From 350ee7ca2ba53a6380f0383f284105a673d9c41e Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Wed, 12 Nov 2014 18:39:02 +0100 Subject: [PATCH] added all my stuff --- announcements/correlationcartoon.jpeg | Bin 0 -> 11140 bytes announcements/evalutation.pdf | Bin 0 -> 40907 bytes announcements/evalutation.tex | 60 ++ linearalgebra/code/Chorthippus_biguttulus.wav | Bin 0 -> 3547004 bytes linearalgebra/code/PeterUndDerWolf.wav | Bin 0 -> 3537480 bytes linearalgebra/code/Tielli-Kraulis.wav | Bin 0 -> 3564968 bytes linearalgebra/code/coordinaterafo2.m | 52 ++ linearalgebra/code/coordinatetrafo.m | 37 + linearalgebra/code/correlationcoefficient.m | 29 + .../{simulations => code}/covareigen.m | 21 +- .../{simulations => code}/covareigen3.m | 25 +- linearalgebra/code/covareigen3examples.m | 19 + .../covareigenexamples.m | 6 +- linearalgebra/code/extdata.mat | Bin 0 -> 2366486 bytes linearalgebra/code/extracellularrecording.m | 54 ++ linearalgebra/code/gaussian.m | 25 + linearalgebra/code/matrix2dtrafos.m | 21 + linearalgebra/code/matrixbox.m | 45 ++ .../code/matrixmultiplicationlatex.m | 85 ++ linearalgebra/code/p-unit_spike_times.mat | Bin 0 -> 162494 bytes linearalgebra/code/p-unit_stimulus.mat | Bin 0 -> 1398570 bytes linearalgebra/code/pca2d.m | 95 +++ linearalgebra/code/pca2dexamples.m | 33 + linearalgebra/code/pca3d.m | 60 ++ linearalgebra/code/pca3dexamples.m | 19 + .../{simulations => code}/plotvector.m | 0 .../{simulations => code}/plotvector3.m | 0 linearalgebra/code/simplematrix2dtrafos.m | 21 + linearalgebra/code/simplematrixbox.m | 21 + linearalgebra/code/soundmixture.m | 72 ++ linearalgebra/code/spikesortingwave.m | 118 +++ .../{simulations => code}/spiketime.m | 0 linearalgebra/code/sta.m | 227 ++++++ linearalgebra/code/stastcexample.m | 31 + linearalgebra/code/stc.m | 66 ++ linearalgebra/exercises/correlations.pdf | Bin 0 -> 113158 bytes linearalgebra/exercises/correlations.tex | 95 +++ linearalgebra/exercises/matrices.pdf | Bin 0 -> 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pointprocesses/code/isireturnmap.m | 24 + pointprocesses/code/isis.m | 15 + pointprocesses/code/isiserialcorr.m | 26 + pointprocesses/code/lifadaptspikes.m | 53 ++ pointprocesses/code/lifboltzmanspikes.m | 51 ++ pointprocesses/code/liffano.m | 23 + pointprocesses/code/lifficurves.m | 36 + .../code/lifinputdiscriminationslope.m | 65 ++ .../code/lifinputdiscriminationtime.m | 51 ++ pointprocesses/code/lifisih.m | 35 + pointprocesses/code/lifisistats.m | 63 ++ pointprocesses/code/lifouadaptspikes.m | 64 ++ pointprocesses/code/lifouspikes.m | 44 ++ pointprocesses/code/lifrateisicorr.m | 34 + pointprocesses/code/lifspikes.m | 38 + pointprocesses/code/pifouspikes.m | 44 ++ pointprocesses/code/pifspikes.m | 38 + pointprocesses/code/poissonisih.m | 27 + pointprocesses/code/poissonisistats.m | 46 ++ pointprocesses/code/poissonspikes.m | 20 + pointprocesses/code/raster.pdf | Bin 0 -> 6050 bytes pointprocesses/code/savefigpdf.m | 28 + pointprocesses/code/spikeraster.m | 17 + pointprocesses/exercises/hompoissonisih.m | 18 + pointprocesses/exercises/hompoissonisistats.m | 46 ++ pointprocesses/exercises/hompoissonspikes.m | 19 + .../exercises/iafisistats-solutions.pdf | Bin 0 -> 210869 bytes pointprocesses/exercises/iafisistats.pdf | Bin 0 -> 81872 bytes pointprocesses/exercises/iafisistats.tex | 142 ++++ pointprocesses/exercises/inversegauss.pdf | Bin 0 -> 14889 bytes pointprocesses/exercises/lifficurves.pdf | Bin 0 -> 6271 bytes pointprocesses/exercises/lifisih08.pdf | Bin 0 -> 16316 bytes pointprocesses/exercises/lifisih16.pdf | Bin 0 -> 5227 bytes pointprocesses/exercises/lifisistats.pdf | Bin 0 -> 7150 bytes pointprocesses/exercises/lifraster10.pdf | Bin 0 -> 3935 bytes pointprocesses/exercises/lifraster15.pdf | Bin 0 -> 5889 bytes pointprocesses/exercises/pifficurves.pdf | Bin 0 -> 6657 bytes pointprocesses/exercises/pifisih01.pdf | Bin 0 -> 15647 bytes pointprocesses/exercises/pifisih10.pdf | Bin 0 -> 5011 bytes pointprocesses/exercises/pifisistats.pdf | Bin 0 -> 5939 bytes pointprocesses/exercises/pifraster02.pdf | Bin 0 -> 3797 bytes pointprocesses/exercises/pifraster10.pdf | Bin 0 -> 6116 bytes .../exercises/poisson-solutions.pdf | Bin 0 -> 199254 bytes pointprocesses/exercises/poisson.pdf | Bin 0 -> 81657 bytes pointprocesses/exercises/poisson.tex | 160 ++++ .../poissoncounthistdist100hz100ms.pdf | Bin 0 -> 3815 bytes .../poissoncounthistdist100hz10ms.pdf | Bin 0 -> 3630 bytes pointprocesses/exercises/poissonfano100hz.pdf | Bin 0 -> 17762 bytes pointprocesses/exercises/poissonisih100hz.pdf | Bin 0 -> 9070 bytes pointprocesses/exercises/poissonisih20hz.pdf | Bin 0 -> 12293 bytes pointprocesses/exercises/poissonisistats.pdf | Bin 0 -> 26757 bytes .../exercises/poissonraster100hz.pdf | Bin 0 -> 6050 bytes .../exercises/poissonserial100hz.pdf | Bin 0 -> 4366 bytes pointprocesses/lecture/Makefile | 142 ++++ pointprocesses/lecture/UT_WBMW_Rot_RGB.pdf | 529 +++++++++++++ .../lecture/beamercolorthemetuebingen.sty | 61 ++ 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pointprocesses/lecture/poissonfano100hz.pdf | Bin 0 -> 17762 bytes pointprocesses/lecture/poissonisih100hz.pdf | Bin 0 -> 6356 bytes .../lecture/poissonisihexp100hz.pdf | Bin 0 -> 8691 bytes pointprocesses/lecture/poissonisihexp20hz.pdf | Bin 0 -> 10378 bytes pointprocesses/lecture/poissonraster100hz.pdf | Bin 0 -> 6700 bytes .../lecture/poissonreturnmap100hz.pdf | Bin 0 -> 233248 bytes pointprocesses/lecture/poissonserial100hz.pdf | Bin 0 -> 4366 bytes pointprocesses/lecture/raster.pdf | Bin 0 -> 6050 bytes pointprocesses/lecture/thumbs.pdf | Bin 0 -> 2873259 bytes pointprocesses/lecture/whitestyles.gp | 67 ++ ...ntroductionToTheTheoryOfPointProcesses.pdf | Bin 0 -> 2365807 bytes .../Eden2003-IntroductionToPointProcesses.pdf | Bin 0 -> 560460 bytes resources/Mallot2014-DatAnal.pdf | Bin 0 -> 1358765 bytes resources/Nieder2013-Matlab_I_Tutorial.pdf | Bin 0 -> 1605066 bytes 160 files changed, 5869 insertions(+), 253 deletions(-) create mode 100644 announcements/correlationcartoon.jpeg 