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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::ParIlu< ValueType, IndexType > Class Template Reference

ParILU is an incomplete LU factorization which is computed in parallel. More...

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

Collaboration diagram for gko::factorization::ParIlu< ValueType, IndexType >:
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Classes

class  Factory
 
struct  parameters_type
 

Public Types

using value_type = ValueType
 
using index_type = IndexType
 
using l_matrix_type = matrix::Csr< ValueType, IndexType >
 
using u_matrix_type = matrix::Csr< ValueType, IndexType >
 
- Public Types inherited from gko::Composition< ValueType >
using value_type = 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 l_matrix_typeget_l_factor () const
 
std::shared_ptr< const u_matrix_typeget_u_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...
 
- 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...
 
- 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::ParIlu< ValueType, IndexType >

ParILU is an incomplete LU factorization which is computed in parallel.

$L$ is a lower unitriangular, while $U$ is an upper triangular matrix, which approximate a given matrix $A$ with $A \approx LU$. Here, $L$ and $U$ have the same sparsity pattern as $A$, which is also called ILU(0).

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

$ F(L, U) = \begin{cases} \frac{1}{u_{jj}} \left(a_{ij}-\sum_{k=1}^{j-1}l_{ik}u_{kj}\right), \quad & i>j \\ a_{ij}-\sum_{k=1}^{i-1}l_{ik}u_{kj}, \quad & i\leq j \end{cases} $

In general, the entries of $L$ and $U$ can be iterated in parallel and in asynchronous fashion, the algorithm asymptotically converges to the incomplete factors $L$ and $U$ fulfilling $\left(R = A - L \cdot U\right)\vert_\mathcal{S} = 0\vert_\mathcal{S}$ where $\mathcal{S}$ is the pre-defined sparsity pattern (in case of ILU(0) the sparsity pattern of the system matrix $A$). The number of ParILU sweeps needed for convergence depends on the parallelism level: For sequential execution, a single sweep is sufficient, for fine-grained parallelism, 3 sweeps are typically generating a good approximation.

The ParILU 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: