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A numerical linear algebra library targeting many-core architectures
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gko::experimental::reorder::Mc64< ValueType, IndexType > Class Template Referencefinal

MC64 is an algorithm for permuting large entries to the diagonal of a sparse matrix. More...

#include <ginkgo/core/reorder/mc64.hpp>

Inheritance diagram for gko::experimental::reorder::Mc64< ValueType, IndexType >:
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Collaboration diagram for gko::experimental::reorder::Mc64< ValueType, IndexType >:
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Classes

struct  parameters_type

Public Types

using value_type = ValueType
using index_type = IndexType
using result_type = Composition<value_type>
using matrix_type = matrix::Csr<value_type, index_type>
Public Types inherited from gko::EnablePolymorphicAssignment< Mc64< default_precision, int32 > >
using result_type
Public Types inherited from gko::ConvertibleTo< Mc64< default_precision, int32 > >
using result_type

Public Member Functions

const parameters_typeget_parameters () const
 Returns the parameters used to construct the factory.
std::unique_ptr< result_typegenerate (std::shared_ptr< const LinOp > system_matrix) const
 Creates a new product from the given components.
Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< Mc64< default_precision, int32 >, LinOpFactory >
std::unique_ptr< Mc64< default_precision, int32 > > create_default (std::shared_ptr< const Executor > exec) const
std::unique_ptr< Mc64< default_precision, int32 > > clone (std::shared_ptr< const Executor > exec) const
Mc64< default_precision, int32 > * copy_from (const PolymorphicObject *other)
Mc64< default_precision, int32 > * move_from (ptr_param< PolymorphicObject > other)
Mc64< default_precision, int32 > * clear ()
Public Member Functions inherited from gko::LinOpFactory
std::unique_ptr< LinOpgenerate (std::shared_ptr< const LinOp > input) const
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< Mc64< default_precision, int32 > >
void convert_to (result_type *result) const override
void move_to (result_type *result) override

Static Public Member Functions

static parameters_type build ()
 Creates a new parameter_type to set up the factory.

Friends

class EnablePolymorphicObject< Mc64< ValueType, IndexType >, LinOpFactory >
class enable_parameters_type< parameters_type, Mc64< ValueType, IndexType > >

Detailed Description

template<typename ValueType = default_precision, typename IndexType = int32>
class gko::experimental::reorder::Mc64< ValueType, IndexType >

MC64 is an algorithm for permuting large entries to the diagonal of a sparse matrix.

This approach can increase numerical stability of e.g. an LU factorization without pivoting. Under the assumption of working on a nonsingular square matrix, the algorithm computes a minimum weight perfect matching on a weighted edge bipartite graph of the matrix. It is described in detail in "On Algorithms for Permuting Large Entries to the Diagonal of a Sparse Matrix" (Duff, Koster, 2001, DOI: 10.1137/S0895479899358443). There are two strategies for choosing the weights supported:

  • Maximizing the product of the absolute values on the diagonal. For this strategy, the weights are computed as $c(i, j) = \log_2(a_i) - \log_2(|a(i, j)|)$ if $a(i, j) \neq 0 $ and $c(i, j) = \infty$ otherwise. Here, a_i is the maximum absolute value in row i of the matrix A. In this case, the implementation computes a row permutation P and row and column scaling coefficients L and R such that the matrix P*L*A*R has values with unity absolute value on the diagonal and smaller or equal entries everywhere else.
  • Maximizing the sum of the absolute values on the diagonal. For this strategy, the weights are computed as $c(i, j) = a_i - |a(i, j)|$ if $a(i, j) \neq 0$ and $c(i, j) =
   \infty$ otherwise. In this case, no scaling coefficients are computed.

This class creates a Combination of two ScaledPermutations representing the row and column permutation and scaling factors computed by this algorithm.

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

◆ generate()

template<typename ValueType = default_precision, typename IndexType = int32>
std::unique_ptr< result_type > gko::experimental::reorder::Mc64< ValueType, IndexType >::generate ( std::shared_ptr< const LinOp > system_matrix) const

Creates a new product from the given components.

The method will create an ComponentsType object from the arguments of this method, and pass it to the generate_impl() function which will create a new AbstractProductType.

Template Parameters
Argstypes of arguments passed to the constructor of ComponentsType
Parameters
argsarguments passed to the constructor of ComponentsType
Returns
an instance of AbstractProductType
Note
This function overrides the default LinOpFactory::generate to return a Permutation instead of a generic LinOp, which would need to be cast to ScaledPermutation again to access its indices. It is only necessary because smart pointers aren't covariant.

◆ get_parameters()

template<typename ValueType = default_precision, typename IndexType = int32>
const parameters_type & gko::experimental::reorder::Mc64< ValueType, IndexType >::get_parameters ( ) const
inline

Returns the parameters used to construct the factory.

Returns
the parameters used to construct the factory.

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