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#include "fourier.hpp"
#include <fftw3.h>
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);
}
Real f(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * fP(p, q) + λ * fP(s, q);
}
Real df(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
}
Real ddf(Real λ, unsigned p, unsigned s, Real q) {
return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
}
FourierTransform::FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags) : n(n), Δω(Δω), Δτ(Δτ) {
a = fftw_alloc_real(2 * n);
â = reinterpret_cast<Complex*>(fftw_alloc_complex(n + 1));
// fftw_init_threads();
// fftw_plan_with_nthreads(FFTW_THREADS);
fftw_import_wisdom_from_filename("fftw.wisdom");
plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a, reinterpret_cast<fftw_complex*>(â), flags);
plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â), a, flags);
fftw_export_wisdom_to_filename("fftw.wisdom");
}
FourierTransform::~FourierTransform() {
fftw_destroy_plan(plan_r2c);
fftw_destroy_plan(plan_c2r);
fftw_free(a);
fftw_free(â);
fftw_cleanup();
}
std::vector<Complex> FourierTransform::fourier(const std::vector<Real>& c) {
for (unsigned i = 0; i < 2 * n; i++) {
a[i] = c[i];
}
fftw_execute(plan_r2c);
std::vector<Complex> ĉ(n + 1);
for (unsigned i = 0; i < n + 1; i++) {
ĉ[i] = â[i] * (Δτ * M_PI);
}
return ĉ;
}
std::vector<Complex> FourierTransform::fourier() {
fftw_execute(plan_r2c);
std::vector<Complex> ĉ(n+1);
for (unsigned i = 0; i < n+1; i++) {
ĉ[i] = â[i] * (Δτ * M_PI);
}
return ĉ;
}
std::vector<Real> FourierTransform::convolve(const std::vector<Real>& Γh, const std::vector<Real>& R) {
a[0] = 0;
for (unsigned i = 1; i < n; i++) {
a[i] = R[i];
a[2 * n - i] = -R[i];
}
fftw_execute(plan_r2c);
for (unsigned i = 1; i < n + 1; i++) {
â[i] *= Γh[i] * (Δτ * M_PI);
}
fftw_execute(plan_c2r);
std::vector<Real> dC(n);
for (unsigned i = 0; i < n; i++) {
dC[i] = a[i] * (Δω / (2 * M_PI));
}
return dC;
}
std::vector<Real> FourierTransform::inverse(const std::vector<Complex>& ĉ) {
for (unsigned i = 0; i < n + 1; i++) {
â[i] = ĉ[i];
}
fftw_execute(plan_c2r);
std::vector<Real> c(2*n);
for (unsigned i = 0; i < 2*n; i++) {
c[i] = a[i] * (Δω / (2 * M_PI));
}
return c;
}
void FourierTransform::writeToA(unsigned i, Real ai) {
a[i] = ai;
}
LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad) : N(N), pad(pad), k(k), Δτ(Δτ) {
τₛ = -0.5 * N;
ωₛ = -0.5 * N;
sₛ = -0.5 * pad * N;
a = reinterpret_cast<Complex*>(fftw_alloc_complex(pad*N));
â = reinterpret_cast<Complex*>(fftw_alloc_complex(pad*N));
fftw_import_wisdom_from_filename("fftw.wisdom");
a_to_â = fftw_plan_dft_1d(pad*N, reinterpret_cast<fftw_complex*>(a), reinterpret_cast<fftw_complex*>(â), FFTW_BACKWARD, 0);
â_to_a = fftw_plan_dft_1d(pad*N, reinterpret_cast<fftw_complex*>(â), reinterpret_cast<fftw_complex*>(a), FFTW_BACKWARD, 0);
fftw_export_wisdom_to_filename("fftw.wisdom");
}
LogarithmicFourierTransform::~LogarithmicFourierTransform() {
fftw_destroy_plan(a_to_â);
fftw_destroy_plan(â_to_a);
fftw_free(a);
fftw_free(â);
fftw_cleanup();
}
Real LogarithmicFourierTransform::τ(unsigned n) const {
return Δτ * (n + τₛ);
}
Real LogarithmicFourierTransform::ω(unsigned n) const {
return Δτ * (n + ωₛ);
}
Real LogarithmicFourierTransform::s(unsigned n) const {
return (n + sₛ) * 2*M_PI / (pad * N * Δτ);
}
Real LogarithmicFourierTransform::t(unsigned n) const {
return exp(τ(n));
}
Real LogarithmicFourierTransform::ν(unsigned n) const {
return exp(ω(n));
}
Complex gamma(Complex z) {
gsl_sf_result logΓ;
gsl_sf_result argΓ;
gsl_sf_lngamma_complex_e(z.real(), z.imag(), &logΓ, &argΓ);
return exp(logΓ.val + 1i * argΓ.val);
}
std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real>& c, bool symmetric) {
std::vector<Complex> ĉ(N);
std::vector<Real> σs = {1};
if (symmetric){
σs.push_back(-1);
}
for (Real σ : σs) {
for (unsigned n = 0; n < pad*N; n++) {
if (n < N) {
a[n] = c[n] * exp((1 - k) * τ(n));
} else {
a[n] = 0;
}
}
fftw_execute(a_to_â);
for (unsigned n = 0; n < pad*N; n++) {
â[(pad*N / 2 + n) % (pad*N)] *= pow(1i * σ, 1i * s(n) - k) * gamma(k - 1i * s(n));
}
fftw_execute(â_to_a);
for (unsigned n = 0; n < N; n++) {
ĉ[n] += exp(-k * ω(n)) * a[(pad - 1)*N+n].real() / (Real)(pad*N);
}
}
return ĉ;
}
std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex>& ĉ) {
std::vector<Real> c(N);
std::vector<Real> σs = {1, -1};
for (Real σ : σs) {
for (unsigned n = 0; n < pad * N; n++) {
if (n < N) {
a[n] = ĉ[n] * exp((1 - k) * ω(n));
} else {
a[n] = 0;
}
}
fftw_execute(a_to_â);
for (unsigned n = 0; n < pad*N; n++) {
â[(pad*N / 2 + n) % (pad*N)] *= pow(-1i * σ, 1i * s(n) - k) * gamma(k - 1i * s(n));
}
fftw_execute(â_to_a);
for (unsigned n = 0; n < N; n++) {
c[n] += exp(-k * τ(n)) * a[(pad - 1)*N+n].real() / (Real)(pad*N) / (2 * M_PI);
}
}
return c;
}
std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ) {
return prefix + "_" + 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";
}
Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ) {
Real e = 0;
for (unsigned i = 0; i < C.size() / 2; i++) {
e += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
}
return e;
}
std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(FourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ) {
for (unsigned i = 0; i < C.size() / 2; i++) {
fft.writeToA(i, R[i] * ddf(λ, p, s, C[i]));
}
for (unsigned i = C.size() / 2; i < C.size(); i++) {
fft.writeToA(i, 0);
}
std::vector<Complex> RddfCt = fft.fourier();
for (unsigned i = 0; i < C.size(); i++) {
fft.writeToA(i, df(λ, p, s, C[i]));
}
std::vector<Complex> dfCt = fft.fourier();
return {RddfCt, dfCt};
}
Real estimateZ(FourierTransform& fft, const std::vector<Real>& C, const std::vector<Complex>& Ct, const std::vector<Real>& R, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real y) {
auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
Real Γ₀ = 1 + τ₀ / 2;
return ((Γ₀ * std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
}
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