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authorAndreas Müller <andreas.mueller@ost.ch>2021-07-28 08:07:03 +0200
committerGitHub <noreply@github.com>2021-07-28 08:07:03 +0200
commit9a8dcc1cf9aa0ddd918008e6f2421b48797c38ec (patch)
treeb5113260e190dfc7a94e4298bf6eb5ae21c08344 /buch/papers/multiplikation/images
parentMerge pull request #50 from paschost/patch-1 (diff)
parentadded first part of paper and code (diff)
downloadSeminarMatrizen-9a8dcc1cf9aa0ddd918008e6f2421b48797c38ec.tar.gz
SeminarMatrizen-9a8dcc1cf9aa0ddd918008e6f2421b48797c38ec.zip
Merge pull request #52 from Nunigan/master
Multiplikation #1
Diffstat (limited to '')
-rw-r--r--buch/papers/multiplikation/images/bigo.pdfbin0 -> 24288 bytes
-rw-r--r--buch/papers/multiplikation/images/bigo.tex107
-rw-r--r--buch/papers/multiplikation/images/mm_visualisation.pdfbin0 -> 21665 bytes
-rw-r--r--buch/papers/multiplikation/images/mm_visualisation.tex45
-rw-r--r--buch/papers/multiplikation/images/strassen.pdfbin0 -> 15850 bytes
-rw-r--r--buch/papers/multiplikation/images/strassen.tex140
6 files changed, 292 insertions, 0 deletions
diff --git a/buch/papers/multiplikation/images/bigo.pdf b/buch/papers/multiplikation/images/bigo.pdf
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diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex
new file mode 100644
index 0000000..e3293e4
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+++ b/buch/papers/multiplikation/images/bigo.tex
@@ -0,0 +1,107 @@
+\documentclass[border=10pt,varwidth]{standalone}
+\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{times}
+\usepackage{geometry}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{mathrsfs}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\usepackage{lipsum}
+\usepackage{amscd}
+\usepackage{graphicx}
+\usepackage{fancyhdr}
+\usepackage{textcomp}
+\usepackage{pgfplots}
+\usepackage{txfonts}
+\usepackage[all]{xy}
+\usepackage{paralist}
+\usepackage[colorlinks=true]{hyperref}
+\usepackage{array}
+\usepackage{tikz}
+\usepackage{slashed}
+\usepackage{pdfpages}
+\usepackage{cite}
+\usepackage{url}
+\usepackage{amsmath,amsfonts,amssymb}
+\usepackage{tikz}
+\usetikzlibrary{arrows,matrix,positioning}
+\usetikzlibrary{overlay-beamer-styles}
+\usetikzlibrary{matrix.skeleton}
+\usetikzlibrary{automata,positioning}
+\usetikzlibrary{decorations.text}
+\usepackage{listings}
+\usepackage{multirow}
+\usepackage{color}
+
+\begin{document}
+
+\begin{tikzpicture}
+\begin{axis}[
+ axis lines = left,
+ xlabel = $n$ (Data Input),
+ ylabel = {$t$ (time)},
+ legend pos=north east,
+ very thick,
+ ymax = 500,
+ yticklabels=\empty,
+ xticklabels=\empty,
+ scale only axis=true,
+ width=12cm, height=6cm,
+ ]
+\addplot [
+ domain= 1:20,
+ samples=100,
+ color=red,
+]
+{1};
+\addlegendentry{$\mathcal{O}(1)$}
+\addplot [
+ domain= 1:20,
+ samples=100,
+ color=green,
+]
+{x};
+\addlegendentry{$\mathcal{O}(n)$}
+\addplot [
+ domain= 1:20,
+ samples=100,
+ color=blue,
+]
+{x^2};
+\addlegendentry{$\mathcal{O}(n^2)$}
+\addplot [
+ domain= 1:10,
+ samples=100,
+ color=purple,
+]
+{x^3};
+\addlegendentry{$\mathcal{O}(n^3)$}
+\addplot [
+ domain= 1:10,
+ samples=100,
+ color=black,
+]
+{exp(x)};
+\addlegendentry{$\mathcal{O}(e^n)$}
+\addplot [
+ domain= 1:20,
+ samples=100,
+ color=orange,
+]
+{log2(x)};
+\addlegendentry{$\mathcal{O}(\log n)$}
+
+\addplot [
+ domain= 1:20,
+ samples=100,
+ color=gray,
+]
+{x*log2(x)};
+\addlegendentry{$\mathcal{O}(n \log n)$}
+\end{axis}
+\end{tikzpicture}
+
+\end{document}
diff --git a/buch/papers/multiplikation/images/mm_visualisation.pdf b/buch/papers/multiplikation/images/mm_visualisation.pdf
new file mode 100644
index 0000000..9309df1
--- /dev/null
+++ b/buch/papers/multiplikation/images/mm_visualisation.pdf
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diff --git a/buch/papers/multiplikation/images/mm_visualisation.tex b/buch/papers/multiplikation/images/mm_visualisation.tex
new file mode 100644
index 0000000..6e8f789
--- /dev/null
+++ b/buch/papers/multiplikation/images/mm_visualisation.tex
@@ -0,0 +1,45 @@
+
+ \begin{tikzpicture}[ampersand replacement=\&]
+
+ \matrix (A)[matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}] at (0,0)
+ {
+ A_{1,1} \& \cdots \& A_{1,k} \& \cdots \& A_{1,n} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ A_{i,1} \& \cdots \& A_{i,k} \& \cdots \& A_{i,n} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ A_{m,1} \& \cdots \& A_{m,k} \& \cdots \& A_{m,n} \\
