update

14 files changed, 127 insertions, 38 deletions

diff --git a/buch/papers/multiplikation/code/MM.py b/buch/papers/multiplikation/code/MM.py
index 626b82d..352771f 100644
--- a/buch/papers/multiplikation/code/MM.py
+++ b/buch/papers/multiplikation/code/MM.py
@@ -174,10 +174,11 @@ def test_perfomance(n):
     plt.plot(n, t_mm_strassen, label='Strassen', lw=5)
     plt.plot(n, t_wino, label='Winograd', lw=5)
     plt.plot(n, t_np, label='NumPy A@B', lw=5)
+    plt.xscale('log', base=2)
     plt.legend()
     plt.xlabel("n")
     plt.ylabel("time (s)")
-    plt.grid(True)
+    plt.grid(True, which="both", ls="-")
     plt.tight_layout()
     # plt.yscale('log')
     plt.legend(fontsize=19)
@@ -198,7 +199,7 @@ def plot(num):
     plt.plot(n, t_mm, label='3 For Loops', lw=5)
     plt.plot(n, t_mm_dc, label='Divide and Conquer', lw=5)
     plt.plot(n, t_mm_strassen, label='Strassen', lw=5)
-    # plt.plot(n, t_wino, label='Winograd', lw=5)
+    plt.plot(n, t_wino, label='Winograd', lw=5)
     plt.plot(n, t_np, label='NumPy A@B', lw=5)
     plt.legend()
     plt.xlabel("n")
@@ -275,22 +276,22 @@ def plot_c_res(ave, num):
 
 # test%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 if __name__ == '__main__':
-    plot_c_res(1, 4096)
+    # plot_c_res(1, 4096)
 
  
     # plot(8)    
-    # n = np.logspace(1,10,10,base=2,dtype=(np.int))
+    n = np.logspace(1,8,8,base=2,dtype=(np.int))
     # n = np.arange(1,50,2)  
-    A = np.random.randint(-10, 10, (5,3))
-    B = np.random.randint(-10, 10, (3,5))
+    # A = np.random.randint(-10, 6, (5,3))
+    # B = np.random.randint(-10, 6, (3,5))
 
-    C = winograd2(A, B)
-    C_test = A@B
-    print(C)
-    print(C_test)
+    # C = winograd2(A, B)
+    # C_test = A@B
+    # print(C)
+    # print(C_test)
     # print(np.equal(C, C_test))
 
-    # t_np = test_perfomance(n)
+    t_np = test_perfomance(n)
     # C = strassen(A, B)
     # C_test = A@B
     
