jacobiplots hinzugefügt

6 files changed, 273 insertions, 2 deletions

diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile
index 5749ae0..f3f783f 100644
--- a/buch/chapters/110-elliptisch/images/Makefile
+++ b/buch/chapters/110-elliptisch/images/Makefile
@@ -4,7 +4,7 @@
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 #
 all:	lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \
-	ellipse.pdf pendel.pdf
+	ellipse.pdf pendel.pdf jacobiplots.pdf
 
 lemniskate.pdf:	lemniskate.tex
 	pdflatex lemniskate.tex
@@ -16,7 +16,7 @@ ekplot.tex:	ellipsenumfang.m
 	octave ellipsenumfang.m
 
 rechteck:	rechteck.cpp
-	g++ `pkg-config --cflags gsl` `pkg-config --libs gsl` -O -Wall -g -std=c++11 rechteck.cpp -o rechteck
+	g++ -O -Wall -g -std=c++11 rechteck.cpp -o rechteck `pkg-config --cflags gsl` `pkg-config --libs gsl`
 
 rechteckpfade.tex:	rechteck
 	./rechteck --outfile rechteckpfade.tex
@@ -36,3 +36,27 @@ ellipse.pdf:	ellipse.tex
 pendel.pdf:	pendel.tex
 	pdflatex pendel.tex
 
