From 5c05517960c4913a10eb526b69f99178ee08ef68 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 7 Jan 2022 20:31:27 +0100 Subject: reorganize chapter 7 --- buch/chapters/060-integral/images/Makefile | 8 +- buch/chapters/060-integral/images/legendre.m | 64 --------------- buch/chapters/060-integral/images/legendre.pdf | Bin 47113 -> 0 bytes buch/chapters/060-integral/images/legendre.tex | 99 ----------------------- buch/chapters/060-integral/images/orthogonal.pdf | Bin 25003 -> 0 bytes buch/chapters/060-integral/images/orthogonal.tex | 79 ------------------ 6 files changed, 1 insertion(+), 249 deletions(-) delete mode 100644 buch/chapters/060-integral/images/legendre.m delete mode 100644 buch/chapters/060-integral/images/legendre.pdf delete mode 100644 buch/chapters/060-integral/images/legendre.tex delete mode 100644 buch/chapters/060-integral/images/orthogonal.pdf delete mode 100644 buch/chapters/060-integral/images/orthogonal.tex (limited to 'buch/chapters/060-integral/images') diff --git a/buch/chapters/060-integral/images/Makefile b/buch/chapters/060-integral/images/Makefile index 790bfb1..28b662e 100644 --- a/buch/chapters/060-integral/images/Makefile +++ b/buch/chapters/060-integral/images/Makefile @@ -4,16 +4,10 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: erf.pdf legendre.pdf orthogonal.pdf +all: erf.pdf erf.pdf: erf.tex erfpunkte.tex pdflatex erf.tex erfpunkte.tex: erfpunkte.m octave erfpunkte.m -legendrepaths.tex: legendre.m - octave legendre.m -legendre.pdf: legendre.tex legendrepaths.tex - pdflatex legendre.tex -orthogonal.pdf: orthogonal.tex legendrepaths.tex - pdflatex orthogonal.tex diff --git a/buch/chapters/060-integral/images/legendre.m b/buch/chapters/060-integral/images/legendre.m deleted file mode 100644 index 8e8317d..0000000 --- a/buch/chapters/060-integral/images/legendre.m +++ /dev/null @@ -1,64 +0,0 @@ -# -# legendre.m -# -# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -# -pkg load miscellaneous -global N; -N = 30; - -function retval = legendrepath(fn, n, name) - global N; - m = n * N; - c = legendrepoly(n) - x = (-m:m)/m; - v = polyval(c, x); - fprintf(fn, "\\def\\legendre%s{\n", name) - fprintf(fn, "\t ({%.5f*\\dx},{%.5f*\\dy})", x(1), v(1)); - for i = (2:length(v)) - fprintf(fn, "\n\t-- ({%.5f*\\dx},{%.5f*\\dy})", x(i), v(i)); - - endfor - fprintf(fn, "\n}\n"); - ci = polyint(conv(c, c)) -polyval(ci, 1) - normalization = sqrt(polyval(ci, 1) - polyval(ci, -1)) - fprintf(fn, "\\def\\normalization%s{%.5f}\n", name, normalization); -endfunction - -function retval = legendreprodukt(fn, a, b, name) - global N; - n = max(a, b); - m = n * N; - pa = legendrepoly(a); - pb = legendrepoly(b); - p = conv(pa, pb); - x = (-m:m)/m; - v = polyval(p, x); - fprintf(fn, "\\def\\produkt%s{\n", name) - fprintf(fn, "\t ({%.5f*\\dx},{%.5f*\\dy})", x(1), v(1)); - for i = (2:length(v)) - fprintf(fn, "\n\t-- ({%.5f*\\dx},{%.5f*\\dy})", x(i), v(i)); - endfor - fprintf(fn, "\n}\n"); -endfunction - -fn = fopen("legendrepaths.tex", "w"); -legendrepath(fn, 1, "one"); -legendrepath(fn, 2, "two"); -legendrepath(fn, 3, "three"); -legendrepath(fn, 4, "four"); -legendrepath(fn, 5, "five"); -legendrepath(fn, 6, "six"); -legendrepath(fn, 7, "seven"); -legendrepath(fn, 