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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FFT_MODULE_H
#define EIGEN_FFT_MODULE_H
#include <complex>
#include <vector>
#include <map>
#include "../../Eigen/Core"
/**
* \defgroup FFT_Module Fast Fourier Transform module
*
* \code
* #include <unsupported/Eigen/FFT>
* \endcode
*
* This module provides Fast Fourier transformation, with a configurable backend
* implementation.
*
* The default implementation is based on kissfft. It is a small, free, and
* reasonably efficient default.
*
* There are currently four implementation backend:
*
* - kissfft(https://github.com/mborgerding/kissfft) : Simple and not so fast, BSD-3-Clause.
* It is a mixed-radix Fast Fourier Transform based up on the principle, "Keep It Simple, Stupid."
* Notice that:kissfft fails to handle "atypically-sized" inputs(i.e., sizes with large factors),a workaround is using
* fftw or pocketfft.
* - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
* - MKL (https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-download.html) : fastest, free -- may be
* incompatible with Eigen in GPL form.
* - pocketfft (https://gitlab.mpcdf.mpg.de/mtr/pocketfft) : faster than kissfft, BSD 3-clause.
* It is a heavily modified implementation of FFTPack, with the following advantages:
* 1.strictly C++11 compliant
* 2.more accurate twiddle factor computation
* 3.very fast plan generation
* 4.worst case complexity for transform sizes with large prime factors is N*log(N), because Bluestein's algorithm is
* used for these cases
*
* \section FFTDesign Design
*
* The following design decisions were made concerning scaling and
* half-spectrum for real FFT.
*
* The intent is to facilitate generic programming and ease migrating code
* from Matlab/octave.
* We think the default behavior of Eigen/FFT should favor correctness and
* generality over speed. Of course, the caller should be able to "opt-out" from this
* behavior and get the speed increase if they want it.
*
* 1) %Scaling:
* Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there
* is a constant gain incurred after the forward&inverse transforms , so
* IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply.
* The downside is that algorithms that worked correctly in Matlab/octave
* don't behave the same way once implemented in C++.
*
* How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x.
*
* 2) Real FFT half-spectrum
* Other libraries use only half the frequency spectrum (plus one extra
* sample for the Nyquist bin) for a real FFT, the other half is the
* conjugate-symmetric of the first half. This saves them a copy and some
* memory. The downside is the caller needs to have special logic for the
* number of bins in complex vs real.
*
* How Eigen/FFT differs: The full spectrum is returned from the forward
* transform. This facilitates generic template programming by obviating
* separate specializations for real vs complex. On the inverse
* transform, only half the spectrum is actually used if the output type is real.
*/
#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
// IWYU pragma: begin_exports
#ifdef EIGEN_FFTW_DEFAULT
// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
#include <fftw3.h>
#include "src/FFT/ei_fftw_impl.h"
namespace Eigen {
// template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work
template <typename T>
struct default_fft_impl : public internal::fftw_impl<T> {};
} // namespace Eigen
#elif defined EIGEN_MKL_DEFAULT
// intel Math Kernel Library: fastest, free -- may be incompatible with Eigen in GPL form
#include "src/FFT/ei_imklfft_impl.h"
namespace Eigen {
template <typename T>
struct default_fft_impl : public internal::imklfft::imklfft_impl<T> {};
} // namespace Eigen
#elif defined EIGEN_POCKETFFT_DEFAULT
// internal::pocketfft_impl: a heavily modified implementation of FFTPack, with many advantages.
#include <pocketfft_hdronly.h>
#include "src/FFT/ei_pocketfft_impl.h"
namespace Eigen {
template <typename T>
struct default_fft_impl : public internal::pocketfft_impl<T> {};
} // namespace Eigen
#else
// internal::kissfft_impl: small, free, reasonably efficient default, derived from kissfft
#include "src/FFT/ei_kissfft_impl.h"
namespace Eigen {
template <typename T>
struct default_fft_impl : public internal::kissfft_impl<T> {};
} // namespace Eigen
#endif
// IWYU pragma: end_exports
