LightKrylov_AbstractVectors

This module provides the base class absract_vector from which all Krylov vectors needs to be derived. To use LightKrylov, you need to extend one of the followings:

abstract_vector_rsp : Real-valued vector with single precision arithmetic.
abstract_vector_rdp : Real-valued vector with double precision arithmetic.
abstract_vector_csp : Complex-valued vector with single precision arithmetic.
abstract_vector_cdp : Complex-valued vector with double precision arithmetic.

To extend either of these abstract types, you need to provide an associated implementation for the following type-bound procedures:

zero(self) : A subroutine zeroing-out the vector.
rand(self, ifnorm) : A subroutine creating a random vector, possibily normalized to have unit-norm (ifnorm = .true.).
scal(self, alpha) : A subroutine computing in-place the scalar multiplication $\mathbf{x} \leftarrow \alpha \mathbf{x}$ .
`axpby(alpha, vec, beta, self) : A subroutine computing in-place the product $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
dot(self, vec) : A function computing the inner product $\alpha = \langle \mathbf{x} \vert \mathbf{y} \rangle$ .
get_size(self) : A function returning the dimension $n$ of the vector $\mathbf{x}$ .

Once these type-bound procedures have been implemented by the user, they will automatically be used to define:

vector addition : add(self, vec) = axpby(1, vec, 1, self)
vector subtraction : sub(self, vec) = axpby(-1, vec, 1, self)
vector norm : norm(self) = sqrt(self%dot(self))

This module also provides the following utility subroutines:

innerprod(X, Y) : Function computing the product $\mathbf{X}^H \mathbf{y}$ between a Krylov basis X and a Krylov vector (resp. basis) Y.
linear_combination(Y, X, V) : Subroutine computing the linear combination $\mathbf{y}_j = \sum_{i=1}^n \mathbf{x}_i v_{ij}$ .
axpby_basis(alpha, X, beta, Y) : In-place computation of $\mathbf{Y} \leftarrow \alpha \mathbf{X} + \beta \mathbf{Y}$ where X and Y are arrays of abstract_vector.
zero_basis(X) : Zero-out a collection of abstract_vectors.
copy_basis(out, from) : Copy a collection of abstract_vectors.
rand_basis(X, ifnorm) : Create a collection of random abstract_vectors. If ifnorm = .true., the vectors are normalized to have unit-norm.

Uses

- LightKrylov_Logger
- LightKrylov_Constants
- stdlib_optval
- LightKrylov_Utils
- stdlib_linalg_blas

Interfaces

public interface Gram

Compute the Gram matrix $\mathbf{G} = \mathbf{X}^H \mathbf{X}$ .

Description

This interface provides methods for computing the Gram matrix associated to a basis of abstract_vector $\mathbf{X}$ .

Example

The example below assumes that you have already extended the abstract_vector_rdp class to define your own my_real_vector type.

    type(my_real_vector), dimension(10) :: X
    real(dp), dimension(:, :), allocatable :: G

    ! ... Part of your code where you initialize everything ...

    G = Gram(X)

    ! ... Rest of your code ...

private function gram_matrix_rsp(X) result(G)

Computes the inner product/Gram matrix associated with the basis $\mathbf{X}$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(in)			::	X(:)

Return Value real(kind=sp), (size(X),size(X))

private function gram_matrix_rdp(X) result(G)

Computes the inner product/Gram matrix associated with the basis $\mathbf{X}$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(in)			::	X(:)

Return Value real(kind=dp), (size(X),size(X))

private function gram_matrix_csp(X) result(G)

Computes the inner product/Gram matrix associated with the basis $\mathbf{X}$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(in)			::	X(:)

Return Value complex(kind=sp), (size(X),size(X))

private function gram_matrix_cdp(X) result(G)

Computes the inner product/Gram matrix associated with the basis $\mathbf{X}$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(in)			::	X(:)

Return Value complex(kind=dp), (size(X),size(X))

public interface axpby_basis

In-place addition of two arrays of extended abstract_vector.

Description

This interface provides methods to add in-place two arrays of extended abstract_vector, i.e.

$\mathbf{Y}_i \leftarrow \alpha \mathbf{X}_i + \beta \mathbf{Y}_i.$

No out-of-place alternative is currently available in LightKrylov. If you do need an out-of-place version, you can combine axpby_basis with copy.

