From c0f54682f4ff0172962a5b11058b75c460669c01 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Mon, 16 Nov 2020 22:04:50 +0100 Subject: [PATCH 01/87] [matrices] update exercise --- programming/exercises/matrices.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/programming/exercises/matrices.tex b/programming/exercises/matrices.tex index 84127a4..00ad06f 100644 --- a/programming/exercises/matrices.tex +++ b/programming/exercises/matrices.tex @@ -14,7 +14,7 @@ %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} \pagestyle{headandfoot} -\header{{\bfseries\large Exercise 3}}{{\bfseries\large Matrices}}{{\bfseries\large 22. Oktober, 2019}} +\header{{\bfseries\large Exercise 3}}{{\bfseries\large Matrices}}{{\bfseries\large 10. Oktober, 2020}} \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} @@ -54,11 +54,11 @@ following pattern: \begin{solution} \code{x = [7 3 5; 1 8 3; 8 6 4];\\disp(size(x))} \end{solution} - \part Use the help to figure out how to get only the size along a certain dimension. Display the sizes of each dimension. + \part Use the help to figure out how to get only the size along a certain dimension. Display the sizes of each dimension separately. \begin{solution} \code{disp(size(x, 1))}\\\code{disp(size(x, 2))} \end{solution} - \part Copy the content at the position 3rd line, 2nd column to a new variable. + \part Copy the content at the position 3rd line, 2nd column into a new variable. \begin{solution} \code{c = x(3, 2)} \end{solution} @@ -109,7 +109,7 @@ following pattern: \code{y = M(:, [2:2:size(M,2)])} \end{solution} - \part Calculate the averages of lines 1, 3, and 5 (use the function \verb+mean+}, see help). + \part Calculate the averages of lines 1, 3, and 5 (use the function \verb+mean+, see help). \begin{solution} \code{mean(M([1 3 5],:), 2)} \end{solution} From 08382f94d45feeca9b18e96ae40df2668fd99944 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 7 Dec 2020 19:21:17 +0100 Subject: [PATCH 02/87] updated statistics exercise instructions --- README.fonts | 14 + .../lecture/pointprocessscetchA.eps | 120 ++++-- .../lecture/pointprocessscetchA.pdf | Bin 2786 -> 2924 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++++++++------ .../lecture/pointprocessscetchB.pdf | Bin 4694 -> 4877 bytes statistics/exercises/exercises01.tex | 5 +- statistics/lecture/diehistograms.py | 12 +- 7 files changed, 379 insertions(+), 161 deletions(-) diff --git a/README.fonts b/README.fonts index ab7a941..638013d 100644 --- a/README.fonts +++ b/README.fonts @@ -1,6 +1,20 @@ Fonts for matplotlib -------------------- +Install Humor Sans font +``` +sudo apt install fonts-humor-sans +``` + +Clear matplotlib font cache: +``` +cd ~/.cache/matplotlib/ +rm -r * +``` + +Older problems +-------------- + Make sure the right fonts are installed: ``` sudo apt-get install ttf-lyx2.0 diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 2383569..67537f6 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: 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begin /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow {currentpoint stroke M 0 vshift R - Blacktext {gsave 0 setgray show grestore} {show} ifelse} def + Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def /Rshow {currentpoint stroke M dup stringwidth pop neg vshift R - Blacktext {gsave 0 setgray show grestore} {show} ifelse} def + Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def /Cshow {currentpoint stroke M dup stringwidth pop -2 div vshift R - Blacktext {gsave 0 setgray show grestore} {show} ifelse} def + Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def /UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def /DL {Color {setrgbcolor Solid {pop []} if 0 setdash} @@ -82,7 +83,7 @@ gnudict begin /PL {stroke userlinewidth setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def 3.8 setmiterlimit -% Default Line colors +% Classic Line colors (version 5.0) /LCw {1 1 1} def /LCb {0 0 0} def 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zSTRCjy!=QwwDN#HuL{Z&ibkW*?qDRu69I-oy-{Gu?gFEb-b4(>1L*;Uq0`-kE%{)m z^fF=9pVO}j8;L-`Ftj}kjzway5M;Wk23Q)rhc SL~j5Bj(`GGRZXqU0RI88|K<|_ diff --git a/statistics/exercises/exercises01.tex b/statistics/exercises/exercises01.tex index 68455b3..22f1131 100644 --- a/statistics/exercises/exercises01.tex +++ b/statistics/exercises/exercises01.tex @@ -15,7 +15,7 @@ \else \newcommand{\stitle}{} \fi -\header{{\bfseries\large Exercise 8\stitle}}{{\bfseries\large Statistics}}{{\bfseries\large December 2nd, 2019}} +\header{{\bfseries\large Exercise 7\stitle}}{{\bfseries\large Statistics}}{{\bfseries\large December 8th, 2020}} \firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: jan.benda@uni-tuebingen.de} \runningfooter{}{\thepage}{} @@ -97,12 +97,13 @@ jan.benda@uni-tuebingen.de} \item Initially test computationally expensive \code{for} loops, vectors, matrices, etc. with small numbers of repetitions and/or sizes. Once it is working use large repetitions and/or sizes for - getting a good statistics. + getting a good statistics, i.e. smooth curves. \item Use the help functions of \code{matlab} (\code{help command} or \code{doc command}) and the internet to figure out how specific \code{matlab} functions are used and what features they offer. In addition, the internet offers a lot of material and suggestions for any question you have regarding your code ! +\item Work in groups! Nevertheless everybody should write down his/her own solution. \item Please upload your solution to the exercises to ILIAS as a zip-archive with the name ``statistics\_\{last name\}\_\{first name\}.zip''. \end{itemize} diff --git a/statistics/lecture/diehistograms.py b/statistics/lecture/diehistograms.py index 2458412..241bde7 100644 --- a/statistics/lecture/diehistograms.py +++ b/statistics/lecture/diehistograms.py @@ -15,7 +15,7 @@ ax1.set_xticks(range(1, 7)) ax1.set_xlabel('x') ax1.set_ylim(0, 98) ax1.set_ylabel('Frequency') -fs = fsC +fs = dict(**fsC) fs['color'] = [fsC['facecolor'], fsE['facecolor']] del fs['facecolor'] ax1.hist([x2, x1], bins, **fs) @@ -26,9 +26,11 @@ ax2.set_xlabel('x') ax2.set_ylim(0, 0.23) ax2.set_ylabel('Probability') ax2.plot([0.2, 6.8], [1.0/6.0, 1.0/6.0], zorder=-10, **lsAm) -if mpl_major > 1: - ax2.hist([x2, x1], bins, density=True, zorder=-5, **fs) -else: - ax2.hist([x2, x1], bins, normed=True, zorder=-5, **fs) +h1, b1 = np.histogram(x1, bins) +h2, b2 = np.histogram(x2, bins) +h1 = h1/np.sum(h1) +h2 = h2/np.sum(h2) +ax2.bar(b1[:-1]+0.3, h1, zorder=-5, width=0.4, **fsC) +ax2.bar(b2[:-1]+0.7, h2, zorder=-5, width=0.4, **fsE) fig.subplots_adjust(left=0.125) fig.savefig('diehistograms.pdf') From e1c6c32db0157894cc2208f6ef1e46efe72fd8c8 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 7 Dec 2020 19:53:13 +0100 Subject: [PATCH 03/87] [statistics] imporved code style --- header.tex | 2 +- plotstyle.py | 2 +- statistics/code/checkmymedian.m | 12 ++++---- statistics/code/correlations.m | 6 ++-- statistics/code/cumulative.m | 2 +- statistics/code/diehistograms.m | 2 +- statistics/code/gaussianpdf.m | 8 +++--- statistics/code/histogramquartiles.m | 20 ++++++------- statistics/code/quartiles.m | 22 +++++++-------- statistics/code/rollthedie.m | 4 +-- statistics/code/sprintfexamples.m | 42 ++++++++++++++-------------- 11 files changed, 61 insertions(+), 61 deletions(-) diff --git a/header.tex b/header.tex index 29f6ba8..4e98c6b 100644 --- a/header.tex +++ b/header.tex @@ -304,7 +304,7 @@ % \newboolean{showexercisesolutions} \setboolean{showexercisesolutions}{true} -\newcommand{\exercisesolutions}{end} % 0: here, 1: chapter, 2: end +\newcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end % we need this also as numbers: \ifthenelse{\equal{\exercisesolutions}{end}}{\newcommand{\exercisesolutionsnum}{2}}{% \ifthenelse{\equal{\exercisesolutions}{chapter}}{\newcommand{\exercisesolutionsnum}{1}}{% diff --git a/plotstyle.py b/plotstyle.py index 7e3ba8c..cb453f3 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -43,7 +43,7 @@ filllw = 1.0 fillec = colors['white'] fillalpha = 0.4 filledge = {'linewidth': filllw, 'joinstyle': 'round'} -if int(mpl.__version__.split('.')[0]) < 2: +if mpl_major < 2: del filledge['joinstyle'] # helper lines: diff --git a/statistics/code/checkmymedian.m b/statistics/code/checkmymedian.m index d2d101d..31c7e1a 100644 --- a/statistics/code/checkmymedian.m +++ b/statistics/code/checkmymedian.m @@ -1,11 +1,11 @@ % check whether the median returned by mymedian % really separates a vector into two halfs -for i = 1:140 % loop over different length - for k = 1:10 % try several times - a = randn( i, 1 ); % generate some data - m = mymedian( a ); % compute median - if length( a(a>m) ) ~= length( a(am)) ~= length(a(a=x1)&(x=x1)&(r=q(1)) & (b=q(1)) & (b=q(2)) & (b=q(2)) & (b=q(3)), h(b>=q(3)), 'FaceColor', [0.5 0 0.5] ); +bar(b(b=q(1)) & (b=q(1)) & (b=q(2)) & (b=q(2)) & (b=q(3)), h(b>=q(3)), 'FaceColor', [0.5 0 0.5]); hold off; diff --git a/statistics/code/quartiles.m b/statistics/code/quartiles.m index 8123733..d78a8db 100644 --- a/statistics/code/quartiles.m +++ b/statistics/code/quartiles.m @@ -1,16 +1,16 @@ -function q = quartiles( x ) +function q = quartiles(x) % returns a vector with the first, second, and third quartile % of the vector x - xs = sort( x ); - if ( length( xs ) == 0 ) % no data + xs = sort(x); + if (length(xs) == 0) % no data q = []; - elseif ( rem( length( xs ), 2 ) == 0 ) % even number of data - index = length( xs )/2; - m = (xs( index ) + xs( index+1 ))/2; - q = [ round( xs(length(xs)/4) ), m, xs(round(3*length(xs)/4)) ]; - else % odd number of data - index = (length( xs ) + 1)/2; - m = xs( index ); - q = [ round( xs(length(xs)/4) ), m, xs(round(3*length(xs)/4)) ]; + elseif (rem(length(xs), 2) == 0) % even number of data + index = length(xs)/2; + m = (xs(index) + xs(index+1))/2; + q = [round(xs(length(xs)/4)), m, xs(round(3*length(xs)/4))]; + else % odd number of data + index = (length(xs) + 1)/2; + m = xs(index); + q = [round(xs(length(xs)/4)), m, xs(round(3*length(xs)/4))]; end end diff --git a/statistics/code/rollthedie.m b/statistics/code/rollthedie.m index 1842da8..1eeefc6 100644 --- a/statistics/code/rollthedie.m +++ b/statistics/code/rollthedie.m @@ -1,4 +1,4 @@ -function x = rollthedie( n ) +function x = rollthedie(n) % return a vector with the result of rolling a die n times - x = randi( [1, 6], n, 1 ); + x = randi([1, 6], n, 1); end diff --git a/statistics/code/sprintfexamples.m b/statistics/code/sprintfexamples.m index b8f6b75..b08a5c2 100644 --- a/statistics/code/sprintfexamples.m +++ b/statistics/code/sprintfexamples.m @@ -1,48 +1,48 @@ % sprintf returns a string. % This string can be used to annotate plots using the text() function. -s = sprintf( 'x=%f', pi ) +s = sprintf('x=%f', pi) % fprintf writes directly to console (or into files). % for fprintf you usually want to add the line break '\n': % '%f' formats floating point numbers: -fprintf( 'x=%f\n', pi ) +fprintf('x=%f\n', pi) % The '%f' formatting string can be anywhere in the string: -fprintf( 'x=%fms\n', pi ) +fprintf('x=%fms\n', pi) % There can be arbitrary many '%' formatting strings: -fprintf( 'x=%fms, y=%fkHz\n', pi, 2*pi ) +fprintf('x=%fms, y=%fkHz\n', pi, 2*pi) % The '%' itself is generated by '%%': -fprintf( 'x=%f%%\n', pi ) +fprintf('x=%f%%\n', pi) % A point followed by a number sets the number of digits after the point: -fprintf( 'x=%.2fms\n', pi ) +fprintf('x=%.2fms\n', pi) % The numbers are appropriately rounded: -fprintf( 'x=%.3fms\n', pi ) +fprintf('x=%.3fms\n', pi) % A number right before the point sets the width of the generated output: -fprintf( 'x=%10.3fms\n', pi ) +fprintf('x=%10.3fms\n', pi) % '%e' also formats floating point numbers but forces to write in % exponential style: -fprintf( 'x=%e\n', pi ) +fprintf('x=%e\n', pi) % again, a point and number set the number of digits after the point. -fprintf( 'x=%.1e\n', pi ) +fprintf('x=%.1e\n', pi) % '%g% formats the floating point number to a given number of valid digits % (default is 5): -fprintf( 'x=%g\n', pi ) +fprintf('x=%g\n', pi) % The number of valid digits is not the number of digits after the point: -fprintf( 'x=%.2g\n', pi ) -fprintf( 'x=%.2g\n', 10.123 ) -fprintf( 'x=%.2g\n', 18765.123 ) -fprintf( 'x=%.5g\n', 18765.123 ) +fprintf('x=%.2g\n', pi) +fprintf('x=%.2g\n', 10.123) +fprintf('x=%.2g\n', 18765.123) +fprintf('x=%.5g\n', 18765.123) % '%d' formats integers: -fprintf( 'x=%d\n', 5 ) +fprintf('x=%d\n', 5) % the number defines the width of the output: -fprintf( 'x=%3d\n', 5 ) +fprintf('x=%3d\n', 5) % precedig the width with a '0' fills up the space with leading zeros: -fprintf( 'x=%03d\n', 5 ) +fprintf('x=%03d\n', 5) % '%s' formats a string: -fprintf( 'x=%s\n', 'hallo' ) +fprintf('x=%s\n', 'hallo') % ... aligned to the right: -fprintf( 'x=%10s\n', 'hallo' ) +fprintf('x=%10s\n', 'hallo') % ... unless the width is negative: -fprintf( 'x=%-10s!\n', 'hallo' ) +fprintf('x=%-10s!\n', 'hallo') From 430bdfb7fd63f4c4559591ace600ccb2ac87bf96 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 7 Dec 2020 22:37:36 +0100 Subject: [PATCH 04/87] [bootstrap] improved code --- bootstrap/code/bootstrapsem.m | 29 ++++++++++++------------ bootstrap/code/correlationsignificance.m | 10 ++++---- statistics/code/correlations.m | 2 +- statistics/code/gaussiankerneldensity.m | 26 ++++++++++----------- 4 files changed, 34 insertions(+), 33 deletions(-) diff --git a/bootstrap/code/bootstrapsem.m b/bootstrap/code/bootstrapsem.m index 18ebae3..f496071 100644 --- a/bootstrap/code/bootstrapsem.m +++ b/bootstrap/code/bootstrapsem.m @@ -1,24 +1,25 @@ nsamples = 100; nresamples = 1000; -% draw a SRS (simple random sample, "Stichprobe") from the population: -x = randn( 1, nsamples ); -fprintf('%-30s %-5s %-5s %-5s\n', '', 'mean', 'stdev', 'sem' ) -fprintf('%30s %5.2f %5.2f %5.2f\n', 'single SRS', mean( x ), std( x ), std( x )/sqrt(nsamples) ) +% draw a simple random sample ("Stichprobe") from the population: +x = randn(1, nsamples); +fprintf('%-30s %-5s %-5s %-5s\n', '', 'mean', 'stdev', 'sem') +fprintf('%30s %5.2f %5.2f %5.2f\n', 'single SRS', mean(x), std(x), std(x)/sqrt(nsamples)) % bootstrap the mean: -mus = zeros(nresamples,1); % vector for storing the means -for i = 1:nresamples % loop for generating the bootstraps +mus = zeros(nresamples,1); % vector for storing the means +for i = 1:nresamples % loop for generating the bootstraps inx = randi(nsamples, 1, nsamples); % range, 1D-vector, number - xr = x(inx); % resample the original SRS - mus(i) = mean(xr); % compute statistic of the resampled SRS + xr = x(inx); % resample the original SRS + mus(i) = mean(xr); % compute statistic of the resampled SRS end -fprintf('%30s %5.2f %5.2f -\n', 'bootstrapped distribution', mean( mus ), std( mus ) ) +fprintf('%30s %5.2f %5.2f -\n', 'bootstrapped distribution', mean(mus), std(mus)) -% many SRS (we can do that with the random number generator, but not in real life!): -musrs = zeros(nresamples,1); % vector for the means of each SRS +% many SRS (we can do that with the random number generator, +% but not in real life!): +musrs = zeros(nresamples,1); % vector for the means of each SRS for i = 1:nresamples - x = randn( 1, nsamples ); % draw a new SRS - musrs(i) = mean( x ); % compute its mean + x = randn(1, nsamples); % draw a new SRS + musrs(i) = mean(x); % compute its mean end -fprintf('%30s %5.2f %5.2f -\n', 'sampling distribution', mean( musrs ), std( musrs ) ) +fprintf('%30s %5.2f %5.2f -\n', 'sampling distribution', mean(musrs), std(musrs)) diff --git a/bootstrap/code/correlationsignificance.m b/bootstrap/code/correlationsignificance.m index f5ccb1c..d9b0fff 100644 --- a/bootstrap/code/correlationsignificance.m +++ b/bootstrap/code/correlationsignificance.m @@ -6,7 +6,7 @@ y = randn(n, 1) + a*x; % correlation coefficient: rd = corr(x, y); -fprintf('correlation coefficient of data r = %.2f\n', rd ); +fprintf('correlation coefficient of data r = %.2f\n', rd); % distribution of null hypothesis by permutation: nperm = 1000; @@ -16,12 +16,12 @@ for i=1:nperm yr=y(randperm(length(y))); % shuffle y rs(i) = corr(xr, yr); end -[h,b] = hist(rs, 20 ); -h = h/sum(h)/(b(2)-b(1)); % normalization +[h,b] = hist(rs, 20); +h = h/sum(h)/(b(2)-b(1)); % normalization % significance: rq = quantile(rs, 0.95); -fprintf('correlation coefficient of null hypothesis at 5%% significance = %.2f\n', rq ); +fprintf('correlation coefficient of null hypothesis at 5%% significance = %.2f\n', rq); if rd >= rq fprintf('--> correlation r=%.2f is significant\n', rd); else @@ -32,7 +32,7 @@ end bar(b, h, 'facecolor', 'b'); hold on; bar(b(b>=rq), h(b>=rq), 'facecolor', 'r'); -plot( [rd rd], [0 4], 'r', 'linewidth', 2 ); +plot([rd rd], [0 4], 'r', 'linewidth', 2); xlabel('Correlation coefficient'); ylabel('Probability density of H0'); hold off; diff --git a/statistics/code/correlations.m b/statistics/code/correlations.m index 9be872c..e6eb0b7 100644 --- a/statistics/code/correlations.m +++ b/statistics/code/correlations.m @@ -3,7 +3,7 @@ corrs = [1.0, 0.6, 0.0, -0.9]; for k = [1:length(corrs)] r = corrs(k); x = randn(n, 1); - y = r*x; % linear dependence of y on x + y = r*x; % linear dependence of y on x % add noise to destroy perfect correlations: y = y + sqrt(1.0-r*r)*randn(n, 1); % compute correlation coefficient of data: diff --git a/statistics/code/gaussiankerneldensity.m b/statistics/code/gaussiankerneldensity.m index 8f97818..b01a1c2 100644 --- a/statistics/code/gaussiankerneldensity.m +++ b/statistics/code/gaussiankerneldensity.m @@ -1,15 +1,15 @@ -data = randn(100, 1); % generate some data -sigma = 0.2; % std. dev. of Gaussian kernel -xmin = -4.0; % minimum x value for kernel density -xmax = 4.0; % maximum x value for kernel density -dx = 0.05*sigma; % step size for kernel density -xg = [-4.0*sigma:dx:4.0*sigma]; % x-axis for single Gaussian kernel +data = randn(100, 1); % generate some data +sigma = 0.2; % std. dev. of Gaussian kernel +xmin = -4.0; % minimum x value for kernel density +xmax = 4.0; % maximum x value for kernel density +dx = 0.05*sigma; % step size for kernel density +xg = [-4.0*sigma:dx:4.0*sigma]; % x-axis for single Gaussian kernel % single Gaussian kernel: kernel = exp(-0.5*(xg/sigma).^2)/sqrt(2.0*pi)/sigma; ng = floor((length(kernel)-1)/2); % half the length of the Gaussian -x = [xmin:dx:xmax+0.5*dx]; % x-axis for kernel density -kd = zeros(1, length(x)); % vector for kernel density -for i = 1:length(data) % for every data value ... +x = [xmin:dx:xmax+0.5*dx]; % x-axis for kernel density +kd = zeros(1, length(x)); % vector for kernel density +for i = 1:length(data) % for every data value ... xd = data(i); % index of data value in kernel density vector: inx = round((xd-xmin)/dx)+1; @@ -17,8 +17,8 @@ for i = 1:length(data) % for every data value ... k0 = inx-ng; % end index for Gaussian in kernel density vector: k1 = inx+ng; - g0 = 1; % start index in Gaussian - g1 = length(kernel); % end index in Gaussian + g0 = 1; % start index in Gaussian + g1 = length(kernel); % end index in Gaussian % check whether left side of Gaussian extends below xmin: if inx < ng+1 % adjust start indices accordingly: @@ -34,7 +34,7 @@ for i = 1:length(data) % for every data value ... % add Gaussian on kernel density: kd(k0:k1) = kd(k0:k1) + kernel(g0:g1); end -kd = kd/length(data); % normalize by number of data points +kd = kd/length(data); % normalize by number of data points % plot the computed kernel density: plot(x, kd, 'b', 'linewidth', 4, 'displayname', 'manual') @@ -45,4 +45,4 @@ plot(x, kd, '--r', 'linewidth', 4, 'displayname', 'ksdensity()') hold off xlabel('x') ylabel('Probability density') -legend('show') \ No newline at end of file +legend('show') From e2f026c53f0cea2b5b1b67f5a3e865a3d52be3c7 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 7 Dec 2020 22:51:10 +0100 Subject: [PATCH 05/87] [pointprocesses] improved code --- pointprocesses/code/binnedRate.m | 2 +- pointprocesses/code/convolutionRate.m | 17 +++++---- pointprocesses/code/counthist.m | 6 ++-- pointprocesses/code/instantaneousRate.m | 2 +- pointprocesses/code/isihist.m | 2 +- pointprocesses/code/rasterplot.m | 36 +++++++++---------- .../lecture/pointprocesses-chapter.tex | 4 +-- 7 files changed, 34 insertions(+), 35 deletions(-) diff --git a/pointprocesses/code/binnedRate.m b/pointprocesses/code/binnedRate.m index e34366c..cf9ad65 100644 --- a/pointprocesses/code/binnedRate.m +++ b/pointprocesses/code/binnedRate.m @@ -18,7 +18,7 @@ function [time, rate] = binned_rate(spikes, bin_width, dt, t_max) rate = zeros(size(time)); h = hist(spikes, bins) ./ bin_width; for i = 2:length(bins) - rate(round(bins(i - 1) / dt) + 1:round(bins(i) / dt)) = h(i); + rate(round(bins(i-1)/dt) + 1:round(bins(i)/dt)) = h(i); end end diff --git a/pointprocesses/code/convolutionRate.m b/pointprocesses/code/convolutionRate.m index a2b1344..4fe5bb8 100644 --- a/pointprocesses/code/convolutionRate.m +++ b/pointprocesses/code/convolutionRate.m @@ -10,19 +10,18 @@ function [time, rate] = convolution_rate(spikes, sigma, dt, t_max) % t_max : the trial duration in seconds. % % Returns: - two vectors containing the time and the rate. +% two vectors containing the time and the rate. -time = 0:dt:t_max - dt; -rate = zeros(size(time)); -spike_indices = round(spikes / dt); -rate(spike_indices) = 1; -kernel = gaussKernel(sigma, dt); - -rate = conv(rate, kernel, 'same'); + time = 0:dt:t_max - dt; + rate = zeros(size(time)); + spike_indices = round(spikes / dt); + rate(spike_indices) = 1; + kernel = gaussKernel(sigma, dt); + rate = conv(rate, kernel, 'same'); end function y = gaussKernel(s, step) x = -4 * s:step:4 * s; - y = exp(-0.5 .* (x ./ s) .^ 2) ./ sqrt(2 * pi) / s; + y = exp(-0.5 .* (x ./ s).^ 2) ./ sqrt(2 * pi) / s; end diff --git a/pointprocesses/code/counthist.m b/pointprocesses/code/counthist.m index 6885b1a..67b4cae 100644 --- a/pointprocesses/code/counthist.m +++ b/pointprocesses/code/counthist.m @@ -37,8 +37,8 @@ function [counts, bins] = counthist(spikes, w) % plot: if nargout == 0 - bar( bins, counts ); - xlabel( 'counts k' ); - ylabel( 'P(k)' ); + bar(bins, counts); + xlabel('counts k'); + ylabel('P(k)'); end end diff --git a/pointprocesses/code/instantaneousRate.m b/pointprocesses/code/instantaneousRate.m index 8928c31..da8ee29 100644 --- a/pointprocesses/code/instantaneousRate.m +++ b/pointprocesses/code/instantaneousRate.m @@ -19,6 +19,6 @@ function [time, rate] = instantaneous_rate(spikes, dt, t_max) spike_indices = [1 round(spikes ./ dt)]; for i = 2:length(spike_indices) - rate(spike_indices(i - 1):spike_indices(i)) = inst_rate(i - 1); + rate(spike_indices(i-1):spike_indices(i)) = inst_rate(i-1); end end diff --git a/pointprocesses/code/isihist.m b/pointprocesses/code/isihist.m index 33ad4f5..00b02c3 100644 --- a/pointprocesses/code/isihist.m +++ b/pointprocesses/code/isihist.m @@ -13,7 +13,7 @@ function [pdf, centers] = isihist(isis, binwidth) if nargin < 2 % compute good binwidth: - nperbin = 200; % average number of data points per bin + nperbin = 200; % average number of data points per bin bins = length(isis)/nperbin; % number of bins binwidth = max(isis)/bins; if binwidth < 5e-4 % half a millisecond diff --git a/pointprocesses/code/rasterplot.m b/pointprocesses/code/rasterplot.m index 0bcdb8d..7b28820 100644 --- a/pointprocesses/code/rasterplot.m +++ b/pointprocesses/code/rasterplot.m @@ -5,25 +5,25 @@ function rasterplot(spikes, tmax) % spikes: a cell array of vectors of spike times in seconds % tmax: plot spike raster upto tmax seconds -ntrials = length(spikes); -for k = 1:ntrials - times = spikes{k}; - times = times(times Date: Tue, 8 Dec 2020 11:48:07 +0100 Subject: [PATCH 06/87] [bootstrap] notes on how to extend the permutation tests --- bootstrap/lecture/bootstrap-chapter.tex | 7 ++++++- bootstrap/lecture/bootstrap.tex | 19 ++++++++++++++++--- 2 files changed, 22 insertions(+), 4 deletions(-) diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index 845b6b1..b61d395 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -17,10 +17,15 @@ \include{bootstrap} \section{TODO} + This chapter easily covers two lectures: \begin{itemize} \item 1. Bootstrapping with a proper introduction of of confidence intervals -\item 2. Permutation test with a proper introduction of statistical tests (dsitribution of nullhypothesis, significance, power, etc.) +\item 2. Permutation test with a proper introduction of statistical tests (distribution of nullhypothesis, significance, power, etc.) \end{itemize} +Add jacknife methods to bootstrapping + +Add permutation test for significant different means of two distributions. + \end{document} diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index 667c833..20f01c2 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -1,8 +1,12 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\chapter{Bootstrap methods} +\chapter{Resampling methods} \label{bootstrapchapter} -\exercisechapter{Bootstrap methods} +\exercisechapter{Resampling methods} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Bootstrapping} Bootstrapping methods are applied to create distributions of statistical measures via resampling of a sample. Bootstrapping offers several @@ -94,7 +98,8 @@ sample. This can be implemented by generating random indices into the data set using the \code{randi()} function. -\section{Bootstrap of the standard error} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Bootstrap of the standard error} Bootstrapping can be nicely illustrated at the example of the \enterm{standard error} of the mean (\determ{Standardfehler}). The @@ -138,7 +143,9 @@ distribution is the standard error of the mean. \end{exercise} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Permutation tests} + Statistical tests ask for the probability of a measured value to originate from a null hypothesis. Is this probability smaller than the desired \entermde{Signifikanz}{significance level}, the @@ -166,6 +173,12 @@ while we conserve all other statistical properties of the data. statistically significant.} \end{figure} +%\subsection{Significance of a difference in the mean} + +%See \url{https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests.} + +\subsection{Significance of correlations} + A good example for the application of a \entermde{Permutationstest}{permutaion test} is the statistical assessment of \entermde[correlation]{Korrelation}{correlations}. Given From 0e30a01a45f0cf232ba86da6b1b3b3ef4a41db01 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Fri, 11 Dec 2020 23:22:40 +0100 Subject: [PATCH 07/87] fixed page breaking of code and exercises --- codestyle/lecture/codestyle.tex | 15 +- debugging/lecture/debugging.tex | 36 +- designpattern/lecture/designpattern.tex | 69 ++-- header.tex | 42 +- plotting/lecture/plotting-chapter.tex | 2 +- plotting/lecture/plotting.tex | 27 +- .../lecture/pointprocessscetchA.eps | 120 ++---- .../lecture/pointprocessscetchA.pdf | Bin 2924 -> 2786 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++------------ .../lecture/pointprocessscetchB.pdf | Bin 4877 -> 4694 bytes programming/code/vectorsize.m | 9 +- programming/code/vectorsize.out | 6 +- programming/lecture/programming.tex | 181 ++++---- 13 files changed, 360 insertions(+), 536 deletions(-) diff --git a/codestyle/lecture/codestyle.tex b/codestyle/lecture/codestyle.tex index 42f7429..01d1d12 100644 --- a/codestyle/lecture/codestyle.tex +++ b/codestyle/lecture/codestyle.tex @@ -204,7 +204,7 @@ random walk\footnote{A random walk is a simple simulation of Brownian (listing \ref{chaoticcode}) then in cleaner way (listing \ref{cleancode}) -\begin{lstlisting}[label=chaoticcode, caption={Chaotic implementation of the random-walk.}] +\begin{pagelisting}[label=chaoticcode, caption={Chaotic implementation of the random-walk.}] num_runs = 10; max_steps = 1000; positions = zeros(max_steps, num_runs); @@ -217,18 +217,15 @@ for step = 2:max_steps x = randn(1); if x<0 positions(step, run)= positions(step-1, run)+1; - elseif x>0 positions(step,run)=positions(step-1,run)-1; end end end -\end{lstlisting} - -\pagebreak[4] +\end{pagelisting} -\begin{lstlisting}[label=cleancode, caption={Clean implementation of the random-walk.}] +\begin{pagelisting}[label=cleancode, caption={Clean implementation of the random-walk.}] num_runs = 10; max_steps = 1000; positions = zeros(max_steps, num_runs); @@ -243,7 +240,7 @@ for run = 1:num_runs end end end -\end{lstlisting} +\end{pagelisting} \section{Using comments} @@ -275,7 +272,6 @@ avoided:\\ \varcode{ x = x + 2; \% add two to x}\\ make it even clearer.}{Steve McConnell} \end{important} -\pagebreak[4] \section{Documenting functions} All pre-defined \matlab{} functions begin with a comment block that describes the purpose of the function, the required and optional @@ -335,8 +331,7 @@ used within the context of another function \matlab{} allows to define within the same file. Listing \ref{localfunctions} shows an example of a local function definition. -\pagebreak[3] -\lstinputlisting[label=localfunctions, caption={Example for local +\pageinputlisting[label=localfunctions, caption={Example for local functions.}]{calculateSines.m} \emph{Local function} live in the same \entermde{m-File}{m-file} as diff --git a/debugging/lecture/debugging.tex b/debugging/lecture/debugging.tex index 6be3277..b83c24e 100644 --- a/debugging/lecture/debugging.tex +++ b/debugging/lecture/debugging.tex @@ -59,14 +59,14 @@ every opening parenthesis must be matched by a closing one or every respective error messages are clear and the editor will point out and highlight most syntax errors. -\begin{lstlisting}[label=syntaxerror, caption={Unbalanced parenthesis error.}] +\begin{pagelisting}[label=syntaxerror, caption={Unbalanced parenthesis error.}] >> mean(random_numbers | Error: Expression or statement is incorrect--possibly unbalanced (, {, or [. Did you mean: >> mean(random_numbers) -\end{lstlisting} +\end{pagelisting} \subsection{Indexing error}\label{index_error} Second on the list of common errors are the @@ -125,7 +125,7 @@ dimensions. The command in line 7 works due to the fact, that matlab automatically extends the matrix, if you assign values to a range outside its bounds. -\begin{lstlisting}[label=assignmenterror, caption={Assignment errors.}] +\begin{pagelisting}[label=assignmenterror, caption={Assignment errors.}] >> a = zeros(1, 100); >> b = 0:10; @@ -136,7 +136,7 @@ outside its bounds. >> size(a) ans = 110 1 -\end{lstlisting} +\end{pagelisting} \subsection{Dimension mismatch error} Similarly, some arithmetic operations are only valid if the variables @@ -154,7 +154,7 @@ in listing\,\ref{dimensionmismatch} does not throw an error but the result is something else than the expected elementwise multiplication. % XXX Some arithmetic operations make size constraints, violating them leads to dimension mismatch errors. -\begin{lstlisting}[label=dimensionmismatch, caption={Dimension mismatch errors.}] +\begin{pagelisting}[label=dimensionmismatch, caption={Dimension mismatch errors.}] >> a = randn(100, 1); >> b = randn(10, 1); >> a + b @@ -171,7 +171,7 @@ result is something else than the expected elementwise multiplication. >> size(c) ans = 100 10 -\end{lstlisting} +\end{pagelisting} @@ -239,7 +239,7 @@ but it requires a deep understanding of the applied functions and also the task at hand. % XXX Converting a series of spike times into the firing rate as a function of time. Many tasks can be solved with a single line of code. But is this readable? -\begin{lstlisting}[label=easyvscomplicated, caption={One-liner versus readable code.}] +\begin{pagelisting}[label=easyvscomplicated, caption={One-liner versus readable code.}] % the one-liner rate = conv(full(sparse(1, round(spike_times/dt), 1, 1, length(time))), kernel, 'same'); @@ -248,7 +248,7 @@ rate = zeros(size(time)); spike_indices = round(spike_times/dt); rate(spike_indices) = 1; rate = conv(rate, kernel, 'same'); -\end{lstlisting} +\end{pagelisting} The preferred way depends on several considerations. (i) How deep is your personal understanding of the programming language? (ii) What @@ -291,7 +291,7 @@ example given in the \matlab{} help and assume that there is a function \varcode{rightTriangle()} (listing\,\ref{trianglelisting}). % XXX Slightly more readable version of the example given in the \matlab{} help system. Note: The variable name for the angles have been capitalized in order to not override the matlab defined functions \code{alpha, beta,} and \code{gamma}. -\begin{lstlisting}[label=trianglelisting, caption={Example function for unit testing.}] +\begin{pagelisting}[label=trianglelisting, caption={Example function for unit testing.}] function angles = rightTriangle(length_a, length_b) ALPHA = atand(length_a / length_b); BETA = atand(length_a / length_b); @@ -300,7 +300,7 @@ function angles = rightTriangle(length_a, length_b) angles = [ALPHA BETA GAMMA]; end -\end{lstlisting} +\end{pagelisting} This function expects two input arguments that are the length of the sides $a$ and $b$ and assumes a right angle between them. From this @@ -337,7 +337,7 @@ The test script for the \varcode{rightTriangle()} function (listing\,\ref{trianglelisting}) may look like in listing\,\ref{testscript}. -\begin{lstlisting}[label=testscript, caption={Unit test for the \varcode{rightTriangle()} function stored in an m-file testRightTriangle.m}] +\begin{pagelisting}[label=testscript, caption={Unit test for the \varcode{rightTriangle()} function stored in an m-file testRightTriangle.m}] tolerance = 1e-10; % preconditions @@ -373,7 +373,7 @@ angles = rightTriangle(1, 1500); smallAngle = (pi / 180) * angles(1); % radians approx = sin(smallAngle); assert(abs(approx - smallAngle) <= tolerance, 'Problem with small angle approximation') -\end{lstlisting} +\end{pagelisting} In a test script we can execute any code. The actual test whether or not the results match our predictions is done using the @@ -390,16 +390,16 @@ executed. We further define a \varcode{tolerance} variable that is used when comparing double values (Why might the test on equality of double values be tricky?). -\begin{lstlisting}[label=runtestlisting, caption={Run the test!}] +\begin{pagelisting}[label=runtestlisting, caption={Run the test!}] result = runtests('testRightTriangle') -\end{lstlisting} +\end{pagelisting} During the run, \matlab{} will put out error messages onto the command line and a summary of the test results is then stored within the \varcode{result} variable. These can be displayed using the function \code[table()]{table(result)}. -\begin{lstlisting}[label=testresults, caption={The test results.}, basicstyle=\ttfamily\scriptsize] +\begin{pagelisting}[label=testresults, caption={The test results.}, basicstyle=\ttfamily\scriptsize] table(result) ans = 4x6 table @@ -411,7 +411,7 @@ _________________________________ ______ ______ ___________ ________ _____ 'testR.../Test_IsoscelesTriangles' true false false 0.004893 [1x1 struct] 'testR.../Test_30_60_90Triangle' true false false 0.005057 [1x1 struct] 'testR.../Test_SmallAngleApprox' true false false 0.0049 [1x1 struct] -\end{lstlisting} +\end{pagelisting} So far so good, all tests pass and our function appears to do what it is supposed to do. But tests are only as good as the programmer who @@ -479,11 +479,11 @@ stopped in debug mode (listing\,\ref{debuggerlisting}). \end{figure} -\begin{lstlisting}[label=debuggerlisting, caption={Command line when the program execution was stopped in the debugger.}] +\begin{pagelisting}[label=debuggerlisting, caption={Command line when the program execution was stopped in the debugger.}] >> simplerandomwalk 6 for run = 1:num_runs K>> -\end{lstlisting} +\end{pagelisting} When stopped in the debugger we can view and change the state of the program at this point, we can also issue commands to try the next diff --git a/designpattern/lecture/designpattern.tex b/designpattern/lecture/designpattern.tex index 1fb191d..5baada5 100644 --- a/designpattern/lecture/designpattern.tex +++ b/designpattern/lecture/designpattern.tex @@ -10,7 +10,8 @@ pattern]{design pattern}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Looping over vector elements} Iterating over vector elements by means of a \mcode{for}-loop is a very commen pattern: -\begin{lstlisting}[caption={\varcode{for}-loop for accessing vector elements by indices}] + +\begin{pagelisting}[caption={\varcode{for}-loop for accessing vector elements by indices}] x = [2:3:20]; % Some vector. for i=1:length(x) % For loop over the indices of the vector. i % This is the index (an integer number) @@ -22,12 +23,14 @@ for i=1:length(x) % For loop over the indices of the vector. % as an argument to a function: do_something(x(i)); end -\end{lstlisting} +\end{pagelisting} +\noindent If the result of the computation within the loop are single numbers that are to be stored in a vector, you should create this vector with the right size before the loop: -\begin{lstlisting}[caption={\varcode{for}-loop for writing a vector}] + +\begin{pagelisting}[caption={\varcode{for}-loop for writing a vector}] x = [1.2 2.3 2.6 3.1]; % Some vector. % Create a vector for the results, as long as the number of loops: y = zeros(length(x),1); @@ -38,13 +41,15 @@ for i=1:length(x) end % Now the result vector can be further processed: mean(y); -\end{lstlisting} +\end{pagelisting} +\noindent The computation within the loop could also result in a vector of some length and not just a single number. If the length of this vector (here 10) is known beforehand, then you should create a matrix of appropriate size for storing the results: -\begin{lstlisting}[caption={\varcode{for}-loop for writing rows of a matrix}] + +\begin{pagelisting}[caption={\varcode{for}-loop for writing rows of a matrix}] x = [2:3:20]; % Some vector. % Create space for results - % as many rows as loops, as many columns as needed: @@ -56,11 +61,13 @@ for i=1:length(x) end % Process the results stored in matrix y: mean(y, 1) -\end{lstlisting} +\end{pagelisting} +\noindent Another possibility is that the result vectors (here of unknown size) need to be combined into a single large vector: -\begin{lstlisting}[caption={\varcode{for}-loop for appending vectors}] + +\begin{pagelisting}[caption={\varcode{for}-loop for appending vectors}] x = [2:3:20]; % Some vector. y = []; % Empty vector for storing the results. for i=1:length(x) @@ -72,14 +79,15 @@ for i=1:length(x) end % Process the results stored in the vector z: mean(y) -\end{lstlisting} +\end{pagelisting} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Scaling and shifting random numbers, zeros, and ones} Random number generators usually return random numbers of a given mean and standard deviation. Multiply those numbers by a factor to change their standard deviation and add a number to shift the mean. -\begin{lstlisting}[caption={Scaling and shifting of random numbers}] + +\begin{pagelisting}[caption={Scaling and shifting of random numbers}] % 100 random numbers drawn from a normal distribution % with mean 0 and standard deviation 1: x = randn(100, 1); @@ -89,18 +97,20 @@ x = randn(100, 1); mu = 4.8; sigma = 2.3; y = randn(100, 1)*sigma + mu; -\end{lstlisting} +\end{pagelisting} +\noindent The same principle can be useful for in the context of the functions \mcode{zeros()} or \mcode{ones()}: -\begin{lstlisting}[caption={Scaling and shifting of \varcode{zeros()} and \varcode{ones()}}] + +\begin{pagelisting}[caption={Scaling and shifting of \varcode{zeros()} and \varcode{ones()}}] x = -1:0.01:2; % Vector of x-values for plotting plot(x, exp(-x.*x)); % Plot for the same x-values a horizontal line with y=0.8: plot(x, zeros(size(x))+0.8); % ... or a line with y=0.5: plot(x, ones(size(x))*0.5); -\end{lstlisting} +\end{pagelisting} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -119,25 +129,26 @@ can plot the values of the $y$ vector against the ones of the $x$ vector. The following scripts compute and plot the function $f(x)=e^{-x^2}$: -\begin{lstlisting}[caption={Plotting a mathematical function --- very detailed}] + +\begin{pagelisting}[caption={Plotting a mathematical function --- very detailed}] xmin = -1.0; xmax = 2.0; dx = 0.01; % Step size x = xmin:dx:xmax; % Vector with x-values. y = exp(-x.*x); % No for loop! '.*' for multiplying the vector elements. plot(x, y); -\end{lstlisting} +\end{pagelisting} -\begin{lstlisting}[caption={Plotting a mathematical function --- shorter}] +\begin{pagelisting}[caption={Plotting a mathematical function --- shorter}] x = -1:0.01:2; y = exp(-x.*x); plot(x, y); -\end{lstlisting} +\end{pagelisting} -\begin{lstlisting}[caption={Plotting a mathematical function --- compact}] +\begin{pagelisting}[caption={Plotting a mathematical function --- compact}] x = -1:0.01:2; plot(x, exp(-x.*x)); -\end{lstlisting} +\end{pagelisting} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -146,28 +157,34 @@ For estimating probabilities or probability densities from histograms we need to normalize them appropriately. The \mcode{histogram()} function does this automatically with the appropriate arguments: -\begin{lstlisting}[caption={Probability density with the \varcode{histogram()}-function}] + +\begin{pagelisting}[caption={Probability density with the \varcode{histogram()}-function}] x = randn(100, 1); % Some real-valued data. histogram(x, 'Normalization', 'pdf'); -\end{lstlisting} -\begin{lstlisting}[caption={Probability with the \varcode{histogram()}-function}] +\end{pagelisting} + +\begin{pagelisting}[caption={Probability with the \varcode{histogram()}-function}] x = randi(6, 100, 1); % Some integer-valued data. histogram(x, 'Normalization', 'probability'); -\end{lstlisting} +\end{pagelisting} + +\noindent Alternatively one can normalize the histogram data as returned by the \code{hist()}-function manually: -\begin{lstlisting}[caption={Probability density with the \varcode{hist()}- and \varcode{bar()}-function}] + +\begin{pagelisting}[caption={Probability density with the \varcode{hist()}- and \varcode{bar()}-function}] x = randn(100, 1); % Some real-valued data. [h, b] = hist(x); % Compute histogram. h = h/sum(h)/(b(2)-b(1)); % Normalization to a probability density. bar(b, h); % Plot the probability density. -\end{lstlisting} -\begin{lstlisting}[caption={Probability with the \varcode{hist()}- and \varcode{bar()}-function}] +\end{pagelisting} + +\begin{pagelisting}[caption={Probability with the \varcode{hist()}- and \varcode{bar()}-function}] x = randi(6, 100, 1); % Some integer-valued data. [h, b] = hist(x); % Compute histogram. h = h/sum(h); % Normalize to probability. bar(b, h); % Plot the probabilities. -\end{lstlisting} +\end{pagelisting} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/header.tex b/header.tex index 4e98c6b..fcaaa87 100644 --- a/header.tex +++ b/header.tex @@ -2,7 +2,7 @@ \title{\textbf{\huge\sffamily\tr{Introduction to\\[1ex] Scientific Computing}% {Einf\"uhrung in die\\[1ex] wissenschaftliche Datenverarbeitung}}} -\author{{\LARGE Jan Grewe \& Jan Benda}\\[5ex]Abteilung Neuroethologie\\[2ex]% +\author{{\LARGE Jan Grewe \& Jan Benda}\\[5ex]Neuroethology Lab\\[2ex]% \includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}\vspace{3ex}} \date{WS 2020/2021\\\vfill% @@ -77,7 +77,7 @@ \setcounter{totalnumber}{2} % float placement fractions: -\renewcommand{\textfraction}{0.2} +\renewcommand{\textfraction}{0.1} \renewcommand{\topfraction}{0.9} \renewcommand{\bottomfraction}{0.0} \renewcommand{\floatpagefraction}{0.7} @@ -209,6 +209,21 @@ \let\l@lstlisting\l@figure \makeatother +% \lstinputlisting wrapped in a minipage to avoid page breaks: +\newcommand{\pageinputlisting}[2][]{\vspace{-2ex}\noindent\begin{minipage}[t]{1\linewidth}\lstinputlisting[#1]{#2}\end{minipage}} + +%%%%% listing environment: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% usage: +% +% \begin{pagelisting}[label=listing1, caption={A script.}] +% >> x = 6 +% \end{pagelisting} +% +% This is the lstlisting environment but wrapped in a minipage to avoid page breaks. +\lstnewenvironment{pagelisting}[1][]% + {\vspace{-2ex}\lstset{#1}\noindent\minipage[t]{1\linewidth}}% + {\endminipage} + %%%%% english, german, code and file terms: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{ifthen} @@ -304,7 +319,7 @@ % \newboolean{showexercisesolutions} \setboolean{showexercisesolutions}{true} -\newcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end +\newcommand{\exercisesolutions}{chapter} % 0: here, 1: chapter, 2: end % we need this also as numbers: \ifthenelse{\equal{\exercisesolutions}{end}}{\newcommand{\exercisesolutionsnum}{2}}{% \ifthenelse{\equal{\exercisesolutions}{chapter}}{\newcommand{\exercisesolutionsnum}{1}}{% @@ -349,11 +364,12 @@ }{% \immediate\write\solutions{\unexpanded{\subsection}{Exercise \thechapter.\arabic{exercisef}}}% \immediate\write\solutions{\unexpanded{\label}{solution\arabic{chapter}-\arabic{exercisef}}}% - \immediate\write\solutions{\unexpanded{\lstinputlisting[belowskip=0ex,aboveskip=0ex,% - nolol=true, title={\textbf{Source code:} \protect\StrSubstitute{#1}{_}{\_}}]}{\codepath#1}}% + \immediate\write\solutions{\unexpanded{\begin{minipage}{1\linewidth}\lstinputlisting[belowskip=0ex,aboveskip=0ex,% + nolol=true, title={\textbf{Source code:} \protect\StrSubstitute{#1}{_}{\_}}]}{\codepath#1}\unexpanded{\end{minipage}}}% \ifthenelse{\equal{#2}{}}{}% - {\immediate\write\solutions{\unexpanded{\lstinputlisting[language={},% - nolol=true, title={\textbf{Output:}}, belowskip=0ex, aboveskip=1ex]}{\codepath#2}}}% + {\immediate\write\solutions{\unexpanded{\begin{minipage}{1\linewidth}\lstinputlisting[language={},% + nolol=true, title={\textbf{Output:}}, belowskip=0ex, aboveskip=1ex]}{\codepath#2}\unexpanded{\end{minipage}}}}% + \immediate\write\solutions{\unexpanded{\vspace*{\fill}}}% \immediate\write\solutions{}% }% }% @@ -362,14 +378,18 @@ { \hypersetup{hypertexnames=false}% \ifthenelse{\equal{\exercisesource}{}}{}% { \addtocounter{lstlisting}{-1}% - \lstinputlisting[belowskip=0pt,aboveskip=1ex,nolol=true,% + \par\noindent\begin{minipage}[t]{1\linewidth}% + \lstinputlisting[belowskip=1ex,aboveskip=-1ex,nolol=true,% title={\textbf{Solution:} \exercisefile}]% {\exercisesource}% + \end{minipage}% \ifthenelse{\equal{\exerciseoutput}{}}{}% { \addtocounter{lstlisting}{-1}% + \par\noindent\begin{minipage}[t]{1\linewidth}% \lstinputlisting[language={},title={\textbf{Output:}},% - nolol=true,belowskip=0pt]% + nolol=true,belowskip=0pt,aboveskip=-0.5ex]% {\exerciseoutput}% + \end{minipage}% }% }% \hypersetup{hypertexnames=true}% @@ -452,12 +472,12 @@ { \captionsetup{singlelinecheck=off,hypcap=false,labelformat={empty},% labelfont={large,sf,it,bf},font={large,sf,it,bf}} \ifthenelse{\equal{#1}{}}% - { \begin{mdframed}[linecolor=importantline,linewidth=1ex,% + { \begin{mdframed}[nobreak=true,linecolor=importantline,linewidth=1ex,% backgroundcolor=importantback,font={\sffamily}]% \setlength{\parindent}{0pt}% \setlength{\parskip}{1ex}% }% - { \begin{mdframed}[linecolor=importantline,linewidth=1ex,% + { \begin{mdframed}[nobreak=true,linecolor=importantline,linewidth=1ex,% backgroundcolor=importantback,font={\sffamily},% frametitle={\captionof{iboxf}{#1}},frametitleaboveskip=-1ex,% frametitlebackgroundcolor=importantline]% diff --git a/plotting/lecture/plotting-chapter.tex b/plotting/lecture/plotting-chapter.tex index 6a96c4a..85d9cc5 100644 --- a/plotting/lecture/plotting-chapter.tex +++ b/plotting/lecture/plotting-chapter.tex @@ -3,7 +3,7 @@ \input{../../header} \lstset{inputpath=../code} -\graphicspath{{images/}} +\graphicspath{{figures/}} \typein[\pagenumber]{Number of first page} \typein[\chapternumber]{Chapter number} diff --git a/plotting/lecture/plotting.tex b/plotting/lecture/plotting.tex index d895f8b..b27b919 100644 --- a/plotting/lecture/plotting.tex +++ b/plotting/lecture/plotting.tex @@ -148,7 +148,7 @@ or the color. For additional options consult the help. The following listing shows a simple line plot with axis labeling and a title -\lstinputlisting[caption={A simple plot showing a sinewave.}, +\pageinputlisting[caption={A simple plot showing a sinewave.}, label=simpleplotlisting]{simple_plot.m} @@ -162,10 +162,10 @@ chosen, and star marker symbols is used. Finally, the name of the curve is set to \emph{plot 1} which will be displayed in a legend, if chosen. -\begin{lstlisting}[label=settinglineprops, caption={Setting line properties when calling \varcode{plot}.}] +\begin{pagelisting}[label=settinglineprops, caption={Setting line properties when calling \varcode{plot}.}] x = 0:0.1:2*pi; y = sin(x); plot( x, y, 'color', 'r', 'linestyle', ':', 'marker', '*', 'linewidth', 1.5, 'displayname', 'plot 1') -\end{lstlisting} +\end{pagelisting} \begin{important}[Choosing the right color.] Choosing the perfect color goes a little bit beyond personal @@ -277,7 +277,7 @@ the last one defines the output format (box\,\ref{graphicsformatbox}). listing\,\ref{niceplotlisting}.}\label{spikedetectionfig} \end{figure} -\begin{ibox}[t]{\label{graphicsformatbox}File formats for digital artwork.} +\begin{ibox}[tp]{\label{graphicsformatbox}File formats for digital artwork.} There are two fundamentally different types of formats for digital artwork: \begin{enumerate} \item \enterm[bitmap]{Bitmaps} (\determ{Rastergrafik}) @@ -322,7 +322,7 @@ the last one defines the output format (box\,\ref{graphicsformatbox}). efficient. \end{ibox} -\lstinputlisting[caption={Script for creating the plot shown in +\pageinputlisting[caption={Script for creating the plot shown in \figref{spikedetectionfig}.}, label=niceplotlisting]{automatic_plot.m} @@ -380,7 +380,7 @@ draw the data. In the example we also provide further arguments to set the size, color of the dots and specify that they are filled (listing\,\ref{scatterlisting1}). -\lstinputlisting[caption={Creating a scatter plot with red filled dots.}, +\pageinputlisting[caption={Creating a scatter plot with red filled dots.}, label=scatterlisting1, firstline=9, lastline=9]{scatterplot.m} We could have used plot for this purpose and set the marker to @@ -395,8 +395,7 @@ manipulate the color we need to specify a length(x)-by-3 matrix. For each dot we provide an individual color (i.e. the RGB triplet in each row of the color matrix, lines 2-4 in listing\,\ref{scatterlisting2}) - -\lstinputlisting[caption={Creating a scatter plot with size and color +\pageinputlisting[caption={Creating a scatter plot with size and color variations. The RGB triplets define the respective color intensity in a range 0:1. Here, we modify only the red color channel.}, label=scatterlisting2, linerange={15-15, 21-23}]{scatterplot.m} @@ -431,7 +430,7 @@ figures\,\ref{regularsubplotsfig}, \ref{irregularsubplotsfig}). also below).}\label{regularsubplotsfig} \end{figure} -\lstinputlisting[caption={Script for creating subplots in a regular +\pageinputlisting[caption={Script for creating subplots in a regular grid \figref{regularsubplotsfig}.}, label=regularsubplotlisting, basicstyle=\ttfamily\scriptsize]{regular_subplot.m} @@ -458,7 +457,7 @@ create a grid with larger numbers of columns and rows, and specify the used cells of the grid by passing a vector as the third argument to \code{subplot()}. -\lstinputlisting[caption={Script for creating subplots of different +\pageinputlisting[caption={Script for creating subplots of different sizes \figref{irregularsubplotsfig}.}, label=irregularsubplotslisting, basicstyle=\ttfamily\scriptsize]{irregular_subplot.m} @@ -516,7 +515,7 @@ its properties. See the \matlab{} help for more information. listing\,\ref{errorbarlisting} for A and C and listing\,\ref{errorbarlisting2} }\label{errorbarplot} \end{figure} -\lstinputlisting[caption={Illustrating estimation errors using error bars. Script that +\pageinputlisting[caption={Illustrating estimation errors using error bars. Script that creates \figref{errorbarplot}. A, B}, label=errorbarlisting, firstline=13, lastline=31, basicstyle=\ttfamily\scriptsize]{errorbarplot.m} @@ -550,7 +549,7 @@ leading to invisibility and a value of one to complete opaqueness. Finally, we use the normal plot command to draw a line connecting the average values (line 12). -\lstinputlisting[caption={Illustrating estimation errors using a shaded area. Script that +\pageinputlisting[caption={Illustrating estimation errors using a shaded area. Script that creates \figref{errorbarplot} C.}, label=errorbarlisting2, firstline=33, basicstyle=\ttfamily\scriptsize]{errorbarplot.m} @@ -575,7 +574,7 @@ listing\,\ref{annotationsplotlisting}. For more options consult the listing\,\ref{annotationsplotlisting}}\label{annotationsplot} \end{figure} -\lstinputlisting[caption={Adding annotations to figures. Script that +\pageinputlisting[caption={Adding annotations to figures. Script that creates \figref{annotationsplot}.}, label=annotationsplotlisting, basicstyle=\ttfamily\scriptsize]{annotations.m} @@ -632,7 +631,7 @@ Lissajous figure. 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The equality sign is the so called @@ -93,8 +94,7 @@ information but it is not suited to be used in programs (see also the \code{who} function that returns a list of all defined variables, listing~\ref{varListing2}). -\newpage -\begin{lstlisting}[label=varListing2, caption={Requesting information about defined variables and their types.}] +\begin{pagelisting}[label=varListing2, caption={Requesting information about defined variables and their types.}] >>class(x) ans = double @@ -110,7 +110,7 @@ x y z x 1x1 8 double y 0x0 0 double z 1x1 2 char -\end{lstlisting} +\end{pagelisting} \begin{important}[Naming conventions] There are a few rules regarding variable names. \matlab{} is @@ -120,7 +120,6 @@ x y z variable names. \end{important} -\pagebreak[4] \subsection{Working with variables} We can certainly work, i.e. do calculations, with variables. \matlab{} knows all basic \entermde[Operator!arithmetic]{Operator!arithmetischer}{arithmetic operators} @@ -131,7 +130,7 @@ such as \code[Operator!arithmetic!1add@+]{+}, \code[Operator!arithmetic!5pow@\^{}]{\^{}}. Listing~\ref{varListing3} shows their use. -\begin{lstlisting}[label=varListing3, caption={Working with variables.}] +\begin{pagelisting}[label=varListing3, caption={Working with variables.}] >> x = 1; >> x + 10 ans = @@ -149,13 +148,12 @@ ans = z = 3 ->> z = z * 5; ->> z +>> z = z * 5 z = 15 >> clear z % deleting a variable -\end{lstlisting} +\end{pagelisting} Note: in lines 2 and 10 the variables have been used without changing their values. Whenever the value of a variable should change, the @@ -271,8 +269,8 @@ step-sizes unequal to 1. Line 5 can be read like: ``Create a variable \varcode{b} and assign the values from 0 to 9 in increasing steps of 1.''. Line 9 reads: ``Create a variable \varcode{c} and assign the values from 0 to 10 in steps of 2''. -\pagebreak -\begin{lstlisting}[label=generatevectorslisting, caption={Creating simple row-vectors.}] + +\begin{pagelisting}[label=generatevectorslisting, caption={Creating simple row-vectors.}] >> a = [0 1 2 3 4 5 6 7 8 9] % Creating a row-vector a = 0 1 2 3 4 5 6 7 8 9 @@ -284,7 +282,7 @@ b = >> c = (0:2:10) c = 0 2 4 6 8 10 -\end{lstlisting} +\end{pagelisting} The length of a vector, that is the number of elements, can be requested using the \code{length()} or \code{numel()} @@ -292,14 +290,14 @@ functions. \code{size()} provides the same information in a slightly, yet more powerful way (listing~\ref{vectorsizeslisting}). The above used vector \varcode{a} has the following size: -\begin{lstlisting}[label=vectorsizeslisting, caption={Size of a vector.}] +\begin{pagelisting}[label=vectorsizeslisting, caption={Size of a vector.}] >> length(a) ans = 10 >> size(a) ans = 1 10 -\end{lstlisting} +\end{pagelisting} The answer provided by the \code{size()} function demonstrates that vectors are nothing else but 2-dimensional matrices in which one @@ -310,7 +308,7 @@ create a column-vector and how the \code[Operator!Matrix!']{'} --- operator is used to transpose the column-vector into a row-vector (lines 14 and following). -\begin{lstlisting}[label=columnvectorlisting, caption={Column-vectors.}] +\begin{pagelisting}[label=columnvectorlisting, caption={Column-vectors.}] >> b = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] % Creating a column-vector b = 1 @@ -333,7 +331,7 @@ b = >> size(b) ans = 1 10 -\end{lstlisting} +\end{pagelisting} \subsubsection{Accessing elements of a vector} @@ -354,7 +352,7 @@ number of elements irrespective of the type of vector. Elements of a vector are accessed via their index. This process is called \entermde{Indizierung}{indexing}. - In \matlab{} the first element has the index one. + In \matlab{} the first element in a vector has the index one. The last element's index equals the length of the vector. \end{important} @@ -365,25 +363,25 @@ individual values by providing a single index or use the \code[Operator!Matrix!:]{:} notation to access multiple values with a single command. -\begin{lstlisting}[label=vectorelementslisting, caption={Access to individual elements of a vector.}] ->> a = (11:20) +\begin{pagelisting}[label=vectorelementslisting, caption={Access to individual elements of a vector.}] +>> a = (11:20) % generate a vector a = 11 12 13 14 15 16 17 18 19 20 ->> a(1) % the 1. element +>> a(1) % the 1. element ans = 11 ->> a(5) % the 5. element +>> a(5) % the 5. element ans = 15 ->> a(end) % the last element +>> a(end) % the last element ans = 20 -\end{lstlisting} +\end{pagelisting} -\begin{lstlisting}[caption={Access to multiple elements.}, label=vectorrangelisting] +\begin{pagelisting}[caption={Access to multiple elements.}, label=vectorrangelisting] >> a([1 3 5]) % 1., 3. and 5. element ans = 11 13 15 ->> a(2:4) % all elements with the indices 2 to 4 +>> a(2:4) % elements at indices 2 to 4 ans = 12 13 14 @@ -394,7 +392,7 @@ ans = >> a(:) % all elements as row-vector ans = 11 12 13 14 15 16 17 18 19 20 -\end{lstlisting} +\end{pagelisting} \begin{exercise}{vectorsize.m}{vectorsize.out} Create a row-vector \varcode{a} with 5 elements. The return value of @@ -403,13 +401,13 @@ ans = \end{exercise} \begin{important}[The : (colon) operator] - The colon \code[Operator!colon@:]{:} operator is often used when working with vectors. It has multiple purposes. + The colon \code[Operator!colon@:]{:} operator is often used when working with vectors. It has multiple purposes.\vspace{-1ex} \begin{enumerate} - \item In the simplest form, \code{x = a:b} with \code{a} and \code{b} being two numbers, it creates - a vector \code{x} containing the numbers \code{a} to \code{b} in integer steps. In \matlab{} the borders $a$ and $b$ are included $[a, b]$ or $a\leq x \leq b$. - \item In the form \code{x = a:c:b} the vector \code{x} uses a \emph{stepsize} of \code{c} to create the range of numbers. - \item When used in the context of indexing such as \code{x(:)} all elements of the vector x are accessed. + \item In the simplest form, \code{x = a:b} with \code{a} and \code{b} being two numbers, it generates + a vector \code{x} containing the numbers \code{a} to \code{b} inclusively in integer steps. + \item In the form \code{x = a:c:b} the vector \code{x} uses a \emph{stepsize} of \code{c} to generate the range of numbers. \item As vectors are often used for indexing in other vectors one use the colon operator to create such vectors implicitely, e.g. \varcode{x(1:2:end)} to access every seond element of \code{x}. + \item Indexing with a single colon, e.g. \code{x(:)}, returns all elements of the vector \code{x} as a row vector. \end{enumerate} \end{important} @@ -423,7 +421,7 @@ how vectors and scalars can be combined with the operators \code[Operator!arithm \code[Operator!arithmetic!4div@/]{/} \code[Operator!arithmetic!5powe@.\^{}]{.\^}. -\begin{lstlisting}[caption={Calculating with vectors and scalars.},label=vectorscalarlisting] +\begin{pagelisting}[caption={Calculations with vectors and scalars.},label=vectorscalarlisting] >> a = (0:2:8) a = 0 2 4 6 8 @@ -447,7 +445,7 @@ ans = >> a .^ 2 % exponentiation ans = 0 4 16 36 64 -\end{lstlisting} +\end{pagelisting} When doing calculations with scalars and vectors the same mathematical operation is done to each element of the vector. In case of, e.g. an @@ -460,7 +458,7 @@ element-wise operations of two vectors, e.g. each element of vector layout (row- or column vectors). Addition and subtraction are always element-wise (listing~\ref{vectoradditionlisting}). -\begin{lstlisting}[caption={Element-wise addition and subtraction of two vectors.},label=vectoradditionlisting] +\begin{pagelisting}[caption={Element-wise addition and subtraction of two vectors.},label=vectoradditionlisting] >> a = [4 9 12]; >> b = [4 3 2]; >> a + b % addition @@ -479,7 +477,7 @@ Matrix dimensions must agree. >> a + d % both vectors must have the same layout! Error using + Matrix dimensions must agree. -\end{lstlisting} +\end{pagelisting} Element-wise multiplication, division, or raising a vector to a given power requires a different operator with a preceding '.'. \matlab{} defines the @@ -489,7 +487,7 @@ following operators for element-wise operations on vectors \code[Operator!arithmetic!5powe@.\^{}]{.\^{}} (listing~\ref{vectorelemmultiplicationlisting}). -\begin{lstlisting}[caption={Element-wise multiplication, division and +\begin{pagelisting}[caption={Element-wise multiplication, division and exponentiation of two vectors.},label=vectorelemmultiplicationlisting] >> a .* b % element-wise multiplication ans = @@ -509,7 +507,7 @@ Matrix dimensions must agree. >> a .* d % Both vectors must have the same layout! Error using .* Matrix dimensions must agree. -\end{lstlisting} +\end{pagelisting} The simple operators \code[Operator!arithmetic!3mul@*]{*}, \code[Operator!arithmetic!4div@/]{/} and @@ -519,7 +517,7 @@ matrix-operations known from linear algebra (Box~ of a row-vectors $\vec a$ with a column-vector $\vec b$ the scalar-poduct (or dot-product) $\sum_i = a_i b_i$. -\begin{lstlisting}[caption={Multiplication of vectors.},label=vectormultiplicationlisting] +\begin{pagelisting}[caption={Multiplication of vectors.},label=vectormultiplicationlisting] >> a * b % multiplication of two vectors Error using * Inner matrix dimensions must agree. @@ -536,14 +534,13 @@ ans = 16 12 8 36 27 18 48 36 24 -\end{lstlisting} - -\pagebreak[4] +\end{pagelisting} To remove elements from a vector an empty value (\code[Operator!Matrix!{[]}]{[]}) is assigned to the respective elements: -\begin{lstlisting}[label=vectoreraselisting, caption={Deleting elements of a vector.}] + +\begin{pagelisting}[label=vectoreraselisting, caption={Deleting elements of a vector.}] >> a = (0:2:8); >> length(a) ans = 5 @@ -556,7 +553,7 @@ a = 4 8 >> length(a) ans = 2 -\end{lstlisting} +\end{pagelisting} In addition to deleting of vector elements one also add new elements or concatenate two vectors. When performing a concatenation the two @@ -718,7 +715,7 @@ remapping, but can be really helpful rows in each column and so on.}\label{matrixlinearindexingfig} \end{figure} -\begin{lstlisting}[label=matrixLinearIndexing, caption={Lineares indexing in matrices.}] +\begin{pagelisting}[label=matrixLinearIndexing, caption={Lineares indexing in matrices.}] >> x = randi(100, [3, 4, 5]); % 3-D matrix filled with random numbers >> size(x) ans = @@ -735,17 +732,17 @@ ans = >> min(x(:)) % or even simpler ans = 4 -\end{lstlisting} +\end{pagelisting} \matlab{} defines functions that convert subscript indices to linear indices and back (\code{sub2ind()} and \code{ind2sub()}). -\begin{ibox}[tp]{\label{matrixmultiplication} The matrix--multiplication.} +\begin{ibox}[t]{\label{matrixmultiplication} The matrix--multiplication.} The matrix--multiplication from linear algebra is \textbf{not} an element--wise multiplication of each element in a matrix \varcode{A} and the respective element of matrix \varcode{B}. It is something completely different. Confusing element--wise and matrix--multiplication is one of the most common mistakes in - \matlab{}. \linebreak + \matlab{}. The matrix--multiplication of two 2-D matrices is only possible if the number of columns in the first matrix agrees with the number of @@ -795,8 +792,7 @@ box~\ref{matrixmultiplication}). To do a matrix-multiplication the inner dimensions of the matrices must agree (box~\ref{matrixmultiplication}). -\pagebreak[4] -\begin{lstlisting}[label=matrixOperations, caption={Two kinds of multiplications of matrices.}] +\begin{pagelisting}[label=matrixOperations, caption={Two kinds of multiplications of matrices.}] >> A = randi(5, [2, 3]) % 2-D matrix A = 1 5 3 @@ -822,7 +818,7 @@ ans = 10 15 20 24 23 35 16 17 25 -\end{lstlisting} +\end{pagelisting} \section{Boolean expressions} @@ -854,7 +850,7 @@ synonymous for the logical values 1 and 0. Listing~\ref{logicaldatatype} exemplifies the use of the logical data type. -\begin{lstlisting}[caption={The logical data type. Please note that the actual \matlab{} output looks a little different.}, label=logicaldatatype] +\begin{pagelisting}[caption={The logical data type. Please note that the actual \matlab{} output looks a little different.}, label=logicaldatatype] >> true ans = 1 >> false @@ -871,7 +867,7 @@ ans = 0 ans = 1 1 1 1 >> logical([1 2 3 4 0 0 10]) ans = 1 1 1 1 0 0 1 -\end{lstlisting} +\end{pagelisting} \varcode{true} and \varcode{false} are reserved keywords that evaluate to the logical values 1 and 0, respectively. If you want to create a @@ -884,7 +880,7 @@ code of each character in ``test'' is non-zero value, thus, the result of casting it to logical is a vector of logicals. A similar thing happens upon casting a vector (or matrix) of numbers to logical. Each value is converted to logical and the result is true for all non-zero -values (line 21). +values (line 15). Knowing how to represent true and false values in \matlab{} using the logical data type allows us to take a step towards more complex @@ -922,8 +918,8 @@ stored in variable \varcode{b}?''. The result of such questions is then given as a logical value. Listing~\ref{relationaloperationslisting} shows examples using relational operators. -\pagebreak -\begin{lstlisting}[caption={Relational Boolean expressions.}, label=relationaloperationslisting] + +\begin{pagelisting}[caption={Relational Boolean expressions.}, label=relationaloperationslisting] >> true == logical(1) ans = 1 >> false ~= logical(1) @@ -941,7 +937,7 @@ ans = 0 0 1 0 0 ans = 0 1 0 0 1 >> [2 0 0 5 0] >= [1 0 3 2 0] ans = 1 1 0 1 1 -\end{lstlisting} +\end{pagelisting} Testing the relations between numbers and scalar variables is straight forward. When comparing vectors, the relational operator will be @@ -1038,7 +1034,7 @@ for implementing such expressions. Listing~\ref{logicaloperatorlisting} shows a few examples and respective illustrations are shown in figure~\ref{logicaloperationsfig}. -\begin{lstlisting}[caption={Boolean expressions.}, label=logicaloperatorlisting] +\begin{pagelisting}[caption={Boolean expressions.}, label=logicaloperatorlisting] >> x = rand(1) % create a single random number in the range [0, 1] x = 0.3452 >> x > 0.25 & x < 0.75 @@ -1049,7 +1045,7 @@ x = 0.4920, 0.9106, 0.7218, 0.8749, 0.1574, 0.0201, 0.9107, 0.8357, 0.0357, 0.47 ans = 1 0 1 0 0 0 0 0 0 1 >> x < 0.25 | x > 0.75 ans = 0 1 0 1 1 1 1 1 1 0 -\end{lstlisting} +\end{pagelisting} \begin{figure}[ht] \includegraphics[]{logical_operations} @@ -1064,7 +1060,6 @@ ans = 0 1 0 1 1 1 1 1 1 0 data.}\label{logicaloperationsfig} \end{figure} -\pagebreak \begin{important}[Assignment and equality operators] The assignment operator \code[Operator!Assignment!=]{=} and the relational equality operator \code[Operator!relational!==]{==} are @@ -1093,7 +1088,7 @@ elements of \varcode{x} where the Boolean expression \varcode{x < 0} evaluates to true and store the result in the variable \varcode{x\_smaller\_zero}''. -\begin{lstlisting}[caption={Logical indexing.}, label=logicalindexing1] +\begin{pagelisting}[caption={Logical indexing.}, label=logicalindexing1] >> x = randn(1, 6) % a vector with 6 random numbers x = -1.4023 -1.4224 0.4882 -0.1774 -0.1961 1.4193 @@ -1110,7 +1105,7 @@ elements_smaller_zero = >> elements_smaller_zero = x(x < 0) elements_smaller_zero = -1.4023 -1.4224 -0.1774 -0.1961 -\end{lstlisting} +\end{pagelisting} \begin{exercise}{logicalVector.m}{logicalVector.out} Create a vector \varcode{x} containing the values 0--10. @@ -1119,8 +1114,7 @@ elements_smaller_zero = \item Display the content of \varcode{y} in the command window. \item What is the data type of \varcode{y}? \item Return only those elements \varcode{x} that are less than 5. - \end{enumerate} - \pagebreak[4] + \end{enumerate}\vspace{-1ex} \end{exercise} \begin{figure}[t] @@ -1142,7 +1136,6 @@ segment of data of a certain time span (the stimulus was on, \begin{exercise}{logicalIndexingTime.m}{} Assume that measurements have been made for a certain time. Usually measured values and the time are stored in two vectors. - \begin{itemize} \item Create a vector that represents the recording time \varcode{t = 0:0.001:10;}. @@ -1150,9 +1143,9 @@ segment of data of a certain time span (the stimulus was on, that has the same length as \varcode{t}. The values stored in \varcode{x} represent the measured data at the times in \varcode{t}. - \item Use logical indexing to select those values that have been - recorded in the time span from 5--6\,s. - \end{itemize} + \item Use logical indexing to select values that have been + recorded in the time span 5--6\,s. + \end{itemize}\vspace{-1ex} \end{exercise} \begin{ibox}[ht]{\label{advancedtypesbox}Advanced data types} @@ -1230,7 +1223,7 @@ As the name already suggests loops are used to execute the same parts of the code repeatedly. In one of the earlier exercises the factorial of five has been calculated as depicted in listing~\ref{facultylisting}. -\begin{lstlisting}[caption={Calculation of the factorial of 5 in five steps}, label=facultylisting] +\begin{pagelisting}[caption={Calculation of the factorial of 5 in five steps}, label=facultylisting] >> x = 1; >> x = x * 2; >> x = x * 3; @@ -1239,7 +1232,7 @@ five has been calculated as depicted in listing~\ref{facultylisting}. >> x x = 120 -\end{lstlisting} +\end{pagelisting} This kind of program solves the taks but it is rather repetitive. The only thing that changes is the increasing factor. The repetition of such @@ -1279,7 +1272,7 @@ a certain purpose. The \varcode{for}-loop is closed with the keyword \code{end}. Listing~\ref{looplisting} shows a simple version of such a for-loop. -\begin{lstlisting}[caption={Example of a \varcode{for}-loop.}, label=looplisting] +\begin{pagelisting}[caption={Example of a \varcode{for}-loop.}, label=looplisting] >> for x = 1:3 % head disp(x) % body end @@ -1288,7 +1281,7 @@ for-loop. 1 2 3 -\end{lstlisting} +\end{pagelisting} \begin{exercise}{factorialLoop.m}{factorialLoop.out} @@ -1308,11 +1301,11 @@ keyword \code{while} that is followed by a Boolean expression. If this can be evaluated to true, the code in the body is executed. The loop is closed with an \code{end}. -\begin{lstlisting}[caption={Basic structure of a \varcode{while} loop.}, label=whileloop] -while x == true % head with a Boolean expression +\begin{pagelisting}[caption={Basic structure of a \varcode{while} loop.}, label=whileloop] +while x == true % head with a Boolean expression % execute this code if the expression yields true end -\end{lstlisting} +\end{pagelisting} \begin{exercise}{factorialWhileLoop.m}{} Implement the factorial of a number \varcode{n} using a \varcode{while}-loop. @@ -1367,7 +1360,7 @@ expression to provide a default case. The last body of the \varcode{if} - \varcode{elseif} - \varcode{else} statement has to be finished with the \code{end} (listing~\ref{ifelselisting}). -\begin{lstlisting}[label=ifelselisting, caption={Structure of an \varcode{if} statement.}] +\begin{pagelisting}[label=ifelselisting, caption={Structure of an \varcode{if} statement.}] if x < y % head % body I, executed only if x < y elseif x > y @@ -1375,7 +1368,7 @@ elseif x > y else % body III, executed only if the previous conditions did not match end - \end{lstlisting} + \end{pagelisting} \begin{exercise}{ifelse.m}{} Draw a random number and check with an appropriate \varcode{if} @@ -1403,7 +1396,7 @@ that were not explicitly stated above (listing~\ref{switchlisting}). As usual the \code{switch} statement needs to be closed with an \code{end}. -\begin{lstlisting}[label=switchlisting, caption={Structure of a \varcode{switch} statement.}] +\begin{pagelisting}[label=switchlisting, caption={Structure of a \varcode{switch} statement.}] mynumber = input('Enter a number:'); switch mynumber case -1 @@ -1413,7 +1406,7 @@ switch mynumber otherwise disp('something else'); end -\end{lstlisting} +\end{pagelisting} \subsubsection{Comparison \varcode{if} and \varcode{switch} -- statements} @@ -1437,7 +1430,7 @@ skip the execution of the body under certain circumstances, one can use the keywords \code{break} and \code{continue} (listings~\ref{continuelisting} and \ref{continuelisting}). -\begin{lstlisting}[caption={Stop the execution of a loop using \varcode{break}.}, label=breaklisting] +\begin{pagelisting}[caption={Stop the execution of a loop using \varcode{break}.}, label=breaklisting] >> x = 1; while true if (x > 3) @@ -1450,9 +1443,9 @@ use the keywords \code{break} and \code{continue} 1 2 3 -\end{lstlisting} +\end{pagelisting} -\begin{lstlisting}[caption={Skipping iterations using \varcode{continue}.}, label=continuelisting] +\begin{pagelisting}[caption={Skipping iterations using \varcode{continue}.}, label=continuelisting] for x = 1:5 if(x > 2 & x < 5) continue; @@ -1463,7 +1456,7 @@ end 1 2 5 -\end{lstlisting} +\end{pagelisting} \begin{exercise}{logicalIndexingBenchmark.m}{logicalIndexingBenchmark.out} Above we claimed that logical indexing is faster and much more @@ -1535,11 +1528,11 @@ has one \entermde{Argument}{argument} $x$ that is transformed into the function's output value $y$. In \matlab{} the syntax of a function declaration is very similar (listing~\ref{functiondefinitionlisting}). -\begin{lstlisting}[caption={Declaration of a function in \matlab{}}, label=functiondefinitionlisting] +\begin{pagelisting}[caption={Declaration of a function in \matlab{}}, label=functiondefinitionlisting] function [y] = functionName(arg_1, arg_2) % ^ ^ ^ % return value argument_1, argument_2 -\end{lstlisting} +\end{pagelisting} The keyword \code{function} is followed by the return value(s) (it can be a list \varcode{[]} of values), the function name and the @@ -1572,7 +1565,7 @@ The following listing (\ref{badsinewavelisting}) shows a function that calculates and displays a bunch of sine waves with different amplitudes. -\begin{lstlisting}[caption={Bad example of a function that displays a series of sine waves.},label=badsinewavelisting] +\begin{pagelisting}[caption={Bad example of a function that displays a series of sine waves.},label=badsinewavelisting] function myFirstFunction() % function head t = (0:0.01:2); frequency = 1.0; @@ -1583,7 +1576,7 @@ function myFirstFunction() % function head hold on; end end -\end{lstlisting} +\end{pagelisting} \varcode{myFirstFunction} (listing~\ref{badsinewavelisting}) is a prime-example of a bad function. There are several issues with it's @@ -1644,7 +1637,7 @@ define (i) how to name the function, (ii) which information it needs Having defined this we can start coding (listing~\ref{sinefunctionlisting}). -\begin{lstlisting}[caption={Function that calculates a sine wave.}, label=sinefunctionlisting] +\begin{pagelisting}[caption={Function that calculates a sine wave.}, label=sinefunctionlisting] function [time, sine] = sinewave(frequency, amplitude, t_max, t_step) % Calculate a sinewave of a given frequency, amplitude, % duration and temporal resolution. @@ -1662,7 +1655,7 @@ function [time, sine] = sinewave(frequency, amplitude, t_max, t_step) time = (0:t_step:t_max); sine = sin(frequency .* time .* 2 .* pi) .* amplitude; end -\end{lstlisting} +\end{pagelisting} \paragraph{II. Plotting a single sine wave} @@ -1689,7 +1682,7 @@ specification of the function: With this specification we can start to implement the function (listing~\ref{sineplotfunctionlisting}). -\begin{lstlisting}[caption={Function for the graphical display of data.}, label=sineplotfunctionlisting] +\begin{pagelisting}[caption={Function for the graphical display of data.}, label=sineplotfunctionlisting] function plotFunction(x_data, y_data, name) % Plots x-data against y-data and sets the display name. % @@ -1701,7 +1694,7 @@ function plotFunction(x_data, y_data, name) % name : the displayname plot(x_data, y_data, 'displayname', name) end -\end{lstlisting} +\end{pagelisting} \paragraph{III. One script to rule them all} @@ -1728,7 +1721,7 @@ Again, we need to specify what needs to be done: The implementation is shown in listing~\ref{sinesskriptlisting}. -\begin{lstlisting}[caption={Control script for the plotting of sine waves.},label=sinesskriptlisting] +\begin{pagelisting}[caption={Control script for the plotting of sine waves.},label=sinesskriptlisting] amplitudes = 0.25:0.25:1.25; frequency = 2.0; duration = 10.0; % seconds @@ -1744,11 +1737,11 @@ for i = 1:length(amplitudes) end hold off legend('show') -\end{lstlisting} +\end{pagelisting} +\pagebreak[4] \begin{exercise}{plotMultipleSinewaves.m}{} Extend the program to plot also a range of frequencies. - \pagebreak[4] \end{exercise} From 3dd0660b21b5d8c973a24e5be7effa7bee7378e7 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 12 Dec 2020 20:34:43 +0100 Subject: [PATCH 08/87] [bootstrap] added difference of mean --- bootstrap/code/correlationsignificance.m | 14 +- bootstrap/code/meandiffsignificance.m | 40 ++++++ bootstrap/code/meandiffsignificance.out | 4 + bootstrap/lecture/bootstrap-chapter.tex | 2 - bootstrap/lecture/bootstrap.tex | 160 ++++++++++++++++++----- bootstrap/lecture/bootstrapsem.py | 2 +- bootstrap/lecture/permuteaverage.py | 103 +++++++++++++++ bootstrap/lecture/permutecorrelation.py | 52 ++++++-- chapter.mk | 3 + plotstyle.py | 7 +- 10 files changed, 326 insertions(+), 61 deletions(-) create mode 100644 bootstrap/code/meandiffsignificance.m create mode 100644 bootstrap/code/meandiffsignificance.out create mode 100644 bootstrap/lecture/permuteaverage.py diff --git a/bootstrap/code/correlationsignificance.m b/bootstrap/code/correlationsignificance.m index d9b0fff..7426cc5 100644 --- a/bootstrap/code/correlationsignificance.m +++ b/bootstrap/code/correlationsignificance.m @@ -1,6 +1,6 @@ % generate correlated data: -n=200; -a=0.2; +n = 200; +a = 0.2; x = randn(n, 1); y = randn(n, 1) + a*x; @@ -11,13 +11,13 @@ fprintf('correlation coefficient of data r = %.2f\n', rd); % distribution of null hypothesis by permutation: nperm = 1000; rs = zeros(nperm,1); -for i=1:nperm - xr=x(randperm(length(x))); % shuffle x - yr=y(randperm(length(y))); % shuffle y +for i = 1:nperm + xr = x(randperm(length(x))); % shuffle x + yr = y(randperm(length(y))); % shuffle y rs(i) = corr(xr, yr); end -[h,b] = hist(rs, 20); -h = h/sum(h)/(b(2)-b(1)); % normalization +[h, b] = hist(rs, 20); +h = h/sum(h)/(b(2)-b(1)); % normalization % significance: rq = quantile(rs, 0.95); diff --git a/bootstrap/code/meandiffsignificance.m b/bootstrap/code/meandiffsignificance.m new file mode 100644 index 0000000..96a328e --- /dev/null +++ b/bootstrap/code/meandiffsignificance.m @@ -0,0 +1,40 @@ +% generate two data sets: +n = 200; +d = 0.2; +x = randn(n, 1); +y = randn(n, 1) + d; + +% difference of sample means: +md = mean(y) - mean(x); +fprintf('difference of means of data d = %.2f\n', md); + +% distribution of null hypothesis by permutation: +nperm = 1000; +xy = [x; y]; % x and y data in one column vector +ds = zeros(nperm,1); +for i = 1:nperm + xyr = xy(randperm(length(xy))); % shuffle data + xr = xyr(1:length(x)); % random x-data + yr = xyr(length(x)+1:end); % random y-data + ds(i) = mean(yr) - mean(xr); % difference of means +end +[h, b] = hist(ds, 20); +h = h/sum(h)/(b(2)-b(1)); % normalization + +% significance: +dq = quantile(ds, 0.95); +fprintf('difference of means of null hypothesis at 5%% significance = %.2f\n', dq); +if md >= dq + fprintf('--> difference of means d=%.2f is significant\n', md); +else + fprintf('--> d=%.2f is not a significant difference of means\n', md); +end + +% plot: +bar(b, h, 'facecolor', 'b'); +hold on; +bar(b(b>=dq), h(b>=dq), 'facecolor', 'r'); +plot([md md], [0 4], 'r', 'linewidth', 2); +xlabel('Difference of means'); +ylabel('Probability density of H0'); +hold off; diff --git a/bootstrap/code/meandiffsignificance.out b/bootstrap/code/meandiffsignificance.out new file mode 100644 index 0000000..e17ad8d --- /dev/null +++ b/bootstrap/code/meandiffsignificance.out @@ -0,0 +1,4 @@ +>> meandiffsignificance +difference of means of data d = 0.18 +difference of means of null hypothesis at 5% significance = 0.17 +--> difference of means d=0.18 is significant diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index b61d395..78d7d3c 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -26,6 +26,4 @@ This chapter easily covers two lectures: Add jacknife methods to bootstrapping -Add permutation test for significant different means of two distributions. - \end{document} diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index 20f01c2..8f72366 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -125,7 +125,6 @@ Via bootstrapping we create a distribution of the mean values (\figref{bootstrapsemfig}) and the standard deviation of this distribution is the standard error of the mean. -\pagebreak[4] \begin{exercise}{bootstrapsem.m}{bootstrapsem.out} Create the distribution of mean values from bootstrapped samples resampled from a single SRS. Use this distribution to estimate the @@ -152,67 +151,156 @@ desired \entermde{Signifikanz}{significance level}, the \entermde{Nullhypothese}{null hypothesis} may be rejected. Traditionally, such probabilities are taken from theoretical -distributions which are based on assumptions about the data. Thus the -applied statistical test has to be appropriate for the type of +distributions which are based on some assumptions about the data. For +example, the data should be normally distributed. Given some data one +has to find an appropriate test that matches the properties of the data. An alternative approach is to calculate the probability density -of the null hypothesis directly from the data itself. To do this, we +of the null hypothesis directly from the data themselves. To do so, we need to resample the data according to the null hypothesis from the SRS. By such permutation operations we destroy the feature of interest -while we conserve all other statistical properties of the data. +while conserving all other statistical properties of the data. + + +\subsection{Significance of a difference in the mean} + +Often we would like to know whether two data sets differ in their +mean. Whether the ears of foxes are larger in southern Europe compared +to the ones from Scandinavia, whether a drug decreases blood pressure +in humans, whether a sensory stimulus increases the firing rate of a +neuron, etc. The \entermde{Nullhypothese}{null hypothesis} is that +they do not differ in their means, i.e. that both data sets come from +the same distribution. But even if the two data sets come from the +same distribution, their sample means may nevertheless differ by +chance. We need to figure out how these differences of the means are +distributed. Only if the measured difference between the means is +significantly larger than the ones obtained by chance we can reject +the null hypothesis and consider the two data sets to differ +significantly in their means. + +We can easily estimate the distribution of the null hypothesis by +putting the data of both data sets in one big bag. By merging the two +data sets we assume that all the data values come from the same +distribution. We then randomly separate the data values into two new +data sets. These random data sets contain data from both original data +sets and thus come from the same distribution. From these random data +sets we compute the difference of their sample means. This procedure +is repeated many, say one thousand, times and each time we get a value +for a difference of means. The distribution of these values is the +distribution of the null hypothesis. It is the distribution of +differences of mean values that we get by chance although the two data +sets come from the same distribution. For a one-sided test that checks +whether the measured difference of means is significantly larger than +zero at a significance level of 5\,\% we compute the value of the +95\,\% percentile of the null distribution. If the measured value is +larger, we can reject the null hypothesis and consider the two data +sets to differ significantly in their means. + +By using the original data to estimate the null hypothesis, we make no +assumption about the properties of the data. We do not need to worry +about the data being normally distributed. We do not need to memorize +which test to use in which situation. And we better understand what we +are testing, because we design the test ourselves. Nowadays, computer +are powerful enough to iterate even ten thousand times over the data +to compute the distribution of the null hypothesis --- with only a few +lines of code. This is why \entermde{Permutationstest}{permutaion + test} are getting quite popular. \begin{figure}[tp] - \includegraphics[width=1\textwidth]{permutecorrelation} - \titlecaption{\label{permutecorrelationfig}Permutation test for - correlations.}{Let the correlation coefficient of a dataset with - 200 samples be $\rho=0.21$. The distribution of the null - hypothesis (yellow), optained from the correlation coefficients of - permuted and therefore uncorrelated datasets is centered around - zero. The measured correlation coefficient is larger than the - 95\,\% percentile of the null hypothesis. The null hypothesis may - thus be rejected and the measured correlation is considered - statistically significant.} + \includegraphics[width=1\textwidth]{permuteaverage} + \titlecaption{\label{permuteaverage}Permutation test for differences + in means.}{We want to test whether two datasets + $\left\{x_i\right\}$ (red) and $\left\{y_i\right\}$ (blue) come + from different distributions by assessing the significance of the + difference in their sample means. The data sets were generated + with a difference in their population means of $d=0.7$. For + generating the distribution of the null hypothesis, i.e. the + distribution of differences in the means if the two data sets come + from the same distribution, we randomly select the same number of + samples from both data sets (top right). This is repeated many + times and results in the desired distribution of differences of + means (bottom). The measured difference is clearly beyond the + 95\,\% percentile of this distribution and thus indicates a + significant difference between the distributions of the two + original data sets.} \end{figure} -%\subsection{Significance of a difference in the mean} +\begin{exercise}{meandiffsignificance.m}{meandiffsignificance.out} +Estimate the statistical significance of a difference in the mean of two data sets. +\vspace{-1ex} +\begin{enumerate} +\item Generate two independent data sets, $\left\{x_i\right\}$ and + $\left\{y_i\right\}$, of $n=200$ samples each, by drawing random + numbers from a normal distribution. Add 0.2 to all the $y_i$ samples + to ensure the population means to differ by 0.2. +\item Calculate the difference between the sample means of the two data sets. +\item Estimate the distribution of the null hypothesis of no + difference of the means by generating new data sets with the same + number of samples randomly selected from both data sets. For this + lump the two data sets together into a single vector. Then permute + the order of the elements in this vector using the function + \varcode{randperm()}, split it into two data sets and calculate + the difference of their means. Repeat this 1000 times. +\item Read out the 95\,\% percentile from the resulting distribution + of the differences in the mean, the null hypothesis using the + \varcode{quantile()} function, and compare it with the difference of + means measured from the original data sets. +\end{enumerate} +\end{exercise} -%See \url{https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests.} \subsection{Significance of correlations} -A good example for the application of a -\entermde{Permutationstest}{permutaion test} is the statistical -assessment of \entermde[correlation]{Korrelation}{correlations}. Given -are measured pairs of data points $(x_i, y_i)$. By calculating the +Another nice example for the application of a +\entermde{Permutationstest}{permutaion test} is testing for +significant \entermde[correlation]{Korrelation}{correlations} +(figure\,\ref{permutecorrelationfig}). Given are measured pairs of +data points $(x_i, y_i)$. By calculating the \entermde[correlation!correlation -coefficient]{Korrelationskoeffizient}{correlation - coefficient} we can quantify how strongly $y$ depends on $x$. The -correlation coefficient alone, however, does not tell whether the -correlation is significantly different from a random correlation. The -\entermde{Nullhypothese}{null hypothesis} for such a situation is that -$y$ does not depend on $x$. In order to perform a permutation test, we -need to destroy the correlation by permuting the $(x_i, y_i)$ pairs, -i.e. we rearrange the $x_i$ and $y_i$ values in a random +coefficient]{Korrelationskoeffizient}{correlation coefficient} we can +quantify how strongly $y$ depends on $x$. The correlation coefficient +alone, however, does not tell whether the correlation is significantly +different from a non-zero correlation that we might get although there +is no true correlation in the data. The \entermde{Nullhypothese}{null + hypothesis} for such a situation is that $y$ does not depend on +$x$. In order to perform a permutation test, we need to destroy the +correlation between the data pairs by permuting the $(x_i, y_i)$ +pairs, i.e. we rearrange the $x_i$ and $y_i$ values in a random fashion. Generating many sets of random pairs and computing the -resulting correlation coefficients yields a distribution of -correlation coefficients that result randomly from uncorrelated +corresponding correlation coefficients yields a distribution of +correlation coefficients that result randomly from truly uncorrelated data. By comparing the actually measured correlation coefficient with this distribution we can directly assess the significance of the -correlation (figure\,\ref{permutecorrelationfig}). +correlation. + +\begin{figure}[tp] + \includegraphics[width=1\textwidth]{permutecorrelation} + \titlecaption{\label{permutecorrelationfig}Permutation test for + correlations.}{Let the correlation coefficient of a dataset with + 200 samples be $\rho=0.21$ (top left). By shuffling the data pairs + we destroy any true correlation (top right). The resulting + distribution of the null hypothesis (bottm, yellow), optained from + the correlation coefficients of permuted and therefore + uncorrelated datasets is centered around zero. The measured + correlation coefficient is larger than the 95\,\% percentile of + the null hypothesis. The null hypothesis may thus be rejected and + the measured correlation is considered statistically significant.} +\end{figure} \begin{exercise}{correlationsignificance.m}{correlationsignificance.out} Estimate the statistical significance of a correlation coefficient. \begin{enumerate} -\item Create pairs of $(x_i, y_i)$ values. Randomly choose $x$-values +\item Generate pairs of $(x_i, y_i)$ values. Randomly choose $x$-values and calculate the respective $y$-values according to $y_i =0.2 \cdot x_i + u_i$ where $u_i$ is a random number drawn from a normal distribution. \item Calculate the correlation coefficient. -\item Generate the distribution of the null hypothesis by generating +\item Estimate the distribution of the null hypothesis by generating uncorrelated pairs. For this permute $x$- and $y$-values \matlabfun{randperm()} 1000 times and calculate for each permutation the correlation coefficient. \item Read out the 95\,\% percentile from the resulting distribution - of the null hypothesis and compare it with the correlation - coefficient computed from the original data. + of the null hypothesis using the \varcode{quantile()} function and + compare it with the correlation coefficient computed from the + original data. \end{enumerate} \end{exercise} diff --git a/bootstrap/lecture/bootstrapsem.py b/bootstrap/lecture/bootstrapsem.py index 3a276bd..837b0b1 100644 --- a/bootstrap/lecture/bootstrapsem.py +++ b/bootstrap/lecture/bootstrapsem.py @@ -24,7 +24,7 @@ for i in range(nresamples) : musrs.append(np.mean(rng.randn(nsamples))) hmusrs, _ = np.histogram(musrs, bins, density=True) -fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.2*figure_height)) +fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.05*figure_height)) fig.subplots_adjust(**adjust_fs(left=4.0, bottom=2.7, right=1.5)) ax.set_xlabel('Mean') ax.set_xlim(-0.4, 0.4) diff --git a/bootstrap/lecture/permuteaverage.py b/bootstrap/lecture/permuteaverage.py new file mode 100644 index 0000000..53cfc0b --- /dev/null +++ b/bootstrap/lecture/permuteaverage.py @@ -0,0 +1,103 @@ +import numpy as np +import scipy.stats as st +import matplotlib.pyplot as plt +import matplotlib.gridspec as gridspec +import matplotlib.ticker as ticker +from plotstyle import * + +rng = np.random.RandomState(637281) + +# generate data that differ in their mein by d: +n = 200 +d = 0.7 +x = rng.randn(n) + d; +y = rng.randn(n); +#x = rng.exponential(1.0, n); +#y = rng.exponential(1.0, n) + d; + +# histogram of data: +db = 0.5 +bins = np.arange(-2.5, 2.6, db) +hx, _ = np.histogram(x, bins) +hy, _ = np.histogram(y, bins) + +# Diference of means, pooled standard deviation and Cohen's d: +ad = np.mean(x)-np.mean(y) +s = np.sqrt(((len(x)-1)*np.var(x)+(len(y)-1)*np.var(y))/(len(x)+len(y)-2)) +cd = ad/s + +# permutation: +nperm = 1000 +ads = [] +xy = np.hstack((x, y)) +for i in range(nperm) : + xyp = rng.permutation(xy) + ads.append(np.mean(xyp[:len(x)])-np.mean(xyp[len(x):])) + +# histogram of shuffled data: +hxp, _ = np.histogram(xyp[:len(x)], bins) +hyp, _ = np.histogram(xyp[len(x):], bins) + +# pdf of the differences of means: +h, b = np.histogram(ads, 20, density=True) + +# significance: +dq = np.percentile(ads, 95.0) +print('Measured difference of means = %.2f, difference at 95%% percentile of permutation = %.2f' % (ad, dq)) +da = 1.0-0.01*st.percentileofscore(ads, ad) +print('Measured difference of means %.2f is at %.2f%% percentile of permutation' % (ad, 100.0*da)) + +ap, at = st.ttest_ind(x, y) +print('Measured difference of means %.2f is at %.2f%% percentile of test' % (ad, ap)) + + +fig = plt.figure(figsize=cm_size(figure_width, 1.8*figure_height)) +gs = gridspec.GridSpec(nrows=2, ncols=2, wspace=0.35, hspace=0.8, + **adjust_fs(fig, left=5.0, right=1.5, top=1.0, bottom=2.7)) + +ax = fig.add_subplot(gs[0,0]) +ax.bar(bins[:-1]-0.25*db, hy, 0.5*db, **fsA) +ax.bar(bins[:-1]+0.25*db, hx, 0.5*db, **fsB) +ax.annotate('', xy=(0.0, 45.0), xytext=(d, 45.0), arrowprops=dict(arrowstyle='<->')) +ax.text(0.5*d, 50.0, 'd=%.1f' % d, ha='center') +ax.set_xlim(-2.5, 2.5) +ax.set_ylim(0.0, 50) +ax.yaxis.set_major_locator(ticker.MultipleLocator(20.0)) +ax.set_xlabel('Original x and y values') +ax.set_ylabel('Counts') + +ax = fig.add_subplot(gs[0,1]) +ax.bar(bins[:-1]-0.25*db, hyp, 0.5*db, **fsA) +ax.bar(bins[:-1]+0.25*db, hxp, 0.5*db, **fsB) +ax.set_xlim(-2.5, 2.5) +ax.set_ylim(0.0, 50) +ax.yaxis.set_major_locator(ticker.MultipleLocator(20.0)) +ax.set_xlabel('Shuffled x and y values') +ax.set_ylabel('Counts') + +ax = fig.add_subplot(gs[1,:]) +ax.annotate('Measured\ndifference\nis significant!', + xy=(ad, 1.2), xycoords='data', + xytext=(ad-0.1, 2.2), textcoords='data', ha='right', + arrowprops=dict(arrowstyle="->", relpos=(1.0,0.5), + connectionstyle="angle3,angleA=-20,angleB=100") ) +ax.annotate('95% percentile', + xy=(0.19, 0.9), xycoords='data', + xytext=(0.3, 5.0), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(0.1,0.0), + connectionstyle="angle3,angleA=40,angleB=80") ) +ax.annotate('Distribution of\nnullhypothesis', + xy=(-0.08, 3.0), xycoords='data', + xytext=(-0.22, 4.5), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0), + connectionstyle="angle3,angleA=60,angleB=150") ) +ax.bar(b[:-1], h, width=b[1]-b[0], **fsC) +ax.bar(b[:-1][b[:-1]>=dq], h[b[:-1]>=dq], width=b[1]-b[0], **fsB) +ax.plot( [ad, ad], [0, 1], **lsA) +ax.set_xlim(-0.25, 0.85) +ax.set_ylim(0.0, 5.0) +ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) +ax.set_xlabel('Difference of means') +ax.set_ylabel('PDF of H0') + +plt.savefig('permuteaverage.pdf') diff --git a/bootstrap/lecture/permutecorrelation.py b/bootstrap/lecture/permutecorrelation.py index c5f0db7..3357140 100644 --- a/bootstrap/lecture/permutecorrelation.py +++ b/bootstrap/lecture/permutecorrelation.py @@ -1,9 +1,11 @@ import numpy as np import scipy.stats as st import matplotlib.pyplot as plt +import matplotlib.gridspec as gridspec +import matplotlib.ticker as ticker from plotstyle import * -rng = np.random.RandomState(637281) +rng = np.random.RandomState(37281) # generate correlated data: n = 200 @@ -19,32 +21,56 @@ rd = np.corrcoef(x, y)[0, 1] nperm = 1000 rs = [] for i in range(nperm) : - xr=rng.permutation(x) - yr=rng.permutation(y) - rs.append( np.corrcoef(xr, yr)[0, 1] ) + xr = rng.permutation(x) + yr = rng.permutation(y) + rs.append(np.corrcoef(xr, yr)[0, 1]) +rr = np.corrcoef(xr, yr)[0, 1] # pdf of the correlation coefficients: h, b = np.histogram(rs, 20, density=True) # significance: rq = np.percentile(rs, 95.0) -print('Measured correlation coefficient = %.2f, correlation coefficient at 95%% percentile of bootstrap = %.2f' % (rd, rq)) +print('Measured correlation coefficient = %.2f, correlation coefficient at 95%% percentile of permutation = %.2f' % (rd, rq)) ra = 1.0-0.01*st.percentileofscore(rs, rd) -print('Measured correlation coefficient %.2f is at %.4f percentile of bootstrap' % (rd, ra)) +print('Measured correlation coefficient %.2f is at %.4f percentile of permutation' % (rd, ra)) rp, ra = st.pearsonr(x, y) print('Measured correlation coefficient %.2f is at %.4f percentile of test' % (rp, ra)) -fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.2*figure_height)) -fig.subplots_adjust(**adjust_fs(left=4.0, bottom=2.7, right=0.5, top=1.0)) +fig = plt.figure(figsize=cm_size(figure_width, 1.8*figure_height)) +gs = gridspec.GridSpec(nrows=2, ncols=2, wspace=0.35, hspace=0.8, + **adjust_fs(fig, left=5.0, right=1.5, top=1.0, bottom=2.7)) + +ax = fig.add_subplot(gs[0,0]) +ax.text(0.0, 4.0, 'r=%.2f' % rd, ha='center') +ax.plot(x, y, **psAm) +ax.set_xlim(-4.0, 4.0) +ax.set_ylim(-4.0, 4.0) +ax.xaxis.set_major_locator(ticker.MultipleLocator(2.0)) +ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) +ax.set_xlabel('x') +ax.set_ylabel('y') + +ax = fig.add_subplot(gs[0,1]) +ax.text(0.0, 4.0, 'r=%.2f' % rr, ha='center') +ax.plot(xr, yr, **psAm) +ax.set_xlim(-4.0, 4.0) +ax.set_ylim(-4.0, 4.0) +ax.xaxis.set_major_locator(ticker.MultipleLocator(2.0)) +ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) +ax.set_xlabel('Shuffled x') +ax.set_ylabel('Shuffled y') + +ax = fig.add_subplot(gs[1,:]) ax.annotate('Measured\ncorrelation\nis significant!', xy=(rd, 1.1), xycoords='data', - xytext=(rd, 2.2), textcoords='data', ha='left', - arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0), + xytext=(rd-0.01, 3.0), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(0.3,0.0), connectionstyle="angle3,angleA=10,angleB=80") ) ax.annotate('95% percentile', xy=(0.14, 0.9), xycoords='data', - xytext=(0.18, 4.0), textcoords='data', ha='left', + xytext=(0.16, 6.2), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.1,0.0), connectionstyle="angle3,angleA=30,angleB=80") ) ax.annotate('Distribution of\nuncorrelated\nsamples', @@ -56,7 +82,9 @@ ax.bar(b[:-1], h, width=b[1]-b[0], **fsC) ax.bar(b[:-1][b[:-1]>=rq], h[b[:-1]>=rq], width=b[1]-b[0], **fsB) ax.plot( [rd, rd], [0, 1], **lsA) ax.set_xlim(-0.25, 0.35) +ax.set_ylim(0.0, 6.0) +ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.set_xlabel('Correlation coefficient') -ax.set_ylabel('Prob. density of H0') +ax.set_ylabel('PDF of H0') plt.savefig('permutecorrelation.pdf') diff --git a/chapter.mk b/chapter.mk index 50d1708..3afd160 100644 --- a/chapter.mk +++ b/chapter.mk @@ -42,6 +42,9 @@ $(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(wildcard $(B watchchapter : while true; do ! make -q chapter && make chapter; sleep 0.5; done +watchplots : + while true; do ! make -q plots && make plots; sleep 0.5; done + cleantex: rm -f *~ rm -f $(BASENAME).aux $(BASENAME).log *.idx diff --git a/plotstyle.py b/plotstyle.py index cb453f3..ecada61 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -33,13 +33,14 @@ colors['white'] = '#FFFFFF' # general settings for plot styles: lwthick = 3.0 lwthin = 1.8 +edgewidth = 0.0 if xkcd_style else 1.0 mainline = {'linestyle': '-', 'linewidth': lwthick} minorline = {'linestyle': '-', 'linewidth': lwthin} -largemarker = {'marker': 'o', 'markersize': 9, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} -smallmarker = {'marker': 'o', 'markersize': 6, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} +largemarker = {'marker': 'o', 'markersize': 9, 'markeredgecolor': colors['white'], 'markeredgewidth': edgewidth} +smallmarker = {'marker': 'o', 'markersize': 6, 'markeredgecolor': colors['white'], 'markeredgewidth': edgewidth} largelinepoints = {'linestyle': '-', 'linewidth': lwthick, 'marker': 'o', 'markersize': 10, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} smalllinepoints = {'linestyle': '-', 'linewidth': 1.4, 'marker': 'o', 'markersize': 7, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} -filllw = 1.0 +filllw = edgewidth fillec = colors['white'] fillalpha = 0.4 filledge = {'linewidth': filllw, 'joinstyle': 'round'} From b76b2d35cce208d129f86594243831d1a9acbf41 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 13 Dec 2020 09:08:05 +0100 Subject: [PATCH 09/87] [bootstrap] generalized intro --- bootstrap/lecture/bootstrap-chapter.tex | 11 +++++- bootstrap/lecture/bootstrap.tex | 51 ++++++++++++++----------- 2 files changed, 37 insertions(+), 25 deletions(-) diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index 78d7d3c..9009d78 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -23,7 +23,14 @@ This chapter easily covers two lectures: \item 1. Bootstrapping with a proper introduction of of confidence intervals \item 2. Permutation test with a proper introduction of statistical tests (distribution of nullhypothesis, significance, power, etc.) \end{itemize} - -Add jacknife methods to bootstrapping +ToDo: +\begin{itemize} +\item Add jacknife methods to bootstrapping +\item Add discussion of confidence intervals to descriptive statistics chapter +\item Have a separate chapter on statistical tests before. What is the + essence of a statistical test (null hypothesis distribution), power + analysis, and a few examples of existing functions for statistical + tests. +\end{itemize} \end{document} diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index 8f72366..f71b268 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -5,20 +5,24 @@ \exercisechapter{Resampling methods} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Bootstrapping} - -Bootstrapping methods are applied to create distributions of -statistical measures via resampling of a sample. Bootstrapping offers several -advantages: +\entermde{Resampling methoden}{Resampling methods} are applied to +generate distributions of statistical measures via resampling of +existing samples. Resampling offers several advantages: \begin{itemize} \item Fewer assumptions (e.g. a measured sample does not need to be normally distributed). \item Increased precision as compared to classical methods. %such as? -\item General applicability: the bootstrapping methods are very +\item General applicability: the resampling methods are very similar for different statistics and there is no need to specialize the method to specific statistic measures. \end{itemize} +Resampling methods can be used for both estimating the precision of +estimated statistics (e.g. standard error of the mean, confidence +intervals) and testing for significane. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Bootstrapping} \begin{figure}[tp] \includegraphics[width=0.8\textwidth]{2012-10-29_16-26-05_771}\\[2ex] @@ -88,20 +92,20 @@ of the statistical population. We can use the bootstrap distribution to draw conclusion regarding the precision of our estimation (e.g. standard errors and confidence intervals). -Bootstrapping methods create bootstrapped samples from a SRS by +Bootstrapping methods generate bootstrapped samples from a SRS by resampling. The bootstrapped samples are used to estimate the sampling distribution of a statistical measure. The bootstrapped samples have -the same size as the original sample and are created by randomly +the same size as the original sample and are generated by randomly drawing with replacement. That is, each value of the original sample -can occur once, multiple time, or not at all in a bootstrapped +can occur once, multiple times, or not at all in a bootstrapped sample. This can be implemented by generating random indices into the data set using the \code{randi()} function. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Bootstrap of the standard error} +\subsection{Bootstrap the standard error} -Bootstrapping can be nicely illustrated at the example of the +Bootstrapping can be nicely illustrated on the example of the \enterm{standard error} of the mean (\determ{Standardfehler}). The arithmetic mean is calculated for a simple random sample. The standard error of the mean is the standard deviation of the expected @@ -121,9 +125,9 @@ population. the standard error of the mean.} \end{figure} -Via bootstrapping we create a distribution of the mean values +Via bootstrapping we generate a distribution of mean values (\figref{bootstrapsemfig}) and the standard deviation of this -distribution is the standard error of the mean. +distribution is the standard error of the sample mean. \begin{exercise}{bootstrapsem.m}{bootstrapsem.out} Create the distribution of mean values from bootstrapped samples @@ -148,17 +152,18 @@ distribution is the standard error of the mean. Statistical tests ask for the probability of a measured value to originate from a null hypothesis. Is this probability smaller than the desired \entermde{Signifikanz}{significance level}, the -\entermde{Nullhypothese}{null hypothesis} may be rejected. +\entermde{Nullhypothese}{null hypothesis} can be rejected. Traditionally, such probabilities are taken from theoretical -distributions which are based on some assumptions about the data. For -example, the data should be normally distributed. Given some data one -has to find an appropriate test that matches the properties of the -data. An alternative approach is to calculate the probability density -of the null hypothesis directly from the data themselves. To do so, we -need to resample the data according to the null hypothesis from the -SRS. By such permutation operations we destroy the feature of interest -while conserving all other statistical properties of the data. +distributions which have been derived based on some assumptions about +the data. For example, the data should be normally distributed. Given +some data one has to find an appropriate test that matches the +properties of the data. An alternative approach is to calculate the +probability density of the null hypothesis directly from the data +themselves. To do so, we need to resample the data according to the +null hypothesis from the SRS. By such permutation operations we +destroy the feature of interest while conserving all other statistical +properties of the data. \subsection{Significance of a difference in the mean} From 68784b0e23125cc3cfe32557a0b4c7ac69c6bddd Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 13 Dec 2020 09:43:44 +0100 Subject: [PATCH 10/87] random fixes and notes --- Makefile | 2 +- chapter.mk | 2 ++ codestyle/lecture/codestyle.tex | 1 + header.tex | 2 +- plotting/lecture/plotting.tex | 28 +++++++++--------- .../lecture/pointprocessscetchA.eps | 4 +-- .../lecture/pointprocessscetchA.pdf | Bin 2786 -> 2786 bytes .../lecture/pointprocessscetchB.eps | 4 +-- .../lecture/pointprocessscetchB.pdf | Bin 4694 -> 4694 bytes scientificcomputing-script.tex | 15 +++++----- 10 files changed, 30 insertions(+), 28 deletions(-) diff --git a/Makefile b/Makefile index a743d0a..b59d881 100644 --- a/Makefile +++ b/Makefile @@ -3,7 +3,7 @@ BASENAME=scientificcomputing-script SUBDIRS=programming debugging plotting codestyle statistics bootstrap regression likelihood pointprocesses designpattern SUBTEXS=$(foreach subd, $(SUBDIRS), $(subd)/lecture/$(subd).tex) -all : script chapters +all : plots chapters index script chapters : for sd in $(SUBDIRS); do $(MAKE) -C $$sd/lecture chapter; done diff --git a/chapter.mk b/chapter.mk index 3afd160..0482aed 100644 --- a/chapter.mk +++ b/chapter.mk @@ -10,6 +10,8 @@ pythonplots : $(PYPDFFILES) $(PYPDFFILES) : %.pdf: %.py ../../plotstyle.py PYTHONPATH="../../" python3 $< + #ps2pdf $@ $(@:.pdf=-temp.pdf) # strip fonts, saves only about 1.5MB + #mv $(@:.pdf=-temp.pdf) $@ cleanpythonplots : rm -f $(PYPDFFILES) diff --git a/codestyle/lecture/codestyle.tex b/codestyle/lecture/codestyle.tex index 01d1d12..8e2ee7e 100644 --- a/codestyle/lecture/codestyle.tex +++ b/codestyle/lecture/codestyle.tex @@ -4,6 +4,7 @@ more months might as well have been written by someone else.