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A numerical linear algebra library targeting many-core architectures
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gko::preconditioner::Isai< IsaiType, ValueType, IndexType > Class Template Reference
Linear Operators » Preconditioners | Linear Operators

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

struct  parameters_type
class  Factory

Public Types

using value_type = ValueType
using index_type = IndexType
using transposed_type
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

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).
Isai & operator= (const Isai &other)
 Copy-assigns an ISAI preconditioner.
Isai & operator= (Isai &&other)
 Move-assigns an ISAI preconditioner.
 Isai (const Isai &other)
 Copy-constructs an ISAI preconditioner.
 Isai (Isai &&other)
 Move-constructs an ISAI preconditioner.
const parameters_type & get_parameters () const
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.
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
Public Member Functions inherited from gko::EnablePolymorphicAssignment< Isai< IsaiType, ValueType, IndexType > >
void convert_to (result_type *result) const override
void move_to (result_type *result) override

Static Public Member Functions

static auto build () -> decltype(Factory::create())
static parameters_type parse (const config::pnode &config, const config::registry &context, const config::type_descriptor &td_for_child=config::make_type_descriptor< ValueType, IndexType >())
 Create the parameters from the property_tree.

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
IsaiTypedetermines if the ISAI is generated for a general square matrix, a lower triangular matrix, an upper triangular matrix or an spd matrix
ValueTypeprecision of matrix elements
IndexTypeprecision of matrix indexes

Member Typedef Documentation

◆ transposed_type

template<isai_type IsaiType, typename ValueType, typename IndexType>
using gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::transposed_type
Initial value:
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>
gko::preconditioner::Isai::Isai
Isai(const Isai &other)
Copy-constructs an ISAI preconditioner.

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

◆ 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)

◆ parse()

template<isai_type IsaiType, typename ValueType, typename IndexType>
parameters_type gko::preconditioner::Isai< IsaiType, ValueType, IndexType >::parse ( const config::pnode & config,
const config::registry & context,
const config::type_descriptor & td_for_child = config::make_type_descriptor< ValueType, IndexType >() )
static

Create the parameters from the property_tree.

Because this is directly tied to the specific type, the value/index type settings within config are ignored and type_descriptor is only used for children configs.

Parameters
configthe property tree for setting
contextthe registry
td_for_childthe type descriptor for children configs. The default uses the value/index type of this class.
Returns
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: