Merge branch 'master' of whale.am28.uni-tuebingen.de:scientificComputing
This commit is contained in:
commit
a32a22b35b
@ -52,10 +52,10 @@ endobj
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||||
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@ -65,10 +65,10 @@ endstream
|
||||
endobj
|
||||
2 0 obj
|
||||
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|
||||
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|
||||
/CreationDate(D:20170116181818)
|
||||
/ModDate(D:20170116181818)
|
||||
/Creator(MATLAB, The MathWorks, Inc. Version 8.3.0.532 \(R2014a\). Operating System: Linux 3.13.0-24-generic #47-Ubuntu SMP Fri May 2 23:30:00 UTC 2014 x86_64.)
|
||||
/Title(/tmp/tpd0b45dc9_ff5a_4aa8_90bd_50aa8e8237b6.ps)>>endobj
|
||||
/Title(/tmp/tp6e6add58_0ada_4a6c_ba7e_63eeba1cbd7c.ps)>>endobj
|
||||
xref
|
||||
0 12
|
||||
0000000000 65535 f
|
||||
@ -85,7 +85,7 @@ xref
|
||||
0000001375 00000 n
|
||||
trailer
|
||||
<< /Size 12 /Root 1 0 R /Info 2 0 R
|
||||
/ID [<8FE161FFCC6D1C11BAD3CE59BA0E3F32><8FE161FFCC6D1C11BAD3CE59BA0E3F32>]
|
||||
/ID [<F0B160FA5B0C72A4E47D89F3F547B465><F0B160FA5B0C72A4E47D89F3F547B465>]
|
||||
>>
|
||||
startxref
|
||||
3070
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@ -1,6 +1,6 @@
|
||||
%% (a) generate correlated data
|
||||
n=1000;
|
||||
a=0.2;
|
||||
n = 1000;
|
||||
a = 0.2;
|
||||
x = randn(n, 1);
|
||||
y = randn(n, 1) + a*x;
|
||||
|
||||
@ -50,7 +50,7 @@ hold on;
|
||||
bar(b, h, 'facecolor', 'b');
|
||||
bar(b(b>=rq), h(b>=rq), 'facecolor', 'r');
|
||||
plot( [rd rd], [0 4], 'r', 'linewidth', 2 );
|
||||
xlim([-0.2 0.2])
|
||||
xlim([-0.25 0.25])
|
||||
xlabel('Correlation coefficient');
|
||||
ylabel('Probability density of H0');
|
||||
hold off;
|
||||
|
||||
Binary file not shown.
@ -15,7 +15,7 @@
|
||||
\else
|
||||
\newcommand{\stitle}{}
|
||||
\fi
|
||||
\header{{\bfseries\large \"Ubung 3\stitle}}{{\bfseries\large Statistik}}{{\bfseries\large 21. Oktober, 2015}}
|
||||
\header{{\bfseries\large \"Ubung\stitle}}{{\bfseries\large Bootstrap}}{{\bfseries\large 17. Januar, 2017}}
|
||||
\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email:
|
||||
jan.benda@uni-tuebingen.de}
|
||||
\runningfooter{}{\thepage}{}
|
||||
@ -84,10 +84,13 @@ jan.benda@uni-tuebingen.de}
|
||||
|
||||
\input{instructions}
|
||||
|
||||
|
||||
\begin{questions}
|
||||
|
||||
\question \qt{Bootstrap des Standardfehlers}
|
||||
Wir wollen den Standardfehler, die Standardabweichung des Mittelwerts,
|
||||
eines Datensatze mit Hilfe der Bootstrapmethode berechnen und mit der
|
||||
Formel ``Standardabweichung geteilt durch Wurzel aus $n$''
|
||||
vergleichen.
|
||||
\begin{parts}
|
||||
\part Lade von Ilias die Datei \code{thymusglandweights.dat} herunter.
|
||||
Darin befindet sich ein Datensatz vom Gewicht der Thymus Dr\"use in 14-Tage alten
|
||||
@ -112,8 +115,11 @@ jan.benda@uni-tuebingen.de}
|
||||
\end{solution}
|
||||
|
||||
|
||||
\continue
|
||||
\question \qt{Student t-Verteilung}
|
||||
Durch Standardabweichungen normierte Mittelwerte sind nicht Gaussverteilt,
|
||||
wenn beide aus Normalverteilten Daten abgesch\"atzt werden.