namespace Eigen {
//
template <typename T_SrcMat, typename T_FftIfc>
struct fft_fwd_proxy;
template <typename T_SrcMat, typename T_FftIfc>
struct fft_inv_proxy;
namespace internal {
template <typename T_SrcMat, typename T_FftIfc>
struct traits<fft_fwd_proxy<T_SrcMat, T_FftIfc> > {
typedef typename T_SrcMat::PlainObject ReturnType;
};
template <typename T_SrcMat, typename T_FftIfc>
struct traits<fft_inv_proxy<T_SrcMat, T_FftIfc> > {
typedef typename T_SrcMat::PlainObject ReturnType;
};
} // namespace internal
template <typename T_SrcMat, typename T_FftIfc>
struct fft_fwd_proxy : public ReturnByValue<fft_fwd_proxy<T_SrcMat, T_FftIfc> > {
typedef DenseIndex Index;
fft_fwd_proxy(const T_SrcMat& src, T_FftIfc& fft, Index nfft) : m_src(src), m_ifc(fft), m_nfft(nfft) {}
template <typename T_DestMat>
void evalTo(T_DestMat& dst) const;
Index rows() const { return m_src.rows(); }
Index cols() const { return m_src.cols(); }
protected:
const T_SrcMat& m_src;
T_FftIfc& m_ifc;
Index m_nfft;
};
template <typename T_SrcMat, typename T_FftIfc>
struct fft_inv_proxy : public ReturnByValue<fft_inv_proxy<T_SrcMat, T_FftIfc> > {
typedef DenseIndex Index;
fft_inv_proxy(const T_SrcMat& src, T_FftIfc& fft, Index nfft) : m_src(src), m_ifc(fft), m_nfft(nfft) {}
template <typename T_DestMat>
void evalTo(T_DestMat& dst) const;
Index rows() const { return m_src.rows(); }
Index cols() const { return m_src.cols(); }
protected:
const T_SrcMat& m_src;
T_FftIfc& m_ifc;
Index m_nfft;
};
template <typename T_Scalar, typename T_Impl = default_fft_impl<T_Scalar> >
class FFT {
public:
typedef T_Impl impl_type;
typedef DenseIndex Index;
typedef typename impl_type::Scalar Scalar;
typedef typename impl_type::Complex Complex;
using Flag = int;
static constexpr Flag Default = 0;
static constexpr Flag Unscaled = 1;
static constexpr Flag HalfSpectrum = 2;
static constexpr Flag Speedy = 32767;
FFT(const impl_type& impl = impl_type(), Flag flags = Default) : m_impl(impl), m_flag(flags) {
eigen_assert((flags == Default || flags == Unscaled || flags == HalfSpectrum || flags == Speedy) &&
"invalid flags argument");
}
inline bool HasFlag(Flag f) const { return (m_flag & (int)f) == f; }
inline void SetFlag(Flag f) { m_flag |= (int)f; }
inline void ClearFlag(Flag f) { m_flag &= (~(int)f); }
inline void fwd(Complex* dst, const Scalar* src, Index nfft) {
m_impl.fwd(dst, src, static_cast<int>(nfft));
if (HasFlag(HalfSpectrum) == false) ReflectSpectrum(dst, nfft);
}
inline void fwd(Complex* dst, const Complex* src, Index nfft) { m_impl.fwd(dst, src, static_cast<int>(nfft)); }
#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
inline void fwd2(Complex* dst, const Complex* src, int n0, int n1) { m_impl.fwd2(dst, src, n0, n1); }
#endif
template <typename Input_>
inline void fwd(std::vector<Complex>& dst, const std::vector<Input_>& src) {
if (NumTraits<Input_>::IsComplex == 0 && HasFlag(HalfSpectrum))
dst.resize((src.size() >> 1) + 1); // half the bins + Nyquist bin
else
dst.resize(src.size());
fwd(&dst[0], &src[0], src.size());
}
template <typename InputDerived, typename ComplexDerived>
inline void fwd(MatrixBase<ComplexDerived>& dst, const MatrixBase<InputDerived>& src, Index nfft = -1) {
typedef typename ComplexDerived::Scalar dst_type;
typedef typename InputDerived::Scalar src_type;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived, InputDerived) // size at compile-time
EIGEN_STATIC_ASSERT(
(internal::is_same<dst_type, Complex>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(InputDerived::Flags) & int(ComplexDerived::Flags) & DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
if (nfft < 1) nfft = src.size();
if (NumTraits<src_type>::IsComplex == 0 && HasFlag(HalfSpectrum))
dst.derived().resize((nfft >> 1) + 1);
else
dst.derived().resize(nfft);
if (src.innerStride() != 1 || src.size() < nfft) {
Matrix<src_type, 1, Dynamic> tmp;
if (src.size() < nfft) {
tmp.setZero(nfft);
tmp.block(0, 0, src.size(), 1) = src;
} else {
tmp = src;
}
fwd(&dst[0], &tmp[0], nfft);
} else {
fwd(&dst[0], &src[0], nfft);
}
}
template <typename InputDerived>
inline fft_fwd_proxy<MatrixBase<InputDerived>, FFT<T_Scalar, T_Impl> > fwd(const MatrixBase<InputDerived>& src,
Index nfft = -1) {
return fft_fwd_proxy<MatrixBase<InputDerived>, FFT<T_Scalar, T_Impl> >(src, *this, nfft);
}
template <typename InputDerived>
