double_gram_schmidt_step Interface

public interface double_gram_schmidt_step

Description

Given an array $X$ of abstract_vector and an abstract_vector (or array of abstract_vectors) $y$ , this subroutine returns a modified vector $y$ orthogonal to all columns of $X$ , i.e.

$y \leftarrow \left( I - XX^H \right) y,$

using a double Gram-Schmidt process. On exit, $y$ is orthogonal to $X$ but does not have unit norm. Note moreover that $X$ is assumed to be an orthonormal set of vectors. The function can also return the projection coefficients $\beta = X^H y$ .

Syntax

    call double_gram_schmidt_step(y, X, info [, if_chk_orthonormal] [, beta])

Arguments

y : abstract_vector (or array of abstract_vector) that needs to be orthogonalize in-place against $X$ . It is an intent(inout) argument.
X : Array of abstract_vector against which $y$ needs to be orthogonalized. Note the function assumes that $X$ is an orthonormal set of vectors, i.e. $X^H X = I$ . If it this is not the case, the result is meaningless. It is an intent(in) argument.
info : integer Information flag.
if_chk_orthonormal (optional) : logical flag to check whether $X$ is an orthonormal set of vectors or not. If the orthonormality returns .false., the function raises an error. Note that this check is computationally expensive and should be disabled in production unless required for better performance. Is is an optional intent(in) argument. Default .true..
beta (optional) : real or complex array containing the coefficients $\beta = X^H y$ . Is is an optional intent(out) argument.

Subroutines

private module subroutine DGS_basis_against_basis_cdp(Y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(inout)			::	Y(:)	Input `abstract_vector` basis to orthogonalize
class(abstract_vector_cdp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
complex(kind=dp),	intent(out),	optional		::	beta(:,:)	Projection coefficients if requested

private module subroutine DGS_basis_against_basis_csp(Y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(inout)			::	Y(:)	Input `abstract_vector` basis to orthogonalize
class(abstract_vector_csp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
complex(kind=sp),	intent(out),	optional		::	beta(:,:)	Projection coefficients if requested

private module subroutine DGS_basis_against_basis_rdp(Y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(inout)			::	Y(:)	Input `abstract_vector` basis to orthogonalize
class(abstract_vector_rdp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
real(kind=dp),	intent(out),	optional		::	beta(:,:)	Projection coefficients if requested

private module subroutine DGS_basis_against_basis_rsp(Y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(inout)			::	Y(:)	Input `abstract_vector` basis to orthogonalize
class(abstract_vector_rsp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
real(kind=sp),	intent(out),	optional		::	beta(:,:)	Projection coefficients if requested

private module subroutine DGS_vector_against_basis_cdp(y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_cdp),	intent(inout)			::	y	Input `abstract_vector` to orthogonalize
class(abstract_vector_cdp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
complex(kind=dp),	intent(out),	optional		::	beta(:)	Projection coefficients if requested

private module subroutine DGS_vector_against_basis_csp(y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_csp),	intent(inout)			::	y	Input `abstract_vector` to orthogonalize
class(abstract_vector_csp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
complex(kind=sp),	intent(out),	optional		::	beta(:)	Projection coefficients if requested

private module subroutine DGS_vector_against_basis_rdp(y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rdp),	intent(inout)			::	y	Input `abstract_vector` to orthogonalize
class(abstract_vector_rdp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
real(kind=dp),	intent(out),	optional		::	beta(:)	Projection coefficients if requested

private module subroutine DGS_vector_against_basis_rsp(y, X, info, if_chk_orthonormal, beta)

Computes one step of the double Gram-Schmidt orthogonalization process of the abstract_vector y against the abstract_vector basis X

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_vector_rsp),	intent(inout)			::	y	Input `abstract_vector` to orthogonalize
class(abstract_vector_rsp),	intent(in)			::	X(:)	Input `abstract_vector` basis to orthogonalize against
integer,	intent(out)			::	info	Information flag.
logical,	intent(in),	optional		::	if_chk_orthonormal	Check that input Krylov vectors `X` form an orthonormal basis (expensive!). Default `.true.`.
real(kind=sp),	intent(out),	optional		::	beta(:)	Projection coefficients if requested