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100644 linearalgebra/exercises/correlations.tex create mode 100644 linearalgebra/exercises/matrices.pdf create mode 100644 linearalgebra/exercises/matrices.tex create mode 100644 linearalgebra/resources/Pillow2007-STC-LNPmodel.pdf delete mode 100644 linearalgebra/simulations/covareigen3examples.m delete mode 100644 linearalgebra/simulations/matrix2dtrafos.m delete mode 100644 linearalgebra/simulations/matrixbox.m delete mode 100644 linearalgebra/simulations/spikesortingwave.m create mode 100644 "moduledescription/Einf\303\274hrung_wissenschaftl_Datenverarbeitung.pdf" create mode 100644 "moduledescription/Einf\303\274hrung_wissenschaftl_Datenverarbeitung.pptx" create mode 100644 moduledescription/Hiwis.odt create mode 100644 moduledescription/Hiwis.pdf create mode 100644 moduledescription/ModuleScientificComputing.doc create mode 100644 moduledescription/ModuleScientificComputing.odt create mode 100644 pointprocesses/code/colorednoisepdf.m create mode 100644 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--- /dev/null +++ b/announcements/evalutation.tex @@ -0,0 +1,60 @@ +\documentclass[pdftex]{beamer} +\usepackage{beamerthemedefault} +\usepackage{multimedia} +\usepackage{wasysym} +\useoutertheme[subsection=false]{smoothbars} +\useinnertheme[shadow=true]{rounded} + +\setbeamercolor{block title}{fg=black,bg=gray} +\setbeamercolor{block title alerted}{use=alerted text,fg=black,bg=alerted text.fg!75!bg} +\setbeamercolor{block title example}{use=example text,fg=black,bg=example text.fg!75!bg} +\setbeamercolor{block body}{parent=normal text,use=block title,bg=block title.bg!25!bg} +\setbeamercolor{block body alerted}{parent=normal text,use=block title alerted,bg=block title alerted.bg!25!bg} +\setbeamercolor{block body example}{parent=normal text,use=block title example,bg=block title example.bg!25!bg} + +\usepackage{hyperref} +\usepackage[english]{babel} % language set to new-german +\usepackage[utf8]{inputenc} % coding of german special characters +\usepackage{graphicx} % \includegraphics[options]{file.eps} +\usepackage{array} +\usepackage{setspace} +\usepackage{color} +\usepackage{eqlist} +\usepackage{wallpaper} + +\definecolor{tug}{HTML}{CC0000} +\newcommand{\rot}[1]{{\color{tug} #1}} +\definecolor{green}{HTML}{1C8C1C} +\newcommand{\gruen}[1]{{\color{green} #1}} +\definecolor{blue}{HTML}{2424AA} +\newcommand{\blau}[1]{{\color{blue} #1}} +\definecolor{gray}{rgb}{0.8,0.8,0.8} +\definecolor{gray2}{rgb}{0.5,0.5,0.5} +\definecolor{gray2}{rgb}{0.5,0.5,0.5} +\newcommand{\grau}[1]{{\color{gray2} #1}} + +\setbeamercolor{footline}{fg=black,bg=gray} + +%\setbeamertemplate{headline}[text line]{ +% \begin{beamercolorbox}[wd=\paperwidth,ht=8ex,dp=4ex]{}%\vskip-4pt +% \insertnavigation{0.85\paperwidth} +% \hskip-1pt\rule{\paperwidth}{0.3pt} +% \end{beamercolorbox} +%} + +\setlength{\unitlength}{0.01\paperwidth} + +\setbeamercolor{background canvas}{bg=} + + +\begin{document} + +\begin{frame} + \frametitle{Evalutation} + In Ilias:\\[2ex] + Go to {\em Evaluation} and fill out the forms!