LightKrylov_AbstractLinops

This module provides the base classes abtract_linop_rsp, abstract_linop_rdp, abstract_linop_csp and abstract_linop_cdp which can be used to define your own linear operators. To do so, you simply need to provide two type-bound procedures:

matvec(self, vec_in, vec_out) : Computes the matrix-vector product.
`rmatvec(self, vec_in, vec_out) : Computes the transpose matrix-vector product.

It also provides extended types to define the identity operator, symmetric linear operators, scalar-multiplication of a linear multiplication, as well as addition of two linear operators.

Uses

- LightKrylov_AbstractVectors
- LightKrylov_Logger
- LightKrylov_Constants
- LightKrylov_Utils
- stdlib_optval
- stdlib_linalg_blas
- LightKrylov_Timer_Utils

Interfaces

public interface adjoint

private function initialize_adjoint_rsp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_linop_rsp),	intent(in)			::	A

Return Value class(adjoint_linop_rsp), allocatable

private function initialize_adjoint_rdp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_linop_rdp),	intent(in)			::	A

Return Value class(adjoint_linop_rdp), allocatable

private function initialize_adjoint_csp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_linop_csp),	intent(in)			::	A

Return Value class(adjoint_linop_csp), allocatable

private function initialize_adjoint_cdp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_linop_cdp),	intent(in)			::	A

Return Value class(adjoint_linop_cdp), allocatable

public interface dense_linop

private function initialize_dense_linop_from_array_rsp(A) result(linop)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	A(:,:)

Return Value type(dense_linop_rsp)

private function initialize_dense_linop_from_array_rdp(A) result(linop)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	A(:,:)

Return Value type(dense_linop_rdp)

private function initialize_dense_linop_from_array_csp(A) result(linop)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	A(:,:)

Return Value type(dense_linop_csp)

private function initialize_dense_linop_from_array_cdp(A) result(linop)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	A(:,:)

Return Value type(dense_linop_cdp)

public interface verify_linop_axioms

private function verify_linop_axioms_rsp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Deals with optional arguments. Run all tests to verify axioms. Generate random vectors. Check additivity. Generate random vectors. generate the identical non-trivial alpha on all ranks

Check homogeneity. Exit if the test fails. Check that the zero vector is mapped to the zero vector. Exit if the test fails. Generate random vectors. Check adjoint consistency.

Arguments

Type	Intent	Optional		Name
class(abstract_linop_rsp),	intent(inout)		::	A	Linear operator whose implementation needs to be tested.
class(abstract_vector_rsp),	intent(in)		::	x	Mold vector from the operator's domain (used to generate random inputs).
integer,	intent(in),	optional	::	ntrials	Number of random samples generated for the tests.
real(kind=sp),	intent(in),	optional	::	tolerance	Tolerance used for the axiom checks.
logical,	intent(in),	optional	::	test_zero_map	Verify explicitly that the operator maps x = 0 to 0? (Default: .true.)
logical,	intent(in),	optional	::	test_adjoint	Verify also the adjoint consistency `<A u, v> = <u, A^H v>`? (Default: .true.)

Return Value logical

private function verify_linop_axioms_rdp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Deals with optional arguments. Run all tests to verify axioms. Generate random vectors. Check additivity. Generate random vectors. generate the identical non-trivial alpha on all ranks

Check homogeneity. Exit if the test fails. Check that the zero vector is mapped to the zero vector. Exit if the test fails. Generate random vectors. Check adjoint consistency.

Arguments

Type	Intent	Optional		Name
class(abstract_linop_rdp),	intent(inout)		::	A	Linear operator whose implementation needs to be tested.
class(abstract_vector_rdp),	intent(in)		::	x	Mold vector from the operator's domain (used to generate random inputs).
integer,	intent(in),	optional	::	ntrials	Number of random samples generated for the tests.
real(kind=dp),	intent(in),	optional	::	tolerance	Tolerance used for the axiom checks.
logical,	intent(in),	optional	::	test_zero_map	Verify explicitly that the operator maps x = 0 to 0? (Default: .true.)
logical,	intent(in),	optional	::	test_adjoint	Verify also the adjoint consistency `<A u, v> = <u, A^H v>`? (Default: .true.)

