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#include "fourier.hpp"
#include <getopt.h>
#include <iostream>
int main(int argc, char* argv[]) {
unsigned p = 2;
unsigned s = 2;
Real λ = 0.5;
Real τ₀ = 0;
unsigned log2n = 8;
Real Δτ = 0.1;
Real k = 0.1;
Real ε = 1e-16;
Real γ = 1;
Real βₘₐₓ = 0.7;
Real Δβ = 0.01;
int opt;
while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:")) != -1) {
switch (opt) {
case 'p':
p = atoi(optarg);
break;
case 's':
s = atoi(optarg);
break;
case '2':
log2n = atoi(optarg);
break;
case 't':
τ₀ = atof(optarg);
break;
case 'b':
βₘₐₓ = atof(optarg);
break;
case 'd':
Δβ = atof(optarg);
break;
case 'g':
γ = atof(optarg);
break;
case 'k':
k = atof(optarg);
break;
case 'D':
Δτ = atof(optarg);
break;
default:
exit(1);
}
}
unsigned N = pow(2, log2n);
LogarithmicFourierTransform fft(N, k, Δτ, 4);
Real Γ₀ = 1.0;
Real μ = Γ₀;
if (τ₀ > 0) {
μ = (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀);
}
std::vector<Real> C(N);
std::vector<Real> R(N);
std::vector<Complex> Ct(N);
std::vector<Complex> Rt(N);
// start from the exact solution for β = 0
for (unsigned n = 0; n < N; n++) {
if (τ₀ > 0) {
C[n] = Γ₀ * (exp(-μ * fft.t(n)) - μ * τ₀ * exp(-fft.t(n) / τ₀)) / (μ - pow(μ, 3) * pow(τ₀, 2));
} else {
C[n] = Γ₀ * exp(-μ * fft.t(n)) / μ;
}
R[n] = exp(-μ * fft.t(n));
Ct[n] = 2 * Γ₀ / (pow(μ, 2) + pow(fft.ν(n), 2)) / (1 + pow(τ₀ * fft.ν(n), 2));
Rt[n] = 1.0 / (μ + 1i * fft.ν(n));
}
Real β = 0;
while (β < βₘₐₓ) {
Real ΔC = 100;
while (ΔC > ε) {
std::vector<Real> RddfC(N);
std::vector<Real> dfC(N);
for (unsigned n = 0; n < N; n++) {
RddfC[n] = R[n] * ddf(λ, p, s, C[n]);
dfC[n] = df(λ, p, s, C[n]);
}
std::vector<Complex> RddfCt = fft.fourier(RddfC, false);
std::vector<Complex> dfCt = fft.fourier(dfC, true);
std::vector<Complex> Rtnew(N);
std::vector<Complex> Ctnew(N);
for (unsigned n = 0; n < N; n++) {
Rtnew[n] = (1.0 + pow(β, 2) * RddfCt[n] * Rt[n]) / (μ + 1i * fft.ν(n));
Ctnew[n] = (2 * Γ₀ * std::conj(Rt[n]) / (1 + pow(τ₀ * fft.ν(n), 2)) + pow(β, 2) * (RddfCt[n] * Ct[n] + dfCt[n] * std::conj(Rt[n]))) / (μ + 1i * fft.ν(n));
}
std::vector<Real> Cnew = fft.inverse(Ctnew);
std::vector<Real> Rnew = fft.inverse(Rtnew);
ΔC = 0;
for (unsigned i = 0; i < N; i++) {
ΔC += std::norm(Ct[i] - Ctnew[i]);
ΔC += std::norm(Rt[i] - Rtnew[i]);
}
ΔC = sqrt(ΔC) / (2*N);
for (unsigned i = 0; i < N; i++) {
C[i] += γ * (Cnew[i] - C[i]);
R[i] += γ * (Rnew[i] - R[i]);
Ct[i] += γ * (Ctnew[i] - Ct[i]);
Rt[i] += γ * (Rtnew[i] - Rt[i]);
}
μ *= C[0];
// std::cerr << ΔC << std::endl;
}
std::cerr << β << " " << μ << " " << Ct[0].real() << std::endl;
β += Δβ;
}
for (unsigned i = 0; i < N; i++) {
std::cout << fft.t(i) << " " << Rt[i].imag() << std::endl;
}
return 0;
}
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