The Incomplete Sparse Approximate Inverse (ISAI) Preconditioner generates an approximate inverse matrix for a given square matrix A, lower triangular matrix L, upper triangular matrix U or symmetric positive (spd) matrix B. More...

#include <ginkgo/core/preconditioner/isai.hpp>

Inheritance diagram for gko::preconditioner::Isai< IsaiType, ValueType, IndexType >:

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Collaboration diagram for gko::preconditioner::Isai< IsaiType, ValueType, IndexType >:

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Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	index_type = IndexType

using	transposed_type = Isai< IsaiType==isai_type::general ? isai_type::general :IsaiType==isai_type::spd ? isai_type::spd :IsaiType==isai_type::lower ? isai_type::upper :isai_type::lower, ValueType, IndexType >

using	Comp = Composition< ValueType >

using	Csr = matrix::Csr< ValueType, IndexType >

using	Dense = matrix::Dense< ValueType >

Public Types inherited from gko::EnablePolymorphicAssignment< Isai< IsaiType, ValueType, IndexType > >
using	result_type = Isai< IsaiType, ValueType, IndexType >

Public Types inherited from gko::ConvertibleTo< Isai< IsaiType, ValueType, IndexType > >
using	result_type = Isai< IsaiType, ValueType, IndexType >

Public Member Functions
std::shared_ptr< const typename std::conditional< IsaiType==isai_type::spd, Comp, Csr >::type >	get_approximate_inverse () const
	Returns the approximate inverse of the given matrix (either a CSR matrix for IsaiType general, upper or lower or a composition of two CSR matrices for IsaiType spd). More...

Isai &	operator= (const Isai &other)
	Copy-assigns an ISAI preconditioner. More...

Isai &	operator= (Isai &&other)
	Move-assigns an ISAI preconditioner. More...

	Isai (const Isai &other)
	Copy-constructs an ISAI preconditioner. More...

	Isai (Isai &&other)
	Move-constructs an ISAI preconditioner. More...

const parameters_type &	get_parameters () const

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...

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

Isai< IsaiType, ValueType, IndexType > *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x)

const Isai< IsaiType, ValueType, IndexType > *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const

Isai< IsaiType, ValueType, IndexType > *	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< Isai< IsaiType, ValueType, IndexType >, LinOp >
std::unique_ptr< Isai< IsaiType, ValueType, IndexType > >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Isai< IsaiType, ValueType, IndexType > >	create_default () const

std::unique_ptr< Isai< IsaiType, ValueType, IndexType > >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Isai< IsaiType, ValueType, IndexType > >	clone () const

Isai< IsaiType, ValueType, IndexType > *	copy_from (const PolymorphicObject *other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Isai< IsaiType, ValueType, IndexType > > *	copy_from (std::unique_ptr< Derived > &&other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Isai< IsaiType, ValueType, IndexType > > *	copy_from (const std::unique_ptr< Derived > &other)

Isai< IsaiType, ValueType, IndexType > *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

Isai< IsaiType, ValueType, IndexType > *	move_from (ptr_param< PolymorphicObject > other)

Isai< IsaiType, ValueType, IndexType > *	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< Isai< IsaiType, ValueType, IndexType > >
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< Isai< IsaiType, ValueType, IndexType > >
void	convert_to (ptr_param< result_type > result) const

void	move_to (ptr_param< result_type > result)

Static Public Member Functions
static auto	build () -> decltype(Factory ::create())

Static Public Attributes
static constexpr isai_type	type {IsaiType}

Friends
class	EnableLinOp< Isai >

class	EnablePolymorphicObject< Isai, LinOp >

class	Isai< isai_type::general, ValueType, IndexType >

class	Isai< isai_type::lower, ValueType, IndexType >

class	Isai< isai_type::upper, ValueType, IndexType >

class	Isai< isai_type::spd, ValueType, IndexType >

Detailed Description

template<isai_type IsaiType, typename ValueType, typename IndexType>
class gko::preconditioner::Isai< IsaiType, ValueType, IndexType >

The Incomplete Sparse Approximate Inverse (ISAI) Preconditioner generates an approximate inverse matrix for a given square matrix A, lower triangular matrix L, upper triangular matrix U or symmetric positive (spd) matrix B.

