From 05d75b0f467b2535db538ecaee461cf0c8b637d1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 27 Jun 2022 20:17:16 +0200
Subject: add stuff for elliptic filters

---
 buch/chapters/110-elliptisch/experiments/KN.cpp | 177 ++++++++++++++++++++++++
 1 file changed, 177 insertions(+)
 create mode 100644 buch/chapters/110-elliptisch/experiments/KN.cpp

(limited to 'buch/chapters/110-elliptisch/experiments/KN.cpp')

diff --git a/buch/chapters/110-elliptisch/experiments/KN.cpp b/buch/chapters/110-elliptisch/experiments/KN.cpp
new file mode 100644
index 0000000..1dcca9e
--- /dev/null
+++ b/buch/chapters/110-elliptisch/experiments/KN.cpp
@@ -0,0 +1,177 @@
+/*
+ * KN.cpp
+ *
+ * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstdlib>
+#include <cstdio>
+#include <cmath>
+#include <iostream>
+#include <fstream>
+#include <sstream>
+#include <getopt.h>
+#include <vector>
+#include <gsl/gsl_sf_elljac.h>
+#include <gsl/gsl_sf_ellint.h>
+
+namespace KN {
+
+bool	debug = false;
+
+static struct option	longopts[] {
+{ "debug",	no_argument,		NULL,	'd' },
+{ "N",		required_argument,	NULL,	'N' },
+{ "outfile",	required_argument,	NULL,	'o' },
+{ "min",	required_argument,	NULL,	'm' },
+{ NULL,		0,			NULL,	 0  }
+};
+
+double	KprimeK(double k) {
+	double	kprime = sqrt(1-k*k);
+	if (debug)
+		printf("%s:%d: k = %f, k' = %f\n", __FILE__, __LINE__, k, kprime);
+	double	v
+		=
+		gsl_sf_ellint_Kcomp(k, GSL_PREC_DOUBLE)
+		/
+		gsl_sf_ellint_Kcomp(kprime, GSL_PREC_DOUBLE)
+		;
+	if (debug)
+		printf("%s:%d: KprimeK(k = %f) = %f\n", __FILE__, __LINE__, k, v);
+	return v;
+}
+
+static const int	L = 100000000;
+static const double	h = 1. / L;
+
+double	Kd(double k) {
+	double	m = 0;
+	if (k < h) {
+		m = 2 * (KprimeK(k) - KprimeK(k / 2)) / k;
+	} else if (k > 1-h) {
+		m = 2 * (KprimeK((1 + k) / 2) - KprimeK(k)) / (1 - k);
+		
+	} else {
+		m = L * (KprimeK(k + h) - KprimeK(k));
+	}
+	if (debug)
+		printf("%s:%d: Kd(%f) = %f\n", __FILE__, __LINE__, k, m);
+	return m;
+}
+
+double	k1(double y) {
+	if (debug)
+		printf("%s:%d: Newton for y = %f\n", __FILE__, __LINE__, y);
+	double	kn = 0.5;
+	double	delta = 1;
+	int	n = 0;
+	while ((fabs(delta) > 0.000001) && (n < 10)) {
+		double	yn = KprimeK(kn);
+		if (debug)
+			printf("%s:%d: k%d = %f, y%d = %f\n", __FILE__, __LINE__, n, kn, n, yn);
+		delta = (yn - y) / Kd(kn);
+		if (debug)
+			printf("%s:%d: delta = %f\n", __FILE__, __LINE__, delta);
+		double	kneu = kn - delta;
+		if (kneu <= 0) {
+			kneu = kn / 4;
+		}
+		if (kneu >= 1) {
+			kneu = (3 + kn) / 4;
+		}
+		kn = kneu;
+		if (debug)
+			printf("%s:%d: kneu = %f, kn = %f\n", __FILE__, __LINE__, kneu, kn);
+		n++;
+	}
+	if (debug)
+		printf("%s:%d: Newton result: k = %f\n", __FILE__, __LINE__, kn);
+	return kn;
+}
+
+double	k1(int N, double k) {
+	return k1(KprimeK(k) / N);
+}
+
+/**
+ * \brief Main function for the slcl program
+ */
+int	main(int argc, char *argv[]) {
+	int	longindex;
+	int	c;
+	int	N = 5;
+	double	kmin = 0.01;
+	std::string	outfilename;
+	while (EOF != (c = getopt_long(argc, argv, "d:N:o:m:",
+		longopts, &longindex)))
+		switch (c) {
+		case 'd':
+			debug = true;
+			break;
+		case 'N':
+			N = std::stoi(optarg);
+			break;
+		case 'o':
+			outfilename = std::string(optarg);
+			break;
+		case 'm':
+			kmin = std::stod(optarg);
+			break;
+		}
+
+	double	d = 0.01;
+	if (outfilename.size() > 0) {
+		FILE	*fn = fopen(outfilename.c_str(), "w");
+		fprintf(fn, "\\def\\KKpath{ ");
+		double	k = d;
+		fprintf(fn, " (0,0)");
+		double	k0 = k/16;
+		while (k0 < k) {
+			fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", k0, KprimeK(k0));
+			k0 *= 2;
+		}
+		while (k < 1-0.5*d) {
+			fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", k, KprimeK(k));
+			k += d;
+		}
+		fprintf(fn, "}\n");
+
+		k0 = 0.97;
+		fprintf(fn, "\\def\\knull{%.4f}\n", k0);
+		double	KK = KprimeK(k0);
+		fprintf(fn, "\\def\\KKnull{%.4f}\n", KK);
+		fprintf(fn, "\\def\\kone{%.4f}\n", k1(N, k0));
+
+		fclose(fn);
+		return EXIT_SUCCESS;
+	}
+
+	for (double k = kmin; k < (1 - d/2); k += d) {
+		if (debug)
+			printf("%s:%d: k = %f\n", __FILE__, __LINE__, k);
+		double	y = KprimeK(k);
+		double	k0 = k1(y);
+		double	kone = k1(N, k0);
+		printf("g(%4.2f) = %10.6f,", k, y);
+		printf("    g'(%.2f) = %10.6f,", k, Kd(k));
+		printf("    g^{-1} = %10.6f,", k0);
+		printf("    k1 = %10.6f,", kone);
+		printf("    g(k1) = %10.6f\n", KprimeK(kone));
+	}
+
+	return EXIT_SUCCESS;
+}
+
+} // namespace KN
+
+int	main(int argc, char *argv[]) {
+	try {
+		return KN::main(argc, argv);
+	} catch (const std::exception& e) {
+		std::cerr << "terminated by exception: " << e.what();
+		std::cerr << std::endl;
+	} catch (...) {
+		std::cerr << "terminated by unknown exception" << std::endl;
+	}
+	return EXIT_FAILURE;
+}
-- 
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