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150
debugging/lecture/debugging.tex
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@ -1,7 +1,10 @@
\chapter{Debugging}
When we write a program from scratch we almost always make
mistakes. Accordingly a quite substantial amount of time is invested
\centerline{\includegraphics[width=0.7\textwidth]{xkcd_debugger}\rotatebox{90}{\footnotesize\url{www.xkcd.com}}}\vspace{4ex}
When writing a program from scratch we almost always make
mistakes. Accordingly, a quite substantial amount of time is invested
into finding and fixing errors. This process is called
\codeterm{debugging}. Don't be frustrated that a self-written program
does not work as intended and produces errors. It is quite exceptional
@ -14,9 +17,40 @@ some hints that help to minimize errors.
\section{Types of errors and error messages}
There are a number of different classes of programming errors.
There are a number of different classes of programming errors and it
is good to know the common ones. When we make a programming error
there are some that will lead to corrupted syntax, or invalid
operations and \matlab{} will \codeterm{throw} an error. Throwing an
error ends the execution of a program and there will be an error
messages shown in the command window. With such messages \matlab{}
tries to explain what went wrong and provide a hint on the possible
cause.
Bugs that lead to the termination of the execution may be annoying but
are generally easier to find and fix than logical errors that stay
hidden and the results of, e.g. an analysis, are seemingly correct.
\begin{important}[Try --- catch]
There are ways to \codeterm{catch} errors during \codeterm{runtime}
(i.e. when the program is executed) and handle them in the program.
\begin{lstlisting}[label=trycatch, caption={Try catch clause}]
try
y = function_that_throws_an_error(x);
catch
y = 0;
end
\end{lstlisting}
This way of solving errors may seem rather convenient but is
risky. Having a function throwing an error and catching it in the
\codeterm{catch} clause will keep your command line clean but may
obscure logical errors! Take care when using the \codeterm{try-catch
clause}.
\end{important}
\paragraph{\codeterm{Syntax error}:}
\subsection{\codeterm{Syntax error}}
The most common and easiest to fix type of error. A syntax error
violates the rules (spelling and grammar) of the programming
language. For example every opening parenthesis must be matched by a
@ -28,26 +62,94 @@ the editor will point out and highlight most \codeterm{syntax error}s.
>> mean(random_numbers
|
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.
Did you mean:
>> mean(random_numbers)
\end{lstlisting}
\subsection{\codeterm{Indexing error}}
Second on the list of common errors are the indexing errors. Usually
\matlab{} gives rather precise infromation about the cause, once you
know what they mean. Consider the following code.
\begin{lstlisting}[label=indexerror, caption={Indexing errors.}]
>> my_array = (1:100);
>> % first try: index 0
>> my_array(0)
Subscript indices must either be real positive integers or logicals.
>> % second try: negative index
>> my_array(-1)
Subscript indices must either be real positive integers or logicals.
>> % third try: a floating point number
>> my_array(5.7)
Subscript indices must either be real positive integers or logicals.
>> % fourth try: a character
>> my_array('z')
Index exceeds matrix dimensions.
>> % fifth try: another character
>> my_array('A')
ans =
65 % wtf ?!?
\end{lstlisting}
The first two indexing attempts in listing \ref{indexerror_listing}
are rather clear. We are trying to access elements with indices that
are invalid. Remember, indices in \matlab{} start with 1. Negative
numbers and zero are not permitted. In the third attemp we index
using a floating point number. This fails because indices have to be
'integer' values. Using a character as an index (fourth attempt)
leads to a different error message that says that the index exceeds
the matrix dimensions. This indicates that we are trying to read data
behind the length of our variable \codevar{my\_array} which has 100
elements.
One could have expected that the character is an invalid index, but
apparently it is valid but simply too large. The fith attempt
finally succeeds. But why? \matlab{} implicitely converts the
\codeterm{char} to a number and uses this number to address the
element in \varcode{my\_array}.
\subsection{\codeterm{Assignment error}}
This error occurs when we want to write data into a vector.
\Paragraph{\codeterm{Indexing error}:}
\paragraph{\codeterm{Assignment error}:}
\paragraph{Name error:}
\paragraph{Arithmetic error:}
\paragraph{Logical error:}
\section{Avoiding errors}
\section{Logical error}
Sometimes a program runs smoothly and terminates without any
error. This, however, does not necessarily mean that the program is
correct. We may have made a \codeterm{logical error}. Logical errors
are hard to find, \matlab{} has no chance to find this error and can
not help us fixing bugs origination from these. We are on our own but
there are a few strategies that should help us.
\begin{enumerate}
\item Be sceptical: especially when a program executes without any
complaint on the first try.
\item Clean code: Structure your code that you can easily read
it. Comment, but only where necessary. Correctly indent your
code. Use descriptive variable and function names.
\item Keep it simple (below).
\item Read error messages, try to understand what \matlab{} wants to
tell.
\item Use scripts and functions and call them from the command
line. \matlab{} can then provide you with more information. It will
then point to the line where the error happens.
\item If you still find yourself in trouble: Apply debugging
strategies to find and fix bugs (below).
\end{enumerate}
\subsection{Avoiding errors}
It would be great if we could just sit down write a program, run it
and be done. Most likely this will not happen. Rather, we will make
mistakes and have to bebug the code. There are a few guidelines that
help to reduce the number of errors.
\subsection{Keep it small and simple}
\subsection{The Kiss principle: 'Keep it small and simple' or 'simple and stupid'}
\shortquote{Debugging time increases as a square of the program's
size.}{Chris Wenham}
@ -67,15 +169,15 @@ the script is just hard.
when you write it, how will you ever debug it?}{Brian Kernighan}
Many tasks within an analysis can be squashed into a single line of
code. This saves some space in the file, reduces the effort of coming up
with variable names and simply looks so much more competent than a
code. This saves some space in the file, reduces the effort of coming
up with variable names and simply looks so much more competent than a
collection of very simple lines. Consider the following listing
(listing~\ref{easyvscomplicated}). Both parts of the listing solve the
same problem but the second one breaks the task down to a sequence of
easy-to-understand commands. Finding logical and also syntactic errors is
much easier in the second case. The first version is perfectly fine
but it requires a deep understanding of the applied
functions and also the task at hand.
easy-to-understand commands. Finding logical and also syntactic errors
is much easier in the second case. The first version is perfectly fine
but it requires a deep understanding of the applied functions and also
the task at hand.
\begin{lstlisting}[label=easyvscomplicated, caption={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?}]
% the one-liner
@ -88,13 +190,13 @@ rate(spike_indices) = 1;
rate = conv(rate, kernel, 'same');
\end{lstlisting}
The preferred way depends on several considerations. (i)
How deep is your personal understanding of the programming language?
(ii) What about the programming skills of your target audience or
other people that may depend on your code? (iii) Is one solution
faster or uses less resources than the other? (iv) How much do you
have to invest into the development of the most elegant solution
relative to its importance in the project? The decision is up to you.
The preferred way depends on several considerations. (i) How deep is
your personal understanding of the programming language? (ii) What
about the programming skills of your target audience or other people
that may depend on your code? (iii) Is one solution faster or uses
less resources than the other? (iv) How much do you have to invest
into the development of the most elegant solution relative to its
importance in the project? The decision is up to you.
\subsection{Read error messages carefully and call programs from the command line.}

4
header.tex
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@ -2,12 +2,12 @@
%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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]\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}\vspace{3ex}}
\date{WS 15/16\\\vfill \centerline{\includegraphics[width=0.7\textwidth]{announcements/correlationcartoon}\rotatebox{90}{\footnotesize\url{www.xkcd.com}}}}
\date{WS 2017/2018\\\vfill \centerline{\includegraphics[width=0.7\textwidth]{announcements/correlationcartoon}\rotatebox{90}{\footnotesize\url{www.xkcd.com}}}}
%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \newcommand{\tr}[2]{#1} % en
% \usepackage[english]{babel}
\newcommand{\tr}[2]{#2} % de
\newcommand{\tr}[2]{#1} % en
\usepackage[ngerman, english]{babel}
%%%% encoding %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

9
plotting/lecture/plotting-chapter.tex
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@ -19,12 +19,15 @@
\section{TODO}
\begin{itemize}
\item Beispiele schlechter plots sollten mehr Bezug zu den Typen von
plots haben, die wir machen!
plots haben, die wir machen! Check WS1617 presentations for examples.
\item subplot
\item Uebersicht zu wichtigen plot Befehlen (plot, scatter, bar, step, ...)
\item Funktionenplotten (siehe auch Design patterns) und untersampleter Sinus
\item Verschiedene Stile fuer Achsenbeschriftung (gross/kleinschreibungen, Kalmmertyp fuer Einheiten), stay with one style!
\item Stay with a coherent style (font type/style/size, colors schemes, line styles/thickness, point styles)
\item Verschiedene Stile fuer Achsenbeschriftung (gross/kleinschreibungen, Klammertyp fuer Einheiten), stay with one style!
\item Stay with a coherent style (font type/style/size, colors schemes, line styles/thickness, point styles), same line style in all plots for the same quantity. How to do consistent line styles in matlab (python: dictionary for kwargs)?
\item Different plots for journal papers and presentations!
\item Color universal design for color blind people:
\url{http://jfly.iam.u-tokyo.ac.jp/color/}
\end{itemize}
\end{document}

5
pointprocesses/lecture/pointprocesses-chapter.tex
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@ -20,6 +20,11 @@
\begin{itemize}
\item Add spikeraster function
\item Multitrial firing rates
\item Choice of bin width for PSTH, kernel width, also in relation sto
stimulus time scale
\item Kernle firing rate: discuss different kernel shapes, in
particular causal kernels (gamma, exponential), relation to synaptic
potentials
\end{itemize}
\end{document}

2
pointprocesses/lecture/pointprocesses.tex
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@ -113,7 +113,7 @@ heisen die Intervalle auch \determ{Interspikeintervalle}
\frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$.
\end{itemize}
\begin{exercise}{isiHist.m}{}
\begin{exercise}{isihist.m}{}
Schreibe eine Funktion \code{isiHist()}, die einen Vektor mit Interspikeintervallen
entgegennimmt und daraus ein normiertes Histogramm der Interspikeintervalle
berechnet.