}{Eagleson's law} +\noindent Cultivating a good code style is not just a matter of good taste but rather is a key ingredient for readability and maintainability of code and, in the end, facilitates reproducibility of scientific diff --git a/header.tex b/header.tex index fcaaa87..ab412ef 100644 --- a/header.tex +++ b/header.tex @@ -319,7 +319,7 @@ % \newboolean{showexercisesolutions} \setboolean{showexercisesolutions}{true} -\newcommand{\exercisesolutions}{chapter} % 0: here, 1: chapter, 2: end +\newcommand{\exercisesolutions}{end} % 0: here, 1: chapter, 2: end % we need this also as numbers: \ifthenelse{\equal{\exercisesolutions}{end}}{\newcommand{\exercisesolutionsnum}{2}}{% \ifthenelse{\equal{\exercisesolutions}{chapter}}{\newcommand{\exercisesolutionsnum}{1}}{% diff --git a/plotting/lecture/plotting.tex b/plotting/lecture/plotting.tex index b27b919..1d30084 100644 --- a/plotting/lecture/plotting.tex +++ b/plotting/lecture/plotting.tex @@ -74,20 +74,20 @@ the data was changed or the same kind of plot has to be created for a number of datasets. \begin{important}[Why manual editing should be avoided.] - On first glance the manual editing of a figure using tools such as - Corel draw, Illustrator, etc.\,appears much more convenient and less - complex than coding everything into the analysis scripts. This, - however, is not entirely true. What if the figure has to be re-drawn - or updated? Then the editing work starts all over again. Rather, - there is a great risk associated with the manual editing - approach. Axes may be shifted, fonts have not been embedded into the - final document, annotations have been copy pasted between figures - and are not valid. All of these mistakes can be found in - publications and then require an erratum, which is not - desirable. Even if it appears more cumbersome in the beginning one - should always try to create publication-ready figures directly from - the data analysis tool using scripts or functions to properly layout - the plot. + On first glance manual editing of a figure using tools such as + inkscape, Corel draw, Illustrator, etc.\,appears much more + convenient and less complex than coding everything into the analysis + scripts. This, however, is not entirely true. What if the figure has + to be re-drawn or updated, because, for example, you got more data? + Then the editing work starts all over again. In addition, there is a + great risk associated with the manual editing approach. Axes may be + shifted, fonts have not been embedded into the final document, + annotations have been copy-pasted between figures and are not + valid. All of these mistakes can be found in publications and then + require an erratum, which is not desirable. Even if it appears more + cumbersome in the beginning, one should always try to generate + publication-ready figures directly from the data analysis tool using + scripts or functions to properly layout and annotate the plot. \end{important} \subsection{Simple plotting} diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 441b034..5a4bb00 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Fri Dec 11 21:08:22 2020 +%%CreationDate: Sun Dec 13 09:18:35 2020 %%DocumentFonts: %%BoundingBox: 50 50 373 135 %%EndComments @@ -433,7 +433,7 @@ SDict begin [ /Author (jan) % /Producer (gnuplot) % /Keywords () - /CreationDate (Fri Dec 11 21:08:22 2020) + /CreationDate (Sun Dec 13 09:18:35 2020) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchA.pdf b/pointprocesses/lecture/pointprocessscetchA.pdf index 3d417334e8f4f0885323a9268c63697c84990acd..b06226f27816fe77a57084746e940457f8cc9dc1 100644 GIT binary patch delta 309 zcmaDP`bc!cQD$CK3nODwGlL{ub5moB$pLKglRq+NVG(U-vEecfF|f2Uw6HQZoqU!> zLn62|PeIouRX157#L(DE!N3YEX=OT@m$eCt3AKgA`nBvr%33M61?WN2()X=q_=x|x%+hB4O3)Y8<{)YZbo z+|bR^#n{Ed(8ATy&C%S^#nIBx$kffwhMRntYZ; zL&B{nQ$g1yRX157#L&=6!N>|MX=OB-m$eCt3AKgA`nBvr%33M61?WC%nC7Dh&!IXP<>W6jOXj4TbEja|&l zEDemEoehnQEM1)~fTGT(&TdXlb~Xf6#B$l$aTS*&7L`;KrKWKinHU>$sj9mAyKw;k D@|;U- diff --git a/pointprocesses/lecture/pointprocessscetchB.eps b/pointprocesses/lecture/pointprocessscetchB.eps index b9863a7..a0b1ee2 100644 --- a/pointprocesses/lecture/pointprocessscetchB.eps +++ b/pointprocesses/lecture/pointprocessscetchB.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchB.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Fri Dec 11 21:08:22 2020 +%%CreationDate: Sun Dec 13 09:18:35 2020 %%DocumentFonts: %%BoundingBox: 50 50 373 237 %%EndComments @@ -433,7 +433,7 @@ SDict begin [ /Author (jan) % /Producer (gnuplot) % /Keywords () - /CreationDate (Fri Dec 11 21:08:22 2020) + /CreationDate (Sun Dec 13 09:18:35 2020) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchB.pdf b/pointprocesses/lecture/pointprocessscetchB.pdf index d172e5c62c65027bc4b578fa5f6b7634f9b9e8ef..6d49213180fa4a5b33b784fef75bb8f5208c60a8 100644 GIT binary patch delta 266 zcmcbna!qA}B{#3Bg^{tTnL(1Sxv8D^SDeWM<;zY~pHUVrXJyVQFS*>}+XbX5{Q@Wa?yQ R;p}4MY-dAA#bj$CX#h%9KrR3P delta 266 zcmcbna!qA}B{#28l97q2fw`%!xru@0WC33J$*J5~7@`W3|8QG#8HN}cS{Yba85vD> zX3A!Z0BYLquZoWL^~vQTfe}dDEGML1w$8 zCMy^kD!}cG6_8{%G%_@>Ff!U)D^SDeWN7YW;b>@JY-VN*q+CqR9Zg-Foy`rMUCqoK Qoh*#)YzV2CY%L@W00J>TyZ`_I diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 4847455..21daaba 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -71,19 +71,18 @@ \includechapter{regression} +\includechapter{likelihood} + % add chapter on generalized linear models (versus ANOVA) -% add chapter on nonlinear fitting (methods, initial values, local minima) - -\includechapter{likelihood} +% add chapter on nonlinear fitting (methods, initial values, local minima, power law fits on log-log data) \includechapter{pointprocesses} % add chapter on time series (amplitude distribution, autocorrelation, crosscorrelation) - %\includechapter{spectral} -% add chapter on digital filtering +% add chapter on filtering and envelopes % add chapter on event detection, signal detection, ROC @@ -97,11 +96,11 @@ %\part{Tools} % Latex -% markdown +% markdown, html % Makefile % version control (git and github) only put source files into repository! % distributed computing (ssh and grid engines) -% data handling (structure, data bases, storage (rsync), backup) +% data handling (structure, storage (rsync), backup, data bases) % data annotation, meta data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -111,7 +110,7 @@ %\chapter{Cheat-Sheet} %%%% solutions: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% \printallsolutions +\printallsolutions %%%% indices: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% From c9dd1ffbe64c39f52d972fa5ad5a091aba1bb53e Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 13 Dec 2020 13:43:27 +0100 Subject: [PATCH 11/87] [bootstrap] expanding exercise by difference of mean permutation test --- bootstrap/exercises/bootstrapmean.m | 2 +- bootstrap/exercises/correlationbootstrap.m | 14 ++--- bootstrap/exercises/correlationsignificance.m | 20 +++---- bootstrap/exercises/exercises01.tex | 54 +++++++++++++++++-- bootstrap/exercises/meandiffpermutation.m | 29 ++++++++++ bootstrap/exercises/meandiffsignificance.m | 48 +++++++++++++++++ bootstrap/exercises/tdistribution.m | 16 +++--- .../exercises/fitting.tex | 0 8 files changed, 152 insertions(+), 31 deletions(-) create mode 100644 bootstrap/exercises/meandiffpermutation.m create mode 100644 bootstrap/exercises/meandiffsignificance.m rename {statistics => regression}/exercises/fitting.tex (100%) diff --git a/bootstrap/exercises/bootstrapmean.m b/bootstrap/exercises/bootstrapmean.m index 6f3b494..686df9e 100644 --- a/bootstrap/exercises/bootstrapmean.m +++ b/bootstrap/exercises/bootstrapmean.m @@ -10,7 +10,7 @@ function [bootsem, mu] = bootstrapmean(x, resample) for i = 1:resample % resample: xr = x(randi(nsamples, nsamples, 1)); - % compute statistics on sample: + % compute statistics of resampled sample: mu(i) = mean(xr); end bootsem = std(mu); diff --git a/bootstrap/exercises/correlationbootstrap.m b/bootstrap/exercises/correlationbootstrap.m index 707285f..8f6f16f 100644 --- a/bootstrap/exercises/correlationbootstrap.m +++ b/bootstrap/exercises/correlationbootstrap.m @@ -1,18 +1,18 @@ %% (a) bootstrap: nperm = 1000; -rb = zeros(nperm,1); +rb = zeros(nperm, 1); for i=1:nperm % indices for resampling the data: inx = randi(length(x), length(x), 1); % resampled data pairs: - xb=x(inx); - yb=y(inx); + xb = x(inx); + yb = y(inx); rb(i) = corr(xb, yb); end %% (b) pdf of the correlation coefficients: -[hb,bb] = hist(rb, 20); -hb = hb/sum(hb)/(bb(2)-bb(1)); % normalization +[hb, bb] = hist(rb, 20); +hb = hb/sum(hb)/(bb(2)-bb(1)); % normalization %% (c) significance: rbq = quantile(rb, 0.05); @@ -25,8 +25,8 @@ end %% plot: hold on; -bar(b, h, 'facecolor', [0.5 0.5 0.5]); -bar(bb, hb, 'facecolor', 'b'); +bar(b, h, 'facecolor', [0.5 0.5 0.5]); % permuation test +bar(bb, hb, 'facecolor', 'b'); % bootstrap bar(bb(bb<=rbq), hb(bb<=rbq), 'facecolor', 'r'); plot([rd rd], [0 4], 'r', 'linewidth', 2); xlim([-0.25 0.75]) diff --git a/bootstrap/exercises/correlationsignificance.m b/bootstrap/exercises/correlationsignificance.m index d44af84..c7b1939 100644 --- a/bootstrap/exercises/correlationsignificance.m +++ b/bootstrap/exercises/correlationsignificance.m @@ -1,4 +1,4 @@ -%% (a) generate correlated data +%% (a) generate correlated data: n = 1000; a = 0.2; x = randn(n, 1); @@ -8,7 +8,7 @@ y = randn(n, 1) + a*x; subplot(1, 2, 1); plot(x, a*x, 'r', 'linewidth', 3); hold on -%scatter(x, y ); % either scatter ... +%scatter(x, y ); % either scatter ... plot(x, y, 'o', 'markersize', 2 ); % ... or plot - same plot. xlim([-4 4]) ylim([-4 4]) @@ -20,20 +20,20 @@ hold off %c = corrcoef(x, y); % returns correlation matrix %rd = c(1, 2); rd = corr(x, y); -fprintf('correlation coefficient = %.2f\n', rd ); +fprintf('correlation coefficient = %.2f\n', rd); %% (e) permutation: nperm = 1000; -rs = zeros(nperm,1); -for i=1:nperm - xr=x(randperm(length(x))); % shuffle x - yr=y(randperm(length(y))); % shuffle y +rs = zeros(nperm, 1); +for i = 1:nperm + xr = x(randperm(length(x))); % shuffle x + yr = y(randperm(length(y))); % shuffle y rs(i) = corr(xr, yr); end %% (g) pdf of the correlation coefficients: -[h,b] = hist(rs, 20); -h = h/sum(h)/(b(2)-b(1)); % normalization +[h, b] = hist(rs, 20); +h = h/sum(h)/(b(2)-b(1)); % normalization %% (h) significance: rq = quantile(rs, 0.95); @@ -49,7 +49,7 @@ subplot(1, 2, 2) hold on; bar(b, h, 'facecolor', 'b'); bar(b(b>=rq), h(b>=rq), 'facecolor', 'r'); -plot( [rd rd], [0 4], 'r', 'linewidth', 2); +plot([rd rd], [0 4], 'r', 'linewidth', 2); xlim([-0.25 0.25]) xlabel('Correlation coefficient'); ylabel('Probability density of H0'); diff --git a/bootstrap/exercises/exercises01.tex b/bootstrap/exercises/exercises01.tex index 0917579..dd2380d 100644 --- a/bootstrap/exercises/exercises01.tex +++ b/bootstrap/exercises/exercises01.tex @@ -15,7 +15,7 @@ \else \newcommand{\stitle}{} \fi -\header{{\bfseries\large Exercise 9\stitle}}{{\bfseries\large Bootstrap}}{{\bfseries\large December 9th, 2019}} +\header{{\bfseries\large Exercise 8\stitle}}{{\bfseries\large Resampling}}{{\bfseries\large December 14th, 2020}} \firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: jan.benda@uni-tuebingen.de} \runningfooter{}{\thepage}{} @@ -86,6 +86,9 @@ jan.benda@uni-tuebingen.de} \begin{questions} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\question \qt{Read chapter 7 of the script on ``resampling methods''!}\vspace{-3ex} + \question \qt{Bootstrap the standard error of the mean} We want to compute the standard error of the mean of a data set by means of the bootstrap method and compare the result with the formula @@ -149,10 +152,10 @@ normally distributed? \continue -\question \qt{Permutation test} \label{permutationtest} +\question \qt{Permutation test of correlations} \label{correlationtest} We want to compute the significance of a correlation by means of a permutation test. \begin{parts} - \part \label{permutationtestdata} Generate 1000 correlated pairs + \part \label{correlationtestdata} Generate 1000 correlated pairs $x$, $y$ of random numbers according to: \begin{verbatim} n = 1000 @@ -188,9 +191,13 @@ correlation coefficient of zero we can conclude that the correlation coefficient of the data indeed quantifies correlated data. We take the same data set that we have generated in exercise -\ref{permutationtest} (\ref{permutationtestdata}). +\ref{correlationtest} (\ref{correlationtestdata}). \begin{parts} - \part Bootstrap 1000 times the correlation coefficient from the data. + \part Bootstrap 1000 times the correlation coefficient from the + data, i.e. generate bootstrap data by randomly resampling the + original data pairs with replacement. Use the \code{randi()} + function for generating random indices that you can use to select a + random sample from the original data. \part Compute and plot the probability density of these correlation coefficients. \part Is the correlation of the original data set significant? @@ -200,6 +207,43 @@ We take the same data set that we have generated in exercise \includegraphics[width=1\textwidth]{correlationbootstrap} \end{solution} + +\continuepage +\question \qt{Permutation test of difference of means} +We want to test whether two data sets come from distributions that +differ in their mean by means of a permutation test. +\begin{parts} + \part Generate two normally distributed data sets $x$ and $y$ + containing each $n=200$ samples. Let's assume the $x$ samples are + measurements of the membrane potential of a mammalian photoreceptor + in darkness with a mean of $-40$\,mV and a standard deviation of + 1\,mV. The $y$ values are the membrane potentials measured under dim + illumination and come from a distribution with the same standard + deviation and a mean of $-40.5$\,mV. See section 5.2 ``Scaling and + shifting random numbers'' in the script. + \part Plot histograms of the $x$ and $y$ data in a single + plot. Choose appropriate bins. + \part Compute the means of $x$ and $y$ and their difference. + \part The null hypothesis is that the $x$ and $y$ data come from the + same distribution. How can you generate new samples $x_r$ and $y_r$ + from the original data that come from the same distribution? + \part Do exactly this 1000 times and compute each time the + difference of the means of the two resampled samples. + \part Compute and plot the probability density of the resulting + distribution of the null hypothesis. + \part Is the difference of the means of the original data sets significant? + \part Repeat this procedure for $y$ samples that are closer or + further apart from the mean of the $x$ data set. For this put the + computations of the permuation test in a function and all the plotting + in another function. +\end{parts} +\begin{solution} + \lstinputlisting{meandiffpermutation.m} + %\lstinputlisting{meandiffplots.m} + \lstinputlisting{meandiffsignificance.m} + \includegraphics[width=1\textwidth]{meandiffsignificance} +\end{solution} + \end{questions} \end{document} \ No newline at end of file diff --git a/bootstrap/exercises/meandiffpermutation.m b/bootstrap/exercises/meandiffpermutation.m new file mode 100644 index 0000000..f8fb58a --- /dev/null +++ b/bootstrap/exercises/meandiffpermutation.m @@ -0,0 +1,29 @@ +function [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha) +% Permutation test for difference of means of two independent samples. +% +% [md, ds] = meandiffpermutation(x, y, nperm, alpha); +% +% Arguments: +% x: vector with the samples of the x data set. +% y: vector with the samples of the y data set. +% nperm: number of permutations run. +% alpha: significance level. +% +% Returns: +% md: difference of the means +% ds: vector containing the differences of the means of the resampled data sets +% dq: difference of the means at a significance of alpha. + + md = mean(x) - mean(y); % measured difference + xy = [x; y]; % merge data sets + % permutations: + ds = zeros(nperm, 1); + for i = 1:nperm + xyr = xy(randperm(length(xy))); % shuffle xy + xr = xyr(1:length(x)); % random x sample + yr = xyr(length(x)+1:end); % random y sample + ds(i) = mean(xr) - mean(yr); + end + % significance: + dq = quantile(ds, 1.0 - alpha); +end diff --git a/bootstrap/exercises/meandiffsignificance.m b/bootstrap/exercises/meandiffsignificance.m new file mode 100644 index 0000000..cf6586d --- /dev/null +++ b/bootstrap/exercises/meandiffsignificance.m @@ -0,0 +1,48 @@ +%% (a) generate data: +n = 200; +mx = -40.0; +my = -40.5; +x = randn(n, 1) + mx; +y = randn(n, 1) + my; + +%% (b) plot histograms: +subplot(1, 2, 1); +bmin = min([x; y]); +bmax = max([x; y]); +bins = bmin:(bmax-bmin)/20.0:bmax; +hist(x, bins, 'facecolor', 'b'); +hold on +hist(y, bins, 'facecolor', 'r'); +xlabel('x and y') +ylabel('counts') +hold off + +% permutation test: +[md, ds, dq] = meandiffpermutation(x, y, nperm, alpha); + +%% (c) difference of means: +fprintf('difference of means = %.2fmV\n', md); + +%% (f) pdf of the differences: +[h, b] = hist(ds, 20); +h = h/sum(h)/(b(2)-b(1)); % normalization + +%% (g) significance: +fprintf('difference of means at 5%% significance = %.2fmV\n', dq); +if md >= dq + fprintf('--> difference of means %.2fmV is significant\n', md); +else + fprintf('--> %.2fmV is not a significant difference of means\n', md); +end + +%% plot: +subplot(1, 2, 2) +bar(b, h, 'facecolor', 'b'); +hold on; +bar(b(b>=dq), h(b>=dq), 'facecolor', 'r'); +plot([md md], [0 4], 'r', 'linewidth', 2); +xlabel('Difference of means'); +ylabel('Probability density of H0'); +hold off; + +savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 6); diff --git a/bootstrap/exercises/tdistribution.m b/bootstrap/exercises/tdistribution.m index 5fe8341..e20aebc 100644 --- a/bootstrap/exercises/tdistribution.m +++ b/bootstrap/exercises/tdistribution.m @@ -1,10 +1,10 @@ %% (a) generate random numbers: n = 100000; -x=randn(n, 1); +x = randn(n, 1); -for nsamples=[3 5 10 50] +for nsamples = [3 5 10 50] nsamples - %% compute mean, standard deviation and t: + % compute mean, standard deviation and t: nmeans = 10000; means = zeros(nmeans, 1); sdevs = zeros(nmeans, 1); @@ -19,14 +19,14 @@ for nsamples=[3 5 10 50] % Gaussian pdfs: msdev = std(means); tsdev = 1.0; - dxg=0.01; + dxg = 0.01; xmax = 10.0; xmin = -xmax; xg = [xmin:dxg:xmax]; pm = exp(-0.5*(xg/msdev).^2)/sqrt(2.0*pi)/msdev; pt = exp(-0.5*(xg/tsdev).^2)/sqrt(2.0*pi)/tsdev; - %% plots + % plots: subplot(1, 2, 1) bins = xmin:0.2:xmax; [h,b] = hist(means, bins); @@ -35,7 +35,7 @@ for nsamples=[3 5 10 50] hold on plot(xg, pm, 'r', 'linewidth', 2) title(sprintf('sample size = %d', nsamples)); - xlim( [-3, 3] ); + xlim([-3, 3]); xlabel('Mean'); ylabel('pdf'); hold off; @@ -48,11 +48,11 @@ for nsamples=[3 5 10 50] hold on plot(xg, pt, 'r', 'linewidth', 2) title(sprintf('sample size = %d', nsamples)); - xlim( [-8, 8] ); + xlim([-8, 8]); xlabel('Student-t'); ylabel('pdf'); hold off; savefigpdf(gcf, sprintf('tdistribution-n%02d.pdf', nsamples), 14, 5); - pause( 3.0 ) + pause(3.0) end diff --git a/statistics/exercises/fitting.tex b/regression/exercises/fitting.tex similarity index 100% rename from statistics/exercises/fitting.tex rename to regression/exercises/fitting.tex From af45ae7f9eb926156a162f8e549e2a8b2f7a2f98 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 13 Dec 2020 23:35:37 +0100 Subject: [PATCH 12/87] [bootstrap] finished code for new exercises --- bootstrap/exercises/exercises01.tex | 4 +- bootstrap/exercises/meandiffpermutation.m | 2 +- bootstrap/exercises/meandiffplot.m | 40 +++++++++++ bootstrap/exercises/meandiffsignificance.m | 77 ++++++++++------------ bootstrap/exercises/savefigpdf.m | 38 +++++------ 5 files changed, 95 insertions(+), 66 deletions(-) create mode 100644 bootstrap/exercises/meandiffplot.m diff --git a/bootstrap/exercises/exercises01.tex b/bootstrap/exercises/exercises01.tex index dd2380d..12ffb94 100644 --- a/bootstrap/exercises/exercises01.tex +++ b/bootstrap/exercises/exercises01.tex @@ -37,7 +37,7 @@ jan.benda@uni-tuebingen.de} commentstyle=\itshape\color{darkgray}, breaklines=true, breakautoindent=true, - columns=flexible, + % columns=flexible, frame=single, xleftmargin=1em, xrightmargin=1em, @@ -239,7 +239,7 @@ differ in their mean by means of a permutation test. \end{parts} \begin{solution} \lstinputlisting{meandiffpermutation.m} - %\lstinputlisting{meandiffplots.m} + \lstinputlisting{meandiffplot.m} \lstinputlisting{meandiffsignificance.m} \includegraphics[width=1\textwidth]{meandiffsignificance} \end{solution} diff --git a/bootstrap/exercises/meandiffpermutation.m b/bootstrap/exercises/meandiffpermutation.m index f8fb58a..5b02a53 100644 --- a/bootstrap/exercises/meandiffpermutation.m +++ b/bootstrap/exercises/meandiffpermutation.m @@ -1,7 +1,7 @@ function [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha) % Permutation test for difference of means of two independent samples. % -% [md, ds] = meandiffpermutation(x, y, nperm, alpha); +% [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha); % % Arguments: % x: vector with the samples of the x data set. diff --git a/bootstrap/exercises/meandiffplot.m b/bootstrap/exercises/meandiffplot.m new file mode 100644 index 0000000..24fd625 --- /dev/null +++ b/bootstrap/exercises/meandiffplot.m @@ -0,0 +1,40 @@ +function meandiffplot(x, y, md, ds, dq, k, nrows) +% Plot histogram of data sets and of null hypothesis for differences in mean. +% +% meandiffplot(x, y, md, ds, dq, k, rows); +% +% Arguments: +% x: vector with the samples of the x data set. +% y: vector with the samples of the y data set. +% md: difference of means of the two data sets. +% ds: vector containing the differences of the means of the resampled data sets +% dq: minimum difference of the means considered significant. +% k: current row for the plot panels. +% nrows: number of rows of panels in the figure. + + %% (b) plot histograms: + subplot(nrows, 2, k*2-1); + bmin = min([x; y]); + bmax = max([x; y]); + bins = bmin:(bmax-bmin)/20.0:bmax; + hist(x, bins, 'facecolor', 'b'); + hold on + hist(y, bins, 'facecolor', 'r'); + xlabel('x and y') + ylabel('counts') + hold off + + %% (f) pdf of the differences: + [h, b] = hist(ds, 20); + h = h/sum(h)/(b(2)-b(1)); % normalization + + %% plot: + subplot(nrows, 2, k*2) + bar(b, h, 'facecolor', 'b'); + hold on; + bar(b(b>=dq), h(b>=dq), 'facecolor', 'r'); + plot([md md], [0 4], 'r', 'linewidth', 2); + xlabel('Difference of means'); + ylabel('Probability density of H0'); + hold off; +end diff --git a/bootstrap/exercises/meandiffsignificance.m b/bootstrap/exercises/meandiffsignificance.m index cf6586d..e234270 100644 --- a/bootstrap/exercises/meandiffsignificance.m +++ b/bootstrap/exercises/meandiffsignificance.m @@ -1,48 +1,37 @@ -%% (a) generate data: n = 200; mx = -40.0; -my = -40.5; -x = randn(n, 1) + mx; -y = randn(n, 1) + my; - -%% (b) plot histograms: -subplot(1, 2, 1); -bmin = min([x; y]); -bmax = max([x; y]); -bins = bmin:(bmax-bmin)/20.0:bmax; -hist(x, bins, 'facecolor', 'b'); -hold on -hist(y, bins, 'facecolor', 'r'); -xlabel('x and y') -ylabel('counts') -hold off - -% permutation test: -[md, ds, dq] = meandiffpermutation(x, y, nperm, alpha); - -%% (c) difference of means: -fprintf('difference of means = %.2fmV\n', md); - -%% (f) pdf of the differences: -[h, b] = hist(ds, 20); -h = h/sum(h)/(b(2)-b(1)); % normalization - -%% (g) significance: -fprintf('difference of means at 5%% significance = %.2fmV\n', dq); -if md >= dq - fprintf('--> difference of means %.2fmV is significant\n', md); -else - fprintf('--> %.2fmV is not a significant difference of means\n', md); +nperm = 1000; +alpha = 0.05; + +%% (h) repeat for various means of the y-data set: +mys = [-40.1, -40.2, -40.5]; +for k=1:length(mys) + + %% (a) generate data: + my = mys(k); + x = randn(n, 1) + mx; + y = randn(n, 1) + my; + + %% (d), (e) permutation test: + [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha); + + %% (c) difference of means: + fprintf('\nmean x = %.1fmV, mean y = %.1fmV\n', mx, my); + fprintf(' difference of means = %.2fmV\n', md); + + %% (g) significance: + fprintf(' difference of means at 5%% significance = %.2fmV\n', dq); + if md >= dq + fprintf(' --> measured difference of means is significant\n'); + else + fprintf(' --> measured difference of means is not significant\n'); + end + + subplot(length(mys), 2, k*2-1); + title(sprintf('mx=%.1fmV, my=%.1fmV', mx, my)) + + %% (b), (f) plot histograms of data and pdf of differences: + meandiffplot(x, y, md, ds, dq, k, length(mys)); end -%% plot: -subplot(1, 2, 2) -bar(b, h, 'facecolor', 'b'); -hold on; -bar(b(b>=dq), h(b>=dq), 'facecolor', 'r'); -plot([md md], [0 4], 'r', 'linewidth', 2); -xlabel('Difference of means'); -ylabel('Probability density of H0'); -hold off; - -savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 6); +savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 10); diff --git a/bootstrap/exercises/savefigpdf.m b/bootstrap/exercises/savefigpdf.m index fbe2dc2..97a28a3 100644 --- a/bootstrap/exercises/savefigpdf.m +++ b/bootstrap/exercises/savefigpdf.m @@ -1,28 +1,28 @@ -function savefigpdf( fig, name, width, height ) +function savefigpdf(fig, name, width, height) % Saves figure fig in pdf file name.pdf with appropriately set page size % and fonts -% default width: -if nargin < 3 - width = 11.7; -end -% default height: -if nargin < 4 - height = 9.0; -end + % default width: + if nargin < 3 + width = 11.7; + end + % default height: + if nargin < 4 + height = 9.0; + end -% paper: -set( fig, 'PaperUnits', 'centimeters' ); -set( fig, 'PaperSize', [width height] ); -set( fig, 'PaperPosition', [0.0 0.0 width height] ); -set( fig, 'Color', 'white') + % paper: + set(fig, 'PaperUnits', 'centimeters'); + set(fig, 'PaperSize', [width height]); + set(fig, 'PaperPosition', [0.0 0.0 width height]); + set(fig, 'Color', 'white') -% font: -set( findall( fig, 'type', 'axes' ), 'FontSize', 12 ) -set( findall( fig, 'type', 'text' ), 'FontSize', 12 ) + % font: + set(findall(fig, 'type', 'axes'), 'FontSize', 12) + set(findall(fig, 'type', 'text'), 'FontSize', 12) -% save: -saveas( fig, name, 'pdf' ) + % save: + saveas(fig, name, 'pdf') end From bd261254a353b50909e2d0786508ca43a86996eb Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 14 Dec 2020 00:05:27 +0100 Subject: [PATCH 13/87] [bootstrap] improved latex and Makefile file structure --- bootstrap/exercises/Makefile | 36 +----- .../{exercises01.tex => resampling-1.tex} | 85 ++------------ exercises.mk | 33 ++++++ exercisesheader.tex | 108 ++++++++++++++++++ .../instructions.tex => exercisestitle.tex | 0 5 files changed, 151 insertions(+), 111 deletions(-) rename bootstrap/exercises/{exercises01.tex => resampling-1.tex} (77%) create mode 100644 exercises.mk create mode 100644 exercisesheader.tex rename bootstrap/exercises/instructions.tex => exercisestitle.tex (100%) diff --git a/bootstrap/exercises/Makefile b/bootstrap/exercises/Makefile index 27691d9..3f8d7db 100644 --- a/bootstrap/exercises/Makefile +++ b/bootstrap/exercises/Makefile @@ -1,34 +1,4 @@ -TEXFILES=$(wildcard exercises??.tex) -EXERCISES=$(TEXFILES:.tex=.pdf) -SOLUTIONS=$(EXERCISES:exercises%=solutions%) +TEXFILES=resampling-1.tex +# resampling2.tex -.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean - -pdf : $(SOLUTIONS) $(EXERCISES) - -exercises : $(EXERCISES) - -solutions : $(SOLUTIONS) - -$(SOLUTIONS) : solutions%.pdf : exercises%.tex instructions.tex - { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) - pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true - rm $(patsubst %.pdf,%,$@).[!p]* - -$(EXERCISES) : %.pdf : %.tex instructions.tex - pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true - -watch : - while true; do ! make -q pdf && make pdf; sleep 0.5; done - -watchexercises : - while true; do ! make -q exercises && make exercises; sleep 0.5; done - -watchsolutions : - while true; do ! make -q solutions && make solutions; sleep 0.5; done - -clean : - rm -f *~ *.aux *.log *.out - -cleanup : clean - rm -f $(SOLUTIONS) $(EXERCISES) +include ../../exercises.mk diff --git a/bootstrap/exercises/exercises01.tex b/bootstrap/exercises/resampling-1.tex similarity index 77% rename from bootstrap/exercises/exercises01.tex rename to bootstrap/exercises/resampling-1.tex index 12ffb94..326fbc6 100644 --- a/bootstrap/exercises/exercises01.tex +++ b/bootstrap/exercises/resampling-1.tex @@ -1,88 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[english]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 8\stitle}}{{\bfseries\large Resampling}}{{\bfseries\large December 14th, 2020}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - % columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\newcommand{\exercisetopic}{Resampling} +\newcommand{\exercisenum}{8} +\newcommand{\exercisedate}{December 14th, 2020} +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} +\input{../../exercisestitle} \begin{questions} diff --git a/exercises.mk b/exercises.mk new file mode 100644 index 0000000..f9d9cd8 --- /dev/null +++ b/exercises.mk @@ -0,0 +1,33 @@ +EXERCISES=$(TEXFILES:.tex=.pdf) +SOLUTIONS=$(EXERCISES:%.pdf=%-solutions.pdf) + +.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean + +pdf : $(SOLUTIONS) $(EXERCISES) + +exercises : $(EXERCISES) + +solutions : $(SOLUTIONS) + +$(SOLUTIONS) : %-solutions.pdf : %.tex ../../exercisesheader.tex ../../exercisestitle.tex + { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) + pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true + rm $(patsubst %.pdf,%,$@).[!p]* + +$(EXERCISES) : %.pdf : %.tex ../../exercisesheader.tex ../../exercisestitle.tex + pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true + +watch : + while true; do ! make -q pdf && make pdf; sleep 0.5; done + +watchexercises : + while true; do ! make -q exercises && make exercises; sleep 0.5; done + +watchsolutions : + while true; do ! make -q solutions && make solutions; sleep 0.5; done + +clean : + rm -f *~ *.aux *.log *.out + +cleanup : clean + rm -f $(SOLUTIONS) $(EXERCISES) diff --git a/exercisesheader.tex b/exercisesheader.tex new file mode 100644 index 0000000..321d22c --- /dev/null +++ b/exercisesheader.tex @@ -0,0 +1,108 @@ +\usepackage[english]{babel} +\usepackage{pslatex} +\usepackage{graphicx} +\usepackage{tikz} +\usepackage{xcolor} +\usepackage{amsmath} +\usepackage{amssymb} + +%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{listings} +\lstset{ + language=Matlab, + basicstyle=\ttfamily\footnotesize, + numbers=left, + numberstyle=\tiny, + title=\lstname, + showstringspaces=false, + commentstyle=\itshape\color{darkgray}, + breaklines=true, + breakautoindent=true, + % columns=flexible, + frame=single, + xleftmargin=1.5em, + xrightmargin=1em, + aboveskip=10pt +} + +%%%%% page style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[left=20mm,right=20mm,top=25mm,bottom=19mm,headsep=2ex,headheight=3ex,footskip=3.5ex]{geometry} +\pagestyle{headandfoot} +\ifprintanswers +\newcommand{\stitle}{Solutions} +\else +\newcommand{\stitle}{} +\fi +\header{{\bfseries\large \exercisenum. \exercisetopic}}{{\bfseries\large\stitle}}{{\bfseries\large\exercisedate}} +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} +\runningfooter{}{\thepage}{} + +\shadedsolutions +\definecolor{SolutionColor}{gray}{0.9} + +\setlength{\baselineskip}{15pt} +\setlength{\parindent}{0.0cm} +\setlength{\parskip}{0.3cm} + +\usepackage{multicol} + +%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[mediumspace,mediumqspace,Gray,squaren]{SIunits} % \ohm, \micro + +%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\cin}[1]{[{\rm #1}]_{\text{in}}} +\newcommand{\cout}[1]{[{\rm #1}]_{\text{out}}} +\newcommand{\units}[1]{\text{#1}} +\newcommand{\K}{\text{K$^+$}} +\newcommand{\Na}{\text{Na$^+$}} +\newcommand{\Cl}{\text{Cl$^-$}} +\newcommand{\Ca}{\text{Ca$^{2+}$}} +\newcommand{\water}{$\text{H}_2\text{O}$} + +\usepackage{dsfont} +\newcommand{\naZ}{\mathds{N}} +\newcommand{\gaZ}{\mathds{Z}} +\newcommand{\raZ}{\mathds{Q}} +\newcommand{\reZ}{\mathds{R}} +\newcommand{\reZp}{\mathds{R^+}} +\newcommand{\reZpN}{\mathds{R^+_0}} +\newcommand{\koZ}{\mathds{C}} +\newcommand{\RT}{{\rm Re\!\ }} +\newcommand{\IT}{{\rm Im\!\ }} +\newcommand{\arccot}{{\rm arccot}} +\newcommand{\sgn}{{\rm sgn}} +\newcommand{\im}{{\rm i}} +\newcommand{\drv}{\mathrm{d}} +\newcommand{\divis}[2]{$^{#1}\!\!/\!_{#2}$} +\newcommand{\vect}[2]{\left( \!\! \begin{array}{c} #1 \\ #2 \end{array} \!\! \right)} +\newcommand{\matt}[2]{\left( \!\! \begin{array}{cc} #1 \\ #2 \end{array} \!\! \right)} +\renewcommand{\Re}{\mathrm{Re}} +\renewcommand{\Im}{\mathrm{Im}} +\newcommand{\av}[1]{\left\langle #1 \right\rangle} + +\newcommand{\pref}[1]{(\ref{#1})} +\newcommand{\eqnref}[1]{(\ref{#1})} + +\newcommand{\hr}{\par\vspace{-5ex}\noindent\rule{\textwidth}{1pt}\par\vspace{-1ex}} + +\newcommand{\qt}[1]{\textbf{#1}\\} + +\newcommand{\code}[1]{\texttt{#1}} + +%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\continue}{\ifprintanswers% +\else +\vfill\hspace*{\fill}$\rightarrow$\newpage% +\fi} +\newcommand{\continuepage}{\ifprintanswers% +\newpage +\else +\vfill\hspace*{\fill}$\rightarrow$\newpage% +\fi} +\newcommand{\newsolutionpage}{\ifprintanswers% +\newpage% +\else +\fi} + +%%%%% hyperref %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue!50!black,linkcolor=blue!50!black,urlcolor=blue!50!black]{hyperref} diff --git a/bootstrap/exercises/instructions.tex b/exercisestitle.tex similarity index 100% rename from bootstrap/exercises/instructions.tex rename to exercisestitle.tex From 4357939cdbaf43fb7453b5adfe5bb36cea4e3874 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 14 Dec 2020 00:17:32 +0100 Subject: [PATCH 14/87] [statistics] improved latex and Makefile file structure --- exercisesheader.tex | 2 + exercisestitle.tex | 1 + statistics/exercises/Makefile | 35 +------- statistics/exercises/instructions.tex | 6 -- .../{exercises01.tex => statistics-1.tex} | 84 ++---------------- .../{exercises02.tex => statistics-2.tex} | 87 ++----------------- .../{exercises03.tex => statistics-3.tex} | 87 ++----------------- 7 files changed, 29 insertions(+), 273 deletions(-) delete mode 100644 statistics/exercises/instructions.tex rename statistics/exercises/{exercises01.tex => statistics-1.tex} (74%) rename statistics/exercises/{exercises02.tex => statistics-2.tex} (69%) rename statistics/exercises/{exercises03.tex => statistics-3.tex} (56%) diff --git a/exercisesheader.tex b/exercisesheader.tex index 321d22c..51a6258 100644 --- a/exercisesheader.tex +++ b/exercisesheader.tex @@ -87,6 +87,8 @@ \newcommand{\qt}[1]{\textbf{#1}\\} +\newcommand{\extra}{--- Optional ---\ \mbox{}} + \newcommand{\code}[1]{\texttt{#1}} %%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/exercisestitle.tex b/exercisestitle.tex index 3041d3e..b97b56b 100644 --- a/exercisestitle.tex +++ b/exercisestitle.tex @@ -4,3 +4,4 @@ {\large Jan Grewe, Jan Benda}\\[-3ex] Neuroethology Lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ \end{center} +\hr diff --git a/statistics/exercises/Makefile b/statistics/exercises/Makefile index 27691d9..fd49c98 100644 --- a/statistics/exercises/Makefile +++ b/statistics/exercises/Makefile @@ -1,34 +1,3 @@ -TEXFILES=$(wildcard exercises??.tex) -EXERCISES=$(TEXFILES:.tex=.pdf) -SOLUTIONS=$(EXERCISES:exercises%=solutions%) +TEXFILES=$(wildcard statistics-?.tex) -.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean - -pdf : $(SOLUTIONS) $(EXERCISES) - -exercises : $(EXERCISES) - -solutions : $(SOLUTIONS) - -$(SOLUTIONS) : solutions%.pdf : exercises%.tex instructions.tex - { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) - pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true - rm $(patsubst %.pdf,%,$@).[!p]* - -$(EXERCISES) : %.pdf : %.tex instructions.tex - pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true - -watch : - while true; do ! make -q pdf && make pdf; sleep 0.5; done - -watchexercises : - while true; do ! make -q exercises && make exercises; sleep 0.5; done - -watchsolutions : - while true; do ! make -q solutions && make solutions; sleep 0.5; done - -clean : - rm -f *~ *.aux *.log *.out - -cleanup : clean - rm -f $(SOLUTIONS) $(EXERCISES) +include ../../exercises.mk diff --git a/statistics/exercises/instructions.tex b/statistics/exercises/instructions.tex deleted file mode 100644 index 3041d3e..0000000 --- a/statistics/exercises/instructions.tex +++ /dev/null @@ -1,6 +0,0 @@ -\vspace*{-7.8ex} -\begin{center} -\textbf{\Large Introduction to Scientific Computing}\\[2.3ex] -{\large Jan Grewe, Jan Benda}\\[-3ex] -Neuroethology Lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} diff --git a/statistics/exercises/exercises01.tex b/statistics/exercises/statistics-1.tex similarity index 74% rename from statistics/exercises/exercises01.tex rename to statistics/exercises/statistics-1.tex index 22f1131..b7acb51 100644 --- a/statistics/exercises/exercises01.tex +++ b/statistics/exercises/statistics-1.tex @@ -1,88 +1,18 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[english]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 7\stitle}}{{\bfseries\large Statistics}}{{\bfseries\large December 8th, 2020}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} +\newcommand{\exercisetopic}{Statistics} +\newcommand{\exercisenum}{7} +\newcommand{\exercisedate}{December 8th, 2020} + +\input{../../exercisesheader} -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- bonus question ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} +\input{../../exercisestitle} \ifprintanswers% \else diff --git a/statistics/exercises/exercises02.tex b/statistics/exercises/statistics-2.tex similarity index 69% rename from statistics/exercises/exercises02.tex rename to statistics/exercises/statistics-2.tex index 4b1cc3c..e58f16b 100644 --- a/statistics/exercises/exercises02.tex +++ b/statistics/exercises/statistics-2.tex @@ -1,89 +1,18 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 7\stitle}}{{\bfseries\large Statistics}}{{\bfseries\large November 21st, 2017}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- bonus question ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\newcommand{\exercisetopic}{Statistics} +\newcommand{\exercisenum}{X2} +\newcommand{\exercisedate}{XXX} + +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} diff --git a/statistics/exercises/exercises03.tex b/statistics/exercises/statistics-3.tex similarity index 56% rename from statistics/exercises/exercises03.tex rename to statistics/exercises/statistics-3.tex index 11e4320..8456122 100644 --- a/statistics/exercises/exercises03.tex +++ b/statistics/exercises/statistics-3.tex @@ -1,89 +1,20 @@ \documentclass[12pt,a4paper,pdftex]{exam} +\newcommand{\exercisetopic}{Statistics -- Random Walk} +\newcommand{\exercisenum}{X3} +\newcommand{\exercisedate}{XXX} + +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} + \usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: L\"osungen} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large \"Ubung 8\stitle}}{{\bfseries\large Statistik}}{{\bfseries\large 29. November, 2016}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} From e37591d2743c8bf447f5c7abe44c8d3796691872 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 14 Dec 2020 10:48:37 +0100 Subject: [PATCH 15/87] renamed further-topics/ to replicability/ --- 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a/further_topics/lectures/images/savage_vickers_2009_title.png b/replicability/lectures/images/savage_vickers_2009_title.png similarity index 100% rename from further_topics/lectures/images/savage_vickers_2009_title.png rename to replicability/lectures/images/savage_vickers_2009_title.png diff --git a/further_topics/lectures/topics-chapter.tex b/replicability/lectures/topics-chapter.tex similarity index 100% rename from further_topics/lectures/topics-chapter.tex rename to replicability/lectures/topics-chapter.tex diff --git a/further_topics/lectures/topics-slides.tex b/replicability/lectures/topics-slides.tex similarity index 100% rename from further_topics/lectures/topics-slides.tex rename to replicability/lectures/topics-slides.tex diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 21daaba..5bacd1b 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -88,18 +88,20 @@ % add chapter on mutual information -% add chapters on linear algebra, PCA, clustering +% add chapters on linear algebra, PCA, clustering, see linearalgebra/ % add chapter on simple machine learning %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\part{Tools} -% Latex +% Latex -> see latex/ % markdown, html % Makefile -% version control (git and github) only put source files into repository! % distributed computing (ssh and grid engines) +% +% see replicability/ : +% version control (git and github) only put source files into repository! % data handling (structure, storage (rsync), backup, data bases) % data annotation, meta data From acc63490f4ac5225b0c4581f2cf2324ab98bdaf6 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 14 Dec 2020 20:21:37 +0100 Subject: [PATCH 16/87] [bootstrap] added matplotlib figure for meandiff --- bootstrap/exercises/meandiffplot.m | 12 +- bootstrap/exercises/meandiffsignificance.m | 6 +- bootstrap/exercises/meandiffsignificance.pdf | Bin 0 -> 8988 bytes .../lecture/pointprocessscetchA.eps | 120 ++++-- .../lecture/pointprocessscetchA.pdf | Bin 2786 -> 2924 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++++++++------ .../lecture/pointprocessscetchB.pdf | Bin 4694 -> 4877 bytes 7 files changed, 365 insertions(+), 162 deletions(-) create mode 100644 bootstrap/exercises/meandiffsignificance.pdf diff --git a/bootstrap/exercises/meandiffplot.m b/bootstrap/exercises/meandiffplot.m index 24fd625..47e8d86 100644 --- a/bootstrap/exercises/meandiffplot.m +++ b/bootstrap/exercises/meandiffplot.m @@ -17,10 +17,12 @@ function meandiffplot(x, y, md, ds, dq, k, nrows) bmin = min([x; y]); bmax = max([x; y]); bins = bmin:(bmax-bmin)/20.0:bmax; - hist(x, bins, 'facecolor', 'b'); + [xh, b] = hist(x, bins); + [yh, b] = hist(y, bins); + bar(bins, xh, 'facecolor', 'b') hold on - hist(y, bins, 'facecolor', 'r'); - xlabel('x and y') + bar(bins, yh, 'facecolor', 'r'); + xlabel('x and y [mV]') ylabel('counts') hold off @@ -34,7 +36,7 @@ function meandiffplot(x, y, md, ds, dq, k, nrows) hold on; bar(b(b>=dq), h(b>=dq), 'facecolor', 'r'); plot([md md], [0 4], 'r', 'linewidth', 2); - xlabel('Difference of means'); - ylabel('Probability density of H0'); + xlabel('Difference of means [mV]'); + ylabel('pdf of H0'); hold off; end diff --git a/bootstrap/exercises/meandiffsignificance.m b/bootstrap/exercises/meandiffsignificance.m index e234270..b5de2fd 100644 --- a/bootstrap/exercises/meandiffsignificance.m +++ b/bootstrap/exercises/meandiffsignificance.m @@ -27,11 +27,11 @@ for k=1:length(mys) fprintf(' --> measured difference of means is not significant\n'); end - subplot(length(mys), 2, k*2-1); - title(sprintf('mx=%.1fmV, my=%.1fmV', mx, my)) - %% (b), (f) plot histograms of data and pdf of differences: meandiffplot(x, y, md, ds, dq, k, length(mys)); + + subplot(length(mys), 2, k*2-1); + title(sprintf('mx=%.1fmV, my=%.1fmV', mx, my)) end savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 10); diff --git 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zA0i=$Km;SxTZPSju9JqyiJuex^z2*_)^X3>;{}o_26_}PZ>&Ax(qDk+YvAWj($n4} zcky4~dsN%Y6Z>}#D@l~hs|-gU18U>;s`!#gc=tep+TQ+nf+rY;0RQ_gM?q2o2&gU$ zvwI_B5El948Fp*f(>(kLo`Gr?NVEVVIS{<(c4=c;pbwd%wmVLG0Z5yU(AllJXJ8T- z_#HrzFc|Vj4vzRA+-~?Az{8usxnobqhKZ{11 z;E<+pBn%11=%RHII9((fjx&X$Owbq{9*#56`@f2_Km!9HHPD?Bc$q@*1|kti7*JW+ I)Y=UAFNvz-!vFvP From 475b3148c84565ebfd6f75be81d3fd667c52fc7f Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 14 Dec 2020 23:57:36 +0100 Subject: [PATCH 17/87] [bootstrap] split exercises --- bootstrap/exercises/Makefile | 3 +- bootstrap/exercises/resampling-1.tex | 66 +--------------------- bootstrap/exercises/resampling-2.tex | 84 ++++++++++++++++++++++++++++ 3 files changed, 87 insertions(+), 66 deletions(-) create mode 100644 bootstrap/exercises/resampling-2.tex diff --git a/bootstrap/exercises/Makefile b/bootstrap/exercises/Makefile index 3f8d7db..c1e988e 100644 --- a/bootstrap/exercises/Makefile +++ b/bootstrap/exercises/Makefile @@ -1,4 +1,3 @@ -TEXFILES=resampling-1.tex -# resampling2.tex +TEXFILES=$(wildcard resampling-?.tex) include ../../exercises.mk diff --git a/bootstrap/exercises/resampling-1.tex b/bootstrap/exercises/resampling-1.tex index 326fbc6..75b8b81 100644 --- a/bootstrap/exercises/resampling-1.tex +++ b/bootstrap/exercises/resampling-1.tex @@ -18,69 +18,6 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Read chapter 7 of the script on ``resampling methods''!}\vspace{-3ex} -\question \qt{Bootstrap the standard error of the mean} -We want to compute the standard error of the mean of a data set by -means of the bootstrap method and compare the result with the formula -``standard deviation divided by the square-root of $n$''. -\begin{parts} - \part Download the file \code{thymusglandweights.dat} from Ilias. - This is a data set of the weights of the thymus glands of 14-day old chicken embryos - measured in milligram. - \part Load the data into Matlab (\code{load} function). - \part Compute histogram, mean, and standard error of the mean of the first 80 data points. - \part Compute the standard error of the mean of the first 80 data - points by bootstrapping the data 500 times. Write a function that - bootstraps the standard error of the mean of a given data set. The - function should also return a vector with the bootstrapped means. - \part Compute the 95\,\% confidence interval for the mean from the - bootstrap distribution (\code{quantile()} function) --- the - interval that contains the true mean with 95\,\% probability. - \part Use the whole data set and the bootstrap method for computing - the dependence of the standard error of the mean from the sample - size $n$. - \part Compare your result with the formula for the standard error - $\sigma/\sqrt{n}$. -\end{parts} -\begin{solution} - \lstinputlisting{bootstrapmean.m} - \lstinputlisting{bootstraptymus.m} - \includegraphics[width=0.5\textwidth]{bootstraptymus-datahist} - \includegraphics[width=0.5\textwidth]{bootstraptymus-meanhist} - \includegraphics[width=0.5\textwidth]{bootstraptymus-samples} -\end{solution} - - -\question \qt{Student t-distribution} -The distribution of Student's t, $t=\bar x/(\sigma_x/\sqrt{n})$, the -estimated mean $\bar x$ of a data set of size $n$ divided by the -estimated standard error of the mean $\sigma_x/\sqrt{n}$, where -$\sigma_x$ is the estimated standard deviation, is not a normal -distribution but a Student-t distribution. We want to compute the -Student-t distribution and compare it with the normal distribution. -\begin{parts} -\part Generate 100000 normally distributed random numbers. -\part Draw from these data 1000 samples of size $n=3$, 5, 10, and -50. For each sample size $n$ ... -\part ... compute the mean $\bar x$ of the samples and plot the -probability density of these means. -\part ... compare the resulting probability densities with corresponding -normal distributions. -\part ... compute Student's $t=\bar x/(\sigma_x/\sqrt{n})$ and compare its -distribution with the normal distribution with standard deviation of -one. Is $t$ normally distributed? Under which conditions is $t$ -normally distributed? -\end{parts} -\newsolutionpage -\begin{solution} - \lstinputlisting{tdistribution.m} - \includegraphics[width=1\textwidth]{tdistribution-n03}\\ - \includegraphics[width=1\textwidth]{tdistribution-n05}\\ - \includegraphics[width=1\textwidth]{tdistribution-n10}\\ - \includegraphics[width=1\textwidth]{tdistribution-n50} -\end{solution} - - -\continue \question \qt{Permutation test of correlations} \label{correlationtest} We want to compute the significance of a correlation by means of a permutation test. \begin{parts} @@ -109,6 +46,7 @@ y = randn(n, 1) + a*x; \includegraphics[width=1\textwidth]{correlationsignificance} \end{solution} +\newsolutionpage \question \qt{Bootstrap the correlation coefficient} The permutation test generates the distribution of the null hypothesis of uncorrelated data and we check whether the correlation coefficient @@ -137,7 +75,7 @@ We take the same data set that we have generated in exercise \end{solution} -\continuepage +\continue \question \qt{Permutation test of difference of means} We want to test whether two data sets come from distributions that differ in their mean by means of a permutation test. diff --git a/bootstrap/exercises/resampling-2.tex b/bootstrap/exercises/resampling-2.tex new file mode 100644 index 0000000..e27d1c0 --- /dev/null +++ b/bootstrap/exercises/resampling-2.tex @@ -0,0 +1,84 @@ +\documentclass[12pt,a4paper,pdftex]{exam} + +\newcommand{\exercisetopic}{Resampling} +\newcommand{\exercisenum}{X2} +\newcommand{\exercisedate}{December 14th, 2020} + +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\input{../../exercisestitle} + +\begin{questions} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\question \qt{Read chapter 7 of the script on ``resampling methods''!}\vspace{-3ex} + +\question \qt{Bootstrap the standard error of the mean} +We want to compute the standard error of the mean of a data set by +means of the bootstrap method and compare the result with the formula +``standard deviation divided by the square-root of $n$''. +\begin{parts} + \part Download the file \code{thymusglandweights.dat} from Ilias. + This is a data set of the weights of the thymus glands of 14-day old chicken embryos + measured in milligram. + \part Load the data into Matlab (\code{load} function). + \part Compute histogram, mean, and standard error of the mean of the first 80 data points. + \part Compute the standard error of the mean of the first 80 data + points by bootstrapping the data 500 times. Write a function that + bootstraps the standard error of the mean of a given data set. The + function should also return a vector with the bootstrapped means. + \part Compute the 95\,\% confidence interval for the mean from the + bootstrap distribution (\code{quantile()} function) --- the + interval that contains the true mean with 95\,\% probability. + \part Use the whole data set and the bootstrap method for computing + the dependence of the standard error of the mean from the sample + size $n$. + \part Compare your result with the formula for the standard error + $\sigma/\sqrt{n}$. +\end{parts} +\begin{solution} + \lstinputlisting{bootstrapmean.m} + \lstinputlisting{bootstraptymus.m} + \includegraphics[width=0.5\textwidth]{bootstraptymus-datahist} + \includegraphics[width=0.5\textwidth]{bootstraptymus-meanhist} + \includegraphics[width=0.5\textwidth]{bootstraptymus-samples} +\end{solution} + + +\question \qt{Student t-distribution} +The distribution of Student's t, $t=\bar x/(\sigma_x/\sqrt{n})$, the +estimated mean $\bar x$ of a data set of size $n$ divided by the +estimated standard error of the mean $\sigma_x/\sqrt{n}$, where +$\sigma_x$ is the estimated standard deviation, is not a normal +distribution but a Student-t distribution. We want to compute the +Student-t distribution and compare it with the normal distribution. +\begin{parts} +\part Generate 100000 normally distributed random numbers. +\part Draw from these data 1000 samples of size $n=3$, 5, 10, and +50. For each sample size $n$ ... +\part ... compute the mean $\bar x$ of the samples and plot the +probability density of these means. +\part ... compare the resulting probability densities with corresponding +normal distributions. +\part ... compute Student's $t=\bar x/(\sigma_x/\sqrt{n})$ and compare its +distribution with the normal distribution with standard deviation of +one. Is $t$ normally distributed? Under which conditions is $t$ +normally distributed? +\end{parts} +\newsolutionpage +\begin{solution} + \lstinputlisting{tdistribution.m} + \includegraphics[width=1\textwidth]{tdistribution-n03}\\ + \includegraphics[width=1\textwidth]{tdistribution-n05}\\ + \includegraphics[width=1\textwidth]{tdistribution-n10}\\ + \includegraphics[width=1\textwidth]{tdistribution-n50} +\end{solution} + +\end{questions} + +\end{document} \ No newline at end of file From d6756d4975ec8c40ea4e5b7bd9ee3bac540c9fd5 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 08:29:29 +0100 Subject: [PATCH 18/87] [bootstrap] exercises here in chapter --- bootstrap/lecture/bootstrap-chapter.tex | 2 + .../lecture/pointprocessscetchA.eps | 120 ++---- .../lecture/pointprocessscetchA.pdf | Bin 2924 -> 2786 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++------------ .../lecture/pointprocessscetchB.pdf | Bin 4877 -> 4694 bytes statistics/lecture/statistics-chapter.tex | 2 + 6 files changed, 158 insertions(+), 355 deletions(-) diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index 9009d78..60c2b5e 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -10,6 +10,8 @@ \setcounter{page}{\pagenumber} \setcounter{chapter}{\chapternumber} +\renewcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 7234511..59681c9 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex -%%Creator: gnuplot 5.2 patchlevel 8 -%%CreationDate: Mon Dec 14 20:03:21 2020 +%%Creator: gnuplot 4.6 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b/statistics/lecture/statistics-chapter.tex index 4331ed1..84833c0 100644 --- a/statistics/lecture/statistics-chapter.tex +++ b/statistics/lecture/statistics-chapter.tex @@ -10,6 +10,8 @@ \setcounter{page}{\pagenumber} \setcounter{chapter}{\chapternumber} +\renewcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} From 9db487fb253b7db18e9ac2df560872c8ccdc010b Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 13:50:42 +0100 Subject: [PATCH 19/87] [regression] updated exercise infrastructure --- regression/exercises/Makefile | 34 +-------- regression/{code => exercises}/checkdescent.m | 0 regression/{code => exercises}/descent.m | 0 regression/{code => exercises}/descentfit.m | 0 ...{exercises01.tex => gradientdescent-1.tex} | 71 ++++--------------- regression/{code => exercises}/linefit.m | 0 6 files changed, 16 insertions(+), 89 deletions(-) rename regression/{code => exercises}/checkdescent.m (100%) rename regression/{code => exercises}/descent.m (100%) rename regression/{code => exercises}/descentfit.m (100%) rename regression/exercises/{exercises01.tex => gradientdescent-1.tex} (64%) rename regression/{code => exercises}/linefit.m (100%) diff --git a/regression/exercises/Makefile b/regression/exercises/Makefile index 27691d9..ba0b38c 100644 --- a/regression/exercises/Makefile +++ b/regression/exercises/Makefile @@ -1,34 +1,4 @@ -TEXFILES=$(wildcard exercises??.tex) -EXERCISES=$(TEXFILES:.tex=.pdf) -SOLUTIONS=$(EXERCISES:exercises%=solutions%) +TEXFILES=$(wildcard gradientdescent-?.tex) -.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean +include ../../exercises.mk -pdf : $(SOLUTIONS) $(EXERCISES) - -exercises : $(EXERCISES) - -solutions : $(SOLUTIONS) - -$(SOLUTIONS) : solutions%.pdf : exercises%.tex instructions.tex - { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) - pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true - rm $(patsubst %.pdf,%,$@).[!p]* - -$(EXERCISES) : %.pdf : %.tex instructions.tex - pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true - -watch : - while true; do ! make -q pdf && make pdf; sleep 0.5; done - -watchexercises : - while true; do ! make -q exercises && make exercises; sleep 0.5; done - -watchsolutions : - while true; do ! make -q solutions && make solutions; sleep 0.5; done - -clean : - rm -f *~ *.aux *.log *.out - -cleanup : clean - rm -f $(SOLUTIONS) $(EXERCISES) diff --git a/regression/code/checkdescent.m b/regression/exercises/checkdescent.m similarity index 100% rename from regression/code/checkdescent.m rename to regression/exercises/checkdescent.m diff --git a/regression/code/descent.m b/regression/exercises/descent.m similarity index 100% rename from regression/code/descent.m rename to regression/exercises/descent.m diff --git a/regression/code/descentfit.m b/regression/exercises/descentfit.m similarity index 100% rename from regression/code/descentfit.m rename to regression/exercises/descentfit.m diff --git a/regression/exercises/exercises01.tex b/regression/exercises/gradientdescent-1.tex similarity index 64% rename from regression/exercises/exercises01.tex rename to regression/exercises/gradientdescent-1.tex index 9e7c5b3..8275723 100644 --- a/regression/exercises/exercises01.tex +++ b/regression/exercises/gradientdescent-1.tex @@ -1,60 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 10\stitle}}{{\bfseries\large Gradient descent}}{{\bfseries\large December 16th, 2019}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solution:}\par\noindent} -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\exercisetopic}{Resampling} +\newcommand{\exercisenum}{9} +\newcommand{\exercisedate}{December 21th, 2020} + +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} +\input{../../exercisestitle} \begin{questions} @@ -96,7 +53,7 @@ the parameter values at the minimum of the cost function and a vector with the value of the cost function at each step of the algorithm. \begin{solution} - \lstinputlisting{../code/descent.m} + \lstinputlisting{descent.m} \end{solution} \part Plot the data and the straight line with the parameter @@ -105,7 +62,7 @@ \part Plot the development of the costs as a function of the iteration step. \begin{solution} - \lstinputlisting{../code/descentfit.m} + \lstinputlisting{descentfit.m} \end{solution} \part For checking the gradient descend method from (a) compare @@ -116,7 +73,7 @@ minimum gradient. What are good values such that the gradient descent gets closest to the true minimum of the cost function? \begin{solution} - \lstinputlisting{../code/checkdescent.m} + \lstinputlisting{checkdescent.m} \end{solution} \part Use the functions \code{polyfit()} and \code{lsqcurvefit()} @@ -124,7 +81,7 @@ line that fits the data. Compare the resulting fit parameters of those functions with the ones of your gradient descent algorithm. \begin{solution} - \lstinputlisting{../code/linefit.m} + \lstinputlisting{linefit.m} \end{solution} \end{parts} diff --git a/regression/code/linefit.m b/regression/exercises/linefit.m similarity index 100% rename from regression/code/linefit.m rename to regression/exercises/linefit.m From 18da3117e5069cf2a15fbef8eb7cd5d2148ad6ed Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 13:56:24 +0100 Subject: [PATCH 20/87] [likelihood] updated exercise infrastructure --- likelihood/exercises/Makefile | 35 +------- likelihood/exercises/instructions.tex | 41 --------- .../{exercises01.tex => likelihood-1.tex} | 87 ++----------------- regression/exercises/gradientdescent-1.tex | 2 +- regression/exercises/instructions.tex | 6 -- 5 files changed, 10 insertions(+), 161 deletions(-) delete mode 100644 likelihood/exercises/instructions.tex rename likelihood/exercises/{exercises01.tex => likelihood-1.tex} (70%) delete mode 100644 regression/exercises/instructions.tex diff --git a/likelihood/exercises/Makefile b/likelihood/exercises/Makefile index 27691d9..cbfb17a 100644 --- a/likelihood/exercises/Makefile +++ b/likelihood/exercises/Makefile @@ -1,34 +1,3 @@ -TEXFILES=$(wildcard exercises??.tex) -EXERCISES=$(TEXFILES:.tex=.pdf) -SOLUTIONS=$(EXERCISES:exercises%=solutions%) +TEXFILES=$(wildcard likelihood-?.tex) -.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean - -pdf : $(SOLUTIONS) $(EXERCISES) - -exercises : $(EXERCISES) - -solutions : $(SOLUTIONS) - -$(SOLUTIONS) : solutions%.pdf : exercises%.tex instructions.tex - { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) - pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true - rm $(patsubst %.pdf,%,$@).[!p]* - -$(EXERCISES) : %.pdf : %.tex instructions.tex - pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true - -watch : - while true; do ! make -q pdf && make pdf; sleep 0.5; done - -watchexercises : - while true; do ! make -q exercises && make exercises; sleep 0.5; done - -watchsolutions : - while true; do ! make -q solutions && make solutions; sleep 0.5; done - -clean : - rm -f *~ *.aux *.log *.out - -cleanup : clean - rm -f $(SOLUTIONS) $(EXERCISES) +include ../../exercises.mk diff --git a/likelihood/exercises/instructions.tex b/likelihood/exercises/instructions.tex deleted file mode 100644 index 7fe599d..0000000 --- a/likelihood/exercises/instructions.tex +++ /dev/null @@ -1,41 +0,0 @@ -\vspace*{-8ex} -\begin{center} -\textbf{\Large Introduction to scientific computing}\\[1ex] -{\large Jan Grewe, Jan Benda}\\[-3ex] -Neuroethology lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} - -% \ifprintanswers% -% \else - -% % Die folgenden Aufgaben dienen der Wiederholung, \"Ubung und -% % Selbstkontrolle und sollten eigenst\"andig bearbeitet und gel\"ost -% % werden. Die L\"osung soll in Form eines einzelnen Skriptes (m-files) -% % im ILIAS hochgeladen werden. Jede Aufgabe sollte in einer eigenen -% % ``Zelle'' gel\"ost sein. Die Zellen \textbf{m\"ussen} unabh\"angig -% % voneinander ausf\"uhrbar sein. Das Skript sollte nach dem Muster: -% % ``variablen\_datentypen\_\{nachname\}.m'' benannt werden -% % (z.B. variablen\_datentypen\_mueller.m). - -% \begin{itemize} -% \item \"Uberzeuge dich von jeder einzelnen Zeile deines Codes, dass -% sie auch wirklich das macht, was sie machen soll! Teste dies mit -% kleinen Beispielen direkt in der Kommandozeile. -% \item Versuche die L\"osungen der Aufgaben m\"oglichst in -% sinnvolle kleine Funktionen herunterzubrechen. -% Sobald etwas \"ahnliches mehr als einmal berechnet werden soll, -% lohnt es sich eine Funktion daraus zu schreiben! -% \item Teste rechenintensive \code{for} Schleifen, Vektoren, Matrizen -% zuerst mit einer kleinen Anzahl von Wiederholungen oder kleiner -% Gr\"o{\ss}e, und benutze erst am Ende, wenn alles \"uberpr\"uft -% ist, eine gro{\ss}e Anzahl von Wiederholungen oder Elementen, um eine gute -% Statistik zu bekommen. -% \item Benutze die Hilfsfunktion von \code{matlab} (\code{help -% commando} oder \code{doc commando}) und das Internet, um -% herauszufinden, wie bestimmte \code{matlab} Funktionen zu verwenden -% sind und was f\"ur M\"oglichkeiten sie bieten. -% Auch zu inhaltlichen Konzepten bietet das Internet oft viele -% Antworten! -% \end{itemize} - -% \fi diff --git a/likelihood/exercises/exercises01.tex b/likelihood/exercises/likelihood-1.tex similarity index 70% rename from likelihood/exercises/exercises01.tex rename to likelihood/exercises/likelihood-1.tex index 4512e91..28b3946 100644 --- a/likelihood/exercises/exercises01.tex +++ b/likelihood/exercises/likelihood-1.tex @@ -1,90 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 11\stitle}}{{\bfseries\large Maximum likelihood}}{{\bfseries\large January 7th, 2020}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\newcommand{\exercisetopic}{Maximum Likelihood} +\newcommand{\exercisenum}{10} +\newcommand{\exercisedate}{January 12th, 2021} +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} diff --git a/regression/exercises/gradientdescent-1.tex b/regression/exercises/gradientdescent-1.tex index 8275723..7e25b0d 100644 --- a/regression/exercises/gradientdescent-1.tex +++ b/regression/exercises/gradientdescent-1.tex @@ -2,7 +2,7 @@ \newcommand{\exercisetopic}{Resampling} \newcommand{\exercisenum}{9} -\newcommand{\exercisedate}{December 21th, 2020} +\newcommand{\exercisedate}{December 22th, 2020} \input{../../exercisesheader} diff --git a/regression/exercises/instructions.tex b/regression/exercises/instructions.tex deleted file mode 100644 index 3041d3e..0000000 --- a/regression/exercises/instructions.tex +++ /dev/null @@ -1,6 +0,0 @@ -\vspace*{-7.8ex} -\begin{center} -\textbf{\Large Introduction to Scientific Computing}\\[2.3ex] -{\large Jan Grewe, Jan Benda}\\[-3ex] -Neuroethology Lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} From 88c6afac1c640b79e34a935d2a959ab88a569e2e Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 14:02:43 +0100 Subject: [PATCH 21/87] [pointprocesses] updated exercise infrastructure --- pointprocesses/exercises/Makefile | 36 +------- pointprocesses/exercises/instructions.tex | 6 -- ...ntprocesses01.tex => pointprocesses-1.tex} | 87 ++----------------- ...ntprocesses02.tex => pointprocesses-2.tex} | 85 ++---------------- ...ntprocesses03.tex => pointprocesses-3.tex} | 87 ++----------------- 5 files changed, 22 insertions(+), 279 deletions(-) delete mode 100644 pointprocesses/exercises/instructions.tex rename pointprocesses/exercises/{pointprocesses01.tex => pointprocesses-1.tex} (72%) rename pointprocesses/exercises/{pointprocesses02.tex => pointprocesses-2.tex} (68%) rename pointprocesses/exercises/{pointprocesses03.tex => pointprocesses-3.tex} (73%) diff --git a/pointprocesses/exercises/Makefile b/pointprocesses/exercises/Makefile index 0b63fb9..0d84b85 100644 --- a/pointprocesses/exercises/Makefile +++ b/pointprocesses/exercises/Makefile @@ -1,35 +1,3 @@ -BASENAME=pointprocesses -TEXFILES=$(wildcard $(BASENAME)??.tex) -EXERCISES=$(TEXFILES:.tex=.pdf) -SOLUTIONS=$(EXERCISES:pointprocesses%=pointprocesses-solutions%) +TEXFILES=$(wildcard pointprocesses-?.tex) -.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean - -pdf : $(SOLUTIONS) $(EXERCISES) - -exercises : $(EXERCISES) - -solutions : $(SOLUTIONS) - -$(SOLUTIONS) : pointprocesses-solutions%.pdf : pointprocesses%.tex instructions.tex - { echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@) - pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true - rm $(patsubst %.pdf,%,$@).[!p]* - -$(EXERCISES) : %.pdf : %.tex instructions.tex - pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true - -watch : - while true; do ! make -q pdf && make pdf; sleep 0.5; done - -watchexercises : - while true; do ! make -q exercises && make exercises; sleep 0.5; done - -watchsolutions : - while true; do ! make -q solutions && make solutions; sleep 0.5; done - -clean : - rm -f *~ *.aux *.log *.out - -cleanup : clean - rm -f $(SOLUTIONS) $(EXERCISES) +include ../../exercises.mk diff --git a/pointprocesses/exercises/instructions.tex b/pointprocesses/exercises/instructions.tex deleted file mode 100644 index 3041d3e..0000000 --- a/pointprocesses/exercises/instructions.tex +++ /dev/null @@ -1,6 +0,0 @@ -\vspace*{-7.8ex} -\begin{center} -\textbf{\Large Introduction to Scientific Computing}\\[2.3ex] -{\large Jan Grewe, Jan Benda}\\[-3ex] -Neuroethology Lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} diff --git a/pointprocesses/exercises/pointprocesses01.tex b/pointprocesses/exercises/pointprocesses-1.tex similarity index 72% rename from pointprocesses/exercises/pointprocesses01.tex rename to pointprocesses/exercises/pointprocesses-1.tex index eb78d42..eed6a5a 100644 --- a/pointprocesses/exercises/pointprocesses01.tex +++ b/pointprocesses/exercises/pointprocesses-1.tex @@ -1,90 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 12\stitle}}{{\bfseries\large Point processes}}{{\bfseries\large January 14th, 2020}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\newcommand{\exercisetopic}{Point Processes} +\newcommand{\exercisenum}{11} +\newcommand{\exercisedate}{January 19th, 2021} +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} diff --git a/pointprocesses/exercises/pointprocesses02.tex b/pointprocesses/exercises/pointprocesses-2.tex similarity index 68% rename from pointprocesses/exercises/pointprocesses02.tex rename to pointprocesses/exercises/pointprocesses-2.tex index c943457..883b0b2 100644 --- a/pointprocesses/exercises/pointprocesses02.tex +++ b/pointprocesses/exercises/pointprocesses-2.tex @@ -1,90 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Point Processes} +\newcommand{\exercisenum}{X2} +\newcommand{\exercisedate}{January 19th, 2021} -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{L\"osungen} -\else -\newcommand{\stitle}{\"Ubung} -\fi -\header{{\bfseries\large \stitle}}{{\bfseries\large Punktprozesse 2}}{{\bfseries\large 27. Oktober, 2015}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} diff --git a/pointprocesses/exercises/pointprocesses03.tex b/pointprocesses/exercises/pointprocesses-3.tex similarity index 73% rename from pointprocesses/exercises/pointprocesses03.tex rename to pointprocesses/exercises/pointprocesses-3.tex index 31bb760..1af6dc7 100644 --- a/pointprocesses/exercises/pointprocesses03.tex +++ b/pointprocesses/exercises/pointprocesses-3.tex @@ -1,90 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: L\"osungen} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large \"Ubung 8\stitle}}{{\bfseries\large Spiketrain Analyse}}{{\bfseries\large 6. Dezember, 2016}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} +\newcommand{\exercisetopic}{Point Processes} +\newcommand{\exercisenum}{X3} +\newcommand{\exercisedate}{January 19th, 2021} +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\input{instructions} - +\input{../../exercisestitle} \begin{questions} From 18c53cb370be6afc7be96a6e4a44c5a5c6fd447d Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 18:55:20 +0100 Subject: [PATCH 22/87] [plotting] updated exercise infrastructure --- plotting/exercises/Makefile | 3 + plotting/exercises/instructions.tex | 12 +-- .../{exercises.tex => plotting-1.tex} | 84 ++----------------- 3 files changed, 13 insertions(+), 86 deletions(-) create mode 100644 plotting/exercises/Makefile rename plotting/exercises/{exercises.tex => plotting-1.tex} (54%) diff --git a/plotting/exercises/Makefile b/plotting/exercises/Makefile new file mode 100644 index 0000000..8e092f8 --- /dev/null +++ b/plotting/exercises/Makefile @@ -0,0 +1,3 @@ +TEXFILES=$(wildcard plotting-?.tex) + +include ../../exercises.mk diff --git a/plotting/exercises/instructions.tex b/plotting/exercises/instructions.tex index 37f737d..8f5d332 100644 --- a/plotting/exercises/instructions.tex +++ b/plotting/exercises/instructions.tex @@ -1,17 +1,11 @@ -\vspace*{-8ex} -\begin{center} -\textbf{\Large Introduction to scientific computing}\\[1ex] -{\large Jan Grewe, Jan Benda}\\[-3ex] -Neuroethology lab \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\ifprintanswers% +\else The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. In contrast to previous exercises, the solutions can not be saved in a single file. Combine the files into a single zip archive and submit it via ILIAS. Name the archive according to the pattern: ``plotting\_\{surname\}.zip''. -% \ifprintanswers% -% \else % % Die folgenden Aufgaben dienen der Wiederholung, \"Ubung und % % Selbstkontrolle und sollten eigenst\"andig bearbeitet und gel\"ost @@ -43,4 +37,4 @@ to the pattern: ``plotting\_\{surname\}.zip''. % Antworten! % \end{itemize} -% \fi +\fi diff --git a/plotting/exercises/exercises.tex b/plotting/exercises/plotting-1.tex similarity index 54% rename from plotting/exercises/exercises.tex rename to plotting/exercises/plotting-1.tex index f66c61c..48c0fd6 100644 --- a/plotting/exercises/exercises.tex +++ b/plotting/exercises/plotting-1.tex @@ -1,88 +1,18 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Plotting} +\newcommand{\exercisenum}{X} +\newcommand{\exercisedate}{December 14th, 2020} -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{: Solutions} -\else -\newcommand{\stitle}{} -\fi -\header{{\bfseries\large Exercise 7\stitle}}{{\bfseries\large Plotting}}{{\bfseries\large November 20, 2019}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: -jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} +\input{../../exercisestitle} + \input{instructions} \begin{questions} From 9a4100386b995311ebd80aedcc91208a0053d0ee Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 19:12:31 +0100 Subject: [PATCH 23/87] [programming] updated exercise infrastructure --- plotting/exercises/plotting-1.tex | 2 +- programming/exercises/Makefile | 11 +++ .../exercises/boolean_logical_indexing.tex | 46 ++++--------- programming/exercises/control_flow.tex | 39 +++-------- programming/exercises/matrices.tex | 45 +++---------- programming/exercises/scripts_functions.tex | 67 +++---------------- programming/exercises/structs_cells.tex | 37 ++-------- programming/exercises/variables_types.tex | 44 +++--------- programming/exercises/vectors.tex | 39 +++-------- programming/exercises/vectors_matrices.tex | 41 +++--------- 10 files changed, 88 insertions(+), 283 deletions(-) create mode 100644 programming/exercises/Makefile diff --git a/plotting/exercises/plotting-1.tex b/plotting/exercises/plotting-1.tex index 48c0fd6..381e43c 100644 --- a/plotting/exercises/plotting-1.tex +++ b/plotting/exercises/plotting-1.tex @@ -6,7 +6,7 @@ \input{../../exercisesheader} -\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} diff --git a/programming/exercises/Makefile b/programming/exercises/Makefile new file mode 100644 index 0000000..7f3247f --- /dev/null +++ b/programming/exercises/Makefile @@ -0,0 +1,11 @@ +TEXFILES= \ + boolean_logical_indexing.tex \ + control_flow.tex \ + matrices.tex \ + scripts_functions.tex \ + structs_cells.tex \ + variables_types.tex \ + vectors_matrices.tex \ + vectors.tex + +include ../../exercises.mk diff --git a/programming/exercises/boolean_logical_indexing.tex b/programming/exercises/boolean_logical_indexing.tex index f166f3d..b1d616d 100644 --- a/programming/exercises/boolean_logical_indexing.tex +++ b/programming/exercises/boolean_logical_indexing.tex @@ -1,39 +1,17 @@ -\documentclass[12pt,a4paper,pdftex, answers]{exam} - -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} \header{{\bfseries\large Exercise 4 - }}{{\bfseries\large Boolean expressions and logical indexing}}{{\bfseries\large 29. Oktober, 2019}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -\newcommand{\code}[1]{\texttt{#1}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\documentclass[12pt,a4paper,pdftex]{exam} + +\newcommand{\exercisetopic}{Logical indexing} +\newcommand{\exercisenum}{4} +\newcommand{\exercisedate}{29. Oktober, 2019} + +\input{../../exercisesheader} + +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to scientific computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. Your solution diff --git a/programming/exercises/control_flow.tex b/programming/exercises/control_flow.tex index 2dd88fd..55c448e 100644 --- a/programming/exercises/control_flow.tex +++ b/programming/exercises/control_flow.tex @@ -1,40 +1,17 @@ -\documentclass[12pt,a4paper,pdftex, answers]{exam} +\documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Control flow} +\newcommand{\exercisenum}{5} +\newcommand{\exercisedate}{5. November, 2019} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 5}}{{\bfseries\large Control Flow}}{{\bfseries\large 05. November, 2019}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to scientific computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethologie \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. Your solution diff --git a/programming/exercises/matrices.tex b/programming/exercises/matrices.tex index 84127a4..3825486 100644 --- a/programming/exercises/matrices.tex +++ b/programming/exercises/matrices.tex @@ -1,40 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 3}}{{\bfseries\large Matrices}}{{\bfseries\large 22. Oktober, 2019}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\exercisetopic}{Matrices} +\newcommand{\exercisenum}{3} +\newcommand{\exercisedate}{22. October, 2019} + +\input{../../exercisesheader} + +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to Scientific Computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} + +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. Your solution diff --git a/programming/exercises/scripts_functions.tex b/programming/exercises/scripts_functions.tex index 2b3282a..dcd919c 100644 --- a/programming/exercises/scripts_functions.tex +++ b/programming/exercises/scripts_functions.tex @@ -1,62 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -%\documentclass[answers,12pt,a4paper,pdftex]{exam} - -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 6}}{{\bfseries\large Scripts and functions}}{{\bfseries\large 06. November, 2018}} -\firstpagefooter{Prof. Jan Benda}{Phone: 29 74 573}{Email: - jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -\newcommand{\code}[1]{\texttt{#1}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newcommand{\exercisetopic}{Scripts and Functions} +\newcommand{\exercisenum}{6} +\newcommand{\exercisedate}{6. November, 2018} + +\input{../../exercisesheader} + +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to Scientific Computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. In contrast diff --git a/programming/exercises/structs_cells.tex b/programming/exercises/structs_cells.tex index a4431bc..b60a81d 100644 --- a/programming/exercises/structs_cells.tex +++ b/programming/exercises/structs_cells.tex @@ -1,40 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Structs and Cell Arrays} +\newcommand{\exercisenum}{6} +\newcommand{\exercisedate}{16. October, 2015} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large \"Ubung 6}}{{\bfseries\large Strukturen und Cell Arrays}}{{\bfseries\large 16. Oktober, 2015}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Einf\"uhrung in die wissenschaftliche Datenverarbeitung}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} Die folgenden Aufgaben dienen der Wiederholung, \"Ubung und Selbstkontrolle und sollten eigenst\"andig bearbeitet und gel\"ost diff --git a/programming/exercises/variables_types.tex b/programming/exercises/variables_types.tex index 3c4f017..89261c4 100644 --- a/programming/exercises/variables_types.tex +++ b/programming/exercises/variables_types.tex @@ -1,41 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[english]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{lipsum} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 1}}{{\bfseries\large Variables und Datatypes}}{{\bfseries\large 03. November, 2020}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\exercisetopic}{Variables und Datatypes} +\newcommand{\exercisenum}{1} +\newcommand{\exercisedate}{3. November, 2020} + +\input{../../exercisesheader} + +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to Scientific Computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. Your solution diff --git a/programming/exercises/vectors.tex b/programming/exercises/vectors.tex index 1ea0e8e..a870b39 100644 --- a/programming/exercises/vectors.tex +++ b/programming/exercises/vectors.tex @@ -1,40 +1,17 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Vectors} +\newcommand{\exercisenum}{2} +\newcommand{\exercisedate}{3. November, 2020} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 2}}{{\bfseries\large Vectors}}{{\bfseries\large 03. November, 2020}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to Scientific Computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} + +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture. You should try to solve them on your own. Your solution diff --git a/programming/exercises/vectors_matrices.tex b/programming/exercises/vectors_matrices.tex index 5726b64..d64c5fa 100644 --- a/programming/exercises/vectors_matrices.tex +++ b/programming/exercises/vectors_matrices.tex @@ -1,40 +1,17 @@ -\documentclass[12pt,a4paper,pdftex, answers]{exam} +\documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Vectors} +\newcommand{\exercisenum}{2} +\newcommand{\exercisedate}{3. November, 2020} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\header{{\bfseries\large Exercise 2}}{{\bfseries\large Vectors}}{{\bfseries\large 03. November, 2020}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} -\runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to Scientific Computing}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} + +\input{../../exercisestitle} The exercises are meant for self-monitoring and revision of the lecture topic. You should try to solve them on your own. Your solution should From 9c6bb91de531393a556529b6e00a5b28b9792449 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 19:16:24 +0100 Subject: [PATCH 24/87] added exercise target to master Makefile --- Makefile | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/Makefile b/Makefile index b59d881..140f584 100644 --- a/Makefile +++ b/Makefile @@ -3,7 +3,7 @@ BASENAME=scientificcomputing-script SUBDIRS=programming debugging plotting codestyle statistics bootstrap regression likelihood pointprocesses designpattern SUBTEXS=$(foreach subd, $(SUBDIRS), $(subd)/lecture/$(subd).tex) -all : plots chapters index script +all : plots chapters index script exercises chapters : for sd in $(SUBDIRS); do $(MAKE) -C $$sd/lecture chapter; done @@ -37,6 +37,11 @@ watchpdf : watchscript : while true; do ! make -s -q script && make script; sleep 0.5; done + +exercises: + for sd in $(SUBDIRS); do if test -d $$sd/exercises; then $(MAKE) -C $$sd/exercises pdf; fi; done + + cleanplots: for sd in $(SUBDIRS); do $(MAKE) -C $$sd/lecture cleanplots; done @@ -46,6 +51,7 @@ cleantex: clean : cleantex for sd in $(SUBDIRS); do $(MAKE) -C $$sd/lecture clean; done + for sd in $(SUBDIRS); do if test -d $$sd/exercises; then $(MAKE) -C $$sd/exercises clean; fi; done cleanall : clean rm -f $(BASENAME).pdf From a097b10024c0e766ba3173f3c50213e8006d5c9f Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 21:30:16 +0100 Subject: [PATCH 25/87] [programming] updated exercise headers --- programming/exercises/boolean_logical_indexing.tex | 2 +- programming/exercises/control_flow.tex | 2 +- programming/exercises/scripts_functions.tex | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/programming/exercises/boolean_logical_indexing.tex b/programming/exercises/boolean_logical_indexing.tex index b1d616d..c7a22dd 100644 --- a/programming/exercises/boolean_logical_indexing.tex +++ b/programming/exercises/boolean_logical_indexing.tex @@ -2,7 +2,7 @@ \newcommand{\exercisetopic}{Logical indexing} \newcommand{\exercisenum}{4} -\newcommand{\exercisedate}{29. Oktober, 2019} +\newcommand{\exercisedate}{17. November, 2020} \input{../../exercisesheader} diff --git a/programming/exercises/control_flow.tex b/programming/exercises/control_flow.tex index 55c448e..f6d8de7 100644 --- a/programming/exercises/control_flow.tex +++ b/programming/exercises/control_flow.tex @@ -2,7 +2,7 @@ \newcommand{\exercisetopic}{Control flow} \newcommand{\exercisenum}{5} -\newcommand{\exercisedate}{5. November, 2019} +\newcommand{\exercisedate}{24. November, 2020} \input{../../exercisesheader} diff --git a/programming/exercises/scripts_functions.tex b/programming/exercises/scripts_functions.tex index dcd919c..d02c5c9 100644 --- a/programming/exercises/scripts_functions.tex +++ b/programming/exercises/scripts_functions.tex @@ -2,7 +2,7 @@ \newcommand{\exercisetopic}{Scripts and Functions} \newcommand{\exercisenum}{6} -\newcommand{\exercisedate}{6. November, 2018} +\newcommand{\exercisedate}{1. December, 2020} \input{../../exercisesheader} From be79d450dfa62b1721125f604d7e15dec93d50be Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 15 Dec 2020 23:18:12 +0100 Subject: [PATCH 26/87] [regression] started to simplify chapter to a 1d problem --- regression/code/meanSquaredErrorLine.m | 1 - regression/code/meansquarederrorline.m | 15 ++ regression/lecture/cubicerrors.py | 36 ++--- regression/lecture/cubicfunc.py | 26 +++- regression/lecture/cubicmse.py | 7 +- regression/lecture/regression-chapter.tex | 111 +++++++++++++- regression/lecture/regression.tex | 167 +++++++++++----------- 7 files changed, 247 insertions(+), 116 deletions(-) delete mode 100644 regression/code/meanSquaredErrorLine.m create mode 100644 regression/code/meansquarederrorline.m diff --git a/regression/code/meanSquaredErrorLine.m b/regression/code/meanSquaredErrorLine.m deleted file mode 100644 index c395934..0000000 --- a/regression/code/meanSquaredErrorLine.m +++ /dev/null @@ -1 +0,0 @@ -mse = mean((y - y_est).^2); diff --git a/regression/code/meansquarederrorline.m b/regression/code/meansquarederrorline.m new file mode 100644 index 0000000..17f9d2f --- /dev/null +++ b/regression/code/meansquarederrorline.m @@ -0,0 +1,15 @@ +n = 40; +xmin = 2.2; +xmax = 3.9; +c = 6.0; +noise = 50.0; + +% generate data: +x = rand(n, 1) * (xmax-xmin) + xmin; +yest = c * x.^3; +y = yest + noise*randn(n, 1); + +% compute mean squared error: +mse = mean((y - y_est).^2); + +fprintf('the mean squared error is %g kg^2\n', mse)) diff --git a/regression/lecture/cubicerrors.py b/regression/lecture/cubicerrors.py index e072d9e..86e608f 100644 --- a/regression/lecture/cubicerrors.py +++ b/regression/lecture/cubicerrors.py @@ -15,28 +15,13 @@ def create_data(): return x, y, c -def plot_data(ax, x, y, c): - ax.plot(x, y, zorder=10, **psAm) - xx = np.linspace(2.1, 3.9, 100) - ax.plot(xx, c*xx**3.0, zorder=5, **lsBm) - for cc in [0.25*c, 0.5*c, 2.0*c, 4.0*c]: - ax.plot(xx, cc*xx**3.0, zorder=5, **lsDm) - ax.set_xlabel('Size x', 'm') - ax.set_ylabel('Weight y', 'kg') - ax.set_xlim(2, 4) - ax.set_ylim(0, 400) - ax.set_xticks(np.arange(2.0, 4.1, 0.5)) - ax.set_yticks(np.arange(0, 401, 100)) - - def plot_data_errors(ax, x, y, c): ax.set_xlabel('Size x', 'm') - #ax.set_ylabel('Weight y', 'kg') + ax.set_ylabel('Weight y', 'kg') ax.set_xlim(2, 4) ax.set_ylim(0, 400) ax.set_xticks(np.arange(2.0, 4.1, 0.5)) ax.set_yticks(np.arange(0, 401, 100)) - ax.set_yticklabels([]) ax.annotate('Error', xy=(x[28]+0.05, y[28]+60), xycoords='data', xytext=(3.4, 70), textcoords='data', ha='left', @@ -52,31 +37,30 @@ def plot_data_errors(ax, x, y, c): yy = [c*x[i]**3.0, y[i]] ax.plot(xx, yy, zorder=5, **lsDm) + def plot_error_hist(ax, x, y, c): ax.set_xlabel('Squared error') ax.set_ylabel('Frequency') - bins = np.arange(0.0, 1250.0, 100) + bins = np.arange(0.0, 11000.0, 750) ax.set_xlim(bins[0], bins[-1]) - #ax.set_ylim(0, 35) - ax.set_xticks(np.arange(bins[0], bins[-1], 200)) - #ax.set_yticks(np.arange(0, 36, 10)) + ax.set_ylim(0, 15) + ax.set_xticks(np.arange(bins[0], bins[-1], 5000)) + ax.set_yticks(np.arange(0, 16, 5)) errors = (y-(c*x**3.0))**2.0 mls = np.mean(errors) ax.annotate('Mean\nsquared\nerror', xy=(mls, 0.5), xycoords='data', - xytext=(800, 3), textcoords='data', ha='left', + xytext=(4500, 6), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.0,0.2), connectionstyle="angle3,angleA=10,angleB=90") ) ax.hist(errors, bins, **fsC) - if __name__ == "__main__": x, y, c = create_data() fig, (ax1, ax2) = plt.subplots(1, 2) - fig.subplots_adjust(wspace=0.2, **adjust_fs(left=6.0, right=1.2)) - plot_data(ax1, x, y, c) - plot_data_errors(ax2, x, y, c) - #plot_error_hist(ax2, x, y, c) + fig.subplots_adjust(wspace=0.4, **adjust_fs(left=6.0, right=1.2)) + plot_data_errors(ax1, x, y, c) + plot_error_hist(ax2, x, y, c) fig.savefig("cubicerrors.pdf") plt.close() diff --git a/regression/lecture/cubicfunc.py b/regression/lecture/cubicfunc.py index e8c0565..45dd67b 100644 --- a/regression/lecture/cubicfunc.py +++ b/regression/lecture/cubicfunc.py @@ -2,7 +2,7 @@ import matplotlib.pyplot as plt import numpy as np from plotstyle import * -if __name__ == "__main__": +def create_data(): # wikipedia: # Generally, males vary in total length from 250 to 390 cm and # weigh between 90 and 306 kg @@ -12,10 +12,20 @@ if __name__ == "__main__": rng = np.random.RandomState(32281) noise = rng.randn(len(x))*50 y += noise + return x, y, c + - fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.4*figure_height)) - fig.subplots_adjust(**adjust_fs(left=6.0, right=1.2)) - +def plot_data(ax, x, y): + ax.plot(x, y, **psA) + ax.set_xlabel('Size x', 'm') + ax.set_ylabel('Weight y', 'kg') + ax.set_xlim(2, 4) + ax.set_ylim(0, 400) + ax.set_xticks(np.arange(2.0, 4.1, 0.5)) + ax.set_yticks(np.arange(0, 401, 100)) + + +def plot_data_fac(ax, x, y, c): ax.plot(x, y, zorder=10, **psA) xx = np.linspace(2.1, 3.9, 100) ax.plot(xx, c*xx**3.0, zorder=5, **lsB) @@ -27,6 +37,14 @@ if __name__ == "__main__": ax.set_ylim(0, 400) ax.set_xticks(np.arange(2.0, 4.1, 0.5)) ax.set_yticks(np.arange(0, 401, 100)) + +if __name__ == "__main__": + x, y, c = create_data() + print(len(x)) + fig, (ax1, ax2) = plt.subplots(1, 2) + fig.subplots_adjust(wspace=0.5, **adjust_fs(fig, left=6.0, right=1.5)) + plot_data(ax1, x, y) + plot_data_fac(ax2, x, y, c) fig.savefig("cubicfunc.pdf") plt.close() diff --git a/regression/lecture/cubicmse.py b/regression/lecture/cubicmse.py index f687885..55ac64b 100644 --- a/regression/lecture/cubicmse.py +++ b/regression/lecture/cubicmse.py @@ -14,6 +14,7 @@ def create_data(): y += noise return x, y, c + def gradient_descent(x, y): n = 20 dc = 0.01 @@ -29,6 +30,7 @@ def gradient_descent(x, y): mses.append(m0) cc -= eps*dmdc return cs, mses + def plot_mse(ax, x, y, c, cs): ms = np.zeros(len(cs)) @@ -54,7 +56,8 @@ def plot_mse(ax, x, y, c, cs): ax.set_ylim(0, 25000) ax.set_xticks(np.arange(0.0, 10.1, 2.0)) ax.set_yticks(np.arange(0, 30001, 10000)) - + + def plot_descent(ax, cs, mses): ax.plot(np.arange(len(mses))+1, mses, **lpsBm) ax.set_xlabel('Iteration') @@ -69,7 +72,7 @@ def plot_descent(ax, cs, mses): if __name__ == "__main__": x, y, c = create_data() cs, mses = gradient_descent(x, y) - fig, (ax1, ax2) = plt.subplots(1, 2) + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) fig.subplots_adjust(wspace=0.2, **adjust_fs(left=8.0, right=0.5)) plot_mse(ax1, x, y, c, cs) plot_descent(ax2, cs, mses) diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 792dfcd..2169854 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -40,6 +40,113 @@ \item Homework is to do the 2d problem with the straight line! \end{itemize} +\subsection{2D fit} + +\begin{exercise}{meanSquaredError.m}{} + Implement the objective function \eqref{mseline} as a function + \varcode{meanSquaredError()}. The function takes three + arguments. The first is a vector of $x$-values and the second + contains the measurements $y$ for each value of $x$. The third + argument is a 2-element vector that contains the values of + parameters \varcode{m} and \varcode{b}. The function returns the + mean square error. +\end{exercise} + + +\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} + Generate 20 data pairs $(x_i|y_i)$ that are linearly related with + slope $m=0.75$ and intercept $b=-40$, using \varcode{rand()} for + drawing $x$ values between 0 and 120 and \varcode{randn()} for + jittering the $y$ values with a standard deviation of 15. Then + calculate the mean squared error between the data and straight lines + for a range of slopes and intercepts using the + \varcode{meanSquaredError()} function from the previous exercise. + Illustrates the error surface using the \code{surface()} function. + Consult the documentation to find out how to use \code{surface()}. +\end{exercise} + +\begin{exercise}{meanSquaredGradient.m}{}\label{gradientexercise}% + Implement a function \varcode{meanSquaredGradient()}, that takes the + $x$- and $y$-data and the set of parameters $(m, b)$ of a straight + line as a two-element vector as input arguments. The function should + return the gradient at the position $(m, b)$ as a vector with two + elements. +\end{exercise} + +\begin{exercise}{errorGradient.m}{} + Extend the script of exercises~\ref{errorsurfaceexercise} to plot + both the error surface and gradients using the + \varcode{meanSquaredGradient()} function from + exercise~\ref{gradientexercise}. Vectors in space can be easily + plotted using the function \code{quiver()}. Use \code{contour()} + instead of \code{surface()} to plot the error surface. +\end{exercise} + + +\begin{exercise}{gradientDescent.m}{} + Implement the gradient descent for the problem of fitting a straight + line to some measured data. Reuse the data generated in + exercise~\ref{errorsurfaceexercise}. + \begin{enumerate} + \item Store for each iteration the error value. + \item Plot the error values as a function of the iterations, the + number of optimization steps. + \item Plot the measured data together with the best fitting straight line. + \end{enumerate}\vspace{-4.5ex} +\end{exercise} + + +\begin{figure}[t] + \includegraphics[width=1\textwidth]{lin_regress}\hfill + \titlecaption{Example data suggesting a linear relation.}{A set of + input signals $x$, e.g. stimulus intensities, were used to probe a + system. The system's output $y$ to the inputs are noted + (left). Assuming a linear relation between $x$ and $y$ leaves us + with 2 parameters, the slope (center) and the intercept with the + y-axis (right panel).}\label{linregressiondatafig} +\end{figure} + +\begin{figure}[t] + \includegraphics[width=1\textwidth]{linear_least_squares} + \titlecaption{Estimating the \emph{mean square error}.} {The + deviation error (orange) between the prediction (red line) and the + observations (blue dots) is calculated for each data point + (left). Then the deviations are squared and the average is + calculated (right).} + \label{leastsquareerrorfig} +\end{figure} + +\begin{figure}[t] + \includegraphics[width=0.75\textwidth]{error_surface} + \titlecaption{Error surface.}{The two model parameters $m$ and $b$ + define the base area of the surface plot. For each parameter + combination of slope and intercept the error is calculated. The + resulting surface has a minimum which indicates the parameter + combination that best fits the data.}\label{errorsurfacefig} +\end{figure} + + +\begin{figure}[t] + \includegraphics[width=0.75\textwidth]{error_gradient} + \titlecaption{Gradient of the error surface.} {Each arrow points + into the direction of the greatest ascend at different positions + of the error surface shown in \figref{errorsurfacefig}. The + contour lines in the background illustrate the error surface. Warm + colors indicate high errors, colder colors low error values. Each + contour line connects points of equal + error.}\label{gradientquiverfig} +\end{figure} + +\begin{figure}[t] + \includegraphics[width=0.45\textwidth]{gradient_descent} + \titlecaption{Gradient descent.}{The algorithm starts at an + arbitrary position. At each point the gradient is estimated and + the position is updated as long as the length of the gradient is + sufficiently large.The dots show the positions after each + iteration of the algorithm.} \label{gradientdescentfig} +\end{figure} + + \subsection{Linear fits} \begin{itemize} \item Polyfit is easy: unique solution! $c x^2$ is also a linear fit. @@ -54,8 +161,8 @@ Fit with matlab functions lsqcurvefit, polyfit \subsection{Non-linear fits} \begin{itemize} \item Example that illustrates the Nebenminima Problem (with error surface) -\item You need got initial values for the parameter! -\item Example that fitting gets harder the more parameter yuo have. +\item You need initial values for the parameter! +\item Example that fitting gets harder the more parameter you have. \item Try to fix as many parameter before doing the fit. \item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test. \end{itemize} diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index e63e3f9..779309b 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -2,99 +2,104 @@ \exercisechapter{Optimization and gradient descent} Optimization problems arise in many different contexts. For example, -to understand the behavior of a given system, the system is probed -with a range of input signals and then the resulting responses are -measured. This input-output relation can be described by a model. Such -a model can be a simple function that maps the input signals to -corresponding responses, it can be a filter, or a system of -differential equations. In any case, the model has some parameters that -specify how input and output signals are related. Which combination -of parameter values are best suited to describe the input-output -relation? The process of finding the best parameter values is an -optimization problem. For a simple parameterized function that maps -input to output values, this is the special case of a \enterm{curve - fitting} problem, where the average distance between the curve and -the response values is minimized. One basic numerical method used for -such optimization problems is the so called gradient descent, which is -introduced in this chapter. - -%%% Weiteres einfaches verbales Beispiel? Eventuell aus der Populationsoekologie? +to understand the behavior of a given neuronal system, the system is +probed with a range of input signals and then the resulting responses +are measured. This input-output relation can be described by a +model. Such a model can be a simple function that maps the input +signals to corresponding responses, it can be a filter, or a system of +differential equations. In any case, the model has some parameters +that specify how input and output signals are related. Which +combination of parameter values are best suited to describe the +input-output relation? The process of finding the best parameter +values is an optimization problem. For a simple parameterized function +that maps input to output values, this is the special case of a +\enterm{curve fitting} problem, where the average distance between the +curve and the response values is minimized. One basic numerical method +used for such optimization problems is the so called gradient descent, +which is introduced in this chapter. \begin{figure}[t] - \includegraphics[width=1\textwidth]{lin_regress}\hfill - \titlecaption{Example data suggesting a linear relation.}{A set of - input signals $x$, e.g. stimulus intensities, were used to probe a - system. The system's output $y$ to the inputs are noted - (left). Assuming a linear relation between $x$ and $y$ leaves us - with 2 parameters, the slope (center) and the intercept with the - y-axis (right panel).}\label{linregressiondatafig} + \includegraphics{cubicfunc} + \titlecaption{Example data suggesting a cubic relation.}{The length + $x$ and weight $y$ of $n=34$ male tigers (blue, left). Assuming a + cubic relation between size and weight leaves us with a single + free parameters, a scaling factor. The cubic relation is shown for + a few values of this scaling factor (orange and red, + right).}\label{cubicdatafig} \end{figure} -The data plotted in \figref{linregressiondatafig} suggest a linear -relation between input and output of the system. We thus assume that a -straight line +For demonstrating the curve-fitting problem let's take the simple +example of weights and sizes measured for a number of male tigers +(\figref{cubicdatafig}). Weight $y$ is proportional to volume +$V$ via the density $\rho$. The volume $V$ of any object is +proportional to its length $x$ cubed. The factor $\alpha$ relating +volume and size cubed depends on the shape of the object and we do not +know this factor for tigers. For the data set we thus expect a cubic +relation between weight and length \begin{equation} - \label{straightline} - y = f(x; m, b) = m\cdot x + b + \label{cubicfunc} + y = f(x; c) = c\cdot x^3 \end{equation} -is an appropriate model to describe the system. The line has two free -parameter, the slope $m$ and the $y$-intercept $b$. We need to find -values for the slope and the intercept that best describe the measured -data. In this chapter we use this example to illustrate the gradient -descent and how this methods can be used to find a combination of -slope and intercept that best describes the system. +where $c=\rho\alpha$, the product of a tiger's density and form +factor, is the only free parameter in the relation. We would like to +find out which value of $c$ best describes the measured data. In the +following we use this example to illustrate the gradient descent as a +basic method for finding such an optimal parameter. \section{The error function --- mean squared error} -Before the optimization can be done we need to specify what exactly is -considered an optimal fit. In our example we search the parameter -combination that describe the relation of $x$ and $y$ best. What is -meant by this? Each input $x_i$ leads to an measured output $y_i$ and -for each $x_i$ there is a \emph{prediction} or \emph{estimation} -$y^{est}(x_i)$ of the output value by the model. At each $x_i$ -estimation and measurement have a distance or error $y_i - -y^{est}(x_i)$. In our example the estimation is given by the equation -$y^{est}(x_i) = f(x_i;m,b)$. The best fitting model with parameters -$m$ and $b$ is the one that minimizes the distances between -observation $y_i$ and estimation $y^{est}(x_i)$ -(\figref{leastsquareerrorfig}). - -As a first guess we could simply minimize the sum $\sum_{i=1}^N y_i - -y^{est}(x_i)$. This approach, however, will not work since a minimal sum -can also be achieved if half of the measurements is above and the -other half below the predicted line. Positive and negative errors -would cancel out and then sum up to values close to zero. A better -approach is to sum over the absolute values of the distances: -$\sum_{i=1}^N |y_i - y^{est}(x_i)|$. This sum can only be small if all -deviations are indeed small no matter if they are above or below the -predicted line. Instead of the sum we could also take the average -\begin{equation} - \label{meanabserror} - f_{dist}(\{(x_i, y_i)\}|\{y^{est}(x_i)\}) = \frac{1}{N} \sum_{i=1}^N |y_i - y^{est}(x_i)| -\end{equation} -Instead of the averaged absolute errors, the \enterm[mean squared -error]{mean squared error} (\determ[quadratischer -Fehler!mittlerer]{mittlerer quadratischer Fehler}) +Before we go ahead finding the optimal parameter value we need to +specify what exactly we consider as an optimal fit. In our example we +search the parameter that describes the relation of $x$ and $y$ +best. What is meant by this? The length $x_i$ of each tiger is +associated with a weight $y_i$ and for each $x_i$ we have a +\emph{prediction} or \emph{estimation} $y^{est}(x_i)$ of the weight by +the model \eqnref{cubicfunc} for a specific value of the parameter +$c$. Prediction and actual data value ideally match (in a perfect +noise-free world), but in general the estimate and measurement are +separated by some distance or error $y_i - y^{est}(x_i)$. In our +example the estimate of the weight for the length $x_i$ is given by +equation \eqref{cubicfunc} $y^{est}(x_i) = f(x_i;c)$. The best fitting +model with parameter $c$ is the one that somehow minimizes the +distances between observations $y_i$ and corresponding estimations +$y^{est}(x_i)$ (\figref{cubicerrorsfig}). + +As a first guess we could simply minimize the sum of the distances, +$\sum_{i=1}^N y_i - y^{est}(x_i)$. This, however, does not work +because positive and negative errors would cancel out, no matter how +large they are, and sum up to values close to zero. Better is to sum +over absolute distances: $\sum_{i=1}^N |y_i - y^{est}(x_i)|$. This sum +can only be small if all deviations are indeed small no matter if they +are above or below the prediction. The sum of the squared distances, +$\sum_{i=1}^N (y_i - y^{est}(x_i))^2$, turns out to be an even better +choice. Instead of the sum we could also minimize the average distance \begin{equation} \label{meansquarederror} f_{mse}(\{(x_i, y_i)\}|\{y^{est}(x_i)\}) = \frac{1}{N} \sum_{i=1}^N (y_i - y^{est}(x_i))^2 \end{equation} -is commonly used (\figref{leastsquareerrorfig}). Similar to the -absolute distance, the square of the errors, $(y_i - y^{est}(x_i))^2$, is -always positive and thus positive and negative error values do not +This is known as the \enterm[mean squared error]{mean squared error} +(\determ[quadratischer Fehler!mittlerer]{mittlerer quadratischer + Fehler}). Similar to the absolute distance, the square of the errors +is always positive and thus positive and negative error values do not cancel each other out. In addition, the square punishes large deviations over small deviations. In chapter~\ref{maximumlikelihoodchapter} we show that minimizing the -mean square error is equivalent to maximizing the likelihood that the +mean squared error is equivalent to maximizing the likelihood that the observations originate from the model, if the data are normally distributed around the model prediction. -\begin{exercise}{meanSquaredErrorLine.m}{}\label{mseexercise}% - Given a vector of observations \varcode{y} and a vector with the - corresponding predictions \varcode{y\_est}, compute the \emph{mean - square error} between \varcode{y} and \varcode{y\_est} in a single - line of code. +\begin{exercise}{meansquarederrorline.m}{}\label{mseexercise} + Simulate $n=40$ tigers ranging from 2.2 to 3.9\,m in size and store + these sizes in a vector \varcode{x}. Compute the corresponding + predicted weights \varcode{yest} for each tiger according to + \eqnref{cubicfunc} with $c=6$\,\kilo\gram\per\meter\cubed. From the + predictions generate simulated measurements of the tiger's weights + \varcode{y}, by adding normally distributed random numbers to the + predictions scaled to a standard deviation of 50\,\kilo\gram. + + Compute the \emph{mean squared error} between \varcode{y} and + \varcode{yest} in a single line of code. \end{exercise} @@ -110,13 +115,13 @@ can be any function that describes the quality of the fit by mapping the data and the predictions to a single scalar value. \begin{figure}[t] - \includegraphics[width=1\textwidth]{linear_least_squares} - \titlecaption{Estimating the \emph{mean square error}.} {The - deviation error, orange) between the prediction (red - line) and the observations (blue dots) is calculated for each data - point (left). Then the deviations are squared and the aveage is + \includegraphics{cubicerrors} + \titlecaption{Estimating the \emph{mean squared error}.} {The + deviation error (orange) between the prediction (red line) and the + observations (blue dots) is calculated for each data point + (left). Then the deviations are squared and the average is calculated (right).} - \label{leastsquareerrorfig} + \label{cubicerrorsfig} \end{figure} Replacing $y^{est}$ in the mean squared error \eqref{meansquarederror} @@ -139,7 +144,7 @@ Fehler!kleinster]{Methode der kleinsten Quadrate}). contains the measurements $y$ for each value of $x$. The third argument is a 2-element vector that contains the values of parameters \varcode{m} and \varcode{b}. The function returns the - mean square error. + mean squared error. \end{exercise} @@ -359,7 +364,7 @@ distance between the red dots in \figref{gradientdescentfig}) is large. \begin{figure}[t] - \includegraphics[width=0.45\textwidth]{gradient_descent} + \includegraphics{cubicmse} \titlecaption{Gradient descent.}{The algorithm starts at an arbitrary position. At each point the gradient is estimated and the position is updated as long as the length of the gradient is From 1b14bca16419b8782b1af6e388b66168f0506676 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 16 Dec 2020 09:25:01 +0100 Subject: [PATCH 27/87] [regression] objective function section done --- chapter.mk | 4 +-- regression/code/meanSquaredError.m | 12 --------- regression/code/meanSquaredErrorCubic.m | 11 ++++++++ regression/code/meansquarederrorline.m | 4 +-- regression/lecture/cubicfunc.py | 2 +- regression/lecture/regression-chapter.tex | 11 -------- regression/lecture/regression.tex | 32 +++++++++++------------ 7 files changed, 31 insertions(+), 45 deletions(-) delete mode 100644 regression/code/meanSquaredError.m create mode 100644 regression/code/meanSquaredErrorCubic.m diff --git a/chapter.mk b/chapter.mk index 0482aed..f642e2e 100644 --- a/chapter.mk +++ b/chapter.mk @@ -10,8 +10,8 @@ pythonplots : $(PYPDFFILES) $(PYPDFFILES) : %.pdf: %.py ../../plotstyle.py PYTHONPATH="../../" python3 $< - #ps2pdf $@ $(@:.pdf=-temp.pdf) # strip fonts, saves only about 1.5MB - #mv $(@:.pdf=-temp.pdf) $@ +#ps2pdf $@ $(@:.pdf=-temp.pdf) # strip fonts, saves only about 1.5MB +#mv $(@:.pdf=-temp.pdf) $@ cleanpythonplots : rm -f $(PYPDFFILES) diff --git a/regression/code/meanSquaredError.m b/regression/code/meanSquaredError.m deleted file mode 100644 index 6eeea7b..0000000 --- a/regression/code/meanSquaredError.m +++ /dev/null @@ -1,12 +0,0 @@ -function mse = meanSquaredError(x, y, parameter) -% Mean squared error between a straight line and data pairs. -% -% Arguments: x, vector of the input values -% y, vector of the corresponding measured output values -% parameter, vector containing slope and intercept -% as the 1st and 2nd element, respectively. -% -% Returns: mse, the mean-squared-error. - - mse = mean((y - x * parameter(1) - parameter(2)).^2); -end diff --git a/regression/code/meanSquaredErrorCubic.m b/regression/code/meanSquaredErrorCubic.m new file mode 100644 index 0000000..bb17137 --- /dev/null +++ b/regression/code/meanSquaredErrorCubic.m @@ -0,0 +1,11 @@ +function mse = meanSquaredError(x, y, c) +% Mean squared error between data pairs and a cubic relation. +% +% Arguments: x, vector of the input values +% y, vector of the corresponding measured output values +% c, the factor for the cubic relation. +% +% Returns: mse, the mean-squared-error. + + mse = mean((y - c*x.^3).^2); +end diff --git a/regression/code/meansquarederrorline.m b/regression/code/meansquarederrorline.m index 17f9d2f..4eca4a3 100644 --- a/regression/code/meansquarederrorline.m +++ b/regression/code/meansquarederrorline.m @@ -10,6 +10,6 @@ yest = c * x.^3; y = yest + noise*randn(n, 1); % compute mean squared error: -mse = mean((y - y_est).^2); +mse = mean((y - yest).