Return Value logical

private function verify_linop_axioms_csp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Deals with optional arguments. Run all tests to verify axioms. Generate random vectors. Check additivity. Generate random vectors. generate the identical non-trivial alpha on all ranks

Check homogeneity. Exit if the test fails. Check that the zero vector is mapped to the zero vector. Exit if the test fails. Generate random vectors. Check adjoint consistency.

Arguments

Type	Intent	Optional		Name
class(abstract_linop_csp),	intent(inout)		::	A	Linear operator whose implementation needs to be tested.
class(abstract_vector_csp),	intent(in)		::	x	Mold vector from the operator's domain (used to generate random inputs).
integer,	intent(in),	optional	::	ntrials	Number of random samples generated for the tests.
real(kind=sp),	intent(in),	optional	::	tolerance	Tolerance used for the axiom checks.
logical,	intent(in),	optional	::	test_zero_map	Verify explicitly that the operator maps x = 0 to 0? (Default: .true.)
logical,	intent(in),	optional	::	test_adjoint	Verify also the adjoint consistency `<A u, v> = <u, A^H v>`? (Default: .true.)

Return Value logical

private function verify_linop_axioms_cdp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Deals with optional arguments. Run all tests to verify axioms. Generate random vectors. Check additivity. Generate random vectors. generate the identical non-trivial alpha on all ranks

Check homogeneity. Exit if the test fails. Check that the zero vector is mapped to the zero vector. Exit if the test fails. Generate random vectors. Check adjoint consistency.

Arguments

Type	Intent	Optional		Name
class(abstract_linop_cdp),	intent(inout)		::	A	Linear operator whose implementation needs to be tested.
class(abstract_vector_cdp),	intent(in)		::	x	Mold vector from the operator's domain (used to generate random inputs).
integer,	intent(in),	optional	::	ntrials	Number of random samples generated for the tests.
real(kind=dp),	intent(in),	optional	::	tolerance	Tolerance used for the axiom checks.
logical,	intent(in),	optional	::	test_zero_map	Verify explicitly that the operator maps x = 0 to 0? (Default: .true.)
logical,	intent(in),	optional	::	test_adjoint	Verify also the adjoint consistency `<A u, v> = <u, A^H v>`? (Default: .true.)

Return Value logical

Derived Types

type, public, extends(abstract_linop_cdp) :: Id_cdp

Utility type to define the Identity operator. Note that the type-bound procedures for matvec and rmatvec do not have to be defined by the user.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => id_matvec_cdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => id_matvec_cdp

type, public, extends(abstract_linop_csp) :: Id_csp

Utility type to define the Identity operator. Note that the type-bound procedures for matvec and rmatvec do not have to be defined by the user.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => id_matvec_csp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => id_matvec_csp

type, public, extends(abstract_linop_rdp) :: Id_rdp

Utility type to define the Identity operator. Note that the type-bound procedures for matvec and rmatvec do not have to be defined by the user.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => id_matvec_rdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => id_matvec_rdp

type, public, extends(abstract_linop_rsp) :: Id_rsp

Utility type to define the Identity operator. Note that the type-bound procedures for matvec and rmatvec do not have to be defined by the user.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => id_matvec_rsp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => id_matvec_rsp

type, public, abstract, extends(abstract_linop_cdp) :: abstract_exptA_linop_cdp

Utility type to define the exponential propagator $\mathbf{\Phi}_\tau$ which is the linear map corresponding to the matrix exponential of the (possibly time-dependent) system Jacobian $\mathbf{L}(t)$ over a time horizon $\tau$ as:

Components

Type	Visibility		Name		Initial
type(lightkrylov_timer),	public	::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public	::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=dp),	public	::	tau			Time horizon for the temporal integration. This variable must be set when the operator is instantiated.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_cdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_cdp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop_csp) :: abstract_exptA_linop_csp

Components

Type	Visibility		Name		Initial
type(lightkrylov_timer),	public	::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public	::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=sp),	public	::	tau			Time horizon for the temporal integration. This variable must be set when the operator is instantiated.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_csp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_csp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop_rdp) :: abstract_exptA_linop_rdp

