linalg_basic – LINALG

Type	Visibility	Attributes		Name		Initial
integer(kind=int32),	public,	parameter	::	LA_HERMITIAN_TRANSPOSE	=	2	Defines a Hermitian transpose operation for a complex-valued matrix.
integer(kind=int32),	public,	parameter	::	LA_NO_OPERATION	=	0	Defines no operation should be performed on the matrix.
integer(kind=int32),	public,	parameter	::	LA_TRANSPOSE	=	1	Defines a transpose operation.

public interface band_diag_mtx_mult

An interface to the banded diagonal matrix multiplication routines.

private pure subroutine band_diag_mtx_mult_dbl(left, m, kl, ku, alpha, a, b)

Performs the matrix operation $A = \alpha A B$ or $A = \alpha B A$ where $A$ is a banded matrix and $B$ is a diagonal matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	left	A logical flag indicating whether to perform the operation $A = \alpha A B$ (TRUE) or $A = \alpha B A$ (FALSE).
integer(kind=int32),	intent(in)		::	m	The number of rows in the banded matrix $A$ .
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
real(kind=real64),	intent(inout),	dimension(:,:)	::	a	The banded matrix to multiply.
real(kind=real64),	intent(in),	dimension(:)	::	b	The diagonal matrix to multiply by.

private pure subroutine band_diag_mtx_mult_cmplx(left, m, kl, ku, alpha, a, b)

Performs the matrix operation $A = \alpha A B$ or $A = \alpha B A$ where $A$ is a banded matrix and $B$ is a diagonal matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	left	A logical flag indicating whether to perform the operation $A = \alpha A B$ (TRUE) or $A = \alpha B A$ (FALSE).
integer(kind=int32),	intent(in)		::	m	The number of rows in the banded matrix $A$ .
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
complex(kind=real64),	intent(inout),	dimension(:,:)	::	a	The banded matrix to multiply.
complex(kind=real64),	intent(in),	dimension(:)	::	b	The diagonal matrix to multiply by.

public interface band_mtx_mult

An interface to the banded matrix multiplication routines.

private pure subroutine band_mtx_vec_mult_dbl(trans, kl, ku, alpha, a, x, beta, y)

Performs the matrix operation $y = \alpha A x + \beta y$ or $y = \alpha A^T A + \beta y$ where $A$ is a banded matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	trans	A logical flag indicating whether to perform the operation $y = \alpha A x + \beta y$ (FALSE) or $y = \alpha A^T x + \beta y$ (TRUE).
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix $A$ .
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix $A$ .
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The banded matrix $A$ to multiply by.
real(kind=real64),	intent(in),	dimension(:)	::	x	The vector $x$ to multiply by.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply by.
real(kind=real64),	intent(inout),	dimension(:)	::	y	On input, the vector $y$ to multiply. On output, the result of the operation.

private pure subroutine band_mtx_vec_mult_cmplx(trans, kl, ku, alpha, a, x, beta, y)

Performs the matrix operation $y = \alpha op(A) x + \beta y$ where $A$ is a banded matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	trans	An integer flag indicating the operation to perform on matrix $A$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix $A$ .
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix $A$ .
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The banded matrix $A$ to multiply by.
complex(kind=real64),	intent(in),	dimension(:)	::	x	The vector $x$ to multiply by.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply by.
complex(kind=real64),	intent(inout),	dimension(:)	::	y	On input, the vector $y$ to multiply. On output, the result of the operation.

public interface band_mtx_to_full_mtx

An interface to the banded matrix to full matrix conversion routines.

private pure subroutine band_to_full_mtx_dbl(kl, ku, b, f)

Converts a banded matrix to a full matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix.
real(kind=real64),	intent(in),	dimension(:,:)	::	b	The banded matrix to convert.
real(kind=real64),	intent(out),	dimension(:,:)	::	f	The full matrix to store the result in.

private pure subroutine band_to_full_mtx_cmplx(kl, ku, b, f)

Converts a banded matrix to a full matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals in the banded matrix.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals in the banded matrix.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	The banded matrix to convert.
complex(kind=real64),	intent(out),	dimension(:,:)	::	f	The full matrix to store the result in.

public interface banded_to_dense

An interface to the banded to dense matrix conversion routines.

private pure function banded_to_dense_dbl(m, kl, ku, a) result(x)

Converts a banded matrix to a dense matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	m	The number of rows in the M-by-N dense matrix.
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals. Must be at least 0.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals. Must be at least 0.
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The (KL+KU+1)-by-N banded matrix.