^2); -fprintf('the mean squared error is %g kg^2\n', mse)) +fprintf('the mean squared error is %.0f kg^2\n', mse) diff --git a/regression/lecture/cubicfunc.py b/regression/lecture/cubicfunc.py index 45dd67b..8b5b44a 100644 --- a/regression/lecture/cubicfunc.py +++ b/regression/lecture/cubicfunc.py @@ -41,7 +41,7 @@ def plot_data_fac(ax, x, y, c): if __name__ == "__main__": x, y, c = create_data() - print(len(x)) + print('n=%d' % len(x)) fig, (ax1, ax2) = plt.subplots(1, 2) fig.subplots_adjust(wspace=0.5, **adjust_fs(fig, left=6.0, right=1.5)) plot_data(ax1, x, y) diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 2169854..8afed44 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -42,17 +42,6 @@ \subsection{2D fit} -\begin{exercise}{meanSquaredError.m}{} - Implement the objective function \eqref{mseline} as a function - \varcode{meanSquaredError()}. The function takes three - arguments. The first is a vector of $x$-values and the second - contains the measurements $y$ for each value of $x$. The third - argument is a 2-element vector that contains the values of - parameters \varcode{m} and \varcode{b}. The function returns the - mean square error. -\end{exercise} - - \begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} Generate 20 data pairs $(x_i|y_i)$ that are linearly related with slope $m=0.75$ and intercept $b=-40$, using \varcode{rand()} for diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 779309b..7fbffbf 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -109,10 +109,10 @@ The mean squared error is a so called \enterm{objective function} or \enterm{cost function} (\determ{Kostenfunktion}). A cost function assigns to a model prediction $\{y^{est}(x_i)\}$ for a given data set $\{(x_i, y_i)\}$ a single scalar value that we want to minimize. Here -we aim to adapt the model parameters to minimize the mean squared -error \eqref{meansquarederror}. In general, the \enterm{cost function} -can be any function that describes the quality of the fit by mapping -the data and the predictions to a single scalar value. +we aim to adapt the model parameter to minimize the mean squared error +\eqref{meansquarederror}. In general, the \enterm{cost function} can +be any function that describes the quality of a fit by mapping the +data and the predictions to a single scalar value. \begin{figure}[t] \includegraphics{cubicerrors} @@ -125,25 +125,23 @@ the data and the predictions to a single scalar value. \end{figure} Replacing $y^{est}$ in the mean squared error \eqref{meansquarederror} -with our model, the straight line \eqref{straightline}, the cost -function reads +with our cubic model \eqref{cubicfunc}, the cost function reads \begin{eqnarray} - f_{cost}(m,b|\{(x_i, y_i)\}) & = & \frac{1}{N} \sum_{i=1}^N (y_i - f(x_i;m,b))^2 \label{msefunc} \\ - & = & \frac{1}{N} \sum_{i=1}^N (y_i - m x_i - b)^2 \label{mseline} + f_{cost}(c|\{(x_i, y_i)\}) & = & \frac{1}{N} \sum_{i=1}^N (y_i - f(x_i;c))^2 \label{msefunc} \\ + & = & \frac{1}{N} \sum_{i=1}^N (y_i - c x_i^3)^2 \label{msecube} \end{eqnarray} -The optimization process tries to find the slope $m$ and the intercept -$b$ such that the cost function is minimized. With the mean squared -error as the cost function this optimization process is also called -method of the \enterm{least square error} (\determ[quadratischer +The optimization process tries to find a value for the factor $c$ such +that the cost function is minimized. With the mean squared error as +the cost function this optimization process is also called method of + \enterm{least squares} (\determ[quadratischer Fehler!kleinster]{Methode der kleinsten Quadrate}). -\begin{exercise}{meanSquaredError.m}{} - Implement the objective function \eqref{mseline} as a function - \varcode{meanSquaredError()}. The function takes three +\begin{exercise}{meanSquaredErrorCubic.m}{} + Implement the objective function \eqref{msecube} as a function + \varcode{meanSquaredErrorCubic()}. The function takes three arguments. The first is a vector of $x$-values and the second contains the measurements $y$ for each value of $x$. The third - argument is a 2-element vector that contains the values of - parameters \varcode{m} and \varcode{b}. The function returns the + argument is the value of the factor $c$. The function returns the mean squared error. \end{exercise} From 3541f30798c6d7722abc41f253112fe152968151 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 16 Dec 2020 15:14:57 +0100 Subject: [PATCH 28/87] [regression] new figure for minimum of a cost function --- regression/code/meanSquaredErrorCubic.m | 2 +- regression/lecture/cubiccost.py | 80 +++++++++++++++++++++++++ regression/lecture/regression.tex | 57 +++++++++--------- 3 files changed, 108 insertions(+), 31 deletions(-) create mode 100644 regression/lecture/cubiccost.py diff --git a/regression/code/meanSquaredErrorCubic.m b/regression/code/meanSquaredErrorCubic.m index bb17137..44870a1 100644 --- a/regression/code/meanSquaredErrorCubic.m +++ b/regression/code/meanSquaredErrorCubic.m @@ -1,4 +1,4 @@ -function mse = meanSquaredError(x, y, c) +function mse = meanSquaredErrorCubic(x, y, c) % Mean squared error between data pairs and a cubic relation. % % Arguments: x, vector of the input values diff --git a/regression/lecture/cubiccost.py b/regression/lecture/cubiccost.py new file mode 100644 index 0000000..0b8d2dc --- /dev/null +++ b/regression/lecture/cubiccost.py @@ -0,0 +1,80 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.ticker as mt +from plotstyle import * + +def create_data(): + # wikipedia: + # Generally, males vary in total length from 250 to 390 cm and + # weigh between 90 and 306 kg + c = 6 + x = np.arange(2.2, 3.9, 0.05) + y = c * x**3.0 + rng = np.random.RandomState(32281) + noise = rng.randn(len(x))*50 + y += noise + return x, y, c + + +def plot_mse(ax, x, y, c): + ccs = np.linspace(0.5, 10.0, 200) + mses = np.zeros(len(ccs)) + for i, cc in enumerate(ccs): + mses[i] = np.mean((y-(cc*x**3.0))**2.0) + imin = np.argmin(mses) + + ax.plot(ccs, mses, **lsAm) + ax.plot(c, 500.0, **psB) + ax.plot(ccs[imin], mses[imin], **psC) + ax.annotate('Minimum of\ncost\nfunction', + xy=(ccs[imin], mses[imin]*1.2), xycoords='data', + xytext=(4, 7000), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0), + connectionstyle="angle3,angleA=10,angleB=90") ) + ax.text(2.2, 500, 'True\nparameter\nvalue') + ax.annotate('', xy=(c-0.2, 500), xycoords='data', + xytext=(4.1, 700), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(1.0,0.0), + connectionstyle="angle3,angleA=-10,angleB=0") ) + ax.set_xlabel('c') + ax.set_ylabel('Mean squared error') + ax.set_xlim(2, 8.2) + ax.set_ylim(0, 10000) + ax.set_xticks(np.arange(2.0, 8.1, 2.0)) + ax.set_yticks(np.arange(0, 10001, 5000)) + + +def plot_mse_min(ax, x, y, c): + ccs = np.arange(0.5, 10.0, 0.05) + mses = np.zeros(len(ccs)) + for i, cc in enumerate(ccs): + mses[i] = np.mean((y-(cc*x**3.0))**2.0) + di = 20 + i0 = 14 + imin = np.argmin(mses[i0::di])*di + i0 + + ax.plot(c, 500.0, **psB) + ax.plot(ccs, mses, **lsAm) + ax.plot(ccs[i0::di], mses[i0::di], **psAm) + ax.plot(ccs[imin], mses[imin], **psC) + ax.annotate('Estimated\nminimum of\ncost\nfunction', + xy=(ccs[imin], mses[imin]*1.2), xycoords='data', + xytext=(4, 6700), textcoords='data', ha='left', + arrowprops=dict(arrowstyle="->", relpos=(0.8,0.0), + connectionstyle="angle3,angleA=0,angleB=85") ) + ax.set_xlabel('c') + ax.set_xlim(2, 8.2) + ax.set_ylim(0, 10000) + ax.set_xticks(np.arange(2.0, 8.1, 2.0)) + ax.set_yticks(np.arange(0, 10001, 5000)) + ax.yaxis.set_major_formatter(mt.NullFormatter()) + + +if __name__ == "__main__": + x, y, c = create_data() + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) + fig.subplots_adjust(**adjust_fs(left=8.0, right=1)) + plot_mse(ax1, x, y, c) + plot_mse_min(ax2, x, y, c) + fig.savefig("cubiccost.pdf") + plt.close() diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 7fbffbf..8867744 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -103,7 +103,7 @@ distributed around the model prediction. \end{exercise} -\section{Objective function} +\section{Cost function} The mean squared error is a so called \enterm{objective function} or \enterm{cost function} (\determ{Kostenfunktion}). A cost function @@ -146,42 +146,39 @@ Fehler!kleinster]{Methode der kleinsten Quadrate}). \end{exercise} -\section{Error surface} -For each combination of the two parameters $m$ and $b$ of the model we -can use \eqnref{mseline} to calculate the corresponding value of the -cost function. The cost function $f_{cost}(m,b|\{(x_i, y_i)\}|)$ is a -function $f_{cost}(m,b)$, that maps the parameter values $m$ and $b$ -to a scalar error value. The error values describe a landscape over the -$m$-$b$ plane, the error surface, that can be illustrated graphically -using a 3-d surface-plot. $m$ and $b$ are plotted on the $x$- and $y$- -axis while the third dimension indicates the error value -(\figref{errorsurfacefig}). +\section{Graph of the cost function} +For each value of the parameter $c$ of the model we can use +\eqnref{msecube} to calculate the corresponding value of the cost +function. The cost function $f_{cost}(c|\{(x_i, y_i)\}|)$ is a +function $f_{cost}(c)$ that maps the parameter value $c$ to a scalar +error value. For a given data set we thus can simply plot the cost +function as a function of $c$ (\figref{cubiccostfig}). \begin{figure}[t] - \includegraphics[width=0.75\textwidth]{error_surface} - \titlecaption{Error surface.}{The two model parameters $m$ and $b$ - define the base area of the surface plot. For each parameter - combination of slope and intercept the error is calculated. The - resulting surface has a minimum which indicates the parameter - combination that best fits the data.}\label{errorsurfacefig} + \includegraphics{cubiccost} + \titlecaption{Minimum of the cost function.}{For a given data set + the cost function, the mean squared error \eqnref{msecube}, as a + function of the unknown parameter $c$ has a minimum close to the + true value of $c$ that was used to generate the data + (left). Simply taking the absolute minimum of the cost function + computed for a pre-set range of values for the parameter $c$, has + the disadvantage to be limited in precision (right) and the + possibility to entirely miss the global minimum if it is outside + the computed range.}\label{cubiccostfig} \end{figure} \begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} - Generate 20 data pairs $(x_i|y_i)$ that are linearly related with - slope $m=0.75$ and intercept $b=-40$, using \varcode{rand()} for - drawing $x$ values between 0 and 120 and \varcode{randn()} for - jittering the $y$ values with a standard deviation of 15. Then - calculate the mean squared error between the data and straight lines - for a range of slopes and intercepts using the - \varcode{meanSquaredError()} function from the previous exercise. - Illustrates the error surface using the \code{surface()} function. - Consult the documentation to find out how to use \code{surface()}. + Then calculate the mean squared error between the data and straight + lines for a range of slopes and intercepts using the + \varcode{meanSquaredErrorCubic()} function from the previous + exercise. Illustrate the error surface using the \code{surface()} + function. \end{exercise} -By looking at the error surface we can directly see the position of -the minimum and thus estimate the optimal parameter combination. How -can we use the error surface to guide an automatic optimization -process? +By looking at the plot of the cost function we can visually identify +the position of the minimum and thus estimate the optimal value for +the parameter $c$. How can we use the error surface to guide an +automatic optimization process? The obvious approach would be to calculate the error surface for any combination of slope and intercept values and then find the position From 99a8a9d91e6e375c7824afefe6ca9e76c9f9a0f0 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Thu, 17 Dec 2020 22:38:07 +0100 Subject: [PATCH 29/87] [regression] improved cost function figure --- regression/lecture/cubiccost.py | 12 +++++++----- regression/lecture/regression.tex | 16 ++++++++-------- 2 files changed, 15 insertions(+), 13 deletions(-) diff --git a/regression/lecture/cubiccost.py b/regression/lecture/cubiccost.py index 0b8d2dc..30d9575 100644 --- a/regression/lecture/cubiccost.py +++ b/regression/lecture/cubiccost.py @@ -49,16 +49,18 @@ def plot_mse_min(ax, x, y, c): mses = np.zeros(len(ccs)) for i, cc in enumerate(ccs): mses[i] = np.mean((y-(cc*x**3.0))**2.0) - di = 20 - i0 = 14 - imin = np.argmin(mses[i0::di])*di + i0 + imin = np.argmin(mses) + di = 25 + i0 = 16 + dimin = np.argmin(mses[i0::di])*di + i0 ax.plot(c, 500.0, **psB) ax.plot(ccs, mses, **lsAm) ax.plot(ccs[i0::di], mses[i0::di], **psAm) - ax.plot(ccs[imin], mses[imin], **psC) + ax.plot(ccs[dimin], mses[dimin], **psD) + #ax.plot(ccs[imin], mses[imin], **psCm) ax.annotate('Estimated\nminimum of\ncost\nfunction', - xy=(ccs[imin], mses[imin]*1.2), xycoords='data', + xy=(ccs[dimin], mses[dimin]*1.2), xycoords='data', xytext=(4, 6700), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.8,0.0), connectionstyle="angle3,angleA=0,angleB=85") ) diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 8867744..2990aef 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -154,6 +154,14 @@ function $f_{cost}(c)$ that maps the parameter value $c$ to a scalar error value. For a given data set we thus can simply plot the cost function as a function of $c$ (\figref{cubiccostfig}). +\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} + Then calculate the mean squared error between the data and straight + lines for a range of slopes and intercepts using the + \varcode{meanSquaredErrorCubic()} function from the previous + exercise. Illustrate the error surface using the \code{surface()} + function. +\end{exercise} + \begin{figure}[t] \includegraphics{cubiccost} \titlecaption{Minimum of the cost function.}{For a given data set @@ -167,14 +175,6 @@ function as a function of $c$ (\figref{cubiccostfig}). the computed range.}\label{cubiccostfig} \end{figure} -\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} - Then calculate the mean squared error between the data and straight - lines for a range of slopes and intercepts using the - \varcode{meanSquaredErrorCubic()} function from the previous - exercise. Illustrate the error surface using the \code{surface()} - function. -\end{exercise} - By looking at the plot of the cost function we can visually identify the position of the minimum and thus estimate the optimal value for the parameter $c$. How can we use the error surface to guide an From fefe1c3726a1ad784da789177b95bce2b465cc95 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Fri, 18 Dec 2020 13:10:53 +0100 Subject: [PATCH 30/87] [regression] text and example for cost function figure --- regression/code/plotcubiccosts.m | 9 ++++++ regression/lecture/regression.tex | 49 ++++++++++++++++--------------- 2 files changed, 34 insertions(+), 24 deletions(-) create mode 100644 regression/code/plotcubiccosts.m diff --git a/regression/code/plotcubiccosts.m b/regression/code/plotcubiccosts.m new file mode 100644 index 0000000..6c90f03 --- /dev/null +++ b/regression/code/plotcubiccosts.m @@ -0,0 +1,9 @@ +cs = 2.0:0.1:8.0; +mses = zeros(length(cs)); +for i = 1:length(cs) + mses(i) = meanSquaredErrorCubic(x, y, cs(i)); +end + +plot(cs, mses) +xlabel('c') +ylabel('mean squared error') diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 2990aef..d903a0b 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -154,12 +154,11 @@ function $f_{cost}(c)$ that maps the parameter value $c$ to a scalar error value. For a given data set we thus can simply plot the cost function as a function of $c$ (\figref{cubiccostfig}). -\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} - Then calculate the mean squared error between the data and straight - lines for a range of slopes and intercepts using the +\begin{exercise}{plotcubiccosts.m}{} + Calculate the mean squared error between the data and the cubic + function for a range of values of the factor $c$ using the \varcode{meanSquaredErrorCubic()} function from the previous - exercise. Illustrate the error surface using the \code{surface()} - function. + exercise. Plot the graph of the cost function. \end{exercise} \begin{figure}[t] @@ -177,20 +176,22 @@ function as a function of $c$ (\figref{cubiccostfig}). By looking at the plot of the cost function we can visually identify the position of the minimum and thus estimate the optimal value for -the parameter $c$. How can we use the error surface to guide an +the parameter $c$. How can we use the cost function to guide an automatic optimization process? -The obvious approach would be to calculate the error surface for any -combination of slope and intercept values and then find the position -of the minimum using the \code{min} function. This approach, however -has several disadvantages: (i) it is computationally very expensive to -calculate the error for each parameter combination. The number of -combinations increases exponentially with the number of free -parameters (also known as the ``curse of dimensionality''). (ii) the -accuracy with which the best parameters can be estimated is limited by -the resolution used to sample the parameter space. The coarser the -parameters are sampled the less precise is the obtained position of -the minimum. +The obvious approach would be to calculate the mean squared error for +a range of parameter values and then find the position of the minimum +using the \code{min} function. This approach, however has several +disadvantages: (i) the accuracy of the estimation of the best +parameter is limited by the resolution used to sample the parameter +space. The coarser the parameters are sampled the less precise is the +obtained position of the minimum (\figref{cubiccostfig}, right). (ii) +the range of parameter values might not include the absolute minimum. +(iii) in particular for functions with more than a single free +parameter it is computationally expensive to calculate the cost +function for each parameter combination. The number of combinations +increases exponentially with the number of free parameters. This is +known as the \enterm{curse of dimensionality}. So we need a different approach. We want a procedure that finds the minimum of the cost function with a minimal number of computations and @@ -206,22 +207,22 @@ to arbitrary precision. m = \frac{f(x + \Delta x) - f(x)}{\Delta x} \end{equation} of a function $y = f(x)$ is the slope of the secant (red) defined - by the points $(x,f(x))$ and $(x+\Delta x,f(x+\Delta x))$ with the + by the points $(x,f(x))$ and $(x+\Delta x,f(x+\Delta x))$ at distance $\Delta x$. - The slope of the function $y=f(x)$ at the position $x$ (yellow) is + The slope of the function $y=f(x)$ at the position $x$ (orange) is given by the derivative $f'(x)$ of the function at that position. It is defined by the difference quotient in the limit of - infinitesimally (orange) small distances $\Delta x$: + infinitesimally (red and yellow) small distances $\Delta x$: \begin{equation} \label{derivative} f'(x) = \frac{{\rm d} f(x)}{{\rm d}x} = \lim\limits_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} \end{equation} \end{minipage}\vspace{2ex} - It is not possible to calculate the derivative, \eqnref{derivative}, - numerically. The derivative can only be estimated using the - difference quotient, \eqnref{difffrac}, by using sufficiently small - $\Delta x$. + It is not possible to calculate the exact value of the derivative, + \eqnref{derivative}, numerically. The derivative can only be + estimated by computing the difference quotient, \eqnref{difffrac} + using sufficiently small $\Delta x$. \end{ibox} \begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} From ca5493624559b9a2efebe9ad79ea1023b49ca9a9 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Fri, 18 Dec 2020 23:37:17 +0100 Subject: [PATCH 31/87] [regression] finished gradient section --- regression/code/meanSquaredGradientCubic.m | 14 ++ regression/code/plotcubicgradient.m | 9 + regression/lecture/regression-chapter.tex | 12 +- regression/lecture/regression.tex | 191 ++++++++++----------- 4 files changed, 115 insertions(+), 111 deletions(-) create mode 100644 regression/code/meanSquaredGradientCubic.m create mode 100644 regression/code/plotcubicgradient.m diff --git a/regression/code/meanSquaredGradientCubic.m b/regression/code/meanSquaredGradientCubic.m new file mode 100644 index 0000000..a7ff6a2 --- /dev/null +++ b/regression/code/meanSquaredGradientCubic.m @@ -0,0 +1,14 @@ +function dmsedc = meanSquaredGradientCubic(x, y, c) +% The gradient of the mean squared error for a cubic relation. +% +% Arguments: x, vector of the x-data values +% y, vector of the corresponding y-data values +% c, the factor for the cubic relation. +% +% Returns: the derivative of the mean squared error at c. + + h = 1e-5; % stepsize for derivatives + mse = meanSquaredErrorCubic(x, y, c); + mseh = meanSquaredErrorCubic(x, y, c+h); + dmsedc = (mseh - mse)/h; +end diff --git a/regression/code/plotcubicgradient.m b/regression/code/plotcubicgradient.m new file mode 100644 index 0000000..0410b1f --- /dev/null +++ b/regression/code/plotcubicgradient.m @@ -0,0 +1,9 @@ +cs = 2.0:0.1:8.0; +mseg = zeros(length(cs)); +for i = 1:length(cs) + mseg(i) = meanSquaredGradientCubic(x, y, cs(i)); +end + +plot(cs, mseg) +xlabel('c') +ylabel('gradient') diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 8afed44..3983848 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -25,19 +25,11 @@ \subsection{Start with one-dimensional problem!} \begin{itemize} -\item Let's fit a cubic function $y=cx^3$ (weight versus length of a tiger)\\ -\includegraphics[width=0.8\textwidth]{cubicfunc} -\item Introduce the problem, $c$ is density and form factor -\item How to generate an artificial data set (refer to simulation chapter) \item How to plot a function (do not use the data x values!) -\item Just the mean square error as a function of the factor c\\ -\includegraphics[width=0.8\textwidth]{cubicerrors} -\item Also mention the cost function for a straight line -\item 1-d gradient, NO quiver plot (it is a nightmare to get this right)\\ -\includegraphics[width=0.8\textwidth]{cubicmse} \item 1-d gradient descend -\item Describe in words the n-d problem. +\item Describe in words the n-d problem (boltzman as example?). \item Homework is to do the 2d problem with the straight line! +\item NO quiver plot (it is a nightmare to get this right) \end{itemize} \subsection{2D fit} diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index d903a0b..776f745 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -152,7 +152,7 @@ For each value of the parameter $c$ of the model we can use function. The cost function $f_{cost}(c|\{(x_i, y_i)\}|)$ is a function $f_{cost}(c)$ that maps the parameter value $c$ to a scalar error value. For a given data set we thus can simply plot the cost -function as a function of $c$ (\figref{cubiccostfig}). +function as a function of the parameter $c$ (\figref{cubiccostfig}). \begin{exercise}{plotcubiccosts.m}{} Calculate the mean squared error between the data and the cubic @@ -181,17 +181,18 @@ automatic optimization process? The obvious approach would be to calculate the mean squared error for a range of parameter values and then find the position of the minimum -using the \code{min} function. This approach, however has several -disadvantages: (i) the accuracy of the estimation of the best +using the \code{min()} function. This approach, however has several +disadvantages: (i) The accuracy of the estimation of the best parameter is limited by the resolution used to sample the parameter space. The coarser the parameters are sampled the less precise is the obtained position of the minimum (\figref{cubiccostfig}, right). (ii) -the range of parameter values might not include the absolute minimum. -(iii) in particular for functions with more than a single free +The range of parameter values might not include the absolute minimum. +(iii) In particular for functions with more than a single free parameter it is computationally expensive to calculate the cost -function for each parameter combination. The number of combinations -increases exponentially with the number of free parameters. This is -known as the \enterm{curse of dimensionality}. +function for each parameter combination at a sufficient +resolution. The number of combinations increases exponentially with +the number of free parameters. This is known as the \enterm{curse of + dimensionality}. So we need a different approach. We want a procedure that finds the minimum of the cost function with a minimal number of computations and @@ -219,110 +220,54 @@ to arbitrary precision. f'(x) = \frac{{\rm d} f(x)}{{\rm d}x} = \lim\limits_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} \end{equation} \end{minipage}\vspace{2ex} - It is not possible to calculate the exact value of the derivative, - \eqnref{derivative}, numerically. The derivative can only be - estimated by computing the difference quotient, \eqnref{difffrac} - using sufficiently small $\Delta x$. + It is not possible to calculate the exact value of the derivative + \eqref{derivative} numerically. The derivative can only be estimated + by computing the difference quotient \eqref{difffrac} using + sufficiently small $\Delta x$. \end{ibox} -\begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} - Some functions that depend on more than a single variable: - \[ z = f(x,y) \] - for example depends on $x$ and $y$. Using the partial derivative - \[ \frac{\partial f(x,y)}{\partial x} = \lim\limits_{\Delta x \to 0} \frac{f(x + \Delta x,y) - f(x,y)}{\Delta x} \] - and - \[ \frac{\partial f(x,y)}{\partial y} = \lim\limits_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x,y)}{\Delta y} \] - one can estimate the slope in the direction of the variables - individually by using the respective difference quotient - (Box~\ref{differentialquotientbox}). \vspace{1ex} - - \begin{minipage}[t]{0.5\textwidth} - \mbox{}\\[-2ex] - \includegraphics[width=1\textwidth]{gradient} - \end{minipage} - \hfill - \begin{minipage}[t]{0.46\textwidth} - For example, the partial derivatives of - \[ f(x,y) = x^2+y^2 \] are - \[ \frac{\partial f(x,y)}{\partial x} = 2x \; , \quad \frac{\partial f(x,y)}{\partial y} = 2y \; .\] - - The gradient is a vector that is constructed from the partial derivatives: - \[ \nabla f(x,y) = \left( \begin{array}{c} \frac{\partial f(x,y)}{\partial x} \\[1ex] \frac{\partial f(x,y)}{\partial y} \end{array} \right) \] - This vector points into the direction of the strongest ascend of - $f(x,y)$. - \end{minipage} - - \vspace{0.5ex} The figure shows the contour lines of a bi-variate - Gaussian $f(x,y) = \exp(-(x^2+y^2)/2)$ and the gradient (thick - arrows) and the corresponding two partial derivatives (thin arrows) - for three different locations. -\end{ibox} - - \section{Gradient} -Imagine to place a small ball at some point on the error surface -\figref{errorsurfacefig}. Naturally, it would roll down the steepest -slope and eventually stop at the minimum of the error surface (if it had no -inertia). We will use this picture to develop an algorithm to find our -way to the minimum of the objective function. The ball will always -follow the steepest slope. Thus we need to figure out the direction of -the steepest slope at the position of the ball. - -The \entermde{Gradient}{gradient} (Box~\ref{partialderivativebox}) of the -objective function is the vector +Imagine to place a ball at some point on the cost function +\figref{cubiccostfig}. Naturally, it would roll down the slope and +eventually stop at the minimum of the error surface (if it had no +inertia). We will use this analogy to develop an algorithm to find our +way to the minimum of the cost function. The ball always follows the +steepest slope. Thus we need to figure out the direction of the slope +at the position of the ball. + +In our one-dimensional example of a single free parameter the slope is +simply the derivative of the cost function with respect to the +parameter $c$. This derivative is called the +\entermde{Gradient}{gradient} of the cost function: \begin{equation} - \label{gradient} - \nabla f_{cost}(m,b) = \left( \frac{\partial f(m,b)}{\partial m}, - \frac{\partial f(m,b)}{\partial b} \right) + \label{costderivative} + \nabla f_{cost}(c) = \frac{{\rm d} f_{cost}(c)}{{\rm d} c} \end{equation} -that points to the strongest ascend of the objective function. The -gradient is given by partial derivatives -(Box~\ref{partialderivativebox}) of the mean squared error with -respect to the parameters $m$ and $b$ of the straight line. There is -no need to calculate it analytically because it can be estimated from -the partial derivatives using the difference quotient -(Box~\ref{differentialquotientbox}) for small steps $\Delta m$ and -$\Delta b$. For example, the partial derivative with respect to $m$ -can be computed as +There is no need to calculate this derivative analytically, because it +can be approximated numerically by the difference quotient +(Box~\ref{differentialquotientbox}) for small steps $\Delta c$: \begin{equation} - \frac{\partial f_{cost}(m,b)}{\partial m} = \lim\limits_{\Delta m \to - 0} \frac{f_{cost}(m + \Delta m, b) - f_{cost}(m,b)}{\Delta m} -\approx \frac{f_{cost}(m + \Delta m, b) - f_{cost}(m,b)}{\Delta m} \; . + \frac{{\rm d} f_{cost}(c)}{{\rm d} c} = + \lim\limits_{\Delta c \to 0} \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} + \approx \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} \end{equation} -The length of the gradient indicates the steepness of the slope -(\figref{gradientquiverfig}). Since want to go down the hill, we -choose the opposite direction. - - -\begin{figure}[t] - \includegraphics[width=0.75\textwidth]{error_gradient} - \titlecaption{Gradient of the error surface.} {Each arrow points - into the direction of the greatest ascend at different positions - of the error surface shown in \figref{errorsurfacefig}. The - contour lines in the background illustrate the error surface. Warm - colors indicate high errors, colder colors low error values. Each - contour line connects points of equal - error.}\label{gradientquiverfig} -\end{figure} - -\begin{exercise}{meanSquaredGradient.m}{}\label{gradientexercise}% - Implement a function \varcode{meanSquaredGradient()}, that takes the - $x$- and $y$-data and the set of parameters $(m, b)$ of a straight - line as a two-element vector as input arguments. The function should - return the gradient at the position $(m, b)$ as a vector with two - elements. +The derivative is positive for positive slopes. Since want to go down +the hill, we choose the opposite direction. + +\begin{exercise}{meanSquaredGradientCubic.m}{} + Implement a function \varcode{meanSquaredGradientCubic()}, that + takes the $x$- and $y$-data and the parameter $c$ as input + arguments. The function should return the derivative of the mean + squared error $f_{cost}(c)$ with respect to $c$ at the position + $c$. \end{exercise} -\begin{exercise}{errorGradient.m}{} - Extend the script of exercises~\ref{errorsurfaceexercise} to plot - both the error surface and gradients using the - \varcode{meanSquaredGradient()} function from - exercise~\ref{gradientexercise}. Vectors in space can be easily - plotted using the function \code{quiver()}. Use \code{contour()} - instead of \code{surface()} to plot the error surface. +\begin{exercise}{plotcubicgradient.m}{} + Using the \varcode{meanSquaredGradientCubic()} function from the + previous exercise, plot the derivative of the cost function as a + function of $c$. \end{exercise} - \section{Gradient descent} Finally, we are able to implement the optimization itself. By now it should be obvious why it is called the gradient descent method. All @@ -381,6 +326,50 @@ large. \end{exercise} +\begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} + Some functions that depend on more than a single variable: + \[ z = f(x,y) \] + for example depends on $x$ and $y$. Using the partial derivative + \[ \frac{\partial f(x,y)}{\partial x} = \lim\limits_{\Delta x \to 0} \frac{f(x + \Delta x,y) - f(x,y)}{\Delta x} \] + and + \[ \frac{\partial f(x,y)}{\partial y} = \lim\limits_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x,y)}{\Delta y} \] + one can estimate the slope in the direction of the variables + individually by using the respective difference quotient + (Box~\ref{differentialquotientbox}). \vspace{1ex} + + \begin{minipage}[t]{0.5\textwidth} + \mbox{}\\[-2ex] + \includegraphics[width=1\textwidth]{gradient} + \end{minipage} + \hfill + \begin{minipage}[t]{0.46\textwidth} + For example, the partial derivatives of + \[ f(x,y) = x^2+y^2 \] are + \[ \frac{\partial f(x,y)}{\partial x} = 2x \; , \quad \frac{\partial f(x,y)}{\partial y} = 2y \; .\] + + The gradient is a vector that is constructed from the partial derivatives: + \[ \nabla f(x,y) = \left( \begin{array}{c} \frac{\partial f(x,y)}{\partial x} \\[1ex] \frac{\partial f(x,y)}{\partial y} \end{array} \right) \] + This vector points into the direction of the strongest ascend of + $f(x,y)$. + \end{minipage} + + \vspace{0.5ex} The figure shows the contour lines of a bi-variate + Gaussian $f(x,y) = \exp(-(x^2+y^2)/2)$ and the gradient (thick + arrows) and the corresponding two partial derivatives (thin arrows) + for three different locations. +\end{ibox} + +The \entermde{Gradient}{gradient} (Box~\ref{partialderivativebox}) of the +objective function is the vector +\begin{equation} + \label{gradient} + \nabla f_{cost}(m,b) = \left( \frac{\partial f(m,b)}{\partial m}, + \frac{\partial f(m,b)}{\partial b} \right) +\end{equation} +that points to the strongest ascend of the objective function. The +gradient is given by partial derivatives +(Box~\ref{partialderivativebox}) of the mean squared error with +respect to the parameters $m$ and $b$ of the straight line. \section{Summary} The gradient descent is an important numerical method for solving From 4b624fe9815f2d489ec72d9a9c3af0c494b63df4 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 19 Dec 2020 10:13:37 +0100 Subject: [PATCH 32/87] [regression] updated gradient descent seciotn text --- regression/lecture/regression.tex | 38 ++++++++++++++++--------------- 1 file changed, 20 insertions(+), 18 deletions(-) diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 776f745..3f8c045 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -272,24 +272,27 @@ the hill, we choose the opposite direction. Finally, we are able to implement the optimization itself. By now it should be obvious why it is called the gradient descent method. All ingredients are already there. We need: (i) the cost function -(\varcode{meanSquaredError()}), and (ii) the gradient -(\varcode{meanSquaredGradient()}). The algorithm of the gradient +(\varcode{meanSquaredErrorCubic()}), and (ii) the gradient +(\varcode{meanSquaredGradientCubic()}). The algorithm of the gradient descent works as follows: \begin{enumerate} -\item Start with some given combination of the parameters $m$ and $b$ - ($p_0 = (m_0, b_0)$). -\item \label{computegradient} Calculate the gradient at the current - position $p_i$. -\item If the length of the gradient falls below a certain value, we - assume to have reached the minimum and stop the search. We are - actually looking for the point at which the length of the gradient - is zero, but finding zero is impossible because of numerical - imprecision. We thus apply a threshold below which we are - sufficiently close to zero (e.g. \varcode{norm(gradient) < 0.1}). +\item Start with some arbitrary value $p_0$ for the parameter $c$. +\item \label{computegradient} Compute the gradient + \eqnref{costderivative} at the current position $p_i$. +\item If the length of the gradient, the absolute value of the + derivative \eqnref{costderivative}, is smaller than some threshold + value, we assume to have reached the minimum and stop the search. + We return the current parameter value $p_i$ as our best estimate of + the parameter $c$ that minimizes the cost function. + + We are actually looking for the point at which the derivative of the + cost function equals zero, but this is impossible because of + numerical imprecision. We thus apply a threshold below which we are + sufficiently close to zero. \item \label{gradientstep} If the length of the gradient exceeds the threshold we take a small step into the opposite direction: \begin{equation} - p_{i+1} = p_i - \epsilon \cdot \nabla f_{cost}(m_i, b_i) + p_{i+1} = p_i - \epsilon \cdot \nabla f_{cost}(p_i) \end{equation} where $\epsilon = 0.01$ is a factor linking the gradient to appropriate steps in the parameter space. @@ -298,11 +301,10 @@ descent works as follows: \Figref{gradientdescentfig} illustrates the gradient descent --- the path the imaginary ball has chosen to reach the minimum. Starting at -an arbitrary position on the error surface we change the position as -long as the gradient at that position is larger than a certain -threshold. If the slope is very steep, the change in the position (the -distance between the red dots in \figref{gradientdescentfig}) is -large. +an arbitrary position we change the position as long as the gradient +at that position is larger than a certain threshold. If the slope is +very steep, the change in the position (the distance between the red +dots in \figref{gradientdescentfig}) is large. \begin{figure}[t] \includegraphics{cubicmse} From 7518f9dd47483e71a3da605324e79942b5d7af2e Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 19 Dec 2020 12:20:18 +0100 Subject: [PATCH 33/87] [regression] gradient descent code --- regression/code/gradientDescentCubic.m | 25 ++++++++ regression/code/plotgradientdescentcubic.m | 29 +++++++++ regression/lecture/regression.tex | 74 +++++++++++++--------- 3 files changed, 99 insertions(+), 29 deletions(-) create mode 100644 regression/code/gradientDescentCubic.m create mode 100644 regression/code/plotgradientdescentcubic.m diff --git a/regression/code/gradientDescentCubic.m b/regression/code/gradientDescentCubic.m new file mode 100644 index 0000000..a495221 --- /dev/null +++ b/regression/code/gradientDescentCubic.m @@ -0,0 +1,25 @@ +function [c, cs, mses] = gradientDescentCubic(x, y, c0, epsilon, threshold) +% Gradient descent for fitting a cubic relation. +% +% Arguments: x, vector of the x-data values. +% y, vector of the corresponding y-data values. +% c0, initial value for the parameter c. +% epsilon: factor multiplying the gradient. +% threshold: minimum value for gradient +% +% Returns: c, the final value of the c-parameter. +% cs: vector with all the c-values traversed. +% mses: vector with the corresponding mean squared errors + c = c0; + gradient = 1000.0; + cs = []; + mses = []; + count = 1; + while abs(gradient) > threshold + cs(count) = c; + mses(count) = meanSquaredErrorCubic(x, y, c); + gradient = meanSquaredGradientCubic(x, y, c); + c = c - epsilon * gradient; + count = count + 1; + end +end diff --git a/regression/code/plotgradientdescentcubic.m b/regression/code/plotgradientdescentcubic.m new file mode 100644 index 0000000..4972a92 --- /dev/null +++ b/regression/code/plotgradientdescentcubic.m @@ -0,0 +1,29 @@ +meansquarederrorline % generate data + +c0 = 2.0; +eps = 0.0001; +thresh = 0.1; +[cest, cs, mses] = gradientDescentCubic(x, y, c0, eps, thresh); + +subplot(2, 2, 1); % top left panel +hold on; +plot(cs, '-o'); +plot([1, length(cs)], [c, c], 'k'); % line indicating true c value +hold off; +xlabel('Iteration'); +ylabel('C'); +subplot(2, 2, 3); % bottom left panel +plot(mses, '-o'); +xlabel('Iteration steps'); +ylabel('MSE'); +subplot(1, 2, 2); % right panel +hold on; +% generate x-values for plottig the fit: +xx = min(x):0.01:max(x); +yy = cest * xx.^3; +plot(xx, yy, 'displayname', 'fit'); +plot(x, y, 'o', 'displayname', 'data'); % plot original data +xlabel('Size [m]'); +ylabel('Weight [kg]'); +legend("location", "northwest"); +pause diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 3f8c045..6e9c591 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -269,9 +269,21 @@ the hill, we choose the opposite direction. \end{exercise} \section{Gradient descent} + +\begin{figure}[t] + \includegraphics{cubicmse} + \titlecaption{Gradient descent.}{The algorithm starts at an + arbitrary position. At each point the gradient is estimated and + the position is updated as long as the length of the gradient is + sufficiently large.The dots show the positions after each + iteration of the algorithm.} \label{gradientdescentcubicfig} +\end{figure} + Finally, we are able to implement the optimization itself. By now it -should be obvious why it is called the gradient descent method. All -ingredients are already there. We need: (i) the cost function +should be obvious why it is called the gradient descent method. From a +starting position on we iteratively walk down the slope of the cost +function against its gradient. All ingredients necessary for this +algorithm are already there. We need: (i) the cost function (\varcode{meanSquaredErrorCubic()}), and (ii) the gradient (\varcode{meanSquaredGradientCubic()}). The algorithm of the gradient descent works as follows: @@ -292,41 +304,45 @@ descent works as follows: \item \label{gradientstep} If the length of the gradient exceeds the threshold we take a small step into the opposite direction: \begin{equation} + \label{gradientdescent} p_{i+1} = p_i - \epsilon \cdot \nabla f_{cost}(p_i) \end{equation} - where $\epsilon = 0.01$ is a factor linking the gradient to + where $\epsilon$ is a factor linking the gradient to appropriate steps in the parameter space. \item Repeat steps \ref{computegradient} -- \ref{gradientstep}. \end{enumerate} -\Figref{gradientdescentfig} illustrates the gradient descent --- the -path the imaginary ball has chosen to reach the minimum. Starting at -an arbitrary position we change the position as long as the gradient -at that position is larger than a certain threshold. If the slope is -very steep, the change in the position (the distance between the red -dots in \figref{gradientdescentfig}) is large. - -\begin{figure}[t] - \includegraphics{cubicmse} - \titlecaption{Gradient descent.}{The algorithm starts at an - arbitrary position. At each point the gradient is estimated and - the position is updated as long as the length of the gradient is - sufficiently large.The dots show the positions after each - iteration of the algorithm.} \label{gradientdescentfig} -\end{figure} - -\begin{exercise}{gradientDescent.m}{} - Implement the gradient descent for the problem of fitting a straight - line to some measured data. Reuse the data generated in - exercise~\ref{errorsurfaceexercise}. - \begin{enumerate} - \item Store for each iteration the error value. - \item Plot the error values as a function of the iterations, the - number of optimization steps. - \item Plot the measured data together with the best fitting straight line. - \end{enumerate}\vspace{-4.5ex} +\Figref{gradientdescentcubicfig} illustrates the gradient descent --- the +path the imaginary ball has chosen to reach the minimum. We walk along +the parameter axis against the gradient as long as the gradient +differs sufficiently from zero. At steep slopes we take large steps +(the distance between the red dots in \figref{gradientdescentcubicfig}) is +large. + +\begin{exercise}{gradientDescentCubic.m}{} + Implement the gradient descent algorithm for the problem of fitting + a cubic function \eqref{cubicfunc} to some measured data pairs $x$ + and $y$ as a function \varcode{gradientDescentCubic()} that returns + the estimated best fitting parameter value $c$ as well as two + vectors with all the parameter values and the corresponding values + of the cost function that the algorithm iterated trough. As + additional arguments that function takes the initial value for the + parameter $c$, the factor $\epsilon$ connecting the gradient with + iteration steps in \eqnref{gradientdescent}, and the threshold value + for the absolute value of the gradient terminating the algorithm. \end{exercise} +\begin{exercise}{plotgradientdescentcubic.m}{} + Use the function \varcode{gradientDescentCubic()} to fit the + simulated data from exercise~\ref{mseexercise}. Plot the returned + values of the parameter $c$ as as well as the corresponding mean + squared errors as a function of iteration step (two plots). Compare + the result of the gradient descent method with the true value of $c$ + used to simulate the data. Inspect the plots and adapt $\epsilon$ + and the threshold to make the algorithm behave as intended. Also + plot the data together with the best fitting cubic relation + \eqref{cubicfunc}. +\end{exercise} \begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} Some functions that depend on more than a single variable: From 891515caf86e1e6eb319bf0df5f28993ef6b18a9 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 19 Dec 2020 13:41:28 +0100 Subject: [PATCH 34/87] [regression] first part n-dim minimization --- regression/code/plotgradientdescentcubic.m | 9 +- regression/lecture/regression.tex | 96 ++++++++++++++++++++-- 2 files changed, 93 insertions(+), 12 deletions(-) diff --git a/regression/code/plotgradientdescentcubic.m b/regression/code/plotgradientdescentcubic.m index 4972a92..6ac54af 100644 --- a/regression/code/plotgradientdescentcubic.m +++ b/regression/code/plotgradientdescentcubic.m @@ -1,4 +1,4 @@ -meansquarederrorline % generate data +meansquarederrorline; % generate data c0 = 2.0; eps = 0.0001; @@ -21,9 +21,8 @@ hold on; % generate x-values for plottig the fit: xx = min(x):0.01:max(x); yy = cest * xx.^3; -plot(xx, yy, 'displayname', 'fit'); -plot(x, y, 'o', 'displayname', 'data'); % plot original data +plot(xx, yy); +plot(x, y, 'o'); % plot original data xlabel('Size [m]'); ylabel('Weight [kg]'); -legend("location", "northwest"); -pause +legend('fit', 'data', 'location', 'northwest'); diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 6e9c591..472f3c6 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -254,7 +254,7 @@ can be approximated numerically by the difference quotient The derivative is positive for positive slopes. Since want to go down the hill, we choose the opposite direction. -\begin{exercise}{meanSquaredGradientCubic.m}{} +\begin{exercise}{meanSquaredGradientCubic.m}{}\label{gradientcubic} Implement a function \varcode{meanSquaredGradientCubic()}, that takes the $x$- and $y$-data and the parameter $c$ as input arguments. The function should return the derivative of the mean @@ -312,12 +312,12 @@ descent works as follows: \item Repeat steps \ref{computegradient} -- \ref{gradientstep}. \end{enumerate} -\Figref{gradientdescentcubicfig} illustrates the gradient descent --- the -path the imaginary ball has chosen to reach the minimum. We walk along -the parameter axis against the gradient as long as the gradient +\Figref{gradientdescentcubicfig} illustrates the gradient descent --- +the path the imaginary ball has chosen to reach the minimum. We walk +along the parameter axis against the gradient as long as the gradient differs sufficiently from zero. At steep slopes we take large steps -(the distance between the red dots in \figref{gradientdescentcubicfig}) is -large. +(the distance between the red dots in \figref{gradientdescentcubicfig} +is large). \begin{exercise}{gradientDescentCubic.m}{} Implement the gradient descent algorithm for the problem of fitting @@ -339,11 +339,78 @@ large. squared errors as a function of iteration step (two plots). Compare the result of the gradient descent method with the true value of $c$ used to simulate the data. Inspect the plots and adapt $\epsilon$ - and the threshold to make the algorithm behave as intended. Also + and the threshold to make the algorithm behave as intended. Finally plot the data together with the best fitting cubic relation \eqref{cubicfunc}. \end{exercise} +The $\epsilon$ parameter in \eqnref{gradientdescent} is critical. If +too large, the algorithm does not converge to the minimum of the cost +function (try it!). At medium values it oscillates around the minimum +but might nevertheless converge. Only for sufficiently small values +(here $\epsilon = 0.0001$) does the algorithm follow the slope +downwards towards the minimum. + +The terminating condition on the absolute value of the gradient +influences how often the cost function is evaluated. The smaller the +threshold value the more often the cost is computed and the more +precisely the fit parameter is estimated. If it is too small, however, +the increase in precision is negligible, in particular in comparison +to the increased computational effort. Have a look at the derivatives +that we plotted in exercise~\ref{gradientcubic} and decide on a +sensible value for the threshold. Run the gradient descent algorithm +and check how the resulting $c$ parameter values converge and how many +iterations were needed. The reduce the threshold (by factors of ten) +and check how this changes the results. + +Many modern algorithms for finding the minimum of a function are based +on the basic idea of the gradient descent. Luckily these algorithms +choose $\epsilon$ in a smart adaptive way and they also come up with +sensible default values for the termination condition. On the other +hand, these algorithm often take optional arguments that let you +control how they behave. Now you know what this is all about. + +\section{N-dimensional minimization problems} + +So far we were concerned about finding the right value for a single +parameter that minimizes a cost function. The gradient descent method +for such one dimensional problems seems a bit like over kill. However, +often we deal with functions that have more than a single parameter, +in general $n$ parameter. We then need to find the minimum in an $n$ +dimensional parameter space. + +For our tiger problem, we could have also fitted the exponent $\alpha$ +of the power-law relation between size and weight, instead of assuming +a cubic relation: +\begin{equation} + \label{powerfunc} + y = f(x; c, \alpha) = f(x; \vec p) = c\cdot x^\alpha +\end{equation} +We then could check whether the resulting estimate of the exponent +$\alpha$ indeed is close to the expected power of three. The +power-law \eqref{powerfunc} has two free parameters $c$ and $\alpha$. +Instead of a single parameter we are now dealing with a vector $\vec +p$ containing $n$ parameter values. Here, $\vec p = (c, +\alpha)$. Luckily, all the concepts we introduced on the example of +the one dimensional problem of tiger weights generalize to +$n$-dimensional problems. We only need to adapt a few things. The cost +function for the mean squared error reads +\begin{equation} + \label{ndimcostfunc} + f_{cost}(\vec p|\{(x_i, y_i)\}) = \frac{1}{N} \sum_{i=1}^N (y_i - f(x_i;\vec p))^2 +\end{equation} + +For two-dimensional problems the graph of the cost function is an +\enterm{error surface} (\determ{{Fehlerfl\"ache}}). The two parameters +span a two-dimensional plane. The cost function assigns to each +parameter combination on this plane a single value. This results in a +landscape over the parameter plane with mountains and valleys and we +are searching for the bottom of the deepest valley. + +When we place a ball somewhere on the slopes of a hill it rolls +downwards and eventually stops at the bottom. The ball always rolls in +the direction of the steepest slope. + \begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} Some functions that depend on more than a single variable: \[ z = f(x,y) \] @@ -388,6 +455,21 @@ that points to the strongest ascend of the objective function. The gradient is given by partial derivatives (Box~\ref{partialderivativebox}) of the mean squared error with respect to the parameters $m$ and $b$ of the straight line. + + + +For example, you measure the response of a passive membrane to a +current step and you want to estimate membrane time constant. Then you +need to fit an exponential function +\begin{equation} + \label{expfunc} + V(t; \tau, \Delta V, V_{\infty}) = \Delta V e^{-t/\tau} + V_{\infty} +\end{equation} +with three free parameters $\tau$, $\Delta y$, $y_{\infty}$ to the +measured time course of the membrane potential $V(t)$. The $(x_i,y_i)$ +data pairs are the sampling times $t_i$ and the corresponding +measurements of the membrane potential $V_i$. + \section{Summary} The gradient descent is an important numerical method for solving From bfb2f66de2f7fab7cb5ad6ffbef83a1bfd52a1d7 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 19 Dec 2020 21:53:19 +0100 Subject: [PATCH 35/87] [regression] finished n-dim minimization --- designpattern/lecture/designpattern.tex | 8 +- regression/code/gradientDescentPower.m | 41 +++++++ regression/code/plotgradientdescentpower.m | 32 ++++++ regression/lecture/regression.tex | 127 +++++++++++++++------ 4 files changed, 166 insertions(+), 42 deletions(-) create mode 100644 regression/code/gradientDescentPower.m create mode 100644 regression/code/plotgradientdescentpower.m diff --git a/designpattern/lecture/designpattern.tex b/designpattern/lecture/designpattern.tex index 5baada5..05ee5ab 100644 --- a/designpattern/lecture/designpattern.tex +++ b/designpattern/lecture/designpattern.tex @@ -72,13 +72,13 @@ x = [2:3:20]; % Some vector. y = []; % Empty vector for storing the results. for i=1:length(x) % The function get_something() returns a vector of unspecified size: - z = get_somehow_more(x(i)); + z = get_something(x(i)); % The content of z is appended to the result vector y: - y = [y; z(:)]; + y = [y, z(:)]; % The z(:) syntax ensures that we append column-vectors. end -% Process the results stored in the vector z: -mean(y) +% Process the results stored in the vector y: +mean(y, 1) \end{pagelisting} diff --git a/regression/code/gradientDescentPower.m b/regression/code/gradientDescentPower.m new file mode 100644 index 0000000..31390eb --- /dev/null +++ b/regression/code/gradientDescentPower.m @@ -0,0 +1,41 @@ +function [p, ps, mses] = gradientDescentPower(x, y, p0, epsilon, threshold) +% Gradient descent for fitting a power-law. +% +% Arguments: x, vector of the x-data values. +% y, vector of the corresponding y-data values. +% p0, vector with initial values for c and alpha. +% epsilon: factor multiplying the gradient. +% threshold: minimum value for gradient +% +% Returns: p, vector with the final parameter values. +% ps: 2D-vector with all the parameter tuples traversed. +% mses: vector with the corresponding mean squared errors + + p = p0; + gradient = ones(1, length(p0)) * 1000.0; + ps = []; + mses = []; + while norm(gradient) > threshold + ps = [ps, p(:)]; + mses = [mses, meanSquaredErrorPower(x, y, p)]; + gradient = meanSquaredGradientPower(x, y, p); + p = p - epsilon * gradient; + end +end + +function mse = meanSquaredErrorPower(x, y, p) + mse = mean((y - p(1)*x.^p(2)).^2); +end + +function gradmse = meanSquaredGradientPower(x, y, p) + gradmse = zeros(size(p, 1), size(p, 2)); + h = 1e-5; % stepsize for derivatives + mse = meanSquaredErrorPower(x, y, p); + for i = 1:length(p) % for each coordinate ... + pi = p; + pi(i) = pi(i) + h; % displace i-th parameter + msepi = meanSquaredErrorPower(x, y, pi); + gradmse(i) = (msepi - mse)/h; + end +end + diff --git a/regression/code/plotgradientdescentpower.m b/regression/code/plotgradientdescentpower.m new file mode 100644 index 0000000..f52bfe7 --- /dev/null +++ b/regression/code/plotgradientdescentpower.m @@ -0,0 +1,32 @@ +meansquarederrorline; % generate data + +p0 = [2.0, 1.0]; +eps = 0.00001; +thresh = 50.0; +[pest, ps, mses] = gradientDescentPower(x, y, p0, eps, thresh); +pest + +subplot(2, 2, 1); % top left panel +hold on; +plot(ps(1,:), ps(2,:), '.'); +plot(ps(1,end), ps(2,end), 'og'); +plot(c, 3.0, 'or'); % dot indicating true parameter values +hold off; +xlabel('Iteration'); +ylabel('C'); +subplot(2, 2, 3); % bottom left panel +plot(mses, '-o'); +xlabel('Iteration steps'); +ylabel('MSE'); +subplot(1, 2, 2); % right panel +hold on; +% generate x-values for plottig the fit: +xx = min(x):0.01:max(x); +yy = pest(1) * xx.^pest(2); +plot(xx, yy); +plot(x, y, 'o'); % plot original data +xlabel('Size [m]'); +ylabel('Weight [kg]'); +legend('fit', 'data', 'location', 'northwest'); +pause + diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 472f3c6..69e7b05 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -319,7 +319,7 @@ differs sufficiently from zero. At steep slopes we take large steps (the distance between the red dots in \figref{gradientdescentcubicfig} is large). -\begin{exercise}{gradientDescentCubic.m}{} +\begin{exercise}{gradientDescentCubic.m}{}\label{gradientdescentexercise} Implement the gradient descent algorithm for the problem of fitting a cubic function \eqref{cubicfunc} to some measured data pairs $x$ and $y$ as a function \varcode{gradientDescentCubic()} that returns @@ -332,7 +332,7 @@ is large). for the absolute value of the gradient terminating the algorithm. \end{exercise} -\begin{exercise}{plotgradientdescentcubic.m}{} +\begin{exercise}{plotgradientdescentcubic.m}{}\label{plotgradientdescentexercise} Use the function \varcode{gradientDescentCubic()} to fit the simulated data from exercise~\ref{mseexercise}. Plot the returned values of the parameter $c$ as as well as the corresponding mean @@ -373,15 +373,14 @@ control how they behave. Now you know what this is all about. \section{N-dimensional minimization problems} So far we were concerned about finding the right value for a single -parameter that minimizes a cost function. The gradient descent method -for such one dimensional problems seems a bit like over kill. However, -often we deal with functions that have more than a single parameter, -in general $n$ parameter. We then need to find the minimum in an $n$ -dimensional parameter space. +parameter that minimizes a cost function. Often we deal with +functions that have more than a single parameter, in general $n$ +parameters. We then need to find the minimum in an $n$ dimensional +parameter space. For our tiger problem, we could have also fitted the exponent $\alpha$ of the power-law relation between size and weight, instead of assuming -a cubic relation: +a cubic relation with $\alpha=3$: \begin{equation} \label{powerfunc} y = f(x; c, \alpha) = f(x; \vec p) = c\cdot x^\alpha @@ -390,11 +389,11 @@ We then could check whether the resulting estimate of the exponent $\alpha$ indeed is close to the expected power of three. The power-law \eqref{powerfunc} has two free parameters $c$ and $\alpha$. Instead of a single parameter we are now dealing with a vector $\vec -p$ containing $n$ parameter values. Here, $\vec p = (c, -\alpha)$. Luckily, all the concepts we introduced on the example of -the one dimensional problem of tiger weights generalize to -$n$-dimensional problems. We only need to adapt a few things. The cost -function for the mean squared error reads +p$ containing $n$ parameter values. Here, $\vec p = (c, \alpha)$. All +the concepts we introduced on the example of the one dimensional +problem of tiger weights generalize to $n$-dimensional problems. We +only need to adapt a few things. The cost function for the mean +squared error reads \begin{equation} \label{ndimcostfunc} f_{cost}(\vec p|\{(x_i, y_i)\}) = \frac{1}{N} \sum_{i=1}^N (y_i - f(x_i;\vec p))^2 @@ -405,22 +404,18 @@ For two-dimensional problems the graph of the cost function is an span a two-dimensional plane. The cost function assigns to each parameter combination on this plane a single value. This results in a landscape over the parameter plane with mountains and valleys and we -are searching for the bottom of the deepest valley. +are searching for the position of the bottom of the deepest valley. -When we place a ball somewhere on the slopes of a hill it rolls -downwards and eventually stops at the bottom. The ball always rolls in -the direction of the steepest slope. - -\begin{ibox}[tp]{\label{partialderivativebox}Partial derivative and gradient} - Some functions that depend on more than a single variable: +\begin{ibox}[tp]{\label{partialderivativebox}Partial derivatives and gradient} + Some functions depend on more than a single variable. For example, the function \[ z = f(x,y) \] - for example depends on $x$ and $y$. Using the partial derivative + depends on both $x$ and $y$. Using the partial derivatives \[ \frac{\partial f(x,y)}{\partial x} = \lim\limits_{\Delta x \to 0} \frac{f(x + \Delta x,y) - f(x,y)}{\Delta x} \] and \[ \frac{\partial f(x,y)}{\partial y} = \lim\limits_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x,y)}{\Delta y} \] - one can estimate the slope in the direction of the variables - individually by using the respective difference quotient - (Box~\ref{differentialquotientbox}). \vspace{1ex} + one can calculate the slopes in the directions of each of the + variables by means of the respective difference quotient + (see box~\ref{differentialquotientbox}). \vspace{1ex} \begin{minipage}[t]{0.5\textwidth} \mbox{}\\[-2ex] @@ -429,37 +424,93 @@ the direction of the steepest slope. \hfill \begin{minipage}[t]{0.46\textwidth} For example, the partial derivatives of - \[ f(x,y) = x^2+y^2 \] are + \[ f(x,y) = x^2+y^2 \vspace{-1ex} \] are \[ \frac{\partial f(x,y)}{\partial x} = 2x \; , \quad \frac{\partial f(x,y)}{\partial y} = 2y \; .\] - The gradient is a vector that is constructed from the partial derivatives: + The gradient is a vector with the partial derivatives as coordinates: \[ \nabla f(x,y) = \left( \begin{array}{c} \frac{\partial f(x,y)}{\partial x} \\[1ex] \frac{\partial f(x,y)}{\partial y} \end{array} \right) \] This vector points into the direction of the strongest ascend of $f(x,y)$. \end{minipage} - \vspace{0.5ex} The figure shows the contour lines of a bi-variate + \vspace{0.5ex} The figure shows the contour lines of a bivariate Gaussian $f(x,y) = \exp(-(x^2+y^2)/2)$ and the gradient (thick - arrows) and the corresponding two partial derivatives (thin arrows) - for three different locations. + arrows) together with the corresponding partial derivatives (thin + arrows) for three different locations. \end{ibox} -The \entermde{Gradient}{gradient} (Box~\ref{partialderivativebox}) of the -objective function is the vector +When we place a ball somewhere on the slopes of a hill, it rolls +downwards and eventually stops at the bottom. The ball always rolls in +the direction of the steepest slope. For a two-dimensional parameter +space of our example, the \entermde{Gradient}{gradient} +(box~\ref{partialderivativebox}) of the cost function is a vector +\begin{equation} + \label{gradientpowerlaw} + \nabla f_{cost}(c, \alpha) = \left( \frac{\partial f_{cost}(c, \alpha)}{\partial c}, + \frac{\partial f_{cost}(c, \alpha)}{\partial \alpha} \right) +\end{equation} +that points into the direction of the strongest ascend of the cost +function. The gradient is given by the partial derivatives +(box~\ref{partialderivativebox}) of the mean squared error with +respect to the parameters $c$ and $\alpha$ of the power law +relation. In general, for $n$-dimensional problems, the gradient is an +$n-$ dimensional vector containing for each of the $n$ parameters +$p_j$ the respective partial derivatives as coordinates: \begin{equation} \label{gradient} - \nabla f_{cost}(m,b) = \left( \frac{\partial f(m,b)}{\partial m}, - \frac{\partial f(m,b)}{\partial b} \right) + \nabla f_{cost}(\vec p) = \left( \frac{\partial f_{cost}(\vec p)}{\partial p_j} \right) +\end{equation} + +The iterative equation \eqref{gradientdescent} of the gradient descent +stays exactly the same, with the only difference that the current +parameter value $p_i$ becomes a vector $\vec p_i$ of parameter values: +\begin{equation} + \label{ndimgradientdescent} + \vec p_{i+1} = \vec p_i - \epsilon \cdot \nabla f_{cost}(\vec p_i) \end{equation} -that points to the strongest ascend of the objective function. The -gradient is given by partial derivatives -(Box~\ref{partialderivativebox}) of the mean squared error with -respect to the parameters $m$ and $b$ of the straight line. +For the termination condition we need the length of the gradient. In +one dimension it was just the absolute value of the derivative. For +$n$ dimensions this is according to the \enterm{Pythagorean theorem} +(\determ[Pythagoras!Satz des]{Satz des Pythagoras}) the square root of +the sum of the squared partial derivatives: +\begin{equation} + \label{ndimabsgradient} + |\nabla f_{cost}(\vec p_i)| = \sqrt{\sum_{i=1}^n \left(\frac{\partial f_{cost}(\vec p)}{\partial p_i}\right)^2} +\end{equation} +The \code{norm()} function implements this. + +\begin{exercise}{gradientDescentPower.m}{} + Adapt the function \varcode{gradientDescentCubic()} from + exercise~\ref{gradientdescentexercise} to implement the gradient + descent algorithm for the power law \eqref{powerfunc}. The new + function takes a two element vector $(c,\alpha)$ for the initial + parameter values and also returns the best parameter combination as + a two-element vector. Use a \varcode{for} loop over the two + dimensions for computing the gradient. +\end{exercise} + +\begin{exercise}{plotgradientdescentpower.m}{} + Use the function \varcode{gradientDescentPower()} to fit the + simulated data from exercise~\ref{mseexercise}. Plot the returned + values of the two parameters against each other. Compare the result + of the gradient descent method with the true values of $c$ and + $\alpha$ used to simulate the data. Observe the norm of the gradient + and inspect the plots to adapt $\epsilon$ (smaller than in + exercise~\ref{plotgradientdescentexercise}) and the threshold (much + larger) appropriately. Finally plot the data together with the best + fitting power-law \eqref{powerfunc}. +\end{exercise} + +\section{Curve fit for arbitrary functions} +So far, all our code for the gradient descent algorithm was tailored +to a specific function, the cubic relation \eqref{cubicfunc} or the +power law \eqref{powerfunc}. +\section{XXX} For example, you measure the response of a passive membrane to a -current step and you want to estimate membrane time constant. Then you +current step and you want to estimate membrane the time constant. Then you need to fit an exponential function \begin{equation} \label{expfunc} From 46affef86d61bd4ae301979bb46ba326a8e676c2 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 19 Dec 2020 22:56:09 +0100 Subject: [PATCH 36/87] [regression] finished main text and exercises --- regression/code/gradientDescent.m | 66 ++++++---- regression/code/gradientDescentPower.m | 41 ------ regression/code/plotgradientdescentpower.m | 4 +- regression/lecture/regression-chapter.tex | 74 ----------- regression/lecture/regression.tex | 141 +++++++++++++-------- 5 files changed, 128 insertions(+), 198 deletions(-) delete mode 100644 regression/code/gradientDescentPower.m diff --git a/regression/code/gradientDescent.m b/regression/code/gradientDescent.m index 1919035..48b976c 100644 --- a/regression/code/gradientDescent.m +++ b/regression/code/gradientDescent.m @@ -1,32 +1,42 @@ -% x, y from exercise 8.3 +function [p, ps, mses] = gradientDescent(x, y, func, p0, epsilon, threshold) +% Gradient descent for fitting a function to data pairs. +% +% Arguments: x, vector of the x-data values. +% y, vector of the corresponding y-data values. +% func, function handle func(x, p) +% p0, vector with initial parameter values +% epsilon: factor multiplying the gradient. +% threshold: minimum value for gradient +% +% Returns: p, vector with the final parameter values. +% ps: 2D-vector with all the parameter vectors traversed. +% mses: vector with the corresponding mean squared errors -% some arbitrary values for the slope and the intercept to start with: -position = [-2.0, 10.0]; + p = p0; + gradient = ones(1, length(p0)) * 1000.0; + ps = []; + mses = []; + while norm(gradient) > threshold + ps = [ps, p(:)]; + mses = [mses, meanSquaredError(x, y, func, p)]; + gradient = meanSquaredGradient(x, y, func, p); + p = p - epsilon * gradient; + end +end + +function mse = meanSquaredError(x, y, func, p) + mse = mean((y - func(x, p)).^2); +end -% gradient descent: -gradient = []; -errors = []; -count = 1; -eps = 0.0001; -while isempty(gradient) || norm(gradient) > 0.1 - gradient = meanSquaredGradient(x, y, position); - errors(count) = meanSquaredError(x, y, position); - position = position - eps .* gradient; - count = count + 1; +function gradmse = meanSquaredGradient(x, y, func, p) + gradmse = zeros(size(p, 1), size(p, 2)); + h = 1e-5; % stepsize for derivatives + mse = meanSquaredError(x, y, func, p); + for i = 1:length(p) % for each coordinate ... + pi = p; + pi(i) = pi(i) + h; % displace i-th parameter + msepi = meanSquaredError(x, y, func, pi); + gradmse(i) = (msepi - mse)/h; + end end -figure() -subplot(2,1,1) -hold on -scatter(x, y, 'displayname', 'data') -xx = min(x):0.01:max(x); -yy = position(1).*xx + position(2); -plot(xx, yy, 'displayname', 'fit') -xlabel('Input') -ylabel('Output') -grid on -legend show -subplot(2,1,2) -plot(errors) -xlabel('optimization steps') -ylabel('error') diff --git a/regression/code/gradientDescentPower.m b/regression/code/gradientDescentPower.m deleted file mode 100644 index 31390eb..0000000 --- a/regression/code/gradientDescentPower.m +++ /dev/null @@ -1,41 +0,0 @@ -function [p, ps, mses] = gradientDescentPower(x, y, p0, epsilon, threshold) -% Gradient descent for fitting a power-law. -% -% Arguments: x, vector of the x-data values. -% y, vector of the corresponding y-data values. -% p0, vector with initial values for c and alpha. -% epsilon: factor multiplying the gradient. -% threshold: minimum value for gradient -% -% Returns: p, vector with the final parameter values. -% ps: 2D-vector with all the parameter tuples traversed. -% mses: vector with the corresponding mean squared errors - - p = p0; - gradient = ones(1, length(p0)) * 1000.0; - ps = []; - mses = []; - while norm(gradient) > threshold - ps = [ps, p(:)]; - mses = [mses, meanSquaredErrorPower(x, y, p)]; - gradient = meanSquaredGradientPower(x, y, p); - p = p - epsilon * gradient; - end -end - -function mse = meanSquaredErrorPower(x, y, p) - mse = mean((y - p(1)*x.^p(2)).^2); -end - -function gradmse = meanSquaredGradientPower(x, y, p) - gradmse = zeros(size(p, 1), size(p, 2)); - h = 1e-5; % stepsize for derivatives - mse = meanSquaredErrorPower(x, y, p); - for i = 1:length(p) % for each coordinate ... - pi = p; - pi(i) = pi(i) + h; % displace i-th parameter - msepi = meanSquaredErrorPower(x, y, pi); - gradmse(i) = (msepi - mse)/h; - end -end - diff --git a/regression/code/plotgradientdescentpower.m b/regression/code/plotgradientdescentpower.m index f52bfe7..206e2bb 100644 --- a/regression/code/plotgradientdescentpower.m +++ b/regression/code/plotgradientdescentpower.m @@ -3,7 +3,7 @@ meansquarederrorline; % generate data p0 = [2.0, 1.0]; eps = 0.00001; thresh = 50.0; -[pest, ps, mses] = gradientDescentPower(x, y, p0, eps, thresh); +[pest, ps, mses] = gradientDescent(x, y, @powerLaw, p0, eps, thresh); pest subplot(2, 2, 1); % top left panel @@ -22,7 +22,7 @@ subplot(1, 2, 2); % right panel hold on; % generate x-values for plottig the fit: xx = min(x):0.01:max(x); -yy = pest(1) * xx.^pest(2); +yy = powerLaw(xx, pest); plot(xx, yy); plot(x, y, 'o'); % plot original data xlabel('Size [m]'); diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 3983848..2ca1ec2 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -23,80 +23,6 @@ \item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom! \end{itemize} -\subsection{Start with one-dimensional problem!} -\begin{itemize} -\item How to plot a function (do not use the data x values!) -\item 1-d gradient descend -\item Describe in words the n-d problem (boltzman as example?). -\item Homework is to do the 2d problem with the straight line! -\item NO quiver plot (it is a nightmare to get this right) -\end{itemize} - -\subsection{2D fit} - -\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise} - Generate 20 data pairs $(x_i|y_i)$ that are linearly related with - slope $m=0.75$ and intercept $b=-40$, using \varcode{rand()} for - drawing $x$ values between 0 and 120 and \varcode{randn()} for - jittering the $y$ values with a standard deviation of 15. Then - calculate the mean squared error between the data and straight lines - for a range of slopes and intercepts using the - \varcode{meanSquaredError()} function from the previous exercise. - Illustrates the error surface using the \code{surface()} function. - Consult the documentation to find out how to use \code{surface()}. -\end{exercise} - -\begin{exercise}{meanSquaredGradient.m}{}\label{gradientexercise}% - Implement a function \varcode{meanSquaredGradient()}, that takes the - $x$- and $y$-data and the set of parameters $(m, b)$ of a straight - line as a two-element vector as input arguments. The function should - return the gradient at the position $(m, b)$ as a vector with two - elements. -\end{exercise} - -\begin{exercise}{errorGradient.m}{} - Extend the script of exercises~\ref{errorsurfaceexercise} to plot - both the error surface and gradients using the - \varcode{meanSquaredGradient()} function from - exercise~\ref{gradientexercise}. Vectors in space can be easily - plotted using the function \code{quiver()}. Use \code{contour()} - instead of \code{surface()} to plot the error surface. -\end{exercise} - - -\begin{exercise}{gradientDescent.m}{} - Implement the gradient descent for the problem of fitting a straight - line to some measured data. Reuse the data generated in - exercise~\ref{errorsurfaceexercise}. - \begin{enumerate} - \item Store for each iteration the error value. - \item Plot the error values as a function of the iterations, the - number of optimization steps. - \item Plot the measured data together with the best fitting straight line. - \end{enumerate}\vspace{-4.5ex} -\end{exercise} - - -\begin{figure}[t] - \includegraphics[width=1\textwidth]{lin_regress}\hfill - \titlecaption{Example data suggesting a linear relation.}{A set of - input signals $x$, e.g. stimulus intensities, were used to probe a - system. The system's output $y$ to the inputs are noted - (left). Assuming a linear relation between $x$ and $y$ leaves us - with 2 parameters, the slope (center) and the intercept with the - y-axis (right panel).}\label{linregressiondatafig} -\end{figure} - -\begin{figure}[t] - \includegraphics[width=1\textwidth]{linear_least_squares} - \titlecaption{Estimating the \emph{mean square error}.} {The - deviation error (orange) between the prediction (red line) and the - observations (blue dots) is calculated for each data point - (left). Then the deviations are squared and the average is - calculated (right).} - \label{leastsquareerrorfig} -\end{figure} - \begin{figure}[t] \includegraphics[width=0.75\textwidth]{error_surface} \titlecaption{Error surface.}{The two model parameters $m$ and $b$ diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 69e7b05..36e1808 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -479,49 +479,73 @@ the sum of the squared partial derivatives: \end{equation} The \code{norm()} function implements this. -\begin{exercise}{gradientDescentPower.m}{} + +\section{Passing a function as an argument to another function} + +So far, all our code for the gradient descent algorithm was tailored +to a specific function, the cubic relation \eqref{cubicfunc}. It would +be much better if we could pass an arbitrary function to our gradient +algorithm. Then we would not need to rewrite it every time anew. + +This is possible. We can indeed pass a function as an argument to +another function. For this use the \code{@}-operator. As an example +let's define a function that produces a standard plot for a function: + +\pageinputlisting[caption={Example function taking a function as argument.}]{funcPlotter.m} + +This function can then be used as follows for plotting a sine wave. We +pass the built in \varcode{sin()} function as \varcode{@sin} as an +argument to our function: + +\pageinputlisting[caption={Passing a function handle as an argument to a function.}]{funcplotterexamples.m} + + +\section{Gradient descent algorithm for arbitrary functions} + +Now we are ready to adapt the gradient descent algorithm from +exercise~\ref{gradientdescentexercise} to arbitrary functions with $n$ +parameters that we want to fit to some data. + +\begin{exercise}{gradientDescent.m}{} Adapt the function \varcode{gradientDescentCubic()} from exercise~\ref{gradientdescentexercise} to implement the gradient - descent algorithm for the power law \eqref{powerfunc}. The new - function takes a two element vector $(c,\alpha)$ for the initial - parameter values and also returns the best parameter combination as - a two-element vector. Use a \varcode{for} loop over the two - dimensions for computing the gradient. + descent algorithm for any function \varcode{func(x, p)} that takes + as first argument the $x$-data values and as second argument a + vector with parameter values. The new function takes a vector $\vec + p_0$ for the initial parameter values and also returns the best + parameter combination as a vector. Use a \varcode{for} loop over the + two dimensions for computing the gradient. \end{exercise} +For testing our new function we need to implement the power law +\eqref{powerfunc}: + +\begin{exercise}{powerLaw.m}{} + Write a function that implements \eqref{powerfunc}. The function + gets as arguments a vector $x$ containing the $x$-data values and + another vector containing as elements the parameters for the power + law, i.e. the factor $c$ and the power $\alpha$. It returns a vector + with the computed $y$ values for each $x$ value. +\end{exercise} + +Now let's use the new gradient descent function to fit a power law to +our tiger data-set: + \begin{exercise}{plotgradientdescentpower.m}{} - Use the function \varcode{gradientDescentPower()} to fit the - simulated data from exercise~\ref{mseexercise}. Plot the returned - values of the two parameters against each other. Compare the result - of the gradient descent method with the true values of $c$ and - $\alpha$ used to simulate the data. Observe the norm of the gradient - and inspect the plots to adapt $\epsilon$ (smaller than in + Use the function \varcode{gradientDescent()} to fit the + \varcode{powerLaw()} function to the simulated data from + exercise~\ref{mseexercise}. Plot the returned values of the two + parameters against each other. Compare the result of the gradient + descent method with the true values of $c$ and $\alpha$ used to + simulate the data. Observe the norm of the gradient and inspect the + plots to adapt $\epsilon$ (smaller than in exercise~\ref{plotgradientdescentexercise}) and the threshold (much larger) appropriately. Finally plot the data together with the best fitting power-law \eqref{powerfunc}. \end{exercise} -\section{Curve fit for arbitrary functions} - -So far, all our code for the gradient descent algorithm was tailored -to a specific function, the cubic relation \eqref{cubicfunc} or the -power law \eqref{powerfunc}. - -\section{XXX} -For example, you measure the response of a passive membrane to a -current step and you want to estimate membrane the time constant. Then you -need to fit an exponential function -\begin{equation} - \label{expfunc} - V(t; \tau, \Delta V, V_{\infty}) = \Delta V e^{-t/\tau} + V_{\infty} -\end{equation} -with three free parameters $\tau$, $\Delta y$, $y_{\infty}$ to the -measured time course of the membrane potential $V(t)$. The $(x_i,y_i)$ -data pairs are the sampling times $t_i$ and the corresponding -measurements of the membrane potential $V_i$. - -\section{Summary} +\section{Fitting non-linear functions to data} The gradient descent is an important numerical method for solving optimization problems. It is used to find the global minimum of an @@ -530,33 +554,44 @@ objective function. Curve fitting is a common application for the gradient descent method. For the case of fitting straight lines to data pairs, the error surface (using the mean squared error) has exactly one clearly defined -global minimum. In fact, the position of the minimum can be analytically -calculated as shown in the next chapter. - -Problems that involve nonlinear computations on parameters, e.g. the -rate $\lambda$ in an exponential function $f(x;\lambda) = e^{\lambda - x}$, do not have an analytical solution for the least squares. To -find the least squares for such functions numerical methods such as -the gradient descent have to be applied. - -The suggested gradient descent algorithm can be improved in multiple -ways to converge faster. For example one could adapt the step size to -the length of the gradient. These numerical tricks have already been -implemented in pre-defined functions. Generic optimization functions -such as \matlabfun{fminsearch()} have been implemented for arbitrary -objective functions, while the more specialized function -\matlabfun{lsqcurvefit()} i specifically designed for optimizations in -the least square error sense. - -%\newpage +global minimum. In fact, the position of the minimum can be +analytically calculated as shown in the next chapter. For linear +fitting problems numerical methods like the gradient descent are not +needed. + +Fitting problems that involve nonlinear functions of the parameters, +e.g. the power law \eqref{powerfunc} or the exponential function +$f(x;\lambda) = e^{\lambda x}$, do not have an analytical solution for +the least squares. To find the least squares for such functions +numerical methods such as the gradient descent have to be applied. + +The suggested gradient descent algorithm is quite fragile and requires +manually tuned values for $\epsilon$ and the threshold for terminating +the iteration. The algorithm can be improved in multiple ways to +converge more robustly and faster. For example one could adapt the +step size to the length of the gradient. These numerical tricks have +already been implemented in pre-defined functions. Generic +optimization functions such as \mcode{fminsearch()} have been +implemented for arbitrary objective functions, while the more +specialized function \mcode{lsqcurvefit()} is specifically designed +for optimizations in the least square error sense. + +\begin{exercise}{plotlsqcurvefitpower.m}{} + Use the \matlab-function \varcode{lsqcurvefit()} instead of + \varcode{gradientDescent()} to fit the \varcode{powerLaw()} function + to the simulated data from exercise~\ref{mseexercise}. Plot the data + and the resulting best fitting power law function. +\end{exercise} + + \begin{important}[Beware of secondary minima!] Finding the absolute minimum is not always as easy as in the case of - fitting a straight line. Often, the error surface has secondary or + fitting a straight line. Often, the cost function has secondary or local minima in which the gradient descent stops even though there is a more optimal solution, a global minimum that is lower than the local minimum. Starting from good initial positions is a good approach to avoid getting stuck in local minima. Also keep in mind - that error surfaces tend to be simpler (less local minima) the fewer + that cost functions tend to be simpler (less local minima) the fewer parameters are fitted from the data. Each additional parameter increases complexity and is computationally more expensive. \end{important} From dea6319e7553d9b9f6b150938c825e5a69db1dc8 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 20 Dec 2020 01:05:02 +0100 Subject: [PATCH 37/87] [regression] finished chapter --- regression/code/meanSquaredErrorCubic.m | 4 +- regression/lecture/cubiccost.py | 2 +- regression/lecture/cubicerrors.py | 4 +- regression/lecture/cubicfunc.py | 4 +- regression/lecture/cubicmse.py | 2 +- regression/lecture/error_surface.py | 56 ---------------- regression/lecture/lin_regress.py | 60 ----------------- regression/lecture/linear_least_squares.py | 65 ------------------ regression/lecture/regression-chapter.tex | 35 ---------- regression/lecture/regression.tex | 76 +++++++++++++++------- 10 files changed, 61 insertions(+), 247 deletions(-) delete mode 100644 regression/lecture/error_surface.py delete mode 100644 regression/lecture/lin_regress.py delete mode 100644 regression/lecture/linear_least_squares.py diff --git a/regression/code/meanSquaredErrorCubic.m b/regression/code/meanSquaredErrorCubic.m index 44870a1..8953d50 100644 --- a/regression/code/meanSquaredErrorCubic.m +++ b/regression/code/meanSquaredErrorCubic.m @@ -1,8 +1,8 @@ function mse = meanSquaredErrorCubic(x, y, c) % Mean squared error between data pairs and a cubic relation. % -% Arguments: x, vector of the input values -% y, vector of the corresponding measured output values +% Arguments: x, vector of the x-data values +% y, vector of the corresponding y-data values % c, the factor for the cubic relation. % % Returns: mse, the mean-squared-error. diff --git a/regression/lecture/cubiccost.py b/regression/lecture/cubiccost.py index 30d9575..ac145fa 100644 --- a/regression/lecture/cubiccost.py +++ b/regression/lecture/cubiccost.py @@ -75,7 +75,7 @@ def plot_mse_min(ax, x, y, c): if __name__ == "__main__": x, y, c = create_data() fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) - fig.subplots_adjust(**adjust_fs(left=8.0, right=1)) + fig.subplots_adjust(**adjust_fs(left=8.0, right=1.2)) plot_mse(ax1, x, y, c) plot_mse_min(ax2, x, y, c) fig.savefig("cubiccost.pdf") diff --git a/regression/lecture/cubicerrors.py b/regression/lecture/cubicerrors.py index 86e608f..d74c3bf 100644 --- a/regression/lecture/cubicerrors.py +++ b/regression/lecture/cubicerrors.py @@ -58,8 +58,8 @@ def plot_error_hist(ax, x, y, c): if __name__ == "__main__": x, y, c = create_data() - fig, (ax1, ax2) = plt.subplots(1, 2) - fig.subplots_adjust(wspace=0.4, **adjust_fs(left=6.0, right=1.2)) + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.9*figure_height)) + fig.subplots_adjust(wspace=0.5, **adjust_fs(left=6.0, right=1.2)) plot_data_errors(ax1, x, y, c) plot_error_hist(ax2, x, y, c) fig.savefig("cubicerrors.pdf") diff --git a/regression/lecture/cubicfunc.py b/regression/lecture/cubicfunc.py index 8b5b44a..3b34c03 100644 --- a/regression/lecture/cubicfunc.py +++ b/regression/lecture/cubicfunc.py @@ -42,8 +42,8 @@ def plot_data_fac(ax, x, y, c): if __name__ == "__main__": x, y, c = create_data() print('n=%d' % len(x)) - fig, (ax1, ax2) = plt.subplots(1, 2) - fig.subplots_adjust(wspace=0.5, **adjust_fs(fig, left=6.0, right=1.5)) + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.9*figure_height)) + fig.subplots_adjust(wspace=0.5, **adjust_fs(fig, left=6.0, right=1.2)) plot_data(ax1, x, y) plot_data_fac(ax2, x, y, c) fig.savefig("cubicfunc.pdf") diff --git a/regression/lecture/cubicmse.py b/regression/lecture/cubicmse.py index 55ac64b..0d956c5 100644 --- a/regression/lecture/cubicmse.py +++ b/regression/lecture/cubicmse.py @@ -73,7 +73,7 @@ if __name__ == "__main__": x, y, c = create_data() cs, mses = gradient_descent(x, y) fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) - fig.subplots_adjust(wspace=0.2, **adjust_fs(left=8.0, right=0.5)) + fig.subplots_adjust(**adjust_fs(left=8.0, right=1.2)) plot_mse(ax1, x, y, c, cs) plot_descent(ax2, cs, mses) fig.savefig("cubicmse.pdf") diff --git a/regression/lecture/error_surface.py b/regression/lecture/error_surface.py deleted file mode 100644 index da0d867..0000000 --- a/regression/lecture/error_surface.py +++ /dev/null @@ -1,56 +0,0 @@ -import numpy as np -from mpl_toolkits.mplot3d import Axes3D -import matplotlib.pyplot as plt -import matplotlib.cm as cm -from plotstyle import * - -def create_data(): - m = 0.75 - n= -40 - x = np.arange(10.,110., 2.5) - y = m * x + n; - rng = np.random.RandomState(37281) - noise = rng.randn(len(x))*15 - y += noise - return x, y, m, n - - -def plot_error_plane(ax, x, y, m, n): - ax.set_xlabel('Slope m') - ax.set_ylabel('Intercept b') - ax.set_zlabel('Mean squared error') - ax.set_xlim(-4.5, 5.0) - ax.set_ylim(-60.0, -20.0) - ax.set_zlim(0.0, 700.0) - ax.set_xticks(np.arange(-4, 5, 2)) - ax.set_yticks(np.arange(-60, -19, 10)) - ax.set_zticks(np.arange(0, 700, 200)) - ax.grid(True) - ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 1.0)) - ax.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 1.0)) - ax.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 1.0)) - ax.invert_xaxis() - ax.view_init(25, 40) - slopes = np.linspace(-4.5, 5, 40) - intercepts = np.linspace(-60, -20, 40) - x, y = np.meshgrid(slopes, intercepts) - error_surf = np.zeros(x.shape) - for i, s in enumerate(slopes) : - for j, b in enumerate(intercepts) : - error_surf[j,i] = np.mean((y-s*x-b)**2.0) - ax.plot_surface(x, y, error_surf, rstride=1, cstride=1, cmap=cm.coolwarm, - linewidth=0, shade=True) - # Minimum: - mini = np.unravel_index(np.argmin(error_surf), error_surf.shape) - ax.scatter(slopes[mini[1]], intercepts[mini[0]], [0.0], color='#cc0000', s=60) - - -if __name__ == "__main__": - x, y, m, n = create_data() - fig = plt.figure() - ax = fig.add_subplot(1, 1, 1, projection='3d') - plot_error_plane(ax, x, y, m, n) - fig.set_size_inches(7., 5.) - fig.subplots_adjust(**adjust_fs(fig, 1.0, 0.0, 0.0, 0.0)) - fig.savefig("error_surface.pdf") - plt.close() diff --git a/regression/lecture/lin_regress.py b/regression/lecture/lin_regress.py deleted file mode 100644 index ae854d5..0000000 --- a/regression/lecture/lin_regress.py +++ /dev/null @@ -1,60 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from plotstyle import * - -def create_data(): - m = 0.75 - n= -40 - x = np.arange(10.,110., 2.5) - y = m * x + n; - rng = np.random.RandomState(37281) - noise = rng.randn(len(x))*15 - y += noise - return x, y, m, n - - -def plot_data(ax, x, y): - ax.plot(x, y, **psA) - ax.set_xlabel('Input x') - ax.set_ylabel('Output y') - ax.set_xlim(0, 120) - ax.set_ylim(-80, 80) - ax.set_xticks(np.arange(0,121, 40)) - ax.set_yticks(np.arange(-80,81, 40)) - - -def plot_data_slopes(ax, x, y, m, n): - ax.plot(x, y, **psA) - xx = np.asarray([2, 118]) - for i in np.linspace(0.3*m, 2.0*m, 5): - ax.plot(xx, i*xx+n, **lsBm) - ax.set_xlabel('Input x') - #ax.set_ylabel('Output y') - ax.set_xlim(0, 120) - ax.set_ylim(-80, 80) - ax.set_xticks(np.arange(0,121, 40)) - ax.set_yticks(np.arange(-80,81, 40)) - - -def plot_data_intercepts(ax, x, y, m, n): - ax.plot(x, y, **psA) - xx = np.asarray([2, 118]) - for i in np.linspace(n-1*n, n+1*n, 5): - ax.plot(xx, m*xx + i, **lsBm) - ax.set_xlabel('Input x') - #ax.set_ylabel('Output y') - ax.set_xlim(0, 120) - ax.set_ylim(-80, 80) - ax.set_xticks(np.arange(0,121, 40)) - ax.set_yticks(np.arange(-80,81, 40)) - - -if __name__ == "__main__": - x, y, m, n = create_data() - fig, axs = plt.subplots(1, 3) - fig.subplots_adjust(wspace=0.5, **adjust_fs(fig, left=6.0, right=1.5)) - plot_data(axs[0], x, y) - plot_data_slopes(axs[1], x, y, m, n) - plot_data_intercepts(axs[2], x, y, m, n) - fig.savefig("lin_regress.pdf") - plt.close() diff --git a/regression/lecture/linear_least_squares.py b/regression/lecture/linear_least_squares.py deleted file mode 100644 index d36fd32..0000000 --- a/regression/lecture/linear_least_squares.py +++ /dev/null @@ -1,65 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from plotstyle import * - -def create_data(): - m = 0.75 - n= -40 - x = np.concatenate( (np.arange(10.,110., 2.5), np.arange(0.,120., 2.0)) ) - y = m * x + n; - rng = np.random.RandomState(37281) - noise = rng.randn(len(x))*15 - y += noise - return x, y, m, n - - -def plot_data(ax, x, y, m, n): - ax.set_xlabel('Input x') - ax.set_ylabel('Output y') - ax.set_xlim(0, 120) - ax.set_ylim(-80, 80) - ax.set_xticks(np.arange(0,121, 40)) - ax.set_yticks(np.arange(-80,81, 40)) - ax.annotate('Error', - xy=(x[34]+1, y[34]+15), xycoords='data', - xytext=(80, -50), textcoords='data', ha='left', - arrowprops=dict(arrowstyle="->", relpos=(0.9,1.0), - connectionstyle="angle3,angleA=50,angleB=-30") ) - ax.plot(x[:40], y[:40], zorder=0, **psAm) - inxs = [3, 13, 16, 19, 25, 34, 36] - ax.plot(x[inxs], y[inxs], zorder=10, **psA) - xx = np.asarray([2, 118]) - ax.plot(xx, m*xx+n, **lsBm) - for i in inxs : - xx = [x[i], x[i]] - yy = [m*x[i]+n, y[i]] - ax.plot(xx, yy, zorder=5, **lsDm) - - -def plot_error_hist(ax, x, y, m, n): - ax.set_xlabel('Squared error') - ax.set_ylabel('Frequency') - bins = np.arange(0.0, 602.0, 50.0) - ax.set_xlim(bins[0], bins[-1]) - ax.set_ylim(0, 35) - ax.set_xticks(np.arange(bins[0], bins[-1], 100)) - ax.set_yticks(np.arange(0, 36, 10)) - errors = (y-(m*x+n))**2.0 - mls = np.mean(errors) - ax.annotate('Mean\nsquared\nerror', - xy=(mls, 0.5), xycoords='data', - xytext=(350, 20), textcoords='data', ha='left', - arrowprops=dict(arrowstyle="->", relpos=(0.0,0.2), - connectionstyle="angle3,angleA=10,angleB=90") ) - ax.hist(errors, bins, **fsD) - - - -if __name__ == "__main__": - x, y, m, n = create_data() - fig, axs = plt.subplots(1, 2) - fig.subplots_adjust(**adjust_fs(fig, left=6.0)) - plot_data(axs[0], x, y, m, n) - plot_error_hist(axs[1], x, y, m, n) - fig.savefig("linear_least_squares.pdf") - plt.close() diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 2ca1ec2..45fdfda 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -23,47 +23,12 @@ \item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom! \end{itemize} -\begin{figure}[t] - \includegraphics[width=0.75\textwidth]{error_surface} - \titlecaption{Error surface.}{The two model parameters $m$ and $b$ - define the base area of the surface plot. For each parameter - combination of slope and intercept the error is calculated. The - resulting surface has a minimum which indicates the parameter - combination that best fits the data.}\label{errorsurfacefig} -\end{figure} - - -\begin{figure}[t] - \includegraphics[width=0.75\textwidth]{error_gradient} - \titlecaption{Gradient of the error surface.} {Each arrow points - into the direction of the greatest ascend at different positions - of the error surface shown in \figref{errorsurfacefig}. The - contour lines in the background illustrate the error surface. Warm - colors indicate high errors, colder colors low error values. Each - contour line connects points of equal - error.}\label{gradientquiverfig} -\end{figure} - -\begin{figure}[t] - \includegraphics[width=0.45\textwidth]{gradient_descent} - \titlecaption{Gradient descent.}{The algorithm starts at an - arbitrary position. At each point the gradient is estimated and - the position is updated as long as the length of the gradient is - sufficiently large.The dots show the positions after each - iteration of the algorithm.} \label{gradientdescentfig} -\end{figure} - - \subsection{Linear fits} \begin{itemize} \item Polyfit is easy: unique solution! $c x^2$ is also a linear fit. \item Example for overfitting with polyfit of a high order (=number of data points) \end{itemize} -\section{Fitting in practice} - -Fit with matlab functions lsqcurvefit, polyfit - \subsection{Non-linear fits} \begin{itemize} diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 36e1808..2db6a31 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -227,6 +227,7 @@ to arbitrary precision. \end{ibox} \section{Gradient} + Imagine to place a ball at some point on the cost function \figref{cubiccostfig}. Naturally, it would roll down the slope and eventually stop at the minimum of the error surface (if it had no @@ -235,10 +236,21 @@ way to the minimum of the cost function. The ball always follows the steepest slope. Thus we need to figure out the direction of the slope at the position of the ball. +\begin{figure}[t] + \includegraphics{cubicgradient} + \titlecaption{Derivative of the cost function.}{The gradient, the + derivative \eqref{costderivative} of the cost function, is + negative to the left of the minimum of the cost function, zero at, + and positive to the right of the minimum (left). For each value of + the parameter $c$ the negative gradient (arrows) points towards + the minimum of the cost function + (right).} \label{gradientcubicfig} +\end{figure} + In our one-dimensional example of a single free parameter the slope is simply the derivative of the cost function with respect to the -parameter $c$. This derivative is called the -\entermde{Gradient}{gradient} of the cost function: +parameter $c$ (\figref{gradientcubicfig}, left). This derivative is called +the \entermde{Gradient}{gradient} of the cost function: \begin{equation} \label{costderivative} \nabla f_{cost}(c) = \frac{{\rm d} f_{cost}(c)}{{\rm d} c} @@ -252,7 +264,8 @@ can be approximated numerically by the difference quotient \approx \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} \end{equation} The derivative is positive for positive slopes. Since want to go down -the hill, we choose the opposite direction. +the hill, we choose the opposite direction (\figref{gradientcubicfig}, +right). \begin{exercise}{meanSquaredGradientCubic.m}{}\label{gradientcubic} Implement a function \varcode{meanSquaredGradientCubic()}, that @@ -275,7 +288,7 @@ the hill, we choose the opposite direction. \titlecaption{Gradient descent.}{The algorithm starts at an arbitrary position. At each point the gradient is estimated and the position is updated as long as the length of the gradient is - sufficiently large.The dots show the positions after each + sufficiently large. The dots show the positions after each iteration of the algorithm.} \label{gradientdescentcubicfig} \end{figure} @@ -378,18 +391,18 @@ functions that have more than a single parameter, in general $n$ parameters. We then need to find the minimum in an $n$ dimensional parameter space. -For our tiger problem, we could have also fitted the exponent $\alpha$ -of the power-law relation between size and weight, instead of assuming -a cubic relation with $\alpha=3$: +For our tiger problem, we could have also fitted the exponent $a$ of +the power-law relation between size and weight, instead of assuming a +cubic relation with $a=3$: \begin{equation} \label{powerfunc} - y = f(x; c, \alpha) = f(x; \vec p) = c\cdot x^\alpha + y = f(x; c, a) = f(x; \vec p) = c\cdot x^a \end{equation} We then could check whether the resulting estimate of the exponent -$\alpha$ indeed is close to the expected power of three. The -power-law \eqref{powerfunc} has two free parameters $c$ and $\alpha$. +$a$ indeed is close to the expected power of three. The +power-law \eqref{powerfunc} has two free parameters $c$ and $a$. Instead of a single parameter we are now dealing with a vector $\vec -p$ containing $n$ parameter values. Here, $\vec p = (c, \alpha)$. All +p$ containing $n$ parameter values. Here, $\vec p = (c, a)$. All the concepts we introduced on the example of the one dimensional problem of tiger weights generalize to $n$-dimensional problems. We only need to adapt a few things. The cost function for the mean @@ -399,12 +412,27 @@ squared error reads f_{cost}(\vec p|\{(x_i, y_i)\}) = \frac{1}{N} \sum_{i=1}^N (y_i - f(x_i;\vec p))^2 \end{equation} +\begin{figure}[t] + \includegraphics{powergradientdescent} + \titlecaption{Gradient descent on an error surface.}{Contour plot of + the cost function \eqref{ndimcostfunc} for the fit of a power law + \eqref{powerfunc} to some data. Here the cost function is a long + and narrow valley on the plane spanned by the two parameters $c$ + and $a$ of the power law. The red line marks the path of the + gradient descent algorithm. The gradient is always perpendicular + to the contour lines. The algorithm quickly descends into the + valley and then slowly creeps on the shallow bottom of the valley + towards the global minimum where it terminates (yellow circle). + } \label{powergradientdescentfig} +\end{figure} + For two-dimensional problems the graph of the cost function is an \enterm{error surface} (\determ{{Fehlerfl\"ache}}). The two parameters span a two-dimensional plane. The cost function assigns to each parameter combination on this plane a single value. This results in a landscape over the parameter plane with mountains and valleys and we -are searching for the position of the bottom of the deepest valley. +are searching for the position of the bottom of the deepest valley +(\figref{powergradientdescentfig}). \begin{ibox}[tp]{\label{partialderivativebox}Partial derivatives and gradient} Some functions depend on more than a single variable. For example, the function @@ -446,13 +474,13 @@ space of our example, the \entermde{Gradient}{gradient} (box~\ref{partialderivativebox}) of the cost function is a vector \begin{equation} \label{gradientpowerlaw} - \nabla f_{cost}(c, \alpha) = \left( \frac{\partial f_{cost}(c, \alpha)}{\partial c}, - \frac{\partial f_{cost}(c, \alpha)}{\partial \alpha} \right) + \nabla f_{cost}(c, a) = \left( \frac{\partial f_{cost}(c, a)}{\partial c}, + \frac{\partial f_{cost}(c, a)}{\partial a} \right) \end{equation} that points into the direction of the strongest ascend of the cost function. The gradient is given by the partial derivatives (box~\ref{partialderivativebox}) of the mean squared error with -respect to the parameters $c$ and $\alpha$ of the power law +respect to the parameters $c$ and $a$ of the power law relation. In general, for $n$-dimensional problems, the gradient is an $n-$ dimensional vector containing for each of the $n$ parameters $p_j$ the respective partial derivatives as coordinates: @@ -468,6 +496,9 @@ parameter value $p_i$ becomes a vector $\vec p_i$ of parameter values: \label{ndimgradientdescent} \vec p_{i+1} = \vec p_i - \epsilon \cdot \nabla f_{cost}(\vec p_i) \end{equation} +The algorithm proceeds along the negative gradient +(\figref{powergradientdescentfig}). + For the termination condition we need the length of the gradient. In one dimension it was just the absolute value of the derivative. For $n$ dimensions this is according to the \enterm{Pythagorean theorem} @@ -479,8 +510,7 @@ the sum of the squared partial derivatives: \end{equation} The \code{norm()} function implements this. - -\section{Passing a function as an argument to another function} +\subsection{Passing a function as an argument to another function} So far, all our code for the gradient descent algorithm was tailored to a specific function, the cubic relation \eqref{cubicfunc}. It would @@ -500,7 +530,7 @@ argument to our function: \pageinputlisting[caption={Passing a function handle as an argument to a function.}]{funcplotterexamples.m} -\section{Gradient descent algorithm for arbitrary functions} +\subsection{Gradient descent algorithm for arbitrary functions} Now we are ready to adapt the gradient descent algorithm from exercise~\ref{gradientdescentexercise} to arbitrary functions with $n$ @@ -524,21 +554,21 @@ For testing our new function we need to implement the power law Write a function that implements \eqref{powerfunc}. The function gets as arguments a vector $x$ containing the $x$-data values and another vector containing as elements the parameters for the power - law, i.e. the factor $c$ and the power $\alpha$. It returns a vector + law, i.e. the factor $c$ and the power $a$. It returns a vector with the computed $y$ values for each $x$ value. \end{exercise} Now let's use the new gradient descent function to fit a power law to -our tiger data-set: +our tiger data-set (\figref{powergradientdescentfig}): \begin{exercise}{plotgradientdescentpower.m}{} Use the function \varcode{gradientDescent()} to fit the \varcode{powerLaw()} function to the simulated data from exercise~\ref{mseexercise}. Plot the returned values of the two parameters against each other. Compare the result of the gradient - descent method with the true values of $c$ and $\alpha$ used to - simulate the data. Observe the norm of the gradient and inspect the - plots to adapt $\epsilon$ (smaller than in + descent method with the true values of $c$ and $a$ used to simulate + the data. Observe the norm of the gradient and inspect the plots to + adapt $\epsilon$ (smaller than in exercise~\ref{plotgradientdescentexercise}) and the threshold (much larger) appropriately. Finally plot the data together with the best fitting power-law \eqref{powerfunc}. From 17bf940101e651cb235be5baa513d09f75723067 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 20 Dec 2020 13:15:40 +0100 Subject: [PATCH 38/87] [regression] smaller steps for derivative --- regression/code/gradientDescent.m | 2 +- regression/code/meanSquaredGradientCubic.m | 2 +- regression/code/plotcubicgradient.m | 2 ++ regression/code/plotgradientdescentcubic.m | 4 +-- regression/code/plotgradientdescentpower.m | 4 +-- regression/lecture/regression.tex | 29 +++++++++++----------- 6 files changed, 21 insertions(+), 22 deletions(-) diff --git a/regression/code/gradientDescent.m b/regression/code/gradientDescent.m index 48b976c..20e0b90 100644 --- a/regression/code/gradientDescent.m +++ b/regression/code/gradientDescent.m @@ -30,7 +30,7 @@ end function gradmse = meanSquaredGradient(x, y, func, p) gradmse = zeros(size(p, 1), size(p, 2)); - h = 1e-5; % stepsize for derivatives + h = 1e-7; % stepsize for derivatives mse = meanSquaredError(x, y, func, p); for i = 1:length(p) % for each coordinate ... pi = p; diff --git a/regression/code/meanSquaredGradientCubic.m b/regression/code/meanSquaredGradientCubic.m index a7ff6a2..99d5b3b 100644 --- a/regression/code/meanSquaredGradientCubic.m +++ b/regression/code/meanSquaredGradientCubic.m @@ -7,7 +7,7 @@ function dmsedc = meanSquaredGradientCubic(x, y, c) % % Returns: the derivative of the mean squared error at c. - h = 1e-5; % stepsize for derivatives + h = 1e-7; % stepsize for derivatives mse = meanSquaredErrorCubic(x, y, c); mseh = meanSquaredErrorCubic(x, y, c+h); dmsedc = (mseh - mse)/h; diff --git a/regression/code/plotcubicgradient.m b/regression/code/plotcubicgradient.m index 0410b1f..d00bf6e 100644 --- a/regression/code/plotcubicgradient.m +++ b/regression/code/plotcubicgradient.m @@ -1,3 +1,5 @@ +meansquarederrorline; % generate data + cs = 2.0:0.1:8.0; mseg = zeros(length(cs)); for i = 1:length(cs) diff --git a/regression/code/plotgradientdescentcubic.m b/regression/code/plotgradientdescentcubic.m index 6ac54af..6aadc12 100644 --- a/regression/code/plotgradientdescentcubic.m +++ b/regression/code/plotgradientdescentcubic.m @@ -1,8 +1,8 @@ meansquarederrorline; % generate data c0 = 2.0; -eps = 0.0001; -thresh = 0.1; +eps = 0.00001; +thresh = 1.0; [cest, cs, mses] = gradientDescentCubic(x, y, c0, eps, thresh); subplot(2, 2, 1); % top left panel diff --git a/regression/code/plotgradientdescentpower.m b/regression/code/plotgradientdescentpower.m index 206e2bb..2d2a08f 100644 --- a/regression/code/plotgradientdescentpower.m +++ b/regression/code/plotgradientdescentpower.m @@ -2,7 +2,7 @@ meansquarederrorline; % generate data p0 = [2.0, 1.0]; eps = 0.00001; -thresh = 50.0; +thresh = 1.0; [pest, ps, mses] = gradientDescent(x, y, @powerLaw, p0, eps, thresh); pest @@ -28,5 +28,3 @@ plot(x, y, 'o'); % plot original data xlabel('Size [m]'); ylabel('Weight [kg]'); legend('fit', 'data', 'location', 'northwest'); -pause - diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 2db6a31..bfff7bb 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -240,11 +240,11 @@ at the position of the ball. \includegraphics{cubicgradient} \titlecaption{Derivative of the cost function.}{The gradient, the derivative \eqref{costderivative} of the cost function, is - negative to the left of the minimum of the cost function, zero at, - and positive to the right of the minimum (left). For each value of - the parameter $c$ the negative gradient (arrows) points towards - the minimum of the cost function - (right).} \label{gradientcubicfig} + negative to the left of the minimum (vertical line) of the cost + function, zero (horizontal line) at, and positive to the right of + the minimum (left). For each value of the parameter $c$ the + negative gradient (arrows) points towards the minimum of the cost + function (right).