Components

Type	Visibility		Name		Initial
type(lightkrylov_timer),	public	::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public	::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=dp),	public	::	tau			Time horizon for the temporal integration. This variable must be set when the operator is instantiated.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_rdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_rdp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop_rsp) :: abstract_exptA_linop_rsp

Components

Type	Visibility		Name		Initial
type(lightkrylov_timer),	public	::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public	::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=sp),	public	::	tau			Time horizon for the temporal integration. This variable must be set when the operator is instantiated.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_rsp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_rsp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_sym_linop) :: abstract_hermitian_linop_cdp

Abstract representation of an abstract hermitian (complex-valued) linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_herm_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_herm_matvec_cdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, abstract, extends(abstract_sym_linop) :: abstract_hermitian_linop_csp

Abstract representation of an abstract hermitian (complex-valued) linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_herm_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_herm_matvec_csp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, abstract :: abstract_linop

Base type to define an abstract linear operator. All other operator types defined in LightKrylov derive from this fundamental one.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, abstract, extends(abstract_linop) :: abstract_linop_cdp

Base type to extend in order to define a complex(dp)-valued linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_cdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_cdp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop) :: abstract_linop_csp

Base type to extend in order to define a complex(sp)-valued linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_csp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_csp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop) :: abstract_linop_rdp

Base type to extend in order to define a real(dp)-valued linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_rdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_rdp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop) :: abstract_linop_rsp

Base type to extend in order to define a real(sp)-valued linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_matvec_rsp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure(abstract_matvec_rsp), public, deferred, pass(self) :: rmatvec	Procedure to compute the reversed matrix-vector product $\mathbf{y} = \mathbf{A}^H \mathbf{x}$ .

type, public, abstract, extends(abstract_linop) :: abstract_sym_linop

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, abstract, extends(abstract_sym_linop) :: abstract_sym_linop_rdp

Abstract representation of an abstract symmetric (real valued) linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_sym_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_sym_matvec_rdp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, abstract, extends(abstract_sym_linop) :: abstract_sym_linop_rsp

Abstract representation of an abstract symmetric (real valued) linear operator.

Components

Type	Visibility	Attributes		Name		Initial
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_sym_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure(abstract_sym_matvec_rsp), public, deferred, pass(self) :: matvec	Procedure to compute the matrix-vector product $\mathbf{y} = \mathbf{Ax}$ .
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data

type, public, extends(abstract_linop_cdp) :: adjoint_linop_cdp

Utility type to define an adjoint linear operator. The definition of matvec and rmatvec are directly inherited from those used to define A. Note that this utility does not compute the adjoint for you. It simply provides a utility to define a new operator with matvec and rmatvec switched.

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_cdp),	public,	allocatable	::	A			Linear operator whose adjoint needs to be defined.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => adjoint_matvec_cdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => adjoint_rmatvec_cdp

type, public, extends(abstract_linop_csp) :: adjoint_linop_csp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_csp),	public,	allocatable	::	A			Linear operator whose adjoint needs to be defined.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => adjoint_matvec_csp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => adjoint_rmatvec_csp

type, public, extends(abstract_linop_rdp) :: adjoint_linop_rdp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rdp),	public,	allocatable	::	A			Linear operator whose adjoint needs to be defined.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => adjoint_matvec_rdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => adjoint_rmatvec_rdp

type, public, extends(abstract_linop_rsp) :: adjoint_linop_rsp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rsp),	public,	allocatable	::	A			Linear operator whose adjoint needs to be defined.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => adjoint_matvec_rsp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => adjoint_rmatvec_rsp

type, public, extends(abstract_linop_cdp) :: axpby_linop_cdp

Utility type to define a composite linear operator $\mathbf{C} = \alpha \mathbf{A} + \beta \mathbf{B}$ . The definitions of matvec and rmatvec are directly inherited from those used to define A and B.

