Matrices done
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@ -102,12 +102,11 @@
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\item Variablen und Datentypen
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\item Vektoren und Matrizen
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\item Boolsche Operationen
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\item Was ist ein Programm
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\item Kontrollstrukturen
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\item Was ist ein Programm, Stil und Kommentare
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\item Vom Problem zum Algorithmus
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\item Skripte und Funktionen
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\item Stil und Kommentare
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\item Graphische Darstellung von Daten
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\item Graphische Darstellung von Neuro Daten, PSTH, Rasterplot, STA
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\item Fortgeschrittene Datenstrukturen
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\item String Parsing
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\item Lesen und schreiben von Dateien, navigieren im Dateisystem
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@ -293,7 +292,7 @@
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\begin{frame}[fragile]
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\frametitle{Vektoren und Matrizen}
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\framesubtitle{Erzeugen von Vektoren}
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\footnotesize
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\tiny
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\begin{lstlisting}[label=arrayListing1]
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>> a = [0 1 2 3 4 5 6 7 8 9] % Erstellen eines Zeilenvektors
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a =
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@ -349,7 +348,7 @@
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\frametitle{Vektoren}
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\framesubtitle{Zugriff auf Inhalte von Vektoren}
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\vspace{-0.5cm}
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\footnotesize
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\tiny
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\begin{lstlisting}
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>> a = (11:20);
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>> a(1) % das 1. Element
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@ -372,7 +371,7 @@
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\frametitle{Vektoren}
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\framesubtitle{Zugriff auf Inhalte von Vektoren}
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\vspace{-0.5cm}
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\footnotesize
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\tiny
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\begin{lstlisting}
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>> a([1 3 5]) % das 1., 3. und 5. Element
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ans =
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@ -394,7 +393,7 @@
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\frametitle{Vektoren}
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\framesubtitle{Grundlegende Operationen}
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\vspace{-0.25cm}
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\footnotesize
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\tiny
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\begin{lstlisting}[label=arrayListing4]
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>> a = (0:2:8);
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>> a + 5 % addiere einen Skalar
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@ -413,13 +412,80 @@
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ans =
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2 6 10
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>>
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>> a(1:2) + a(2:4) % Addierte Vektoren muessen die gleiche Groesse haben!
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>> a(1:2) + a(2:4) % Vektoren muessen gleich gro{\ss} sein!
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??? Error using ==> plus
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Matrix dimensions must agree.
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Vektoren}
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\framesubtitle{Grundlegende Operationen}
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\vspace{-0.25cm}
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\tiny
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Wie bekomme ich Informationen \"uber einen Vektor?
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\begin{lstlisting}
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>> a = (0:2:8);
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>> % die Laenge eines
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>> length(a)
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ans =
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5
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>>
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>> size(a)
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ans =
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1 5
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>>
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Vektoren}
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\framesubtitle{Grundlegende Operationen}
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\vspace{-0.25cm}
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L\"oschen von Elementen:
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\tiny
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\begin{lstlisting}
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>> a = (0:2:8);
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>> length(a)
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ans =
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5
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>>
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>> a(1) = [] % loesche das erste Element
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a =
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2 4 6 8
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>> a([1 3]) = []
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a =
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4 8
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>> length(a)
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ans =
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2
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Vektoren}
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\framesubtitle{Grundlegende Operationen}
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\vspace{-0.25cm}
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\tiny
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Verkettung von Vektoren:
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\begin{lstlisting}
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>> a = (0:2:8);
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>> b = (10:2:19);
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>>
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>> c = [a b] % erstelle einen Vektor aus einer Liste von Vektoren
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c =
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0 2 4 6 8 10 12 14 16 18
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>> length(c)
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ans =
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10
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>> length(a) + length(b)
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ans =
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10
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Vektoren}
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\framesubtitle{\"Ubungen}
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@ -447,4 +513,263 @@
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\end{enumerate}
