Ginkgo Generated from branch based on master. Ginkgo version 1.7.0
A numerical linear algebra library targeting many-core architectures
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Classes | Public Types | Public Member Functions | Static Public Member Functions | List of all members
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< ValueType >
using value_type = ValueType
 
using transposed_type = Composition<ValueType>
 
- Public Types inherited from gko::EnablePolymorphicAssignment< ConcreteLinOp >
using result_type
 
- Public Types inherited from gko::ConvertibleTo< ResultType >
using result_type = ResultType
 

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.
 
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.
 
Compositionoperator= (Composition &&)
 Move-assigns a Composition.
 
 Composition (const Composition &)
 Copy-constructs a Composition.
 
 Composition (Composition &&)
 Move-constructs a Composition.
 
- Public Member Functions inherited from gko::EnableLinOp< ConcreteLinOp, PolymorphicBase >
const ConcreteLinOpapply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
 
ConcreteLinOpapply (ptr_param< const LinOp > b, ptr_param< LinOp > x)
 
const ConcreteLinOpapply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const
 
ConcreteLinOpapply (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< AbstractObject, PolymorphicBase >
std::unique_ptr< AbstractObjectcreate_default (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< AbstractObjectcreate_default () const
 
std::unique_ptr< AbstractObjectclone (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< AbstractObjectclone () const
 
AbstractObjectcopy_from (const PolymorphicObject *other)
 
template<typename Derived >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, AbstractObject > * copy_from (std::unique_ptr< Derived > &&other)
 
template<typename Derived >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, AbstractObject > * copy_from (const std::unique_ptr< Derived > &other)
 
AbstractObjectcopy_from (const std::shared_ptr< const PolymorphicObject > &other)
 
AbstractObjectmove_from (ptr_param< PolymorphicObject > other)
 
AbstractObjectclear ()
 
- 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.
 
void remove_logger (ptr_param< const Logger > logger)
 
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< ConcreteLinOp >
void convert_to (result_type *result) const override
 Converts the implementer to an object of type result_type.
 
void move_to (result_type *result) override
 Converts the implementer to an object of type result_type by moving data from this object.
 
- Public Member Functions inherited from gko::ConvertibleTo< ResultType >
virtual void convert_to (result_type *result) const =0
 Converts the implementer to an object of type result_type.
 
void convert_to (ptr_param< result_type > result) const
 
virtual void move_to (result_type *result)=0
 Converts the implementer to an object of type result_type by moving data from this object.
 
void move_to (ptr_param< result_type > result)
 

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< ConcreteType >
template<typename... Args>
static std::unique_ptr< ConcreteTypecreate (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

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