gko::factorization::ParIct< ValueType, IndexType > Class Template Reference

ParICT is an incomplete threshold-based Cholesky factorization which is computed in parallel. More...

#include <ginkgo/core/factorization/par_ict.hpp>

Inheritance diagram for gko::factorization::ParIct< ValueType, IndexType >:

Collaboration diagram for gko::factorization::ParIct< ValueType, IndexType >:

Classes
class	Factory
struct	parameters_type

Public Types
using	value_type = ValueType
using	index_type = IndexType
using	matrix_type = matrix::Csr< ValueType, IndexType >
Public Types inherited from gko::Composition< ValueType >
using	value_type = ValueType
using	transposed_type = Composition< ValueType >

Public Member Functions
std::shared_ptr< const matrix_type >	get_l_factor () const
std::shared_ptr< const matrix_type >	get_lt_factor () const
const parameters_type &	get_parameters () const
Public Member Functions inherited from gko::Composition< ValueType >
const std::vector< std::shared_ptr< const LinOp > > &	get_operators () const noexcept
	Returns a list of operators of the composition. More...
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...
Composition &	operator= (const Composition &)
	Copy-assigns a Composition. More...
Composition &	operator= (Composition &&)
	Move-assigns a Composition. More...
	Composition (const Composition &)
	Copy-constructs a Composition. More...
	Composition (Composition &&)
	Move-constructs a Composition. More...
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)

Static Public Member Functions
template<typename... Args>
static std::unique_ptr< Composition< ValueType > >	create (Args &&... args)=delete
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. More...
Static Public Member Functions inherited from gko::EnableCreateMethod< Composition< ValueType > >
static std::unique_ptr< Composition< ValueType > >	create (Args &&... args)

Detailed Description

template<typename ValueType = default_precision, typename IndexType = int32>
class gko::factorization::ParIct< ValueType, IndexType >

ParICT is an incomplete threshold-based Cholesky factorization which is computed in parallel.

\(L\) is a lower triangular matrix which approximates a given symmetric positive definite matrix \(A\) with \(A \approx LL^T\). Here, \(L\) has a sparsity pattern that is improved iteratively based on its element-wise magnitude. The initial sparsity pattern is chosen based on the lower triangle of \(A\).

One iteration of the ParICT algorithm consists of the following steps:

1. Calculate the residual \(R = A - LL^T\).
2. Add new non-zero locations from \(R\) to \(L\). The new non-zero locations are initialized from the corresponding residual entries.

3. Execute a fixed-point iteration on \(L\) according to

   \[ F(L)_{ij} = \begin{cases} \frac{1}{l_{jj}} \left( a_{ij} - \sum_{k=1}^{j-1} l_{ik} l_{jk} \right), & i \neq j, \\ \sqrt{ a_{ij} - \sum_{k=1}^{j-1} l_{ik} l_{jk} }, & i = j. \end{cases} \]

4. Remove the smallest entries (by magnitude) from \(L\).
5. Execute a fixed-point iteration on the (now sparser) \(L\).

This ParICT algorithm thus improves the sparsity pattern and the approximation of \(L\) simultaneously.

References

• Anzt, H., Chow, E., Dongarra, J. ParILUT — A Parallel Threshold ILU for GPUs. 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 231–241. https://doi.org/10.1109/IPDPS.2019.00033

Template Parameters

ValueType	Type of the values of all matrices used in this class
IndexType	Type of the indices of all matrices used in this class

Member Function Documentation

parse()

template<typename ValueType = default_precision, typename IndexType = int32>

static parameters_type gko::factorization::ParIct< 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

config	the property tree for setting
context	the registry
td_for_child	the type descriptor for children configs. The default uses the value/index type of this class.

Returns

parameters

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

• ginkgo/core/factorization/par_ict.hpp