|
||||
Die Verteilung von $t=\bar x/(\sigma_x/\sqrt{m})$ folgt vielmehr
|
||||
der Student t-Verteilung.
|
||||
\begin{parts}
|
||||
\part Erzeuge 100000 normalverteilte Zufallszahlen.
|
||||
\part Ziehe daraus 1000 Stichproben vom Umfang $m=3$, 5, 10, oder 50.
|
||||
@ -123,6 +129,7 @@ dieser Mittelwerte.
|
||||
\part Berechne ausserdem die Gr\"o{\ss}e $t=\bar x/(\sigma_x/\sqrt{m})$
|
||||
(Standardabweichung $\sigma_x$) und vergleiche diese mit der Normalverteilung mit Standardabweichung Eins. Ist $t$ normalverteilt, bzw. unter welchen Bedingungen ist $t$ normalverteilt?
|
||||
\end{parts}
|
||||
\newsolutionpage
|
||||
\begin{solution}
|
||||
\lstinputlisting{tdistribution.m}
|
||||
\includegraphics[width=1\textwidth]{tdistribution-n03}\\
|
||||
@ -132,7 +139,10 @@ dieser Mittelwerte.
|
||||
\end{solution}
|
||||
|
||||
|
||||
\question \qt{Korrelationen}
|
||||
\continue
|
||||
\question \qt{Permutationstest}
|
||||
Wir wollen die Signifikanz einer Korrelation durch einen
|
||||
Permutationstest bestimmen.
|
||||
\begin{parts}
|
||||
\part Erzeuge 1000 korrelierte Zufallszahlen $x$, $y$ durch
|
||||
\begin{verbatim}
|
||||
|
||||
@ -4,38 +4,3 @@
|
||||
{\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}
|
||||
|
||||
\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
|
||||
|
||||
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@ -4,10 +4,13 @@ all : pdf
|
||||
|
||||
include ../../chapter.mk
|
||||
|
||||
# script:
|
||||
pdf : chapter
|
||||
include ../../slides.mk
|
||||
|
||||
clean : cleanchapter
|
||||
# script and slides:
|
||||
pdf : chapter slides
|
||||
|
||||
clean : cleanchapter cleanslides
|
||||
|
||||
cleanall : clean cleanallchapter cleanallslides
|
||||
|
||||
cleanall : clean cleanchapter
|
||||
|
||||
|
||||
529
bootstrap/lecture/UT_WBMW_Rot_RGB.pdf
Normal file
529
bootstrap/lecture/UT_WBMW_Rot_RGB.pdf
Normal file
File diff suppressed because one or more lines are too long
61
bootstrap/lecture/beamercolorthemetuebingen.sty
Normal file
61
bootstrap/lecture/beamercolorthemetuebingen.sty
Normal file
@ -0,0 +1,61 @@
|
||||
% Copyright 2007 by Till Tantau
|
||||
%
|
||||
% This file may be distributed and/or modified
|
||||
%
|
||||
% 1. under the LaTeX Project Public License and/or
|
||||
% 2. under the GNU Public License.
|
||||
%
|
||||
% See the file doc/licenses/LICENSE for more details.