Return Value real(kind=real64), allocatable, dimension(:,:)

The M-by-N dense matrix.

private pure function banded_to_dense_cmplx(m, kl, ku, a) result(x)

Converts a banded matrix to a dense matrix.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	m	The M-by-N dense matrix.
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals. Must be at least 0.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals. Must be at least 0.
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The (KL+KU+1)-by-N banded matrix.

Return Value complex(kind=real64), allocatable, dimension(:,:)

The M-by-N dense matrix.

public interface dense_to_banded

An interface to the dense to banded matrix conversion routines.

private pure function dense_to_banded_dbl(a, kl, ku) result(x)

Converts a banded matrix stored in dense format to a compressed form.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix to convert.
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals. Must be at least 0.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals. Must be at least 0.

Return Value real(kind=real64), allocatable, dimension(:,:)

The (KL+KU+1)-by-N banded matrix.

private pure function dense_to_banded_cmplx(a, kl, ku) result(x)

Converts a banded matrix stored in dense format to a compressed form.

The banded matrix is stored in a compressed form supplied column by column. The following code segment transfers between a full matrix to the bonded matrix storage scheme. \code{fortran} do j = 1, n k = ku + 1 - j do i = max(1, j - ku), min(n, j + kl) a(k + i, j) = matrix(i, j) end do end do \endcode

Arguments

Type	Intent	Attributes		Name
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix to convert.
integer(kind=int32),	intent(in)		::	kl	The number of subdiagonals. Must be at least 0.
integer(kind=int32),	intent(in)		::	ku	The number of superdiagonals. Must be at least 0.

Return Value complex(kind=real64), allocatable, dimension(:,:)

The (KL+KU+1)-by-N banded matrix.

public interface det

An interface to the determinant routines.

private pure function det_dbl(a) result(x)

Computes the determinant of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N matrix on which to operate.

Return Value real(kind=real64)

The determinant of the matrix.

private pure function det_cmplx(a) result(x)

Computes the determinant of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The matrix on which to operate.

Return Value complex(kind=real64)

The determinant of the matrix.

public interface diag_mtx_mult

An interface to the diagonal matrix multiplication routines.

private pure subroutine diag_mtx_mult_mtx(lside, trans, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A op(B) + \beta C$ or $C = \alpha op(B) A + \beta C$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
logical,	intent(in)		::	trans	A logical flag indicating if the matrix $B$ should be transposed.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
real(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
real(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine diag_mtx_mult_mtx2(lside, alpha, a, b)

Performs the matrix operation $B = \alpha A B$ or $B = \alpha B A$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
real(kind=real64),	intent(inout),	dimension(:,:)	::	b	The matrix $B$ in the operation.

private pure subroutine diag_mtx_mult_mtx3(lside, trans, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A op(B) + \beta C$ or $C = \alpha B A + \beta C$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
logical,	intent(in)		::	trans	A logical flag indicating if the matrix $B$ should be transposed.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
real(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
complex(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine diag_mtx_mult_mtx4(lside, opb, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A op(B) + \beta C$ or $C = \alpha op(B) A + \beta C$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
integer(kind=int32),	intent(in)		::	opb	An integer flag indicating the operation to perform on matrix $B$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
complex(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine diag_mtx_mult_mtx_cmplx(lside, opb, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A op(B) + \beta C$ or $C = \alpha op(B) A + \beta C$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
integer(kind=int32),	intent(in)		::	opb	An integer flag indicating the operation to perform on matrix $B$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
complex(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine diag_mtx_mult_mtx2_cmplx(lside, alpha, a, b)

Performs the matrix operation $B = \alpha A B$ or $B = \alpha B A$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
complex(kind=real64),	intent(inout),	dimension(:,:)	::	b	The matrix $B$ in the operation.

private pure subroutine diag_mtx_mult_mtx_mix(lside, opb, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A op(B) + \beta C$ or $C = \alpha op(B) A + \beta C$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
integer(kind=int32),	intent(in)		::	opb	An integer flag indicating the operation to perform on matrix $B$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
complex(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine diag_mtx_mult_mtx2_mix(lside, alpha, a, b)

