psfun_d_krylov_mod

The psfun_d_krylov_mod contains the generic call to a Krylov subspace method for the computation of $y = f(A) x$ , for $A$ large and sparse.

The various Krylov methods are contained in associated submodules, the idea is to have different methods, associated to the same orthogonalization method in the same submodule

Uses

- psb_base_mod
- psb_krylov_mod
- amg_prec_mod
- psfun_d_serial_mod
- ogpf
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Used by

- Descendants:
- psfun_d_arnoldi_mod
- psfun_d_lanczos_mod
- psfun_d_sai_mod
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Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses. Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Interfaces

psfun_d_arnoldi psfun_d_lanczos psfun_d_saiarnoldi

Subroutines

psfun_d_parallel_apply psfun_d_plot_info psfun_d_prec_build psfun_d_prec_init

Interfaces

interface

Simple polynomial method based on the Arnoldi orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

public module subroutine psfun_d_arnoldi(fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Simple polynomial method based on the Arnoldi orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

Arguments

Type	Intent	Optional	Attributes		Name
type(psfun_d_serial),	intent(inout)			::	fun	Function object
type(psb_dspmat_type),	intent(in)			::	a	Distribute sparse matrix
type(psb_desc_type),	intent(in)			::	desc_a	Descriptor for the sparse matrix
type(psb_d_vect_type),	intent(inout)			::	y	Output vector
type(psb_d_vect_type),	intent(inout)			::	x	Input vector
real(kind=psb_dpk_),	intent(in)			::	eps	Requested tolerance
integer(kind=psb_ipk_),	intent(out)			::	info	Output flag
integer(kind=psb_ipk_),	intent(in),	optional		::	itmax	Maximum number of iteration
integer(kind=psb_ipk_),	intent(in),	optional		::	itrace	Trace for logoutput
integer(kind=psb_ipk_),	intent(in),	optional		::	istop	Stop criterion
integer(kind=psb_ipk_),	intent(out),	optional		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(out),	optional		::	err	Last estimate error
real(kind=psb_dpk_),	intent(out),	optional	allocatable	::	res(:)	Vector of the residuals

interface

Simple polynomial method based on the Lanczos orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

public module subroutine psfun_d_lanczos(fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Simple polynomial method based on the Lanczos orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

Arguments

Type	Intent	Optional	Attributes		Name
type(psfun_d_serial),	intent(inout)			::	fun	Function object
type(psb_dspmat_type),	intent(in)			::	a	Distribute sparse matrix
type(psb_desc_type),	intent(in)			::	desc_a	Descriptor for the sparse matrix
type(psb_d_vect_type),	intent(inout)			::	y	Output vector
type(psb_d_vect_type),	intent(inout)			::	x	Input vector
real(kind=psb_dpk_),	intent(in)			::	eps	Requested tolerance
integer(kind=psb_ipk_),	intent(out)			::	info	Output flag
integer(kind=psb_ipk_),	intent(in),	optional		::	itmax	Maximum number of iteration
integer(kind=psb_ipk_),	intent(in),	optional		::	itrace	Trace for logoutput
integer(kind=psb_ipk_),	intent(in),	optional		::	istop	Stop criterion
integer(kind=psb_ipk_),	intent(out),	optional		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(out),	optional		::	err	Last estimate error
real(kind=psb_dpk_),	intent(out),	optional	allocatable	::	res(:)	Vector of the residuals

interface

This interface contains the Shift-and-Invert method based on Arnoldi orthogonalization.

public module subroutine psfun_d_saiarnoldi(fun, a, kryl, prec, tau, desc_a, initmax, initrace, inistop, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Shift-and-invert method based on the Arnoldi orthogonalization procedure the method builds a basis $V_k$ for the shifted Krylov subspace

Arguments

Type	Intent	Optional	Attributes		Name
type(psfun_d_serial),	intent(inout)			::	fun	Function object
type(psb_dspmat_type),	intent(in)			::	a	Distribute sparse matrix
character(len=*),	intent(in)			::	kryl	Krylov method for the solution of inner systems
type(amg_dprec_type),	intent(inout)			::	prec	Preconditioner for the inner method
real(kind=psb_dpk_),	intent(in)			::	tau	Shift parameter of the method
type(psb_desc_type),	intent(in)			::	desc_a	Descriptor for the sparse matrix
integer(kind=psb_ipk_),	intent(in)			::	initmax	Maximum number of iteration (inner method)
integer(kind=psb_ipk_),	intent(in)			::	initrace	Trace for logoutput (inner method)
integer(kind=psb_ipk_),	intent(in)			::	inistop	Stop criterion (inner method)
type(psb_d_vect_type),	intent(inout)			::	y	Output vector
type(psb_d_vect_type),	intent(inout)			::	x	Input vector
real(kind=psb_dpk_),	intent(in)			::	eps	Requested tolerance
integer(kind=psb_ipk_),	intent(out)			::	info	Output flag
integer(kind=psb_ipk_),	intent(in),	optional		::	itmax	Maximum number of iteration
integer(kind=psb_ipk_),	intent(in),	optional		::	itrace	Trace for logoutput
integer(kind=psb_ipk_),	intent(in),	optional		::	istop	Stop criterion
integer(kind=psb_ipk_),	intent(out),	optional		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(out),	optional		::	err	Last estimate error
real(kind=psb_dpk_),	intent(out),	optional	allocatable	::	res(:)	Vector of the residuals

