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#include <getopt.h>
#include <vector>
#include <cmath>
#include <iostream>
#include <fftw3.h>
#include <complex>
using Real = double;
using Complex = std::complex<Real>;
using namespace std::complex_literals;
unsigned p = 2;
Real f(Real q) {
return 0.5 * pow(q, p);
}
Real df(Real q) {
return 0.5 * p * pow(q, p - 1);
}
Real ddf(Real q) {
return 0.5 * p * (p - 1) * pow(q, p - 2);
}
int main(int argc, char* argv[]) {
Real Δω = 1e-3;
Real Δτ = 1e-3;
Real τ₀ = 0;
Real y = 0.5;
unsigned iterations = 10;
int opt;
while ((opt = getopt(argc, argv, "d:T:t:y:I:")) != -1) {
switch (opt) {
case 'd':
Δω = atof(optarg);
break;
case 'T':
Δτ = atof(optarg);
break;
case 't':
τ₀ = atof(optarg);
break;
case 'y':
y = atof(optarg);
break;
case 'I':
iterations = (unsigned)atof(optarg);
break;
default:
exit(1);
}
}
Real z = (-1+sqrt(1+2*τ₀)) / (2 * τ₀);
Real Γ₀ = 1;
Real ωₘₐₓ = 1 / Δτ;
unsigned N = 2 * ωₘₐₓ / Δω + 1;
unsigned n = ωₘₐₓ / Δω + 1;
std::vector<Complex> Ĉ(N / 2 + 1);
std::vector<Real> C(N);
std::vector<Complex> Ř(N / 2 + 1);
std::vector<Real> R(N);
for (unsigned i = 0; i < n; i++) {
Real τ = i * Δτ * M_PI;
C[i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
C[N - 1 - i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
}
/*
for (unsigned it = 0; it < iterations; it++) {
for (unsigned i = 0; i < n; i++) {
Real ω = i * Δω;
ĉ[i] = Γ₀ / ((pow(z, 2) + pow(ω, 2)) * (1 + pow(τ₀ * ω ,2)));
}
}
ř[i] = (z - 1i * ω) / (pow(z, 2) + pow(ω, 2));
std::vector<Real> c(n);
*/
fftw_plan test = fftw_plan_dft_r2c_1d(N, C.data(), reinterpret_cast<fftw_complex*>(Ĉ.data()), 0);
for (unsigned i = 0; i < n; i++) {
Real τ = i * Δτ * M_PI;
C[i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
C[N - 1 - i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
}
fftw_execute(test);
for (unsigned i = 0; i < Ĉ.size(); i++) {
std::cout << i * Δτ * M_PI << " " << Ĉ[i].real() << std::endl;
}
/*
for (unsigned i = 0; i < Ĉ.size(); i++) {
std::cout << i * Δω << " " << Ĉ[i].real() * Δω / (2 * M_PI) << std::endl;
}
*/
return 0;
}
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