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\end{frame}
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\begin{frame}{Matrizen}
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\vspace{-0.5cm}
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\begin{figure}
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\centering
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\includegraphics[width=0.65\columnwidth]{./images/matrices}
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\end{figure}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Matrizen}
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\framesubtitle{Erzeugen von Matrizen}
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\tiny
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\begin{lstlisting}
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>> a = [1 2 3; 4 5 6; 7 8 9]
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>> a =
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1 2 3
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4 5 6
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7 8 9
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>>
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>>
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>> b = ones(3,3,2);
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>> b
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b(:,:,1) =
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1 1 1
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1 1 1
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1 1 1
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b(:,:,2) =
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1 1 1
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1 1 1
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1 1 1
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\end{lstlisting}
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\end{frame}
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\begin{frame}
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\frametitle{Matrizen}
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\framesubtitle{Indexierung und Zugriff auf Inhalte}
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\vspace{-0.5cm}
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\begin{figure}
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\centering
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\includegraphics[width=0.9\columnwidth]{./images/matrixIndexing}
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\end{figure}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Matrizen}
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\framesubtitle{Indexierung}
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\tiny
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\begin{lstlisting}
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>> x = roundi(100, [3, 4, 5]); % 3-D Matrix mit Zufallszahlen
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>>
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>> x(1,1,1); % obere linke Ecke
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ans(1,1,1) =
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14
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>>
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>> x(1,1,:) % obere linke Ecke entlang der 3. Dimension
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ans(1,1,:) =
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14
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ans(:,:,2) =
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58
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ans(:,:,3) =
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4
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ans(:,:,4) =
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93
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ans(:,:,5) =
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56
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>>
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Matrizen}
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\framesubtitle{Grundlegende Operationen}
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\vspace{-0.5 cm}
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\tiny
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\begin{lstlisting}
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>> A = randi(10, [3, 3]) % 2-D Matrix
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A =
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3 8 2
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2 10 3
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10 7 1
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>> B = randi(10, [3, 3]) % dto
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B =
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2 1 7
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1 5 9
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5 10 5
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>>
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>> A*B % Matrix Multiplikation
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ans =
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24 63 103
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29 82 119
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32 55 138
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>>
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>> A.*B % Elementweise Multiplikation
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ans =
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6 8 14
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2 50 27
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50 70 5
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>>
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Matrizen}
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\framesubtitle{\"Ubungen}
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\begin{enumerate}
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\item Erstelle eine 5 x 5 Matrix die Zufallszahlen enth\"alt (nutze die
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MATLAB Funktion \verb+randn()+, benutze die Hilfe. Was macht sie?).
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\begin{enumerate}
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\item Gib alle Elemente der ersten Zeile aus.
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\item Gib alle Elemente der zweiten Spalte aus.
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\item Greife mit einem einzigen Kommando auf die Elemnte jeder
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2. Spalte zu und speichere die Daten in einer neuen Variable.
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\end{enumerate}
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\item Erstelle eine 3-D Matrix aus drei 2-D Matrizen. Benutze die
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\verb+cat()+ Funktion f\"ur diesen Zweck ( schaue in der Hilfe
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nach, wie sie benutzt wird).
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\begin{enumerate}
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\item Gib alle Elemente des ersten ``Blattes'' aus (Index 1 in der 3. Dimension).
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\end{enumerate}
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\item Erstelle eine 3-D Matrix mithilfe der Funktion
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\verb+ones()+. Multipliziere das erste Blatt mit 1, das zweite mit
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2, dritte mit 3 etc.
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\end{enumerate}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Matrizen}
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\framesubtitle{\"Ubungen}
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\begin{enumerate}\setcounter{enumi}{3}
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\item Erstelle folgende Variablen \verb+x = [1 5 9]+ and
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\verb+y = [7 1 5]+ und \verb+M = [3 1 6; 5 2 7]+. Welche der
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folgenden Operationen funktionieren? Wenn nicht, warum
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funktioneieren sie nicht? Teste Deine Vorhersagen.
