From af933f9379edbe5b8b73ed5a12ca154b76485257 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Wed, 28 Oct 2015 09:16:00 +0100
Subject: [PATCH 1/3] Improved spike statistik code.
---
pointprocesses/code/isis.m | 6 +--
pointprocesses/code/isiserialcorr.m | 3 +-
pointprocesses/code/plotspikestats.m | 73 ++++++++++++++++++++++++++++
3 files changed, 75 insertions(+), 7 deletions(-)
create mode 100644 pointprocesses/code/plotspikestats.m
diff --git a/pointprocesses/code/isis.m b/pointprocesses/code/isis.m
index b0b95ff..cfd0cea 100644
--- a/pointprocesses/code/isis.m
+++ b/pointprocesses/code/isis.m
@@ -5,11 +5,7 @@ function isivec = isis( spikes )
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
+ isivec = [ isivec; difftimes(:) ];
end
end
diff --git a/pointprocesses/code/isiserialcorr.m b/pointprocesses/code/isiserialcorr.m
index d5b44c1..0daac23 100644
--- a/pointprocesses/code/isiserialcorr.m
+++ b/pointprocesses/code/isiserialcorr.m
@@ -8,8 +8,7 @@ function isicorr = isiserialcorr( isis, maxlag )
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 );
+ isicorr(k) = corr( isis(1:end-lag), isis(lag+1:end) );
end
end
diff --git a/pointprocesses/code/plotspikestats.m b/pointprocesses/code/plotspikestats.m
new file mode 100644
index 0000000..cede720
--- /dev/null
+++ b/pointprocesses/code/plotspikestats.m
@@ -0,0 +1,73 @@
+%% 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:
+subplot(1, 3, 1);
+spikeraster(poissonspikes, 1.0);
+title('Poisson');
+
+subplot(1, 3, 2);
+spikeraster(pifouspikes, 1.0);
+title('PIF OU');
+
+subplot(1, 3, 3);
+spikeraster(lifadaptspikes, 1.0);
+title('LIF adapt');
+
+%% isi histograms:
+maxisi = 300.0;
+subplot(1, 3, 1);
+poissonisis = isis(poissonspikes);
+isihist(poissonisis, 0.001);
+xlim([0, maxisi])
+title('Poisson');
+
+subplot(1, 3, 2);
+pifouisis = isis(pifouspikes);
+isihist(pifouisis, 0.001);
+xlim([0, maxisi])
+title('PIF OU');
+
+subplot(1, 3, 3);
+lifadaptisis = isis(lifadaptspikes);
+isihist(lifadaptisis, 0.001);
+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');
From dbe0a2173c7e0cb9a43d8d58d6200a73bdca6d75 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Wed, 28 Oct 2015 17:07:34 +0100
Subject: [PATCH 2/3] Updated pointprocess exercises and code
---
pointprocesses/code/counthist.m | 35 ++++++++++++++++--------
pointprocesses/code/isihist.m | 8 ++++--
pointprocesses/code/isis.m | 7 ++++-
pointprocesses/code/isiserialcorr.m | 13 ++++++---
pointprocesses/code/plotspikestats.m | 41 +++++++++++++++++++++++-----
pointprocesses/code/poissonspikes.m | 10 ++++---
pointprocesses/code/spikeraster.m | 8 ++++--
7 files changed, 89 insertions(+), 33 deletions(-)
diff --git a/pointprocesses/code/counthist.m b/pointprocesses/code/counthist.m
index 9abb225..15d431e 100644
--- a/pointprocesses/code/counthist.m
+++ b/pointprocesses/code/counthist.m
@@ -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
+% computes count histogram and compare them with Poisson distribution
+%
+% [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 ) ) );
- n = [ n nn ];
- end
- rate = (length(spikes{k})-1)/(spikes{k}(end) - spikes{k}(1));
+ 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 );
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
-
diff --git a/pointprocesses/code/isihist.m b/pointprocesses/code/isihist.m
index afd69d4..17974cc 100644
--- a/pointprocesses/code/isihist.m
+++ b/pointprocesses/code/isihist.m
@@ -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
diff --git a/pointprocesses/code/isis.m b/pointprocesses/code/isis.m
index cfd0cea..e693ea8 100644
--- a/pointprocesses/code/isis.m
+++ b/pointprocesses/code/isis.m
@@ -1,10 +1,15 @@
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} );
+ % difftimes(:) ensures a column vector
+ % regardless of the type of vector spikes{k}
isivec = [ isivec; difftimes(:) ];
end
end
diff --git a/pointprocesses/code/isiserialcorr.m b/pointprocesses/code/isiserialcorr.m
index 0daac23..c93fb5e 100644
--- a/pointprocesses/code/isiserialcorr.m
+++ b/pointprocesses/code/isiserialcorr.m
@@ -1,13 +1,18 @@
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
+ 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
diff --git a/pointprocesses/code/plotspikestats.m b/pointprocesses/code/plotspikestats.m
index cede720..a664eca 100644
--- a/pointprocesses/code/plotspikestats.m
+++ b/pointprocesses/code/plotspikestats.m
@@ -1,5 +1,4 @@
%% load data:
-
clear all
% alternative 1:
% pro: no structs. contra: global unknown variables
@@ -22,35 +21,37 @@ x = load( 'lifadapt.mat' );
lifadaptspikes = x.spikes;
%% spike raster plots:
+tmax = 1.0;
subplot(1, 3, 1);
-spikeraster(poissonspikes, 1.0);
+spikeraster(poissonspikes, tmax);
title('Poisson');
subplot(1, 3, 2);
-spikeraster(pifouspikes, 1.0);
+spikeraster(pifouspikes, tmax);
title('PIF OU');
subplot(1, 3, 3);
-spikeraster(lifadaptspikes, 1.0);
+spikeraster(lifadaptspikes, tmax);
title('LIF adapt');
%% isi histograms:
maxisi = 300.0;