diff --git a/buch/papers/multiplikation/code/meas_1024.pdf b/buch/papers/multiplikation/code/meas_1024.pdf
index fd0a108..7b7a133 100644
--- a/buch/papers/multiplikation/code/meas_1024.pdf
+++ b/buch/papers/multiplikation/code/meas_1024.pdf
diff --git a/buch/papers/multiplikation/code/meas_1024.txt b/buch/papers/multiplikation/code/meas_1024.txt
index c5ce619..ab507a2 100644
--- a/buch/papers/multiplikation/code/meas_1024.txt
+++ b/buch/papers/multiplikation/code/meas_1024.txt
@@ -1,6 +1,6 @@
 2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 2.560000000000000000e+02 5.120000000000000000e+02 1.024000000000000000e+03
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-6.675720214843750000e-06 7.200241088867187500e-05 5.540847778320312500e-04 3.144979476928710938e-03 2.545046806335449219e-02 2.083067893981933594e-01 1.659256219863891602e+00 1.319160294532775879e+01 1.046767003536224365e+02 9.679818902015686035e+02
-1.668930053710937500e-05 1.628398895263671875e-04 7.648468017578125000e-04 4.426956176757812500e-03 2.922415733337402344e-02 1.800994873046875000e-01 1.286747694015502930e+00 9.412034273147583008e+00 6.263725924491882324e+01 4.427414393424987793e+02
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+2.789497375488281250e-05 1.049041748046875000e-04 5.528926849365234375e-04 4.555702209472656250e-03 1.871442794799804688e-02 1.530685424804687500e-01 1.194762229919433594e+00 8.298985958099365234e+00 6.836994743347167969e+01 5.373736469745635986e+02
+1.835823059082031250e-05 7.867813110351562500e-06 1.001358032226562500e-05 5.412101745605468750e-05 4.267692565917968750e-05 1.184940338134765625e-04 2.441406250000000000e-04 6.957054138183593750e-04 2.217054367065429688e-03 1.880884170532226562e-02
diff --git a/buch/papers/multiplikation/code/meas_128.pdf b/buch/papers/multiplikation/code/meas_128.pdf
index ed1ec63..c54648f 100644
--- a/buch/papers/multiplikation/code/meas_128.pdf
+++ b/buch/papers/multiplikation/code/meas_128.pdf
diff --git a/buch/papers/multiplikation/code/meas_128.txt b/buch/papers/multiplikation/code/meas_128.txt
index 976bbdf..f3a5beb 100644
--- a/buch/papers/multiplikation/code/meas_128.txt
+++ b/buch/papers/multiplikation/code/meas_128.txt
@@ -1,6 +1,6 @@
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-6.675720214843750000e-06 1.251697540283203125e-04 4.818439483642578125e-04 3.490447998046875000e-03 2.465796470642089844e-02 2.014584541320800781e-01 1.630620479583740234e+00
-2.408027648925781250e-05 2.126693725585937500e-04 1.172780990600585938e-03 4.364490509033203125e-03 3.148293495178222656e-02 2.010228633880615234e-01 1.429297924041748047e+00
-2.932548522949218750e-05 1.466274261474609375e-04 4.270076751708984375e-04 2.837419509887695312e-03 1.723575592041015625e-02 1.308519840240478516e-01 1.015527009963989258e+00
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+1.239776611328125000e-05 5.507469177246093750e-05 3.888607025146484375e-04 2.762079238891601562e-03 2.097773551940917969e-02 1.672370433807373047e-01 1.410297393798828125e+00
+5.483627319335937500e-06 5.888938903808593750e-05 3.871917724609375000e-04 3.364324569702148438e-03 2.481031417846679688e-02 2.047052383422851562e-01 1.712310314178466797e+00
+1.358985900878906250e-05 1.189708709716796875e-04 6.430149078369140625e-04 5.586385726928710938e-03 3.101944923400878906e-02 1.874091625213623047e-01 1.327976465225219727e+00
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diff --git a/buch/papers/multiplikation/code/meas_256.pdf b/buch/papers/multiplikation/code/meas_256.pdf
index 5f049dc..4ca7102 100644
--- a/buch/papers/multiplikation/code/meas_256.pdf
+++ b/buch/papers/multiplikation/code/meas_256.pdf
diff --git a/buch/papers/multiplikation/code/meas_256.txt b/buch/papers/multiplikation/code/meas_256.txt
index 15035c6..2ca4447 100644
--- a/buch/papers/multiplikation/code/meas_256.txt
+++ b/buch/papers/multiplikation/code/meas_256.txt
@@ -1,6 +1,6 @@
 2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 6.400000000000000000e+01 1.280000000000000000e+02 2.560000000000000000e+02
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diff --git a/buch/papers/multiplikation/code/meas_32.pdf b/buch/papers/multiplikation/code/meas_32.pdf
index 94c3731..b926095 100644
--- a/buch/papers/multiplikation/code/meas_32.pdf
+++ b/buch/papers/multiplikation/code/meas_32.pdf
diff --git a/buch/papers/multiplikation/code/meas_32.txt b/buch/papers/multiplikation/code/meas_32.txt
index afdb6d5..0fdc18d 100644
--- a/buch/papers/multiplikation/code/meas_32.txt
+++ b/buch/papers/multiplikation/code/meas_32.txt
@@ -1,6 +1,6 @@
 2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01
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diff --git a/buch/papers/multiplikation/code/meas_64.pdf b/buch/papers/multiplikation/code/meas_64.pdf
index 3a90949..92af29b 100644
--- a/buch/papers/multiplikation/code/meas_64.pdf
+++ b/buch/papers/multiplikation/code/meas_64.pdf
diff --git a/buch/papers/multiplikation/code/meas_64.txt b/buch/papers/multiplikation/code/meas_64.txt
index ae6ff9b..b4fc7a1 100644
--- a/buch/papers/multiplikation/code/meas_64.txt
+++ b/buch/papers/multiplikation/code/meas_64.txt
@@ -1,6 +1,6 @@
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+3.504753112792968750e-05 1.106262207031250000e-04 4.322528839111328125e-04 2.696514129638671875e-03 2.188420295715332031e-02 1.477701663970947266e-01
+3.218650817871093750e-05 1.144409179687500000e-05 7.390975952148437500e-06 4.625320434570312500e-05 3.814697265625000000e-05 5.435943603515625000e-05
diff --git a/buch/papers/multiplikation/loesungsmethoden.tex b/buch/papers/multiplikation/loesungsmethoden.tex
index 7ee0b6e..0f6aa6b 100755
--- a/buch/papers/multiplikation/loesungsmethoden.tex
+++ b/buch/papers/multiplikation/loesungsmethoden.tex
@@ -295,9 +295,58 @@ Die Implementation kann Algorithmus \ref{multiplikation:alg:winograd} entnommen
 	\end{algorithmic}
 \end{algorithm}
 
