This LinOp implements a 2D Fourier matrix using the FFT algorithm. More...

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

Inheritance diagram for gko::matrix::Fft2:

Collaboration diagram for gko::matrix::Fft2:

Public Types
using	value_type = std::complex< double >

using	index_type = int64

using	transposed_type = Fft2

Public Types inherited from gko::EnableCloneable< Fft2 >
using	result_type = Fft2

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< 2 >	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
virtual void	validate_data () const
	Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge.

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< Fft2 >
std::unique_ptr< Fft2 >	clone (std::shared_ptr< const Executor > exec) const
	Creates a clone of the object. More...

std::unique_ptr< Fft2 >	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< Fft2 >	create_default () const

std::unique_ptr< Fft2 >	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< Fft2 >	create (std::shared_ptr< const Executor > exec)
	Creates an empty Fourier matrix. More...

static std::unique_ptr< Fft2 >	create (std::shared_ptr< const Executor > exec, size_type size)
	Creates an Fourier matrix with the given dimensions. More...

static std::unique_ptr< Fft2 >	create (std::shared_ptr< const Executor > exec, size_type size1, size_type size2, bool inverse=false)
	Creates an Fourier matrix with the given dimensions. More...

Friends
class	EnableCloneable< Fft2 >

Detailed Description

This LinOp implements a 2D Fourier matrix using the FFT algorithm.

For indexing purposes, the first dimension is the major axis.

It implements complex-to-complex forward and inverse FFT.

For a power-of-two sizes \(n_1, n_2\) with corresponding root of unity \(\omega = e^{-2\pi i / (n_1 n_2)}\) for forward DFT and \(\omega = e^{2 \pi i / (n_1 n_2)}\) for inverse DFT it computes

\[ x_{k_1 n_2 + k_2} = \sum_{i_1=0}^{n_1-1} \sum_{i_2=0}^{n_2-1} \omega^{i_1 k_1 + i_2 k_2} b_{i_1 n_2 + i_2} \]

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, https://doi.org/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::Fft2::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() [1/3]

static std::unique_ptr<Fft2> gko::matrix::Fft2::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() [2/3]

static std::unique_ptr<Fft2> gko::matrix::Fft2::create	(	std::shared_ptr< const Executor >	exec,
		size_type	size
	)

static

Creates an Fourier matrix with the given dimensions.

Parameters

exec	the executor to create the matrix on
size	size of both FFT dimensions

Returns: A smart pointer to the newly created matrix.

◆ create() [3/3]

static std::unique_ptr<Fft2> gko::matrix::Fft2::create	(	std::shared_ptr< const Executor >	exec,
		size_type	size1,
		size_type	size2,
		bool	inverse = `false`
	)

static

Creates an Fourier matrix with the given dimensions.

Parameters

exec	the executor to create the matrix on
size1	size of the first FFT dimension
size2	size of the second FFT dimension
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::Fft2::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::Fft2::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::Fft2::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::Fft2::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::Fft2::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() [1/3]

◆ create() [2/3]

◆ create() [3/3]

◆ transpose()

◆ write() [1/4]

◆ write() [2/4]

◆ write() [3/4]

◆ write() [4/4]