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pointprocesses/lecture/pointprocessscetchA.tex
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@ -1,95 +0,0 @@
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@ -1,130 +0,0 @@
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programming/exercises/boolean_logical_indexing_de.tex Normal file
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@ -0,0 +1,108 @@
\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 \"Ubung
3}}{{\bfseries\large Boolesche Ausdr\"ucke, logisches
Indizieren}}{{\bfseries\large 31. Oktober, 2016}}
\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
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:\newline
``boolesche\_ausdruecke\_\{nachname\}.m'' benannt werden
(z.B. variablen\_datentypen\_mueller.m).
\section{Boolesche Ausdr\"ucke}
\begin{questions}
\question Gegeben sind zwei Vektoren \verb+x = [1 5 2 8 9 0 1]+ und
\verb+y = [5 2 2 6 0 0 2]+. F\"uhre aus und erkl\"are.
\begin{parts}
\part \verb+x > y+
\part \verb+y < x+
\part \verb+x == y+
\part \verb+x ~= y+
\part \verb+x & ~y+
\part \verb+x | y+
\end{parts}
\question Finde heraus, was die Funktionen \verb+bitand+ und \verb+bitor+ machen.
\begin{parts}
\part F\"uhre aus und erkl\"are: \verb+bitand(10, 8)+
\part F\"uhre aus und erkl\"are: \verb+bitor(10, 8)+
\end{parts}
\item Implementiere folgende Boolesche Ausdr\"ucke. Teste mit
zuf\"alligen ganzzahlingen Werten f\"ur \verb+x+ und \verb+y+.
\begin{parts}
\part Das Ergebnis sei wahr, wenn \verb+x+ gr\"o{\ss}er als \verb+y+ und die
Summe aus \verb+x+ und \verb+y+ nicht kleiner als 100 ist.
\part Das Ergebnis sei wahr, wenn \verb+x+ und \verb+y+ ungleich 0
oder \verb+x+ und \verb+y+ gleich sind.
\end{parts}
\end{questions}
\newpage
\section{Logische Indizierung}
Boolesche Ausdr\"ucke k\"onnen benutzt werden um aus Vektoren und
Matrizen die Elemente herauszusuchen, die einem bestimmeten Kriterium
entsprechen.
\begin{questions}
\question Gegeben sind \verb+x = (1:10)+ und
\verb+y = [3 1 5 6 8 2 9 4 7 0]+. Versuche die Ausgaben folgender
Anweisungen zu verstehen. Erkl\"are die Ergebnisse.
\begin{parts}
\part \verb+x < 5+
\part \verb+x( x < 5) )+
\part \verb+x( (y <= 2) )+
\part \verb+x( (x > 2) | (y < 8) )+
\part \verb+x( (x == 0) & (y == 0) )+
\end{parts}
\question Teste den Zufallsgenerator:
\begin{parts}
\part Erzeuge eine 100x100 2-D Matrize mit Zufallswerten zwischen
0 und 100 (\verb+randi+). Ersetze die Werte der Elemente, die in
folgende Klassen fallen: \verb+x < 33+ mit 0,
\verb+x >= 33 und x < 66+ mit 1 und alle \verb+x >= 66+ auf 2.
\part Ermittle die Anzahl Elemente f\"ur jede Klasse mithilfe eines
Booleschen Ausdrucks (\verb+sum+ kann eingesetzt werden um die
Anzahl Treffer zu ermitteln).
\end{parts}
\end{questions}
\end{document}

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\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 \"Ubung 4}}{{\bfseries\large Kontrollstrukturen}}{{\bfseries\large 08. November, 2016}}
\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
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:
``control\_flow\_\{nachname\}.m'' benannt werden
(z.B. control\_flow\_mueller.m).
\begin{questions}
\question Implementiere \code{for} Schleifen bei denen die Laufvariable:
\begin{parts}
\part ... von 0 bis 10 l\"auft. Gib den Wert der Laufvariable im
Schleifenk\"orper aus.
\part ... von 10 bis 0 l\"auft. Gib den Wert der Laufvariable aus.
\part ... von 0 bis 1 in einer Schrittweite von 0.1 l\"auft. Gib
die Laufvariable aus.
\end{parts}
\question Zugriff auf Elemente in Vektoren:
\begin{parts}
\part Definiere einen Vektor \code{x} mit Werten von 1:100.
\part Benutze eine \code{for} Schleife um jedes Element von
\code{x} auszugeben indem die Laufvariable zum indizieren benutzt wird.
\part ... gleiches nur ohne eine Laufvariable zu nutzen.
\end{parts}
\question Erzeuge einen Vektor \verb+x+ mit 50 Zufallszahlen im
Bereich 0 - 10.
\begin{parts}
\part Benutze eine Schleife um das arithmetische Mittel zu
berechnen. Der Mittelwert ist definiert als:
$\overline{x}=\frac{1}{n}\sum\limits_{i=0}^{n}x_i $.
\part Benutze eine Schleife um die Standardabweichung zu
bestimmen:
$\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n}(x_i-\overline{x})^2}$).
\part Suche in der MATLAB Hilfe nach Funktionen, die das f\"ur
dich tun :-).
\end{parts}
\question Implementiere eine \code{while} Schleife
\begin{parts}
\part ... die 100 mal durchlaufen wird. Gib den aktuellen
Durchlauf im Schleifenk\"orper aus.
\part ... die endlos l\"auft. Sie kann mir \code{Strg + C}
abgebrochen werden.
\end{parts}
\question Nutze eine endlose \code{while} Schleife um einzeln die
Elemente eines Vektor der L\"ange 10 auszugeben.
\question Benutze eine endlose \verb+while+ Schleife um so lange
Zufallszahlen (\verb+randn+) zu ziehen, bis eine Zahl gr\"o{\ss}er
1.33 gezogen wurde.
\begin{parts}
\part Z\"ahle die Anzahl n\"otiger Versuche.
\part Nuzte eine \code{for} Schleife um den vorherigen Test
1000 mal laufen zu lassen. Merke Dir alle Anzahlen und berechne den
Mittelwert davon.
\part Plotte die Anzahl notwendiger Versuche.
\part Spiele mit der Schwelle, was passiert?
\end{parts}
\question Erstelle \verb+x+ einen Vektor mit 10 Zufallszahlen im
Bereich 0:10.
\begin{parts}
\part Benutze eine \code{for} Schleife um all die Elemente zu
loeschen (\code{x(index) = [];}), die kleiner als 5 sind.
\part Loesche alle Elemente die kleiner als 5 und groesser als 2
sind.
\part Kann man das gleiche auch ohne eine Schleife erledigen?
\end{parts}
\question Teste den Zufallsgenerator! Dazu z\"ahle die Anzahl der
Elemente, die durch folgende Grenzen getrennt werden [0.0, 0.2,
0.4, 0.6, 0.8, 1.0]. Speichere die Ergebnisse in einem passenden
Vektor. Nutze eine Schleife um 1000 Zufallszahlen mit
\verb+rand()+ (siehe Hilfe) zu ziehen. Was waere die Erwartung,
was kommt heraus?
\question String parsing: Mitunter werden Dateinamen von
Datens\"atzen benutzt um anzuzeigen, unter welchen Bedingungen die
Daten gewonnen wurden. Man muss also den Dateinamen parsen und die
f\"ur einen relevante Information herausfiltern.
\begin{parts}
\part Erstelle eine Variable
\verb+filename = '2015-10-12_100Hz_1.25V.dat'+. Der Unterstrich
ist offensichtlich das verwendete Trennzeichen.
\part Benutze eine \verb+for+ Schleife um durch alle Zeichen zu
laufen. Vergleiche jedes Zeichen mit dem Unterstrich und merke
Dir die Positionen in einem Vektor.
\part Benutze eine zweite Schleife um durch diesen
Positionsvektor zu laufen und benutze die darin enthaltene
Information um den \code{filename} in Teile zu schneiden.
\part Gib die einzelnen Teile auf dem Bildschirm aus.
\end{parts}
\end{questions}
\end{document}

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\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 \"Ubung 5}}{{\bfseries\large Skripte und Funktionen}}{{\bfseries\large 15. November, 2016}}
\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
Die folgenden Aufgaben dienen der Wiederholung, \"Ubung und
Selbstkontrolle und sollten eigenst\"andig bearbeitet und gel\"ost
werden. Im Gegensatz zu den vorherigen \"Ubungsbl\"attern k\"onnen die
L\"osungen nicht mehr in einer Datei gemacht werden. Die L\"osungen
also als zip-Archiv auf ILIAS hochladen. Das Archiv sollte nach dem Muster:
``skripte\_funktionen\_\{nachname\}.zip'' benannt werden.
\begin{questions}
\question Berechne die Fakult\"at einer Zahl.
\begin{parts}
\part Version 1: Schreibe eine Skript, das die Fakult\"at von 5 berechnet und das
Resultat auf dem Bildschirm ausgibt.
\begin{solution}
\lstinputlisting{factorialscripta.m}
\end{solution}
\part Version 2: Wie Version 1, aber als Funktion, die als
Argument die Zahl, von der die Fakult\"at berechnet werden soll,
\"ubernimmt.
\begin{solution}
\lstinputlisting{printfactorial.m}
\lstinputlisting{factorialscriptb.m}
\end{solution}
\part Version 3: Wie Version 2, die Funktion soll den berechneten
Wert nicht ausgeben, sondern als Funktionswert zur\"uckgeben. Das
aufrufende Skript soll dann den berechneten Wert auf dem
Bildschirm ausgeben.
\begin{solution}
\lstinputlisting{myfactorial.m}
\lstinputlisting{factorialscriptc.m}
\end{solution}
\end{parts}
\question Grafische Darstellung einer Sinuswelle.
\begin{parts}
\part Implementiere eine Funktion, die einen Sinus mit der
Amplitude 1 und der Frequenz $f = $ 50\,Hz plottet ($\sin(2\pi \cdot
f \cdot t)$). Rufe die Funktion auf.
\begin{solution}
\lstinputlisting{plotsine50.m}
\lstinputlisting{plotsinea.m}
\end{solution}
\part Erweitere die Funktion so, dass die L\"ange der Zeitachse,
die Amplitude, und die Frequenz als Argumente \"ubergeben werden
k\"onnen. Die Schrittweite soll in der Funktion aus der Frequenz
berechnet werden.
\begin{solution}
\lstinputlisting{plotsine.m}
\lstinputlisting{plotsineb.m}
\end{solution}
\part Verlagere alle plot Befehle in das aufrufende Skript
und ver\"andere die Funktion so, dass sie sowohl den Sinus als
auch die Zeitachse zur\"uckgibt.
\begin{solution}
\lstinputlisting{sinewave.m}
\lstinputlisting{plotsinec.m}
\end{solution}
\part Schreibe eine zweite Funktion, die den Sinus plotted und
daf\"ur die Zeitachse und den Sinus als Argument erh\"alt. Diese
Funktion soll die Achsen richtig beschriften. Schreibe ein kleines
Skript, dass beide Funktionen aufruft, um einen Sinus von 5\,Hz
mit der Amplitude 2 \"uber 1.5 Sekunden zu plotten.
\begin{solution}
\lstinputlisting{plotsinewave.m}
\lstinputlisting{plotsined.m}
\end{solution}
\end{parts}
%\question Schreibe eine Funktion, die bin\"are Datens\"atze
%('signal.bin' und 'signal2.bin' vom Montag) liest und die Daten als
%Vektor zur\"uckgibt. Welche Argumente muss die Funktion
%\"ubernehmen?
\question Random Walk.
\begin{parts}
\part Lies die Aufgabe bis zum Ende durch. \"Uberlege dir dann ein
geeignetes ``Programmlayout'' aus Funktionen und Skripten.
Was w\"are eine geeigente Funktion f\"ur diese Aufgabe? Welche
Argumente sollte sie entgegennehmen? Was soll sie berechnen und
zur\"uckgeben?
\begin{solution}
One function that computes one realisation of a random walk.
Scripts for plotting and analysis.
\lstinputlisting{randomwalkthresh.m}
\end{solution}
\part Simuliere und plotte die Positionen von 10 Realisationen
eines random walk mit gleichen Wahrscheinlichkeiten f\"ur beide
Richtungen. Jeder Walker startet an der Position 0 und soll so
lange laufen, bis er den Wert 50 \"uberschreitet oder den Wert
$-50$ unterschreitet.
\begin{solution}
\lstinputlisting{randomwalkscriptb.m}
\end{solution}
\part Jetzt wollen wir die Wahrscheinlichkeit $p$ f\"ur eine
Bewegung zu gr\"o{\ss}eren Positionen im Bereich $0.5 \le p < 0.8$
variieren. Simuliere 10 Realisationen des random walk f\"ur vier
verschiedene Wahrscheinlichkeiten.
\begin{solution}
\lstinputlisting{randomwalkscriptc.m}
\end{solution}
\part Wie entwickelt sich die mittlere ben\"otigte Schrittanzahl
in Abh\"angigkeit der Wahrscheinlichkeit? Stelle die Mittelwerte
und die Standardabweichungen graphisch dar.
\begin{solution}
\lstinputlisting{randomwalkscriptd.m}
\end{solution}
\end{parts}
%\question Modellierung des exponentiellen Wachstums einer isolierten
%Population. Das exponentielle Wachstum einer isolierten Population
%wird \"uber folgende Differentialgleichung beschrieben:
%\begin{equation}
% \frac{dN}{dt} = N \cdot r,
%\end{equation}
%mit $N$ der Populationsgr\"o{\ss}e und $r$ der Wachstumsrate.
%\begin{parts}
% \part L\"ose die Gleichung numerisch mit dem Euler Verfahren.
% \part Implementiere eine Funktion, die die Populationsgr\"o{\ss}e
% und die Zeit zur\"uckgibt.
% \part Plotte die Populationsgr\"o{\ss}e als Funktion der Zeit.
%\end{parts}
%\question Etwas realistischer ist das logistische Wachstum einer
%isolierten Population, bei der das Wachstum durch eine Kapazit\"at
%gedeckelt ist. Sie wird mit folgender Differentialgleichung
%beschrieben:
%\begin{equation}
% \frac{dN}{dt} = N \cdot r \cdot \left( 1 - \frac{N}{K} \right)
%\end{equation}
%mit $N$ der Population, der Wachstumsrate $r$ und $K$ der ``tragenden''
%Kapazit\"at.
%\begin{parts}
% \part Implementiere die L\"osung des logistischen Wachstums in
% einer Funktion. Benutze das Euler Verfahren. Die Funktion soll die
% Parameter $r$, $K$ sowie den Startwert von $N$ als Argumente
% \"ubernehmen.
% \part Die Funktion soll die Populationsgr\"o{\ss}e und die Zeit
% zur\"uckgeben.
% \part Simuliere das Wachstum mit einer Anzahl unterschiedlicher
% Startwerte f\"ur $N$.
% \part Stelle die Ergebnisse in einem Plot graphisch dar.
% \part Plotte das Wachstum $dN/dt$ als Funktion der
% Populationsgr\"o{\ss}e $N$.
%\end{parts}
\end{questions}
\end{document}