Example

    type(my_real_vector), dimension(10) :: X
    type(my_real_vector), dimension(10) :: Y
    real(dp), dimension(10)             :: alpha, beta

    ! ... Whatever your code is doing ...

    call axpby_basis(alpha, X, beta, Y)

    ! ... Rest of your code ...

private impure elemental subroutine axpby_basis_rsp(alpha, x, beta, y)

Compute in-place $\mathbf{Y} \leftarrow \alpha \mathbf{X} + \beta \mathbf{Y}$ where X and Y are arrays of abstract_vector and alpha and beta are real(sp) numbers.

Arguments

Type	Intent		Name
real(kind=sp),	intent(in)	::	alpha	Scalar multipliers.
class(abstract_vector_rsp),	intent(in)	::	x	Input/Ouput array of `abstract_vector`.
real(kind=sp),	intent(in)	::	beta	Scalar multipliers.
class(abstract_vector_rsp),	intent(inout)	::	y	Array of `abstract_vector` to be added/subtracted to `X`.

private impure elemental subroutine axpby_basis_rdp(alpha, x, beta, y)

Compute in-place $\mathbf{Y} \leftarrow \alpha \mathbf{X} + \beta \mathbf{Y}$ where X and Y are arrays of abstract_vector and alpha and beta are real(dp) numbers.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	alpha	Scalar multipliers.
class(abstract_vector_rdp),	intent(in)	::	x	Input/Ouput array of `abstract_vector`.
real(kind=dp),	intent(in)	::	beta	Scalar multipliers.
class(abstract_vector_rdp),	intent(inout)	::	y	Array of `abstract_vector` to be added/subtracted to `X`.

private impure elemental subroutine axpby_basis_csp(alpha, x, beta, y)

Compute in-place $\mathbf{Y} \leftarrow \alpha \mathbf{X} + \beta \mathbf{Y}$ where X and Y are arrays of abstract_vector and alpha and beta are complex(sp) numbers.

Arguments

Type	Intent		Name
complex(kind=sp),	intent(in)	::	alpha	Scalar multipliers.
class(abstract_vector_csp),	intent(in)	::	x	Input/Ouput array of `abstract_vector`.
complex(kind=sp),	intent(in)	::	beta	Scalar multipliers.
class(abstract_vector_csp),	intent(inout)	::	y	Array of `abstract_vector` to be added/subtracted to `X`.

private impure elemental subroutine axpby_basis_cdp(alpha, x, beta, y)

Compute in-place $\mathbf{Y} \leftarrow \alpha \mathbf{X} + \beta \mathbf{Y}$ where X and Y are arrays of abstract_vector and alpha and beta are complex(dp) numbers.

Arguments

Type	Intent		Name
complex(kind=dp),	intent(in)	::	alpha	Scalar multipliers.
class(abstract_vector_cdp),	intent(in)	::	x	Input/Ouput array of `abstract_vector`.
complex(kind=dp),	intent(in)	::	beta	Scalar multipliers.
class(abstract_vector_cdp),	intent(inout)	::	y	Array of `abstract_vector` to be added/subtracted to `X`.

public interface copy

This interface provides methods to copy an array X of abstract_vector into another array Y. Note that Y needs to be pre-allocated.

Example

    type(my_real_vector), dimension(10) :: X
    type(my_real_vector), dimension(10) :: Y

    ! ... Your code ...

    call copy(Y, X)

    ! ... Your code ...

private impure elemental subroutine copy_vector_rsp(out, from)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(out)			::	out
class(abstract_vector_rsp),	intent(in)			::	from

private impure elemental subroutine copy_vector_rdp(out, from)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(out)			::	out
class(abstract_vector_rdp),	intent(in)			::	from

private impure elemental subroutine copy_vector_csp(out, from)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(out)			::	out
class(abstract_vector_csp),	intent(in)			::	from

private impure elemental subroutine copy_vector_cdp(out, from)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(out)			::	out
class(abstract_vector_cdp),	intent(in)			::	from

public interface dense_vector

private function initialize_dense_vector_from_array_rsp(x) result(vec)

Arguments

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

Return Value type(dense_vector_rsp)

private function initialize_dense_vector_from_array_rdp(x) result(vec)

Arguments

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

Return Value type(dense_vector_rdp)

private function initialize_dense_vector_from_array_csp(x) result(vec)

Arguments

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

Return Value type(dense_vector_csp)

private function initialize_dense_vector_from_array_cdp(x) result(vec)

Arguments

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

Return Value type(dense_vector_cdp)

public interface innerprod

Compute the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{y}$ or matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$ .

