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fft_utils.hh
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/**
* file fft_utils.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 06 Dec 2017
*
* @brief collection of functions used in the context of spectral operations
*
* @section LICENCE
*
* Copyright (C) 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#ifndef FFT_UTILS_H
#define FFT_UTILS_H
#include <valarray>
#include <array>
#include <Eigen/Dense>
#include "common/common.hh"
namespace muSpectre {
/**
* compute fft frequencies (in time (or length) units of of sampling
* periods), see numpy's fftfreq function for reference
*/
std::valarray<Real> fft_freqs(size_t nb_samples) {
std::valarray<Real> retval(nb_samples);
Int N = (nb_samples-1)/2 + 1; // needs to be signed int for neg freqs
for (Int i = 0; i < N; ++i) {
retval[i] = i;
}
for (Int i = N; i < Int(nb_samples); ++i) {
retval[i] = -Int(nb_samples)/2+i-N;
}
return retval;
}
/**
* compute fft frequencies in correct length or time units
*/
std::valarray<Real> fft_freqs(size_t nb_samples, Real length) {
return fft_freqs(nb_samples)/length;
}
/**
* Get fft_freqs for a grid
*/
template <size_t dim>
std::array<std::valarray<Real>, dim> fft_freqs(Ccoord_t<dim> sizes) {
std::array<std::valarray<Real>, dim> retval{};
for (size_t i = 0; i < dim; ++i) {
retval[i] = std::move(fft_freqs(sizes[i]));
}
return retval;
}
/**
* simple class encapsulating the creation, and retrieval of
* wave vectors
*/
template <Dim_t dim>
class FFT_freqs
{
public:
using Vector = Eigen::Matrix<Real, dim, 1>;
//! Default constructor
FFT_freqs() = delete;
//! constructor with problem sizes
FFT_freqs(Ccoord_t<dim> sizes)
: freqs{fft_freqs(sizes)} {}
//! Copy constructor
FFT_freqs(const FFT_freqs &other) = delete;
//! Move constructor
FFT_freqs(FFT_freqs &&other) = default;
//! Destructor
virtual ~FFT_freqs() noexcept = default;
//! Copy assignment operator
FFT_freqs& operator=(const FFT_freqs &other) = delete;
//! Move assignment operator
FFT_freqs& operator=(FFT_freqs &&other) = default;
//! get unnormalised wave vector (in sampling units)
inline Vector get_xi(const Ccoord_t<dim> ccoord) const;
//! get normalised wave vector
inline Vector get_unit_xi(const Ccoord_t<dim> ccoord) const{
auto && xi = this->get_xi(std::move(ccoord));
return xi/xi.norm();
}
protected:
const std::array<std::valarray<Real>, dim> freqs;
private:
};
template <Dim_t dim>
typename FFT_freqs<dim>::Vector
FFT_freqs<dim>::get_xi(const Ccoord_t<dim> ccoord) const {
Vector retval{};
for (Dim_t i = 0; i < dim; ++i) {
retval(i) = ccoord[i];
}
return retval;
}
} // muSpectre
#endif /* FFT_UTILS_H */

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