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_cdp),	public,	allocatable	::	A			Underlying linear operators.
class(abstract_linop_cdp),	public,	allocatable	::	B			Underlying linear operators.
complex(kind=dp),	public		::	alpha			Scaling factors.
complex(kind=dp),	public		::	beta			Scaling factors.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
logical,	public		::	transA	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.
logical,	public		::	transB	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => axpby_matvec_cdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => axpby_rmatvec_cdp

type, public, extends(abstract_linop_csp) :: axpby_linop_csp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_csp),	public,	allocatable	::	A			Underlying linear operators.
class(abstract_linop_csp),	public,	allocatable	::	B			Underlying linear operators.
complex(kind=sp),	public		::	alpha			Scaling factors.
complex(kind=sp),	public		::	beta			Scaling factors.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
logical,	public		::	transA	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.
logical,	public		::	transB	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => axpby_matvec_csp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => axpby_rmatvec_csp

type, public, extends(abstract_linop_rdp) :: axpby_linop_rdp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rdp),	public,	allocatable	::	A			Underlying linear operators.
class(abstract_linop_rdp),	public,	allocatable	::	B			Underlying linear operators.
real(kind=dp),	public		::	alpha			Scaling factors.
real(kind=dp),	public		::	beta			Scaling factors.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
logical,	public		::	transA	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.
logical,	public		::	transB	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => axpby_matvec_rdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => axpby_rmatvec_rdp

type, public, extends(abstract_linop_rsp) :: axpby_linop_rsp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rsp),	public,	allocatable	::	A			Underlying linear operators.
class(abstract_linop_rsp),	public,	allocatable	::	B			Underlying linear operators.
real(kind=sp),	public		::	alpha			Scaling factors.
real(kind=sp),	public		::	beta			Scaling factors.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
logical,	public		::	transA	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.
logical,	public		::	transB	=	.false.	Logical flag to control whether $\mathbf{A}$ and/or $\mathbf{B}$ need to be transposed.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => axpby_matvec_rsp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => axpby_rmatvec_rsp

type, public, extends(abstract_linop_cdp) :: dense_linop_cdp

Components

Type	Visibility	Attributes		Name		Initial
complex(kind=dp),	public,	allocatable	::	data(:,:)
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => dense_matvec_cdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => dense_rmatvec_cdp

type, public, extends(abstract_linop_csp) :: dense_linop_csp

Components

Type	Visibility	Attributes		Name		Initial
complex(kind=sp),	public,	allocatable	::	data(:,:)
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => dense_matvec_csp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => dense_rmatvec_csp

type, public, extends(abstract_linop_rdp) :: dense_linop_rdp

Components

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public,	allocatable	::	data(:,:)
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => dense_matvec_rdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => dense_rmatvec_rdp

type, public, extends(abstract_linop_rsp) :: dense_linop_rsp

Components

Type	Visibility	Attributes		Name		Initial
real(kind=sp),	public,	allocatable	::	data(:,:)
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => dense_matvec_rsp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => dense_rmatvec_rsp

type, public, extends(abstract_linop_cdp) :: scaled_linop_cdp

Defines a scaled linear operator $\mathbf{B} = \sigma \mathbf{A}$ with $\mathbf{A}$ a complex(dp)-valued operator and $\sigma \in \mathbb{R}\ ) or \( \mathbb{C}$ .

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_cdp),	public,	allocatable	::	A			Base linear operator to be scaled.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
complex(kind=dp),	public		::	sigma			Scaling factor.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_cdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_cdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => scaled_matvec_cdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => scaled_rmatvec_cdp

type, public, extends(abstract_linop_csp) :: scaled_linop_csp

Defines a scaled linear operator $\mathbf{B} = \sigma \mathbf{A}$ with $\mathbf{A}$ a complex(sp)-valued operator and $\sigma \in \mathbb{R}\ ) or \( \mathbb{C}$ .

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_csp),	public,	allocatable	::	A			Base linear operator to be scaled.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
complex(kind=sp),	public		::	sigma			Scaling factor.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_csp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_csp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => scaled_matvec_csp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => scaled_rmatvec_csp

type, public, extends(abstract_linop_rdp) :: scaled_linop_rdp

Defines a scaled linear operator $\mathbf{B} = \sigma \mathbf{A}$ with $\mathbf{A}$ a real-valued operator and $\sigma \in \mathbb{R}$ . The definitions of matvec and rmatvec are directly inherited from those used to define A and do not have to be defined by the user.