Description

This interface provides methods for computing the inner products between a basis of real or complex vectors $\mathbf{X}$ and a single vector $\mathbf{y}$ or another basis $\mathbf{Y}$ . Depending on the case, it returns a one-dimensional array $\mathbf{v}$ or a two-dimensional array $\mathbf{M}$ with the same type as $\mathbf{X}$ .

Example

The example below assumes that you have already extended the abstract_vector_rdp class to define your own my_real_vector type.

    type(my_real_vector), dimension(10) :: X
    type(my_real_vector)                :: y
    real(dp), dimension(:), allocatable :: v

    ! ... Part of your code where you initialize everything ...

    v = innerprod(X, y)

    ! ... Rest of your code ...

Similarly, for computing the matrix of inner products between two bases

    type(my_real_vector), dimension(10) :: X
    type(my_real_vector), dimension(10) :: Y
    real(dp), dimension(:, :), allocatable :: M

    ! ... Part of your code where you initialize everything ...

    M = innerprod(X, Y)

    ! ... Rest of your code ...

private function innerprod_vector_rsp(X, y) result(v)

Computes the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{v}$ between a basis X of abstract_vector and v, a single abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_rsp),	intent(in)			::	y	Bases of `abstract_vector` whose inner products need to be computed.

Return Value real(kind=sp), (size(X))

Resulting inner-product vector.

private function innerprod_matrix_rsp(X, Y) result(M)

Computes the inner product matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$ between two bases of abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_rsp),	intent(in)			::	Y(:)	Bases of `abstract_vector` whose inner products need to be computed.

Return Value real(kind=sp), (size(X),size(Y))

Resulting inner-product matrix.

private function innerprod_vector_rdp(X, y) result(v)

Computes the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{v}$ between a basis X of abstract_vector and v, a single abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_rdp),	intent(in)			::	y	Bases of `abstract_vector` whose inner products need to be computed.

Return Value real(kind=dp), (size(X))

Resulting inner-product vector.

private function innerprod_matrix_rdp(X, Y) result(M)

Computes the inner product matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$ between two bases of abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_rdp),	intent(in)			::	Y(:)	Bases of `abstract_vector` whose inner products need to be computed.

Return Value real(kind=dp), (size(X),size(Y))

Resulting inner-product matrix.

private function innerprod_vector_csp(X, y) result(v)

Computes the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{v}$ between a basis X of abstract_vector and v, a single abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_csp),	intent(in)			::	y	Bases of `abstract_vector` whose inner products need to be computed.

Return Value complex(kind=sp), (size(X))

Resulting inner-product vector.

private function innerprod_matrix_csp(X, Y) result(M)

Computes the inner product matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$ between two bases of abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_csp),	intent(in)			::	Y(:)	Bases of `abstract_vector` whose inner products need to be computed.

Return Value complex(kind=sp), (size(X),size(Y))

Resulting inner-product matrix.

private function innerprod_vector_cdp(X, y) result(v)

Computes the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{v}$ between a basis X of abstract_vector and v, a single abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_cdp),	intent(in)			::	y	Bases of `abstract_vector` whose inner products need to be computed.

Return Value complex(kind=dp), (size(X))

Resulting inner-product vector.

private function innerprod_matrix_cdp(X, Y) result(M)

Computes the inner product matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$ between two bases of abstract_vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(in)			::	X(:)	Bases of `abstract_vector` whose inner products need to be computed.
class(abstract_vector_cdp),	intent(in)			::	Y(:)	Bases of `abstract_vector` whose inner products need to be computed.

Return Value complex(kind=dp), (size(X),size(Y))

Resulting inner-product matrix.

public interface linear_combination

Given a set of extended abstract_vectors and coefficients, return the corresponding linear combinations.

