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Merge branch 'master' of raven.am28.uni-tuebingen.de:scientificComputing

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Jan Grewe 2015-10-30 19:16:44 +01:00
commit 91f1f3663e
17 changed files with 213 additions and 69 deletions
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6
bootstrap/lecture/bootstrap-chapter.tex
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@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

6
designpattern/lecture/designpattern-chapter.tex
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@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

16
designpattern/lecture/designpattern.tex
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@ -62,7 +62,7 @@ sigma = 2.3;
y = randn(100, 1)*sigma + mu;
\end{lstlisting}
Das ist manchmal auch sinnvoll f\"ur \code{zeros} oder \code{ones}:
Das gleiche Prinzip ist manchmal auch sinnvoll f\"ur \code{zeros} oder \code{ones}:
\begin{lstlisting}
x = -1:0.01:2; % Vektor mit x-Werten
plot(x, exp(-x.*x));
@ -75,11 +75,14 @@ plot(x, ones(size(x))*0.5);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{for Schleifen \"uber Vektoren}
Manchmal m\"ochte man doch mit einer for-Schleife \"uber einen Vektor iterieren:
Manchmal m\"ochte man doch mit einer for-Schleife \"uber einen Vektor iterieren.
\begin{lstlisting}
x = [2:3:20]; % irgendein Vektor
for i=1:length(x)
% Benutze den Wert des Vektors x an der Stelle des Indexes i:
for i=1:length(x) % Mit der for-Schleife "loopen" wir ueber den Vektor
i % das ist der Index der die Elemente des Vektors nacheinander indiziert.
x(i) % das ist der Wert des i-ten Elements des Vektors x.
a = x(i); % die Variable a bekommt den Wert des i-ten Elements des Vektors x zugewiesen.
% Benutze den Wert:
do_something( x(i) );
end
\end{lstlisting}
@ -89,7 +92,7 @@ sollten wir uns vor der Schleife schon einen Vektor f\"ur die Ergebnisse
erstellen:
\begin{lstlisting}
x = [2:3:20]; % irgendein Vektor
y = zeros(size(x)); % Platz fuer die Ergebnisse
y = zeros(length(x),1); % Platz fuer die Ergebnisse, genauso viele wie Loops der Schleife
for i=1:length(x)
% Schreibe den Rueckgabewert der Funktion get_something an die i-te
% Stelle von y:
@ -125,7 +128,8 @@ for i=1:length(x)
% Die Funktion get_something gibt uns einen Vektor zurueck:
z = get_something( x(i) );
% dessen Inhalt h\"angen wir an unseren Ergebnissvektor an:
y = [y z(:)];
y = [y; z(:)];
% z(:) stellt sicher, das wir auf jeden Fall einen Spaltenvektoren aneinanderreihen.
end
% jetzt koennen wir dem Ergebnisvektor weiter bearbeiten:
mean(y)

6
likelihood/lecture/likelihood-chapter.tex
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@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

31
pointprocesses/code/counthist.m
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@ -1,24 +1,36 @@
function [counts, bins] = counthist(spikes, w)
% computes count histogram and compare them with Poisson distribution
% spikes: a cell array of vectors of spike times
% w: observation window duration for computing the counts
%
% [counts, bins] = counthist(spikes, w)
% spikes: a cell array of vectors of spike times in seconds
% w: observation window duration in seconds for computing the counts
% 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)
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 ) ) );
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
rate = (length(spikes{k})-1)/(spikes{k}(end) - spikes{k}(1));
% 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 );
if nargout == 0
bar( bins, counts );
@ -26,12 +38,11 @@ function [counts, bins] = counthist(spikes, w)
% Poisson distribution:
rate = mean( r );
x = 0:1:maxn+10;
l = rate*w;
y = l.^x.*exp(-l)./factorial(x);
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

8
pointprocesses/code/isihist.m
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@ -1,7 +1,9 @@
function isihist( isis, binwidth )
% plot histogram of isis
% isis: vector of interspike intervals
% binwidth: optional width to be used for the isi bins
% plot histogram of interspike intervals
%
% isihist(isis, binwidth)
% isis: vector of interspike intervals in seconds
% binwidth: optional width in seconds to be used for the isi bins
if nargin < 2
nperbin = 200; % average number of data points per bin

