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::EnableCloneable< Fft >
using	result_type = Fft

Public Types inherited from gko::ConvertibleTo< ResultType >
using	result_type = ResultType

Public Member Functions
std::unique_ptr< LinOp >	transpose () const override
	Returns a LinOp representing the transpose of the Transposable object. More...

std::unique_ptr< LinOp >	conj_transpose () const override
	Returns a LinOp representing the conjugate transpose of the Transposable object. More...

void	write (matrix_data< std::complex< float >, int32 > &data) const override
	Writes a matrix to a matrix_data structure. More...

void	write (matrix_data< std::complex< float >, int64 > &data) const override
	Writes a matrix to a matrix_data structure. More...

void	write (matrix_data< std::complex< double >, int32 > &data) const override
	Writes a matrix to a matrix_data structure. More...

void	write (matrix_data< std::complex< double >, int64 > &data) const override
	Writes a matrix to a matrix_data structure. More...

dim< 1 >	get_fft_size () const

bool	is_inverse () const

Public Member Functions inherited from gko::LinOp
void	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
	Applies a linear operator to a vector (or a sequence of vectors). More...

void	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const
	Performs the operation x = alpha * op(b) + beta * x. More...

const dim< 2 > &	get_size () const noexcept
	Returns the size of the operator. More...

virtual bool	apply_uses_initial_guess () const
	Returns true if the linear operator uses the data given in x as an initial guess. More...

LinOp &	operator= (const LinOp &)=default
	Copy-assigns a LinOp. More...

LinOp &	operator= (LinOp &&other)
	Move-assigns a LinOp. More...

	LinOp (const LinOp &)=default
	Copy-constructs a LinOp. More...

	LinOp (LinOp &&other)
	Move-constructs a LinOp. More...

Public Member Functions inherited from gko::PolymorphicObject
PolymorphicObject &	operator= (const PolymorphicObject &)

std::shared_ptr< const Executor >	get_executor () const noexcept
	Returns the Executor of the object. More...

Public Member Functions inherited from gko::log::EnableLogging< PolymorphicObject >
void	add_logger (std::shared_ptr< const Logger > logger) override

void	remove_logger (const Logger *logger) override

void	remove_logger (ptr_param< const Logger > logger)

const std::vector< std::shared_ptr< const Logger > > &	get_loggers () const override

void	clear_loggers () override

Public Member Functions inherited from gko::log::Loggable
void	remove_logger (ptr_param< const Logger > logger)

Public Member Functions inherited from gko::EnableCloneable< Fft >
std::unique_ptr< Fft >	clone (std::shared_ptr< const Executor > exec) const
	Creates a clone of the object. More...

std::unique_ptr< Fft >	clone () const
	Creates a clone of the object. More...

void	convert_to (result_type *result) const override
	Converts the implementer to an object of type result_type. More...

void	move_to (result_type *result) override
	Converts the implementer to an object of type result_type by moving data from this object. More...

std::unique_ptr< Fft >	create_default () const

std::unique_ptr< Fft >	create_default (std::shared_ptr< const Executor > exec) const

Public Member Functions inherited from gko::ConvertibleTo< ResultType >
void	convert_to (ptr_param< result_type > result) const

void	move_to (ptr_param< result_type > result)

Public Member Functions inherited from gko::Cloneable
std::unique_ptr< Cloneable >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Cloneable >	clone () const

Cloneable *	copy_from (ptr_param< const Cloneable > other)

Cloneable *	move_from (ptr_param< Cloneable > other)

std::unique_ptr< Cloneable >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Cloneable >	create_default () const

Static Public Member Functions
static std::unique_ptr< Fft >	create (std::shared_ptr< const Executor > exec)
	Creates an empty Fourier matrix. More...

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. More...

Friends
class	EnableCloneable< Fft >

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]

static 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]

static 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.

◆ write() [1/4]

void gko::matrix::Fft::write ( matrix_data< std::complex< double >, int32 > & data ) const

overridevirtual

Writes a matrix to a matrix_data structure.

Parameters

data	the matrix_data structure

Implements gko::WritableToMatrixData< std::complex< double >, int32 >.

◆ write() [2/4]

void gko::matrix::Fft::write ( matrix_data< std::complex< double >, int64 > & data ) const

overridevirtual

Writes a matrix to a matrix_data structure.

Parameters

data	the matrix_data structure

Implements gko::WritableToMatrixData< std::complex< double >, int64 >.

◆ write() [3/4]

void gko::matrix::Fft::write ( matrix_data< std::complex< float >, int32 > & data ) const

overridevirtual

Writes a matrix to a matrix_data structure.

Parameters

data	the matrix_data structure

Implements gko::WritableToMatrixData< std::complex< float >, int32 >.

◆ write() [4/4]

void gko::matrix::Fft::write ( matrix_data< std::complex< float >, int64 > & data ) const

overridevirtual

Writes a matrix to a matrix_data structure.

Parameters

data	the matrix_data structure

Implements gko::WritableToMatrixData< std::complex< float >, int64 >.

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

ginkgo/core/matrix/fft.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Function Documentation

◆ conj_transpose()

◆ create() [1/2]

◆ create() [2/2]

◆ transpose()

◆ write() [1/4]

◆ write() [2/4]

◆ write() [3/4]

◆ write() [4/4]