This LinOp implements a 1D Fourier matrix using the FFT algorithm. More...

#include <ginkgo/core/matrix/fft.hpp>

Inheritance diagram for gko::matrix::Fft:

Collaboration diagram for gko::matrix::Fft:

Public Types
using	value_type = std::complex<double>
using	index_type = int64
using	transposed_type = Fft
Public Types inherited from gko::EnablePolymorphicAssignment< Fft >
using	result_type

Public Member Functions
std::unique_ptr< LinOp >	transpose () const override
	Returns a LinOp representing the transpose of the Transposable object.
std::unique_ptr< LinOp >	conj_transpose () const override
	Returns a LinOp representing the conjugate transpose of the Transposable object.
void	write (matrix_data< std::complex< float >, int32 > &data) const override
void	write (matrix_data< std::complex< float >, int64 > &data) const override
void	write (matrix_data< std::complex< double >, int32 > &data) const override
void	write (matrix_data< std::complex< double >, int64 > &data) const override
dim< 1 >	get_fft_size () const
bool	is_inverse () const
Public Member Functions inherited from gko::EnableLinOp< Fft >
const Fft *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
Public Member Functions inherited from gko::EnablePolymorphicAssignment< Fft >
void	convert_to (result_type *result) const override
void	move_to (result_type *result) override

Static Public Member Functions
static std::unique_ptr< Fft >	create (std::shared_ptr< const Executor > exec)
	Creates an empty Fourier matrix.
static std::unique_ptr< Fft >	create (std::shared_ptr< const Executor > exec, size_type size=0, bool inverse=false)
	Creates an Fourier matrix with the given dimensions.

Friends
class	EnablePolymorphicObject< Fft, LinOp >

Detailed Description

This LinOp implements a 1D Fourier matrix using the FFT algorithm.

It implements forward and inverse DFT.

For a power-of-two size n with corresponding root of unity $\omega = e^{-2\pi i / n}$ for forward DFT and $\omega = e^{2 \pi i / n}$ for inverse DFT it computes

$\‍[ x_k = \sum_{j=0}^{n-1} \omega^{jk} b_j \‍]$

without normalization factors.

The Reference and OpenMP implementations support only power-of-two input sizes, as they use the Radix-2 algorithm by J. W. Cooley and J. W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series," Mathematics of Computation, vol. 19, no. 90, pp. 297–301, 1965, doi: 10.2307/2003354. The CUDA and HIP implementations use cuSPARSE/hipSPARSE with full support for non-power-of-two input sizes and special optimizations for products of small prime powers.

Member Function Documentation

◆ conj_transpose()

std::unique_ptr< LinOp > gko::matrix::Fft::conj_transpose ( ) const

overridevirtual

Returns a LinOp representing the conjugate transpose of the Transposable object.

Returns: a pointer to the new conjugate transposed object

Implements gko::Transposable.

◆ create() [1/2]

std::unique_ptr< Fft > gko::matrix::Fft::create ( std::shared_ptr< const Executor > exec )

static

Creates an empty Fourier matrix.

Parameters

exec	Executor associated to the matrix

Returns: A smart pointer to the newly created matrix.

◆ create() [2/2]

std::unique_ptr< Fft > gko::matrix::Fft::create	(	std::shared_ptr< const Executor >	exec,
		size_type	size = 0,
		bool	inverse = false )

static

Creates an Fourier matrix with the given dimensions.

Parameters

size	size of the matrix
inverse	true to compute an inverse DFT instead of a normal DFT

Returns: A smart pointer to the newly created matrix.

◆ transpose()

std::unique_ptr< LinOp > gko::matrix::Fft::transpose ( ) const

overridevirtual

Returns a LinOp representing the transpose of the Transposable object.

Returns: a pointer to the new transposed object

Implements gko::Transposable.

The documentation for this class was generated from the following file:

ginkgo/core/matrix/fft.hpp

Public Types

Public Member Functions