13
pointprocesses/code/isis.m
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@ -1,15 +1,16 @@
function isivec = isis( spikes )
% returns a single list of isis computed from all trials in spikes
% spikes: a cell array of vectors of spike times
%
% isivec = isis( spikes )
% spikes: a cell array of vectors of spike times in seconds
% isivec: a column vector with all the interspike intervalls
isivec = [];
for k = 1:length(spikes)
difftimes = diff( spikes{k} );
if ( size( difftimes, 1 ) == 1 )
isivec = [ isivec difftimes ];
elseif ( size( difftimes, 2 ) == 1 )
isivec = [ isivec difftimes' ];
end
% difftimes(:) ensures a column vector
% regardless of the type of vector spikes{k}
isivec = [ isivec; difftimes(:) ];
end
end

16
pointprocesses/code/isiserialcorr.m
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@ -1,15 +1,19 @@
function isicorr = isiserialcorr( isis, maxlag )
% serial correlation of isis
% isis: vector of interspike intervals
% maxlag: the maximum lag
% serial correlation of interspike intervals
%
% isicorr = isiserialcorr( isis, maxlag )
% isis: vector of interspike intervals in seconds
% maxlag: the maximum lag in seconds
% isicorr: vector with the serial correlations for lag 0 to maxlag
lags = 0:maxlag;
isicorr = zeros( size( lags ) );
for k = 1:length(lags)
lag = lags(k);
if length( isis ) > lag+10
cc = corrcoef( [ isis(1:end-lag)', isis(1+lag:end)' ] );
isicorr(k) = cc( 1, 2 );
if length( isis ) > lag+10 % ensure "enough" data
% DANGER: the arguments to corr must be column vectors!
% We insure this in the isis() function that generats the isis.
isicorr(k) = corr( isis(1:end-lag), isis(lag+1:end) );
end
end

100
pointprocesses/code/plotspikestats.m Normal file
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@ -0,0 +1,100 @@
%% 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);

4
pointprocesses/code/poissonspikes.m
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@ -1,9 +1,11 @@
function spikes = poissonspikes( trials, rate, tmax )
% Generate spike times of a homogeneous poisson process
%
% spikes = poissonspikes( trials, rate, tmax )
% 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
% spikes: a cell array of vectors of spike times in seconds
dt = 3.33e-5;
p = rate*dt; % probability of event per bin of width dt

6
pointprocesses/code/spikeraster.m
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@ -1,6 +1,8 @@
function spikeraster(spikes, tmax)
% Display a spike raster of the spike times given in spikes.
% spikes: a cell array of vectors of spike times
%
% spikeraster(spikes, tmax)
% spikes: a cell array of vectors of spike times in seconds
% tmax: plot spike raster upto tmax seconds
ntrials = length(spikes);
@ -16,8 +18,10 @@ for k = 1:ntrials
end
if tmax < 1.5
xlabel( 'Time [ms]' );
xlim([0.0 1000.0*tmax]);
else
xlabel( 'Time [s]' );
xlim([0.0 tmax]);
end
ylabel( 'Trials');
ylim( [ 0.3 ntrials+0.7 ] )

6
pointprocesses/lecture/pointprocesses-chapter.tex
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@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

6
scientificcomputing-script.tex
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@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

14
statistics/lecture/diehistograms.py
View File

@ -2,8 +2,9 @@ import numpy as np
import matplotlib.pyplot as plt
# roll the die:
x1 = np.random.random_integers( 1, 6, 100 )
x2 = np.random.random_integers( 1, 6, 500 )
rng = np.random.RandomState(57281)
x1 = rng.random_integers( 1, 6, 100 )
x2 = rng.random_integers( 1, 6, 500 )
bins = np.arange(0.5, 7, 1.0)
plt.xkcd()
@ -14,7 +15,10 @@ ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.set_xlim(0, 7)
ax.set_xticks( range(1, 7) )
ax.set_xlabel( 'x' )
ax.set_ylim(0, 98)
ax.set_ylabel( 'Frequency' )
ax.hist([x2, x1], bins, color=['#FFCC00', '#FFFF66' ])
@ -23,9 +27,13 @@ ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.set_xlim(0, 7)
ax.set_xticks( range(1, 7) )
ax.set_xlabel( 'x' )
ax.set_ylim(0, 0.23)
ax.set_ylabel( 'Probability' )
ax.hist([x2, x1], bins, normed=True, color=['#FFCC00', '#FFFF66' ])
ax.plot([0.2, 6.8], [1.0/6.0, 1.0/6.0], '-r', lw=2, zorder=1)
ax.hist([x2, x1], bins, normed=True, color=['#FFCC00', '#FFFF66' ], zorder=10)
plt.tight_layout()
fig.savefig( 'diehistograms.pdf' )
#plt.show()

