From dc1bb1d760c10ccdde5da9a45b3328d987a3bf28 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 13 Feb 2021 16:34:50 +0100 Subject: rref stuff --- buch/chapters/10-vektorenmatrizen/images/Makefile | 5 +- buch/chapters/10-vektorenmatrizen/images/rref.pdf | Bin 0 -> 15112 bytes buch/chapters/10-vektorenmatrizen/images/rref.tex | 253 ++++++++++++++++++++++ 3 files changed, 257 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/10-vektorenmatrizen/images/rref.pdf create mode 100644 buch/chapters/10-vektorenmatrizen/images/rref.tex (limited to 'buch/chapters/10-vektorenmatrizen/images') diff --git a/buch/chapters/10-vektorenmatrizen/images/Makefile b/buch/chapters/10-vektorenmatrizen/images/Makefile index 664dff5..2c94e8a 100644 --- a/buch/chapters/10-vektorenmatrizen/images/Makefile +++ b/buch/chapters/10-vektorenmatrizen/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: ideale.pdf gausszahlen.pdf strukturen.pdf +all: ideale.pdf gausszahlen.pdf strukturen.pdf rref.pdf ideale.pdf: ideale.tex pdflatex ideale.tex @@ -13,3 +13,6 @@ gausszahlen.pdf: gausszahlen.tex strukturen.pdf: strukturen.tex pdflatex strukturen.tex + +rref.pdf: rref.tex + pdflatex rref.tex diff --git a/buch/chapters/10-vektorenmatrizen/images/rref.pdf b/buch/chapters/10-vektorenmatrizen/images/rref.pdf new file mode 100644 index 0000000..56fbfee Binary files /dev/null and b/buch/chapters/10-vektorenmatrizen/images/rref.pdf differ diff --git a/buch/chapters/10-vektorenmatrizen/images/rref.tex b/buch/chapters/10-vektorenmatrizen/images/rref.tex new file mode 100644 index 0000000..9b2bf50 --- /dev/null +++ b/buch/chapters/10-vektorenmatrizen/images/rref.tex @@ -0,0 +1,253 @@ +% +% rref.tex -- Visualisierung des Gauss-Algorithmus +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{0.21} +\def\r{0.4} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\pivot#1#2{ + \fill[color=red!20] ({#1-0.5},{-#2+0.5}) circle[radius=\r]; + \draw[color=red] ({#1-0.5},{-#2+0.5}) circle[radius=\r]; +} + +\def\spalteoben#1#2#3{ + \fill[color=blue!20] ({(#1)-0.5+\r},{-(#3)}) + -- ({(#1)-0.5+\r},{-(#2)+0.5}) arc (0:180:\r) + -- ({(#1)-0.5-\r},{-(#3)}) -- cycle; + \draw[color=blue] ({(#1)-0.5+\r},{-(#3)}) + -- ({(#1)-0.5+\r},{-(#2)+0.5}) arc (0:180:\r) + -- ({(#1)-0.5-\r},{-(#3)}); +} + +\def\spalteunten#1#2#3{ + \fill[color=blue!20] ({(#1)-0.5-\r},{-(#2)+1}) + -- ({(#1)-0.5-\r},{-(#3)+0.5}) arc (-180:0:\r) + -- ({(#1)-0.5+\r},{-(#2)+1}); + \draw[color=blue] ({(#1)-0.5-\r},{-(#2)+1}) + -- ({(#1)-0.5-\r},{-(#3)+0.5}) arc (-180:0:\r) + -- ({(#1)-0.5+\r},{-(#2)+1}); +} + +\def\fuellung{ + \fill[color=gray!50] (0,0) rectangle (8,-6); +} +\def\rahmen{ + \draw (0,0) rectangle (8,-6); + \draw (7,0) -- (7,-6); +} + +\def\eins#1#2{ + \fill[color=gray] ({#1-1},{-#2}) rectangle ({#1},{-#2+1}); +} + +\def\null#1#2#3{ + \fill[color=white] ({#1-1-0.01},{-#3-0.01}) + rectangle ({#1+0.01},{-#2+1+0.01}); +} + +\fill[color=darkgreen!20] (-1.0,-10.81) rectangle (67.0,5); +\fill[color=orange!20] (-1.0,-27) rectangle (67.0,-11.94); + +\node at (33,2) [above] {Vorwärtsreduktion}; +\node at (33,-24) [below] {Rückwärtseinsetzen}; + +\draw[->] (9,-3.375)--(11,-3.375); +\draw[->] (21,-3.375)--(23,-3.375); +\draw[->] (33,-3.375)--(35,-3.375); +\draw[->] (45,-3.375)--(47,-3.375); + +\draw[->] (57,-3.375) .. controls (62,-3.375) .. (62,-7.5); +\draw[->] (62,-15.375) .. controls (62,-19.375) .. (57,-19.375); + +\draw[<-] (9,-19.375)--(11,-19.375); +\draw[<-] (21,-19.375)--(23,-19.375); +\draw[<-] (33,-19.375)--(35,-19.375); +\draw[<-] (45,-19.375)--(47,-19.375); + +\begin{scope}[xshift=-0.5cm,scale=1.125] +\fuellung +\pivot{1}{1} +\spalteoben{1}{2}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=11.5cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\pivot{2}{2} +\spalteoben{2}{3}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=23.54cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\pivot{3}{3} +\spalteoben{3}{4}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=35.5cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\pivot{5}{4} +\spalteoben{5}{5}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=47.5cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\pivot{7}{5} +\spalteoben{7}{6}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=57.5cm,yshift=-8cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\rahmen +\end{scope} + +\begin{scope}[xshift=47.5cm,yshift=-16cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\spalteunten{7}{1}{4} +\rahmen +\end{scope} + +\begin{scope}[xshift=35.5cm,yshift=-16cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\null{7}{1}{4} +\spalteunten{5}{1}{3} +\rahmen +\end{scope} + +\begin{scope}[xshift=23.5cm,yshift=-16cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\null{7}{1}{4} +\null{5}{1}{3} +\spalteunten{3}{1}{2} +\rahmen +\end{scope} + +\begin{scope}[xshift=11.5cm,yshift=-16cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\null{7}{1}{4} +\null{5}{1}{3} +\null{3}{1}{2} +\spalteunten{2}{1}{1} +\rahmen +\end{scope} + +\begin{scope}[xshift=-0.5cm,yshift=-16cm,scale=1.125] +\fuellung +\eins{1}{1} +\null{1}{2}{6} +\eins{2}{2} +\null{2}{3}{6} +\eins{3}{3} +\null{3}{4}{6} +\null{4}{4}{6} +\eins{5}{4} +\null{5}{5}{6} +\null{6}{5}{6} +\eins{7}{5} +\null{7}{6}{6} +\null{7}{1}{4} +\null{5}{1}{3} +\null{3}{1}{2} +\null{2}{1}{1} +\rahmen +\end{scope} + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1