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#pragma once
#include <cmath>
#include <fftw3.h>
#include <complex>
#include <vector>
#include <tuple>
#include <gsl/gsl_sf_gamma.h>
#ifndef FFTW_THREADS
#define FFTW_THREADS 1
#endif
using Real = double;
using Complex = std::complex<Real>;
using namespace std::complex_literals;
Real f(Real λ, unsigned p, unsigned s, Real q);
Real df(Real λ, unsigned p, unsigned s, Real q);
Real ddf(Real λ, unsigned p, unsigned s, Real q);
class FourierTransform {
private:
Real* a;
Complex* â;
fftw_plan plan_r2c;
fftw_plan plan_c2r;
unsigned n;
Real Δω;
Real Δτ;
public:
FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags = 0);
~FourierTransform();
std::vector<Complex> fourier(const std::vector<Real>& c);
std::vector<Complex> fourier();
std::vector<Real> inverse(const std::vector<Complex>& ĉ);
void writeToA(unsigned i, Real ai);
std::vector<Real> convolve(const std::vector<Real>& Γh, const std::vector<Real>& R);
};
class LogarithmicFourierTransform {
private:
Complex* a;
Complex* â;
fftw_plan a_to_â;
fftw_plan â_to_a;
unsigned N;
unsigned pad;
Real k;
Real Δτ;
Real τₛ;
Real ωₛ;
Real sₛ;
public:
LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad = 4);
~LogarithmicFourierTransform();
Real τ(unsigned n) const;
Real ω(unsigned n) const;
Real t(unsigned n) const;
Real ν(unsigned n) const;
Real s(unsigned n) const;
std::vector<Complex> fourier(const std::vector<Real>& c, bool symmetric);
std::vector<Real> inverse(const std::vector<Complex>& ĉ);
};
Complex gamma(Complex z);
std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ);
Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ);
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);
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);
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