|
||||
|
||||
\usepackage{color}
|
||||
\definecolor{karminrot}{RGB}{165,30,55}
|
||||
\definecolor{gold}{RGB}{180,160,105}
|
||||
\definecolor{anthrazit}{RGB}{50 ,65 ,75 }
|
||||
|
||||
\mode<presentation>
|
||||
|
||||
\setbeamercolor*{normal text}{fg=anthrazit,bg=white}
|
||||
\setbeamercolor*{alerted text}{fg=anthrazit}
|
||||
\setbeamercolor*{example text}{fg=anthrazit}
|
||||
\setbeamercolor*{structure}{fg=gold,bg=karminrot}
|
||||
|
||||
\providecommand*{\beamer@bftext@only}{%
|
||||
\relax
|
||||
\ifmmode
|
||||
\expandafter\beamer@bftext@warning
|
||||
\else
|
||||
\expandafter\bfseries
|
||||
\fi
|
||||
}
|
||||
\providecommand*{\beamer@bftext@warning}{%
|
||||
\ClassWarning{beamer}
|
||||
{Cannot use bold for alerted text in math mode}%
|
||||
}
|
||||
|
||||
\setbeamerfont{alerted text}{series=\beamer@bftext@only}
|
||||
|
||||
\setbeamercolor{palette primary}{fg=karminrot,bg=white}
|
||||
\setbeamercolor{palette secondary}{fg=gold,bg=white}
|
||||
\setbeamercolor{palette tertiary}{fg=anthrazit,bg=white}
|
||||
\setbeamercolor{palette quaternary}{fg=black,bg=white}
|
||||
|
||||
\setbeamercolor{sidebar}{bg=karminrot!100}
|
||||
|
||||
\setbeamercolor{palette sidebar primary}{fg=karminrot}
|
||||
\setbeamercolor{palette sidebar secondary}{fg=karminrot}
|
||||
\setbeamercolor{palette sidebar tertiary}{fg=karminrot}
|
||||
\setbeamercolor{palette sidebar quaternary}{fg=karminrot}
|
||||
|
||||
\setbeamercolor{item projected}{fg=black,bg=black!20}
|
||||
|
||||
\setbeamercolor*{block body}{}
|
||||
\setbeamercolor*{block body alerted}{}
|
||||
\setbeamercolor*{block body example}{}
|
||||
\setbeamercolor*{block title}{parent=structure}
|
||||
\setbeamercolor*{block title alerted}{parent=alerted text}
|
||||
\setbeamercolor*{block title example}{parent=example text}
|
||||
|
||||
\setbeamercolor*{titlelike}{parent=structure}
|
||||
|
||||
\mode
|
||||
<all>
|
||||
110
bootstrap/lecture/bootstrap-slides.tex
Normal file
110
bootstrap/lecture/bootstrap-slides.tex
Normal file
@ -0,0 +1,110 @@
|
||||
\documentclass{beamer}
|
||||
|
||||
%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\title[]{Scientific Computing --- Bootstrap methods}
|
||||
\author[]{Jan Benda}
|
||||
\institute[]{Neuroethology}
|
||||
\date[]{WS 16/17}
|
||||
\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
|
||||
|
||||
%%%%% beamer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\mode<presentation>
|
||||
{
|
||||
\usetheme{Singapore}
|
||||
\setbeamercovered{opaque}
|
||||
\usecolortheme{tuebingen}
|
||||
\setbeamertemplate{navigation symbols}{}
|
||||
\usefonttheme{default}
|
||||
\useoutertheme{infolines}
|
||||
% \useoutertheme{miniframes}
|
||||
}
|
||||
|
||||
%\AtBeginSection[]
|
||||
%{
|
||||
% \begin{frame}<beamer>
|
||||
% \begin{center}
|
||||
% \Huge \insertsectionhead
|
||||
% \end{center}
|
||||
% \end{frame}
|
||||
%}
|
||||
|
||||
\setbeamertemplate{blocks}[rounded][shadow=true]
|
||||
\setcounter{tocdepth}{1}
|
||||
|
||||
%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage[english]{babel}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{bm}
|
||||
\usepackage{pslatex} % nice font for pdf file
|
||||
%\usepackage{multimedia}
|
||||
|
||||
\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}}
|
||||
|
||||
%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage{graphicx}
|
||||
\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}}
|
||||
|
||||
%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage{listings}
|
||||
\lstset{
|
||||
basicstyle=\ttfamily,
|
||||
numbers=left,
|
||||
showstringspaces=false,
|
||||
language=Matlab,
|
||||
commentstyle=\itshape\color{darkgray},
|
||||
keywordstyle=\color{blue},
|
||||
stringstyle=\color{green},
|
||||
backgroundcolor=\color{blue!10},
|
||||
breaklines=true,
|
||||
breakautoindent=true,
|
||||
columns=flexible,
|
||||
frame=single,
|
||||
captionpos=b,
|
||||
xleftmargin=1em,
|
||||
xrightmargin=1em,
|
||||
aboveskip=10pt
|
||||
}
|
||||
|
||||
\graphicspath{{figures/}}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{document}
|
||||
|
||||
\begin{frame}[plain]
|
||||
\frametitle{}
|
||||
\vspace{-1cm}
|
||||
\titlepage % erzeugt Titelseite
|
||||
\end{frame}
|
||||
|
||||
\subsection{Bootstrap distribution}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}
|
||||
\frametitle{Sampling distribution}
|
||||
\includegraphics[width=1\textwidth]{srs1}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Theoretical sampling distribution}
|
||||
\includegraphics[width=1\textwidth]{srs2}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Bootstrap distribution}
|
||||
\includegraphics[width=1\textwidth]{srs3}\\[1ex]
|
||||
\begin{itemize}
|
||||
\item Resampling with replacement.