+binwidth = 0.002;
subplot(1, 3, 1);
poissonisis = isis(poissonspikes);
-isihist(poissonisis, 0.001);
+isihist(poissonisis, binwidth);
xlim([0, maxisi])
title('Poisson');
subplot(1, 3, 2);
pifouisis = isis(pifouspikes);
-isihist(pifouisis, 0.001);
+isihist(pifouisis, binwidth);
xlim([0, maxisi])
title('PIF OU');
subplot(1, 3, 3);
lifadaptisis = isis(lifadaptspikes);
-isihist(lifadaptisis, 0.001);
+isihist(lifadaptisis, binwidth);
xlim([0, maxisi])
title('LIF adapt');
@@ -71,3 +72,29 @@ 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/poissonspikes.m b/pointprocesses/code/poissonspikes.m
index 6a75f40..37f2234 100644
--- a/pointprocesses/code/poissonspikes.m
+++ b/pointprocesses/code/poissonspikes.m
@@ -1,9 +1,11 @@
function spikes = poissonspikes( 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
+%
+% 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
+% 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
diff --git a/pointprocesses/code/spikeraster.m b/pointprocesses/code/spikeraster.m
index 7d4c12f..cde46dc 100644
--- a/pointprocesses/code/spikeraster.m
+++ b/pointprocesses/code/spikeraster.m
@@ -1,7 +1,9 @@
function spikeraster(spikes, tmax)
% Display a spike raster of the spike times given in spikes.
-% spikes: a cell array of vectors of spike times
-% tmax: plot spike raster upto tmax seconds
+%
+% spikeraster(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
@@ -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 ] )
From 3ca3c7b49972148e4a69499d78f49d7b11cea545 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Wed, 28 Oct 2015 22:36:48 +0100
Subject: [PATCH 3/3] Changed colors for listings. Small improvements on the
script.
---
bootstrap/lecture/bootstrap-chapter.tex | 6 +++---
.../lecture/designpattern-chapter.tex | 6 +++---
designpattern/lecture/designpattern.tex | 16 ++++++++++------
likelihood/lecture/likelihood-chapter.tex | 6 +++---
.../lecture/pointprocesses-chapter.tex | 6 +++---
scientificcomputing-script.tex | 6 +++---
statistics/lecture/diehistograms.py | 14 +++++++++++---
statistics/lecture/pdfhistogram.py | 19 ++++++++++++-------
statistics/lecture/statistics-chapter.tex | 6 +++---
statistics/lecture/statistics.tex | 7 +++++--
10 files changed, 56 insertions(+), 36 deletions(-)
diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex
index d185cd4..53099ed 100644
--- a/bootstrap/lecture/bootstrap-chapter.tex
+++ b/bootstrap/lecture/bootstrap-chapter.tex
@@ -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,
diff --git a/designpattern/lecture/designpattern-chapter.tex b/designpattern/lecture/designpattern-chapter.tex
index 08ff012..e821287 100644
--- a/designpattern/lecture/designpattern-chapter.tex
+++ b/designpattern/lecture/designpattern-chapter.tex
@@ -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,
diff --git a/designpattern/lecture/designpattern.tex b/designpattern/lecture/designpattern.tex
index c581b9b..93ef588 100644
--- a/designpattern/lecture/designpattern.tex
+++ b/designpattern/lecture/designpattern.tex
@@ -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)
diff --git a/likelihood/lecture/likelihood-chapter.tex b/likelihood/lecture/likelihood-chapter.tex
index 732acbe..2a82f79 100644
--- a/likelihood/lecture/likelihood-chapter.tex
+++ b/likelihood/lecture/likelihood-chapter.tex
@@ -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,
diff --git a/pointprocesses/lecture/pointprocesses-chapter.tex b/pointprocesses/lecture/pointprocesses-chapter.tex
index 44af27e..1e68316 100644
--- a/pointprocesses/lecture/pointprocesses-chapter.tex
+++ b/pointprocesses/lecture/pointprocesses-chapter.tex
@@ -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,
diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex
index 65e8b2b..e4049a8 100644
--- a/scientificcomputing-script.tex
+++ b/scientificcomputing-script.tex
@@ -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,
diff --git a/statistics/lecture/diehistograms.py b/statistics/lecture/diehistograms.py
index a8832e0..c80c68a 100644
--- a/statistics/lecture/diehistograms.py
+++ b/statistics/lecture/diehistograms.py
@@ -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()
diff --git a/statistics/lecture/pdfhistogram.py b/statistics/lecture/pdfhistogram.py
index a61460e..1faa52d 100644
--- a/statistics/lecture/pdfhistogram.py
+++ b/statistics/lecture/pdfhistogram.py
@@ -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' )
diff --git a/statistics/lecture/statistics-chapter.tex b/statistics/lecture/statistics-chapter.tex
index d43ca3e..1d13265 100644
--- a/statistics/lecture/statistics-chapter.tex
+++ b/statistics/lecture/statistics-chapter.tex
@@ -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,
diff --git a/statistics/lecture/statistics.tex b/statistics/lecture/statistics.tex
index 85ce58d..2ca6481 100644
--- a/statistics/lecture/statistics.tex
+++ b/statistics/lecture/statistics.tex
@@ -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