linalg_cholesky

public interface cholesky_factor

private subroutine cholesky_factor_dbl(a, upper, err)

Computes the Cholesky factorization of a symmetric, positive definite matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(inout),		dimension(:,:)	::	a	On input, the N-by-N matrix to factor. On output, the factored matrix is returned in either the upper or lower triangular portion of the matrix, dependent upon the value of upper.
logical,	intent(in),	optional		::	upper	An optional input that, if specified, provides control over whether the factorization is computed as $A = U^T U$ (set to true), or as $A = L L^T$ (set to false). The default is true such that $A = U^T U$ .
class(errors),	intent(inout),	optional,	target	::	err	The error object to be updated.

private subroutine cholesky_factor_cmplx(a, upper, err)

Computes the Cholesky factorization of a symmetric, positive definite matrix.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(inout),		dimension(:,:)	::	a	On input, the N-by-N matrix to factor. On output, the factored matrix is returned in either the upper or lower triangular portion of the matrix, dependent upon the value of upper.
logical,	intent(in),	optional		::	upper	An optional input that, if specified, provides control over whether the factorization is computed as $A = U^H U$ (set to true), or as $A = L L^H$ (set to false). The default is true such that $A = U^H U$ .
class(errors),	intent(inout),	optional,	target	::	err	The error object to be updated.

public interface cholesky_rank1_downdate

private subroutine cholesky_rank1_downdate_dbl(r, u, work, err)

Computes the rank 1 downdate to a Cholesky factored matrix $A = R^T R$ such that $A_1 = A - \vec{u} \vec{u}^T$ . This operation only works if the new matrix $A_1$ is positive definite.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(inout),		dimension(:,:)	::	r	On input, the N-by-N upper triangular matrix $R$ . On output, the updated matrix $R_1$ .
real(kind=real64),	intent(inout),		dimension(:)	::	u	On input, the N-element vector $\vec{u}$ . On output, the rotation sines used to transform $R$ to $R_1$ .
real(kind=real64),	intent(out),	optional,	target, dimension(:)	::	work	An optional argument that if supplied prevents local memory allocation. If provided, the array must have at least N elements. Additionally, this workspace array is used to contain the rotation cosines used to transform $R$ to $R_1$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

private subroutine cholesky_rank1_downdate_cmplx(r, u, work, err)

Computes the rank 1 downdate to a Cholesky factored matrix $A = R^H R$ such that $A_1 = A - \vec{u} \vec{u}^H$ . This operation only works if the new matrix $A_1$ is positive definite.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(inout),		dimension(:,:)	::	r	On input, the N-by-N upper triangular matrix $R$ . On output, the updated matrix $R_1$ .
complex(kind=real64),	intent(inout),		dimension(:)	::	u	On input, the N-element vector $\vec{u}$ . On output, the rotation sines used to transform $R$ to $R_1$ .
real(kind=real64),	intent(out),	optional,	target, dimension(:)	::	work	An optional argument that if supplied prevents local memory allocation. If provided, the array must have at least N elements. Additionally, this workspace array is used to contain the rotation cosines used to transform $R$ to $R_1$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

public interface cholesky_rank1_update

private subroutine cholesky_rank1_update_dbl(r, u, work, err)

Computes the rank 1 update to a Cholesky factored matrix $A = R^T R$ such that $A_1 = A + \vec{u} \vec{u}^T$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(inout),		dimension(:,:)	::	r	On input, the N-by-N upper triangular matrix $R$ . On output, the updated matrix $R_1$ .
real(kind=real64),	intent(inout),		dimension(:)	::	u	On input, the N-element vector $\vec{u}$ . On output, the rotation sines used to transform $R$ to $R_1$ .
real(kind=real64),	intent(out),	optional,	target, dimension(:)	::	work	An optional argument that if supplied prevents local memory allocation. If provided, the array must have at least N elements. Additionally, this workspace array is used to contain the rotation cosines used to transform $R$ to $R_1$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

private subroutine cholesky_rank1_update_cmplx(r, u, work, err)

Computes the rank 1 update to a Cholesky factored matrix $A = R^H R$ such that $A_1 = A + \vec{u} \vec{u}^H$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(inout),		dimension(:,:)	::	r	On input, the N-by-N upper triangular matrix $R$ . On output, the updated matrix $R_1$ .
complex(kind=real64),	intent(inout),		dimension(:)	::	u	On input, the N-element vector $\vec{u}$ . On output, the rotation sines used to transform $R$ to $R_1$ .
real(kind=real64),	intent(out),	optional,	target, dimension(:)	::	work	An optional argument that if supplied prevents local memory allocation. If provided, the array must have at least N elements. Additionally, this workspace array is used to contain the rotation cosines used to transform $R$ to $R_1$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

public interface solve_cholesky

private subroutine solve_cholesky_mtx(upper, a, b, err)

Solves the system of Cholesky factored equations $A X = R^T R X = B$ or $A X = L L^T X = B$ .

