kexpm – LightKrylov

public interface kexpm

Description

This interface provides methods to evaluate the matrix-vector product $c = \exp(\tau A) b$ based on the Arnoldi method.

Syntax

    call kexpm(c, A, b, tau, tol, info [, trans] [, kdim])

Arguments

c : Output vector (or vectors). It is an intent(out) argument.

A : Linear operator to be exponentiated. It is an intent(in) argument.

b : Vector to be multiplied by $\exp(\tau A)$ . It is an intent(in) argument.

tau : real (singe or double) time over which the matrix exponential needs to be computed. It is an intent(in) argument.

info : integer Information flag.

trans (optional) : Whether $A$ or $A^H$ is being used. (default trans=.false.)

kdim (optional) : Dimension of the Krylov subspace used in the Arnoldi method.

Module Procedures

private subroutine kexpm_vec_rsp(c, A, b, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_rsp),	intent(out)		::	c	Best approximation of $\exp(\tau \mathbf{A}) \mathbf{b}$ in the computed Krylov subspace
class(abstract_linop_rsp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_rsp),	intent(in)		::	b	Input vector on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=sp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=sp),	intent(in)		::	tol	Solution tolerance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_mat_rsp(C, A, B, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_rsp),	intent(out)		::	C(:)	Best Krylov approximation of $\mathbf{C} = \exp(\tau \mathbf{A}) \mathbf{B}$ .
class(abstract_linop_rsp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_rsp),	intent(in)		::	B(:)	Input matrix on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=sp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=sp),	intent(in)		::	tol	Solution toleance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose ?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_vec_rdp(c, A, b, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_rdp),	intent(out)		::	c	Best approximation of $\exp(\tau \mathbf{A}) \mathbf{b}$ in the computed Krylov subspace
class(abstract_linop_rdp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_rdp),	intent(in)		::	b	Input vector on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=dp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=dp),	intent(in)		::	tol	Solution tolerance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_mat_rdp(C, A, B, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_rdp),	intent(out)		::	C(:)	Best Krylov approximation of $\mathbf{C} = \exp(\tau \mathbf{A}) \mathbf{B}$ .
class(abstract_linop_rdp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_rdp),	intent(in)		::	B(:)	Input matrix on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=dp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=dp),	intent(in)		::	tol	Solution toleance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose ?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_vec_csp(c, A, b, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_csp),	intent(out)		::	c	Best approximation of $\exp(\tau \mathbf{A}) \mathbf{b}$ in the computed Krylov subspace
class(abstract_linop_csp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_csp),	intent(in)		::	b	Input vector on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=sp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=sp),	intent(in)		::	tol	Solution tolerance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_mat_csp(C, A, B, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_csp),	intent(out)		::	C(:)	Best Krylov approximation of $\mathbf{C} = \exp(\tau \mathbf{A}) \mathbf{B}$ .
class(abstract_linop_csp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_csp),	intent(in)		::	B(:)	Input matrix on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=sp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=sp),	intent(in)		::	tol	Solution toleance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose ?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_vec_cdp(c, A, b, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_cdp),	intent(out)		::	c	Best approximation of $\exp(\tau \mathbf{A}) \mathbf{b}$ in the computed Krylov subspace
class(abstract_linop_cdp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_cdp),	intent(in)		::	b	Input vector on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=dp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=dp),	intent(in)		::	tol	Solution tolerance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

private subroutine kexpm_mat_cdp(C, A, B, tau, tol, info, trans, kdim)

Arguments

Type	Intent	Optional		Name
class(abstract_vector_cdp),	intent(out)		::	C(:)	Best Krylov approximation of $\mathbf{C} = \exp(\tau \mathbf{A}) \mathbf{B}$ .
class(abstract_linop_cdp),	intent(in)		::	A	Linear operator to be exponentiated.
class(abstract_vector_cdp),	intent(in)		::	B(:)	Input matrix on which to apply $\exp(\tau \mathbf{A})$ .
real(kind=dp),	intent(in)		::	tau	Time horizon for the exponentiation.
real(kind=dp),	intent(in)		::	tol	Solution toleance based on error estimates.
integer,	intent(out)		::	info	Information flag.
logical,	intent(in),	optional	::	trans	Use transpose ?
integer,	intent(in),	optional	::	kdim	Maximum size of the Krylov subspace.

kexpm Interface

Contents

Module Procedures

public interface kexpm

Description

Syntax

Arguments

Module Procedures

private subroutine kexpm_vec_rsp(c, A, b, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_mat_rsp(C, A, B, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_vec_rdp(c, A, b, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_mat_rdp(C, A, B, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_vec_csp(c, A, b, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_mat_csp(C, A, B, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_vec_cdp(c, A, b, tau, tol, info, trans, kdim)

Arguments

private subroutine kexpm_mat_cdp(C, A, B, tau, tol, info, trans, kdim)

Arguments