num::detail Namespace Reference

Classes
struct	CubicSigma
struct	CubicSigma< 2 >
struct	CubicSigma< 3 >
struct	SpikyDW
struct	SpikyDW< 2 >
struct	SpikyDW< 3 >

Functions
template<class Op > requires LinearOperator<Op, Vector, Vector>
LanczosResult	lanczos_operator_impl (const Op &A, idx k, real tol, idx max_steps, Backend backend)
real	normalise (Vector &v)
	Normalise v in-place; returns the old norm.
Matrix	dense_expm_pade6 (const Matrix &A)
template<class Op > requires LinearOperator<Op, Vector, Vector>
SolverResult	cg_operator_impl (const Op &A, const Vector &b, Vector &x, real tol, idx max_iter, Backend backend)
Vector	minres_projected_solve (const std::vector< real > &alpha, const std::vector< real > &beta, real beta0, idx m, Backend backend)
SolverResult	run (const linalg::SPDMatrix< Matrix > &A, const Vector &b, Vector &u, const CG &a)
template<class Op > requires SPDLinearOperator<Op, Vector, Vector>
SolverResult	run (const Op &A, const Vector &b, Vector &u, const CG &a)
SolverResult	run (const Matrix &A, const Vector &b, Vector &u, const GMRES &a)
SolverResult	run (const SparseMatrix &A, const Vector &b, Vector &u, const GMRES &a)
template<class Op > requires LinearOperator<Op, Vector, Vector>
SolverResult	run (const Op &A, const Vector &b, Vector &u, const GMRES &a)
template<class Op > requires SymmetricLinearOperator<Op, Vector, Vector>
SolverResult	run (const Op &A, const Vector &b, Vector &u, const MINRES &a)
template<class Op , class M > requires SPDLinearOperator<Op, Vector, Vector> && Preconditioner<M>
SolverResult	run (const Op &A, const Vector &b, Vector &u, const PCG< M > &a)

Function Documentation

cg_operator_impl()

template<class Op >
requires LinearOperator<Op, Vector, Vector>

SolverResult num::detail::cg_operator_impl	(	const Op &	A,
		const Vector &	b,
		Vector &	x,
		real	tol,
		idx	max_iter,
		Backend	backend
	)

Definition at line 38 of file cg.hpp.

References num::axpy(), num::beta(), num::dot(), num::e, num::SolverResult::iterations, num::scale(), and num::BasicVector< T >::size().

Referenced by num::cg().

dense_expm_pade6()

Matrix num::detail::dense_expm_pade6

(

const Matrix &

A

)

Definition at line 14 of file expv.cpp.

References num::lu(), num::lu_solve(), num::matmul(), num::BasicMatrix< T >::rows(), and num::scale().

Referenced by num::expv().

lanczos_operator_impl()

template<class Op >
requires LinearOperator<Op, Vector, Vector>

LanczosResult num::detail::lanczos_operator_impl	(	const Op &	A,
		idx	k,
		real	tol,
		idx	max_steps,
		Backend	backend
	)

Definition at line 33 of file lanczos.hpp.

References num::axpy(), num::beta(), num::dot(), num::e, num::eig_sym(), num::kernel::subspace::mgs_orthogonalize(), num::EigenResult::values, and num::EigenResult::vectors.

Referenced by num::lanczos().

minres_projected_solve()

Vector num::detail::minres_projected_solve ( const std::vector< real > &  alpha, const std::vector< real > &  beta, real  beta0, idx  m, Backend  backend  )

inline

Definition at line 22 of file minres.hpp.

References num::beta(), num::qr(), and num::qr_solve().

Referenced by num::minres().

normalise()

real num::detail::normalise ( Vector &  v )

inline

Normalise v in-place; returns the old norm.

Definition at line 34 of file power.hpp.

References num::e, and num::BasicVector< T >::size().

Referenced by num::inverse_iteration(), num::power_iteration(), and num::rayleigh_iteration().

run() [1/7]

SolverResult num::detail::run ( const linalg::SPDMatrix< Matrix > &  A, const Vector &  b, Vector &  u, const CG &  a  )

inline

Definition at line 60 of file solve.hpp.

References num::CG::backend, num::cg(), num::CG::max_iter, and num::CG::tol.

Referenced by num::solve(), and num::solve().

run() [2/7]

SolverResult num::detail::run ( const Matrix &  A, const Vector &  b, Vector &  u, const GMRES &  a  )

inline

Definition at line 70 of file solve.hpp.

References num::GMRES::backend, num::gmres(), num::GMRES::max_iter, num::GMRES::restart, and num::GMRES::tol.

run() [3/7]

template<class Op >
requires SPDLinearOperator<Op, Vector, Vector>

SolverResult num::detail::run	(	const Op &	A,
		const Vector &	b,
		Vector &	u,
		const CG &	a
	)

Definition at line 66 of file solve.hpp.

References num::CG::backend, num::cg(), num::CG::max_iter, and num::CG::tol.

run() [4/7]

template<class Op >
requires LinearOperator<Op, Vector, Vector>

SolverResult num::detail::run	(	const Op &	A,
		const Vector &	b,
		Vector &	u,
		const GMRES &	a
	)

Definition at line 80 of file solve.hpp.

References num::gmres(), num::GMRES::max_iter, num::GMRES::restart, and num::GMRES::tol.

run() [5/7]

template<class Op >
requires SymmetricLinearOperator<Op, Vector, Vector>

SolverResult num::detail::run	(	const Op &	A,
		const Vector &	b,
		Vector &	u,
		const MINRES &	a
	)

Definition at line 86 of file solve.hpp.

References num::MINRES::backend, num::MINRES::max_iter, num::minres(), and num::MINRES::tol.

run() [6/7]

template<class Op , class M >
requires SPDLinearOperator<Op, Vector, Vector> && Preconditioner<M>

SolverResult num::detail::run	(	const Op &	A,
		const Vector &	b,
		Vector &	u,
		const PCG< M > &	a
	)

Definition at line 92 of file solve.hpp.

References num::PCG< M >::backend, num::PCG< M >::max_iter, num::pcg(), num::PCG< M >::preconditioner, and num::PCG< M >::tol.

run() [7/7]

SolverResult num::detail::run ( const SparseMatrix &  A, const Vector &  b, Vector &  u, const GMRES &  a  )

inline

Definition at line 74 of file solve.hpp.

References num::gmres(), num::GMRES::max_iter, num::GMRES::restart, and num::GMRES::tol.