Description

This interface provides methods for computing linear combinations of a set of abstract_vectors. Depending on its input, it either computes

$\mathbf{y} = \sum_{i=1}^n \alpha_i \mathbf{x}_i,$

i.e. a single vector, or

$\mathbf{y}_j = \sum_{i=1}^n \alpha_{ij} \mathbf{x}_i,$

i.e. a set of vectors of the same type as $\mathbf{X}$ .

Example

    type(my_real_vector), dimension(10) :: X
    real(dp), dimension(m, n)           :: B
    type(my_real_vector)                :: Y

    ! ... Whatever your code is doing ...

    call linear_combination(Y, X, B)

    ! ... Rest of your code ...

private subroutine linear_combination_vector_rsp(y, X, v)

Given X and v, this function return $\mathbf{y} = \mathbf{Xv}$ where y is an abstract_vector, X an array of abstract_vector and v a Fortran array containing the coefficients of the linear combination.

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_rsp),	intent(out),	allocatable	::	y	Ouput vector.
class(abstract_vector_rsp),	intent(in)		::	X(:)	Krylov basis.
real(kind=sp),	intent(in)		::	v(:)	Coordinates of `y` in the Krylov basis `X`.

private subroutine linear_combination_matrix_rsp(Y, X, B)

Given X and B, this function computes $\mathbf{Y} = \mathbf{XB}$ where X and Y are arrays of abstract_vector, and B is a 2D Fortran array.

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_rsp),	intent(out),	allocatable	::	Y(:)	Output matrix.
class(abstract_vector_rsp),	intent(in)		::	X(:)	Krylov basis.
real(kind=sp),	intent(in)		::	B(:,:)	Coefficients of the linear combinations.

private subroutine linear_combination_vector_rdp(y, X, v)

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_rdp),	intent(out),	allocatable	::	y	Ouput vector.
class(abstract_vector_rdp),	intent(in)		::	X(:)	Krylov basis.
real(kind=dp),	intent(in)		::	v(:)	Coordinates of `y` in the Krylov basis `X`.

private subroutine linear_combination_matrix_rdp(Y, X, B)

Given X and B, this function computes $\mathbf{Y} = \mathbf{XB}$ where X and Y are arrays of abstract_vector, and B is a 2D Fortran array.

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_rdp),	intent(out),	allocatable	::	Y(:)	Output matrix.
class(abstract_vector_rdp),	intent(in)		::	X(:)	Krylov basis.
real(kind=dp),	intent(in)		::	B(:,:)	Coefficients of the linear combinations.

private subroutine linear_combination_vector_csp(y, X, v)

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_csp),	intent(out),	allocatable	::	y	Ouput vector.
class(abstract_vector_csp),	intent(in)		::	X(:)	Krylov basis.
complex(kind=sp),	intent(in)		::	v(:)	Coordinates of `y` in the Krylov basis `X`.

private subroutine linear_combination_matrix_csp(Y, X, B)

Given X and B, this function computes $\mathbf{Y} = \mathbf{XB}$ where X and Y are arrays of abstract_vector, and B is a 2D Fortran array.

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_csp),	intent(out),	allocatable	::	Y(:)	Output matrix.
class(abstract_vector_csp),	intent(in)		::	X(:)	Krylov basis.
complex(kind=sp),	intent(in)		::	B(:,:)	Coefficients of the linear combinations.

private subroutine linear_combination_vector_cdp(y, X, v)

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_cdp),	intent(out),	allocatable	::	y	Ouput vector.
class(abstract_vector_cdp),	intent(in)		::	X(:)	Krylov basis.
complex(kind=dp),	intent(in)		::	v(:)	Coordinates of `y` in the Krylov basis `X`.

private subroutine linear_combination_matrix_cdp(Y, X, B)

Given X and B, this function computes $\mathbf{Y} = \mathbf{XB}$ where X and Y are arrays of abstract_vector, and B is a 2D Fortran array.

Arguments

Type	Intent	Attributes		Name
class(abstract_vector_cdp),	intent(out),	allocatable	::	Y(:)	Output matrix.
class(abstract_vector_cdp),	intent(in)		::	X(:)	Krylov basis.
complex(kind=dp),	intent(in)		::	B(:,:)	Coefficients of the linear combinations.

public interface rand_basis

This interface provides methods to create an array X of random abstract_vector. It is a simple wrapper around X(i)%rand(ifnorm).

