fgmres – LightKrylov

public interface fgmres

Description

Solve a square linear system of equations

$Ax = b$

using the Flexible Generalized Minimum RESidual (FGMRES) method.

References

Saad Y. and Schultz M. H. "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems." SIAM Journal on Scientific and Statistical Computing, 7(3), 1986.

Syntax

    call fgmres(A, b, x, info [, rtol] [, atol] [, preconditioner] [, options] [, transpose])

Arguments

A : Linear operator derived from one of the abstract_linop provided by the AbstractLinops module. It is an intent(inout) argument.
b : Right-hand side vector derived from one the abstract_vector types provided by the AbstractVectors module. It needs to have the same type and kind as A. It is an intent(in) argument.
x : On entry, initial guess for the solution. On exit, the solution computed by gmres. It is a vector derived from one the abstract_vector types provided by the AbstractVectors module. It needs to have the same type and kind as A. It is an intent(inout) argument.
info : integer information flag.
rtol (optional) : real relative tolerance for the solver.
atol (optional) : real absolute tolerance for the solver.
preconditioner (optional) : Right preconditioner used to solve the system. It needs to be consistent with the abstract_preconditioner interface. It is an intent(in) argument.
options (optional) : Container for the gmres options given by the gmres_opts type. It is an intent(in) argument.
transpose (optional): logical flag controlling whether $Ax = b$ or $A^H x = b$ is being solved.

Subroutines

private module subroutine dense_fgmres_cdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
complex(kind=dp),	intent(in)		::	A(:,:)	Linear operator to be inverted.
complex(kind=dp),	intent(in)		::	b(:)	Right-hand side vector.
complex(kind=dp),	intent(inout)		::	x(:)	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=dp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=dp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_cdp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine dense_fgmres_csp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
complex(kind=sp),	intent(in)		::	A(:,:)	Linear operator to be inverted.
complex(kind=sp),	intent(in)		::	b(:)	Right-hand side vector.
complex(kind=sp),	intent(inout)		::	x(:)	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=sp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=sp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_csp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine dense_fgmres_rdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
real(kind=dp),	intent(in)		::	A(:,:)	Linear operator to be inverted.
real(kind=dp),	intent(in)		::	b(:)	Right-hand side vector.
real(kind=dp),	intent(inout)		::	x(:)	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=dp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=dp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_rdp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine dense_fgmres_rsp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
real(kind=sp),	intent(in)		::	A(:,:)	Linear operator to be inverted.
real(kind=sp),	intent(in)		::	b(:)	Right-hand side vector.
real(kind=sp),	intent(inout)		::	x(:)	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=sp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=sp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_rsp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine fgmres_cdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
class(abstract_linop_cdp),	intent(inout)		::	A	Linear operator to be inverted.
class(abstract_vector_cdp),	intent(in)		::	b	Right-hand side vector.
class(abstract_vector_cdp),	intent(inout)		::	x	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=dp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=dp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_cdp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine fgmres_csp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
class(abstract_linop_csp),	intent(inout)		::	A	Linear operator to be inverted.
class(abstract_vector_csp),	intent(in)		::	b	Right-hand side vector.
class(abstract_vector_csp),	intent(inout)		::	x	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=sp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=sp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_csp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine fgmres_rdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
class(abstract_linop_rdp),	intent(inout)		::	A	Linear operator to be inverted.
class(abstract_vector_rdp),	intent(in)		::	b	Right-hand side vector.
class(abstract_vector_rdp),	intent(inout)		::	x	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=dp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=dp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_rdp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

private module subroutine fgmres_rsp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

Type	Intent	Optional		Name
class(abstract_linop_rsp),	intent(inout)		::	A	Linear operator to be inverted.
class(abstract_vector_rsp),	intent(in)		::	b	Right-hand side vector.
class(abstract_vector_rsp),	intent(inout)		::	x	Solution vector.
integer,	intent(out)		::	info	Information flag.
real(kind=sp),	intent(in),	optional	::	rtol	Relative solver tolerance
real(kind=sp),	intent(in),	optional	::	atol	Absolute solver tolerance
class(abstract_precond_rsp),	intent(inout),	optional	::	preconditioner	Preconditioner (optional).
class(abstract_opts),	intent(in),	optional	::	options	GMRES options.
logical,	intent(in),	optional	::	transpose	Whether $\mathbf{A}$ or $\mathbf{A}^H$ is being used.
class(abstract_metadata),	intent(out),	optional	::	meta	Metadata.

fgmres Interface

Contents

Subroutines

public interface fgmres

Description

Syntax

Arguments

Subroutines

private module subroutine dense_fgmres_cdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine dense_fgmres_csp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine dense_fgmres_rdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine dense_fgmres_rsp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine fgmres_cdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine fgmres_csp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine fgmres_rdp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments

private module subroutine fgmres_rsp(A, b, x, info, rtol, atol, preconditioner, options, transpose, meta)

Arguments