From 59ce7227fc98c47b0f7c9299a87661c71b07113e Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 3 Nov 2015 00:02:15 +0100 Subject: [PATCH] Vectors finished --- .../lecture/pointprocessscetchA.eps | 6 +- .../lecture/pointprocessscetchB.eps | 6 +- programming/lectures/programming.tex | 491 ++++++++++++++++++ scientificcomputing-script.tex | 2 +- .../lecture/images/psth_comparison.pdf | Bin 184616 -> 103782 bytes .../lecture/images/reconstruction.pdf | Bin 103467 -> 18671 bytes spike_trains/lecture/images/sta.pdf | Bin 96577 -> 11386 bytes spike_trains/lecture/psth_sta.tex | 113 ++-- 8 files changed, 578 insertions(+), 40 deletions(-) create mode 100644 programming/lectures/programming.tex diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 17a8e91..f862701 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Wed Oct 28 18:47:55 2015 +%%CreationDate: Mon Nov 2 19:55:25 2015 %%DocumentFonts: %%BoundingBox: 50 50 373 135 %%EndComments @@ -430,10 +430,10 @@ SDict begin [ /Title (pointprocessscetchA.tex) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 4) - /Author (benda) + /Author (jan) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed Oct 28 18:47:55 2015) + /CreationDate (Mon Nov 2 19:55:25 2015) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchB.eps b/pointprocesses/lecture/pointprocessscetchB.eps index 19d3b78..a246da8 100644 --- a/pointprocesses/lecture/pointprocessscetchB.eps +++ b/pointprocesses/lecture/pointprocessscetchB.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchB.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Wed Oct 28 18:47:56 2015 +%%CreationDate: Mon Nov 2 19:57:38 2015 %%DocumentFonts: %%BoundingBox: 50 50 373 237 %%EndComments @@ -430,10 +430,10 @@ SDict begin [ /Title (pointprocessscetchB.tex) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 4) - /Author (benda) + /Author (jan) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed Oct 28 18:47:56 2015) + /CreationDate (Mon Nov 2 19:57:38 2015) /DOCINFO pdfmark end } ifelse diff --git a/programming/lectures/programming.tex b/programming/lectures/programming.tex new file mode 100644 index 0000000..414b8a8 --- /dev/null +++ b/programming/lectures/programming.tex @@ -0,0 +1,491 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{\tr{Programming basics}{Grundlagen der Programmierung in Matlab}} + +\section{Variablen und Datentypen} + +\subsection{Variablen} + +Eine Variable ist ein Zeiger auf eine Stelle im Speicher. Dieser +Zeiger hat einen Namen, den Variablennamen, und einen Datentyp +(Abbildung \ref{variablefig}).Im Speicher wird der Wert der Variablen +bin\"ar gespeichert. Wird auf den Wert der Variable zugegriffen, wird +dieses Bitmuster je nach Datentyp interpretiert. Das Beispiel in +Abbildung \ref{variablefig} zeigt, dass das gleiche Bitmuster im einen +Fall als 8-Bit Integer Datentyp zur Zahl 38 interpretiert wird und im +anderen Fall als Character zum kaufm\"annischen ``und'' ausgewertet +wird. In Matlab sind Datentypen nicht von sehr zentraler +Bedeutung. Wir werden uns dennoch sp\"ater etwas genauer mit ihnen +befassen. + +\begin{figure} +\centering +\begin{subfigure}{.5\textwidth} + \includegraphics[width=0.8\textwidth]{variable} + \label{variable:a} +\end{subfigure}% +\begin{subfigure}{.5\textwidth} + \includegraphics[width=.8\textwidth]{variableB} + \label{variable:b} +\end{subfigure} +\caption{\textbf{Variablen.} Variablen sind Zeiger auf eine Adresse + im Speicher, die einen Namen und einen Datentypen beinhalten. Im + Speicher ist der Wert der Variable bin\"ar gespeichert. Abh\"angig + vom Datentyp wird dieses Bitmuster unterschiedlich + interpretiert.