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@ -15,7 +15,7 @@
%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
\pagestyle{headandfoot}
\header{{\bfseries\large \"Ubung 1}}{{\bfseries\large Variablen und Datentypen}}{{\bfseries\large 18. Oktober, 2016}}
\header{{\bfseries\large Exercise 1}}{{\bfseries\large Variables und Datatypes}}{{\bfseries\large 17. Oktober, 2017}}
\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
jan.grewe@uni-tuebingen.de}
\runningfooter{}{\thepage}{}
@ -26,221 +26,198 @@
\renewcommand{\baselinestretch}{1.15}
\newcommand{\code}[1]{\texttt{#1}}
\renewcommand{\solutiontitle}{\noindent\textbf{L\"osung:}\par\noindent}
\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\vspace*{-6.5ex}
\begin{center}
\textbf{\Large Einf\"uhrung in die wissenschaftliche Datenverarbeitung}\\[1ex]
\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} \\
Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
\end{center}
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:\linebreak
``variablen\_datentypen\_\{nachname\}.m'' benannt werden
(z.B. variablen\_datentypen\_mueller.m).
The exercises are meant for self-monitoring, revision of the lecture
topic. 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'' benannt werden
(e.g. variables\_datentypes\_mueller.m).
\begin{questions}
\question Erzeugen und L\"oschen von Variablen:
\question Creating and deleting variables:
\begin{parts}
\part Erzeuge zwei Variablen \code{a}, \code{b} und weise ihnen
unterschiedliche Werte zu. Schlie{\ss}e die Zeilen mit einem
Semikolon ab. Erstelle eine Variable \code{c} die leer ist.
\part Create two new variables \code{a}, \code{b} and assign arbitrary values to them. End each command with a semicolon. Create a variable \code{c} that is empty.
\begin{solution}
\code{a = 1;} \code{b = 2;} \code{c = [];}
\end{solution}
\part Lass die Werte der Variablen ausgeben.
\part Print the varaibles and their content in the matlab command line
\begin{solution}
\code{disp(a)}; \code{disp(b)}; \code{disp(c)}
\end{solution}
\part Benuzte die Kommandozeile um herauszufinden, welche Variablen
es im Workspace gibt.
\part Use the appropriate command to find out which variables have been created.
\begin{solution}
\code{who}
\end{solution}
\part Benuzte die Kommandozeile um herauszufinden, welche Datentypen sie haben.
\part Use the appropriate command to additionally display the data type.
\begin{solution}
\code{whos} oder \code{class(a)}, \code{class(b)}, \code{class(c)}
\code{whos} or \code{class(a)}, \code{class(b)}, \code{class(c)}
\end{solution}
\part Finde in der Hilfe mehr Information \"uber das \code{clear} Kommando.
\part Use the help system to learn about the \code{clear} command.
\begin{solution}
\code{help clear}
\end{solution}
\part L\"osche eine Variable.
\part Delete a single variable.
\begin{solution}
\code{clear a}
\end{solution}
\part L\"osche alle \"ubrigen Variablen.
\part Delete all remaining variables.
\begin{solution}
\code{clear all} oder einfach \code{clear}
\code{clear all} or simply \code{clear}
\end{solution}
\end{parts}
\question Operationen auf Variablen:
\question Working with variables:
\begin{parts}
\part Erstelle die Variablen \code{a} und \code{b} und weise ihnen
beliebige Werte zu.
\part Create two new variables \code{a}, \code{b} and assign arbitrary numeric values.
\begin{solution}
\code{a = 5; b = 3.14;}
\end{solution}
\part Addiere beliebige andere Zahlen zu den Variablen \code{a} und \code{b}.
\part Add a number to \code{a} and \code{b}.
\begin{solution}
\code{a + 5} \code{b + 7.28}
\end{solution}
\part Addiere die Variablen.
\part Add the variables themselves.
\begin{solution}
\code{a + b}
\end{solution}
\part Mulipliziere die Variablen miteinander.
\part Multiply \code{a} and \code{b}.
\begin{solution}
\code{a * b}
\end{solution}
\part \"Andern sich die urspr\"unglichen Werte der Variablen?
\part Do \code{a} and \code{b} change?
\begin{solution}
Nein, die Operationen benutzen die Werte der Variablen. Die
Variablen bleiben unver\"andert.
No, we make use of the stored values, the values remaing untouched.
\end{solution}
\part F\"uhre eine beliebige Berechnungen mit den Variablen aus und
weise die Ergebnisse einer neuen Variable \code{x} zu.
\part Execute any arithmetic operation with \code{a} and \code{b} and store the result in a new variabel \code{x}.
\begin{solution}
\code{x = a * b;}
\end{solution}
\part Weise \code{a} und \code{b} neue Werte zu. Hat sich etwas am
Wert von \code{x} ge\"andert?
\part Assign new values to \code{a} and \code{b}. Did \code{x} change?
\begin{solution}
Nein, der Variablen \code{x} wird ein Wert zugewiesen, der sich
nicht \"andert bis der Variablen ein neuer Wert zugewiesen
wird. Die Variable 'x' speichert das Resultat der Rechnung
\textbf{nicht} die Anweisung.
No, the content of \code{x} does not change, it stores a value, \textbf{not} a recipe.
\end{solution}
\end{parts}
\question Berechne die Fakult\"at von 5:
\question Calculate the faculty of 5:
\begin{parts}
\part Erzeuge eine Variable \code{x} und weise ihr den Wert 1 zu.
\part Berechne den ersten Schritt (\code{*2}) und weise das Ergebnis \code{x}
zu.
\part Fahre schrittweise fort, bis die Fakult\"at von 5 berechnet ist. \code{x}
sollte nun das Endergebnis enthalten.
\part Create a variable \code{x} an assign the value 1.
\part In a first step multiply \code{x} with 2 and assign the result to \code{x} itself.
\part Proceed in a similar manner until x stores $5!$.
\end{parts}
\begin{solution}
\code{x = 1;} \\ \code{x = x * 2;}\\ \code{x = x * 3;} \\ \code{x = x * 4;} \\ \code{x = x * 5;}\\ \code{disp(x)}\\
\code{ 120}
\end{solution}
\question Erstelle eine Variable, die einen beliebigen Text enth\"alt. Was
ist ihr Datentyp?
\question Create a variable and assign a string to it. What is the data type of that variable?
\begin{solution}
\code{x = 'einfacher Text'}\\ \code{class(x)\\ char}
\code{x = 'some text'}\\ \code{class(x)\\ char}
\end{solution}
\question Was sind die gr\"o{\ss}ten Zahlen, die in den Integer 8, 16, 32
und 64 bit Datentypen abgelegt werden k\"onnen?
\question List the largest numbers that can stored in 8, 16, 32
and 64 bit integer data types?
\begin{solution}
\verb+2^8 / 2 - 1+\\
\verb+2^16 / 2 - 1+\\
\verb+2^32 / 2 - 1+\\
\verb+2^64 / 2 - 1+
\end{solution}
\question Erstelle eine Variable des 8 Bit Integer Datentyps und weise
ihr einen Wert zu. Addiere \code{300}. Welchen Wert enth\"alt nun die
Variable? Warum?
\question Create an 8 bit integer variable \code{x} and assign a
valid numeric value to it. Add \code{300} and re-assign the result
to \code{x}. Which value is now stored in \code{x}? Why?
\begin{solution}
\code{x = int8(35);\\x = x + 300;\\ disp(x)\\ 127}\\
Der Datentype int8 kann nur Werte von -128 bis 127 speichern.
The int8 dtype can only store values between -128 and 127.
\end{solution}
\question Erkl\"are die Ausgaben von \code{int8(1024)} und \code{uint8(1024)}.
\question Explain the output of the follwoing commands: \code{int8(1024)} and \code{uint8(1024)}.
\begin{solution}
Der int8 Datentyp kann Werte von -128 bis maximal 127 ablegen. Der
uint8 Typ ist \textit{unsigned}, er speichert Werte zwischen 0 und
255.
int8 can store values between -128 and 127. uint8 is
\textit{unsigned}, ist stores values between 0 and 255.
\end{solution}
\question Typkonvertierung:
\question Typeconversion:
\begin{parts}
\part F\"uhre aus: \code{x = 131.333}. Welchen Datentyp hat die
Variable \code{x}?
\part Execute: \code{x = 131.333}. What is the datatype of \code{x}?
\begin{solution}
Sie hat den Typ \textit{double}.
\textit{double}.
\end{solution}
\part Wandle \code{x} in den speichereffizientesten Integer Datentypen um.
\part Convert \code{x} to the most efficient integer datatype.
\begin{solution}
\code{x = uint8(x);}\\Ben\"otigt 8 bit anstelle der 64 bit f\"ur
den double.
\code{x = uint8(x);}\\Needs 8 bit instead of 64 bit for double.
\end{solution}
\part Welchen Wert hat nun \code{x} ?
\part What is the value stored in \code{x} after conversion?
\begin{solution}
131
\end{solution}
\end{parts}
\question Flie{\ss}kommazahlen 1: Endliche Pr\"azision bei Addition
\question Floating point numbers I: Limited precision during additions
\begin{parts}
\part Weise der Variablen \code{a} eine Zahl mit Nachkommastellen zu.
\part Create the variable \code{a} and assign an arbitrary floting point number.
\begin{solution}
\code{a = 3.14;}
\end{solution}
\part Eine weitere Variable \code{b} soll den Wert \code{a+0.001}
haben. Was ist das Ergebnis von \code{b-a} ?
\part A second variable \code{b} stores the value \code{a+0.001}. What is the result of \code{b-a} ?
\begin{solution}
\code{b = a + 0.001;}\\ \code{disp(b - a)\\0.001}\\
Alles ok, Ergebnis wie erwartet.
All cool, result as expected.
\end{solution}
\part Einer dritte Variable \code{c} soll der Wert \code{a+1e-16}
zugewiesen werden. Was ist das Ergebnis von \code{c-a} ? Warum?
\part Create a third variable \code{c} and assign \code{a+1e-16}. What is the result of \code{c-a}? Why?
\begin{solution}
Das Ergebnis ist 0! Auch die double Werte haben nur eine endliche
P\"azision in den Nachkommastellen.
Result is 0! Also with doubles there is a limited precision in
the decimal part.
\end{solution}
\part Berechne \verb=(2^52 + 1) - 2^52= sowie
\part Calculate \verb=(2^52 + 1) - 2^52= and
\verb=(2^53 + 1) - 2^53=.
\begin{solution}
Im Ersten Fall ist das Ergebnis = 1, im Zweiten = 0. Bei so
gro{\ss}en Zahlen k\"onnen so kleine Unterschiede nicht mehr
aufgel\"ost werden.
First command results in = 1, in the second case = 0. With such
high numbers, small differences (1!) cannot be resolved.
\end{solution}
\part Berechne \code{sqrt(1+1e-16)-1} . Ist das richtig? Warum?
\part Calculate \code{sqrt(1+1e-16)-1}. Is the result correct? Why (not)?
\begin{solution}
Die Wurzel von 1 + etwas sollte nicht 1 sein! Das Ergebnis
sollte nicht 0 sein.
Square root of something larger than 1 should not be 1 and thus
the result must not be 0.
\end{solution}
\part Vergleiche mit dem Ergebnis beim Addieren einer etwas
gr\"o{\ss}eren Zahl (z.B. 1e-8).
\part Compare wwith the result when adding a slightly largern number (e.g. 1e-8).
\begin{solution}
Hier sollte das Ergebnis ungleich 0 sein.
Result is not equal to zero.
\end{solution}
\end{parts}
\question Flie{\ss}kommazahlen 2: Endliche Pr\"azision bei Multiplikation
\question Floating point numbers II: Limited precision during multiplications.
\begin{parts}
\part Weise der Variablen \code{a} die Zahl \code{4/3} zu.
\part Die Variable \code{b} soll den Wert \code{3*(a-1)} erhalten.
\part Welches Ergebnis erwartest du f\"ur \code{b-1} ?
\part Create a variable \code{a} and assign \code{4/3}.
\part Variable \code{b} should contain the value \code{3*(a-1)}.
\part What do you expect for \code{b-1}?
\begin{solution}
\code{a = 4/3;}\\ \code{b = 3 * (a-1)}\\
b sollte nun 1 sein. d.h., \code{b-1} sollte 0 sein.
\code{a = 4/3;}\\ \code{b = 3 * (a-1)}\\
b should be 1. i.e., \code{b-1} should give 0.
\end{solution}
\part Berechne mit matlab \code{b-1} !
\part Calculate with matlab \code{b-1}!
\begin{solution}
\code{disp(b - 1)\\ -2.2204e-16}\\ Aufgrund von Rundungsfehlern
kommt es zu diesem Ergebnis.
\code{disp(b - 1)\\ -2.2204e-16}\\ Due to rounding mistakes.
\end{solution}
\part Was sollte \code{sin(pi)} ergeben ? Was sagt matlab?
\part What should be the result of \code{sin(pi)}? What gives matlab?
\begin{solution}
Sollte 0 sein, ist es aber nicht. Wie oben, Rundungsfehler
f\"uhren zu diesen Abweichungen.
Should be 0, but it is not. See above, due to rounding errors we
get some deviation.
\end{solution}
\end{parts}
\end{questions}
\end{document}
\end{document}

