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This commit is contained in:
Tobias Wood
@@ -1,5 +1,5 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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// for linear algebra.
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//
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// Copyright (C) 2009 Mark Borgerding mark a borgerding net
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//
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@@ -15,67 +15,68 @@
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#include <map>
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#include "../../Eigen/Core"
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/**
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* \defgroup FFT_Module Fast Fourier Transform module
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*
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* \code
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* #include <unsupported/Eigen/FFT>
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* \endcode
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*
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* This module provides Fast Fourier transformation, with a configurable backend
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* implementation.
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*
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* The default implementation is based on kissfft. It is a small, free, and
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* reasonably efficient default.
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*
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* There are currently four implementation backend:
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*
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* - kissfft(https://github.com/mborgerding/kissfft) : Simple and not so fast, BSD-3-Clause.
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* It is a mixed-radix Fast Fourier Transform based up on the principle, "Keep It Simple, Stupid."
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* Notice that:kissfft fails to handle "atypically-sized" inputs(i.e., sizes with large factors),a workaround is using fftw or pocketfft.
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* - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
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* - 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.
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* - pocketfft (https://gitlab.mpcdf.mpg.de/mtr/pocketfft) : faster than kissfft, BSD 3-clause.
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* It is a heavily modified implementation of FFTPack, with the following advantages:
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* 1.strictly C++11 compliant
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* 2.more accurate twiddle factor computation
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* 3.very fast plan generation
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* 4.worst case complexity for transform sizes with large prime factors is N*log(N), because Bluestein's algorithm is used for these cases
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*
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* \section FFTDesign Design
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*
|
||||
* The following design decisions were made concerning scaling and
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* half-spectrum for real FFT.
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*
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||||
* The intent is to facilitate generic programming and ease migrating code
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* from Matlab/octave.
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* We think the default behavior of Eigen/FFT should favor correctness and
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* generality over speed. Of course, the caller should be able to "opt-out" from this
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* behavior and get the speed increase if they want it.
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||||
*
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||||
* 1) %Scaling:
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* Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there
|
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* is a constant gain incurred after the forward&inverse transforms , so
|
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* IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply.
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* The downside is that algorithms that worked correctly in Matlab/octave
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* don't behave the same way once implemented in C++.
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*
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* How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x.
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*
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* 2) Real FFT half-spectrum
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* Other libraries use only half the frequency spectrum (plus one extra
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* sample for the Nyquist bin) for a real FFT, the other half is the
|
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* conjugate-symmetric of the first half. This saves them a copy and some
|
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* memory. The downside is the caller needs to have special logic for the
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* number of bins in complex vs real.
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*
|
||||
* How Eigen/FFT differs: The full spectrum is returned from the forward
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* transform. This facilitates generic template programming by obviating
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* separate specializations for real vs complex. On the inverse
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* transform, only half the spectrum is actually used if the output type is real.
|
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*/
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||||
|
||||
* \defgroup FFT_Module Fast Fourier Transform module
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*
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* \code
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* #include <unsupported/Eigen/FFT>
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* \endcode
|
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*
|
||||
* This module provides Fast Fourier transformation, with a configurable backend
|
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* implementation.
|
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*
|
||||
* 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.
|
||||
*/
|
||||
|
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#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
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|
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@@ -83,356 +84,308 @@
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#ifdef EIGEN_FFTW_DEFAULT
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// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
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# include <fftw3.h>
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# include "src/FFT/ei_fftw_impl.h"
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namespace Eigen {
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//template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work
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template <typename T> struct default_fft_impl : public internal::fftw_impl<T> {};
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||||
}
|
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#include <fftw3.h>
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#include "src/FFT/ei_fftw_impl.h"
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namespace Eigen {
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// template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work
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template <typename T>
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struct default_fft_impl : public internal::fftw_impl<T> {};
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} // namespace Eigen
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#elif defined EIGEN_MKL_DEFAULT
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// intel Math Kernel Library: fastest, free -- may be incompatible with Eigen in GPL form
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# include "src/FFT/ei_imklfft_impl.h"
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namespace Eigen {
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template <typename T> struct default_fft_impl : public internal::imklfft::imklfft_impl<T> {};
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}
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#include "src/FFT/ei_imklfft_impl.h"
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namespace Eigen {
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template <typename T>
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struct default_fft_impl : public internal::imklfft::imklfft_impl<T> {};
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} // namespace Eigen
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#elif defined EIGEN_POCKETFFT_DEFAULT
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// internal::pocketfft_impl: a heavily modified implementation of FFTPack, with many advantages.