-\subsection{Weitere Algorithmen}
+\subsection{Basic Linear Algebra Subprograms (BLAS)}
+
+die gebr\"uchlichen Methode f\"ur die Anwendung einer optimierten Matrizenmultiplikation ist die Verwendung einer Subrutine aus den \textit{Basic Linear Algebra Subprograms (BLAS)}  \cite{multiplikation:BLAS}.
+Die meisten Numerischen Bibliotheken von High-Level Skriptsprachen wie \texttt{Matlab}, \texttt{NumPy (Python)}, \texttt{GNU Octave} oder \texttt{Mathematica} ben\"utzen eine Form von \textit{BLAS}. 
+
+\textit{BLAS} sind dabei in drei unterschiedliche Levels aufgeteilt.
+
+\begin{itemize}
+	\item Level 1
+	\begin{itemize}
+		\item Operationen der Art: $\mathbf{y} \leftarrow \alpha \mathbf{x}+\mathbf{y}$
+		\item Dieses Level hat $\mathcal{O}(n)$ karakteristik 
+	\end{itemize}
+	\item Level 2
+	\begin{itemize}
+		\item Operationen der Art: $\mathbf{y} \leftarrow \alpha \mathbf{A}\mathbf{x}+\beta  \mathbf{y}$
+		\item Dieses Level hat $\mathcal{O}\left(n^2\right)$ karakteristik 
+		\end{itemize}
+		\item Level 3
+		\begin{itemize}
+			\item Operationen der Art: $\mathbf{C} \leftarrow \alpha \mathbf{A}\mathbf{B}+\beta\mathbf{C}$
+			\item Dieses Level hat $\mathcal{O}\left(n^3\right)$ karakteristik 
+			\end{itemize}
+\end{itemize}
+
+Die \textit{BLAS} sind auf die modernen Computer Prozessoren optimiert und k\"onnen dank einer ausgek\"ugelter Verwedung der Speicher Architektur zur erheblichen Leistungoprimierung f\"uhren.
+
+
+\subsubsection{General Matrix Multiplication (GEMM)}
+
+Die \textit{Double-GEMM} ist in \cite{multiplikation:DGEMM} definiert als:
+
+\textit{DGEMM  performs one of the matrix-matrix operations}
+$$
+ C := \alpha \cdot op( A )\cdot op( B ) + \beta \cdot C,
+ $$
+ \textit{where  op( X ) is one of}
+$$
+op( X ) = X  \quad \text{ or } \quad  op( X ) = X^T,
+$$
+ \textit{alpha and beta are scalars, and A, B and C are matrices, with op( A )
+ an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+ }
+
+Die Implementaion von $\alpha\mathbf{A}\mathbf{B} + \beta \mathbf{C} = \mathbf{C}$, wobei  $\alpha = 1.0$ und $\beta = 0.0$ in der \texttt{C}-Version von \textit{BLAS}, ist als
+\begin{lstlisting}[style=multiplikationC]
+cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
+      m, n, k, 1, A, m , B, k, 0, C, m);
+\end{lstlisting}
+definiert.
+
 
-\textcolor{red}{TODO: BLAS}
 
 \section{Implementation}
 \rhead{Implementation}
diff --git a/buch/papers/multiplikation/main.tex b/buch/papers/multiplikation/main.tex
index 8d0a8df..fb1908e 100755
--- a/buch/papers/multiplikation/main.tex
+++ b/buch/papers/multiplikation/main.tex
@@ -4,6 +4,28 @@
 %
 % (c) 2021 Hochschule Rapperswil
 %
+\definecolor{mygreen}{RGB}{28,172,0} % color values Red, Green, Blue
+\definecolor{mylilas}{RGB}{170,55,241}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\lstdefinestyle{multiplikationC}{
+  numbers=left,
+  belowcaptionskip=1\baselineskip,
+  breaklines=true,
+  frame=l,
+  framerule=0pt,
+  framesep=-1pt,
+  xleftmargin=1em,
+  language=C,
+  showstringspaces=false,
+  basicstyle=\ttfamily,
+  keywordstyle=\bfseries\color{green!40!black},
+  commentstyle=\itshape\color{purple!40!black},
+  identifierstyle=\color{blue},
+  stringstyle=\color{red},
+  numberstyle=\ttfamily\tiny,
+  backgroundcolor=\color{backcolour}
+}
+
 \chapter{Schnelle Matrizen Multiplikation\label{chapter:multiplikation}}
 \lhead{FMM}
 \begin{refsection}
diff --git a/buch/papers/multiplikation/references.bib b/buch/papers/multiplikation/references.bib
index 63cb976..8815386 100755
--- a/buch/papers/multiplikation/references.bib
+++ b/buch/papers/multiplikation/references.bib
@@ -83,3 +83,20 @@
 	day = {28}
 }
 
+@online{multiplikation:BLAS,
+	title = {BLAS (Basic Linear Algebra Subprograms)},
+	url = {http://www.netlib.org/blas/},
+	date = {2021-08-01},
+	year = {2021},
+	month = {8},
+	day = {01}
+}
+
+@online{multiplikation:DGEMM,
+	title = {DGEMM},
+	url = {http://www.netlib.org/lapack/explore-html/d1/d54/group__double__blas__level3_gaeda3cbd99c8fb834a60a6412878226e1.html#gaeda3cbd99c8fb834a60a6412878226e1},
+	date = {2021-08-01},
+	year = {2021},
+	month = {8},
+	day = {01}
+}