+jacobi:	jacobi.cpp
+	g++ -O -Wall -g -std=c++11 jacobi.cpp -o jacobi `pkg-config --cflags gsl` `pkg-config --libs gsl`
+
+test:	blubb.tex
+
+blubb.tex:	jacobi
+	./jacobi --umax=14 --outfile=blubb.tex blubb 0.7
+
+jacobipaths.tex:	jacobi Makefile
+	./jacobi --umax=13 --steps=200 --outfile=jacobipaths.tex \
+		zero 0.00 \
+		one 0.2 \
+		two 0.4 \
+		three 0.6 \
+		four 0.8 \
+		five 0.9 \
+		six 0.99 \
+		seven 0.999 \
+		eight 0.9999 \
+		nine 0.99999 \
+		ten 1.0
+
+jacobiplots.pdf:	jacobiplots.tex jacobipaths.tex
+	pdflatex jacobiplots.tex
diff --git a/buch/chapters/110-elliptisch/images/jacobi.cpp b/buch/chapters/110-elliptisch/images/jacobi.cpp
new file mode 100644
index 0000000..438fe48
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/jacobi.cpp
@@ -0,0 +1,154 @@
+/*
+ * jacobi.cpp
+ *
+ * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstdlib>
+#include <cstdio>
+#include <cmath>
+#include <gsl/gsl_sf_elljac.h>
+#include <vector>
+#include <iostream>
+#include <sstream>
+#include <fstream>
+#include <getopt.h>
+
+namespace jacobi {
+
+static struct option	longopts[] {
+{ "k",		required_argument,	NULL,	'k' },
+{ "m",		required_argument,	NULL,	'm' },
+{ "outfile",	required_argument,	NULL,	'o' },
+{ "infile",	required_argument,	NULL,	'i' },
+{ "umin",	required_argument,	NULL,	'f' },
+{ "umax",	required_argument,	NULL,	't' },
+{ "steps",	required_argument,	NULL,	's' },
+{ NULL,		0,			NULL,	 0  }
+};
+
+/**
+ * \brief A class to contain a single plot
+ */
+class jacobiplot : public std::vector<std::pair<double,double> > {
+	std::string	punkt(std::pair<double,double> x) const {
+		char	buffer[128];
+		snprintf(buffer, sizeof(buffer), "({%.4f*\\dx},{%.4f*\\dy})",
+			x.first, x.second);
+		return std::string(buffer);
+	}
+public:
+	jacobiplot() { }
+	void	write(std::ostream& out, const std::string& name) const {
+		out << "\\def\\" << name << "{" << std::endl;
+		auto	i = begin();
+		out << punkt(*i);
+		for (i++; i != end(); i++) {
+			out << std::endl << " -- " << punkt(*i);
+		}
+		out << std::endl << "}" << std::endl;
+	}
+};
+
+/**
+ * \brief A class containing all three basic functions
+ */
+class jacobiplots {
+	jacobiplot	_sn;
+	jacobiplot	_cn;
+	jacobiplot	_dn;
+	double	_m;
+public:
+	const jacobiplot&	sn() const { return _sn; }
+	const jacobiplot&	cn() const { return _cn; }
+	const jacobiplot&	dn() const { return _dn; }
+	jacobiplots(double m) : _m(m) { }
+	double	m() const { return _m; }
+	void	add(double umin, double umax, int steps) {
+		_sn.clear();
+		_cn.clear();
+		_dn.clear();
+		double	h = (umax - umin) / steps;
+		for (int i = 0; i <= steps; i++) {
+			double	u = umin + i * h;
+			double	snvalue, cnvalue, dnvalue;
+			gsl_sf_elljac_e(u, m(), &snvalue, &cnvalue, &dnvalue);
+			_sn.push_back(std::make_pair(u, snvalue));
+			_cn.push_back(std::make_pair(u, cnvalue));
+			_dn.push_back(std::make_pair(u, dnvalue));
+		}
+	}
+	void	write(std::ostream& out, const std::string& name) const {
+		out << "% name=" << name << ", m=" << m() << std::endl;
+		out << "\\def\\m" << name << "{" << m() << "}" << std::endl;
+		_sn.write(out, std::string("sn") + name);
+		_cn.write(out, std::string("cn") + name);
+		_dn.write(out, std::string("dn") + name);
+	}
+};
+
+int	main(int argc, char *argv[]) {
+	int	c;
+	int	longindex;
+	std::ostream	*out = &std::cout;
+	std::string	infilename;
+	int	steps = 100;
+	double	umin = 0;
+	double	umax = 10;
+	while (EOF != (c = getopt_long(argc, argv, "o:i:f:t:s:", longopts,
+		&longindex)))
+		switch (c) {
+		case 'o':
+			out = new std::ofstream(optarg);
+			(*out) << "%" << std::endl;
+			(*out) << "% " << optarg << std::endl;
+			(*out) << "%" << std::endl;
+			break;
+		case 'i':
+			infilename = std::string(optarg);
+			break;
+		case 'f':
+			umin = std::stod(optarg);
+			break;
+		case 't':
+			umax = std::stod(optarg);
+			break;
+		case 's':
+			steps = std::stoi(optarg);
+			break;