}\label{variablefig} +\end{figure} + + +\subsection{Erzeugen von Variablen} +In Matlab kann eine Variable auf der Kommandozeile, in einem Skript +oder einer Funktion an beliebiger Stelle erzeugen. Das folgende +Listing zeigt zwei M\"oglichkeiten: +\footnotesize +\begin{lstlisting}[label=varListing1, caption=Erzeugen von Variablen] +>> y = [] +y = + [] +>> +>> x = 38 +x = + 38 +\end{lstlisting} +\normalsize + +Die Zeile 1 kann etwa so gelesen werden:''Erzeuge eine Variable mit +dem Namen y und weise ihr einen leeren Wert zu.'' Das +Gleichheitszeichen ist der sogenannte +\textit{Zuweisungsoperator}. Zeile 5 definiert eine Variable x, der +nun der Zahlenwert 38 zugewiesen wird. Da Matlab, wenn nicht anders +angegeben immer den ``double'' Datentypen benutzt, haben beide +Variablen diesen Datentyp. + +\footnotesize +\begin{lstlisting}[label=varListing2, caption={Erfragen des Datentyps einer Variable, Listen aller definierten Variablen.}] +>>disp(class(x)) + double +>> +>> who % oder whos um mehr Information zu bekommen +\end{lstlisting} +\normalsize + +Bei der Namensgebung ist zu beachten, dass Matlab auf Gro{\ss}- und +Kleinschreibung achtet und ein Variablennane mit einem alphabethischen +Zeichen beginnen muss. Des Weiteren sind Umlaute, Sonder- und +Leerzeichen in Variablennamen nicht erlaubt. + + +\subsection{Arbeiten mit Variablen} + +Nat\"urlich kann man mit den Variablen auch arbeiten, bzw +rechnen. Matlab kennt alle normalen arithmetischen Operatoren wie +\code{+, -, *. /}. Die Potenz wird \"uber das Dach Symbol \code{\^} +dargestellt. Das folgende Listing zeigt, wie sie benutzt werden. + +\footnotesize +\begin{lstlisting}[label=varListing3, caption={Rechnen mit Variablen.}] +>> x = 1; +>> x + 10 +ans = + 11 +>> +>> x % x wurde nicht veraendert +ans = + 1 +>> +>> y = 2; +>> +>> x + y +ans = + 3 +>> +>> z = x + y +z = + 3 +>> +>> z = z * 5; +>> z +z = + 15 +>> +>> clear z +\end{lstlisting} +\normalsize + +Beachtenswert ist z.B. in Zeilen 3 und 6, dass wir mit dem Inhalt +einer Variablen rechnen k\"onnen, ohne dass dadurch ihr Wert +ver\"andert w\"urde. Wenn der Wert einer Variablen ver\"andert werden +soll, dann muss dieser der Variable expliyit zugewiesen werden (mit +dem \code{=} Zuweisungsoperator, z.B. Zeilen 16, 20). Zeile 25 zeigt +wie eine einzelne Variable gel\"oscht wird. + + +\subsection{Datentypen} + +Der Datentyp bestimmt, wie die im Speicher abgelegten Bitmuster +interpretiert werden. Die Wichtigsten Datentpyen sind folgende: + +\begin{itemize} +\item \textit{integer} - Ganze Zahlen. Hier gibt es mehrere + Unterarten, die wir in Matlab (meist) ignorieren k\"onnen. +\item \textit{double} - Flie{\ss}kommazahlen. +\item \textit{complex} - Komplexe Zahlen. +\item \textit{logical} - Boolesche Werte, die als wahr + (\textit{true}) oder falsch (\textit{false}) interpretiert werden. +\item \textit{char} - ASCII Zeichen +\end{itemize} + +Unter den numerischen Datentypen gibt es verschiedene Arten mit +unterschiedlichem Speicherbedarf und Wertebreich. + +\begin{table}[] +\centering +\caption{Gel\"aufige Datentypen und ihr Wertebereich.} +\label{dtypestab} +\begin{tabular}{l|l|c|cl} +Datentyp & Speicherbedarf & Wertebereich & Beispiel \\ \cline{1-4} +double & 64 bit & & Flie{\ss}kommazahlen.