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#include "fourier.hpp"
#include <fstream>
#include <fftw3.h>
#include <getopt.h>
#include <iostream>
Real energy(const std::vector<Real>& C, std::vector<Real>& R, Real λ, unsigned p, unsigned s, Real Δτ) {
Real I = 0;
for (unsigned σ = 0; σ < C.size(); σ++) {
I += Δτ * df(λ, p, s, C[σ]) * R[σ];
}
return I;
}
int main(int argc, char* argv[]) {
unsigned p = 3;
unsigned s = 4;
Real λ = 0.5;
Real τₘₐₓ = 1e3;
Real τ₀ = 0;
Real β₀ = 0;
Real βₘₐₓ = 1;
Real Δβ = 1e-2;
unsigned iterations = 10;
unsigned log2n = 8;
Real ε = 1e-14;
int opt;
while ((opt = getopt(argc, argv, "T:2:t:0:b:d:I:")) != -1) {
switch (opt) {
case 'T':
τₘₐₓ = atof(optarg);
break;
case '2':
log2n = atof(optarg);
break;
case 't':
τ₀ = atof(optarg);
break;
case '0':
β₀ = atof(optarg);
break;
case 'b':
βₘₐₓ = atof(optarg);
break;
case 'd':
Δβ = atof(optarg);
break;
case 'I':
iterations = (unsigned)atof(optarg);
break;
default:
exit(1);
}
}
unsigned N = pow(2, log2n);
Real Δτ = (1 + τ₀ / 2) * τₘₐₓ / M_PI / N;
Real Δω = M_PI / ((1 + τ₀ / 2) * τₘₐₓ);
FourierTransform fft(N, Δω, Δτ, FFTW_ESTIMATE);
Real Γ₀ = 1;
Real μ = 1;
if (τ₀ > 0) {
μ = (sqrt(1+4*Γ₀*τ₀) - 1) / (2 * τ₀);
}
Real τ = 0;
std::vector<Real> C(N);
std::vector<Real> R(N);
std::vector<Real> Γ(N);
std::vector<Real> Γh(N+1);
Γh[0] = Γ₀;
for (unsigned i = 0; i < N; i++) {
Real τ = i * Δτ;
Real ω = (i + 1) * Δω * M_PI;
if (τ₀ > 0) {
C[i] = (Γ₀ / μ) * (exp(-μ * τ) - μ * τ₀ * exp(-τ / τ₀)) / (1 - pow(μ * τ₀, 2));
Γ[i] = (Γ₀ / τ₀) * exp(-τ / τ₀);
} else {
C[i] = (Γ₀ / μ) * exp(-μ * τ);
}
Γh[i+1] = Γ₀ / (1 + pow(ω * τ₀, 2));
R[i] = exp(-μ * τ);
}
for (Real β = β₀; β < βₘₐₓ; β += Δβ) {
Real Rerr = 100;
while (sqrt(Rerr / N) > ε) {
/* First step: integrate R from C */
std::vector<Real> R₊(N);
R₊[0] = 1;
for (unsigned i = 1; i < N; i++) {
Real I = 0;
for (unsigned j = 0; j <= i; j++) {
I += R[i - j] * ddf(λ, p, s, C[i - j]) * R[j] * Δτ;
}
Real dR = -μ * R₊[i - 1] + pow(β, 2) * I;
R₊[i] = R₊[i - 1] + dR * Δτ;
}
Rerr = 0;
for (unsigned i = 0; i < N; i++) {
Rerr += pow(R[i] - R₊[i], 2);
}
R = R₊;
/* Second step: integrate C from R */
std::vector<Real> dC = fft.convolve(Γh, R);
Real Cₜ₊₁ = 0;
for (unsigned i = 0; i < N; i++) {
Real Cₜ = Cₜ₊₁ + dC[N - i - 1] * Δτ;
C[N - i - 1] = Cₜ;
Cₜ₊₁ = Cₜ;
}
/* Third step: adjust μ */
μ *= C[0];
std::cerr << β << " " << sqrt(Rerr / N) << std::endl;
}
std::ofstream outfile(fourierFile("Ci", p, s, λ, τ₀, β, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
outfile.write((const char*)(C.data()), N * sizeof(Real));
outfile.close();
std::ofstream outfileR(fourierFile("Ri", p, s, λ, τ₀, β, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
outfileR.write((const char*)(R.data()), N * sizeof(Real));
outfileR.close();
}
return 0;
}
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