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\documentclass[12pt,a4paper,pdftex]{exam}
\usepackage[german]{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 \"Ubung 1}}{{\bfseries\large Variablen und Datentypen}}{{\bfseries\large 18. Oktober, 2016}}
\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{L\"osung:}\par\noindent}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
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:\linebreak
``variablen\_datentypen\_\{nachname\}.m'' benannt werden
(z.B. variablen\_datentypen\_mueller.m).
\begin{questions}
\question Erzeugen und L\"oschen von Variablen:
\begin{parts}
\part Erzeuge zwei Variablen \code{a}, \code{b} und weise ihnen
unterschiedliche Werte zu. Schlie{\ss}e die Zeilen mit einem
Semikolon ab. Erstelle eine Variable \code{c} die leer ist.
\begin{solution}
\code{a = 1;} \code{b = 2;} \code{c = [];}
\end{solution}
\part Lass die Werte der Variablen ausgeben.
\begin{solution}
\code{disp(a)}; \code{disp(b)}; \code{disp(c)}
\end{solution}
\part Benuzte die Kommandozeile um herauszufinden, welche Variablen
es im Workspace gibt.
\begin{solution}
\code{who}
\end{solution}
\part Benuzte die Kommandozeile um herauszufinden, welche Datentypen sie haben.
\begin{solution}
\code{whos} oder \code{class(a)}, \code{class(b)}, \code{class(c)}
\end{solution}
\part Finde in der Hilfe mehr Information \"uber das \code{clear} Kommando.
\begin{solution}
\code{help clear}
\end{solution}
\part L\"osche eine Variable.
\begin{solution}
\code{clear a}
\end{solution}
\part L\"osche alle \"ubrigen Variablen.
\begin{solution}
\code{clear all} oder einfach \code{clear}
\end{solution}
\end{parts}
\question Operationen auf Variablen:
\begin{parts}
\part Erstelle die Variablen \code{a} und \code{b} und weise ihnen
beliebige Werte zu.
\begin{solution}
\code{a = 5; b = 3.14;}
\end{solution}
\part Addiere beliebige andere Zahlen zu den Variablen \code{a} und \code{b}.
\begin{solution}
\code{a + 5} \code{b + 7.28}
\end{solution}
\part Addiere die Variablen.
\begin{solution}
\code{a + b}
\end{solution}
\part Mulipliziere die Variablen miteinander.
\begin{solution}
\code{a * b}
\end{solution}
\part \"Andern sich die urspr\"unglichen Werte der Variablen?
\begin{solution}
Nein, die Operationen benutzen die Werte der Variablen. Die
Variablen bleiben unver\"andert.
\end{solution}
\part F\"uhre eine beliebige Berechnungen mit den Variablen aus und
weise die Ergebnisse einer neuen Variable \code{x} zu.
\begin{solution}
\code{x = a * b;}
\end{solution}
\part Weise \code{a} und \code{b} neue Werte zu. Hat sich etwas am
Wert von \code{x} ge\"andert?
\begin{solution}
Nein, der Variablen \code{x} wird ein Wert zugewiesen, der sich
nicht \"andert bis der Variablen ein neuer Wert zugewiesen
wird. Die Variable 'x' speichert das Resultat der Rechnung
\textbf{nicht} die Anweisung.
\end{solution}
\end{parts}
\question Berechne die Fakult\"at von 5:
\begin{parts}
\part Erzeuge eine Variable \code{x} und weise ihr den Wert 1 zu.
\part Berechne den ersten Schritt (\code{*2}) und weise das Ergebnis \code{x}
zu.
\part Fahre schrittweise fort, bis die Fakult\"at von 5 berechnet ist. \code{x}
sollte nun das Endergebnis enthalten.
\end{parts}
\begin{solution}
\code{x = 1;} \\ \code{x = x * 2;}\\ \code{x = x * 3;} \\ \code{x = x * 4;} \\ \code{x = x * 5;}\\ \code{disp(x)}\\
\code{ 120}
\end{solution}
\question Erstelle eine Variable, die einen beliebigen Text enth\"alt. Was
ist ihr Datentyp?
\begin{solution}
\code{x = 'einfacher Text'}\\ \code{class(x)\\ char}
\end{solution}
\question Was sind die gr\"o{\ss}ten Zahlen, die in den Integer 8, 16, 32
und 64 bit Datentypen abgelegt werden k\"onnen?
\begin{solution}
\verb+2^8 / 2 - 1+\\
\verb+2^16 / 2 - 1+\\
\verb+2^32 / 2 - 1+\\
\verb+2^64 / 2 - 1+
\end{solution}
\question Erstelle eine Variable des 8 Bit Integer Datentyps und weise
ihr einen Wert zu. Addiere \code{300}. Welchen Wert enth\"alt nun die
Variable? Warum?
\begin{solution}
\code{x = int8(35);\\x = x + 300;\\ disp(x)\\ 127}\\
Der Datentype int8 kann nur Werte von -128 bis 127 speichern.
\end{solution}
\question Erkl\"are die Ausgaben von \code{int8(1024)} und \code{uint8(1024)}.
\begin{solution}
Der int8 Datentyp kann Werte von -128 bis maximal 127 ablegen. Der
uint8 Typ ist \textit{unsigned}, er speichert Werte zwischen 0 und
255.
\end{solution}
\question Typkonvertierung:
\begin{parts}
\part F\"uhre aus: \code{x = 131.333}. Welchen Datentyp hat die
Variable \code{x}?
\begin{solution}
Sie hat den Typ \textit{double}.
\end{solution}
\part Wandle \code{x} in den speichereffizientesten Integer Datentypen um.
\begin{solution}
\code{x = uint8(x);}\\Ben\"otigt 8 bit anstelle der 64 bit f\"ur
den double.
\end{solution}
\part Welchen Wert hat nun \code{x} ?
\begin{solution}
131
\end{solution}
\end{parts}
\question Flie{\ss}kommazahlen 1: Endliche Pr\"azision bei Addition
\begin{parts}
\part Weise der Variablen \code{a} eine Zahl mit Nachkommastellen zu.
\begin{solution}
\code{a = 3.14;}
\end{solution}
\part Eine weitere Variable \code{b} soll den Wert \code{a+0.001}
haben. Was ist das Ergebnis von \code{b-a} ?
\begin{solution}
\code{b = a + 0.001;}\\ \code{disp(b - a)\\0.001}\\
Alles ok, Ergebnis wie erwartet.
\end{solution}
\part Einer dritte Variable \code{c} soll der Wert \code{a+1e-16}
zugewiesen werden. Was ist das Ergebnis von \code{c-a} ? Warum?
\begin{solution}
Das Ergebnis ist 0! Auch die double Werte haben nur eine endliche
P\"azision in den Nachkommastellen.
\end{solution}
\part Berechne \verb=(2^52 + 1) - 2^52= sowie
\verb=(2^53 + 1) - 2^53=.
\begin{solution}
Im Ersten Fall ist das Ergebnis = 1, im Zweiten = 0. Bei so
gro{\ss}en Zahlen k\"onnen so kleine Unterschiede nicht mehr
aufgel\"ost werden.
\end{solution}
\part Berechne \code{sqrt(1+1e-16)-1} . Ist das richtig? Warum?
\begin{solution}
Die Wurzel von 1 + etwas sollte nicht 1 sein! Das Ergebnis
sollte nicht 0 sein.
\end{solution}
\part Vergleiche mit dem Ergebnis beim Addieren einer etwas
gr\"o{\ss}eren Zahl (z.B. 1e-8).
\begin{solution}
Hier sollte das Ergebnis ungleich 0 sein.
\end{solution}
\end{parts}
\question Flie{\ss}kommazahlen 2: Endliche Pr\"azision bei Multiplikation
\begin{parts}
\part Weise der Variablen \code{a} die Zahl \code{4/3} zu.
\part Die Variable \code{b} soll den Wert \code{3*(a-1)} erhalten.
\part Welches Ergebnis erwartest du f\"ur \code{b-1} ?
\begin{solution}
\code{a = 4/3;}\\ \code{b = 3 * (a-1)}\\
b sollte nun 1 sein. d.h., \code{b-1} sollte 0 sein.
\end{solution}
\part Berechne mit matlab \code{b-1} !
\begin{solution}
\code{disp(b - 1)\\ -2.2204e-16}\\ Aufgrund von Rundungsfehlern
kommt es zu diesem Ergebnis.
\end{solution}
\part Was sollte \code{sin(pi)} ergeben ? Was sagt matlab?
\begin{solution}
Sollte 0 sein, ist es aber nicht. Wie oben, Rundungsfehler
f\"uhren zu diesen Abweichungen.
\end{solution}
\end{parts}
\end{questions}
\end{document}