+ };
+
+ \node [right=0.1 of A] (mul) {$\cdot$};
+
+
+ \matrix (B)[right=0.1 of mul, matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}]
+ {
+ B_{1,1} \& \cdots \& B_{1,j} \& \cdots \& B_{1,p} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ B_{k,1} \& \cdots \& B_{k,j} \& \cdots \& B_{k,p} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ B_{n,1} \& \cdots \& B_{n,j} \& \cdots \& B_{n,p} \\
+ };
+
+ \node [right=0.1 of B] (eq) {$=$};
+
+ \matrix (C)[right=0.1 of eq, matrix of math nodes, label skeleton, left delimiter=[,right delimiter={]}]
+ {
+ C_{1,1} \& \cdots \& C_{1,j} \& \cdots \& C_{1,p} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ C_{i,1} \& \cdots \& C_{i,j} \& \cdots \& C_{i,p} \\
+ \vdots \& \& \vdots \& \& \vdots \\
+ C_{m,1} \& \cdots \& C_{m,j} \& \cdots \& C_{m,p} \\
+ };
+
+
+ \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=green, fit=(A-3-1)(A-3-5)] {};
+ \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=blue, fit=(B-1-3)(B-5-3)] {};
+ \node[opacity=0.5, rounded corners=2pt, inner sep=-1pt, fill=red, fit=(C-3-3)] {};
+
+
+ \end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/papers/multiplikation/images/strassen.pdf b/buch/papers/multiplikation/images/strassen.pdf
new file mode 100644
index 0000000..9899dcb
--- /dev/null
+++ b/buch/papers/multiplikation/images/strassen.pdf
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diff --git a/buch/papers/multiplikation/images/strassen.tex b/buch/papers/multiplikation/images/strassen.tex
new file mode 100644
index 0000000..797772b
--- /dev/null
+++ b/buch/papers/multiplikation/images/strassen.tex
@@ -0,0 +1,140 @@
+\documentclass[border=10pt]{standalone}
+\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{times}
+\usepackage{geometry}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{mathrsfs}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\usepackage{lipsum}
+\usepackage{amscd}
+\usepackage{graphicx}
+\usepackage{fancyhdr}
+\usepackage{textcomp}
+\usepackage{pgfplots}
+\usepackage{txfonts}
+\usepackage[all]{xy}
+\usepackage{paralist}
+\usepackage[colorlinks=true]{hyperref}
+\usepackage{array}
+\usepackage{tikz}
+\usepackage{slashed}
+\usepackage{pdfpages}
+\usepackage{cite}
+\usepackage{url}
+\usepackage{amsmath,amsfonts,amssymb}
+\usepackage{tikz}
+\usetikzlibrary{arrows,matrix,positioning}
+\usetikzlibrary{overlay-beamer-styles}
+\usetikzlibrary{matrix.skeleton}
+\usetikzlibrary{automata,positioning}
+\usetikzlibrary{decorations.text}
+\usepackage{listings}
+\usepackage{multirow}
+\usepackage{color}
+
+\begin{document}
+
+\begin{tikzpicture}[ampersand replacement=\&]
+
+\foreach \i in {1,...,4}
+{
+ \small{
+ \matrix (X\i)[matrix of math nodes,nodes in empty cells,
+ nodes = {draw, minimum size=10mm,
+ anchor=center,
+ inner sep=0pt, outer sep=0pt},
+ column sep=-\pgflinewidth,
+ row sep=-\pgflinewidth,
+ ] at (0,-\i*5)
+ {
+ A_{11}B_{11} \& A_{12}B_{11} \& A_{21}B_{11} \& A_{22}B_{11} \\
+ A_{11}B_{21} \& A_{12}B_{21} \& A_{21}B_{21} \& A_{22}B_{21} \\
+ A_{11}B_{11} \& A_{12}B_{12} \& A_{21}B_{12} \& A_{22}B_{12} \\
+ A_{11}B_{22} \& A_{12}B_{22} \& A_{21}B_{22} \& A_{22}B_{22} \\
+ };}
+
+ \foreach \j in {1,...,7}
+ {
+ \matrix(M\i\j)[matrix of math nodes,nodes in empty cells,
+ nodes = {draw, minimum size=10mm,
+ anchor=center,
+ inner sep=0pt, outer sep=0pt},
+ column sep=-\pgflinewidth,
+ row sep=-\pgflinewidth,
+ ] at (\j*5,-\i*5)
+ {
+ \& \& \& \\
+ \& \& \& \\
+ \& \& \& \\
+ \& \& \& \\
+ };
+ }
+}
+
+\huge{
+ \node at (-3,-20) {$C_{22}=$};
+ \node at (-3,-15) {$C_{21}=$} ;
+ \node at (-3,-10) {$C_{12}=$} ;
+ \node at (-3,-5) {$C_{11}=$} ;
+
+ \node at (5,-2) {I};
+ \node at (10,-2) {II};
+ \node at (15,-2) {III};
+ \node at (20,-2) {IV};
+ \node at (25,-2) {V};
+ \node at (30,-2) {VI};
+ \node at (35,-2) {VII};
+}
+
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X1-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X2-4-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X3-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-3-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-4-4)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M43-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M43-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-3-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-3-1)] {};
+\end{tikzpicture}
+
+\end{document}