|
||||
\item Size of resample equals size of original sample.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
|
||||
@ -1 +1 @@
|
||||
printfaculty(5);
|
||||
printfactorial(5);
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
function x = mufactorial(n)
|
||||
function x = myfactorial(n)
|
||||
% return the factorial of n
|
||||
x = 1;
|
||||
for i = 1:n
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
function printfaculty(n)
|
||||
% compute the faculty of n and print it
|
||||
function printfactorial(n)
|
||||
% compute the factorial of n and print it
|
||||
x = 1;
|
||||
for i = 1:n
|
||||
x = x * i;
|
||||
|
||||
@ -26,6 +26,7 @@
|
||||
\item Matrizen erstmal 2-D und nur kurz n-D
|
||||
\item Zusammenfassung von Fehlermeldungen bezueglich Matrizen und Vektoren
|
||||
\item Random-walk behutsam mit einer Schleife, dann zwei Schleifen. Plus Bildchen.
|
||||
\item Random-Walk with drift is model for decision making! See resoures/GoldShadlen2007 paper, Figure 2. Das wird auch in Systems Neurosciene \texttt{9 - Kognitive Kontrolle II.pdf} behandelt.
|
||||
\item Doppelte for-Schleife
|
||||
\item File output and input (load, save, fprintf, scanf) (extra chapter?)
|
||||
\item help() und doc()
|
||||
|
||||
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11
projects/project_fano_time/solution/counthist.m
Normal file
11
projects/project_fano_time/solution/counthist.m
Normal file
@ -0,0 +1,11 @@
|
||||
function [counts, cbins] = counthist(spikes, tmin, tmax, T, cmax)
|
||||
tbins = tmin+T/2:T:tmax;
|
||||
cbins = 0.5:cmax;
|
||||
counts = zeros(1, length(cbins));
|
||||
for k = 1:length(spikes)
|
||||
times = spikes{k};
|
||||
n = hist(times((times>=tmin)&(times<=tmax)), tbins);
|
||||
counts = counts + hist(n, cbins);
|
||||
end
|
||||
counts = counts / sum(counts);
|
||||
end
|
||||
23
projects/project_fano_time/solution/discriminability.m
Normal file
23
projects/project_fano_time/solution/discriminability.m
Normal file
@ -0,0 +1,23 @@
|
||||
function [d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax)
|
||||
[c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
|
||||
[c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
|
||||
thresholds = 0:cmax;
|
||||
true1s = zeros(length(thresholds), 1);
|
||||
true2s = zeros(length(thresholds), 1);
|
||||
false1s = zeros(length(thresholds), 1);
|
||||
false2s = zeros(length(thresholds), 1);
|
||||
for k = 1:length(thresholds)
|
||||
th = thresholds(k);
|
||||
t1 = sum(c1(b1<=th));
|
||||
f1 = sum(c1(b1>th));
|
||||
t2 = sum(c2(b2>=th));
|
||||
f2 = sum(c2(b2<th));
|
||||
true1s(k) = t1;
|
||||
true2s(k) = t2;
|
||||
false1s(k) = f1;
|
||||
false2s(k) = f2;
|
||||
end
|
||||
%pratio = (true1s + true2s)./(false1s+false2s);
|
||||
pratio = (true1s + true2s)/2;
|
||||
d = max(pratio);
|
||||
end
|
||||
71
projects/project_fano_time/solution/fanotime.m
Normal file
71
projects/project_fano_time/solution/fanotime.m
Normal file
@ -0,0 +1,71 @@
|
||||
%% general settings for the model neuron:
|
||||
trials = 10;
|
||||
tmax = 50.0;
|
||||
D = 0.01;
|
||||
|
||||
%% generate and plot spiketrains for two inputs:
|
||||
I1 = 14.0;
|
||||
I2 = 15.0;
|
||||
spikes1 = lifspikes(trials, I1, tmax, D);
|
||||
spikes2 = lifspikes(trials, I2, tmax, D);
|
||||
subplot(1, 2, 1);
|
||||
tmin = 10.0;
|
||||
spikeraster(spikes1, tmin, tmin+2.0);
|
||||
title(sprintf('I_1=%g', I1))