\\ \cline{1-4} +int & 64 bit & $-2^{31} bis 2^{31}-1$ & Ganzzahlige Werte \\ \cline{1-4} +int16 & 64 bit & $-2^{15} bis 2^{15}-1$ & Digitalisierte Spannungen. \\ \cline{1-4} +uint8 & 64 bit & 0 bis 255 & Digitalisierte Imaging Daten. \\ \cline{1-4} + & & & +\end{tabular} +\end{table} + + +Matlab arbeitet meist mit dem ``double'' Datentyp wenn numerische +Daten gespeichert werden. Dennoch lohnt es sich, sich ein wenig mit +den Datentypen auseinanderzusetzen. Ein Szenario, dass in der +Neurobiologie nicht selten ist, ist, dass wir die elektrische +Aktivit\"at einer Nervenzelle messen. Die gemessenen Spannungen werden +mittels Messkarte digitalisiert und auf dem Rechner +gespeichert. Typischerweise k\"onnen mit solchen Messkarten Spannungen +im Bereich $\pm 10$\,V gemessen werden. Die Aufl\"osung der Wandler +betr\"agt typischerweise 16 bit. Das heisst, dass der gesamte +Spannungsbereich in $2^{16}$ Schritte aufgeteilt ist. Um Speicherplatz +zu sparen ist es sinnvoll, die gemessenen Daten als ``int16'' Werte im +Rechner abzulegen. Die Daten als ``echte'' Spannungen, also als +Flie{\ss}kommawerte, abzulegen w\"urde den 4-fachen Speicherplatz +ben\"otigen. + + + +\section{Vektoren und Matrizen} + +\begin{definition}[Vektoren und Matrizen] + Vektoren und Matrizen sind die wichtigsten Datenstrukturen in + Matlab. In andern Programmiersprachen spricht man von ein- + bzw. mehrdimensionalen Feldern. Felder sind Datenstrukturen, die + mehrere Werte des geleichen Datentyps in einer Variablen + vereinen. Da Matalb seinen Ursprung in der Verarbeitung von + mathematischen Vektoren und Matrizen hat werden sie hier auch so + genannt.\\ + + In Wahrheit existiert auch in Matlab kein Unterschied zwischen + beiden Datenstrukturen. Im Hintergrund sind auch Vektoren + 2-diemsensionale Matrizen bei denen eine Dimension die Gr\"o{\ss}e 1 + hat. +\end{definition} + + +\subsection{Vektoren} + +Im Gegensatz zu den Variablen, die einzelene Werte beinhalten, +Skalare, kann ein Vektor mehrere Werte des gleichen Datentyps +beinhalten (Abbildung \ref{vectorfig} B). Die Variable ``test'' +enth\"alt in diesem Beispiel vier ganzzahlige Werte. + + +\begin{figure} + \includegraphics[width=0.8\columnwidth]{scalarArray} + \caption{\textbf{Skalare und Vektoren. A)} Eine skalare Variable kann + genau einen Wert tragen. \textbf{B)} Ein Vektor kann mehrer + Werte des gleichen Datentyps (z.B. ganzzahlige Integer Werte) + beinhalten. Matlab kennt den Zeilen- (row-) und Spaltenvektor + (columnvector).}\label{vectorfig} +\end{figure} + +Das folgende Listing zeigt, wie einfache Vektoren erstellt werden +k\"onnen. + +\footnotesize +\begin{lstlisting}[label=arrayListing1, caption={Erstellen einfacher Zeilenvektoren.}] +>> a = [0 1 2 3 4 5 6 7 8 9] % Erstellen eines Zeilenvektors + a = + 0 1 2 3 4 5 6 7 8 9 +>> +>> b = (0:9) % etwas bequemer + b = + 0 1 2 3 4 5 6 7 8 9 +>> +>> c = (0:2:10) + c = + 0 2 4 6 8 10 +\end{lstlisting} +\normalsize + +Die L\"ange eines Vektors kann mithilfe der Funktion \code{length()} +bestimmt werden. \"Ahnliche Information kann man \"uber die Funktion +\code{size()} erhalten. Im Falle des Vektors \code{a} von oben erh\"alt +man folgende Ausgabe: + +\footnotesize +\begin{lstlisting}[label=arrayListing2, caption={Gr\"o{\ss}e von Vektoren.}] +>> length(a) +ans = + 10 +>> size(a) +ans = + 1 10 +\end{lstlisting} +\normalsize + +Diese Ausgabe zeigt, dass Vektoren im Grunde 2-dimensional sind. Bei +einem Zeilenvektor hat die erste Dimension die Gr\"o{\ss}e +1. \code{length(a)} gibt die l\"angste Ausdehnung an. + +\footnotesize +\begin{lstlisting}[label=arrayListing3, caption={Spaltenvektoren.}] +>> b = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] % Erstellen eines Spaltenvektors + b = + 1 + 2 + .... + 9 + 10 +>> length(b) +ans = + 10 +>> size(b) +ans = + 10 1 +>> b = b'; % Transponieren +>> size(b) +ans = + 1 10 +\end{lstlisting} + +Der \code{'}- Operator transponiert den Spaltenvektor zu einem +Zeilenvektor. + +\subsubsection{Zugriff auf Inhalte von Vektoren} +\begin{figure} + \includegraphics[width=0.4\columnwidth]{arrayIndexing} + \caption{\textbf{Indices von Vektoren.