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\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 \"Ubung
2}}{{\bfseries\large Vektoren und Matrizen}}{{\bfseries\large 12. Oktober, 2015}}
\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{L\"osung:}\par\noindent}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
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:
\linebreak ``vektoren\_matrizen\_\{nachname\}.m'' benannt werden
(z.B. vektoren\_matrizen\_mueller.m).
\begin{questions}
\section*{Vektoren}
\question Erzeuge Vektoren mit folgendem Inhalt:
\begin{parts}
\part Von 1 bis 10 in ganzzahligen Schritten.
\begin{solution}
\code{a = 1:10;}
\end{solution}
\part Von 0 bis 20 in 2er Schritten.
\begin{solution}
\code{a = 0:2:20;}
\end{solution}
\part Mit \textbf{absteigendem} Inhalt von 100 bis 0.
\begin{solution}
\code{a = 100:-1:0;}
\end{solution}
\part In 10 Schritten von 0 bis 1.
\begin{solution}
\code{a = 0:0.1:1;}
\end{solution}
\part In 11 Schritten von 0 bis 1.
\begin{solution}
\code{a = 0:1/11:1;}
\end{solution}
\part In 50 Schritten von 0 bis $2\pi$ ($\pi$ ist als Konstante
\code{pi} in Matlab definiert).
\begin{solution}
\code{a = 0:2*pi/50:2*pi;}
\end{solution}
\end{parts}
\question Rechnen mit Vektoren:
\begin{parts}
\part Definiere einen Vektor \code{x = [3 2 6 8];}
\part Wie gro{\ss} ist der Vektor? Benutze die Funktionen
\code{size} und \code{length}. Was ist der Unterschied zwischen
den beiden Funktionen?
\begin{solution}
\code{x = [3 2 6 8]; \\ disp(length(x));\\ 4\\ disp(size(x))\\ 1 4}
\end{solution}
\part Wie \"andern sich \code{size} und \code{length} des
Vektors wenn er transponiert wird?
\begin{solution}
L\"ange \"andert sich nicht. R\"uckgabewert von size ist invertiert.
\end{solution}
\part Addiere 5 zu jedem Element von \verb+x+.
\begin{solution}
\code{disp(x + 5)}
\end{solution}
\part Multipliziere jedes Element von \code{x} mit 2;
\begin{solution}
\code{disp(x * 2)}
\end{solution}
\part Definiere einen zweiten Vektor (\verb+y = [4 1 3 5];+).
Stelle sicher, dass \code{x} wieder in seiner urspr\"unglichen
Form ist.
\part Addiere beide Vektoren \code{x + y}.
\begin{solution}
\code{y = [4 1 3 5]; \\disp(x + y)\\7 3 9 13}
\end{solution}
\part Subtrahiere beide Vektoren \code{x - y}.
\begin{solution}
\code{disp(x - y)\\-1 1 3 3}
\end{solution}
\part Multipliziere beide Vektoren \code{x * y}.
\begin{solution}
\code{disp(x * y)\\Error using *. Inner matrix dimension must agree.}
\end{solution}
\part Erkl\"are die Fehlermeldung.
\begin{solution}
* ist der Operator f\"ur die Matrixmultiplikation. Bei dieser
muessen die inneren Dimensionen \"uebereinstimmen.\linebreak
\code{disp(size(x))\\1 4 \\disp(size(y)) \\ 1 4}\\
(m,n)*(n,o) w\"are ok.
\end{solution}
\part Was m\"usste man machen, damit \code{mtimes} bzw. der
\code{*} Operator funktionieren?
\begin{solution}
y m\"usste transponiert werden: \code{x * y'}
\end{solution}
\part Multipliziere die Vektoren elementweise (\code{x .* y})
und weise das Ergebnis eine neuen Variablen zu.
\begin{solution}
\code{z = x .* y;}
\end{solution}
\end{parts}
\question Erzeugen von Vektoren mit Helferfunktionen:
\begin{parts}
\part Erstelle einen 100 Elemente langen Vektor mit der Funktion
\code{ones} (siehe Hilfe). Was macht sie?
\begin{solution}
\code{ones(100,1)} erzeugt einen Vektor bei dem alle Elemente mit 1 gef\"ullt sind.
\end{solution}
\part Erstelle einen 100 Elemente langen Vektor mit der Funktion
\code{zeros}. Was macht diese?
\begin{solution}
\code{zeros(100,1)} erzeugt einen Vektor bei dem alle Elemente mit 0 gef\"ullt sind.
\end{solution}
\part Erstelle einen 100 Elemente langen Vektor in dem jedes
Element den Wert 4.5 hat.
\begin{solution}
\code{ones(100,1) * 4.5}
\end{solution}
\part Erzeuge einen Vektor mit 100 Zufallszahlen (\code{rand},
siehe Hilfe).
\begin{solution}
\code{x = rand(100,1)}
\end{solution}
\part Erzeuge einen Vektor mit 100 Werten zwischen 0 und 1
mithilfe der Funktion \code{linspace}.
\begin{solution}
\code{x = linspace(0,1,100)}
\end{solution}
\end{parts}
\question Indizieren in Vektoren:
\begin{parts}
\part Erzeuge einen Vektor mit 100 Elementen (0 - 100).
\begin{solution}
\code{x = linspace(0,100,100);}
\end{solution}
\part Gib jeweils den ersten, den letzten, den 5., 24. und den
vorletzten Wert aus.
\begin{solution}
\code{disp(x(1))\\ disp(x(end))\\ disp(x(5))\\ disp(x(24))\\ disp(x(end-1))}
\end{solution}
\part Gib die ersten 10 Werte aus.
\begin{solution}
\code{x(1:10)}
\end{solution}
\part Gib die letzten 10 Werte aus.
\begin{solution}
\code{disp(x(end-9:end))}
\end{solution}
\part Versuche den Wert an der Stelle 0 auszugeben.
\begin{solution}
\code{x(0)\\ Subscript indices must either be real positive integers or logicals.}
\end{solution}
\part Versuche den Wert an der Stelle 110 auszugeben.
\begin{solution}
\code{x(110)\\ Index exceeds matrix dimensions.}
\end{solution}
\part Gib die Werte an den Stellen 3, 15, und 42 zusammen als
Vektor aus.
\begin{solution}
\code{disp(x([3 15 42]))}
\end{solution}
\part Gib 10 zuf\"allig ausgew\"ahlte Werte aus (benutze
\verb+randi+ um die Indizes zu erstellen).
\begin{solution}
\code{x(randi(100,10,1))}
\end{solution}
\end{parts}
\question Erzeuge eine Variable und speichere etwas Text in ihr,
so dass mindestens 2 Worte vorhanden sind. (z.B. \code{x = 'some
text'}). Benutze die Indizierung um die W\"orter einzeln
auszugeben.
\begin{solution}
\code{x = 'some text'; \\ disp(x(1:4))\\disp(x(6:end))}
\end{solution}
\newpage
\section*{Matrizen}
\question Erstelle folgende Matrix
\[ A = \left( \begin{array}{ccc} 7 & 3 & 5 \\ 1 & 8 & 3 \\ 8 & 6 &
4 \end{array} \right) \]
\begin{parts}
\part Benutze die Funktion \code{size} um die Gr\"o{\ss}e vpm \code{A} anzeeigen zu lassen.
\begin{solution}
\code{x = [7 3 5; 1 8 3; 8 6 4];\\disp(size(x))}
\end{solution}
\part Finde heraus, wie man \code{size} aufruft um nur die L\"ange entlang einer einzelnen Dimension auszugeben. Gib einzeln die L\"angen beider Dimensionen aus.
\begin{solution}
\code{disp(size(x, 1))}\\\code{disp(size(x, 2))}
\end{solution}
\part Gib das Element in der 3. Zeile und 2. Spalte aus.
\begin{solution}
\code{x(3,2)}
\end{solution}
\part Gib jeweils alle Elemente der 1., 2. und 3. Zeile aus.
\begin{solution}
\code{disp(x([1 2 3],:));}
\end{solution}
\part Gib jeweils alle Elemente der 1., 2., und 3. Spalte aus.
\begin{solution}
\code{disp(x(:, 1))\\ disp(x(:, 2))\\ disp(x(:, 3))}
\end{solution}
\part Erh\"ohe das Element in der 2. Zeile und 3. Spalte um Eins.
\begin{solution}
\code{x(2,3) = x(2,3) + 1;}
\end{solution}
\part Ziehe von allen Elementen der 1. Zeile 5 ab.
\begin{solution}
\code{x(1,:) = x(1,:) - 5;}
\end{solution}
\part Multipliziere alle Elementen der 3. Spalte mit 2.
\begin{solution}
\code{x(:,3) = x(:,3) * 2;}
\end{solution}
\end{parts}
\question Erstelle eine $5 \times 5$ Matrix \code{M} die
Zufallszahlen enth\"alt (nutze die MATLAB Funktion
\verb+randn()+. Benutze die Hilfe: Was macht die Funktion?).
\begin{parts}
\part Gib das Element in der 2. Zeile und 3. Spalte aus.
\begin{solution}
\code{M = randn(5, 5);}
\code{disp(M(2,3))}
\end{solution}
\part Gib jeweils alle Elemente der 1., 3. und letzten Zeile aus.
\begin{solution}
\code{disp(M(1,:)) \\ disp(M(3,:))\\ disp(M(size(M,1), :))}
\end{solution}
\part Gib jeweils alle Elemente der 2. und 4. Spalte aus.
\begin{solution}
\code{disp(M(:,2))\\ disp(M(:,4))}
\end{solution}
\part Greife mit einem einzigen Kommando auf die Elemente jeder
zweiten Spalte zu und speichere die Daten in einer neuen Variable.
\begin{solution}
\code{y = M(:, [2:2:size(M,2)])}
\end{solution}
\part Berechne jeweils den Mittelwert der 1., 3. und 5. Zeile
(Funktion \code{mean}, siehe Hilfe).
\begin{solution}
\code{mean(M([1 3 5],:), 2)}
\end{solution}
\part Berechne die Summe aller Werte der 2. und 4. Spalte
(Funktion \code{sum}, siehe Hilfe).
\begin{solution}
\code{sum(M(:, [2 4]), 1)}
\end{solution}
\part Berechne die Summe aller Elemente der Matrize.
\begin{solution}
\code{sum(M(:))}
\end{solution}
\part Ersetze die Elemente der 2. Zeile mit denen der 4.
\begin{solution}
\code{M(2,:) = M(4,:)}
\end{solution}
\part F\"uhre folgendes Kommando aus: \code{M(1:2,1) = [1, 2,
3]}. Was k\"onnte die Absicht dieses Codes gewesen sein? Was
bedeutet die Fehlermeldung?
\begin{solution}
\code{M(1:2,1) = [1, 2,3];\\ Subscripted assignment dimension
mismatch.} \\ Der einzuf\"ugende Vektor hat 3 Elemente, die
Auswahl von M in die geschrieben werden soll hat nur die
Gr\"o{\ss}e 2;
\end{solution}
\end{parts}
\question Matrizen k\"onnen neben der ``normalen''
\textit{subscript} Indizierung auch \textit{linear} indiziert werden
(siehe Hilfe \"uber Indexing oder Funktionen \verb+sub2ind+ oder
\verb+ind2sub+).
\begin{parts}
\part Erstelle eine 2-D Matrix mit Zufallszahlen mit der Dimensionalit\"at
\verb+[10,10]+.
\begin{solution}
\code{x = randn(10, 10)}
\end{solution}
\part Wie viele Werte enth\"alt sie?
\begin{solution}
\code{disp(numel(x))}
\end{solution}
\part Benutze das lineare Indizieren um 50 zuf\"allige Werte
auszuw\"ahlen.
\begin{solution}
\code{x(randi(100, 50, 1)])}
\end{solution}
\part Wo liegt der Vorteil gegen\"uber der \textit{subscript}
Indizierung?
\begin{solution}
Die Matrize ist 2-dimensional. Wenn mit dem subscript index
zugegriffen werden soll, dann muss auf die Dimensionen
einzeln geachtet werden. Mit dem linearen Indexieren kann einfach
einen Vektor mit n Indices benutzt werden. Wenn es auch noch eine
eindeutige (ohne doppelte) Auswahl sein soll, dann muss bei
2-D viel komplexer kontrollieren.
\end{solution}
\part Berechne die Summe aller Werte mit einem Funktionsaufruf..
\begin{solution}
\code{sum(x(:))} oder \code{sum(sum(x))}
\end{solution}
\end{parts}
\question Erstelle folgende Variablen \verb+x = [1 5 9]+ and
\verb+y = [7 1 5]+ und \verb+M = [3 1 6; 5 2 7]+. Welche der
folgenden Operationen funktionieren? Wenn nicht, warum funktionieren
sie nicht? Teste Deine Vorhersagen.
\begin{parts}
\part \code{x + y}
\begin{solution}
Funktioniert!
\end{solution}
\part \code{x * M}
\begin{solution}
Matrixmultiplikation Funktioniert nicht! Inner dimensions must agree!
\end{solution}
\part \code{x + y'}
\begin{solution}
Funktioniert nicht! Die Dimensionalit\"aten passen nicht.
\end{solution}
\part \code{M - [x y]}
\begin{solution}
Funktioniert nicht! \code{[x y] ist ein Zeilenvektor der L\"ange
6, M ist eine Martix.}
\end{solution}
\part \code{[x; y]}
\begin{solution}
Funktioniert! Gr\"o{\ss}e: 2 3
\end{solution}
\part \code{M - [x; y]}
\begin{solution}
Funktioniert!
\end{solution}
\end{parts}
\question Erstelle eine 3-D Matrix aus drei 2-D Matrizen. Benutze
die \verb+cat()+ Funktion f\"ur diesen Zweck (schaue in der Hilfe
nach, wie sie benutzt wird).
\begin{parts}
\part Gib alle Elemente des ersten ``Blattes'' aus (Index 1 der 3. Dimension).
\begin{solution}
\code{x = randn(5,5); \\y = randn(5, 5);\\ z = cat(3, x, y);\\disp(z(:,:,1))}
\end{solution}
\end{parts}
\question Erzeuge eine $5 \times 5 \times 5$ Matrix die mit
ganzzahligen, gleichverteilten Zufallszahlen zwischen 0 und 100
gef\"ullt ist.
\begin{parts}
\part Berechne den Mittelwert aller Bl\"atter dieser Matrix
(benutze \verb+mean()+, siehe Hilfe).
\begin{solution}
\code{x = round(rand(5,5,5) .* 100);\\ Disp(mean(mean(x(:,:,1))))\\ disp(mean(mean(x(:,:,2)))) \\ disp(mean(mean(x(:,:,3))))}
\end{solution}
\end{parts}
\end{questions}
\end{document}

