Ginkgo Generated from branch based on main. Ginkgo version 1.10.0
A numerical linear algebra library targeting many-core architectures
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gko::factorization::ParIc< ValueType, IndexType > Class Template Reference

ParIC is an incomplete Cholesky factorization which is computed in parallel. More...

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

Inheritance diagram for gko::factorization::ParIc< ValueType, IndexType >:
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Collaboration diagram for gko::factorization::ParIc< 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< default_precision >
using value_type
using transposed_type
Public Types inherited from gko::EnablePolymorphicAssignment< Composition< default_precision > >
using result_type
Public Types inherited from gko::ConvertibleTo< Composition< default_precision > >
using result_type

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< default_precision >
const std::vector< std::shared_ptr< const LinOp > > & get_operators () const noexcept
 Returns a list of operators of the composition.
std::unique_ptr< LinOptranspose () const override
 Returns a LinOp representing the transpose of the Transposable object.
std::unique_ptr< LinOpconj_transpose () const override
 Returns a LinOp representing the conjugate transpose of the Transposable object.
Compositionoperator= (const Composition &)
 Copy-assigns a Composition.
 Composition (const Composition &)
 Copy-constructs a Composition.
Public Member Functions inherited from gko::EnableLinOp< Composition< default_precision > >
const Composition< default_precision > * apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< Composition< default_precision >, LinOp >
std::unique_ptr< Composition< default_precision > > create_default (std::shared_ptr< const Executor > exec) const
std::unique_ptr< Composition< default_precision > > clone (std::shared_ptr< const Executor > exec) const
Composition< default_precision > * copy_from (const PolymorphicObject *other)
Composition< default_precision > * move_from (ptr_param< PolymorphicObject > other)
Composition< default_precision > * clear ()
Public Member Functions inherited from gko::LinOp
LinOpapply (ptr_param< const LinOp > b, ptr_param< LinOp > x)
 Applies a linear operator to a vector (or a sequence of vectors).
const LinOpapply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
LinOpapply (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.
const LinOpapply (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.
virtual bool apply_uses_initial_guess () const
 Returns true if the linear operator uses the data given in x as an initial guess.
LinOpoperator= (const LinOp &)=default
 Copy-assigns a LinOp.
LinOpoperator= (LinOp &&other)
 Move-assigns a LinOp.
 LinOp (const LinOp &)=default
 Copy-constructs a LinOp.
 LinOp (LinOp &&other)
 Move-constructs a LinOp.
Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< LinOp >
std::unique_ptr< LinOpcreate_default (std::shared_ptr< const Executor > exec) const
std::unique_ptr< LinOpclone (std::shared_ptr< const Executor > exec) const
LinOpcopy_from (const PolymorphicObject *other)
LinOpmove_from (ptr_param< 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.
std::unique_ptr< PolymorphicObjectcreate_default () const
 Creates a new "default" object of the same dynamic type as this object.
std::unique_ptr< PolymorphicObjectclone (std::shared_ptr< const Executor > exec) const
 Creates a clone of the object.
std::unique_ptr< PolymorphicObjectclone () const
 Creates a clone of the object.
PolymorphicObjectcopy_from (const PolymorphicObject *other)
 Copies another object into this object.
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.
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.
PolymorphicObjectcopy_from (const std::shared_ptr< const PolymorphicObject > &other)
 Copies another object into this object.
PolymorphicObjectmove_from (ptr_param< PolymorphicObject > other)
 Moves another object into this object.
PolymorphicObjectclear ()
 Transforms the object into its default state.
std::shared_ptr< const Executorget_executor () const noexcept
 Returns the Executor of the object.
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.
void remove_logger (const Logger *logger) override
 Removes a logger from the list of subscribed loggers.
const std::vector< std::shared_ptr< const Logger > > & get_loggers () const override
 Returns the vector containing all loggers registered at this object.
void clear_loggers () override
 Remove all loggers registered at this object.
Public Member Functions inherited from gko::log::Loggable
void remove_logger (ptr_param< const Logger > logger)
Public Member Functions inherited from gko::EnablePolymorphicAssignment< Composition< default_precision > >
void convert_to (result_type *result) const override
void move_to (result_type *result) override

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.
Static Public Member Functions inherited from gko::EnableCreateMethod< Composition< default_precision > >
static std::unique_ptr< Composition< default_precision > > create (Args &&... args)

Detailed Description

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

ParIC is an incomplete Cholesky factorization which is computed in parallel.

$L$ is a lower triangular matrix, which approximates a given matrix $A$ with $A \approx LL^H$. Here, $L + L^H$ has the same sparsity pattern as $A$, which is also called IC(0).

The ParIC algorithm generates the incomplete factors iteratively, using a fixed-point iteration of the form

$F(L) =
\begin{cases}
    \sqrt{a_{ii}-\sum_{k=1}^{i-1}|l_{ik}|^2}, \quad & i == j \\
    a_{ij}-\sum_{k=1}^{i-1}l_{ik}u_{kj}, \quad & i < j
\end{cases}
$

In general, the entries of $L$ can be iterated in parallel and in asynchronous fashion, the algorithm asymptotically converges to the incomplete factors $L$ and $L^H$ fulfilling $\left(R = A - L \cdot
L^H\right)\vert_\mathcal{S} = 0\vert_\mathcal{S}$ where $\mathcal{S}$ is the pre-defined sparsity pattern (in case of IC(0) the sparsity pattern of the system matrix $A$). The number of ParIC sweeps needed for convergence depends on the parallelism level: For sequential execution, a single sweep is sufficient, for fine-grained parallelism, the number of sweeps necessary to get a good approximation of the incomplete factors depends heavily on the problem. On the OpenMP executor, 3 sweeps usually give a decent approximation in our experiments, while GPU executors can take 10 or more iterations.

The ParIC algorithm in Ginkgo follows the design of E. Chow and A. Patel, Fine-grained Parallel Incomplete LU Factorization, SIAM Journal on Scientific Computing, 37, C169-C193 (2015).

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

Member Function Documentation

◆ parse()

template<typename ValueType = default_precision, typename IndexType = int32>
parameters_type gko::factorization::ParIc< 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

References gko::Composition< default_precision >::Composition(), and gko::PolymorphicObject::get_executor().


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