From 240303051f23580172b8e478ed23ae11694ee98c Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 3 Nov 2015 18:29:19 +0100 Subject: [PATCH] matrices almost done --- .../lecture/pointprocessscetchA.eps | 6 +- .../lecture/pointprocessscetchB.eps | 6 +- programming/lectures/programming.tex | 166 +++++++++++++++++- .../lectures/vectors_matrices-slides.tex | 2 +- .../lecture/images/psth_comparison.pdf | Bin 103782 -> 22263 bytes .../lecture/images/reconstruction.pdf | Bin 18671 -> 18683 bytes spike_trains/lecture/images/sta.pdf | Bin 11386 -> 11418 bytes 7 files changed, 164 insertions(+), 16 deletions(-) diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index f862701..041fcf8 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: Mon Nov 2 19:55:25 2015 +%%CreationDate: Tue Nov 3 17:29:16 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 (jan) + /Author (grewe) % /Producer (gnuplot) % /Keywords () - /CreationDate (Mon Nov 2 19:55:25 2015) + /CreationDate (Tue Nov 3 17:29:16 2015) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchB.eps b/pointprocesses/lecture/pointprocessscetchB.eps index a246da8..81e21bf 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: Mon Nov 2 19:57:38 2015 +%%CreationDate: Tue Nov 3 18:24:39 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 (jan) + /Author (grewe) % /Producer (gnuplot) % /Keywords () - /CreationDate (Mon Nov 2 19:57:38 2015) + /CreationDate (Tue Nov 3 18:24:39 2015) /DOCINFO pdfmark end } ifelse diff --git a/programming/lectures/programming.tex b/programming/lectures/programming.tex index 414b8a8..55465ce 100644 --- a/programming/lectures/programming.tex +++ b/programming/lectures/programming.tex @@ -432,33 +432,181 @@ Dimensions of matrices being concatenated are not consistent. \subsection{Matrizen} +Im Gegesatz zu den 1-dimensionalen Vektoren k\"onnen Martizen +n-dimensional sein, das hei{\ss}t, dass sie beliebig viele Dimensionen +haben k\"onnen. Von praktischer Bedeutung sind allerdings nur Matrizen +mit bis zu vier Dimensionen. Meist beschr\"ankt es sich jedoch auf 2- +bis 3-d Matrizen (Abbildung \ref{matrixfig} A,B). + \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} + \caption{\textbf{Matrizen. A)} Eine Variable (``test'') die eine + 2-dimensionale Matrize ist. \textbf{B)} Illustration einer + 3-dimensionalen Matrize. Die Pfeile zeigen den Rang der + Dimensionen an.}\label{matrixfig} \end{figure} +Erzeugt werden Matrizen sehr \"ahnlich zu den Vektoren (Listing +\ref{matrixListing}). Die Definition einer Matrize wird, wie beim +Vektor, durch \code{[]} eingeschlossen. Das \code{;} trennt die +einzelnen Zeilen der Matrize. + +\footnotesize +\begin{lstlisting}[label=matrixListing, caption={Erzeugen von Matrizen.}] +>> a = [1 2 3; 4 5 6; 7 8 9] +>> a = + 1 2 3 + 4 5 6 + 7 8 9 +>> +>> b = ones(3,3,2); +>> b + + b(:,:,1) = + 1 1 1 + 1 1 1 + 1 1 1 + + b(:,:,2) = + 1 1 1 + 1 1 1 + 1 1 1 +\end{lstlisting} +\normalsize + +Zur Defintion von mehr-dimensionalen Matrizen ist die Notation in +Zeile 1 nicht wirklich geeignet. Es gibt allerdings eine Reihe von +Helferfunktionen, die n-dimensionale Matrizen erstellen k\"onnen +(z.B. \code{ones}, Zeile 7). Sollte sich die Notwendigkeit ergeben +mehrdimensionale Matrizen zusammenzuf\"ugen hilft die \code{cat} +Funktion. + +Um Informationen \"uber die Gr\"{\ss}e einer Matrize zu bekommen ist +die Funktion \code{length} nicht geeignet. Wie oben erw\"ahnt gibt sie +die Gr\"o{\ss}e der l\"angsten Dimension aus. Wann immer es um +Matrizen geht, wird \code{size} benutzt. \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} + \caption{\textbf{Indices von Matrizen.} Jedes Feld einer Matrize + wird durch einen Index individuell angesprochen. Der Index setzt + sich aus so vielen Zahlen zusammen wie es Dimensionen gibt (links + 2, rechts 3). Dabei steht die 1. Stelle immer f\"ur die Zeile, die + 2. f\"uer die Spalte und die dritte f\"ur das Blatt, + etc.. }\label{matrixindexingfig} \end{figure} +Der Zugriff auf Inhalte von Matrizen erfolgt \"uber den Index +(Abbildung \ref{matrixindexingfig}, Listing +\ref{matrixIndexing}). \"Ahnlich zu den Positionen in einem +Koordinatensystem wird jede Zelle einer Matrize mit einem Index +angesprochen, der aus $n$ Zahlen besteht wobei $n$ die +Dimensionalit\"at der Matrize ist. Diese Art des Zugriffs wird +\textit{subsript indexing} genannt. + +\footnotesize +\begin{lstlisting}[caption={Zugriff auf Inhalte von Matrizen, + Indexierung.