Class to solve linear equations using Gauss-Seidel iteration [7]. More...

#include <num_collect/linear/gauss_seidel_iterative_solver.h>

Inheritance diagram for num_collect::linear::gauss_seidel_iterative_solver< Matrix >:

Collaboration diagram for num_collect::linear::gauss_seidel_iterative_solver< Matrix >:

Public Types
using	base_type
	Type of the base class.

using	vector_type = Eigen::VectorX<scalar_type>
	Type of vectors.

Public Types inherited from num_collect::linear::iterative_solver_base< gauss_seidel_iterative_solver< Matrix > >
enum

using	matrix_type
	Type of matrices.

using	MatrixType
	Type of matrices. (For Eigen library.)

using	real_scalar_type
	Type of real scalars.

using	RealScalar
	Type of real scalars. (For Eigen library.)

using	Scalar
	Type of scalars. (For Eigen library.)

using	scalar_type
	Type of scalars.

using	storage_index_type
	Type of indices in storages.

using	StorageIndex
	Type of indices in storages. (For Eigen library.)

Public Member Functions
	gauss_seidel_iterative_solver ()=default
	Constructor.

void	compute (const matrix_type &coeff)
	Prepare to solve.

auto	iterations () const noexcept -> index_type
	Get the number of iterations.

auto	residual_rate () const noexcept -> scalar_type
	Get the rate of the last residual.

template<base::concepts::dense_vector_of< scalar_type > Right, base::concepts::dense_vector_of< scalar_type > Solution>
void	solve_vector_in_place (const Right &right, Solution &solution) const
	Iterate repeatedly until stop criterion is satisfied for a vector.

Public Member Functions inherited from num_collect::linear::iterative_solver_base< gauss_seidel_iterative_solver< Matrix > >
	iterative_solver_base ()
	Constructor.

void	_solve_impl (const Right &right, Solution &solution) const
	Internal function to solve for a right-hand-side vector.

void	_solve_with_guess_impl (const Right &right, Solution &solution) const
	Internal function to solve for a right-hand-side vector.

auto	cols () const noexcept -> Eigen::Index
	Get the number of columns.

auto	compute (const matrix_type &coeff) -> gauss_seidel_iterative_solver< Matrix > &
	Initialize this solver using a coefficient matrix.

auto	max_iterations () const noexcept -> index_type
	Get the maximum number of iterations.

auto	max_iterations (index_type val) -> gauss_seidel_iterative_solver< Matrix > &
	Set the maximum number of iterations.

auto	rows () const noexcept -> Eigen::Index
	Get the number of rows.

auto	solve (const Right &right) const -> Eigen::Solve< gauss_seidel_iterative_solver< Matrix >, Right >
	Solve a linear equation.

auto	solve_with_guess (const Right &right, const Solution &solution) const -> Eigen::SolveWithGuess< gauss_seidel_iterative_solver< Matrix >, Right, Solution >
	Solve a linear equation with a guess of the solution.

auto	tolerance () const noexcept -> real_scalar_type
	Get the tolerance of rate of residual.

auto	tolerance (const real_scalar_type &val) -> gauss_seidel_iterative_solver< Matrix > &
	Set the tolerance of rate of residual.

Private Member Functions
template<base::concepts::dense_vector_of< scalar_type > Right, base::concepts::dense_vector_of< scalar_type > Solution>
void	iterate (const matrix_type &coeff_ref, const Right &right, Solution &solution) const
	Iterate once.

Private Attributes
vector_type	diag_ {}
	Diagonal coefficients.

vector_type	inv_diag_ {}
	Inverse of diagonal coefficients.

index_type	iterations_ {}
	Number of iterations.

scalar_type	residual_ {}
	Last residual.

scalar_type	residual_rate_ {}
	Rate of last residual.

Additional Inherited Members
Protected Types inherited from num_collect::linear::iterative_solver_base< gauss_seidel_iterative_solver< Matrix > >
using	Base
	Base class.

Protected Member Functions inherited from num_collect::linear::iterative_solver_base< gauss_seidel_iterative_solver< Matrix > >
auto	coeff () const noexcept -> const matrix_type &
	Get the coefficient matrix.

Detailed Description

template<base::concepts::sparse_matrix Matrix>
class num_collect::linear::gauss_seidel_iterative_solver< Matrix >

Class to solve linear equations using Gauss-Seidel iteration [7].

Template Parameters

Matrix Type of the matrix.

Definition at line 64 of file gauss_seidel_iterative_solver.h.

Member Typedef Documentation

◆ base_type

template<base::concepts::sparse_matrix Matrix>

using num_collect::linear::gauss_seidel_iterative_solver< Matrix >::base_type

Initial value:

iterative_solver_base<gauss_seidel_iterative_solver<Matrix>>

Type of the base class.

Definition at line 72 of file gauss_seidel_iterative_solver.h.

◆ vector_type

template<base::concepts::sparse_matrix Matrix>

using num_collect::linear::gauss_seidel_iterative_solver< Matrix >::vector_type = Eigen::VectorX<scalar_type>

Type of vectors.

Definition at line 85 of file gauss_seidel_iterative_solver.h.

Member Function Documentation

◆ compute()

template<base::concepts::sparse_matrix Matrix>

void num_collect::linear::gauss_seidel_iterative_solver< Matrix >::compute ( const matrix_type & coeff )

inline

Prepare to solve.

Parameters

[in] coeff Coefficient matrix.

Definition at line 97 of file gauss_seidel_iterative_solver.h.

◆ iterate()

template<base::concepts::sparse_matrix Matrix>

template<base::concepts::dense_vector_of< scalar_type > Right, base::concepts::dense_vector_of< scalar_type > Solution>

void num_collect::linear::gauss_seidel_iterative_solver< Matrix >::iterate	(	const matrix_type &	coeff_ref,
		const Right &	right,
		Solution &	solution ) const