6
programming/lecture/programming-chapter.tex
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@ -28,7 +28,11 @@
\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 File handling: (extra chapter?)
\begin{itemize}
\item output and input (load, save, fprintf, scanf)
\item dir() function
\end{itemize}
\item help() und doc()
\item A box about sampling of contiunous data.
\item A box about foo and bar?

54
programming/lecture/programming.tex
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@ -1009,6 +1009,60 @@ segment of data of a certain time span (the stimulus was on,
\end{itemize}
\end{exercise}
\begin{ibox}[ht]{\label{whenscriptsbox}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{}-
specific advanced data structures that make life easier (mostly). We
will introduce them breifly here and refer to the \matlab{} help for
further information. \textbf{Note: Some of these data types are
more recent additions to the matlab language. One should consider
this if downward compatibility is desired/needed.}
\textbf{Structures} Arrays of named fields that each can contain
arbitrary data types. \codeterm{Structures} can have sub-structures
and thus can build a trees. Structures are often used to combine
data and mtadata in a single variable.
\textbf{Cell arrays} Arrays of variables that contain different
types. Unlike structures, the entries of a \codeterm{Cell array} are
not named. Indexing in \codeterm{Cell arrays} requires a special
operator the \code{\{\}}. \matlab{} uses \codeterm{Cell arrays} for
example when strings of different lengths should be stored in the
same variable: \varcode{months = \{'Januar', 'February', 'March',
'April', 'May', 'Jun'\};}. Note the curly braces that are used to
create the array and are also used for indexing.
\textbf{Tables} Tabular structure that allows to have columns of
varying type combined with a header (much like a spreadsheet).
\textbf{Timetables} Array of values that are associated with a
timestamp. For example one can store measurements, that are made in
irregular intervals togehter with the measurement time in a single
variable. Without the \codeterm{Timetable} data type at least two
variables (one storing the time, the other the measurement) would be
required. \codeterm{Timetables} offer specific convenience functions
to work with timestamps.
\textbf{Maps} In a \codeterm{map} a \codeterm{value} is associated
with an arbitrary \codeterm{key}. The \codeterm{key} is not
restricted to be an integer but can be almost anything. Maps are an
alternative to structures with the additional advantage that the key
can be used during indexing: \varcode{my\_map('key')}.
\textbf{Categorical arrays} are used to stored values that come from
a limited set of values, e.g. Months. Such categories can then be
used for filter operations. \codeterm{Categorical arrays} are often
used in conjunctions with \codeterm{Tables}.
\begin{lstlisting}[caption={Using Categorical arrays}, label=categoricallisting]
>> months = categorical({'Jan', 'Feb', 'Jan', 'Dec'});
>> events = [10, 2, 18, 20 ];
>> events(months == 'Jan')
ans =
10 18
\end{lstlisting}
\end{ibox}
\section{Control flow}\label{controlstructsec}

22
projects/Makefile
View File

@ -1,9 +1,15 @@
all:
for d in `ls -d project_*/`; do \
echo "Processing $$d" ; \
a=$$(echo $$d*.tex) ; \
rm $${a%.tex}.zip ; \
cd $$d; $(MAKE) zip ; cd .. ; \
all: projects evalutation
evaluation: evaluation.pdf
evaluation.pdf: evaluation.tex
pdflatex $<
projects:
for d in `ls -d project_*`; do \
if test "x$$d" != "xproject_template"; then \
echo "Processing $$d" ; \
cd $$d; $(MAKE) zip ; cd .. ; \
fi \
done
mv project_*/*zip .
@ -11,8 +17,10 @@ all:
clean:
for d in `ls -d project_*/`; do \
echo "Cleaning up $$d" ; \
cd $$d; $(MAKE) clean ; cd .. ; \
$(MAKE) -C $$d clean ; \
done
rm -f *~
rm -f evaluation.aux evaluation.log
rm -f *.zip
rm -rf auto

