diff options
Diffstat (limited to 'buch/chapters/070-orthogonalitaet/images/weight.tex')
| -rw-r--r-- | buch/chapters/070-orthogonalitaet/images/weight.tex | 174 |
1 files changed, 174 insertions, 0 deletions
diff --git a/buch/chapters/070-orthogonalitaet/images/weight.tex b/buch/chapters/070-orthogonalitaet/images/weight.tex new file mode 100644 index 0000000..796f09a --- /dev/null +++ b/buch/chapters/070-orthogonalitaet/images/weight.tex @@ -0,0 +1,174 @@ +% +% weight.tex -- Einfluss der Gewichtsfunktion auf die möglichen Funktionen +% +% (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} +\begin{document} +\def\skala{6} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{hell}{rgb}{0.4,0.4,1} + +\xdef\sfour{0.16} +\xdef\sthree{0.20} +\xdef\stwo{0.27} +\xdef\sone{0.45} + +\begin{scope} + \clip (-1,-1) rectangle (1,1); + + \xdef\s{0.16} + \fill[color=blue!40] + plot[domain=0.7:0.99,samples=20] + ({\x},{\s*exp(-0.48*ln(1-\x))}) + -- (1,1) -- (1,-1) -- + plot[domain=0.99:0.7,samples=20] + ({\x},{-\s*exp(-0.48*ln(1-\x))}) + -- cycle; + + \xdef\s{0.20} + \fill[color=blue!40] + plot[domain=0.033:0.33,samples=20] + ({\x},{\s*exp(-0.28*ln(1/3-\x))}) + -- ({1/3},1) -- + plot[domain=0.34:0.6333,samples=20] + ({\x},{\s*exp(-0.28*ln(\x-1/3))}) + -- + plot[domain=0.6333:0.34,samples=20] + ({\x},{-\s*exp(-0.28*ln(\x-1/3))}) + -- ({1/3},-1) -- + plot[domain=0.333:0.033,samples=20] + ({\x},{-\s*exp(-0.28*ln(1/3-\x))}) + -- cycle; + + \xdef\s{0.27} + \fill[color=blue!40] + (-0.6333,-\s) rectangle (-0.0333,\s); + + \xdef\s{0.45} + \fill[color=blue!40] + (-1,0) + -- + plot[domain=-0.99:-0.7,samples=100] + ({\x},{\s*exp(0.48*ln(1+\x))}) + -- + plot[domain=-0.7:-0.99,samples=100] + ({\x},{-\s*exp(0.48*ln(1+\x))}) + -- + cycle; + +\end{scope} + +\def\rechteck#1#2{ + \fill[color=hell!#1] + ({#2/300},1) rectangle ({(#2+1.1)/300},-1); +} + +\def\verlauf{ + \foreach\x in {0,1,...,100.1}{ + \rechteck{\x}{\x} + \rechteck{\x}{-\x} + } +} + +\def\rand{ + plot[domain=0.7:0.99,samples=20] + ({\x},{\sfour*exp(-0.48*ln(1-\x))}) + -- (1,1) -- (1,-1) -- + plot[domain=0.99:0.7,samples=20] + ({\x},{-\sfour*exp(-0.48*ln(1-\x))}) + -- + plot[domain=0.6333:0.34,samples=20] + ({\x},{-\sthree*exp(-0.28*ln(\x-1/3))}) + -- ({1/3},-1) -- + plot[domain=0.333:0.033,samples=20] + ({\x},{-\sthree*exp(-0.28*ln(1/3-\x))}) + -- + (-0.0333,-\stwo) -- (-0.6333,-\stwo) + -- + plot[domain=-0.7:-0.998,samples=100] + ({\x},{-\sone*exp(0.48*ln(1+\x))}) + -- + (-1,0) + -- + plot[domain=-0.998:-0.7,samples=100] + ({\x},{\sone*exp(0.48*ln(1+\x))}) + -- + (-0.6333,\stwo) -- (-0.0333,\stwo) + -- + plot[domain=0.033:0.33,samples=20] + ({\x},{\sthree*exp(-0.28*ln(1/3-\x))}) + -- ({1/3},1) -- + plot[domain=0.34:0.6333,samples=20] + ({\x},{\sthree*exp(-0.28*ln(\x-1/3))}) + -- cycle; +} + +\begin{scope} + \clip (-1,-1) rectangle (1,1); + \begin{scope} + \clip \rand; + \fill[left color=hell,right color=white] + (-1,-1) rectangle (-0.6666,1); + \fill[left color=white,right color=hell] + (-0.6666,-1) rectangle (-0.3333,1); + \fill[left color=hell,right color=white] + (-0.3333,-1) rectangle (0,1); + \fill[left color=white,right color=hell] + (0,-1) rectangle (0.3333,1); + \fill[left color=hell,right color=white] + (0.3333,-1) rectangle (0.6666,1); + \fill[left color=white,right color=hell] + (0.6666,-1) rectangle (1,1); + \end{scope} + \draw[color=white,line width=0.5pt] \rand; + \draw[color=white,line width=0.5pt] ({-2/3},-1) -- ({-2/3},1); + \draw[color=white,line width=0.5pt] ({2/3},-1) -- ({2/3},1); +\end{scope} + +\draw[->] (-1.1,0) -- (1.1,0) coordinate[label={$x$}]; +\draw[->] (0,-1.1) -- (0,1.1) coordinate[label={right:$y$}]; + +\begin{scope} + \clip (-1,-1) rectangle (1,1); + + \input{weightfunction.tex} + +\end{scope} + +\draw[line width=0.2pt] (-1,-1) -- (-1,1); +\draw[line width=0.2pt] ({-1/3},-1) -- ({-1/3},1); + +\draw ({-1/3},{-0.1/\skala}) -- ({-1/3},{0.1/\skala}); +\draw ({1/3},{-0.1/\skala}) -- ({1/3},{0.1/\skala}); +\draw (1,{-0.1/\skala}) -- (1,{0.1/\skala}); + +\node at (-1,0) [below left] {$-1$}; +\node at (1,0) [below right] {$1$}; + +\def\marke#1#2#3{ + \fill[color=white,opacity=0.7] + ({#1-0.03},{#2-0.12}) + rectangle + ({#1+0.03},{#2+0.12}); +} + +\marke{-1}{0.2}{} +\node at (-1,0.2) [rotate=90] {$\alpha=-1.9$}; +\marke{-1/3}{0.2}{} +\node at ({-1/3},0.2) [rotate=90] {$\alpha=-0.9$}; +\marke{1/3}{0.2}{} +\node at ({1/3},0.2) [rotate=90] {$\alpha=1$}; +\marke{1}{0.2}{} +\node at (1,0.2) [rotate=90] {$\alpha=2$}; + +\end{tikzpicture} +\end{document} + |