8, "eight"); -legendrepath(fn, 9, "nine"); -legendrepath(fn, 10, "ten"); - -legendreprodukt(fn, 4, 7, "ortho"); -legendreprodukt(fn, 4, 4, "vier"); -legendreprodukt(fn, 7, 7, "sieben"); - -fclose(fn); - - diff --git a/buch/chapters/060-integral/images/legendre.pdf b/buch/chapters/060-integral/images/legendre.pdf deleted file mode 100644 index 554dc35..0000000 Binary files a/buch/chapters/060-integral/images/legendre.pdf and /dev/null differ diff --git a/buch/chapters/060-integral/images/legendre.tex b/buch/chapters/060-integral/images/legendre.tex deleted file mode 100644 index 8409da0..0000000 --- a/buch/chapters/060-integral/images/legendre.tex +++ /dev/null @@ -1,99 +0,0 @@ -% -% legendre.tex -- plots of legendre polynomials -% -% (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{6.5} -\input{legendrepaths.tex} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\definecolor{fone}{rgb}{1,0,0} -\definecolor{ftwo}{rgb}{1.0,0,0.8} -\definecolor{fthree}{rgb}{0.8,0,1} -\definecolor{ffour}{rgb}{0,0,1} -\definecolor{ffive}{rgb}{0,0.8,1} -\definecolor{fsix}{rgb}{0,1,1} -\definecolor{fseven}{rgb}{0,0.6,0} -\definecolor{feight}{rgb}{0.2,1,0.6} -\definecolor{fnine}{rgb}{0.6,0.8,0.2} -\definecolor{ften}{rgb}{1,0.4,0} - -\def\dx{1} -\def\dy{0.25} - -\def\achsen{ - \draw[->] ({-1-(0.1/\skala)},0) -- ({1+(0.3/\skala)},0) - coordinate[label={$x$}]; - \draw[->] (0,{-(\dy)-(0.1/\skala)}) -- (0,{(\dy)+(0.3/\skala)}) - coordinate[label={right:$y$}]; - \foreach \x in {-1,-0.9,...,1.001}{ - \draw ({\dx*\x},{-0.05/\skala}) -- ({\dx*\x},{0.05/\skala}); - } - \foreach \x in {-1,-0.5,0.5,1}{ - \draw ({-0.05/\skala},{\dy*\x}) -- ({0.05/\skala},{\dy*\x}); - \node at ({\dx*\x},{-0.05/\skala}) [below] {$\mathstrut\x$}; - \node at ({-0.05/\skala},{\dy*\x}) [left] {$\mathstrut\x$}; - } -} - -\begin{scope}[yshift=0cm] - \node[color=fone] at (-0.70,{-0.9*\dy}) [right] {$n=1\mathstrut$}; - \node[color=ftwo] at (-0.90,{0.9*\dy}) [right] {$n=2\mathstrut$}; - \draw[line width=1.4pt,color=fone] \legendreone; - \draw[line width=1.4pt,color=ftwo] \legendretwo; - \achsen -\end{scope} - -\begin{scope}[yshift=-0.6cm] - \node[color=fthree] at (-0.96,{-0.9*\dy}) [right] {$n=3\mathstrut$}; - \node[color=ffour] at (-0.96,{0.9*\dy}) [right] {$n=4\mathstrut$}; - \draw[line width=1.4pt,color=fthree] \legendrethree; - \draw[line width=1.4pt,color=ffour] \legendrefour; - \achsen -\end{scope} - -\begin{scope}[yshift=-1.2cm] - \node[color=ffive] at (-0.96,{-0.9*\dy}) [right] {$n=5\mathstrut$}; - \node[color=fsix] at (-0.96,{0.9*\dy}) [right] {$n=6\mathstrut$}; - \draw[line width=1.4pt,color=ffive] \legendrefive; - \draw[line width=1.4pt,color=fsix] \legendresix; - \achsen -\end{scope} - -\begin{scope}[yshift=-1.8cm] - \node[color=fseven] at (-0.96,{-0.9*\dy}) [right] {$n=7\mathstrut$}; - \node[color=feight] at (-0.96,{0.9*\dy}) [right] {$n=8\mathstrut$}; - \draw[line width=1.4pt,color=fseven] \legendreseven; - \draw[line width=1.4pt,color=feight] \legendreeight; - \achsen -\end{scope} - -\begin{scope}[yshift=-2.4cm] - \node[color=fnine] at (-0.96,{-0.9*\dy}) [right] {$n=9\mathstrut$}; - \node[color=ften] at (-0.96,{0.9*\dy}) [right] {$n=10\mathstrut$}; - \draw[line width=1.4pt,color=fnine] \legendrenine; - \draw[line