Arguments

Type	Intent	Optional	Attributes		Name
logical,	intent(in)			::	upper	Set to true if $A$ is factored such that $A = R^T R$ ; else, set to false if $A$ is factored such that $A = L L^T$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N Cholesky factored matrix as returned by cholesky_factor.
real(kind=real64),	intent(inout),		dimension(:,:)	::	b	On input, the N-by-NRHS matrix $B$ . On output, the resulting N-by-NRHS matrix $X$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

private subroutine solve_cholesky_mtx_cmplx(upper, a, b, err)

Solves the system of Cholesky factored equations $A X = R^H R X = B$ or $A X = L L^H X = B$ .

Arguments

Type	Intent	Optional	Attributes		Name
logical,	intent(in)			::	upper	Set to true if $A$ is factored such that $A = R^H R$ ; else, set to false if $A$ is factored such that $A = L L^H$ .
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N Cholesky factored matrix as returned by cholesky_factor.
complex(kind=real64),	intent(inout),		dimension(:,:)	::	b	On input, the N-by-NRHS matrix $B$ . On output, the resulting N-by-NRHS matrix $X$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

private subroutine solve_cholesky_vec(upper, a, b, err)

Solves the system of Cholesky factored equations $A \vec{x} = R^T R \vec{x} = \vec{b}$ or $A \vec{x} = L L^T \vec{x} = \vec{b}$ .

Arguments

Type	Intent	Optional	Attributes		Name
logical,	intent(in)			::	upper	Set to true if $A$ is factored such that $A = R^T R$ ; else, set to false if $A$ is factored such that $A = L L^T$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N Cholesky factored matrix as returned by cholesky_factor.
real(kind=real64),	intent(inout),		dimension(:)	::	b	On input, the N-element vector $\vec{b}$ . On output, the resulting N-element vector $\vec{x}$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

private module subroutine solve_cholesky_vec_cmplx(upper, a, b, err)

Solves the system of Cholesky factored equations $A \vec{x} = R^H R \vec{x} = \vec{b}$ or $A \vec{x} = L L^H \vec{x} = \vec{b}$ .

Arguments

Type	Intent	Optional	Attributes		Name
logical,	intent(in)			::	upper	Set to true if $A$ is factored such that $A = R^H R$ ; else, set to false if $A$ is factored such that $A = L L^H$ .
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N Cholesky factored matrix as returned by cholesky_factor.
complex(kind=real64),	intent(inout),		dimension(:)	::	b	On input, the N-element vector $\vec{b}$ . On output, the resulting N-element vector $\vec{x}$ .
class(errors),	intent(inout),	optional,	target	::	err	An error object to report any errors that occur.

linalg_cholesky Module

Contents

Interfaces

Uses

Interfaces

public interface cholesky_factor

private subroutine cholesky_factor_dbl(a, upper, err)

Arguments

private subroutine cholesky_factor_cmplx(a, upper, err)

Arguments

public interface cholesky_rank1_downdate

private subroutine cholesky_rank1_downdate_dbl(r, u, work, err)

Arguments

private subroutine cholesky_rank1_downdate_cmplx(r, u, work, err)

Arguments

public interface cholesky_rank1_update

private subroutine cholesky_rank1_update_dbl(r, u, work, err)

Arguments

private subroutine cholesky_rank1_update_cmplx(r, u, work, err)

Arguments

public interface solve_cholesky

private subroutine solve_cholesky_mtx(upper, a, b, err)

Arguments

private subroutine solve_cholesky_mtx_cmplx(upper, a, b, err)

Arguments

private subroutine solve_cholesky_vec(upper, a, b, err)

Arguments

private module subroutine solve_cholesky_vec_cmplx(upper, a, b, err)

Arguments