44
projects/disclaimer.tex
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@ -1,44 +0,0 @@
\fbox{\parbox{0.985\linewidth}{ \small
{\bf Evaluation criteria:}
Each project has three elements that are graded: (i) the code,
(ii) the slides/figures, and (iii) the presentation.
\vspace{1ex}
The {\bf code} and the {\bf presentation} should be uploaded to
ILIAS at latest on Thursday, February 9th, 12:59h. We will
store all presentations on one computer to allow fast
transitions between talks. The presentations start on Thursday,
February 9th at 1:00h c.t.. Please hand in your presentation as
a pdf file. Bundle everything (the pdf, the code, and the data)
into a {\em single} zip-file.
\vspace{1ex}
The {\bf code} should be executable without any further
adjustments from our side. A single \texttt{main.m} script should
coordinate the analysis by calling functions and sub-scripts and
should produce the {\em same} figures that you use in your
slides. The code should be properly commented and comprehensible
by a third person (use proper and consistent variable and
function names).
\vspace{1ex}
\textbf{Please write your name and matriculation number as a
comment at the top of the \texttt{main.m} script.}
\vspace{1ex}
The {\bf presentation} should be {\em at most} 10min long and be
held in English. In the presentation you should (i) briefly
describe the problem, (ii) present figures introducing, showing,
and discussing your results, and (iii) explain how you solved
the problem algorithmically (don't show your entire code). All
data-related figures you show in the presentation should be
produced by your program. It is always a good idea to illustrate
the problem with basic plots of the raw-data. Make sure the axis
labels are large enough!
}}

44
projects/evaluation.tex Normal file
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@ -0,0 +1,44 @@
\documentclass[12pt,a4paper]{article}
\usepackage[ngerman]{babel}
\usepackage{pslatex}
%%%%% page style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[left=10mm,right=10mm,top=10mm,bottom=10mm,headsep=0ex,headheight=0ex,footskip=0ex]{geometry}
\pagestyle{empty}
\newcounter{studentnum}
\newcommand{\num}{\rule{0pt}{5.8ex}{\stepcounter{studentnum}\small \arabic{studentnum}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\sffamily
\section*{Scientific computing WS16/17}
\begin{tabular}{|p{0.15\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|p{0.07\textwidth}|}
\hline
Name & \multicolumn{5}{l|}{Code} & \multicolumn{3}{l|}{Functions} & Figures \\
& runs & docu & variable function script names & style & extras & NOT \newline used as scripts & docu & sep. \newline algo./ plot & saved \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\num & & & & & & & & & \\ \hline
\end{tabular}
\end{document}

56
projects/header.tex Normal file
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@ -0,0 +1,56 @@
\usepackage{pslatex}
\usepackage[mediumspace,mediumqspace,squaren]{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}
\header{{\bfseries\large Scientific Computing}}{{\bfseries\large Project: \ptitle}}{{\bfseries\large Januar 24th, 2017}}
\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}{\vfill\hspace*{\fill}$\rightarrow$\newpage}
%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\qt}[1]{\textbf{#1}\\}
\newcommand{\code}[1]{\texttt{#1}}

59
projects/instructions.tex Normal file
View File

@ -0,0 +1,59 @@
\setlength{\fboxsep}{2ex}
\fbox{\parbox{1\linewidth}{\small
{\bf Evaluation criteria:}
Each project has three elements that are graded: (i) the code,
(ii) the slides/figures, and (iii) the presentation.
\vspace{1ex}
{\bf Dates:}
The {\bf code} and the {\bf presentation} should be uploaded to
ILIAS at latest on Thursday, February 9th, 12:59h. We will
store all presentations on one computer to allow fast
transitions between talks. The presentations start on Thursday,
February 9th at 1:00h c.t..
\vspace{1ex}
{\bf Files:}
Please hand in your presentation as a pdf file. Bundle
everything (the pdf, the code, and the data) into a {\em single}
zip-file.
\vspace{1ex}
{\bf Code:}
The {\bf code} should be executable without any further
adjustments from our side. A single \texttt{main.m} script
should coordinate the analysis by calling functions and
sub-scripts and should produce the {\em same} figures
(\texttt{saveas()}-function, pdf or png format) that you use in
your slides. The code should be properly commented and
comprehensible by a third person (use proper and consistent
variable and function names).
% Hint: make the zip file you want to upload, unpack it
% somewhere else and check if your main script is running.
\vspace{1ex}
\emph{Please write your name and matriculation number as a
comment at the top of the \texttt{main.m} script.}
\vspace{1ex}
{\bf Presentation:}
The {\bf presentation} should be {\em at most} 10min long and be
held in English. In the presentation you should (i) briefly
describe the problem, (ii) present figures introducing, showing,
and discussing your results, and (iii) explain how you solved
the problem algorithmically (don't show your entire code). All
data-related figures you show in the presentation should be
produced by your program --- no editing or labeling by
PowerPoint or other software. It is always a good idea to
illustrate the problem with basic plots of the raw-data. Make
sure the axis labels are large enough!
}}

25
projects/project.mk Normal file
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@ -0,0 +1,25 @@
BASENAME=$(subst project_,,$(notdir $(CURDIR)))
latex:
pdflatex $(BASENAME).tex
pdflatex $(BASENAME).tex
pdf: $(BASENAME).pdf
$(BASENAME).pdf : $(BASENAME).tex ../header.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
clean:
rm -f *~ code/*~ solution/*~ data/*~
rm -rf *.log *.aux *.out auto
rm -f `basename *.tex .tex`.pdf
rm -f *.zip
zip: latex
rm -f zip $(BASENAME).zip
zip $(BASENAME).zip *.pdf *.m data/* $(ZIPFILES)

11
projects/project_adaptation_fit/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat data/*.mat
include ../project.mk

32
projects/project_adaptation_fit/adaptation_fit.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Adaptation time-constant}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Estimating the adaptation time-constant.}

11
projects/project_eod/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf data/*.mat
include ../project.mk

32
projects/project_eod/eod.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{EOD waveform}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

80
projects/project_eod/solution/fit_eod.py Normal file
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@ -0,0 +1,80 @@
import matplotlib.pyplot as plt
import numpy as np
from IPython import embed
import scipy.io as scio
def load_data(filename):
data = scio.loadmat(filename)
t = data['t']
eod = data['eod']
return t[0], eod[0]
def eod_model(p, t):
b_0 = p[0]
omega_0 = p[1]
params = p[2:]
n = len(params)/2
eod = np.zeros(t.shape)
for i in range(n):
eod += params[i*2] * np.sin(2 * np.pi * t * (i+1) * omega_0 + params[i*2+1])
eod += b_0
return eod
def fit_error(p, t, y):
y_dash = eod_model(p,t)
err = np.mean((y - y_dash)**2)
return err
def gradient(p, t, y, scale=None):
if scale is None:
scale = np.ones(len(p))
grad = np.zeros(len(p))
h = 0.002
for i in range(len(p)):
p_temp = list(p)
p_temp[i] = p[i] + scale[i] * h
grad[i] = (fit_error(p_temp, t, y) - fit_error(p, t, y)) / h
return grad
def gradient_descent(t, y):
count = 80
b_0 = np.mean(y)
omega_0 = 650
params = [b_0, omega_0, np.min(y) + np.max(y), np.pi/2, (np.min(y) + np.max(y))/2, np.pi/3, (np.min(y) + np.max(y))/4, np.pi/4, (np.min(y) + np.max(y))/5, np.pi]
scale = np.ones(len(params))
scale[1] = 1000
eps = 0.01
grad = None
errors = []
plt.axis([0, t[count], -3, 3.5])
plt.ion()
plt.plot(t[:count], y[:count])
l = None
while (grad is None) or (np.linalg.norm(grad) > 0.01):
errors.append(fit_error(params, t[:count], y[:count]))
grad = gradient(params, t[:count], y[:count])
params -= eps * scale * grad
if l is None:
l = plt.plot(t[:count], eod_model(params, t[:count]))
else:
l[0].set_data(t[:count], eod_model(params, t[:count]))
plt.title("norm: %.2f, freq: %.2f" % (np.linalg.norm(grad), params[1]))
plt.pause(0.005)
embed()
exit()
if __name__ == "__main__":
datafile = '../data/EOD_data.mat'
t, eod = load_data(datafile)
# eod = eod_model([0.0, 600, 1.0, 0.0], t[:100])
gradient_descent(t, eod)
embed()
exit()

11
projects/project_eyetracker/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf data/*.mat
include ../project.mk

32
projects/project_eyetracker/eyetracker.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Eye tracker}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Analysis of eye trajectories.}

11
projects/project_fano_slope/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

54
projects/project_fano_slope/fano_slope.tex
View File

@ -1,52 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Stimulus discrimination}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

2
projects/project_fano_slope/lifboltzmannspikes.m
View File

@ -20,7 +20,7 @@ function spikes = lifboltzmannspikes(trials, input, tmax, gain)
for k=1:trials
times = [];
j = 1;
v = vreset;
v = vreset + (vthresh - vreset) * rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + inb)*dt/tau;

13
projects/project_fano_slope/solution/fanoslope.m
View File

@ -76,7 +76,8 @@ plot(false2s, true1s);
T = 0.1;
gains = 0.01:0.01:1.0;
cmax = 100;
ds = zeros(length(gains), 1);
dstt = zeros(length(gains), 1);
dsff = zeros(length(gains), 1);
for k = 1:length(gains)
gain = gains(k);
spikes1 = lifboltzmannspikes(trials, I1, tmax, gain);
@ -84,9 +85,11 @@ for k = 1:length(gains)
[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;
dstt(k) = d;
dsff(k) = min(false1s + false2s);
end
figure()
plot(gains, ds)
plot(gains, dstt);
hold on;
plot(gains, dsff);
hold off;

2
projects/project_fano_slope/solution/lifboltzmannspikes.m
View File

@ -20,7 +20,7 @@ function spikes = lifboltzmannspikes(trials, input, tmax, gain)
for k=1:trials
times = [];
j = 1;
v = vreset;
v = vreset + (vthresh - vreset) * rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + inb)*dt/tau;

11
projects/project_fano_test/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat
include ../project.mk

0
projects/project_fano_test/fano.mat → projects/project_fano_test/data/fano.mat
View File

35
projects/project_fano_test/fano.tex → projects/project_fano_test/fano_test.tex
View File

@ -1,37 +1,16 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Fabian Sinz}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Fano factor test}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question The Fano factor $F=\frac{\sigma^2}{\mu}$ relates the
variance of a spike count $\sigma^2$ to the mean spike count

11
projects/project_fano_time/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

54
projects/project_fano_time/fano_time.tex
View File

@ -1,52 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Stimulus discrimination}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

2
projects/project_fano_time/lifspikes.m
View File

@ -19,7 +19,7 @@ function spikes = lifspikes(trials, input, tmax)
for k=1:trials
times = [];
j = 1;
v = vreset + (vthresh-vreset)*rand(1);
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:length(noise)
v = v + (- v + noise(i) + input)*dt/tau;

2
projects/project_fano_time/solution/lifspikes.m
View File

@ -19,7 +19,7 @@ function spikes = lifspikes(trials, input, tmax)
for k=1:trials
times = [];
j = 1;
v = vreset + (vthresh-vreset)*rand(1);
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:length(noise)
v = v + (- v + noise(i) + input)*dt/tau;

