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#include <getopt.h>
#include <vector>
#include <cmath>
#include <iostream>
#include <fftw3.h>
#include <complex>
#include <fstream>
using Real = double;
using Complex = std::complex<Real>;
using namespace std::complex_literals;
inline Real fP(unsigned p, Real q) {
return 0.5 * pow(q, p);
}
inline Real dfP(unsigned p, Real q) {
return 0.5 * p * pow(q, p - 1);
}
inline Real ddfP(unsigned p, Real q) {
return 0.5 * p * (p - 1) * pow(q, p - 2);
}
inline Real f(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * fP(p, q) + λ * fP(s, q);
}
inline Real df(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
}
inline Real ddf(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
}
class FourierTransform {
private:
std::vector<Real> a;
std::vector<Complex> â;
fftw_plan plan_r2c;
fftw_plan plan_c2r;
Real Δω;
Real Δτ;
public:
FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags = 0) : a(2 * n), â(n + 1), Δω(Δω), Δτ(Δτ) {
plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a.data(), reinterpret_cast<fftw_complex*>(â.data()), flags);
plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â.data()), a.data(), flags);
}
~FourierTransform() {
fftw_destroy_plan(plan_r2c);
fftw_destroy_plan(plan_c2r);
fftw_cleanup();
}
std::vector<Complex> fourier(const std::vector<Real>& c) {
a = c;
fftw_execute(plan_r2c);
std::vector<Complex> ĉ(â.size());
for (unsigned i = 0; i < â.size(); i++) {
ĉ[i] = â[i] * (Δτ * M_PI);
}
return ĉ;
}
std::vector<Real> inverse(const std::vector<Complex>& ĉ) {
â = ĉ;
fftw_execute(plan_c2r);
std::vector<Real> c(a.size());
for (unsigned i = 0; i < a.size(); i++) {
c[i] = a[i] * (Δω / (2 * M_PI));
}
return c;
}
};
int main(int argc, char* argv[]) {
unsigned p = 2;
unsigned s = 2;
Real λ = 0.5;
Real τ₀ = 0;
Real y₀ = 0;
Real yₘₐₓ = 0.5;
Real Δy = 0.05;
unsigned log2n = 8;
Real τₘₐₓ = 20;
int opt;
while ((opt = getopt(argc, argv, "p:s:2:T:t:0:y:d:")) != -1) {
switch (opt) {
case 'p':
p = atoi(optarg);
break;
case 's':
s = atoi(optarg);
break;
case '2':
log2n = atoi(optarg);
break;
case 'T':
τₘₐₓ = atof(optarg);
break;
case 't':
τ₀ = atof(optarg);
break;
case '0':
y₀ = atof(optarg);
break;
case 'y':
yₘₐₓ = atof(optarg);
break;
case 'd':
Δy = atof(optarg);
break;
default:
exit(1);
}
}
unsigned n = pow(2, log2n);
Real Δτ = τₘₐₓ / M_PI / n;
Real Δω = M_PI / τₘₐₓ;
Real y = y₀;
FourierTransform fft(n, Δω, Δτ, FFTW_ESTIMATE);
while (y += Δy, y <= yₘₐₓ) {
std::vector<Real> C(2 * n);
std::vector<Real> R(2 * n);
std::string file_end = std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
std::ifstream cfile("C_"+file_end, std::ios::binary);
if (cfile.is_open()) {
cfile.read((char*)(C.data()), C.size() * sizeof(Real));
cfile.close();
std::ifstream rfile("R_"+file_end, std::ios::binary);
rfile.read((char*)(R.data()), R.size() * sizeof(Real));
rfile.close();
Real energy = 0;
for (unsigned i = 0; i < n; i++) {
energy += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
}
std::vector<Complex> Ct = fft.fourier(C);
std::cout << y << " " << energy << " " << Ct[0].real() << std::endl;
}
}
return 0;
}
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