IterativeSolvers.hpp File Reference

Contains (sequential/threaded) iterative solvers. More...

#include <functional>
#include "StrumpackOptions.hpp"
#include "sparse/CompressedSparseMatrix.hpp"
#include "dense/DenseMatrix.hpp"

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Namespaces
	strumpack

Typedefs
template<typename T >
using	strumpack::iterative::SPMV = std::function< void(const T *, T *)>
template<typename T >
using	strumpack::iterative::PREC = std::function< void(T *)>

Functions
template<typename scalar_t , typename real_t = typename RealType<scalar_t>::value_type>
real_t	strumpack::iterative::GMRes (const SPMV< scalar_t > &A, const PREC< scalar_t > &M, std::size_t n, scalar_t *x, const scalar_t *b, real_t rtol, real_t atol, int &totit, int maxit, int restart, GramSchmidtType GStype, bool non_zero_guess, bool verbose)
template<typename scalar_t , typename real_t = typename RealType<scalar_t>::value_type>
real_t	strumpack::iterative::BiCGStab (const SPMV< scalar_t > &A, const PREC< scalar_t > &M, std::size_t n, scalar_t *x, const scalar_t *b, real_t rtol, real_t atol, int &totit, int maxit, bool non_zero_guess, bool verbose)
template<typename scalar_t , typename integer_t , typename real_t = typename RealType<scalar_t>::value_type>
void	strumpack::iterative::IterativeRefinement (const CompressedSparseMatrix< scalar_t, integer_t > &A, const std::function< void(DenseMatrix< scalar_t > &)> &M, DenseMatrix< scalar_t > &x, const DenseMatrix< scalar_t > &b, real_t rtol, real_t atol, int &totit, int maxit, bool non_zero_guess, bool verbose)
template<typename scalar_t , typename real_t = typename RealType<scalar_t>::value_type>
void	strumpack::iterative::IterativeRefinement (const DenseMatrix< scalar_t > &A, const std::function< void(DenseMatrix< scalar_t > &)> &M, DenseMatrix< scalar_t > &x, const DenseMatrix< scalar_t > &b, real_t rtol, real_t atol, int &totit, int maxit, bool non_zero_guess, bool verbose)

Detailed Description

Contains (sequential/threaded) iterative solvers.

Function Documentation

BiCGStab()

template<typename scalar_t , typename real_t = typename RealType<scalar_t>::value_type>

real_t strumpack::iterative::BiCGStab	(	const SPMV< scalar_t > &	A,
		const PREC< scalar_t > &	M,
		std::size_t	n,
		scalar_t *	x,
		const scalar_t *	b,
		real_t	rtol,
		real_t	atol,
		int &	totit,
		int	maxit,
		bool	non_zero_guess,
		bool	verbose
	)

http://www.netlib.org/templates/matlab/bicgstab.m

IterativeRefinement() [1/2]

template<typename scalar_t , typename integer_t , typename real_t = typename RealType<scalar_t>::value_type>

void strumpack::iterative::IterativeRefinement	(	const CompressedSparseMatrix< scalar_t, integer_t > &	A,
		const std::function< void(DenseMatrix< scalar_t > &)> &	M,
		DenseMatrix< scalar_t > &	x,
		const DenseMatrix< scalar_t > &	b,
		real_t	rtol,
		real_t	atol,
		int &	totit,
		int	maxit,
		bool	non_zero_guess,
		bool	verbose
	)

Iterative refinement, with a sparse matrix, to solve a linear system M^{-1}Ax=M^{-1}b.

Template Parameters

scalar_t	scalar type
integer_t	integer type used in A
real_t	real type, can be derived from the scalar_t type

Parameters

A	dense matrix A
M	routine to apply M^{-1} to a matrix
x	on output this contains the solution, on input this can be the initial guess. This always has to be allocated to the correct size (A.rows() x b.cols())
b	the right hand side, should have A.rows() rows
rtol	relative stopping tolerance
atol	absolute stopping tolerance
totit	on output this will contain the number of iterations that were performed
maxit	maximum number of iterations
non_zero_guess	x use x as an initial guess

IterativeRefinement() [2/2]

template<typename scalar_t , typename real_t = typename RealType<scalar_t>::value_type>

void strumpack::iterative::IterativeRefinement	(	const DenseMatrix< scalar_t > &	A,
		const std::function< void(DenseMatrix< scalar_t > &)> &	M,
		DenseMatrix< scalar_t > &	x,
		const DenseMatrix< scalar_t > &	b,
		real_t	rtol,
		real_t	atol,
		int &	totit,
		int	maxit,
		bool	non_zero_guess,
		bool	verbose
	)

Iterative refinement, with a dense matrix, to solve a linear system M^{-1}Ax=M^{-1}b.

Template Parameters

scalar_t	scalar type
real_t	real type, can be derived from the scalar_t type

Parameters

A	dense matrix A
direct_solve	routine to apply M^{-1} to a matrix
x	on output this contains the solution, on input this can be the initial guess. This always has to be allocated to the correct size (A.rows() x b.cols())
b	the right hand side, should have A.rows() rows
rtol	relative stopping tolerance
atol	absolute stopping tolerance
totit	on output this will contain the number of iterations that were performed
maxit	maximum number of iterations
non_zero_guess	x use x as an initial guess