\\[6ex] + \includegraphics[width=0.8\textwidth]{correlationcartoon} +\end{frame} + + +\end{document} diff --git a/linearalgebra/code/Chorthippus_biguttulus.wav b/linearalgebra/code/Chorthippus_biguttulus.wav new file mode 100644 index 0000000000000000000000000000000000000000..2c5706877ba3a7d80c2e0df072e22b630dcd1ebb GIT binary patch literal 3547004 zcmXus1>99t`ab+acXy|>fGCo-qM%};j@>ir&+f5x#!*Kd9c#uOb?n3z6a_^@kq}V2 zQ@Z=S-|Ni(mCx}xXYaMwy5qWIA*UR1@#WXGu3ab;$`r~L4u88) zsQp3NLis}N!iDEuci!>Jv@I+sRw~Rb_9|>HRx4~Rt}m`EZZ0+}R4Pm@{$6~pxT*Mc zv2EeIV%fslV&lT>Vwu8o#d3ua#oC2Q#ae|K#iIYWD*WvJtl}JZHx^r~vs0mZp;@6q zp{E)<73viBD>N?jE_C#(hC7W5U2%MIs_(0d-=hEL z;tIbP7C-d=ov!~-oLjsJk3Sce7x(x*7Y!4Nv;2Qvu|A46d2V)bh9@?V!s_BU|NpG` zYq3sYeerX34JmFf9!O3%7pD}v_=-CNvR?5Ew&i@UX3z3?o`en<1Cc>1Kc7R{TB zj}+?`E+|$g+@+QK(fN3BOK~`vJ&Bfgi@TJV?#eG{++A!^*it;zr*olJVO6n3VIKL6 zbbYnw_gC{^GVVe<`;$&r{8u2og9}TPEJsR_^tRO{vIyQFaE{f;UyW3D9-f#yW(%2oZ)$ zLd_@cuhUwC!WtaR$IVzzEux_+g(`(bP_lrgekaR$;nWcpI#&MM*DZ 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+ hist( nc(:,1), 50, 'b' ); + xlabel( 'new x' ); + ylabel( 'n_newx' ); end diff --git a/linearalgebra/simulations/covareigen3.m b/linearalgebra/code/covareigen3.m similarity index 64% rename from linearalgebra/simulations/covareigen3.m rename to linearalgebra/code/covareigen3.m index c11f2de..636d9cb 100644 --- a/linearalgebra/simulations/covareigen3.m +++ b/linearalgebra/code/covareigen3.m @@ -20,25 +20,40 @@ function covareigen3( x, y, z ) ylabel( 'y' ); zlabel( 'z' ); grid on; - + % plot eigenvectors: quiver3( ones( 1, 3 ).*mean( x ), ones( 1, 3 )*mean(y), ones( 1, 3 )*mean(z), v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', v(3,:).*sqrt(diag(d))', 'r', 'LineWidth', 3, 'AutoScale', 'off', 'AutoScaleFactor', 1.0, 'MaxHeadSize', 0.7 ) %axis( 'equal' ); hold off; + % 2D scatter plots: + subplot( 2, 6, 4 ); + scatter( x, y, 'b', 'filled', 'MarkerEdgeColor', 'white' ); + xlabel( 'x' ) + ylabel( 'y' ) + subplot( 2, 6, 5 ); + scatter( x, z, 'b', 'filled', 'MarkerEdgeColor', 'white' ); + xlabel( 'x' ) + ylabel( 'z' ) + subplot( 2, 6, 6 ); + scatter( y, z, 'b', 'filled', 'MarkerEdgeColor', 'white' ); + xlabel( 'y' ) + ylabel( 'z' ) + % sort the eigenvalues: [d,inx] = sort( diag(d), 'descend' ); - subplot( 2, 2, 2 ); + subplot( 2, 2, 4 ); hold on; % subtract means: x = x - mean( x ); y = y - mean( y ); % project onto eigenvectors: - nx = [ x y z ] * v(:,inx(1)); - ny = [ x y z ] * v(:,inx(2)); - scatter( nx, ny, 'b', 'filled', 'MarkerEdgeColor', 'white' ); + nx = [ x y z ] * v(:,inx); + scatter( nx(:,1), nx(:,2), 'b', 'filled', 'MarkerEdgeColor', 'white' ); + xlabel( 'ex' ) + ylabel( 'ey' ) axis( 'equal' ); hold off; diff --git a/linearalgebra/code/covareigen3examples.m b/linearalgebra/code/covareigen3examples.m new file mode 100644 index 0000000..f27c76c --- /dev/null +++ b/linearalgebra/code/covareigen3examples.m @@ -0,0 +1,19 @@ +scrsz = get( 0, 'ScreenSize' ); +set( 0, 'DefaultFigurePosition', [ scrsz(3)/2 scrsz(4)/2 scrsz(3)/2 