11
projects/project_input_resistance/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf data/*.mat
include ../project.mk

32
projects/project_input_resistance/input_resistance.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Cellular properties}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Estimating cellular properties of different cell types.}

11
projects/project_isicorrelations/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

53
projects/project_isicorrelations/isicorrelations.tex
View File

@ -1,55 +1,16 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Interspike-intervall correlations}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question You are recording the activity of a neuron in response to
constant stimuli of intensity $I$ (think of that, for example,

2
projects/project_isicorrelations/lifadaptspikes.m
View File

@ -32,7 +32,7 @@ function spikes = lifadaptspikes( trials, input, tmaxdt, D, tauadapt, adaptincr
for k=1:trials
times = [];
j = 1;
v = vreset;
v = vreset + (vthresh-vreset)*rand();
a = 0.0;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )

11
projects/project_isipdffit/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

54
projects/project_isipdffit/isipdffit.tex
View File

@ -1,52 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{ISI distributions}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

2
projects/project_isipdffit/lifouspikes.m
View File

@ -28,7 +28,7 @@ function spikes = lifouspikes( trials, input, tmaxdt, D, outau )
times = [];
j = 1;
n = 0.0;
v = vreset;
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
n = n + ( - n + noise(i))*dt/outau;

2
projects/project_isipdffit/pifouspikes.m
View File

@ -28,7 +28,7 @@ function spikes = pifouspikes( trials, input, tmaxdt, D, outau )
times = [];
j = 1;
n = 0.0;
v = vreset;
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
n = n + ( - n + noise(i))*dt/outau;

11
projects/project_isipdffit/solution/invgauss.m Normal file
View File

@ -0,0 +1,11 @@
function p = invgauss(x, mu, D)
if abs(x) < 1e-8
p = zeros(size(x))
else
if x < 0
x = -x;
end
p = exp(-(x-mu).^2./4.0./D./x./mu./mu)./sqrt(4.*pi.*D.*x.^3.0);
end
p(p<1e-16) = 1e-16;
end

72
projects/project_isipdffit/solution/isipdffit.m Normal file
View File

@ -0,0 +1,72 @@
%% check Pig implementation:
mu = 0.01;
D = 1.0;
dx=0.0001;
x = dx:dx:10.0;
for D = [0.1 1 10 100]
for mu = [0.01 0.03 0.1 .03]
%pig = exp(-(x-mu).^2/4.0/D./x./mu/mu)./sqrt(4*pi*D*x.^3.0);
pig = invgauss(x,mu,D);
P = sum(pig)*dx;
mig = sum(x.*pig)*dx;
qig = sum(x.*x.*pig)*dx;
vig = qig - mig*mig;
dig = 0.5*vig/mig^3;
fprintf('Integral=%.3f\n', P);
fprintf('Average=%.3f = %.3f\n', mig, mu);
%fprintf('Variance=%.3f\n', vig);
fprintf('Diffusion=%.3f = %.3f\n\n', dig, D);
plot(x, pig)
hold on
plot([mu mu], [0 max(pig)], 'k')
hold off
xmax = 3.0*mu;
if xmax < 0.1
xmax = 0.1;
end
xlim([0 xmax])
text(0.6, 0.8, sprintf('D=%.3g', D), 'units', 'normalized')
pause( 1.0 )
end
end
%% fit to data:
trials = 1;
tmax = 100.0;
input = 10.0; % the input I
Dnoise = 1.0; % noise strength
outau = 0.1; % correlation time of the noise in seconds
%for input = [9.5 10.1 11.7 15.9]
% spikes = lifouspikes(trials, input, tmax, Dnoise, outau);
for input = [1.0 2.0 5.0 10.0]
spikes = pifouspikes(trials, input, tmax, Dnoise, outau);
isis = diff(spikes{1});
mu = mean(isis);
fprintf('mean firing rate = %.0f Hz\n', 1.0/mu)
v = var(isis);
D = 0.5*v/mu^3;
[h,b] = hist(isis, 0:0.001:1);
h = h/sum(h)/(b(2)-b(1));
bar(b, h);
hold on;
dx=0.0001;
x = dx:dx:max(isis);
pig = exp(-(x-mu).^2/4.0/D./x./mu/mu)./sqrt(4*pi*D*x.^3.0);
plot(x, pig, 'r', 'linewidth', 2);
% mle fit:
phat = mle(isis, 'pdf', @invgauss, 'start', [0.1 0.1] );
mu = phat(1);
D = phat(2);
pig = exp(-(x-mu).^2/4.0/D./x./mu/mu)./sqrt(4*pi*D*x.^3.0);
plot(x, pig, 'c', 'linewidth', 2);
xlim([0 4.0*mu])
hold off;
pause( 4.0 )
end

11
projects/project_lif/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

56
projects/project_lif/lif.tex
View File

@ -1,53 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Integrate-and-fire neuron}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
@ -89,6 +50,9 @@ time = [0.0:dt:tmax]; % t_i
and compute $V(t)$ for $t_{max}=50$\,ms. Plot $V(t)$ and compare it to
the expected result of $V(t) = \exp(-t/\tau)$.
Vary the time step $\Delta t$ by factors of 10 and discuss
accuracy of numerical solutions. What is a good time step?
Why is $V=0$ the resting potential of this neuron?
\part Response of the passive membrane to a step input.

11
projects/project_mutualinfo/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat
include ../project.mk

0
projects/project_mutualinfo/decisions.mat → projects/project_mutualinfo/data/decisions.mat
View File

34
projects/project_mutualinfo/mutualinfo.tex
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@ -1,36 +1,16 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Mutual information}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question A subject was presented two possible objects for a very
brief time ($50$\,ms). The task of the subject was to report which of

11
projects/project_noiseficurves/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

2
projects/project_noiseficurves/lifspikes.m
View File

@ -18,7 +18,7 @@ function spikes = lifspikes(trials, input, tmax, D)
for k=1:trials
times = [];
j = 1;
v = vreset;
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + input)*dt/tau;

54
projects/project_noiseficurves/noiseficurves.tex
View File

@ -1,55 +1,17 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
%%%%% 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=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Neural tuning and noise}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{REPLACE BY SUBTHRESHOLD RESONANCE PROJECT!}
\begin{questions}
\question You are recording the activity of a neuron in response to
constant stimuli of intensity $I$ (think of that, for example,

2
projects/project_noiseficurves/solution/lifspikes.m
View File

@ -18,7 +18,7 @@ function spikes = lifspikes(trials, input, tmax, D)
for k=1:trials
times = [];
j = 1;
v = vreset;
v = vreset + (vthresh-vreset)*rand();
noise = sqrt(2.0*D)*randn(n, 1)/sqrt(dt);
for i=1:n
v = v + (- v + noise(i) + input)*dt/tau;

11
projects/project_numbers/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat data/*.mat
include ../project.mk

32
projects/project_numbers/numbers.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Number coding}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

11
projects/project_onset_fi/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat data/*.mat
include ../project.mk

32
projects/project_onset_fi/onset_fi.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Onset f-I curve}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Quantifying the responsiveness of a neuron using the F-I curve.}

3
projects/project_pca_natural_images/Makefile Normal file
View File

@ -0,0 +1,3 @@
ZIPFILES=
include ../project.mk

0
projects/project_pca_natural_img/natimg.jpg → projects/project_pca_natural_images/data/natimg.jpg
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35
projects/project_pca_natural_img/pca_natural_images.tex → projects/project_pca_natural_images/pca_natural_images.tex Executable file → Normal file
View File

@ -1,33 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Fabian Sinz}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Image statistics}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

11
projects/project_pca_natural_img/Makefile
View File

@ -1,11 +0,0 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
clean:
rm -rf *.log *.aux *.zip *.out auto *.bbl *.blg
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.jpg

11
projects/project_photoreceptor/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat data/*.mat
include ../project.mk

32
projects/project_photoreceptor/photoreceptor.tex
View File

@ -1,32 +1,14 @@
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
%\shadedsolutions
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{Photoreceptor activity}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
% \begin{flushright}
% \gradetable[h][questions]
% \end{flushright}
\begin{center}
\input{../disclaimer.tex}
\end{center}
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Analysis of insect photoreceptor data.}

11
projects/project_populationvector/Makefile
View File

@ -1,10 +1,3 @@
latex:
pdflatex *.tex > /dev/null
pdflatex *.tex > /dev/null
ZIPFILES=
clean:
rm -rf *.log *.aux *.zip *.out auto
rm -f `basename *.tex .tex`.pdf
zip: latex
zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
include ../project.mk

0
projects/project_populationvector/population01.mat → projects/project_populationvector/data/population01.mat
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0
projects/project_populationvector/population02.mat → projects/project_populationvector/data/population02.mat
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0
projects/project_populationvector/population03.mat → projects/project_populationvector/data/population03.mat
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projects/project_populationvector/population04.mat → projects/project_populationvector/data/population04.mat
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projects/project_populationvector/population05.mat → projects/project_populationvector/data/population05.mat
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projects/project_populationvector/population06.mat → projects/project_populationvector/data/population06.mat
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projects/project_populationvector/population07.mat → projects/project_populationvector/data/population07.mat
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projects/project_populationvector/population08.mat → projects/project_populationvector/data/population08.mat
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projects/project_populationvector/population09.mat → projects/project_populationvector/data/population09.mat
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projects/project_populationvector/population10.mat → projects/project_populationvector/data/population10.mat
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0
projects/project_populationvector/population11.mat → projects/project_populationvector/data/population11.mat
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0
projects/project_populationvector/population12.mat → projects/project_populationvector/data/population12.mat
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projects/project_populationvector/population13.mat → projects/project_populationvector/data/population13.mat
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0
projects/project_populationvector/population14.mat → projects/project_populationvector/data/population14.mat
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0
projects/project_populationvector/population15.mat → projects/project_populationvector/data/population15.mat
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0
projects/project_populationvector/population16.mat → projects/project_populationvector/data/population16.mat
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0
projects/project_populationvector/population17.mat → projects/project_populationvector/data/population17.mat
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projects/project_populationvector/population18.mat → projects/project_populationvector/data/population18.mat
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0
projects/project_populationvector/population19.mat → projects/project_populationvector/data/population19.mat
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0
projects/project_populationvector/population20.mat → projects/project_populationvector/data/population20.mat
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0
projects/project_populationvector/population21.mat → projects/project_populationvector/data/population21.mat
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0
projects/project_populationvector/population22.mat → projects/project_populationvector/data/population22.mat
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0
projects/project_populationvector/population23.mat → projects/project_populationvector/data/population23.mat
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0
projects/project_populationvector/population24.mat → projects/project_populationvector/data/population24.mat
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0
projects/project_populationvector/population25.mat → projects/project_populationvector/data/population25.mat
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0
projects/project_populationvector/population26.mat → projects/project_populationvector/data/population26.mat
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0
projects/project_populationvector/population27.mat → projects/project_populationvector/data/population27.mat
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projects/project_populationvector/population28.mat → projects/project_populationvector/data/population28.mat
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projects/project_populationvector/population29.mat → projects/project_populationvector/data/population29.mat
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