|
||||
subplot(1, 2, 2);
|
||||
spikeraster(spikes2, tmin, tmin+2.0);
|
||||
title(sprintf('I_2=%g', I2))
|
||||
%savefigpdf(gcf(), 'spikeraster.pdf')
|
||||
|
||||
%% spike count histograms:
|
||||
Ts = [0.01 0.1 0.5 1.0];
|
||||
cmax = 100;
|
||||
figure()
|
||||
for k = 1:length(Ts)
|
||||
T = Ts(k);
|
||||
[c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
|
||||
[c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
|
||||
subplot(2, 2, k)
|
||||
bar(b1, c1, 'r');
|
||||
hold on;
|
||||
bar(b2, c2, 'b');
|
||||
xlim([0 cmax])
|
||||
title(sprintf('T=%gms', 1000.0*T))
|
||||
hold off;
|
||||
end
|
||||
|
||||
%% discrimination measure:
|
||||
T = 0.1;
|
||||
cmax = 20;
|
||||
[d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
|
||||
figure()
|
||||
subplot(1, 3, 1);
|
||||
plot(thresholds, true1s, 'b');
|
||||
hold on;
|
||||
plot(thresholds, true2s, 'b');
|
||||
plot(thresholds, false1s, 'r');
|
||||
plot(thresholds, false2s, 'r');
|
||||
hold off;
|
||||
% Ratio:
|
||||
subplot(1, 3, 2);
|
||||
fprintf('discriminability = %g\n', d);
|
||||
plot(thresholds, pratio);
|
||||
% ROC:
|
||||
subplot(1, 3, 3);
|
||||
plot(false2s, true1s);
|
||||
|
||||
%% discriminability:
|
||||
Ts = 0.01:0.01:1.0;
|
||||
cmax = 100;
|
||||
ds = zeros(length(Ts), 1)
|
||||
for k = 1:length(Ts)
|
||||
T = Ts(k);
|
||||
[c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
|
||||
[c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
|
||||
[d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
|
||||
ds(k) = d;
|
||||
end
|
||||
figure()
|
||||
plot(Ts, ds)
|
||||
|
||||
|
||||
39
projects/project_fano_time/solution/lifspikes.m
Normal file
39
projects/project_fano_time/solution/lifspikes.m
Normal file
@ -0,0 +1,39 @@
|
||||
function spikes = lifspikes(trials, input, tmaxdt, D)
|
||||
% Generate spike times of a leaky integrate-and-fire neuron.
|
||||
% trials: the number of trials to be generated
|
||||
% input: the stimulus either as a single value or as a vector
|
||||
% tmaxdt: in case of a single value stimulus the duration of a trial
|
||||
% in case of a vector as a stimulus the time step
|
||||
% D: the strength of additive white noise
|
||||
|
||||
tau = 0.01;
|
||||
if nargin < 4
|
||||
D = 1e0;
|
||||
end
|
||||
vreset = 0.0;
|
||||
vthresh = 10.0;
|
||||
dt = 5e-5;
|
||||
|
||||
if max(size(input)) == 1
|
||||
input = input * ones(ceil(tmaxdt/dt), 1);
|
||||
else
|
||||
dt = tmaxdt;
|
||||
end
|
||||
spikes = cell(trials, 1);
|
||||
for k=1:trials
|
||||
times = [];
|
||||
j = 1;
|
||||
v = vreset + (vthresh-vreset)*rand(1);
|
||||
noise = sqrt(2.0*D)*randn(length(input), 1)/sqrt(dt);
|
||||
for i=1:length(noise)
|
||||
v = v + (- v + noise(i) + input(i))*dt/tau;
|
||||
if v >= vthresh
|
||||
v = vreset;
|
||||
spiketime = i*dt;
|
||||
times(j) = spiketime;
|
||||
j = j + 1;
|
||||
end
|
||||
end
|
||||
spikes{k} = times;
|
||||
end
|
||||
end
|
||||
28
projects/project_fano_time/solution/savefigpdf.m
Normal file
28
projects/project_fano_time/solution/savefigpdf.m
Normal file
@ -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
|
||||
|
||||
30
projects/project_fano_time/solution/spikeraster.m
Normal file
30
projects/project_fano_time/solution/spikeraster.m
Normal file
@ -0,0 +1,30 @@
|
||||
function spikeraster(spikes, tmin, tmax)
|
||||
% Display a spike raster of the spike times given in spikes.