Performs the matrix operation $B = \alpha A B$ or $B = \alpha B A$ where $A$ is a diagonal matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	A logical flag indicating if the diagonal matrix is on the left.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:)	::	a	The diagonal matrix $A$ in the operation.
complex(kind=real64),	intent(inout),	dimension(:,:)	::	b	The matrix $B$ in the operation.

private pure subroutine diag_mtx_sparse_mult(lside, alpha, a, b)

Performs the matrix operation $B = \alpha A B$ or $B = \alpha B A$ where $A$ is a diagonal matrix and $B$ is a sparse matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside
real(kind=real64),	intent(in)		::	alpha
real(kind=real64),	intent(in),	dimension(:)	::	a
class(csr_matrix),	intent(inout)		::	b

public interface extract_diagonal

An interface to the diagonal extraction routines.

private pure function extract_diagonal_dbl(a) result(diag)

Extracts the diagonal of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix.

Return Value real(kind=real64), allocatable, dimension(:)

The MIN(M, N) element array for the diagonal elements.

private pure function extract_diagonal_cmplx(a) result(diag)

Extracts the diagonal of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix.

Return Value complex(kind=real64), allocatable, dimension(:)

The MIN(M, N) element array for the diagonal elements.

private pure function extract_diagonal_csr(a) result(diag)

Extracts the diagonal of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(csr_matrix),	intent(in)			::	a	The M-by-N matrix.

Return Value real(kind=real64), allocatable, dimension(:)

The MIN(M, N) element array for the diagonal elements.

public interface extract_lower_triangular

An interface to the lower triangular matrix extraction routines.

private pure function extract_lower_triangular_dbl(x) result(rst)

Extracts the lower triangular portion of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix.

Return Value real(kind=real64), allocatable, dimension(:,:)

The M-by-K lower triangular matrix where K = MIN(M, N).

private pure function extract_lower_triangular_cmplx(x) result(rst)

Extracts the lower triangular portion of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix.

Return Value complex(kind=real64), allocatable, dimension(:,:)

The M-by-K lower triangular matrix where K = MIN(M, N).

public interface extract_upper_triangular

An interface to the upper triangular matrix extraction routines.

private pure function extract_upper_triangular_dbl(x) result(rst)

Extracts the upper triangular portion of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix.

Return Value real(kind=real64), allocatable, dimension(:,:)

The K-by-N upper triangular matrix where K = MIN(M, N).

private pure function extract_upper_triangular_cmplx(x) result(rst)

Extracts the upper triangular portion of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix.

Return Value complex(kind=real64), allocatable, dimension(:,:)

The K-by-N upper triangular matrix where K = MIN(M, N).

public interface mtx_mult

An interface to the matrix multiplication routines.

private pure subroutine mtx_mult_mtx(transa, transb, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A B + \beta C$ .

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	transa	A logical flag indicating if the matrix $A$ should be transposed.
logical,	intent(in)		::	transb	A logical flag indicating if the matrix $B$ should be transposed.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix $A$ in the operation.
real(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
real(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine mtx_mult_vec(trans, alpha, a, b, beta, c)

Performs the matrix-vector operation $C = \alpha A B + \beta C$ .

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	trans	A logical flag indicating if the matrix $A$ should be transposed.
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix $A$ in the operation.
real(kind=real64),	intent(in),	dimension(:)	::	b	The vector $B$ in the operation.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the vector $C$ .
real(kind=real64),	intent(inout),	dimension(:)	::	c	The vector $C$ in the operation.

private pure subroutine cmtx_mult_mtx(opa, opb, alpha, a, b, beta, c)

Performs the matrix operation $C = \alpha A B + \beta C$ .

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	opa	An integer flag indicating the operation to perform on matrix $A$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
integer(kind=int32),	intent(in)		::	opb	An integer flag indicating the operation to perform on matrix $B$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix $A$ in the operation.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	The matrix $B$ in the operation.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the matrix $C$ .
complex(kind=real64),	intent(inout),	dimension(:,:)	::	c	The matrix $C$ in the operation.

private pure subroutine cmtx_mult_vec(opa, alpha, a, b, beta, c)

Performs the matrix-vector operation $C = \alpha A B + \beta C$ .