Using the preconditioner computes $aiA * x$ , $aiU * x$ , $aiL * x$ or $aiC^T * aiC * x$ (depending on the type of the Isai) for a given vector x (may have multiple right hand sides). aiA, aiU and aiL are the approximate inverses for A, U and L respectively. aiC is an approximation to C, the exact Cholesky factor of B (This is commonly referred to as a Factorized Sparse Approximate Inverse, short FSPAI).

The sparsity pattern used for the approximate inverse of A, L and U is the same as the sparsity pattern of the respective matrix. For B, the sparsity pattern used for the approximate inverse is the same as the sparsity pattern of the lower triangular half of B.

Note that, except for the spd case, for a matrix A generally ISAI(A)^T != ISAI(A^T).

For more details on the algorithm, see the paper Incomplete Sparse Approximate Inverses for Parallel Preconditioning, which is the basis for this work.

Note: GPU implementations can only handle the vector unit width width (warp size for CUDA) as number of elements per row in the sparse matrix. If there are more than width elements per row, the remaining elements will be ignored.

Template Parameters

IsaiType	determines if the ISAI is generated for a general square matrix, a lower triangular matrix, an upper triangular matrix or an spd matrix
ValueType	precision of matrix elements
IndexType	precision of matrix indexes

Constructor & Destructor Documentation

◆ Isai() [1/2]

template<isai_type IsaiType, typename ValueType , typename IndexType >

gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::Isai ( const Isai< IsaiType, ValueType, IndexType > & other )

Copy-constructs an ISAI preconditioner.

Inherits the executor, shallow-copies the matrix and parameters.

◆ Isai() [2/2]

template<isai_type IsaiType, typename ValueType , typename IndexType >

gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::Isai ( Isai< IsaiType, ValueType, IndexType > && other )

Move-constructs an ISAI preconditioner.

Inherits the executor, moves the matrix and parameters. The moved-from object is empty (0x0 with nullptr matrix and default parameters)

Member Function Documentation

◆ conj_transpose()

template<isai_type IsaiType, typename ValueType , typename IndexType >

std::unique_ptr<LinOp> gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::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.

◆ get_approximate_inverse()

template<isai_type IsaiType, typename ValueType , typename IndexType >

std::shared_ptr<const typename std::conditional<IsaiType == isai_type::spd, Comp, Csr>::type> gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::get_approximate_inverse ( ) const

inline

Returns the approximate inverse of the given matrix (either a CSR matrix for IsaiType general, upper or lower or a composition of two CSR matrices for IsaiType spd).

Returns: the generated approximate inverse

References gko::as().

◆ operator=() [1/2]

template<isai_type IsaiType, typename ValueType , typename IndexType >

Isai& gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::operator= ( const Isai< IsaiType, ValueType, IndexType > & other )

Copy-assigns an ISAI preconditioner.

Preserves the executor, shallow-copies the matrix and parameters. Creates a clone of the matrix if it is on the wrong executor.

◆ operator=() [2/2]

template<isai_type IsaiType, typename ValueType , typename IndexType >

Isai& gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::operator= ( Isai< IsaiType, ValueType, IndexType > && other )

Move-assigns an ISAI preconditioner.

Preserves the executor, moves the matrix and parameters. Creates a clone of the matrix if it is on the wrong executor. The moved-from object is empty (0x0 with nullptr matrix and default parameters)

◆ transpose()

template<isai_type IsaiType, typename ValueType , typename IndexType >

std::unique_ptr<LinOp> gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::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/preconditioner/isai.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

template<isai_type IsaiType, typename ValueType, typename IndexType> class gko::preconditioner::Isai< IsaiType, ValueType, IndexType >

Constructor & Destructor Documentation

◆ Isai() [1/2]

◆ Isai() [2/2]

Member Function Documentation

◆ conj_transpose()

◆ get_approximate_inverse()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ transpose()

template<isai_type IsaiType, typename ValueType, typename IndexType>
class gko::preconditioner::Isai< IsaiType, ValueType, IndexType >