inline fft_inv_proxy<MatrixBase<InputDerived>, FFT<T_Scalar, T_Impl> > inv(const MatrixBase<InputDerived>& src,
Index nfft = -1) {
return fft_inv_proxy<MatrixBase<InputDerived>, FFT<T_Scalar, T_Impl> >(src, *this, nfft);
}
inline void inv(Complex* dst, const Complex* src, Index nfft) {
m_impl.inv(dst, src, static_cast<int>(nfft));
if (HasFlag(Unscaled) == false) scale(dst, Scalar(1. / nfft), nfft); // scale the time series
}
inline void inv(Scalar* dst, const Complex* src, Index nfft) {
m_impl.inv(dst, src, static_cast<int>(nfft));
if (HasFlag(Unscaled) == false) scale(dst, Scalar(1. / nfft), nfft); // scale the time series
}
template <typename OutputDerived, typename ComplexDerived>
inline void inv(MatrixBase<OutputDerived>& dst, const MatrixBase<ComplexDerived>& src, Index nfft = -1) {
typedef typename ComplexDerived::Scalar src_type;
typedef typename ComplexDerived::RealScalar real_type;
typedef typename OutputDerived::Scalar dst_type;
const bool realfft = (NumTraits<dst_type>::IsComplex == 0);
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived, OutputDerived) // size at compile-time
EIGEN_STATIC_ASSERT(
(internal::is_same<src_type, Complex>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(OutputDerived::Flags) & int(ComplexDerived::Flags) & DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
if (nfft < 1) { // automatic FFT size determination
if (realfft && HasFlag(HalfSpectrum))
nfft = 2 * (src.size() - 1); // assume even fft size
else
nfft = src.size();
}
dst.derived().resize(nfft);
// check for nfft that does not fit the input data size
Index resize_input = (realfft && HasFlag(HalfSpectrum)) ? ((nfft / 2 + 1) - src.size()) : (nfft - src.size());
if (src.innerStride() != 1 || resize_input) {
// if the vector is strided, then we need to copy it to a packed temporary
Matrix<src_type, 1, Dynamic> tmp;
if (resize_input) {
size_t ncopy = (std::min)(src.size(), src.size() + resize_input);
tmp.setZero(src.size() + resize_input);
if (realfft && HasFlag(HalfSpectrum)) {
// pad at the Nyquist bin
tmp.head(ncopy) = src.head(ncopy);
tmp(ncopy - 1) = real(tmp(ncopy - 1)); // enforce real-only Nyquist bin
} else {
size_t nhead, ntail;
nhead = 1 + ncopy / 2 - 1; // range [0:pi)
ntail = ncopy / 2 - 1; // range (-pi:0)
tmp.head(nhead) = src.head(nhead);
tmp.tail(ntail) = src.tail(ntail);
if (resize_input <
0) { // shrinking -- create the Nyquist bin as the average of the two bins that fold into it
tmp(nhead) = (src(nfft / 2) + src(src.size() - nfft / 2)) * real_type(.5);
} else { // expanding -- split the old Nyquist bin into two halves
tmp(nhead) = src(nhead) * real_type(.5);
tmp(tmp.size() - nhead) = tmp(nhead);
}
}
} else {
tmp = src;
}
inv(&dst[0], &tmp[0], nfft);
} else {
inv(&dst[0], &src[0], nfft);
}
}
template <typename Output_>
inline void inv(std::vector<Output_>& dst, const std::vector<Complex>& src, Index nfft = -1) {
if (nfft < 1)
nfft = (NumTraits<Output_>::IsComplex == 0 && HasFlag(HalfSpectrum)) ? 2 * (src.size() - 1) : src.size();
dst.resize(nfft);
inv(&dst[0], &src[0], nfft);
}
#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
inline void inv2(Complex* dst, const Complex* src, int n0, int n1) {
m_impl.inv2(dst, src, n0, n1);
if (HasFlag(Unscaled) == false) scale(dst, 1. / (n0 * n1), n0 * n1);
}
#endif
inline impl_type& impl() { return m_impl; }
private:
template <typename T_Data>
inline void scale(T_Data* x, Scalar s, Index nx) {
#if 1
for (int k = 0; k < nx; ++k) *x++ *= s;
#else
if (((ptrdiff_t)x) & 15)
Matrix<T_Data, Dynamic, 1>::Map(x, nx) *= s;
else
Matrix<T_Data, Dynamic, 1>::MapAligned(x, nx) *= s;
// Matrix<T_Data, Dynamic, Dynamic>::Map(x,nx) * s;
#endif
}
inline void ReflectSpectrum(Complex* freq, Index nfft) {
// create the implicit right-half spectrum (conjugate-mirror of the left-half)
Index nhbins = (nfft >> 1) + 1;
for (Index k = nhbins; k < nfft; ++k) freq[k] = conj(freq[nfft - k]);
}
impl_type m_impl;
int m_flag;
};
template <typename T_SrcMat, typename T_FftIfc>
template <typename T_DestMat>
inline void fft_fwd_proxy<T_SrcMat, T_FftIfc>::evalTo(T_DestMat& dst) const {
m_ifc.fwd(dst, m_src, m_nfft);
}
template <typename T_SrcMat, typename T_FftIfc>
template <typename T_DestMat>
inline void fft_inv_proxy<T_SrcMat, T_FftIfc>::evalTo(T_DestMat& dst) const {
m_ifc.inv(dst, m_src, m_nfft);
}
} // namespace Eigen
#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
#endif