scrsz(4)/2 ] ); + +n = 10000; + +% three distributions: +x = randn( n, 1 ); +y = randn( n, 1 ); +z = randn( n, 1 ); +dx = [ 0 8 0 0 ]; +dy = [ 0 0 8 0 ]; +dz = [ 0 0 0 8 ]; +for k = 1:4 + x((k-1)*n/4+1:k*n/4) = x((k-1)*n/4+1:k*n/4) + dx(k); + y((k-1)*n/4+1:k*n/4) = y((k-1)*n/4+1:k*n/4) + dy(k); + z((k-1)*n/4+1:k*n/4) = z((k-1)*n/4+1:k*n/4) + dz(k); +end +f = figure( 1 ); +covareigen3( x, y, z ); diff --git a/linearalgebra/simulations/covareigenexamples.m b/linearalgebra/code/covareigenexamples.m similarity index 88% rename from linearalgebra/simulations/covareigenexamples.m rename to linearalgebra/code/covareigenexamples.m index f360e8c..2f7a480 100644 --- a/linearalgebra/simulations/covareigenexamples.m +++ b/linearalgebra/code/covareigenexamples.m @@ -5,11 +5,11 @@ set( 0, 'DefaultFigurePosition', [ scrsz(3)/2 scrsz(4)/2 scrsz(3)/2 scrsz(4)/2 ] n = 10000; x = randn( n, 1 ); f = figure( 1 ); -for r = 0.01:0.199:1 +for r = 0.01:0.19:1 fprintf( 'Correlation = %g\n', r ); clf( f ); y = r*x + sqrt(1-r^2)*randn( n, 1 ); - covareigen( x, y, 2, 5.0, 3.0 ); + covareigen( x, y, 0, 5.0, 3.0 ); key = waitforbuttonpress; end return @@ -29,7 +29,7 @@ for d = 0:1:5 x = [ x1; x2 ]; y = [ y1+d2; y2-d2 ]; scrsz = get(0,'ScreenSize'); - covareigen( x, y, 1, 10.0, 7.0 ); + covareigen( x, y, 0, 10.0, 7.0 ); %key = waitforbuttonpress; pause( 1.0 ); end diff --git a/linearalgebra/code/extdata.mat b/linearalgebra/code/extdata.mat new file mode 100644 index 0000000000000000000000000000000000000000..619c0c1011a5c90e918cacc7637bbc0b2fd30837 GIT binary patch literal 2366486 zcmb@tWpEuq&nBA0%*-4!Guy|^%*@Qp_OTtuF;g5fvtwpvW@d)tV`k=?_wH`(_f_qW zd#hF@m872O*7K*;Ga8M8h`PLpC@Cis3#o#LI-{kHy#)iQvb~ABrIV`zAE}hQqP7SZ z2Lq{?tA&ZXg*mB{BOj@nha;(?lP4)D8z~zr-#_NyB4uM?{=85$Rtj;)2>eHc_6DNmF~Ee?6)jjCaBQP<=0yJ-GWk)eiOfyI!;|MPFBC!eOg+7OIFE4A<-;KZvXeCEPCR%G^_59ev-p&6cX{w zK^HD!yu~Cw)+wv|*8cN2(~6fm2BAaqXq4^7C9hUfhEsrxyN^k9cf&mjVr)dM`9WA* z7D|2xfO0+Amtt%%PV3CpDf(vbI(bV6N@a=@LDI*xH%nqXFy?AL@YiMt5t`?nd6wIP 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zmsL3Dl-ED6tnj>}n!jMm+N7|*+^Qg!25$c;><11j(B3bfQTRQ@d4==T6@_tqLt)=~M`8c;MBzFA z3x(&4uN4@nq4E`e&lBor-xuXadBR(oAKKX4;K#qDyJkPbz=kqas)}5(-xM(9Y{5;Q{<>$Vd thresh & voltage(1:end-2) voltage(3:end) ) + 1; +spiketimes = time(inx); +spikevoltage = voltage(inx); +tinx = inx; +for k=1:2 + inx = find( ( spiketimes(2:end-1)-spiketimes(1:end-2)>0.005 | spikevoltage(2:end-1) > spikevoltage(1:end-2) ) & ( spiketimes(3:end)-spiketimes(2:end-1)>0.005 | spikevoltage(2:end-1) > spikevoltage(3:end) ) )+1; + spiketimes = spiketimes(inx); + spikevoltage = spikevoltage(inx); + tinx = tinx(inx); +end +scatter( spiketimes(spiketimes<1.0), spikevoltage(spiketimes<1.0), 100.0, 'r', 'filled' ); +%scatter( t(tinx), v(tinx), 100.0, 'r', 'filled' ); +hold off; + +% save data to file: +save( 'extdata', 'time', 'voltage', 'spiketimes', 'waveformt', 'waveform1', 'waveform2' ); diff --git a/linearalgebra/code/gaussian.m b/linearalgebra/code/gaussian.m new file mode 100644 index 0000000..cdac6d5 --- /dev/null +++ b/linearalgebra/code/gaussian.m @@ -0,0 +1,25 @@ +% Gaussian density from histogram: +x = randn( 1000000, 1 ); +[ n, c ] = hist( x, 100 ); +n = n/sum(n)/(c(2)-c(1)); +bar( c, n ); +hold on; +% equation p(x): +xx = -5:0.01:5; +p=exp(-xx.