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/*
* 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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