}, label=matrixIndexing] +>> x = randi(100, [3, 4, 5]); % 3-D Matrix mit Zufallszahlen +>> size(x) +ans = + 3 4 5 +>> x(1,1,1); % obere linke Ecke + ans(1,1,1) = + 14 + >> +>> x(1,1,:) % obere linke Ecke entlang der 3. Dimension +ans(1,1,:) = + 14 +ans(:,:,2) = + 58 +ans(:,:,3) = + 4 +ans(:,:,4) = + 93 +ans(:,:,5) = + 56 +\end{lstlisting} +\normalsize + +Alternativ zum \textit{subscript indexing} k\"onnen die Zellen einer +Matrize auch \textit{linear} angesprochen werden (Abbildung +\ref{matrixlinearindexingfig}). Diese Art der Adressierung ist nicht +so intuituiv verst\"andlich, kann aber sehr hilfreich sein. Der +``linare'' Index einer Zelle reicht von 1 bis \code{numel(M)} +Elemente. Wobei dieser erst entlang der 1. Dimension, dann der 2., +3. etc. Dimension ansteigt. Listing \ref{matrixLinearIndexing} zeigt +ein Beispiel fuer den Einsatz des linearen Indexierens z.B. wenn man +den Minimalwert aller Elemente einer Matrize ermitteln m\"ochte.. + \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} + \caption{\textbf{Lineares Indexieren von Matrizen.} Der Index steigt + linear von 1 bis zur Anzahl Elemente in der Matrize an. Dabei + steigt der Index zuerst entlang der ersten, zweiten, dritten und + weiterer Dimensionen an.}\label{matrixlinearindexingfig} \end{figure} +\begin{lstlisting}[label=matrixLinearIndexing, caption={Lineares Indexieren in Matrizen.}] +>> x = randi(100, [3, 4, 5]); % 3-D Matrix mit Zufallszahlen +>> size(x) +ans = + 3 4 5 +>> numel(x) +ans = + 60 +>> min(min(min(x))) % Minumum uber die Zeilen, Spalten, Blaetter... +ans = + 4 +>> min(x(:)) % oder so +ans = + 4 +\end{lstlisting} + +Beim Rechnen mit Matrizen gelten die gleichen Regeln wie bei +Vektoren. Matrizen k\"onnen solange elementweise miteinander +Verrechnet werden, wie die Dimensionalit\"aten +\"ubereinstimmen. Besondere Vorsicht sollte man immer dann walten +lassen, wenn man Matrizen miteinander mulitplizieren, dividieren oder +postenzieren will. Hier ist es wichtig sich klarzumachen was man will: +Eine elementweise multiplikation (\code{.*} Operator, Listing +\ref{matrixOperations} Zeile 18) oder ob eine Matrixmultiplikation +(\code{*} Operator, Listing \ref{matrixOperations} Zeile 12) +durchgef\"uhrt werden soll. + +\footnotesize +\begin{lstlisting}[label=matrixOperations, caption={Zwei Arten von Multiplikationen auf Matrizen.}] +>> A = randi(10, [3, 3]) % 2-D Matrix + A = + 3 8 2 + 2 10 3 + 10 7 1 +>> B = randi(10, [3, 3]) % dto + B = + 2 1 7 + 1 5 9 + 5 10 5 +>> +>> A * B % Matrix Multiplikation + ans = + 24 63 103 + 29 82 119 + 32 55 138 +>> +>> A .* B % Elementweise Multiplikation + ans = + 6 8 14 + 2 50 27 + 50 70 5 +>> +\end{lstlisting} +\normalsize \section{Boolesche Operationen} + \section{Logisches Indizieren} diff --git a/programming/lectures/vectors_matrices-slides.tex b/programming/lectures/vectors_matrices-slides.tex index 991526a..1c60e02 100644 --- a/programming/lectures/vectors_matrices-slides.tex +++ b/programming/lectures/vectors_matrices-slides.tex @@ -413,7 +413,7 @@ \framesubtitle{Indexierung} \tiny \begin{lstlisting} ->> x = roundi(100, [3, 4, 5]); % 3-D Matrix mit Zufallszahlen +>> x = randi(100, [3, 4, 5]); % 3-D Matrix mit Zufallszahlen >> >> x(1,1,1); % obere linke Ecke ans(1,1,1) = diff --git a/spike_trains/lecture/images/psth_comparison.pdf b/spike_trains/lecture/images/psth_comparison.pdf index 59e49f7ca0deaf76012bbd76e7641ec92c48e1e9..73d9dd3b4fd9972e321e96c24c10490127a26680 100644 GIT binary patch delta 13168 zcmZ{}bzBr&&^Amr64JSVbnUWqry|lwOLupJOCuc%Qj#JaOA1PNN~ef~bhm`?F6#5W z&wbzDyMMr(IdkT^=9)QYe?QnLMZ2s(gjFL#0)}e#`(3{ILwaZykR4`jK*{v>!lKYA z0vZLlJs(}XYk&4@_w+hceX}-2+kvkqo7wU9G=B8{;`Zt)vrXCGsoQz2%(Q)l*v#oe zgm5pz@}nCww%n`F-^K6P8ji5M&0BCzjxQzIv(=?fI(Q6CE?y&Bwl*z^3XEz$FS#<_ zsnStsZQ@(krdc`Y0JW@QoTB0G6Z^jKf>^)iYo2+=Tqshst4Bz=#;4bs-W5bC)9PbI zTSe~Lg!q;H(&d!XU`Qf>qfI?#ZKL;0LEycOP6|zcb+c>c-R8%ODArekdOF)xLK{ag 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