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# include<pocketfft_hdronly.h>
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# include"src/FFT/ei_pocketfft_impl.h"
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namespace Eigen {
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||||
template <typename T>
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struct default_fft_impl : public internal::pocketfft_impl<T> {};
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}
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#else
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#include <pocketfft_hdronly.h>
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#include "src/FFT/ei_pocketfft_impl.h"
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namespace Eigen {
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template <typename T>
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struct default_fft_impl : public internal::pocketfft_impl<T> {};
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} // namespace Eigen
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#else
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// internal::kissfft_impl: small, free, reasonably efficient default, derived from kissfft
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# include "src/FFT/ei_kissfft_impl.h"
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namespace Eigen {
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template <typename T>
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struct default_fft_impl : public internal::kissfft_impl<T> {};
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}
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#include "src/FFT/ei_kissfft_impl.h"
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namespace Eigen {
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template <typename T>
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struct default_fft_impl : public internal::kissfft_impl<T> {};
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} // namespace Eigen
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#endif
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|
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// IWYU pragma: end_exports
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|
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namespace Eigen {
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|
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|
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//
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template<typename T_SrcMat,typename T_FftIfc> struct fft_fwd_proxy;
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template<typename T_SrcMat,typename T_FftIfc> struct fft_inv_proxy;
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//
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template <typename T_SrcMat, typename T_FftIfc>
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struct fft_fwd_proxy;
|
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template <typename T_SrcMat, typename T_FftIfc>
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struct fft_inv_proxy;
|
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|
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namespace internal {
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template<typename T_SrcMat,typename T_FftIfc>
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struct traits< fft_fwd_proxy<T_SrcMat,T_FftIfc> >
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{
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template <typename T_SrcMat, typename T_FftIfc>
|
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struct traits<fft_fwd_proxy<T_SrcMat, T_FftIfc> > {
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typedef typename T_SrcMat::PlainObject ReturnType;
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};
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template<typename T_SrcMat,typename T_FftIfc>
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struct traits< fft_inv_proxy<T_SrcMat,T_FftIfc> >
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{
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template <typename T_SrcMat, typename T_FftIfc>
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struct traits<fft_inv_proxy<T_SrcMat, T_FftIfc> > {
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typedef typename T_SrcMat::PlainObject ReturnType;
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};
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}
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} // namespace internal
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|
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template<typename T_SrcMat,typename T_FftIfc>
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struct fft_fwd_proxy
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: public ReturnByValue<fft_fwd_proxy<T_SrcMat,T_FftIfc> >
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{
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template <typename T_SrcMat, typename T_FftIfc>
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struct fft_fwd_proxy : public ReturnByValue<fft_fwd_proxy<T_SrcMat, T_FftIfc> > {
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typedef DenseIndex Index;
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fft_fwd_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
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fft_fwd_proxy(const T_SrcMat& src, T_FftIfc& fft, Index nfft) : m_src(src), m_ifc(fft), m_nfft(nfft) {}
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|
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template<typename T_DestMat> void evalTo(T_DestMat& dst) const;
|
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template <typename T_DestMat>
|
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void evalTo(T_DestMat& dst) const;
|
||||
|
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Index rows() const { return m_src.rows(); }
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Index cols() const { return m_src.cols(); }
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protected:
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const T_SrcMat & m_src;
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T_FftIfc & m_ifc;
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|
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protected:
|
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const T_SrcMat& m_src;
|
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T_FftIfc& m_ifc;
|
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Index m_nfft;
|
||||
};
|
||||
|
||||
template<typename T_SrcMat,typename T_FftIfc>
|
||||
struct fft_inv_proxy
|
||||
: public ReturnByValue<fft_inv_proxy<T_SrcMat,T_FftIfc> >
|
||||
{
|
||||
template <typename T_SrcMat, typename T_FftIfc>
|
||||
struct fft_inv_proxy : public ReturnByValue<fft_inv_proxy<T_SrcMat, T_FftIfc> > {
|
||||
typedef DenseIndex Index;
|
||||
|
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fft_inv_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
|
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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;
|
||||
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;
|
||||
|
||||
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;
|
||||
|
||||
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;
|
||||
|
||||
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");
|
||||
}
|
||||
|
||||
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
|
||||
bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;}
|
||||
inline void SetFlag(Flag f) { m_flag |= (int)f; }
|
||||
|
||||
inline
|
||||
void SetFlag(Flag f) { m_flag |= (int)f;}
|
||||
inline void ClearFlag(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 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));
|
||||
}
|
||||
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);
|
||||
}
|
||||
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 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, 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)
|
||||
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);
|
||||
}
|
||||
|
||||
if (nfft<1)
|
||||
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();
|
||||
|
||||
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 );
|
||||
}
|
||||
dst.derived().resize(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 );
|
||||
}
|
||||
// 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());
|
||||
|
||||
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);
|
||||
}
|
||||
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);
|
||||
} 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);
|
||||
}
|
||||
|
||||
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);
|
||||
}
|
||||
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; }
|
||||
|
||||
inline
|
||||
impl_type & impl() {return m_impl;}
|
||||
private:
|
||||
|
||||
template <typename T_Data>
|
||||
inline
|
||||
void scale(T_Data * x,Scalar s,Index nx)
|
||||
{
|
||||
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;
|
||||
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
|
||||
}
|
||||
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]);
|
||||
}
|
||||
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;
|
||||
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_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);
|
||||
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"
|
||||
|
||||
|
||||
Reference in New Issue
Block a user