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A numerical linear algebra library targeting many-core architectures
Classes | Public Types | Public Member Functions | Static Public Member Functions | List of all members
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>

Collaboration diagram for gko::factorization::ParIct< ValueType, IndexType >:
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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 Types inherited from gko::EnablePolymorphicAssignment< Composition< ValueType > >
using result_type = Composition< ValueType >
 
- Public Types inherited from gko::ConvertibleTo< Composition< ValueType > >
using result_type = Composition< ValueType >
 

Public Member Functions

std::shared_ptr< const matrix_typeget_l_factor () const
 
std::shared_ptr< const matrix_typeget_lt_factor () const
 
const parameters_typeget_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< LinOptranspose () const override
 Returns a LinOp representing the transpose of the Transposable object. More...
 
std::unique_ptr< LinOpconj_transpose () const override
 Returns a LinOp representing the conjugate transpose of the Transposable object. More...
 
- Public Member Functions inherited from gko::EnableLinOp< Composition< ValueType > >
const Composition< ValueType > * apply (const LinOp *b, LinOp *x) const
 
Composition< ValueType > * apply (const LinOp *b, LinOp *x)
 
const Composition< ValueType > * apply (const LinOp *alpha, const LinOp *b, const LinOp *beta, LinOp *x) const
 
Composition< ValueType > * apply (const LinOp *alpha, const LinOp *b, const LinOp *beta, LinOp *x)
 
- Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< Composition< ValueType >, LinOp >
std::unique_ptr< Composition< ValueType > > create_default (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< Composition< ValueType > > create_default () const
 
std::unique_ptr< Composition< ValueType > > clone (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< Composition< ValueType > > clone () const
 
Composition< ValueType > * copy_from (const PolymorphicObject *other)
 
Composition< ValueType > * copy_from (std::unique_ptr< PolymorphicObject > other)
 
Composition< ValueType > * clear ()
 
- Public Member Functions inherited from gko::LinOp
LinOpapply (const LinOp *b, LinOp *x)
 Applies a linear operator to a vector (or a sequence of vectors). More...
 
const LinOpapply (const LinOp *b, LinOp *x) const
 Applies a linear operator to a vector (or a sequence of vectors). More...
 
LinOpapply (const LinOp *alpha, const LinOp *b, const LinOp *beta, LinOp *x)
 Performs the operation x = alpha * op(b) + beta * x. More...
 
const LinOpapply (const LinOp *alpha, const LinOp *b, const LinOp *beta, 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...
 
- Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< LinOp >
std::unique_ptr< LinOpcreate_default (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< LinOpcreate_default () const
 
std::unique_ptr< LinOpclone (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< LinOpclone () const
 
LinOpcopy_from (const PolymorphicObject *other)
 
LinOpcopy_from (std::unique_ptr< PolymorphicObject > other)
 
LinOpclear ()
 
- Public Member Functions inherited from gko::PolymorphicObject
PolymorphicObjectoperator= (const PolymorphicObject &)
 
std::unique_ptr< PolymorphicObjectcreate_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< PolymorphicObjectcreate_default () const
 Creates a new "default" object of the same dynamic type as this object. More...
 
std::unique_ptr< PolymorphicObjectclone (std::shared_ptr< const Executor > exec) const
 Creates a clone of the object. More...
 
std::unique_ptr< PolymorphicObjectclone () const
 Creates a clone of the object. More...
 
PolymorphicObjectcopy_from (const PolymorphicObject *other)
 Copies another object into this object. More...
 
PolymorphicObjectcopy_from (std::unique_ptr< PolymorphicObject > other)
 Moves another object into this object. More...
 
PolymorphicObjectclear ()
 Transforms the object into its default state. More...
 
std::shared_ptr< const Executorget_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
 Adds a new logger to the list of subscribed loggers. More...
 
void remove_logger (const Logger *logger) override
 Removes a logger from the list of subscribed loggers. More...
 
- Public Member Functions inherited from gko::EnablePolymorphicAssignment< Composition< ValueType > >
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...
 

Static Public Member Functions

template<typename... Args>
static std::unique_ptr< Composition< ValueType > > create (Args &&... args)=delete
 
static auto build () -> decltype(Factory ::create())
 
- 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. Calculating the residual $R = A - LL^T$
  2. Adding new non-zero locations from $R$ to $L$. The new non-zero locations are initialized based on the corresponding residual value.
  3. Executing a fixed-point iteration on $L$ according to $ F(L) = \begin{cases} \frac{1}{l_{jj}} \left(a_{ij}-\sum_{k=1}^{j-1}l_{ik}l_{jk}\right), \quad & i \neq j \\ \sqrt{a_{ij}-\sum_{k=1}^{j-1}l_{ik}l_{jk}}, \quad & i = j \\ \end{cases} $
  4. Removing the smallest entries (by magnitude) from $L$
  5. Executing a fixed-point iteration on the (now sparser) $L$

This ParICT algorithm thus improves the sparsity pattern and the approximation of $L$ simultaneously.

The implementation follows the design of H. Anzt et al., ParILUT - A Parallel Threshold ILU for GPUs, 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 231–241.

Template Parameters
ValueTypeType of the values of all matrices used in this class
IndexTypeType of the indices of all matrices used in this class

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