} \label{gradientcubicfig} \end{figure} In our one-dimensional example of a single free parameter the slope is @@ -263,9 +263,9 @@ can be approximated numerically by the difference quotient \lim\limits_{\Delta c \to 0} \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} \approx \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} \end{equation} -The derivative is positive for positive slopes. Since want to go down -the hill, we choose the opposite direction (\figref{gradientcubicfig}, -right). +Choose, for example, $\Delta c = 10^{-7}$. The derivative is positive +for positive slopes. Since want to go down the hill, we choose the +opposite direction (\figref{gradientcubicfig}, right). \begin{exercise}{meanSquaredGradientCubic.m}{}\label{gradientcubic} Implement a function \varcode{meanSquaredGradientCubic()}, that @@ -361,7 +361,7 @@ The $\epsilon$ parameter in \eqnref{gradientdescent} is critical. If too large, the algorithm does not converge to the minimum of the cost function (try it!). At medium values it oscillates around the minimum but might nevertheless converge. Only for sufficiently small values -(here $\epsilon = 0.0001$) does the algorithm follow the slope +(here $\epsilon = 0.00001$) does the algorithm follow the slope downwards towards the minimum. The terminating condition on the absolute value of the gradient @@ -373,7 +373,7 @@ to the increased computational effort. Have a look at the derivatives that we plotted in exercise~\ref{gradientcubic} and decide on a sensible value for the threshold. Run the gradient descent algorithm and check how the resulting $c$ parameter values converge and how many -iterations were needed. The reduce the threshold (by factors of ten) +iterations were needed. Then reduce the threshold (by factors of ten) and check how this changes the results. Many modern algorithms for finding the minimum of a function are based @@ -508,7 +508,8 @@ the sum of the squared partial derivatives: \label{ndimabsgradient} |\nabla f_{cost}(\vec p_i)| = \sqrt{\sum_{i=1}^n \left(\frac{\partial f_{cost}(\vec p)}{\partial p_i}\right)^2} \end{equation} -The \code{norm()} function implements this. +The \code{norm()} function implements this given a vector with the +partial derivatives. \subsection{Passing a function as an argument to another function} @@ -568,10 +569,8 @@ our tiger data-set (\figref{powergradientdescentfig}): parameters against each other. Compare the result of the gradient descent method with the true values of $c$ and $a$ used to simulate the data. Observe the norm of the gradient and inspect the plots to - adapt $\epsilon$ (smaller than in - exercise~\ref{plotgradientdescentexercise}) and the threshold (much - larger) appropriately. Finally plot the data together with the best - fitting power-law \eqref{powerfunc}. + adapt $\epsilon$ and the threshold if necessary. Finally plot the + data together with the best fitting power-law \eqref{powerfunc}. \end{exercise} From cd90a132a6b2f885239c66ffba09a4a44ae60b94 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 13:39:11 +0100 Subject: [PATCH 39/87] [programming] update exercises --- .../exercises/boolean_logical_indexing.tex | 8 +++---- programming/exercises/control_flow.tex | 14 +++++------ programming/exercises/scripts_functions.tex | 23 ++++++++++--------- 3 files changed, 23 insertions(+), 22 deletions(-) diff --git a/programming/exercises/boolean_logical_indexing.tex b/programming/exercises/boolean_logical_indexing.tex index f166f3d..762b2b6 100644 --- a/programming/exercises/boolean_logical_indexing.tex +++ b/programming/exercises/boolean_logical_indexing.tex @@ -1,4 +1,4 @@ -\documentclass[12pt,a4paper,pdftex, answers]{exam} +\documentclass[12pt, a4paper, pdftex]{exam} \usepackage[german]{babel} \usepackage{natbib} @@ -14,7 +14,7 @@ %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} \pagestyle{headandfoot} \header{{\bfseries\large Exercise 4 - }}{{\bfseries\large Boolean expressions and logical indexing}}{{\bfseries\large 29. Oktober, 2019}} + }}{{\bfseries\large Boolean expressions \& logical indexing}}{{\bfseries\large 17. November, 2020}} \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} @@ -40,8 +40,8 @@ lecture. You should try to solve them on your own. Your solution should be submitted as a single script (m-file) in the Ilias system. Each task should be solved in its own ``cell''. Each cell must be executable on its own. The file should be named according to the -following pattern: ``variables\_datatypes\_\{lastname\}.m'' -(e.g. variables\_datentypes\_mueller.m). +following pattern: ``boolean\_logical\_indexing\_\{lastname\}.m'' +(e.g. boolean\_logical\_indexing\_mueller.m). \section{Boolean expressions} diff --git a/programming/exercises/control_flow.tex b/programming/exercises/control_flow.tex index 2dd88fd..96e352a 100644 --- a/programming/exercises/control_flow.tex +++ b/programming/exercises/control_flow.tex @@ -1,4 +1,4 @@ -\documentclass[12pt,a4paper,pdftex, answers]{exam} +\documentclass[12pt,a4paper,pdftex]{exam} \usepackage[german]{babel} \usepackage{natbib} @@ -14,7 +14,7 @@ %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} \pagestyle{headandfoot} -\header{{\bfseries\large Exercise 5}}{{\bfseries\large Control Flow}}{{\bfseries\large 05. November, 2019}} +\header{{\bfseries\large Exercise 5}}{{\bfseries\large Control Flow}}{{\bfseries\large 24. November, 2020}} \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} @@ -41,13 +41,13 @@ lecture. You should try to solve them on your own. Your solution should be submitted as a single script (m-file) in the Ilias system. Each task should be solved in its own ``cell''. Each cell must be executable on its own. The file should be named according to the -following pattern: ``variables\_datatypes\_\{lastname\}.m'' -(e.g. variables\_datentypes\_mueller.m). +following pattern: ``control\_flow\_\{lastname\}.m'' +(e.g. control\_flow\_mueller.m). \begin{questions} - \question Implement \code{for} loops in which the \emph{running variable}: + \question Implement \code{for} loops in which the \emph{running variable}: \begin{parts} - \part ... assumes values from 0 to 10. Print (\code{disp}) the value of the running variable for each iteration step. + \part ... assumes values from 0 to 10. Display (\code{disp}) the value of the running variable for each iteration of the loop. \begin{solution} for i = 1:10 disp(i); end; \end{solution} @@ -252,7 +252,7 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m'' \part Create a variable \verb+filename = '2015-10-12_100Hz_1.25V.dat'+. Obviously, the underscore was used as a delimiter. - \part Use a \verb+for+ loop to find the positions of the underscores and store these in a vector. + \part Use a \verb+for+ loop to find the positions of the underscores and store these positions in a vector. \begin{solution} \begin{verbatim} positions = []; diff --git a/programming/exercises/scripts_functions.tex b/programming/exercises/scripts_functions.tex index 2b3282a..f53f881 100644 --- a/programming/exercises/scripts_functions.tex +++ b/programming/exercises/scripts_functions.tex @@ -16,9 +16,9 @@ %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} \pagestyle{headandfoot} -\header{{\bfseries\large Exercise 6}}{{\bfseries\large Scripts and functions}}{{\bfseries\large 06. November, 2018}} -\firstpagefooter{Prof. Jan Benda}{Phone: 29 74 573}{Email: - jan.benda@uni-tuebingen.de} +\header{{\bfseries\large Exercise 6}}{{\bfseries\large Scripts and functions}}{{\bfseries\large 01. December, 2020}} +\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74 588}{Email: + jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} \setlength{\baselineskip}{15pt} @@ -71,7 +71,7 @@ to the pattern: ``scripts\_functions\_\{surname\}.zip''. \begin{parts} \part{} Version 1: Write a script that calculates the factorial of 5 and - prints out the result. + displays the result on the command line. \begin{solution} \lstinputlisting{factorialscripta.m} \end{solution} @@ -86,8 +86,8 @@ to the pattern: ``scripts\_functions\_\{surname\}.zip''. \part{} Version 3: like version 2, but the calculated result should not be - printed on the command line but returned by the function. Write a - script that calls the function and prints out the result. + displayed on the command line but returned by the function. Write a + script that calls the function, accepts the returned value and then displays the result. \begin{solution} \lstinputlisting{myfactorial.m} \lstinputlisting{factorialscriptc.m} @@ -116,7 +116,7 @@ to the pattern: ``scripts\_functions\_\{surname\}.zip''. \part{} Write a script that calls the function and controls the - plotting. Change the function in a way that it returns a proper + plotting. Change the function in a way that it returns time-axis and the calculated sinwave. \begin{solution} \lstinputlisting{sinewave.m} @@ -148,10 +148,11 @@ to the pattern: ``scripts\_functions\_\{surname\}.zip''. \begin{parts} \part{} - Read the exercise completely before starting the implementation - and then come up with a proper program layout of scripts and - functions. What would be a suitable function to solve the task? Which - arguments should it take? Which results should it return? + Read the exercise instructions completely before you start + implementing a solution. Analyze the requirements and then come up with a + program layout of scripts and functions. What would be a + suitable function to solve the core task? Which arguments should it + take? Which results should it return? \begin{solution} One function that computes one realisation of a random walk. Scripts for plotting and analysis. From beab805065e8c91ac9db86eb505395f2e0492205 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 13:39:30 +0100 Subject: [PATCH 40/87] [programming] code fixes --- programming/exercises/plotsinewave.m | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/programming/exercises/plotsinewave.m b/programming/exercises/plotsinewave.m index f2960da..25667a3 100644 --- a/programming/exercises/plotsinewave.m +++ b/programming/exercises/plotsinewave.m @@ -2,12 +2,12 @@ function plotsinewave(time, sine) % plot precomputed sinewave % time: vector with timepoints % sine: corresponding vector with sinewave -if time(end)-time(1) <= 1.0 - plot(1000.0*time, sine); +if time(end) - time(1) <= 1.0 + plot(1000.0 * time, sine); xlabel('Time [ms]'); else plot(time, sine); xlabel('Time [s]'); end -ylim([1.2*min(sine) 1.2*max(sine)]); +ylim([1.2 * min(sine) 1.2 * max(sine)]); ylabel('Sinewave'); From fe7707063613401c47be405024b044a5e8503ae1 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 13:41:49 +0100 Subject: [PATCH 41/87] [progamming] fixes to colon operator box --- programming/lecture/programming.tex | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/programming/lecture/programming.tex b/programming/lecture/programming.tex index e05e381..44c025e 100644 --- a/programming/lecture/programming.tex +++ b/programming/lecture/programming.tex @@ -362,8 +362,8 @@ number of elements irrespective of the type of vector. Listings~\ref{vectorelementslisting} and~\ref{vectorrangelisting} show how the index is used to access elements of a vector. One can access individual values by providing a single index or use the -\code[Operator!Matrix!:]{:} notation to access multiple values with a -single command. +\code[Operator!Matrix!:]{:} operator to access multiple values with a +single command (see also the info box below \ref{important:colon_operator}). \begin{lstlisting}[label=vectorelementslisting, caption={Access to individual elements of a vector.}] >> a = (11:20) @@ -403,13 +403,14 @@ ans = \end{exercise} \begin{important}[The : (colon) operator] + \label{important:colon_operator} The colon \code[Operator!colon@:]{:} operator is often used when working with vectors. It has multiple purposes. \begin{enumerate} \item In the simplest form, \code{x = a:b} with \code{a} and \code{b} being two numbers, it creates a vector \code{x} containing the numbers \code{a} to \code{b} in integer steps. In \matlab{} the borders $a$ and $b$ are included $[a, b]$ or $a\leq x \leq b$. - \item In the form \code{x = a:c:b} the vector \code{x} uses a \emph{stepsize} of \code{c} to create the range of numbers. + \item In the form \code{x = a:c:b} the vector \code{x} uses a \emph{stepsize} of \code{c} to create the range of numbers ranging from $a$ to $b$ in steps of $c$. \item When used in the context of indexing such as \code{x(:)} all elements of the vector x are accessed. - \item As vectors are often used for indexing in other vectors one use the colon operator to create such vectors implicitely, e.g. \varcode{x(1:2:end)} to access every seond element of \code{x}. + \item Vectors are often used for indexing in other vectors. To do so the colon operator is used to create such vectors implicitely, e.g. \varcode{x(1:2:end)} to access every second element of \code{x}. \end{enumerate} \end{important} From 591c9982280c59e408a08136d8073be103be213b Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 13:43:21 +0100 Subject: [PATCH 42/87] [programming] add box on string type --- programming/lecture/programming.tex | 51 +++++++++++++++++++++++++++-- 1 file changed, 48 insertions(+), 3 deletions(-) diff --git a/programming/lecture/programming.tex b/programming/lecture/programming.tex index 44c025e..e123739 100644 --- a/programming/lecture/programming.tex +++ b/programming/lecture/programming.tex @@ -176,11 +176,12 @@ As mentioned above, the data type associated with a variable defines how the sto part. \item \enterm{logical}: Boolean values that can be evaluated to \code{true} or \code{false}. -\item \enterm{character}: ASCII characters. +\item \enterm{character}: Unicode characters. +\item \enterm{string}: Strings of unicode characters, i.e. text. \end{itemize} There is a variety of numeric data types that require different amounts of memory and have different ranges of values that can be -represented (table~\ref{dtypestab}). +represented (table~\ref{dtypestab}). There are also more advanced data types which will not be used in this chapter but see box~\ref{box:advanced_dtypes} and box about strings \ref{box:strings}. \begin{table}[t] \centering @@ -1156,7 +1157,7 @@ segment of data of a certain time span (the stimulus was on, \end{itemize} \end{exercise} -\begin{ibox}[ht]{\label{advancedtypesbox}Advanced data types} +\begin{ibox}[!ht]{\label{advancedtypesbox}Advanced data types} Thoughout this script and the exercises we will limit ourselves to the basic data types introduced above (int, double, char, scalars, vectors, matrices and strings). There are, however, \matlab{}- @@ -1212,6 +1213,50 @@ ans = \end{ibox} +\begin{ibox}[!ht]{\label{box:string_dtype}The \enterm[string]{string} data type} + With release 2017a \matlab{} introduced the string data type which offers more convenience for handling text. A string scalar is created using double quotes: \varcode{s = "Hello world!";}. + The string object \varcode{s} now offers several methods to work on the stored information. Some of the most commonly used methods are listed below. Refer to the documentation for complete descriptions. + \begin{enumerate} + \item \varcode{append} -- appends another string to the string and returns the new string. As with the other functions the original is not affected.\vspace{-0.5em} + \item \varcode{contains} -- searches the string for the occurence of a another string, which is passed as an argument. Returns a logical that is true if the pattern was found.\vspace{-0.5em} + \item \varcode{split} -- splits the string into substrings. By default a blank is used as delimiter. You can pass any other string as an argument to spilt the string at each occurence of the passed pattern. Returns a vector of substrings.\vspace{-0.5em} + \item \varcode{join} -- The opposite of spilt. \varcode{join} takes a vector of strings and concatenates them to a single string. By default a blank is used as delimiter.\vspace{-0.5em} + \item \varcode{lower} -- returns a version of the string in which all characters are lower case. This is particularly useful when one compares user input or string arguments in a function in an case insensitive way.\vspace{-0.5em} + \item \varcode{upper} -- as above but all characters are converted to upper case. + \end{enumerate} + \paragraph{Example:} + A dataset is recorded on a specific recording date using an experimental subject and applying certain stimulus conditions. The recorded data should be stored in a file that contains this information separated by undersores. + + \begin{lstlisting}[basicstyle=\ttfamily\scriptsize, caption={Using \varcode{join} to combine strings.}, label=usingjoin] +date = "2020-12-24"; +subject = "subjectA"; +condition = "control"; +file_extension = ".dat"; + +filename = join([date, subject, condition], "_"); +filename = filename.append(file_extension) + +disp(filename) + +ans = + "2020-12-24_subjectA_control.dat" + \end{lstlisting} + + When reading the dataset during the analysis, we may want to extract the stimulus condtion or the subject name. + + \begin{lstlisting}[basicstyle=\ttfamily\scriptsize, caption={Using \varcode{split} to cut a string at a delimiter.}, label=usingsplit] +disp(filename) +ans = + "2020-12-24_subjectA_control.dat" + +filename = filename.erase(".dat"); % remove file extension +string_parts = filename.split("_"); % split at the underscore +% string_parts is a vector of the substrings +date = string_parts(1); +subject = string_parts(2); +condition = string_parts(3); + \end{lstlisting} +\end{ibox} \section{Control flow}\label{controlstructsec} Generally, a program is executed line by line from top to From e0178658b031118ce61dc482abe00c7201280cac Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 13:44:25 +0100 Subject: [PATCH 43/87] [programming] add box on sprintf --- programming/lecture/programming-chapter.tex | 2 +- programming/lecture/programming.tex | 34 +++++++++++++++++++-- 2 files changed, 33 insertions(+), 3 deletions(-) diff --git a/programming/lecture/programming-chapter.tex b/programming/lecture/programming-chapter.tex index 2a76f64..941c688 100644 --- a/programming/lecture/programming-chapter.tex +++ b/programming/lecture/programming-chapter.tex @@ -19,7 +19,7 @@ \section{TODO} \begin{itemize} \item Ausgabeformat: \varcode{format} ? -\item Expliziter die \varcode{(a:b:c)} Notation einf\"uhren! +\item Expliziter die \varcode{(a:b:c)} Notation einf\"uhren! Done! \item Mathematische Funktionen sin(), cos(), exp() \item Rundungsfunktionen round(), floor(), ceil() \item Zeitvektoren, deltat, Umrechnung Zeit und Index. diff --git a/programming/lecture/programming.tex b/programming/lecture/programming.tex index e123739..6681f61 100644 --- a/programming/lecture/programming.tex +++ b/programming/lecture/programming.tex @@ -1749,6 +1749,36 @@ function plotFunction(x_data, y_data, name) end \end{lstlisting} +\begin{ibox}[!ht]{\label{box:sprintf}\enterm[Format strings]{Formatted strings} with \mcode{sprintf}.} + We can use \varcode{disp} to dispaly the content of a variable on the command line. But how can we embed variable contents nicely into a text and store it in a variable or show it on the command line? \varcode{sprintf} is the standard function to achieve this. We introduce only a fraction of its real might here. For a more complete description visit the \matlab{} help or e.g. \url{https://en.wikipedia.org/wiki/Printf_format_string}. + + Consider the following code: + \begin{lstlisting}[commentstyle=\color{black}, basicstyle=\ttfamily\scriptsize, caption={Using sprintf.}] +n = 100; +numbers = randn(n, 1); + +sprintf("Drawing %i random numbers yields an average of %.3f and a standard deviation of %.3f.", n, mean(numbers), std(numbers)) + +ans = + "Drawing 100 random numbers yields an average of -0.121 and a standard deviation of 0.921." + + \end{lstlisting} + \varcode{sprintf} takes a variable number of arguments. The first one is the string that contains placehoders for the variable content. Here we used three placehoders (two different types, \varcode{\%i, \%.2f}). Accordingly, \varcode{sprintf} expects three additional arguments (\varcode{n, mean(numbers), std(numbers)}). These are the content we want to show in the text. The function will try to convert the variable content and format is according to the placehoder type: + + \footnotesize + \begin{tabular}{l||p{4cm}|p{7.5cm}} + type & purpose & example \\ \hline \hline + \%i & integer values & \varcode{sprintf("I drew \%i numbers", 100)}\\ \hline + \%s & string values & \varcode{name = "John Doe";} \varcode{sprintf("My name is \%s", name)}\\ \hline + \%f & double values, accepts width and precision arguments & \varcode{sprintf("Number pi is \%.2f", pi)}\\ \hline + \%g & double values, uses exponential style when appropriate& \varcode{sprintf("Large int \%g", 1000000)} + \end{tabular} + \normalsize + + Simplified, the placehoder has the form \varcode{\%[width][.precision]type}. Square brackets indicates optional parameters. \varcode{width} controls the total number of characters used for the content. \varcode{.precision} controls how many of the total characters may de devoted to the positions after the decimal point. The example above (\varcode{\%.2f}) limits the output of the $\pi$ to 2 positions after the decimal point. + + Many programming languages offer versions of \varcode{sprintf} that work essentially in the same way. +\end{ibox} \paragraph{III. One script to rule them all} @@ -1774,7 +1804,7 @@ Again, we need to specify what needs to be done: The implementation is shown in listing~\ref{sinesskriptlisting}. -\begin{lstlisting}[caption={Control script for the plotting of sine waves.},label=sinesskriptlisting] +\begin{lstlisting}[caption={Control script for the plotting of sine waves. Note the use of \varcode{sprintf} in the function call in line 11. This function creates a so called formatted string based on the passed string which contains placeholders for variables. For some more details see~\ref{box:sprintf}.},label=sinesskriptlisting] amplitudes = 0.25:0.25:1.25; frequency = 2.0; duration = 10.0; % seconds @@ -1785,7 +1815,7 @@ hold on for i = 1:length(amplitudes) [x_data, y_data] = sinewave(frequency, amplitudes(i), ... duration, stepsize); - plotFunction(x_data, y_data, sprintf('freq: %5.2f, ampl: %5.2f',... + plotFunction(x_data, y_data, sprintf("freq: %5.2f, ampl: %5.2f",... frequency, amplitudes(i))) end hold off From ecc37f8f679fe450fdb0b642bdc5e2c4deea5087 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 14:04:08 +0100 Subject: [PATCH 44/87] [progamming] fix --- programming/lecture/programming.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/programming/lecture/programming.tex b/programming/lecture/programming.tex index 47e9873..0c63aba 100644 --- a/programming/lecture/programming.tex +++ b/programming/lecture/programming.tex @@ -1813,7 +1813,7 @@ for i = 1:length(amplitudes) end hold off legend('show') -\end{pagelisting} +\end{lstlisting} \pagebreak[4] \begin{exercise}{plotMultipleSinewaves.m}{} @@ -1861,4 +1861,4 @@ legend('show') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\printsolutions +% \printsolutions From 46bd94e05d52ef80572a5a35ea398b404072f04a Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Sun, 20 Dec 2020 14:11:11 +0100 Subject: [PATCH 45/87] more ignores, real fix of pagelisting --- .gitignore | 2 +- programming/lecture/programming.tex | 6 +++--- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/.gitignore b/.gitignore index 2c353b4..94ae568 100644 --- a/.gitignore +++ b/.gitignore @@ -26,4 +26,4 @@ *.vrb __* pointprocesses/lecture/pointprocessscetch*.tex - +*.DS_Store diff --git a/programming/lecture/programming.tex b/programming/lecture/programming.tex index 0c63aba..b75cc0d 100644 --- a/programming/lecture/programming.tex +++ b/programming/lecture/programming.tex @@ -1797,7 +1797,7 @@ Again, we need to specify what needs to be done: The implementation is shown in listing~\ref{sinesskriptlisting}. -\begin{lstlisting}[caption={Control script for the plotting of sine waves. Note the use of \varcode{sprintf} in the function call in line 11. This function creates a so called formatted string based on the passed string which contains placeholders for variables. For some more details see~\ref{box:sprintf}.},label=sinesskriptlisting] +\begin{pagelisting}[caption={Control script for the plotting of sine waves. Note the use of \varcode{sprintf} in the function call in line 11. This function creates a so called formatted string based on the passed string which contains placeholders for variables. For some more details see~\ref{box:sprintf}.},label=sinesskriptlisting] amplitudes = 0.25:0.25:1.25; frequency = 2.0; duration = 10.0; % seconds @@ -1813,7 +1813,7 @@ for i = 1:length(amplitudes) end hold off legend('show') -\end{lstlisting} +\end{pagelisting} \pagebreak[4] \begin{exercise}{plotMultipleSinewaves.m}{} @@ -1861,4 +1861,4 @@ legend('show') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% \printsolutions +\printsolutions From c2e4d4e40cf24bc697f05989fe996070a544bd41 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 20 Dec 2020 21:24:46 +0100 Subject: [PATCH 46/87] [regression] note on evolution --- regression/lecture/regression-chapter.tex | 23 ++--- regression/lecture/regression.tex | 103 +++++++++++++++++----- 2 files changed, 94 insertions(+), 32 deletions(-) diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 45fdfda..8798b2a 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -23,20 +23,23 @@ \item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom! \end{itemize} -\subsection{Linear fits} +\subsection{New chapter: non-linear fits} \begin{itemize} -\item Polyfit is easy: unique solution! $c x^2$ is also a linear fit. -\item Example for overfitting with polyfit of a high order (=number of data points) -\end{itemize} - - -\subsection{Non-linear fits} -\begin{itemize} -\item Example that illustrates the Nebenminima Problem (with error surface) +\item Move 8.7 to this new chapter. +\item Example that illustrates the Nebenminima Problem (with error + surface). Maybe data generate from $1/x$ and fitted with + $\exp(\lambda x)$ induces local minima. \item You need initial values for the parameter! \item Example that fitting gets harder the more parameter you have. -\item Try to fix as many parameter before doing the fit. +\item Try to fix as many parameters before doing the fit. \item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test. +\item Impoartant box: summary of fit howtos. +\end{itemize} + +\subsection{New chapter: linear fits --- generalized linear models} +\begin{itemize} +\item Polyfit is easy: unique solution! $c x^3$ is also a linear fit. +\item Example for \emph{overfitting} with polyfit of a high order (=number of data points) \end{itemize} diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index bfff7bb..de9630c 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -576,34 +576,36 @@ our tiger data-set (\figref{powergradientdescentfig}): \section{Fitting non-linear functions to data} -The gradient descent is an important numerical method for solving +The gradient descent is a basic numerical method for solving optimization problems. It is used to find the global minimum of an objective function. -Curve fitting is a common application for the gradient descent method. -For the case of fitting straight lines to data pairs, the error -surface (using the mean squared error) has exactly one clearly defined -global minimum. In fact, the position of the minimum can be -analytically calculated as shown in the next chapter. For linear -fitting problems numerical methods like the gradient descent are not -needed. +Curve fitting is a specific optimization problem and a common +application for the gradient descent method. For the case of fitting +straight lines to data pairs, the error surface (using the mean +squared error) has exactly one clearly defined global minimum. In +fact, the position of the minimum can be analytically calculated as +shown in the next chapter. For linear fitting problems numerical +methods like the gradient descent are not needed. Fitting problems that involve nonlinear functions of the parameters, e.g. the power law \eqref{powerfunc} or the exponential function -$f(x;\lambda) = e^{\lambda x}$, do not have an analytical solution for -the least squares. To find the least squares for such functions -numerical methods such as the gradient descent have to be applied. - -The suggested gradient descent algorithm is quite fragile and requires -manually tuned values for $\epsilon$ and the threshold for terminating -the iteration. The algorithm can be improved in multiple ways to -converge more robustly and faster. For example one could adapt the -step size to the length of the gradient. These numerical tricks have -already been implemented in pre-defined functions. Generic -optimization functions such as \mcode{fminsearch()} have been -implemented for arbitrary objective functions, while the more -specialized function \mcode{lsqcurvefit()} is specifically designed -for optimizations in the least square error sense. +$f(t;\tau) = e^{-t/\tau}$, do in general not have an analytical +solution for the least squares. To find the least squares for such +functions numerical methods such as the gradient descent have to be +applied. + +The suggested gradient descent algorithm requires manually tuned +values for $\epsilon$ and the threshold for terminating the iteration. +The algorithm can be improved in multiple ways to converge more +robustly and faster. Most importantly, $\epsilon$ is made dependent +on the changes of the gradient from one iteration to the next. These +and other numerical tricks have already been implemented in +pre-defined functions. Generic optimization functions such as +\mcode{fminsearch()} have been implemented for arbitrary objective +functions, while the more specialized function \mcode{lsqcurvefit()} +is specifically designed for optimizations in the least square error +sense. \begin{exercise}{plotlsqcurvefitpower.m}{} Use the \matlab-function \varcode{lsqcurvefit()} instead of @@ -626,5 +628,62 @@ for optimizations in the least square error sense. \end{important} +\section{Evolution as an optimization problem} + +Evolution is a biological implementation of an optimization +algorithm. The objective function is an organism's fitness. This needs +to be maximized (this is the same as minimizing the negative fitness). +The parameters of this optimization problem are all the many genes on +the DNA. This is a very high-dimensional optimization problem. By +cross-over and mutations a population of a species moves along the +high-dimensional parameter space. Selection processes make sure that +only organisms with higher fitness pass on their genes to the next +generations. In this way the algorithm is not directed towards higher +fitness, as the gradient descent method would be. Rather, some +neighborhood of the parameter space is randomly probed. That way it is +even possible to escape a local maximum and find a potentially better +maximum. For this reason, \enterm{genetic algorithms} try to mimic +evolution in the context of high-dimensional optimization problems, in +particular with discrete parameter values. In biological evolution, +the objective function, however, is not a fixed function. It may +change in time by changing abiotic and biotic environmental +conditions, making this a very complex but also interesting +optimization problem. + +How should a neuron or neural network be designed? As a particular +aspect of the general evolution of a species, this is a fundamental +question in the neurosciences. Maintaining a neural system is +costly. By their simple presence neurons incur costs. They need to be +built and maintained, they occupy space and consume +resources. Equipping a neuron with more ion channels also costs. And +neural activity makes it more costly to maintain concentration +gradients of ions. This all boils down to the consumption of more ATP, +the currency of metabolism. On the other hand each neuron provides +some useful function. In the end, neurons make the organism to behave +in some sensible way to increase the overall fitness of the +organism. On the level of neurons that means that they should +faithfully represent and process behaviorally relevant sensory +stimuli, make a sensible decision, store some important memory, or +initiate and control movements in a directed way. Unfortunately there +is a tradeoff. Better neural function usually involves higher +costs. More ion channels reduce intrinsic noise which usually favors +the precision of neural responses. Higher neuronal activity improves +the quality of the encoding of sensory stimuli. More neurons are +required for more complex computations. And so on. + +Understanding why a neuronal system is designed in some specific way +requires to also understand these tradeoffs. The number of neurons, +the number and types of ion channels, the length of axons, the number +of synapses, the way neurons are connected, etc. are all parameters +that could be optimized. For the objective function the function of +the neurons needs to be quantified, for example by measures from +information or detection theory, and their dependence on the +parameters. From these benefits the costs need to be subtracted. And +then one is interested in finding the maximum of the resulting +objective function. Maximization (or minimization) problems are not +only a tool for data analysis, rather they are at the core of many --- +not only biological or neuroscientific --- problems. + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \printsolutions From 4b18c855b90352322d015d2f26a2a44154a09456 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 20 Dec 2020 23:16:56 +0100 Subject: [PATCH 47/87] [regression] first exercise --- header.tex | 6 +- regression/code/funcPlotter.m | 4 + regression/code/funcplotterexamples.m | 2 + regression/code/plotlsqcurvefitpower.m | 13 ++ regression/code/powerLaw.m | 9 ++ .../{fitting.tex => exercises00-de.tex} | 0 regression/exercises/expdecay.m | 4 + regression/exercises/expdecaydata.m | 10 ++ regression/exercises/expdecaydescent.m | 34 +++++ regression/exercises/expdecayplot.m | 29 +++++ regression/exercises/gradientdescent-1.tex | 116 ++++++++++-------- regression/exercises/gradientdescent-2.tex | 92 ++++++++++++++ regression/lecture/cubicgradient.py | 89 ++++++++++++++ regression/lecture/powergradientdescent.py | 67 ++++++++++ regression/lecture/regression.tex | 44 +++---- 15 files changed, 444 insertions(+), 75 deletions(-) create mode 100644 regression/code/funcPlotter.m create mode 100644 regression/code/funcplotterexamples.m create mode 100644 regression/code/plotlsqcurvefitpower.m create mode 100644 regression/code/powerLaw.m rename regression/exercises/{fitting.tex => exercises00-de.tex} (100%) create mode 100644 regression/exercises/expdecay.m create mode 100644 regression/exercises/expdecaydata.m create mode 100644 regression/exercises/expdecaydescent.m create mode 100644 regression/exercises/expdecayplot.m create mode 100644 regression/exercises/gradientdescent-2.tex create mode 100644 regression/lecture/cubicgradient.py create mode 100644 regression/lecture/powergradientdescent.py diff --git a/header.tex b/header.tex index ab412ef..a1b8961 100644 --- a/header.tex +++ b/header.tex @@ -72,14 +72,14 @@ \newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}} % maximum number of floats: -\setcounter{topnumber}{2} -\setcounter{bottomnumber}{0} +\setcounter{topnumber}{1} +\setcounter{bottomnumber}{1} \setcounter{totalnumber}{2} % float placement fractions: \renewcommand{\textfraction}{0.1} \renewcommand{\topfraction}{0.9} -\renewcommand{\bottomfraction}{0.0} +\renewcommand{\bottomfraction}{0.9} \renewcommand{\floatpagefraction}{0.7} % spacing for floats: diff --git a/regression/code/funcPlotter.m b/regression/code/funcPlotter.m new file mode 100644 index 0000000..ed4936e --- /dev/null +++ b/regression/code/funcPlotter.m @@ -0,0 +1,4 @@ +function funcPlotter(func) + x = 0:0.1:10.0; + plot(x,func(x)); +end diff --git a/regression/code/funcplotterexamples.m b/regression/code/funcplotterexamples.m new file mode 100644 index 0000000..7b12d06 --- /dev/null +++ b/regression/code/funcplotterexamples.m @@ -0,0 +1,2 @@ +funcPlotter(@sin); + diff --git a/regression/code/plotlsqcurvefitpower.m b/regression/code/plotlsqcurvefitpower.m new file mode 100644 index 0000000..3d39605 --- /dev/null +++ b/regression/code/plotlsqcurvefitpower.m @@ -0,0 +1,13 @@ +meansquarederrorline; % generate data +p0 = [2.0, 1.0]; +pest = lsqcurvefit(@powerLaw, p0, x, y) + +hold on; +% generate x-values for plottig the fit: +xx = min(x):0.01:max(x); +yy = powerLaw(xx, pest); +plot(xx, yy); % plot fit +plot(x, y, 'o'); % plot original data +xlabel('Size [m]'); +ylabel('Weight [kg]'); +legend('fit', 'data', 'location', 'northwest'); diff --git a/regression/code/powerLaw.m b/regression/code/powerLaw.m new file mode 100644 index 0000000..f51898e --- /dev/null +++ b/regression/code/powerLaw.m @@ -0,0 +1,9 @@ +function y = powerLaw(x, p) +% Power law function y = c*x^alpha. +% +% Arguments: x, vector of the x-data values. +% p, vector with parameter values c and alpha +% +% Returns: y, vector of the computed y-data values. + y = p(1)*x.^p(2); +end diff --git a/regression/exercises/fitting.tex b/regression/exercises/exercises00-de.tex similarity index 100% rename from regression/exercises/fitting.tex rename to regression/exercises/exercises00-de.tex diff --git a/regression/exercises/expdecay.m b/regression/exercises/expdecay.m new file mode 100644 index 0000000..febd36a --- /dev/null +++ b/regression/exercises/expdecay.m @@ -0,0 +1,4 @@ +function x = expdecay(t, tau) +% return the exponential function x = e^{-t/tau} + x = exp(-t./tau); +end diff --git a/regression/exercises/expdecaydata.m b/regression/exercises/expdecaydata.m new file mode 100644 index 0000000..c15f8f4 --- /dev/null +++ b/regression/exercises/expdecaydata.m @@ -0,0 +1,10 @@ +tau = 10.0; % membrane time constant in ms +dt = 0.05; % sampling interval in ms +noisesd = 0.05; % measurement noise in mV + +time = 0.0:dt:5*tau; % time vector +voltage = expdecay(time, tau); % exponential decay +voltage = voltage + noisesd*randn(1, length(voltage)); % plus noise + +plot(time, voltage); + diff --git a/regression/exercises/expdecaydescent.m b/regression/exercises/expdecaydescent.m new file mode 100644 index 0000000..02434ed --- /dev/null +++ b/regression/exercises/expdecaydescent.m @@ -0,0 +1,34 @@ +function [tau, taus, mses] = expdecaydescent(t, x, tau0, epsilon, threshold) +% Gradient descent for fitting a decaying exponential. +% +% Arguments: t, vector of time points. +% x, vector of the corresponding measured data values. +% tau0, initial value for the time constant. +% epsilon: factor multiplying the gradient. +% threshold: minimum value for gradient +% +% Returns: tau, the final value of the time constant. +% taus: vector with all the tau-values traversed. +% mses: vector with the corresponding mean squared errors + tau = tau0; + gradient = 1000.0; + taus = []; + mses = []; + count = 1; + while abs(gradient) > threshold + taus(count) = tau; + mses(count) = expdecaymse(t, x, tau); + gradient = expdecaygradient(t, x, tau); + tau = tau - epsilon * gradient; + count = count + 1; + end +end + +function mse = expdecaymse(t, x, tau) + mse = mean((x - expdecay(t, tau)).^2); +end + +function gradient = expdecaygradient(t, x, tau) + h = 1e-7; % stepsize for derivative + gradient = (expdecaymse(t, x, tau+h) - expdecaymse(t, x, tau))/h; +end diff --git a/regression/exercises/expdecayplot.m b/regression/exercises/expdecayplot.m new file mode 100644 index 0000000..fac8bfe --- /dev/null +++ b/regression/exercises/expdecayplot.m @@ -0,0 +1,29 @@ +expdecaydata; % generate data + +tau0 = 2.0; +eps = 1.0; +thresh = 0.00001; +[tauest, taus, mses] = expdecaydescent(time, voltage, tau0, eps, thresh); + +subplot(2, 2, 1); % top left panel +hold on; +plot(taus, '-o'); +plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau value +hold off; +xlabel('Iteration'); +ylabel('tau'); +subplot(2, 2, 3); % bottom left panel +plot(mses, '-o'); +xlabel('Iteration steps'); +ylabel('MSE'); +subplot(1, 2, 2); % right panel +hold on; +% generate x-values for plottig the fit: +tt = 0.0:0.01:max(time); +xx = expdecay(tt, tauest); +plot(time, voltage, '.'); % plot original data +plot(tt, xx, '-r'); % plot fit +xlabel('Time [ms]'); +ylabel('Voltage [mV]'); +legend('data', 'fit', 'location', 'northeast'); +pause diff --git a/regression/exercises/gradientdescent-1.tex b/regression/exercises/gradientdescent-1.tex index 7e25b0d..3340e58 100644 --- a/regression/exercises/gradientdescent-1.tex +++ b/regression/exercises/gradientdescent-1.tex @@ -1,6 +1,6 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\newcommand{\exercisetopic}{Resampling} +\newcommand{\exercisetopic}{Gradient descent} \newcommand{\exercisenum}{9} \newcommand{\exercisedate}{December 22th, 2020} @@ -15,67 +15,83 @@ \begin{questions} - \question We want to fit the straigth line \[ y = mx+b \] to the - data in the file \emph{lin\_regression.mat}. - - In the lecture we already prepared the cost function - (\code{meanSquaredError()}), and the gradient - (\code{meanSquaredGradient()}) (read chapter 8 ``Optimization and - gradient descent'' in the script, in particular section 8.4 and - exercise 8.4!). With these functions in place we here want to - implement a gradient descend algorithm that finds the minimum of the - cost function and thus the slope and intercept of the straigth line - that minimizes the squared distance to the data values. - - The algorithm for the descent towards the minimum of the cost - function is as follows: - \begin{enumerate} - \item Start with some arbitrary parameter values (intercept $b_0$ - and slope $m_0$, $\vec p_0 = (b_0, m_0)$ for the slope and the - intercept of the straight line. - \item \label{computegradient} Compute the gradient of the cost function - at the current values of the parameters $\vec p_i$. - \item If the magnitude (length) of the gradient is smaller than some - small number, the algorithm converged close to the minimum of the - cost function and we abort the descent. Right at the minimum the - magnitude of the gradient is zero. However, since we determine - the gradient numerically, it will never be exactly zero. This is - why we just require the gradient to be sufficiently small - (e.g. \code{norm(gradient) < 0.1}). - \item \label{gradientstep} Move against the gradient by a small step - $\epsilon = 0.01$: - \[\vec p_{i+1} = \vec p_i - \epsilon \cdot \nabla f_{cost}(m_i, b_i)\] - \item Repeat steps \ref{computegradient} -- \ref{gradientstep}. - \end{enumerate} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question \qt{Read sections 8.1 -- 8.5 of chapter 8 on ``optimization + and gradient descent!}\vspace{-3ex} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question \qt{Fitting the time constant of an exponential function} + Let's assume we record the membrane potential from a photoreceptor + neuron. We define the resting potential of the neuron to be at + 0\,mV. By means of a brief current injection we increase the + membrane potential by exactly 1\,mV. We then record how the membrane + potential decays exponentially down to the resting potential. We are + interested in the membrane time constant and therefore want to fit + an exponential function to the recorded time course of the membrane + potential. \begin{parts} - \part Implement the gradient descent in a function that returns - the parameter values at the minimum of the cost function and a vector - with the value of the cost function at each step of the algorithm. + \part Implement (and document!) the exponential function + \begin{equation} + \label{expfunc} + x(t) = e^{-t/\tau} + \end{equation} + with the membrane time constant $\tau$ as a matlab function + \code{expdecay(t, tau)} that takes as arguments a vector of + time points and the membrane time constant. The function returns + \eqnref{expfunc} computed for each time point as a vector. \begin{solution} - \lstinputlisting{descent.m} + \lstinputlisting{expdecay.m} \end{solution} - \part Plot the data and the straight line with the parameter - values that you found with the gradient descent method. + \part Let's first generate the data. Set the membrane time + constant to 10\,ms. Generate a time vector with sample times + between zero and five times the membrane time constant and a + sampling interval of 0.05\,ms. Then compute a vector containing + the corresponding measurements of the membrane potential using the + \code{expdecay()} function and adding some measurement noise with + a standard deviation of 0.05\.mV (\code{randn()} function). Also + plot the data. + \begin{solution} + \lstinputlisting{expdecaydata.m} + \end{solution} - \part Plot the development of the costs as a function of the - iteration step. + \part Implement the gradient descent algorithm for finding the + least squares for the exponential function \eqref{expfunc}. The + function takes as arguments the measured data, an initial value + for the estimation of the membrane time constant, the $\epsilon$ + factor, and the threshold for the length of the gradient where to + terminate the algorithm. The function should return the estimated + membrane time constant at the minimum of the mean squared error, a + vector with the time constants, and a vector with the mean squared + errors for each step of the algorithm. \begin{solution} - \lstinputlisting{descentfit.m} + \lstinputlisting{expdecaydescent.m} \end{solution} - \part For checking the gradient descend method from (a) compare - its result for slope and intercept with the position of the - minimum of the cost function that you get when computing the cost - function for many values of the slope and intercept and then using - the \code{min()} function. Vary the value of $\epsilon$ and the - minimum gradient. What are good values such that the gradient - descent gets closest to the true minimum of the cost function? + \part Call the gradient descent function with the generated data. + Watch the value of the gradient and of tau and adapt $\epsilon$ + and the threshold accordingly (they differ quite dramatically from + the ones in the script for the cubic fit). + + \part Generate three plots: (i) the values of the time constant + for each iteration step, (ii) the mean squared error for each + iteration step, and (iii) the measured data and the fitted + exponential function. \begin{solution} - \lstinputlisting{checkdescent.m} + \lstinputlisting{expdecayplot.m} \end{solution} + \end{parts} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question \qt{Read sections 8.6 -- 8.8 of chapter 8 on ``optimization + and gradient descent!}\vspace{-3ex} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question \qt{Fitting the full exponential function} + \begin{parts} + \part Use the functions \code{polyfit()} and \code{lsqcurvefit()} provided by matlab to find the slope and intercept of a straight line that fits the data. Compare the resulting fit parameters of diff --git a/regression/exercises/gradientdescent-2.tex b/regression/exercises/gradientdescent-2.tex new file mode 100644 index 0000000..e10be99 --- /dev/null +++ b/regression/exercises/gradientdescent-2.tex @@ -0,0 +1,92 @@ +\documentclass[12pt,a4paper,pdftex]{exam} + +\newcommand{\exercisetopic}{Gradient descent} +\newcommand{\exercisenum}{9} +\newcommand{\exercisedate}{December 22th, 2020} + +\input{../../exercisesheader} + +\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\input{../../exercisestitle} + +\begin{questions} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question We want to fit the straigth line \[ y = mx+b \] to the + data in the file \emph{lin\_regression.mat}. + + In the lecture we already prepared the cost function + (\code{meanSquaredError()}), and the gradient + (\code{meanSquaredGradient()}) (read chapter 8 ``Optimization and + gradient descent'' in the script, in particular section 8.4 and + exercise 8.5!). With these functions in place we here want to + implement a gradient descend algorithm that finds the minimum of the + cost function and thus the slope and intercept of the straigth line + that minimizes the squared distance to the data values. + + The algorithm for the descent towards the minimum of the cost + function is as follows: + \begin{enumerate} + \item Start with some arbitrary parameter values (intercept $b_0$ + and slope $m_0$, $\vec p_0 = (b_0, m_0)$ for the slope and the + intercept of the straight line. + \item \label{computegradient} Compute the gradient of the cost function + at the current values of the parameters $\vec p_i$. + \item If the magnitude (length) of the gradient is smaller than some + small number, the algorithm converged close to the minimum of the + cost function and we abort the descent. Right at the minimum the + magnitude of the gradient is zero. However, since we determine + the gradient numerically, it will never be exactly zero. This is + why we just require the gradient to be sufficiently small + (e.g. \code{norm(gradient) < 0.1}). + \item \label{gradientstep} Move against the gradient by a small step + $\epsilon = 0.01$: + \[\vec p_{i+1} = \vec p_i - \epsilon \cdot \nabla f_{cost}(m_i, b_i)\] + \item Repeat steps \ref{computegradient} -- \ref{gradientstep}. + \end{enumerate} + + \begin{parts} + \part Implement the gradient descent in a function that returns + the parameter values at the minimum of the cost function and a vector + with the value of the cost function at each step of the algorithm. + \begin{solution} + \lstinputlisting{descent.m} + \end{solution} + + \part Plot the data and the straight line with the parameter + values that you found with the gradient descent method. + + \part Plot the development of the costs as a function of the + iteration step. + \begin{solution} + \lstinputlisting{descentfit.m} + \end{solution} + + \part For checking the gradient descend method from (a) compare + its result for slope and intercept with the position of the + minimum of the cost function that you get when computing the cost + function for many values of the slope and intercept and then using + the \code{min()} function. Vary the value of $\epsilon$ and the + minimum gradient. What are good values such that the gradient + descent gets closest to the true minimum of the cost function? + \begin{solution} + \lstinputlisting{checkdescent.m} + \end{solution} + + \part Use the functions \code{polyfit()} and \code{lsqcurvefit()} + provided by matlab to find the slope and intercept of a straight + line that fits the data. Compare the resulting fit parameters of + those functions with the ones of your gradient descent algorithm. + \begin{solution} + \lstinputlisting{linefit.m} + \end{solution} + + \end{parts} + +\end{questions} + +\end{document} diff --git a/regression/lecture/cubicgradient.py b/regression/lecture/cubicgradient.py new file mode 100644 index 0000000..e8557d1 --- /dev/null +++ b/regression/lecture/cubicgradient.py @@ -0,0 +1,89 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.ticker as mt +from plotstyle import * + +def create_data(): + # wikipedia: + # Generally, males vary in total length from 250 to 390 cm and + # weigh between 90 and 306 kg + c = 6 + x = np.arange(2.2, 3.9, 0.05) + y = c * x**3.0 + rng = np.random.RandomState(32281) + noise = rng.randn(len(x))*50 + y += noise + return x, y, c + + +def gradient_descent(x, y): + n = 20 + dc = 0.01 + eps = 0.0001 + cc = 1.1 + cs = [] + mses = [] + for k in range(n): + m0 = np.mean((y-(cc*x**3.0))**2.0) + m1 = np.mean((y-((cc+dc)*x**3.0))**2.0) + dmdc = (m1 - m0)/dc + cs.append(cc) + mses.append(m0) + cc -= eps*dmdc + return cs, mses + + +def plot_gradient(ax, x, y, c): + ccs = np.linspace(0.5, 10.0, 200) + mses = np.zeros(len(ccs)) + for i, cc in enumerate(ccs): + mses[i] = np.mean((y-(cc*x**3.0))**2.0) + cmin = ccs[np.argmin(mses)] + gradient = np.diff(mses)/(ccs[1]-ccs[0]) + + ax.plot([cmin, cmin], [-10000, 10000], **lsSpine) + ax.plot([ccs[0], ccs[-1]], [0, 0], **lsSpine) + ax.plot(ccs[:-1], gradient, **lsBm) + ax.set_xlabel('c') + ax.set_ylabel('Derivative') + ax.set_xlim(0, 10) + ax.set_ylim(-10000, 10000) + ax.set_xticks(np.arange(0.0, 10.1, 2.0)) + ax.set_yticks(np.arange(-10000, 10001, 10000)) + ax.set_yticklabels(['', '0', '']) + + +def plot_mse(ax, x, y, c): + ccs = np.linspace(0.5, 10.0, 200) + mses = np.zeros(len(ccs)) + for i, cc in enumerate(ccs): + mses[i] = np.mean((y-(cc*x**3.0))**2.0) + cmin = ccs[np.argmin(mses)] + gradient = np.diff(mses)/(ccs[1]-ccs[0]) + + ay = 1500.0 + asB = dict(arrowprops=dict(arrowstyle="->", shrinkA=0, shrinkB=0, + color=lsB['color'], lw=2)) + ax.annotate('', xy=(3.0, ay), xytext=(1.0, ay), **asB) + ax.annotate('', xy=(5.0, ay), xytext=(3.8, ay), **asB) + ax.annotate('', xy=(6.2, ay), xytext=(7.4, ay), **asB) + ax.annotate('', xy=(8.0, ay), xytext=(10.0, ay), **asB) + ax.plot([cmin, cmin], [0, 30000], **lsSpine) + ax.plot(ccs, mses, zorder=10, **lsAm) + ax.set_xlabel('c') + ax.set_ylabel('Mean squared error') + ax.set_xlim(0, 10) + ax.set_ylim(0, 25000) + ax.set_xticks(np.arange(0.0, 10.1, 2.0)) + ax.set_yticks(np.arange(0, 30001, 10000)) + ax.set_yticklabels(['0', '', '', '']) + + +if __name__ == "__main__": + x, y, c = create_data() + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) + fig.subplots_adjust(wspace=0.5, **adjust_fs(left=5.0, right=1.2)) + plot_gradient(ax1, x, y, c) + plot_mse(ax2, x, y, c) + fig.savefig("cubicgradient.pdf") + plt.close() diff --git a/regression/lecture/powergradientdescent.py b/regression/lecture/powergradientdescent.py new file mode 100644 index 0000000..56566e3 --- /dev/null +++ b/regression/lecture/powergradientdescent.py @@ -0,0 +1,67 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.ticker as mt +from plotstyle import * + + +def power_law(x, c, a): + return c*x**a + + +def create_data(): + # wikipedia: + # Generally, males vary in total length from 250 to 390 cm and + # weigh between 90 and 306 kg + c = 6.0 + x = np.arange(2.2, 3.9, 0.05) + y = power_law(x, c, 3.0) + rng = np.random.RandomState(32281) + noise = rng.randn(len(x))*50 + y += noise + return x, y, c + + +def gradient_descent(x, y, func, p0): + n = 20000 + h = 1e-7 + ph = np.identity(len(p0))*h + eps = 0.00001 + p = p0 + ps = np.zeros((n, len(p0))) + mses = np.zeros(n) + for k in range(n): + m0 = np.mean((y-func(x, *p))**2.0) + gradient = np.array([(np.mean((y-func(x, *(p+ph[:,i])))**2.0) - m0)/h + for i in range(len(p))]) + ps[k,:] = p + mses[k] = m0 + p -= eps*gradient + return ps, mses + + +def plot_gradient_descent(ax, x, y, c, ps, mses): + cs = np.linspace(0.0, 10.0, 300) + bs = np.linspace(1.0, 5.5, 180) + mse = np.zeros((len(bs), len(cs))) + for i in range(len(bs)): + for k in range(len(cs)): + mse[i, k] = np.mean((y-power_law(x, cs[k], bs[i]))**2.0) + z = np.log10(mse) + ax.contourf(cs, bs, z, levels=(3.3, 3.36, 3.5, 4.0, 4.5, 5.5, 6.5, 7.5, 8.5), + cmap='Blues_r') + ax.plot(ps[::5,0], ps[::5,1], **lsBm) + ax.plot(ps[-1,0], ps[-1,1], **psC) + ax.set_xlabel('c') + ax.set_ylabel('a') + ax.yaxis.set_major_locator(mt.MultipleLocator(1.0)) + ax.set_aspect('equal') + + +if __name__ == "__main__": + x, y, c = create_data() + ps, mses = gradient_descent(x, y, power_law, [1.0, 1.0]) + fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.3*figure_height)) + fig.subplots_adjust(**adjust_fs(left=4.5, right=1.0)) + plot_gradient_descent(ax, x, y, c, ps, mses) + fig.savefig("powergradientdescent.pdf") + plt.close() diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index de9630c..be49cfe 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -198,7 +198,20 @@ So we need a different approach. We want a procedure that finds the minimum of the cost function with a minimal number of computations and to arbitrary precision. -\begin{ibox}[t]{\label{differentialquotientbox}Difference quotient and derivative} +\section{Gradient} + +\begin{figure}[t] + \includegraphics{cubicgradient} + \titlecaption{Derivative of the cost function.}{The gradient, the + derivative \eqref{costderivative} of the cost function, is + negative to the left of the minimum (vertical line) of the cost + function, zero (horizontal line) at, and positive to the right of + the minimum (left). For each value of the parameter $c$ the + negative gradient (arrows) points towards the minimum of the cost + function (right).} \label{gradientcubicfig} +\end{figure} + +\begin{ibox}[b]{\label{differentialquotientbox}Difference quotient and derivative} \includegraphics[width=0.33\textwidth]{derivative} \hfill \begin{minipage}[b]{0.63\textwidth} @@ -226,8 +239,6 @@ to arbitrary precision. sufficiently small $\Delta x$. \end{ibox} -\section{Gradient} - Imagine to place a ball at some point on the cost function \figref{cubiccostfig}. Naturally, it would roll down the slope and eventually stop at the minimum of the error surface (if it had no @@ -236,17 +247,6 @@ way to the minimum of the cost function. The ball always follows the steepest slope. Thus we need to figure out the direction of the slope at the position of the ball. -\begin{figure}[t] - \includegraphics{cubicgradient} - \titlecaption{Derivative of the cost function.}{The gradient, the - derivative \eqref{costderivative} of the cost function, is - negative to the left of the minimum (vertical line) of the cost - function, zero (horizontal line) at, and positive to the right of - the minimum (left). For each value of the parameter $c$ the - negative gradient (arrows) points towards the minimum of the cost - function (right).} \label{gradientcubicfig} -\end{figure} - In our one-dimensional example of a single free parameter the slope is simply the derivative of the cost function with respect to the parameter $c$ (\figref{gradientcubicfig}, left). This derivative is called @@ -434,7 +434,7 @@ landscape over the parameter plane with mountains and valleys and we are searching for the position of the bottom of the deepest valley (\figref{powergradientdescentfig}). -\begin{ibox}[tp]{\label{partialderivativebox}Partial derivatives and gradient} +\begin{ibox}[t]{\label{partialderivativebox}Partial derivatives and gradient} Some functions depend on more than a single variable. For example, the function \[ z = f(x,y) \] depends on both $x$ and $y$. Using the partial derivatives @@ -642,13 +642,13 @@ generations. In this way the algorithm is not directed towards higher fitness, as the gradient descent method would be. Rather, some neighborhood of the parameter space is randomly probed. That way it is even possible to escape a local maximum and find a potentially better -maximum. For this reason, \enterm{genetic algorithms} try to mimic -evolution in the context of high-dimensional optimization problems, in -particular with discrete parameter values. In biological evolution, -the objective function, however, is not a fixed function. It may -change in time by changing abiotic and biotic environmental -conditions, making this a very complex but also interesting -optimization problem. +maximum. For this reason, \enterm[genetic algorithm]{genetic + algorithms} try to mimic evolution in the context of +high-dimensional optimization problems, in particular with discrete +parameter values. In biological evolution, the objective function, +however, is not a fixed function. It may change in time by changing +abiotic and biotic environmental conditions, making this a very +complex but also interesting optimization problem. How should a neuron or neural network be designed? As a particular aspect of the general evolution of a species, this is a fundamental From 84a21ed91ff21abf234988299141ba0d79e9fff3 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 14:10:15 +0100 Subject: [PATCH 48/87] [regression] added note on uniqe parameters --- .../lecture/pointprocessscetchA.eps | 120 ++++-- .../lecture/pointprocessscetchA.pdf | Bin 2786 -> 2924 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++++++++------ .../lecture/pointprocessscetchB.pdf | Bin 4694 -> 4877 bytes regression/lecture/regression-chapter.tex | 7 +- 5 files changed, 360 insertions(+), 156 deletions(-) diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 59681c9..bdf6699 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex -%%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Mon Dec 14 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zFOd*RAcB$fR^j76RYXJN#82sdwrQ>iOW$jEX2B#f)`0Boqvt@l_!l7hVf{S<4Yc>j zUHljL9@X~t()-)PN)aXTD#205fZAqzS^P+WIFDe0+TP7^1TQcQ3I6v$z@Q`iNH{`A z7e+S*=_CJp0=pR;LOlHmUcqYT14Dv{q+sygwo99Y1pAW6YP-$Q3qaab1R4R}dn+h7 z5Dfedph(zmo&VzCi2uRCFh6*qP?*jSUKr{J9UO^3@97l(voIWq#{6K`fzm1BhG$GM zI5+~0M4RK#7*h)!6Qm9d28E+=2$ZfF5{=fy8vI|y86Xx5qy&4AgD;T@K0qV_2?HuC Jo7-9d{{_=$;!OYm diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index 8798b2a..cfc984b 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -28,18 +28,21 @@ \item Move 8.7 to this new chapter. \item Example that illustrates the Nebenminima Problem (with error surface). Maybe data generate from $1/x$ and fitted with - $\exp(\lambda x)$ induces local minima. + $c\exp(\lambda x)$ induces local minima. \item You need initial values for the parameter! \item Example that fitting gets harder the more parameter you have. \item Try to fix as many parameters before doing the fit. +\item Ensure that all parameters in the function are unique, e.g. $a e^{x-c} = be^x$. \item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test. -\item Impoartant box: summary of fit howtos. +\item Important box: summary of fit howtos. \end{itemize} \subsection{New chapter: linear fits --- generalized linear models} \begin{itemize} \item Polyfit is easy: unique solution! $c x^3$ is also a linear fit. \item Example for \emph{overfitting} with polyfit of a high order (=number of data points) +\item Higher order and cross terms +\item Link function, logistic regression \end{itemize} From f5c3bb6139fa2ec7ca5cfeab6544a4c8b4d99850 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 19:58:19 +0100 Subject: [PATCH 49/87] [regression] finished exercise --- regression/code/gradientDescent.m | 9 +- regression/exercises/exp2errorsurface.m | 15 ++++ regression/exercises/exp2fit.m | 15 ++++ regression/exercises/exp2fit.pdf | Bin 0 -> 29836 bytes regression/exercises/exp2func.m | 4 + regression/exercises/exp2plot.m | 27 ++++++ regression/exercises/exp2plot.pdf | Bin 0 -> 185733 bytes regression/exercises/expdecaydata.m | 2 +- regression/exercises/expdecayplot.m | 10 +-- regression/exercises/expdecayplot.pdf | Bin 0 -> 179679 bytes regression/exercises/gradientdescent-1.tex | 96 +++++++++++++++++---- regression/exercises/gradientdescent.m | 39 +++++++++ regression/exercises/savefigpdf.m | 28 ++++++ 13 files changed, 217 insertions(+), 28 deletions(-) create mode 100644 regression/exercises/exp2errorsurface.m create mode 100644 regression/exercises/exp2fit.m create mode 100644 regression/exercises/exp2fit.pdf create mode 100644 regression/exercises/exp2func.m create mode 100644 regression/exercises/exp2plot.m create mode 100644 regression/exercises/exp2plot.pdf create mode 100644 regression/exercises/expdecayplot.pdf create mode 100644 regression/exercises/gradientdescent.m create mode 100644 regression/exercises/savefigpdf.m diff --git a/regression/code/gradientDescent.m b/regression/code/gradientDescent.m index 20e0b90..3fb9643 100644 --- a/regression/code/gradientDescent.m +++ b/regression/code/gradientDescent.m @@ -13,7 +13,7 @@ function [p, ps, mses] = gradientDescent(x, y, func, p0, epsilon, threshold) % mses: vector with the corresponding mean squared errors p = p0; - gradient = ones(1, length(p0)) * 1000.0; + gradient = ones(size(p0)) * 1000.0; ps = []; mses = []; while norm(gradient) > threshold @@ -29,13 +29,12 @@ function mse = meanSquaredError(x, y, func, p) end function gradmse = meanSquaredGradient(x, y, func, p) - gradmse = zeros(size(p, 1), size(p, 2)); + gradmse = zeros(size(p)); h = 1e-7; % stepsize for derivatives + ph = eye(length(p))*h; % ... for each parameter mse = meanSquaredError(x, y, func, p); for i = 1:length(p) % for each coordinate ... - pi = p; - pi(i) = pi(i) + h; % displace i-th parameter - msepi = meanSquaredError(x, y, func, pi); + msepi = meanSquaredError(x, y, func, p + ph(:,i)); gradmse(i) = (msepi - mse)/h; end end diff --git a/regression/exercises/exp2errorsurface.m b/regression/exercises/exp2errorsurface.m new file mode 100644 index 0000000..7dc4e4f --- /dev/null +++ b/regression/exercises/exp2errorsurface.m @@ -0,0 +1,15 @@ +expdecaydata; % generate data +close all; + +cs = 0.5:0.02:1.5; % range of c values +taus = 4.0:0.2:16.0; % range of tau values +msesurf = zeros(length(taus), length(cs)); % mean squared error +for i = 1:length(taus) + for k = 1:length(cs) + msesurf(i, k) = mean((voltage - ... + exp2func(time, [cs(k), taus(i)])).^2); + end +end +%surface(cs, taus, mses) +%contour(cs, taus, mses) +contourf(cs, taus, log10(msesurf)) diff --git a/regression/exercises/exp2fit.m b/regression/exercises/exp2fit.m new file mode 100644 index 0000000..47e833a --- /dev/null +++ b/regression/exercises/exp2fit.m @@ -0,0 +1,15 @@ +expdecaydata; +close all; + +p0 = [0.5, 6.0]; +pest = lsqcurvefit(@(p, x) exp2func(x, p), p0, time, voltage); +fprintf('c=%4.1fmV, tau=%4.1fms\n', pest(1), pest(2)); + +hold on; +plot(time, voltage) +plot(time, exp2func(time, pest), 'LineWidth', 2) +hold off; +xlabel('time [ms]') 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Z!0fc~_Wg%tg&-p0!uV`#Dmtq8{|DimXl?)i literal 0 HcmV?d00001 diff --git a/regression/exercises/exp2func.m b/regression/exercises/exp2func.m new file mode 100644 index 0000000..6bdb6c0 --- /dev/null +++ b/regression/exercises/exp2func.m @@ -0,0 +1,4 @@ +function x = exp2func(t, p) +% return the exponential function x = c*e^{-t/tau} + x = p(1)*exp(-t./p(2)); +end diff --git a/regression/exercises/exp2plot.m b/regression/exercises/exp2plot.m new file mode 100644 index 0000000..cc2dd91 --- /dev/null +++ b/regression/exercises/exp2plot.m @@ -0,0 +1,27 @@ +... + +p0 = [0.5, 6.0]; +[pest, ps, mses] = gradientdescent(time, voltage, @exp2func, p0, 1.0, 0.00001); +fprintf('c=%4.1fmV, tau=%4.1fms\n', pest(1), pest(2)); + +subplot(1, 2, 1); +hold on; +%surface(cs, taus, msesurf); +%plot3(ps(1,:), ps(2,:), mses, '.r'); +%view(80, 35); +contourf(cs, taus, log10(msesurf)); +plot(ps(1,:), ps(2,:), '.r'); +hold off; +xlabel('c [mV]') +ylabel('tau [ms]') +zlabel('mse [mV^2]') + +subplot(1, 2, 2); +hold 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sampling interval in ms noisesd = 0.05; % measurement noise in mV -time = 0.0:dt:5*tau; % time vector +time = 0.0:dt:6*tau; % time vector voltage = expdecay(time, tau); % exponential decay voltage = voltage + noisesd*randn(1, length(voltage)); % plus noise diff --git a/regression/exercises/expdecayplot.m b/regression/exercises/expdecayplot.m index fac8bfe..68ea89b 100644 --- a/regression/exercises/expdecayplot.m +++ b/regression/exercises/expdecayplot.m @@ -8,7 +8,7 @@ thresh = 0.00001; subplot(2, 2, 1); % top left panel hold on; plot(taus, '-o'); -plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau value +plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau hold off; xlabel('Iteration'); ylabel('tau'); @@ -19,11 +19,9 @@ ylabel('MSE'); subplot(1, 2, 2); % right panel hold on; % generate x-values for plottig the fit: -tt = 0.0:0.01:max(time); -xx = expdecay(tt, tauest); -plot(time, voltage, '.'); % plot original data -plot(tt, xx, '-r'); % plot fit 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zeros(size(p)); - h = 1e-3; % stepsize for derivative + h = 1e-7; % stepsize for derivative ph = eye(length(p))*h; % ... for each parameter mse = meansquarederror(t, x, func, p); for i = 1:length(p) % for each coordinate ... From 60a94c9ce6e528ac45fa875abfc16be80a217b46 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 22:07:36 +0100 Subject: [PATCH 51/87] some fixes --- bootstrap/lecture/bootstrap.tex | 10 +++++----- bootstrap/lecture/bootstrapsem.py | 2 +- regression/lecture/regression.tex | 18 +++++++++++++++--- 3 files changed, 21 insertions(+), 9 deletions(-) diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index f71b268..66a526f 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -5,7 +5,7 @@ \exercisechapter{Resampling methods} -\entermde{Resampling methoden}{Resampling methods} are applied to +\entermde{Resampling-Methoden}{Resampling methods} are applied to generate distributions of statistical measures via resampling of existing samples. Resampling offers several advantages: \begin{itemize} @@ -80,10 +80,10 @@ distribution of average values around the true mean of the population Alternatively, we can use \enterm{bootstrapping} (\determ[Bootstrap!Verfahren]{Bootstrapverfahren}) to generate new -samples from one set of measurements -(\entermde{Resampling}{resampling}). From these bootstrapped samples -we compute the desired statistical measure and estimate their -distribution (\entermde{Bootstrap!Verteilung}{bootstrap distribution}, +samples from one set of measurements by means of resampling. From +these bootstrapped samples we compute the desired statistical measure +and estimate their distribution +(\entermde{Bootstrap!Verteilung}{bootstrap distribution}, \subfigref{bootstrapsamplingdistributionfig}{c}). Interestingly, this distribution is very similar to the sampling distribution regarding its width. The only difference is that the bootstrapped values are diff --git a/bootstrap/lecture/bootstrapsem.py b/bootstrap/lecture/bootstrapsem.py index 837b0b1..d431111 100644 --- a/bootstrap/lecture/bootstrapsem.py +++ b/bootstrap/lecture/bootstrapsem.py @@ -24,7 +24,7 @@ for i in range(nresamples) : musrs.append(np.mean(rng.randn(nsamples))) hmusrs, _ = np.histogram(musrs, bins, density=True) -fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.05*figure_height)) +fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.1*figure_height)) fig.subplots_adjust(**adjust_fs(left=4.0, bottom=2.7, right=1.5)) ax.set_xlabel('Mean') ax.set_xlim(-0.4, 0.4) diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index be49cfe..83060fd 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -362,7 +362,8 @@ too large, the algorithm does not converge to the minimum of the cost function (try it!). At medium values it oscillates around the minimum but might nevertheless converge. Only for sufficiently small values (here $\epsilon = 0.00001$) does the algorithm follow the slope -downwards towards the minimum. +downwards towards the minimum. Change $\epsilon$ by factors of ten to +adapt it to a specific problem. The terminating condition on the absolute value of the gradient influences how often the cost function is evaluated. The smaller the @@ -560,7 +561,7 @@ For testing our new function we need to implement the power law \end{exercise} Now let's use the new gradient descent function to fit a power law to -our tiger data-set (\figref{powergradientdescentfig}): +our tiger data-set: \begin{exercise}{plotgradientdescentpower.m}{} Use the function \varcode{gradientDescent()} to fit the @@ -573,12 +574,21 @@ our tiger data-set (\figref{powergradientdescentfig}): data together with the best fitting power-law \eqref{powerfunc}. \end{exercise} +Note that in our specific example on tiger sizes and weights the +simulated data look on a first glance like being linearly related +(\figref{cubicdatafig}). The true cubic relation between weights and +sizes is not that obvious, because of the limited range of tiger +sizes. Nevertheless, the cost function has a minimum at the bottom of +a valley that is very narrow in the direction of the expontent +(\figref{powergradientdescentfig}). The exponent of about three is +thus clearly defined by the data. + \section{Fitting non-linear functions to data} The gradient descent is a basic numerical method for solving optimization problems. It is used to find the global minimum of an -objective function. +objective function. Curve fitting is a specific optimization problem and a common application for the gradient descent method. For the case of fitting @@ -650,6 +660,8 @@ however, is not a fixed function. It may change in time by changing abiotic and biotic environmental conditions, making this a very complex but also interesting optimization problem. +\subsection{Optimal design of neural systems} + How should a neuron or neural network be designed? As a particular aspect of the general evolution of a species, this is a fundamental question in the neurosciences. Maintaining a neural system is From 5a6cca59d3a700125411e487f7ff2cb6de555ca5 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 23 Dec 2020 18:16:27 +0100 Subject: [PATCH 52/87] [regression] n-dim is simply n times 1 dim --- regression/lecture/regression.tex | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 83060fd..2d13b96 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -259,6 +259,7 @@ There is no need to calculate this derivative analytically, because it can be approximated numerically by the difference quotient (Box~\ref{differentialquotientbox}) for small steps $\Delta c$: \begin{equation} + \label{costderivativediff} \frac{{\rm d} f_{cost}(c)}{{\rm d} c} = \lim\limits_{\Delta c \to 0} \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} \approx \frac{f_{cost}(c + \Delta c) - f_{cost}(c)}{\Delta c} @@ -443,7 +444,7 @@ are searching for the position of the bottom of the deepest valley and \[ \frac{\partial f(x,y)}{\partial y} = \lim\limits_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x,y)}{\Delta y} \] one can calculate the slopes in the directions of each of the - variables by means of the respective difference quotient + variables by means of the respective difference quotients (see box~\ref{differentialquotientbox}). \vspace{1ex} \begin{minipage}[t]{0.5\textwidth} @@ -489,6 +490,10 @@ $p_j$ the respective partial derivatives as coordinates: \label{gradient} \nabla f_{cost}(\vec p) = \left( \frac{\partial f_{cost}(\vec p)}{\partial p_j} \right) \end{equation} +Despite the fancy words this simply means that we need to calculate the +derivatives in the very same way as we have done it for the case of a +single parameter, \eqnref{costderivativediff}, for each parameter +separately. The iterative equation \eqref{gradientdescent} of the gradient descent stays exactly the same, with the only difference that the current @@ -497,7 +502,8 @@ parameter value $p_i$ becomes a vector $\vec p_i$ of parameter values: \label{ndimgradientdescent} \vec p_{i+1} = \vec p_i - \epsilon \cdot \nabla f_{cost}(\vec p_i) \end{equation} -The algorithm proceeds along the negative gradient +For each parameter we subtract the corresponding derivative multiplied +with $\epsilon$. The algorithm proceeds along the negative gradient (\figref{powergradientdescentfig}). For the termination condition we need the length of the gradient. In From a63dd2f2fe468b143619bb27b0fd7dd168565060 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 23 Dec 2020 18:48:59 +0100 Subject: [PATCH 53/87] [regression] expandend exercise according to feedback from Alex --- regression/exercises/expdecaydescent.m | 9 ------ regression/exercises/expdecaygradient.m | 11 +++++++ regression/exercises/expdecaygradientplot.m | 15 +++++++++ regression/exercises/expdecaymse.m | 10 ++++++ regression/exercises/expdecaymseplot.m | 13 ++++++++ regression/exercises/expdecayplot.m | 2 +- regression/exercises/gradientdescent-1.tex | 35 +++++++++++++++++++-- 7 files changed, 82 insertions(+), 13 deletions(-) create mode 100644 regression/exercises/expdecaygradient.m create mode 100644 regression/exercises/expdecaygradientplot.m create mode 100644 regression/exercises/expdecaymse.m create mode 100644 regression/exercises/expdecaymseplot.m diff --git a/regression/exercises/expdecaydescent.m b/regression/exercises/expdecaydescent.m index 02434ed..b75b63b 100644 --- a/regression/exercises/expdecaydescent.m +++ b/regression/exercises/expdecaydescent.m @@ -23,12 +23,3 @@ function [tau, taus, mses] = expdecaydescent(t, x, tau0, epsilon, threshold) count = count + 1; end end - -function mse = expdecaymse(t, x, tau) - mse = mean((x - expdecay(t, tau)).^2); -end - -function gradient = expdecaygradient(t, x, tau) - h = 1e-7; % stepsize for derivative - gradient = (expdecaymse(t, x, tau+h) - expdecaymse(t, x, tau))/h; -end diff --git a/regression/exercises/expdecaygradient.m b/regression/exercises/expdecaygradient.m new file mode 100644 index 0000000..1b10400 --- /dev/null +++ b/regression/exercises/expdecaygradient.m @@ -0,0 +1,11 @@ +function gradient = expdecaygradient(t, x, tau) +% Gradient of MSE for a decaying exponential. +% +% Arguments: t, vector of time points. +% x, vector of the corresponding measured data values. +% tau, value for the time constant. +% +% Returns: gradient: the derivative of the MSE with respect to tau. + h = 1e-7; % stepsize for derivative + gradient = (expdecaymse(t, x, tau+h) - expdecaymse(t, x, tau))/h; +end diff --git a/regression/exercises/expdecaygradientplot.m b/regression/exercises/expdecaygradientplot.m new file mode 100644 index 0000000..62baf42 --- /dev/null +++ b/regression/exercises/expdecaygradientplot.m @@ -0,0 +1,15 @@ +... + +gradients = zeros(length(taus), 1); +for i = 1:length(taus) + gradients(i) = expdecaygradient(time, voltage, taus(i)); +end + +subplot(2, 1, 2) +plot(taus, gradients); +xlabel('tau [ms]') +ylabel('gradient [mV^2/ms]') +savefigpdf(gcf, 'expdecaygradientplot.pdf', 10, 10); + + + diff --git a/regression/exercises/expdecaymse.m b/regression/exercises/expdecaymse.m new file mode 100644 index 0000000..4e16dd6 --- /dev/null +++ b/regression/exercises/expdecaymse.m @@ -0,0 +1,10 @@ +function mse = expdecaymse(t, x, tau) +% Mean squared error for a decaying exponential. +% +% Arguments: t, vector of time points. +% x, vector of the corresponding measured data values. +% tau, value for the time constant. +% +% Returns: mse: mean squared error + mse = mean((x - expdecay(t, tau)).^2); +end diff --git a/regression/exercises/expdecaymseplot.m b/regression/exercises/expdecaymseplot.m new file mode 100644 index 0000000..1e1ebd9 --- /dev/null +++ b/regression/exercises/expdecaymseplot.m @@ -0,0 +1,13 @@ +expdecaydata; % generate data +close all; + +taus = 0.0:0.1:20.0; +mses = zeros(length(taus), 1); +for i = 1:length(taus) + mses(i) = expdecaymse(time, voltage, taus(i)); +end + +subplot(2, 1, 1) +plot(taus, mses); +xlabel('tau [ms]') +ylabel('mean squared error [mV^2]') diff --git a/regression/exercises/expdecayplot.m b/regression/exercises/expdecayplot.m index 68ea89b..baa6d16 100644 --- a/regression/exercises/expdecayplot.m +++ b/regression/exercises/expdecayplot.m @@ -11,7 +11,7 @@ plot(taus, '-o'); plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau hold off; xlabel('Iteration'); -ylabel('tau'); +ylabel('tau [ms]'); subplot(2, 2, 3); % bottom left panel plot(mses, '-o'); xlabel('Iteration steps'); diff --git a/regression/exercises/gradientdescent-1.tex b/regression/exercises/gradientdescent-1.tex index b4df7b3..b940202 100644 --- a/regression/exercises/gradientdescent-1.tex +++ b/regression/exercises/gradientdescent-1.tex @@ -56,6 +56,29 @@ \lstinputlisting{expdecaydata.m} \end{solution} + \part Write a function that returns the mean squared error. The + function takes as arguments the measured data (time points and + corresponding voltage measurements) and a value for the membrane + time constant at which the mean squred error should be + evaluated. Plot the mean squared error as a function of $\tau$. + \begin{solution} + \lstinputlisting{expdecaymse.m} + \lstinputlisting{expdecaymseplot.m} + \end{solution} + + \part Write a function that returns the gradient of the mean + squared error, i.e. its derivative with respect to the $\tau$ + parameter. The function takes as arguments the measured data + (time points and corresponding voltage measurements) and a value + for the membrane time constant at which the gradient should be + evaluated. Plot the gradient as a function of $\tau$. + \begin{solution} + \lstinputlisting{expdecaygradient.m} + \newsolutionpage + \lstinputlisting{expdecaygradientplot.m} + \includegraphics{expdecaygradientplot} + \end{solution} + \part Implement the gradient descent algorithm for finding the least squares for the exponential function \eqref{expfunc}. The function takes as arguments the measured data, an initial value @@ -78,7 +101,6 @@ for each iteration step, (ii) the mean squared error for each iteration step, and (iii) the measured data and the fitted exponential function. - \newsolutionpage \begin{solution} \lstinputlisting{expdecayplot.m} \includegraphics{expdecayplot} @@ -140,9 +162,16 @@ \part Plot the path of the gradient descent algorithm into the error surface. - Why appears (potentially) the path of the gradient descent - algorithm not perpendicular to the contour lines of the error + Why does (potentially) the path of the gradient descent algorithm + appear to be not perpendicular to the contour lines of the error surface? + \begin{solution} + Because on the plot the $c$ and $\tau$ axes are (in general) not + equally scaled. That is a unit step in $c$ direction covers a + physical distance on paper or the screen than a unit stpe in + $\tau$ direction. Use \code{axis equal} to force the plot to + have equally scaled $c$ and $\tau$ axes. + \end{solution} \part Plot the data together with the fitted exponential function. From c011e90fdd335bfc9fff7bd7226b8aefc535452c Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 23 Dec 2020 23:04:09 +0100 Subject: [PATCH 54/87] removed texpicture command where not needed --- bootstrap/lecture/bootstrap-slides.tex | 1 - replicability/lectures/topics-chapter.tex | 4 ---- replicability/lectures/topics-slides.tex | 1 - statistics/lecture/statistics-slides.tex | 1 - 4 files changed, 7 deletions(-) diff --git a/bootstrap/lecture/bootstrap-slides.tex b/bootstrap/lecture/bootstrap-slides.tex index 31e5655..3801d64 100644 --- a/bootstrap/lecture/bootstrap-slides.tex +++ b/bootstrap/lecture/bootstrap-slides.tex @@ -49,7 +49,6 @@ %%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} -\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}} %%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{listings} diff --git a/replicability/lectures/topics-chapter.tex b/replicability/lectures/topics-chapter.tex index 32acf92..e3bfbde 100644 --- a/replicability/lectures/topics-chapter.tex +++ b/replicability/lectures/topics-chapter.tex @@ -59,10 +59,6 @@ % figures: \setlength{\fboxsep}{0pt} -\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{#1.tex}}} -%\newcommand{\texpicture}[1]{\fbox{\sffamily\footnotesize\input{#1.tex}}} -%\newcommand{\texpicture}[1]{\setlength{\fboxsep}{2mm}\fbox{#1}} -%\newcommand{\texpicture}[1]{} \newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}} % maximum number of floats: diff --git a/replicability/lectures/topics-slides.tex b/replicability/lectures/topics-slides.tex index 295e684..157d1ab 100644 --- a/replicability/lectures/topics-slides.tex +++ b/replicability/lectures/topics-slides.tex @@ -50,7 +50,6 @@ %%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} -\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}} %%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{listings} diff --git a/statistics/lecture/statistics-slides.tex b/statistics/lecture/statistics-slides.tex index dc1af03..e143170 100644 --- a/statistics/lecture/statistics-slides.tex +++ b/statistics/lecture/statistics-slides.tex @@ -49,7 +49,6 @@ %%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} -\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}} %%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{listings} From 5e9ad55d1cea5848b36c1480a30048a259f6da06 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 27 Dec 2020 21:39:20 +0100 Subject: [PATCH 55/87] ideas for more chapters --- header.tex | 2 + pointprocesses/code/isiserialcorr.m | 1 - pointprocesses/lecture/pointprocesses.tex | 2 +- scientificcomputing-script.tex | 61 ++++++++++++++++++----- simulations/lecture/simulations.tex | 18 +++---- statistics/lecture/statistics-chapter.tex | 17 +++++-- 6 files changed, 73 insertions(+), 28 deletions(-) diff --git a/header.tex b/header.tex index a1b8961..464bb56 100644 --- a/header.tex +++ b/header.tex @@ -1,6 +1,8 @@ %%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title{\textbf{\huge\sffamily\tr{Introduction to\\[1ex] Scientific Computing}% {Einf\"uhrung in die\\[1ex] wissenschaftliche Datenverarbeitung}}} +%\title{\textbf{\huge\sffamily\tr{Scientific Computing for Neurobiologists}% +% {Wissenschaftliche Datenverarbeitung f\"ur Neurobiologen}}} \author{{\LARGE Jan Grewe \& Jan Benda}\\[5ex]Neuroethology Lab\\[2ex]% \includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}\vspace{3ex}} diff --git a/pointprocesses/code/isiserialcorr.m b/pointprocesses/code/isiserialcorr.m index e5b07fb..21bb474 100644 --- a/pointprocesses/code/isiserialcorr.m +++ b/pointprocesses/code/isiserialcorr.m @@ -32,4 +32,3 @@ function isicorr = isiserialcorr(isivec, maxlag) ylabel('\rho_k') end end - diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index 1cf796e..d25cf08 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -50,7 +50,7 @@ spike trains leads into the realm of the so called \entermde[point \end{itemize} \end{ibox} -\begin{figure}[t] +\begin{figure}[tb] \texpicture{pointprocessscetch} \titlecaption{\label{pointprocessscetchfig} Statistics of point processes.}{A point process is a sequence of instances in time diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 5bacd1b..64db445 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -39,8 +39,22 @@ \listofiboxfs +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \mainmatter +% add introduction: +% - data analysis skills way beyond basic statistical test are at the +% core of modern neuroscience +% - *understanding* of basic concepts of data analysis concepts is important +% - most concepts are also quite relevant for the brain itself! +% - modern approaches: +% * open source science (open data, open code, open algorithmns in contrast +% to closed source license models) +% * knowledge is freedom ... +% * do not consume what companies offer you but know what you want and implement it +% * python as a modern and popular programming language in modern science +% (i.e. machine learning, others?) with a strong community support. + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \part{Programming basics} @@ -57,10 +71,10 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \part{Data analysis} +%\part{Basic statistics} +% With an intro saying statistical tests are overrated! -% add chapter on simulations (draw random numbers, draw random functions, euler forward, odeint) -% !!! this would be a nice and simple starter !!! -% introduces derivatives which are also needed for fitting +% add chapter on stochastic simulations (draw random numbers, draw random functions) %\includechapter{simulations} \includechapter{statistics} @@ -71,32 +85,53 @@ \includechapter{regression} +% add chapter on nonlinear fitting (methods, initial values, local minima, power law fits on log-log data) + \includechapter{likelihood} -% add chapter on generalized linear models (versus ANOVA) +% add chapter on multivariate analysis/generalized linear models (in addition to ANOVA) -% add chapter on nonlinear fitting (methods, initial values, local minima, power law fits on log-log data) -\includechapter{pointprocesses} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\part{Time series} + +% add chapter on simulations of dynamical systems/time series (euler +% forward, odeint, iterated maps, dynamical system, bifurcations?) +% !!! this would be a nice and simple starter !!! +% introduces derivatives which are also needed for fitting % add chapter on time series (amplitude distribution, autocorrelation, crosscorrelation) %\includechapter{spectral} -% add chapter on filtering and envelopes +% add chapter on filtering (1. order, butter and kernel convolution) and envelopes -% add chapter on event detection, signal detection, ROC +% add chapter on event detection (local maxima, threshold crossings, +% peak detection), signal detection, ROC -% add chapter on mutual information +\includechapter{pointprocesses} -% add chapters on linear algebra, PCA, clustering, see linearalgebra/ +% add a chapter on simulating point-processes/spike trains +% (Poisson spike trains, integrate-and-fire models) + +% add chapter on information theory, mutual information, stimulus reconstruction, coherence + +% add a chapter on Bayesian inference (the Neuroscience of it and a +% bit of application for statistical problems). -% add chapter on simple machine learning %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\part{Machine learning} +% add chapters on linear algebra, PCA, clustering, see linearalgebra/ + +% add chapter on simple machine learning, perceptron + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\part{Tools} -% Latex -> see latex/ -% markdown, html + +% add chapter on Markup and LaTeX -> see latex/ +% with an introduction on mark-up in general, an outlook to markdown, html, xml, jason, yaml + % Makefile % distributed computing (ssh and grid engines) % diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index 6d69396..0c1d3d1 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -12,14 +12,14 @@ well controlled data sets that are free of confounding pecularities of real data sets. With simulated data we can also test our own analysis functions. More importantly, by means of simulations we can explore possible outcomes of our experiments before we even started the -experiment or we can explore possible results for regimes that we +experiment. We could even explore possible results for regimes that we cannot test experimentally. How dynamical systems, like for example -predator-prey interactions or the activity of neurons, evolve in time -is a central application for simulations. Computers becoming available -from the second half of the twentieth century on pushed the exciting -field of nonlinear dynamical systems forward. Conceptually, many kinds -of simulations are very simple and are implemented in a few lines of -code. +predator-prey interactions or the activity of neurons or whole brains, +evolve in time is a central application for simulations. The advent of +computers at the second half of the twentieth century pushed the +exciting field of nonlinear dynamical systems forward. Conceptually, +many kinds of simulations are very simple and are implemented in a few +lines of code. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Random numbers} @@ -83,8 +83,8 @@ given distribution like, for example, the normal distribution. This simulates repeated measurements of some quantity (e.g., weight of tigers or firing rate of neurons). Doing so we must specify from which probability distribution the data should originate from and what are -the parameters (mean, standard deviation, shape parameters, etc.) -that distribution. How to illuastrate and quantify univariate data, no +the parameters of that distribution (mean, standard deviation, shape +parameters, ...). How to illustrate and quantify univariate data, no matter whether they have been actually measured or whether they have been simulated as described in the following, is described in chapter~\ref{descriptivestatisticschapter}. diff --git a/statistics/lecture/statistics-chapter.tex b/statistics/lecture/statistics-chapter.tex index 84833c0..c8edb4b 100644 --- a/statistics/lecture/statistics-chapter.tex +++ b/statistics/lecture/statistics-chapter.tex @@ -20,12 +20,21 @@ \section{TODO} \begin{itemize} -\item The content of this lecture easily covers two lectures! -\item 1. mymedian and debugging, rolling a die, normalized histogram -\item 2. densities, quantiles, cumulative distribution, kernel histogram -\item Adapt the exercises to that! +\item Statistics is to estimate some parameter from data (see below). +\item Introduce this concept on a range of examples: mean, other + parameters of a distribution, parameters of a function. +\item This is also what the brain needs to do: estimate some + information about the environment from noisy/incomplete data! \end{itemize} +\section{Exercises} +The content of this lecture easily covers two lectures! +\begin{enumerate} +\item mymedian and debugging, rolling a die, normalized histogram +\item densities, quantiles, cumulative distribution, kernel histogram +\end{enumerate} + Adapt the exercises to that! + \end{document} From a50cc4ff7b170ae239ff9a49495b2f6a5192ea81 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 27 Dec 2020 23:15:19 +0100 Subject: [PATCH 56/87] [simulations] added exponential distribution --- pointprocesses/lecture/pointprocesses.tex | 1 + simulations/code/exprandom.m | 8 +++ simulations/code/exprandom.out | 3 ++ simulations/code/probability.m | 6 +++ simulations/code/probability.out | 1 + simulations/lecture/simulations.tex | 63 +++++++++++++++++++++-- 6 files changed, 77 insertions(+), 5 deletions(-) create mode 100644 simulations/code/exprandom.m create mode 100644 simulations/code/exprandom.out create mode 100644 simulations/code/probability.m create mode 100644 simulations/code/probability.out diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index d25cf08..5849a9a 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -1,6 +1,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Spiketrain analysis} +\label{pointprocesseschapter} \exercisechapter{Spiketrain analysis} \entermde[action potential]{Aktionspotential}{Action potentials} diff --git a/simulations/code/exprandom.m b/simulations/code/exprandom.m new file mode 100644 index 0000000..6e20a9b --- /dev/null +++ b/simulations/code/exprandom.m @@ -0,0 +1,8 @@ +n = 10000; +lambda = 50.0; % event rate +t = exprnd(1.0/lambda, n, 1); % exponentially distributed random numbers +m = mean(t); % mean time interval +s = std(t); % corresponding standard deviation +fprintf('Generated n=%d exponentially distributed random time intervals\n', n); +fprintf(' with rate=%.0fHz (-> mean=%.3fs, std=%.3fs)\n', lambda, 1.0/lambda, 1.0/lambda); +fprintf('Measured mean=%.3fs, std=%.3fs\n', m, s); diff --git a/simulations/code/exprandom.out b/simulations/code/exprandom.out new file mode 100644 index 0000000..2c91625 --- /dev/null +++ b/simulations/code/exprandom.out @@ -0,0 +1,3 @@ +Generated n=10000 exponentially distributed random time intervals + with rate=50Hz (-> mean=0.020s, std=0.020s) +Measured mean=0.020s, std=0.020s diff --git a/simulations/code/probability.m b/simulations/code/probability.m new file mode 100644 index 0000000..c7da8d4 --- /dev/null +++ b/simulations/code/probability.m @@ -0,0 +1,6 @@ +n = 20; % number of coin flips +P = 0.6; % probability of head +u = rand(n, 1); % n random numbers between 0 and 1 +heads = u < P; % true if head showed up +nheads = sum(heads); % number of heads +fprintf('Of %d coin flips, %d heads showed up.\n', n, nheads); diff --git a/simulations/code/probability.out b/simulations/code/probability.out new file mode 100644 index 0000000..8ae62ee --- /dev/null +++ b/simulations/code/probability.out @@ -0,0 +1 @@ +Of 20 coin flips, 12 heads showed up. diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index 0c1d3d1..15cb87f 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -38,7 +38,8 @@ generator!pseudo]{pseudo random number generators}. In rare cases this periodicity can induce problems in simulations whenever more random numbers than the period of the random number generator are used. Luckily, nowadays the periods of random nunmber generators are -very large, $2^{64}$, $2^{128}$, or even larger. +very large. Periods are at least in the range of $2^{64}$, that is +about $10^{18}$, or even larger. The pseudo randomness of numerical random number generators also has an advantage. They allow to repeat exactly the same sequence of @@ -124,15 +125,66 @@ mean we just add the desired mean $\mu$ to the random numbers: \end{exercise} \subsection{Other probability densities} -\code{rand()} -gamma +We can draw random numbers not only from normal +distributions. Functions are provided that let you draw random numbers +of almost any probability distribution. They differ in their shape and +in the number of parameters they have. Most probability distributions +are parameterized by a location parameter that usually coincides with +their mean, and a scale parameter that often coincides with their +standard deviation. Some distributions have additional shape +parameters. + +For example, the time intervals $t$ between randomly generated action +potentials (a so called Poisson spike train, see +chapter~\ref{pointprocesseschapter}) are exponentially distributed --- +as are the intervals between state transitions of ion channels, or the +intervals between radioactive decays. The exponential distribution is +only defined for positive time intervals: +\begin{equation} + \label{expdistribution} + p_{exp}(t) = \lambda e^{-\lambda t} \; , \quad t \ge 0, \; \lambda > 0 +\end{equation} +The exponential distribution is parameterized by a single rate +parameter $\lambda$ measured in Hertz. It defines how often per time +unit the event happens. Both the mean interval between the events and +the corresponding standard deviation equal the inverse rate. + +\begin{exercise}{exprandom.m}{exprandom.out} + Draw $n=10\,000$ random time intervals from an exponential + distribution with rate $\lambda=50$\,Hz. Calculate the mean and the + standard deviation of the random numbers and compare them with the + expected values. +\end{exercise} + +The gamma distribution (\code{gamrnd()}) phenomenologically describes +various types of interspike interval dsitributions +(chapter~\ref{pointprocesseschapter}). scale and shape. exercise. + + \code{rand()} between xmin +and xmax. + +\subsection{Simulating probabilities} +Simulating events that happen with some probability $P$ is also +possible. That could be the probability of head showing up when +flipping a coin, getting an action potential within some time, a ion +channel to open, ... For this draw a random number $u_i$ from a +uniform distribution between zero and one (\code{rand()}). If the +random number is lower than $P$, the event happens, if it is larger +the event does not occur. + +\begin{exercise}{probability.m}{probability.out} + Let's flip a coin 20 times. The coin is biased and shows head with a + probability of $P=0.6$. Count the number of heads. +\end{exercise} \subsection{Random integers} \code{randi()} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Bivariate data and static nonlinearities} +\section{Bivariate data} + +\subsection{Static nonlinearities} \begin{figure}[t] \includegraphics[width=1\textwidth]{staticnonlinearity} @@ -147,7 +199,8 @@ gamma Example: mechanotransduciton! -draw (and plot) random functions (in statistics chapter?) +draw (and plot) random functions. + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Dynamical systems} From d50b0be404b60464f3f8bac7db54cac3390094c1 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 28 Dec 2020 20:36:59 +0100 Subject: [PATCH 57/87] [simulations] added uniform distribution --- simulations/code/exprandom.m | 16 +++--- simulations/code/exprandom.out | 6 +- simulations/code/unirandom.m | 16 ++++++ simulations/code/unirandom.out | 3 + simulations/lecture/simulations.tex | 88 ++++++++++++++++++++--------- 5 files changed, 92 insertions(+), 37 deletions(-) create mode 100644 simulations/code/unirandom.m create mode 100644 simulations/code/unirandom.out diff --git a/simulations/code/exprandom.m b/simulations/code/exprandom.m index 6e20a9b..be9c5a3 100644 --- a/simulations/code/exprandom.m +++ b/simulations/code/exprandom.m @@ -1,8 +1,8 @@ -n = 10000; -lambda = 50.0; % event rate -t = exprnd(1.0/lambda, n, 1); % exponentially distributed random numbers -m = mean(t); % mean time interval -s = std(t); % corresponding standard deviation -fprintf('Generated n=%d exponentially distributed random time intervals\n', n); -fprintf(' with rate=%.0fHz (-> mean=%.3fs, std=%.3fs)\n', lambda, 1.0/lambda, 1.0/lambda); -fprintf('Measured mean=%.3fs, std=%.3fs\n', m, s); +n = 200; % number of time intervals +rate = 50.0; % event rate +t = exprnd(1.0/rate, n, 1); % exponentially distributed intervals +m = mean(t); % mean time interval +s = std(t); % corresponding standard deviation +fprintf('Generated n=%d random time intervals with rate=%.0fHz:\n', n, rate); +fprintf(' Expected mean interval=%.3fs, std=%.3fs\n', 1.0/rate, 1.0/rate); +fprintf(' Measured mean interval=%.3fs, std=%.3fs\n', m, s); diff --git a/simulations/code/exprandom.out b/simulations/code/exprandom.out index 2c91625..7053ee8 100644 --- a/simulations/code/exprandom.out +++ b/simulations/code/exprandom.out @@ -1,3 +1,3 @@ -Generated n=10000 exponentially distributed random time intervals - with rate=50Hz (-> mean=0.020s, std=0.020s) -Measured mean=0.020s, std=0.020s +Generated n=200 random time intervals with rate=50Hz: + Expected mean interval=0.020s, std=0.020s + Measured mean interval=0.020s, std=0.019s diff --git a/simulations/code/unirandom.m b/simulations/code/unirandom.m new file mode 100644 index 0000000..0c6f1fb --- /dev/null +++ b/simulations/code/unirandom.m @@ -0,0 +1,16 @@ +n = 10000; % number of action potentials +T = 100.0; % total time interval +spikes = sort(T*rand(n, 1)); % sorted times of action potentials +isis = diff(spikes); % interspike intervals +rate = n/T; % firing rate +misi = mean(isis); % mean interspike interval +sisi = std(isis); % and standard deviation +fprintf('firing rate = %.1fHz\n', rate); +fprintf(' mean ISI = %.1fms\n', 1000.0*misi); % inverse of rate +fprintf(' std ISI = %.1fms\n', 1000.0*sisi); % same as mean +hist(1000.0*isis, 50); % exponential distribution +xlabel('ISI [ms]'); +ylabel('count'); + + + diff --git a/simulations/code/unirandom.out b/simulations/code/unirandom.out new file mode 100644 index 0000000..4abe24c --- /dev/null +++ b/simulations/code/unirandom.out @@ -0,0 +1,3 @@ +firing rate = 100.0Hz + mean ISI = 10.0ms + std ISI = 10.0ms diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index 15cb87f..c4dbfa1 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -79,24 +79,28 @@ script is run. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Univariate data} -The most basic type of simulation is to draw random numbers from a -given distribution like, for example, the normal distribution. This -simulates repeated measurements of some quantity (e.g., weight of -tigers or firing rate of neurons). Doing so we must specify from which +A basic type of stochastic simulations is to draw random numbers from +a given distribution like, for example, the normal distribution. This +simulates repeated measurements of some quantity (weight of tigers, +firing rate of neurons). Doing so we must specify from which probability distribution the data should originate from and what are the parameters of that distribution (mean, standard deviation, shape -parameters, ...). How to illustrate and quantify univariate data, no -matter whether they have been actually measured or whether they have -been simulated as described in the following, is described in +parameters). How to illustrate and quantify univariate data, no matter +whether they have been actually measured or whether they have been +simulated as described in the following, is described in chapter~\ref{descriptivestatisticschapter}. \subsection{Normally distributed data} -For drawing numbers $x_i$ from a normal distribution we use the -\code{randn()} function. This function returns normally distributed -numbers $\xi_i$ with zero mean and unit standard deviation. For -changing the standard deviation we need to multiply the returned data -values with the required standard deviation $\sigma$. For changing the -mean we just add the desired mean $\mu$ to the random numbers: +For drawing numbers from a normal distribution +\begin{equation} + p_{norm}(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2} +\end{equation} +with zero mean and unit standard deviation we use the \code{randn()} +function. This function returns normally distributed numbers $\xi_i$ +with zero mean and unit standard deviation. For changing the standard +deviation we need to multiply the returned data values with the +required standard deviation $\sigma$. For changing the mean we just +add the desired mean $\mu$ to the random numbers: \begin{equation} x_i = \sigma \xi_i + \mu \end{equation} @@ -144,24 +148,44 @@ only defined for positive time intervals: \label{expdistribution} p_{exp}(t) = \lambda e^{-\lambda t} \; , \quad t \ge 0, \; \lambda > 0 \end{equation} -The exponential distribution is parameterized by a single rate -parameter $\lambda$ measured in Hertz. It defines how often per time -unit the event happens. Both the mean interval between the events and -the corresponding standard deviation equal the inverse rate. +A single rate parameter $\lambda$ measured in Hertz parameterizes the +exponential distribution. It defines how often per time unit the event +happens. Both the mean interval between the events and the +corresponding standard deviation equal the inverse rate. \begin{exercise}{exprandom.m}{exprandom.out} - Draw $n=10\,000$ random time intervals from an exponential - distribution with rate $\lambda=50$\,Hz. Calculate the mean and the - standard deviation of the random numbers and compare them with the - expected values. + Draw $n=200$ random time intervals from an exponential distribution + with rate $\lambda=50$\,Hz. Calculate the mean and the standard + deviation of the random numbers and compare them with the expected + values. \end{exercise} -The gamma distribution (\code{gamrnd()}) phenomenologically describes -various types of interspike interval dsitributions -(chapter~\ref{pointprocesseschapter}). scale and shape. exercise. +The \code{rand()} function returns uniformly distributed random +numbers between zero and one +\begin{equation} + p_{uni}(x) = \left\{\begin{array}{rcl} 1 & ; & 0 \le x < 1 \\ + 0 & ; & \text{else} \end{array}\right. +\end{equation} +For random numbers $x_i$ uniformly distributed between $x_{\rm min}$ +and $x_{\rm max}$ we multiply by the desired range $x_{\rm max} - +x_{\rm min}$ and add $x_{\rm min}$ to the numbers $u_i$ returned by +\code{rand()}: +\begin{equation} + x_i = (x_{\rm max} - x_{\rm min}) u_i + x_{\rm min} +\end{equation} + +\begin{exercise}{unirandom.m}{unirandom.out} + Simulate the times of $n=10\,000$ action potentials occuring + randomly within a time interval of 100\,s using the \code{rand()} + function. Sort the times using \code{sort()}, compute the time + intervals between the action potentials (interspike intervals, ISIs) + using the \code{diff()} function, plot a histogram of the interspike + intervals in milliseconds, and compute the mean and standard + deviation of the interspike intervals, also in milliseconds. Compare + the mean ISI with the firing rate (number of action potentials per + time). +\end{exercise} - \code{rand()} between xmin -and xmax. \subsection{Simulating probabilities} Simulating events that happen with some probability $P$ is also @@ -177,6 +201,18 @@ the event does not occur. probability of $P=0.6$. Count the number of heads. \end{exercise} +Random walk! Have a figure with a few 1D random walks and the +increasing standard deviation as a sheded area behind. + + + + + + +The gamma distribution (\code{gamrnd()}) phenomenologically describes +various types of interspike interval dsitributions +(chapter~\ref{pointprocesseschapter}). scale and shape. exercise. + \subsection{Random integers} \code{randi()} From 7b61bd1e85391bd40e8e5e220b9c88d065e0ad54 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 28 Dec 2020 21:20:09 +0100 Subject: [PATCH 58/87] [simulations] added random walk --- scientificcomputing-script.tex | 4 +++ simulations/lecture/simulations.tex | 39 +++++++++++++++++++++++++++-- 2 files changed, 41 insertions(+), 2 deletions(-) diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 64db445..ee064c9 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -46,6 +46,10 @@ % - data analysis skills way beyond basic statistical test are at the % core of modern neuroscience % - *understanding* of basic concepts of data analysis concepts is important +% - math is the universal language of natural sciences, including neuroscience. +% it is the most precise way to express relation. +% We therefore expose you to some mathematical equations +% that do not go beyond what you learned at school. % - most concepts are also quite relevant for the brain itself! % - modern approaches: % * open source science (open data, open code, open algorithmns in contrast diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index c4dbfa1..7f91e19 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -160,6 +160,13 @@ corresponding standard deviation equal the inverse rate. values. \end{exercise} + +\subsection{Uniformly distributed random numbers} + +\begin{figure}[t] + Exponential distribution of ISIs. +\end{figure} + The \code{rand()} function returns uniformly distributed random numbers between zero and one \begin{equation} @@ -201,12 +208,40 @@ the event does not occur. probability of $P=0.6$. Count the number of heads. \end{exercise} -Random walk! Have a figure with a few 1D random walks and the -increasing standard deviation as a sheded area behind. +\subsection{Random walks} +A basic concept for stochastic models is the random walk. A walker +starts at some initial position $x_0$. It then takes steps to the +right, $x_n = x_{n-1} + 1$, with some probability $P_r$ or to the +left, $x_n = x_{n-1} - 1$, with probability $P_l = 1-P_r$. +For a symmetric random walk, the probabilities to step to the left or +to the right are the same, $P_r = P_l = \frac{1}{2}$. The average +position of many walkers is then independent of the iteration step and +equals the initial position $x_0$. The standard deviation of the +walker positions, however, grows with the square root of the number of +iteration steps $n$: $\sigma_{x_n} = \sqrt{n}$. +\begin{figure}[tb] + Have a figure with a few 1D random walks and the increasing standard + deviation as a shaded area behind. And with absorbing boundary. +\end{figure} +The sub-threshold membrane potential of a neuron can be modeled as a +one-dimensional random walk. The thousands of excitatory and +inhibitory synaptic inputs of a principal neuron in the brain make the +membrane potential to randomly step upwards or downwards. Once the +membrane potential hits a firing threshold an action potential is +generated and the membrane potential is reset to the resting +potential. The firing threshold in this context is often called an +``absorbing boundary''. The time it takes from the initial position to +cross the threshold is the ``first-passage time''. For neurons this is +the interspike interval. For symmetric random walks the first-passage +times are again exponentially distributed. ??? Is that so ??? + +% Gerstein and Mandelbrot 1964 + +Higher dimensions, Brownian motion. The gamma distribution (\code{gamrnd()}) phenomenologically describes From 2bac236768fc484b952dbe7d4574864fd7fa622b Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 29 Dec 2020 19:01:23 +0100 Subject: [PATCH 59/87] [simulations] added random walk figures --- plotstyle.py | 2 +- simulations/lecture/randomwalkone.py | 34 +++++++ simulations/lecture/randomwalktwo.py | 37 +++++++ simulations/lecture/simulations.tex | 146 +++++++++++++++------------ 4 files changed, 155 insertions(+), 64 deletions(-) create mode 100644 simulations/lecture/randomwalkone.py create mode 100644 simulations/lecture/randomwalktwo.py diff --git a/plotstyle.py b/plotstyle.py index ecada61..694bdb0 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -22,7 +22,7 @@ colors['orange'] = '#FF9900' colors['lightorange'] = '#FFCC00' colors['yellow'] = '#FFF720' colors['green'] = '#99FF00' -colors['blue'] = '#0010CC' +colors['blue'] = '#0020BB' colors['gray'] = '#A7A7A7' colors['black'] = '#000000' colors['white'] = '#FFFFFF' diff --git a/simulations/lecture/randomwalkone.py b/simulations/lecture/randomwalkone.py new file mode 100644 index 0000000..6fec50f --- /dev/null +++ b/simulations/lecture/randomwalkone.py @@ -0,0 +1,34 @@ +import numpy as np +import matplotlib.pyplot as plt +from plotstyle import * + +def random_walk(n, p, rng): + steps = rng.rand(n) + steps[steps>=p] = 1 + steps[steps=0*p)&(steps<1*p)] = +1 + xsteps[(steps>=1*p)&(steps<2*p)] = -1 + ysteps[(steps>=2*p)&(steps<3*p)] = +1 + ysteps[(steps>=3*p)&(steps<4*p)] = -1 + x = np.hstack(((0.0,), np.cumsum(xsteps))) + y = np.hstack(((0.0,), np.cumsum(ysteps))) + return x, y + +if __name__ == "__main__": + fig, ax = plt.subplots(figsize=cm_size(figure_width, 0.65*figure_width)) + fig.subplots_adjust(**adjust_fs(fig, right=1.0)) + rng = np.random.RandomState(42281) + nmax = 500 + lcs = [colors['blue'], colors['red'], colors['orange'], + colors['yellow'], colors['green']] + for k in range(len(lcs)): + x, y = random_walk(nmax, rng) + ls = dict(**lsAm) + ls['color'] = lcs[k%len(lcs)] + ax.plot(x, y, **ls) + ax.set_xlabel('Position $x_n$') + ax.set_ylabel('Position $y_n$') + ax.set_xlim(-30, 30) + ax.set_ylim(-20, 20) + ax.set_xticks(np.arange(-30, 31, 10)) + ax.set_yticks(np.arange(-20, 21, 10)) + fig.savefig("randomwalktwo.pdf") + plt.close() diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index 7f91e19..4c7cdac 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -1,8 +1,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\chapter{Simulations} -\label{simulationschapter} -\exercisechapter{Simulations} +\chapter{Stochastic simulations} +\label{stochasticsimulationschapter} +\exercisechapter{Stochastic simulations} The real power of computers for data analysis is the possibility to run simulations. Experimental data of almost unlimited sample sizes @@ -23,23 +23,37 @@ lines of code. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Random numbers} + +\begin{figure}[t] + \includegraphics{randomnumbers} + \titlecaption{\label{randomnumbersfig} Random numbers.} {Numerical + random number generators return sequences of numbers that are as + random as possible. The returned values approximate a given + probability distribution. Here, for example, a uniform + distribution between zero and one (top left). The serial + correlation (auto-correlation) of the returned sequences is zero + at any lag except for zero (bottom left). However, by setting a + seed, defining the state, or spawning the random number generator, + the exact same sequence can be generated (right).} +\end{figure} + At the heart of many simulations are random numbers that we get from \enterm[random number generator]{random number generators}. These are numerical algorithms that return sequences of numbers that appear to -be as random as possible. If we draw random numbers using, for -example, the \code{rand()} function, then these numbers are indeed -uniformly distributed and have a mean of one half. Subsequent numbers -are independent of each other, i.e. the autocorrelation function is -zero everywhere except at lag zero. However, numerical random number -generators have a period, after which they repeat the exact same -sequence of numbers. This differentiates them from truely random -numbers and hence they are called \enterm[random number -generator!pseudo]{pseudo random number generators}. In rare cases this -periodicity can induce problems in simulations whenever more random -numbers than the period of the random number generator are -used. Luckily, nowadays the periods of random nunmber generators are -very large. Periods are at least in the range of $2^{64}$, that is -about $10^{18}$, or even larger. +be as random as possible (\figref{randomnumbersfig}). If we draw +random numbers using, for example, the \code{rand()} function, then +these numbers are indeed uniformly distributed and have a mean of one +half. Subsequent numbers are independent of each other, i.e. the +autocorrelation function is zero everywhere except at lag +zero. However, numerical random number generators have a period, after +which they repeat the exact same sequence of numbers. This +differentiates them from truely random numbers and hence they are +called \enterm[random number generator!pseudo]{pseudo random number + generators}. In rare cases this periodicity can induce problems in +simulations whenever more random numbers than the period of the random +number generator are used. Luckily, nowadays the periods of random +nunmber generators are very large. Periods are at least in the range +of $2^{64}$, that is about $10^{18}$, or even larger. The pseudo randomness of numerical random number generators also has an advantage. They allow to repeat exactly the same sequence of @@ -64,19 +78,6 @@ script is run. the sequence. This is the serial correlation at lag one. \end{exercise} -\begin{figure}[t] - \includegraphics[width=1\textwidth]{randomnumbers} - \titlecaption{\label{randomnumbersfig} Random numbers.} {Numerical - random number generators return sequences of numbers that are as - random as possible. The returned values approximate a given - probability distribution. Here, for example, a uniform - distribution between zero and one (top left). The serial - correlation (auto-correlation) of the returned sequences is zero - at any lag except for zero (bottom left). However, by setting a - seed, defining the state, or spawning the random number generator, - the exact same sequence can be generated (right).} -\end{figure} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Univariate data} A basic type of stochastic simulations is to draw random numbers from @@ -91,6 +92,18 @@ simulated as described in the following, is described in chapter~\ref{descriptivestatisticschapter}. \subsection{Normally distributed data} + +\begin{figure}[t] + \includegraphics{normaldata} + \titlecaption{\label{normaldatafig} Generating normally distributed + data.}{With the help of a computer the weight of 300 tigers can be + measured in no time using the \code{randn()} function (left). By + construction we then even know the population distribution (red + line, right), its mean (here 220\,kg) and standard deviation + (40\,kg) from which the simulated data values were drawn (yellow + histogram).} +\end{figure} + For drawing numbers from a normal distribution \begin{equation} p_{norm}(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2} @@ -100,22 +113,12 @@ function. This function returns normally distributed numbers $\xi_i$ with zero mean and unit standard deviation. For changing the standard deviation we need to multiply the returned data values with the required standard deviation $\sigma$. For changing the mean we just -add the desired mean $\mu$ to the random numbers: +add the desired mean $\mu$ to the random numbers +(\figref{normaldatafig}): \begin{equation} x_i = \sigma \xi_i + \mu \end{equation} -\begin{figure}[t] - \includegraphics[width=1\textwidth]{normaldata} - \titlecaption{\label{normaldatafig} Generating normally distributed - data.}{With the help of a computer the weight of 300 tigers can be - measured in no time using the \code{randn()} function (left). By - construction we then even know the population distribution (red - line, right), its mean (here 220\,kg) and standard deviation - (40\,kg) from which the simulated data values were drawn (yellow - histogram).} -\end{figure} - \begin{exercise}{normaldata.m}{normaldata.out} Write a little script that generates $n=100$ normally distributed data simulating the weight of Bengal tiger males with mean 220\,kg @@ -211,37 +214,54 @@ the event does not occur. \subsection{Random walks} A basic concept for stochastic models is the random walk. A walker -starts at some initial position $x_0$. It then takes steps to the -right, $x_n = x_{n-1} + 1$, with some probability $P_r$ or to the -left, $x_n = x_{n-1} - 1$, with probability $P_l = 1-P_r$. - -For a symmetric random walk, the probabilities to step to the left or -to the right are the same, $P_r = P_l = \frac{1}{2}$. The average -position of many walkers is then independent of the iteration step and -equals the initial position $x_0$. The standard deviation of the -walker positions, however, grows with the square root of the number of -iteration steps $n$: $\sigma_{x_n} = \sqrt{n}$. +starts at some initial position $x_0$. At every iteration $n$ it takes +a step $\delta_n$: $x_n = x_{n-1} + \delta_n$. The walker either steps +to the right ($\delta_n = +1$) with some probability $P_r$ or to the +left ($\delta_n = -1$) with probability $P_l = 1-P_r$. + +For a symmetric random walk (\figref{randomwalkonefig}), the +probabilities to step to the left or to the right are the same, $P_r = +P_l = \frac{1}{2}$. The average position of many walkers is then +independent of the iteration step and equals the initial position +$x_0$. The variance of each step is $\sigma_{\delta_n} = 1$. Since +each step is independent of the steps before, the variances of each +step add up such that the total variance of the walker position at +step $n$ equals $\sigma_{x_n}^2 = n$. The standard deviation of the +walker positions grows with the square root of the number of iteration +steps $n$: $\sigma_{x_n} = \sqrt{n}$. \begin{figure}[tb] - Have a figure with a few 1D random walks and the increasing standard - deviation as a shaded area behind. And with absorbing boundary. + \includegraphics{randomwalkone} + \titlecaption{\label{randomwalkonefig} Random walk in one + dimension.}{Twelve symmetric random walks starting at $x_0=0$. The + ensemble average of the position of the random walkers is zero + (blue line) and the standard deviation increases with the square + root of the number of steps taken (shaded area).} \end{figure} The sub-threshold membrane potential of a neuron can be modeled as a one-dimensional random walk. The thousands of excitatory and inhibitory synaptic inputs of a principal neuron in the brain make the membrane potential to randomly step upwards or downwards. Once the -membrane potential hits a firing threshold an action potential is -generated and the membrane potential is reset to the resting -potential. The firing threshold in this context is often called an -``absorbing boundary''. The time it takes from the initial position to -cross the threshold is the ``first-passage time''. For neurons this is -the interspike interval. For symmetric random walks the first-passage +membrane potential hits a threshold an action potential is generated +and the membrane potential is reset to the resting potential. The +threshold in this context is often called an ``absorbing +boundary''. The time it takes from the initial position to cross the +threshold is the ``first-passage time''. For neurons this is the +interspike interval. For symmetric random walks the first-passage times are again exponentially distributed. ??? Is that so ??? % Gerstein and Mandelbrot 1964 -Higher dimensions, Brownian motion. +Higher dimensions (\figref{randomwalktwofig}), Brownian motion. Crystal growth. + +\begin{figure}[tb] + \includegraphics{randomwalktwo} + \titlecaption{\label{randomwalktwofig} Random walk in two + dimensions.}{Fivehundred steps of five random walkers that in each + iteration take a step either up, down, to the left, or to the + right.} +\end{figure} The gamma distribution (\code{gamrnd()}) phenomenologically describes @@ -258,7 +278,7 @@ various types of interspike interval dsitributions \subsection{Static nonlinearities} \begin{figure}[t] - \includegraphics[width=1\textwidth]{staticnonlinearity} + \includegraphics{staticnonlinearity} \titlecaption{\label{staticnonlinearityfig} Generating data fluctuating around a function.}{The conductance of the mechontransducer channels in hair cells of the inner ear is a @@ -268,7 +288,7 @@ various types of interspike interval dsitributions distributed (right, red line).} \end{figure} -Example: mechanotransduciton! +Example: mechanotransduciton! (\figref{staticnonlinearityfig}) draw (and plot) random functions. From 16aa2b8f4b987843799717600c341fdd2a92463f Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 29 Dec 2020 23:45:46 +0100 Subject: [PATCH 60/87] [simulations] added random walk neuron figures --- plotstyle.py | 2 + simulations/lecture/randomwalkneuron.py | 58 ++++++++++++++ simulations/lecture/randomwalkone.py | 32 +++++--- simulations/lecture/randomwalktwo.py | 1 + simulations/lecture/simulations.tex | 100 ++++++++++++++++-------- 5 files changed, 150 insertions(+), 43 deletions(-) create mode 100644 simulations/lecture/randomwalkneuron.py diff --git a/plotstyle.py b/plotstyle.py index 694bdb0..5cbf30e 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -52,6 +52,8 @@ lsSpine = {'c': colors['black'], 'linestyle': '-', 'linewidth': 1, 'clip_on': Fa lsGrid = {'c': colors['gray'], 'linestyle': '--', 'linewidth': 1} lsMarker = {'c': colors['black'], 'linestyle': '-', 'linewidth': 2} +psMarker = dict({'color': colors['black'], 'linestyle': 'none'}, **largemarker) + # line (ls), point (ps), and fill styles (fs). # Each style is derived from a main color as indicated by the capital letter. diff --git a/simulations/lecture/randomwalkneuron.py b/simulations/lecture/randomwalkneuron.py new file mode 100644 index 0000000..da248ce --- /dev/null +++ b/simulations/lecture/randomwalkneuron.py @@ -0,0 +1,58 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.gridspec as gridspec +from plotstyle import * + +def random_walk(n, p, rng): + steps = rng.rand(n) + steps[steps>=1.0-p] = 1 + steps[steps<1.0-p] = -1 + x = np.hstack(((0.0,), np.cumsum(steps))) + return x + +def random_walk_neuron(n, p, thresh, rng): + x = random_walk(n, p, rng) + spikes = [] + j = -1 + i = 1 + while i > 0: + if j > 0: + spikes.append(j+i) + j += i + 1 + x[j:] -= x[j] + i = np.argmax(x[j:] >= thresh - 0.1) + return x, spikes + + +if __name__ == "__main__": + fig = plt.figure() + spec = gridspec.GridSpec(nrows=1, ncols=2, width_ratios=[2, 1], wspace=0.4, + **adjust_fs(fig, left=6.5, right=1.5)) + ax = fig.add_subplot(spec[0, 0]) + rng = np.random.RandomState(52281) + p = 0.6 + thresh = 10.0 + nmax = 500 + n = np.arange(0.0, nmax+1, 1.0) + x, spikes = random_walk_neuron(nmax, p, thresh, rng) + ax.axhline(0.0, **lsGrid) + ax.axhline(thresh, **lsAm) + ax.plot(n, x, **lsBm) + for tspike in spikes: + ax.plot([tspike, tspike], [12.0, 16.0], **lsC) + ax.set_xlabel('Time') + ax.set_ylabel('Potential') + ax.set_xlim(0, nmax) + ax.set_ylim(-10, 17) + ax.set_yticks(np.arange(-10, 11, 10)) + ax = fig.add_subplot(spec[0, 1]) + nmax = 100000 + x, spikes = random_walk_neuron(nmax, p, thresh, rng) + isis = np.diff(spikes) + ax.hist(isis, np.arange(0.0, 151.0, 10.0), **fsAs) + ax.set_xlabel('ISI') + ax.set_ylabel('Count') + ax.set_xticks(np.arange(0, 151, 50)) + ax.set_yticks(np.arange(0, 401, 100)) + fig.savefig("randomwalkneuron.pdf") + plt.close() diff --git a/simulations/lecture/randomwalkone.py b/simulations/lecture/randomwalkone.py index 6fec50f..9b4724a 100644 --- a/simulations/lecture/randomwalkone.py +++ b/simulations/lecture/randomwalkone.py @@ -4,31 +4,39 @@ from plotstyle import * def random_walk(n, p, rng): steps = rng.rand(n) - steps[steps>=p] = 1 - steps[steps=1.0-p] = 1 + steps[steps<1.0-p] = -1 x = np.hstack(((0.0,), np.cumsum(steps))) return x -if __name__ == "__main__": - fig, ax = plt.subplots() - fig.subplots_adjust(**adjust_fs(fig, right=1.0)) - rng = np.random.RandomState(52281) - nmax = 80 +def plot_random_walk(ax, nmax, p, rng, ymin=-20.0, ymax=20.0): nn = np.linspace(0.0, nmax, 200) - ax.fill_between(nn, np.sqrt(nn), -np.sqrt(nn), **fsAa) - ax.axhline(0.0, **lsAm) + m = 2*p-1 + v = 4*p*(1-p) + ax.fill_between(nn, m*nn+np.sqrt(nn*v), m*nn-np.sqrt(nn*v), **fsAa) + ax.plot([0.0, nmax], [0.0, m*nmax], **lsAm) lcs = [colors['red'], colors['orange'], colors['yellow'], colors['green']] n = np.arange(0.0, nmax+1, 1.0) for k in range(12): - x = random_walk(nmax, 0.5, rng) + x = random_walk(nmax, p, rng) ls = dict(**lsAm) ls['color'] = lcs[k%len(lcs)] ax.plot(n, x, **ls) ax.set_xlabel('Iteration $n$') ax.set_ylabel('Position $x_n$') ax.set_xlim(0, nmax) - ax.set_ylim(-20, 20) - ax.set_yticks(np.arange(-20, 21, 10)) + ax.set_ylim(ymin, ymax) + ax.set_yticks(np.arange(ymin, ymax+1.0, 10.0)) + + +if __name__ == "__main__": + fig, (ax1, ax2) = plt.subplots(2, 1, figsize=cm_size(figure_width, 2.0*figure_height)) + fig.subplots_adjust(**adjust_fs(fig, right=1.0)) + rng = np.random.RandomState(52281) + plot_random_walk(ax1, 80, 0.5, rng) + ax1.text(5.0, 20.0, 'symmetric', va='center') + plot_random_walk(ax2, 80, 0.6, rng, -10.0, 30.0) + ax2.text(5.0, 30.0, 'with drift', va='center') fig.savefig("randomwalkone.pdf") plt.close() diff --git a/simulations/lecture/randomwalktwo.py b/simulations/lecture/randomwalktwo.py index 39a58b9..79221d1 100644 --- a/simulations/lecture/randomwalktwo.py +++ b/simulations/lecture/randomwalktwo.py @@ -27,6 +27,7 @@ if __name__ == "__main__": ls = dict(**lsAm) ls['color'] = lcs[k%len(lcs)] ax.plot(x, y, **ls) + ax.plot([0], [0], **psMarker) ax.set_xlabel('Position $x_n$') ax.set_ylabel('Position $y_n$') ax.set_xlim(-30, 30) diff --git a/simulations/lecture/simulations.tex b/simulations/lecture/simulations.tex index 4c7cdac..f2deb1d 100644 --- a/simulations/lecture/simulations.tex +++ b/simulations/lecture/simulations.tex @@ -212,31 +212,69 @@ the event does not occur. \end{exercise} -\subsection{Random walks} -A basic concept for stochastic models is the random walk. A walker -starts at some initial position $x_0$. At every iteration $n$ it takes -a step $\delta_n$: $x_n = x_{n-1} + \delta_n$. The walker either steps -to the right ($\delta_n = +1$) with some probability $P_r$ or to the -left ($\delta_n = -1$) with probability $P_l = 1-P_r$. - -For a symmetric random walk (\figref{randomwalkonefig}), the -probabilities to step to the left or to the right are the same, $P_r = -P_l = \frac{1}{2}$. The average position of many walkers is then -independent of the iteration step and equals the initial position -$x_0$. The variance of each step is $\sigma_{\delta_n} = 1$. Since -each step is independent of the steps before, the variances of each -step add up such that the total variance of the walker position at -step $n$ equals $\sigma_{x_n}^2 = n$. The standard deviation of the -walker positions grows with the square root of the number of iteration -steps $n$: $\sigma_{x_n} = \sqrt{n}$. +The gamma distribution (\code{gamrnd()}) phenomenologically describes +various types of interspike interval dsitributions +(chapter~\ref{pointprocesseschapter}). scale and shape. exercise. + +\subsection{Random integers} +\code{randi()} + + +\section{Random walks} +A basic concept for stochastic models is the \enterm{random walk}. A +walker starts at some initial position $x_0$. At every iteration $n$ +it takes a step $\delta_n$: $x_n = x_{n-1} + \delta_n$. The walker +either steps to the right ($\delta_n = +1$) with some probability $p$ +or to the left ($\delta_n = -1$) with probability $q = 1-p$. \begin{figure}[tb] \includegraphics{randomwalkone} \titlecaption{\label{randomwalkonefig} Random walk in one - dimension.}{Twelve symmetric random walks starting at $x_0=0$. The - ensemble average of the position of the random walkers is zero - (blue line) and the standard deviation increases with the square - root of the number of steps taken (shaded area).} + dimension.}{Twelve random walks starting at $x_0=0$. The ensemble + average of the position of the random walkers marked by the blue + line and the corresponding standard deviation by the shaded + area. The standard deviation increases with the square root of the + number of steps taken. The top plot shows a symmetric random walk + where the probability of a step to the right equals the one for a + step to the left ($p=q=\frac{1}{2}$). The bottom plot shows a + random walk with drift. Here the probability of taking a step to + the right ($p=0.6$) is larger than the probability for a step to + the left ($q=0.4$).} +\end{figure} + +For a \enterm[random walk!symmetric]{symmetric random walk} +(\figref{randomwalkonefig} top), the probabilities for a step to the +left or to the right are the same, $p = q = \frac{1}{2}$. The average +position of many walkers is then independent of the iteration step and +equals the initial position $x_0$. The variance of each step is +$\sigma_{\delta_n}^2 = p \cdot 1^2 + q \cdot(-1)^2 = 1$. Since each +step is independent of the steps before, the variances of all the +steps add up such that the total variance of the walker position at +step $n$ equals $\sigma_{x_n}^2 = \sum_{i=1}^n \sigma_{\delta_n}^2 = +n$. The standard deviation of the walker positions grows with the +square root of the number of iteration steps $n$: $\sigma_{x_n} = +\sqrt{n}$. + +\enterm[random walk!with drift]{Random walks with drift} are biased to +one direction (\figref{randomwalkonefig} bottom). The probability to +step to the left does not equal the probability to step to the right, +$p \ne q$. Consequently, the average step is no longer zero. Instead +it equals $\mu_{\delta_n} = p \cdot 1 + q \cdot (-1) = 2p - 1$. The +average position grows proportional to the number of iterations: +$\mu_{x_n} = n(2p - 1)$. The variance of each step turns out to be +$\sigma_{\delta_n}^2 = 4pq$ (this indeed equals one for +$p=q=\frac{1}{2}$). Again, because of the independence of the steps, +the variance of the position at the $n$-th iteration, $\sigma_{x_n}^2 += 4pqn$, is proportional to $n$ and the standard deviation, +$\sigma_{x_n} = 2\sqrt{pqn}$, grows with the square root of $n$. + +\begin{exercise}{}{} + Random walk exercise. +\end{exercise} + +\begin{figure}[tb] + \includegraphics{randomwalkneuron} + \titlecaption{\label{randomwalkneuronfig} Random walk spiking neuron.}{.} \end{figure} The sub-threshold membrane potential of a neuron can be modeled as a @@ -253,23 +291,23 @@ times are again exponentially distributed. ??? Is that so ??? % Gerstein and Mandelbrot 1964 -Higher dimensions (\figref{randomwalktwofig}), Brownian motion. Crystal growth. +\begin{exercise}{}{} + Random walk neuron exercise. +\end{exercise} \begin{figure}[tb] \includegraphics{randomwalktwo} \titlecaption{\label{randomwalktwofig} Random walk in two - dimensions.}{Fivehundred steps of five random walkers that in each - iteration take a step either up, down, to the left, or to the - right.} + dimensions.}{Fivehundred steps of five random walkers starting at + the origin (black dot) and taking steps of distance one either up, + down, to the left, or to the right with equal probability.} \end{figure} +Higher dimensions (\figref{randomwalktwofig}), Brownian motion. Crystal growth. -The gamma distribution (\code{gamrnd()}) phenomenologically describes -various types of interspike interval dsitributions -(chapter~\ref{pointprocesseschapter}). scale and shape. exercise. - -\subsection{Random integers} -\code{randi()} +\begin{exercise}{}{} + Random walk in 2D exercise. +\end{exercise} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% From 2a65c1c1cc151014b35703a0dac0cc0b05330099 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 2 Jan 2021 12:02:11 +0100 Subject: [PATCH 61/87] added a few more general notes --- regression/lecture/regression-chapter.tex | 2 ++ scientificcomputing-script.tex | 13 ++++++++----- 2 files changed, 10 insertions(+), 5 deletions(-) diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index cfc984b..05c049a 100644 --- a/regression/lecture/regression-chapter.tex +++ b/regression/lecture/regression-chapter.tex @@ -21,6 +21,8 @@ \subsection{Notes} \begin{itemize} \item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom! +\item Gradient ascent is used by bacteria and worms (and others) to + approach food sources along chemical and temperature gradients (using biased random walks). \end{itemize} \subsection{New chapter: non-linear fits} diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index ee064c9..8df08d8 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -51,9 +51,10 @@ % We therefore expose you to some mathematical equations % that do not go beyond what you learned at school. % - most concepts are also quite relevant for the brain itself! +% The brain also needs to analyse the data coming in from the senses. % - modern approaches: % * open source science (open data, open code, open algorithmns in contrast -% to closed source license models) +% to closed source license models), FAIR % * knowledge is freedom ... % * do not consume what companies offer you but know what you want and implement it % * python as a modern and popular programming language in modern science @@ -75,7 +76,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \part{Data analysis} -%\part{Basic statistics} +%\subpart{Basic statistics} % With an intro saying statistical tests are overrated! % add chapter on stochastic simulations (draw random numbers, draw random functions) @@ -97,7 +98,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\part{Time series} +%\subpart{Time series} % add chapter on simulations of dynamical systems/time series (euler % forward, odeint, iterated maps, dynamical system, bifurcations?) @@ -124,7 +125,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\part{Machine learning} +%\subpart{Machine learning} % add chapters on linear algebra, PCA, clustering, see linearalgebra/ @@ -135,6 +136,7 @@ % add chapter on Markup and LaTeX -> see latex/ % with an introduction on mark-up in general, an outlook to markdown, html, xml, jason, yaml +% make notes, data, and texts understandable by computers! % Makefile % distributed computing (ssh and grid engines) @@ -142,7 +144,8 @@ % see replicability/ : % version control (git and github) only put source files into repository! % data handling (structure, storage (rsync), backup, data bases) -% data annotation, meta data +% data annotation, meta data, FAIR + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \appendix From 9bfc39b82c2ef538f3f89b8651909bceb4d02b05 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Fri, 8 Jan 2021 19:21:46 +0100 Subject: [PATCH 62/87] [regression] added matlab figure to exercise --- regression/exercises/expdecaygradientplot.pdf | Bin 0 -> 6783 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 regression/exercises/expdecaygradientplot.pdf diff --git a/regression/exercises/expdecaygradientplot.pdf b/regression/exercises/expdecaygradientplot.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ac46b86631214847b795f131c83ea7d156f59031 GIT binary patch literal 6783 zcmai32UJtr(pKrANtL1y5TrvwFOd$?Boyg2K!6}55CQ}Q5fBjRRZ)pZN02TZMd?Tf zQF`x4FN%~ux$oZl-}k?_)_=0H&e`A0o|!$fXP>iXcn#DwMZltx0N%Gn#qR)MAP9(Z za05Uf05JnJ%E`wOjt26pc)}cA;XqBO0nikV_C}zPKygt?QILqSzKVgd7WAGx5HCg@ z<>=!9M`G@vVV!E*Q?SO^5>1A+Ji z0E&tLIMRurS^RGcfMR-ZqzlFsD1nEJfMS{mcMRSdF->>8EOode$_Wm{&-2FMRd@if zuiC7?l<;(TO&yz!4B6@lNN~TlB1*e_*|wA8J7p-PgKU;?&%mr!Xzl^jRbC>F)?mam<6`-J~PouUj~?+Oy%@EpPoofolzZ$9%6_ zJ369|Li%Zsx-Np6&o=nBFMjR4e#QwqCObV7^W8q_g>Kg<*_{96O?&t<|G_v~z#UE3 zaAI%PO=*AhYvs$e4~$_Zc~WbUUu0(Hr;o3VonNvFzC7|1I&;2~G<;MlHgk@0S&FB%ZBSEP_)HQ3Z|_hlqa!?=Xlw9~&-ensLyk7d|vHUW@0@X4d@$S3?bu{wAAw$k6ln z%g@xFRawE3->sZCw#o(12gvqMLBpIg!N&_n-(H`ePvsxapthBQPPU<*aTjz}j$D>U z3&fyoP8jNO7Zh>cO+^9i^n*VFdeMFb{o5ISV%;hRUrK2t@=*WINedz`le1!7R4qA zqL+cqdv7tw1N2zAsck&P_QO>uDgDV|xl6UO)r94k$-qzKCEJ9-FQeU~rnKE%~B{*h%MV;7^2A;w;-hQ0ahGTfQdsHLGtn11CLe$oh(yje9JUl{{g!Z4UNhR&j@}kdk#Bpaj+7x?3(M{ z7u2^k@%k9)Ke;`FZmy5A>K(~aw^xE80<)*N5%n34T8JiNd4 z^8$;caHDp;DP(Z$_1JN?f=_nu*dRODX*1RF5j(qk+G8HS7#-rqCAFK!)Y2{}tzd=@ zV7>vWxBA(`k{oTI^ZpAf00XXsN75gtx4rS6B{LYDL>)8ONUec^@y~eeQ{navD8vj zx4x%w>m9dGqdA!vT+QVuv=@RLfN|xIHfjx%+WF+a4Z63SXzQ>+SJhuD8u`Df%JJ&S z&Z<1p*X9Ewu76OBPkRdcmE+tuTN%1Mzs-2NYmHjSCkJtsj2=p+W(Y)N5`&9z#PAk$ zcyu{ayi}EoG>IBaU-Zqk`NVXJ7kcEnJ<4C&%X{BR;CD-0c5ehi(ckUt(}Y#&k$!4& zVJ3-nEB|V}RC4)Yx5*JxSQZm*^Vp}^CNrVT zO5&<1=m~@9edZP&z+;m3yqLk_C5|n=gsF(#Zj3?|!I^ff=ZIqy_p(d~1cL8EHIU&?9$yWu4*o zNw%yf5LR{IKDiobo^nqYCtqmX%$j53aqbxd1REQ40X(ek8&C(M{M z4`+VojJ$ugKlV%-Zg~WmeK5YmVSl+oAlJENRh%wrGxf=BKATSz#q`8tF8;~NX7(Cj zyD@>T%^giM(}$}rdjk=u0dAf=@ZD89$ zR*e>=`vD!O_v0cip2tx6q*-x7PAsVRDlV?tYlO>e2fits6xy5i=B|b+rpxaph&T zcyW6OC$*DE*(-aqCKP!cpG8y%4YrVua`2c(2vp0vGZw*`&Dp8r?)IexrzUg7qHg$U zPJiU%aLodd%WqB#%x^@bHk&v|z-b?Tqeg_c3^^B(EZnGdV`;wytr4G>z64&=CiCYd zFXA&pz^NAbhkJlCN_B4UTFSJJR(L$WDujQNxlj3dy~~6>=4~e?8YboWm6VS4 zdsdK)^YW|Ru`;?^ofsec_u34t9i1kchO9`MIj_0()fX%zRLQADH$t-Yb?HdBJm&N&SSZ2HLdCwaAJz(IyJdX z#3)}sT$827gnVOV8(ZMoN0Uo~R`RYf+FQ3yT!j6woR4&EkT+Y*VP1WSQPs9n&xSL2`NdtGB0wT(5{|Y#=$v!R+332 z!jja}^W3}xz=0ET_^MGcAHCDsRw?_l>Fl{D6q0cH)<9ogW~`Q}69fNR*}++cts`~% zSQ%i;Ue!GyAkHZ~zm4Z+qXlREGmC7e_lohV@y%U$rM-zcnznix8r zVnJkK0RfWUut@DOcc$3al9c!*3l*zOFg@|6T3c8>w(b^YQJ%{j6NJIf9%c)HL=F<< z*sD`4%sEJG-&k3eOq#cb+1Ij>UW+PjZKSBLOtVNAqSI)Ai3~867v2rS3N3^$qkk&CjRW4L{Fz$sboe38(fa~O#i9nB|W8xJ*yl)z`jHE zO*m{ef+LA`;|BAPw)up<^1}glx}tVfq2w{G$RPTASM2K4z;zQ&5VKex<{FddT)FG! 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These parameters can be simply a mean, +a standard deviation, or any other parameter needed to describe the +distribution the data a re originating from, a correlation +coefficient, or some parameters of a function describing a particular +dependence between the data. The brain faces exactly the same +problem. Given the activity pattern of some neurons (the data) it +needs to infer some aspects (parameters) of the environment and the +internal state of the body in order to generate some useful +behavior. One possible approach to estimate parameters from data are +\enterm[maximum likelihood estimator]{maximum likelihood estimators} +(\enterm[mle|see{maximum likelihood estimator}]{mle}, +\determ{Maximum-Likelihood-Sch\"atzer}). They choose the parameters +such that they maximize the likelihood of the specific data values to +originate from a specific distribution. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Maximum Likelihood} +\section{Maximum likelihood} Let $p(x|\theta)$ (to be read as ``probability(density) of $x$ given -$\theta$.'') the probability (density) distribution of $x$ given the -parameters $\theta$. This could be the normal distribution +$\theta$.'') the probability (density) distribution of data value $x$ +given parameter values $\theta$. This could be the normal distribution \begin{equation} \label{normpdfmean} p(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \end{equation} defined by the mean $\mu$ and the standard deviation $\sigma$ as -parameters $\theta$. If the $n$ independent observations of $x_1, -x_2, \ldots x_n$ originate from the same probability density -distribution (they are \enterm[i.i.d.|see{independent and identically - distributed}]{i.i.d.}, \enterm{independent and identically - distributed}) then the conditional probability $p(x_1,x_2, \ldots -x_n|\theta)$ of observing $x_1, x_2, \ldots x_n$ given some specific -parameter values $\theta$ is given by +parameters $\theta$. If the $n$ observations $x_1, x_2, \ldots, x_n$ +are independent of each other and originate from the same probability +density distribution (they are \enterm[i.i.d.|see{independent and + identically distributed}]{i.i.d.}, \enterm{independent and + identically distributed}), then the conditional probability +$p(x_1,x_2, \ldots, x_n|\theta)$ of observing the particular data +values $x_1, x_2, \ldots, x_n$ given some specific parameter values +$\theta$ of the probability density is given by the product of the +probability densities of each data value: \begin{equation} - p(x_1,x_2, \ldots x_n|\theta) = p(x_1|\theta) \cdot p(x_2|\theta) - \ldots p(x_n|\theta) = \prod_{i=1}^n p(x_i|\theta) \; . + \label{probdata} + p(x_1,x_2, \ldots, x_n|\theta) = p(x_1|\theta) \cdot p(x_2|\theta) + \ldots, p(x_n|\theta) = \prod_{i=1}^n p(x_i|\theta) \; . \end{equation} Vice versa, the \entermde{Likelihood}{likelihood} of the parameters $\theta$ -given the observed data $x_1, x_2, \ldots x_n$ is +given the observed data $x_1, x_2, \ldots, x_n$ is \begin{equation} - {\cal L}(\theta|x_1,x_2, \ldots x_n) = p(x_1,x_2, \ldots x_n|\theta) \; . + \label{likelihood} + {\cal L}(\theta|x_1,x_2, \ldots, x_n) = p(x_1,x_2, \ldots, x_n|\theta) \; . \end{equation} -Note: the likelihood ${\cal L}$ is not a probability in the +Note, that the likelihood ${\cal L}$ is not a probability in the classic sense since it does not integrate to unity ($\int {\cal - L}(\theta|x_1,x_2, \ldots x_n) \, d\theta \ne 1$). - -When applying maximum likelihood estimations we are interested in the -parameter values + L}(\theta|x_1,x_2, \ldots, x_n) \, d\theta \ne 1$). For given +observations $x_1, x_2, \ldots, x_n$, the likelihood +\eqref{likelihood} is a function of the parameters $\theta$. This +function has a global maximum for some specific parameter values. At +this maximum the probability \eqref{probdata} to observe the measured +data values is the largest. + +Maximum likelihood estimators just find the parameter values \begin{equation} - \theta_{mle} = \text{argmax}_{\theta} {\cal L}(\theta|x_1,x_2, \ldots x_n) + \theta_{mle} = \text{argmax}_{\theta} {\cal L}(\theta|x_1,x_2, \ldots, x_n) \end{equation} -that maximize the likelihood. $\text{argmax}_xf(x)$ is the value of -the argument $x$ for which the function $f(x)$ assumes its global -maximum. Thus, we search for the parameter values $\theta$ at which -the likelihood ${\cal L}(\theta)$ reaches its maximum. For these -paraemter values the measured data most likely originated from the -corresponding distribution. +that maximize the likelihood \eqref{likelihood}. +$\text{argmax}_xf(x)$ is the value of the argument $x$ for which the +function $f(x)$ assumes its global maximum. Thus, we search for the +parameter values $\theta$ at which the likelihood ${\cal L}(\theta)$ +reaches its maximum. For these parameter values the measured data most +likely originated from the corresponding distribution. The position of a function's maximum does not change when the values of the function are transformed by a strictly monotonously rising function such as the logarithm. For numerical reasons and reasons that -we will discuss below, we search for the maximum of the logarithm of -the likelihood -(\entermde[likelihood!log-]{Likelihood!Log-}{log-likelihood}): - +we discuss below, we instead search for the maximum of the logarithm +of the likelihood +(\entermde[likelihood!log-]{Likelihood!Log-}{log-likelihood}) \begin{eqnarray} - \theta_{mle} & = & \text{argmax}_{\theta}\; {\cal L}(\theta|x_1,x_2, \ldots x_n) \nonumber \\ - & = & \text{argmax}_{\theta}\; \log {\cal L}(\theta|x_1,x_2, \ldots x_n) \nonumber \\ + \theta_{mle} & = & \text{argmax}_{\theta}\; {\cal L}(\theta|x_1,x_2, \ldots, x_n) \nonumber \\ + & = & \text{argmax}_{\theta}\; \log {\cal L}(\theta|x_1,x_2, \ldots, x_n) \nonumber \\ & = & \text{argmax}_{\theta}\; \log \prod_{i=1}^n p(x_i|\theta) \nonumber \\ & = & \text{argmax}_{\theta}\; \sum_{i=1}^n \log p(x_i|\theta) \label{loglikelihood} \end{eqnarray} +which is the sum of the logarithms of the probabilites of each +observation. Let's illustrate the concept of maximum likelihood +estimation on the arithmetic mean. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Example: the arithmetic mean} -Suppose that the measurements $x_1, x_2, \ldots x_n$ originate from a -normal distribution \eqnref{normpdfmean} and we consider the mean -$\mu$ as the only parameter $\theta$. Which value of $\theta$ -maximizes the likelihood of the data? +\subsection{Arithmetic mean} +Suppose that the measurements $x_1, x_2, \ldots, x_n$ originate from a +normal distribution \eqref{normpdfmean} and we do not know the +population mean $\mu$ of the normal distribution +(\figrefb{mlemeanfig}). In this setting $\mu$ is the only parameter +$\theta$. Which value of $\mu$ maximizes the likelihood of the data? \begin{figure}[t] \includegraphics[width=1\textwidth]{mlemean} \titlecaption{\label{mlemeanfig} Maximum likelihood estimation of the mean.}{Top: The measured data (blue dots) together with three - different possible normal distributions with different means - (arrows) the data could have originated from. Bottom left: the - likelihood as a function of $\theta$ i.e. the mean. It is maximal - at a value of $\theta = 2$. Bottom right: the - log-likelihood. Taking the logarithm does not change the position - of the maximum.} + normal distributions differing in their means (arrows) from which + the data could have originated from. Bottom left: the likelihood + as a function of the parameter $\mu$. For the data it is maximal + at a value of $\mu = 2$. Bottom right: the log-likelihood. Taking + the logarithm does not change the position of the maximum.} \end{figure} -The log-likelihood \eqnref{loglikelihood} +With the normal distribution \eqref{normpdfmean} and applying +logarithmic identities, the log-likelihood \eqref{loglikelihood} reads \begin{eqnarray} - \log {\cal L}(\theta|x_1,x_2, \ldots x_n) - & = & \sum_{i=1}^n \log \frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x_i-\theta)^2}{2\sigma^2}} \nonumber \\ - & = & \sum_{i=1}^n - \log \sqrt{2\pi \sigma^2} -\frac{(x_i-\theta)^2}{2\sigma^2} \; . + \log {\cal L}(\mu|x_1,x_2, \ldots, x_n) + & = & \sum_{i=1}^n \log \frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x_i-\mu)^2}{2\sigma^2}} \nonumber \\ + & = & \sum_{i=1}^n - \log \sqrt{2\pi \sigma^2} -\frac{(x_i-\mu)^2}{2\sigma^2} \; . \end{eqnarray} Since the logarithm is the inverse function of the exponential ($\log(e^x)=x$), taking the logarithm removes the exponential from the -normal distribution. To calculate the maximum of the log-likelihood, -we need to take the derivative with respect to $\theta$ and set it to -zero: +normal distribution. This is the second reason why it is useful to +maximize the log-likelihood. To calculate the maximum of the +log-likelihood, we need to take the derivative with respect to $\mu$ +and set it to zero: \begin{eqnarray} - \frac{\text{d}}{\text{d}\theta} \log {\cal L}(\theta|x_1,x_2, \ldots x_n) & = & \sum_{i=1}^n - \frac{2(x_i-\theta)}{2\sigma^2} \;\; = \;\; 0 \nonumber \\ - \Leftrightarrow \quad \sum_{i=1}^n x_i - \sum_{i=1}^n \theta & = & 0 \nonumber \\ - \Leftrightarrow \quad n \theta & = & \sum_{i=1}^n x_i \nonumber \\ - \Leftrightarrow \quad \theta & = & \frac{1}{n} \sum_{i=1}^n x_i \;\; = \;\; \bar x + \frac{\text{d}}{\text{d}\mu} \log {\cal L}(\mu|x_1,x_2, \ldots, x_n) & = & \sum_{i=1}^n - \frac{\text{d}}{\text{d}\mu} \log \sqrt{2\pi \sigma^2} - \frac{\text{d}}{\text{d}\mu} \frac{(x_i-\mu)^2}{2\sigma^2} \;\; = \;\; 0 \nonumber \\ + \Leftrightarrow \quad \sum_{i=1}^n - \frac{2(x_i-\mu)}{2\sigma^2} & = & 0 \nonumber \\ + \Leftrightarrow \quad \sum_{i=1}^n x_i - \sum_{i=1}^n \mu & = & 0 \nonumber \\ + \Leftrightarrow \quad n \mu & = & \sum_{i=1}^n x_i \nonumber \\ + \Leftrightarrow \quad \mu & = & \frac{1}{n} \sum_{i=1}^n x_i \;\; = \;\; \bar x \end{eqnarray} -Thus, the maximum likelihood estimator is the arithmetic mean. That -is, the arithmetic mean maximizes the likelihood that the data -originate from a normal distribution centered at the arithmetic mean +Thus, the maximum likelihood estimator of the population mean of +normally distributed data is the arithmetic mean. That is, the +arithmetic mean maximizes the likelihood that the data originate from +a normal distribution centered at the arithmetic mean (\figref{mlemeanfig}). Equivalently, the standard deviation computed from the data, maximizes the likelihood that the data were generated from a normal distribution with this standard deviation. @@ -123,6 +144,17 @@ from a normal distribution with this standard deviation. the maxima with the mean calculated from the data. \end{exercise} +Comparing the values of the likelihood with the ones of the +log-likelihood shown in \figref{mlemeanfig}, shows the numerical +reason for taking the logarithm of the likelihood. The likelihood +values can get very small, because we multiply many, potentially small +probability densities with each other. The likelihood quickly gets +smaller than the samlles number a floating point number of a computer +can represent. Try it by increasing the number of data values in the +exercise. Taking the logarithm avoids this problem. The log-likelihood +assumes well behaving numbers that can be handled well by the +computer. + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Fitting probability distributions} @@ -130,32 +162,39 @@ Consider normally distributed data with unknown mean and standard deviation. From the considerations above we just have seen that a Gaussian distribution with mean at the arithmetic mean and standard deviation equal to the standard deviation computed from the data is -the best Gaussian distribution that fits the data best in a maximum -likelihood sense, i.e. the likelihood that the data were generated -from this distribution is the largest. Fitting a Gaussian distribution -to data is very simple: just compute the two parameter of the Gaussian -distribution as the arithmetic mean and a standard deviation directly -from the data. - -For non-Gaussian distributions (e.g. a Gamma-distribution), however, -such simple analytical expressions for the parameters of the -distribution do not exist, e.g. the shape parameter of a -\entermde[distribution!Gamma-]{Verteilung!Gamma-}{Gamma-distribution}. How -do we fit such a distribution to some data? That is, how should we -compute the values of the parameters of the distribution, given the -data? +the Gaussian that fits the data best in a maximum likelihood sense, +i.e. the likelihood that the data were generated from this +distribution is the largest. Fitting a Gaussian distribution to data +is very simple: just compute the two parameter of the Gaussian +distribution $\mu$ and $\sigma$ as the arithmetic mean and a standard +deviation, respectively, directly from the data. + +For non-Gaussian distributions, for example a +\entermde[distribution!Gamma-]{Verteilung!Gamma-}{Gamma-distribution} +\begin{equation} + \label{gammapdf} + p(x|\alpha,\beta) \sim x^{\alpha-1}e^{-\beta x} \; , +\end{equation} +however, such simple analytical expressions for the parameters of the +distribution do not exist. This is the case, for example, for the +shape parameter $\alpha$ of the Gamma-distribution. How do we fit such +a distribution to some data? That is, how should we compute the +values of the parameters of the distribution, given the data? A first guess could be to fit the probability density function by minimization of the squared difference to a histogram of the measured -data. For several reasons this is, however, not the method of choice: -(i) Probability densities can only be positive which leads, for small -values in particular, to asymmetric distributions. (ii) The values of -a histogram estimating the density are not independent because the -integral over a density is unity. The two basic assumptions of -normally distributed and independent samples, which are a prerequisite -make the minimization of the squared difference \eqnref{chisqmin} to a -maximum likelihood estimation, are violated. (iii) The histogram -strongly depends on the chosen bin size \figref{mlepdffig}). +data in the same way as we fit a a function to some data. For several +reasons this is, however, not the method of choice: (i) Probability +densities can only be positive which leads, for small values in +particular, to asymmetric distributions of the estimated histogram +around the true density. (ii) The values of a histogram estimating the +density are not independent because the integral over a density is +unity. The two basic assumptions of normally distributed and +independent samples, which are a prerequisite for making the +minimization of the squared difference to a maximum likelihood +estimation (see next section), are violated. (iii) The estimation of +the probability density by means of a histogram strongly depends on +the chosen bin size \figref{mlepdffig}). \begin{figure}[t] \includegraphics[width=1\textwidth]{mlepdf} @@ -173,11 +212,10 @@ Instead we should stay with maximum-likelihood estimation. Exactly in the same way as we estimated the mean value of a Gaussian distribution above, we can numerically fit the parameter of any type of distribution directly from the data by means of maximizing the -likelihood. We simply search for the parameter $\theta$ of the -desired probability density function that maximizes the -log-likelihood. In general this is a non-linear optimization problem -that is solved with numerical methods such as the gradient descent -\matlabfun{mle()}. +likelihood. We simply search for the parameter values of the desired +probability density function that maximize the log-likelihood. In +general this is a non-linear optimization problem that is solved with +numerical methods such as the gradient descent \matlabfun{mle()}. \begin{exercise}{mlegammafit.m}{mlegammafit.out} Generate a sample of gamma-distributed random numbers and apply the @@ -191,12 +229,16 @@ that is solved with numerical methods such as the gradient descent When fitting a function of the form $f(x;\theta)$ to data pairs $(x_i|y_i)$ one tries to adapt the parameter $\theta$ such that the -function best describes the data. With maximum likelihood we search -for the parameter value $\theta$ for which the likelihood that the data -were drawn from the corresponding function is maximal. If we assume -that the $y_i$ values are normally distributed around the function -values $f(x_i;\theta)$ with a standard deviation $\sigma_i$, the -log-likelihood is +function best describes the data. In +chapter~\ref{gradientdescentchapter} we simply assumed that ``best'' +means minimizing the squared distance between the data and the +function. With maximum likelihood we search for the parameter value +$\theta$ for which the likelihood that the data were drawn from the +corresponding function is maximal. + +If we assume that the $y_i$ values are normally distributed around the +function values $f(x_i;\theta)$ with a standard deviation $\sigma_i$, +the log-likelihood is \begin{eqnarray} \log {\cal L}(\theta|(x_1,y_1,\sigma_1), \ldots, (x_n,y_n,\sigma_n)) & = & \sum_{i=1}^n \log \frac{1}{\sqrt{2\pi \sigma_i^2}}e^{-\frac{(y_i-f(x_i;\theta))^2}{2\sigma_i^2}} \nonumber \\ @@ -218,18 +260,17 @@ the position of the minimum: \theta_{mle} = \text{argmin}_{\theta} \; \sum_{i=1}^n \left( \frac{y_i-f(x_i;\theta)}{\sigma_i} \right)^2 \;\; = \;\; \text{argmin}_{\theta} \; \chi^2 \end{equation} The sum of the squared differences normalized by the standard -deviation is also called $\chi^2$. The parameter $\theta$ which -minimizes the squared differences is thus the one that maximizes the -likelihood that the data actually originate from the given -function. Minimizing $\chi^2$ therefore is a maximum likelihood +deviation is also called $\chi^2$ (chi squared). The parameter +$\theta$ which minimizes the squared differences is thus the one that +maximizes the likelihood of the data to actually originate from the +given function. Therefore, minimizing $\chi^2$ is a maximum likelihood estimation. From the mathematical considerations above we can see that the minimization of the squared difference is a maximum-likelihood estimation only if the data are normally distributed around the function. In case of other distributions, the log-likelihood -\eqnref{loglikelihood} needs to be adapted accordingly and be -maximized respectively. +\eqnref{loglikelihood} needs to be adapted accordingly. \begin{figure}[t] \includegraphics[width=1\textwidth]{mlepropline} @@ -377,7 +418,7 @@ orientation $\phi$ of an edge is given by The log-likelihood of the edge orientation $\phi$ given the activity pattern in the population $r_1$, $r_2$, ... $r_n$ is thus \begin{equation} - {\cal L}(\phi|r_1, r_2, \ldots r_n) = \sum_{i=1}^n \log p_i(r_i|\phi) + {\cal L}(\phi|r_1, r_2, \ldots, r_n) = \sum_{i=1}^n \log p_i(r_i|\phi) \end{equation} The angle $\phi$ that maximizes this likelihood is then an estimate of the orientation of the edge. diff --git a/likelihood/lecture/mlemean.py b/likelihood/lecture/mlemean.py index a1fb974..e18618d 100644 --- a/likelihood/lecture/mlemean.py +++ b/likelihood/lecture/mlemean.py @@ -52,7 +52,7 @@ for i, theta in enumerate(thetas) : p=np.prod(ps,axis=0) # plot it: ax = fig.add_subplot(spec[1, 0]) -ax.set_xlabel(r'Parameter $\theta$') +ax.set_xlabel(r'Parameter $\mu$') ax.set_ylabel('Likelihood') ax.set_xticks(np.arange(1.6, 2.5, 0.4)) ax.annotate('Maximum', @@ -68,7 +68,7 @@ ax.annotate('', ax.plot(thetas, p, **lsAm) ax = fig.add_subplot(spec[1, 1]) -ax.set_xlabel(r'Parameter $\theta$') +ax.set_xlabel(r'Parameter $\mu$') ax.set_ylabel('Log-Likelihood') ax.set_ylim(-50,-20) ax.set_xticks(np.arange(1.6, 2.5, 0.4)) diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex index 2d13b96..6199650 100644 --- a/regression/lecture/regression.tex +++ b/regression/lecture/regression.tex @@ -1,4 +1,5 @@ \chapter{Optimization and gradient descent} +\label{gradientdescentchapter} \exercisechapter{Optimization and gradient descent} Optimization problems arise in many different contexts. For example, From 454c7178c7f4dc81cc9a5d375b8786f09ee65caa Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 9 Jan 2021 19:48:59 +0100 Subject: [PATCH 64/87] [likelihood] improved text --- likelihood/lecture/likelihood-chapter.tex | 7 +- likelihood/lecture/likelihood.tex | 334 +++++++++++++--------- likelihood/lecture/mlecoding.py | 43 +-- 3 files changed, 232 insertions(+), 152 deletions(-) diff --git a/likelihood/lecture/likelihood-chapter.tex b/likelihood/lecture/likelihood-chapter.tex index 736d9eb..40021f4 100644 --- a/likelihood/lecture/likelihood-chapter.tex +++ b/likelihood/lecture/likelihood-chapter.tex @@ -20,12 +20,11 @@ \section{TODO} \begin{itemize} -\item Fitting psychometric functions: +\item Fitting psychometric functions, logistic regression: Variable $x_i$, responses $r_i$ either 0 or 1. - $p(x_i, \theta)$ is Weibull or Boltzmann function. + $p(x_i, \theta)$ is Weibull or Boltzmann or logistic function. Likelihood is $L = \prod p(x_i, \theta)^{r_i} (1-p(x_i, \theta))^{1-r_i}$. - Use fminsearch for fitting. -\item GLM model fitting? + Use fminsearch for fitting? \end{itemize} \end{document} diff --git a/likelihood/lecture/likelihood.tex b/likelihood/lecture/likelihood.tex index cae9ff0..ea0cfd4 100644 --- a/likelihood/lecture/likelihood.tex +++ b/likelihood/lecture/likelihood.tex @@ -7,15 +7,15 @@ The core task of statistics is to infer from measured data some parameters describing the data. These parameters can be simply a mean, a standard deviation, or any other parameter needed to describe the -distribution the data a re originating from, a correlation -coefficient, or some parameters of a function describing a particular -dependence between the data. The brain faces exactly the same -problem. Given the activity pattern of some neurons (the data) it -needs to infer some aspects (parameters) of the environment and the -internal state of the body in order to generate some useful -behavior. One possible approach to estimate parameters from data are -\enterm[maximum likelihood estimator]{maximum likelihood estimators} -(\enterm[mle|see{maximum likelihood estimator}]{mle}, +distribution the data are originating from, a correlation coefficient, +or some parameters of a function describing a particular dependence +between the data. The brain faces exactly the same problem. Given the +activity pattern of some neurons (the data) it needs to infer some +aspects (parameters) of the environment and the internal state of the +body in order to generate some useful behavior. One possible approach +to estimate parameters from data are \enterm[maximum likelihood +estimator]{maximum likelihood estimators} (\enterm[mle|see{maximum + likelihood estimator}]{mle}, \determ{Maximum-Likelihood-Sch\"atzer}). They choose the parameters such that they maximize the likelihood of the specific data values to originate from a specific distribution. @@ -124,7 +124,7 @@ and set it to zero: \Leftrightarrow \quad \sum_{i=1}^n - \frac{2(x_i-\mu)}{2\sigma^2} & = & 0 \nonumber \\ \Leftrightarrow \quad \sum_{i=1}^n x_i - \sum_{i=1}^n \mu & = & 0 \nonumber \\ \Leftrightarrow \quad n \mu & = & \sum_{i=1}^n x_i \nonumber \\ - \Leftrightarrow \quad \mu & = & \frac{1}{n} \sum_{i=1}^n x_i \;\; = \;\; \bar x + \Leftrightarrow \quad \mu & = & \frac{1}{n} \sum_{i=1}^n x_i \;\; = \;\; \bar x \label{arithmeticmean} \end{eqnarray} Thus, the maximum likelihood estimator of the population mean of normally distributed data is the arithmetic mean. That is, the @@ -173,28 +173,28 @@ For non-Gaussian distributions, for example a \entermde[distribution!Gamma-]{Verteilung!Gamma-}{Gamma-distribution} \begin{equation} \label{gammapdf} - p(x|\alpha,\beta) \sim x^{\alpha-1}e^{-\beta x} \; , + p(x|\alpha,\beta) \sim x^{\alpha-1}e^{-\beta x} \end{equation} -however, such simple analytical expressions for the parameters of the -distribution do not exist. This is the case, for example, for the -shape parameter $\alpha$ of the Gamma-distribution. How do we fit such -a distribution to some data? That is, how should we compute the -values of the parameters of the distribution, given the data? - -A first guess could be to fit the probability density function by -minimization of the squared difference to a histogram of the measured -data in the same way as we fit a a function to some data. For several -reasons this is, however, not the method of choice: (i) Probability -densities can only be positive which leads, for small values in -particular, to asymmetric distributions of the estimated histogram -around the true density. (ii) The values of a histogram estimating the -density are not independent because the integral over a density is -unity. The two basic assumptions of normally distributed and -independent samples, which are a prerequisite for making the -minimization of the squared difference to a maximum likelihood -estimation (see next section), are violated. (iii) The estimation of -the probability density by means of a histogram strongly depends on -the chosen bin size \figref{mlepdffig}). +with a shape parameter $\alpha$ and a rate parameter $\beta$ +(\figrefb{mlepdffig}), in general no such simple analytical +expressions for estimating the parameters directly from the data do +not exist. How do we fit such a distribution to the data? That is, +how should we compute the values of the parameters of the +distribution, given the data? + +A first guess could be to fit the probability density function by a +\enterm{least squares} fit to a normalized histogram of the measured data in +the same way as we fit a function to some data. For several reasons +this is, however, not the method of choice: (i) Probability densities +can only be positive which leads, in particular for small values, to +asymmetric distributions of the estimated histogram around the true +density. (ii) The values of a histogram estimating the density are not +independent because the integral over a density is unity. The two +basic assumptions of normally distributed and independent samples, +which are a prerequisite for making the minimization of the squared +difference to a maximum likelihood estimation (see next section), are +violated. (iii) The estimation of the probability density by means of +a histogram strongly depends on the chosen bin size. \begin{figure}[t] \includegraphics[width=1\textwidth]{mlepdf} @@ -203,9 +203,9 @@ the chosen bin size \figref{mlepdffig}). order Gamma-distribution. The maximum likelihood estimation of the probability density function is shown in orange, the true pdf is shown in red. Right: normalized histogram of the data together - with the real (red) and the fitted probability density - functions. The fit was done by minimizing the squared difference - to the histogram.} + with the true probability density (red) and the probability + density function obtained by a least squares fit to the + histogram.} \end{figure} Instead we should stay with maximum-likelihood estimation. Exactly in @@ -228,13 +228,13 @@ numerical methods such as the gradient descent \matlabfun{mle()}. \section{Curve fitting} When fitting a function of the form $f(x;\theta)$ to data pairs -$(x_i|y_i)$ one tries to adapt the parameter $\theta$ such that the +$(x_i|y_i)$ one tries to adapt the parameters $\theta$ such that the function best describes the data. In chapter~\ref{gradientdescentchapter} we simply assumed that ``best'' means minimizing the squared distance between the data and the -function. With maximum likelihood we search for the parameter value -$\theta$ for which the likelihood that the data were drawn from the -corresponding function is maximal. +function. With maximum likelihood we search for those parameter +values $\theta$ that maximize the likelihood of the data to be drawn +from the corresponding function. If we assume that the $y_i$ values are normally distributed around the function values $f(x_i;\theta)$ with a standard deviation $\sigma_i$, @@ -242,35 +242,49 @@ the log-likelihood is \begin{eqnarray} \log {\cal L}(\theta|(x_1,y_1,\sigma_1), \ldots, (x_n,y_n,\sigma_n)) & = & \sum_{i=1}^n \log \frac{1}{\sqrt{2\pi \sigma_i^2}}e^{-\frac{(y_i-f(x_i;\theta))^2}{2\sigma_i^2}} \nonumber \\ - & = & \sum_{i=1}^n - \log \sqrt{2\pi \sigma_i^2} -\frac{(y_i-f(x_i;\theta))^2}{2\sigma_i^2} \\ + & = & \sum_{i=1}^n - \log \sqrt{2\pi \sigma_i^2} -\frac{(y_i-f(x_i;\theta))^2}{2\sigma_i^2} \end{eqnarray} -The only difference to the previous example is that the averages in -the equations above are now given as the function values -$f(x_i;\theta)$. The parameter $\theta$ should be the one that -maximizes the log-likelihood. The first part of the sum is independent -of $\theta$ and can thus be ignored when computing the the maximum: +The only difference to the previous example of the arithmetic mean is +that the means $\mu$ in the equations above are given by the function +values $f(x_i;\theta)$. The parameters $\theta$ should maximize the +log-likelihood. The first term in the sum is independent of $\theta$ +and can be ignored when computing the the maximum. From the second +term we pull out the constant factor $-\frac{1}{2}$: \begin{eqnarray} & = & - \frac{1}{2} \sum_{i=1}^n \left( \frac{y_i-f(x_i;\theta)}{\sigma_i} \right)^2 \end{eqnarray} We can further simplify by inverting the sign and then search for the -minimum. Also the factor $1/2$ can be ignored since it does not affect -the position of the minimum: +minimum. Also the factor $\frac{1}{2}$ can be ignored since it does +not affect the position of the minimum: \begin{equation} \label{chisqmin} \theta_{mle} = \text{argmin}_{\theta} \; \sum_{i=1}^n \left( \frac{y_i-f(x_i;\theta)}{\sigma_i} \right)^2 \;\; = \;\; \text{argmin}_{\theta} \; \chi^2 \end{equation} -The sum of the squared differences normalized by the standard -deviation is also called $\chi^2$ (chi squared). The parameter +The sum of the squared differences between the $y$-data values and the +function values, normalized by the standard deviation of the data +around the function, is called $\chi^2$ (chi squared). The parameter $\theta$ which minimizes the squared differences is thus the one that maximizes the likelihood of the data to actually originate from the -given function. Therefore, minimizing $\chi^2$ is a maximum likelihood -estimation. +given function. + +Whether minimizing $\chi^2$ or the \enterm{mean squared error} +\eqref{meansquarederror} introduced in +chapter~\ref{gradientdescentchapter} does not matter. The latter is +the mean and $\chi^2$ is the sum of the squared differences. They +simply differ by the constant factor $n$, the number of data pairs, +which does not affect the position of the minimum. $\chi^2$ is more +general in that it allows for different standard deviations for each +data pair. If they are all the same ($\sigma_i = \sigma$), the common +standard deviation can be pulled out of the sum and also does not +influence the position of the minimum. Both \enterm{least squares} and +minimizing $\chi^2$ are maximum likelihood estimators of the +parameters $\theta$ of a function. From the mathematical considerations above we can see that the minimization of the squared difference is a maximum-likelihood estimation only if the data are normally distributed around the function. In case of other distributions, the log-likelihood -\eqnref{loglikelihood} needs to be adapted accordingly. +\eqref{loglikelihood} needs to be adapted accordingly. \begin{figure}[t] \includegraphics[width=1\textwidth]{mlepropline} @@ -283,26 +297,32 @@ function. In case of other distributions, the log-likelihood the normal distribution of the data around the line (right histogram).} \end{figure} +Let's go on and calculate the minimum \eqref{chisqmin} of $\chi^2$ +analytically for a simple function. -\subsection{Example: simple proportionality} -The function of a line with slope $\theta$ through the origin is -\[ f(x) = \theta x \; . \] -The $\chi^2$-sum is thus -\[ \chi^2 = \sum_{i=1}^n \left( \frac{y_i-\theta x_i}{\sigma_i} \right)^2 \; . \] -To estimate the minimum we again take the first derivative with -respect to $\theta$ and equate it to zero: -\begin{eqnarray} - \frac{\text{d}}{\text{d}\theta}\chi^2 & = & \frac{\text{d}}{\text{d}\theta} \sum_{i=1}^n \left( \frac{y_i-\theta x_i}{\sigma_i} \right)^2 \nonumber \\ - & = & \sum_{i=1}^n \frac{\text{d}}{\text{d}\theta} \left( \frac{y_i-\theta x_i}{\sigma_i} \right)^2 \nonumber \\ - & = & -2 \sum_{i=1}^n \frac{x_i}{\sigma_i} \left( \frac{y_i-\theta x_i}{\sigma_i} \right) \nonumber \\ - & = & -2 \sum_{i=1}^n \left( \frac{x_i y_i}{\sigma_i^2} - \theta \frac{x_i^2}{\sigma_i^2} \right) \;\; = \;\; 0 \nonumber \\ -\Leftrightarrow \quad \theta \sum_{i=1}^n \frac{x_i^2}{\sigma_i^2} & = & \sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2} \nonumber -\end{eqnarray} + +\subsection{Straight line trough the origin} +The function of a straight line with slope $m$ through the origin +is +\[ f(x) = m x \; . \] +With this specific function, $\chi^2$ reads +\[ \chi^2 = \sum_{i=1}^n \left( \frac{y_i-m x_i}{\sigma_i} \right)^2 +\; . \] To calculate the minimum we take the first derivative with +respect to $m$ and equate it to zero: \begin{eqnarray} -\Leftrightarrow \quad \theta & = & \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n \frac{x_i^2}{\sigma_i^2}} \label{mleslope} + \frac{\text{d}}{\text{d}m}\chi^2 & = & \sum_{i=1}^n \frac{\text{d}}{\text{d}m} \left( \frac{y_i-m x_i}{\sigma_i} \right)^2 \nonumber \\ + & = & -2 \sum_{i=1}^n \frac{x_i}{\sigma_i} \left( \frac{y_i-m x_i}{\sigma_i} \right) \nonumber \\ + & = & -2 \sum_{i=1}^n \left( \frac{x_i y_i}{\sigma_i^2} - m \frac{x_i^2}{\sigma_i^2} \right) \;\; = \;\; 0 \nonumber \\ +\Leftrightarrow \quad m \sum_{i=1}^n \frac{x_i^2}{\sigma_i^2} & = & \sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2} \nonumber \\ +\Leftrightarrow \quad m & = & \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n \frac{x_i^2}{\sigma_i^2}} \label{mleslope} \end{eqnarray} -This is an analytical expression for the estimation of the slope -$\theta$ of the regression line (\figref{mleproplinefig}). +This is an analytical expression for the estimation of the slope $m$ +of the regression line (\figref{mleproplinefig}). We do not need to +apply numerical methods like the gradient descent to find the slope +that minimizes the squared differences. Instead, we can compute the +slope directly from the data by means of \eqnref{mleslope}, very much +like we calculate the mean of some data by means of the arithmetic +mean \eqref{arithmeticmean}. \subsection{Linear and non-linear fits} A gradient descent, as we have done in the previous chapter, is not @@ -317,47 +337,68 @@ or the coefficients $a_k$ of a polynomial \matlabfun{polyfit()}. Parameters that are non-linearly combined can not be calculated -analytically. Consider for example the rate $\lambda$ of the -exponential decay +analytically. Consider, for example, the factor $c$ and the rate +$\lambda$ of the exponential decay \[ y = c \cdot e^{\lambda x} \quad , \quad c, \lambda \in \reZ \; . \] Such cases require numerical solutions for the optimization of the cost function, e.g. the gradient descent \matlabfun{lsqcurvefit()}. \subsection{Relation between slope and correlation coefficient} -Let us have a closer look on \eqnref{mleslope}. If the standard -deviation of the data $\sigma_i$ is the same for each data point, -i.e. $\sigma_i = \sigma_j \; \forall \; i, j$, the standard deviation drops -out of \eqnref{mleslope} and we get +Let us have a closer look on \eqnref{mleslope} for the slope of a line +through the origin. If the standard deviation of the data $\sigma_i$ +is the same for each data point, i.e. $\sigma_i = \sigma_j \; \forall +\; i, j$, the standard deviation drops out and \eqnref{mleslope} +simplifies to \begin{equation} \label{whitemleslope} - \theta = \frac{\sum_{i=1}^n x_i y_i}{\sum_{i=1}^n x_i^2} + m = \frac{\sum_{i=1}^n x_i y_i}{\sum_{i=1}^n x_i^2} \end{equation} -To see what this expression is, we need to standardize the data. We -make the data mean free and normalize them to their standard -deviation, i.e. $x \mapsto (x - \bar x)/\sigma_x$. The resulting -numbers are also called \entermde[z-values]{z-Wert}{$z$-values} or -$z$-scores and they have the property $\bar x = 0$ and $\sigma_x = -1$. $z$-scores are often used in Biology to make quantities that -differ in their units comparable. For standardized data the variance +To see what the nominator and the denominator of this expression +describe, we need to subtract from the data their mean value. We make +the data mean free, i.e. $x \mapsto x - \bar x$ and $y \mapsto y - +\bar y$ . For mean-free data the variance \begin{equation} - \sigma_x^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar x)^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 = 1 + \sigma_x^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar x)^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 \end{equation} -is given by the mean squared data and equals one. -The covariance between $x$ and $y$ also simplifies to +is given by the mean squared data. In the same way, the covariance +between $x$ and $y$ simplifies to \begin{equation} \text{cov}(x, y) = \frac{1}{n} \sum_{i=1}^n (x_i - \bar x)(y_i - - \bar y) =\frac{1}{n} \sum_{i=1}^n x_i y_i + \bar y) =\frac{1}{n} \sum_{i=1}^n x_i y_i \; , +\end{equation} +the averaged product between pairs of $x$ and $y$ values. Expanding +the fraction in \eqnref{whitemleslope} by $\frac{1}{n}$ we get +\begin{equation} + \label{meanfreeslope} + m = \frac{\frac{1}{n}\sum_{i=1}^n x_i y_i}{\frac{1}{n}\sum_{i=1}^n x_i^2} + = \frac{\text{cov}(x, y)}{\sigma_x^2} \end{equation} -the averaged product between pairs of $x$ and $y$ values. Recall that -the correlation coefficient $r_{x,y}$, -\eqnref{correlationcoefficient}, is the covariance normalized by the -product of the standard deviations of $x$ and $y$, -respectively. Therefore, in case the standard deviations equal one, -the correlation coefficient is identical to the covariance. -Consequently, for standardized data the slope of the regression line -\eqnref{whitemleslope} simplifies to + +Recall that the correlation coefficient $r_{x,y}$ is the covariance +normalized by the product of the standard deviations of $x$ and $y$: +\begin{equation} + \label{meanfreecorrcoef} + r_{x,y} = \frac{\text{cov}(x, y)}{\sigma_x\sigma_y} +\end{equation} +If furthermore the standard deviations of $x$ and $y$ are the same, +i.e. $\sigma_x = \sigma_y$, the slope of a line trough the origin is +identical to the correlation coefficient. + +This relation between slope and correlation coefficient in particular +holds for standardized data that have been made mean free and have +been normalized by their standard deviation, i.e. $x \mapsto (x - \bar +x)/\sigma_x$ and $y \mapsto (y - \bar x)/\sigma_y$. The resulting +numbers are called \entermde[z-value]{z-Wert}{$z$-values} or +\enterm[z-score]{$z$-scores}. Their mean equals zero and their +standard deviation one. $z$-scores are often used to make quantities +that differ in their units comparable. For standardized data the +denominators for both the slope \eqref{meanfreeslope} and the +correlation coefficient \eqref{meanfreecorrcoef} equal one. For +standardized data, both the slope of the regression line and the +corelation coefficient reduce to the covariance between the $x$ and +$y$ data: \begin{equation} - \theta = \frac{1}{n} \sum_{i=1}^n x_i y_i = \text{cov}(x,y) = r_{x,y} + m = \frac{1}{n} \sum_{i=1}^n x_i y_i = \text{cov}(x,y) = r_{x,y} \end{equation} For standardized data the slope of the regression line is the same as the correlation coefficient! @@ -365,63 +406,100 @@ correlation coefficient! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Neural coding} +Maximum likelihood estimators are not only a central concept for data +analysis. Neural systems face the very same problem. They also need to +estimate parameters of the internal and external environment based on +the activity of neurons. + In sensory systems certain aspects of the environment are encoded in the neuronal activity of populations of neurons. One example of such a population code is the tuning of neurons in the primary visual cortex -(V1) to the orientation of an edge or bar in the visual -stimulus. Different neurons respond best to different edge -orientations. Traditionally, such a tuning is measured by analyzing -the neuronal response strength (e.g. the firing rate) as a function of -the orientation of a black bar and is illustrated and summarized -with the so called \enterm{tuning-curve} (\determ{Abstimmkurve}, +(V1) to the orientation of a bar in the visual stimulus. Different +neurons respond best to different bar orientations. Traditionally, +such a tuning is measured by analyzing the neuronal response strength +(e.g. the firing rate) as a function of the orientation of a black bar +and is illustrated and summarized with the so called +\enterm{tuning-curve} (\determ{Abstimmkurve}, figure~\ref{mlecodingfig}, top). \begin{figure}[tp] \includegraphics[width=1\textwidth]{mlecoding} \titlecaption{\label{mlecodingfig} Maximum likelihood estimation of - a stimulus parameter from neuronal activity.}{Top: Tuning curve of - an individual neuron as a function of the stimulus orientation (a - dark bar in front of a white background). The stimulus that evokes - the strongest activity in that neuron is the bar with the vertical - orientation (arrow, $\phi_i=90$\,\degree). The red area indicates - the variability of the neuronal activity $p(r|\phi)$ around the - tuning curve. Center: In a population of neurons, each neuron may - have a different tuning curve (colors). A specific stimulus (the - vertical bar) activates the individual neurons of the population - in a specific way (dots). Bottom: The log-likelihood of the - activity pattern will be maximized close to the real stimulus + a stimulus parameter from neuronal activity.}{Top: Tuning curve + $r_i(\phi;c,\phi_i)$ of a specific neuron $i$ as a function of the + orientation $\phi$ of a stimulus, a dark bar in front of a white + background. The preferred stimulus $\phi_i$ of that neuron, the + one that evokes the strongest firing rate response, is a bar with + vertical orientation (arrow, $\phi_i=90$\,\degree). The width of + the red area indicates the variability of the neuronal activity + $\sigma_i$ around the tuning curve. Center: In a population of + neurons, each neuron may have a different tuning curve (colors). A + specific stimulus activates the individual neurons of the + population in a specific way (dots). Bottom: The log-likelihood of + the activity pattern has a maximum close to the real stimulus orientation.} \end{figure} The brain, however, is confronted with the inverse problem: given a certain activity pattern in the neuronal population, what is the -stimulus (here the orientation of an edge)? In the sense of maximum -likelihood, a possible answer to this question would be: the stimulus -for which the particular activity pattern is most likely given the -tuning of the neurons. +stimulus? In our example, what is the orientation of the bar? In the +sense of maximum likelihood, a possible answer to this question would +be: the stimulus for which the particular activity pattern is most +likely given the tuning of the neurons and the noise (standard +deviation) of the responses. Let's stay with the example of the orientation tuning in V1. The -tuning $\Omega_i(\phi)$ of the neurons $i$ to the preferred edge -orientation $\phi_i$ can be well described using a van-Mises function -(the Gaussian function on a cyclic x-axis) (\figref{mlecodingfig}): +tuning of the firing rate $r_i(\phi)$ of neuron $i$ to the preferred +bar orientation $\phi_i$ can be well described using a van-Mises +function (the Gaussian function on a cyclic x-axis) +(\figref{mlecodingfig}): \begin{equation} - \Omega_i(\phi) = c \cdot e^{\cos(2(\phi-\phi_i))} \quad , \quad c \in \reZ + \label{bartuningcurve} + r_i(\phi; c, \phi_i) = c \cdot e^{\cos(2(\phi-\phi_i))} \quad , \quad c > 0 \end{equation} +Note the factor two in the cosine, because the response of the neuron +is the same for a bar turned by 180\,\degree. + If we approximate the neuronal activity by a normal distribution -around the tuning curve with a standard deviation $\sigma=\Omega/4$, -which is proportional to $\Omega$, then the probability $p_i(r|\phi)$ -of the $i$-th neuron showing the activity $r$ given a certain -orientation $\phi$ of an edge is given by +around the tuning curve with a standard deviation $\sigma_i$, then the +probability $p_i(r|\phi)$ of the $i$-th neuron having the observed +activity $r$, given a certain orientation $\phi$ of a bar is \begin{equation} - p_i(r|\phi) = \frac{1}{\sqrt{2\pi}\Omega_i(\phi)/4} e^{-\frac{1}{2}\left(\frac{r-\Omega_i(\phi)}{\Omega_i(\phi)/4}\right)^2} \; . + p_i(r|\phi) = \frac{1}{\sqrt{2\pi\sigma_i^2}} e^{-\frac{1}{2}\left(\frac{r-r_i(\phi; c, \phi_i)}{\sigma_i}\right)^2} \; . \end{equation} -The log-likelihood of the edge orientation $\phi$ given the +The log-likelihood of the bar orientation $\phi$ given the activity pattern in the population $r_1$, $r_2$, ... $r_n$ is thus \begin{equation} {\cal L}(\phi|r_1, r_2, \ldots, r_n) = \sum_{i=1}^n \log p_i(r_i|\phi) \end{equation} -The angle $\phi$ that maximizes this likelihood is then an estimate of -the orientation of the edge. +The angle $\phi_{mle}$ that maximizes this likelihood is an estimate +of the true orientation of the bar (\figref{mlecodingfig}). + +The noisiness of the neuron's responses as quantified by $\sigma_i$ +usually is a function of the neuron's mean firing rate $r_i$, +\eqnref{bartuningcurve}: $\sigma_i = \sigma_i(r_i)$. This dependence +has a major impact of the maximum likelihood estimation. Usually, the +stronger the response of a neuron, the higher its firing rate, the +lower the noise. In this case, strong responses will have a stronger +influence on the position of the maximum of the log-likelihood. + +Whether neural systems really implement maximum likelihood estimators +is another question. There are many ways how a stimulus property can +be read out from the activity of a population of neurons. The simplest +one being a ``winner takes all'' rule. The preferred stimulus +parameter of the neuron with the strongest response is the +estimate. Another possibility is to compute a population vector. The +estimated stimulus parameter is the sum of the preferred stimulus +parameters of all neurons in the population weighted by the activity +of the neurons. In case of angular stimulus parameters, like the +orientation of the bar in our example, a vector pointing in the +direction of the angle is used instead of the angle to incorporate the +cyclic nature of the parameter. + +Using maximum likelihood estimators for analyzing neural population +activity gives us an upper bound of how well a stimulus parameter is +encoded in the activity of the neurons. The brain would not be able to +do better. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/likelihood/lecture/mlecoding.py b/likelihood/lecture/mlecoding.py index 3edd5a5..8be385f 100644 --- a/likelihood/lecture/mlecoding.py +++ b/likelihood/lecture/mlecoding.py @@ -5,11 +5,9 @@ import matplotlib.gridspec as gridspec from plotstyle import * rng = np.random.RandomState(4637281) -lmarg=0.1 -rmarg=0.1 fig = plt.figure(figsize=cm_size(figure_width, 2.8*figure_height)) -spec = gridspec.GridSpec(nrows=4, ncols=1, height_ratios=[4, 4, 1, 3], hspace=0.2, +spec = gridspec.GridSpec(nrows=4, ncols=1, height_ratios=[4, 5, 1, 3], hspace=0.2, **adjust_fs(fig, left=4.0)) ax = fig.add_subplot(spec[0, 0]) ax.set_xlim(0.0, np.pi) @@ -17,7 +15,7 @@ ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) ax.set_ylim(0.0, 3.5) ax.yaxis.set_major_locator(plt.NullLocator()) -ax.text(-0.2, 0.5*3.5, 'Activity', rotation='vertical', va='center') +ax.text(-0.2, 0.5*3.5, 'Firing rate', rotation='vertical', va='center') ax.annotate('Tuning curve', xy=(0.42*np.pi, 2.5), xycoords='data', xytext=(0.3*np.pi, 3.2), textcoords='data', ha='right', @@ -32,27 +30,34 @@ ax.text(0.52*np.pi, 0.7, 'preferred\norientation') xx = np.arange(0.0, 2.0*np.pi, 0.01) pp = 0.5*np.pi yy = np.exp(np.cos(2.0*(xx+pp))) -ax.fill_between(xx, yy+0.25*yy, yy-0.25*yy, **fsBa) +ss = 1.0/(0.75+2.0*yy) +ax.fill_between(xx, yy+ss, yy-ss, **fsBa) ax.plot(xx, yy, **lsB) ax = fig.add_subplot(spec[1, 0]) ax.set_xlim(0.0, np.pi) ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) -ax.set_ylim(0.0, 3.0) +ax.set_ylim(-0.1, 3.5) ax.yaxis.set_major_locator(plt.NullLocator()) -ax.text(-0.2, 0.5*3.5, 'Activity', rotation='vertical', va='center') +ax.text(-0.2, 0.5*3.5, 'Firing rate', rotation='vertical', va='center') xx = np.arange(0.0, 1.0*np.pi, 0.01) prefphases = np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi) responses = [] -xresponse = 0.475*np.pi +sigmas = [] +xresponse = 0.41*np.pi +ax.annotate('Orientation of bar', + xy=(xresponse, -0.1), xycoords='data', + xytext=(xresponse, 3.1), textcoords='data', ha='left', zorder=-10, + arrowprops=dict(arrowstyle="->", relpos=(0.0,0.0)) ) for pp, ls, ps in zip(prefphases, [lsE, lsC, lsD, lsB, lsD, lsC, lsE], [psE, psC, psD, psB, psD, psC, psE]) : yy = np.exp(np.cos(2.0*(xx+pp))) - #ax.plot(xx, yy, color=cm.autumn(2.0*np.abs(pp/np.pi-0.5), 1)) ax.plot(xx, yy, **ls) y = np.exp(np.cos(2.0*(xresponse+pp))) - responses.append(y + rng.randn()*0.25*y) + s = 1.0/(0.75+2.0*y) + responses.append(y + rng.randn()*s) + sigmas.append(s) ax.plot(xresponse, y, **ps) responses = np.array(responses) @@ -68,25 +73,23 @@ ax = fig.add_subplot(spec[3, 0]) ax.set_xlim(0.0, np.pi) ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) -ax.set_ylim(-1600, 0) +ax.set_ylim(-210, 0) ax.yaxis.set_major_locator(plt.NullLocator()) ax.set_xlabel('Orientation') -ax.text(-0.2, -800, 'Log-Likelihood', rotation='vertical', va='center') +ax.text(-0.2, -100, 'Log-Likelihood', rotation='vertical', va='center') phases = np.linspace(0.0, 1.1*np.pi, 100) probs = np.zeros((len(responses), len(phases))) -for k, (pp, r) in enumerate(zip(prefphases, responses)) : +for k, (pp, r, sigma) in enumerate(zip(prefphases, responses, sigmas)) : y = np.exp(np.cos(2.0*(phases+pp))) - sigma = 0.1*y - probs[k,:] = np.exp(-0.5*((r-y)/sigma)**2.0)/np.sqrt(2.0*np.pi)/sigma + probs[k,:] = np.exp(-0.5*((r-y)/sigma)**2.0)/np.sqrt(2.0*np.pi*sigma**2) loglikelihood = np.sum(np.log(probs), 0) -maxl = np.max(loglikelihood) maxp = phases[np.argmax(loglikelihood)] ax.annotate('', - xy=(maxp, -1600), xycoords='data', - xytext=(maxp, -30), textcoords='data', + xy=(maxp, -210), xycoords='data', + xytext=(maxp, -10), textcoords='data', arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5), connectionstyle="angle3,angleA=80,angleB=90") ) -ax.text(maxp+0.05, -1100, 'most likely\norientation\ngiven the responses') -ax.plot(phases, loglikelihood, **lsA) +ax.text(maxp+0.05, -150, 'most likely\norientation\ngiven the responses') +ax.plot(phases, loglikelihood, clip_on=False, **lsA) plt.savefig('mlecoding.pdf') From 10f71d5661696996564d9300da0f8a2a8c9b9761 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 9 Jan 2021 19:55:54 +0100 Subject: [PATCH 65/87] [likelihood] updated exercise --- likelihood/exercises/likelihood-1.tex | 3 +++ likelihood/lecture/likelihood.tex | 22 +++++++++++----------- 2 files changed, 14 insertions(+), 11 deletions(-) diff --git a/likelihood/exercises/likelihood-1.tex b/likelihood/exercises/likelihood-1.tex index 28b3946..c0b7f3d 100644 --- a/likelihood/exercises/likelihood-1.tex +++ b/likelihood/exercises/likelihood-1.tex @@ -15,6 +15,9 @@ \begin{questions} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\question \qt{Read chapter 9 on ``Maximum likelihood estimation''!}\vspace{-3ex} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Maximum likelihood of the standard deviation} Let's compute the likelihood and the log-likelihood for the estimation diff --git a/likelihood/lecture/likelihood.tex b/likelihood/lecture/likelihood.tex index ea0cfd4..255ddd5 100644 --- a/likelihood/lecture/likelihood.tex +++ b/likelihood/lecture/likelihood.tex @@ -411,17 +411,6 @@ analysis. Neural systems face the very same problem. They also need to estimate parameters of the internal and external environment based on the activity of neurons. -In sensory systems certain aspects of the environment are encoded in -the neuronal activity of populations of neurons. One example of such a -population code is the tuning of neurons in the primary visual cortex -(V1) to the orientation of a bar in the visual stimulus. Different -neurons respond best to different bar orientations. Traditionally, -such a tuning is measured by analyzing the neuronal response strength -(e.g. the firing rate) as a function of the orientation of a black bar -and is illustrated and summarized with the so called -\enterm{tuning-curve} (\determ{Abstimmkurve}, -figure~\ref{mlecodingfig}, top). - \begin{figure}[tp] \includegraphics[width=1\textwidth]{mlecoding} \titlecaption{\label{mlecodingfig} Maximum likelihood estimation of @@ -440,6 +429,17 @@ figure~\ref{mlecodingfig}, top). orientation.} \end{figure} +In sensory systems certain aspects of the environment are encoded in +the neuronal activity of populations of neurons. One example of such a +population code is the tuning of neurons in the primary visual cortex +(V1) to the orientation of a bar in the visual stimulus. Different +neurons respond best to different bar orientations. Traditionally, +such a tuning is measured by analyzing the neuronal response strength +(e.g. the firing rate) as a function of the orientation of a black bar +and is illustrated and summarized with the so called +\enterm{tuning-curve} (\determ{Abstimmkurve}, +figure~\ref{mlecodingfig}, top). + The brain, however, is confronted with the inverse problem: given a certain activity pattern in the neuronal population, what is the stimulus? In our example, what is the orientation of the bar? In the From e5fd1ecb32e1dadb341d606e501ad659a269150e Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 9 Jan 2021 23:23:47 +0100 Subject: [PATCH 66/87] [pointprocesses] updated some figures --- pointprocesses/lecture/isihexamples.py | 26 +++--- pointprocesses/lecture/pointprocesses.tex | 95 ++++++++++---------- pointprocesses/lecture/rasterexamples.py | 40 ++++----- pointprocesses/lecture/returnmapexamples.py | 19 ++-- pointprocesses/lecture/serialcorrexamples.py | 6 +- 5 files changed, 101 insertions(+), 85 deletions(-) diff --git a/pointprocesses/lecture/isihexamples.py b/pointprocesses/lecture/isihexamples.py index b1c7daa..674bbd7 100644 --- a/pointprocesses/lecture/isihexamples.py +++ b/pointprocesses/lecture/isihexamples.py @@ -55,11 +55,11 @@ def plotisih( ax, isis, binwidth=None ) : binwidth = 5e-4 h, b = np.histogram(isis, np.arange(0.0, np.max(isis)+binwidth, binwidth), density=True) ax.text(0.9, 0.85, 'rate={:.0f}Hz'.format(1.0/np.mean(isis)), ha='right', transform=ax.transAxes) - ax.text(0.9, 0.75, 'mean={:.0f}ms'.format(1000.0*np.mean(isis)), ha='right', transform=ax.transAxes) - ax.text(0.9, 0.65, 'CV={:.2f}'.format(np.std(isis)/np.mean(isis)), ha='right', transform=ax.transAxes) + ax.text(0.9, 0.7, 'mean={:.0f}ms'.format(1000.0*np.mean(isis)), ha='right', transform=ax.transAxes) + ax.text(0.9, 0.55, 'CV={:.2f}'.format(np.std(isis)/np.mean(isis)), ha='right', transform=ax.transAxes) ax.set_xlabel('ISI', 'ms') ax.set_ylabel('p(ISI)', '1/s') - ax.bar( 1000.0*b[:-1], h, bar_fac*1000.0*np.diff(b), facecolor=colors['blue']) + ax.bar( 1000.0*b[:-1], h, bar_fac*1000.0*np.diff(b), **fsA) # parameter: rate = 20.0 @@ -85,16 +85,18 @@ x[x<0.0] = 0.0 inhspikes = pifspikes(x, trials, dt, D=0.3) fig, (ax1, ax2) = plt.subplots(1, 2) -fig.subplots_adjust(**adjust_fs(fig, top=1.5)) -ax1.set_title('stationary') -ax1.set_xlim(0.0, 200.0) -ax1.set_ylim(0.0, 40.0) -plotisih(ax1, isis(homspikes)) +fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) +ax1.set_xlim(0.0, 150.0) +ax1.set_ylim(0.0, 31.0) +ax1.set_xticks(np.arange(0.0, 151.0, 50.0)) +ax1.set_yticks(np.arange(0.0, 31.0, 10.0)) +plotisih(ax1, isis(homspikes), 0.005) -ax2.set_title('non-stationary') -ax2.set_xlim(0.0, 200.0) -ax2.set_ylim(0.0, 40.0) -plotisih(ax2, isis(inhspikes)) +ax2.set_xlim(0.0, 150.0) +ax2.set_ylim(0.0, 31.0) +ax2.set_xticks(np.arange(0.0, 151.0, 50.0)) +ax2.set_yticks(np.arange(0.0, 31.0, 10.0)) +plotisih(ax2, isis(inhspikes), 0.005) plt.savefig('isihexamples.pdf') plt.close() diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index 5849a9a..81bbb9a 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -1,36 +1,41 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\chapter{Spiketrain analysis} +\chapter{Spike-train analysis} \label{pointprocesseschapter} -\exercisechapter{Spiketrain analysis} +\exercisechapter{Spike-train analysis} \entermde[action potential]{Aktionspotential}{Action potentials} -(\enterm[spike|seealso{action potential}]{spikes}) are the carriers of -information in the nervous system. Thereby it is the time at which the -spikes are generated that is of importance for information -transmission. The waveform of the action potential is largely -stereotyped and therefore does not carry information. - -The result of the pre-processing of electrophysiological recordings are -series of spike times, which are termed \enterm{spiketrains}. If -measurements are repeated we get several \enterm{trials} of -spiketrains (\figref{rasterexamplesfig}). - -Spiketrains are times of events, the action potentials. Analyzing -spike trains leads into the realm of the so called \entermde[point - process]{Punktprozess}{point processes}. - -\begin{figure}[ht] +(\enterm[spike|seealso{action potential}]{spikes}) carry information +within neural systems. More precisely, the times at which action +potentials are generated contain the information. The waveform of the +action potential is largely stereotyped and therefore conveys no +information. Analyzing the statistics of spike times and their +relation to sensory stimuli or motor actions is central to +neuroscientific research. With multi-electrode arrays it is nowadays +possible to record from hundreds or even thousands of neurons +simultaneously. The open challenge is how to analyze such data sets in +order to understand how neural systems work. Let's start with the +basics in this chapter. + +The result of the pre-processing of electrophysiological recordings +are series of spike times, which are termed \enterm[spike train]{spike + trains}. If measurements are repeated we get several \enterm{trials} +of spike trains (\figref{rasterexamplesfig}). Spike trains are lists +of times of events, the action potentials. Analyzing spike trains +leads into the realm of the statistics of so called \entermde[point +process]{Punktprozess}{point processes}. + +\begin{figure}[bt] \includegraphics[width=1\textwidth]{rasterexamples} - \titlecaption{\label{rasterexamplesfig}Raster-plot.}{Raster-plots of - ten trials of data illustrating the times of the action - potentials. Each vertical dash illustrates the time at which an - action potential was observed. Each line displays the events of - one trial. Shown is a stationary point process (homogeneous point + \titlecaption{\label{rasterexamplesfig}Raster plot.}{Raster plots of + ten trials of data illustrating the times of action + potentials. Each vertical stroke illustrates the time at which an + action potential was observed. Each row displays the events of one + trial. Shown is a stationary point process (homogeneous point process with a rate $\lambda=20$\;Hz, left) and an non-stationary - point process (perfect integrate-and-fire neuron driven by - Ohrnstein-Uhlenbeck noise with a time-constant $\tau=100$\,ms, - right).} + point process with a rate that varies in time (noisy perfect + integrate-and-fire neuron driven by Ohrnstein-Uhlenbeck noise with + a time-constant $\tau=100$\,ms, right).} \end{figure} @@ -43,7 +48,7 @@ spike trains leads into the realm of the so called \entermde[point crosses some threshold. For example:\vspace{-1ex} \begin{itemize} \item Action potentials/heart beat: created by the dynamics of the - neuron/sinoatrial node + neuron/sinoatrial node. \item Earthquake: defined by the dynamics of the pressure between tectonical plates. \item Communication calls in crickets/frogs/birds: shaped by @@ -59,21 +64,21 @@ spike trains leads into the realm of the so called \entermde[point $T_i=t_{i+1}-t_i$ and the number of events $n_i$. } \end{figure} +\noindent A temporal \entermde{Punktprozess}{point process} is a stochastic -process that generates a sequence of events at times $\{t_i\}$, $t_i -\in \reZ$. In the neurosciences, the statistics of point processes is -of importance since the timing of neuronal events (action potentials, -post-synaptic potentials, events in EEG or local-field recordings, -etc.) is crucial for information transmission and can be treated as -such a process. +process that generates a sequence of events at times $\{t_i\}$. In +the neurosciences, the statistics of point processes is of importance +since the timing of neuronal events (action potentials, post-synaptic +potentials, events in EEG or local-field recordings, etc.) is crucial +for information transmission and can be treated as such a process. The events of a point process can be illustrated by means of a raster plot in which each vertical line indicates the time of an event. The event from two different point processes are shown in -\figref{rasterexamplesfig}. Point processes can be described using -the intervals between successive events $T_i=t_{i+1}-t_i$ and the -number of observed events within a certain time window $n_i$ -(\figref{pointprocessscetchfig}). +\figref{rasterexamplesfig}. In addition to the event times, point +processes can be described using the intervals $T_i=t_{i+1}-t_i$ +between successive events or the number of observed events within a +certain time window $n_i$ (\figref{pointprocessscetchfig}). \begin{exercise}{rasterplot.m}{} Implement a function \varcode{rasterplot()} that displays the times of @@ -94,7 +99,7 @@ real-valued variables: \begin{figure}[t] \includegraphics[width=0.96\textwidth]{isihexamples}\vspace{-2ex} - \titlecaption{\label{isihexamplesfig}Interspike interval + \titlecaption{\label{isihexamplesfig}Interspike-interval histograms}{of the spike trains shown in \figref{rasterexamplesfig}.} \end{figure} @@ -144,7 +149,7 @@ the interval $T_i$. The parameter $k$ is called the \enterm{lag} (\determ{Verz\"ogerung}) $k$. Stationary and non-stationary return maps are distinctly different \figref{returnmapfig}. -\begin{figure}[t] +\begin{figure}[tp] \includegraphics[width=1\textwidth]{returnmapexamples} \includegraphics[width=1\textwidth]{serialcorrexamples} \titlecaption{\label{returnmapfig}Interspike interval @@ -314,7 +319,7 @@ The homogeneous Poisson process has the following properties: \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms} \titlecaption{\label{hompoissoncountfig}Distribution of counts of a - Poisson spiketrain.}{The count statistics was generated for two + Poisson spike train.}{The count statistics was generated for two different windows of width $W=10$\,ms (left) and width $W=100$\,ms (right). The red line illustrates the corresponding Poisson distribution \eqnref{poissoncounts}.} @@ -324,7 +329,7 @@ The homogeneous Poisson process has the following properties: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Time-dependent firing rate} -So far we have discussed stationary spiketrains. The statistical properties +So far we have discussed stationary spike trains. The statistical properties of these did not change within the observation time (stationary point processes). Most commonly, however, this is not the case. A sensory neuron, for example, might respond to a stimulus by modulating its @@ -351,7 +356,7 @@ justifications, their pros- and cons. \begin{figure}[tp] \includegraphics[width=\columnwidth]{isimethod} - \titlecaption{Instantaneous firing rate.}{The recorded spiketrain + \titlecaption{Instantaneous firing rate.}{The recorded spike train (top). Arrows illustrate the interspike intervals and numbers give the intervals in milliseconds. The inverse of the interspike intervals is the \emph{instantaneous firing rate} @@ -412,7 +417,7 @@ methods make an assumption about the relevant observation time-scale \begin{figure}[tp] \includegraphics[width=\columnwidth]{binmethod} \titlecaption{Estimating the PSTH using the binning method.}{The - same spiketrain as shown in \figref{instratefig} (top). Vertical + same spike train as shown in \figref{instratefig} (top). Vertical gray lines indicate the borders between adjacent bins in which the number of action potentials is counted (red numbers). The firing rate is then the histogram normalized to the binwidth @@ -448,8 +453,8 @@ time-scale. \begin{figure}[tp] \includegraphics[width=\columnwidth]{convmethod} \titlecaption{Estimating the firing rate using the convolution - method.}{The same spiketrain as in \figref{instratefig} (top). The - convolution of the spiketrain with a kernel replaces each spike + method.}{The same spike train as in \figref{instratefig} (top). The + convolution of the spike train with a kernel replaces each spike event with the kernel (red). A Gaussian kernel is used here, but other kernels are also possible. If the kernel is properly normalized the firing rate results directly form the superposition diff --git a/pointprocesses/lecture/rasterexamples.py b/pointprocesses/lecture/rasterexamples.py index 042bda2..f616c18 100644 --- a/pointprocesses/lecture/rasterexamples.py +++ b/pointprocesses/lecture/rasterexamples.py @@ -1,5 +1,6 @@ import numpy as np import matplotlib.pyplot as plt +from plotstyle import * def hompoisson(rate, trials, duration) : spikes = [] @@ -8,8 +9,8 @@ def hompoisson(rate, trials, duration) : t = 0.0 while t < duration : t += np.random.exponential(1/rate) - times.append( t ) - spikes.append( times ) + times.append(t) + spikes.append(times) return spikes def inhompoisson(rate, trials, dt) : @@ -18,7 +19,7 @@ def inhompoisson(rate, trials, dt) : for k in range(trials) : x = np.random.rand(len(rate)) times = dt*np.nonzero(x= vthresh : v = vreset times.append(k*dt) - spikes.append( times ) + spikes.append(times) return spikes # parameter: @@ -64,23 +65,22 @@ x[x<0.0] = 0.0 # pif spike trains: inhspikes = pifspikes(x, trials, dt, D=0.3) -fig = plt.figure( figsize=(9,4) ) -ax = fig.add_subplot(1, 2, 1) -ax.set_title('stationary') -ax.set_xlim(0.0, duration) -ax.set_ylim(-0.5, trials-0.5) -ax.set_xlabel('Time [s]') -ax.set_ylabel('Trials') -ax.eventplot(homspikes, colors=[[0, 0, 0]], linelength=0.8) +fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.5*figure_width)) +fig.subplots_adjust(**adjust_fs(fig, left=4.0, right=1.0, top=1.2)) -ax = fig.add_subplot(1, 2, 2) -ax.set_title('non-stationary') -ax.set_xlim(0.0, duration) -ax.set_ylim(-0.5, trials-0.5) -ax.set_xlabel('Time [s]') -ax.set_ylabel('Trials') -ax.eventplot(inhspikes, colors=[[0, 0, 0]], linelength=0.8) +ax1.set_title('stationary') +ax1.set_xlim(0.0, duration) +ax1.set_ylim(-0.5, trials-0.5) +ax1.set_xlabel('Time [s]') +ax1.set_ylabel('Trial') +ax1.eventplot(homspikes, colors=[lsA['color']], linelength=0.8, lw=1) + +ax2.set_title('non-stationary') +ax2.set_xlim(0.0, duration) +ax2.set_ylim(-0.5, trials-0.5) +ax2.set_xlabel('Time [s]') +ax2.set_ylabel('Trial') +ax2.eventplot(inhspikes, colors=[lsA['color']], linelength=0.8, lw=1) -plt.tight_layout() plt.savefig('rasterexamples.pdf') plt.close() diff --git a/pointprocesses/lecture/returnmapexamples.py b/pointprocesses/lecture/returnmapexamples.py index db9326d..99bf88d 100644 --- a/pointprocesses/lecture/returnmapexamples.py +++ b/pointprocesses/lecture/returnmapexamples.py @@ -40,19 +40,21 @@ def pifspikes(input, trials, dt, D=0.1) : spikes.append( times ) return spikes + def isis( spikes ) : isi = [] for k in range(len(spikes)) : isi.extend(np.diff(spikes[k])) return np.array( isi ) -def plotreturnmap(ax, isis, lag=1, max=None) : + +def plotreturnmap(ax, isis, lag=1, max=1.0) : ax.set_xlabel(r'ISI$_i$', 'ms') ax.set_ylabel(r'ISI$_{i+1}$', 'ms') - if max != None : - ax.set_xlim(0.0, 1000.0*max) - ax.set_ylim(0.0, 1000.0*max) - ax.scatter(1000.0*isis[:-lag], 1000.0*isis[lag:], c=colors['blue']) + ax.set_xlim(0.0, 1000.0*max) + ax.set_ylim(0.0, 1000.0*max) + isiss = isis[isis Date: Sun, 10 Jan 2021 20:37:40 +0100 Subject: [PATCH 67/87] [pointprocesses] python version of sketch --- plotstyle.py | 2 + pointprocesses/lecture/firingrates.py | 26 +++--- pointprocesses/lecture/isihexamples.py | 88 ++++++++++-------- pointprocesses/lecture/pointprocesses.tex | 9 +- pointprocesses/lecture/rasterexamples.py | 85 ++++++++++-------- pointprocesses/lecture/returnmapexamples.py | 94 -------------------- pointprocesses/lecture/serialcorrexamples.py | 94 +++++++++++++------- 7 files changed, 179 insertions(+), 219 deletions(-) delete mode 100644 pointprocesses/lecture/returnmapexamples.py diff --git a/plotstyle.py b/plotstyle.py index 5cbf30e..add3e40 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -37,6 +37,7 @@ edgewidth = 0.0 if xkcd_style else 1.0 mainline = {'linestyle': '-', 'linewidth': lwthick} minorline = {'linestyle': '-', 'linewidth': lwthin} largemarker = {'marker': 'o', 'markersize': 9, 'markeredgecolor': colors['white'], 'markeredgewidth': edgewidth} +largeopenmarker = {'marker': 'o', 'markersize': 7, 'markerfacecolor': colors['white'], 'markeredgewidth': 2} smallmarker = {'marker': 'o', 'markersize': 6, 'markeredgecolor': colors['white'], 'markeredgewidth': edgewidth} largelinepoints = {'linestyle': '-', 'linewidth': lwthick, 'marker': 'o', 'markersize': 10, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} smalllinepoints = {'linestyle': '-', 'linewidth': 1.4, 'marker': 'o', 'markersize': 7, 'markeredgecolor': colors['white'], 'markeredgewidth': 1} @@ -88,6 +89,7 @@ fsAa = {'facecolor': colors['blue'], 'edgecolor': 'none', 'alpha': fillalpha} lsB = dict({'color': colors['red']}, **mainline) lsBm = dict({'color': colors['red']}, **minorline) psB = dict({'color': colors['red'], 'linestyle': 'none'}, **largemarker) +psBo = dict({'markeredgecolor': colors['red'], 'linestyle': 'none'}, **largeopenmarker) psBm = dict({'color': colors['red'], 'linestyle': 'none'}, **smallmarker) lpsB = dict({'color': colors['red']}, **largelinepoints) lpsBm = dict({'color': colors['red']}, **smalllinepoints) diff --git a/pointprocesses/lecture/firingrates.py b/pointprocesses/lecture/firingrates.py index 087e7ee..1195e3a 100644 --- a/pointprocesses/lecture/firingrates.py +++ b/pointprocesses/lecture/firingrates.py @@ -6,7 +6,7 @@ import matplotlib.pyplot as plt from plotstyle import * -def get_instantaneous_rate(times, max_t=30., dt=1e-4): +def instantaneous_rate(times, max_t=30., dt=1e-4): time = np.arange(0., max_t, dt) indices = np.asarray(times / dt, dtype=int) intervals = np.diff(np.hstack(([0], times))) @@ -19,12 +19,12 @@ def get_instantaneous_rate(times, max_t=30., dt=1e-4): def plot_isi_rate(spike_times, max_t=30, dt=1e-4): times = np.squeeze(spike_times[0][0])[:50000] - time, rate = get_instantaneous_rate(times, max_t=50000*dt) + time, rate = instantaneous_rate(times, max_t=50000*dt) rates = np.zeros((len(rate), len(spike_times))) for i in range(len(spike_times)): - _, rates[:, i] = get_instantaneous_rate(np.squeeze(spike_times[i][0])[:50000], - max_t=50000*dt) + _, rates[:, i] = instantaneous_rate(np.squeeze(spike_times[i][0])[:50000], + max_t=50000*dt) avg_rate = np.mean(rates, axis=1) rate_std = np.std(rates, axis=1) @@ -48,7 +48,7 @@ def plot_isi_rate(spike_times, max_t=30, dt=1e-4): plt.close() -def get_binned_rate(times, bin_width=0.05, max_t=30., dt=1e-4): +def binned_rate(times, bin_width=0.05, max_t=30., dt=1e-4): time = np.arange(0., max_t, dt) bins = np.arange(0., max_t, bin_width) bin_indices = np.asarray(bins / dt, np.int) @@ -62,10 +62,10 @@ def get_binned_rate(times, bin_width=0.05, max_t=30., dt=1e-4): def plot_bin_rate(spike_times, bin_width, max_t=30, dt=1e-4): times = np.squeeze(spike_times[0][0]) - time, rate = get_binned_rate(times) + time, rate = binned_rate(times) rates = np.zeros((len(rate), len(spike_times))) for i in range(len(spike_times)): - _, rates[:, i] = get_binned_rate(np.squeeze(spike_times[i][0])) + _, rates[:, i] = binned_rate(np.squeeze(spike_times[i][0])) avg_rate = np.mean(rates, axis=1) rate_std = np.std(rates, axis=1) @@ -93,7 +93,7 @@ def plot_bin_rate(spike_times, bin_width, max_t=30, dt=1e-4): plt.close() -def get_convolved_rate(times, sigma, max_t=30., dt=1.e-4): +def convolved_rate(times, sigma, max_t=30., dt=1.e-4): time = np.arange(0., max_t, dt) kernel = spst.norm.pdf(np.arange(-8*sigma, 8*sigma, dt),loc=0,scale=sigma) indices = np.asarray(times/dt, dtype=int) @@ -105,11 +105,11 @@ def get_convolved_rate(times, sigma, max_t=30., dt=1.e-4): def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): times = np.squeeze(spike_times[0][0]) - time, rate = get_convolved_rate(times, sigma) + time, rate = convolved_rate(times, sigma) rates = np.zeros((len(rate), len(spike_times))) for i in range(len(spike_times)): - _, rates[:, i] = get_convolved_rate(np.squeeze(spike_times[i][0]), sigma) + _, rates[:, i] = convolved_rate(np.squeeze(spike_times[i][0]), sigma) avg_rate = np.mean(rates, axis=1) rate_std = np.std(rates, axis=1) @@ -139,9 +139,9 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): def plot_comparison(spike_times, bin_width, sigma, max_t=30., dt=1e-4): times = np.squeeze(spike_times[0][0]) - time, conv_rate = get_convolved_rate(times, bin_width/np.sqrt(12.)) - time, inst_rate = get_instantaneous_rate(times) - time, binn_rate = get_binned_rate(times, bin_width) + time, conv_rate = convolved_rate(times, bin_width/np.sqrt(12.)) + time, inst_rate = instantaneous_rate(times) + time, binn_rate = binned_rate(times, bin_width) fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, figsize=cm_size(figure_width, 1.8*figure_height)) fig.subplots_adjust(**adjust_fs(fig, left=6.0, right=1.5, bottom=3.0, top=1.0)) diff --git a/pointprocesses/lecture/isihexamples.py b/pointprocesses/lecture/isihexamples.py index 674bbd7..9d0f7c0 100644 --- a/pointprocesses/lecture/isihexamples.py +++ b/pointprocesses/lecture/isihexamples.py @@ -2,6 +2,15 @@ import numpy as np import matplotlib.pyplot as plt from plotstyle import * + +rate = 20.0 +trials = 10 +duration = 100.0 +dt = 0.001 +drate = 50.0 +tau = 0.1; + + def hompoisson(rate, trials, duration) : spikes = [] for k in range(trials) : @@ -13,6 +22,7 @@ def hompoisson(rate, trials, duration) : spikes.append( times ) return spikes + def inhompoisson(rate, trials, dt) : spikes = [] p = rate*dt @@ -40,12 +50,27 @@ def pifspikes(input, trials, dt, D=0.1) : spikes.append( times ) return spikes + +def oupifspikes(rate, trials, duration, dt, D, drate, tau): + # OU noise: + rng = np.random.RandomState(54637281) + time = np.arange(0.0, duration, dt) + x = np.zeros(time.shape)+rate + n = rng.randn(len(time))*drate*tau/np.sqrt(dt) + rate + for k in range(1,len(x)) : + x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau + x[x<0.0] = 0.0 + spikes = pifspikes(x, trials, dt, D) + return spikes + + def isis( spikes ) : isi = [] for k in range(len(spikes)) : isi.extend(np.diff(spikes[k])) return isi + def plotisih( ax, isis, binwidth=None ) : if binwidth == None : nperbin = 200.0 # average number of isis per bin @@ -61,42 +86,29 @@ def plotisih( ax, isis, binwidth=None ) : ax.set_ylabel('p(ISI)', '1/s') ax.bar( 1000.0*b[:-1], h, bar_fac*1000.0*np.diff(b), **fsA) -# parameter: -rate = 20.0 -drate = 50.0 -trials = 10 -duration = 100.0 -dt = 0.001 -tau = 0.1; + +def plot_hom_isih(ax): + homspikes = hompoisson(rate, trials, duration) + ax.set_xlim(0.0, 150.0) + ax.set_ylim(0.0, 31.0) + ax.set_xticks(np.arange(0.0, 151.0, 50.0)) + ax.set_yticks(np.arange(0.0, 31.0, 10.0)) + plotisih(ax, isis(homspikes), 0.005) + + +def plot_inhom_isih(ax): + inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + ax.set_xlim(0.0, 150.0) + ax.set_ylim(0.0, 31.0) + ax.set_xticks(np.arange(0.0, 151.0, 50.0)) + ax.set_yticks(np.arange(0.0, 31.0, 10.0)) + plotisih(ax, isis(inhspikes), 0.005) -# homogeneous spike trains: -homspikes = hompoisson(rate, trials, duration) - -# OU noise: -rng = np.random.RandomState(54637281) -time = np.arange(0.0, duration, dt) -x = np.zeros(time.shape)+rate -n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate -for k in range(1,len(x)) : - x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau -x[x<0.0] = 0.0 - -# pif spike trains: -inhspikes = pifspikes(x, trials, dt, D=0.3) - -fig, (ax1, ax2) = plt.subplots(1, 2) -fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) -ax1.set_xlim(0.0, 150.0) -ax1.set_ylim(0.0, 31.0) -ax1.set_xticks(np.arange(0.0, 151.0, 50.0)) -ax1.set_yticks(np.arange(0.0, 31.0, 10.0)) -plotisih(ax1, isis(homspikes), 0.005) - -ax2.set_xlim(0.0, 150.0) -ax2.set_ylim(0.0, 31.0) -ax2.set_xticks(np.arange(0.0, 151.0, 50.0)) -ax2.set_yticks(np.arange(0.0, 31.0, 10.0)) -plotisih(ax2, isis(inhspikes), 0.005) - -plt.savefig('isihexamples.pdf') -plt.close() + +if __name__ == "__main__": + fig, (ax1, ax2) = plt.subplots(1, 2) + fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) + plot_hom_isih(ax1) + plot_inhom_isih(ax2) + plt.savefig('isihexamples.pdf') + plt.close() diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index 81bbb9a..da03d13 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -60,8 +60,8 @@ process]{Punktprozess}{point processes}. \texpicture{pointprocessscetch} \titlecaption{\label{pointprocessscetchfig} Statistics of point processes.}{A point process is a sequence of instances in time - $t_i$ that can be characterized through the inter-event-intervals - $T_i=t_{i+1}-t_i$ and the number of events $n_i$. } + $t_i$ that can be also characterized by inter-event intervals + $T_i=t_{i+1}-t_i$ and event counts $n_i$.} \end{figure} \noindent @@ -150,9 +150,8 @@ the interval $T_i$. The parameter $k$ is called the \enterm{lag} maps are distinctly different \figref{returnmapfig}. \begin{figure}[tp] - \includegraphics[width=1\textwidth]{returnmapexamples} \includegraphics[width=1\textwidth]{serialcorrexamples} - \titlecaption{\label{returnmapfig}Interspike interval + \titlecaption{\label{returnmapfig}Interspike-interval correlations}{of the spike trains shown in \figref{rasterexamplesfig}. Upper panels show the return maps and lower panels the serial correlations of successive intervals @@ -191,7 +190,7 @@ with itself and is always 1. % \begin{figure}[t] % \includegraphics[width=0.48\textwidth]{poissoncounthist100hz10ms}\hfill % \includegraphics[width=0.48\textwidth]{poissoncounthist100hz100ms} -% \titlecaption{\label{countstatsfig}Count Statistik.}{} +% \titlecaption{\label{countstatsfig}Count statistic.