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\begin{enumerate}
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\item \begin{verbatim} x + y \end{verbatim}
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\item \begin{verbatim} x * M \end{verbatim}
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\item \begin{verbatim} x + y' \end{verbatim}
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\item \begin{verbatim} M - [x y] \end{verbatim}
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\item \begin{verbatim} [x; y] \end{verbatim}
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\item \begin{verbatim} M - [x; y] \end{verbatim}
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\end{enumerate}
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\item Erzeuge eine 5 x 5 x 5 Matrix die mit ganzzahligen
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Zufallszahlen zwischen 0 und 100 gefuellt ist.
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\begin{enumerate}
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\item Berechne den Mittelwert aller Bl\"atter dieser Matrix (benutze \verb+mean()+, siehe Hilfe).
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\end{enumerate}
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\end{enumerate}
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\end{frame}
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\begin{frame}[plain]
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\huge{Boolesche Operationen}
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\end{frame}
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\begin{frame}
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\frametitle{Boolesche Operationen}
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\framesubtitle{Was ist das?}\pause
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\end{frame}
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\begin{frame}
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\frametitle{Boolesche Operationen}
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\framesubtitle{Logische Operatoren}
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\begin{table}[th]
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\begin{center}
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\begin{tabular}{c|c}
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\hline
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\textbf{Operator} & \textbf{Beschreibung} \\ \hline
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$\sim$ & logisches NOT\\
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$\&$ & logisches UND\\
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$|$ & logisches ODER\\
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$\&\&$ & short-circuit logical AND\\
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$\|$ & short-circuit logical OR\\
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\hline
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\end{tabular}
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\end{center}
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Das auschliessende ODER (XOR) ist nur als Funktion \verb+xor(A, B)+ verf\"ugbar.
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\end{table}
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\end{frame}
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\subsection{Relational operators}
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\begin{frame}
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\frametitle{Boolesche Operationen}
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\framesubtitle{Relationale Operatoren}
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\begin{table}[th]
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\begin{center}
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\begin{tabular}{c|c}
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\hline
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\textbf{Operator} & \textbf{Beschreibung} \\ \hline
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$<$ & kleiner als\\
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$>$ & gr\"o\{ss}er als \\
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$==$ & gleich \\
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$>=$ & gr\"o\{ss}er oder gleich\\
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$<=$ & kleiner oder gleich\\
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$\sim=$ & ungleich\\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\end{frame}
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\subsection{Logical operators}
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\subsection{Boolean operations}
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\begin{frame}[fragile]{Boolean operations}{Examples}
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\tiny
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\begin{lstlisting}[label=booleanListing1]
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>> x = [2 0 0 5 0] & [1 0 3 2 0]
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x =
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1 0 0 1 0
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>>
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>> ~([2 0 0 5 0] & [1 0 3 2 0])
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ans =
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0 1 1 0 1
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>> [2 0 0 5 0] | [1 0 3 2 0]
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ans =
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1 0 1 1 0
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\end{lstlisting}
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\end{frame}
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\subsection{Exercises}
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\begin{frame}[fragile]{Boolean operations}{Exercises}
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\vspace{-0.5cm}
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\begin{enumerate}
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\item Given are two vectors \verb+x = [1 5 2 8 9 0 1]+ and
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\verb+y = [5 2 2 6 0 0 2]+. Execute and explain the following commands.
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\begin{enumerate}
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\item \verb+x > y+
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\item \verb+y < x+
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\item \verb+x == y+
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\item \verb+x ~= y+
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\item \verb+x & ~y+
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\item \verb+x | y+
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\end{enumerate}
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\item One can use boolean operations for so called logical indexing:
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Given are \verb+x = 1:10+ and \verb+y = [3 1 5 6 8 2 9 4 7 0]+. Try
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to understand the following commands.
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\begin{enumerate}
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\item \verb+x( (y <= 2) )+
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\item \verb+x( (x > 2) | (y < 8) )+
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\item \verb+x( (x == 0) & (y == 0) )+
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\end{enumerate}
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\item Play around with boolean operations.
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\end{enumerate}
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\end{frame}
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\end{document}
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