gko::experimental::reorder::Mc64< ValueType, IndexType > Class Template Reference

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 >:

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

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 Member Functions
const parameters_type &	get_parameters () const
	Returns the parameters used to construct the factory. More...
std::unique_ptr< result_type >	generate (std::shared_ptr< const LinOp > system_matrix) const
Public Member Functions inherited from gko::LinOpFactory
std::unique_ptr< LinOp >	generate (std::shared_ptr< const LinOp > input) const
Public Member Functions inherited from gko::PolymorphicObject
virtual void	validate_data () const
	Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge.
PolymorphicObject &	operator= (const PolymorphicObject &)
std::shared_ptr< const Executor >	get_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
void	remove_logger (const Logger *logger) override
void	remove_logger (ptr_param< const Logger > logger)
const std::vector< std::shared_ptr< const Logger > > &	get_loggers () const override
void	clear_loggers () override
Public Member Functions inherited from gko::log::Loggable
void	remove_logger (ptr_param< const Logger > logger)

Static Public Member Functions
static parameters_type	build ()
	Creates a new parameter_type to set up the factory.

Friends
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, https://doi.org/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

ValueType	Type of the values of all matrices used in this class
IndexType	Type 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

Parameters

system_matrix

the source matrix to compute the reordering for.

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.

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

• ginkgo/core/reorder/mc64.hpp