|
||||
%
|
||||
% spikeraster(spikes, tmax)
|
||||
% spikes: a cell array of vectors of spike times in seconds
|
||||
% tmin: plot spike raster starting at tmin seconds
|
||||
% tmax: plot spike raster upto tmax seconds
|
||||
|
||||
ntrials = length(spikes);
|
||||
for k = 1:ntrials
|
||||
times = spikes{k};
|
||||
times = times((times>=tmin) & (times<=tmax));
|
||||
if tmax < 1.5
|
||||
times = 1000.0*times; % conversion to ms
|
||||
end
|
||||
for i = 1:length( times )
|
||||
line([times(i) times(i)],[k-0.4 k+0.4], 'Color', 'k');
|
||||
end
|
||||
end
|
||||
if (tmax-tmin) < 1.5
|
||||
xlabel('Time [ms]');
|
||||
xlim([1000.0*tmin 1000.0*tmax]);
|
||||
else
|
||||
xlabel('Time [s]');
|
||||
xlim([tmin tmax]);
|
||||
end
|
||||
ylabel('Trials');
|
||||
ylim([0.3 ntrials+0.7 ]);
|
||||
end
|
||||
|
||||
File diff suppressed because one or more lines are too long
15
slides.mk
Normal file
15
slides.mk
Normal file
@ -0,0 +1,15 @@
|
||||
# slides:
|
||||
slides : $(BASENAME)-slides.pdf
|
||||
|
||||
$(BASENAME)-slides.pdf : $(BASENAME)-slides.tex $(PYPDFFILES) $(GPTTEXFILES)
|
||||
pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
|
||||
|
||||
watchslides :
|
||||
while true; do ! make -q slides && make slides; sleep 0.5; done
|
||||
|
||||
cleanslides :
|
||||
rm -f *~
|
||||
rm -f $(BASENAME)-slides.aux $(BASENAME)-slides.log $(BASENAME)-slides.out $(BASENAME)-slides.idx
|
||||
|
||||
cleanallslides : cleanslides
|
||||
rm -f $(BASENAME)-slides.pdf
|
||||
34
statistics/exercises/randomwalkfirstpassagetime.py
Normal file
34
statistics/exercises/randomwalkfirstpassagetime.py
Normal file
@ -0,0 +1,34 @@
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
# first passage time of random walker
|
||||
# the average of the first passage time grows
|
||||
# the more experiments you average (n)
|
||||
# eventually diverges to infinity
|
||||
# see https://www.math.ucdavis.edu/~tracy/courses/math135A/UsefullCourseMaterial/firstPassage.pdf last paragraph
|
||||
|
||||
p = 0.5
|
||||
thresh = 1.0
|
||||
rep = 1
|
||||
rn = 10000
|
||||
n = 2
|
||||
meantimes = np.zeros(rep)
|
||||
for i in range(rep):
|
||||
times = np.zeros(n)
|
||||
for k in range(n):
|
||||
xx = 0.0
|
||||
xxinx = 0
|
||||
while True:
|
||||
r = np.random.rand(rn)
|
||||
x = np.zeros(len(r))
|
||||
x[r < p] = 1.0
|
||||
x[r >= p]= -1.0
|
||||
y = xx + np.cumsum(x)
|
||||
inx = np.where(y > thresh)[0]
|
||||
if len(inx) > 0:
|
||||
times[k] = xxinx + inx[0]
|
||||
break
|
||||
xx = y[-1]
|
||||
xxinx += len(x)
|
||||
meantimes[i] = np.mean(times)
|
||||
print np.mean(meantimes)
|
||||
Reference in New Issue
Block a user