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	opa	An integer flag indicating the operation to perform on matrix $A$ . Possible options are: LA_NO_OPERATION: No operation is performed on matrix. LA_TRANSPOSE: The transpose of matrix is used. LA_HERMITIAN_TRANSPOSE: The Hermitian transpose of matrix is used.
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the product of $A$ and $B$ .
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The matrix $A$ in the operation.
complex(kind=real64),	intent(in),	dimension(:)	::	b	The vector $B$ in the operation.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply the vector $C$ .
complex(kind=real64),	intent(inout),	dimension(:)	::	c	The vector $C$ in the operation.

public interface mtx_rank

An interface to the matrix rank routines.

private pure function mtx_rank_dbl(a, tol) result(rnk)

Computes the rank of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The matrix.
real(kind=real64),	intent(in),	optional		::	tol	An optional input, that if supplied, overrides the default tolerance on singular values such that singular values less than this tolerance are treated as zero. The default tolerance is: MAX(M, N) * EPS * MAX(S). If the supplied value is less than the smallest value that causes an overflow if inverted, the tolerance reverts back to its default value, and the operation continues; however, a warning message is issued.

Return Value integer(kind=int32)

The rank of the matrix.

private pure function mtx_rank_cmplx(a, tol) result(rnk)

Computes the rank of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The matrix.
real(kind=real64),	intent(in),	optional		::	tol	An optional input, that if supplied, overrides the default tolerance on singular values such that singular values less than this tolerance are treated as zero. The default tolerance is: MAX(M, N) * EPS * MAX(S). If the supplied value is less than the smallest value that causes an overflow if inverted, the tolerance reverts back to its default value, and the operation continues; however, a warning message is issued.

Return Value integer(kind=int32)

The rank of the matrix.

public interface rank1_update

An interface to the rank-1 update routines.

private pure subroutine rank1_update_dbl(alpha, x, y, a)

Performs a rank-1 update of a matrix of the form $A = \alpha x y^T + A$ .

Arguments

Type	Intent	Attributes		Name
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the outer product of $x$ and $y$ .
real(kind=real64),	intent(in),	dimension(:)	::	x	The vector $x$ in the outer product.
real(kind=real64),	intent(in),	dimension(:)	::	y	The vector $y$ in the outer product.
real(kind=real64),	intent(inout),	dimension(:,:)	::	a	The matrix $A$ to update.

private pure subroutine rank1_update_cmplx(alpha, x, y, a)

Performs a rank-1 update of a matrix of the form $A = \alpha x y^H + A$ .

Arguments

Type	Intent	Attributes		Name
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply the outer product of $x$ and $y$ .
complex(kind=real64),	intent(in),	dimension(:)	::	x	The vector $x$ in the outer product.
complex(kind=real64),	intent(in),	dimension(:)	::	y	The vector $y$ in the outer product.
complex(kind=real64),	intent(inout),	dimension(:,:)	::	a	The matrix $A$ to update.

public interface recip_mult_array

An interface to the reciprocal multiplication routines.

private pure subroutine recip_mult_array_dbl(a, x)

Computes the product of a scalar and a vector, where the scalar is the reciprocal of the scalar A.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	a	The scalar A, which is the reciprocal of the scalar to multiply by.
real(kind=real64),	intent(inout),		dimension(:)	::	x	On input, the vector to multiply. On output, the product of the vector and the scalar reciprocal.

public interface swap

An interface to the swap routines.

private pure subroutine swap_dbl(x, y)

Swaps the contents of two arrays.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(inout),		dimension(:)	::	x	On input, the first array to swap. On output, the contents of the first array are copied to the second array.
real(kind=real64),	intent(inout),		dimension(:)	::	y	On input, the second array to swap. On output, the contents of the second array are copied to the first array.

private pure subroutine swap_cmplx(x, y)

Swaps the contents of two arrays.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(inout),		dimension(:)	::	x	On input, the first array to swap. On output, the contents of the first array are copied to the second array.
complex(kind=real64),	intent(inout),		dimension(:)	::	y	On input, the second array to swap. On output, the contents of the second array are copied to the first array.

public interface trace

An interface to the trace routines.

private pure function trace_dbl(x) result(y)

Computes the trace of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The matrix.

Return Value real(kind=real64)

The trace of the matrix.

private pure function trace_cmplx(x) result(y)

Computes the trace of a matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	x	The matrix.

