This LinOp implements a 3D Fourier matrix using the FFT algorithm. More...

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

Inheritance diagram for gko::matrix::Fft3:

Collaboration diagram for gko::matrix::Fft3:

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

using	index_type = int64

using	transposed_type = Fft3

Public Types inherited from gko::EnablePolymorphicAssignment< Fft3 >
using	result_type = Fft3

Public Types inherited from gko::ConvertibleTo< Fft3 >
using	result_type = Fft3

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< 3 >	get_fft_size () const

bool	is_inverse () const

Public Member Functions inherited from gko::EnableLinOp< Fft3 >
const Fft3 *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const

Fft3 *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x)

const Fft3 *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const

Fft3 *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x)

Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< Fft3, LinOp >
std::unique_ptr< Fft3 >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Fft3 >	create_default () const

std::unique_ptr< Fft3 >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Fft3 >	clone () const

Fft3 *	copy_from (const PolymorphicObject *other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Fft3 > *	copy_from (std::unique_ptr< Derived > &&other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Fft3 > *	copy_from (const std::unique_ptr< Derived > &other)

Fft3 *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

Fft3 *	move_from (ptr_param< PolymorphicObject > other)

Fft3 *	clear ()

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

const LinOp *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const

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

const LinOp *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const

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

std::unique_ptr< LinOp >	create_default () const

std::unique_ptr< LinOp >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< LinOp >	clone () const

LinOp *	copy_from (const PolymorphicObject *other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > *	copy_from (std::unique_ptr< Derived > &&other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > *	copy_from (const std::unique_ptr< Derived > &other)

LinOp *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

LinOp *	move_from (ptr_param< PolymorphicObject > other)

LinOp *	clear ()

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

std::unique_ptr< PolymorphicObject >	create_default (std::shared_ptr< const Executor > exec) const
	Creates a new "default" object of the same dynamic type as this object. More...

std::unique_ptr< PolymorphicObject >	create_default () const
	Creates a new "default" object of the same dynamic type as this object. More...

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

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

PolymorphicObject *	copy_from (const PolymorphicObject *other)
	Copies another object into this object. More...

template<typename Derived , typename Deleter >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > *	copy_from (std::unique_ptr< Derived, Deleter > &&other)
	Moves another object into this object. More...

template<typename Derived , typename Deleter >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > *	copy_from (const std::unique_ptr< Derived, Deleter > &other)
	Copies another object into this object. More...

PolymorphicObject *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)
	Copies another object into this object. More...

PolymorphicObject *	move_from (ptr_param< PolymorphicObject > other)
	Moves another object into this object. More...

PolymorphicObject *	clear ()
	Transforms the object into its default state. More...

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::EnablePolymorphicAssignment< Fft3 >
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...

Public Member Functions inherited from gko::ConvertibleTo< Fft3 >
void	convert_to (ptr_param< result_type > result) const

void	move_to (ptr_param< result_type > result)

Friends
class	EnablePolymorphicObject< Fft3, LinOp >

class	EnableCreateMethod< Fft3 >

Additional Inherited Members
Static Public Member Functions inherited from gko::EnableCreateMethod< ConcreteType >
template<typename... Args>
static std::unique_ptr< ConcreteType >	create (Args &&... args)

Detailed Description

This LinOp implements a 3D 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 $n_1, n_2, n_3$ with corresponding root of unity $\omega = e^{-2\pi i / (n_1 n_2 n_3)}$ for forward DFT and $\omega = e^{2 \pi i / (n_1 n_2 n_3)}$ for inverse DFT it computes

$x_{k_1 n_2 n_3 + k_2 n_3 + k_3} = \sum_{i_1=0}^{n_1-1} \sum_{i_2=0}^{n_2-1} \sum_{i_3=0}^{n_3-1} \omega^{i_1 k_1 + i_2 k_2 + i_3 k_3} b_{i_1 n_2 n_3 + i_2 n_3 + i_3}$

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::Fft3::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.

◆ transpose()

std::unique_ptr<LinOp> gko::matrix::Fft3::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::Fft3::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::Fft3::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::Fft3::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::Fft3::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

Friends

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ conj_transpose()

◆ transpose()

◆ write() [1/4]

◆ write() [2/4]

◆ write() [3/4]

◆ write() [4/4]