Example

    type(my_real_vector), dimension(10) :: X
    logical                             :: ifnorm = .true.

    ! ... Your code ...

    call rand_basis(X, ifnorm)

    ! ... Your code ...

private impure elemental subroutine rand_basis_rsp(X, ifnorm)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(inout)			::	X
logical,	intent(in),	optional		::	ifnorm

private impure elemental subroutine rand_basis_rdp(X, ifnorm)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(inout)			::	X
logical,	intent(in),	optional		::	ifnorm

private impure elemental subroutine rand_basis_csp(X, ifnorm)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(inout)			::	X
logical,	intent(in),	optional		::	ifnorm

private impure elemental subroutine rand_basis_cdp(X, ifnorm)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(inout)			::	X
logical,	intent(in),	optional		::	ifnorm

public interface zero_basis

This interface provides methods to zero-out a collection of abstract_vector X. It is a simple wrapper around X(i)%zero().

Example

    type(my_real_vector), dimension(10) :: X

    ! ... Your code ...

    call zero_basis(X)

    ! ... Your code ...

private impure elemental subroutine zero_basis_rsp(X)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(inout)			::	X

private impure elemental subroutine zero_basis_rdp(X)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(inout)			::	X

private impure elemental subroutine zero_basis_csp(X)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(inout)			::	X

private impure elemental subroutine zero_basis_cdp(X)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(inout)			::	X

Derived Types

type, public, abstract :: abstract_vector

Base abstract type from which all other types of vectors used in LightKrylov are being derived from.

type, public, abstract, extends(abstract_vector) :: abstract_vector_cdp

Abstract type to define complex(dp)-valued vectors. Derived-types defined by the user should be extending one such class.

Type-Bound Procedures

procedure, public, pass(self) :: add => add_cdp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure(abstract_axpby_cdp), public, deferred, pass(self) :: axpby	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_cdp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure(abstract_dot_cdp), public, deferred, pass(self) :: dot	Computes the dot product between two `abstract_vector_cdp`.
procedure(abstract_get_size_cdp), public, deferred, pass(self) :: get_size	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_cdp	Computes the norm of the `abstract_vector`.
procedure(abstract_rand_cdp), public, deferred, pass(self) :: rand	Creates a random `abstract_vector_cdp`.
procedure(abstract_scal_cdp), public, deferred, pass(self) :: scal	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_cdp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure(abstract_zero_cdp), public, deferred, pass(self) :: zero	Sets an `abstract_vector_cdp` to zero.

type, public, abstract, extends(abstract_vector) :: abstract_vector_csp

Abstract type to define complex(sp)-valued vectors. Derived-types defined by the user should be extending one such class.

Type-Bound Procedures

procedure, public, pass(self) :: add => add_csp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure(abstract_axpby_csp), public, deferred, pass(self) :: axpby	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_csp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure(abstract_dot_csp), public, deferred, pass(self) :: dot	Computes the dot product between two `abstract_vector_csp`.
procedure(abstract_get_size_csp), public, deferred, pass(self) :: get_size	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_csp	Computes the norm of the `abstract_vector`.
procedure(abstract_rand_csp), public, deferred, pass(self) :: rand	Creates a random `abstract_vector_csp`.
procedure(abstract_scal_csp), public, deferred, pass(self) :: scal	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_csp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure(abstract_zero_csp), public, deferred, pass(self) :: zero	Sets an `abstract_vector_csp` to zero.

type, public, abstract, extends(abstract_vector) :: abstract_vector_rdp

Abstract type to define real(dp)-valued vectors. Derived-types defined by the user should be extending one such class.

Type-Bound Procedures

procedure, public, pass(self) :: add => add_rdp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure(abstract_axpby_rdp), public, deferred, pass(self) :: axpby	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_rdp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure(abstract_dot_rdp), public, deferred, pass(self) :: dot	Computes the dot product between two `abstract_vector_rdp`.
procedure(abstract_get_size_rdp), public, deferred, pass(self) :: get_size	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_rdp	Computes the norm of the `abstract_vector`.
procedure(abstract_rand_rdp), public, deferred, pass(self) :: rand	Creates a random `abstract_vector_rdp`.
procedure(abstract_scal_rdp), public, deferred, pass(self) :: scal	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_rdp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure(abstract_zero_rdp), public, deferred, pass(self) :: zero	Sets an `abstract_vector_rdp` to zero.

type, public, abstract, extends(abstract_vector) :: abstract_vector_rsp

Abstract type to define real(sp)-valued vectors. Derived-types defined by the user should be extending one such class.

Type-Bound Procedures

procedure, public, pass(self) :: add => add_rsp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure(abstract_axpby_rsp), public, deferred, pass(self) :: axpby	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_rsp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure(abstract_dot_rsp), public, deferred, pass(self) :: dot	Computes the dot product between two `abstract_vector_rsp`.
procedure(abstract_get_size_rsp), public, deferred, pass(self) :: get_size	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_rsp	Computes the norm of the `abstract_vector`.
procedure(abstract_rand_rsp), public, deferred, pass(self) :: rand	Creates a random `abstract_vector_rsp`.
procedure(abstract_scal_rsp), public, deferred, pass(self) :: scal	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_rsp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure(abstract_zero_rsp), public, deferred, pass(self) :: zero	Sets an `abstract_vector_rsp` to zero.

type, public, extends(abstract_vector_cdp) :: dense_vector_cdp

Components

Type	Visibility	Attributes		Name		Initial
complex(kind=dp),	public,	allocatable	::	data(:)
integer,	public		::	n

Type-Bound Procedures

procedure, public, pass(self) :: add => add_cdp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure, public, pass(self) :: axpby => dense_axpby_cdp	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_cdp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure, public, pass(self) :: dot => dense_dot_cdp	Computes the dot product between two `abstract_vector_cdp`.
procedure, public, pass(self) :: get_size => dense_get_size_cdp	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_cdp	Computes the norm of the `abstract_vector`.
procedure, public, pass(self) :: rand => dense_rand_cdp	Creates a random `abstract_vector_cdp`.
procedure, public, pass(self) :: scal => dense_scal_cdp	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_cdp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure, public, pass(self) :: zero => dense_zero_cdp	Sets an `abstract_vector_cdp` to zero.

type, public, extends(abstract_vector_csp) :: dense_vector_csp

Components

Type	Visibility	Attributes		Name		Initial
complex(kind=sp),	public,	allocatable	::	data(:)
integer,	public		::	n

Type-Bound Procedures

procedure, public, pass(self) :: add => add_csp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure, public, pass(self) :: axpby => dense_axpby_csp	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_csp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure, public, pass(self) :: dot => dense_dot_csp	Computes the dot product between two `abstract_vector_csp`.
procedure, public, pass(self) :: get_size => dense_get_size_csp	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_csp	Computes the norm of the `abstract_vector`.
procedure, public, pass(self) :: rand => dense_rand_csp	Creates a random `abstract_vector_csp`.
procedure, public, pass(self) :: scal => dense_scal_csp	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_csp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure, public, pass(self) :: zero => dense_zero_csp	Sets an `abstract_vector_csp` to zero.

type, public, extends(abstract_vector_rdp) :: dense_vector_rdp

Components

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public,	allocatable	::	data(:)
integer,	public		::	n

Type-Bound Procedures

procedure, public, pass(self) :: add => add_rdp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure, public, pass(self) :: axpby => dense_axpby_rdp	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_rdp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure, public, pass(self) :: dot => dense_dot_rdp	Computes the dot product between two `abstract_vector_rdp`.
procedure, public, pass(self) :: get_size => dense_get_size_rdp	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_rdp	Computes the norm of the `abstract_vector`.
procedure, public, pass(self) :: rand => dense_rand_rdp	Creates a random `abstract_vector_rdp`.
procedure, public, pass(self) :: scal => dense_scal_rdp	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_rdp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure, public, pass(self) :: zero => dense_zero_rdp	Sets an `abstract_vector_rdp` to zero.

type, public, extends(abstract_vector_rsp) :: dense_vector_rsp

Components

Type	Visibility	Attributes		Name		Initial
real(kind=sp),	public,	allocatable	::	data(:)
integer,	public		::	n