19
statistics/lecture/pdfhistogram.py
View File

@ -2,9 +2,10 @@ import numpy as np
import matplotlib.pyplot as plt
# normal distribution:
rng = np.random.RandomState(6281)
x = np.arange( -4.0, 4.0, 0.01 )
g = np.exp(-0.5*x*x)/np.sqrt(2.0*np.pi)
r = np.random.randn( 100 )
r = rng.randn( 100 )
plt.xkcd()
@ -15,9 +16,10 @@ ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.set_xlabel( 'x' )
ax.set_xlim(-3.2, 3.2)
ax.set_xticks( np.arange( -3.0, 3.1, 1.0 ) )
ax.set_ylabel( 'Frequency' )
#ax.set_ylim( 0.0, 0.46 )
#ax.set_yticks( np.arange( 0.0, 0.45, 0.1 ) )
ax.set_yticks( np.arange( 0.0, 41.0, 10.0 ) )
ax.hist(r, 5, color='#CC0000')
ax.hist(r, 20, color='#FFCC00')
@ -27,11 +29,14 @@ ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.set_xlabel( 'x' )
ax.set_xlim(-3.2, 3.2)
ax.set_xticks( np.arange( -3.0, 3.1, 1.0 ) )
ax.set_ylabel( 'Probability density p(x)' )
#ax.set_ylim( 0.0, 0.46 )
#ax.set_yticks( np.arange( 0.0, 0.45, 0.1 ) )
ax.hist(r, 5, normed=True, color='#CC0000')
ax.hist(r, 20, normed=True, color='#FFCC00')
ax.set_ylim(0.0, 0.44)
ax.set_yticks( np.arange( 0.0, 0.41, 0.1 ) )
ax.plot(x, g, '-b', lw=2, zorder=-1)
ax.hist(r, 5, normed=True, color='#CC0000', zorder=-10)
ax.hist(r, 20, normed=True, color='#FFCC00', zorder=-5)
plt.tight_layout()
fig.savefig( 'pdfhistogram.pdf' )

6
statistics/lecture/statistics-chapter.tex
View File

@ -163,9 +163,9 @@
numbers=left,
showstringspaces=false,
language=Matlab,
commentstyle=\itshape\color{darkgray},
keywordstyle=\color{blue},
stringstyle=\color{green},
commentstyle=\itshape\color{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
backgroundcolor=\color{blue!10},
breaklines=true,
breakautoindent=true,

7
statistics/lecture/statistics.tex
View File

@ -111,7 +111,8 @@ Wahrscheinlichkeitsverteilung der Messwerte ab.
to their sum.}{Histogramme des Ergebnisses von 100 oder 500 mal
W\"urfeln. Links: das absolute Histogramm z\"ahlt die Anzahl des
Auftretens jeder Augenzahl. Rechts: Normiert auf die Summe des
Histogramms werden die beiden Messungen vergleichbar.}}
Histogramms werden die beiden Messungen untereinander als auch
mit der theoretischen Verteilung $P=1/6$ vergleichbar.}}
\end{figure}
Bei ganzzahligen Messdaten (z.B. die Augenzahl eines W\"urfels)
@ -142,7 +143,9 @@ Meistens haben wir es jedoch mit reellen Messgr\"o{\ss}en zu tun.
normalverteilten Messwerten. Links: Die H\"ohe des absoluten
Histogramms h\"angt von der Klassenbreite ab. Rechts: Bei auf
das Integral normierten Histogrammen werden auch
unterschiedliche Klassenbreiten vergleichbar.}}
unterschiedliche Klassenbreiten untereinander vergleichbar und
auch mit der theoretischen Wahrschinlichkeitsdichtefunktion
(blau).}}
\end{figure}
Histogramme von reellen Messwerten m\"ussen auf das Integral 1