}{} % \end{figure} Counting the number of events $n_i$ (counts) in time windows $i$ of duration $W$ yields positive integer random numbers that are commonly quantified diff --git a/pointprocesses/lecture/rasterexamples.py b/pointprocesses/lecture/rasterexamples.py index f616c18..07b8628 100644 --- a/pointprocesses/lecture/rasterexamples.py +++ b/pointprocesses/lecture/rasterexamples.py @@ -2,6 +2,15 @@ import numpy as np import matplotlib.pyplot as plt from plotstyle import * + +rate = 20.0 +trials = 10 +duration = 2.0 +dt = 0.001 +drate = 50.0 +tau = 0.1; + + def hompoisson(rate, trials, duration) : spikes = [] for k in range(trials) : @@ -13,6 +22,7 @@ def hompoisson(rate, trials, duration) : spikes.append(times) return spikes + def inhompoisson(rate, trials, dt) : spikes = [] p = rate*dt @@ -40,47 +50,44 @@ def pifspikes(input, trials, dt, D=0.1) : spikes.append(times) return spikes -# parameter: -rate = 20.0 -drate = 50.0 -trials = 10 -duration = 2.0 -dt = 0.001 -tau = 0.1; - -# homogeneous spike trains: -homspikes = hompoisson(rate, trials, duration) -# OU noise: -rng = np.random.RandomState(54637281) -time = np.arange(0.0, duration, dt) -x = np.zeros(time.shape)+rate -n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate -for k in range(1,len(x)) : - x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau -x[x<0.0] = 0.0 - -# inhomogeneous spike trains: -#inhspikes = inhompoisson(x, trials, dt) -# pif spike trains: -inhspikes = pifspikes(x, trials, dt, D=0.3) +def oupifspikes(rate, trials, duration, dt, D, drate, tau): + # OU noise: + rng = np.random.RandomState(54637281) + time = np.arange(0.0, duration, dt) + x = np.zeros(time.shape)+rate + n = rng.randn(len(time))*drate*tau/np.sqrt(dt) + rate + for k in range(1,len(x)) : + x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau + x[x<0.0] = 0.0 + spikes = pifspikes(x, trials, dt, D) + return spikes -fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.5*figure_width)) -fig.subplots_adjust(**adjust_fs(fig, left=4.0, right=1.0, top=1.2)) + +def plot_homogeneous_spikes(ax): + homspikes = hompoisson(rate, trials, duration) + ax.set_title('stationary') + ax.set_xlim(0.0, duration) + ax.set_ylim(-0.5, trials-0.5) + ax.set_xlabel('Time [s]') + ax.set_ylabel('Trial') + ax.eventplot(homspikes, colors=[lsA['color']], linelength=0.8, lw=1) -ax1.set_title('stationary') -ax1.set_xlim(0.0, duration) -ax1.set_ylim(-0.5, trials-0.5) -ax1.set_xlabel('Time [s]') -ax1.set_ylabel('Trial') -ax1.eventplot(homspikes, colors=[lsA['color']], linelength=0.8, lw=1) + +def plot_inhomogeneous_spikes(ax): + inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + ax.set_title('non-stationary') + ax.set_xlim(0.0, duration) + ax.set_ylim(-0.5, trials-0.5) + ax.set_xlabel('Time [s]') + ax.set_ylabel('Trial') + ax.eventplot(inhspikes, colors=[lsA['color']], linelength=0.8, lw=1) -ax2.set_title('non-stationary') -ax2.set_xlim(0.0, duration) -ax2.set_ylim(-0.5, trials-0.5) -ax2.set_xlabel('Time [s]') -ax2.set_ylabel('Trial') -ax2.eventplot(inhspikes, colors=[lsA['color']], linelength=0.8, lw=1) -plt.savefig('rasterexamples.pdf') -plt.close() +if __name__ == "__main__": + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.5*figure_width)) + fig.subplots_adjust(**adjust_fs(fig, left=4.0, right=1.0, top=1.2)) + plot_homogeneous_spikes(ax1) + plot_inhomogeneous_spikes(ax2) + plt.savefig('rasterexamples.pdf') + plt.close() diff --git a/pointprocesses/lecture/returnmapexamples.py b/pointprocesses/lecture/returnmapexamples.py deleted file mode 100644 index 99bf88d..0000000 --- a/pointprocesses/lecture/returnmapexamples.py +++ /dev/null @@ -1,94 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from plotstyle import * - -def hompoisson(rate, trials, duration) : - spikes = [] - for k in range(trials) : - times = [] - t = 0.0 - while t < duration : - t += np.random.exponential(1/rate) - times.append( t ) - spikes.append( times ) - return spikes - -def inhompoisson(rate, trials, dt) : - spikes = [] - p = rate*dt - for k in range(trials) : - x = np.random.rand(len(rate)) - times = dt*np.nonzero(x= vthresh : - v = vreset - times.append(k*dt) - spikes.append( times ) - return spikes - - -def isis( spikes ) : - isi = [] - for k in range(len(spikes)) : - isi.extend(np.diff(spikes[k])) - return np.array( isi ) - - -def plotreturnmap(ax, isis, lag=1, max=1.0) : - ax.set_xlabel(r'ISI$_i$', 'ms') - ax.set_ylabel(r'ISI$_{i+1}$', 'ms') - ax.set_xlim(0.0, 1000.0*max) - ax.set_ylim(0.0, 1000.0*max) - isiss = isis[isis Date: Sun, 10 Jan 2021 20:54:23 +0100 Subject: [PATCH 68/87] no more gnuplot! --- chapter.mk | 19 +- header.tex | 4 - .../lecture/pointprocesses-slides.tex | 5 +- pointprocesses/lecture/pointprocesses.tex | 6 +- pointprocesses/lecture/pointprocesses_de.tex | 2 +- pointprocesses/lecture/pointprocessscetch.gpt | 205 ---- .../lecture/pointprocessscetchA.eps | 546 ----------- .../lecture/pointprocessscetchA.gpt | 62 -- .../lecture/pointprocessscetchA.pdf | 84 -- .../lecture/pointprocessscetchB.eps | 891 ------------------ .../lecture/pointprocessscetchB.gpt | 204 ---- .../lecture/pointprocessscetchB.pdf | Bin 4877 -> 0 bytes pointprocesses/lecture/pointprocesssketch.py | 69 ++ pointprocesses/lecture/whitestyles.gp | 67 -- scientificcomputing-script.tex | 1 - 15 files changed, 77 insertions(+), 2088 deletions(-) delete mode 100644 pointprocesses/lecture/pointprocessscetch.gpt delete mode 100644 pointprocesses/lecture/pointprocessscetchA.eps delete mode 100644 pointprocesses/lecture/pointprocessscetchA.gpt delete mode 100644 pointprocesses/lecture/pointprocessscetchA.pdf delete mode 100644 pointprocesses/lecture/pointprocessscetchB.eps delete mode 100644 pointprocesses/lecture/pointprocessscetchB.gpt delete mode 100644 pointprocesses/lecture/pointprocessscetchB.pdf create mode 100644 pointprocesses/lecture/pointprocesssketch.py delete mode 100644 pointprocesses/lecture/whitestyles.gp diff --git a/chapter.mk b/chapter.mk index f642e2e..44553f5 100644 --- a/chapter.mk +++ b/chapter.mk @@ -1,5 +1,5 @@ # plots: -plots : pythonplots gnuplots +plots : pythonplots # python plots: PYFILES=$(wildcard *.py) @@ -16,21 +16,6 @@ $(PYPDFFILES) : %.pdf: %.py ../../plotstyle.py cleanpythonplots : rm -f $(PYPDFFILES) - -# gnuplot plots: -GPTFILES=$(wildcard *.gpt) -GPTTEXFILES=$(GPTFILES:.gpt=.tex) - -gnuplots : $(GPTTEXFILES) - -$(GPTTEXFILES) : %.tex: %.gpt whitestyles.gp - gnuplot whitestyles.gp $< - epstopdf $*.eps - -cleangnuplots : - rm -f $(GPTTEXFILES) - - # script: chapter : $(BASENAME)-chapter.pdf @@ -52,7 +37,7 @@ cleantex: rm -f $(BASENAME).aux $(BASENAME).log *.idx rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out $(BASENAME)-chapter.idx $(BASENAME)-chapter-solutions.tex $(BASENAME)-solutions.tex -cleanplots: cleanpythonplots cleangnuplots +cleanplots: cleanpythonplots cleanchapter : cleanplots cleantex diff --git a/header.tex b/header.tex index 464bb56..2f2360d 100644 --- a/header.tex +++ b/header.tex @@ -68,10 +68,6 @@ \pagecolor{white} %%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% gnuplot figures: -\newcommand{\texinputpath}{} -\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{\texinputpath#1.tex}}} -\newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}} % maximum number of floats: \setcounter{topnumber}{1} diff --git a/pointprocesses/lecture/pointprocesses-slides.tex b/pointprocesses/lecture/pointprocesses-slides.tex index ff49cb2..75a084c 100644 --- a/pointprocesses/lecture/pointprocesses-slides.tex +++ b/pointprocesses/lecture/pointprocesses-slides.tex @@ -49,7 +49,6 @@ %%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} -\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}} %%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{listings} @@ -95,7 +94,7 @@ \begin{frame} \frametitle{Point process} \vspace{-3ex} - \texpicture{pointprocessscetchA} + \includegraphics{pointprocesssketch} A point process is a stochastic (or random) process that generates a sequence of events at times $\{t_i\}$, $t_i \in \reZ$. @@ -113,7 +112,7 @@ \begin{frame} \frametitle{Point process} - \texpicture{pointprocessscetchB} + \includegraphics{pointprocesssketch} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index da03d13..f2286e2 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -57,8 +57,8 @@ process]{Punktprozess}{point processes}. \end{ibox} \begin{figure}[tb] - \texpicture{pointprocessscetch} - \titlecaption{\label{pointprocessscetchfig} Statistics of point + \includegraphics{pointprocesssketch} + \titlecaption{\label{pointprocesssketchfig} Statistics of point processes.}{A point process is a sequence of instances in time $t_i$ that can be also characterized by inter-event intervals $T_i=t_{i+1}-t_i$ and event counts $n_i$.} @@ -78,7 +78,7 @@ event from two different point processes are shown in \figref{rasterexamplesfig}. In addition to the event times, point processes can be described using the intervals $T_i=t_{i+1}-t_i$ between successive events or the number of observed events within a -certain time window $n_i$ (\figref{pointprocessscetchfig}). +certain time window $n_i$ (\figref{pointprocesssketchfig}). \begin{exercise}{rasterplot.m}{} Implement a function \varcode{rasterplot()} that displays the times of diff --git a/pointprocesses/lecture/pointprocesses_de.tex b/pointprocesses/lecture/pointprocesses_de.tex index 4b0850f..60c0f80 100644 --- a/pointprocesses/lecture/pointprocesses_de.tex +++ b/pointprocesses/lecture/pointprocesses_de.tex @@ -56,7 +56,7 @@ erzeugt. Zum Beispiel: \end{ibox} \begin{figure}[t] - \texpicture{pointprocessscetch} + \includegraphics{pointprocesssketch} \titlecaption{\label{pointprocessscetchfig} Statistik von Punktprozessen.}{Ein Punktprozess ist eine Abfolge von Zeitpunkten $t_i$ die auch durch die Intervalle $T_i=t_{i+1}-t_i$ diff --git a/pointprocesses/lecture/pointprocessscetch.gpt b/pointprocesses/lecture/pointprocessscetch.gpt deleted file mode 100644 index d045938..0000000 --- a/pointprocesses/lecture/pointprocessscetch.gpt +++ /dev/null @@ -1,205 +0,0 @@ -set term epslatex size 11.4cm, 6.4cm -set out 'pointprocessscetch.tex' - -set border 0 -set lmarg 4 -set rmarg 1 -set tmarg 1 -set bmarg 1 -set xrange [0:11] -unset xtics -set yrange [-0.7:1.8] -unset ytics -set label 1 at graph -0.07, graph 1.1 - -set multiplot - -set origin 0, 0.7 -set size 1, 0.3 -set label 1 '\normalsize Event times $\{t_i\}$' -set arrow 1 from 0, 0.5 to 11, 0.5 head filled -set label 2 'Time' at 11, -0.3 center -set label 3 "$t_{1}$" at 0.724649, -0.6 center -set label 4 "$t_{2}$" at 1.67586, -0.6 center -set label 5 "$t_{3}$" at 3.02389, -0.6 center -set label 6 "$t_{4}$" at 3.57466, -0.6 center -set label 7 "$t_{5}$" at 4.15121, -0.6 center -set label 8 "$t_{6}$" at 5.00412, -0.6 center -set label 9 "$t_{7}$" at 6.64549, -0.6 center -set label 10 "$t_{8}$" at 7.81657, -0.6 center -set label 11 "$t_{9}$" at 9.77964, -0.6 center -plot '-' w l lt 1 lc rgb 'black' lw 10 -0.724649 0 -0.724649 1 - -1.67586 0 -1.67586 1 - -3.02389 0 -3.02389 1 - -3.57466 0 -3.57466 1 - -4.15121 0 -4.15121 1 - -5.00412 0 -5.00412 1 - -6.64549 0 -6.64549 1 - -7.81657 0 -7.81657 1 - -9.77964 0 -9.77964 1 -e -unset label 3 -unset label 4 -unset label 5 -unset label 6 -unset label 7 -unset label 8 -unset label 9 -unset label 10 -unset label 11 - -set origin 0, 0.4 -set label 1 '\normalsize Intervals $\{T_i\}, \; T_i = t_{i+1} - t_i$' -set label 3 "$T_{1}$" at 1.20025, -0.5 center -set arrow 3 from 0.724649, 0.2 to 1.67586, 0.2 heads -set label 4 "$T_{2}$" at 2.34987, -0.5 center -set arrow 4 from 1.67586, 0.2 to 3.02389, 0.2 heads -set label 5 "$T_{3}$" at 3.29927, -0.5 center -set arrow 5 from 3.02389, 0.2 to 3.57466, 0.2 heads -set label 6 "$T_{4}$" at 3.86293, -0.5 center -set arrow 6 from 3.57466, 0.2 to 4.15121, 0.2 heads -set label 7 "$T_{5}$" at 4.57767, -0.5 center -set arrow 7 from 4.15121, 0.2 to 5.00412, 0.2 heads -set label 8 "$T_{6}$" at 5.82481, -0.5 center -set arrow 8 from 5.00412, 0.2 to 6.64549, 0.2 heads -set label 9 "$T_{7}$" at 7.23103, -0.5 center -set arrow 9 from 6.64549, 0.2 to 7.81657, 0.2 heads -set label 10 "$T_{8}$" at 8.79811, -0.5 center -set arrow 10 from 7.81657, 0.2 to 9.77964, 0.2 heads -plot '-' w l lt 1 lc rgb 'black' lw 10 -0.724649 0 -0.724649 1 - 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4 "$t_{2}$" at 1.67586, -0.6 center -set label 5 "$t_{3}$" at 3.02389, -0.6 center -set label 6 "$t_{4}$" at 3.57466, -0.6 center -set label 7 "$t_{5}$" at 4.15121, -0.6 center -set label 8 "$t_{6}$" at 5.00412, -0.6 center -set label 9 "$t_{7}$" at 6.64549, -0.6 center -set label 10 "$t_{8}$" at 7.81657, -0.6 center -set label 11 "$t_{9}$" at 9.77964, -0.6 center -plot '-' w l lt 1 lc rgb 'black' lw 10 -0.724649 0 -0.724649 1 - -1.67586 0 -1.67586 1 - -3.02389 0 -3.02389 1 - -3.57466 0 -3.57466 1 - -4.15121 0 -4.15121 1 - -5.00412 0 -5.00412 1 - -6.64549 0 -6.64549 1 - -7.81657 0 -7.81657 1 - -9.77964 0 -9.77964 1 -e -unset label 3 -unset label 4 -unset label 5 -unset label 6 -unset label 7 -unset label 8 -unset label 9 -unset label 10 -unset label 11 - -set origin 0, 0.4 -set label 1 '\normalsize Intervals $\{T_i\}, \; T_i = t_{i+1} - t_i$' -set label 3 "$T_{1}$" at 1.20025, -0.5 center -set arrow 3 from 0.724649, 0.2 to 1.67586, 0.2 heads -set label 4 "$T_{2}$" at 2.34987, -0.5 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6.64549, 7.81657, 9.77964] + + +def plot_spikes(ax, spikes): + ax.show_spines('') + ax.text(-0.06, 1.1, r'Event times $\{t_i\}$', transform=ax.transAxes) + ax.annotate('', xy=(0.0, 0.5), xytext=(11.0, 0.5), zorder=-10, + arrowprops=dict(arrowstyle='<-')) + ax.text(10.5, -0.2, 'Time') + for i, t in enumerate(spikes): + ax.plot([t, t], [0.0, 1.0], **lsA) + ax.text(t, -0.6, '$t_{%d}$' % i, ha='center') + ax.set_xlim(0.0, 11.0) + ax.set_ylim(-0.7, 1.2) + + +def plot_isis(ax, spikes): + ax.show_spines('') + ax.text(-0.06, 1.1, r'Intervals $\{T_i\}, \; T_i = t_{i+1} - t_i$', transform=ax.transAxes) + ax.annotate('', xy=(0.0, 0.5), xytext=(11.0, 0.5), zorder=-10, + arrowprops=dict(arrowstyle='<-')) + ax.text(10.5, -0.2, 'Time') + for i in range(len(spikes)): + t1 = spikes[i] + ax.plot([t1, t1], [0., 1.], **lsA) + if i > 0: + t0 = spikes[i-1] + ax.annotate('', xy=(t0, 0.2), xytext=(t1, 0.2), arrowprops=dict(arrowstyle='<->')) + ax.text(0.5*(t0+t1), -0.6, '$T_{%d}$' % i, ha='center') + ax.set_xlim(0.0, 11.0) + ax.set_ylim(-0.7, 1.2) + + +def plot_counts(ax, spikes): + ax.show_spines('l') + ax.text(-0.06, 1.1, r'Event counts $\{ n_i \}$', transform=ax.transAxes) + ax.annotate('', xy=(0.0, 0.0), xytext=(11.0, 0.0), zorder=-10, + arrowprops=dict(arrowstyle='<-')) + ax.text(10.5, -2.0, 'Time') + c = 0 + t0 = 0.0 + for i, t in enumerate(spikes): + ax.plot([t0, t], [c, c], zorder=10, clip_on=False, **lsBm) + ax.plot([t], [c], zorder=20, clip_on=False, **psBo) + c += 1 + ax.plot([t], [c], zorder=30, clip_on=False, **psB) + t0 = t + ax.plot([t0, 10.5], [c, c], zorder=10, **lsBm) + ax.set_xlim(0.0, 11.0) + ax.set_ylim(0, 11) + ax.set_yticks(np.arange(0.0, 11.0, 2.0)) + + +if __name__ == "__main__": + fig = plt.figure(figsize=cm_size(figure_width, 1.7*figure_height)) + gs = gridspec.GridSpec(3, 1, height_ratios=[2, 2, 4]) + gs.update(hspace=0.6, **adjust_fs(fig, bottom=1.5, top=1.5, left=3.0, right=1.5)) + ax1, ax2, ax3 = [fig.add_subplot(gs[i,0]) for i in range(3)] + plot_spikes(ax1, spikes) + plot_isis(ax2, spikes) + plot_counts(ax3, spikes) + plt.savefig('pointprocesssketch.pdf') + plt.close() diff --git a/pointprocesses/lecture/whitestyles.gp b/pointprocesses/lecture/whitestyles.gp deleted file mode 100644 index 1eeb255..0000000 --- a/pointprocesses/lecture/whitestyles.gp +++ /dev/null @@ -1,67 +0,0 @@ -set tics scale 0.8 -set tics out -set format '$%g$' -unset grid -unset key - -# on white background: -set style line 1 lt -1 lc rgb "black" lw 2 # border -set border back ls 1 -set style line 2 lt 1 lc rgb "black" lw 4 pt 7 ps 2 # thick line -set style line 3 lt 1 lc rgb "black" lw 2 # thin line -set style line 4 lt 3 lc rgb "black" lw 1 # grid line - -set style line 10 lt 1 lc rgb "#00DD00" lw 6 # stimulus thick, AM -set style line 11 lt 1 lc rgb "#00DD00" lw 3 # stimulus thin, AM -set style line 15 lt 1 lc rgb "black" lw 15 # stimulus bar - -set style line 20 lt 1 lc rgb "yellow" lw 4 # thin spikes cell 1 -set style line 21 lt 1 lc rgb "orange" lw 4 # thin spikes cell 2 -set style line 22 lt 1 lc rgb "yellow" lw 6 # thick spikes cell 1 -set style line 23 lt 1 lc rgb "orange" lw 6 # thick spikes cell 2 -set style line 24 lt 1 lc rgb "blue" lw 22 # big sync spikes -set style line 25 lt 1 lc rgb "blue" lw 6 # thick sync spikes -set style line 26 lt 1 lc rgb "orange" lw 4 # all spikes - -set style line 30 lt 1 lc rgb "dark-red" lw 6 pt 7 ps 2 # firing rate 1 thick -set style line 31 lt 1 lc rgb "red" lw 6 pt 7 ps 2 # firing rate 2 thick -set style line 32 lt 1 lc rgb "orange" lw 6 pt 7 ps 2 # firing rate 3 thick -set style line 33 lt 1 lc rgb "blue" lw 6 pt 7 ps 2 # firing rate 4 thick -set style line 34 lt 1 lc rgb "gray" lw 6 # firing rate gray thick -set style line 35 lt 1 lc rgb "dark-red" lw 3 pt 7 ps 0.7 # firing rate 1 thin -set style line 36 lt 1 lc rgb "red" lw 3 # firing rate 2 thin -set style line 37 lt 1 lc rgb "orange" lw 3 # firing rate 3 thin -set style line 38 lt 1 lc rgb "blue" lw 3 # firing rate 4 thin -set style line 39 lt 1 lc rgb "gray" lw 3 # firing rate gray thin - -set style line 40 lt 1 lc rgb "green" lw 6 pt 5 ps 2 # onset f-I curve thick -set style line 41 lt 1 lc rgb "green" lw 3 pt 5 ps 2 # onset f-I curve thin -set style line 42 lt 1 lc rgb "red" lw 6 pt 7 ps 2 # steady-state f-I curve thick -set style line 43 lt 1 lc rgb "red" lw 3 pt 7 ps 2 # steady-state f-I curve thin -set style line 44 lt 1 lc rgb "blue" lw 6 pt 9 ps 2 # adapted f-I curve thick -set style line 45 lt 1 lc rgb "blue" lw 3 pt 9 ps 2 # adapted f-I curve thin -set style line 47 lt 1 lc rgb "cyan" lw 6 # adaptation level thick -set style line 48 lt 1 lc rgb "cyan" lw 3 # adaptation level thin -set style line 49 lt 1 lc rgb "yellow" lw 3 pt 7 ps 4 # current adaptation point - -set style line 50 lt 1 lc rgb "dark-red" lw 4 # membrane voltage 1 -set style line 51 lt 1 lc rgb "red" lw 4 # membrane voltage 2 -set style line 52 lt 1 lc rgb "orange" lw 4 # membrane voltage 3 -set style line 55 lt 1 lc rgb "orange" lw 4 # nerve potential - -set style line 60 lt 1 lc rgb "blue" lw 4 # gating variable -set style line 61 lt 1 lc rgb "cyan" lw 4 # gating variable average - -set style line 70 lt 1 lc rgb "red" lw 4 # ionic current -set style line 71 lt 1 lc rgb "orange" lw 4 # ionic current average - -set style line 80 lt 1 lc rgb "#77FFFF" lw 4 pt 13 ps 2.4# baseline -set style line 81 lt 1 lc rgb "#FF5533" lw 4 pt 9 ps 2.8 # beat -set style line 82 lt 1 lc rgb "yellow" lw 4 pt 7 ps 2.4 # chirp -set style line 83 lt 1 lc rgb "#FF7700" lw 4 pt 11 ps 2.8# beat shuffled -set style line 84 lt 1 lc rgb "#FFAA00" lw 4 pt 5 ps 2.2 # chirp shuffled - -set style line 90 lt 1 lc rgb "#77FFFF" lw 2 # EOD thin -set style line 91 lt 1 lc rgb "#77FFFF" lw 4 # EOD thick - -set term epslatex input color dashed rounded size 11.4cm, 6.6cm diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 8df08d8..27b369c 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -5,7 +5,6 @@ \newcommand{\includechapter}[1]{% \graphicspath{{#1/lecture/}{#1/lecture/figures/}{#1/images/}}% \setcodepath{#1/code}% - \renewcommand{\texinputpath}{#1/lecture/}% \include{#1/lecture/#1}% } From f111d20976017dbf27de1dc463aaa7dc89abc270 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 11 Jan 2021 16:55:54 +0100 Subject: [PATCH 69/87] [likelihood] small fixes --- likelihood/lecture/likelihood.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/likelihood/lecture/likelihood.tex b/likelihood/lecture/likelihood.tex index 255ddd5..7ea2b6c 100644 --- a/likelihood/lecture/likelihood.tex +++ b/likelihood/lecture/likelihood.tex @@ -476,12 +476,12 @@ The angle $\phi_{mle}$ that maximizes this likelihood is an estimate of the true orientation of the bar (\figref{mlecodingfig}). The noisiness of the neuron's responses as quantified by $\sigma_i$ -usually is a function of the neuron's mean firing rate $r_i$, -\eqnref{bartuningcurve}: $\sigma_i = \sigma_i(r_i)$. This dependence -has a major impact of the maximum likelihood estimation. Usually, the -stronger the response of a neuron, the higher its firing rate, the -lower the noise. In this case, strong responses will have a stronger -influence on the position of the maximum of the log-likelihood. +usually is a function of the neuron's mean firing rate $r_i$: +$\sigma_i = \sigma_i(r_i)$. This dependence has a major impact on the +maximum likelihood estimation. Usually, the stronger the response of a +neuron, the higher its firing rate, the lower the noise. In this case, +strong responses have a stronger influence on the position of the +maximum of the log-likelihood. Whether neural systems really implement maximum likelihood estimators is another question. There are many ways how a stimulus property can From 4046210b436fdb3a533bc19bd6d77ea7075e1a00 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 11 Jan 2021 21:41:32 +0100 Subject: [PATCH 70/87] [likelihood] fixed exercise --- likelihood/exercises/likelihood-1.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/likelihood/exercises/likelihood-1.tex b/likelihood/exercises/likelihood-1.tex index c0b7f3d..2da6ac2 100644 --- a/likelihood/exercises/likelihood-1.tex +++ b/likelihood/exercises/likelihood-1.tex @@ -51,10 +51,10 @@ of the standard deviation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Maximum-likelihood estimator of a line through the origin} In the lecture we derived the following equation for an -maximum-likelihood estimate of the slope $\theta$ of a straight line +maximum-likelihood estimate of the slope $m$ of a straight line through the origin fitted to $n$ pairs of data values $(x_i|y_i)$ with standard deviation $\sigma_i$: -\[\theta = \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n +\[ m = \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n \frac{x_i^2}{\sigma_i^2}} \] \begin{parts} \part \label{mleslopefunc} Write a function that takes two vectors @@ -105,7 +105,7 @@ normally-distributed data. Such parameter need to be estimated numerically by means of maximum-likelihood from the data. Let us demonstrate this approach by means of data that are drawn from a -gamma distribution, +gamma distribution. \begin{parts} \part Find out which \code{matlab} function computes the probability-density function of the gamma distribution. @@ -123,7 +123,7 @@ gamma distribution, \part Compute and plot a properly normalized histogram of these random numbers. - \part Find out which \code{matlab} function fit a distribution to a + \part Find out which \code{matlab} function fits a distribution to a vector of random numbers according to the maximum-likelihood method. How do you need to use this function in order to fit a gamma distribution to the data? From 06ae3bb84e8286b1f28b0ab6552d00b74f2034d8 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 11 Jan 2021 21:52:54 +0100 Subject: [PATCH 71/87] [spectral] added crosscorrelations notebook --- spectral/code/crosscorrelation.ipynb | 1602 ++++++++++++++++++++++++++ 1 file changed, 1602 insertions(+) create mode 100644 spectral/code/crosscorrelation.ipynb diff --git a/spectral/code/crosscorrelation.ipynb b/spectral/code/crosscorrelation.ipynb new file mode 100644 index 0000000..0973ec8 --- /dev/null +++ b/spectral/code/crosscorrelation.ipynb @@ -0,0 +1,1602 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Correlation coefficient, autocorrelation, and cross-correlograms" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "Initialize python" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import scipy.stats as stats\n", + "import scipy.signal as sig\n", + "import matplotlib.pylab as plt\n", + "%matplotlib inline" + ], + "language": "python", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A function for printing out x-y values:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def printdata( x, y ) :\n", + " print 'x ||', ' | '.join( [ '%5.2f' % v for v in x[:10] ] ), '...'\n", + " print 'y ||', ' | '.join( [ '%5.2f' % v for v in y[:10] ] ), '...'" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Correlations coefficient (Pearson r)" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Paired data (independent)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.random.randn( 1000 )\n", + "y = np.random.randn( 1000 )\n", + "printdata( x, y )" + ], + "language": "python", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "x || -0.56 | 2.81 | 2.90 | 0.95 | -0.11 | 0.85 | 0.19 | 0.55 | 0.69 | -0.69 ...\n", + "y || -1.23 | 0.81 | -0.18 | -0.99 | 0.59 | -1.31 | -0.18 | 0.84 | -0.79 | 0.26 ...\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Pearson's correlation coefficient" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plotcorr( x, y ) :\n", + " r = stats.pearsonr( x, y )\n", + " plt.scatter( x, y )\n", + " plt.xlabel( 'x' )\n", + " plt.ylabel( 'y' )\n", + " plt.text( 0.05, 0.9, 'Pearson r = %.2f' % r[0], transform=plt.gca().transAxes )\n", + " plt.show()\n", + "\n", + "plt.title( 'Independent data' )\n", + "plotcorr( x, y )\n" + ], + "language": "python", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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yUFIjOHLkKJLyquvSpUu8fv16jnW///57TpkyhevXr3+sfDcmk4uDMiZ1uj50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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mean $$\\langle x \\rangle = \\frac{1}{N}\\sum_{i=1}^N x_i$$\n", + "\n", + "Variance $$\\sigma_{x,x}^2 = \\langle (x - \\langle x \\rangle)^2 \\rangle$$\n", + "\n", + "Covariance $$\\sigma_{x,y}^2 = \\langle (x - \\langle x \\rangle) (y - \\langle y \\rangle) \\rangle$$\n", + "\n", + "Pearson's correlation coefficient $$r_{x,y}=\\frac{\\sigma_{x,y}^2}{\\sqrt{\\sigma_{x,x}^2 \\sigma_{y,y}^2}}$$\n", + "\n", + "* Correlation coefficient is the covariance normalized by the variance: $$-1 < r < 1$$\n", + "* positively correlated: $$r>0$$\n", + "* negatively correlated, anti-correlated: $$r<0$$\n", + "* uncorrelated: $$r \\sim 0$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for r, t in zip( [ 1.0, 0.8, 0.5, 0.0, -0.7, -1.0 ],\n", + " [ 'perfectly correlated', 'positively correlated', 'weakly positively correlated', \n", + " 'uncorrelated', 'negatively correlated', 'perfectly anticorrelated' ] ) :\n", + " z = x*10.0\n", + " plt.title( t )\n", + " plotcorr( z, r*x+np.sqrt(1.0-r*r)*y )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Ap3F1LSM39wLOzs46JBVCXzJrSNRJd911F+HhdwBhQDe0k8O+BH4GXkBrCfQB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\nGViP1hp4DxiDdnLY3wADbdq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5kwkJCQVcPv/3f/9Hk8lDccl8TSCQwFxaLFW4adOme3qXFStW0GTyUdxO02ky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kJMLCwnDy5Mkcsn3++edo3bo1GjVqhMaNGz/Qc65duxY9evQAAERHR2Pbtm13vDa3miTB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XsNlsaNu2LUJCQgAA5cvXxKFD0UhLexPALlgsA3HixO/w9/cvWIEFuWLlylXo3n0wkpKG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kAAAg\nAElEQVSPRaSviGwVkYGydOnbIuIWkUdEZISIICLfiMidInKpiBSIyGsikiwiXeXw4fqyatVqmTv3\ndSkq2iwiG8Tj+VFatNglwWBQDh1aK7t3vyj79r0jl102Sb777rsjJ/RfYGXKlJGPPlot111XSa68\n0isrVy6VM88885THc7lckpaWJsFg8DTOstT+J+xXCkjHtccff5yaNWvidruPq2j4H5reUe2DDz4g\nFKpEnP2zG5EUgsG2XHzx5bRu3Rmv9zKU0bIO2y7D22+/XWKMjz76iPLla+JyuUlPzysuJNq/fz8T\nJ06jevWGuN1hlL0z00AgK8yYt+Ny5TF37lzWrFlDJJJJONyPcLgtFSvWZs2aNcRiMT777DNTMRsk\n3gnsMCr5HDYQig+3O5Vp06aRk1OFOHTUmXiuIBGOSi2xkxFpgtvdDpGFuFzNzDyfSPj8BUSieDyp\naG7gMny+JP72t78BClP06TOUWrWaM3ToSHbu3MnBgwfxeHzEu4eBJpwn4WD/ujupgUpleFEdoUYJ\nx8cQKUcw2IiaNZuglcfOZ29SoUKtI+Qd3O4K1K7dlKVLl/7m71SpldqvZSfrO/8jnvbjjz/m008/\npW3btr+bQPDmm28SjTb5mdPJoEeP/uzfv59AIJzgeMHnu4xZs2YddSwHQ967dy9XXHElOTlV8Pk6\nog1PRhIMptKsWVsDh9yGk7j1+5sxb948AL7++mvuvvtuypevim3nYdtladeuC9999x1Dh15EOJyN\n210TkZvweNqbIFAdpYfuQyUsklCBuC8N7NMUpXMGDayzqxieUepoEVrRHCLOQNmDx2NjWS1McNyD\nVghfiSZ08xEZgMfThqSkcowcOY6srDw8nk6I3EUgcAH16rWkqKiIHj0G4Pd3Q2se5qBMp0qU7AUw\n2gSFmmjuoirxgrmfEAnRr98Qxo27HJ9vVMJ5s6hYsQ62nUa83uJVE+TmY1mZR1STn25bv349PXsO\nolmzs5k58+bfZVP0Uvt92O8iEDj2ewoEP/74I5mZFXC7b0HkM7zeK8nPLyjmdWui12n5WEQo1Jb7\n77//mOP99NNPJCeXM05X+fKOrHIgcCYeT8h8lmyceCEuVzKWVZamTc9g27ZtnH/+KPx+R3P/IJbV\nndzcqgQCgxB5Dbe7G6FQJrNmzSIYzESx/jgDRXMAzs/7UMZRngkQTnewvmjyuRoiboLBFGy7TsJ5\nB/H7k2jevA0iLrNS745STBujzW3mmaBwByJnmHs611zramw7l88//5y9e/cyevR40tMrm+t7zXmv\nJlzvQTSh3hhNlp+BVk/fhUhjatduzHnn/YGxYy8jNTUXZRT1QCSLYLAaI0eOJhRKxeVKMUHAGftW\nhg4dyapVq6hXrw1ly9agVq3GNGt2NhdfPL44oX2qtmXLFpKTc3C7ZyDyLLbdnLFjJ/yiMUut1I5l\npYHgV7T169fTvPlZZGRUpH377mzevJmDBw/y5ptvMmPGDCwrjVBoCOFwU5o1O/O47JHhwy9Ci4/2\nGod2DiJTjVOqY5yUUxTmVL2ej7KJRpGVVYnatVuYnx0n+ZDhxx8q/l002oxXXnnFCJ2dR7x6+C40\nqez8/CkuV5DMzFwUDnrGBIRPEsa/gf79B5GTk4/HczUiy/F4euNyJeFyFaAKp04S+Vq08XsSWtD1\nBloJnUScOfUdIukEAqls2rSpxPPRSuI30F4I55hAtQtlKaWhbCa/CV6t0XqCyrjd1RD5C37/BUbu\neQTaJOdbRJ6nceMO7N+/n+rVG5HYdMjlup5+/YaY5/Qg2t2sMyJnEggMpbCw+S+Sg7j77ruxrEEJ\nz/IbAoHwaWk3WWql9nM7Wd/p/bVyDx06dJCtW7ce8fsZM2ZIt27dTnica6+9tvj/27ZtK23btj0N\nszs1q1y5srz11tLin/fs2SONGrWVL774SVwuW6LRJJkwoY7k5/eQbt26mYTp0W3Nmo9FZJyIWOY3\nF4nI1eLx/ChFRZ+JSAfRBK+ISCsRCYjIPNGkaVv57rsqUliYJp999owcPNhWRGISCCyWQ4cOiCZR\n/yYieRKL/SRer1caN24qr7/+uoi0FpFUEXlNUlOTZd++HrJvX10JBO6TVq1aCcTk1Vf3m+t5ReR9\nEakmmqB9VypVqiM33TRTxoyZLKtXPyHffvuVQAURWSMiHhH5UETaiMjVInKDiBSZ/waJyB0iki2a\nABcRSReRLCksTJO8vLwSz+eqqy6TceOGyt69V4jIyyISMZ8EROSPItJYRKaJJqvfMNcISSz2pYhk\nycGDF4nX+5mI7DbXFhHZLNFoWAKBgMyYMUUGDRoje/d+Ky7XTrHt2ZKfP0KKirqLyEBz/MMikiMH\nDvwoGzbUlI8++kjq1at3zO/0eOZyuURJAo4ViYjrlMYqtVL7uS1fvlyWL19+6gP8SgHphOz3tiP4\nuU2ZcjWBwACcKl6PZxrduw84oXOHDx+FyjQ4K/JL8XrTqFWrEZoMrURcEfVJs5J2EtWHcbvzWLZs\nGVWr1iMSqUU4XIWGDduQkpJjVuCtDawSpkyZakyffgNZWRWxrKoEAmUpLGzG9u3bmTNnDk2atEDz\nAHXQKmCt9lVoKIxqJzUmEskpIZesCVnb7CDilcMK6SxDKZ5O1e1fUHgpDZFFqC5QY0RC1K/fms8/\n//yIZ7Ro0VN07z6QWrUa4/XmmnPPMeN9hUpdO7IQi1HaazzZbFm9CQYjuN3jcbmuIBRKLyEE99JL\nL9Gnz/kMHjyCv/3tb8yfP59Q6By0H8M9iCw0O5wiwuFqv6hV49atW0lNLYvHcy0iT2LbjRk//opT\nHq/USu14drK+8z8eCI7X+u6/PRD06DEIFWxznOAKatRoekLnfv/995QrVx2Ppx4uV30sK4OPP/44\nobJ2PIqFt0ckZETbOhnYogf5+QUcPny4WBJ5zZo1XHbZJDQ5+xfiKp+R/2vvzOOiqvo//pl95g6r\ngqAioogLO2qaW7nhvltpmpn6ZGVl5eOSmllPuWFaWtYvLU1t0TTXcsE9slRyDZdEJUFTHxERQbZh\nPr8/7mUYHrQAgcE479eL14u5c+85n7kD53vPOd+FwDOUpAZcuvQL7tq1i/v372dubi6tViunT39H\nGczPKp/hhDL4/U6VyotBQaF8+OF2HDFiJNPT0wt9Bl/fhko/nsrgmU3g30q9hhACI5Q2r1LeQNYr\nelwVbTMIJFClmktnZy/OmzeP69evZ4sWndmoUQu++eY7tFgsjIuLo07nptyT7izwgnKjvNzVh/np\nN+SgtwMEPqSrqzdjYmL45JND2KdPv0IxG3cjLS2Nbm61KC+ZDVMMTAQNhpEMDW1135lCExISOGTI\nKHbo0Jfz5y8Um8WCcuOBMATr1q2jj48PjUYjvby82K1bt7ueV9kNQVTUPEpSJ+Up1EKD4RmOGDGG\nFouF3333HRctWsQjR47c8/o7d+5w69at3LJli22QHT16LPX60cpM4VdqtZEcPHg4fXwaUM5s6Uu1\n2ptDh44q1FZeXh51OhPt88nIKR4aKQP1JPbsObjQNWPHjqdOV4eyB469e2gggWOUpFH85JNP7ql/\n0KBBlPMTdaO8p6GlSuWmDMouyowgTXlyH0c5d9AqxRi4E+hFOTL4jHKsFuUZSX8CMZSk1hw/fgrn\nz59Pvf5FynsEjShvYLtSjlyuR9mtdBjlzKxjCARTo6nGo0ePsl27bnRyiqCz80CazR788ccfSZK/\n/PILFyxYwA0bNtgG5Js3bxaJ/larPfj440OZmppaqr8RgcARPBCGoLhUdkOQm5vLAQOeosHgRqPR\nky1bdmRKSgo7d+5DJ6cWNJlG02Ty4sqVXxW7zZs3bzIw8CE6OwfTySmIQUEt+O2339LZuTULlpFu\nUas1FnpCt1gsShTtbbsB/UllgAwl0JNDh/7Ldv66deuVATtMeVJ/hbKb6k/KIJ1Ak6kuO3fuzXbt\nevGdd2bb0mRbLBZ+/PHHNBjcKOc0WqgYKVfF6HgpT/wm5biW8vJZHuU6Dc9R3oydozx116fsLpq/\ngexLOQbgDKtXr8vFixdTkvKXhJKVPlwoeySdpRx5XV0xRs4EZlKnM3HZsmU0m9uzoDraBvr5BXPB\ngkWUJB8aDGNoNkewR4+BHDXqRTZr1p46Xa1CRtHVtf19RfNWBqxWa5HZnOCfjTAEDuDatWtMSkqi\n1Wrlpk2b6OTUjAWeO8cpSW4l8g7Jzs7mL7/8wgMHDjAnJ4cbNmygi0sXuwEqmzqduchT6oABT1Gt\n7kZ5aeRjZUCOJFCdJpObLUHe7du3KUnulF1I51PeUxirGAwnyumaJRoM7tRoplCukvYon3jiafbr\nN5R6vYcywL9kp2mPMhjnp6Z4kvJew1zF4JyjHK/gRfvMqLIh0v2PARuj6FjPmjUDmJycTD+/QKrV\njxH4j52RsW+noZ0RcmO1aj4MCAimSjXB7pz/UpLcqdNJlPcoSOAmVSpXarUvUA6Kc6PspZVHYBud\nnDzvWansQWDPnj10d69FjcZAb+/697XPIXhwEIbAwXz22Wc0m4fbDT4WqtXaUme3JOVZgqdnXWo0\n7xLYR6NxEDt37mN7Pzs7m9euXWNGRgaffno01erqlNe5vQm4sFmzNraoXpI8c+aMUmQ9UxmkE5kf\nEyAHne1WDEMHu8+RSnkztjPl6N7xLFyx7SjlGcFUyr77acq5JkVLviunSXmPypN6Y8rJ5L5Wjt2m\nXOayNzUadzZuHE61WkedzkRnZ0/Ky0k6RXeycs02pf1fKCe/e5TyXsnrimG4SMBKrXYiW7WKVGYy\n+bOrnZT3M/JfHybgRJVKQw+POty3bx9//fVXNmnSgq6utdm+fU+mpKTc199IRfHf//6XTk6elJMY\nWgmsYrVqtUWuoSqAMAQOZvPmzdTrq1FOd5xNjeYNhoWVLmOkPQkJCezZ8wnWqNGQ7u512bp1Vx44\ncIArVnxJg8GZBkM11qrVgHFxcUxPT+eWLVv42Wefcf7892kyuVKrNbF+/RCePXuW6enpNJncKaeC\nsB8USXmzdS3lZaJOdsdvKYZgJeU1/FjlCfxbystJIZQrjV1VjkcrT9ULKAfGaRgYGM569ZpQrkWw\nkPJspRPlCOGalGcknpQLzUylp2dNJTp6JIGN1Gr9WLAsNEk5fzblvYjZdlpPUN47IOVIaR21Wonh\n4W145coV1q8fQrV6DuX4jdmUU2jn34MsGgxuTEpKIkn+8MMP1GpdKCcDPEvgGXp5Nah0/v8ZGRnc\nvn07t23bxoyMDJLybMDVta3dfSGdnQN46tQpB6sVlDfCEDiQr776hiaTJ43GdpSXL9Rs2vQRXrp0\nqUzanzjxDUpSS8pP7EtpMsl7E0Cc8o/+GX18GtoGqdOnT9Nk8qRcAMdKlWoB69eX89n37NmXBZu2\nUymnx9ioPGlvJPAbAYkazVTldXvlMx2jvOSzjXLB+UZKG+4E1rNgmciDgJp+fkH87bffbBuyKSkp\nyrJUfp2CGZSX0TYpBiNKGXTzK6rNo7x85aEYCLPS5xzFKD1GeQ8i30NJ3guQZyG/EkigJHkUigxO\nSEhgSEgrqtUaenr60tvbnzrdKwQ202jsy/bt5RKkGzZsoE7nQjkTqr17rI7ff/99mXynZcH169dZ\nr14QnZ1b09m5Df38Annt2jWeOXNGSTF+Q9GeSIPBhcnJyY6WLChnhCFwEBaLhUajC+VNUBK4Q0lq\nyD179pRJ+z/88AN1Ok/lafwQ5WjYHtTr+xZ64lOrTXz11XHcuXMnV65cSSenwXbvW6nVGnn79m0+\n//xYpa3elGcFZsreQrOVJ253Dh48jIMHj6TRWJNy6ucJBMKVAVn2Emra9BHGxcXx6aeHU6XyUAbx\njwmY2bFjtyLlN0kyNjaWWq1EOfVDIOU9ifx1fx/KSzvhBKazIJZiMQFnGgwelCubPUx5huLK5557\njp6edSknqRuvGI2JlJeLAvnSS+Puek/zDeb169c5bNhourr6Ua12pl7vyu7dB7JOnUAC7yh95c8Y\n/iSg46efflrq7zI5OZlXrlwps1nFyJEvUqd72aZRp3uNw4c/T5IcN24yzeZ6NJufoiTVZlTU+2XS\np6ByIwyBg0hNTVXq9hYsszg7P86vviq+x9C9WLduHU2mWpQ3MRcoA92v1Gj6Uq+vy4I191+VwfRN\nSlIdvvLKODo5NaGcxkJexzeZXGmxWBgZ2Zfy+vwjlJdoCoyJSmXm0KEFLpP79++nk5Mnzeb+1Gqr\n02Sqxv79BxQKLiPJ9evX09W1LtVqfwIzaTD8i02aNGd2dnaRz7Rx40a6uNSgSqVhgwbhXLx4MQ0G\nF8ppKLYohqG+YqTWUK6325sazSvU6z3o4hJGk6k2e/V6ghaLhadOnaJGY6KcufWo8lnasFWrdjZv\np79i/PgpNBr7U46FyKLJ1JtGowfleg5tKOdPmkmgPrVa97+Mf7kXubm5HDhwGPV6FxoM1di2bdci\n97A0tG3bkwWzMRLYxNatu9ve/+mnn7hs2TLGxsbed1+CBwNhCCqAc+fOMTS0NXU6ifXqhTA2NpZW\nq5V+fkFUqRYqxuAIJcmzTKpgNW3aQVnuyP9HjyLwEF1dvTl48AiazfVoMnWnvNTznXJOHM3m6oyM\n7E2TqR7N5kE0mTy5evW3PHHiBE0mH8r5eWoqhuWqct0+As40mfqzTp1GvHHjBkkyMTGRrVp1pMHQ\ngsC7NBiC2bLlI4We+C9evKgkt8uxzUCcnEK4f//+e342+3xM7u61KKfdts8QelQxBrUp711kUKPR\n8+DBgzx58qTtqTo9PV3xBsr/HLmUpMBiz8hatepGeakr/x6vp5dXAE2m3pTjHF4iIFGt1nPBgkWl\n+BbJ2bPfs4s7yaXBMJT9+g1m3bpB1Okkhoe35YULF0rc7uTJ02ky9aS8+Z9Fk6kPJ04sXW1jwT8D\nYQjKmdzcXPr4NKRaPZ/yBuo3dHHx4o0bN3j27FnWqxdMrdZISXLjmjVry6TPsLBHlKfk/EHqA/r7\nhzMhIYGkHBw1atQo6vX2y0AXCDjRySmQRmNdBgSE8+jRoyTJffv2UZIaU16WSae8Tl9Nee1GOWVE\nb6rVoZwwYRJJ8vz588ogf4Vy4reWBFrQ3b02O3ToQR+fQLZt21U5J9911kpn5/C7lvKMjo7m1KnT\nuGjRIpsXy7Rp05X+/QvNUGRd05Tff2a1aj53vU9Tp75Ns7mxMiPqyEcf7VGs2QBJDh/+vLJPYCVg\npV4/hiNGvMDhw5+nm1st1qrViIsWfXxfT/C9ej3JwhXo9ioeXmspB69FsW7dJsXWnE9WVhZ79XqC\ner1cA7t794H35aUmePARhqCcOXfuHM1m30IDlavrI4XSF9y+fbtM0wcsW7acklRfmf6vpCQVzZ1/\n+vRpSpIH5U3XBKrVjalSvagMbLk0GgfwzTf/Q1JexpKLwdtvsP5OAJTTOnelnJnzeRqN1ennF0ov\nL3/q9fUobyw/zYIlsLeUzKPHqVa/SYPBg0bjIALfU68fw4CAcGZmZvLWrVu2p/f58xdSkvwIvEmT\nqRfDwlozOzubM2bMUMpJOrFgA/w8VSonSlJzJUDPk+vWrbvnvdq4cSPfeGMalyxZUqLawf/973+V\nDdeWdHZuQX//0DLfVB0/fjINhoJ7p1ZPUTyhCv6WJKkmL168WKr2k5OTef369TLVLHgwEYagnElO\nTlbSEOQnU8ugJNW1PW2XFytWfMmHH+7KRx7pdc9I1927d7NBgwi6u/vQxaWussyTP8gsZ58+BQnx\nVq5cqWzuJlJ2BR2uFG0xsmBPwUrZLTSKwM9K+ojmLFz5K0aZHcivnZyCOGjQ02zZsgtHjBjDHTt2\nsEYNP2q1El1dvbhz506liM95Wx9OTu24du1afvDBBzQah1B2Xa1OOQrZzIULP+bq1au5aNEinjhx\notzu8Z07d7hjxw7u3LmzXHztb926pUSNN6OLS1t6etalyVSX+XUogCvU6cz3XftAIBCGoAKYMuUt\nms0B1GrH0WxuysGDR9BqtTInJ4ebN2/mV199xcTExArXde3aNf7222/MyMjg0KHPUq8fowzmOTSZ\nevPtt2cUOj8q6n2q1WYC1alS9aHBUFMxBFl2A30LAluV37+iTueuLA2lUd4LGEDZi4cEsilJvoyL\niyMpD6zyun9+GctdNJs9qFbrWLCPQJrNT3Hp0qVMSUlhrVoNqNePIDCBBoMH5837Z3m5ZGdnc/fu\n3YyOjmZaWhr79x9Ks7k5tdrXKEn1+dZbMx0tUfAPQBiCCmL79u2cM2cO165dS6vVyqysLLZo0YFO\nTi3o7Pw4nZw8i9QsLk9mzXqPBoMrnZ0b0929Fnfu3Mng4JY0m+tTkmqzY8deRdaNL1++TIPBnQWJ\n6q5S3nDuTeB7yvmHalLeRyCBlWzQoBmHDRtNnU6iXu/C6tX9aDS2ITCIGk19hoQ0ty2LnTp1ikZj\n4aUPV9c2DA1tRa32X8psZB0lqbptkzQ5OZkzZszkuHETuXv37nt+3tjYWHbv/jjbtu3Jzz5bWukC\nvIpLXl4e16xZw6ioqL/NjioQFBdhCBzE1KlTqdd3YkH+mzUMCGhaIX3HxsZSknwIXLL1XaOGH0+d\nOsXXXnuNEydOtEXK2nPkyBG6uIQUGqjljdpGlNNDdFNmCPnpJKrZqmrdunWLycnJzMrKYqNGTanR\ntCEwk2ZzU44ePZYkuWjRx8r1PyrXT6BO587Jk6dSrfagvEHtQ3f3miVa246Li1MqiS1SDEljfvDB\nh2V2PwWCB52Sjp0q5aJKiUqlQiWWZ2PJkqV44YVXkJf3GoD/KEcvwcXlIdy6daVc+tyzZw++/fZb\neHl5wd3dHVOnxiIj40vlXUKtNsBkckN29mCoVJlQq9eic+dIDB7cF0OHDoFKpcLt27dRp05D3Lq1\nGEBvAFshV+dqC2AH5AplfgD6ALAAeBxqdSvcuZOOM2fOICYmBmlpaZgxYynu3DkNQAcgFQaDH5KS\n4tGz5xDExroB2ALgWQAaqFSfwtXVBamp3wNoCgAwGIZh1qymGD16NMxmMwDg4sWLWLZsOXJycjF4\n8OMIDQ21ffYJEybjvfe0AN5RjhyAr++zuHjxt3K51wLBg0aJx85yMEZlRiWXR5LMzMxUNj+XUA6A\nSiRgoVb7Ert2HVAufU6YMEUpVNOJQC/q9a5KwNl15idh02qrK0/M+U/6bxDoSEkK4vTp79ra+vnn\nn+nhUYdarYkqlZnAZ3bXTKbswRNLwEKN5m0GBz/Mb79dQ5OpBo3G52k0tqJG40372AFJ8uGFCxfY\npk13yl5I9nmAPqJG4045EVx+AFtP6nRmarVGBgSEc/fu3XRx8aJGM5Yq1RRKkkchL6nx41+nSjXF\nrs39rFs3pFzutUDwIFLSsbNSj7QPgiH4888/lXw/JPAe5cheHQMCIsrFle/ixYvUaJwJvGg3EM6j\nj08gjUZPuro+TGfnGgwIaE5gu905yymnhk6g0ehSaE3darUyLS2NzzzzvLIkdJNAPAE/url50cnJ\ngyqVhiEhrZiYmEhXV28CB5V28ygnkRtB4Dy12ikMCAinxWLh1q1bFT/5r+10bGKNGo1oMnWhnOlz\nnmJs5HxIavV7dHGpTbV6WiHtrVsXFC86ffq0sjQ0n8A3lKQG/OijexfQEQiqGsIQVDB5eXmsVasB\n5Vw4VgI/0mSqXmpf8L/jwIED1Gprs7AL54+sVy+C586dY0xMDG/cuMGZM+cqCeriKSeQa0I5SdtN\n6nSmu26uZmZmslu3/lSpdASM9PcP4Z9//mnziCJlo6FWa1ng8kjqdD2p1VanSuXKWrUa2QLdSPL1\n1ydTo/FTZhXHKEmhfP/9hRw7diLr1g1hnToNaTI9afdZrFSptAQ+sju2m8HBhTO4Hj16lP37P8VO\nnfpzxYov73m/Tp06xfXr1/PkyZNl8wUIBA8AwhA4gFOnTtHXtwk1GgOdnT34ww8/lFtfN2/eVHLy\nhFL28kkj0IEvvlg4sVpeXh4nTJhKFxdvFhSg30+TqTuHDBl1j9Zl/s4Dp3XrLtRqX1OMwdeU8wKt\nJxBHk6knn376uUJtvf/+QtasGUBv7wZ89905hdrfvn07zeYgO8NyhAaDi+Jf/zOBE5Sk5pw1670S\n36sFCxbRZPKii0svSpI35879oMRtCAQPIsIQOJD09PQKcWPct2+f4vapJaBhx449/zKlwLFjx9iu\nXQ82bPgQX3110l2TwJWEa9eusXXrLtRodDQanalWv2L39H6JTk4exW7LarVywICn6OQURCenJylJ\nnlyzZi2XLPmcdeoE0tu7AadN+8/fRmpbrVauWrWKL7zwCqOi5vLChQs0Gt0oF6ohgSQajdWYlJRE\ni8XCY8eO8ejRo/ddkF4gqIw8MIZg/PjxbNy4MUNDQ9m/f/+7Fgd/0AxBRWK1WpmSkuLQgcxqtXLh\nwoU0Gu1zHMUSMNPNzZubN28udjs7duzg8uXLbeU08zlx4gS7d3+cDz3UmXPnvn9PgzBx4hs0mZpQ\nTl+to0plotHYxE4X6eLSjLt27WKzZo/QbG5AJ6eGDA1tVeRvLz4+nlu3bi1VAjiBoDLwwBiC6Oho\n2z/1pEmTOGnSpCLnCENQeqxWK5cs+Zy9ej3J554by8uXL5dLP/nRwDrdSAKzKJeG/IzAfkqSB+Pj\n40vd9vnz5+nk5EmVagGBHyhJD/H1198scl5WVha1WgPlMpajKZe73Kts3O9kflZVs9mDzz33Mg2G\np5RN7jwaDKNscQ8k+cEHH9Fk8qSra2eaTB5csmRpqfULBI7igTEE9qxbt45Dhw4tclwYgtIzdepb\nNJvDCCynVjueNWrULbfKVMnJyZw69Q2qVEbKJSrlJ3Bn50H88ssvabFYuGLFCr7zzjvcunVrsduN\nioqiTmfvHXWWbm61ipx369YtpdCNCwuqcZFq9UAaDG40mWrQycmD0dHRbN++D+PPcVUAABVPSURB\nVAtSdZPAD2zZsgtJOdW20ViNwB/MT8RnNLqJil6CB46Sjp3qsgthKD1Lly5Fjx49HC3jH8X8+R8g\nI2MTgKdhscxFenpLrFu3rsTtkMS8eQvg6xuMevXCsHjxZ0XOqV69Ot5++y3o9VoAPsrRHJAn4enp\niZ49H8cLL3yK6dMz8NhjL+Ptt2cWq2+1Wg2VKtfuiAUqVdE/WRcXF7Ro0QaAHkB+UBlhMKThww+j\ncO7cUaSk/InIyEg0bRoIo3ENgDwAVhgM3yIiIhAAkJiYCIMhAEBdpY2G0Otr49KlS8XSKxA8sJSP\nPZLp3Lkzg4ODi/xs2rTJds67777LAQPuHngFgNOnT7f9lFXZxweJ5ctXMiSkLUND2/HLL4tX7Swn\nJ4d6vX2RFtJkeoYff/xxifufNSuKOl0AgQMEYihJ9blq1eq7nrt06ReUJG+aTKPo5BTBrl37sU2b\nLorXUoiyTHOFOp3E9PT0v+07KSmJrq7eVKv/Q+BrSlIQZ8yYc9dzb968ydatOxBwpko1iiZTe4aF\ntS6SRTQ9PZ0tW3ak2VyXZnM9Nm3ajmlpaSTlTXA5A2t+jMReOjl5iGyggkrPnj17Co2VJR3aHbr2\nsmzZMrZuXfSfNZ9ytlOVnlWrVit5+7cS2EJJ8uXatd/95TVy1K8rNRpXysXhF1OlWkhn5xolzoh6\n6dIlajSelGsc5C+lrGS3bo/f85ojR47wk08+4aZNm9i5c19qtcMpR1t/T7kS2mkajR68cuVKsTTE\nx8dz6NB/sUuXx2zJ5bZv387Q0LasXz+C06e/W6iQy4kTJ7hgwQKuXLnynp5UeXl5PHnyJOPi4ooU\ngdm4cRMlyZ1mc13bcpJA8KDxwBiCrVu3MjAw8C+jb6u6IZDXs1fbDcJfsXPne6etOH/+PE0mDxbU\n7P2KGo0LO3fuZ0sNXRL+/e9JlKuDLbbTMJtPPPHM316bl5dHjUZHuSxj/rWjqFL1YMOGEaV2sz14\n8CBNJk/KhXN+oSQ9zMmTp5eqrf8lISGBDz3UgSaTO/39Q3jw4MEyaVcgqGhKOnY6bI/g5ZdfRnp6\nOiIjIxEREYExY8Y4SkqlxWDQA0izO3ILRqP+nucfP34cOl0rAOHKkSHQ6fRYseJjBAUFlbj/lJQ0\nAF0ATAHwJoDXoVK9g2nT/v2316rVahiNzgD+UI4QwEn4+ydi165NUKlUJdYDAF99tRqZmS8C6A/g\nYdy5839YvnxVqdqyx2Kx4NFHe+Dw4a7IzDyD8+fHoVu3/khNTb3vtgWCyo7WUR3Hx8c7qutKj9Vq\nRUxMDNq1C8e+fa8jKysVACFJUZgyZdM9r/P19YXFchxAKgA3yBunOahevXqpdDzxRB+sXj0ad+7M\nAxADrTYaI0c+g+Dg4GJd/957s/Hvf3dDZuZwGI2/oV69PBw+HAuj0VgqPRaLBWvXrgfQ0+5oCgyG\n0rVnT0JCAm7cuAOrdZJy5BlYrZ/j6NGj6NChw323LxBUZhxmCAR3Jy8vD716PYGffjoDtdofKlUe\nunX7Gd7eXnjxxa1o3rz5Pa9t1qwZRo0ahM8/D4dWGw6L5WcsWfIp9Pp7zyL+im7duuGjj97BG2/M\nRE5OFp566knMnftusa9//vln0ahRA+zduw81akRixIgRpTYCgJx6OzVVAvAdACOAWgDewfTpH5S6\nzXzc3NyQm3sTwA0A1QFkwWK5BDc3t/tuWyCo7Ih6BJWMb775Bs8++yEyMvZBzu+/Eb6+U3Dx4sli\ntxEbG4vExESEhoYiICCgzLTFx8cjJiYG1apVQ69evaDVVuxzxIYNGzB8+BKkpX0M4GMAt6HVLsfV\nq4mlnvXYM27cZCxevAmZmX1hMu1Gly4N8N13K0u9jCUQOIqSjp3CEFQy5syZgzfeuA6L5T3lSCoM\nhjrIyrrtUF3R0dHo338oVKruUKnOIiTEGfv2bYFOpytVeyRx6dIlaDQa1KxZE59++hmmT59tm3m8\n//7sIobm+vXrCAgIxa1b7wB4BDrdhwgNPYHY2L1lMliTxObNm3H8+HE0aNAAgwYNglpdKUJtBIIS\nIQrTPODs3r1bcRlNImClRvMWW7To6GhZrFmzAYEdivePhWZzey5fvrxUbaWlpfHhhzvRaKxBg6Ea\nmzd/RMk2+iuB85Sk9pw4cdpdrz1x4gSbNn2Unp712KvXIBH1KxDchZKOnWJGUAmZM2c+pk17A2q1\nAX5+9bFz50b4+Pj8/YXliNHojOzsJMib0IBWOw4zZnhj4sSJJW5r9OixWLEiFdnZywDkQqPpibw8\nZwAblDMOwt9/DM6dO1xW8gWCKkVJx04x762ETJo0DmlpKUhKOovTp391uBEAgJYtH4FW+w7k2sW/\nQ6dbjbZt25aqrYMHjyE7ewQADQAj8vJGArhgd8YFuLm53rdmgUBQPIQhqKQYjUZ4enpWmo3KNWuW\nISLiKNRqE4zGFujZsy1WrFiNr7/+usSztkaN6kOr3aa8skKv3waT6TL0+pHQaMZDksbigw/+U/Yf\nQiAQ3BWxNCQoERkZGXj00R44edINWVmPwmxeiVGjIrFgQVSx27h69SoefrgjUlKcAGTDz0/C+vVf\nYsOGDcjKyka/fn1LFQAnEAhkhNeQoFzZuXMn+vefiPT0XyFPKFOg1fogNfU6zGZzsdvJzMzEoUOH\noNFo0LJly1J7HwkEgqKUdOwUAWWCEpGRkQG12gsFq4puUKv1yMrKKpEhMJlMePTRR8tFo0AgKBli\nj0BQItq2bQuN5gRUqk8AnIJe/xJCQ8NRrVo1R0sTCASlRBgCQYmoXr06fvppBx566Dt4e/dDz55p\n2L59XaXZ1BYIBCVH7BEIyh2S+OabVfjhh92oXbsGJk0aVyYpIQQCwd0Rm8WCSsfbb89EVNRXuHPn\nJeh0x+HltQdxcYfg6ipiBQSC8kAYAkGlgiRMJldkZ/+G/FrAZnMfLFo0EMOHD3esOIHgH4qILBZU\nKkgiLy8H+akp5GPVkJ2dfc9rrl69igsXLiAvL68CFAoEAmEIBCCJhIQE/PHHH2U+A1Or1Rg48EmY\nTMMAHALwGdTqLejWrVuRc61WK5566ln4+QUiJOQRhIa2wvXr18tUj0AgKIowBFWcjIwMtG3bFUFB\nbRAY2Art2/dEZmZmmfbxxRefYOTIhvD3fwGtW69FTEw0fH19i5z3+eefY/36U8jOTsSdO0mIj2+L\nUaPGlqkWgUBQFIcYgmnTpiEsLAzh4eHo1KkTkpKSHCFDAGDKlLdx5Eh1ZGYmIjMzEYcOSXjzzRll\n2ofRaMRHH72Hc+cOY//+bQgPD7/reQcPHsedO08AcAKgQm7uCBw5crxMtQgEgqI4xBBMnDgRx48f\nx7Fjx9CvXz+8/fbbjpAhAHDo0AlkZT0FOchch6ysoTh40DGDb2CgP0ymaMgZTgG1eisCAvwdokUg\nqEo4xBA4Ozvbfk9PT4eHh4cjZAgABAY2gF7/PQACIAyGHxASUri8JUkcOHAAGzZsQGJiYrlpeeml\nF9G8uRVmcxBcXFrB0/P/8PnnC8qtP4FAIOMw99GpU6di5cqVkCQJBw4cuGuRcOE+Wv7cvHkTrVtH\n4vLlXABW+PpK2L8/2ubjTxLPPPMCvvsuGhpNECyWA1i7dgW6d+9eLnry8vJw+PBhZGZmolmzZnBy\nciqXfgSCfzKVJo4gM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J2FHQas/DbDbfdr03C0k0b94cdvspKBviBAFoCGAgkpI23PBeHx8/KBvZAwBh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8ALh06SoGg4vMShaiAkmLQFSo9u3bs3nzfrSlrN2A+4B1aPMN3gbS0bbNzKJ2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\n/eaCz+5tEAAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Time series data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A time axis:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "tmax=500.0\n", + "deltat = 0.01 # 10 msec resolution\n", + "time = np.arange( 0.0, tmax, deltat )\n", + "print 'time ||', ' | '.join( [ '%5.2f' % v for v in time[:10] ] ), '...'" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time || 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 ...\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And some white noise:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "white_noise = np.random.randn( len( time ) )\n", + "printdata( time, white_noise )\n", + "tseg = (time>10.0) & (time<15.0)\n", + "plt.plot( time[tseg], white_noise[tseg] )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.ylabel( 'Signal' )\n", + "plt.show()\n", + "plt.hist( white_noise, 50 )\n", + "plt.xlabel( 'Signal' )\n", + "plt.ylabel( 'Count' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "x || 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 ...\n", + "y || 1.72 | -0.09 | -0.22 | 0.78 | -1.09 | 1.61 | -0.50 | -1.33 | -0.62 | -0.09 ...\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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CIzxuL9tOv365RMBjyX1kmxs6NNo8Alm/VBi67UFrSMYNtt/eP4/F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\nX30VDQ0NeOSRR9DZ2YkLLrgA999/P1544QXMnDkTV1xxRehxr7rqKjz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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Low-pass filtered white noise:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "colored_noise = np.zeros( len( white_noise ) )\n", + "x = 0.0\n", + "for k in xrange( len( white_noise ) ) :\n", + " x += ( 8.0*white_noise[k] - x )*0.03\n", + " colored_noise[k] = x\n", + "printdata( time, colored_noise )\n", + "plt.plot( time[tseg], colored_noise[tseg] )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.ylabel( 'Signal' )\n", + "plt.show()\n", + "plt.hist( colored_noise, 50 )\n", + "plt.xlabel( 'Signal' )\n", + "plt.ylabel( 'Count' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "x || 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 ...\n", + "y || 0.41 | 0.38 | 0.31 | 0.49 | 0.21 | 0.59 | 0.46 | 0.12 | -0.03 | -0.05 ...\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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6O6nGfV6e9wSSmUkn2+jRSjzju98Ffv1r4PrrQxuz2sKwIhjt7TTZlJWR1dPW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\nQveZRRv05vdSC0ZvL71HOF1SIhiC4GDKy4EDB8w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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Autocorrelation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Autocorrelation shows how a timeseries correlates with itself, if you shift the timeseries against itself by various time lags. With no time shift (lag = 0) the timeseries is obviously perfectly correlated with itself:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plotdatacorr( time, data, lagi, tseg, title ) :\n", + " plt.figure( figsize=(16, 5))\n", + " plt.subplot( 1, 2, 1 )\n", + " plt.title( title )\n", + " plt.plot( time[tseg], data[tseg], 'b-', lw=2 )\n", + " if lagi > 0 :\n", + " plt.plot( time[tseg], data[lagi:][tseg[:-lagi]], 'r-' )\n", + " else :\n", + " plt.plot( time[tseg], data[tseg], 'r-' )\n", + " plt.subplot( 1, 2, 2 )\n", + " plt.title( title )\n", + " if lagi > 0 :\n", + " plotcorr( data[:-lagi], data[lagi:] )\n", + " else :\n", + " plotcorr( data, data )\n", + " \n", + "tseg = (time>10.0) & (time<11.0)\n", + "plotdatacorr( time, white_noise, 0, tseg, 'White noise' )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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d3ScxxhYXyrKZsRaZySKCu9k/1EMcMh4P2HATNlnjx3SlJRI8hyF9SGu1tVig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\ngJ8DCWw7rtApIotK6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fIDBwBFZrgxLSPmb3SWlODsxKWYPft+8eF9PpROxNVhaMIYMKnzCcnc2ktBRv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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Time lags" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we shift the time series data by a range of lags. For the colored noise we see that the correlation decreases with increasing lags." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = [ 0.1, 0.5, 1.0 ] # lags in seconds\n", + "for lag in lags :\n", + " lagi = int( lag/deltat ) # lag in indices\n", + " tseg = (time>10.0) & (time<15.0)\n", + " plotdatacorr( time, colored_noise, lagi, tseg, 'Lag %gs' % lag )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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//qvEx/9FnTp13P0DAwPZvHkdLVqsRq+vQq1aE/nuu9VU0S548rBnzx5ycsp7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\n/qKL7E2VKoHysyHh5FhGYNw/NnJywo9gEIDSqOQIUPrTT1JKjROCxf1ly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o71I4LEkehR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9PQiLJZY5c2bi7a0HtOEPffD2rgmcALYAfezTR4GxgI65c99h8uTJLm3vqaee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/1c8zsIbO5DEN0ChYiOMP/fhQAl3rR/AwpRLURgMsaMkb0qdi9SPR82/QsYf0AQmYwg+i0zNhXM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ZSUraxfX5Fnnnkx3/2CcX5EsYPSJk1g+XLYsCFvJeGcitKlZV08fDinUtq2Lfz1V4Eq1Z5S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\nwR6yWqcU1NZCtWsXvETHsiSUCiGEEKK8kVAqiofWiqxQoUwM3xXFx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9c+eUaoPE+yB8N7UofeghJTS8vNRjZ4jSQuGUliihRKmbmxKjuQ3fNRrB27vY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889dZtGgx6emTgDsJBEaxfftxTJ48mSlT3sPvz2DXrmT69y/+lIb/sh0WUFq3rvdzw4aFX5c/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+vMPjYzTg4E8bciNfkHcx3aIKV5lGmnHlJ9rXVVe5vx+hBNDJRGqnESLtckLr+8LS7XUyiv\n9VlgLgMH3srUqXfyyCP3Ex7e0Yz/YDNu7Uyf42nSpAUORyY2W2P++GMXY8dOZOLE/6JJAauYVZgZ\nYzv6HM9Ahahm4Pc3AtqQlvYto0ePYd++fbRvfxkrV/Zl794ZfPGFn6uv7ktJ/P+Kcw5KmzSBFStg\nw4bclYQTolw52RCzWxFdLqmnEycWW1//jqIopYcOqa9ut+7GrUXnrbVKsueUhjiyp6YG32B36QL/\n/S/cems+VetChsOh0/T7A5V4CxLvv685iFtuOfH13AodnTVQmpamD3moldJTrVPq8cDUqdCokYqD\nFTYiIgSl4eFw0UWnVkqLAUot9TtaqZZFVkqzQ+mpCgoD9OlTuDZz+zqfxPUG9p1uQWk+hzHvsKA0\nPV0nGx0dyCkND4dPP4UXXijcsT0efbZK7KclcRqiefPm9OzZk7i4OMaM+S/p6X5UMGcx0JmMDDeJ\nRbGjB8W2bduYM2cOGzduzHO7kSOHMW3acwwYcIiIiCUIRMIAP07ndkqXLs1zzz3H6tWr8PuTEDR8\njwAnHCl7exFwLUZ22T1AKnb7TSQmHsXhcBIZ+QxS974GIvD5bKSnD6Zfv7tINqXBR4x4lMjITUg1\nXIfAbQZS/Srh91+FgOhTpEw+hlS/DARAHyCQWWH2tyOL7ePABgRUKQjYMlCe6GBkPy6DQC3KHPMx\nMw5VEPg8aPrRHSnDO8xY+czrjZFiuMlsMwzlou41jz1oyZr1KM+1pRkzn9nvc1TwBzOmTpSXWcu8\nVgmpw1NMn5worzbajFd9BJT/Q9bnCASa8Wb/WNNHCOSpno/grxQC/FRklZ6AIPsqlK/7PrIV3wNY\nf2t3orzfdGRxbmbG6WnTz9ZAQ5zOMGrUOJ+NG3fj82WZ/Q4Cr/HWWx/Qo0cPdu8+hNvd14xxnDnv\nCDNmO/j993VkZS3A7f6O9PTfef/9WbRo0ZTzzquOJgf8BAojdUKfhZFIUb/ajOt1wO9kZmawaNEi\n/P52SOVujNs9hWXLvifV+iddEv8v4pyD0gJH2bKwY4fktuxyXsWKgtbT0Yd774Vffin4vocO6e57\n5swALV14YeD9nOy7IYyIiBPzeLPnqg0ZAh98UPwrO1jqzw03FHzf+fNzfr1FC/3OnlN61kDp3r0q\nCBNqKA0PFxjkpA5YSumcOSdK4YWJVq00i3T4MHz00clQumGD1g+GYrHv+v0Bt2mNGvpd1Oq71jBa\nE2J5KaWg70Vh688EW36HDtW6vXDiEA4aBA89Ho03JQ2XpxigNC0tsIRWWpo+kw0bCij//FMzPtY1\nzG+43VLgi2IBLomSKGA89tiTzJu3F7//c5Q392/gVaKjYygbgsKAb7/9Ho0bt6VPn5dp2bITzz2X\n94T3tddey8svP899992N1v10YrPVoGrVffTp04ennnoB5Q/+hoCzNsoD/A3B4TSkgN6DFLQGQBV8\nvuNkZv7K0aOzSE/PQJDkRgWMagDjcDgqsnv3bvbu3UvXrj1JSemLQHQ9gol3kY20OrLjBlRYFSz6\nD1JTF5jtrAIftZBaVxGBqrXMjFW9NgkpfZUJrG+6ImhUVpr995nfP6E8x1nIjroMQVwkAtTVqCrv\nv5GV1lpaxY6Az4WgvCNSZsejHMrzzHhNQ6oqCO7TkRI4x7y2CKmst5nz7o+g8mEEz98h+B2J1EhL\nrexv9v/V9BEEasuQGvsVAvLpqKrxPtPmnqCx2G/GrQsC5hVmHMaYsfSYfWxmXIea9/8gK6sMO3a8\nzO7db+D1ljXHeAl9XkqRkJBA48b1iIj4mgAMf4LU7p3IdmxHkAtQGo+nETt37iQmpoxpt6l5fxmy\nIbuRsjzC9O8xpOb3JzKyAv/733TS0qyldEDKMyQlJfH2228zZcoUDh60LO0l8U+NEig9VZQrp9yl\nwnroQhFPPAH/+tfJC33mJyxZ5IMPREt33qkbfCuKGUrhRG4/U8M4Zox+FyYFISexr3r1ACxkzykt\n1vXVCwKle/aIpopq301JCUiFINrJLa/Uqr6bnp5v5TLXGDxYhYss/3V2KH3nHfj4Yz0uBvvuoUM6\nlbJlA7xbmGH0esVRNltggia/SmlUVM51nfIbW7cqn3vcuECOc3CbL78Mm3ZHkZSQRljmaVJKGzXS\nhEZCgr6YTz9dsGN7PLrWWVn5X7O3JEqiiPHhh9PJyHgXwUsf4Hbs9iF8/vlU7EWcVU1MTOT++x/G\n7V5OevpC3O41jBz5DH/++Wee+23atIkpU6YiS246cCter5+IiAiystIIQIEdqWsjsNnaY7fXQcrX\nXAR31rqVS8y2vyKAjEcK30QEcmmAj5SUHTRv3p777nuQjIwrEDx0RXBcGq2HWQYpjm+iSrX3oWVH\njiJQfA/B6RGsojeCyHSkLC5AQDfe9GGNOfZvwABzbj5UQOlqVMRoodn/U2C4ac+qJovZ34GssFZu\nUSezTwsEkfNRXqdVFCIDVabNQgBZA4HY+8Bk034cUlojzc9tCLavRgBrRxD4Msq/fMSMUUUzPs+Z\nfo5BIDwd5cp2M+3cgJREK8KQmnyvGRenuV5fmtfGI2tuBlKYbzfjeRTZmu1IlT5i2vGZtt417dvN\nNWmHcnetCtTLgBSqVavGf/7zKFWrbkUTCc+b998zY+xF1/9/5vVN+HxLaNasGXFxVVDBp0NI5baq\nBl9ktq1rzg0zhpkcP/4kc+fWxuvdYs7rBaAdnTp1oWnTNgwYsJBBg76nYcOWp/zOlMTZHYX+Szpj\nxgwaNWqEw+Fg9erVuW43d+5cGjRoQL169Rg/fnxhmztzUbasFJmi5MYVNcqXV6GQ/Hj9soe1z+HD\noqd33oF69QLvWzePWVmnBUqLsmxlUcIqHAsFzyvNPuxXXKF0Nmu4ztqc0t27BaVFVUrd7pO97rlZ\naa11Si0YCWVkb/Pw4QCUFIN910oXt4YQCjeMVjHi8PCAeplfKC3qENatKwbMqU3LyZ9GFE5PGhH+\nNDLs0aG5bDlBqaWUWh0C2LUL5s5VKkR+w+MJ5KmGogBcSZREtnC73YwY8TTdul3Po48O5fjx44SF\nRaB8PyuOYrPVY/DgkWQWcXJkyZIleL3W0iEAcWRmVj+ljXf58uXYbFcgeAjD73+GP//cSK9e/ahf\nPx5ZX71IFXwXuBi/vzU+32EEIhcjlbA9gpe+SDUbjQBprXntKQQPmxC4lsLr7cQ33yzH47Fs9M+b\ntqojGHoErdNpFQTah8DoJVSg6CqUA/m52a4CUkHDECRbkYBspt+ivMbDCFbKmj7HmeNuRupgOgLO\nz5Gd9BfgNQSzdyJoXI6US5DCG27GwIp2CMxvR4qeHcFbFFJSHyCQ51kGwV1XBK7hCCpfQICXbvrn\nQSqfparbkLIYheD7CmSlXYAU4pbmXK81fV6CcnLnILtumhnXdNPOBShP9jszTk+b15MQpP6ObM/v\noGtfE9miV5o+Tzb7zEV27S/MtTqAzbae2NgWREdfy2efTSUyMpLExEQSEvYiYP3AtGXlRzVC8D8C\nTSi0oGPHfxEfH8/zz4+iVKlZOBznoetfCUH+U+jzNRSB7o9oIkN2XanDqeb8fgPas379Zo4e9ZOe\nPoO0tNUkJjbj9tvvx2390y2Jf1wUGkqbNGnCrFmz6NChQ67beL1eHnroIebOncvGjRuZPn06fxTU\nqnWmo1w5WLcu4N87UxEZWbiFMNPSdIOYnJwzLQUrpcUk8QU7m87UMNrtgcIvp7JMZo/sw16//omw\ncNpzSo8dg19/zXs7v19KafXqRYfSjIyToTQ/SunpgFKPR2uUJiYWGEonTJCDNLfYY5xQRYVSa5iC\nCw/l174byiHMDqUpKfqdRhR/bUglmlRsMdGhKbyd3b4bHa3P7cGDsu+CrOXx8dCxI+S3gqnXq8+2\n05n7UlmffQYrV4bgJEriXAy/30/Pnr2ZOHEVCxf2YfLkfVxyyeWMGjWEyMjeyGo4GJiH1zuXbdtS\nWbJkSZHalNKajIAEBFI7TmkLrlixIm73GgIVdjcCMcybt5pnnhlKhQrzEXA0QFVOpyFw6IiAw2/2\n2Y0qwL6OlLfzzPsPoVzUhij/EVRAJxpYgd/vQYrbaNPnLAQRZZFq9xICYjeyEjdFKmJ3VA33GgQg\nLlSoKRIVMnoIAdJjKMdwN4Ldi8z71tItUxDcJZht3jGvX45UyZWmT8MRdH5m+nK1GZNqwCBz7i8j\nCMxAQG5Hdt7bEDBej4DwLaQeDjXnfRkCwgoIqKeb9m8359EWTWbUNOd5D7I5v4lAP8Mcp7XZpwFS\nR38y7b1qrtu/zZjcghTon5DN9wZzHlMQLP+OANhUymOvuSYz0KTBVpSPejEC2g1m+9fM8dua6zTe\n9HEofn8KqalbcTgcrFy5huTkZHbt2kVExPlmLNub419LdHRDwsNHc/nlF+JyHcZuP8o111zLt99+\ngc/nIzk5mTfeeJFnn72WF198jt9//4mnnnqMmJibsdkuQpMFU81YJJnPyPWmfx4E3MtwOn0cOHAA\nqfibgWP4/QdZunQvLVu253jJhOU/MgoNpQ0aNOCCCy7Ic5tffvmFunXrUrt2bVwuFzfeeCOzZ88u\nbJNnJsqVk+3sTENpVFThldLy5XXzdiooPQ1K6ZkcRquCakGG0e8/efvsw2Q9tybLix1KExNV+Cev\nOHRIIBAVVXT7rtt9cinX3JRSj0eDdvx4PiuJFSCyfwcOHdKgd+4MixfnO6fUAkyQfTW3CFZKC1Ic\nKXtYk7bBw5FfpTSUQxjcpt8fWHImjSiiSCOaVByx0bkfoCDhcp04OVGtmkCxbNmAh79DB2jWDLp2\nzT+UWhWlIXeldPz4wlf2LYlzPnbt2sWyZT+Tnj4D6I3b/R47diTTrFkT3nprLHb7cARCK4A4bLay\nZBR0pjNbXHTRRURGOpAqGQdcisvl5MEHn6R379vZa1WtzhZXXnklXu9OtK7m3UhpHIbPF09qaiqH\nDu1g9uyZOBylUEXWZkiVbAh8TUTEZdStm4LT+R1SrTohe+obBGAuCSlTm0yrvxJYhqQhNpsNu/1t\npMT2RFbUcmZ8zkP5iDYCS4v4gx73RiqYG5hMREQEgtUFKHdyAwLVXcjy2xipcLMQiB02fbbg3Sr8\n0wbZTz81/bLW72yAlE0/AuvHkGo73hy7KlJEUxFghpttZiFQs6KhGRMvAuxdZhsHAj0rfkNgHGP6\nFmGO3ZOAsnzMjPkuAvmSh9Dt+StIucxC6nGUOb6NQBGnqgQKJIHA14YAPdqcxxQEwtvQtT2ObLwO\nZJe1lu2xQBYE+UfMuW7D663CsWOdGTnyKcqXr8pddw3A49mOrnMqUoZtlC7t58MPpzB37hesXfsr\nF198KZs27WDAgP/QuXMPunW7g/7932T8+FeIiYlh/fr1XHJJGy688CLq1m3AAw88xMqVC4iOPo5y\nnW831+1Kcx3vB1IpXXohYWE10Rq6T5jxWInP9zvbt9fngQcG8tFHH/H555/z0ksvMW3atCI7Gkqi\n+KM4s9/Yu3cvNYIopHr16vz888/F2WTow5qprF79zPYjr8qjucWXXypvq3x5JZdZ5WKD4xyC0shI\n8Vx+hzEzE1q2DKyxakVuUJrb85BGftVsy7oLobHv5hdKg+20xaGUBsvWllJqRT6V0u3bA4+zF94K\nDgtKq1cPKJpFte9akZ91SiG0Q2i5Bdxu/RwyKUqpRBNFGlGkkRWZw9+IwkR2pbRhQ6VBtGihak+l\nS8Mdd2jb6tXhxRfzd1y3O28oPXwYVq0iNIutlsS5GF6vF5vNgW7YAWzYbC68Xi8333wzr776Lr/9\ndgyP5wB2+8eEhW2jXbt2RWqzcuXKzJnzOb163URq6hEcjhhstkv47bcHWb9+MUuXdmTz5jWUyvY/\n3OFwEBbmx+3ejuCjK/BfsrIyad36WQBWr/4dv785gkgnUtqexeFw4vPt5JJL+tC7dw/++99NQZNu\nOxDY+BF03IjspNUQMP3PPH8Dv/8KmjaN46+/1hEWFs7AgcOpV+88tm/fTmZmJhs3buaTT/5E6uwA\npMQeQaAVhhTEOwkL+wGnc5Np80JUMKk7sprGInXPqtaagaDtGFJ+D6H8zE8QiLUjAGlbzTHeRxCc\nbo6fgUDQmvlrbMboOQQ4LyEFs5vZ5xWUt1oBQZAf2Zu/QbmRjdDEQD+UKzvZnOd4ZCueaM75K3Mu\nDjPOpdBkwnYEqx2RQjkc2V/TEUhfg1Ta/eYc+5r2LgS2oGrFlyO1uyyC3ucQXHZA4AtSpG9DFZev\nNWOznHvv7cdbb72Kx5OI3x9jzvd+cwwXUlYXAFvwemuxZcuT1K0Lu3f3ICPDhtd7MbCWhIQ/uPnm\nfixYsIC33/4Iv/9xoBNbtw4ASuHzrTdj14r77ptIVFRDUlLmIavuk+zePZ6EhBdZt+5nPvxwKrNn\nf8Nvv23C709BcL8XpzOF2bPnceml16I82Z0EcoBtuN2dmT59GJ99lkRGxkIcjjZERGTyyivvsHTp\nPFzFepNWEkWJPJXSbt260aRJk5N+5syZk9duf4ctJD6wMxwWUZ1ppbQw9t2xY6UglS+vm7mcvoin\nIac0mKOCV9U53WEppfkdxo0bTwZSODWEFmuho9hYqFXrxLy8nGLvXoiL0+PTbd8FQWmoldLsIGwp\npVbkE0qvuy7w2MqrzCksccJyQEPo7Lv5Wac0eLtQhXW81NQTldLSJBNDCjsSi15FFDg5p7RWLf2O\ni1Oi62uvwWWX6ad+fXml85MHZOWTQs7rN//wg45/ily8kiiJ3KJ27do0adKA8HDl94WFDaJyZbjw\nwgux2WzMmzeTXr281K59F506LWHFiu8pE1ydvJDRtWtXkpL289df2/D73bjdnwDdyMp6hpSUmixe\nvDjH/Vq2vBCB0GpkkZ1EpUrVOM9U6Fu+fA0+370Ivpxobc3SeL378Xj+YsaM72nbti3Vq28iIqIP\ndvsTREb2pl27FtjttbHZKmO3L2LSpOfp1+8SBDLXmNZ3AbE0bNiIpKQEDh78kyefHErv3r0ZNmwY\nI0eO5NixLGQdjs0vpYoAACAASURBVEEQdgGBHMSdKL9zGB7Pt2RlOQgPfwitm3k1suquRkB57O/2\nZFN1I5vtQVRZuCbwqHntbbOtB4FqOrLggpTXrgjcZiIFrjuyhQ5GQOo37T6MoM6DcmD/Zdr5FUHo\nX+b5U8hiaq0BOhJZdmcgAHwUAXEa8DPQA9l/qyNo3m22vdCMzX5zThtQnml1ZGMeYPodhkB4IYLn\ni822D6JCTVnIqrwdTR4sQoo3CCzDTb9uANpgt+9h+vSZ+Hyd8fv/wOl8k3LlyiJLsQspuj+hyYna\ngI2srCH8+ecmDh3ag8ORgYocnQf0IDOzD1OmfIHf3wyBdXt8vg74fD3QZ3AaUAafbz0pKTMJ2Mrb\nkpExjTlzPqNmzZo89dRIVq9ewe2330B0dBsiI+8jKqodY8aM5uKLL6Z//7uJjm6L3W4VkcpCKvBk\nvN7HyMiYCfyM1/szqanfsmFDFp9//jklcfZGnrfPCxYsyOvtU0ZcXBy7LbkB2L17N9XzUBxHjRr1\n9+NOnTrRqVOnIrUfkjhboNRaUqEgkZysir3WOWRf0gZOS05pcLfP5DxFQdaGhNwBJDuEZh/WYp2E\nCwvTGjU9e+a9XWJi4LqfTvuuBYmpqaEnqvh4Vdu9+261k5p6olKaT/tup04qfPXmm3lDobWMS/ny\nAdX0n2zfBbFhUpLWB7bmNdKIIoZUDlCJg4dDVJA9WCmNjJRMW7++oDQsDPr1C2zrcKiQ2969p17X\nNrt9N1tO6aJ581hUvryswk8+GZpzKYlzKux2OwsXzuaxx4azcuU4GjWqxwsvLCTc/A0sU6YM06e/\nUyxt22w2YmNjkXplFc3xAx4cwXkHQREf34iffgoqXsgF7N9/iPPPb8Lixd/SsOF5LFgwB0GRDeUp\ndjTblsLv/xcHDhxg7dqfeO+990hKSqZbt5ncfvuD2Gz34/PdA3zLiBHPsnz5Qj7//GLS0+9ANuPJ\nuFyRXHllZ0BVhIcPH8OWLTvp0KEVQ4c+RuPG9Zg/fzZe72Fk+60d1JdIAlVwHYSFxdO5cxizZw9E\nILQMFQOqAwzC5XqGzMx4pAZ2QXmslyG1Mg2pjlcgmK1rxjEcqahvIzg8iGD0CaQafoVyRB3m90yk\nTCaacyyPFM+3EdD3Qpbg+Uix9Ji+OhCYVULgbUPw+C2aNPCbbY6ZbdYAHyFo62fO4zIElg2Qvdaa\ndHsILfeyGKmjNlQIqBaC0TmmLRAYpwNlcbns1K17iG3bUsnMPM+M/VZk+fUiBfVaHI7HSElpQGam\n0h6ysn7H4+lKTMzD+HzTSUvbhNToT80x7gB+olKlOCIjI4mKKo3HswvZtkFFrfogkLVmfpcidfo+\nBOFtCbgR2qHcV4Bj2O2OEypav/POa/TpM5/t27fTvPltfzsTXnhhHD17dmP16tV88MFnbNlSAa83\nE5utKllZj5q9G6LPQDJebyMOW7OxJXFWRkgoxJ+L3NCqVSu2bt3KX3/9RbVq1fjkk0+YPn16rscJ\nhtKzJiz77pmG0sjIgLSR30hOFgVa1XbPUE7p2bK2cUGVUqsQTPY4o/ZdyF2lDI7jxwN27eKw70ZE\n5J5TakWoofShh+DDD2HhwgBRWe05HPkmOJtNYhrkPYyWCFeqVPEVOjqd9l2ASZPgkktg8mR46im9\n5iEML3YOEsL1moKVUuuL16BB7rbamjVh2DBNPFgdyymCP4s52Hc7RUTQqW9fvX7DDYx+9tkQnExJ\nnGsRExPDG2+8dEbajo2N5brrbuCrr64hLe0ewsIWU7FiMh07dsxx+2uv7c706Q+TltYZWUuH4fff\nxd695bnxxruZP38m77xTn9TUBkhl3IKUPJDSN5/mzR8kNjaWgQMH4vP5+Omnn9izZz9e7zNABn7/\n/Xi9H7Nnzx7++GMVzZq1Jjk5A2iA37+ZmJgYMjIyaN26M7t2tcXj6cOyZe+watU6pk17m08/ncHO\nnVURXO5GFuLpCM4GIevlYmy21WzcGEcgn/NPZKsFFbOpal5zoZzJLghc/zTHeg3lxs5A6uVapBB2\nRArqeFRQymn6YuWXJqKCTg6kHu5F8Pmz2ecrVPToRQSElxAAO5DammX6Ykdw3BupkQeQLbgdgude\nKM+0JcpDvQ7lelqxzRwjFVln3zV9T0bLvrRE67T+ZsbIh4A8zJyLDwH31WRlLeCttybx5ZdfMmHC\nlwhi55qxegiH4yXCwz1cdFFTVqyoiwB7P1CezMx0tm/fxNKlS1myZAlvvTWdzMw+wDxstrFERmbx\n4YeC2IkTx/Lwwz1JS7sL5R7/iSC+JQLYxki17Ueg4JMTAXh1YBw2W2n8/nbYbDuoWrUWlSrVJj09\nhe7de/LBB69z+eWXk1N06dKFLl26MHjwYA4fPsy+ffv417+6kpW1GhXGetdcjx3Y7TPp0KF/jscp\nibMjCj0tPmvWLGrUqMGKFSvo0aMH3bt3ByAhIYEePXoA4HQ6ee2117j88suJj4+nT58+NLQqL/5T\nokwZuP9+ySVnMgpT6Cg5WdUurb6fISi96y79vuGGYjl8vqOgSmlua5r+Y6DUUg6Lw74bGZm3fdfq\nZyjD4RBRrV8fmKCxLmavXgWS4fNT/TZUUJqXUpq9/ezHDzWUXnyxlmVKSVHqpcJGKtEcouIJAmaR\nIrt9F7TubN++OW9fowbMnp13OWQ4USnNyb6bkCDwnToVzj+/aOdQEiVxhmLatLd54onL6NZtBnff\nHcHKlYuJsiZ3giIrK4sKFSpw773XExHRBalC9YBn8PluZePGdZQuXZpduzZSpswxBDxOVGW1FDZb\nM0aMeIRWrVoBsG/fPuLjL+LSS/9NenoiyiGNBapw7NhGnnnmeebNm0dGRhiqCjuLrKwF3HLLXfz4\n448cOBCJx/M60Jv09C+YPXsWrVp1ZP78OTRrFklk5GzCwxNQfuVEpEouwm6/kGbN3mPx4rnYbNZt\n6ZNImRyKYOYLMjN/Av5A1V77mL5dB39PqN0BrEJFiWKQmviK2X4Egkc/Ast+yLI7HhiHAKal6ZcL\nWYYbIqvtJASF1ox2JlL9uiDoDa54OwdVJM4wx6uJgBTTvgNBshflnVrVha9G9uErzb4ppn+Jpu3S\nCO46mnG5F4FoDCpg9TaC/c0oD/ZX/P7DDB8+lmnTvkZwfFXQWF1OjRqlWLZsDm+88TKqeFsVFYmq\nQ9myFZk/fz433HADM2fOJzNzlhmbr3G52jJ06KC/J0pcLheNGtUlOnoydvtGpCIfAFJwOudjsz2D\n3R5ursUOYBVhYWE4nfVxOkvRsOEyIiOPYbNdit8/g1274jlypBZpaX/w9ddu7r57ADlFZmYmQ4c+\nRXz8v+jYsSe7d++mTJkyjBnzBJGRl+F0xhAW9hgOxx7KlevD1Klv0LRp0xyPVRJnRxRaKb3uuuu4\nLjg5y0S1atX4+uuv/37evXv3v4H1Hxl2O7z++qm3K+4oaE5pZqZuCNPTlWtns+UNpVlZxWbf7dED\nNm+GOnWK5fD5joJCaXJyzq+f0ZxSyB+UHjsWUErPhH3X6SyegWjUCJYvV9VWCNiEP/20QIcpKJSG\novpu8BBajz0egagFvdmLA4aa60FDeOCA0s2tSCOK1MiKvPFGiBrJXugIwNz45hg1a2qgLM90bnGq\n6rsWlDZvXvi+l0RJnOFwOp08+eR/8nSgp6Wl0bHjlWzadAi7PZqoqGhstgqkp08AwrDZ5lCnjlxS\n5cqVY9++P5k0aRJPPDEGj+c94EJcrtEsWPAjQ4c+BkC/fvezffvlZGWNRTDUHuXqVcPv786iRY1Z\nvHgIfn8ttI7lEOBrMjJSSUtLw2azKr+C4CuCLVsu5eqrb6Jy5crExGygTp0oype/lB9+uB2nM5bK\nlUvx448bqVatGuvXr8ftPo6gLBmpel8iG+gtyIYLKugzDhW5SUcAF4PAKhzlnDZCwLkNWV/LIXCc\njhTU/UhRTUD5p1bsBs5HNtulSE3+BanLzRHcfoTgdq75HYWU2YEoZzMSrb1pQwC7H63Xud2cVziy\n/qaZfi9Fa6haf4D7m+2mIXitTGAt2famT9+YfiQiwJ6BYDwRAXYCNlsky5dXIDNzGILlR1H+6Tjg\nWzIzyxEREYHX68Xvt6Gc5LeBBPbv78lDD73JwoXLOH48EdmhFZmZ9di3bx8Ar746maFDXyItbRQ2\n227s9mew22sSFVWap58eRYsWzahcuTI33ngXmzY9iMfTD5frS+LiyrB27Ub8fj9Lly6lb98J+P1P\nmxbammvtJCPjv8ydm3MhsQcfHMy0aRtIS5sAbKRt2y7Y7Q7Cw6sRFVWKOXM+oW3btv8/6tucI1Hc\nt88lEaooaPXdYKKKitL+eRU6ysg4GTxCGKdYPei0REHtu/mF0uw5pcU4jIr8KqVVq+rxmSh0FGqJ\nz4r4eJgyBb76ShVdU1JyzpU+ReQHSi2lvDjsuzZbYAjd7sBnM1hohuIZxkaN4PvvwdxTAILS6DqV\niA7RijA5KqV5hZUecSoozW7fzb69BaUlURL/z+O5555n/fpKZGR8D9hxOp+kYsXPgPq4XNVwufYy\nffrcv7ePiIigdOnSOJ3X4PH0AsDjeZ3Fi0uRlZWF0+lkzZrVZGW9jGCqHKrwugZZUdsDyfj9bRCM\n2REE3kzNmvW49NJLiY19nJSUIfh83VCl2I74fGPZvHkCW7aMx+9/hmPHJtGixV9s2bKGo0ePUrNm\nTcqWLcvmzZtp27YTqanpqEjPAwh8LWBMJbCEyofAWFQddgdSdGshlfB6pDCCCvU0Q1BYzuzrQNbd\n85CCuRwYhcDVhQoNzUfW0tvNGBw3bSxGym0yKpb0GbLt1kPW4Qxk/bXWXd2D1NyGyHq7DhUmOoJy\nTfsjpdWDLL5lTd9vNf0vj2zK45BKGWMex5p+WkvDPYlss+PNuHfB5dpOVtZSMjPfN+fcAVUuboEs\nxPNJSFjMRRddTGamD4+nDALnFcjiHU5a2kPMnFmbzp078N13j+DxvARsw+9/j3ff9XH99dczfvyr\npKVNAy7C7we//xBPPhnN00+PJjgWLfqahx76D6tXDyY+/gImTVrwdzVpl8uF359GQMV2m3F1AFuI\njc25AN/UqR+Snr4RKbwpZGaWBVbjdpcF3uW22x5ky5bVOe5bEmdnhKiqRUkUexTUvhvsPY2K0k9e\nSumxY/muXvpPjdOllBb7MLpckuzyIqTgnFLrGhcm/P7CKaXFIfGBiGrdOpg+XbmHqanFBqU5KaXZ\noTE/kZN9F3L+PJ4uKM0eaUSRFpPH+jgFjeyFjk4VNWtqgAqqlAb/nfP5JAFbkzElURL/j2PDhu1k\nZFyBdRuXldWao0cTychIIDNzMxMmPE0j82X/7bffmD17NhkZGdhsOwkUn9mDyxXxdxGlWrXqYLPN\nN+9lAt8hgEtBttkMZB+1bh3bYbPt45ZbrmfQoKHcd98t/Otfv2G3344K4nyM7LRR+P2PAS1wu99k\n1aqVDB/+DK1ataVSpTi6dbuWyZPfIjX1NpQTeQUCuLEI+IYha2wZBCCXoDxBFyqc0x2pkPea160I\nx+VyEhXVAymXD5u+jzXnsgAV/umCLLqvIPtsM6TZvIdU0F+QMvkasr+WQpVww8z7yokViEYgmOqP\nQPEXIN78LAbuQSruQQReLwLPIGhNQ3BtxXnmWn1mtq+Kcl9t5rkV+4HVOBw9qFatCr17p/DAAw3N\nZKr1T8Vn9vMioG2G3/8wKSkZuN0fIzjehPKSrf/3UTidZRg9eig1amxGBZjuBN7C7X6Txx8fi8/n\nI1jf8vud+Hwn15kpW7Ys06ZN4Y8/VvD55/+jSpUqf7/XoUMH4uK8puL1B9hsXXE4quF0Pk1k5M1M\nnjz+pOMBOJ0uAsWgNqLPgQWwfdixY0OO+5XE2RslSuk/JQpq3w0mqsjI3JVSC1iSk//fQ2lxKaXZ\nn+ezCGzhw5LZgiW27BGcU1qunMgnJQViYgrWVlaWLOzZKz/mBqUej/pXXEppmTIwfLhySI8cKTal\nNCtL79ntGmJrdZ1du3LePq/Iyb4LOa+bezrsux076jPbsKFExblztVZpekwxFzrKKy67TDmld96Z\n93Z55ZQeOSJQLXarQkmUxJmPtm2bMXfuR6Sl9UUQMRC3+x7gadLT13HnnR2ZP38RlStXYcqUj3A6\nm5GZ+TMVKpTF57uO9PQWREW9z9ixY/+2N06d+jodOlxOVtZ0UlK24/MdQzbKZ5A11IHW0LwTqITD\n8V8qVKjM888vIi3tOiIjv6JDh1J069aWZcu+Aw6SmfkNUBm324eA8Dher5vPPvuNrKx9QBRLl97G\n/v1LEVTEI8VvCAK8X7DZ6gLx+P0rzDHeRmD1HlJxQXDqQQWJGgENCAsbQf/+/alRoxKPPz4Gr7ci\ngsppyG5bDUFoAoKyTATEnVGeaAay61oQ3gGpqmEI2C9F0LjRbDsbgakdKaEOZHu9CanKTyHr7W0o\nP7Q6Ko50C4LVLgicP0GwNQ7BfUOUOzscWYufQ/mzm4DD5pr0AlbTtGljRo4cTJ8+d5GVlYHWJ30I\nwbf1fzkZKcep5pwvQ0rsAwiUxwH/xuH4iAoVwmnevDnt2rVh+/a7zbEAlpKSksqAAfcwZsxtpKWN\nBfYQFfUON9/8IwWJ8PBwVqz4jmeeGc/WrQto3fo6ypSJJSUlhcsum0/zXNIxhg0bwjPPXENa2mDs\n9iX4fGsI5N9+Tu3a/7AaNiVRAqX/mCioUppf+26wUlq5ctH7eRZHqJTSUy0Bc1rY3vJ+5gWlllJq\nt6voy7ZtBc+1y8m6G9x+9vB4BL7FBaUgKAVYsUJQWohZgFNBabBKarMF7Odbtxa4qRztu7n14XQo\npQ0aqE5UTAw89pigNI0o3LHFoJTm174bHg7t2hXcvhsMpQkJJSppSZwz8cgjA1i27Ffmzq2OzRZG\nRsZBBEwOZNHszYwZc7HbfWRmbkAK0moOHerC/7V33vFNld8ffydt0ia0QhmlQIGWPaWIgKggw4KK\nIIiy3CI4UQRR/LlAvyxxoYgoMh04KTigiiiiCCIIIkNllL0LFNo0TZvm98fT26YhaZuu9MJ5v159\nZd3x9OQmuZ/7Oc85kyc/xLFjJ+jW7V169uyZu82WLVuya9ffbNiwgenT3+Hbb2NQ4qkOqhLtLyiX\nsgFgIDs7mJQUK3Z7IhBKevqD/PJLY9at+4YDBw5w7Ngx2rV7gjvvfJB//x2M3d4Fq/UDoqKas2fP\ncJTzCXb7o5w79wBW69vYbE+gBOczhIRcwiuvTOHYsROsXbuONWsaY7cvRTl+l6EEmkZzgoJm4nS+\nDkzHaNzNiBF3kp3t5N13P8bpbIIScUEot7AXyj1MRM3N1C7YPo4SZ/Ny/uf3UIWFaqCEWySqDcts\n4CeUi7w3Z7urcuJlRqUVZ6Mq0d6DmttaK2fs96KKHIFybbcQEvI6LpcJh2M30BUlrJ7OiXc/lGh1\nolJ3jTn7mIzBkInLtRrogNOZTmJiDImJHXPWTUS5wffmjG8Z0JuQkO5kZNxLaOivOJ1hZGa+hxL1\n0ZhMt9KwYQInT75Hq1at+OCDREwmE0OH9ufLL4djs7UCqmC1jub22wfw1FNjCA8P48MP36Zy5TAm\nTkwsVkHTypUrM22af9XSx417gvr1o1my5HsiI2M5dy6Szz9vgskUTXDwMb788tvCNyJUKESU6oXi\nOKVab1OLxXf6rnbyeBE5paWdvuspUstVlPrCvdARqLZA//3nvyj1lroLBafvhoWVXfquO2azSt+t\nXt3vVQsTpe7zSUG1zzQYVHFYfwtV+5O+6+mUlpW213S89n9MYyzXNOpQejvQnPVz54rmlAJUqqQC\n4HAo13P2bHj++fzLuDulYWH5+zadOZPXwksQLnCCg4NZsuRjDh8+jMPhoE2bjpw9uxk1zzAL2ILT\neTUuVzJ5KY2X4XIFMXToUCIjvWdGREREEB8fT0hICD/+OJD09JlAX0JDv8blqkVGxrcoRzIDq/UK\nsrMzyEv3NBMUVJmMjAxuuOGG3G2uWfM9b7zxJjt3buPqq0ewa1cSr7++BodjGGDAaFxDkyYNWbRo\nFs8+O5XU1Ghuv/0RHnnkQdLS0ujbdwirVq1GdR+chkqz7YbR+DjZ2R8AJ7BY3qBHj3b8889r1KpV\nk4ED72DChMmcOdOBrKz7UUV+ElCVaTVX1oWad/oHyi0ENcf0MpQQvAk1L7Quea1etN/QQai5oR2A\nhcBWVHpvo5z4v4yaD5sMtM6JkQWVHnuVW8SvAF7hyiuvZs6cDTRo0AQlmBfmvP4VSqC+kjPefajC\nR/OBR3G5QlAurCVnP41Rc0L/DyWAb0UVUPoHuBaDoQ0dO1aiYcN/adToMq67bhx9+w4mOfkZXK4M\nZs58i3vvvfu84yIyMpJmzRqyffttWCwwcuSD/N//jcVgMPDwww/w8MMPnLdOWWMwGBg6dAhDh+ZV\ndX/++SdJTk6mefPmuXNWBf0golQvFKfQUd26quytlr7rLc3RbFbzBk+cKIe808CineCXdvque3EY\nk6mcsgcLE6XuTikoUVocm68gUeqtZ055OKUaJpP6TJRB+q67U6otX68e7NunhKk/hbsKc0oLmlNa\n1tpeC91ybuCqKqW8cZNJfYiKeiwYDCo9+/RpWLhQzRn2Jkq1QHp+J6alUXqVmgSh9MnOzmbKlFdZ\nvDiR6tUjmDbtBVq3bl2ibdauXZvdu3czdOgA3n23Ky5XH9T8ytoogbIc5ey1BD7hkkvCqF7AhbzF\nixN4//1PsFpDmTz5aRYseIuMjAwGDrybyZNfQ7X6qAmcJSvrGDVrRnL48LNkZQ0mKGgxVao4aNWq\nVb5tVqpUiWeeeTr3cUpKCosXd+Xo0S7AJZjNW5g58ycaNWrEypVL8q07atTT/PbbJbhcZ1FzLq8H\n3sNgiKN+/U9JTr6C0FALL730LCNG3AfAffeNZOzYN7Hbu6HmcTZGzdWMz9nq1UAEQUHVcDrnoNJy\nN6Aq1/6Jmi8KStT1QTmM2agWM2NzXluISqn9GiX6n0cVKbobJQhfz9nOFJQwfQ7lto5ECdbrgRAs\nltcYMWI4b7zxMgDNm7dmx46lqJTfKJRTm4HB8B8uVzTKtV4HPImazzqOvPY0T6GKPdly3qeonNd2\nACeAp3C5unLu3ETmzn07N8b79//DiRMnqFKlCiEeP1Tbt29n0KD72Lp1K2pO6fMYjdOoUycKo7Hi\nlaVp2LAhDaUdmG4RUaoXNNezqKSkQHS0EqUFpe8aDFCjBuzefcE7pWXVp9T9grPWfafMKYoodb/I\n0Lgx/Pqr//upiOm7GpqiKgdRCiqE+/Ypbe+PKC3MKS0ofbcY/5pfuB/Lpb4vs1m5l/4cCxERcOoU\nHD3q/fWMjLyBeh6DaWn+z5kWhHJk7NhnmTXrp5z2Gf+xZk0Ptmz5ndgS9EtbtWoVvXvfikrLvIyM\njGUEBcUB1TGb3+aBB4Yzc+aVGAxWwsLMfPfdEp9i4sMPP+b++5/GZnsJOE1i4v9Ys+YH2uS04MrO\nNjBlSkuys+tgNB7mscceYtSoB7n33kf5+++BtGjRnDlzVhBayNW0ypUr89dfv7Fy5UocDgddu3al\natWqXpddvXodGRnTUY5lKnAHRuMMwsOTSUz8mSYeX8Z//fUXixYtxW7fhnI2D6DmZJpQKbUNgIOY\nzWcJCnKSnl4dVWH4U5SbagBeQwm+SqiU6AkosdoBNY80BeUWd0KJ1S0oJ3U4qjBUGqqNTVbO/VGo\nHqSghOK9QE0MBoiLu4bx4/8PgG3btjFwYF8mTJgMNEWl6H5OSMhtfPDBu9xxxwgyMr7L2XZtlAi9\nI2e7oai5uN+gUnbbAbeghHQ34CXgagyGL7DbrezYsYMmTZowYcJkFi9eTrVqEbz66vjcnrUAp06d\nonPnnpw69TTKSX4HmI/N9j4vvzw69yKAIJQWIkr1QnGc0ujovHV9iVJQqmrr1gtelBa10JHLBXv3\nFt0pdRel5WY2a4WOfOHplMbEwEcf+b+fipy+q70RxVBT2r9UmCh1fz+180Z/ix0VVOgICk7f9awv\nVdq4h65MRKk2jaCoREQop9SXKHVP3/U8BlNTxSkVKjSzZ8/BZvsdiMHl6oXDsZ3FixczZsyYQtf1\nxbBho7DZ5gB9ARehoX247joTf/zxK6dOXcKsWZ8RF3c5CxfOIjY2luAC+kdPnjwDm202WiprWloq\n77wzl1mzpgNw8OBhjMa6OBz9CQ1dxn//7SYqKorlyz/3e9wWi4Ubb7yx0OXq149m584xKPe3KpBM\np04t+fTT76ijVaBz4+jRo5hMTVCCNBtVTKgKQUERuFztCAu7iqysjdxxxx3s2bOfVasuIzOzM6oN\nTE+UeOxJZOT7nDzpIjs7GNWaJhIlbB/LuTWhHNZ/yCuEpNXlmI8StOEoUer+5RqKcj5DsFi68/ff\nqVx++TU8/fQoRo58CqezEQZDVVyu17FaOwAzePbZ/2PXrr04HOkodzYDlVLsPl2hKpBFSMjTmEwp\n1KxZhd2730LNlx2YM8YuuFzp7NjRmvbtu9C3b2+WLt2DzTYJ2EnXrtezadNvNG6s+tvOnTsXm60S\nymluhJpTWxM4g8t1foVdQSgpFc97F7xTVKf00CG4/XZ1Mqh9YRfUEgaUqnI6L5r03cK0/euvqzmE\nf//t/XXP33RPp7RcKMgpdbnOF6WVK+cvClNUfInS0FDf1XcvAKfUc04p5L23/oaxJOm7ZZ0dVeai\n9MyZ4onSY8e8v+5+PHpzSkWUChUY5VDmXUw0GDIICgoiOzubI0eOYPMnGyqHkyePoQobARiw2y9j\n377DnDx5Fenpe7DZ9rB5czXef39hgYIUIC0tBVVB9kuUoAvOafkBBw8e5KOPPsFu/xl4Hrt9FUuW\nfEf16vX47rvv/B53YZw5c4brrhvAypXfoBzSJJQAfITMzCCvghQgLi4Oh2MjykmshJqPeZrhw6/l\nzz9XMWfOu1In5AAAIABJREFU3TRpEstHH61i3bpUjMYjGAybgCdQrupQwMz69T8RGxuaE4efga8J\nDQ1C9foENb/zMGo+6keoYkcPocRqB5T7OooaNWpgsbwOzAW+IiTkXmrVqgpMxGb7itTUlRw4cBn3\n3/8I6elDcDhScbneAB7H6fyDhIR5NGkSy4QJ7+JybUP1Qe0BnEJVwv0RlaL9LHA9PXqEk5AwlR07\nNlO1am2UmDaixPGmnDH+D5vtST7/fCk220JUm5/7cDgGk5CQAMCkSdN49tnp2O0dUUJ8FKpCcRoW\nyxjGjCn/OaTChY+IUr2gOWOFXZ3avFk5Yvv3qzKbUDSnFC4ap7QwUfr00wW/7tke1D1sZZ1umUtB\notRmUwNxPwHx7OlYVHyl71os3vevE6e0OOm72jUbf0WpP+m7nk5pWYvSMk/fTU5W80SLStWqap0j\nR7y/XpBTKqJUqOCMGfMYVustwEcYjS9gsSTSqVMnGja8lAYNLiUiIpJXXnmjSNtyuVzs2bOHdu3a\nYTJNQIndnVitC0hLyyQjYxDqFC8Yu/1WNm4suGfjO++8x5Ejyai01InAlYSGTmP48DsBOHv2LCZT\nVVT1V1COXyynTo3l5ptvZ9euXf4HpACGDh3OTz9VweV6GBiCEpgAd7Bt21af64WEhOT8Rr+EEopP\nAyE0bFgPp9PJqlWr+OcfK6mpmzl3biUZGaNR7VJeyvn7HYOhP7fccjdJSSdRLV7SgNXY7XYslvdR\nhZBaosTq9agCR51RbWKMqNTbT7BahzBx4rN8/30CPXp8zRVXzOTtt5+hUqVwXK4rckZswOG4AqfT\nCHyO6kk6CHiBrKz+bN26lW+/XUlGxqOoasMRqHmq0aiU5gGoOawvYrVu5c47h3LttddiMpn47LMF\nVKo0iEqVeuasm4USqeBy1UAlS+YVizMaUzGbzSQnJ/Pii/8jI+N31NzZ34FPMBovp1atusyc+QIP\nPXQ/ALt27SIxMZE9e/YU8Z0VBN+IKNULRqM6GStoHiHkKaTfflONCGvWVGfWBYlSrRXMReKUFnYx\nurDpPZ7CwX0OaWFvT6kRElKwovKsOufZ07Go+Ju+63DkHW9lTTnPKdXu+6vt/UnfveCcUpdLCc2i\nUr++uqBWlPRdmVMq6Ixnn32KN98czfXXf8Uddxzjzz/XMGLEaPbvvxO7/QQOx3ZeeOF1fi1k/n96\nejpdu/amVaurWbduE0bjV0AlzObLmDp1HFdd1QmzOQHl5jkJDV1CXFwzn9vLyspi1KjROBxrUK1O\n1hEUdJLJk5+lffv2ADRq1IiqVYMJCpqEchTfQhXPuReD4bpCx+wPa9asITHxWxyOqaj+qMsA7Yvy\nC2rWjPK57qZNm3A6Y1FtXCJRPUFDmDRpOl26DGD27D+w2/8ENuescRshIUZU6m4foC4u12z+/HMN\n2dmnUcWLQlFzNIdw8829mDx5IA88cA09e16F1fojwcEOVKpuMDCS4OCZ9O79E48+OpgXX3yVvn0H\nEx0dxU8/LWHYsHvo1u0qQkNfRV1IOInV+h6RkdVQRYny5mwYDCGcO3eOdevWoea0avwNOAkLiyIu\nrgUm0y6Cg0fy0EN9GDhwYO5SPXr04K23XiYzcwOqANMI1JzY2Vit4xk6tA9W6wBgDkFB4wgL+4Eh\nQ4aQnJyMyVQd5TaDKkZVj3HjBnPo0A7uvltdqJg+/W0uvfRKBg9+lVatOvL++/OK8O4Kgm9kTqme\nCAtTZ8sFnfBriungQVWNZedOdTZdWPqu2Vw+7lYA0UyUwrRZTIyqDwXQvTu0bw833aTaKAJkZfle\nt9xEqfsJeXa2qsCjqWlvorS0ndLCCh3lpHyVKaXolG7ZAuPHw9SpqqBRQaK0tNN3Cyp0pHun1Gg8\n/1gsiAYNVEGuM2e8//PuF0m8zSn1kdInCBUBg8HAsGH3MGzYPbnPbdv2B9nZP+Q8qofT2YeNGzdy\n9dVXA+B0Opk3bx5btuwgLq4ld999N+PHT2L9eit2+z6UtzAUOExQ0H4MBgOvvvo/1q+/jn37muNy\nOWnevA4TJrznc1ypqak5SVgNcp4xY7XGUcut76/ZbGb16kSGDBnB2rUTUe1HvgMsGAz/Uq3awPO2\nWxz27NlDr179cLmqAttRonIlUA+ohsFwiPnzl/lcv0qVKsBRVKrp3aj2LxmcPm0nb17qIlTv0M2Y\nTLNo1qwlu3YdJzXVhSp0tI+QkEqkpztQRYyuRKXxbmLx4hSWLPmOhISPiY+PJy0tjV9//ZWEhK/4\n448dVK++gylTfiYjI4Pu3fuRnv4JEMNnnz2KwTCaefNm8sYbkzl48E6+/74yBgMMH/4YI0eOoH37\nrpw+3RdVnfc/LJbFfPhhFPv2dQB+AK4DqgEJNGzYkJ9//pE6depw5swZQkNDvRaYmjHjAxyOuagW\nNwDZhIdPYNy4R+jc+So6d76K7777herVq/B///cbNWvWJCIiAqvVSWrqnJwYLickZD+PP/44hpyr\n8AcPHmTcuOex2/8kPb0+sJORIzvQr1+fAqs7C0JBiCjVE3XrKhfBR38xIO+stnbt/M5npUrnT4bU\niIy84F1SUOGDwgvVRLldhI2NhSlT8r9e0LScgmoPlSruonDTJhgxAjZuVI+9pTFWqqSWdzr9q55T\n3EJHnuqqLCiBUxocrDSP06kuMnz4ISQkQIcOMG6cCiHkD6P2ESmuU1qcPqW6L3QUEeGfsm7QQLWB\nqV0bTp48/3V3pzQkRD3Ozlb7kPRdQYdERtbnyJGfgBsAOybTWurV6wGoFN0BA+5gxYqD2Gw3YrXO\nJTHxZ06cSMFuvwM1fxGUcHid9PREnnrqah5++AE2bfqVrVu3YjQaadWqFUFevkzS09PZtWsX1atX\np0GDpuza9T+czrHAGpzOn+nY8ZV8y9evX5/ffvuO2bPnMmrUc2RlvYPJ9Cdt21bL15e0JKxcuRKX\nqzdwM6p67EAgieDgTOrWNdCly6388ccfXHrppVT2MuUoLi6OHj068P33LVFzbQ+jhOYAVK/PSaiU\n27sIDa1JkyaN+eqrz7jhhlvZvbsfdnscFst8pk2bQmamnccfvx6Xqx+qD6mV9PQ1wFoGDLiF06eP\nUqlSJXr16kWvXr3yjeO5517Abh8OdM2J9XSWLu0CzMRqtbJs2RfY7XaCgoIw5VwdPHlyHy+//BpL\nl75FtWqVGTr0dYYP/z8yM98DzgFfEBLyHPPnz2Xw4MG5+6pSwBSJzMxMVA9TjUrUqFGd//3vTczm\npRgM+1i58hsuu+yy3CXMZjM//vgtffsOISlpBJGR9fnyy8X5xOb+/fsxmxtht9fPeaYxZnM0Bw8e\nFFEqFBsRpXoiJkaVhXUr2X0emhho2jT/8w8/7HudyMgLfj4pqD6ToERpVpZvcek+Z9T9fHr6dPj5\nZ4iPP38djYCI0rNnC59bZzSq51JT/Xuv/RGlLpcK7HXXna+uyoISOKUGgwqhzabCqLmfWki9idLS\ndkqLkr577bX+7ctfytwp9Sd1F5QoPXIEbr0VPv9cHVPu+fFnz6rvQch7E+12lQkiolTQIZ98Mofe\nvW/BaGyP07mT+PgO3HTTTQD8888/rFixGpttFxCKzfYI33zTkFtv7UNIyDdkZPRHCa6vURVS62K3\np+JyuTCZTLRt29bnfv/++2+6d+9NRkYlHI6jjBhxL1brCrZseYlq1erw4YcfE6N91jwYPvxeWrVq\nzm+//UatWh0YOHCgV9FbHMLCwjAaD6FSaVcAnxEcvIm5c2fzwANjWbiwDmbzBqZPn82WLevOE6YG\ng4HlyxfTtGl7du26j7zKtyMANV/XaJxDq1btSUz8gqioKAwGA+vX/8ScOXM4duw43brNo3v37gB0\n796d119/nUWLgrHbf0RdCLgGhyOL06dP+xRgVapcgtm82e2cYC9hYfkv/ns6m0ajkXHjnqBjx3b0\n6zeY779fTmamE9XW5RrgToKDJ9HU8/yuAEaOvJtRo0Zis70BnCMk5CUOHw7Hbv+X9PRwYBEDBtxF\nUlL+yo4tW7Zk9+4tOJ1Or+9t48aNycraDaxHFXZaTXb2URo0aHDesoJQVESU6onYWEhKKngZh0Op\nr7vuyv98lO85GDRoABdBs+HQUGXAHD6sihTXr+99OXdh8NBDefcffVT9eaNLF1i9GjwulpYd7qLU\nZss/aJvN+8m5lsLrjyj1J303M1OpnM6di779kmAwqCsLxVRT7qJUm2eshbEgUVpac0oLSt8dPBje\nfbfsExjKxSn1h+ho9Z527AiLF6uLHJs2waWXqoCdPJn/opy7KJWWMIIO6dKlC//+u5kNGzZQvXp1\nOnXqlJsimZaWRnBwNdScRgArwcERjBhxF5s3j2XXrpbYbHaU8FpESMgD9OhxU+76BXHTTUM5efIl\nVHrscebMuYJly+bRpUuXIq3fqVMnOnXqVMz/+nxOnz7Nhx9+yJkzZ6he/RBZWYOw2+OwWj/hpZem\n8tRTL2KzfQ5cTUYGHD8+mAULFvColx9lo9FI9+5Xs3//dzgcN+U89y3wOxZLPapVq0RCwre56cnH\njh1jwoQpHDhwjOuu60K3bt1yt9W6dWtGjx7Np5/GoyrfxgBfY7VaffZW3bJlS05K7Y/AbTgcsYSG\nvs/06e8UGofk5GT69h1EauoiVJXdr4EbgSlYLCto27ZRbt/YojB8+DCMRiNvv/0KISEmWrfuz4IF\nFtQcWIC+HDhwt8/1fV1sqFGjBosWzWPo0OuBMAwGG4sXf8wlF0HWnVB2iCjVE7Gx8M8/BS/jcKjJ\nj56itCCaN4cyKOleEYmJUaI0KalwUTprFsTFFW27X3wBn3wCd95ZKsMsHHdRmJaW36L15RgVp9iR\nP06pe2pleWEylUiUggqjJkK1MBaUvlva1Xe9pe+GhpZPRn2ZO6X+isTgYPU917GjWt/hgJEjYdIk\n6NEDTpwAd2fC/TiUQkeCTqlduzZ9+/Y97/mWLVsSHp5OWtoUnM4BBAV9SkSEi8svv5wNG35m06ZN\nbNy4kddfn82pU/3p0aM7779fuPDJzs5m797tqMqyAJFkZ/fk77//5pprrindf84Np9PJrFnv8ttv\nm2jevAFjxozCYrGQnJzMpZdewalT7cnKqoXJdIK77qqK1XqGa699ixtuuIEJEyahBKHC4YghJcX3\nFcIpU8azalUPjhy5HDAQGZlJYuImjEYj9erVy22Pk5KSQuvW7UlObkh2dktWrnyfnTuTeOONqbnb\natWqFZMnP8eTT8ZhNkdhNKbw7beLc1r85GflypX07TuYjIy7CAq6ipCQRB5++B4GDlxKx44dC43R\njh07CApqiBKkoBzjCOrWfYsRI+7iiSce97rfgnCfx7xixQo++ughHI7ngOoYDB/SqFFrv7an0bdv\nH06cOMjhw4epU6eO1zmtguAPIkr1REwMLF9+/vN79qi+pG3bBkYY6IjYWFWYOCkJunbNe/7FF2Hh\nQli/Pk+URkcXfbs1aqhz53LDU5S6O6W+RGlxih35K0p9FdMqK8zmEovSjIw8EaqFUXNOyzJ9t6A+\npeX1Ea5wTinAypXqw2c2K5Wemqq+30A5pe6i1PNzIE6pcAFhsVj49dfvufPOh/jnn/do0aIFCxd+\nR0jOl0mHDh3o0KEDDz74oF/bNRqN1K7diEOHlqLmWqYQFLSKpk0HlP4/4cadd97PkiX/YrPdRmjo\nDyxdej1r1/7AO+/M4sSJLmRmzgEgK6sLP/88iR07fs9d98Yb+7B48aPY7a8BuwkJmcf113/rc18R\nERFs2bKWdevW4XK5uOKKK7yKpueff4ETJ84CTYDNpKeHM2PGdF57bXI+8ffoow9x222DOHr0KLGx\nsVh99F9+9NFnsdneA/rjdILLdT/h4ZcUSZAC1KlTh4yMXcBxVPXgA8BZTp7Mpleva0ss/OLj43n4\n4cG8+WZjzOZILBYHCQm+C0cVhsVioeFFkGknlA8iSvWEr/Tdzz9Xc03feUdEaSFoBWo9w/jCC+p2\n/vzyFwbFoqD03dJ0Sv1N3y3voJWCKHVP3y2KU1rahY689SktrzCWqVNqMhVPlGoVyTSn9Nw5VY0X\nlCitUSNv2dDQ/E6piFLhAiMmJobVq4svGnyxePEH9Ox5EzANh2Mvd999O9f6OYk9LS2NH374gezs\nbLp37+618JDG8ePH+eKLL3A4DgJh2O0j+OefNqxbt44TJ06TmdnYbenGpKScybf++++/SVDQKL75\n5mrCwiozY8ZsLi+ovgaqZ6kv5/f06dPcc88jLF36Narq8H2oti9dyM7OIjs7+zxHslq1alSrVq3A\nfapx54m0zMyGnDzpo++yF2JjY3nooft47bXmKLf0V2ACJtOP7N+/P7dFT0l4+eWXGD36YZKTk2nU\nqFHuRQ5BCDTSp1RPxMSo1h+qdnseKSnKTQARpYWg1W3Yu9f76y6XDkVpUdN3w8PzRGlmJmzYUPh+\nfM3T8+aU2u26T98typzSc+fUcbJ6tcoy/euvgvejhdwzjJoo1faljQUuIKfU30JHnus7HPmdUm/p\nu1rQZE6pIBSZDh06sHfvDr799lU2b17NjBmvFGkuqcbJkydp2bI9d9wxnbvuepcmTeI4cOCAz+Uz\nMjIwGkMAzWE0YjRWISMjgz59rsNqfRv4AziExfIkfften299i8XCwoXvcurUQfbv3+Y13dkf+vYd\nwvLlVmAT8CTQG1Wptylt216em97rjXXr1tG2bReio5szbNgjpLv9Ft500w1YLE+hHM4/gJf56KOP\n2VCU39scpk2bSERECFADWA50IyNjDdH+pG8VQlRUFC1bthRBKlQoRJTqibAwddJ17Fj+58+ezTvz\nFVFaIL6cUg2jUSei1GLJUzP+OKVnz6r0yDVrYNCgwvdz/Lj3FkSaGPzpp/z7Le85fWaz9/TiIuAu\nCotS6MhkUrtyOqFNG7jmGpXuXdi50YkT6tYzjJrz+umneX1xtf2WVxjLfE5pcZxS9/U1UXrmjHqT\nXC5V1EhDnFJBKDZVqlThqquuokmTJn6v+9xz/+Pw4R6cO/cj584lkpx8J6NHPwuoNiTHjx8n261f\ndXR0NC1aNMVsfgjYQFDQJKzWw3To0IFrr72WGTP+R40aAwkLa8vAgXWZPn2qjz37JjMzkyeffI7G\njS/niiviWbdundfl0tPTWbt2FQ7HOyhXcyiquu08goMTmDXrLa/rZWdns379enr0uJHNmx/g0KHP\n+PjjI9xxx/25y7z22iT6968NNEO1tXmFM2dm0rPnTdiL2MjcaDTy00/LiYxchsnUDWiP0ViFbt1u\nYNGiT4seEEHQGSJK9Ya3FF5xSouMN1HqbjwHBfmullqhCA/Pe8/T0pRS0nrZFOaU3nab6m2TlJTf\npvOGL1EKSk3dfnve40CIghI4pe7Op69CR57ThjQh+bdb9fyC+t5mZUFysioU7Jn11asXtM6pL/H2\n2+pWe0vLK4zuoSv14/2yy5R6Ly4mkwpIZqb6jtPmk7q7Oe5OqRQ6EoRyY/fug2RmXp372Om8ir/+\n2s4XX3xJ5co1qFevObVqNWDz5s2AatXyww9L6d/fQWzscHr02MjatSsJz/kivueeuzh+PIlz544z\nf/47xXLwRo4cy4wZv7Fr1wx+//1Orr22D/9qV/zcMJlMOam52gV+F/AvVuurfPjhLK8psjt37iQ2\ntiVXXdUTmy0VSANaY7fPY+nSz3HlnEiEhIQwbNhtVK7cDuWW3g0MIDPTyl5fKVpeaNOmDZs3/0ZQ\nkAv4nfT0XaSnr2LYsAc56a2HsyBcAIgo1RuxsefnnoooLTLR0coNPXw4T4B4zunThVPqnorrrUqP\nL1G6f79y2rU08B07zl8uKytPqZ844VuU3nijcqk05z41NTBOaSmI0qI4pe7rFMYHH8DSpUpHgRKk\nnpX1zWaYNk3d37Qp/34vCKd0zBjI6fVXLMxmOHVK3T9z5vzUXchzSl0u38e9IAjFZv/+/bz33nvU\nqdOU4GAr1avXJzExkR49OmG1zgJSATvwOnv27GXIkGGkp/9ERkYyx49PpmfPfjhzLphGRETwySdz\nmTDhCU6dSmHw4Pv59lvfxYr85aOPPiY9fT5wBXAHDscQvvrqq/OWCw4O5rnnnqdSpe7AJCyW/rRp\nE87p08cZNGig12337j2QAwceIivrDLAVeAH4EzhGSIg1X+pznTp1cDj+A5JzntlHZuZxIj1+S1eu\nXEnDhnFUrRrNrbfexTmPmg/79+/HbG4IaG0AWmMy1WPfvn1+RkYQ9IGIUr0RE+PdKdW+zDIyKria\nCiwmk6qj4nLlOVzuhWtSU3UoSr0pKl/pu1o6k3YMbdt2/nJ9+sCqVep+QU6pwaB65rgrqgvMKfX8\nd3y1aXE/lzh0SLUG6tdPhQ98h1Drbb95M2RnB9YprXDHu6co9ay8C3lO6alTSsn76KknCIL/vP32\nuzRp0ob77x/L4cPxOJ2HSE6eS79+Q+nT53p69owCIoDKwGmczjvIymoD5HyxMYQzZ1KZPXs2Z3N+\naD/44CMeeOA5Nmx4jN9/v4+BA+/jhx9+KJXxms0hwOncx0FBZ3w6rs89N46PP57GmDEpTJ7cjbVr\nf8Ds40vQ4XCwa9ffuFwP5zzTCOgGTMFqvZ7x45/Lt3zTpk155JHhWK3tCAsbjNXaiSlTJubra7pj\nxw769h3Mnj3/4/TpNXz9dTZDhtyXbzuxsbFkZiYBWmrOZrKyDhCjFccQhAsMEaV6Q5zSEuOZwqvV\nUAGdilJvispbufqOHeHXX9X9vXvVP7h1a/5lsrNVz5wjOdUCCxKloFI0//xT3deZU6oNNSUlb1qi\nw5FnusH54lATkZ64G8452WqAEqjgO4SRkVCnjgrdrl3l75RWeFGanOM0pKTA6dPnz1HVnNK//4ZW\nrcp/jIJwgbJ//37Gjn2GjIx+KDd0EkqA9sDh6MmaNWsYN24UFktd4BJUBduvgW2AVjl3K5mZaTzx\nRALNml3GLbfczoMPPo3N9gaq/+at2GzjmTlzYamM+fnnn8JqvRmYSXDw44SH/8yQIUN8Lt+3b19e\neWUqjz32GBatyIAXTCYTlSvXANbkPGPDZPqDG25w8PHHr/LEE6POW+fll1/ixx8/ZdasPvz223JG\njXok3+uqavEA4EagPhkZM/nuu69y04ABIiMjmTNnJhbLNVxySRxWaw/mz3+v0ArAgqBXpCWM3oiO\nhq+/zv+ciFK/0ArYHT6sbnUvSovqlHbpovJIT5+GAwegceM8K08jKUlZxykpKpf57NmCK6i2agXa\nVW6dOqVaISJQIczIUNrcbAbPAowDBsC8eedvy30b7qJ01y51W5Cub91aidd//il/p7RM03dLiuaU\nmkzKKfV20UNzSrdsKdn8VUEQ8pGUlITRWBtIQDmh9YA5QH/gX6pWvZUWLVqQnn4MWIlKmXUA9QgJ\naY3T2ZysrD+AuaSlDSEtbQhffqkVxluCEqUGIB2zOe+LNiUlhaCgIMKKcWXuscceoV69Onz55XIi\nIyMYO3YdNdxbSBUTg8HAokXzGDDgZoKDr8Tp3E7fvl346KP3C6xY3LFjR5/9SS+55BKCgvah5rMa\ngL1YrZect70hQwYRH9+Dffv2ERMTI4JUuKARUao3wsLyzlw1RJT6hSZGNFfKXZSeO6dDUerNKfWm\naoKDYexY1ctk2TKlzj0LHWmup1ZYplo1NQnXF5dckrcNnTml2nHgXsw6I8N36i6ArzZ+7mHcuDHv\n/s6d6rYgUaq19ktLC+ycUvf7FQKTSYnSOnXU8ejtuNac0q1boZCehYIgFJ169eqRlrYb+AzVLmUz\nqkLtRCIjU0hLS2PDhg0YDBm4XFphIDOhoTcwalRNPvvsG/bseQ0YAuwCvgMmoKrdPgH0A7pitU5i\nzJhlpKen06/fbfz00/e4XNkMGnQbCxbMIsjPlPz+/fvTv3//UomBO9dddx3bt29g48aNREVF0alT\nJ79a6Hhy6623MmnSdPbvvxW7vRVW61xeeWWS12WrV69Odc+pC4JwAVJsUfr5558zfvx4/vnnH/74\n4w8uu+wyr8vFxMTkXBEKwmQysX79+mIPVkCdrbqfAbtcys3SGmw6HBW8bGzg0c5rNR2ve6fUW5NN\nX1bbU0+pdZctUyf7nu2FtmxR7lNKinJRC7vK7NkvtbxFaSk4pUeP5j3ncBQsSkNC4OBB6Nw5/9Ru\n9+tE7hnRRRGlWtaY3V7+Tqn79YYKNx1Tc0qjo9XcZ2/Hl7tTeu+9gRmnIFwgOBwOnn/+f/z441pq\n1LgEs7kKDkfvnFfjgCY0anSOQ4dSeeSRb8nO3kTlyrU5e3YK2dn/B2zHYFjGoEGJuFwm3nzzM9LT\nBwILUeJ0ZM62GgDtuekmK888s4z27dszcuRYVq8OIjPzFOAgIeFG2rR5k7FjHy/3OPiifv361K9f\nv1S2ZbVa2bhxNXPmzOH48ZP06DGf7iUpDCcIFwDFFqWtW7cmISGB+++/v8DlDAYDq1atyjfBWygB\nnk6pzabOlM3mPEVVodVU4NHOa705pboTpdoEyKCgoolSyJuXV7s27N6d/7WTJ6FhQxWUo0cLVlOQ\nX5SmppZ/+m5cHBTzJMGbU1qYKAWl5T3rjblfJ3Kv1q91IygojKGh6tZuL3+ntEIXq9VEaZ06sHat\n9+MrNFQFbds2mVMqCCVk8OB7SUw8TXr6GIzGn8jOXoaaI9oSOIbFcoD9+1NxONYCrYE0QkJaUL36\nHJKTX8JkMjNr1kzi4uJo0aIFSUkj+PLLqmRnO3G53C8aZWIymVmyZFHuM6tX/47dPgEwA2ZstvtY\nteobxo4txwCUM2FhYTz22GOBHoYgVBiKXeioWbNmRW647D5xWyghlSrlF6UpKSr/TxMpIkoLRTvh\n9+aUuqfvVrh0RnfMZlX9Vss3rVKl8PRdDU2U1qlzfvru6dNK5KWkwH//QWGfcYslr0pQIJzSqVOh\nXbtxdConAAAYp0lEQVRirerNKS0sfVfDM2tLWyc7O//xpAnXRo18b0sTpenp5e+UhobChg35+65W\nGDRRGhGhBnrs2PmBCQtT/0DNmr5LIwuCUCg2m42vv/6S9PQvgOvIzp5KSEhTzObOVK58HRZLHCNH\nDkd5GTkNlqlERkZTzp27BLM5jHnz3ufOO1XvarPZzKefzsdmO8fOnf8SHr4Ug+ElYBEm0wDGj38y\n3/4bNKhHUNDqnEcuzOZfaNy4Xvn884IgVAjKvPquwWDg2muv5fLLL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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The autocorrelation function is the correlation coefficient plotted against the lags:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plotautocorr( data, deltat, lags, rmin=0.0 ) :\n", + " auto_corr = []\n", + " for lag in lags :\n", + " lagi = int( lag/deltat )\n", + " if lagi > 0 :\n", + " r = stats.pearsonr( data[:-lagi], data[lagi:] )\n", + " elif lagi < 0 :\n", + " r = stats.pearsonr( data[-lagi:], data[:lagi] )\n", + " else :\n", + " r = stats.pearsonr( data[:], data[:] )\n", + " auto_corr.append( r[0] )\n", + " plt.plot( lags, auto_corr )\n", + " plt.xlabel( 'Lag [s]' )\n", + " plt.ylabel( 'Autocorrelation' )\n", + " plt.ylim( rmin, 1.0 )\n", + " plt.show()\n", + " \n", + "lags = np.arange( 0.0, 2.0, 0.05 )\n", + "plt.title( 'Colored noise' )\n", + "plotautocorr( colored_noise, deltat, lags )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The time it needs for the autocorrelation to drop to zero is the correlation time of the time series. The correlation time is often measured as the time consant of the exponential decay of the autocorrelation. The colored noise example shown has a correlation time of about 0.5 s.\n", + "\n", + "You can also plot the autocorrelation for negative time lags. However, the autocorrelation is symmetric and therefore the negative lags do not provide any new information about the time series." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = np.arange( -2.0, 2.0, 0.05 )\n", + "plt.title( 'Colored noise' )\n", + "plotautocorr( colored_noise, deltat, lags )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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000/LGorIHMXFwFdf2dfchcpERwMffABY8aZAqoGMFoaXX35ZP8bg4OCA4uJi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\nFRUJX19fce7cOVFQUCCCg4N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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The white noise data has no correlation except for the time lag at zero, where every time series has a correlation coefficient of one. White noise has an infinitesimal small correlation time. You cannot predict any future value of white noise from the knowledge of the previous ones." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.title( 'White noise' )\n", + "plotautocorr( white_noise, deltat, lags )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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554CYGODpp4HDh/WXa20F8vLEGsPDgeBgse6vvzb8OltagKoqcd35+cD+/eJz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\nYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In python (similar to other programming languages) the numpy.correlate() function just computes $$c_k = \\sum_{n} x_{n+k} x_n$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "acc = np.correlate( colored_noise, colored_noise, mode='full' )\n", + "lags = deltat*(np.arange( len( acc ) ) - len( acc )/2)\n", + "plt.plot(lags, acc)\n", + "plt.xlim( -2.0, 2.0 )\n", + "plt.ylim( 0.0, 60000.0 )\n", + "plt.xlabel( 'Lag [s]' )\n", + "plt.ylabel( 'Autocorrelation' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but we want\n", + "$$\\rho_k = \\frac{\\frac{1}{N}\\sum_n (x_{n+k}-\\langle x \\rangle)(x_n-\\langle x \\rangle)}{\\frac{1}{N}\\sum_n (x_n-\\langle x \\rangle)^2}$$\n", + "In order to get the correlation coefficients from that we need to first subtract the mean of the data before we then compute the covariance with the correlate function. The result we then divide by the number of available data to turn the sum into an average. Finally we divide by the variance of the data to get the correlation coefficient." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# subtract mean:\n", + "x = colored_noise - np.mean( colored_noise )\n", + "# \"covariance\":\n", + "acc = np.correlate( x, x, mode='full' )\n", + "# divide by n to make it a mean:\n", + "acc /= np.arange( len( acc ) )+1\n", + "# divide by variance to make it a correlation coefficient:\n", + "acc /= np.var( x )\n", + "lags = deltat*(np.arange( len( acc ) ) - len( acc )/2)\n", + "plt.plot(lags, acc)\n", + "plt.xlim( -2.0, 2.0 )\n", + "plt.ylim( 0.0, 1.0 )\n", + "plt.xlabel( 'Lag [s]' )\n", + "plt.ylabel( 'Autocorrelation' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another example: white noise filtered by a resonance filter - a band-pass filter with peak-gain at about 2Hz. This produces a almost periodic but not perfectly periodic signal." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "band_noise = np.zeros( len( white_noise ) )\n", + "x = 0.0\n", + "y = 0.0\n", + "w0 = 2.0*np.pi*2.0\n", + "xi = 0.1\n", + "for k in xrange( len( white_noise ) ) :\n", + " y += (-2.0*xi*w0*y-w0*w0*x+white_noise[k])*deltat\n", + " x += y*deltat\n", + " band_noise[k] = x\n", + "tseg = (time>20.0) & (time<25.0)\n", + "plt.plot( time[tseg], band_noise[tseg], 'b-' )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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X5HK66SZ95/3BD6i1x6ZN9PrXv6YHQFaW/2ONBDONWhTyTFpEY0A7pMc6MUYB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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For such quasi-periodic signal we have positive and negative autocorrelations in dependence on the lag." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = np.arange( 0.125, 0.6, 0.125 )\n", + "for lag in lags :\n", + " lagi = int( lag/deltat )\n", + " tseg = (time>20.0) & (time<25.0)\n", + " plotdatacorr( time, band_noise, lagi, tseg, 'Lag %gs' % lag )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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LF4wxwI7pJTftmkzaDVoppRT8738/kZb2JFANcCE9/Rk2bSrc6+lKNWtWB0yI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\nB10MJpY7eNYJUu63vvdzgprjHbxU6LpPnAC4ud23iYPznKA96KC/g9Psm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US3EVTgqBXg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YnVmk9iYipJQEAhg2CuNYjeQoF4sdsflPvvfyTDGMuWLZPg4EoCboEZAneJqrLzDMK1UiBE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\n5Y0q5bFx4/owLiKiPuLi4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7//3PyciYDvwT8LE8a61kKpgZzcLd8g84ISGBLl1uIzl5KobRhqNHX+PkycdZ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waF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\nfJ7A8tYzKzbAkSYnJzE+Po7GxkaEQiHo9XoA92/9EAqFFI4uO0TWkJIjV8P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Lw5kzUEx/NOY1BNqeDGsCrJQhIyODZcuW0aFDB958801at27NjBkzuHDhAk2aNOHee+8l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kUK9Fyk1t+DNgdSbHzq2ZgXRJsn19o4nkAbC0/a/FyMYoBfR6ryChv/FDSPT6D1Vhep2OUR3Cej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\ngfXbxdZPp6NNhoVow+NC64O3LP9X0DnwjUgx7YXG2fUG6GNl9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QfmkJvbm0aN6lKvXj1A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brB1Td/p5TKsJ37+4IFC3L8+HGCgoLYunUr7du3Z/fu3fjd9WK0dxklS8rT3804eBAaNswT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\nzJ49W6/DKjhqw/Pnz5elWbp0qTF16lRXFdHtO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9QD/gGbKzzwGv8+ijN/HAA/fhWujCMnLkOM6ebQLMBP4G+gOjgSzgF/75p7kd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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting autocorrelation function is periodic with a frequency of about 2Hz. In addition this periodic correlation decays towards zero with larger lags." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = np.arange( -2.0, 2.0, 0.02 )\n", + "plotautocorr( band_noise, deltat, lags, rmin=-1.0 )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a final example a pure sine wave with 2Hz. It has as a 2Hz sine wave as an autocorrelation with infinite correlation time." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sine = np.sin( 2.0*np.pi*2.0*time)\n", + "#sine += 10.0*white_noise\n", + "tseg = (time>20.0) & (time<26.0)\n", + "plt.title( 'Sine wave with 2Hz' )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.plot( time[tseg], sine[tseg] )\n", + "plt.show()\n", + "lags = np.arange( -3.0, 3.0, 0.02 )\n", + "plt.title( 'Autocorrelation of sine wave' )\n", + "plotautocorr( sine, deltat, lags, rmin=-1.0 )\n", + "#plt.psd( sine, 1024, Fs=1.0/deltat )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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h0z5jotMKn5MtBclXxPLJts8OlBV9lXpjivTF8ukcvbW2WtuQBuDliKmpvDzR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\n0fh09RWv+Dyp0/cT/DoEkx1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2gTEW1EAEQtSDjUal7Xa+wMiFgs8uIyFC0ehNH4iMJKKNLzaW12VEnC4YjYVk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\nsrKygl7Xr18/AEDfvn3x85//HJs2bdJ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+ "text": [ + "" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at the sine wave autocorrelation in more detail." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = np.arange( 0.0, 0.57, 0.5/8 )\n", + "for lag in lags :\n", + " lagi = int( lag/deltat )\n", + " tseg = (time>20.0) & (time<22.0)\n", + " plotdatacorr( time, sine, lagi, tseg, 'Lag %gs' % lag )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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SHVRIuvtnBDvrfqYVUkAlhw+7//i+qmnPUcYIxLRkvkeOn7soHAdGTuyq9cjx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AFyUZP/3pT2lsbKSwsJBJkyZx9913A6oM9s9//jNTp05l8+bNpKend7md9evX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\nipmO4zFpaABSUrTPYPVcYhTHbYVnsFK0SAIyDsBHAfwWwP8GMJaJCfU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hAI8DqIVptoR9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++lW48UboqqMQMz/4AXzlK/D5z8PPfuaOTM9xyinw29/2bA51g7Iy+OUvOT5n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btm3Mnj2b6dOn87Of/Yz777+fxMREnn76ab7xjW8wZcoU4uLiuP3223vsaxhG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xQrFpk31zaC0zZ6q5oHHclH3bNujshNNOg+xse46ZlDRwPV6Iy56c09sLH300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XGtS//OUvXZ8dJO24uLiY0rDS7o2NjZxzzjnMnz+fRYsWUVxczGWXXeaKnIqi\nKCYQsoaaQvSIUCg05Gxmb378Y/j2t+GKK6CzjkLc/Pd/w7e+Bd/8Jvz613E09Nvfwssvw733OiMY\nwD33wHPPwQMPONemw7S0QE6O/K2vh5Ej42+zrU3abGqCAwckgBYTliVhwY8/dibMaLc5frykoE6a\n5EybLnDDDXDXXXDzzbBqlTNtfve78KMfwX/+J9x6axwN/fCHotg773RGMIDbb4eaGvh//8+5Nh1m\nzx65DLOzZaw4USB5/35Znp2ZCQcPxrHV8OHD0lBdXfzl122ammT/sNpa2arLA2K5ryg90e9QURRF\ncZJY7iuBjrA6nU4HDkYonI5OQCAiFB9+KM7qjBnOOKsgNV/szOq4MqLLy8WSd8pZBYkKBiDV0elI\nXnhbjowVJ6PeEIgIq/29LVzojLMKMh9TUiL+Zj+7dETOhg2yPsIpZxXESZ0xQ6qyKYqiKIqiREhC\nOKxO2roLFogPsnGjVNuMGadTT0EMyMpKWYxoKG5MIoBD26i4MYkAxk8kWJbzxX3C24o7I9rptZIg\nXuB770m1KUNx4/crvL24xoobv18QiMkdRVEURVHMIrAO66FDUlMlLQ2OPtq5dnNyJAjQ2irRwpho\naxOP196PxSlSU2HuXKMLL7kRyQtvLy6/0A3HCIw3wrdvl8zO8eOdzVqePFnSs/fskf1EY6K2Vh6d\n2044xpgxkn66dauz7TqI8WPFjSIuAYh8K4qiKIpiFoF1WD/6SP4edZRUCXYSO/30gw9ibGDrVqlS\nmpPjmExdzJtndEqd/Z3Nn+9su3Z7MesEpPSz04JBoHTiZP2QUMiBsbJxo+z16VRObDgB0ouT6FhR\nFEVRFCWRCKzDahtjTkZXbebM6dlH1Hz4oTuCgbQbc+jXXSyr+zuzv0OnsLct+uQTiX7HhFt6mTpV\nCvw0NDjftgO4pZPwNnWsREdTk8xrDRsmWyw7if11xqyTjg4pTDZ7tmMydXH00TLbqEV8FEVRFEWJ\nkMA6rLYd6oYRbht8Mdu6H37ojmAg7RpqhO/e3V3Fd+JEZ9vOzpYU1NbWGLM8GxrEqZw61VnBoNvr\n+Phj59t2APtyccMvdGSsuOWwGjxWPvlE/MLp053PECkpkd20du+WqsFRs2MHjB4dRznuQcjLk8Fc\nWel824qiKIqiJCSBd1jdNMKNjhoZGKEIj3q7sXVdXHr5+GNxKmPe52MIDI7mGe+wujW5Y7BO3MwQ\nSUnpDo5QlkwtAAAgAElEQVTG9PHd/P0Co/WiKIqiKIp5qMPaD9OmyW4OFRUxFuT94AP3DL4JE8RZ\nralxp/04cDPqDXE6R27qBKTtuBYNukNbm0TzwL0MT5Asz6gL8to55G7pZeZM2LZN9lkyDDd/v8Lb\n1bGiKIqiKErQCaTDWlcH1dWyrd/kyc63n5oKs2bJc7u4U8S0tMCnn3Y34DShkLGpjkYb4W5G8sBY\nnWzbJtszFRc7ty9uOGPHyhxKQ4NM8ETFnj3itDq5L244I0ZIfuyWLe60Hwc6VswbK4qiKIqimEkg\nHVbb1pk9290MT4ghELBli3gHI0Y4LlMXhqbUuZnmCHEW+EnSNEe3HaPwtqP++LZO3MgftzFUL24W\nwgpvV8eKoiiKoihBJ9AOq5s2lW3wRW1XuZ1OB0am1FlWdzTaLSN81ixZn7dli0QNo8JtvZSWSoWb\n+nr3+ogBt9O0w9uOaay4KRgYOVYaG2Vv3LQ0KbrkBjFPIrS3Sw65G/njNrNnx5hDriiKoihKMhJI\nh9XtSF542zFFjdw2wg1MqauqgoMHJUV0/Hh3+sjIgClTxKbevDmKE+vrpXxxaak7gkF3pZuoc8jd\nxcuxErVf6HYkD4wcK3Yx6RkzxGl1g8JCSQHft08yryPm008lRTs72x3BAEaNgjFjoLzcvT4URVEU\nRUkYAumwepnmaKQRbmClYC8co/D2o9LLRx/JRq4pLl/uBqY6BiIl2E0M1IkXYyUU6g6SRjVWvNAJ\nGKkXRVEURVHMJNAOq5uBzMmTJaK3c6cUeYoYL1KCx46VzRurq93tJwq80El4+1HZul7oBIxLP21t\nlUh0KCT+ulvYX+3HH0eR5el2hWCb6dNlX9GmJnf7iQIdKxg3VhKRyy67jAkTJjB37twBj7nuuuuY\nPn068+fPp6yszEPpFEVRFCVyAuew7t8vO7pkZUltI7cYNqzbyI/Y4GtqEuN4xgzX5OrCsFRHLyJ5\n4e1H9dG9ihoZppMtW8RpnTxZxotb5OZCQQEcOSJrMyNi507ZO2rcOPcEA+lj6lTYtMndfqJAxwrG\njZVE5NJLL2Xt2rUDvv/MM8+wdetWtmzZwt13382VV17poXRKNIRCoa5HNMdGcryiKEoQCJzDau8p\naRfgcRPbYbX7HJKtW2WdZHq6WyJ1M2uWUUa4/R25GckLbz9inYB8T24LBqKTqARzF690Et5HxB//\nk0+8EQySVi8xjRWv9GLY71cicuqppzJ69OgB33/yySe55JJLADjhhBOoq6ujxsD9vZOdUCgLyAJm\nARmDOqHyXg5Q0PnIUadVUZSEIHAOq11sx4sgpt1HxAV+Nm/2RjCQfgwy+LzSi11Vdds2aGuL8KRN\nm7zRS3GxVLlpbHS/rwgwfqzMnOmaPD2YMSPKKl3u0dwstYZSUqSAmJtErRPLkrC8VxfMpk1GrcNP\nNqqrqykqKur6v7CwkKqqKh8lSi4kAppLKDSGUGhkv46lvJYObAY+Bp4GRgzihGYDXwQqOh/ndr4W\niSx5nbKkqpOrKIpxpPotQLTYxpcXtq7dR8QG36ZN3hnhM2fCU09509cQ7N8PtbVSWHTiRHf7ysqS\nCqhVVZJ9PXXqECc0N0v66eTJ7goGkkc+daoY/QsWuN/fEBg/Vrya3Jk5E55/3pu+hmDbNvHRpkyR\nZehuUlwsfezaBYcOQU7OECdUV8sgHjXKXcEA8vJEuJoayM93vz+lX6xeEwYDOSqrVq3qer506VKW\nLl3qolSJj3zPWcA1wOeAnwIvDnD08cCkzuenMXicYThwQdgxXwGeiUCWHGA1kAtcAewa6iMoiqJE\nzLp161i3bl1cbQTOYbWDil5GjSIOZG7eDCef7Jo8PTAowhquEy8mZmfMEId106YIHNatW6GkxL39\nQ3pjR/MMcFiNHyunn+6aPD2YMQP+53+86WsIvNTJsGEwbZosFd28GY45ZogTvMwQge7fMHVYfaGg\noIDKysqu/6uqqigoKOj32HCHVXGK2cCtnc9PBkYRCoX6TCLAm0i0tBhYCwxW2a4JuA84u/P/+4Gh\nNi3PBm4GLu78/x7E0VUURXGG3hOdt9xyS9RtBDYl2IuokZ1+unWr7P05JF5GWEtKYO9eOHzYm/4G\nwUudhPcTUTTPy9RTkL4MmUjQCGsntk4MSD81eqx4+fsF0pchqdrJyIoVK7j33nsBeOONN8jNzWXC\nhAk+S5U4SJrtaEKhUYRC/a0lbQLs36RW+nNExXltRtavTga+BDT149TaNALPAfnAROBZoGEISS3g\nSNj/RwY6sA/dac0jO/9qKrGiKO4QqAhre7s4j9DtTLpJdrZUP62ulnVnQ0bzvIxQDBsmeYVbtsD8\n+d70OQBeRo3C+4nIL/TSMQLp66WXvOtvAGprZTltVpb7adog6afp6TJWGhpk7AxIc7Mc6PYiTpu8\nPImw79kDPhvkRo8VvyKsiit89atf5eWXX2bfvn0UFRVxyy230NraCsDKlSs588wzeeaZZ5g2bRpZ\nWVn8/ve/91nixKE75fcPwBQk9ffdXkdtB/4Z+DzwCyAdy+obDbWsI53tlXf+P/DEm2VZncce6vHa\n4DQCP0TWyo4GvgPUDnGO/Rkzge8BZwG/Bn49QJRYURQlPgLlsFZUiK07aVIE67EcYuZMsa03bx7C\nYd2/X/YQ8dIgtiMUPjusRkeNNm+Gk05yVZ4ezJwJv/yld/0NQHjBJS8mve30048+kjmUhQsHOfjT\nT8XD9SpNG7qjrD47rMaPldNOc1WeHsycCa+/7l1/ScaDDz445DGrV6/2QJJk5QpgRefzPyApwEK3\nY/kn4CkkCtoyYEvROIDROovdstyGJN3VRdHGdODfOp/fBeikh6Io7hColGCvoxPhfQ0ZCLCjE16m\nxBhS/VSjRmHYOvF5htn+brzO8Azve0C8Tj0FHSumZiMYoBNFcYfqsOe7gGE93rUsC8s6jGXtx7Ka\nfY1Kiiz1WNaBKOXYh6Qzg0R1m5wXTlEUhYA5rF5HJ8L7GtKu8nqtJBixXjI8TdsrW7e0VIJzdvrp\noHjtHI0dK+HGvXu967MfvNzSxibibVS8nkQAI9ZL2mnamZmy1MALwn+/BrVDW1qkkplXadogIfny\ncslMUZSAIus4hxMKpfVaw/kkcBnwIyRldqibVRA5hFQ5vgv4DDAsKodXvrsRhELDdP2roiiDEiiH\n1egIq9fRCTAiQmGnaU+c6F2atp1+CpJ+OiC1tSKc12mgBqzN0whrLwzQiddp2gBjxsgS3oYG2d5m\nQLZtg6IiWYjsFcOHy/qO8nLv+lQUB+lex/nvwPVARtgazsNIKvAqoBbLGqy6b/CQz3gQeAX4L2Aj\n0Tjl8t2NRioUXwZkqtOqKMqABMph1QhrLwyofuqHTsL7G1Qvtk68vgkaEM3TCGsvDNKJ0WPFawzI\nElGU2BmN7F/6feBO4CZkT1M7zbYdyxqsqm+wkc9opzZbUX7OkUgU+rtIwabzXJFRUZTEIFAOqx8R\nVnsLz6oqaGwc5EA/Iqxjxogztm+ft/2G4YdOwvsb1Nb1wzEC36N5HR3dkWcvP354hHVQu8WPCOvU\nqRLJa2vztt8wjB4rfvx+gRFZIooSOynI9jE2kwhYLUsf6aDnd1cEaIRVUZT+CYzDevgwVFZCaipM\nnuxdv6mpEaSfdnTIQk4v9toJJxTyPXKkUaN+8FknlZXQ1AT5+TBypHf9jhkDo0fDoUNQUzPAQQcO\ndAvnJSNGSN66j+mnOlb6wYDIt6LEzkHgWuBt4O9ItPCArxIFhxBwKfAB8DQSqU7MSLSiKPETGIfV\nLuwzZYo4kV4yZKpjZaUsFBt080mXmD7dCIfVa189ovTTzZu9FwySViehUAR62bJFBPNjrVKS6kXH\niqK4RStQiRQeOhvYm7Dpv85zCCgDTgG+DjTod6coyoAExmHdtk3+2tFOL7H3X7Vl6MO2bf4IBtLv\ngIK5j196GVIn9pt+XTDbt0vk3Qd0rAyAj2PFsnSs9IvPv1+KEg1S1TaXUCiDUEjSV2SNal3nw78l\nB0FD1rweinE7HVsXWZ2P7E6daEqxoiQqgXNYbePLSyIywv0QDKRfO/zsMa2tsGOHBMu8TNMGySjN\nzJRCwHV1/RxgWfK9+KGXrCzIzYWdO73vG8PHil86AV/Hyp49sgY+N1eSMbzE/ro//XSAOZTDh2H/\nfu/22gmnqEjyx5ubve9bUaJmFHAOUA78GchSJ8k3RgBTgfeBt5D1w8MGPUNRlOCiDmsEGG+E+xSh\nqKiQfVgLCmSJoJeEQt1bRvb78ffvh5QU770DGx+dI+MjrEk4Vvz8/crJgXHjxCfsdw7l009lc+Nh\nPhh7qanitG7f7n3fihI1DcD/ABOA04GL/BUnqckC7kCc1qOAHyATCoqiJCLqsEaAGuH946dOwvvt\n9+P7qRNIWr3oWOkfHSuD4KNeFCU60gG7+qIFfOKjLMlOOxC+/n0TsqZYUZREJHAOqx9Ro5ISCT5U\nVQ2QueanwTd2rGzVccD7yoR+6iS8XzXCuwlfK+nHxx9UJ/YbfullyhSpEuzD2mIdK4OgDqsSGJqA\nzwLfRgotve+vOElNHfAdYCXwz8g+uIf8FEhRFBcJhMPq51pJkH1YS0rEGeiTuWZ7CH5ZoqGQbwaf\nKVGjfjNv/TbCfSomU1MjayVHj5aH10yYIEt4a2v7mUM5fFhe9GOtJMii59Gjobra867ta9TYseLX\n7xeow6oEBsvqQBylHwMvAYe0sq1PyPd+BLgb+ANwRHWhKAlMIBzWHTtkrWRhIQwf7o8MA6bU7dsn\n67D88A5sktxh1ahRN37rZNC1xfZayRQff3aSVC86VhQlPqQqrRRYkgq3ljpIPhOuh1h1YetVi2cp\nitnEbTmuXbuWWbNmMX36dG6//fY+769bt45Ro0axcOFCFi5cyK233hp1H34be+F997Gr/Db2QI1w\nNcK78Fsn4X3rWOnGb73oWFGU2BFnJgsYDgxX5yZBED1mI3pNJxQKRAxHUZKSuEZne3s711xzDWvX\nruWjjz7iwQcf5OOPP+5z3JIlSygrK6OsrIybbrop6n78NvbC+zbWCPe4Iq1lScDM7t4PiotlbXF1\nNTQ19XrTz8rNAGPGyFrJ2lpPu/V7rSQMMlb81gn4MlYOHYK9eyU7ZNIkT7vuYkCdtLVBZaU/ay1s\npkyRtRbt7f7JoCgDIE5NJvBLZA3rq0CmOq0Bp9tZ/RGi17fRbYoUxVzicljXr1/PtGnTKC0tJS0t\njYsuuognnniiz3Hxps2owzoEPkQo7LWSeXmyt6QfDLi2uLFRNmf1a60k+La2WMfKEPiokylT/MuG\nHj9e1hbX1fWaQ6mslDf9WmsBsrY4L8+XtcWKEhmpwDc6nx/X+VCCTwtwVefzuUhBLUVRTCQu86m6\nupqioqKu/wsLC6nuZXSEQiFef/115s+fz5lnnslHH30UdT8mGeF9gjMmGOE+FPjxu4iMTb/O0aef\nSsTIz7WSoA5rfw6rn6Ff8GWsmKATe/4kXJ6uf/wexOBbkTJFiYwmurewqQc+9FEWxVne6/x7GHjX\nT0EURRmEuCz6SFInFi1aRGVlJRs2bODaa6/l3HPPjbofEww+u5BMn8w1E4zwwkIp/nTkiGddmqCT\n8P7VCBdM0EsgIqweFksxQSfh/fcZK37/foGuY1WMRTLE2oHjgbOBmUCzFlwKOKK/FmAxcBYwA5mM\nUBTFRFLjObmgoIDKysqu/ysrKyksLOxxTE5OTtfz5cuXc9VVV1FbW0teXl6f9latWtX1fOnSpSxd\nutT3fSVtsrNly46aGslcKy7ufMMEI3zYMMmN3b4dZs/2pEsTdBLev5EO69Sp8PrrnnV38KCslRwx\nAiZO9KzbPthri6uqZA4lI4PutZKlpf4JBpJ6CpIXO2aMJ13qWIkAhxzWdevWsW7duvjlUZQwLKut\nc4L+6c7/1VlNBCzL6tTrMz1eUxTFPOJyWI899li2bNlCeXk5kyZN4uGHH+bBBx/scUxNTQ3jx48n\nFAqxfv16LMvq11mFng6rza5dYvSOGePfWkmbadPEYd22rdNhbWyE+np/vQMb2+Dz2GH1Ozhj998j\nVXvbNjjqKF/k6cHUqXDffZ51F+4Y+ZkNnZYmfum2bWFzKBUVkJ/v71pJ6Lm22COH1b42jR0rxxmw\nHm/qVPjzn+Nuxp7otLnlllviblNRQB2ZREX1qijBIC6zNjU1ldWrV7Ns2TJmz57NhRdeyFFHHcWa\nNWtYs2YNAI8++ihz585lwYIFXH/99Tz00ENR9WEX07FTcv0kPC2464nf+0raTJnSXbbXA0zRSx+d\ngHwPfgsGSauTcBm69GKKTiBp9aJjRVFiR/frVAZCrw1FcZ+4Iqwgab7Lly/v8drKlSu7nl999dVc\nffXVMbdvG1d+7rpgY2czlpd3vrB9uxmCgQi3Y4dn3Zmil5IS+VteLssSQyHM0UtBAezZAy0tkJ7u\nenem6AR0rNi0tUlwGbqvVb/ooxMwRy8e/34pSjR078PaDkgaqUbmFAjf9qgD6NBrQ1FcwoDQ4OCo\nER4hpaW9LFH3OHIEdu+W1E+/9pW0GTUKRo+WfVj37EH2Pt2xw/+1kgCpqfIFVVV50p2OlQjxcKxU\nVUmRtkmTZG2xn9jr7quqxJHmwAGZ5Rk92le5ANlap7ERGhr8lkRRetDtkPwKOILuw6rY9Nyj9wjw\nGrqXq6K4Q2AcVhP8DzXCBbsbu7iO39h62bEDWfScmyt7O5qAh3oxcax0Bc3Ky5NyrJikk+HDxXFu\nb+/c8tT+/TLBuAqFJAStUVbFSFKBr3c+131YlXBSgX/qfH4sUk1aURSnMd5hte1KE2zdPg5rebkZ\nlij4YoSboBPopReTdAJJq5d+J3dM0YsPkzsm6AR0rChKbDQBH3c+131YlXCagI86nx8ENvooi6Ik\nLsY7rCYZ4YWFUl+puhpaWzErwjpmjKyVrHd/HzGjjXCTdAKeGeGWZZZejM5GsCN5HqwzMun3C3Ss\nKEq0dO/DegJwJrIPa4uuU1TCro0TkWtjBrpHr6K4g9EOq711I/hfsASkbk5BgSyTrKq0zDL4QiHP\nCpeoER4FHhnhe/bI2uK8PBg50vXuhiQ/X8bL3r3QuPewOds/gWyqnJXVuejZXXSsRIE6rIqhWFYb\ncAh4FqjBstyfGFaCQd9r46DPEilKYmK0wxpesMTv7RttbIOvauMBcRJNKFhi45HBZ9K6PFAjHMzT\nSUpK9yTTrjd2yIJnE7Z/svFIL3YXpuhFx4qixIZlWV0PRQlHrw1FcR+DLMi+mBadgG6D78C7Bq3J\ns/HYOTJFL2qEm6cT0LEC5umlz1gxSS/qsCqKoiiK0g9x78PqJqYZe9Bt3x3+uNwswSBpjfAee7Ee\nKSdkimAgOeQ1Na7vxWqaTqB7rBz5yLBJBPBkrDQ3w86dUkm7qMjVriKmy2HdbsGecrP0og6rEgDC\ntyzRiJriFHpdKcrgaIQ1SroCEp8mpxFeXy/bN2ZkyNaJJmDvxdpypE08BFO8A/BsL1aTCi7Z2GPF\nStKxYtd1KiqSy8AE7L1Ymyv3YGVlyXpeU9C9WBXDEaciBxgOpBIKuTcJqSQPcl1lACOA4bqPq6L0\ng9EOq2nrv6BbluE7DUunA0+M8HCdmPSbWloKRVTSMnqCq5HMmPBAL6atYYWwsbKr3CzBwPOxYgr2\nXqzFHdtpmVTqtzg90b1YFeMZCXwbOAJsAnLUuVDiQq6fTOA+5Lp6EcjU60pRemG0w2pihNVOP809\nkJxRIxN1AvLRJ7Od+jzDBAO5aJJQL7ajNkrHilGUlBg8VjQtWDGaBuAGIARMAb7srzhKgpANnN/5\n/BTgKB9lURQzUYc1SoqKJBCQ37Sd1kKDBANP9mI1USfQ7bDWZBomGLhuhLe3Q0VFd1emYMuSf8RA\nh9WDvVh1rMSAOqyK0WQAf+983gK85qMsSuJQD2zrfL4f2OqjLIpiJsY6rE1N3QVLCgv9lqab9HQo\nmGRRwg6q00r9FqcnHuzFauJaSZCPXUo5O0KGCQauG+E7d0Jrq+x9mpHhWjdRk58PY9PqSbNaaMwY\n67c4PfFgL1aTHdZkHSuKEh+NwLnAcmAmUOmvOErgkQJLFrAIOAuYBbRr4SVF6YWxDqsdMTKpYInN\nooIaGsli+16DCpbYuGzwmbhWErqjRpuaS/0WpS9JqpOUFDhpYjnllLKjwsD1OC7rxcQ1rJDcY0VR\n4kGciMPAWqAcOKiOhRI3ltUMHASeAfZhWYd8lkhRzMNYh9VUYw9gYd4OdlBipl3lssFnB29N00tp\nKZSwg/frS/wWpS9JqhOABaN1rJiml2QeK8nE2rVrmTVrFtOnT+f222/v8/66desYNWoUCxcuZOHC\nhdx6660+SBk8LMvq8VAUJ9BrSlEGx7DYZTemGnsAszIrktYItyPfJYbZuiUlUEcF62tKsCyzKhhT\nWOjqXqym6gTgqCwZK5T7LUk/uDhWmppE5ampMHGiK13ETGmJRRGVvFVT7LcofVGH1RHa29u55ppr\neOGFFygoKOC4445jxYoVHHVUz2IuS5Ys4cknn/RJSkVRFEWJDGMjrLbDaqIRPnlYcjqsBw9CXZ2s\nkxwzxpUuYmZUVhv57GZrcyF79/otTS9sr8WlvVhth7XYRP8jSceKrerCQlmHbxLFGXtpIJvN1Vm0\ntfktTS90L1ZHWL9+PdOmTaO0tJS0tDQuuuginnjiiT7HaTRHURRFCQLGOqy2HWmiwzqpdQcVFCed\nER7uGBkVwQTYuZO6tHG0kZZ0erEnd0x0WCe1JOdYMVknI2p2sCu1mPZ2qK72W5pe6F6sjlBdXU1R\nUVHX/4WFhVT3UnYoFOL1119n/vz5nHnmmXz00Udei5kQhEKhHg9F8Qu9DpVExliH1eQIa15DRVIa\n4SZH8qio4ECOCKZ6MQcdK640Hx9JPFaShUgM1kWLFlFZWcmGDRu49tprOffccz2QLLGQ7zkHKADG\nAznqLCieI07qSORanApk6nWoJBy6hjUGMvZVUEkxVVWynUhamt8ShWHvxXrwIIwc6WjTphvhR8YW\nQ62hwRmXjHDLMlsvmfvFYW0xUSfhe7E6fHM3WSdUVHBkXDEcSK6xkkwUFBRQWdm95UplZSWFvfaH\ny8nJ6Xq+fPlyrrrqKmpra8nLy+vT3qpVq7qeL126lKVLlzouczDJAS4C1gDtwPnAc75KpCQr44B3\ngVHAb4B/81ccRQlj3bp1rFu3Lq42jHRYW1slVS0UMmsPVpuUygpaJxbTsUvWqhm1z2J4St3cuY42\nbboR3lFYDJsNtXVLS+Fvf3O82QMHZMlfTg6MGuV48/HR0kJK7T72p03kyB44fBgyM/0WKozsbBFo\n715ZO+kgOlbiQFOC4+bYY49ly5YtlJeXM2nSJB5++GEefPDBHsfU1NQwfvx4QqEQ69evx7Ksfp1V\n6OmwKuGkIQ5rCDGnLgL+7qtESrLyRcRZBbgAuMpHWRSlJ70nOm+55Zao2zAyJbi6Gjo6YNIkV4qq\nxkdjIxw+TM6UcYChBp9LEQqTq9FSUUHaNBEsWXViXAZQdTWhiRMpLJV5MSN9EB0r5qER1rhJTU1l\n9erVLFu2jNmzZ3PhhRdy1FFHsWbNGtasWQPAo48+yty5c1mwYAHXX389Dz30kM9SB5FW4AHAAto6\nnx/2VSIlWXkSqO98/hCQ4aMsiuI8RkZYTS64REUFFBVROjnE318z1K5y2Qg3Mmq0Ywc5y5YDqhNj\n2LEDiospGQ5btsjH77Wrhv/Yejn+eEebNbnoEjt2kLNE17AmOsuXL2f58uU9Xlu5cmXX86uvvpqr\nr77aa7ESjEPAI8AziPPaDDT5KpGSrOwFCpHU4Bp04kRJNIx0WE0uuERFBRQXd62tNdKucsngM9oI\nr6hgzMJuI9zIvVh373Z80bPpOqG4mNLOid5kGSvh64rDCrWaQ0UF445Rh1VR4sWyrM7iNod6vKYo\nXmJfc3ItNvR4TVESBSNTgk0uuJSsDmtbW/cWGCauK6aigpFzisnNlbWS+/b5LVAvXNqL1egIa5KO\nlb17obkZRo+WtcVGceQIHDxIwUJZs1tZiXl7sU6YAIcOyfILRTEcy7J6PBTFL/Q6VBIZox1WjbDG\niAtG+K5d0N4O+fkwfLijTcdPfb0ses7NNVsvJSWOC6YOa5y4MFaM1kllJRQWMiIzhYkTxVndudNv\noXqhe7EqiqIoihKGOqzR0mmE27IlmxFusk4IhZLWOTJZL6oTg7DHCiTdb5iiKIqiKMHESIfV+KJL\nJSUUFUkgwN6L1SjGjoWmJtmL1SGMjhp16gRIWufISL3s2AElJWbrxI56O5hCZfy64iQdK4qiKIqi\nBBPjHNaODslaA0Md1s7Kp8OHy7Y7HR2OL0uMn1BIDD4HU+qMNsI7dQLJZYS3tEiqdkqKXItGYVce\nKipi4kSpM7Wncy9Wo8jJ6d6L1SGMn0RIwrGiKF4TCoUIhbIJhUZ3FsNRFHOR6zWTUCiPUChdr1nF\nOIxzWHfvFkN83DixI42ivV0qD3VWHUomg89oIzwszTGZdFJVJX5hQYHUdDKK2lrZRHnkSFJSuief\njFyWqGPFPNRhVQKMGPsZwHXAj4FCQiHTNpVXFEGu1xzgXOAnwLGd/yuKORjnsBq9frWmRkp/jhgB\nBMDg277dsebUCHeAJNUJqF6MIUnHiqJ4z0XAD4HLgL8AplUrVJRwCoE/ApcAzwMtGmVVjMI4hzUo\nBUugW0ZbZqMoKenOrXaAoBjh4ToxrrJ7YaFMeji0j0hQdAI6VoxhgLFiHA7rRFG8J7vXc9NuSIoS\nTiZgO6jDgWE+yqIofTHWYTXW2AvzpG0ZjTT4iosdzb80fiKhU7BRo2RZYkMD1NX5LFdv0tIk192h\nfUSM1klnwSWbZBkrR47IWt20NNl21yjsAgGdyigqkpcrK+Uto5gwAQ4ckOJxihJIftP5+BvwFZ9l\nUbRI+lUAACAASURBVJSh+AT4HvAKcDHqsCqmYZzDGpTiPhAAI9whwerr5ZGZCXl5jjTpHK2tsvC5\ns+pQKJQ8ejF+cqefsWLkGlYHdWIHBQsLpRiWUezZAyNHQkYGAFlZMGaM1AzYs8dn2XqTkiJfokZZ\nlQBiWRZwBLgR+DKwCWj0VSZFGQi5XhuBnwPnAWuBQ52vK4oZmGZSqRHuFC45RsYtadi5U6IxaWld\nLyWLXoye3BlgrOgkgo/00gkkz1hRFK+xLAvLqsWy9mNZh9X4V4xGrte6zuv1oF6vinGowxoNgxjh\nxo3tiRNh3z5obo67qSDpBNQ5MgJ1WM2jn7Fi9DpWdVgVRVEURcFgh9XIdXm9DL6cHCka3Nzs6DaO\nzjBsmKTJVlfH3ZQa4Q7ikBFub3NqN2kcvfRir5esqpLdoYxi7FhZfNrQEHdTQdIJJM9EgqIoiqIo\nwcUoh/XQIamzMWKE2JDGETSDr6TEEcGCNIkAAdCJA/mXtbVw+LAUmRo1ygG5nKS5Gfbv71F1aPhw\nyM8XZ3XXLh9l6w974bMD6yV1rDiIQ79fiqIoiqIEG6McVqPXSjY0SBSmlydttMHnUPVT46NGvbwD\n43Xi4CSCkTqpqpLo/rCeVQaNXy/pgGDGrysO2lgx8mJRFEVRFMVLjHVYjcOOTvTypI03wh2wRI02\nwntVbgbVie/0E8mDADhHiT6RkKRjRVFMJBQKdT7Su54rSlCRazhNr2XFNdRhjRQ1wgOjl0mTZFeM\nXbtkyw6jyM2VTS/r6+NqJmg6gcQfK/Y2p9C9ZtcogpYSXFQkX6hxFe0UJT7EoM8BlgCrgClAlp8i\nKUrMhEIpQB6yj+tFQJY6rYrjqMMaKQMY4Yle4KetTeo2hUJQUOCQXE5hWf1GjdLSRFbLcqTmlLPY\n6yXj1IuOFYdxQCd798ry3bw8yM52SC6nOHxYigSMG9fj5QkTID1dlhw3mrZNZFaWPIyraKcoTjAe\neBH4D+BNoEWNfCWgZAHPAv8FPAic7q84SkJilMNqp6UFpWAJGB6hcKBoyc6dEjnKz5fCOUZRXy8O\nYD9VhxJdL0Y7rP1MIoDqxFcqKyVimdLzJz8lpTsa7EDNKefRwktKwjIRsNf55wFpgxyrKCbTBoSn\nFU32SxAlgTHKYTXa4OunYAkYboQXFcW9SazxVU9LSvqt0GW0XhwoJhMIvfQi0XVi/ITbAIIlul4U\nxUzeBX4DbAOuB1L9FUdRYiYduAzYAjwD/NZfcZSExKhfSKMd1gGiRvn5kJoKe/ZIEeGMDB9kG4ic\nHAmL7t8f8z5BQdQJJH4xGaP1MkQ2gpE6KSyUdIL29j7VjSPFaJ0k8VhRFNOwLKsz/ffbQDsSaT2I\npeu1lUByEHgNOAaJgzXotaw4jlER1qoq+VtY6K8c/TKAET5sWLe8RqbUxWnwBbEaLQQgahSHYM3N\nUlBq2LAeW52agWXJZ+un6tCYMTKhU18fd80p5xk+XBaf7t4dcxNGO6xJOlYUxVQsy8Ky6rCsQ51/\n1cBXgolcywc7H3otK+5glMPa3i5FQEaM8FuSXrS3S/RlAE86kYvJqBHuAnHqxJ7YKSiQ6L5R7N8v\nAzgnp89bdr0pSMzJnaCOlUT+/VIURVEUJfgY5bCCocbe7t0SfRmg6lAiO0dqhLtAnIVkgqoTMFwv\nSTpWEvn3S1EURVGU4GOUw3rssbBggd9S9MMQRrjRBp9DzpGxhWQiMMKNy06ZNEkmQVpbYzrdaJ0M\nslYSEnusGF90KYgOq1YJVhRFUZSkx6iEwrfe8luCARikwiYYbvAVF8P69TGfbnzUaAC9jBoFI0fC\nwYNw4IAEyI0hLU1y33fujMm7CapOIAAFfjZvjunUw4dh375u1RpFR4fkkfezrhh6bmvT0dFn5xt/\nGT9eFjwbV9FOURRFURSvMMk0MZcIo0bGGuExetJ1deLwZWXB6NEOyxUvra1QUyPRygFIVL0EtRAW\nBGByJ0bB7DW5/Wx16j81NTKDM4DDl5kpRcRbW+OqOeUOKSlSO8DIRc+K4g2hUKjroSiJhl7bSiSY\nZlqZSZKuywuP5Bn3W1Jd3b2n0AAkqnNkfIQ1CR3WIOsEEvc3TFGCjhjy6cBwIEsNeyVhEEc1G9nW\nKZVQaJRe38qAqMMaCUMYfL1T6owiPx9qa2UvlChRI9xF4libF2S9GK2TJHZYE3UiQVGCjBjvWcA/\ngCbgv1GnVUksCoHdwGHgLGCkv+IoxqIOayQMYfBlZ8sayeZm2LvXQ7kiYdgw2f/E3gslCtQId5Hi\n4phyle1tTu0mjGOI9PmCAonWV1dDW5uHckXCmDEyiA8divrUIKdpg+FjRQsvKUnNycCizuffBEyr\nIqgosZINXAOMBdKAG1C3RBkIvTIiYYhCMmC4wRejc2R0NdpE0EkMgu3fL/VncnOlqJRRNDVJhauJ\nEwc8ZPhwCfrbWxsbhb1RbAx60bHiIjH+filKYrARsCfRPgBMm+lTlFg5AvyN7kmY13yURTEddViH\n4tAhiboMUWY2EQv8BDmSB6oTz6mqkhDqEFWHjHeOEk0vSTpWFCUxaARmAWcDJwGtWMbt1aYosdAO\nPA8sBD4P3AjU+SqRYi7qsA6FnU43xJqRRFybp2mOLmJHjaI0PIKuEwiAXhLNYQ36em91WJUkRRzT\nQ8BO4GmgAcsyrVCGosRG9/W9AXgBOKKTMcqAqMM6FGqEB9YInzRJlvDu2hVTzSl3yc2VSGR9fVSn\nBV0nkHhjpaOj57Y2xhH0yZ2iIkMr2imK+1iW1eOhKImEXt9KpKjDOhRJaoS3tsoaw1BIsjyNwq48\nNIReUlO7Za+u9kCuaIlhbZ7RDmsEqaeQeNG8PXugpUVqNmVluSRXrDQ2ymPcuEEPGzdO1hfX1kJD\ng0eyRUpmJuTkGFjRTlEURVEUL1CHdSgSwWGNocrmzp0S0Jg0CdLTXZIrVurqJDo5atSQhxqtlxic\nI+OL+0QxVoxcLxnDWLE/h5E6qayUCOUQSxpSUnpuz2UcWilYURRFUZIWdViHIoIKm2C4Y1RUJIJF\nkW5hdCQvQp2A4XqJw2ENsl6M10kiRb0TaawYOcOhKIqiKIrbxO2wrl27llmzZjF9+nRuv/32fo+5\n7rrrmD59OvPnz6esrCzeLr0lwjTH/HxIS5OstcOHPZArGrKzISMD9u2L+BSji/tEqBMwPJoXg8Nq\ntF4SIRuhoEDSC9rbIz7FaIc1icdKspPw92ZFURQlaYjLYW1vb+eaa65h7dq1fPTRRzz44IN8/PHH\nPY555pln2Lp1K1u2bOHuu+/myiuvjEtgz4nQCDc+pS5Kg89oIzxCnYDhzlGUaY5NTVBTI4WkBtnq\n1B/sdcURVB3Ky5NliQcPRl1zyn2GD4exY6VSV4QkylhJtLXFyUxS3JuVfgmFQj0eipJo6DWenMTl\nsK5fv55p06ZRWlpKWloaF110EU888USPY5588kkuueQSAE444QTq6uqoqamJp1vvaG+XaEuEVYeM\ndo6S1GE13giPIpxVVSV/CwvFaTWKvXvFC83OHvLQUCgAeknCsZJIv19B4Wc/+xkHDhxwvN2Evzcr\n/SLGeyZwJrJva6Ya9EpCIddzDnAc8FX0Gk8e4nJYq6urKQqLqBQWFlLdqxxrf8dU2Za36ezaJdGW\n4cMjOtxogy/KaF4iFPcBw3USo2MUdJ2A4emnUY4Vo4suJcpYSdCiSzU1NRx33HFccMEFrF271rFt\nHRL+3qwMwEjgemTP1r8A3+58TVESieOAN4EHgEfQazw5SI3n5EhnNXrfhAc6b9WqVV3Ply5dytKl\nS2MVzRmiKFgChht8UUbzjI8axVBIxrKGLJbqLZMmyZ4ora2yAHoIEkUnoGPFM5Ks6NK6detYt26d\n+/I4xG233cYPfvADnnvuOe655x6uueYaLrjgAi6//HKmTp0ac7sJf29WBiANODbs/2M6X1OUROIE\nwP6tWgi0+iiLEglO3JvjclgLCgqoDFuwWVlZSWFh4aDHVFVVUTBAim34TdEIoihYAoZHjYqL4Y03\nIjrUsgwv7hOFXkaOlN1v6uth/34JmBtDaqpU66quhtLSIQ833jGKYawY6xx98klEhzY2ynWVng7j\nx7ssV7R0dEgeea/f5IEIX4Pf3m5Y2vm4cXDokFS0y8wc8LDeztQtt9zigXDxkZKSQn5+PhMmTGDY\nsGEcOHCAL3/5y3zuc5/jzjvvjKnNhL83KwPQANwKLEYM+luBRl8lUhTn+TVwCVAK/Cdg2t6LSm+c\nuDfHlRJ87LHHsmXLFsrLy2lpaeHhhx9mxYoVPY5ZsWIF9957LwBvvPEGubm5TJgwIZ5uvSNKIzxR\n1uXV1UFDgyxHzM11Wa5oaWmR9ZJRVB0y3jmKUDCjJxESzWGNUDDb3i8qksJrRrF7N4weDSNGRHR4\nRoY43W1tcqpR2FXtjKxoFzs//elPOeaYY7jxxhs55ZRT+OCDD/jlL3/JO++8w2OPPRZzuwl/b1YG\noBnYDOQDE4CPgSZfJVIUJ5GskDpgHrJe+zHAtOqNihvEFWFNTU1l9erVLFu2jPb2di6//HKOOuoo\n1qxZA8DKlSs588wzeeaZZ5g2bRpZWVn8/ve/d0RwT6iogFmzIj48UYzw8EieUSm0INHIiRMlOhkh\nxcWwcaN8rkWLXJQtFkpKIg7JGx1h3bEDTjwx4sMTcawYR5STCCCH79kjp0ZYa847bL3MnOm3JI5R\nW1vLY489RkmvtO2UlBT+8pe/xNxuwt+blX6xU7zt1G7LOuSnOIriCpbVGnaNq7OaLMTlsAIsX76c\n5cuX93ht5cqVPf5fvXp1vN34Q0UFfOELER8enlLX0WFYxCU/Hw4ckL1Rhoi4JJoRniiR70TSi60T\nY9PnkzDqDXL422/LqSed5JJcsZKAlYIHS4uaPXt2XG0n9L1ZGRSnincpiqnoNZ58mORSmUeUBl9W\nFowZI1mre/a4KFcspKTIWrYIqkAmUjVaSIxonr3NqX2KcUSpl4ICid7v3Ck1p4wiL0+EOnhwyEN1\nrHhIglYKVhRFURRlcNRhHYwoK5+C4QZfhJU2jXeMEk0nEQi2b58Ex0ePhpwcD+SKhiNHZOFzfn7E\np6SnS2Z3R4c4rUYRCkWsFx0rHhJl9WZFURRFURIDdVgH4uBBibKMHh3VaYmQ6mi0ER5l5WYIQPXm\noOvErkQbZQ688c5R0PUSw1hJhN8vRVEURVESC3VYB8JOp4uy6lAiGOGJuC7PPtU47DTHIdZjJJpO\nwHC9JILDmmhjRR1WRVEURUlK1GEdCDXCE8YInzhR9pTcvRuam12SK1ZGjhThDhwY9DCjdRJDJA+C\nP1Y6Onpua2McieawFhVJNL+jw29JFCWhCIVChEJjCIXGEgqldlVgVZSgI9f28M5rO0+v7QCjDutA\nJKnD2toqawpTUgzc1sKuPBSlXlJTJWMVIqo55T0R6CXRivtA8NNPd++W8TJuHGRmeiRXpDQ0yNri\nsWOjOm3cOBg+XOZPDpm2I0ZGhkzwGFfRTlGCixjw2cBPgXuAicAwP0VSFAcZAZQC9wN3AhnqtAYU\ndVgHIoaCJWC4wxrBnp/V1eIXTpoEaWkeyRUpBw6IUCNHRn2q0XqJwmE1MsKapGPFaJ1UVsa0pMGu\nN2U3YRxR7FusKEokZAOrgK8DZyNOa/T3WEUxk3TgIeAM4HLgX9EJmWCiDutAxJjmaHTUqKhIrNBB\n1ksabYTHqBMIfuElo/WSpNkIRuskjrFi9G+YrmNVFIexgKaw/01bN6Mo8RCi5zXdBOiykiCS6rcA\nxhKjET5+vGzZsX8/NDbK3qzGkJUlj717RdB+SMTiPmC4cxTB/pKJqJfwSQTLijoY6C4FBbBrF7S1\nSU55PxjtsCbqWFGHVVEcphH4ITAcGA3cCAxeU0FRgkMj8CXg/wOqgDXIJI0SNDTCOhAxGnwpKd0F\nWIxMqRvC4FMj3AeG2F/yyBFZtpeaGtVWp97Q0SFfagxVh0aPlvmThgaor3dBtnhIT5cFnbt2DXhI\nIk4iQADGipGCKUowsSwLOAz8ALgBqO18TVGCj2W1AruAbwG3A0f0+g4o6rD2R1ubGKoxVh0KssGX\nqA6rneYYRJ3YhaIKC6WgsFHs3QvZ2TGlEoRCwU4/TdSxEuTfL0VRoseyLCyrHstSZ1VJPOT6rsWy\nDur1HWDUYe2PXbskupKeHtPpRht8Q6SfJmI1WjBcJxE6RommEzBcLzpWzGMInezYAa+/LvMoiqIo\niqIkBuqw9keMVU9tjI/mDRLOMj5qFKNe7IzViopBa075w8SJsG8ftLT0+3ai6gQMd46SdKwE+ffr\ngQfglFPgjjs8lElRFEVRFFdRh7U/4qiwCcGtSGtvc2ofZhxx6GXkSMjNlfWg+/Y5LFe8pKaK01pd\n3e/bRuskkSOsg4yVhgaorZU9S8eN81iuoWhvl2vJ3nw4SsL3LG5vd1AuJxg3TqrZNTb2+7bRY0VR\nFEVRlJhQh7U/ktQIP3BADPGcHBg1ymO5hqK5WTzNiRNjbsJ4vQwww2F0cR+HJneM1ckAgtkF1YqK\npNCaUezeDXl54k3HwIgRMGFC91J+owiFurfn6gej07QVRfn/27vz6KrO89D/360BBEgMYhAaEQhk\nMRgBwSaOS4xjhI0xFOKshDpNaJOb368ZblbSW8fkZrDdxi6+6U2axGmd5Zu0uCt1XN8a8K2HGMfG\ndmy4uAbXtcEMMkJCQjIgJgmBpn3/eLQ1oCPpDHt4z9nPZ62zJKRz9nm1n/0e3me/k1JKxcW0ppYZ\nQpqw9u+dMGqLEZAeo4KChFYdSoW4GMelupJsoxGMvomQYExA64pSKjqWZfU+lEpm/a9lvZ7Nowlr\nJAk2+Ppva9Nt2v7EeXmyh0hb26BfGd074UIj3Pi5eSM0wlMxLhoTD2jCqgmrUj6wrHFADvBRYByW\nFXnPaqVMJwnqWOAjQCEwXpNWw2jCGkmCC8mMHQtTpkBHBzQ1uVguN6SlySS1CEPqjG7sJRgTSM5G\neP95xXFsdeq9BONSWCi9+Q0NUl+MMmmSTOKMsEms1pUAzZgRsUv+/Hm4cEF2WJo0KYByKRUi0phP\nB94HdgN7gAxt5KskNQH4G+DfgWPAvGCLowbRhDWSBOflQXLuL2l0I9yFmBg9/HSI7TpOnZLpu7m5\nst2pUdraJEOYNi3uQ2Rmykhv2x5yzangWFZo60oyfn71H6atbWal/FABFPR8vwBp9CuVjDqB1T3f\nZwJrAB0xYBJNWK92/ryM4504MaHDGN1DEUWDzzhhGOYYITswPiZFRQmvOmR8XJItYQ1DXUm2mCiV\nkt4D/qPn+xeAiwGWRalEZAC/AGzgLPAYksQqU2jCejWnsZfgLXpt8Lks1RvhxcURN4lN9ZiA4T3f\nenPHPCN8fhk5r1ipFGPbNnAZWAZMBf4QaOv5uVLJ5jzwc2AykA+YtkS+0oT1ai43wpOxwZeqjfD8\nfNnytKkJLl92qVxuGT8eRo2SzT37SfWYQPItvNTVJXuUgsHzilM5YS0ulgBctaKd0XVFqRRk213A\nFeA0cFmTVZW05Nq9iPSuXsG2L+r1bBhNWK/mwoIlYHiDL8J8yfZ22XMxLU0WwjGKs/JQgi3R9HQZ\nwQp9CYdRIiRHRvcahbSuNDbKHqXTpsGYMQGVaygXL8qk58mTEzrMlCnyt507J9OUjZKVJasqXbWi\nnSasSvnPtu3eh1LJTK9ls2nCerWw9BpdNf6yvl7ywsJC6YU0SnMzjB4NOTkJH8ro5GiYhNXIRnhY\nRiNcVVeMjkldnStTGpz1ppxDGifZ4qKUUkqpuGnCejUXVtgEw+flFRcP2iTW6MaeSzEBw+MSYbuO\nMMTF+IQ1mW4ihKWuRIiL0fOKlVJKKRU3TViv5lKv0dSp0inY3AwtLS6Uy01jx0pv5alTvT8yurHn\nUkwg+ZKjMMSlf2Jk3EicwsK+McA9whATSK660tEhe/laloFTGpRSSimVEE1Yr+ZSgy8trW9BFmOH\n1PVr8BndaxTSRnhbm9xTyMyE6dMDLFck3d1yYbuw6tDEibLHbGsrnD3rQtnclJkpk1UbGnp/pHXF\nAFfVlYYGuSTz82XtMqWU+SzL6n0oZbr+16tes/7ThLW/zk7pTXHpFn0yNfiMX9zHpUa48XOL+xXM\nudFRXJzwVqfu+/BDWdl47NiED2VZyRWXsNQV/fxSSnlFGvzjkC1ExmFZ4zUJUMaSazMHmATkAjl6\nvfrMtGZwsBoaIC9PelVcYHQj/KrVT43vNXKpJZqMjfBUjwkYHpeQ1hX9/FJKeWcisBlo6HkUBFsc\npYY1DlgJfAg0AauA7EBLFDaasPbn4oIlkASLlvQrmNENPhfj4oxgra01cL5kfj6cOSPbkhCemIDh\nCWtI64p+fimlvNMObOr5fjywEW2SKnNlIddrRs9jEzA60BKFjX469Be2RnhPwWwbamr6fmwcF+OS\nkyNbOF6+PGDNKTOkp0NBQe8msWGJCSRBctRTV86fl3m2WVmysJpROjtlM2Vns+EEOYeprx+w5pQZ\npkyBS5d6V7Qzuq4opSLIBHb0fH8ZeBroHvrpSgXqCvAUYPc8nkJuuii/aMLaX00NzJzp2uGSJWE9\ndUoW+Jk0CSZMCLhcV2trg3PnpPfRJckSF6cR7uIl6Z6Q1hUnoS4tTXirU/fV18sCUS6tOjR6tCz2\n1dUlebBRnI1ieyZ6G11XlFIRnAfuAeYBxcDRYIuj1LBagG3AzJ7HvwIXAy1R2GjC2l9NjbREXZIs\njXCnsefin+4epyfPxVWHjJ6bl0xxcbFgyRKT/gmrcVz+/AL9DFNKecO2beAScBA4DVzs+ZlS5pFr\n8yJwvOeh16vfNGHtz+UGnzNf8sQJ6aUwyrRpcOECtLWZ3djTRngo4mJ0TPot8BOmmIDhNxJ64tLd\n3XcjQVcJVip52LY94KGUyfR6DZYmrP253Gs0ZozkhR0d0NTk2mHd4WwUW1trdq+RyzGB5EiOOjpk\nhGdammtTEt3jTHp2MTsoKJC/9eRJaDdtWsiECfI3nztndsIatrrSs/DShx/KOmVTpsh+vkoppZRK\nLZqwOrq7ZT6Uy6t2JMNiMkY3wj3sYTU2JsePc+KEXJKFha5NSXRPczNkZMDEia4dMjNTklbb7l1z\nyhzOfEmtK2ZJhpgopZRSKmGasDpOnoTcXFn+00XG91CY3uAL6ZDgsMUENC4J07qilFJKqRSkCavD\n5SGOjmRq8Bk5/8uDuBgdk55h2jXHZH5EWGIChsclGZKjsNWVZPj8CkBzczNVVVWUl5ezatUqzp07\nF/F5paWlLFy4kMWLF3P99df7XEqlEmdZFpaVjWWNwzJu2XYVFnIdZmFZE/Q69JAmrI6Q9hrZpjf4\nPIhLfr4MQf3wQ9k1xyg5OZCVxYcHzwAGJ0YeFMzoBX5KSrhypJbmZhmEMW1a0AW6SmenTHp2Vnpz\nidGfX0VFUF/P8Q9kRTsj60oAtmzZQlVVFYcPH+aWW25hy5YtEZ9nWRa7du1i//797N271+dSKpUY\nSQzGAd8HNgNjNVlQvuu7Dv8E+GugGMsaHWiZUpUmrI4wNsJnzKCjupZLl2Q6ootTEt3R1gZnz7q6\nBysMXMjIuPmSADNm0HpQLhgjG+FhvLkzYwZth/piYly7qKEBpk6VzVNdNHkyjB0L58/LwyhZWZCb\ny/nDsqKdkXUlAE8//TSbNm0CYNOmTWzfvn3I5+pKlyp5TQJ+DnwL+B7wl4BpG8mrcLgFeAT4CrAT\nSA+2OClKE1aHx41wUxct6T4mBTOysVdbKz1GLu7B6tC4JCCMCWtIY+KsNwUal2TR1NREXl4eAHl5\neTQNsUS9ZVmsXLmSpUuX8uijj/pZRKVckIYkrY7JaKKggjG53/e5gGn7WKaGjKALYIyaGvjUp1w/\nrNGNveJiMptOYNFNaamB9y48aoSD4XEpKSHj1fD2sJp6EyGzMXwxAYnL++9LXbn2Wk/eIm52SQmZ\n+2uBG8yc0uCRqqoqGhsbB/38gQceGPBvmVsVeTjA66+/Tn5+PqdOnaKqqoqKigqWL1/uSXmVct85\n4KtANtAO3A00B1oiFVa/AT4OzEOGp5u2tUNq0ITV4VGDzxmld/YsXLwoUxSNMWYMl0eNZ1rHh5SW\nTg+6NIOFNGHtKixh/LlaLMv1KYmJc/Zg9biH1bYNG3ZbUMCYC01k0EFpaWbQpRkspHXl0uQSpnfU\nMnmyYZ+tHtu5c+eQv8vLy6OxsZHp06dz8uRJpg0x4Tq/Z6rF1KlT2bBhA3v37h0yYb3vvvt6v1+x\nYgUrVqyIu+xKucG2O7GsDMDpaDirQ9yV72zb7rkp+M2en3QCLQGWyEy7du1i165dCR1DE1bwbA9W\n6BtSd+SIvMW8ea6/RUJOjy2hpLU2dAmryXOLz4wroZi95u7Bmp7uyYTniRNh/Hi4cEHeZvLkkV/j\nm8xMzo3Oo6CtgdJSA7vyamrgYx/z5NAmJ6ynxpRQwlEze70Dsm7dOrZu3co999zD1q1bWb9+/aDn\nXLp0ia6uLnJycmhtbeWFF17g3nvvHfKY/RNWpUxh251BF0EpvVEShatvdN5///0xH8PAcaABOHkS\nJk2CMWM8ObzJydGJtBmUUGtmgy+kvUZ1IY0JmB2XsNYVkz+/jK4rAdm8eTM7d+6kvLycl156ic2b\nNwPQ0NDAmjVrAGhsbGT58uUsWrSIZcuWcccdd7Bq1aogi62UUkoNSXtYIdSN8OqOEmZw3MwGX0gT\n1iNXSlgRwpiAxOXddyUuixd79jZxOdpbVwyc5xfSunK0vYTFptaVgOTm5vLiiy8O+nlBQQHPPPMM\nALNmzeLtt9/2u2hKKaVUXLSHFXxLWE1bTMa24b2L0gg3csESnxrh3d2evEXc3j83nUmcZXbR5aCL\nMlhI68qFC5IclWUcD80erA5TYwLw7gWDb7gppZRSyhWasILnjXDn0MeOefYWcTl9Gg53lDInpEOe\nrwAAIABJREFUoyY0e7A6xo2DKVPgyhWIsNhmoI4dT6OOYuZnG5ghHD8eyrpy/DjUUMqCcTVmLQYF\nnu3B6nB2ljpxAtrbPXmLuL3XOJlMOpg91bRNYpVSppNVtLOxrClY1sQhV9RWKhZyXY3Hsib3fNXr\nyg2asILnCevMmX1vY5KaGjjGTMoyaoIuymAe7sHqMD4u6TVBF2WwkNaV48cNrisexyQzE4qKZERG\nXZ1nbxOXmuMWx5jJbBPjopQyXA5wA/DPwDeAsZpcqITI9ZMDbES2u9kA5Oh15QJNWCG0Paw1NdJr\nVNx5TFqjJvE4JmB+XIo6DCsYhL6uhDEmYGZcbLuv57uw3aCCKaWMJwlEG/A0sAq4D7g+yCKplDER\n+AVQBfwDMDbY4qQITVjB8wZfYaH0UjQ2ykhXU9TUwHkmYqdnwJkzQRdnIB8a4U5vnkmN8I4OGXpZ\nw0xyzxtUMPB0D1ZH/5iYdA+lpgaOM4Pc1jro6gq6OAOFtK40NcHly3AyayZjGg0qmFIqiXT0+96w\nOQ8qSXUCzuIo3T3/VonShNXDPVgd6el9hzdpqKNTlpapM81qiUJoG+EnTsgleT53Jum1BhUMZE5x\nWpone7A6pkyR+cUXLsjbmaKmBq6QRfv4KbLAkUlCWld6P7+mGPj5pZQymuydmQWsRIZufhX4j0DL\npFJFC/Bp4AlkSLDeCHGDJqwe78HqcNqTJiasnUUGNvh8bISbGJOOoplmFQx8iYllmR2XzuJwxsXk\nz68OEz+/lFJJoAVJUr8KPAa09iSySsVHrp+LwHPAV4AXgYt6XblAE1YfGntgdg9FRrmBDb6Q9xpl\nzik1q2CgdQXInKN1xRS9n18mxkQpZTzbtrHtK9j2GWxbkwrlDrmuLvVcV216XblEE9aQNsKd6YgA\n2fNLzeo6AV/i0n8v1k5Dphg4YZhUkQetrdDSEmh5BvCprpi2wM/FizLFOysLsipKzSkYeL4Hq8O0\nzy/oqys515bKP7RRoJRSSqUkTVhDmrCePg2XLsl0xLHzDeuh8HgPVkdWFhQUyBo6J054+lZRcxrh\npTMtuS5NiktI68rxnu1wZ8wAa5ZhdcXjPVgdBQWycFxTk3xumMCpKwVzJ8CoUfKhppRSSqmUowmr\nz71GpnRk9iZGpUiGYFIj3Ic9WB2mzZccEJfSUnMKBr4nrKb86YPqiikFA99i0n/hOCeBD5rRn2FK\nqVCwLAvLysGyJmNZE3S/TdVLrw13acJaUyNdJx4zrdfIaezNmIG0+I4fl+VpTeBTTMDwuJjWCA95\nXTEyMQppXXH2YAVD64pSKiTGAyuQFWH/DBiniYnqMR64Cbk2voxeG4nRhNWnHoq8PBmC2twsW3YE\nbUAjfOxYGRt88mSAJerHp5iAWfMlnT1YLatnSqJJjXAf9mB19B+NYMK0xAF1pahIxsW2G7JMvY91\nxaSE1dmDNTcXcnIwq64opUJBko924F+R7XEeAuYGWiZlBrk2rgBPIdfGFmBeoGVKduFOWJ09WH3o\nobAss5KjAY1w5xsTCgahbYQ7e7AWFPRMSTSpEX72rFzEHu7B6pgwQXaaamuTxCRoA+pKRoYEqLY2\nwBL1E9KbO0Z/fimlQsQGOvt9fyXAsiiz2EBHv+8NudGdpOJOWJubm6mqqqK8vJxVq1Zx7ty5iM8r\nLS1l4cKFLF68mOuvvz7ugnqisVEa4B7vweowaW7eoAafSXPzjh/3PWE14U+P2Ag3oWDQlxj5NJzF\n6LhoXQmc0TFRSoWCbFcyCrgV+A3wRUBvnKlI18Z/AaoDLVOyizth3bJlC1VVVRw+fJhbbrmFLVu2\nRHyeZVns2rWL/fv3s3fv3rgL6gkfeyfArN68iA0+EwoGoe1hHTImJoyL9TExgiSJiwm0rgiTYqKU\nCpGLwL8DXwX+BWjRfTdVjxbgTeTaeAK9NhITd8L69NNPs2nTJgA2bdrE9u3bh3yusQE6diyQRvgH\nH/j2lhH134N1QIMv6II5fIxLUZGsgNrQIHPigjQoJpMmydfm5gBKc5WQ1pX+e7Dm5fX80JS60tkp\n48id5Xs9ZkpMYIjRCLW1skeVUkr5xLZtbLsN2z6DbWtCovrItXFFrw2XxJ2wNjU1kdfTgsvLy6Np\niMlmlmWxcuVKli5dyqOPPhrv23mjuhrKynx7u1mz5GvQDT5nL8Xc3H5TEsvKgi8YQGsrnDsn8wR9\nkJEhU5j7J/FBqe4ZLdJ7SVqWOXEJaV1x3n/WrH6joU2JSV2dZNEe78HqmDYNxo2T6hn0PZRBdWXM\nGJg8GerrAyuTUkoppbyRMdwvq6qqaGxsHPTzBx54YMC/Za+hyHPbXn/9dfLz8zl16hRVVVVUVFSw\nfPnyBIrsoupquOkm395u9mz5evSob28ZkfP+A/KPsrK+VmCQPvhAunJ82IPVMXu2vO3Ro1BR4dvb\nDjJsXK67LpAy9aquhttv9+3ttK5EweebCM79k3fekbfOzfXtrQcZNi4+9TgrpZQbpP2cA2QiCzhd\n0N64FCBxzUbmsnYB5zWuCRg2Yd25c+eQv8vLy6OxsZHp06dz8uRJpk2bFvF5+fn5AEydOpUNGzaw\nd+/eIRPW++67r/f7FStWsGLFihGKn6DqavjCF7x9j36cXqNjx2TkWnq6b289wKDeCZCxsadPy9Ks\nPi1CFZHPjXDoe7ugc5CIcQlpcmR8TI4elW75IPdUC6iuOAlrUPdQ2ttl9G//ldedwu169ll2vfJK\nMAVTSqkY9SWrtwNfAp4GfoVlWZrcJD1nj96vA78DfqpxTcCwCetw1q1bx9atW7nnnnvYunUr69ev\nH/ScS5cu0dXVRU5ODq2trbzwwgvce++9Qx6zf8LqC58bfNnZMoKvqUlGrgXVERCxEZ6eLmNjP/gA\n5s8PpFxAaBPWCxfkfkFWFvTc4xFlZfDGG4GVC5C5krW1fZMYfVBSIsO16+uDvYcSsa44XYvNzTIM\nNSghrSvHj8v2TyUlV42GLitjRWsrK/r9P3L//ff7Xj6llIpNGvBrIB34BPBb4FCgJVKJkRsRo4En\nkR7WW5Ck1bDFZ5NI3OMuN2/ezM6dOykvL+ell15i8+bNADQ0NLBmzRoAGhsbWb58OYsWLWLZsmXc\ncccdrFq1yp2SJ6qlxde5kg4TGnwRG+HOD4Lu0jp6NJSNcOe9Z826ajS0CTGprfV1riT0zS2GYBd/\njVhXnLGxQccl5HXFyM8vpZSKWRcD93LtGOa5KnlcvQ9rwCt7Jrm4e1hzc3N58cUXB/28oKCAZ555\nBoBZs2bx9ttvx186LwUwVxL6Osyqq+Hmm319615GN/iqq2HtWl/fUhvhIwigJw/6/vTqapg3z/e3\nB6KIS5B7S4e0h3XYmAQ96VkppWKWBtwBfAEZEnwq2OKohNm2jWWNR/Zh/QrwImDAYo1JLO6ENelV\nV/et7OIjbfCNIIBGuAlzi4eMSVGR7KsS9LjYENYVZ65kWlqEHX2CvpFg25qwDnUTIei5xUopFSVJ\nbCzgNWAf0Aa06TzHlODs0ftfkd7VSxrXBPjbvWiSAHuNnLcPwpBzJSH4RnhHh+wr6eN+nyBbdUyf\nLglKULtiDNkIT0+X8xHkNiohrSvOXMniYhg16qpfBl1XPvxQKnHvvlT+uHpucRCGrCu5uXJ34cwZ\n38uklFLxkv06L/fs16lJTaoYGNdWjWuCNGH1WdCN8P6NvUGjoYNuhNfWSubo41xJhylxidiRGXRc\nApgrCUkQkyBHIwT0+WXC3OIh42LK3GKllPKZbC85EcvKwbImDLnVpPJeXyyye75qLNygCavP+u8v\nGcTNloj7FzpmzpSksavL1zL1CigmEPy+n8PGJehGuAF1JQgak8iCjEt39zA9rM4PNWFVSoWIJETj\nkJWG30a2UhkfZJFCqy8W3wXeBe4GxmnS6gJNWH02ZQrk5MjQ3CBGrg3b2BszRgpYV+drmXoF2AgP\nsjfvyhU55Wlpfb1XAwTZCLdtGY4cQFycucU1NcHcQxm2rhQWyrY2ly75WqZeIa0rJ0/C5cvyMTU+\nUntME1alVCh9HlgDlAG/RFekDVI+8BdAKfAdYFKgpUkV4UxYA5orCX2j1iCYdtWwjXDnF0GOwQxh\nI7ymRvLCkpIIcyUh2Jg0NclcyQkTfH/rsWNlnnVHRzD3UIatK0HPLQ5pXTH680sppQLTf45GHWFe\nUzV4zcjiWQAtwPkAy5I6wpmw1tZKSzhiduA9oxt8s2cHm7AGsBotGB6TkN5EAMPjEnRd0YR1ME1Y\nlVKh9BpwJ3A/UEVfwqT81wHcCPwAuAGwdcElF4QzYQ0wMQJt8A3JkEa4358rI8bEmVvc2TnEEzwU\n0rrS3d3XeWpsXdGbO4NpwqqUChlJhlqBp4C/As5g290xH0cWC7J0vmWMBp+3i8B+5ObBu0gvq0pU\nOBPWgFY9dTjtzCNH/H3fy5dlaGV6+hBzJUEK53fBoG81lYDiMnmyjHq9cAFO+bxn97CL+4AMyc3L\nk6TVbyGtKw0NUl+mTpU55xEFVVcuXICWFllROwD99y32+x7KiHWlsFA+3Do6fCuTUkoFTbZQsbHt\nzrh68yxrHJADLAbGaNIaJTlPOcBkoBIYCzjx6OiNi0pcOBPWQ4fgmmsCe/vycvl6+LC/7+usTDxz\n5jCjocvL/S8YyMaO48cPsZKK9ywruLgcOiRfh70kg4pLSOuK0TE5fFjeO6AGxdixsjdtZ6f/W9uM\nGJe0NNi9GzIzfSuTUkolM0m6MoHDwD7gFWC0Jq1Rmw4cR1Zo/hWSwCq3hTNhdRp8AXEaW4cO+Tv8\n1GlbD9sInzNHejr9XpY14JhA33nxOweJKi5BJ0cB0ZhEENK6Ytt97xfwn6+UUilmEZJ4AVwHZAVY\nlmSzCtnKBmSlZp0/7IVwJqwB9xrl5ckww3Pn4PRp/97X6Z0YtrE3bpzsGeH38NOAYwJ958U5T364\nfFlWCU5P7xtqGdE11/hbMJBh2gEnR86Q4Opqf4efRlVXSkqkAre2+lKmXiGtK/X1sovQlCmQm+vf\n+yqlVOp7C3A+0J8D2gMsS7LZBnzY8/0/4AwLVu4KX8J65YpMUAtgSxuHZQXTQxFVrxEE03MU0l4j\nZ5GnYYdpQzAxaWiQOysBbGnjGDdOhp92dEhi75eo6kp6ukym9Hsea0jrStSfX0oppaImcywvI3Mw\n85HVhtuinnspCw5NxLJGYVnjUnIosfyN47CsMVhWVu/fKefoPDAD6aH+NnAh0LKmqvAlrEePSrIa\n8BynIHooouo1gmB680Laa6QxGZnG5SoGxMXomCillIqJbXcAV4BGYklWxQRkKGwT8DIwIQWT1lHA\nTOB9ZK5vGTAaANtuQRL+JqBVF1nySPgSVgN6J8DwHoqQ9rDOmSNfjx71bwpv1DEpKZHliy9d8rxM\nvQyICfhfV65ckd7ctLQoFkj2u644EzmdizUgRn9+KaWUilnfSsOxJlxXgB8Dk4DrgS/G9GqTttIZ\nuiw5yJZBM4CSnu+ze38b/7lT0QpfwmpA7wT430Nx5ow8xo2D/PwRnux3r9GVKzJBbdhJnN4bNw6K\nivwdfhp1r1EQw09DWleqq2X67ojDtMH/utLQIBfqxIn+vWcEJSVybhoa4OJFf95Te1ij8+STTzJ/\n/nzS09PZt2/fkM97/vnnqaioYM6cOTz00EM+llAplVoygAM939vAO1G9SpLDbCAdyMCyguuZlbJM\nQP6WDCzr6nmoHcieqo73AJ/3dQu58CWshvQa+b1dR//VNUf8PPC716i6WlrABmxFEWRcRuR3XLSu\njCyImBhwEyE93f89cnWF4Ohce+21bNu2jY9//ONDPqerq4uvfe1rPP/88xw4cIDHH3+cgwcP+lhK\npVTqaAHWAl8Bbgb2xPDaQuAkcAm4DRh5a0NJLkdjWeOjSnDl+Tk9c0+Hev4E4DPI0N7jQO5Vz70A\n/DVwF/BZ4AfI3FXll/AlrIb1Gvk1/DSqfSUdpaXQ1OTf8FNDYgIDtxzyQ0xx8bs3z5C4JEVM/BoG\ndOiQMRmbn3G5ckX2fLWsvkRZRVZRUUH5CNfI3r17mT17NqWlpWRmZrJx40Z27NjhUwmVUqlEhsG2\nAH+P7OHaEuXQ2Gzga8BUZB/YzYyUlkgSORb4L8BfAlOxrIwRnp8L3A98GRgzRNLahSyYlA4UAP8f\n0tsq5O9pAx4H/pnY5/mqRIUvYTWk1yg7GwoKoL0djh/3/v1i6p1w9lg5etTTMvUyJCbgb29e/2Ha\nBQVRvMDP3rwrV+DECRkXG7AZM/qGn7a0eP9+MdWVyZMhIwM+/HDk57rBkB5W8LeufPCBDNMuLYXR\no71/v1RXX19PcXFx77+Lioqor68PsERKqWTWfw5n9IncZeA1ZBgxwBtRvu6TwM+BbwDPMPw2MhOA\np4A/R+bZbgIiJazp9PUMd/eUa+CQ3/j+RuWWoW9LpKLmZskQ8/KCLgkg7c6GBumh8Hr6Zky9Rs4T\nDx2ChQs9K1OvQ4fgox/1/n2i4GevUUzDtEEK98gjnpapV3V1X6YYMGf46YEDcs6WLPH2/eKuK358\nrhw6BDfd5P37RMHPuhJzTFJcVVUVjY2Ng37+4IMPsnbt2hFfH+s8sfvuu6/3+xUrVrBixYqYXq+U\nUoN1Inu+LgWmIEliWxSvm9bv+ylIgjkUG5h81WvTIzzvPLJY1D8BdciwYOWWXbt2sWvXroSOEa6E\n1enJM2Q1svJyePllKdbq1d6+V8zzv/zszTt8GD7/eX/eawR+9hrFHRPb9v4aNqjXG6QofiWsccdl\nmDmDrjEoLkbXlRS3c+fOhF5fWFhIXV1d77/r6uooKioa8vn9E1allHKDbds9N8/2DfjZyB4BlgGz\ngK+P8NxOpFf174F64EdEWiypryzPxVgWFY2rb3Tef//9MR8jXAmrQfO/wL8eiq6uvoVRov7zr7kG\nErwbEjWD4lJaKp2KJ07I8NPs7BFfEreYVz2dMkX2Wjl1CqZNG/n5iTAoJuBfXTl7Vk7v2LFQWBjl\ni/yaW9zeDnV1Uey144/+MfH6HoquEByfoRpcS5cu5ciRI9TU1FBQUMATTzzB448/7nPplFJhF2tS\n2JdY/v89P+kAWod5xSVk79RbkaHAQ8+v1QTVbOGaw3rgAMybF3Qpes2dK18PHBj+eYk6dkymJBYW\nwviRF2ATc+d6XzCQ7KCjI4q9dvyRnt7XKH7/fW/fyzm9MV2SfsUlpHXFOf7cuTEkYH7F5PBhY4Zp\ng9w/mTJFbuycOOHte8VVV0Jq27ZtFBcXs2fPHtasWcPqnuE7DQ0NrFmzBoCMjAwefvhhbr31VubN\nm8dnPvMZ5jqVTCmlDCZzSM/2PIZf4Eme29rz3GZNSpNYuBLW996DBQuCLkWv+fPl67vvervI6Lvv\nDny/qMyfLxlb93BzA1zgxMSQYdowMC5eijsu773nSXkGMLiueCmumCxYEMqYgD9xse2+0xtTXEJq\nw4YN1NXV0dbWRmNjI889J0PcCgoKeOaZZ3qft3r1ag4dOsTRo0f59re/HVRxlVJKqRGFL2E1qMVT\nVCQ9nmfOeLvIqNPYi6mtO3485OZCTY0XRepjWEygrzhe5iCXLsnKp/17dKPiR3LU3Q0HDxrVneV0\n/hw+LCNjvRJXYjRzpowUuHjRkzL1MrCuOJ8pXl6SdXVyaqdO9X4kvFJKKaXME56EtaVFskIDtulw\nWJY/yVHcvRPz5/vTpRXCRvj770vPUXl5jNt0+BGTY8dku5aox497b9w4WUm7s7NvPrYX4rq5k54u\nEzq9HhZsYF0x+vNLKaWUUikhPAnrgQNQUSGNS4MY3eDzozcvpMMcE7qJ8N573o4hNzAm4E9diWtI\nMIS+rhj5+aWUUkqplBCehNXA4XTQ1/70Kjnq7OxbPCjmEZ5ez5d0JqcZFpeyMun1rKuDCxe8eY+4\nE6Np06RrvqnJ9TL1MjAm4P2NhNOnZRBGdjaUlMT4Yq/ryuXLUFsLc+Z49x5x6J+wejXd3Ym3Ybm6\nUkoppXwSnoTVwOF04H0PxdGjMudvxgzIyYnxxV4PP21slOTLsIlp6ener0ob19BTkPO1YIG3cTG0\nrng9VLt/T17Ma4B5XVfef1/GRBuyQrBj8mSYPl3mZB/3aJ917WFVSimlwi08CauBw+lgYCPci1Ge\ncSdGIF2yhw/LRq5eMHCFYIfXvXkJNcK97s0ztK54fXMn7l5v8H5IsKExAW9vJHR399000oRVKaWU\nCqdwJawGtnjy8mQx3nPn4ORJ94+fUGI0bpx0n1RXu1qmXobGBLxNjlpaZPHlzEyYPTuOA3iZsHZ2\nyk0KA/dkrKiAtDQZNXD5svvHT6iulJTA+fNSkb0Q0rpy/Lj03ubny+ekUkoppcInHAnruXPyiHli\nmvf6rxTsRW9eQr1Gzgu96mY0dOgpeBsTp8fommskaY2ZlzGprpabFOPGeXP8BGRlyfziri44dMj9\n4ydUV9LSJMn3svs3hHUl4c8vpZRSSiW9cCSsBw7I8NY0M/9cL4fUJTQk2Hmhl5MGQzjMMeGYzJ8v\n17RXY8gNjQl4Fxdn/a/+7xEzrSuuSzgmSimllEp6ZmVw/+2/eXeb3uBb9F71ULS3y+hOy5LhlHHx\nqjfP0BWCHaWlMHasDNNubnb32An3Gk2ZIt2NJ064VqZeIa0rjY0S5wkToKAgzoN4VVdaW6GhQbqX\nDeSsPn7woIwod5P2sCqllFLKrIT19GnYs8f94779Nixa5P5xXVJZKV/373f3uO++Kw3I8nJJvuKy\naJGcP7cdOwbjx8syowZKS4Nrr5Xv3Y6Lczwn7nHxKi4hrSv9YxL3GmBexeSddyRjy8hw/9gumDBB\nbvBcvuz+UG1X6opSSimlkppZCetHPgJvveX+cd96C5Yscf+4Llm0SBrJ774LV664d9x9++TrRz6S\nwEEqKqQnz+0NSQ2PCfSdN+c8usG2XYrLkiWhrCvOOXvrLXdHRLsSk8WLJWF1e0NSw2MC3tSV1lbZ\nzScjo+/mkVJKKaXCx6yEdckSd1s8AB0dkgka3GuUnS0L8DhFdYuTzyTU1s3IgIUL3e852rcvwezA\ne855c/OS/OADWUw2L09WPo3bRz7ifl05fVoWJzN06ClIT96kSXDqFNTXu3dc51QmVFdyc2W49pEj\nrpSpVxLVFTfvofzHf0juP3++jIBXSimlVDiZlbAuWiQZW0eHe8c8eFBWB87Odu+YHvCih8KVXiPw\npjcviXqN3PzT+8ckoe1nvYjJ/v3SS2jo4mQg58yLGwnOqXSlrrh9IyGJ6oqRn19KKaWUSmpmtUyz\nsyW5PHjQvWPu22d8Yw/c76Ho6JAeCnChc9ntRrgzLtbwuMybB6NGSYeZWyOiXen1BulqbGuT1YLc\nkgSJEbhfV06fhtpameddXp7gwdy+kXD5slyAho+JXbxYvu7f796IaNfqilJKKaWSmlkJK7jf4Hvr\nraS4Re92r9HBgzIftqwMJk5M8GBuzy2urZUNSONejtUfo0a5v/CSa71GTlej211aSVBX3O7Nc46z\naBGkpyd4MLeHar/zjmTRho+JnTYNioqgpcW9EdGuDNNWSimlVNIzL2F1u8GXBD150NdD8c477oyI\ndm2II0hXY02NrILihiSJCbibHNm2y71GbteVkPawujr01LmJ4NaKUElyEwHcHULf1ia7XqWl6QrB\nSimlVNiZl7C62cPa1SXjYp1s0GATJsDs2dIreuBA4sdztXdi1ChZ+cSthZeSpNcb3O35rq2VvT6n\nTIHi4sSP52pdOXsWPvzQhTGx3isrkx2RTp6UR6JcrStTp0rhPvjAhYORNDcRwN268p//KR/fc+cm\nsCWXUkoppVKCeQnr4sXSzdjVlfixDh2SpVgnTEj8WD5ws4fC1R5WcHf4aRL2sLoZkyVLElxwyeFm\nD+vbb0tXVsJjYr2XltZ3D8qNP9/4upIkN3eM/vxSSimlVNIyL2GdMEGSzPffT/xYSdQ7Ae4NdXQ6\nlsHFzmW3evOccbFJEpcFC2Rnn/ffl/l5iXB91dNZs2SPnNOnEz9WEsUE3EuOzp2TztCsLOnNc4Vb\ndaW9XSajL1yY+LF80L+HNdGFl3T+qlJKKaUc5iWsANdfD3v2JH6cPXvkWEniuuvka6J/+jvvwKVL\nks9Mnpx4uQD3YlJTI92LroyJ9V5WluQLtg1vvpnYsXbvlq9OnBOWlgZLl2pdSYDz+sWL5caEK9yq\nK/v2yRDtJBkTm58PhYWyonai9xtdrytKKaWUSlpmJqwf/zi8+mrix3n1VTlWkli2TBbPffvtxLZR\ncU7d8uXulAuQrK2xUeY5JuK11yQmroyJ9YdzHhO5JNvb+xrhf/AHiZeplxt1xbaTrq44MXn99cRm\nD3hSVz72Mfj3f5cJ6YlIspiAO3XlzBlZcCkrS+7HKKWUUirczExYly+XxCYRzc1w/HhSLLjkGDtW\nGmjd3fDGG/Efxzl1rrZ109OlIZ5oXJKwEe4UN5FG+L59svLp3LmyLo9r3Kgrhw/DmDGyB3KSKCyU\nEQQXLsiIgng5MXX1khw/Hq65RpLWRLz2msuZtPec85jIJfn738vXj35U1ntTSimlVLiZmbDOnQsX\nL8KJE/Ef4/e/lxaPa+P8/JFocuR0lvU/lms+/vHEk6MkbIQ7xd29W3pK4+FJTx5It/w77yS25VAS\n3kSAxHvz2tpkmLdlwY03ulcuIPGe7+5u+QxLsrriXEavvBL/zj6efX4ppZRSKimZmbBaloybTCQ5\nSsLECBJvhB86BKdOwfTpsv2Hq5YvT6wR7gwpXrDAvTL5YOpUqKiQBCfexV89a4SPHSur+/7f/xv/\nMZK0riR6c2fvXrkBsXAhTJzoXrmAxHu+331XLrzp090rkw/mzoXcXKivl+nq8fDs5o5SSimlkpKZ\nCSsk3kORpL1GN94o+fqbb0qCFKv+w4Fdnya6dKkMHz1/Pr7X//73ciMiCbZOuVoiyVHnm/w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L46abburxXsuyep1TX393g0ceeYQvfOELTJw4kQkTJnD++ecD8Kc//anzf582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Aww8/zPz58xk7dix//etf+fWvf+3K8QVBEHyN6RHsDOVXvzJNMM1bbrFxwAsv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UPkdkhGI6HKPeg2l5Tp166jCeMzGaJzMdp2X8kH3U25lrvR0cfWVkv/SV6XD0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ZHiHaeOaMdBr7jBmjgsiIGDtWmsl0x+bNRovcOsck7HVxHQYMUJNg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+ "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Crosscorrelation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A crosscorrelation is computed between two different time series x(t) and y(t): $$\\rho_{x,y}(\\tau) = \\frac{\\langle (x(t-\\tau)-\\langle x \\rangle) (y(t) -\\langle y \\rangle)\\rangle}{\\sqrt{\\sigma_{x,x}^2 \\sigma_{y,y}^2}}$$\n", + "\n", + "For an example we generate a low-pass filtered version of the colored noise. The low-pass filtering introduces a time shift such that the filtered signal lags behind the original colored noise signal." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "nyq = 0.5/deltat\n", + "lowf = 0.5\n", + "low = lowf/nyq\n", + "b, a = sig.butter( 4, low, btype='lowpass' )\n", + "filtered_noise = sig.lfilter( b, a, colored_noise )\n", + "filtered_noise += 0.1*np.random.randn( len(filtered_noise) )\n", + "\n", + "tseg = (time>10.0) & (time<15.0)\n", + "plt.plot( time[tseg], colored_noise[tseg], '-b' )\n", + "plt.plot( time[tseg], filtered_noise[tseg], '-r' )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.ylabel( 'Signal' )\n", + "plt.show() " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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qMREY/sy9NGMk4/wAYQC085dPFCBMUnqQm0snrquLVtvYWBGYfvQolQKVf4MX\nsCmBJ74RwnA6RQkWf81RAB1yQYF7zo6WSSoxkY7X6VSaIWtqlGNSL778MrBjN4yWFuUAzM+n0LTM\nTGHrZcJwuaLWh8GEIQfoyYSRmkqPTzpJ+d5gEgZbM477KCmHg8zb0aYw2tpoIEycqAy/lNcl2fHJ\nJim7nSZlII12ZKh9GHrXWcCAWYqLYcmE4XRSPYPPPqNkk/R0+rBTTwUKCpS/KzXVM2GoyQIgiaS3\nw15eHg2Q3Fw6lokTSd45HORQ2LePttw+CKOzkyxYPT1i8dVLGHY7/Z5gFHPcvZuElnxdnE7qrKil\nMLh1sUwYHR1ifBlBEJPmvaOri5x56iJrJ5xA2f2ZmUK6M2E4HMSi9fV0QiwW5QWKUA/nzk5Sg1w/\nkyETRl8fHba60HKwCOOEE4D58+n+ca8wopUweEE84QSxjgLKiSsTBpukbDbaQQaLMPxVGPxevwiD\nTVJc+fDEEwVTXXUV8OKLyhal3ghDC9/7Hpmo9GDYMCKNk06iVO3rrgM+/5z+t2cP9dE4+WSfhNHc\nTOMsNVVkzeohjLY2YPRo4xn6nlBU5D7ey8upx7taYeTlUcAYHz+DO7kZhT+qxC/U11NSphSGDYAm\nU1eXO2GwJzk3l0yP//wnvZ7VY2Mj2XrV0R4ffeTewTHIYIXhqY0LQNeisZGuC/s7u7qISAKZ+4yy\nMlF6aFASxsaNGzFx4kSUlpbiwQcfdPt/eXk5MjIyMHPmTMycORP3ejH6Ohw0fqKNMDgqZsoUWpfY\nFyAv2nLgj6wwhg9XOvMDJYzubqHY/SEMnwVfmTC++opu162jXXxpKT2eM0d8cWEhEBurMLV5NUkF\nipkzgVdfBR57DLjrLsoH4ZX+hRdo23zGGboJIy3NGGHU14v1LFjl4tV+MT79aoUhm654rezro/d6\n69znCbwDDnpV8d5e4NFH3b9IljSvvy7KImRkKAmjs5PMjPn5wNVXU92UuDjaDLS3A//+N71PzXjP\nPhvyvA1WGHa7csMg+ys6OkQu4jvv0CGzugiWCdBqpSk26Aijt7cXN910EzZu3Ig9e/bgxRdfxF6O\nz5cwf/587Ny5Ezt37sRdd93l8fNYYUSbD4MXes7O5h1GW5sIc1ObpDhUMz9fTOhAFUZMDJnte3r8\nI4zOTlrv//73/icrKkTWNINXLN7R/e//0u5tzBja5s6eLRzV/auam0lK+pFBJYyYGIpHHjECuOce\n9xNQU0N+QdEJAAAgAElEQVSkIps/vvqKFpubbhpYHW02ul6pqcK6oYcweCFoawuOwgCUmwBAHLo6\nRyMjQ5xWJgwmGn8UBv9uT+91OqnOlWEcOAD87GfiMZ80LvESF0dJmBwlolYYAAVcZGQATz1Fk+fX\nv6aQ69//XmyvbTZSwbfcIg44aANNG6wwABF/ASgVRkeH+Bk//jFNnbo6ZXRToGAzt78EFDHC2LZt\nG8aNG4dRo0YhPj4el112GV5//XW317l0bmPa2/UpjBtuALZ7KVEUbLDCAGjA8IBgQgDcCaO2lhak\nlJTgmaQA4cew2437MO68k47rvvv6n3zrLQqhlSHvzouLxbY2LY0ik9j7zyFgUP0ulcJgx1xINwGp\nqURw2dm00Njt9LseeIAUyb33UrjmW28BcFcYycnGCAPQlzCpB/ImABCnX23yt1jE5oQJgzci/hAG\np7l4CtE9dsx9aOgC507wnFcrjMxM+jGeCCM2liY3T6iYGBFGtnKl8InYbKRUHnuM/qf2RIcAnZ3i\nsEb3R5HHxdE6wP4JWWHYbDTWamr0t2ENByJGGMeOHUOJ1JuyuLgYx1TxZBaLBZs3b8b06dOxcOFC\n7PFStCcxUV9Vzj//mTIsg4FXX/Uty9WEwWqYCSMmRmlztlppB5eZSQsLT2ibzT3m3ijYj9HSYkxh\n2Gxktdm8mUy9fX1w95i6XMqV6sQTxf3kZKGBMzIUccTefBgAnQ8jUUiG8PDDpIK4yQATxoYNtEi1\ntAibwZtvAlD6MGpraTIbIYykJGM1wHxBHczAx6hGQQFdAv5fIITBUclywqLTKQiktZWOxbDJij+Y\nJ3FjI51oDtPmQeuJMLKyiOhvu0185nXXUQju3LkUi56drbQL1taGTWHw0M7Pp7nIxPGjHwELFigV\nBkDXqro6uggjgPqHgcGiQxPNmjULFRUVsFqt2LBhAxYvXoz9Hp1TK/Hpp2RFmDmzDGVlZR4/99Ah\n/45ZRkcH1YDh9queIBNGVpYYEA4HWUcyM5ULSHIyTbaRI4U/45ZbaDO0dGlgxywrDCOE0dpKi01J\nCYmAlhYgs6NDTDIunXv77eJNcvKcfILOPluU7wDcfRgqGRXS0tw//7nysdVKB/TBB+RYTU8X5UP6\nt+ZMGC0tZF4cNkyfE5gJI9jtbnkTwLkd0qEqUFBA443/x05Vf3wYDgdd7k8/pUUvJgZ44glaex96\niIiEixQbqoHE0oUrYzY2UnnmTz6h53mLzoTBPoyWFhqkPFDkyLnkZIqIY/NpZiadBE5A2bEjbAqD\nh3ZeHt2fMoWscCefTNOlrU2pRJub6dDkPK1AUV5ejvLycr/fHzHCKCoqQgUPEAAVFRUoVmXopkmx\nZOeddx5uuOEGNDU1IVuuJ9SP/PyVOOMMYnEvXAFAJD0FAlbPbW36CUOtMPLy3GsJsX07J0cQBjfJ\nCdQkxYuLUcLg4wFosWxu7icM3p7yLlw2KcorhWy0z8wkX0Y/FCapX/1KaeBFmMtaWCwknzjUdsQI\n+o2xsQP2HpuNzkF9PW2I8/OVdmhP4IUgWP4Lhnx+WlooMviee9xfxwEUwTBJOZ30uy+/nK7dBRfQ\n56qVh82mQRivvkqZ/loNRWTCyMig3dW0aUQYXHUYICJ//30a0AkJwIcfUl7PoUPAD3/o/eCZMGpq\naOLu3x82hcHjPDeX7k+eDLz2Gu2TkpNFSG1aGvFfczMNx2AqjLIy5WZ61apVht4fMZPU7NmzceDA\nARw5cgRdXV14+eWXsUiVelxbWzvgw9i2bRtcLpcmWQB00vUsLrLjORDIhOEN8g5arTDy890Jg8mn\nqIgGUUeHsOYEunDy+eHcECOQCaOpCXRgPMl4pdi3j+TQs88qQ3W8rJIKk9QJJ7i1FItIHaTvf59+\nJF9kaWve3EzXzGqlfw8bZswkFWyFoc7g/81vSMSpcc89JKjYzxEIYbS3C17nselw0Lz64osBdw/+\n/Gf3nALs3k092LUgEwZAJ41L2xcVKScLq4iEBAopKisj5vblPMnMJIfcc8+RemlocCeMY8c0Djww\nyMU+R46kMc+V+RMTRY/2xkZhqmIfRjAVRqCIGGHExcVh9erVOOecczB58mRceumlmDRpEtasWYM1\na9YAANauXYupU6dixowZ+NnPfoaXXnrJ4+elpOgrDRJIExIZvJb4qs3jTWHMnStK+zN4bS0sFFnf\nvCAFWk8tLo7mqt7S5jLUCkNBGMeOiYygCRPIdpaaKkIxvBCGL2d+RAjj6qtpgeLw4BEjBlZaNkkZ\nIYzt22kdi4sLvsKQx7w339Tw4fST+FjZJOWvwuDfwYEJTBjr1olgpPvvJ7OVAk1NnqsE79hBt2ed\nRU4zzpsAaHzdfLP7exISyFly8sn6HESZmeJHT51KB602Sd1330C/lkDw97+Lj2GF8cUXVNMrMVHw\nX3OzIIymJkEYTU1EGP62ZQ0FImaSAsjMdN555ymeWy5VZLvxxhtx44036vosvQqDd2PqvsdGwSZQ\nXwpD3kFnZQn/XVsbMHaswjoDQCzkhYU0gLjAawDFVQdw6BBVAR8/3rh5y40w2tuVJqmZM4H/+R/R\nzyI1larFHj7skzC8OfPDXh+st5cWncceo0w4gAhjzx7g179Gc/P9A4Rht9N54cxvT+Np0ya6nTfP\nvwXaG4xk8KekKN1O8q1ecD9zNeE4naIjrny93DY5jY1KJfHQQySLvv2WPnTqVKo9smQJ7ah4tczI\n0LY18+DRKjipBVn5TpkC/Pe/7gqDU/IDxI9+RHumq64SCmPqVPpfYiKNoWuvpZ+1ebNSYRQW0jxr\nbAxuWG2gGDKZ3mwH9DYhu7poM5KaGvjE1WuS0lIYWl3RGLxBys6m31NXJ8LuglUozp8QXa8Ko6qK\ntq/nnCP0c1YWGWkBj4ThckWhwuALwMlhABFGfT3w6KMDeRhsWuLwZ28qw+GgvIRTTgm9wvBFGEYU\nRkuLKADL4Ex1drDz+1lhqEN6NQmjqQlYtYp8XnffTQv05s1UVVM+QYcPCwM+J3+qwZNLCtX2Cp5E\n//0vMH26tsJoafEvGkADiYm019i6VTnOmTCefloEuDidNLcWLyaR3txMFjOtqjiRQkQVRjCRkuI7\n0cvpFKH+Tmdg9Vn8IQy2/3d10c7D2846M5PGbG0tLQIPPuh/sx3G9OlU7NMoYSxYAPz0pB3Ag+8i\nJ/0XaG6OV4bVVlQow2gB4Ac/AL77XeGc1ABv5mNjPX+3vIMOK2TC4N2r04keuwNpaSmahOHJHNTU\nRIFhXKk2mJAJ1Vd+jRyirMeHsXcvWWdkkc+1sJgYeL45HHSd1JVW6+pAi/OJJ9Ib2TewciUdrMVC\nfo3Dh4kUuCMiIJIQ+vo8Z5rx4NHrGb72WpL2p59OJsfqapKHTid9d1IS/bggScGkJODii2key2bg\nFSvEfopfV1tLY2n+fNqj/OMfdEjqisSRxJBSGLLk1gLv6oORQVxXR2PVH4WhJ9xw7FilwrjqKn3l\nyL1h2zYymxgtM/L228Dsgy8Bd9yBBx9JUCqMpiZqGcY+DEZ8PDHkRRd5nOx6iCtizX9GjhRl1ftL\nsQNAams1khN6Udi6D7HoGRh33hRGc7P4iFBESbGJqLnZ+26U54fLpc8kZbfTmu10Eu8DgvS4uZdM\nGICIQOTrWlcH4DvfEclPjY3k51q7lkp1XHUVmaCOHSOVyqvq6NF0wlJSvKclsxdfb/nVggIK7wJE\nF0b+IStWkAMmyITB50oe69dco9wAJiXRKeCYHo6+i40N/iYjEAw5heHLNMC+jkAJw+kk5jfi9GaF\nodXkRgY7yPbupQmnV237Qny82EwZDtFNTCRja3k57I3ddJC9vcCaNVQE0I/m1FFPGOnpNKu5nElr\nKzYcLIVrVgzGpOVjJnLhrH8Jz9bdBodjvcePamqihSA/P/j9J9gktX8/uYy8nc/YWDqfHR107uPj\naV0cPpyqb6ijcTj5buNGing+cEA4vNevp/w42YeRlCQIo7CQ1vIBkxQri6Ym0csCoPt/+AOd4+9+\nVxDGxInKHsWeICsSo8jJEfLV6SQllJERdMLgn9rX5/11VVXkCgREc8lgVQUIFoaMwpg0KbwKo6uL\nxtumTaIInRZkpy4rDF9hrTzpk5Lo9cEobQzQRo2jMQwTRlMTcMkl6EzJQm+TZON98klg2TK/jseX\nwxuIYFOsCRNoBc7Lo217ZuaAV7vhxXfw+hNV2IhzMfHpWzGvdQO6vvVcNpsjq849lxLLgwlWGLt3\n6+uRwnOko4N+0tGjNH65mq0M3rx/+aXYiLFJiuujyQpj1Cixzl58MfCLX0iE0dpKKyYnsjCWLydb\n6Y4dxDIyYegxM/msiOkFcpRCbS1t6Q8fpmNtaiICCRBJSXRuHnmEKvp7QnIynR45a2DUqOjyXwBD\niDAWLdKvMIJBGFx98tVXRRFMNVwumsxaCkNPHgSbL4JFGAANYG6KZAiNjUB2NnpSMuCyS4Rx9CiF\n//gBPaaxiCmM4mIqf75+Pdnfly4Fzj4bxyxFiD3rTFhTLNiBE5FURWUD4rd/4vGjWGGEAkyoegmD\n50hHB43Hbdvo+TfecO9Oy4TxxRdiXsl+GC7FDwjCYJSVUXv1AcJoaRGZfPLgi4sjZQEIk1R8PNlk\n9RDGvfcqG80YBSvjvj4KHzx8mI71tdfIlBYgmDDYwuntdYDSX2ESRghRXBx+hcGLgKew8u5uGvs8\nULiscGWlvuJ/TBhGCgX6AtfcMlytsn/V60tNh6XFLggjLc3v4kh6TVIRrUDMBe9uvRWYMQN7MAXJ\nyTSGmpGFhGqygad84Zkw2IcRCjChVlQo/fSewP4WuRgeQCWYFi5UvlZNGC6XMgeDI3sAJWFMSD2G\n1BTXQGkuADR+qqq0PbgnnkjnuKCABkRKCvkZ9Mix9HQyL/iLGTPoNi6OYs4PHBAhZIDnya0TSUm+\nTdCAOKcyQYwcaRJGSGFEYTgctKvyF52dIkCD/WZqyP4LRlYW8J//uLdh1EIg88ATkpL8LDHSTxiu\ntAyUVfw/YcMIYERHtQ9DA33TZ2Kj6xwkJQnCsPSzWXx9f7Y7N0A/6SRgwwa4XKIuXijAJc4dDn1K\nVDZJzZpFGeB39rdTV8f7t7TQRuzQIfpZXV2eFYbTKQjjo/wLMbtrM9LSgLbW/gqE77xDSQhahDF9\nOh1IfDwN0NRUYlhOhQ4lbr6Z6vZbrZQwqJbeH3/s18dy4cXERM8h9DJKSkjU/OY34rm5c92DDyON\nIUUYvhQGh9VaraRiA4k66uoSDkx5E9LeLsyqWoSRnU3ZsHo6i/Iio2Vf9hd+E0ZjI032jAxcUfOw\nSFlX1X7Si48+ogAZXz6MaCKMju9djCeSfgGLRRAGALQk5yPW3l/7Y/FiyinYvh149VU4HPQbAq00\n7AlGy73wZqmzk5zcK1cKZaLOKLbbyczFix+nK8iE4XQSYfX1iejjHDTA2liBuDggNb5T+aFaUish\nQRTASkryvboGE+ecQ+UPfv97Ink1SbG5q7PTvf+LF8jRZ3qiIi0WikSXSfvCC0nYRhOGFGH4Uhg8\nqbjnRCDo6qKd2UMPKQnDahV11TwpDLsdOO00fd/zzTfAX/4S2LHKYJOUV1x5JdkhZPQrDEum0j5m\nT/BPYdTWUg26waQw5PaqVivQGkuE0Zg5FvGt/VFAlZWitlZLi+H+6UbBJjs9Zg9AmKTkwAeOwquu\nBi69VLyWCYPBhKE2SfEOOj+/39xptw90WcpPdaIvJZVWQ8B3UgErjHBj+XI6mbKsHzaMyGT1anL2\n3HCD7o/jPJXOTv3XZjDAI2GkpqYiLS1N8y89lDMgALBE9lSHn5NgrFZBGP62mezsJL/cLbdQlElP\nj1CvXNzQk8I4+WT9c4LLBAQLuhTGP/5BPSEY3d20MqSnIzZLmZ1WnTQG/oDbg/o6lohFSWlATRg9\nqeQEaMkZg0RHP2E0NwvDvd2uaJATCiQm0nHpLSXOKpzVNkBrZH4+7RG2biWH9bFj2oShZZJiwsjL\nA9JSXYrStfkpDvSmZVLmKaCPMCK5ul5wgbg/bRrlGD3+OJ0MdRq7F/BLu7r0maQGCzwSRltbG1pb\nWzX/WgycuHAiJkZMIC00NNCgtlrFJpC7lRkFk0F8PP05nZQ8CpA9EtAOG83O1meOChV0m6TYI/rF\nF8Af/0isZbEgLkcQxqVjt+PdBe692PWASWCwKozCQmD1k3FAaipa88ciydFvkpIJo6VloCdzqJCT\nQ9ZCoyYp+fVjxpA/r6+PDv+LLwRhTJggYhrUJilWGIcOkTlq7Fjg2ssdZJOtrgbq6pCX3IbeRKuw\ntfjy/kdKYTAuv1wUfOO6aHwyfPR7l8FrkL/VoaMVuoMr6+rq0CEZ5kaMGBGSAwoUvIPSyo6sr6di\nf21tooQBRzIZheywTUxUlkznBB2tsNG77gqticIXfJqkeKRznN8vf0kOy/PPBwDE5aSjC/FIQDc+\naZ+B8a1e6np4AZOAHh9GtPRplwkjNha47DIAt2ehs2AkErtaMTynC9UtLQqFEWrCyMsjK5jeXSyb\npNSLGJc1aWkhezon3Q0bRr4OrlDQ1CT2Eqww3nmHImPT0oDf3WEHVoN2ZBdcgDO7LkZPvJXeFB8f\n/QoDEBd54kRygjscFIZmt5NJQkeIYXc3/QwuiBBN2dqBwKcPY926dSgtLcXo0aMxf/58jBo1yq3C\nbDTBmx9DVhjc9Mbf3atsbkpIUCbv8fdrmaTGjIlsqJxXhfHll6IdIRMHh75Mnw4AiMnMwF4L2Ska\nbbGKDmFGMNgVxgCyspA2Kgd2VzpSm/rD5Xgw1NWhtTW0u8u8PNqs6N3FZmSQxcgTYQC0Ju7dS/lr\nY8YAzzxDhRMdDmp5wh1tea698w7VGwNAHx4XR4RRV4eJXbvQldBf3iM/3zdhFBYqEzoiAb7IWVkU\nRVVcTM7v3l7d8fhdXUSgdjuNcW/10gYTfBLGXXfdhU8++QTjx4/H4cOH8d5772HOnDnhODa/4C3H\nor6eFmurVagAf3evsnpITKQ1YtYsalXpjTAiDa+EsXw5FWcDxElk4mB5vnAhfpP+KJoefBpOJ/wm\nDD7vg54wTjsNw04vRSNyMBb9ZMuJNmEwScmEoWdjPnIkhYF7IwyAXFinnkrmqHPPJYHgcFCgAtdG\nKi4mXti9uz+L2WYjZhk7lpyETU0Y4/wK9m4rbcrz832bpBYvpoilSEJOgHr4YbLL7d1Lz+k0S3V1\n0fltaho65ihAB2HEx8cjNzcXfX196O3txRlnnIHt27eH49j8grdCcKwweIcE+L8Yyf6JhAQy2WZn\nK78/GgnDq0mqtVV0vOEfUVsLPPooTWQAGDUKX2V/B/vmEbGEWmFEq9N7AE88geKzJ6PZko1x6K99\nVFFBO5OeHrTZekJOGBUVtKnXY1plwlArH06wZpSXU3AGIyWFvuebb4Bx4+i5tDRK8j/11H4L5tGj\nxES5ufQFNhtGtHyFxvZ+JnvgAe/1MaIFcXH0xxeuqEiE1+r03zJh9PZG3sIWTPj0YWRlZaG1tRXz\n5s3DlVdeifz8fKRGMWUWFJDPSt2YyOUSCkNWxbLCcDhok+Srjh6X/OAJxgpjMBCGV4XR2kqlFp58\nUiiM2loqkSC9yeUS8z5QwhhMeRiahAEyN1RnTMIC2ztwxcXBUlFB4W1WKzqanEhLC53TKi+P8nT0\nTslRo2h+8ILGsFhIZXR00Jrf0aG0DFmtVBsqLk5ZEO83v5GCTORyMdnZQH094tEJW3e/AV+rd2y0\nIjlZOBtHjBDzwYDCYL4J5YYh3PCpMF577TVYrVY88sgjOPfcczFu3Di8EUiKdIhx7rnAm28qn+OG\nRZxwJTO+vBitXUsVOH2hq4vIgqNH2IehJoz160OTrR0IvBJGWxtw3XW0MvCP0OgRyUEkQOgVRrQ6\nvdUoveMi/ADr0FtQJBpTWK24ZPV3cObXT4TsmPLyaJ3Wu4v1pDAAyg2aNUs85mg/QBSOVZt7TzkF\nOOPo8yTfuXRzRQUdWP+Cm9RKFWX9DWGPCNLShHefJRVg2CQFRFc/i0DhkzBSU1MRGxuL+Ph4LF26\nFCtWrEBOFJ+Bc84B3ntP+dxzz1H1TLmLY3U19WuRF6O2Nn0LoFo5sMLIyhKE0ddHG/W77gro5wQd\nXk1SbNhmR1BvLxlhvWRzH/dO735M/tnZaInJQE92f/hoWhpgtWJ47S6cv15fm2F/wNE3nZ3eX8fg\ny1tf704Yr71G5np2M8jzJTOT3FiaZq+lS2mM/PKX9OGvv06PR4/GlrI78FYXxZFHC/HrwpYtIgGK\nCSM72xBhMImHqixMJOCTMF555RWUlpYiPT096Il7GzduxMSJE1FaWooHH9SO51+xYgVKS0sxffp0\n7Ny50+dnFhe7t4Xcv58awMjF2QoKaGzLg5hbJPqCOlxWrTA2bybbbkqK/kZg4YJHhdHdTUkpXPzN\n4SDTQn6+W32dDz8Ujk9/O1kOGac3IzERcyc04/Dj/fK2tRWwWtFr6Q+PCeGPyMvTaIXqBWxq0gr1\nLCwUyXqyafall6gCuVd8/jn5uhYtooPKysLhn/wO9/bcAUA/qUUFZHnFhFFSopswurvF2I5iC75h\n+CSM22+/HevWrUNLS0tQE/d6e3tx0003YePGjdizZw9efPFF7OVIhH6sX78eBw8exIEDB/DUU0/h\n+uuv9/m5yckkfeXkvaoquoDqaD21Q5UbyPmCOiFPrTAAIg091UPDDY+EwSnJbLdzOulHzJ3r9tJ5\n88gp+vnndK79aUmg14cRTU5vh8N7PH2y1YK25Dwy7F92GWC1ItbVf3L8lWI68MMfGnv9qFG0iGkV\nGb7zTqovxRURGHFxQBx63HtEsJ2JS5Tz6tjfqVBuQzqoCEMGJx3m5ioTrrxAtkIcV4RRUFCASSEw\nxG/btg3jxo3DqFGjEB8fj8suuwyvv/664jXr1q3DkiVLAABz5syBzWZDrY8iUBYLLdyyUuAkPTVh\nqO3jegnj/vuVC11CAq0H6elKW3I0EkZmpofe4HKcJWc/fvSRSF9XYdgwSs3w18cwGE1SvspvDJT7\n/u1vgeuvH1hxOzPzA+sM5wOPPCLSZ/Rg5EjPvyM+nky1Z52l8c+vvurPVpTQ3k67kP/5H3rMHt5+\nhSFHJPqrRiMOi4WI8pZbgKefpsAQHxiqhOEzSmr27Nm49NJLsXjxYiT0nwGLxYILL7wwoC8+duwY\nSiTZV1xcjK1bt/p8TWVlJYapy2qqkJVF87O5meT1sWO0Q1Iv4FoKw2Yj/4OnFg89PcCf/qQ06ycm\n0mRQO9SjMRn+pz/tz0Hp7KQfwwcse0GtVpLeb7wB3Ojd/s4LutFWkoOVMLxF0CUnq8rS9BNG34jR\nYmfqclHXrYsuCtpxxcdTgp1esMLwhJISMkG5oaGBnH9yiCC3E2RDPRPGGWcAjY0KE96gVRgAbZy6\nuigk7Te/oZyll16iyK+qKrd6P8ctYdjtdiQnJ+Ptt99WPB8oYVh0dvBxqUIrPL1v5cqVA/djYspw\n4YVlOHSIFsdjx6jQpDrfUL075sKFdrtnRxUvCDab8nMAWnt5/S0oiE6FMeCOmH82LQC7d9NjuUqe\n1Ur5GKedBpxwgtfP89dkNBijpHyV31ATRk+CFUAsEscVC4Vhs1EEhjrT7tZbge9/nyr/hRi+CMMj\nGhtpglRVicHd3EySlT3l/MHSAvqf/wA/+ckgVhgMNiUMH049Cv7wB+DnP6f/qYrScSQlEF2EUV5e\njvLycr/f75MwnnvuOb8/3BuKiopQUVEx8LiiogLFcliGxmsqKytR5GGLJxPGp59SSCtAIaA9PVQ/\nT801WgoDEJsmLfCglxcxXvSsVkEezz0Xfc1PFPjwQ2XWrawweCFTmx804K8C6O4m8vJFGHJXt0jD\nVza13FAIAGxdViTEpiE9P08QBvsyDh9WkvFXX1EkQRgIY+5c4Kab/HgjHzu397PZRI9uHksaSQfn\nn09ugGhUGLNm0VTQvahnZ9Nv/Oc/iTh7ezXfLCuMaErcKysrQ5k0xlatWmXo/T4J4+abb4bFYhnY\n6VssFmRkZGD27Nn4Ade49wOzZ8/GgQMHcOTIERQWFuLll1/Giy++qHjNokWLsHr1alx22WXYsmUL\nMjMzfZqjAHH9pk6lENsxY7TrhWn5MADyY3iS+FqVcNUD4/33ad4bboMaDnz9tZj4crMY2Ydh1Z9o\nFYgP4777RJsET8jMVKq5SMKowmjssCI3MZWcpUwY7CT75hslYbS26gvRCwJyc4Fly3S88MgRZTNq\nmTAOHiRnx513EmGkpVEGo4cstcTE6CSMnTvp57CbtreXKrt4tQ4UFVHZc4uFnHmNjTQJduwgW/bJ\nJysII9pysQKBT8Lo6OjAvn37cMkll8DlcuGVV17B6NGjsWvXLmzatAl//OMf/fviuDisXr0a55xz\nDnp7e7Fs2TJMmjQJa9asAQAsX74cCxcuxPr16zFu3DikpKTg2Wef1fXZHMQ1fjzw1ls0rrWgpTAs\nFu+Oby3CkBUGENny5T5x7rmip6z842WTVE4O/QhPJ06Cvwqjq4v8S75i1NUBDJHACy+QWVOP01se\nH+2woisxjVZo9krLhCGjrS3yP1SNBQvInsQbi8ZGuuBHj1KIHEBNYIqLRbSJhxOUlBS9Jil5w/Ph\nh9QA7RPPLdrp97IpLjmZ7N6NjWRWaGsD/vY3dHeLsH1119fBDJ8/5YsvvsDHH3+MuP5ffcMNN+D0\n00/HRx99hKlTpwb05eedd55b5dvly5crHq9evdrw5/KcHD0aWLOGAla0wP2QGU4nKc62Ns+frTXo\no1F6egRP6JISsWO87Tay2/H/kpNJJulAID4MPWVTMjMjv45WVJAFyajCaI9JQXdiGiU3sN2Yz7ma\nMFpb9YXohRN1dcrCbI2NFBp35AiRxkknUYLbddfR/9lco4FoVRiAcg2oqxtoFugZRUUU9VJbSwOi\nre+rbygAACAASURBVI0U5KFDVM4XNL4zM4cWWQA6wmptNhvapBW0ra0NTU1NiIuLQ5LR0JgwYfJk\nWg+nTaN5KGf2y1DvjtvbaXPtqQETv0YNVhiDgjB4Qk+ZIhav558nZlX3M9aBQHwYeggjNZU+P5KR\nUh0dNI4ME4bFiu7kNPJNfP01PdnURGYMrq/PiDaF0dVFUl1hY2ukyJGDBylY4sIL6eRwJeOLLvKo\nSpOSoo8wOJ5GJoyGBuKB2FgvqTNLlwIrVhBxlJQQeezdS5uA6mrg6NGorCMXDOhK3Js5cyaWLl2K\npUuXYubMmbjtttvgcDhwlmawdoTw738P3H3mGRrTV1xBZim56qYMLYWhlzDkz+SB4TELOFJwudzT\nc5kwJkygH1xZSSGf7e0DTZKMIBCTlJ4JZbFE3o/R0UFrpy+nt5owHC4repLTaBAePkwfVFFBj9Wr\nURh9GLrAxydLaiaMXbtoK75wIT1/+eV0e//9HuOOOfQ8msAtDmQia2yk4+zr8zLmTj2VvOWLF9Oc\nycig7MlvvqHz8/XXxy9hLFu2DB9//DEWL16MCy64AB9//DGuu+46pKSk4KGHHgrHMeqDVHEwNpYu\nVmwsKcT+3j9u0HJ6Z2d7J4yODqpXJaeMJCbSYuEpdyNsqK5WepEPHBBlyRlsdiospB/7wQd0gpYv\nV9Z914lAnN56J1Sk/RhMGEYVhgMp6LWm0wApKaHktocecieM7m5ataLJJMVOejkscN8+8m3V1wMz\nZpCyaGrSJa2j0STF41Ytohg+j/d736MMx6++Es9NngwcOiTCajs6AFUwz2CGRwvb3r17MWnSJOzY\nsQMWi2Ugga6mpgY1NTWYJZe1jAb4Mdm0nN6+CEOrnlBCQpS0YKyqArZtE485ExEgteFyiXjxggJy\nxn70Ee2KnnzSr68MRGHobY0baT9Ge7s+k5S6F8uW4ovhmnAWJgO0uHLQhhw1BQinWTQpDD4+ngyb\nN1NjJFYQl1xCtzor60Wj05ungjzf5cui+3ivv54u/PnnU1hmP2EkJIBMVbffLlTYIIdHwnj44Yfx\n9NNP49Zbb9VMltu0aVNID8ww/KjVo6UwcnK8DxQtwuB6fREHN/RgtLfTYtTTA/z5z6RAeEUbPpx+\n7NdfU78LP2HU6d3XJ3wSg0lh2O00PrxdZ/VxNvZloaekf0G98ELK8J48mSTqww+L/tBtbTSo+M1N\nTWTeUDd1CSdkhfHee6RE2QT99de6IuhkRLPCkPN8GhuFUvS2cVTgl78U948cAT75BF2J/ePbbg9p\nHbFww6MR5brrrkN1dTXKy8uxadMmLF26FGlpaTjhhBOwdu3acB6jPgSoMLhgoR4fRtQqDO58w4zH\nP8RuF6GQbW3A3XdT9lZODjl7Aqi/bFRhvPUWsGSJfqc3QIcXaR9GXR2NF29RL9nZymHodEpjZdEi\nMhd++SWZdZKSRPx3ayuFara2UiLAzTdTBFIkwYTR1kZE8a9/iQquEyYYtr8aIYwxY6hCeqjhSWGw\nD183YcgoLQX27UNXF1Bw+BMKSzbEPtENj1d9+fLlSOwP//nwww9xxx13YMmSJcjIyHALfY0KBKgw\nOjpoQUhJ8e3DUAeHRZXCAEQJZrmOSWMj2aAdDipNkZpKhFFZ6bvPshcYJYyqKlpUjSiMvDwdoY4h\nBHOwr2ucna0chorNRVoaNZzghTYnR7y4rY3sbqmpdO1CWKhQE11d7okHfAybN9MtN0XyE0ZMUocP\n+8iDCBI8+TDWrCGO9GuNnzIFqK6Gta0OJdvWUgQOEF3mxgDgkTD6+vqQ3b+QvPzyy1i+fDkuuugi\n3HvvvThw4EDYDlA3mpoMt/SSFUZzM034pCTjCiMxMUoUBhMGb8fVhHHkiNJJyY2wAiQMvU7vjg4R\nhWKEMGbPVgYZhBu80PkijJwcpcLw2j8jNpZMgS6XKMvCNi3uXBcu7NgBXHutePzeexRbGh8PcA05\nhyMgwjBqkgpH/SW1wujrozYFpaXE334RRlwcMG8eJtWWw2qvEZu3IWKW8kgYvb296O5fCd59912c\nIaUv96gKbUUFYmIoWuHzz+mq//jH7rHuKiQkANu30zy46Saa8MnJxn0YCQlRojDYeapFGE1NNCOq\nq90JI0wmqZ/+lDZc7e3GnN6nnSY2upEAn0Z1eXw11Cap9nYvG4lDhyh9vLVVP2HU1gIbNxo9fHfs\n3w/86EficUuLckFbtowSDYuKRFICELDCiDbCUCuMY8foElitGpWHjWDuXIxt3o4kW414Lpoi4AKA\nR8K4/PLLMX/+fCxatAhWqxXz5s0DABw4cACZmg0VIozsbOCJJyh0cfhw4G9/A774wutb4uNpM3XK\nKVSsMDfX90DRMknNn08ldSIOWWF8+y2wZ4943NhIUS6Ae7PhABSGEad3XR1F+hpVGGPHimTaSIA3\nEL6qD6ek0CLEr1f4MNSoqKAFuaaGCCItja6DN8L4/e+B886jAdqfUewXKiuVc4MJgxV6WxuRChcD\n5XDrABWGkSipcCoMdnofOiSmiK+No1eMGoW89m+R2Dz0CMOjC+/OO+/EmWeeiZqaGpx99tmI6be9\nulwuPP7442E7QN3IyaFJ9MUXVCa2qMjnloY3VXfdRb4pVhi+TFK5ue5f7aHPUHghE4a8HWbCOPts\nmhW8igXJJKWXMHgddDrp0viqVMvg5L2WFvdzHw7wwuFLYVgsYs0fPtyHSaq4mD7w8GFaTLKy6EQ2\nNXmuTcPX6513aHPkr9pob6ex4nJRTkVLC62era3UBczhIOaTCWPvXvH9fiA+3q0CuCZ41x+OIhJq\nhaEmDL8VxsiRGNbxLRK6+wkjLm7om6QAYO7cubjggguQItlbxo8fH305GIBIz29spKQ07hrnBSkp\nNAe40VFurn8+jKgBLzTqrXhzMy1Ec+eS3pYdr0DYTFJMGM3N9D4jdXZSU5U5DsFCSQmZJb2ho4PK\n499+u+/Pk33ZPsdKQQEVg7z7bmJENkl5Igw2DR04QCfj9tv9y5psb6e5sXUrlSlhB1FjI63qzJBM\nGBMm0LHptSFqIC5OH2Fw4BhnYYcSah+GTBi8DrhcZJUzhBEjUNJxALHO/h8zcuSQURiRzk0OHoYP\nJ3nP99VZVBq4/XbaYOXn0xrqy4exfTtFUERpCS36vRkZyhCT2FgyTyUnUzltWevn5NB5CqCGgRGn\nNy8GNptxn09qqveikP6islLk03lCRwcFlnmoq6eAHCmlizAAOjFMGF9+ST82Ntb9xLIDdft2utYP\nPUTh0kbBCoNXQj4Bf/qTcmHjMNqpU8V9PxEXp2+csPstHG5StcKoqxOXJDmZlpOHHxbP6UZhITJ7\nm9Cb1t8PedSo6KnRHyCGDmEUFor7OgkDIDNCbCyRhi8fBjteo44wfvhD8ti1tdFuZtcu8b+xY4HP\nPqMfN2MGFU5jjBxJSREBQK/CWLVKEAZgnDC4KGgo8PHH3v/Pbav1YMwYEgAAbeK9Rs/JvV24a926\ndWTf1JJUHJr52WdiAfJn58qEwW1jeXX+wx8o8x+gC8s+izlzAo460GuSYk7s7Q3o63RBTRgtLbTf\nAmgdeOwxkZNnKACzXwm2n3YWsU1xcfR0AQsQQ4cwhg9X3rda6SJxdJCOt/vyYTgcwC9+oasRXXhw\nwQWU2PCvf1H4o8NBlVF37xaOyilTyORQWkr26QcfFO9PTaVdZQDQ4/Tu6wNWrlSacY06NUNlkgIo\nd5FRU0OJ2DK0Ah08Yfp04mvOofT6PnnrmplJq1VlJTBvnlJSdXfTdbbZiGQOHxaLfXU17WBlNvaF\n9na6KFVV7p3CeLPBk4GPLcAwQL0mKebBcBCG2und0iJUpFoZGg24OKXgCGyP/w3YsIFMwSZhRBmY\nMAoKlAojJ4fKd/uYULNmURl0LR/Gpk2kRP7xD5qvUdNJb8cO0QzJbqffO2kSbYcmTqTnp0yh2edH\n6XI9SEig8+Wt5Sfv5GJjaRMdE+O/SWrlyuCXmJAJ7+23ReoBQKfSH8LghcdrQvQFF4ie0JmZZDIs\nLaWQcFkh//SnFMRhs9H/u7sFmezdS2Pg2DHxuf/3f97tPzzAv/2WxoeMXbuIuCZOFD+at90BQC9h\nsMIIl0kqPl6QVEsL7akAQRgffkgxNNz/Si8O941EQnIskbkOf+pgwdAhjMJCmp233UaZXlarGH1/\n/Svwq195ffszz1C8v5bCOHyYbr/6KqBAkeDD6RRmCpuNFhEmCr4dN45mBT8OMhISaIf+pz95lu28\ndqWlUTRpWpr/JqlVq8T1CBbktVXtEuCOaexv9oUZM8Qm/Z57fLw4N5e62gG0KJ9+OoWz5ucrFcZz\nz9Gtzebe3IWLTbI/oqKC5sCRI0QiWhGNMmFwm9hrrqHSJbt2UW2M998nwkhODkqdbr0+jHCapHp6\niH+PHKHHHCQGCK4sKSGrrlHCUOQZsbUDoEmye3eghx4xDB3CKC4mm+svfiGipHbupP/V1dFE0gEt\np7dsColEWKdHOBzC0V9fTwtMaSmtbtxIOCWFWg+GUGFwSoAn0xQ/n54ukqL8MUnxTjBYXcx6ekgt\nxscL1aImDCPqAqANxUUXUauIlSt1vIEHlDq3iQmjp4fMRxxBpSaMTz+lWyaMt94Sj7dsAR591P07\nmTCOHhUK4+qrae4cOSLYPDnZ/bj8hF4fBl+HcCmMkSNpXDkcSoXB17yggKIodS4fA1DkGTFhdHRQ\n2D/3EQFop8XmxUGAodNAcPRopWMuJUVECx07pi/EBXRtOUSdTU8OB+00KioirDDWrqUidgkJtIh0\ndIgVrqKCiLGwkMwXY8fSypqcDPzzn+6mhyAhIYGsIgCtQ1q5FUwYfAmSkvxTGGx1CZZJqrOTTo/V\nSotFXp47YSxcaLxSx+OPG3Ap+CIMm43UBx+Eukosr2S8cWDFUV1Nf0eOCNsLQ1YYo0bRCUhPF4Ob\n2TwtLWgDXq9JisdKuBRGQoJIh5F9GHyKkpJEbo0RaBLGww9T1V85UOFPf6K1SyaRKEZEFEZTUxMW\nLFiA8ePH4+yzz4bNQ8jZqFGjMG3aNMycORMne2qbJ0N24MnhKQ4HlWTWQRqJiTR3ZCcX+5KBCBPG\nTTeRyQIQEpd9GN98QwMxP59WrNmzaaFJTibDeoiaC8vrkKdwZNkkBdAh+ePD4EovwSIMVg/p6WKB\nVxc59BVBpYWUFGUMhlcwYaj9BGlpFLF0993EZBkZ7gpj5kxxnxWG3U6fWV1NDNvbK2wuDF4Nu7po\nQJ91Fm00hg+nE8KEMWkSJQkGAUYJI1wKIy5OmJw44R5QEoTR8vrcdsbNJHX4MH1RW5uYFE1NPksY\nRRMiQhgPPPAAFixYgP379+O73/0uHnjgAc3XWSwWlJeXY+fOndgmNwbSA16ROH7c4dAdl1lcrLyG\nDoew6ESMMPr6iMWYXJkwjh4lRbFnDy0ssbGkQpKTBWGEECeeKO57Igy1wvDXJMXXJFiNeLQIgwPq\n+HbsWMHRIUFqKilHtZ9gzBjgqafI/yYnd8gtUEePplI4V14pCKO1lQYrEwYg4nwZspOupIRqiefm\nkg9wzBgxdywWP5IQtKHXhxFuhREfTxy8axddAl7kL71UWPOMEgYLuoHgGCaMykoxiBMSqIx9c7NJ\nGL6wbt06LOmP/1+yZAlee+01j691GaxAOwAe9JMnqz/Q51u1CKO0lMgigCoa/mPvXlocensFYbBj\n5ehR0tRZWe7b2jPOCDjhyhemT6c1qrTUt8I47TS69dckxdaXUBIGHysvXD5zKQKFxUJODzUmT6bd\nZ2enGHQTJ4r7nHR5//0U581Ks6VFSRjjx5P6lCFH7KgvxLhxISnkpFdhsHoMVx5GXBz5/T/5RPgv\nAIqGXLGC7hslDLc6aUwYx44p5fHq1fRiebF56CEKd45SRIQwamtrMaw/aWnYsGGo9ZB7b7FYcNZZ\nZ2H27Nl4+umnjX0Jz3I1YegYtVqEkZVF1ztElh3v2LlTGNfVCuPbb2nrPm6cO2E884wo7xBCpKbS\n6famME44QUQN+asweJgE2ySVluaZMLxWnA0lZJ9TVhbwxhvAK6/Q1vWBB0hp8GI/fz45U/fsoR8y\nfjwtOlVVFLbF9tUvvqAfK8cNqzFxYkClYjxBr9O7q4vMwuEwSbHCOOEEMj16slhnZZHAk/N1vEGT\nMBwOz0pC9qi/+GJghSVDjJAtfwsWLEANO+Ik3HfffYrHFotFswUsAHz88ccYPnw46uvrsWDBAkyc\nOHGgaq4aK6WQlLKyMpRx5jcTxtSpVHaho4NKoB84AFxxheZnaRFGSor+Ynl+4/HHgZ/8xP2L5NVV\nrTC6u4VzMoJNObzV4FJPIH99GIyKCmVEi7/o6KBjiajC8IQJE+ik9vaSqvje98T/fvUrIhDZOX3T\nTZSa3NICnHwy8MgjdP/qq2mn09JCq6Ivs+zddxvupqcHRnwYVmt4FcaUKaSS5cR7GVlZtGSUlurL\n+HYr3W+1umf+ZWXRwKuuVhJGW1tIu/OVl5ejvLzc7/eHjDDe8eIsGzZsGGpqalBQUIDq6mrk5+dr\nvm54/445Ly8PF1xwAbZt26aLMACIwGmuLLhuHbW97OigifPf/wrC+PBDRV/rkSOBl18WH8WEEXKs\nWkULw5tvUkMbju2T43plwuBKd+np5Ezw13wXBHirwaVux+qPSUouLX7nnfTzOefNX3gzSXV20gLH\nkTRhh9VKTtLTT9e2g1qtypN47bW08nV20uaoo4NUZ0kJ9XNfvZpWvLIy6nUBUEa5GiEa6EYIIzk5\nvAojLY2sgp4Sco0KLjeFwX5EuYtUQQF9cG4uKcO+PiJqLhEQIpSVlaGsrGzg8apVqwy9PyImqUWL\nFuH5558HADz//PNYvHix22ucTida+0MJHQ4H3n77bUydOlX/l4wZQ54s3oZmZIg+kXa7CIex24Ez\nz1SUD7n4YrqGW7ag//vDRBgdHbS7uPNOZWSLHKMpm6Rmz6b7dXXA9dcDN9wQhoPUhlYLzgULgF//\n2n3HdcklVC3BCOQ0ksbG4ISuc40oNWGkpNAxc/HAiGX2c9UCPYRRWCga0qenU/LdSSfRe48epdcf\nOCD8JZs3ezdNBRlGnN7hVhgAxR3861/arzOaiuJGGJz1KQ/iYcPIrDhihFAaQMgVRqCICGHccccd\neOeddzB+/Hi8//77uOOOOwAAVVVVOP/88wEANTU1mDdvHmbMmIE5c+bge9/7Hs4++2z9X2Kx0KRh\nw2RamrCb2O0ibr29nUanFBtttQJzZvei5AYyA4SFMFwuOhabjVYvOVabY/Czs5UKIy2NFpQo6ICo\nRRj79gG/+x1tquQJ9MMfGk8LsViA666jTZrLFZxq0bIPg0+xmjAi3np31CjtSCU1YQAiRDchgZTq\nwoUirO+GG6iT3qWX0uOsrLBW0TTiw7Baw6swfEFvlj/DY3Ow8eNpIOfmCsLIzhZxvS5X1BNGRBL3\nsrOz8e6777o9X1hYiDfffBMAMGbMGHz++eeBfxnXoYiLE6uazUaEwYs0QB5VKY07O64FRTvfBLq7\n4XDEh54wurtJ5bBzW00YEybQtlxWGCkptGuMguJWWiVVRo8W/oYAWikM4Kmn6BI+/nhw+tEwYSQk\nKAkjJ4cmfcT8FzKefFLbefaDH4gCkww5l4Obd7BptriYInAYYe6aadQkFW6F4QsTJuj3RatNsAMo\nLCQ1MXo0bfRmzaJ53t1N12n2bFqTqqrI7ySHUEcJhk6mtycMHw789rd0XzZJtbfTSsbb4ro6xbY3\nK65/BWlvDw9h8GrLpig5jq+1lWzUM2ZQhAxACkNrlxkhaCkMDuSy2YLnB+BNcTAVhlyinRVGZyft\nLCNOGJ6uLysFGVpFAtmcJS8+EfB1RaPTW6/CAKjgM7tDfcGjwhg+nK7RHXdQZBurv//9Xwp2YZP7\nk08SaTz5pL4vDCOGTi0pT4iPpxo5gPDMcoWz3btFb2NVaG9WbL9R2+kMj0lKru8DuCsMjoQ6epSU\nCCuMKIEWYbCv3m4PHmHwZjtYCiM5mYZId7fI0GWTlNee3NEILcLIyCBnahjCq73BiA8jXE5vdcUU\nbzDSk1yTMIqLqbtibi6ZGeUM4JtvJhMV1wWrq4tcA3sfGPoKQ4asMNi2wRnkdXWKl6ZbSGG4HGEm\nDE7AYsLo7KT76emUJZeZSbWhmpqiYPsr4IkwEhNJYQTDJMXfAwRfYXR30yIVG0vPtbbS0IiiU+wb\n6sKEgCALOcwsAjCiMFJSwqcw9LpxEhPp2DZsAM4+27tfwy2sFhChs//5j7tPKjOTouF4s9jb631H\n5FHChB5DX2HIkAlj5EgKW2QmVykMJoz2RqeiZEDIIBNGQoJYEe+8E3j1VVIYMTHA8uXAX/5Cfxde\nGOKD0g8tH4bDQdVKgmmSYoURCGG89BLlRzFhcBMoNlEkJFCqw913DzLCuPVW7Zatu3cbKG4VGhhx\negeqMHp7ya3nq7GXEYVhsdDYu+IK36XOva7nw4dr+xw5mo3hiTCOHQtDQphnHN+EwR5ZwE1hpLno\neVuVEx7SRIIL3p5/+y3tFD/9lBKxtm/vP6D+aK/TTgPefZciYKZPD8OB6YMnhcGEEWyF4XD4n/F9\nxRX0x2G1bJLiBSQhQfS0CHazppAiLk67FEwISn0YRTid3lxZw1fPop4eY5UbWC23tVHSvScTm18C\nwBNh3HILFU5l6E03DxGOP8J4/30ihxEjROxzfLybwkjpI4Vhr3YOtDb2G5995tnR+Je/UDw8b8+5\np8XWraQuPviAnmfCGD+e7J9XXhngQQUXasLo66PFNicnNAojP99/lcGf0dZGayk7vWXCYGgUKzDh\nB8Lp9GYF4Cs61YjCAMRmpa2N3A7qEl2MoBGGy0VJxvv20f033xSmLT0OoRDg+COMNWvofkGBWMRH\njHBTGCl9pDBaawNUGC4XZWF/9ZX2/996i3wS3G0eEM2Pfv5zYRPh0RoTQ8b1s84K4KCCDzVhsMM4\nJSW4Tm/OEs/MNNbGWgYTBpcXUSsMWfF7KHNmwiDC5fQuL6eam4BvwmhqMjYuZcJoafH8+R7Dar2B\nA1qYwTo7aRK1tRF5VFVRS19WGBHK1Tj+CAMAlixRxqGPGuW2Mlh7SWG01QdIGBwqxBEQahw7RqVJ\nOK0cIK9aXx/F2p96Kh2bXERxzJioyL2QIZcG6e4mHx43JwqmSSoxkVSBXDDQn88ARPCZmjAYsbEi\n7cVEYIiLI9XgK6I3EIWxdi3QX0ACgPc19eBBavXxgx/o/3weN9yhz5PJy2+FAShbejY1EWE0NdGX\ndneLJnEmYYQBfBXXrFGGII4cSQqjsZEuhMuF5G4iDGd9gCYptkV+9BF9tjoZ8dgx9ybVWVlECCee\nSKM6LE6UwJCcLLjx66/JB9DWRmog2HkYqamkDIx2wmPwsbDCkE1ScXHid/zjH5QsaCJwWCxEwL6I\ngLsg+qMwXniBSsYxvK2pu3ZRKS1PBQe1wPtN9pHoLbapC0wY06bRbUICrR2trYIwAFpHAN8OGhnv\nv09RHEHA8UUYvBIkJioJIzeXLkBuLm1v7rkHSV0t6IMFHU2SwlAv7HrAhLF7N/kjrr9e/K+vj0af\nenZEpOlGYMjLE1Y92WEcCoWRkqKs/2QUPJk9KQyeiz/8IZUjMREc6PFjBOL0bm6mtfWJJ0jheiOM\n+nrlZl4PmDC4L5U3hWF4vPN6dNlldDtmDPlYWWFwIm97OyVhGiGMzz4DNm0yeEDaOL4IQ/aSyiYp\ndXbWs88isasV9rgcdNn6FUZPD13EDRvc+3iqIZu3Ghqox0BFhbKGFf9Py7A7CAmjsFCcFiYMgAij\ntTV4CiMjg8y9gRCG7MNISxN5GEwYcnFgE8GDHj9GILWkeBPOnWa1CIMFfkMDDFsOeNyERGGMHUsd\nm9j0PG0aNU7r66NNJ/+4sWPJ/2qzUXa4HlRWBi266vglDFlhqLN3KiuR2FyNmthitDc6qaoCj46F\nC0UnIC24XBQWe/fdpCgaG6lDS0MD/dXUkJ2ju5tGnjquLz4+qjK49WL4cDGR5Jo77LMPFmHMmQP8\n+9/B82Gw01uOkjIJIzTQk4sRqMIAaCxq5QUBZIay22kqBqowgkoYycnUE5Y3r1OniioUe/ZQ1GRs\nLNWfSk6mvsF//SuF4ftKOKmspJPDB+5yUcl7T35VLzi+CGPkSHHVmTBSUugCLFokXldcjJTtH2BH\nwimIra9B6Zhe5ejwtjXh3uF//COwYweNzPx82hXs3Uue4eXLaRu+ebPoW8rIzo46h7YeZGfTKXI6\nyTTFizJzX7BMUhYLXbpgKgy1ScokjNBAr0nKX6c3b8ILCz0TRmcnTcH6euMKw4hJyu8NUlIS/ZWW\nKglj9WqqOPzHP9IJ+uYbOkk/+hFZPQDKIpejLXt6aFfE4brFxTTIY2KA3/zGr37txxdh/PnPwqeQ\nkUGrQ24uja7XXwe+/326P38++jKz8VXneCx1/AklW/6lHB3esn1YxbS20nc1NtJ3lJQoQ2u3b6ew\nDrWsHITmKIAW8oICMkvV1lJE8EknBV9hMAJxeqsVhjoPwySM0MAIYRg1SXV3Exl85zs0DrUIw+US\nr/NHYfC48aYwvv2W6oP6XYklNZXM5aNHi5a6jBEjBBtyEsjRo6I96OHDYo1hR0pODimJc8+l59kM\n8Mor2kmePnB8EUZ8vFjB8vKAP/yBLhBvHfLy6G/2bPTNmIXuLmqqFLNrp5Iw1Bljn38O3HWX+//Y\nDJWToySMmBgijE8/JRMXb7/j4iiMdpCC/Rh1dZRzKNdiCnZplUBMUnwsHR10fGqF8fzzyo6LJoID\nXz4Ml8t/k1RzM62zH3xA11CLMORuiv46vbOyxOdoKYzKSrIm6XUvuGH4cAqxHzuWTsKkScDDD9P/\n2CrCCgMQvdsBmhAcecIHxwf7xhuUPlBRQd8xf75fh3d8EYaM2FhK10xNFXbD/Hz6u/pqWB5/KCyZ\nuQAAGlJJREFUHOnoX5G+/JIuwIQJwMqVytLjAPDss8B991HNJ84aAkhd1NRQ7F5JiVA3p59O5qqu\nLhoE3IN5/XrgmWdC/tNDhYIC8q25XMIUFaqS/oGYpLi5YkwMKSO10/uccyhCykRw4UthcKkOvXWn\nZNhs7nEsasJgU39Xl39O76QkpRVHS2HY7dpFgw1h5EhRzdbpFL2I+QutVpHO3tMjCKO1VQTcMGHE\nxND9uDg6QRUVStViEMdXtVotyITBCiMjA3EZGfhZzf+g8bPzkbNwDoWlnXgi/W3YQNvnk0+m9/HF\nXbGCRu7s2RTl8M03tI0tLhYXculS4PzzqbRHXh6tWBxbPciRk0MO7/x84YY580zy+Qe7WKo/hPH1\n18IsAdBcAtyLD5oIDXwRAVtR9ORrqNHcrOy97Y0wdu2iaWnUhJ+YKFyR2dnaCsNuD3JvKi4FAogC\nksnJyh7FaoXx+us06QAyY/H6lplJJixuW+0HTML4wx9EWehp/7+984+J8r7j+PsOuQLl+NUiAw+L\nKIjg8WNa7NrpyPRUiljRtDrTlVKXbN2sS3XrthintCmzW5osmcmSLbP1j84sbrvSho3qutHYroxW\nxVq1lTqZKD80CKzAIgLP/vj0y/NwPHf3HNzzPHfH55UQ7o7n7r4899zzfj6/Cylg/QWJaTHA+vuB\nsjLqORAXR0flv/5FA41EUEootnBuFhcD3/se8MQTJCDz5smm4uOP0+S8kZHAL3FCnJQU+jIp6wwt\nFjLQgk1CAhVp/f3vJEpa2LGD8gxWrJDXC3iv9GaCiz8L4+ZNuujQ2ndKSX//VMHwbIYpLhR++UuK\nHwfa9DUpiRwILpec5Cg4d47O0UGxMAQxMfLsHtGCF5D9vGJHnT1LFsd//0v3N22icxRAwXPlP9DR\nMSPBmL0uKUFRkew/WbOG0mGVWCzkbgLoKBRH5blz5GtUjnn9ylfoQ0lJoSP/5k1ySWVkyAGmxET6\nwBMSwqKCOxBSUugqPpDq2elSWkqGm/heaEE09710iT6m116j+56V3ow++BOCjg66IJ6OhSGKMAW+\nLIzOTvXRIf746U9pWN5PfkIWs/L1CwspftLfH0TB2LGD8oAB2X8KyIKxbJncOPXhhyeb3J9+ShbJ\n3r3yY4mJZGHMwCVlimAcO3YMBQUFiIqKwunTp71u19jYiLy8POTk5OC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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now we cross correlate the two signals." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plotcrosscorr( datax, datay, deltat, lags, rmin=0.0 ) :\n", + " cross_corr = []\n", + " for lag in lags :\n", + " lagi = int( lag/deltat )\n", + " if lagi > 0 :\n", + " r = stats.pearsonr( datax[:-lagi], datay[lagi:] )\n", + " elif lagi < 0 :\n", + " r = stats.pearsonr( datax[-lagi:], datay[:lagi] )\n", + " else :\n", + " r = stats.pearsonr( datax[:], datay[:] )\n", + " cross_corr.append( r[0] )\n", + " plt.plot( lags, cross_corr )\n", + " plt.xlabel( 'Lag [s]' )\n", + " plt.ylabel( 'Cross-correlation' )\n", + " plt.ylim( rmin, 1.0 )\n", + " plt.show()\n", + "\n", + "lags = np.arange( -2.0, 2.0, 0.05 ) \n", + "plotcrosscorr( colored_noise, filtered_noise, deltat, lags, rmin=-0.1 )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are several things to note in contrast to the auto correlation:\n", + "* the maximum cross correlation can be smaller than one (here this occurs because of the filtering and because of the added independent noise)\n", + "* the maximum cross correlation is not at zero lag\n", + "* the cross-correlation function is not symmetric with respect to lag zero\n", + "* the shifted peak tells us that the filtered noise lags behind the colored noise\n", + "* and again there is a finite correlation time between the two signals." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Point process data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Point process data are sets of time points $t_i$. As a countinuous time series, point processes can be expressed as delta function combs:\n", + "$$ x(t) = \\sum_{i=1}^n \\delta(t-t_i) $$\n", + "This is a sum of Dirac delta functions shifted to the time points $t_i$ of the point process." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Generate periodic time points that occur every 12 seconds with some jitter:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def printpoints( x ) :\n", + " print 'ti ||', ' | '.join( [ '%5.2f' % v for v in x[:10] ] ), '...'\n", + "\n", + "tmax = 10000.0\n", + "period = 12.0\n", + "periodic_chirps = np.arange( 0.0, tmax, period )\n", + "periodic_chirps += 0.1*np.random.randn( len( periodic_chirps ) )\n", + "printpoints( periodic_chirps )" + ], + "language": "python", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ti || -0.07 | 12.07 | 24.02 | 35.91 | 48.05 | 60.06 | 72.05 | 83.97 | 95.94 | 108.08 ...\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.eventplot( periodic_chirps[periodic_chirps<100.0], colors=[['#ff0000']] )\n", + "plt.xlabel( 'Time [s]' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The mean of the point process is\n", + "$$\\langle x \\rangle = \\frac{1}{T}\\int x(t) dt = \\frac{1}{T}\\int \\sum_{i=1}^n \\delta(t-t_i) dt = \\frac{1}{T} \\sum_{i=1}^n \\int \\delta(t-t_i) dt = \\frac{1}{T} \\sum_{i=1}^n 1 = \\frac{n}{T} = r$$\n", + "its average rate $r$ (number of events per time).\n", + "\n", + "However, the variance of a point process is not defined/infinity:\n", + "$$\\begin{array}{rcl}\n", + "\\sigma^2_{x,x} & = & \\langle x^2 \\rangle - \\langle x \\rangle^2\\\\\n", + "& = & \\frac{1}{T}\\int x^2(t) dt - r^2\\\\\n", + "& = & \\frac{1}{T}\\int \\sum_{i=1}^n \\delta(t-t_i) \\sum_{k=1}^n \\delta(t-t_k) dt - r^2\\\\\n", + "& = & \\frac{1}{T} \\sum_{i=1}^n \\sum_{k=1}^n \\int \\delta(t-t_i)\\delta(t-t_k) dt - r^2\\\\\n", + "& = & \\frac{1}{T} \\sum_{i=1}^n \\sum_{k=1}^n \\delta(t_k-t_i) - r^2\\\\\n", + "& = & \\frac{1}{T} \\sum_{i=1}^n \\delta(0) - r^2\n", + "\\end{array}$$\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "rate = len(periodic_chirps)/tmax\n", + "print('rate: %g Hz' % rate)\n", + "print('inverse period: %g Hz' % (1.0/period))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "rate: 0.0834 Hz\n", + "inverse period: 0.0833333 Hz\n" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "For computing the auto or cross correlation we need to convert point process data to a time series.\n", + "\n", + "One way to do this is to use the histogram function and create a time series that is one whenever there is an event and zero otherwise. After multiplying the histogram with the inverse binwidth, this is an approximation of the delta function comb. The mean over the time series is then the expeted firing rate." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "deltat = 0.02 # 20 msec resolution\n", + "time = np.arange( 0.0, tmax, deltat )\n", + "data, time = np.histogram( periodic_chirps, time )\n", + "data /= deltat\n", + "print('rate: %g Hz' % (np.mean(data)))\n", + "plt.plot( time[time<100.0], data[time[:-1]<100.0], 'r-' )\n", + "plt.ylim( -5, 60 )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "rate: 0.0833002 Hz\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 54 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variance of this time series depends on the bin width:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "deltats = np.arange(0.01, 0.2, 0.01)\n", + "variances = []\n", + "for dt in deltats :\n", + " vtime = np.arange( 0.0, tmax, dt )\n", + " vdata, vtime = np.histogram( periodic_chirps, vtime )\n", + " vdata /= dt\n", + " variances.append(np.var(vdata))\n", + "plt.xlabel('Time bin [s]')\n", + "plt.ylabel('Variance [Hz^2]')\n", + "plt.plot(deltats, variances)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In particular, the variance diverges for small time bins." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Autocorrelation of this point process:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lags = np.arange( -30.0, 30.0, 0.1 )\n", + "plotautocorr( data, deltat, lags, rmin=-0.1 )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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zZsxQbW2tJGnZsmXmdQa4BAQCLnt+v7/R/Y098KZHjx5at26doqKi9Nlnn+nL\nL79UTExMs8cfOnSotm3b1uhr3H0ekYQpI6AVDhw4oFGjRsntduvBBx/U3//+90bbde/evUUXpr3x\nxhtci4CIwQNyAACSGCEAAOoQCAAASQQCAKAOgQAAkEQgAADqEAgAAEnS/wN298/6DMuk8QAAAABJ\nRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This depends on the bin width of the time series:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "deltat = 1.0 # 1 sec resolution\n", + "time = np.arange( 0.0, tmax, deltat )\n", + "data, time = np.histogram( periodic_chirps, time )\n", + "plotautocorr( data, deltat, lags, rmin=-0.1 )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GviLT82uhGBBmzpyJFStWoK6uDnV1dVi+fDlmzpypuOGqqiqkpaUhJSUFMTExKC4uRmVl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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively to the histogram binning we can convolve the point-process with a Gaussian kernel with some standard deviation. The standard deviation of the Gaussian determines its width and thus is the equivalent to the bins of the histogram method.\n", + "\n", + "Convolution of the delta function comb simplifies to placing the kernel $k(t)$ at each time point and summing up:\n", + "$$ \\begin{array}{rcl}\n", + " x * k & = & \\int_{\\infty}^{\\infty} x(\\tau) k(t-\\tau) d\\tau \\\\\n", + " & = & \\int_{\\infty}^{\\infty} \\sum_i \\delta(\\tau-t_i) k(t-\\tau) d\\tau \\\\\n", + " & = & \\sum_i \\int_{\\infty}^{\\infty} \\delta(\\tau-t_i) k(t-\\tau) d\\tau \\\\ \n", + " & = & \\sum_i k(t-t_i)\n", + "\\end{array}$$\n", + "\n", + "So let's convolve the point process with Gaussian kernels:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def gauss_convolve( time, points, sd ) :\n", + " gtime = np.arange( -4.0*sd, 4.0*sd, time[1]-time[0] )\n", + " gauss = stats.norm.pdf( gtime, scale=sd )\n", + " ngauss = len( gauss )/2\n", + " data = np.zeros( len( time ) )\n", + " for x in points :\n", + " inx = int(x/deltat)\n", + " if inx-ngauss < 0 :\n", + " n = ngauss-inx\n", + " data[:inx+ngauss] += gauss[n:]\n", + " elif inx + ngauss >= len( data ) :\n", + " n = inx+ngauss-len(data)\n", + " data[inx-ngauss:] += gauss[:-n]\n", + " else :\n", + " data[inx-ngauss:inx+ngauss] += gauss\n", + " return data\n", + "\n", + "deltat = 0.01 # 10 msec resolution for plotting\n", + "time = np.arange( 0.0, tmax, deltat )\n", + "data = gauss_convolve( time, periodic_chirps, 0.3 )\n", + "plt.plot( time[time<50.0], data[time<50.0], 'r-' )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 67 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is now a time series and we can compute the autocorrelation as usual:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plotautocorr( data, deltat, lags, rmin=-0.2 )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the peak values and the negative values. The latter get larger, the wider we make the kernel.\n", + "\n", + "The autocorrelation thus heavily depends on the bin width we choose!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can compute the autocorrelation integral for point processes before we turn the point process into a time series:\n", + "$$ \\begin{array}{rcl}\n", + " \\int x(t) x(t-\\tau) dt & = & \\int \\sum_i \\delta(t-t_i) \\sum_k \\delta(t-\\tau-t_k) dt \\\\\n", + " & = & \\int \\sum_i \\sum_k \\delta(t-t_i) \\delta(t-\\tau-t_k) dt \\\\\n", + " & = & \\sum_i \\sum_k \\int \\delta(t-t_i) \\delta(t-\\tau-t_k) dt \\\\\n", + " & = & \\sum_i \\sum_k \\delta(\\tau + t_k-t_i) \\\\\n", + " & = & \\sum_k \\sum_i \\delta(\\tau -(t_i-t_k)) \n", + " \\end{array} $$\n", + "\n", + "That is, shift one point-process to the times of the other point process and compute a histogram or kernel density." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " def points_autocorr( data, lags ) :\n", + " rel = []\n", + " for x in data :\n", + " rel.extend( data[(data>=x+lags[0]) & (data<=x+lags[-1])] - x )\n", + " h,_ = np.histogram( rel, lags )\n", + " return h\n", + "\n", + "h = points_autocorr( periodic_chirps, lags )\n", + "plt.xlabel( 'Lag [s]' )\n", + "plt.plot( lags[:-1], h )\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 69 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Better is it to normalize the result to probabilities, i.e. rates." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for bin_width in [0.2, 1.0, 6.0, 12.0] :\n", + " lags = np.arange( -50.0, 50.0+0.5*bin_width, bin_width )\n", + " h = points_autocorr( periodic_chirps, lags )\n", + " plt.xlabel( 'Lag [s]' )\n", + " plt.ylim(0.0, 1.1/bin_width)\n", + " plt.plot( [lags[0], lags[-1]], [rate, rate], 'r')\n", + " plt.plot( lags[:-1], h/(lags[1]-lags[0])/len(periodic_chirps), 'b' )\n", + " plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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kkZ2C2V+7JtcssaO0zYgOCrHQltCwesI8LU1+rt7SYAqxsMtks7NlfLVtFxPB\nPXtmGkYasl1lfkZ12JnUqm84mg4KsTBicBwLezVQ0kEdNvsYUGlAFHpPRoYuqMSCDW6yDtXVOJRi\nwWbPTIJ7s7Q0aDpUXxNKsVCtg4IGSjqok9DsGxoaUF5ejrKyMuzfvz/qMbt27UJZWRkqKytx5syZ\n8Z8XFxdj5cqVWL16NW655RbrVDtAfr6cDBwZSXysXT0ngEZDNrJTlJ0TYBSeMCj0qAEavWoKbdOI\nDrsqglKFjHgvhsNh7Ny5E6+88goKCwtRXV2N+vp6VFRUjB9z7NgxnDt3Ds3NzXjzzTfx0EMP4eTJ\nkwAAn8+HxsZG5Nsxc2kz6enS8Ds7gYUL4x9r99jshx/qO9auhhy5U1SitWbsTurLlxMfFw5LrQUF\n1muYPVt+/uCgjEk8KBic1TtlRTJvnswPIRJPQtudI3pufL29sqLLqp2yUo24PftTp06htLQUxcXF\n8Pv92Lp1K44cOTLpmKNHj+L+++8HANx6663o6enB1atXx18XRvcMI4TehLIzqfX2ZoeGZCleTo49\nOijEQq+Gri5Zspqebr0Gny+1YhEMWrtTViQzZujfLtLupxzV1yMViGv2ra2tWLJkyfj/i4qK0Nra\nqvsYn8+H9evXo6qqCs8995yVuh1Bb4+BSlIHAvYktaYjVWJhdy213iEUCrGw2+Ao6KCgIRWIO4zj\n0+kcsXrvf/vb37B48WIEg0HU1taivLwc69atm3bcnj17xv9dU1ODmpoaXb/Xbij0GCgZXKrEgorB\nUSi9tLNHDUzc+JYtS6xDdSxS/QtVjY2NaGxsNP3+uGZfWFiIlpaW8f+3tLSgqKgo7jGffPIJCgsL\nAQCLFy8GAAQCAWzatAmnTp1KaPaUoJBQqWZwFJKaY+GMBio6KGhwgqkd4b179xp6f9xhnKqqKjQ3\nN+PixYsIhUI4fPgw6uvrJx1TX1+PX/3qVwCAkydPIi8vDwsWLMDg4CD6+voAAAMDAzh+/Dhuvvlm\nQ+JUQ6ERaZNgiTaJ8EpSt7cnrgrySixUazCig8pTTiqbfbLE7dlnZGTg4MGDqKurQzgcxvbt21FR\nUYFDhw4BAHbs2IE77rgDx44dQ2lpKbKzs/H8888DANra2rB582YAwOjoKO677z5s2LDB5tOxlkAA\nePfdxMfZ2ZD9fllJ0dUVf70ZJ5L60qX4xwhhbyyysyd2ioo3EU3B4LSdsuwqRMvPl0tTjIzINhIL\nu/db1ROb35wIAAAS4UlEQVSLgQHZNqzcKSsSI3Monw42eJK4Zg8AGzduxMaNGyf9bMeOHZP+f/Dg\nwWnvW7p0Kc6ePZukPLXomZS0s8wvUodWVRELJwzuH/+If0xfn/2lbVosEpn98uX2amhujn+MnUto\nAPpLg4NB4MYb7dEAyFh8/HH8Y+wuHsjOlk++icphg0GgstIeDakAf4M2DnomJTs75SqEdpT5aejp\nPTlh9olufE48JlOJhWoNVHRQ0KC3HDbVJ2iThc0+Dnobst0NiEJD1nPjY4NzToMRHarLUCnFwstj\n9mz2caDSgCj0qinFQs+NT/VTjt0aNB2qrwmF66FXB5s9E5OCAjkePzoa+xgnGjKFXnUgkHh9HCpm\n70RvVvX1AGgYHIXrASR+wvD6ujgAm31c0tPlWjCdnbGP8UpS69kpyqkeXLykHhuTlUt2TpjPmSOX\nphgain0MhSe+4WFZCWP1TllTNaRCJ6CvT+78lmg9IzfDZp+ARI2IQkMeHgauX5frwajU4VQPLp6G\n7m5ZqROvHDFZfD5ZGUU9Ftr2kHZVwQBykbzMzPidAAo54vVePcBmnxAKjUiPBruTWtMRrydJJRZO\nJDUFHRQ0aDq4XdCHzT4BFHqzepLJiZKyRD1JLyU1BR0U2iaQuF1QmKBls2ezT0gio6UwQcsG56wG\nKjooaNCrQ/UELZs9m31CKBhtovVxKCU1G5zES71ZCjr0XA8vf6EKYLNPCIWGPGOG/Ep4rE0iKCS1\nU6Vt2k5RAwPRX3fCZIH4T3xOLKEByM/v7pa/LxpOxiJWu7h+Xa7fY9emOno0ANyzB9jsExKvETlR\n5qdHB4WJOM18s7Pt1ZDoq/EUxqmdWEIDkKWEubmxS4MpdAI0DXYXD+TkxC+HZbNns09IPIPTtr+z\ns8xPjw6nHlHjGZxTJqtHBwWDoxILp9pFvLbpxPXQ0wlgs2fiEi+ZnGrIiXRQMTinYkFBBwUNVHRQ\nuvGp7hBRhs0+ARSSiYoOChqo6KCggYoOChoo6aAKm30C4k2Cea0haxqifTXeq7FQqYGKDgoa4ung\ndXEkbPYJ0CbBurqmv0ahITupIytrYqcoVRqA+EmtLRFgN3l5clI6FJr+mpPDe7Fioe2UNXeucxqo\ndgIGBuSYvt3FA9Rhs9dBrMlRJ8cjY2kIhaT52rnYlR4dTid1NA3XrsldsjIz7deQliaf+jo6pr9G\nweA6OuzdKSuSWbNkpyhaJ4DCjY979RI2ex3EmhylMEGr9WSdSOp4OigktZMaNB1Ub3xOdkSA2JOj\nFCZoeXJWwmavAwo9BgoaEulQXW6owuBU64ingUq78FqOUIXNXgcUGhEFDVR0UNBARQcFDVR0UNBA\nGTZ7HVB5XI+2SQQntRoNVHRQ0EBFBwUNlGGz1wGFx/XMTLlb1NT1cbyY1LF2iqIQCyeX0ADkfE1X\n1/RF8lTMX0yNxdCQ/GP3pjrxNAA8Zq/BZq+DWEnd2elMmZ9GtJuOCoOb+pRz/brcp3f2bGc0xNop\nioLZd3XZv1NWJH6/jHt39+SfU4iFpsHudXE0cnNlWxwejq7D67DZ6yBaQ+7ulknmVFLH0uF0ryXe\nDceppAai33QoGZyTxNKhuhrH6VjEWh+HzV7CZq8DKg2Igg4KNxyAzlOOapMFaBgthbZJSQdF2Ox1\nQKEXqelQ3ZApaKCig4IGKjooaKCkgyJs9jqINgmmogdH4aZDJZliPWGonr+gEgsK7cLp6xFPB0/Q\nstnrwu+XFSCR6+OoaMgUhi6ys2X5Z+ROURQMTsViV/n5QG+vXIdGg0IsRkdl1VZ+vjoNAI0hrYEB\n2Ta8vi4OwGavm6mNmUpS9/Y6m9TaJFhkQlGIRV+f3L5x1iznNKSny9hH7hRFIRadnXIBNLt3yopE\nM1NqnQAVxQNUYbPXCUWzd3Kxq0imPmFQiIWqcdmpOigMXajoUQPTe9VebhcUYbPXCTdkWjooPF1o\nOijEQrUGKjqi3Xx5vF7CZq8TKg2ZosFRKL2kEgsK49RUYkHlKYd79hI2e51QMLhAYPL6OFSSmkIP\njmOhVkMsHV698VGEzV4nFBJq1iw5Cdnbq04DQCMWeXnA4ODEV+MpxEII55fQAOTvi+wEqOhRA5Nj\nMTwsr49Tm+pE0wCw2UfCZq+TyCEUJ7e/i6ZDa8wqDU6LxfCw/DNnjrMatPVxtJ2iVBqcFoueHrl1\n44wZzmrIzJS/V1skj8KNT8sPp6tgtE6Atl2kqnZBETZ7nUSOEWtJ7cT2d1OJTChVk0+RsQgG1SQ1\nMP3GRyEWqoyFSiy0G5+qWPh8k7eLVBULirDZ64RCj5qKDgoaqOiYevPlWKjVQEkHNdjsdUKhRw3Q\n6D1RSabIIRSOhXodnCO0YbPXybx5cvJtbIyTmlJSU4qFyiEDCgZHoW1S0kENNnudzJgxsUmE1xty\nTo5cD2ZwkGNRUCDbRDhMIxbhsLM7ZUXTANCIxeCgXFIkJ0eNDmqw2RtAa0QUGnI4LE1GRVJHbhJB\nIRbaeiwqFrvKyJA7JHV10YhFV5fUk5HhvIbZs6W5UukEaBp4XRwJm70BKBmcisWuItGGUCjEQvWj\nOgUdkRpUDSX5fNwuKMNmbwCtEakep25vV9+QKSRU5PVQHQvV14TC9YjUwTlCDzZ7A3BS09JBoTcL\nTPRmKZRecrug0wmgBpu9AfgRlZYOCjdfTQeFWKjWQEUHlU4ANdjsDUChIWdlyXH68+fVJ3V7u9rH\n9fx8oL8fuHxZfSyCQfmtTdUGp7o3GwjI69HfL+eUVGlQnacUYbM3AIWk1nS89576oYvLl9UsdqWR\nliYN/4MP1F+Pjz6Sy2fMnKlGg7ZI3kcfqW8XTU1qNtXRmDtX7lx25QqbfSRs9gYIBIBz59QmNTCR\nUKoN7v33ZemnytK2QIBGLFRroKJD06DyhpOWJtvl+++rvyaUYLM3AAWTBSaMVnVSq9ZARQcFDVR0\nUNCg6VB906EGm70BAgE5bEGhIavWQUEDFR0UNFDRQUEDJR2USGj2DQ0NKC8vR1lZGfbv3x/1mF27\ndqGsrAyVlZU4c+aMofemEtr69aobkPb7VSe1ag1UdFDQQEUHBQ2UdFAirtmHw2Hs3LkTDQ0NaGpq\nwgsvvID3339/0jHHjh3DuXPn0NzcjJ/97Gd46KGHdL831cjMlJt0GGlAjY2Nluug0JBzcwG/Hxge\nblQnAhMxsOtxXc/1o9YJ0Lupjlvbpvb709MbHd9UhzJxzf7UqVMoLS1FcXEx/H4/tm7diiNHjkw6\n5ujRo7j//vsBALfeeit6enrQ1tam672pSCBgzFjsSCjt96vYKUtDWx+np6dRnQjIWGRmynVZ7EDP\n9ZsxQ1YkqR4fnj9fVqL4/fqOt6Ntzpkj40EhFrNmNfK6OBHENfvW1lYsWbJk/P9FRUVobW3Vdczl\ny5cTvjcVmT+fRq8lP1/NYldTdahYfGyqhkBA/WJXmg6va9A6Aap1UGib1Ihr9j6dGSS0nY49wIIF\n8o9qDap7TpoO1QlFKRaqdVBom1R0LFhg39NeqhK3b1hYWIiWlpbx/7e0tKCoqCjuMZ988gmKioow\nMjKS8L0AUFJSovumQoUXXwS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+ "text": [ + "" + ] + } + ], + "prompt_number": 91 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, what we want to compute is\n", + "$$\\begin{array}{rcl}\n", + "\\rho_{x,y}(\\tau) & = & \\frac{\\langle (x(t-\\tau)-\\langle x \\rangle) (y(t) -\\langle y \\rangle)\\rangle}{\\sqrt{\\sigma_{x,x}^2 \\sigma_{y,y}^2}} \\\\\n", + " & = & \\frac{\\langle x(t-\\tau) y(t) \\rangle-\\langle x \\rangle\\langle y \\rangle}{\\sqrt{\\sigma_{x,x}^2 \\sigma_{y,y}^2}} \\\\\n", + " & = & \\frac{\\frac{1}{T}\\int x(t-\\tau) y(t) dt - \\frac{1}{T}\\int x(t) dt \\cdot \\frac{1}{T} \\int y(t) dt}{\\sqrt{\\frac{1}{T}\\int x(t)^2 dt \\cdot \\frac{1}{T}\\int y(t)^2 dt}} \\\\\n", + "\\end{array}$$\n", + "\n", + "We still need to subtract the average firing rates (shuffle corrector) and divide by the variance..." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hn=(h/tmax-(len(periodic_chirps)/tmax)**2)\n", + "plt.plot(lags[:-1], hn)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 71 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file From 849f1d8f0d6135d1f9a87b18832c24333435e128 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 11 Jan 2021 22:00:25 +0100 Subject: [PATCH 72/87] [logisitc] added code on AUC interpretation --- logistic/code/logistic.py | 156 +++++++++++++++++++++++++++++++++ scientificcomputing-script.tex | 24 +++-- 2 files changed, 174 insertions(+), 6 deletions(-) create mode 100644 logistic/code/logistic.py diff --git a/logistic/code/logistic.py b/logistic/code/logistic.py new file mode 100644 index 0000000..18d500c --- /dev/null +++ b/logistic/code/logistic.py @@ -0,0 +1,156 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.stats import ttest_ind, mannwhitneyu + + +def auc(n, dx, uniform=False, plot=False): + # loser: + if uniform: + x0 = np.random.rand(n) + else: + x0 = np.random.randn(n)*0.3 + y0 = np.zeros(len(x0)) + # winner: + if uniform: + x1 = np.random.rand(n) + dx + else: + x1 = np.random.randn(n)*0.3 + dx + y1 = np.ones(len(x1)) + + # combine into a single table: + data = np.zeros((len(x0) + len(y0), 2)) + data[:len(x0),0] = x0 + data[:len(x0),1] = y0 + data[len(x0):,0] = x1 + data[len(x0):,1] = y1 + + # fraction of overlapping data values: + si = np.argsort(data[:,0]) + i0 = np.argmax(data[si,1] != data[si[0],1]) + i1 = len(data) - 1 - np.argmax(data[si[::-1],1] != data[si[-1],1]) + overlap = (i1-i0+1)/len(data) + + # Cohen's d: + m0 = np.mean(data[data[:,1] < 0.5,0]) + v0 = np.var(data[data[:,1] < 0.5,0]) + m1 = np.mean(data[data[:,1] > 0.5,0]) + v1 = np.var(data[data[:,1] > 0.5,0]) + cohensd = (m1 - m0)/np.sqrt(0.5*(v0+v1)) + + # t-test: + ttest, p = ttest_ind(data[data[:,1] > 0.5,0], data[data[:,1] < 0.5,0]) + + # Mann-Whitney U: + mannu, p = mannwhitneyu(data[data[:,1] < 0.5,0], data[data[:,1] > 0.5,0]) + + # ROC: + thresh = np.arange(np.min(data[:,0])-0.1, np.max(data[:,0])+0.2, 0.01) + true_pos = np.zeros(len(thresh)) + false_pos = np.zeros(len(thresh)) + for k in range(len(thresh)): + true_pos[k] = np.sum(data[data[:,0] > thresh[k],1] > 0.5)/np.sum(data[:,1] > 0.5) + false_pos[k] = np.sum(data[data[:,0] > thresh[k],1] < 0.5)/np.sum(data[:,1] < 0.5) + + # AUC: + droc = 0.001 + xroc = np.arange(0.0, 1.0+droc, droc) + yroc = np.interp(xroc, false_pos[::-1], true_pos[::-1]) + auc = np.sum(yroc)*droc + + if plot: + fig = plt.figure() + ax = fig.add_subplot(211) + ax.axvline(data[si[i0],0], color='k') + ax.axvline(data[si[i1],0], color='k', lw=2) + ax.plot(data[:,0], data[:,1], 'o') + ax.plot(data[data[:,1] < 0.5,0], np.zeros(len(data[data[:,1] < 0.5,0]))-0.5, 'or') + ax.plot(data[data[:,1] > 0.5,0], np.zeros(len(data[data[:,1] > 0.5,0]))-0.5, 'og') + ax.text(0.5*(data[si[i0],0]+data[si[i1],0]), 0.65, 'overlap=%.0f%%' % (100.0*overlap), ha='center') + ax.text(0.5*(data[si[i0],0]+data[si[i1],0]), 0.35, "Cohen's d=%.2f" % cohensd, ha='center') + ax.set_xlabel('x') + ax.set_yticks([0, 1]) + ax.set_yticklabels(['Lose', 'Win']) + if uniform: + ax.set_title('Uniformly distributed data') + else: + ax.set_title('Normally distributed data') + + ax = fig.add_subplot(223) + ax.plot(thresh, true_pos, '-og', label='TP') + ax.plot(thresh, false_pos, '-or', label='FP') + ax.legend() + ax.set_xlabel('threshold') + + ax = fig.add_subplot(224) + ax.plot(false_pos, true_pos, '-o') + ax.fill_between(xroc, yroc) + ax.text(0.5, 0.5, 'AUC=%.0f%%' % (100.0*auc)) + ax.set_xlabel('FP') + ax.set_ylabel('TP') + fig.tight_layout() + plt.show() + + return auc, overlap, cohensd, ttest, mannu + + +# demo: +auc(20, 0.5, True, True) +auc(20, 0.5, False, True) + +# AUC versus overlap: +n = 100 +aucs_uni = [] +overlaps_uni = [] +cohensd_uni = [] +ttest_uni = [] +mannu_uni = [] +aucs_norm = [] +overlaps_norm = [] +cohensd_norm = [] +ttest_norm = [] +mannu_norm = [] +for frac in np.arange(-1.5, 1.5, 0.02): + a, o, d, t, u = auc(n, frac, True, False) + aucs_uni.append(a) + overlaps_uni.append(o) + cohensd_uni.append(d) + ttest_uni.append(t) + mannu_uni.append(u) + a, o, d, t, u = auc(n, frac, False, False) + aucs_norm.append(a) + overlaps_norm.append(o) + cohensd_norm.append(d) + ttest_norm.append(t) + mannu_norm.append(u) + +fig, axs = plt.subplots(2, 2) +ax = axs[0, 0] +ax.plot([0.0, 1.0, 0.0], [0.0, 0.5, 1.0], 'k') +ax.plot(overlaps_uni, aucs_uni, 'o', label='uniform pdfs') +ax.plot(overlaps_norm, aucs_norm, 'o', label='normal pdfs') +ax.set_ylim(0, 1) +ax.set_xlabel('fraction of overlapping data') +ax.set_ylabel('AUC') +ax.legend(loc='center left') +ax = axs[0, 1] +ax.plot(cohensd_uni, aucs_uni, 'o', label='uniform pdfs') +ax.plot(cohensd_norm, aucs_norm, 'o', label='normal pdfs') +ax.set_ylim(0, 1) +ax.set_xlabel("Cohen's d") +ax.set_ylabel('AUC') +#ax.legend(loc='center left') +ax = axs[1, 1] +ax.plot(ttest_uni, aucs_uni, 'o', label='uniform pdfs') +ax.plot(ttest_norm, aucs_norm, 'o', label='normal pdfs') +ax.set_ylim(0, 1) +ax.set_xlabel("Student t") +ax.set_ylabel('AUC') +ax = axs[1, 0] +ax.plot(mannu_uni, aucs_uni, 'o', label='uniform pdfs') +ax.plot(mannu_norm, aucs_norm, 'o', label='normal pdfs') +ax.set_ylim(0, 1) +ax.set_xlabel("Mann-Whitney U") +ax.set_ylabel('AUC') +fig.savefig('aucoverlap.pdf') +plt.show() + diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 27b369c..13ca240 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -56,6 +56,7 @@ % to closed source license models), FAIR % * knowledge is freedom ... % * do not consume what companies offer you but know what you want and implement it +% * no screenshots on how to use a stupid GUI program % * python as a modern and popular programming language in modern science % (i.e. machine learning, others?) with a strong community support. @@ -128,22 +129,33 @@ % add chapters on linear algebra, PCA, clustering, see linearalgebra/ +% add chapter on logistic regression, see logistic/ + % add chapter on simple machine learning, perceptron %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\part{Tools} % add chapter on Markup and LaTeX -> see latex/ -% with an introduction on mark-up in general, an outlook to markdown, html, xml, jason, yaml -% make notes, data, and texts understandable by computers! +% - if you know LaTeX you also know how to better use word/libreoffice +% - with an introduction on mark-up in general, an outlook to markdown, html, xml, jason, yaml +% - make notes, data, and texts understandable by computers! +% - easily generate markup from python scripts via mako . + +% bash basics: +% - calling a (python) script/program with arguments +% - files: ls, cp, mkdir, find, etc. +% - text file manipulations: grep, diff, sed, awk +% - pipes, for loop, if, test % Makefile + % distributed computing (ssh and grid engines) -% + % see replicability/ : -% version control (git and github) only put source files into repository! -% data handling (structure, storage (rsync), backup, data bases) -% data annotation, meta data, FAIR +% - version control (git and github) only put source files into repository! +% - data handling (structure, storage (rsync), backup, data bases) +% - data annotation, meta data, FAIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% From c5d5d94d1b874e92786a8c5469bd7b5ec7a9a49f Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Fri, 15 Jan 2021 17:58:34 +0100 Subject: [PATCH 73/87] [pointprocesses] improved count statistics --- pointprocesses/lecture/countexamples.py | 49 ++++++++++ pointprocesses/lecture/fanoexamples.py | 107 ++++++++++++++++++++++ pointprocesses/lecture/pointprocesses.tex | 99 ++++++++++++++------ 3 files changed, 225 insertions(+), 30 deletions(-) create mode 100644 pointprocesses/lecture/countexamples.py create mode 100644 pointprocesses/lecture/fanoexamples.py diff --git a/pointprocesses/lecture/countexamples.py b/pointprocesses/lecture/countexamples.py new file mode 100644 index 0000000..7e0f98f --- /dev/null +++ b/pointprocesses/lecture/countexamples.py @@ -0,0 +1,49 @@ +import numpy as np +from scipy.stats import poisson +import matplotlib.pyplot as plt +from plotstyle import * + + +rate = 20.0 +trials = 10 +duration = 200.0 + + +def hompoisson(rate, trials, duration) : + spikes = [] + for k in range(trials) : + times = [] + t = 0.0 + while t < duration : + t += np.random.exponential(1/rate) + times.append( t ) + spikes.append( times ) + return spikes + + +def plot_count_hist(ax, spikes, win, pmax): + counts = [] + for times in spikes: + c, _ = np.histogram(times, np.arange(0.0, duration, win)) + counts.extend(c) + cb = np.arange(0.0, 15.5, 1.0) + h, b = np.histogram(counts, cb, density=True) + ax.bar(b[:-1], h, bar_fac, **fsA) + ax.plot(cb, poisson.pmf(cb, rate*win), **lsBm) + ax.plot(cb, poisson.pmf(cb, rate*win), **psBm) + ax.text(0.9, 0.9, 'T=%.0fms' % (1000.0*win), transform=ax.transAxes, ha='right') + ax.set_xlim(-0.5, 10.5) + ax.set_ylim(0.0, pmax) + ax.set_xticks(np.arange(0.0, 11.0, 5.0)) + ax.set_xlabel('Counts k') + ax.set_ylabel('P(k)') + + +if __name__ == "__main__": + spikes = hompoisson(rate, trials, duration) + fig, (ax1, ax2) = plt.subplots(1, 2) + fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) + plot_count_hist(ax1, spikes, 0.02, 0.7) + plot_count_hist(ax2, spikes, 0.2, 0.25) + plt.savefig('countexamples.pdf') + plt.close() diff --git a/pointprocesses/lecture/fanoexamples.py b/pointprocesses/lecture/fanoexamples.py new file mode 100644 index 0000000..dc68c0e --- /dev/null +++ b/pointprocesses/lecture/fanoexamples.py @@ -0,0 +1,107 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.ticker as mpt +from plotstyle import * + + +rate = 20.0 +trials = 20 +duration = 100.0 +dt = 0.001 +drate = 50.0 +tau = 0.1; + + +def hompoisson(rate, trials, duration) : + spikes = [] + for k in range(trials) : + times = [] + t = 0.0 + while t < duration : + t += np.random.exponential(1/rate) + times.append( t ) + spikes.append( times ) + return spikes + + +def inhompoisson(rate, trials, dt) : + spikes = [] + p = rate*dt + for k in range(trials) : + x = np.random.rand(len(rate)) + times = dt*np.nonzero(x= vthresh : + v = vreset + times.append(k*dt) + spikes.append( times ) + return spikes + + +def oupifspikes(rate, trials, duration, dt, D, drate, tau): + # OU noise: + rng = np.random.RandomState(54637281) + time = np.arange(0.0, duration, dt) + x = np.zeros(time.shape)+rate + n = rng.randn(len(time))*drate*tau/np.sqrt(dt) + rate + for k in range(1,len(x)) : + x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau + x[x<0.0] = 0.0 + spikes = pifspikes(x, trials, dt, D) + return spikes + + +def plot_count_fano(ax1, ax2, spikes): + wins = np.logspace(-2, 0.0, 200) + mean_counts = np.zeros(len(wins)) + var_counts = np.zeros(len(wins)) + for k, win in enumerate(wins): + counts = [] + for times in spikes: + c, _ = np.histogram(times, np.arange(0.0, duration, win)) + counts.extend(c) + mean_counts[k] = np.mean(counts) + var_counts[k] = np.var(counts) + ax1.plot(mean_counts, var_counts, **lsA) + ax1.set_xlabel('Mean count') + ax1.set_xlim(0.0, 20.0) + ax1.set_ylim(0.0, 20.0) + ax2.plot(1000.0*wins, var_counts/mean_counts, **lsB) + ax2.set_xlabel('Window', 'ms') + ax2.set_ylim(0.0, 1.2) + ax2.set_xscale('log') + ax2.set_xticks([10, 100, 1000]) + ax2.set_xticklabels(['10', '100', '1000']) + + +if __name__ == "__main__": + homspikes = hompoisson(rate, trials, duration) + inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + fig, axs = plt.subplots(2, 2) + fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) + plot_count_fano(axs[0,0], axs[0,1], homspikes) + axs[0,0].text(0.1, 0.95, 'Poisson', transform=axs[0,0].transAxes) + axs[0,0].set_xlabel('') + axs[0,1].set_xlabel('') + axs[0,0].xaxis.set_major_formatter(mpt.NullFormatter()) + axs[0,1].xaxis.set_major_formatter(mpt.NullFormatter()) + plot_count_fano(axs[1,0], axs[1,1], inhspikes) + axs[1,0].text(0.1, 0.95, 'OU noise', transform=axs[1,0].transAxes) + fig.text(0.01, 0.58, 'Count variance', va='center', rotation='vertical') + fig.text(0.53, 0.58, 'Fano factor', va='center', rotation='vertical') + plt.savefig('fanoexamples.pdf') + plt.close() diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index f2286e2..d13d0ab 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -187,40 +187,79 @@ with itself and is always 1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Count statistics} -% \begin{figure}[t] -% \includegraphics[width=0.48\textwidth]{poissoncounthist100hz10ms}\hfill -% \includegraphics[width=0.48\textwidth]{poissoncounthist100hz100ms} -% \titlecaption{\label{countstatsfig}Count statistic.}{} -% \end{figure} -Counting the number of events $n_i$ (counts) in time windows $i$ of duration $W$ -yields positive integer random numbers that are commonly quantified -using the following measures: -\begin{itemize} -\item Histogram of the counts $n_i$. -\item Average number of counts: $\mu_n = \langle n \rangle$. -\item Variance of counts: $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$. -\item \entermde{Fano Faktor}{Fano factor} (variance of counts divided by average count): $F = \frac{\sigma_n^2}{\mu_n}$. -\end{itemize} -Of particular interest is the \enterm[firing rate!average]{average - firing rate} $r$ (spike count per time interval, \determ{Feuerrate}) -that is given in Hertz +\begin{figure}[t] + \includegraphics{countexamples} + \titlecaption{\label{countstatsfig}Count statistics.}{The + distribution of the number of events $k$ (blue) counted within + windows of 20\,ms (left) or 200\,ms duration (right) of the + homogeneous Poisson spike train with a rate of 20\,Hz shown in + \figref{rasterexamplesfig}. For Poisson spike trains these + distributions are given by Poisson distributions (red).} +\end{figure} + +The most commonly used measure for characterizing spike trains is the +\enterm[firing rate!average]{average firing rate}. The firing rate $r$ +is the average number of spikes counted within some time interval $W$ \begin{equation} \label{firingrate} - r = \frac{\langle n \rangle}{W} \; . + r = \frac{\langle n \rangle}{W} \end{equation} +and is neasured in Hertz. The average of the spike counts is taken +over trials. For stationary spike trains (no change in statistics, in +particular the firing rate, over time), the firing rate based on the +spike count equals the inverse average interspike interval +$1/\mu_{ISI}$. + +The firing rate based on an averaged spike counts is one example of +many statistics based on event counts. Stationary spike trains can be +split into many segments $i$, each of duration $W$, and the number of +events $n_i$ in each of the segments can be counted. The integer event +counts can be quantified in the usual ways: +\begin{itemize} +\item Histogram of the counts $n_i$ (\figref{countstatsfig}). +\item Average number of counts: $\mu_n = \langle n \rangle$. +\item Variance of counts: + $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$. +\end{itemize} +Because spike counts are unitless and positive numbers, the +\begin{itemize} +\item \entermde{Fano Faktor}{Fano factor} (variance of counts divided + by average count): $F = \frac{\sigma_n^2}{\mu_n}$. +\end{itemize} +is an additional measure quantifying event counts. + +Note that all of these statistics depend on the chosen window length +$W$. The average spike count, for example, grows linearly with $W$ for +sufficiently large time windows: $\langle n \rangle = r W$, +\eqnref{firingrate}. Doubling the counting window doubles the spike +count. As does the spike-count variance (\figref{fanofig}). At smaller +time windows the statistics of the event counts might depend on the +particular duration of the counting window. There might be an optimal +time window for which the variance of the spike count is minimal. The +Fano factor plotted as a function of the time window illustrates such +properties of point processes (\figref{fanofig}). + +This also has consequences for information transmission in neural +systems. The lower the variance in spike count relative to the +averaged count, the higher the signal-to-noise ratio at which +information encoded in the mean spike count is transmitted. -% \begin{figure}[t] -% \begin{minipage}[t]{0.49\textwidth} -% Poisson process $\lambda=100$\,Hz:\\ -% \includegraphics[width=1\textwidth]{poissonfano100hz} -% \end{minipage} -% \hfill -% \begin{minipage}[t]{0.49\textwidth} -% LIF $I=10$, $\tau_{adapt}=100$\,ms:\\ -% \includegraphics[width=1\textwidth]{lifadaptfano10-100ms} -% \end{minipage} -% \titlecaption{\label{fanofig}Fano factor.}{} -% \end{figure} +\begin{figure}[t] + \includegraphics{fanoexamples} + \titlecaption{\label{fanofig} + Count variance and Fano factor.}{Variance of event counts as a + function of mean counts obtained by varying the duration of the + count window (left). Dividing the count variance by the respective + mean results in the Fano factor that can be plotted as a function + of the count window (right). For Poisson spike trains the variance + always equals the mean counts and consequently the Fano factor + equals one irrespective of the count window (top). A spike train + with positive correlations between interspike intervals (caused by + Ohrnstein-Uhlenbeck noise) has a minimum in the Fano factor, that + is an analysis window for which the relative count variance is + minimal somewhere close to the correlation time scale of the + interspike intervals (bottom).} +\end{figure} \begin{exercise}{counthist.m}{} Implement a function \varcode{counthist()} that calculates and plots From bd610a9b1dbafdc9375cd0027bca041dc7f2ceea Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 16 Jan 2021 10:50:27 +0100 Subject: [PATCH 74/87] [pointprocesses] imrpoved count and fano plots --- pointprocesses/lecture/countexamples.py | 10 ++++++---- pointprocesses/lecture/fanoexamples.py | 11 ++++++++--- pointprocesses/lecture/pointprocesses.tex | 10 +++++----- 3 files changed, 19 insertions(+), 12 deletions(-) diff --git a/pointprocesses/lecture/countexamples.py b/pointprocesses/lecture/countexamples.py index 7e0f98f..8c8a8f3 100644 --- a/pointprocesses/lecture/countexamples.py +++ b/pointprocesses/lecture/countexamples.py @@ -5,8 +5,8 @@ from plotstyle import * rate = 20.0 -trials = 10 -duration = 200.0 +trials = 20 +duration = 100.0 def hompoisson(rate, trials, duration) : @@ -28,7 +28,7 @@ def plot_count_hist(ax, spikes, win, pmax): counts.extend(c) cb = np.arange(0.0, 15.5, 1.0) h, b = np.histogram(counts, cb, density=True) - ax.bar(b[:-1], h, bar_fac, **fsA) + ax.bar(b[:-1], h, bar_fac, align='center', **fsA) ax.plot(cb, poisson.pmf(cb, rate*win), **lsBm) ax.plot(cb, poisson.pmf(cb, rate*win), **psBm) ax.text(0.9, 0.9, 'T=%.0fms' % (1000.0*win), transform=ax.transAxes, ha='right') @@ -44,6 +44,8 @@ if __name__ == "__main__": fig, (ax1, ax2) = plt.subplots(1, 2) fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) plot_count_hist(ax1, spikes, 0.02, 0.7) - plot_count_hist(ax2, spikes, 0.2, 0.25) + ax1.set_yticks(np.arange(0.0, 0.7, 0.2)) + plot_count_hist(ax2, spikes, 0.2, 0.22) + ax2.set_yticks(np.arange(0.0, 0.25, 0.1)) plt.savefig('countexamples.pdf') plt.close() diff --git a/pointprocesses/lecture/fanoexamples.py b/pointprocesses/lecture/fanoexamples.py index dc68c0e..228b473 100644 --- a/pointprocesses/lecture/fanoexamples.py +++ b/pointprocesses/lecture/fanoexamples.py @@ -76,23 +76,27 @@ def plot_count_fano(ax1, ax2, spikes): counts.extend(c) mean_counts[k] = np.mean(counts) var_counts[k] = np.var(counts) - ax1.plot(mean_counts, var_counts, **lsA) + ax1.plot(mean_counts, var_counts, zorder=100, **lsA) ax1.set_xlabel('Mean count') ax1.set_xlim(0.0, 20.0) ax1.set_ylim(0.0, 20.0) + ax1.set_xticks(np.arange(0.0, 21.0, 10.0)) + ax1.set_yticks(np.arange(0.0, 21.0, 10.0)) ax2.plot(1000.0*wins, var_counts/mean_counts, **lsB) ax2.set_xlabel('Window', 'ms') ax2.set_ylim(0.0, 1.2) ax2.set_xscale('log') ax2.set_xticks([10, 100, 1000]) ax2.set_xticklabels(['10', '100', '1000']) + ax2.xaxis.set_minor_locator(mpt.NullLocator()) + ax2.set_yticks(np.arange(0.0, 1.2, 0.5)) if __name__ == "__main__": homspikes = hompoisson(rate, trials, duration) inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) fig, axs = plt.subplots(2, 2) - fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5)) + fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=2.0)) plot_count_fano(axs[0,0], axs[0,1], homspikes) axs[0,0].text(0.1, 0.95, 'Poisson', transform=axs[0,0].transAxes) axs[0,0].set_xlabel('') @@ -100,8 +104,9 @@ if __name__ == "__main__": axs[0,0].xaxis.set_major_formatter(mpt.NullFormatter()) axs[0,1].xaxis.set_major_formatter(mpt.NullFormatter()) plot_count_fano(axs[1,0], axs[1,1], inhspikes) + axs[1,1].axhline(1.0, **lsGrid) axs[1,0].text(0.1, 0.95, 'OU noise', transform=axs[1,0].transAxes) fig.text(0.01, 0.58, 'Count variance', va='center', rotation='vertical') - fig.text(0.53, 0.58, 'Fano factor', va='center', rotation='vertical') + fig.text(0.51, 0.58, 'Fano factor', va='center', rotation='vertical') plt.savefig('fanoexamples.pdf') plt.close() diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index d13d0ab..65947c3 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -189,11 +189,11 @@ with itself and is always 1. \begin{figure}[t] \includegraphics{countexamples} - \titlecaption{\label{countstatsfig}Count statistics.}{The - distribution of the number of events $k$ (blue) counted within - windows of 20\,ms (left) or 200\,ms duration (right) of the - homogeneous Poisson spike train with a rate of 20\,Hz shown in - \figref{rasterexamplesfig}. For Poisson spike trains these + \titlecaption{\label{countstatsfig}Count statistics.}{Probability + distributions of counting $k$ events $k$ (blue) within windows of + 20\,ms (left) or 200\,ms duration (right) of a homogeneous Poisson + spike train with a rate of 20\,Hz + (\figref{rasterexamplesfig}). For Poisson spike trains these distributions are given by Poisson distributions (red).} \end{figure} From 0f0dfafd56f6eec2c0683a8f54f10f31d4132a78 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sun, 17 Jan 2021 23:57:06 +0100 Subject: [PATCH 75/87] [pointprocesses] better incorporated Poisson spike train --- header.tex | 19 +- pointprocesses/lecture/isihexamples.py | 2 + pointprocesses/lecture/pointprocesses.tex | 313 ++++++++++++---------- 3 files changed, 192 insertions(+), 142 deletions(-) diff --git a/header.tex b/header.tex index 2f2360d..73288b8 100644 --- a/header.tex +++ b/header.tex @@ -222,11 +222,26 @@ {\vspace{-2ex}\lstset{#1}\noindent\minipage[t]{1\linewidth}}% {\endminipage} -%%%%% english, german, code and file terms: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%% english and german terms: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{ifthen} +% \enterm[en-index]{term}: Typeset term and add it to the index of english terms +% +% \determ[de-index]{term}: Typeset term and add it to the index of german terms +% +% \entermde[en-index]{de-index}{term}: Typeset term and add it to the index of english terms +% and de-index to the index of german terms +% +% how to specificy an index: +% \enterm{term} - just put term into the index +% \enterm[en-index]{term} - typeset term and put en-index into the index +% \enterm[statistics!mean]{term} - mean is a subentry of statistics +% \enterm[statistics!average|see{statistics!mean}]{term} - cross reference to statistics mean +% \enterm[statistics@\textbf{statistics}]{term} - put index at statistics but use +% \textbf{statistics} for typesetting in the index + % \enterm[english index entry]{} -% typeset the term in italics and add it (or the optional argument) to +% typeset the term in italics and add it (or rather the optional argument) to % the english index. \newcommand{\enterm}[2][]{\textit{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[enterm]{#2}}{\protect\sindex[enterm]{#1}}} diff --git a/pointprocesses/lecture/isihexamples.py b/pointprocesses/lecture/isihexamples.py index 9d0f7c0..c3e2d87 100644 --- a/pointprocesses/lecture/isihexamples.py +++ b/pointprocesses/lecture/isihexamples.py @@ -93,6 +93,8 @@ def plot_hom_isih(ax): ax.set_ylim(0.0, 31.0) ax.set_xticks(np.arange(0.0, 151.0, 50.0)) ax.set_yticks(np.arange(0.0, 31.0, 10.0)) + tt = np.linspace(0.0, 0.15, 100) + ax.plot(1000.0*tt, rate*np.exp(-rate*tt), **lsB) plotisih(ax, isis(homspikes), 0.005) diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index 65947c3..f1a57f9 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -34,7 +34,7 @@ process]{Punktprozess}{point processes}. trial. Shown is a stationary point process (homogeneous point process with a rate $\lambda=20$\;Hz, left) and an non-stationary point process with a rate that varies in time (noisy perfect - integrate-and-fire neuron driven by Ohrnstein-Uhlenbeck noise with + integrate-and-fire neuron driven by Ornstein-Uhlenbeck noise with a time-constant $\tau=100$\,ms, right).} \end{figure} @@ -87,15 +87,60 @@ certain time window $n_i$ (\figref{pointprocesssketchfig}). are stored as vectors of times within a cell array. \end{exercise} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Homogeneous Poisson process} + +The Gaussian distribution is, because of the central limit theorem, +the standard distribution for continuous measures. The equivalent in +the realm of point processes is the +\entermde[distribution!Poisson]{Verteilung!Poisson-}{Poisson distribution}. + +In a \entermde[Poisson process!homogeneous]{Poissonprozess!homogener}{homogeneous Poisson + process} the events occur at a fixed rate $\lambda=\text{const}$ and +are independent of both the time $t$ and occurrence of previous events +(\figref{hompoissonfig}). The probability of observing an event within +a small time window of width $\Delta t$ is given by +\begin{equation} + \label{hompoissonprob} + P = \lambda \cdot \Delta t \; . +\end{equation} + +In an \entermde[Poisson process!inhomogeneous]{Poissonprozess!inhomogener}{inhomogeneous Poisson + process}, however, the rate $\lambda$ depends on time: $\lambda = +\lambda(t)$. + +\begin{exercise}{poissonspikes.m}{} + Implement a function \varcode{poissonspikes()} that uses a homogeneous + Poisson process to generate events at a given rate for a certain + duration and a number of trials. The rate should be given in Hertz + and the duration of the trials is given in seconds. The function + should return the event times in a cell-array. Each entry in this + array represents the events observed in one trial. Apply + \eqnref{hompoissonprob} to generate the event times. +\end{exercise} + +\begin{exercise}{hompoissonspikes.m}{} + Implement a function \varcode{hompoissonspikes()} that uses a + homogeneous Poisson process to generate spike events at a given rate + for a certain duration and a number of trials. The rate should be + given in Hertz and the duration of the trials is given in + seconds. The function should return the event times in a + cell-array. Each entry in this array represents the events observed + in one trial. Apply \eqnref{poissonintervals} to generate the event + times. +\end{exercise} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Interval statistics} The intervals $T_i=t_{i+1}-t_i$ between successive events are real positive numbers. In the context of action potentials they are -referred to as \entermde{Interspikeintervalle}{interspike - intervals}. The statistics of interspike intervals are described -using common measures for describing the statistics of stochastic -real-valued variables: +referred to as \entermde[interspike +interval]{Interspikeintervall}{interspike intervals}, in short +\entermde[ISI|see{interspike + interval}]{ISI|see{Interspikeintervall}}{ISI}s. The statistics of +interspike intervals are described using common measures for +describing the statistics of real-valued variables: \begin{figure}[t] \includegraphics[width=0.96\textwidth]{isihexamples}\vspace{-2ex} @@ -110,19 +155,45 @@ real-valued variables: trial are stored as vectors within a cell-array. \end{exercise} -%\subsection{First order interval statistics} \begin{itemize} \item Probability density $p(T)$ of the intervals $T$ - (\figref{isihexamplesfig}). Normalized to $\int_0^{\infty} p(T) \; dT - = 1$. -\item Average interval: $\mu_{ISI} = \langle T \rangle = - \frac{1}{n}\sum\limits_{i=1}^n T_i$. -\item Standard deviation of the interspike intervals: $\sigma_{ISI} = \sqrt{\langle (T - \langle T - \rangle)^2 \rangle}$\vspace{1ex} -\item \entermde[coefficient of variation]{Variationskoeffizient}{Coefficient of variation}: - $CV_{ISI} = \frac{\sigma_{ISI}}{\mu_{ISI}}$. -\item \entermde[diffusion coefficient]{Diffusionskoeffizient}{Diffusion coefficient}: $D_{ISI} = - \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$. + (\figref{isihexamplesfig}). Normalized to $\int_0^{\infty} p(T) \; + dT = 1$. Commonly referred to as the \enterm[interspike + interval!histogram]{interspike interval histogram}. Its shape + reveals many interesting aspects like locking or bursting that + cannot be inferred from the mean or standard deviation. A particular + reference is the exponential distribution of intervals + \begin{equation} + \label{hompoissonexponential} + p_{exp}(T) = \lambda e^{-\lambda T} + \end{equation} + of a homogeneous Poisson spike train with rate $\lambda$. +\item Mean interval: $\mu_{ISI} = \langle T \rangle = + \frac{1}{n}\sum\limits_{i=1}^n T_i$. The average time it takes from + one event to the next. The inverse of the mean interval is identical + with the mean rate $\lambda$ (number of events per time, see below) + of the process. +\item Standard deviation of intervals: $\sigma_{ISI} = \sqrt{\langle + (T - \langle T \rangle)^2 \rangle}$. Periodically spiking neurons + have little variability in their intervals, whereas many cortical + neurons cover a wide range with their intervals. The standard + deviation of homogeneous Poisson spike trains, $\sigma_{ISI} = + \frac{1}{\lambda}$, also equals the inverse rate. Whether the + standard deviation of intervals is low or high, however, is better + quantified by the +\item \entermde[coefficient of + variation]{Variationskoeffizient}{Coefficient of variation}, the + standard deviation of the ISIs relative to their mean: + \begin{equation} + \label{cvisi} + CV_{ISI} = \frac{\sigma_{ISI}}{\mu_{ISI}} + \end{equation} + Homogeneous Poisson spike trains have an CV of exactly one. The + lower the CV the more regularly firing a neuron is firing. CVs + larger than one are also possible in spike trains with small + intervals separated by really long ones. +%\item \entermde[diffusion coefficient]{Diffusionskoeffizient}{Diffusion coefficient}: $D_{ISI} = +% \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$. \end{itemize} \begin{exercise}{isihist.m}{} @@ -142,12 +213,33 @@ real-valued variables: \end{exercise} \subsection{Interval correlations} -So called \entermde[return map]{return map}{return maps} are used to -illustrate interdependencies between successive interspike -intervals. The return map plots the delayed interval $T_{i+k}$ against -the interval $T_i$. The parameter $k$ is called the \enterm{lag} -(\determ{Verz\"ogerung}) $k$. Stationary and non-stationary return -maps are distinctly different \figref{returnmapfig}. +Intervals are not just numbers without an order, like weights of +tigers. Intervals are temporally ordered and there could be temporal +structure in the sequence of intervals. For example, short intervals +could be followed by more longer ones, and vice versa. Such +dependencies in the sequence of intervals do not show up in the +interval histogram. We need additional measures to also quantify the +temporal structure of the sequence of intervals. + +We can use the same techniques we know for visualizing and quantifying +correlations in bivariate data sets, i.e. scatter plots and +correlation coefficients. We form $(x,y)$ data pairs by taking the +series of intervals $T_i$ as $x$-data values and pairing them with the +$k$-th next intervals $T_{i+k}$ as $y$-data values. The parameter $k$ +is called \enterm{lag} (\determ{Verz\"ogerung}). For lag one we pair +each interval with the next one. A \entermde[return map]{return + map}{Return map} illustrates dependencies between successive +intervals by simply plotting the intervals $T_{i+k}$ against the +intervals $T_i$ in a scatter plot (\figref{returnmapfig}). For Poisson +spike trains there is no structure beyond the one expected from the +exponential interspike interval distribution, hinting at neighboring +interspike intervals being independent of each other. For the spike +train based on an Ornstein-Uhlenbeck process the return map is more +clustered along the diagonal, hinting at a positive correlation +between succeeding intervals. That is, short intervals are more likely +to be followed by short ones and long intervals more likely by long +ones. This temporal structure was already clearly visible in the spike +raster shown in \figref{rasterexamplesfig}. \begin{figure}[tp] \includegraphics[width=1\textwidth]{serialcorrexamples} @@ -165,16 +257,34 @@ maps are distinctly different \figref{returnmapfig}. the mean firing rate of the spike trains.} \end{figure} -Such dependencies can be further quantified using the +Such dependencies can be further quantified by \entermde[correlation!serial]{Korrelation!serielle}{serial - correlations} \figref{returnmapfig}. The serial correlation is the -correlation coefficient of the intervals $T_i$ and the intervals -delayed by the lag $T_{i+k}$: -\[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} -= {\rm corr}(T_{i+k}, T_i) \] The resulting correlation coefficient -$\rho_k$ is usually plotted against the lag $k$ -\figref{returnmapfig}. $\rho_0=1$ is the correlation of each interval -with itself and is always 1. + correlations}. These are the correlation coefficients between the +intervals $T_{i+k}$ and $T_i$ in dependence on lag $k$: +\begin{equation} + \label{serialcorrelation} + \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} += {\rm corr}(T_{i+k}, T_i) +\end{equation} +The serial correlations $\rho_k$ are usually plotted against the lag +$k$ for a range small range of lags +(\figref{returnmapfig}). $\rho_0=1$ is the correlation of each +interval with itself and always equals one. + +If the serial correlations all equal zero, $\rho_k =0$ for $k>0$, then +the length of an interval is independent of all the previous +ones. Such a process is a \enterm{renewal process} +(\determ{Erneuerungsprozess}). Each event, each action potential, +erases the history. The occurrence of the next event is independent of +what happened before. To a first approximation an action potential +erases all information about the past from the membrane voltage and +thus spike trains may approximate renewal processes. + +However, other variables like the intracellular calcium concentration +or the states of slowly switching ion channels may carry information +from one interspike interval to the next and thus introducing +correlations. Such non-renewal dynamics can then be described by the +non-zero serial correlations (\figref{returnmapfig}). \begin{exercise}{isiserialcorr.m}{} Implement a function \varcode{isiserialcorr()} that takes a vector of @@ -204,7 +314,7 @@ is the average number of spikes counted within some time interval $W$ \label{firingrate} r = \frac{\langle n \rangle}{W} \end{equation} -and is neasured in Hertz. The average of the spike counts is taken +and is measured in Hertz. The average of the spike counts is taken over trials. For stationary spike trains (no change in statistics, in particular the firing rate, over time), the firing rate based on the spike count equals the inverse average interspike interval @@ -216,7 +326,14 @@ split into many segments $i$, each of duration $W$, and the number of events $n_i$ in each of the segments can be counted. The integer event counts can be quantified in the usual ways: \begin{itemize} -\item Histogram of the counts $n_i$ (\figref{countstatsfig}). +\item Histogram of the counts $n_i$. For homogeneous Poisson spike + trains with rate $\lambda$ the resulting probability distributions + follow a Poisson distribution (\figref{countstatsfig}), where the + probability of counting $k$ events within a time window $W$ is given by + \begin{equation} + \label{poissondist} + P(k) = \frac{(\lambda W)^k e^{\lambda W}}{k!} + \end{equation} \item Average number of counts: $\mu_n = \langle n \rangle$. \item Variance of counts: $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$. @@ -224,20 +341,29 @@ counts can be quantified in the usual ways: Because spike counts are unitless and positive numbers, the \begin{itemize} \item \entermde{Fano Faktor}{Fano factor} (variance of counts divided - by average count): $F = \frac{\sigma_n^2}{\mu_n}$. + by average count) + \begin{equation} + \label{fano} + F = \frac{\sigma_n^2}{\mu_n} + \end{equation} + is a commonly used measure for quantifying the variability of event + counts relative to the mean number of events. In particular for + homogeneous Poisson processes the Fano factor equals one, + independently of the time window $W$. \end{itemize} is an additional measure quantifying event counts. -Note that all of these statistics depend on the chosen window length -$W$. The average spike count, for example, grows linearly with $W$ for -sufficiently large time windows: $\langle n \rangle = r W$, -\eqnref{firingrate}. Doubling the counting window doubles the spike -count. As does the spike-count variance (\figref{fanofig}). At smaller -time windows the statistics of the event counts might depend on the -particular duration of the counting window. There might be an optimal -time window for which the variance of the spike count is minimal. The -Fano factor plotted as a function of the time window illustrates such -properties of point processes (\figref{fanofig}). +Note that all of these statistics depend in general on the chosen +window length $W$. The average spike count, for example, grows +linearly with $W$ for sufficiently large time windows: $\langle n +\rangle = r W$, \eqnref{firingrate}. Doubling the counting window +doubles the spike count. As does the spike-count variance +(\figref{fanofig}). At smaller time windows the statistics of the +event counts might depend on the particular duration of the counting +window. There might be an optimal time window for which the variance +of the spike count is minimal. The Fano factor plotted as a function +of the time window illustrates such properties of point processes +(\figref{fanofig}). This also has consequences for information transmission in neural systems. The lower the variance in spike count relative to the @@ -255,9 +381,9 @@ information encoded in the mean spike count is transmitted. always equals the mean counts and consequently the Fano factor equals one irrespective of the count window (top). A spike train with positive correlations between interspike intervals (caused by - Ohrnstein-Uhlenbeck noise) has a minimum in the Fano factor, that - is an analysis window for which the relative count variance is - minimal somewhere close to the correlation time scale of the + an Ornstein-Uhlenbeck process) has a minimum in the Fano factor, + that is an analysis window for which the relative count variance + is minimal somewhere close to the correlation time scale of the interspike intervals (bottom).} \end{figure} @@ -271,99 +397,6 @@ information encoded in the mean spike count is transmitted. \end{exercise} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Homogeneous Poisson process} - -The Gaussian distribution is, because of the central limit theorem, -the standard distribution for continuous measures. The equivalent in -the realm of point processes is the -\entermde[distribution!Poisson]{Verteilung!Poisson-}{Poisson distribution}. - -In a \entermde[Poisson process!homogeneous]{Poissonprozess!homogener}{homogeneous Poisson - process} the events occur at a fixed rate $\lambda=\text{const}$ and -are independent of both the time $t$ and occurrence of previous events -(\figref{hompoissonfig}). The probability of observing an event within -a small time window of width $\Delta t$ is given by -\begin{equation} - \label{hompoissonprob} - P = \lambda \cdot \Delta t \; . -\end{equation} - -In an \entermde[Poisson process!inhomogeneous]{Poissonprozess!inhomogener}{inhomogeneous Poisson - process}, however, the rate $\lambda$ depends on time: $\lambda = -\lambda(t)$. - -\begin{exercise}{poissonspikes.m}{} - Implement a function \varcode{poissonspikes()} that uses a homogeneous - Poisson process to generate events at a given rate for a certain - duration and a number of trials. The rate should be given in Hertz - and the duration of the trials is given in seconds. The function - should return the event times in a cell-array. Each entry in this - array represents the events observed in one trial. Apply - \eqnref{hompoissonprob} to generate the event times. -\end{exercise} - -\begin{figure}[t] - \includegraphics[width=1\textwidth]{poissonraster100hz} - \titlecaption{\label{hompoissonfig}Rasterplot of spikes of a - homogeneous Poisson process with a rate $\lambda=100$\,Hz.}{} -\end{figure} - -\begin{figure}[t] - \includegraphics[width=0.45\textwidth]{poissonisihexp20hz}\hfill - \includegraphics[width=0.45\textwidth]{poissonisihexp100hz} - \titlecaption{\label{hompoissonisihfig}Distribution of interspike - intervals of two Poisson processes.}{The processes differ in their - rate (left: $\lambda=20$\,Hz, right: $\lambda=100$\,Hz). The red - lines indicate the corresponding exponential interval distribution - \eqnref{poissonintervals}.} -\end{figure} - -The homogeneous Poisson process has the following properties: -\begin{itemize} -\item Intervals $T$ are exponentially distributed (\figref{hompoissonisihfig}): - \begin{equation} - \label{poissonintervals} - p(T) = \lambda e^{-\lambda T} \; . - \end{equation} -\item The average interval is $\mu_{ISI} = \frac{1}{\lambda}$ . -\item The variance of the intervals is $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$ . -\item Thus, the coefficient of variation is always $CV_{ISI} = 1$ . -\item The serial correlation is $\rho_k =0$ for $k>0$, since the - occurrence of an event is independent of all previous events. Such a - process is also called a \enterm{renewal process} (\determ{Erneuerungsprozess}). -\item The number of events $k$ within a temporal window of duration - $W$ is Poisson distributed: -\begin{equation} - \label{poissoncounts} - P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} -\end{equation} -(\figref{hompoissoncountfig}) -\item The Fano Faktor is always $F=1$ . -\end{itemize} - -\begin{exercise}{hompoissonspikes.m}{} - Implement a function \varcode{hompoissonspikes()} that uses a - homogeneous Poisson process to generate spike events at a given rate - for a certain duration and a number of trials. The rate should be - given in Hertz and the duration of the trials is given in - seconds. The function should return the event times in a - cell-array. Each entry in this array represents the events observed - in one trial. Apply \eqnref{poissonintervals} to generate the event - times. -\end{exercise} - -\begin{figure}[t] - \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill - \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms} - \titlecaption{\label{hompoissoncountfig}Distribution of counts of a - Poisson spike train.}{The count statistics was generated for two - different windows of width $W=10$\,ms (left) and width $W=100$\,ms - (right). The red line illustrates the corresponding Poisson - distribution \eqnref{poissoncounts}.} -\end{figure} - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Time-dependent firing rate} From 20332e2013bdcb5781df804c73dc9c2bfac49068 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 18 Jan 2021 13:13:35 +0100 Subject: [PATCH 76/87] [pointprocesses] improved chapter --- pointprocesses/code/counthist.m | 25 +- pointprocesses/code/isihist.m | 2 +- pointprocesses/code/isis.m | 2 - pointprocesses/code/isiserialcorr.m | 16 +- pointprocesses/code/plotisiserialcorr.m | 16 ++ pointprocesses/code/rasterplot.m | 30 +- pointprocesses/lecture/fanoexamples.py | 40 ++- pointprocesses/lecture/pointprocesses.tex | 330 +++++++++++++--------- pointprocesses/lecture/rasterexamples.py | 2 +- scientificcomputing-script.tex | 3 +- 10 files changed, 272 insertions(+), 194 deletions(-) create mode 100644 pointprocesses/code/plotisiserialcorr.m diff --git a/pointprocesses/code/counthist.m b/pointprocesses/code/counthist.m index 67b4cae..2f5b746 100644 --- a/pointprocesses/code/counthist.m +++ b/pointprocesses/code/counthist.m @@ -1,16 +1,11 @@ -function [counts, bins] = counthist(spikes, w) -% Compute and plot histogram of spike counts. +function counthist(spikes, w) +% Plot histogram of spike counts. % -% [counts, bins] = counthist(spikes, w) +% counthist(spikes, w) % % Arguments: % spikes: a cell array of vectors of spike times in seconds -% w: observation window duration in seconds for computing the counts -% -% Returns: -% counts: the histogram of counts normalized to probabilities -% bins: the bin centers for the histogram - +% w: duration of window in seconds for computing the counts % collect spike counts: tmax = spikes{1}(end); n = []; @@ -21,12 +16,12 @@ function [counts, bins] = counthist(spikes, w) % for tk = 0:w:tmax-w % nn = sum((times >= tk) & (times < tk+w)); % %nn = length(find((times >= tk) & (times < tk+w))); -% n = [n nn]; +% n = [n, nn]; % end % alternative 2: use the hist() function to do that! tbins = 0.5*w:w:tmax-0.5*w; nn = hist(times, tbins); - n = [n nn]; + n = [n, nn]; end % histogram of spike counts: @@ -36,9 +31,7 @@ function [counts, bins] = counthist(spikes, w) counts = counts / sum(counts); % plot: - if nargout == 0 - bar(bins, counts); - xlabel('counts k'); - ylabel('P(k)'); - end + bar(bins, counts); + xlabel('counts k'); + ylabel('P(k)'); end diff --git a/pointprocesses/code/isihist.m b/pointprocesses/code/isihist.m index 00b02c3..a24989c 100644 --- a/pointprocesses/code/isihist.m +++ b/pointprocesses/code/isihist.m @@ -8,7 +8,7 @@ function [pdf, centers] = isihist(isis, binwidth) % binwidth: optional width in seconds to be used for the isi bins % % Returns: -% pdf: vector with probability density of interspike intervals in Hz +% pdf: vector with pdf of interspike intervals in Hertz % centers: vector with centers of interspikeintervalls in seconds if nargin < 2 diff --git a/pointprocesses/code/isis.m b/pointprocesses/code/isis.m index 65a346b..509dcc5 100644 --- a/pointprocesses/code/isis.m +++ b/pointprocesses/code/isis.m @@ -5,11 +5,9 @@ function isivec = isis(spikes) % % Arguments: % spikes: a cell array of vectors of spike times in seconds -% isivec: a column vector with all the interspike intervalls % % Returns: % isivec: a column vector with all the interspike intervalls - isivec = []; for k = 1:length(spikes) difftimes = diff(spikes{k}); diff --git a/pointprocesses/code/isiserialcorr.m b/pointprocesses/code/isiserialcorr.m index 21bb474..1b813fc 100644 --- a/pointprocesses/code/isiserialcorr.m +++ b/pointprocesses/code/isiserialcorr.m @@ -1,15 +1,15 @@ -function isicorr = isiserialcorr(isivec, maxlag) +function [isicorr, lags] = isiserialcorr(isivec, maxlag) % serial correlation of interspike intervals % % isicorr = isiserialcorr(isivec, maxlag) % % Arguments: % isivec: vector of interspike intervals in seconds -% maxlag: the maximum lag in seconds +% maxlag: the maximum lag % % Returns: % isicorr: vector with the serial correlations for lag 0 to maxlag - +% lags: vector with the lags corresponding to isicorr lags = 0:maxlag; isicorr = zeros(size(lags)); for k = 1:length(lags) @@ -21,14 +21,4 @@ function isicorr = isiserialcorr(isivec, maxlag) isicorr(k) = corr(isivec(1:end-lag), isivec(lag+1:end)); end end - - if nargout == 0 - % plot: - plot(lags, isicorr, '-b'); - hold on; - scatter(lags, isicorr, 50.0, 'b', 'filled'); - hold off; - xlabel('Lag k') - ylabel('\rho_k') - end end diff --git a/pointprocesses/code/plotisiserialcorr.m b/pointprocesses/code/plotisiserialcorr.m new file mode 100644 index 0000000..3f21418 --- /dev/null +++ b/pointprocesses/code/plotisiserialcorr.m @@ -0,0 +1,16 @@ +function isicorr = plotisiserialcorr(isivec, maxlag) +% plot serial correlation of interspike intervals +% +% plotisiserialcorr(isivec, maxlag) +% +% Arguments: +% isivec: vector of interspike intervals in seconds +% maxlag: the maximum lag + [isicorr, lags] = isiserialcorr(isivec, maxlag); + plot(lags, isicorr, '-b'); + hold on; + scatter(lags, isicorr, 20.0, 'b', 'filled'); + hold off; + xlabel('Lag k') + ylabel('\rho_k') +end diff --git a/pointprocesses/code/rasterplot.m b/pointprocesses/code/rasterplot.m index 7b28820..ccbfe60 100644 --- a/pointprocesses/code/rasterplot.m +++ b/pointprocesses/code/rasterplot.m @@ -2,21 +2,35 @@ function rasterplot(spikes, tmax) % Display a spike raster of the spike times given in spikes. % % rasterplot(spikes, tmax) +% +% Arguments: % spikes: a cell array of vectors of spike times in seconds -% tmax: plot spike raster upto tmax seconds - +% tmax: plot spike raster up to tmax seconds + in_msecs = tmax < 1.5 + spiketimes = []; + trials = []; ntrials = length(spikes); for k = 1:ntrials times = spikes{k}; times = times(times0$, then the length of an interval is independent of all the previous @@ -282,15 +325,21 @@ thus spike trains may approximate renewal processes. However, other variables like the intracellular calcium concentration or the states of slowly switching ion channels may carry information -from one interspike interval to the next and thus introducing -correlations. Such non-renewal dynamics can then be described by the -non-zero serial correlations (\figref{returnmapfig}). +from one interspike interval to the next and thus introduce +correlations between intervals. Such non-renewal dynamics is then +characterized by the non-zero serial correlations +(\figref{returnmapfig}). \begin{exercise}{isiserialcorr.m}{} - Implement a function \varcode{isiserialcorr()} that takes a vector of - interspike intervals as input argument and calculates the serial - correlation. The function should further plot the serial - correlation. + Implement a function \varcode{isiserialcorr()} that takes a vector + of interspike intervals as input argument and calculates the serial + correlations up to some maximum lag. +\end{exercise} + +\begin{exercise}{plotisiserialcorr.m}{} + Implement a function \varcode{plotisiserialcorr()} that takes a + vector of interspike intervals as input argument and generates a + plot of the serial correlations. \end{exercise} @@ -326,10 +375,11 @@ split into many segments $i$, each of duration $W$, and the number of events $n_i$ in each of the segments can be counted. The integer event counts can be quantified in the usual ways: \begin{itemize} -\item Histogram of the counts $n_i$. For homogeneous Poisson spike - trains with rate $\lambda$ the resulting probability distributions - follow a Poisson distribution (\figref{countstatsfig}), where the - probability of counting $k$ events within a time window $W$ is given by +\item Histogram of the counts $n_i$ appropriately normalized to + probability distributions. For homogeneous Poisson spike trains with + rate $\lambda$ the resulting probability distributions follow a + Poisson distribution (\figref{countstatsfig}), where the probability + of counting $k$ events within a time window $W$ is given by \begin{equation} \label{poissondist} P(k) = \frac{(\lambda W)^k e^{\lambda W}}{k!} @@ -338,7 +388,7 @@ counts can be quantified in the usual ways: \item Variance of counts: $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$. \end{itemize} -Because spike counts are unitless and positive numbers, the +Because spike counts are unitless and positive numbers the \begin{itemize} \item \entermde{Fano Faktor}{Fano factor} (variance of counts divided by average count) @@ -351,7 +401,6 @@ Because spike counts are unitless and positive numbers, the homogeneous Poisson processes the Fano factor equals one, independently of the time window $W$. \end{itemize} -is an additional measure quantifying event counts. Note that all of these statistics depend in general on the chosen window length $W$. The average spike count, for example, grows @@ -372,33 +421,33 @@ information encoded in the mean spike count is transmitted. \begin{figure}[t] \includegraphics{fanoexamples} - \titlecaption{\label{fanofig} - Count variance and Fano factor.}{Variance of event counts as a - function of mean counts obtained by varying the duration of the - count window (left). Dividing the count variance by the respective - mean results in the Fano factor that can be plotted as a function - of the count window (right). For Poisson spike trains the variance - always equals the mean counts and consequently the Fano factor - equals one irrespective of the count window (top). A spike train - with positive correlations between interspike intervals (caused by - an Ornstein-Uhlenbeck process) has a minimum in the Fano factor, - that is an analysis window for which the relative count variance - is minimal somewhere close to the correlation time scale of the - interspike intervals (bottom).} + \titlecaption{\label{fanofig} Fano factor.}{Counting events in time + windows of given duration and then dividing the variance of the + counts by their mean results in the Fano factor. Here, the Fano + factor is plotted as a function of the duration of the window used + to count events. For Poisson spike trains the variance always + equals the mean counts and consequently the Fano factor equals one + irrespective of the count window (left). A spike train with + positive correlations between interspike intervals (caused by an + Ornstein-Uhlenbeck process) has a minimum in the Fano factor, that + is an analysis window for which the relative count variance is + minimal somewhere close to the correlation time scale of the + interspike intervals (right).