Type-Bound Procedures

procedure, public, pass(self) :: add => add_rsp	Adds two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{x} + \mathbf{y}$ .
procedure, public, pass(self) :: axpby => dense_axpby_rsp	In-place computation of $\mathbf{y} \leftarrow \alpha \mathbf{x} + \beta \mathbf{y}$ .
procedure, public, pass(self) :: chsgn => chsgn_rsp	Change the sign of a vector, i.e. $\mathbf{x} \leftarrow -\mathbf{x}$ .
procedure, public, pass(self) :: dot => dense_dot_rsp	Computes the dot product between two `abstract_vector_rsp`.
procedure, public, pass(self) :: get_size => dense_get_size_rsp	Return size of specific abstract vector
procedure, public, pass(self) :: norm => norm_rsp	Computes the norm of the `abstract_vector`.
procedure, public, pass(self) :: rand => dense_rand_rsp	Creates a random `abstract_vector_rsp`.
procedure, public, pass(self) :: scal => dense_scal_rsp	Compute the scalar-vector product.
procedure, public, pass(self) :: sub => sub_rsp	Subtracts two `abstract_vector`, i.e. $\mathbf{y} \leftarrow \mathbf{y} - \mathbf{x}$ .
procedure, public, pass(self) :: zero => dense_zero_rsp	Sets an `abstract_vector_rsp` to zero.

LightKrylov_AbstractVectors Module

Contents

Interfaces

Derived Types

Uses

Interfaces

public interface Gram

Description

Example

private function gram_matrix_rsp(X) result(G)

Arguments

Return Value real(kind=sp), (size(X),size(X))

private function gram_matrix_rdp(X) result(G)

Arguments

Return Value real(kind=dp), (size(X),size(X))

private function gram_matrix_csp(X) result(G)

Arguments

Return Value complex(kind=sp), (size(X),size(X))

private function gram_matrix_cdp(X) result(G)

Arguments

Return Value complex(kind=dp), (size(X),size(X))

public interface axpby_basis

Description

Example

private impure elemental subroutine axpby_basis_rsp(alpha, x, beta, y)

Arguments

private impure elemental subroutine axpby_basis_rdp(alpha, x, beta, y)

Arguments

private impure elemental subroutine axpby_basis_csp(alpha, x, beta, y)

Arguments

private impure elemental subroutine axpby_basis_cdp(alpha, x, beta, y)

Arguments

public interface copy

Example

private impure elemental subroutine copy_vector_rsp(out, from)

Arguments

private impure elemental subroutine copy_vector_rdp(out, from)

Arguments

private impure elemental subroutine copy_vector_csp(out, from)

Arguments

private impure elemental subroutine copy_vector_cdp(out, from)

Arguments

public interface dense_vector

private function initialize_dense_vector_from_array_rsp(x) result(vec)

Arguments

Return Value type(dense_vector_rsp)

private function initialize_dense_vector_from_array_rdp(x) result(vec)

Arguments

Return Value type(dense_vector_rdp)

private function initialize_dense_vector_from_array_csp(x) result(vec)

Arguments

Return Value type(dense_vector_csp)

private function initialize_dense_vector_from_array_cdp(x) result(vec)

Arguments

Return Value type(dense_vector_cdp)

public interface innerprod

Description

Example

private function innerprod_vector_rsp(X, y) result(v)

Arguments

Return Value real(kind=sp), (size(X))

private function innerprod_matrix_rsp(X, Y) result(M)

Arguments

Return Value real(kind=sp), (size(X),size(Y))

private function innerprod_vector_rdp(X, y) result(v)

Arguments

Return Value real(kind=dp), (size(X))

private function innerprod_matrix_rdp(X, Y) result(M)

Arguments

Return Value real(kind=dp), (size(X),size(Y))

private function innerprod_vector_csp(X, y) result(v)

Arguments

Return Value complex(kind=sp), (size(X))

private function innerprod_matrix_csp(X, Y) result(M)

Arguments

Return Value complex(kind=sp), (size(X),size(Y))

private function innerprod_vector_cdp(X, y) result(v)

Arguments

Return Value complex(kind=dp), (size(X))

private function innerprod_matrix_cdp(X, Y) result(M)