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rdp),	public,	allocatable	::	A			Base linear operator to be scaled.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=dp),	public		::	sigma			Scaling factor.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rdp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rdp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => scaled_matvec_rdp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => scaled_rmatvec_rdp

type, public, extends(abstract_linop_rsp) :: scaled_linop_rsp

Components

Type	Visibility	Attributes		Name		Initial
class(abstract_linop_rsp),	public,	allocatable	::	A			Base linear operator to be scaled.
type(lightkrylov_timer),	public		::	matvec_timer	=	lightkrylov_timer('matvec timer')
type(lightkrylov_timer),	public		::	rmatvec_timer	=	lightkrylov_timer('rmatvec timer')
real(kind=sp),	public		::	sigma			Scaling factor.

Type-Bound Procedures

procedure, public, pass(self) :: apply_matvec => apply_matvec_rsp	Wrapper for matvec including the counter increment
procedure, public, pass(self) :: apply_rmatvec => apply_rmatvec_rsp	Wrapper for rmatvec including the counter increment
procedure, public, pass(self) :: finalize_timer => finalize_linop_timer	Finalize timers and print complete history_info
procedure, public, pass(self) :: get_counter	Return matvec/rmatvec counter value
procedure, public, pass(self) :: matvec => scaled_matvec_rsp
procedure, public, pass(self) :: print_timer_info	Print current timing data
procedure, public, pass(self) :: reset_counter	Reset matvec/rmatvec counter
procedure, public, pass(self) :: reset_timer => reset_linop_timer	Reset current timing data
procedure, public, pass(self) :: rmatvec => scaled_rmatvec_rsp

LightKrylov_AbstractLinops Module

Contents

Interfaces

Derived Types

Uses

Interfaces

public interface adjoint

private function initialize_adjoint_rsp(A) result(B)

Arguments

Return Value class(adjoint_linop_rsp), allocatable

private function initialize_adjoint_rdp(A) result(B)

Arguments

Return Value class(adjoint_linop_rdp), allocatable

private function initialize_adjoint_csp(A) result(B)

Arguments

Return Value class(adjoint_linop_csp), allocatable

private function initialize_adjoint_cdp(A) result(B)

Arguments

Return Value class(adjoint_linop_cdp), allocatable

public interface dense_linop

private function initialize_dense_linop_from_array_rsp(A) result(linop)

Arguments

Return Value type(dense_linop_rsp)

private function initialize_dense_linop_from_array_rdp(A) result(linop)

Arguments

Return Value type(dense_linop_rdp)

private function initialize_dense_linop_from_array_csp(A) result(linop)

Arguments

Return Value type(dense_linop_csp)

private function initialize_dense_linop_from_array_cdp(A) result(linop)

Arguments

Return Value type(dense_linop_cdp)

public interface verify_linop_axioms

private function verify_linop_axioms_rsp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Arguments

Return Value logical

private function verify_linop_axioms_rdp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Arguments

Return Value logical

private function verify_linop_axioms_csp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Arguments

Return Value logical

private function verify_linop_axioms_cdp(A, x, ntrials, tolerance, test_zero_map, test_adjoint) result(success)

Arguments

Return Value logical

Derived Types

type, public, extends(abstract_linop_cdp) :: Id_cdp

Components

Type-Bound Procedures

type, public, extends(abstract_linop_csp) :: Id_csp

Components

Type-Bound Procedures

type, public, extends(abstract_linop_rdp) :: Id_rdp

Components

Type-Bound Procedures

type, public, extends(abstract_linop_rsp) :: Id_rsp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_linop_cdp) :: abstract_exptA_linop_cdp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_linop_csp) :: abstract_exptA_linop_csp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_linop_rdp) :: abstract_exptA_linop_rdp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_linop_rsp) :: abstract_exptA_linop_rsp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_sym_linop) :: abstract_hermitian_linop_cdp

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_sym_linop) :: abstract_hermitian_linop_csp

Components

Type-Bound Procedures

type, public, abstract :: abstract_linop

Components

Type-Bound Procedures

type, public, abstract, extends(abstract_linop) :: abstract_linop_cdp