} Jedes Feld eines Vektors hat + einen Index mit dem auf den jeweiligen Inhalt zugegriffen werden + kann.}\label{vectorindexingfig} +\end{figure} + +Der Zugriff auf die Inhalte eines Vektors erfolgt \"uber den Index +(Abbildung \ref{vectorindexingfig}). Jedes Feld in einem Vektor hat +einen \textit{Index} \"uber den auf die Werte des Vektors zugegriffen +werden kann. Dabei spielt es keine Rolle, ob es sich um einen Zeilen- +oder Spaltenvektor handlet. \textbf{Achtung!} Anders als viele andere +Sprachen beginnt Matlab mit dem Index 1. Die Listings +\ref{arrayListing4} und \ref{arrayListing5} zeigen wie man mit dem +Index auf die Inhalte zugreifen kann. + +\footnotesize +\begin{lstlisting}[label=arrayListing4, caption={Zugriff auf den Inhalt von Vektoren I}] +>> a = (11:20); +>> a(1) % das 1. Element +ans = + 11 +>> a(5) % das 5. Element +ans = + 15 +>> a(end) % das letzte Element +ans = + 20 +\end{lstlisting} +\normalsize + +Hierbei kann man auf einzelne Werte zugreifen oder, analog zur +Erzeugung von Vektoren, die \code{:} Notation verwenden um auf mehrere +Element gleichzeitig zuzugreifen. + +\footnotesize +\begin{lstlisting}[caption={Zugriff auf den Inhalt von Vektoren I}, label=arrayListing5] +>> a([1 3 5]) % das 1., 3. und 5. Element +ans = + 11 13 15 +>> a(2:4) % alle element von Index 2 bis 4 +ans = + 12 13 14 +>> a(1:2:end) %jedes zweite Element +ans = + 11 13 15 17 19 +\end{lstlisting} +\normalsize + +\paragraph{Frage:} +Der R\"uckgabewert von \code{size(a)} ist wieder ein Vektor der +L\"ange 2. Wie k\"onnte man also die Gr\"o{\ss}e von \code{a} in der +zweiten Dimension herausfinden? + +\paragraph{Antwort:} +Man speichert den R\"uckgabewert in einer Variable (\code{s = size(a);}) +und gibt den Inhalt an der Stelle 2 aus (\code{disp(s(2))}). + + +\subsubsection{Operationen auf Vektoren} + +Nat\"urlich kann man mit Vektoren auch rechnen. Listing +\ref{arrayListing5} zeigt Rechnungen mit Vektoren. + +\footnotesize +\begin{lstlisting}[caption={Rechnen mit Vektoren.},label=arrayListing5] +>> a = (0:2:8); +>> a + 5 % addiere einen Skalar +ans = + 5 7 9 11 13 + +>> a - 5 % subtrahiere einen Skalar +ans = + -5 -3 -1 1 3 + +>> a .* 2 % Multiplication +ans = + 0 4 8 12 16 + +>> a ./ 2 % Division +ans = + 0 1 2 3 4 + +>> a(1:3) + a(2:4) % Addieren von 2 Vektoren +ans = + 2 6 10 +>> +>> a(1:2) + a(2:4) % Vektoren muessen gleich gross sein! + ??? Error using ==> plus + Matrix dimensions must agree. +\end{lstlisting} +\normalsize + +Wird ein Vektor mit einem skalaren Wert verrechnet, dann ist das +Problemlos m\"oglich. Bei der Multiplikation (Zeile 10), der Division +(Zeile 14) und auch der Potenzierung sollte man mit vorangestellem '.' +klar machen, dass es sich um einen \textit{elementweise} Verarbeitung +handelt. F\"ur diese elementweisen Operationen kennt Matlab die +Operatoren \code{.*, ./} und \code{.\^}. Die einfachen Operatoren sind +im Kontext von Vektoren und Matrizen anders belegt, als man es +vielleicht erwarten w\"urde. Es sind dann die entsprechenden +Matrixoperationen, die man aus der linearen Algebrar kennt (s.u.). + +Zu Beachten ist des Weiteren noch die Fehlermeldung am SChluss von +Listing \ref{arrayListing5}. Wenn zwei Vektoren (elementweise) +miteinander verrechnet werden sollen muss nicht nur die Anzahl Element +übereinstimmen sondern es muss auch das Layout (Zeilen- oder +Spaltenvektoren) \"ubereinstimmen. + + +Will man Elemente aus einem Vektor entfernen, dann weist man den +entsprechenden Zellen einen leeren Wert (\code{[]}) zu. + +\footnotesize +\begin{lstlisting}[label=arrayListing6, caption={L\"oschen von Elementen aus einem Vektor.