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/*
* jacobi.cpp
*
* (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
*/
#include <cstdlib>
#include <vector>
#include <iostream>
#include <sstream>
#include <fstream>
#include <memory>
#include <getopt.h>
#include <cmath>
/**
* \brief Pfad-Klasse
*/
class pfad {
std::ostringstream *_inhalt;
std::string _name;
int _punkte;
public:
pfad(const pfad&) = delete;
pfad(const std::string name) : _name(name), _punkte(0) {
_inhalt = new std::ostringstream();
}
~pfad() {
if (_inhalt) {
delete _inhalt;
}
}
void add(const std::pair<double,double>& XY) {
if (_punkte == 0) {
*_inhalt << "\\def\\" + _name + "{\n\t";
} else {
*_inhalt << "\n\t-- ";
}
*_inhalt << "({";
*_inhalt << XY.first;
*_inhalt << "*\\dx},{";
*_inhalt << XY.second;
*_inhalt << "*\\dy})";
_punkte++;
}
void operator()(const std::pair<double,double>& XY) {
add(XY);
}
std::string macro() const {
std::string result = _inhalt->str();
result = result + ";\n}\n";
return result;
}
};
typedef std::shared_ptr<pfad> pfad_ptr;
#define c(k) ((k)+a+b)
std::vector<double> jacobiP(double a, double b, double x, int n) {
std::vector<double> result;
double p0 = 1.;
result.push_back(p0);
double p1 = (a - b)/2. + (1. + (a + b)/2.) * x;
result.push_back(p1);
int i = 1;
while (i++ < n) {
double p;
p = c(2*i-1) * (c(2*i-2) * c(2*i) * x + a*a - b*b) * p1
- 2. * (i-1.+a) * (i-1.+b) * c(2*i) * p0;
p /= 2 * i * c(i) * c(2*i-2);
result.push_back(p);
p0 = p1;
p1 = p;
}
return result;
}
std::string jacobiPlots(const std::string& prefix,
double a, double b, int n, int N) {
std::vector<pfad_ptr> pfade;
for (int j = 0; j <= n; j++) {
char c = 'a' + j;
std::string name = prefix;
name.append(1, c);
pfad_ptr p(new pfad(name));
pfade.push_back(p);
}
for (int i = -N; i <= N; i++) {
double x = i / (double)N;
std::vector<double> r = jacobiP(a, b, x, n);
for (int j = 0; j <= n; j++) {
std::pair<double,double> XY
= std::make_pair(x, r[j]);
pfade[j]->add(XY);
}
}
std::ostringstream result;
for (int j = 0; j <= n; j++) {
result << pfade[j]->macro();
}
return result.str();
}
std::string jacobiWeight(const std::string& prefix,
double a, double b, int N) {
std::ostringstream out;
out << "\\def\\" << prefix << "weight{" << std::endl;
int _punkte = 0;
int starti = -N;
int endi = N;
if (b < 0) {
starti += 1;
}
if (a < 0) {
endi -= 1;
}
for (int i = starti; i <= endi; i++) {
double x = i / (double)N;
double y = pow(1-x, a) * pow(1+x, b);
if (_punkte > 0) {
out << std::endl << "\t-- ";
}
out << "({" << x << "*\\dx},{" << y << "*\\dwy})";
_punkte++;
}
out << std::endl << "}" << std::endl;
return out.str();
}
struct option options[] = {
{ "a", required_argument, NULL, 'a' },
{ "b", required_argument, NULL, 'b' },
{ "degree", required_argument, NULL, 'n' },
{ "points", required_argument, NULL, 'N' },
{ "prefix", required_argument, NULL, 'p' },
{ "outfile", required_argument, NULL, 'o' },
{ NULL, 0, NULL, 0 }
};
int main(int argc, char *argv[]) {
int n = 10;
int N = 100;
double a = 1;
double b = 1;
std::string outfilename;
std::string prefix("prefix");
int c;
while (EOF != (c = getopt_long(argc, argv, "a:b:n:N:o:p:", options,
NULL)))
switch (c) {
case 'a':
a = std::stod(optarg);
break;
case 'b':
b = std::stod(optarg);
break;
case 'n':
n = std::stoi(optarg);
break;
case 'N':
N = std::stoi(optarg);
break;
case 'o':
outfilename = std::string(optarg);
break;
case 'p':
prefix = std::string(optarg);
break;
}
std::string result = jacobiPlots(prefix, a, b, n, N);
result.append(jacobiWeight(prefix, a, b, N));
if (outfilename.size() == 0) {
std::cout << result;
return EXIT_SUCCESS;
}
std::ofstream out(outfilename.c_str());
out << result;
out.close();
return EXIT_SUCCESS;
}
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