num_collect::ode::impl::gmres< Vector > Class Template Reference

Class to solve linear equations using generalized minimal residual (GMRES) [7]. More...

#include <num_collect/ode/impl/gmres.h>

Inheritance diagram for num_collect::ode::impl::gmres< Vector >:

Collaboration diagram for num_collect::ode::impl::gmres< Vector >:

Public Types
using	matrix_type = Eigen::MatrixX<scalar_type>
	Type of matrices.
using	scalar_type = typename vector_type::Scalar
	Type of scalars.
using	vector_type = Vector
	Type of vectors.

Public Member Functions
auto	max_subspace_dim (index_type val) -> gmres &
	Set the maximum number of dimensions of subspace.
template<typename CoeffFunction >
void	solve (CoeffFunction &&coeff_function, const vector_type &rhs, vector_type &solution)
	Solve.

Private Attributes
matrix_type	basis_ {}
	Basis of subspace.
matrix_type	hessenberg_ {}
	Hessenberg matrix.
index_type	max_subspace_dim_ {default_max_subspace_dim}
	Maximum number of dimensions of subspace.
Eigen::ColPivHouseholderQR< matrix_type >	qr_ {}
	QR decomposition.
vector_type	residual_ {}
	Residual.
Eigen::VectorX< scalar_type >	temp_rhs_ {}
	Temporary vector for solving internal equation.
Eigen::VectorX< scalar_type >	temp_sol_ {}
	Temporary vector for solving internal equation.

Static Private Attributes
static constexpr index_type	default_max_subspace_dim = 2
	Default maximum number of dimensions of subspace.

Detailed Description

template<base::concepts::real_scalar_dense_vector Vector>
class num_collect::ode::impl::gmres< Vector >

Class to solve linear equations using generalized minimal residual (GMRES) [7].

Template Parameters

Vector

Type of vectors.

Definition at line 45 of file gmres.h.

Member Typedef Documentation

matrix_type

template<base::concepts::real_scalar_dense_vector Vector>

using num_collect::ode::impl::gmres< Vector >::matrix_type = Eigen::MatrixX<scalar_type>

Type of matrices.

Definition at line 54 of file gmres.h.

scalar_type

template<base::concepts::real_scalar_dense_vector Vector>

using num_collect::ode::impl::gmres< Vector >::scalar_type = typename vector_type::Scalar

Type of scalars.

Definition at line 51 of file gmres.h.

vector_type

template<base::concepts::real_scalar_dense_vector Vector>

using num_collect::ode::impl::gmres< Vector >::vector_type = Vector

Type of vectors.

Definition at line 48 of file gmres.h.

Member Function Documentation

max_subspace_dim()

template<base::concepts::real_scalar_dense_vector Vector>

auto num_collect::ode::impl::gmres< Vector >::max_subspace_dim ( index_type val ) -> gmres&

inline

Set the maximum number of dimensions of subspace.

Parameters

[in]

val

Value.

Returns

This.

Definition at line 122 of file gmres.h.

solve()

template<base::concepts::real_scalar_dense_vector Vector>

template<typename CoeffFunction >

void num_collect::ode::impl::gmres< Vector >::solve ( CoeffFunction && coeff_function, const vector_type & rhs, vector_type & solution )

inline

Solve.

coeff_function is assumed to have a signature like:

void coeff_function(const variable_type& target, variable_type& result);

Template Parameters

CoeffFunction

Type of the function to multiply coefficient matrix.

Parameters

[in]	coeff_function	Function to multiply coefficient matrix.
[in]	rhs	Right-hand-side vector.
[in,out]	solution	Solution. (Given vector is used as the initial solution.)

Definition at line 73 of file gmres.h.

Member Data Documentation

basis_

template<base::concepts::real_scalar_dense_vector Vector>

matrix_type num_collect::ode::impl::gmres< Vector >::basis_ {}

private

Basis of subspace.

Definition at line 141 of file gmres.h.

default_max_subspace_dim

template<base::concepts::real_scalar_dense_vector Vector>

index_type num_collect::ode::impl::gmres< Vector >::default_max_subspace_dim = 2

staticconstexprprivate

Default maximum number of dimensions of subspace.

Definition at line 132 of file gmres.h.

hessenberg_

template<base::concepts::real_scalar_dense_vector Vector>

matrix_type num_collect::ode::impl::gmres< Vector >::hessenberg_ {}

private

Hessenberg matrix.

Definition at line 144 of file gmres.h.

max_subspace_dim_

template<base::concepts::real_scalar_dense_vector Vector>

index_type num_collect::ode::impl::gmres< Vector >::max_subspace_dim_ {default_max_subspace_dim}

private

Maximum number of dimensions of subspace.

Definition at line 135 of file gmres.h.

qr_

template<base::concepts::real_scalar_dense_vector Vector>

Eigen::ColPivHouseholderQR<matrix_type> num_collect::ode::impl::gmres< Vector >::qr_ {}

private

QR decomposition.

Definition at line 153 of file gmres.h.

residual_

template<base::concepts::real_scalar_dense_vector Vector>

vector_type num_collect::ode::impl::gmres< Vector >::residual_ {}

private

Residual.

Definition at line 138 of file gmres.h.

temp_rhs_

template<base::concepts::real_scalar_dense_vector Vector>

Eigen::VectorX<scalar_type> num_collect::ode::impl::gmres< Vector >::temp_rhs_ {}

private

Temporary vector for solving internal equation.

Definition at line 147 of file gmres.h.

temp_sol_

template<base::concepts::real_scalar_dense_vector Vector>

Eigen::VectorX<scalar_type> num_collect::ode::impl::gmres< Vector >::temp_sol_ {}

private

Temporary vector for solving internal equation.

Definition at line 150 of file gmres.h.

---

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

• include/num_collect/ode/impl/gmres.h