}] +>> a = (0:2:8); +>> length(a) +ans = + 5 + +>> a(1) = [] % loesche das erste Element +a = 2 4 6 8 + +>> a([1 3]) = [] +a = 4 8 + +>> length(a) +ans = + 2 +\end{lstlisting} + +Neben dem L\"oschen von Vektorinhalten kann man Vektoren auch +erweitern oder zusammensetzen. Auch hier muss das Layout der Vektoren +\"ubereinstimmen (Listing \ref{arrayListing7}, Zeile 12). Will man +einen Vektor erweitern, kann man \"uber das Ende hinaus +zuweisen. Matlab erweitert dann die Variable. Auch hierbei muss auf +das Layout geachtet werden. Zudem ist dieser Vorgang +``rechenintensiv'' und man sollte, soweit m\"oglich, vermeiden +Vektoren bei Bedarf einfach zu erweitern. + +\footnotesize +\begin{lstlisting}[caption={Zusammenf\"ugen und erweitern von Vektoren.}, label=arrayListing7] +>> a = (0:2:8); +>> b = (10:2:19); +>> c = [a b] % erstelle einen Vektor aus einer Liste von Vektoren + c = + 0 2 4 6 8 10 12 14 16 18 +>> length(c) +ans = + 10 +>> length(a) + length(b) +ans = + 10 +>> c = [a b']; +Error using horzcat +Dimensions of matrices being concatenated are not consistent. + +>> b(6:8) = [1 2 3 4]; +\end{lstlisting} + + +\subsection{Matrizen} + +\begin{figure} + \includegraphics[width=0.5\columnwidth]{matrices} + \caption{\textbf{Indices von Vektoren.} Jedes Feld eines Vektors hat + einen Index mit dem auf den jeweiligen Inhalt zugegriffen werden + kann.}\label{vectorindexingfig} +\end{figure} + + +\begin{figure} + \includegraphics[width=0.9\columnwidth]{matrixIndexing} + \caption{\textbf{Indices von Vektoren.} Jedes Feld eines Vektors hat + einen Index mit dem auf den jeweiligen Inhalt zugegriffen werden + kann.}\label{vectorindexingfig} +\end{figure} + +\begin{figure} + \includegraphics[width=0.9\columnwidth]{matrixLinearIndexing} + \caption{\textbf{Indices von Vektoren.} Jedes Feld eines Vektors hat + einen Index mit dem auf den jeweiligen Inhalt zugegriffen werden + kann.}\label{vectorindexingfig} +\end{figure} + + + +\section{Boolesche Operationen} + + +\section{Logisches Indizieren} + + +\section{Kontrollstrukturen} + +\begin{definition}[Kontrollstrukturen] + In der Regel wird ein Programm Zeile f\"ur Zeile von oben nach unten + ausgef\"uhrt. Manchmal muss der Kontrollfluss aber so gesteuert + werden, dass bestimmte Teile des Programmcodes wiederholt oder nur + unter bestimmten Bedingungen ausgef\"uhrt werden. Von grosser + Bedeutung sind hier zwei Strukturen: + \begin{enumerate} + + \item Schleifen. + \item Bedingte Anweisungen und Verzweigungen. + \end{enumerate} +\end{definition} + + +\section{Skripte und Funktionen} + + +\section{Graphische Darstellung von Daten} + + +\begin{figure} + \includegraphics[width=0.9\columnwidth]{./images/convincing} + \caption{Die Folgen schlecht annotierter + Plots. \url{www.xkcd.com}} \label{xkcdplotting} +\end{figure} \ No newline at end of file diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index 891303c..faeaf4d 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -1,4 +1,4 @@ -\documentclass[12pt]{report} +g\documentclass[12pt]{report} \input{header} diff --git a/spike_trains/lecture/images/psth_comparison.pdf b/spike_trains/lecture/images/psth_comparison.pdf index b9a52751a1ff3cffbd1460a057e49e782a92d511..0e37e5953adae427364a14c499c01a187ce9a886 100644 GIT binary patch delta 28217 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