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test_RungeKutta.cpp
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test_RungeKutta.cpp
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#include "RungeKutta.h"
#include "PruferTransformer.h"
#include "OrthogonalPolynomials.h"
#include <iostream>
#include "math.h"
using namespace std;
void test_Prufer_for_Legendre2()
{
cout << "test RungeKutta4 for Prufer Transform of Legendre2:\n";
LegendrePolys Pn(mpz_class(2));
polynomial p2 = Pn.getPm(2);
vector<polynomial> coeff_ODE = Pn.coefficientsOfODE(2);
PruferTransformer prufer2(p2,coeff_ODE);
auto dx_dtheta = prufer2.get_dx_dtheta();
vector<mpf_class> initial = {0,prufer2.theta_x_value(0)};
RungeKutta4 RK4(initial,dx_dtheta);
mpf_class h = -1e-3;
mpf_class end_x = -pi/2.0;
mpf_class end_y = RK4.compute(h, end_x);
cout << "Legendre polynomial P2's smallest root>0 is :" << end_y <<"\n";
cout << "should be about " << 1.0/sqrt(3) << endl;
cout << "P2(" << end_y <<") = " << p2(end_y) << endl;
cout << "P2(" << 1.0/sqrt(3) << ") = " << p2(1.0/sqrt(3)) << endl;
}
void test_Prufer_for_Legendre4()
{
cout << "test RungeKutta4 for Prufer Transform of Legendre4:\n";
LegendrePolys Pn(mpz_class(4));
polynomial p4 = Pn.getPm(4);
vector<polynomial> coeff_ODE = Pn.coefficientsOfODE(4);
PruferTransformer prufer4(p4,coeff_ODE);
auto dx_dtheta = prufer4.get_dx_dtheta();
vector<mpf_class> initial = {0,prufer4.theta_x_value(0)};
RungeKutta4 RK4(initial,dx_dtheta);
mpf_class h = -1e-3;
mpf_class end_x = -pi/2.0;
mpf_class end_y = RK4.compute(h, end_x);
cout << "Legendre polynomial P4's smallest root>0 is :" << end_y <<"\n";
cout << "P4(" << end_y <<") = " << p4(end_y) << endl;
}
void test_set_initial()
{
cout << "test RungeKutta4 for Legendre4 with set initial condtion:\n";
LegendrePolys Pn(mpz_class(4));
polynomial p4 = Pn.getPm(4);
vector<polynomial> coeff_ODE = Pn.coefficientsOfODE(4);
PruferTransformer prufer4(p4,coeff_ODE);
auto dx_dtheta = prufer4.get_dx_dtheta();
vector<mpf_class> initial = {0,prufer4.theta_x_value(0)};
RungeKutta4 RK4(initial,dx_dtheta);
mpf_class h = -1e-3;
mpf_class end_x = -pi/2.0;
mpf_class end_y = RK4.compute(h, end_x);
cout << "Legendre polynomial P4's smallest root>0 is :" << end_y <<"\n";
cout << "P4(" << end_y <<") = " << p4(end_y) << endl;
vector<mpf_class> initial2 = {pi/2.0,end_y};
RK4.set_initial_condition(initial2);
mpf_class end_y2 = RK4.compute(h, end_x);
cout << "Legendre polynomial P4's second root>0 is :" << end_y2 <<"\n";
cout << "P4(" << end_y2 <<") = " << p4(end_y2) << endl;
}
int main()
{
test_Prufer_for_Legendre2();
test_Prufer_for_Legendre4();
test_set_initial();
return 0;
}