+		}
+
+	if (infilename.size() == 0) {
+		while ((optind + 1) < argc) {
+			std::string	name(argv[optind++]);
+			double	m = std::stod(argv[optind++]);
+			jacobiplots	j(m);
+			j.add(umin, umax, steps);
+			j.write(*out, name);
+		}
+	} else {
+		std::ifstream	infile(infilename);
+		while (!infile.eof()) {
+			std::string	name;
+			double	m;
+			infile >> name;
+			infile >> m;
+			jacobiplots	j(m);
+			j.add(umin, umax, steps);
+			j.write(*out, name);
+		}
+	}
+
+	return EXIT_SUCCESS;
+}
+
+} // namespace jacobi
+
+int	main(int argc, char *argv[]) {
+	try {
+		return jacobi::main(argc, argv);
+	} catch (const std::exception& x) {
+		std::cerr << "cannot build sn/cn/dn file: " << x.what();
+		std::cerr << std::endl;
+	}
+	return EXIT_FAILURE;
+}
diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
new file mode 100644
index 0000000..c1885c9
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.tex b/buch/chapters/110-elliptisch/images/jacobiplots.tex
new file mode 100644
index 0000000..4fc572e
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.tex
@@ -0,0 +1,93 @@
+%
+% jacobiplots.tex -- template for standalon tikz images
+%
+% (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{1}
+\def\dx{1}
+\def\dy{2}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\input{jacobipaths.tex}
+\def\piticks{
+	\draw (3.1415,-0.1) -- (3.1415,0.1);
+	\node at (3.1415,0) [below] {$\pi$};
+	\draw (6.2831,-0.1) -- (6.2831,0.1);
+	\node at (6.2831,0) [below] {$2\pi$};
+	\draw (9.4248,-0.1) -- (9.4248,0.1);
+	\node at (9.4248,0) [below] {$3\pi$};
+	\draw (12.5664,-0.1) -- (12.5664,0.1);
+	\node at (12.5664,0) [below] {$4\pi$};
+}
+\def\mlabel#1{
+%\fill[color=gray!50] (-0.2,-6) rectangle (7.0,2.3);
+\fill[color=gray!50] (-0.2,1.65) rectangle (7.0,2.3);
+\draw[line width=0.5pt] (-0.2,-6) rectangle (7.0,2.3);
+\begin{scope}[scale=0.5]
+\node at (6.5,{\dy+2}) {$m = #1$};
+\end{scope}
+}
+\def\jacobiplot#1#2#3#4{
+
+
+\begin{scope}[scale=0.5]
+\draw[->] (-0.1,0) -- (13.5,0) coordinate[label={$u$}];
+\piticks
+\draw[->] (0,-2.1) -- (0,2.5) coordinate[label={right:$\operatorname{sn}(u,k)$}];
+\draw[color=red#4] #1;
+\end{scope}
+
+\begin{scope}[yshift=-2.5cm,scale=0.5]
+\draw[->] (-0.1,0) -- (13.5,0) coordinate[label={$u$}];
+\piticks
+\draw[->] (0,-2.1) -- (0,2.5) coordinate[label={right:$\operatorname{cn}(u,k)$}];
+\draw[color=blue#4] #2;
+\end{scope}
+
+\begin{scope}[yshift=-5.5cm,scale=0.5]
+\draw[->] (-0.1,0) -- (13.5,0) coordinate[label={$u$}];
+\piticks
+\draw[->] (0,-0.1) -- (0,3.5) coordinate[label={right:$\operatorname{dn}(u,k)$}];
+\draw[color=darkgreen#4] #3;
+\end{scope}
+
+}
+%\input{blubb.tex}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\begin{scope}
+\mlabel{\mone}
+\jacobiplot{\snzero}{\cnzero}{\dnzero}{!50}
+\jacobiplot{\snone}{\cnone}{\dnone}{}
+\end{scope}
+
+\begin{scope}[xshift=7.3cm]
+\mlabel{\mfive}
+\jacobiplot{\snzero}{\cnzero}{\dnzero}{!50}
+\jacobiplot{\snfive}{\cnfive}{\dnfive}{}
+\end{scope}
+
+\begin{scope}[xshift=0cm,yshift=-8.4cm]
+\mlabel{\mseven}
+\jacobiplot{\snzero}{\cnzero}{\dnzero}{!50}
+%\jacobiplot{\sneight}{\cneight}{\dneight}{}
+\jacobiplot{\snseven}{\cnseven}{\dnseven}{}
+\end{scope}
+
+\begin{scope}[xshift=7.3cm,yshift=-8.4cm]
+\mlabel{\mnine}
+\jacobiplot{\snzero}{\cnzero}{\dnzero}{!50}
+\jacobiplot{\snnine}{\cnnine}{\dnnine}{}
+\end{scope}
+
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/110-elliptisch/images/rechteck.pdf b/buch/chapters/110-elliptisch/images/rechteck.pdf
index ea5869d..6209897 100644
--- a/buch/chapters/110-elliptisch/images/rechteck.pdf
+++ b/buch/chapters/110-elliptisch/images/rechteck.pdf
diff --git a/buch/chapters/110-elliptisch/images/unvollstaendig.pdf b/buch/chapters/110-elliptisch/images/unvollstaendig.pdf
index f28495c..491f328 100644
--- a/buch/chapters/110-elliptisch/images/unvollstaendig.pdf
+++ b/buch/chapters/110-elliptisch/images/unvollstaendig.pdf