Return Value complex(kind=real64)

The trace of the matrix.

public interface tri_mtx_mult

An interface to the triangular matrix multiplication routines.

private pure subroutine tri_mtx_mult_dbl(upper, alpha, a, beta, b)

Performs the matrix operation $B = \alpha A^T A + \beta B$ or $B = \alpha A A^T + \beta B$ where $A$ is a triangular matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	upper	A logical flag indicating whether the matrix A is upper triangular (TRUE) or lower triangular (FALSE).
real(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The triangular matrix $A$ to multiply by.
real(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply by.
real(kind=real64),	intent(inout),	dimension(:,:)	::	b	On input, the matrix $B$ to multiply. On output, the result of the operation.

private pure subroutine tri_mtx_mult_cmplx(upper, alpha, a, beta, b)

Performs the matrix operation $B = \alpha A^T A + \beta B$ or $B = \alpha A A^T + \beta B$ where $A$ is a triangular matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	upper	A logical flag indicating whether the matrix A is upper triangular (TRUE) or lower triangular (FALSE).
complex(kind=real64),	intent(in)		::	alpha	The scalar $\alpha$ to multiply by.
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The triangular matrix $A$ to multiply by.
complex(kind=real64),	intent(in)		::	beta	The scalar $\beta$ to multiply by.
complex(kind=real64),	intent(inout),	dimension(:,:)	::	b	On input, the matrix $B$ to multiply. On output, the result of the operation.

linalg_basic Module

Contents

Variables

Interfaces

Functions

Uses

Variables

Interfaces

public interface band_diag_mtx_mult

private pure subroutine band_diag_mtx_mult_dbl(left, m, kl, ku, alpha, a, b)

Arguments

private pure subroutine band_diag_mtx_mult_cmplx(left, m, kl, ku, alpha, a, b)

Arguments

public interface band_mtx_mult

private pure subroutine band_mtx_vec_mult_dbl(trans, kl, ku, alpha, a, x, beta, y)

Arguments

private pure subroutine band_mtx_vec_mult_cmplx(trans, kl, ku, alpha, a, x, beta, y)

Arguments

public interface band_mtx_to_full_mtx

private pure subroutine band_to_full_mtx_dbl(kl, ku, b, f)

Arguments

private pure subroutine band_to_full_mtx_cmplx(kl, ku, b, f)

Arguments

public interface banded_to_dense

private pure function banded_to_dense_dbl(m, kl, ku, a) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function banded_to_dense_cmplx(m, kl, ku, a) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)

public interface dense_to_banded

private pure function dense_to_banded_dbl(a, kl, ku) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function dense_to_banded_cmplx(a, kl, ku) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)

public interface det

private pure function det_dbl(a) result(x)

Arguments

Return Value real(kind=real64)

private pure function det_cmplx(a) result(x)

Arguments

Return Value complex(kind=real64)

public interface diag_mtx_mult

private pure subroutine diag_mtx_mult_mtx(lside, trans, alpha, a, b, beta, c)

Arguments

private pure subroutine diag_mtx_mult_mtx2(lside, alpha, a, b)

Arguments

private pure subroutine diag_mtx_mult_mtx3(lside, trans, alpha, a, b, beta, c)

Arguments

private pure subroutine diag_mtx_mult_mtx4(lside, opb, alpha, a, b, beta, c)

Arguments

private pure subroutine diag_mtx_mult_mtx_cmplx(lside, opb, alpha, a, b, beta, c)

Arguments

private pure subroutine diag_mtx_mult_mtx2_cmplx(lside, alpha, a, b)

Arguments

private pure subroutine diag_mtx_mult_mtx_mix(lside, opb, alpha, a, b, beta, c)

Arguments

private pure subroutine diag_mtx_mult_mtx2_mix(lside, alpha, a, b)

Arguments

private pure subroutine diag_mtx_sparse_mult(lside, alpha, a, b)

Arguments

public interface extract_diagonal

private pure function extract_diagonal_dbl(a) result(diag)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

private pure function extract_diagonal_cmplx(a) result(diag)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)

private pure function extract_diagonal_csr(a) result(diag)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

public interface extract_lower_triangular

private pure function extract_lower_triangular_dbl(x) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function extract_lower_triangular_cmplx(x) result(rst)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)