^2/2.0)/sqrt(2.0*pi); +plot( xx, p, 'r', 'LineWidth', 3 ) + +% with mean=2 and sigma=0.5: +mu = 2.0; +sig = 0.5; +x = sig*x + mu; +[ n, c ] = hist( x, 100 ); +n = n/sum(n)/(c(2)-c(1)); +bar( c, n ); +% equation: +p=exp(-(xx-mu).^2/2.0/sig^2)/sqrt(2.0*pi*sig^2); +plot( xx, p, 'r', 'LineWidth', 3 ) +hold off; +xlabel( 'x' ); +ylabel( 'p(x)' ); +title( 'Gaussian distribution' ); diff --git a/linearalgebra/code/matrix2dtrafos.m b/linearalgebra/code/matrix2dtrafos.m new file mode 100644 index 0000000..2bd7546 --- /dev/null +++ b/linearalgebra/code/matrix2dtrafos.m @@ -0,0 +1,21 @@ +% Visualize some common matrix transformations +% in a 2D coordinate system + +disp( 'Click into the plot to advance to the next matrix' ) +matrixbox( [ 1 0; 0 1], 'Identity' ); +matrixbox( [ 2 0; 0 1], 'Scale x' ); +matrixbox( [ 1 0; 0 2], 'Scale y' ); +matrixbox( [ 2 0; 0 2], 'Scale x and y' ); +matrixbox( [ 0.5 0; 0 0.5], 'Scale x and y' ); +matrixbox( [ -1 0; 0 1], 'Flip x' ); +matrixbox( [ 1 0; 0 -1], 'Flip y' ); +matrixbox( [ -1 0; 0 -1], 'Flip both' ); +matrixbox( [ 1 2; 0 1], 'Shear x' ); +matrixbox( [ 1 0; 2 1], 'Shear y' ); +matrixbox( [ 0.5 1; 1 0.5], 'Something A' ); +matrixbox( [ 0.5 1; 1.2 0.6], 'Something B' ); +% rotation matrices: +for deg = 0:10:360 + phi = deg*pi/180.0; + matrixbox( [ cos(phi) -sin(phi); sin(phi) cos(phi)], sprintf( 'Rotate %.0f', deg ) ); +end diff --git a/linearalgebra/code/matrixbox.m b/linearalgebra/code/matrixbox.m new file mode 100644 index 0000000..6cc0aa1 --- /dev/null +++ b/linearalgebra/code/matrixbox.m @@ -0,0 +1,45 @@ +function matrixbox( m, s ) +% visualizes the effect of a matrix m on a set of vectors forming a box +% m: a 2x2 matrix +% s: a string plotted as the title of the plot +% this function is called by matrix2dtrafos.m + + % the 5 vectors that point into the cornes of a unit square: + v = [ 0 1 1 0 0; + 0 0 1 1 0 ]; + % transform v by means of m into new vector w: + w = m*v; + clf; + hold on; + % axis: + plot( [-2 2], [0 0], 'k', 'LineWidth', 1 ); + plot( [0 0], [-2 2], 'k', 'LineWidth', 1 ); + % old vectors: + plot( v(1,:), v(2,:), 'k', 'LineWidth', 1.0 ) + quiver( v(1,1), v(2,1), v(1,3), v(2,3), 1.0, 'k', 'LineWidth', 2.0 ); + scatter( v(1,2), v(2,2), 60.0, 'filled', 'k' ); + % transformed vectors: + plot( w(1,:), w(2,:), 'b', 'LineWidth', 2.0 ) + quiver( w(1,1), w(2,1), w(1,3), w(2,3), 1.0, 'b', 'LineWidth', 3.0 ); + scatter( w(1,2), w(2,2), 100.0, 'filled', 'b' ); + % eigenvectors: + [ev ed] = eig(m); + n = ev*ed; + if isreal( n ) + quiver( [0 0], [0 0], n(1,:), n(2,:), 1.0, 'r', 'LineWidth', 2.0 ); + text( 0.1, 0.2, sprintf( '\\lambda_1 = %.3g', ed(1,1) ), 'Units', 'normalized' ) + text( 0.1, 0.1, sprintf( '\\lambda_2 = %.3g', ed(2,2) ), 'Units', 'normalized' ) + end + hold off; + xlim( [ -2 2 ] ); + ylim( [ -2 2 ] ); + axis( 'equal' ); + m( abs(m) < 1e-3 ) = 0.0; % make zeros really a zero + text( 0.7, 0.15, 'A =', 'Units', 'normalized' ) + text( 0.8, 0.2, sprintf( '%.3g', m(1,1) ), 'Units', 'normalized' ) + text( 0.9, 0.2, sprintf( '%.3g', m(1,2) ), 'Units', 'normalized' ) + text( 0.8, 0.1, sprintf( '%.3g', m(2,1) ), 'Units', 'normalized' ) + text( 0.9, 0.1, sprintf( '%.3g', m(2,2) ), 'Units', 'normalized' ) + title( s ); + waitforbuttonpress; +end diff --git a/linearalgebra/code/matrixmultiplicationlatex.m b/linearalgebra/code/matrixmultiplicationlatex.m new file mode 100644 index 0000000..dbb66de --- /dev/null +++ b/linearalgebra/code/matrixmultiplicationlatex.m @@ -0,0 +1,85 @@ +% open a file to write in the LaTeX commands: +f = fopen( 'matrices.tex','w'); +fprintf( f, '\\documentclass{exam}\n' ); +fprintf( f, '\\usepackage{amsmath}\n' ); +fprintf( f, '\\begin{document}\n' ); + +for k = 1:40 + + % compute row and column numbers: + pd = rand( 1, 1 ); + if pd < 0.05 + % row vector multiplication that might not be possible: + am = 1; + an = randi( [ 2 4 ]); + bm = randi( [ 2 4 ]); + bn = 1; + elseif pd < 0.1 + % column vector multiplication that might not be possible: + am = randi( [ 2 4 ]); + an = 1; + bm = 1; + bn = randi( [ 2 4 ]); + elseif pd < 0.4 + % row vector multiplication that is possible: + am = 1; + an = randi( [ 2 4 ]); + bm = an; + bn = 1; + elseif pd < 0.5 + % column vector multiplication that is possible: + am = randi( [ 2 4 ]); + an = 1; + bm = 1; + bn = am; + elseif pd < 0.6 + % matrix multiplication that might not be possible: + am = randi( [ 2 4 ]); + an = randi( [ 2 4 ]); + bm = randi( [ 2 4 ]); + bn = randi( [ 2 4 ]); + else + % matrix multiplication that is possible: + am = randi( [ 2 4 ]); + an = randi( [ 2 4 ]); + bm = an; + bn = randi( [ 2 4 ]); + end + % generate the matrices: + a = randi( [-4 4], am, an ); + b = randi( [-4 4], bm, bn ); + % write them out as LaTeX code: + % matrix a: + fprintf( f, ' \\[ \\begin{pmatrix}' ); + for r = 1:size( a, 1 ) + for c = 1:size( a, 2 ) + if c > 1 + fprintf( f, ' &' ); + end + fprintf( f, ' %d', a(r,c) ); + end + if r < size( a, 1 ) + fprintf( f, ' \\\\' ); + end + end + fprintf( f, ' \\end{pmatrix} \\cdot\n' ); + % matrix b: + fprintf( f, ' \\begin{pmatrix}' ); + for r = 1:size( b, 1 ) + for c = 1:size( b, 2 ) + if c > 1 + fprintf( f, ' &' ); + end + fprintf( f, ' %d', b(r,c) ); + end + if r < size( b, 1 ) + fprintf( f, ' \\\\' ); + end + end + fprintf( f, ' \\end{pmatrix} = \\]\n\n' ); + +end + +% close the document and the file: +fprintf( f, '\\end{document}\n' ); +fclose( f ); diff --git a/linearalgebra/code/p-unit_spike_times.mat b/linearalgebra/code/p-unit_spike_times.mat new file mode 100644 index 0000000000000000000000000000000000000000..75f53e63fa60c1e5b0ecc719adedba9175db2bbc GIT binary patch literal 162494 zcma%iWl$VUuq{pq?!h4h*8ss?g1bAx2^L%z3GNzPgS)%C1r~R=1r}d?S-9V=y6^w% z>QmKIH8a)yqess4C`)K5Nk~$EW9Ot+me69ewsWvzrB-wJ;co5h>L^GptE8eQ!OO!+ 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