Derived Types

type, public :: psfun_d_krylov

Components

Type	Visibility		Name		Initial
integer(kind=psb_ipk_),	public	::	irst	=	10	Size for subspace restarting (inner method)
integer(kind=psb_ipk_),	public	::	istopc	=	1	Stopping criterion (inner method)
integer(kind=psb_ipk_),	public	::	itmax	=	200	Maximum number of iterations (inner method)
integer(kind=psb_ipk_),	public	::	itrace	=	0	Trace for the solution (inner method)
character(len=20),	public	::	kmethd	=	'CG'	Method for the solution of the linear system
character(len=20),	public	::	kname	=	'ARNOLDI'	Name of the Krylov method
type(amg_dprec_type),	public	::	prec			Preconditioner for the inner solution method
real(kind=psb_dpk_),	public	::	tau	=	dzero	Shift for shift-and-invert methods

Type-Bound Procedures

procedure, public, pass(meth) :: apply => psfun_d_parallel_apply
procedure, public, pass(meth) :: plot => psfun_d_plot_info
procedure, public, pass(meth) :: precbuild => psfun_d_prec_build
procedure, public, pass(meth) :: precinit => psfun_d_prec_init
generic, public :: set => setstring, setinteger
procedure, public, pass(meth) :: setinteger => psfun_d_setinteger
procedure, public, pass(meth) :: setstring => psfun_d_setstring

Subroutines

public subroutine psfun_d_parallel_apply(meth, fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

This is the generic function for applying every implemented Krylov method. The general iteration parameters (like the number of iteration, the stop criterion to be used, and the verbosity of the trace) can be passed directly to this routine. All the constitutive parameters of the actual method, and the information relative to the function are instead contained in the meth and fun objects. The Descriptor object `desc_a' contains the properties of the parallel environment.

Arguments

Type	Intent	Optional	Attributes		Name
class(psfun_d_krylov),	intent(inout)			::	meth	Krylov method object
type(psfun_d_serial),	intent(inout)			::	fun	Function object
type(psb_dspmat_type),	intent(in)			::	a	Distribute sparse matrix
type(psb_desc_type),	intent(in)			::	desc_a	Descriptor for the sparse matrix
type(psb_d_vect_type),	intent(inout)			::	y	Output vector
type(psb_d_vect_type),	intent(inout)			::	x	Input vector
real(kind=psb_dpk_),	intent(in)			::	eps	Requested tolerance
integer(kind=psb_ipk_),	intent(out)			::	info	Output flag
integer(kind=psb_ipk_),	intent(in),	optional		::	itmax	Maximum number of iteration
integer(kind=psb_ipk_),	intent(in),	optional		::	itrace	Trace for logoutput
integer(kind=psb_ipk_),	intent(in),	optional		::	istop	Stop criterion
integer(kind=psb_ipk_),	intent(out),	optional		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(out),	optional		::	err	Last estimate error
real(kind=psb_dpk_),	intent(out),	optional	allocatable	::	res(:)	Vector of the residuals

public subroutine psfun_d_plot_info(meth, fun, iter, res, info)

This function plots the convergence history of the Krylov method

Arguments

Type	Intent	Attributes		Name
class(psfun_d_krylov),	intent(inout)		::	meth	Krylov method
type(psfun_d_serial),	intent(inout)		::	fun	Function object
integer(kind=psb_ipk_),	intent(in)		::	iter	Number of iteration
real(kind=psb_dpk_),	intent(in),	dimension(:)	::	res	Residual vector
integer(kind=psb_ipk_),	intent(out)		::	info	Result of the Gnuplot call

public subroutine psfun_d_prec_build(meth, a, desc_a, info)

This function builds the AMG4PSBLAS preconditioner for the inner solve in a Rational Krylov method

Arguments

Type	Intent		Name
class(psfun_d_krylov),	intent(inout)	::	meth	Krylov method
type(psb_dspmat_type),	intent(inout)	::	a	Sparse matrix
type(psb_desc_type),	intent(inout)	::	desc_a	Descriptor for the sparse matrix
integer(kind=psb_ipk_)		::	info	Result of the init call

public subroutine psfun_d_prec_init(meth, ctxt, ptype, info)

This function performs the init of the preconditioner for the inner solve in the rational Krylov method

Arguments

Type	Intent		Name
class(psfun_d_krylov),	intent(inout)	::	meth	Krylov method
type(psb_ctxt_type),	intent(in)	::	ctxt	Parallel context
character(len=20),	intent(in)	::	ptype	PSBLAS/AMG4PSBLAS preconditioner
integer(kind=psb_ipk_)		::	info	Result of the init call

psfun_d_krylov_mod Module

Contents

Interfaces

Derived Types

Subroutines

Uses

Used by

Descendants:

Contents

Interfaces

Derived Types

Subroutines

Interfaces

interface

public module subroutine psfun_d_arnoldi(fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Arguments

interface

public module subroutine psfun_d_lanczos(fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Arguments

interface

public module subroutine psfun_d_saiarnoldi(fun, a, kryl, prec, tau, desc_a, initmax, initrace, inistop, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Arguments

Derived Types

type, public :: psfun_d_krylov

Components

Type-Bound Procedures

Subroutines

public subroutine psfun_d_parallel_apply(meth, fun, a, desc_a, y, x, eps, info, itmax, itrace, istop, iter, err, res)

Arguments

public subroutine psfun_d_plot_info(meth, fun, iter, res, info)

Arguments

public subroutine psfun_d_prec_build(meth, a, desc_a, info)

Arguments

public subroutine psfun_d_prec_init(meth, ctxt, ptype, info)

Arguments