width=1.4pt,color=ften] \legendreten; - \achsen -\end{scope} - -%\draw[line width=1.4pt,color=ftwo] \legendretwo; -%\draw[line width=1.4pt,color=fthree] \legendrethree; -%\draw[line width=1.4pt,color=ffour] \legendrefour; -%\draw[line width=1.4pt,color=ffive] \legendrefive; -%\draw[line width=1.4pt,color=fsix] \legendresix; -%\draw[line width=1.4pt,color=fseven] \legendreseven; -%\draw[line width=1.4pt,color=feight] \legendreeight; -%\draw[line width=1.4pt,color=fnine] \legendrenine; -%\draw[line width=1.4pt,color=ften] \legendreten; - -\end{tikzpicture} -\end{document} - diff --git a/buch/chapters/060-integral/images/orthogonal.pdf b/buch/chapters/060-integral/images/orthogonal.pdf deleted file mode 100644 index f7abb5e..0000000 Binary files a/buch/chapters/060-integral/images/orthogonal.pdf and /dev/null differ diff --git a/buch/chapters/060-integral/images/orthogonal.tex b/buch/chapters/060-integral/images/orthogonal.tex deleted file mode 100644 index 8600281..0000000 --- a/buch/chapters/060-integral/images/orthogonal.tex +++ /dev/null @@ -1,79 +0,0 @@ -% -% orthogonal.tex -- plots of legendre polynomials -% -% (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} -\input{legendrepaths.tex} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\definecolor{fone}{rgb}{1,0,0} -\definecolor{ftwo}{rgb}{1.0,0,0.8} -\definecolor{fthree}{rgb}{0.8,0,1} -\definecolor{ffour}{rgb}{0,0,1} -\definecolor{ffive}{rgb}{0,0.8,1} -\definecolor{fsix}{rgb}{0,1,1} -\definecolor{fseven}{rgb}{0,0.6,0} -\definecolor{feight}{rgb}{0.2,1,0.6} -\definecolor{fnine}{rgb}{0.6,0.8,0.2} -\definecolor{ften}{rgb}{1,0.4,0} - -\def\dx{1} -\def\Dy{3} -\def\dy{3} - -\begin{scope} -\clip (-1,-0.6) rectangle (1,1); - -%\pgfmathparse{\Dy/(\normalizationfour*\normalizationfour)} -%\xdef\dy{\pgfmathresult} -\fill[color=ffour!70,opacity=0.5] (-1,0) -- \produktvier -- (1,0) -- cycle; - -%\pgfmathparse{\Dy/(\normalizationeight*\normalizationeight)} -%\xdef\dy{\pgfmathresult} -\fill[color=fseven!70,opacity=0.5] (-1,0) -- \produktsieben -- (1,0) -- cycle; - -%\pgfmathparse{\Dy/(\normalizationfour*\normalizationeight)} -%\xdef\dy{\pgfmathresult} -\fill[color=red!50,opacity=0.5] (-1,0) -- \produktortho -- (1,0) -- cycle; - -%\pgfmathparse{\Dy/\normalizationfour} -%\xdef\dy{\pgfmathresult} -%\draw[line width=1.4pt,color=ffour] \legendrefour; -% -%\pgfmathparse{\Dy/\normalizationeight} -%\xdef\dy{\pgfmathresult} -%\draw[line width=1.4pt,color=feight] \legendreeight; - -%\pgfmathparse{\Dy/(\normalizationfour*\normalizationeight)} -%\xdef\dy{\pgfmathresult} -\draw[line width=1.4pt,color=red] \produktortho; - -\end{scope} - -\draw[->] ({-1-(0.1/\skala)},0) -- ({1+(0.3/\skala)},0) - coordinate[label={$x$}]; -\draw[->] (0,{-{0.2*\Dy}-(0.1/\skala)}) -- (0,{1+(0.3/\skala)}) - coordinate[label={right:$y$}]; -\foreach \x in {-1,-0.9,...,1.001}{ - \draw ({\dx*\x},{-0.1/\skala}) -- ({\dx*\x},{0.1/\skala}); -} -\foreach \y in {-0.2,-0.1,0.1,0.2,0.3}{ - \draw ({-0.1/\skala},{\Dy*\y}) -- ({0.1/\skala},{\Dy*\y}); - \node at ({-0.1/\skala},{\Dy*\y}) [left] {$\mathstrut\y$}; -} -\foreach \x in {-1,-0.5,0.5,1}{ - \node at ({\dx*\x},{-0.1/\skala}) [below] {$\mathstrut\x$}; -} - -\end{tikzpicture} -\end{document} - -- cgit v1.2.1