krylovsolvers

Convenience functions for solving linear systems by Krylov methods. More...

Functions
uint	solve_cg_avector (void *A, addeval_t addeval_A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method and a general matrix type A. More...
uint	solve_cg_amatrix_avector (pcamatrix A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method. More...
uint	solve_cg_sparsematrix_avector (pcsparsematrix A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method. More...
uint	solve_cg_hmatrix_avector (pchmatrix A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method. More...
uint	solve_cg_h2matrix_avector (pch2matrix A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method. More...
uint	solve_cg_dh2matrix_avector (pcdh2matrix A, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the conjugate gradient method. More...
uint	solve_pcg_avector (void *A, addeval_t addeval_A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_pcg_amatrix_avector (pcamatrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_pcg_sparsematrix_avector (pcsparsematrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_pcg_hmatrix_avector (pchmatrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_pcg_h2matrix_avector (pch2matrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_pcg_dh2matrix_avector (pcdh2matrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter)
	Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method. More...
uint	solve_gmres_avector (void *A, addeval_t addeval_A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_gmres_amatrix_avector (pcamatrix A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_gmres_sparsematrix_avector (pcsparsematrix A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_gmres_hmatrix_avector (pchmatrix A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_gmres_h2matrix_avector (pch2matrix A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_gmres_dh2matrix_avector (pcdh2matrix A, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the generalized minimal residual method. More...
uint	solve_pgmres_avector (void *A, addeval_t addeval_A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...
uint	solve_pgmres_amatrix_avector (pcamatrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...
uint	solve_pgmres_sparsematrix_avector (pcsparsematrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...
uint	solve_pgmres_hmatrix_avector (pchmatrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...
uint	solve_pgmres_h2matrix_avector (pch2matrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...
uint	solve_pgmres_dh2matrix_avector (pcdh2matrix A, prcd_t prcd, void *pdata, pcavector b, pavector x, real eps, uint maxiter, uint kmax)
	Solve a linear system with the preconditioned generalized minimal residual method. More...

Detailed Description

Convenience functions for solving linear systems by Krylov methods.

Function Documentation

uint solve_cg_amatrix_avector	(	pcamatrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_cg_avector	(	void *	A,
		addeval_t	addeval_A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method and a general matrix type A.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
addeval_A	General callback function for evaluation of a matrix A.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_cg_dh2matrix_avector	(	pcdh2matrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_cg_h2matrix_avector	(	pch2matrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_cg_hmatrix_avector	(	pchmatrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_cg_sparsematrix_avector	(	pcsparsematrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_gmres_amatrix_avector	(	pcamatrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_gmres_avector	(	void *	A,
		addeval_t	addeval_A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
addeval_A	General callback function for evaluation of a matrix A.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_gmres_dh2matrix_avector	(	pcdh2matrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_gmres_h2matrix_avector	(	pch2matrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_gmres_hmatrix_avector	(	pchmatrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_gmres_sparsematrix_avector	(	pcsparsematrix	A,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pcg_amatrix_avector	(	pcamatrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pcg_avector	(	void *	A,
		addeval_t	addeval_A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
addeval_A	General callback function for evaluation of a matrix A.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pcg_dh2matrix_avector	(	pcdh2matrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pcg_h2matrix_avector	(	pch2matrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pcg_hmatrix_avector	(	pchmatrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pcg_sparsematrix_avector	(	pcsparsematrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter
	)

Solve a self-adjoint positive definite system with the preconditioned conjugate gradient method.

Parameters

A	System matrix, has to be self-adjoint and positive definite.
prcd	Callback function for preconditioner.
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.

Returns

Number of iterations.

uint solve_pgmres_amatrix_avector	(	pcamatrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pgmres_avector	(	void *	A,
		addeval_t	addeval_A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
addeval_A	General callback function for evaluation of a matrix A.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pgmres_dh2matrix_avector	(	pcdh2matrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pgmres_h2matrix_avector	(	pch2matrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pgmres_hmatrix_avector	(	pchmatrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.

uint solve_pgmres_sparsematrix_avector	(	pcsparsematrix	A,
		prcd_t	prcd,
		void *	pdata,
		pcavector	b,
		pavector	x,
		real	eps,
		uint	maxiter,
		uint	kmax
	)

Solve a linear system with the preconditioned generalized minimal residual method.

Parameters

A	System matrix, should be invertible.
prcd	Callback function for preconditioner .
pdata	Data for prcd callback function.
b	Right-hand side vector.
x	Initial guess, will be overwritten by approximate solution.
eps	Relative accuracy , the method stops if .
maxiter	Maximal number of iterations. maxiter=0 means that the number of iterations is not bounded.
kmax	Maximal dimension of Krylov subspace.

Returns

Number of iterations.