} \end{figure} \begin{exercise}{counthist.m}{} Implement a function \varcode{counthist()} that calculates and plots the distribution of spike counts observed in a certain time - window. The function should take two input arguments: (i) a - cell-array of vectors containing the spike times in seconds observed - in a number of trials, and (ii) the duration of the time window that - is used to evaluate the counts. + window. The function should take two input arguments: a cell-array + of vectors containing the spike times in seconds observed in a + number of trials, and the duration of the time window that is used + to evaluate the counts. \end{exercise} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Time-dependent firing rate} +\label{nonstationarysec} So far we have discussed stationary spike trains. The statistical properties of these did not change within the observation time (stationary point @@ -566,6 +615,7 @@ relevate time-scale. \end{exercise} \section{Spike-triggered Average} +\label{stasec} The graphical representation of the neuronal activity alone is not sufficient tot investigate the relation between the neuronal response diff --git a/pointprocesses/lecture/rasterexamples.py b/pointprocesses/lecture/rasterexamples.py index 07b8628..7a9f4f0 100644 --- a/pointprocesses/lecture/rasterexamples.py +++ b/pointprocesses/lecture/rasterexamples.py @@ -85,7 +85,7 @@ def plot_inhomogeneous_spikes(ax): if __name__ == "__main__": - fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.5*figure_width)) + fig, (ax1, ax2) = plt.subplots(1, 2) fig.subplots_adjust(**adjust_fs(fig, left=4.0, right=1.0, top=1.2)) plot_homogeneous_spikes(ax1) plot_inhomogeneous_spikes(ax2) diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 13ca240..016a6a4 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -116,9 +116,10 @@ \includechapter{pointprocesses} % add a chapter on simulating point-processes/spike trains -% (Poisson spike trains, integrate-and-fire models) +% (Poisson spike trains, LMP models, integrate-and-fire models, full HH like models) % add chapter on information theory, mutual information, stimulus reconstruction, coherence +% move STA here! % add a chapter on Bayesian inference (the Neuroscience of it and a % bit of application for statistical problems). From 51da7aa567719723a519056d7d6def708afa4783 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 18 Jan 2021 18:58:37 +0100 Subject: [PATCH 77/87] [likelihood] solved standard deviation problem --- likelihood/exercises/likelihood-1.tex | 3 ++- likelihood/exercises/mlestd.m | 16 ++++++++++------ likelihood/exercises/mlestd.pdf | Bin 10259 -> 75531 bytes 3 files changed, 12 insertions(+), 7 deletions(-) diff --git a/likelihood/exercises/likelihood-1.tex b/likelihood/exercises/likelihood-1.tex index 2da6ac2..8c86079 100644 --- a/likelihood/exercises/likelihood-1.tex +++ b/likelihood/exercises/likelihood-1.tex @@ -37,10 +37,11 @@ of the standard deviation. \end{parts} \begin{solution} \lstinputlisting{mlestd.m} + \lstinputlisting[language={}]{mlestd.out} \includegraphics[width=1\textwidth]{mlestd}\\ The more data the smaller the product of the probabilities ($\approx - p^n$ with $0 \le p < 1$) and the smaller the sum of the logarithms + p^n$ if $0 \le p < 1$) and the smaller the sum of the logarithms of the probabilities ($\approx n\log p$, note that $\log p < 0$). The product eventually gets smaller than the precision of the diff --git a/likelihood/exercises/mlestd.m b/likelihood/exercises/mlestd.m index 8c61e4b..c08f4c1 100644 --- a/likelihood/exercises/mlestd.m +++ b/likelihood/exercises/mlestd.m @@ -6,16 +6,19 @@ for k = 1:length(ns) fprintf('\nn=%d\n', n); % draw random numbers: x = randn(n,1)*sigma+mu; - fprintf(' mean of the data is %.2f\n', mean(x)) - fprintf(' standard deviation of the data is %.2f\n', std(x)) + datamean = mean(x); + fprintf(' mean %.3f\n', datamean) + % we assume the mean to be given, therefore dof=n: + fprintf(' standard deviation %.3f\n', std(x, 1)) % standard deviation as parameter: - psigs = 1.0:0.01:3.0; + psigs = 1.0:0.001:3.0; % matrix with the probabilities for each x and psigs: lms = zeros(length(x), length(psigs)); for i=1:length(psigs) psig = psigs(i); - p = exp(-0.5*((x-mu)/psig).^2.0)/sqrt(2.0*pi)/psig; + % same mean as for the standard deviation of the data: + p = exp(-0.5*((x-datamean)/psig).^2.0)/sqrt(2.0*pi)/psig; lms(:,i) = p; end lm = prod(lms, 1); % likelihood @@ -24,8 +27,9 @@ for k = 1:length(ns) if length(maxlm) > 1 maxlm = maxlm(1); end - fprintf(' likelihood: standard deviation of the data is %.2f\n', maxlm) - fprintf(' log-likelihood: standard deviation of the data is %.2f\n', psigs(loglm==max(loglm))) + maxloglm = psigs(loglm==max(loglm)); + fprintf(' likelihood: standard deviation %.3f\n', maxlm) + fprintf(' log-likelihood: standard deviation %.3f\n', maxloglm) % plot likelihood of standard deviation: subplot(2, 2, 2*k-1); diff --git a/likelihood/exercises/mlestd.pdf b/likelihood/exercises/mlestd.pdf index 4732ba4cede4ae175352b52bfb0103b7d38458d7..c321734e0a955b8b8d300aa13df80a23c36b14f0 100644 GIT binary patch literal 75531 zcmX_mWmH^E)9n+1;4rvraJRuBz~I5%nZaQOf-`6!xVyW%GdLu;OK=ZP&;Y?DAMgEf z|8-S&?Y*mNRiCxaYI-%0EIT&`9~yl{WmPpAH#HZvBg76(R1}R<&Dqhy&D_$Nno05t z*xbgFT2@t!TF27a#n#b*numjrgNt2LMN&;uUR6t&`V|J`Xzm8Hba0h(27j@!HFx0w 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zZ!(XmLIsar&frDG?vSqV#>ik`+G`5&PF0t|W7mCn$*}H6k^A{XJPDWYk)jB6yoo#x z_Ux61k?{Dny?q4i8}c_`fLA)iZC&+Vj9L%54p3<`RoIR3u_t+jeZK0G$xcgv z{31wFwh1_MEbH5nemTca?Va8_*K+WgG$de$!>=;1qH(vh9%>JS2AWT~9JSQXz*$BF z9@trHY~q&ZH6zw}Dr&Rq6y5Y6g4sAqw3F=nGcl^xMAk zk;8xs4P`DV<~%(wG&%kD0J0#TA(`^DR;qycRQk8Iu4Mo!0!IB9XQ)P Date: Mon, 18 Jan 2021 19:09:56 +0100 Subject: [PATCH 78/87] [pointprocesses] fixed exercises --- pointprocesses/code/rasterplot.m | 13 ++----------- pointprocesses/{code => exercises}/lifadapt.mat | Bin pointprocesses/{code => exercises}/pifou.mat | Bin pointprocesses/exercises/pointprocesses-1.tex | 2 +- pointprocesses/{code => exercises}/poisson.mat | Bin 5 files changed, 3 insertions(+), 12 deletions(-) rename pointprocesses/{code => exercises}/lifadapt.mat (100%) rename pointprocesses/{code => exercises}/pifou.mat (100%) rename pointprocesses/{code => exercises}/poisson.mat (100%) diff --git a/pointprocesses/code/rasterplot.m b/pointprocesses/code/rasterplot.m index ccbfe60..beb1970 100644 --- a/pointprocesses/code/rasterplot.m +++ b/pointprocesses/code/rasterplot.m @@ -6,16 +6,12 @@ function rasterplot(spikes, tmax) % Arguments: % spikes: a cell array of vectors of spike times in seconds % tmax: plot spike raster up to tmax seconds - in_msecs = tmax < 1.5 spiketimes = []; trials = []; ntrials = length(spikes); for k = 1:ntrials times = spikes{k}; times = times(times Date: Mon, 18 Jan 2021 23:03:30 +0100 Subject: [PATCH 79/87] [pointprocesses] improved spike count and fano factor exercises --- pointprocesses/code/counthist.m | 37 --------- pointprocesses/code/fano.m | 39 ---------- pointprocesses/code/fanoplot.m | 33 -------- pointprocesses/code/fanoplots.m | 9 --- pointprocesses/code/hompoissonspikes.m | 3 - pointprocesses/code/isihist.m | 14 +--- pointprocesses/code/isis.m | 4 +- pointprocesses/code/isiserialcorr.m | 5 +- pointprocesses/code/plotcounthist.m | 38 ++++----- pointprocesses/code/plotfanofactor.m | 31 ++++++++ pointprocesses/code/plotisihist.m | 15 +--- pointprocesses/code/plotisiserialcorr.m | 2 - pointprocesses/code/rasterplot.m | 4 +- pointprocesses/lecture/pointprocesses.tex | 95 ++++++++++++++--------- 14 files changed, 109 insertions(+), 220 deletions(-) delete mode 100644 pointprocesses/code/counthist.m delete mode 100644 pointprocesses/code/fano.m delete mode 100644 pointprocesses/code/fanoplot.m delete mode 100644 pointprocesses/code/fanoplots.m create mode 100644 pointprocesses/code/plotfanofactor.m diff --git a/pointprocesses/code/counthist.m b/pointprocesses/code/counthist.m deleted file mode 100644 index 2f5b746..0000000 --- a/pointprocesses/code/counthist.m +++ /dev/null @@ -1,37 +0,0 @@ -function counthist(spikes, w) -% Plot histogram of spike counts. -% -% counthist(spikes, w) -% -% Arguments: -% spikes: a cell array of vectors of spike times in seconds -% w: duration of window in seconds for computing the counts - % collect spike counts: - tmax = spikes{1}(end); - n = []; - r = []; - for k = 1:length(spikes) - times = spikes{k}; -% alternative 1: count the number of spikes in each window: -% for tk = 0:w:tmax-w -% nn = sum((times >= tk) & (times < tk+w)); -% %nn = length(find((times >= tk) & (times < tk+w))); -% n = [n, nn]; -% end -% alternative 2: use the hist() function to do that! - tbins = 0.5*w:w:tmax-0.5*w; - nn = hist(times, tbins); - n = [n, nn]; - end - - % histogram of spike counts: - maxn = max(n); - [counts, bins] = hist(n, 0:1:maxn+10); - % normalize to probabilities: - counts = counts / sum(counts); - - % plot: - bar(bins, counts); - xlabel('counts k'); - ylabel('P(k)'); -end diff --git a/pointprocesses/code/fano.m b/pointprocesses/code/fano.m deleted file mode 100644 index a73cada..0000000 --- a/pointprocesses/code/fano.m +++ /dev/null @@ -1,39 +0,0 @@ -function fano( spikes ) -% computes fano factor as a function of window size -% spikes: a cell array of vectors of spike times - - tmax = spikes{1}(end); - windows = 0.01:0.05:0.01*tmax; - mc = windows; - vc = windows; - ff = windows; - fs = windows; - for j = 1:length(windows) - w = windows( j ); - % collect counts: - n = []; - for k = 1:length(spikes) - for tk = 0:w:tmax-w - nn = sum( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) ); - %nn = length( find( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) ) ); - n = [ n nn ]; - end - end - % statistics for current window: - mc(j) = mean( n ); - vc(j) = var( n ); - ff(j) = vc( j )/mc( j ); - fs(j) = sqrt(vc( j )/mc( j )); - end - - subplot( 1, 2, 1 ); - scatter( mc, vc, 'filled' ); - xlabel( 'Mean count' ); - ylabel( 'Count variance' ); - - subplot( 1, 2, 2 ); - scatter( 1000.0*windows, fs, 'filled' ); - xlabel( 'Window W [ms]' ); - ylabel( 'Fano factor' ); -end - diff --git a/pointprocesses/code/fanoplot.m b/pointprocesses/code/fanoplot.m deleted file mode 100644 index b53c42f..0000000 --- a/pointprocesses/code/fanoplot.m +++ /dev/null @@ -1,33 +0,0 @@ -function fanoplot(spikes, titles) -% computes and plots fano factor as a function of window size -% spikes: a cell array of vectors of spike times -% titles: string that is used as a title for the plots - windows = logspace(-3.0, -0.5, 100); - mc = windows; - vc = windows; - ff = windows; - for j = 1:length(windows) - w = windows(j); - counts = spikecounts(spikes, w); - % statistics for current window: - mc(j) = mean(counts); - vc(j) = var(counts); - ff(j) = vc(j)/mc(j); - end - - subplot(1, 2, 1); - scatter(mc, vc, 'filled'); - title(titles); - xlabel('Mean count'); - ylabel('Count variance'); - - subplot(1, 2, 2); - scatter(1000.0*windows, ff, 'filled'); - title(titles); - xlabel('Window [ms]'); - ylabel('Fano factor'); - xlim(1000.0*[windows(1) windows(end)]) - ylim([0.0 1.1]); - set(gca, 'XScale', 'log'); -end - diff --git a/pointprocesses/code/fanoplots.m b/pointprocesses/code/fanoplots.m deleted file mode 100644 index 949eb91..0000000 --- a/pointprocesses/code/fanoplots.m +++ /dev/null @@ -1,9 +0,0 @@ -spikes{1} = poissonspikes; -spikes{2} = pifouspikes; -spikes{3} = lifadaptspikes; -idents = {'poisson', 'pifou', 'lifadapt'}; -for k = 1:3 - figure(k) - fanoplot(spikes{k}, titles{k}); - savefigpdf(gcf, sprintf('fanoplots%s.pdf', idents{k}), 20, 7); -end diff --git a/pointprocesses/code/hompoissonspikes.m b/pointprocesses/code/hompoissonspikes.m index e5caf62..9fe8446 100644 --- a/pointprocesses/code/hompoissonspikes.m +++ b/pointprocesses/code/hompoissonspikes.m @@ -2,8 +2,6 @@ function spikes = hompoissonspikes(rate, trials, tmax) % Generate spike times of a homogeneous poisson process % using the exponential interspike interval distribution. % -% spikes = hompoissonspikes(rate, trials, tmax) -% % Arguments: % rate: the rate of the Poisson process in Hertz % trials: number of trials that should be generated @@ -11,7 +9,6 @@ function spikes = hompoissonspikes(rate, trials, tmax) % % Returns: % spikes: a cell array of vectors of spike times in seconds - spikes = cell(trials, 1); mu = 1.0/rate; nintervals = 2*round(tmax/mu); diff --git a/pointprocesses/code/isihist.m b/pointprocesses/code/isihist.m index a24989c..6c89b38 100644 --- a/pointprocesses/code/isihist.m +++ b/pointprocesses/code/isihist.m @@ -1,25 +1,13 @@ function [pdf, centers] = isihist(isis, binwidth) % Compute normalized histogram of interspike intervals. % -% [pdf, centers] = isihist(isis, binwidth) -% % Arguments: % isis: vector of interspike intervals in seconds -% binwidth: optional width in seconds to be used for the isi bins +% binwidth: width in seconds to be used for the ISI bins % % Returns: % pdf: vector with pdf of interspike intervals in Hertz % centers: vector with centers of interspikeintervalls in seconds - - if nargin < 2 - % compute good binwidth: - nperbin = 200; % average number of data points per bin - bins = length(isis)/nperbin; % number of bins - binwidth = max(isis)/bins; - if binwidth < 5e-4 % half a millisecond - binwidth = 5e-4; - end - end bins = 0.5*binwidth:binwidth:max(isis); % histogram data: [nelements, centers] = hist(isis, bins); diff --git a/pointprocesses/code/isis.m b/pointprocesses/code/isis.m index 509dcc5..d5eb7d6 100644 --- a/pointprocesses/code/isis.m +++ b/pointprocesses/code/isis.m @@ -1,13 +1,11 @@ function isivec = isis(spikes) % returns a single list of isis computed from all trials in spikes % -% isivec = isis(spikes) -% % Arguments: % spikes: a cell array of vectors of spike times in seconds % % Returns: -% isivec: a column vector with all the interspike intervalls +% isivec: a column vector with all the interspike intervals isivec = []; for k = 1:length(spikes) difftimes = diff(spikes{k}); diff --git a/pointprocesses/code/isiserialcorr.m b/pointprocesses/code/isiserialcorr.m index 1b813fc..fc5ec17 100644 --- a/pointprocesses/code/isiserialcorr.m +++ b/pointprocesses/code/isiserialcorr.m @@ -1,8 +1,6 @@ function [isicorr, lags] = isiserialcorr(isivec, maxlag) % serial correlation of interspike intervals % -% isicorr = isiserialcorr(isivec, maxlag) -% % Arguments: % isivec: vector of interspike intervals in seconds % maxlag: the maximum lag @@ -16,8 +14,7 @@ function [isicorr, lags] = isiserialcorr(isivec, maxlag) lag = lags(k); if length(isivec) > lag+10 % ensure "enough" data % NOTE: the arguments to corr must be column vectors! - % We insure this in the isis() function that - % generates the isivec. + % We insure this already in the isis() function. isicorr(k) = corr(isivec(1:end-lag), isivec(lag+1:end)); end end diff --git a/pointprocesses/code/plotcounthist.m b/pointprocesses/code/plotcounthist.m index 7a0a51d..c487e9a 100644 --- a/pointprocesses/code/plotcounthist.m +++ b/pointprocesses/code/plotcounthist.m @@ -1,24 +1,14 @@ -w = 0.1; -cmax = 8; -pmax = 0.5; -subplot(1, 3, 1); -counthist(poissonspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('Poisson'); - -subplot(1, 3, 2); -counthist(pifouspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('PIF OU'); - -subplot(1, 3, 3); -counthist(lifadaptspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('LIF adapt'); -savefigpdf(gcf, 'counthist.pdf', 20, 7); \ No newline at end of file +function counthist(spikes, w) +% Plot histogram of spike counts. +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% w: duration of window in seconds for computing the counts + n = counts(spikes, w); + maxn = max(n); + [counts, bins] = hist(n, 0:1:maxn+10); + counts = counts / sum(counts); + bar(bins, counts); + xlabel('counts k'); + ylabel('P(k)'); +end diff --git a/pointprocesses/code/plotfanofactor.m b/pointprocesses/code/plotfanofactor.m new file mode 100644 index 0000000..7335bdf --- /dev/null +++ b/pointprocesses/code/plotfanofactor.m @@ -0,0 +1,31 @@ +function plotfanofactor(spikes, wmin, wmax) +% Compute and plot Fano factor as a function of window size. +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% wmin: minimum window size in seconds +% wmax: maximum window size in seconds + windows = logspace(log10(wmin), log10(wmax), 100); + mc = zeros(1, length(windows)); + vc = zeros(1, length(windows)); + for k = 1:length(windows) + w = windows(k); + n = counts(spikes, w); + mc(k) = mean(n); + vc(k) = var(n); + end + + subplot(1, 2, 1); + scatter(mc, vc, 'filled'); + xlabel('Mean count'); + ylabel('Count variance'); + + subplot(1, 2, 2); + scatter(1000.0*windows, vc ./ mc, 'filled'); + xlabel('Window [ms]'); + ylabel('Fano factor'); + xlim(1000.0*[windows(1) windows(end)]) + ylim([0.0 1.1]); + set(gca, 'XScale', 'log'); +end + diff --git a/pointprocesses/code/plotisihist.m b/pointprocesses/code/plotisihist.m index 2f3cf93..bfdf179 100644 --- a/pointprocesses/code/plotisihist.m +++ b/pointprocesses/code/plotisihist.m @@ -1,24 +1,13 @@ function plotisihist(isis, binwidth) % Plot and annotate histogram of interspike intervals. % -% plotisihist(isis, binwidth) -% % Arguments: % isis: vector of interspike intervals in seconds -% binwidth: optional width in seconds to be used for the isi bins - - % compute normalized histogram: - if nargin < 2 - [pdf, centers] = isihist(isis); - else - [pdf, centers] = isihist(isis, binwidth); - end - - % plot: +% binwidth: width in seconds to be used for the ISI bins + [pdf, centers] = isihist(isis, binwidth); bar(1000.0*centers, pdf); % milliseconds on x-axis xlabel('ISI [ms]') ylabel('p(ISI) [1/s]') - % annotation: misi = mean(isis); sdisi = std(isis); text(0.95, 0.8, sprintf('mean=%.1f ms', 1000.0*misi), ... diff --git a/pointprocesses/code/plotisiserialcorr.m b/pointprocesses/code/plotisiserialcorr.m index 3f21418..ce806e3 100644 --- a/pointprocesses/code/plotisiserialcorr.m +++ b/pointprocesses/code/plotisiserialcorr.m @@ -1,8 +1,6 @@ function isicorr = plotisiserialcorr(isivec, maxlag) % plot serial correlation of interspike intervals % -% plotisiserialcorr(isivec, maxlag) -% % Arguments: % isivec: vector of interspike intervals in seconds % maxlag: the maximum lag diff --git a/pointprocesses/code/rasterplot.m b/pointprocesses/code/rasterplot.m index beb1970..7551552 100644 --- a/pointprocesses/code/rasterplot.m +++ b/pointprocesses/code/rasterplot.m @@ -1,8 +1,6 @@ function rasterplot(spikes, tmax) % Display a spike raster of the spike times given in spikes. % -% rasterplot(spikes, tmax) -% % Arguments: % spikes: a cell array of vectors of spike times in seconds % tmax: plot spike raster up to tmax seconds @@ -21,7 +19,7 @@ function rasterplot(spikes, tmax) ones(1, length(times)) * (k+0.4); ... ones(1, length(times)) * nan]]; end - % convert matrices into simple vectors of (x,y) pairs: + % convert matrices into column vectors of (x,y) pairs: spiketimes = spiketimes(:); trials = trials(:); % plotting this is lightning fast: diff --git a/pointprocesses/lecture/pointprocesses.tex b/pointprocesses/lecture/pointprocesses.tex index 8a297ee..f6796d2 100644 --- a/pointprocesses/lecture/pointprocesses.tex +++ b/pointprocesses/lecture/pointprocesses.tex @@ -239,19 +239,18 @@ describing univariate data sets of real numbers: \begin{exercise}{isihist.m}{} Implement a function \varcode{isihist()} that calculates the - normalized interspike interval histogram. The function should take - two input arguments; (i) a vector of interspike intervals and (ii) - the width of the bins used for the histogram. It returns the + normalized interspike interval histogram. The function should take a + vector of interspike intervals and the width of the bins to be used + for the histogram as input arguments. The function returns the probability density as well as the centers of the bins. \end{exercise} \begin{exercise}{plotisihist.m}{} - Implement a function that takes the returned values of - \varcode{isihist()} as input arguments and then plots the data. The - plot should show the histogram with the x-axis scaled to - milliseconds and should be annotated with the average ISI, the - standard deviation, and the coefficient of variation of the ISIs - (\figref{isihexamplesfig}). + Implement a function that uses the \varcode{isihist()} function from + the previous exercise to plot an ISI histogram. The plot shows the + histogram with the x-axis scaled to milliseconds, annotated with the + average ISI, the standard deviation, and the coefficient of + variation of the ISIs (\figref{isihexamplesfig}). \end{exercise} \subsection{Interval correlations} @@ -332,8 +331,8 @@ characterized by the non-zero serial correlations \begin{exercise}{isiserialcorr.m}{} Implement a function \varcode{isiserialcorr()} that takes a vector - of interspike intervals as input argument and calculates the serial - correlations up to some maximum lag. + of interspike intervals as input and computes serial correlations up + to some maximum lag. \end{exercise} \begin{exercise}{plotisiserialcorr.m}{} @@ -398,27 +397,10 @@ Because spike counts are unitless and positive numbers the \end{equation} is a commonly used measure for quantifying the variability of event counts relative to the mean number of events. In particular for - homogeneous Poisson processes the Fano factor equals one, - independently of the time window $W$. + homogeneous Poisson processes the Fano factor equals exactly one and + is independent of the time window $W$. \end{itemize} -Note that all of these statistics depend in general on the chosen -window length $W$. The average spike count, for example, grows -linearly with $W$ for sufficiently large time windows: $\langle n -\rangle = r W$, \eqnref{firingrate}. Doubling the counting window -doubles the spike count. As does the spike-count variance -(\figref{fanofig}). At smaller time windows the statistics of the -event counts might depend on the particular duration of the counting -window. There might be an optimal time window for which the variance -of the spike count is minimal. The Fano factor plotted as a function -of the time window illustrates such properties of point processes -(\figref{fanofig}). - -This also has consequences for information transmission in neural -systems. The lower the variance in spike count relative to the -averaged count, the higher the signal-to-noise ratio at which -information encoded in the mean spike count is transmitted. - \begin{figure}[t] \includegraphics{fanoexamples} \titlecaption{\label{fanofig} Fano factor.}{Counting events in time @@ -435,13 +417,52 @@ information encoded in the mean spike count is transmitted. interspike intervals (right).} \end{figure} -\begin{exercise}{counthist.m}{} - Implement a function \varcode{counthist()} that calculates and plots - the distribution of spike counts observed in a certain time - window. The function should take two input arguments: a cell-array - of vectors containing the spike times in seconds observed in a - number of trials, and the duration of the time window that is used - to evaluate the counts. +Note that all of these statistics depend in general on the chosen +window length $W$ used for counting the events. The average spike +count, for example, grows linearly with $W$ for sufficiently large +time windows: $\langle n \rangle = r W$, \eqnref{firingrate}. Doubling +the counting window doubles the spike count. As does the spike-count +variance (\figref{fanofig}). At smaller time windows the statistics of +the event counts might depend on the particular duration of the +counting window. There could be an optimal time window for which the +variance of the spike count is minimal. The Fano factor plotted as a +function of the time window illustrates such properties of point +processes in a single graph (\figref{fanofig}). + +This also has consequences for information transmission in neural +systems. The membrane time constant of a post-synaptic neuron defines +a counting window. If input spikes arrive within about one time +constant they are added up. The lower the variance in spike count +relative to the averaged count, the higher the signal-to-noise ratio +at which information encoded in the mean spike count is +transmitted. If the membrane time constant of the target neuron +matches the counting window where the Fano factor is minimal, then +information is potentially transmitted at the highest possible +signal-to-noise ratio. For this reason, the Fano factor is used in the +Neurosciences to quantify and analyze reliability of neuronal +responses. + +\begin{exercise}{counts.m}{} + Write a function \varcode{counts()} that counts the number of spikes + in windows of given duration and returns the counts in a single + vector. Spike times are passed as a cell-array of vectors, + containing the spike times in seconds observed in a number of + trials, to the function. +\end{exercise} + +\begin{exercise}{plotcounthist.m}{} + Write a function that takes a cell-array with spike times as input + and plots a normalized histogram of the spike counts counted in + windows of a given duration. +\end{exercise} + +\begin{exercise}{plotfanofactor.m}{} + Write a function that takes a cell-array with spike times as input + and plots in one plot count variances a function of the + corresponding mean counts and in a second plot the Fano factor as a + function of the duration of the count window in logarithmic + scale. Two arguments of the function take the minimum and maximum + duration of the count window. \end{exercise} From 030332051ac851a580adbea10532ef1e9fc0afa7 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 18 Jan 2021 23:05:17 +0100 Subject: [PATCH 80/87] [likelihood] add mlestd.out --- likelihood/exercises/mlestd.out | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 likelihood/exercises/mlestd.out diff --git a/likelihood/exercises/mlestd.out b/likelihood/exercises/mlestd.out new file mode 100644 index 0000000..947a8cd --- /dev/null +++ b/likelihood/exercises/mlestd.out @@ -0,0 +1,11 @@ +n=50 + mean 3.189 + standard deviation 1.953 + likelihood: standard deviation 1.953 + log-likelihood: standard deviation 1.953 + +n=1000 + mean 3.094 + standard deviation 1.995 + likelihood: standard deviation 1.000 + log-likelihood: standard deviation 1.995 From 2bc8119e2e3424d1e4a757343cd0ceea1cd8a6bd Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 18 Jan 2021 23:18:14 +0100 Subject: [PATCH 81/87] [likelihood] added mlestd.out and fixed mlestd.pdf --- exercises.mk | 2 +- likelihood/exercises/mlestd.out | 14 +++++++------- likelihood/exercises/mlestd.pdf | Bin 75531 -> 10259 bytes 3 files changed, 8 insertions(+), 8 deletions(-) diff --git a/exercises.mk b/exercises.mk index f9d9cd8..ae68f24 100644 --- a/exercises.mk +++ b/exercises.mk @@ -27,7 +27,7 @@ watchsolutions : while true; do ! make -q solutions && make solutions; sleep 0.5; done clean : - rm -f *~ *.aux *.log *.out + rm -f *~ *.aux *.log $(EXERCISES:.pdf=.out) $(SOLUTIONS:.pdf=.out) cleanup : clean rm -f $(SOLUTIONS) $(EXERCISES) diff --git a/likelihood/exercises/mlestd.out b/likelihood/exercises/mlestd.out index 947a8cd..25fec42 100644 --- a/likelihood/exercises/mlestd.out +++ b/likelihood/exercises/mlestd.out @@ -1,11 +1,11 @@ n=50 - mean 3.189 - standard deviation 1.953 - likelihood: standard deviation 1.953 - log-likelihood: standard deviation 1.953 + mean 3.468 + standard deviation 1.833 + 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zPwatgFltB;;T}I{$*{0qy_RS4W$G1N#0QBWM!-$)~3UCfVQlv~@K9 z(N`P1oarBYpn~sDj2S|q(WxQ7&rSQFAP_h>I$u_mCBruegZtxXFUHM~h}XrNYwF_6 z@p?qOwjRNhWJWaACFq*r@g!57y?c!@|2xZ Date: Tue, 19 Jan 2021 00:10:39 +0100 Subject: [PATCH 82/87] [pointprocesses] moved exercise codes to exercise folder --- pointprocesses/code/counts.m | 25 ++++++ pointprocesses/code/plotcounthist.m | 2 +- pointprocesses/code/spikecounts.m | 30 ------- pointprocesses/code/spikecountshists.m | 17 ---- pointprocesses/exercises/counts.m | 25 ++++++ pointprocesses/exercises/fanoplot.m | 32 ++++++++ pointprocesses/exercises/fanoplots.m | 9 ++ pointprocesses/exercises/isihist.m | 29 +++++++ pointprocesses/exercises/isis.m | 16 ++++ pointprocesses/exercises/isiserialcorr.m | 21 +++++ pointprocesses/exercises/plotisihist.m | 31 +++++++ .../{code => exercises}/plotisihs.m | 0 pointprocesses/exercises/plotisiserialcorr.m | 14 ++++ pointprocesses/exercises/plotpoissonisih.m | 12 +++ .../{code => exercises}/plotserialcorr.m | 8 +- .../{code => exercises}/plotspikeraster.m | 0 pointprocesses/exercises/pointprocesses-1.tex | 82 +++++++++++++------ pointprocesses/exercises/pointprocesses-2.tex | 4 +- pointprocesses/exercises/rasterplot.m | 43 ++++++++++ pointprocesses/exercises/spikecountshists.m | 22 +++++ 20 files changed, 341 insertions(+), 81 deletions(-) create mode 100644 pointprocesses/code/counts.m delete mode 100644 pointprocesses/code/spikecounts.m delete mode 100644 pointprocesses/code/spikecountshists.m create mode 100644 pointprocesses/exercises/counts.m create mode 100644 pointprocesses/exercises/fanoplot.m create mode 100644 pointprocesses/exercises/fanoplots.m create mode 100644 pointprocesses/exercises/isihist.m create mode 100644 pointprocesses/exercises/isis.m create mode 100644 pointprocesses/exercises/isiserialcorr.m create mode 100644 pointprocesses/exercises/plotisihist.m rename pointprocesses/{code => exercises}/plotisihs.m (100%) create mode 100644 pointprocesses/exercises/plotisiserialcorr.m create mode 100644 pointprocesses/exercises/plotpoissonisih.m rename pointprocesses/{code => exercises}/plotserialcorr.m (53%) rename pointprocesses/{code => exercises}/plotspikeraster.m (100%) create mode 100644 pointprocesses/exercises/rasterplot.m create mode 100644 pointprocesses/exercises/spikecountshists.m diff --git a/pointprocesses/code/counts.m b/pointprocesses/code/counts.m new file mode 100644 index 0000000..90e53ef --- /dev/null +++ b/pointprocesses/code/counts.m @@ -0,0 +1,25 @@ +function n = counts(spikes, w) +% Count spikes in time windows. +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% w: duration of window in seconds for computing the counts +% +% Returns: +% n: vector with spike counts + tmax = spikes{1}(end); + n = []; + for k = 1:length(spikes) + times = spikes{k}; +% alternative 1: count the number of spikes in each window: +% for tk = 0:w:tmax-w +% nn = sum((times >= tk) & (times < tk+w)); +% % nn = length(find((times >= tk) & (times < tk+w))); +% n = [n, nn]; +% end +% alternative 2: use the hist() function to do that! + tbins = 0.5*w:w:tmax-0.5*w; + nn = hist(times, tbins); + n = [n, nn]; + end +end diff --git a/pointprocesses/code/plotcounthist.m b/pointprocesses/code/plotcounthist.m index c487e9a..ddfa7fc 100644 --- a/pointprocesses/code/plotcounthist.m +++ b/pointprocesses/code/plotcounthist.m @@ -1,4 +1,4 @@ -function counthist(spikes, w) +function plotcounthist(spikes, w) % Plot histogram of spike counts. % % Arguments: diff --git a/pointprocesses/code/spikecounts.m b/pointprocesses/code/spikecounts.m deleted file mode 100644 index c3eef4f..0000000 --- a/pointprocesses/code/spikecounts.m +++ /dev/null @@ -1,30 +0,0 @@ -function counts = spikecounts(spikes, w) -% Compute vector of spike counts. -% -% counts = spikecounts(spikes, w) -% -% Arguments: -% spikes: a cell array of vectors of spike times in seconds -% w: observation window duration in seconds for computing the counts -% -% Returns: -% counts: vector of spike counts - - % collect spike counts: - tmax = spikes{1}(end); - counts = []; - for k = 1:length(spikes) - times = spikes{k}; -% method 1: count the number of spikes in each window: -% for tk = 0:w:tmax-w -% nn = sum((times >= tk) & (times < tk+w)); -% %nn = length(times((times >= tk) & (times < tk+w))); -% %nn = length(find((times >= tk) & (times < tk+w))); -% counts = [counts nn]; -% end -% method 2: use the hist() function to do that! - tbins = 0.5*w:w:tmax-0.5*w; - nn = hist(times, tbins); - counts = [counts nn]; - end -end diff --git a/pointprocesses/code/spikecountshists.m b/pointprocesses/code/spikecountshists.m deleted file mode 100644 index 5876386..0000000 --- a/pointprocesses/code/spikecountshists.m +++ /dev/null @@ -1,17 +0,0 @@ -w = 0.1; -bins = 0.0:1.0:10.0; - -counts{1} = spikecounts(poissonspikes, w); -counts{2} = spikecounts(pifouspikes, w); -counts{3} = spikecounts(lifadaptspikes, w); -titles = {'Poisson', 'PIF OU', 'LIF adapt'}; -for k = 1:3 - subplot(1, 3, k); - [h, b] = hist(counts{k}, bins); - bar(b, h/sum(h)); - title(titles{k}) - xlabel('Spike count'); - xlim([-0.5, 8.5]); - ylim([0.0 0.8]); -end -savefigpdf(gcf, 'spikecountshists.pdf', 20, 7); diff --git a/pointprocesses/exercises/counts.m b/pointprocesses/exercises/counts.m new file mode 100644 index 0000000..90e53ef --- /dev/null +++ b/pointprocesses/exercises/counts.m @@ -0,0 +1,25 @@ +function n = counts(spikes, w) +% Count spikes in time windows. +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% w: duration of window in seconds for computing the counts +% +% Returns: +% n: vector with spike counts + tmax = spikes{1}(end); + n = []; + for k = 1:length(spikes) + times = spikes{k}; +% alternative 1: count the number of spikes in each window: +% for tk = 0:w:tmax-w +% nn = sum((times >= tk) & (times < tk+w)); +% % nn = length(find((times >= tk) & (times < tk+w))); +% n = [n, nn]; +% end +% alternative 2: use the hist() function to do that! + tbins = 0.5*w:w:tmax-0.5*w; + nn = hist(times, tbins); + n = [n, nn]; + end +end diff --git a/pointprocesses/exercises/fanoplot.m b/pointprocesses/exercises/fanoplot.m new file mode 100644 index 0000000..671ced9 --- /dev/null +++ b/pointprocesses/exercises/fanoplot.m @@ -0,0 +1,32 @@ +function fanoplot(spikes, titles) +% Plots fano factor as a function of window size. +% +% Arguments: +% spikes: a cell array of vectors of spike times +% titles: string that is used as a title for the plots + windows = logspace(-3.0, -0.5, 100); + mc = zeros(1, length(windows)); + vc = zeros(1, length(windows)); + for j = 1:length(windows) + w = windows(j); + spikecounts = counts(spikes, w); + mc(j) = mean(spikecounts); + vc(j) = var(spikecounts); + end + + subplot(1, 2, 1); + scatter(mc, vc, 'filled'); + title(titles); + xlabel('Mean count'); + ylabel('Count variance'); + + subplot(1, 2, 2); + scatter(1000.0*windows, vc ./ mc, 'filled'); + title(titles); + xlabel('Window [ms]'); + ylabel('Fano factor'); + xlim(1000.0*[windows(1) windows(end)]) + ylim([0.0 1.1]); + set(gca, 'XScale', 'log'); +end + diff --git a/pointprocesses/exercises/fanoplots.m b/pointprocesses/exercises/fanoplots.m new file mode 100644 index 0000000..949eb91 --- /dev/null +++ b/pointprocesses/exercises/fanoplots.m @@ -0,0 +1,9 @@ +spikes{1} = poissonspikes; +spikes{2} = pifouspikes; +spikes{3} = lifadaptspikes; +idents = {'poisson', 'pifou', 'lifadapt'}; +for k = 1:3 + figure(k) + fanoplot(spikes{k}, titles{k}); + savefigpdf(gcf, sprintf('fanoplots%s.pdf', idents{k}), 20, 7); +end diff --git a/pointprocesses/exercises/isihist.m b/pointprocesses/exercises/isihist.m new file mode 100644 index 0000000..a24989c --- /dev/null +++ b/pointprocesses/exercises/isihist.m @@ -0,0 +1,29 @@ +function [pdf, centers] = isihist(isis, binwidth) +% Compute normalized histogram of interspike intervals. +% +% [pdf, centers] = isihist(isis, binwidth) +% +% Arguments: +% isis: vector of interspike intervals in seconds +% binwidth: optional width in seconds to be used for the isi bins +% +% Returns: +% pdf: vector with pdf of interspike intervals in Hertz +% centers: vector with centers of interspikeintervalls in seconds + + if nargin < 2 + % compute good binwidth: + nperbin = 200; % average number of data points per bin + bins = length(isis)/nperbin; % number of bins + binwidth = max(isis)/bins; + if binwidth < 5e-4 % half a millisecond + binwidth = 5e-4; + end + end + bins = 0.5*binwidth:binwidth:max(isis); + % histogram data: + [nelements, centers] = hist(isis, bins); + % normalization (integral = 1): + pdf = nelements / sum(nelements) / binwidth; +end + diff --git a/pointprocesses/exercises/isis.m b/pointprocesses/exercises/isis.m new file mode 100644 index 0000000..d5eb7d6 --- /dev/null +++ b/pointprocesses/exercises/isis.m @@ -0,0 +1,16 @@ +function isivec = isis(spikes) +% returns a single list of isis computed from all trials in spikes +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% +% Returns: +% isivec: a column vector with all the interspike intervals + isivec = []; + for k = 1:length(spikes) + difftimes = diff(spikes{k}); + % difftimes(:) ensures a column vector + % regardless of the type of vector in spikes{k} + isivec = [isivec; difftimes(:)]; + end +end diff --git a/pointprocesses/exercises/isiserialcorr.m b/pointprocesses/exercises/isiserialcorr.m new file mode 100644 index 0000000..fc5ec17 --- /dev/null +++ b/pointprocesses/exercises/isiserialcorr.m @@ -0,0 +1,21 @@ +function [isicorr, lags] = isiserialcorr(isivec, maxlag) +% serial correlation of interspike intervals +% +% Arguments: +% isivec: vector of interspike intervals in seconds +% maxlag: the maximum lag +% +% Returns: +% isicorr: vector with the serial correlations for lag 0 to maxlag +% lags: vector with the lags corresponding to isicorr + lags = 0:maxlag; + isicorr = zeros(size(lags)); + for k = 1:length(lags) + lag = lags(k); + if length(isivec) > lag+10 % ensure "enough" data + % NOTE: the arguments to corr must be column vectors! + % We insure this already in the isis() function. + isicorr(k) = corr(isivec(1:end-lag), isivec(lag+1:end)); + end + end +end diff --git a/pointprocesses/exercises/plotisihist.m b/pointprocesses/exercises/plotisihist.m new file mode 100644 index 0000000..2f3cf93 --- /dev/null +++ b/pointprocesses/exercises/plotisihist.m @@ -0,0 +1,31 @@ +function plotisihist(isis, binwidth) +% Plot and annotate histogram of interspike intervals. +% +% plotisihist(isis, binwidth) +% +% Arguments: +% isis: vector of interspike intervals in seconds +% binwidth: optional width in seconds to be used for the isi bins + + % compute normalized histogram: + if nargin < 2 + [pdf, centers] = isihist(isis); + else + [pdf, centers] = isihist(isis, binwidth); + end + + % plot: + bar(1000.0*centers, pdf); % milliseconds on x-axis + xlabel('ISI [ms]') + ylabel('p(ISI) [1/s]') + % annotation: + misi = mean(isis); + sdisi = std(isis); + text(0.95, 0.8, sprintf('mean=%.1f ms', 1000.0*misi), ... + 'Units', 'normalized', 'HorizontalAlignment', 'right') + text(0.95, 0.7, sprintf('std=%.1f ms', 1000.0*sdisi), ... + 'Units', 'normalized', 'HorizontalAlignment', 'right') + text(0.95, 0.6, sprintf('CV=%.2f', sdisi/misi), ... + 'Units', 'normalized', 'HorizontalAlignment', 'right') +end + diff --git a/pointprocesses/code/plotisihs.m b/pointprocesses/exercises/plotisihs.m similarity index 100% rename from pointprocesses/code/plotisihs.m rename to pointprocesses/exercises/plotisihs.m diff --git a/pointprocesses/exercises/plotisiserialcorr.m b/pointprocesses/exercises/plotisiserialcorr.m new file mode 100644 index 0000000..ce806e3 --- /dev/null +++ b/pointprocesses/exercises/plotisiserialcorr.m @@ -0,0 +1,14 @@ +function isicorr = plotisiserialcorr(isivec, maxlag) +% plot serial correlation of interspike intervals +% +% Arguments: +% isivec: vector of interspike intervals in seconds +% maxlag: the maximum lag + [isicorr, lags] = isiserialcorr(isivec, maxlag); + plot(lags, isicorr, '-b'); + hold on; + scatter(lags, isicorr, 20.0, 'b', 'filled'); + hold off; + xlabel('Lag k') + ylabel('\rho_k') +end diff --git a/pointprocesses/exercises/plotpoissonisih.m b/pointprocesses/exercises/plotpoissonisih.m new file mode 100644 index 0000000..2218196 --- /dev/null +++ b/pointprocesses/exercises/plotpoissonisih.m @@ -0,0 +1,12 @@ +maxisi = 300.0; +poissonisis = isis(poissonspikes); +rate = 1.0/mean(poissonisis); +plotisihist(poissonisis, 0.001); +tt = linspace(0.0, 0.001*maxisi, 200); +pexp = rate*exp(-tt*rate); +hold on; +plot(1000.0*tt, pexp, 'r') +hold off; +xlim([0, maxisi]) +title('Poisson'); +savefigpdf(gcf, 'poissonisihist.pdf', 10, 7); diff --git a/pointprocesses/code/plotserialcorr.m b/pointprocesses/exercises/plotserialcorr.m similarity index 53% rename from pointprocesses/code/plotserialcorr.m rename to pointprocesses/exercises/plotserialcorr.m index 05f3ea8..ab33e50 100644 --- a/pointprocesses/code/plotserialcorr.m +++ b/pointprocesses/exercises/plotserialcorr.m @@ -1,17 +1,17 @@ maxlag = 10; rrange = [-0.5, 1.05]; subplot(1, 3, 1); -isiserialcorr(poissonisis, maxlag); +plotisiserialcorr(poissonisis, maxlag); ylim(rrange) title('Poisson'); subplot(1, 3, 2); -isiserialcorr(pifouisis, maxlag); +plotisiserialcorr(pifouisis, maxlag); ylim(rrange) title('PIF OU'); subplot(1, 3, 3); -isiserialcorr(lifadaptisis, maxlag); +plotisiserialcorr(lifadaptisis, maxlag); ylim(rrange) title('LIF adapt'); -savefigpdf(gcf, 'serialcorr.pdf', 20, 7); \ No newline at end of file +savefigpdf(gcf, 'serialcorr.pdf', 20, 7); diff --git a/pointprocesses/code/plotspikeraster.m b/pointprocesses/exercises/plotspikeraster.m similarity index 100% rename from pointprocesses/code/plotspikeraster.m rename to pointprocesses/exercises/plotspikeraster.m diff --git a/pointprocesses/exercises/pointprocesses-1.tex b/pointprocesses/exercises/pointprocesses-1.tex index 2da20f9..6edb623 100644 --- a/pointprocesses/exercises/pointprocesses-1.tex +++ b/pointprocesses/exercises/pointprocesses-1.tex @@ -15,6 +15,9 @@ \begin{questions} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \question \qt{Read in chapter 10 on ``Spike-train analysis'' sections 10.1 -- 10.5!}\vspace{-3ex} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Statistics of interspike intervals} Download the files \code{poisson.mat}, @@ -61,11 +64,12 @@ of the spike. When appropriate, the function should use milliseconds for the time axis instead of seconds. - Use this function to plot the first second of the - spike rasters of the three neurons. + Use this function to plot the first second of the spike rasters of + the three neurons. Carefully look at the raster plots. How do the + spike rasters differ between the three neurons? \begin{solution} - \lstinputlisting{../code/rasterplot.m} - \lstinputlisting{../code/plotspikeraster.m} + \lstinputlisting{rasterplot.m} + \lstinputlisting{plotspikeraster.m} \mbox{}\\[-3ex] \colorbox{white}{\includegraphics[width=1\textwidth]{spikeraster}} \end{solution} @@ -73,7 +77,7 @@ \part Write a function that returns a single vector containing the interspike intervals of all trials of spike times. \begin{solution} - \lstinputlisting{../code/isis.m} + \lstinputlisting{isis.m} \end{solution} \part Write a function that computes an estimate of the @@ -90,33 +94,51 @@ the standard deviation and the coefficient of variation and display them in the plot as well. - Use this and the previous functions to compare the - interspike interval statistics of the three neurons. + Use this and the previous functions to compare the interspike + interval statistics of the three neurons. How do the ISI + histograms differ between the three neurons? \begin{solution} - \lstinputlisting{../code/isihist.m} - \lstinputlisting{../code/plotisihist.m} - \lstinputlisting{../code/plotisihs.m} + \lstinputlisting{isihist.m} + \lstinputlisting{plotisihist.m} + \lstinputlisting{plotisihs.m} \mbox{}\\[-3ex] \colorbox{white}{\includegraphics[width=1\textwidth]{isihist}} \end{solution} + + \part Compare the interspike interval histogram of the Poisson + spike train to the expected exponential distribution + \[ p(T) = \lambda e^{-\lambda T} \; .\] of a Poisson process with + firing rate $\lambda$. Estimate the firing rate from the inverse + of the mean interspike interval. + \begin{solution} + \lstinputlisting{plotpoissonisih.m} + %\mbox{}\\[-3ex] + %\colorbox{white}{\includegraphics[width=1\textwidth]{poissonisihist}} + \end{solution} % XXX Add return map!!! XXX - \part Write a function that computes and plots the serial - correlations of interspike intervals for lags upto - \code{maxlag}. The serial correlations $\rho_k$ for lag $k$ of the - interspike intervals $T_i$ are the correlation coefficients - between interspike intervals $T_i$ and the intervals $T_{i+k}$ - that are shifted by lag $k$: + \part Write a function that computes the serial correlations of + interspike intervals for lags up to \code{maxlag}. The serial + correlations $\rho_k$ for lag $k$ of the interspike intervals + $T_i$ are the correlation coefficients between interspike + intervals $T_i$ and the intervals $T_{i+k}$ that are shifted by + lag $k$: \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm - var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] + var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] + + Write another function that plots the serial correlations. - Use this function to compare the serial correlations of the - interspike intervals of the three neurons. + Use the functions to compare the serial correlations of the + interspike intervals of the three neurons. What do the serial + correlations mean? How do they relate to what you see in the + raster plots? Do the serial correlations of the Poisson spike + train match the expectations? \begin{solution} - \lstinputlisting{../code/isiserialcorr.m} - \lstinputlisting{../code/plotserialcorr.m} + \lstinputlisting{isiserialcorr.m} + \lstinputlisting{plotisiserialcorr.m} + \lstinputlisting{plotserialcorr.m} \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}} \end{solution} @@ -127,16 +149,22 @@ \question \qt{Statistics of spike counts} Now let's have a look at the statistics of the spike counts. \begin{parts} - \part Write a function that counts and returns the number of - spikes in windows of a given width $W$. + \part Write a function that counts and returns a vector with the + number of spikes in windows of a given width $W$. Use this function to generate a properly normalized histogram of spike counts for the data of the three types of neurons. Use 100\,ms for the window width. + + Compare the distributions with the Poisson distribution expected + for a Poisson spike train: + \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] where + $\lambda$ is the rate of the spike train that you should estimate + from the data. \begin{solution} - \lstinputlisting{../code/spikecounts.m} + \lstinputlisting{counts.m} \newsolutionpage - \lstinputlisting{../code/spikecountshists.m} + \lstinputlisting{spikecounthists.m} \colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}} \end{solution} @@ -148,9 +176,9 @@ (the mean spike count increases for larger window widths). The other plot showing the Fano factor as a function of window width. \begin{solution} - \lstinputlisting{../code/fanoplot.m} + \lstinputlisting{fanoplot.m} \newsolutionpage - \lstinputlisting{../code/fanoplots.m} + \lstinputlisting{fanoplots.m} \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspoisson}} \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspifou}} \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotslifadapt}} diff --git a/pointprocesses/exercises/pointprocesses-2.tex b/pointprocesses/exercises/pointprocesses-2.tex index 883b0b2..cd7a2f3 100644 --- a/pointprocesses/exercises/pointprocesses-2.tex +++ b/pointprocesses/exercises/pointprocesses-2.tex @@ -103,7 +103,7 @@ f\"ur gen\"ugend kleine $\Delta t$. soll. Hinweis: es gibt eine \code{matlab} Funktion, die die Fakult\"at $n!$ berechnet. \begin{solution} - \lstinputlisting{../code/counthist.m} + \lstinputlisting{counthist.m} \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}} \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}} \end{solution} @@ -115,7 +115,7 @@ f\"ur gen\"ugend kleine $\Delta t$. den Ergebnissen angefertigt werden: (i) Varianz gegen Mittelwert der counts. (ii) Fano Faktor als Funktion der Fensterbreite. \begin{solution} - \lstinputlisting{../code/fano.m} + \lstinputlisting{fanoplot.m} \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}} \end{solution} diff --git a/pointprocesses/exercises/rasterplot.m b/pointprocesses/exercises/rasterplot.m new file mode 100644 index 0000000..ccbfe60 --- /dev/null +++ b/pointprocesses/exercises/rasterplot.m @@ -0,0 +1,43 @@ +function rasterplot(spikes, tmax) +% Display a spike raster of the spike times given in spikes. +% +% rasterplot(spikes, tmax) +% +% Arguments: +% spikes: a cell array of vectors of spike times in seconds +% tmax: plot spike raster up to tmax seconds + in_msecs = tmax < 1.5 + spiketimes = []; + trials = []; + ntrials = length(spikes); + for k = 1:ntrials + times = spikes{k}; + times = times(times Date: Tue, 19 Jan 2021 00:24:14 +0100 Subject: [PATCH 83/87] [pointprocesses] fixed exercise code references --- pointprocesses/exercises/pointprocesses-1.tex | 6 +++--- pointprocesses/exercises/pointprocesses-2.tex | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/pointprocesses/exercises/pointprocesses-1.tex b/pointprocesses/exercises/pointprocesses-1.tex index 6edb623..44cab5a 100644 --- a/pointprocesses/exercises/pointprocesses-1.tex +++ b/pointprocesses/exercises/pointprocesses-1.tex @@ -1,6 +1,6 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\newcommand{\exercisetopic}{Point Processes} +\newcommand{\exercisetopic}{Point processes} \newcommand{\exercisenum}{11} \newcommand{\exercisedate}{January 19th, 2021} @@ -116,6 +116,7 @@ %\colorbox{white}{\includegraphics[width=1\textwidth]{poissonisihist}} \end{solution} + \continuepage % XXX Add return map!!! XXX \part Write a function that computes the serial correlations of interspike intervals for lags up to \code{maxlag}. The serial @@ -144,7 +145,6 @@ \end{parts} - \continuepage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Statistics of spike counts} Now let's have a look at the statistics of the spike counts. @@ -164,7 +164,7 @@ \begin{solution} \lstinputlisting{counts.m} \newsolutionpage - \lstinputlisting{spikecounthists.m} + \lstinputlisting{spikecountshists.m} \colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}} \end{solution} diff --git a/pointprocesses/exercises/pointprocesses-2.tex b/pointprocesses/exercises/pointprocesses-2.tex index cd7a2f3..8af40c9 100644 --- a/pointprocesses/exercises/pointprocesses-2.tex +++ b/pointprocesses/exercises/pointprocesses-2.tex @@ -103,7 +103,7 @@ f\"ur gen\"ugend kleine $\Delta t$. soll. Hinweis: es gibt eine \code{matlab} Funktion, die die Fakult\"at $n!$ berechnet. \begin{solution} - \lstinputlisting{counthist.m} + %\lstinputlisting{counthist.m} \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}} \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}} \end{solution} From 73c6d35536530a857d8fce2859f1ca035956a2fd Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 19 Jan 2021 12:59:54 +0100 Subject: [PATCH 84/87] [pointprocesses] finished solution of first exercise --- pointprocesses/exercises/fanoplots.m | 4 ++-- .../exercises/fanoplotslifadapt.pdf | Bin 18196 -> 5969 bytes pointprocesses/exercises/fanoplotspifou.pdf | Bin 18088 -> 5963 bytes pointprocesses/exercises/fanoplotspoisson.pdf | Bin 17508 -> 5895 bytes pointprocesses/exercises/isihist.pdf | Bin 23441 -> 7656 bytes pointprocesses/exercises/plotisihs.m | 7 ++++--- pointprocesses/exercises/plotpoissonisih.m | 7 ++++--- pointprocesses/exercises/plotspikeraster.m | 8 ++++++++ pointprocesses/exercises/pointprocesses-1.tex | 19 +++++++++++++----- pointprocesses/exercises/rasterplot.m | 2 +- .../{code => exercises}/savefigpdf.m | 0 pointprocesses/exercises/serialcorr.pdf | Bin 6595 -> 4208 bytes pointprocesses/exercises/spikecountshists.pdf | Bin 4640 -> 4407 bytes pointprocesses/exercises/spikeraster.pdf | Bin 10709 -> 17411 bytes 14 files changed, 33 insertions(+), 14 deletions(-) rename pointprocesses/{code => exercises}/savefigpdf.m (100%) diff --git a/pointprocesses/exercises/fanoplots.m b/pointprocesses/exercises/fanoplots.m index 949eb91..49d7343 100644 --- a/pointprocesses/exercises/fanoplots.m +++ b/pointprocesses/exercises/fanoplots.m @@ -1,9 +1,9 @@ spikes{1} = poissonspikes; spikes{2} = pifouspikes; spikes{3} = lifadaptspikes; -idents = {'poisson', 'pifou', 'lifadapt'}; +titles = {'poisson', 'pifou', 'lifadapt'}; for k = 1:3 figure(k) fanoplot(spikes{k}, titles{k}); - savefigpdf(gcf, 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.../exercises/iafisistats-solutions.pdf | Bin 210869 -> 0 bytes pointprocesses/exercises/iafisistats.pdf | Bin 81872 -> 0 bytes pointprocesses/exercises/iafisistats.tex | 142 ------------- .../{code => exercises}/inversegauss.m | 0 .../{code => exercises}/inversegaussplot.m | 0 .../{code => exercises}/lifficurves.m | 0 pointprocesses/{code => exercises}/lifisih.m | 0 .../{code => exercises}/lifisistats.m | 0 pointprocesses/exercises/pointprocesses-2.tex | 200 ++++++++---------- pointprocesses/exercises/pointprocesses-3.tex | 163 -------------- .../exercises/pointprocesses01-de.tex | 198 ----------------- .../exercises/poisson-solutions.pdf | Bin 199254 -> 0 bytes .../poissoncounthistdist100hz100ms.pdf | Bin 3815 -> 0 bytes .../poissoncounthistdist100hz10ms.pdf | Bin 3630 -> 0 bytes pointprocesses/exercises/poissonfano100hz.pdf | Bin 17762 -> 0 bytes pointprocesses/exercises/poissonisihist.pdf | Bin 0 -> 7119 bytes pointprocesses/exercises/poissonisistats.pdf | Bin 26757 -> 0 bytes .../exercises/poissonraster100hz.pdf | Bin 6050 -> 0 bytes .../exercises/poissonserial100hz.pdf | Bin 4366 -> 0 bytes pointprocesses/exercises/psth.tex | 48 ++--- 25 files changed, 106 insertions(+), 730 deletions(-) delete mode 100644 pointprocesses/exercises/counthist.pdf delete mode 100644 pointprocesses/exercises/hompoissonisih.m delete mode 100644 pointprocesses/exercises/hompoissonisistats.m delete mode 100644 pointprocesses/exercises/hompoissonspikes.m delete mode 100644 pointprocesses/exercises/iafisistats-solutions.pdf delete mode 100644 pointprocesses/exercises/iafisistats.pdf delete mode 100644 pointprocesses/exercises/iafisistats.tex rename pointprocesses/{code => exercises}/inversegauss.m (100%) rename pointprocesses/{code => exercises}/inversegaussplot.m (100%) rename pointprocesses/{code => exercises}/lifficurves.m (100%) rename pointprocesses/{code => exercises}/lifisih.m (100%) rename pointprocesses/{code => exercises}/lifisistats.m (100%) delete mode 100644 pointprocesses/exercises/pointprocesses-3.tex delete mode 100644 pointprocesses/exercises/pointprocesses01-de.tex delete mode 100644 pointprocesses/exercises/poisson-solutions.pdf delete mode 100644 pointprocesses/exercises/poissoncounthistdist100hz100ms.pdf delete mode 100644 pointprocesses/exercises/poissoncounthistdist100hz10ms.pdf delete mode 100644 pointprocesses/exercises/poissonfano100hz.pdf create mode 100644 pointprocesses/exercises/poissonisihist.pdf delete mode 100644 pointprocesses/exercises/poissonisistats.pdf delete mode 100644 pointprocesses/exercises/poissonraster100hz.pdf delete mode 100644 pointprocesses/exercises/poissonserial100hz.pdf diff --git a/pointprocesses/exercises/Makefile b/pointprocesses/exercises/Makefile index 0d84b85..2bbd561 100644 --- a/pointprocesses/exercises/Makefile +++ b/pointprocesses/exercises/Makefile @@ -1,3 +1,3 @@ -TEXFILES=$(wildcard pointprocesses-?.tex) +TEXFILES=$(wildcard pointprocesses-?.tex) psth.tex include ../../exercises.mk diff 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a/pointprocesses/exercises/hompoissonisih.m b/pointprocesses/exercises/hompoissonisih.m deleted file mode 100644 index cd2bc06..0000000 --- a/pointprocesses/exercises/hompoissonisih.m +++ /dev/null @@ -1,18 +0,0 @@ -% generate spike times: -rate = 20.0; -spikes = hompoissonspikes( 10, rate, 50.0 ); -% isi histogram: -isivec = isis( spikes ); -isihist( isivec ); -hold on -% theoretical density: -xmax = 5.0/rate; -x = 0:0.0001:xmax; -y = rate*exp(-rate*x); -plot( 1000.0*x, y, 'r', 'LineWidth', 3 ); -% plot details: -title( sprintf( 'Poisson spike trains, rate=%g Hz, nisi=%d', rate, length( isivec ) ) ) -xlim( [ 0.0 1000.0*xmax ] ) -ylim( [ 0.0 1.1*rate ] ) -legend( 'data', 'poisson' ) -hold off diff --git a/pointprocesses/exercises/hompoissonisistats.m b/pointprocesses/exercises/hompoissonisistats.m deleted file mode 100644 index 7ca3cf3..0000000 --- a/pointprocesses/exercises/hompoissonisistats.m +++ /dev/null @@ -1,46 +0,0 @@ -rates = 1:1:100; -avisi = []; -sdisi = []; -cvisi = []; - -for rate = rates - spikes = hompoissonspikes( 10, rate, 100.0 ); - isivec = isis( spikes ); - av = mean( isivec ); - sd = std( isivec ); - cv = sd/av; - avisi = [ avisi av ]; - sdisi = [ sdisi sd ]; - cvisi = [ cvisi cv ]; -end - -f = figure; -subplot( 1, 3, 1 ); -scatter( rates, 1000.0*avisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ); -title( 'Mean ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 2 ); -scatter( rates, 1000.0*sdisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ) -title( 'Standard deviation ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 3 ); -scatter( rates, cvisi, 'b', 'filled' ); -hold on; -plot( rates, ones( size( rates ) ), 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 2 ] ) -title( 'CV' ); -legend( 'simulation', 'theory' ); diff --git a/pointprocesses/exercises/hompoissonspikes.m b/pointprocesses/exercises/hompoissonspikes.m deleted file mode 100644 index 43b4e5c..0000000 --- a/pointprocesses/exercises/hompoissonspikes.m +++ /dev/null @@ -1,19 +0,0 @@ -function spikes = hompoissonspikes( trials, rate, tmax ) -% Generate spike times of a homogeneous poisson process -% trials: number of trials that should be generated -% rate: the rate of the Poisson process in Hertz -% tmax: the duration of each trial in seconds -% returns a cell array of vectors of spike times - - dt = 3.33e-5; - p = rate*dt; - if p > 0.2 - p = 0.2 - dt = p/rate; - end - x = rand( trials, ceil(tmax/dt) ); - spikes = cell( trials, 1 ); - for k=1:trials - spikes{k} = find( x(k,:) < p ) * dt; - end -end diff --git a/pointprocesses/exercises/iafisistats-solutions.pdf b/pointprocesses/exercises/iafisistats-solutions.pdf deleted file mode 100644 index d1b6c63e4cb56e1d9b20a4fab168fe0c3cb86974..0000000000000000000000000000000000000000 GIT binary patch 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a/pointprocesses/exercises/iafisistats.tex +++ /dev/null @@ -1,142 +0,0 @@ -\documentclass[addpoints,10pt]{exam} -\usepackage{url} -\usepackage{color} -\usepackage{hyperref} -\usepackage{graphicx} - -\pagestyle{headandfoot} -\runningheadrule -\firstpageheadrule - -\firstpageheader{Scientific Computing}{Integrate-and-fire models}{Oct 28, 2014} -%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014} -\firstpagefooter{}{}{} -\runningfooter{}{}{} -\pointsinmargin -\bracketedpoints - -%\printanswers -\shadedsolutions - -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - basicstyle=\ttfamily, - numbers=left, - showstringspaces=false, - language=Matlab, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - captionpos=t, - xleftmargin=2em, - xrightmargin=1em, - aboveskip=10pt, - %title=\lstname, - title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext} - } - - -\begin{document} - -\sffamily -%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{questions} - \question \textbf{Statistics of integrate-and-fire neurons} - For the following use different variants of the leaky integrate-and-fire models provided in \texttt{lifspikes.m}, - \texttt{lifouspikes.m}, and \texttt{lifadaptspikes.m} do generate some spike train data. - Use the functions you wrote for the Poisson process to analyze the statistics of the spike trains. - \begin{parts} - \part Generate a few trials of the two models for two different inputs - that result in qualitatively different spike trains and display - them in a raster plot. Decide for a noise strength (good values to try are 0.001, 0.01, 0.1, 1). - \begin{solution} - \begin{lstlisting} -spikes = pifspikes( 10, 1.0, 0.5, 0.01 ); -%spikes = pifspikes( 10, 10.0, 0.5, 0.01 ); -%spikes = lifspikes( 10, 11.0, 0.5, 0.001 ); -%spikes = lifspikes( 10, 15.0, 0.5, 0.001 ); -spikeraster( spikes ) - \end{lstlisting} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster02}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster10}}\\ - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster10}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster15}} - \end{solution} - - - \part The inverse Gaussian describes the interspike interval distribution of a PIF driven with white noise: - \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \] - where $\langle T \rangle$ is the mean interspike interval and - \[ D = \frac{\langle(T - \langle T \rangle)^2\rangle}{2 \langle T \rangle^3} \] - is the diffusion coefficient (variance of the interspike intervals - $T$ divided by two times the mean cubed). Show in two plots how - this distribution depends on $\langle T \rangle$ and $D$. - \begin{solution} - \lstinputlisting{simulations/inversegauss.m} - \lstinputlisting{simulations/inversegaussplot.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{inversegauss}} - \end{solution} - - \part Extent your function plotting an interspike interval histogram - to also report the diffusion coefficient $D$. - \begin{solution} - \begin{lstlisting} -... -% annotation: -misi = mean( isis ); -sdisi = std( isis ); -disi = sdisi^2.0/2.0/misi^3; -text( 0.6, 0.7, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' ) -text( 0.6, 0.6, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' ) -text( 0.6, 0.5, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' ) -text( 0.6, 0.4, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' ) -... - \end{lstlisting} - \end{solution} - - \part Compare intersike interval histograms obtained from the LIF and PIF models with the inverse Gaussian. - \begin{solution} - \lstinputlisting{simulations/lifisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih01}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih10}}\\ - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih08}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih16}} - \end{solution} - - \part Plot the firing rate (inverse mean interspike interval), - mean interspike interval, the corresponding standard deviation, - CV, and diffusion coefficient as a function of the input to the LIF - and the PIF with noise strength set to 0.01. - \begin{solution} - \lstinputlisting{simulations/lifisistats.m} - Leaky integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.8\textwidth]{lifisistats}}\\ - Perfect integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.8\textwidth]{pifisistats}} - \end{solution} - - \part Plot the firing rate as a function of input of the LIF and the PIF for various values - of the noise strength. - \begin{solution} - \lstinputlisting{simulations/lifficurves.m} - Leaky integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.7\textwidth]{lifficurves}}\\ - Perfect integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.7\textwidth]{pifficurves}} - \end{solution} - - \part Use the functions for computing serial correlations, count statistics and fano factors - to further explore the statistics of the integrate-and-fire models! - - \end{parts} - -\end{questions} - - -\end{document} diff --git a/pointprocesses/code/inversegauss.m b/pointprocesses/exercises/inversegauss.m similarity index 100% rename from pointprocesses/code/inversegauss.m rename to pointprocesses/exercises/inversegauss.m diff --git a/pointprocesses/code/inversegaussplot.m b/pointprocesses/exercises/inversegaussplot.m similarity index 100% rename from pointprocesses/code/inversegaussplot.m rename to pointprocesses/exercises/inversegaussplot.m diff --git a/pointprocesses/code/lifficurves.m b/pointprocesses/exercises/lifficurves.m similarity index 100% rename from pointprocesses/code/lifficurves.m rename to pointprocesses/exercises/lifficurves.m diff --git a/pointprocesses/code/lifisih.m b/pointprocesses/exercises/lifisih.m similarity index 100% rename from pointprocesses/code/lifisih.m rename to pointprocesses/exercises/lifisih.m diff --git a/pointprocesses/code/lifisistats.m b/pointprocesses/exercises/lifisistats.m similarity index 100% rename from pointprocesses/code/lifisistats.m rename to pointprocesses/exercises/lifisistats.m diff --git a/pointprocesses/exercises/pointprocesses-2.tex b/pointprocesses/exercises/pointprocesses-2.tex index 8af40c9..87ffff3 100644 --- a/pointprocesses/exercises/pointprocesses-2.tex +++ b/pointprocesses/exercises/pointprocesses-2.tex @@ -1,12 +1,12 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\newcommand{\exercisetopic}{Point Processes} -\newcommand{\exercisenum}{X2} +\newcommand{\exercisetopic}{Integrate-and-fire models} +\newcommand{\exercisenum}{13} \newcommand{\exercisedate}{January 19th, 2021} \input{../../exercisesheader} -\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} +\firstpagefooter{Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} @@ -14,113 +14,97 @@ \input{../../exercisestitle} \begin{questions} + \question \textbf{Statistics of integrate-and-fire neurons} + For the following use different variants of the leaky integrate-and-fire models provided in \texttt{lifspikes.m}, + \texttt{lifouspikes.m}, and \texttt{lifadaptspikes.m} do generate some spike train data. + Use the functions you wrote for the Poisson process to analyze the statistics of the spike trains. + \begin{parts} + \part Generate a few trials of the two models for two different inputs + that result in qualitatively different spike trains and display + them in a raster plot. Decide for a noise strength (good values to try are 0.001, 0.01, 0.1, 1). + \begin{solution} + \begin{lstlisting} +spikes = pifspikes( 10, 1.0, 0.5, 0.01 ); +%spikes = pifspikes( 10, 10.0, 0.5, 0.01 ); +%spikes = lifspikes( 10, 11.0, 0.5, 0.001 ); +%spikes = lifspikes( 10, 15.0, 0.5, 0.001 ); +spikeraster( spikes ) + \end{lstlisting} + \mbox{}\\[-3ex] + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster02}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster10}}\\ + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster10}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster15}} + \end{solution} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\question \qt{Homogener Poisson Prozess} -Wir wollen den homogenen Poisson Prozess benutzen um Spikes zu generieren, -mit denen wir die Analysfunktionen des vorherigen \"Ubungszettel \"uberpr\"ufen k\"onnen. - -Ein homogener Poisson Prozess mit der Rate $\lambda$ (gemessen in Hertz) ist ein Punktprozess, -bei dem die Wahrschienlichkeit eines Ereignisses unabh\"angig von der Zeit $t$ und -unabh\"angig von vorherigen Ereignissen ist. -Die Wahrscheinlichkeit $P$ eines Ereignisses innerhalb eines Bins der Breite $\Delta t$ ist -\[ P = \lambda \cdot \Delta t \] -f\"ur gen\"ugend kleine $\Delta t$. -\begin{parts} - - \part Schreibe eine Funktion die $n$ homogene Poisson Spiketrains - einer gegebenen Dauer $T_{max}$ mit Rate $\lambda$ erzeugt. - \begin{solution} - \lstinputlisting{hompoissonspikes.m} - \end{solution} - - \part Benutze diese Funktion um einige Trials von Spikes zu erzeugen - und plotte diese als Spikeraster. - \begin{solution} - \begin{lstlisting} - spikes = hompoissonspikes( 10, 100.0, 0.5 ); - spikeraster( spikes ) - \end{lstlisting} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=0.7\textwidth]{poissonraster100hz}} - \end{solution} - - \part Berechne Histogramme aus den Interspikeintervallen von $n$ - Poisson Spiketrains mit der Rate $\lambda=100$\,Hz. Ver\"andere - \"uber die Dauer $T_{max}$ der Spiketrains und die Anzahl $n$ der - Trials die Anzahl der Intervalle und ver\"andere auch die Binbreite - des Histograms (fang mit 1\,ms an). Wieviele Interspikeintervalle - werden ben\"otigt, um ein ``sch\"ones'' Histogramm zu erhalten? Wie - lange m\"usste man also von dem Neuron ableiten? - \begin{solution} - About 5000 intervals for 25 bins. This corresponds to a $5000 / - 100\,\hertz = 50\,\second$ recording of a neuron firing with - 100\,\hertz. - \end{solution} - - \part Vergleiche Interspike-Intervall Histogramme von Poisson-Spikes - verschiedener Raten $\lambda$ mit der theoretisch zu erwartenden Verteilung - der Intervalle $T$ des Poisson Prozesses - \[ p(T) = \lambda e^{-\lambda T} \; .\] - \begin{solution} - \lstinputlisting{hompoissonisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih100hz}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih20hz}} - \end{solution} - - \part \extra Was pasiert mit den Histogrammen, wenn die Binbreite - der Histogramme kleiner als das bei der Erzeugung der Poisson - Spiketrains verwendete $\Delta t$ ist? - \begin{solution} - Die Bins zwischen der durch $\Delta t$ vorgegebenen - Diskretisierung haben den Wert 0. Dadurch werden aber die anderen - durch die Normierung h\"oher als sie sein sollten. - \end{solution} - - \part Plotte den Mittelwert der Interspikeintervalle, die - dazugeh\"orige Standardabweichung und den Variationskoeffizienten - als Funktion der Rate $\lambda$ des Poisson Prozesses. Vergleiche - die Ergebnisse mit den theoretischen Erwartungen (siehe Vorlesungsskript). - \begin{solution} - \lstinputlisting{hompoissonisistats.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonisistats}} - \end{solution} - - \part Plotte die seriellen Korrelationen von Poisson-Spiketrains und - erkl\"are kurz das Ergebniss. - \begin{solution} - \mbox{}\\[-2ex]\hspace*{2cm} - \colorbox{white}{\includegraphics[width=0.8\textwidth]{poissonserial100hz}}\\ - Alle Korrelationen zwischen Interspikeintervallen sind Null, da - beim Poisson Prozess das Auftreten jedes Spikes unabh\"angig von - den vorherigen Spikes ist. - \end{solution} - - \part Vergleiche Histogramme von Spikecounts gez\"ahlt in Fenstern - der Breite $W$ mit der Poisson Verteilung - \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] - wobei die Rate $\lambda$ aus den Daten bestimmt werden - soll. Hinweis: es gibt eine \code{matlab} Funktion, die die - Fakult\"at $n!$ berechnet. - \begin{solution} - %\lstinputlisting{counthist.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}} - \end{solution} - - \part Schreibe eine Funktion, die die mittlere Anzahl, die Varianz - und den Fano-Faktor der Anzahl der Spikes in einem Fenster der - Breite $W$ bestimmt. Benutze die Funktion, um diese Parameter f\"ur - verschiedene Fensterbreiten $W$ zu bestimmen. Zwei Plots sollen aus - den Ergebnissen angefertigt werden: (i) Varianz gegen Mittelwert der counts. - (ii) Fano Faktor als Funktion der Fensterbreite. - \begin{solution} - \lstinputlisting{fanoplot.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}} - \end{solution} - -\end{parts} + \part The inverse Gaussian describes the interspike interval distribution of a PIF driven with white noise: + \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \] + where $\langle T \rangle$ is the mean interspike interval and + \[ D = \frac{\langle(T - \langle T \rangle)^2\rangle}{2 \langle T \rangle^3} \] + is the diffusion coefficient (variance of the interspike intervals + $T$ divided by two times the mean cubed). Show in two plots how + this distribution depends on $\langle T \rangle$ and $D$. + \begin{solution} + \lstinputlisting{inversegauss.m} + \lstinputlisting{inversegaussplot.m} + \colorbox{white}{\includegraphics[width=0.98\textwidth]{inversegauss}} + \end{solution} + + \part Extent your function plotting an interspike interval histogram + to also report the diffusion coefficient $D$. + \begin{solution} + \begin{lstlisting} +... +% annotation: +misi = mean( isis ); +sdisi = std( isis ); +disi = sdisi^2.0/2.0/misi^3; +text( 0.6, 0.7, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' ) +text( 0.6, 0.6, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' ) +text( 0.6, 0.5, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' ) +text( 0.6, 0.4, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' ) +... + \end{lstlisting} + \end{solution} + + \part Compare intersike interval histograms obtained from the LIF and PIF models with the inverse Gaussian. + \begin{solution} + \lstinputlisting{lifisih.m} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih01}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih10}}\\ + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih08}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih16}} + \end{solution} + + \part Plot the firing rate (inverse mean interspike interval), + mean interspike interval, the corresponding standard deviation, + CV, and diffusion coefficient as a function of the input to the LIF + and the PIF with noise strength set to 0.01. + \begin{solution} + \lstinputlisting{lifisistats.m} + Leaky integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.8\textwidth]{lifisistats}}\\ + Perfect integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.8\textwidth]{pifisistats}} + \end{solution} + + \part Plot the firing rate as a function of input of the LIF and the PIF for various values + of the noise strength. + \begin{solution} + \lstinputlisting{lifficurves.m} + Leaky integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.7\textwidth]{lifficurves}}\\ + Perfect integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.7\textwidth]{pifficurves}} + \end{solution} + + \part Use the functions for computing serial correlations, count statistics and fano factors + to further explore the statistics of the integrate-and-fire models! + + \end{parts} + \end{questions} + \end{document} diff --git a/pointprocesses/exercises/pointprocesses-3.tex b/pointprocesses/exercises/pointprocesses-3.tex deleted file mode 100644 index 1af6dc7..0000000 --- a/pointprocesses/exercises/pointprocesses-3.tex +++ /dev/null @@ -1,163 +0,0 @@ -\documentclass[12pt,a4paper,pdftex]{exam} - -\newcommand{\exercisetopic}{Point Processes} -\newcommand{\exercisenum}{X3} -\newcommand{\exercisedate}{January 19th, 2021} - -\input{../../exercisesheader} - -\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{document} - -\input{../../exercisestitle} - -\begin{questions} - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \question \qt{Statistik von Spiketrains 2} - In Ilias findet ihr die Dateien \code{poisson.mat}, - \code{pifou.mat}, und \code{lifadapt.mat}. Jede dieser Dateien - enth\"alt mehrere Trials von Spiketrains von einer bestimmten Art - von Neuron. Die Spikezeiten sind in Sekunden gemessen. - - Mit den folgenden Aufgaben wollen wir die Statistik der Spiketrains - der drei Neurone miteinander vergleichen. - - Bereits im letzten \"Ubungszettel erstellte Funktionen d\"urfen (sollen!) - wiederverwendet werden. - \begin{parts} - \part Lade die Spiketrains aus den drei Dateien. Stelle sie in Rasterplots dar. - - \part Plotte die Interspike-Intervall Verteilungen. - - Annotiere die Plots mit dem Mittelwert, der - Standardabweichung, und dem Variationskoeffizienten der - Interspikeintervalle, sowie der mittleren Feuerrate. - - \part Vergleiche die ISI-Histogramme mit der ISI Verteilung eines Poisson Prozesses - der Rate $\lambda$: - \[ p(T) = \lambda e^{-\lambda T} \; .\] - - \part Erstelle Return-Maps f\"ur die drei Spiketrains, also jedes - Interspike-Intervall $T_{i+1}$ gegen das vorherige Intervall $T_i$ - geplottet. - - \part Schreibe eine Funktion, die die seriellen Korrelationen der - Interspikeintervalle f\"ur Lags bis zu \code{maxlag} berechnet und - plottet. Die Seriellen Korrelationen $\rho_k$ f\"ur Lag $k$ der - Interspikeintervalle $T_i$ sind die Korrelationskoeffizienten - zwischen den Interspikeintervallen $T_i$ und den um das Lag $k$ - verschobenen Intervallen $T_{i+k}$: - \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - - \langle T \rangle) \rangle}{\langle (T_i - \langle T - \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm - var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] - - Benutze diese Funktion, um die Interspikeintervall-Korrelationen - der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isiserialcorr.m} - \lstinputlisting{../code/plotserialcorr.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}} - \end{solution} - - \end{parts} - - \continue - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \question \qt{Homogener Poisson Prozess} - Wir wollen den homogenen Poisson Prozess benutzen um Spikes zu - generieren, mit denen wir die Analysfunktionen des vorherigen - Aufgaben \"uberpr\"ufen k\"onnen. - - Ein homogener Poisson Prozess mit der Rate $\lambda$ (gemessen in - Hertz) ist ein Punktprozess, bei dem die Wahrscheinlichkeit eines - Ereignisses unabh\"angig von der Zeit $t$ und unabh\"angig von - vorherigen Ereignissen ist. Wenn wir die Zeitachse in kleine Bins - der Breite $\Delta t$ einteilen, dann ist - \[ P = \lambda \cdot \Delta t \] - die Wahrscheinlichkeit innerhalb eines Bins ein Ereignis (``spike'') - zu erhalten. $\Delta t$ muss daf\"ur klein genug sein, so dass $P<0.1$. - \begin{parts} - - \part Schreibe eine Funktion die $n$ homogene Poisson Spiketrains - einer gegebenen Dauer $T_{max}$ mit Rate $\lambda$ erzeugt. - - Falls das nicht gelingt, benutze f\"ur die folgenden Aufgaben - soweit m\"oglich spikes aus der Datei \code{poisson.mat}. - \begin{solution} - \lstinputlisting{hompoissonspikes.m} - \end{solution} - - \part Benutze diese Funktion um einige Trials von Spikes zu erzeugen - und plotte diese als Spikeraster. - \begin{solution} - \begin{lstlisting} - spikes = hompoissonspikes( 10, 100.0, 0.5 ); - spikeraster( spikes ) - \end{lstlisting} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=0.7\textwidth]{poissonraster100hz}} - \end{solution} - - \part Berechne Histogramme aus den Interspikeintervallen von $n$ - Poisson Spiketrains mit der Rate $\lambda=100$\,Hz. Wie viele bins - werden f\"ur ein ``sch\"ones'' ISI-Histogramm ungef\"ahr ben\"otigt? - Ver\"andere \"uber die Dauer $T_{max}$ der Spiketrains und die - Anzahl $n$ der Trials die Anzahl der Intervalle. Wieviele - Interspikeintervalle werden ben\"otigt, um ein ``sch\"ones'' - Histogramm zu erhalten? Wie lange m\"usste man also von dem Neuron - ableiten? - \begin{solution} - About 5000 intervals for 25 bins. This corresponds to a $5000 / - 100\,\hertz = 50\,\second$ recording of a neuron firing with - 100\,\hertz. - \end{solution} - - \part Vergleiche Interspike-Intervall Histogramme von Poisson-Spikes - verschiedener Raten $\lambda$ mit der theoretisch zu erwartenden Verteilung - der Intervalle $T$ des Poisson Prozesses - \[ p(T) = \lambda e^{-\lambda T} \; .\] - Achte darauf, dass die Bins des Histograms nicht kleiner als $\Delta t$ sind! - \begin{solution} - \lstinputlisting{hompoissonisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih100hz}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih20hz}} - \end{solution} - - \part \extra Was passiert mit den Histogrammen, wenn die Binbreite - der Histogramme kleiner als das bei der Erzeugung der Poisson - Spiketrains verwendete $\Delta t$ ist? - \begin{solution} - Die Bins zwischen der durch $\Delta t$ vorgegebenen - Diskretisierung haben den Wert 0. Dadurch werden aber die anderen - durch die Normierung h\"oher als sie sein sollten. - \end{solution} - - \part Plotte den Mittelwert der Interspikeintervalle, die - dazugeh\"orige Standardabweichung und den Variationskoeffizienten - als Funktion der Rate $\lambda$ des Poisson Prozesses. Vergleiche - die Ergebnisse mit den theoretischen Erwartungen (siehe Vorlesungsskript). - \begin{solution} - \lstinputlisting{hompoissonisistats.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonisistats}} - \end{solution} - - \part Plotte die seriellen Korrelationen von Poisson-Spiketrains und - erkl\"are kurz das Ergebniss. - \begin{solution} - \mbox{}\\[-2ex]\hspace*{2cm} - \colorbox{white}{\includegraphics[width=0.8\textwidth]{poissonserial100hz}}\\ - Alle Korrelationen zwischen Interspikeintervallen sind Null, da - beim Poisson Prozess das Auftreten jedes Spikes unabh\"angig von - den vorherigen Spikes ist. - \end{solution} - - \end{parts} - - -\end{questions} - -\end{document} diff --git a/pointprocesses/exercises/pointprocesses01-de.tex b/pointprocesses/exercises/pointprocesses01-de.tex deleted file mode 100644 index ea8674d..0000000 --- a/pointprocesses/exercises/pointprocesses01-de.tex +++ /dev/null @@ -1,198 +0,0 @@ -\documentclass[12pt,a4paper,pdftex]{exam} - -\usepackage[german]{babel} -\usepackage{pslatex} -\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro -\usepackage{xcolor} -\usepackage{graphicx} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} - -%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} -\ifprintanswers -\newcommand{\stitle}{L\"osungen} -\else -\newcommand{\stitle}{\"Ubung} -\fi -\header{{\bfseries\large \stitle}}{{\bfseries\large Punktprozesse}}{{\bfseries\large 27. Oktober, 2015}} -\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: -jan.benda@uni-tuebingen.de} -\runningfooter{}{\thepage}{} - -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} - -%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{listings} -\lstset{ - language=Matlab, - basicstyle=\ttfamily\footnotesize, - numbers=left, - numberstyle=\tiny, - title=\lstname, - showstringspaces=false, - commentstyle=\itshape\color{darkgray}, - breaklines=true, - breakautoindent=true, - columns=flexible, - frame=single, - xleftmargin=1em, - xrightmargin=1em, - aboveskip=10pt -} - -%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{dsfont} -\newcommand{\naZ}{\mathds{N}} -\newcommand{\gaZ}{\mathds{Z}} -\newcommand{\raZ}{\mathds{Q}} -\newcommand{\reZ}{\mathds{R}} -\newcommand{\reZp}{\mathds{R^+}} -\newcommand{\reZpN}{\mathds{R^+_0}} -\newcommand{\koZ}{\mathds{C}} - -%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\continue}{\ifprintanswers% -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\continuepage}{\ifprintanswers% -\newpage -\else -\vfill\hspace*{\fill}$\rightarrow$\newpage% -\fi} -\newcommand{\newsolutionpage}{\ifprintanswers% -\newpage% -\else -\fi} - -%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\newcommand{\qt}[1]{\textbf{#1}\\} -\newcommand{\pref}[1]{(\ref{#1})} -\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}} -\newcommand{\code}[1]{\texttt{#1}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{document} - -\input{instructions} - - -\begin{questions} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \question \qt{Statistik von Spiketrains} - In Ilias findet ihr die Dateien \code{poisson.mat}, - \code{pifou.mat}, und \code{lifadapt.mat}. Jede dieser Dateien - enth\"alt mehrere Trials von Spiketrains von einer bestimmten Art - von Neuron. Die Spikezeiten sind in Sekunden gemessen. - - Mit den folgenden Aufgaben wollen wir die Statistik der Spiketrains - der drei Neurone miteinander vergleichen. - \begin{parts} - \part Lade die Spiketrains aus den drei Dateien. Achte darauf, - dass sie verschiedene Variablen\-namen bekommen. - \begin{solution} - \begin{lstlisting} - clear all - % not so good: - load poisson.mat - whos - poissonspikes = spikes; - load pifou.mat; - pifouspikes = spikes; - load lifadapt.mat; - lifadaptspikes = spikes; - clear spikes; - % better: - clear all - x = load( 'poisson.mat' ); - poissonspikes = x.spikes; - x = load( pifou.mat' ); - pifouspikes = x.spikes; - x = load( 'lifadapt.mat' ); - lifadaptspikes = x.spikes; - \end{lstlisting} - \end{solution} - - \part Schreibe eine Funktion, die die Spikezeiten der ersten - $t_{max}$ Sekunden in einem Rasterplot visualisiert. In jeder - Zeile des Rasterplots wird ein Spiketrain dargestellt. Jeder - einzelne Spike wird als senkrechte Linie zu der Zeit des - Auftretens des Spikes geplottet. Benutze die Funktion, um die - Spikeraster der ersten 1\,s der drei Neurone nebeneinander zu plotten. - \begin{solution} - \lstinputlisting{../code/spikeraster.m} - \lstinputlisting{../code/plotspikeraster.m} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=1\textwidth]{spikeraster}} - \end{solution} - - \part Schreibe eine Funktion, die einen einzigen Vektor mit den - Interspikeintervallen aller Trials von Spikezeiten zur\"uckgibt. - \begin{solution} - \lstinputlisting{../code/isis.m} - \end{solution} - - \part Schreibe eine Funktion, die ein normiertes Histogramm aus - einem Vektor von Interspikeintervallen, gegeben in Sekunden, - berechnet und dieses mit richtiger Achsenbeschriftung plottet. - Die Interspikeintervalle sollen dabei in Millisekunden angegeben - werden. Die Funktion soll zus\"atzlich den Mittelwert, die - Standardabweichung, und den Variationskoeffizienten der - Interspikeintervalle berechnen und diese im Plot mit angeben. - - Benutze die vorherige und diese Funktion, um die - Interspikeintervall Verteilung der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isihist.m} - \lstinputlisting{../code/plotisih.m} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=1\textwidth]{isihist}} - \end{solution} - - \part Schreibe eine Funktion, die die seriellen Korrelationen der - Interspikeintervalle f\"ur Lags bis zu \code{maxlag} berechnet und - plottet. Die Seriellen Korrelationen $\rho_k$ f\"ur Lag $k$ der - Interspikeintervalle $T_i$ sind die Korrelationskoeffizienten - zwischen den Interspikeintervallen $T_i$ und den um das Lag $k$ - verschobenen Intervallen $T_{i+k}$: - \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - - \langle T \rangle) \rangle}{\langle (T_i - \langle T - \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm - var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] - - Benutze diese Funktion, um die Interspikeintervall-Korrelationen - der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isiserialcorr.m} - \lstinputlisting{../code/plotserialcorr.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}} - \end{solution} - - \part Schreibe eine Funktion, die aus Spikezeiten - Histogramme aus der Anzahl von Spikes, die in Fenstern gegebener L\"ange $W$ - gez\"ahlt werden, erzeugt und plottet. - - Wende diese Funktion auf die drei - Datens\"atze an. Probiere verschiedene Fenstergr\"o{\ss}en $W$ aus. - \begin{solution} - \lstinputlisting{../code/counthist.m} - \lstinputlisting{../code/plotcounthist.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{counthist}} - \end{solution} - - - \end{parts} - -\end{questions} - -\end{document} \ No newline at end of file diff --git a/pointprocesses/exercises/poisson-solutions.pdf b/pointprocesses/exercises/poisson-solutions.pdf deleted file mode 100644 index 4546a8db101133710506c5cb390747a99382e77f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 199254 zcmb@s1yChT(=LeH0E4@`yTjn_?(XjH&cWSnaCe6R26r9Yox$Dhp7;Il-Pn!qM(lrM z_r!^g?&|8StjescswW?EMNx5jW(IaR^4W!<6*vweCL#x8Ya%{AI7V4Bdka@fA{I7Q zcA|fOaE#(swytK*M2zCLMy_U}W+o1%W^nxca4xRSW=3{!o@?FOGA{e=$UScw*GV{D z?xB5eyEUtorpdWA-KNTCs)+i8mXWQRX_8`v!~4aLy=6jy#Z;&%?d9V`zCy8|{P*7w z_7AB0#*V9cH}w79r6{4WrOce)GN`hsN)rnxI`k+!nhY?#)OA&URNZbf?M9z*oA^GO zbgU9ozGqEFm7R6Whfeu3a2~3tn;sfn4f{6q(%gOY(4BwdSic-U%>VqW=!|MF_ 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b/pointprocesses/exercises/psth.tex @@ -1,42 +1,20 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Time-dependent firing rates} +\newcommand{\exercisenum}{12} +\newcommand{\exercisedate}{January 19th, 2021} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} \header{{\bfseries\large Exercise - }}{{\bfseries\large Time-dependent firing rate}}{{\bfseries\large January, 14, 2020}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solution}\par\noindent} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to scientific computing.}\\[1ex] - {\large Jan Grewe, Jan Benda}\\[-3ex] - Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\ -\end{center} +\input{../../exercisestitle} \begin{questions} + \question Plot the time-dependent firing rate of a neuron. Calculate the firing rate from the \emph{instantaneous firing rate} (based on the interspike interval). Use the \code{lifoustim.mat}. The dataset @@ -45,14 +23,14 @@ duration of each trial is 30 seconds. \begin{parts} - \part{} Write a function that takes three arguments: the spike + \part Write a function that takes three arguments: the spike times of a single trial, the trial duration and the temporal resolution. The function should return two variables: the time axis and the time-dependent firing rate. - \part{} Write a script that applies the above function to estimate + \part Write a script that applies the above function to estimate the time-dependent firing rate of each trial. Plot the firing rates of the individual responses and the average response as a function of time into the same graph. - \part{} Extend your program that it saves the figure with the width and height of 8.5\,cm using a fontsize of 10\,pt for labels. + \part Extend your program that it saves the figure with the width and height of 8.5\,cm using a fontsize of 10\,pt for labels. See Chapter 3 in the script, or browse the Matlab help for more information. Store the figure in pdf format. \end{parts} @@ -65,10 +43,10 @@ \question{} Some trials are different than the others. \begin{parts} - \part{} Use a rasterplot to identify them. In which sense + \part Use a rasterplot to identify them. In which sense are they different? Save the rasterplot in pdf format. Use the same figure specifications as above and make sure it is properly labeled. - \part{} Identify those trials in which the spike count + \part Identify those trials in which the spike count deviates more than $2\sigma$ (twice the standard deviation) from the average. \end{parts} \end{questions} From 25dd6ac2c7c0a2081fe4bb5aa377f38ca2e59c75 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 19 Jan 2021 13:51:22 +0100 Subject: [PATCH 86/87] [pointprocesses] cleaned up code --- pointprocesses/code/colorednoisepdf.m | 10 -- pointprocesses/code/colorednoisepdfisifit.m | 24 ----- pointprocesses/code/counthistpoisson.m | 55 ---------- pointprocesses/code/isireturnmap.m | 24 ----- pointprocesses/code/plotspikestats.m | 100 ------------------ pointprocesses/code/poissonisih.m | 27 ----- pointprocesses/code/poissonisistats.m | 46 -------- pointprocesses/code/psth.m | 14 --- pointprocesses/code/spikerate.m | 12 --- .../lecture/pointprocesses-chapter.tex | 1 - pointprocesses/lecture/raster.pdf | Bin 6050 -> 0 bytes pointprocesses/lecture/thumbs.pdf | Bin 2873259 -> 0 bytes 12 files changed, 313 deletions(-) delete mode 100644 pointprocesses/code/colorednoisepdf.m delete mode 100644 pointprocesses/code/colorednoisepdfisifit.m delete mode 100644 pointprocesses/code/counthistpoisson.m delete mode 100644 pointprocesses/code/isireturnmap.m delete mode 100644 pointprocesses/code/plotspikestats.m delete mode 100644 pointprocesses/code/poissonisih.m delete mode 100644 pointprocesses/code/poissonisistats.m delete mode 100644 pointprocesses/code/psth.m delete mode 100644 pointprocesses/code/spikerate.m delete mode 100644 pointprocesses/lecture/raster.pdf delete mode 100644 pointprocesses/lecture/thumbs.pdf diff --git a/pointprocesses/code/colorednoisepdf.m b/pointprocesses/code/colorednoisepdf.m deleted file mode 100644 index 28f421b..0000000 --- a/pointprocesses/code/colorednoisepdf.m +++ /dev/null @@ -1,10 +0,0 @@ -function pcn = colorednoisepdf( x, misi, epsilon, tau ) -% returns the ISI pdf for PIF with colored noise drive -% x: the input ISI -% misis: the mean isi -% epsilon: a parameter -% tau: the correlation time of the noise - gamma1 = x/tau+exp(-x/tau)-1.0; - gamma2 = 1.0-exp(-x/tau); - pcn=exp(-(x-misi).^2./(4.0*epsilon*tau.^2.*gamma1)).*(((misi-x).*gamma2+2*gamma1*tau).^2./(2*gamma1*tau^2)-epsilon*(gamma2.^2-2*gamma1.*exp(-x/tau))) ./ (2*tau*sqrt(4*pi*epsilon*gamma1.^3)); -end diff --git a/pointprocesses/code/colorednoisepdfisifit.m b/pointprocesses/code/colorednoisepdfisifit.m deleted file mode 100644 index 1c653c0..0000000 --- a/pointprocesses/code/colorednoisepdfisifit.m +++ /dev/null @@ -1,24 +0,0 @@ -% misi = 0.02; -% epsilon = 1.0; -% tau = 0.1; -x=0:0.002:0.1; -% pcn = colorednoisepdf( x, misi, epsilon, tau )+10.0*randn( size( x ) ); -% plot( x, pcn ); - -spikes = lifouspikes( 10, 15, 50.0, 1.0, 1.0 ); -isivec = isis( spikes ); -misi = mean( isivec ); -1.0/misi -isibins = 0:0.0005:0.1; -[ n, c ] = hist( isivec, isibins ); -n = n / sum(n)/(isibins(2)-isibins(1)); -bar( c, n ); - -beta0 = [ 1.0, 0.01 ]; -b = nlinfit(c(1:end-2), n(1:end-2), @(b,x)(colorednoisepdf(x, misi, b(1), b(2))), beta0) - -pcn = colorednoisepdf( x, misi, b(1), b(2) ); -hold on -plot( x, pcn, 'r', 'LineWidth', 3 ); -hold off - diff --git a/pointprocesses/code/counthistpoisson.m b/pointprocesses/code/counthistpoisson.m deleted file mode 100644 index 9d9889a..0000000 --- a/pointprocesses/code/counthistpoisson.m +++ /dev/null @@ -1,55 +0,0 @@ -function [counts, bins] = counthist(spikes, w) -% computes count histogram and compare with Poisson distribution -% -% [counts, bins] = counthist(spikes, w) -% -% Arguments: -% spikes: a cell array of vectors of spike times in seconds -% w: observation window duration in seconds for computing the counts -% -% Returns: -% counts: the histogram of counts normalized to probabilities -% bins: the bin centers for the histogram - - % collect spike counts: - tmax = spikes{1}(end); - n = []; - r = []; - for k = 1:length(spikes) - times = spikes{k}; -% alternative 1: count the number of spikes in each window: -% for tk = 0:w:tmax-w -% nn = sum( ( times >= tk ) & ( times < tk+w ) ); -% %nn = length( find( ( times >= tk ) & ( times < tk+w ) ) ); -% n = [ n nn ]; -% end -% alternative 2: use the hist function to do that! - tbins = 0.5*w:w:tmax-0.5*w; - nn = hist(times, tbins); - n = [ n nn ]; - % the rate of the spikes: - rate = (length(times)-1)/(times(end) - times(1)); - r = [ r rate ]; - end - - % histogram of spike counts: - maxn = max( n ); - [counts, bins ] = hist( n, 0:1:maxn+10 ); - % normalize to probabilities: - counts = counts / sum( counts ); - - % plot: - if nargout == 0 - bar( bins, counts ); - hold on; - % Poisson distribution: - rate = mean( r ); - x = 0:1:maxn+10; - a = rate*w; - y = a.^x.*exp(-a)./factorial(x); - plot( x, y, 'r', 'LineWidth', 3 ); - hold off; - xlabel( 'counts k' ); - ylabel( 'P(k)' ); - end -end diff --git a/pointprocesses/code/isireturnmap.m b/pointprocesses/code/isireturnmap.m deleted file mode 100644 index d790e13..0000000 --- a/pointprocesses/code/isireturnmap.m +++ /dev/null @@ -1,24 +0,0 @@ -function isireturnmap( isis, lag2 ) -% plot return maps for lag 1 and lag lag2 - - clf; - subplot( 1, 2, 1 ); - lag = 1; - scatter( 1000.0*isis(1:end-lag)', 1000.0*isis(1+lag:end)', 'b', 'filled', 'MarkerEdgeColor', 'white' ); - xlabel( 'ISI T_i [ms]' ); - ylabel( 'ISI T_{i+1} [ms]' ); - maxisi = max( isis ); - maxy = ceil(maxisi/10)*10.0; - xlim( [0 1.5*maxy ]) - ylim( [0 maxy ]) - - subplot( 1, 2, 2 ); - lag = lag2; - scatter( 1000.0*isis(1:end-lag)', 1000.0*isis(1+lag:end)', 'b', 'filled', 'MarkerEdgeColor', 'white' ); - xlabel( 'ISI T_i [ms]' ); - ylabel( 'ISI T_{i+2} [ms]' ); - xlim( [0 1.5*maxy ]) - ylim( [0 maxy ]) - -end - diff --git a/pointprocesses/code/plotspikestats.m b/pointprocesses/code/plotspikestats.m deleted file mode 100644 index a664eca..0000000 --- a/pointprocesses/code/plotspikestats.m +++ /dev/null @@ -1,100 +0,0 @@ -%% load data: -clear all -% alternative 1: -% pro: no structs. contra: global unknown variables -load poisson.mat -whos -poissonspikes = spikes; -load pifou.mat; -pifouspikes = spikes; -load lifadapt.mat; -lifadaptspikes = spikes; -clear spikes; -% alternative 2: -% pro: clean code. contra: structs that we do not really know yet -clear all -x = load( 'poisson.mat' ); -poissonspikes = x.spikes; -x = load( 'pifou.mat' ); -pifouspikes = x.spikes; -x = load( 'lifadapt.mat' ); -lifadaptspikes = x.spikes; - -%% spike raster plots: -tmax = 1.0; -subplot(1, 3, 1); -spikeraster(poissonspikes, tmax); -title('Poisson'); - -subplot(1, 3, 2); -spikeraster(pifouspikes, tmax); -title('PIF OU'); - -subplot(1, 3, 3); -spikeraster(lifadaptspikes, tmax); -title('LIF adapt'); - -%% isi histograms: -maxisi = 300.0; -binwidth = 0.002; -subplot(1, 3, 1); -poissonisis = isis(poissonspikes); -isihist(poissonisis, binwidth); -xlim([0, maxisi]) -title('Poisson'); - -subplot(1, 3, 2); -pifouisis = isis(pifouspikes); -isihist(pifouisis, binwidth); -xlim([0, maxisi]) -title('PIF OU'); - -subplot(1, 3, 3); -lifadaptisis = isis(lifadaptspikes); -isihist(lifadaptisis, binwidth); -xlim([0, maxisi]) -title('LIF adapt'); - -%% serial correlations: -maxlag = 10; -rrange = [-0.5, 1.05]; -subplot(1, 3, 1); -isiserialcorr(poissonisis, maxlag); -ylim(rrange) -title('Poisson'); - -subplot(1, 3, 2); -isiserialcorr(pifouisis, maxlag); -ylim(rrange) -title('PIF OU'); - -subplot(1, 3, 3); -isiserialcorr(lifadaptisis, maxlag); -ylim(rrange) -title('LIF adapt'); - -%% spike counts: -w = 0.1; -cmax = 8; -pmax = 0.5; -subplot(1, 3, 1); -counthist(poissonspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('Poisson'); - -subplot(1, 3, 2); -counthist(pifouspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('PIF OU'); - -subplot(1, 3, 3); -counthist(lifadaptspikes, w); -xlim([0 cmax]) -set(gca, 'XTick', 0:2:cmax) -ylim([0 pmax]) -title('LIF adapt'); -savefigpdf(gcf, 'counthist.pdf', 20, 7); diff --git a/pointprocesses/code/poissonisih.m b/pointprocesses/code/poissonisih.m deleted file mode 100644 index f006e2b..0000000 --- a/pointprocesses/code/poissonisih.m +++ /dev/null @@ -1,27 +0,0 @@ -rate = 100.0; -trials = 50; -tmax = 100.0; - -% generate spikes: -spikes = poissonspikes( trials, rate, tmax ); -% interspike intervals: -isivec = isis( spikes ); -% histogram -f = figure( 1 ); -isihist( isivec ); -hold on -% theoretical density: -xmax = 5.0/rate; -x = 0:0.0001:xmax; -y = rate*exp(-rate*x); -plot( 1000.0*x, y, 'r', 'LineWidth', 3 ); -% plot details: -title( sprintf( 'Poisson spike trains, rate=%g Hz, nisi=%d', rate, length( isivec ) ) ) -xlim( [ 0.0 1000.0*xmax ] ) -ylim( [ 0.0 1.1*rate ] ) -legend( 'data', 'poisson' ) -hold off - -% serial correlations: -f = figure( 2 ); -isiserialcorr( isivec, 10 ); diff --git a/pointprocesses/code/poissonisistats.m b/pointprocesses/code/poissonisistats.m deleted file mode 100644 index 0c97e3d..0000000 --- a/pointprocesses/code/poissonisistats.m +++ /dev/null @@ -1,46 +0,0 @@ -rates = 1:1:100; -avisi = []; -sdisi = []; -cvisi = []; - -for rate = rates - spikes = poissonspikes( 10, rate, 100.0 ); - isivec = isis( spikes ); - av = mean( isivec ); - sd = std( isivec ); - cv = sd/av; - avisi = [ avisi av ]; - sdisi = [ sdisi sd ]; - cvisi = [ cvisi cv ]; -end - -f = figure; -subplot( 1, 3, 1 ); -scatter( rates, 1000.0*avisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ); -title( 'Mean ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 2 ); -scatter( rates, 1000.0*sdisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ) -title( 'Standard deviation ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 3 ); -scatter( rates, cvisi, 'b', 'filled' ); -hold on; -plot( rates, ones( size( rates ) ), 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 2 ] ) -title( 'CV' ); -legend( 'simulation', 'theory' ); diff --git a/pointprocesses/code/psth.m b/pointprocesses/code/psth.m deleted file mode 100644 index 87da768..0000000 --- a/pointprocesses/code/psth.m +++ /dev/null @@ -1,14 +0,0 @@ -function p = psth(spikes, dt, tmax) -% plots a PSTH of the spikes with binwidth dt - t = 0.0:dt:tmax+dt; - p = zeros(1, length(t)); - for k=1:length(spikes) - times = spikes{k}; - [h, b] = hist(times, t); - p = p + h; - end - p = p/length(spikes)/dt; - t(end) = []; - p(end) = []; - plot(t, p); -end diff --git a/pointprocesses/code/spikerate.m b/pointprocesses/code/spikerate.m deleted file mode 100644 index 4efdedb..0000000 --- a/pointprocesses/code/spikerate.m +++ /dev/null @@ -1,12 +0,0 @@ -function r = spikerate(spikes, duration) -% returns the average spike rate of the spikes -% for the first duration seconds -% spikes: a cell array of vectors of spike times - - 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import * rate = 20.0 trials = 20 -duration = 100.0 +duration = 500.0 dt = 0.001 drate = 50.0 tau = 0.1; - + def hompoisson(rate, trials, duration) : spikes = [] for k in range(trials) : @@ -19,8 +21,8 @@ def hompoisson(rate, trials, duration) : t = 0.0 while t < duration : t += np.random.exponential(1/rate) - times.append( t ) - spikes.append( times ) + times.append(t) + spikes.append(times) return spikes @@ -30,7 +32,7 @@ def inhompoisson(rate, trials, dt) : for k in range(trials) : x = np.random.rand(len(rate)) times = dt*np.nonzero(x= vthresh : v = vreset times.append(k*dt) - spikes.append( times ) + spikes.append(times) return spikes @@ -65,8 +67,7 @@ def oupifspikes(rate, trials, duration, dt, D, drate, tau): return spikes -def plot_count_fano(ax1, ax2, spikes): - wins = np.logspace(-2, 0.0, 200) +def count_stats(spikes, wins): mean_counts = np.zeros(len(wins)) var_counts = np.zeros(len(wins)) for k, win in enumerate(wins): @@ -76,6 +77,10 @@ def plot_count_fano(ax1, ax2, spikes): counts.extend(c) mean_counts[k] = np.mean(counts) var_counts[k] = np.var(counts) + return mean_counts, var_counts + + +def plot_count_fano(ax1, ax2, wins, mean_counts, var_counts): ax1.plot(mean_counts, var_counts, zorder=100, **lsA) ax1.set_xlabel('Mean count') ax1.set_xlim(0.0, 20.0) @@ -92,37 +97,47 @@ def plot_count_fano(ax1, ax2, spikes): ax2.set_yticks(np.arange(0.0, 1.2, 0.5)) -def plot_fano(ax, spikes): - wins = np.logspace(-2, 0.0, 200) - mean_counts = np.zeros(len(wins)) - var_counts = np.zeros(len(wins)) - for k, win in enumerate(wins): - counts = [] - for times in spikes: - c, _ = np.histogram(times, np.arange(0.0, duration, win)) - counts.extend(c) - mean_counts[k] = np.mean(counts) - var_counts[k] = np.var(counts) +def plot_fano(ax, wins, mean_counts, var_counts): ax.plot(1000.0*wins, var_counts/mean_counts, **lsB) ax.set_xlabel('Window', 'ms') ax.set_ylim(0.0, 1.2) ax.set_xscale('log') - ax.set_xticks([10, 100, 1000]) - ax.set_xticklabels(['10', '100', '1000']) + ax.set_xticks([1, 10, 100, 1000]) + ax.set_xticklabels(['1', '10', '100', '1000']) ax.xaxis.set_minor_locator(mpt.NullLocator()) ax.set_yticks(np.arange(0.0, 1.2, 0.5)) if __name__ == "__main__": - homspikes = hompoisson(rate, trials, duration) - inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + if not os.path.exists('fanoexamples.json'): + homspikes = hompoisson(rate, trials, duration) + inhspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + wins = np.logspace(-3, 0.0, 100) + hom_mean_counts, hom_var_counts = count_stats(homspikes, wins) + inh_mean_counts, inh_var_counts = count_stats(inhspikes, wins) + with open('fanoexamples.json', 'w') as df: + json.dump({'wins': wins.tolist(), + 'hom_mean_counts': hom_mean_counts.tolist(), + 'hom_var_counts': hom_var_counts.tolist(), + 'inh_mean_counts': inh_mean_counts.tolist(), + 'inh_var_counts': inh_var_counts.tolist()}, df, indent=4) + else: + with open('fanoexamples.json', 'r') as sf: + data = json.load(sf) + wins = np.array(data['wins']) + hom_mean_counts = np.array(data['hom_mean_counts']) + hom_var_counts = np.array(data['hom_var_counts']) + inh_mean_counts = np.array(data['inh_mean_counts']) + inh_var_counts = np.array(data['inh_var_counts']) fig, (ax1, ax2) = plt.subplots(1, 2) fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=2.0)) - plot_fano(ax1, homspikes) + plot_fano(ax1, wins, hom_mean_counts, hom_var_counts) ax1.set_ylabel('Fano factor') ax1.text(0.1, 0.95, 'Poisson', transform=ax1.transAxes) - plot_fano(ax2, inhspikes) ax2.axhline(1.0, **lsGrid) + plot_fano(ax2, wins, inh_mean_counts, inh_var_counts) + ax2.annotate('', xy=(45.0, 0.0), xytext=(45.0, 0.4), arrowprops=dict(arrowstyle="->")) + ax2.text(60.0, 0.25, 'most\nreliable', va='center') ax2.text(0.1, 0.95, 'OU noise', transform=ax2.transAxes) plt.savefig('fanoexamples.pdf') plt.close() diff --git a/pointprocesses/lecture/serialcorrexamples.json b/pointprocesses/lecture/serialcorrexamples.json new file mode 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plotstyle import * # parameter: rate = 20.0 -trials = 10 +trials = 20 duration = 500.0 dt = 0.001 drate = 50.0 @@ -91,41 +93,59 @@ def plotserialcorr(ax, isis, maxlag=10) : ax.set_xlim(0.0, maxlag) ax.set_ylim(-1.0, 1.0) ax.plot([0, 10], [0.0, 0.0], **lsGrid) - ax.plot(lags, corr, clip_on=False, zorder=100, **lpsAm) + ax.plot(lags, corr, clip_on=False, zorder=100, **lpsBm) -def plot_hom_returnmap(ax, spikes): - plotreturnmap(ax, isis(spikes)[:200], 1, 0.3) +def plot_hom_returnmap(ax, isis): + plotreturnmap(ax, isis[:200], 1, 0.3) ax.set_xticks(np.arange(0.0, 301.0, 100.0)) ax.set_yticks(np.arange(0.0, 301.0, 100.0)) -def plot_inhom_returnmap(ax, spikes): - plotreturnmap(ax, isis(spikes)[:200], 1, 0.3) +def plot_inhom_returnmap(ax, isis): + plotreturnmap(ax, isis[:200], 1, 0.3) ax.set_ylabel('') ax.set_xticks(np.arange(0.0, 301.0, 100.0)) ax.set_yticks(np.arange(0.0, 301.0, 100.0)) -def plot_hom_serialcorr(ax, spikes): - plotserialcorr(ax, isis(spikes)) +def plot_hom_serialcorr(ax, isis): + plotserialcorr(ax, isis) + ax.annotate('independent\nintervals', xy=(2.5, 0.05), xytext=(4.0, 0.4), + arrowprops=dict(arrowstyle="->", relpos=(0.0,0.0), + connectionstyle="angle3,angleA=20,angleB=70")) ax.set_ylim(-0.2, 1.0) -def plot_inhom_serialcorr(ax, spikes): - plotserialcorr(ax, isis(spikes)) +def plot_inhom_serialcorr(ax, isis): + plotserialcorr(ax, isis) + ax.annotate('positive\ncorrelations', xy=(1.5, 0.28), xytext=(3.5, 0.5), + arrowprops=dict(arrowstyle="->", relpos=(0.0,0.4), + connectionstyle="angle3,angleA=20,angleB=60")) ax.set_ylabel('') ax.set_ylim(-0.2, 1.0) if __name__ == "__main__": - homspikes = hompoisson(rate, trials, duration) - inhomspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + data_file = 'serialcorrexamples.json' + if not os.path.exists(data_file): + homspikes = hompoisson(rate, trials, duration) + inhomspikes = oupifspikes(rate, trials, duration, dt, 0.3, drate, tau) + homisis = isis(homspikes) + inhomisis = isis(inhomspikes) + with open(data_file, 'w') as df: + json.dump({'homisis': homisis.tolist(), + 'inhomisis': inhomisis.tolist()}, df, indent=4) + else: + with open(data_file, 'r') as sf: + data = json.load(sf) + homisis = np.array(data['homisis']) + inhomisis = np.array(data['inhomisis']) fig, axs = plt.subplots(2, 2, figsize=cm_size(figure_width, 1.8*figure_height)) fig.subplots_adjust(**adjust_fs(fig, left=6.5, right=1.5)) - plot_hom_returnmap(axs[0,0], homspikes) - plot_inhom_returnmap(axs[0,1], inhomspikes) - plot_hom_serialcorr(axs[1,0], homspikes) - plot_inhom_serialcorr(axs[1,1], inhomspikes) + plot_hom_returnmap(axs[0,0], homisis) + plot_inhom_returnmap(axs[0,1], inhomisis) + plot_hom_serialcorr(axs[1,0], homisis) + plot_inhom_serialcorr(axs[1,1], inhomisis) plt.savefig('serialcorrexamples.pdf') plt.close()

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zqpl81c$FjHN<#MZflUl@H^teo$C0{J+3zYP4Kjk}zaQU|6s_GK5RvxYjWU9(f1JC28*Jg*?79L3((*Y6V7cA*8?x zax(Hz^cQyN0^@1$rF=ju{*B-#s;U1?doq5DyFR4G6p&Ap9RB9FNGqN%%)E z)YP~n^`yCuc>n_uf^7u{x?3Vcxe$`(I(l4^hW=pNTL1dj25}=JLjRMph+w2AtrVBE z6s^>M{kRn5nTZr^#0%V zlx1YWas7W_(o+AkJ!R$p`K+{p^nX7a8tm%rhYbFgIKTn}L%ELG{|`Af4Dbx(0_* threshold + ps = [ps, p(:)]; + mses = [mses, meansquarederror(t, x, func, p)]; + gradient = msegradient(t, x, func, p); + p = p - epsilon * gradient; + end +end + +function mse = meansquarederror(t, x, func, p) + mse = mean((x - func(t, p)).^2); +end + +function gradmse = msegradient(t, x, func, p) + gradmse = zeros(size(p)); + h = 1e-3; % stepsize for derivative + ph = eye(length(p))*h; % ... for each parameter + mse = meansquarederror(t, x, func, p); + for i = 1:length(p) % for each coordinate ... + msepi = meansquarederror(t, x, func, p(:) + ph(:,i)); + gradmse(i) = (msepi - mse)/h; + end +end diff --git a/regression/exercises/savefigpdf.m b/regression/exercises/savefigpdf.m new file mode 100644 index 0000000..97a28a3 --- /dev/null +++ b/regression/exercises/savefigpdf.m @@ -0,0 +1,28 @@ +function savefigpdf(fig, name, width, height) +% Saves figure fig in pdf file name.pdf with appropriately set page size +% and fonts + + % default width: + if nargin < 3 + width = 11.7; + end + % default height: + if nargin < 4 + height = 9.0; + end + + % paper: + set(fig, 'PaperUnits', 'centimeters'); + set(fig, 'PaperSize', [width height]); + set(fig, 'PaperPosition', [0.0 0.0 width height]); + set(fig, 'Color', 'white') + + % font: + set(findall(fig, 'type', 'axes'), 'FontSize', 12) + set(findall(fig, 'type', 'text'), 'FontSize', 12) + + % save: + saveas(fig, name, 'pdf') + +end + From f6b52d32cb4aaf723ef053f3d89857b02a5a1a50 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 21:33:13 +0100 Subject: [PATCH 50/87] [regression] some more files --- .../lecture/pointprocessscetchA.eps | 4 ++-- .../lecture/pointprocessscetchA.pdf | 16 ++++++++-------- .../lecture/pointprocessscetchB.eps | 4 ++-- .../lecture/pointprocessscetchB.pdf | Bin 4877 -> 4877 bytes regression/code/gradientDescent.m | 2 +- regression/exercises/exp2plot.pdf | Bin 185733 -> 192680 bytes regression/exercises/gradientdescent.m | 2 +- 7 files changed, 14 insertions(+), 14 deletions(-) diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index bdf6699..910c42e 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex %%Creator: gnuplot 5.2 patchlevel 8 -%%CreationDate: Thu Dec 17 09:43:52 2020 +%%CreationDate: Mon Dec 21 20:05:25 2020 %%DocumentFonts: %%BoundingBox: 50 50 373 135 %%EndComments @@ -441,7 +441,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 8) % /Producer (gnuplot) % /Keywords () - /CreationDate (Thu Dec 17 09:43:52 2020) + /CreationDate (Mon Dec 21 20:05:25 2020) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchA.pdf b/pointprocesses/lecture/pointprocessscetchA.pdf index 8d6a7dd..05bcdac 100644 --- a/pointprocesses/lecture/pointprocessscetchA.pdf +++ b/pointprocesses/lecture/pointprocessscetchA.pdf @@ -43,12 +43,12 @@ endobj - -2020-12-17T09:43:53+01:00 -Thu -De-c T17: 0:9:43::2 + +2020-12-21T20:05:25+01:00 +Mon -De-c T21: 2:0:05::5 gnuplot 5.2 patchlevel 8 - -pointprocessscetchA.texgnuplot plot + +pointprocessscetchA.texgnuplot plot @@ -58,8 +58,8 @@ endstream endobj 2 0 obj <>endobj @@ -77,7 +77,7 @@ xref 0000000814 00000 n trailer << /Size 10 /Root 1 0 R /Info 2 0 R -/ID [] +/ID [] >> startxref 2571 diff --git a/pointprocesses/lecture/pointprocessscetchB.eps b/pointprocesses/lecture/pointprocessscetchB.eps index f58e266..10279c1 100644 --- a/pointprocesses/lecture/pointprocessscetchB.eps +++ b/pointprocesses/lecture/pointprocessscetchB.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchB.tex %%Creator: gnuplot 5.2 patchlevel 8 -%%CreationDate: Thu Dec 17 09:43:53 2020 +%%CreationDate: Mon Dec 21 20:05:26 2020 %%DocumentFonts: %%BoundingBox: 50 50 373 237 %%EndComments @@ -441,7 +441,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 8) % /Producer (gnuplot) % /Keywords () - /CreationDate (Thu Dec 17 09:43:53 2020) + /CreationDate (Mon Dec 21 20:05:26 2020) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchB.pdf b/pointprocesses/lecture/pointprocessscetchB.pdf index 87d8a5e4e097ae7cc05a829f89b73411017123ce..c466f9ad7701242b720ddaee1f5b52077b184707 100644 GIT binary patch delta 291 zcmeBG>s8xe%foA6VVP)XWRRw7o|KY2`2mmoC{4ACfVBf}6Q11kelDdxMnK0Jm>QXFb`;EKj5TsGc5`yIa4|G6uyiptak4Zqb2T<{bTI?6 n-JDEa?Q96Dh~=`g<0>vmEGnreN=@T3F*P#bQdM>JcjE#8Ki*7+ delta 291 zcmeBG>s8xe%foAtXla(5YMH2OZeeCH`2mmoC{4ACfVL-P;=ODhv&D^ugiuDlu& zAsM9#x-O}@$qFHc=2i*@R$xghdxhUNyACdQ`5n;ix78DkBN&CQKnEnUnkoE%+^jUA1h9UWaPj14T@ 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