solve_triangular_system

private pure function solve_tri_mtx(lside, upper, trans, nounit, alpha, a, b) result(x)

Solves a triangular system of equations of the form $op(A) X = \alpha B$ or $X op(A) = \alpha B$ where $A$ is a triangular matrix (either upper or lower) for the unknown $X$ .

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	Set to true to solve $op(A) X = \alpha B$ ; else, set to false to solve $X op(A) = \alpha B$ .
logical,	intent(in)		::	upper	Set to true if $A$ is upper triangular; else, set to false if $A$ is lower triangular.
logical,	intent(in)		::	trans	Set to true if $op(A) = A^T$ ; else, set to false if $op(A) = A$ .
logical,	intent(in)		::	nounit	Set to true if $A$ is unit-triangular (ones on the diagonal); else, false if $A$ is not unit-triangular.
real(kind=real64),	intent(in)		::	alpha	The scalar multiplier $\alpha$ .
real(kind=real64),	intent(in),	dimension(:,:)	::	a	If lside is true, the M-by-M triangular matrix $A$ ; else, $A$ is N-by-N if lside is false.
real(kind=real64),	intent(in),	dimension(:,:)	::	b	The M-by-N matrix $B$ .

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

The M-by-N matrix $X$ .

private pure function solve_tri_mtx_cmplx(lside, upper, trans, nounit, alpha, a, b) result(x)

Solves a triangular system of equations of the form $op(A) X = \alpha B$ or $X op(A) = \alpha B$ where $A$ is a triangular matrix (either upper or lower) for the unknown $X$ .

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	lside	Set to true to solve $op(A) X = \alpha B$ ; else, set to false to solve $X op(A) = \alpha B$ .
logical,	intent(in)		::	upper	Set to true if $A$ is upper triangular; else, set to false if $A$ is lower triangular.
logical,	intent(in)		::	trans	Set to true if $op(A) = A^H$ ; else, set to false if $op(A) = A$ .
logical,	intent(in)		::	nounit	Set to true if $A$ is unit-triangular (ones on the diagonal); else, false if $A$ is not unit-triangular.
complex(kind=real64),	intent(in)		::	alpha	The scalar multiplier $\alpha$ .
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	If lside is true, the M-by-M triangular matrix $A$ ; else, $A$ is N-by-N if lside is false.
complex(kind=real64),	intent(in),	dimension(:,:)	::	b	On input, The M-by-N matrix $B$ .

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

The M-by-N matrix $X$ .

private pure function solve_tri_vec(upper, trans, nounit, a, b) result(x)

Solves the triangular system $op(A) \vec{x} = \vec{b}$ where $A$ is a triangular matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	upper	Set to true if $A$ is upper triangular; else, set to false if $A$ is lower triangular.
logical,	intent(in)		::	trans	Set to true if $op(A) = A^T$ ; else, set to false if $op(A) = A$ .
logical,	intent(in)		::	nounit	Set to true if $A$ is unit-triangular (ones on the diagonal); else, false if $A$ is not unit-triangular.
real(kind=real64),	intent(in),	dimension(:,:)	::	a	The N-by-N triangular matrix $A$ .
real(kind=real64),	intent(in),	dimension(:)	::	b	The N-element vector $\vec{b}$ .

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

The N-element vector $\vec{x}$ .

private pure function solve_tri_vec_cmplx(upper, trans, nounit, a, b) result(x)

Solves the triangular system $op(A) \vec{x} = \vec{b}$ where $A$ is a triangular matrix.

Arguments

Type	Intent	Attributes		Name
logical,	intent(in)		::	upper	Set to true if $A$ is upper triangular; else, set to false if $A$ is lower triangular.
logical,	intent(in)		::	trans	Set to true if $op(A) = A^T$ ; else, set to false if $op(A) = A$ .
logical,	intent(in)		::	nounit	Set to true if $A$ is unit-triangular (ones on the diagonal); else, false if $A$ is not unit-triangular.
complex(kind=real64),	intent(in),	dimension(:,:)	::	a	The N-by-N triangular matrix $A$ .
complex(kind=real64),	intent(in),	dimension(:)	::	b	The N-element vector $\vec{b}$ .

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

The N-element vector $\vec{x}$ .

solve_triangular_system Interface

Contents

Module Procedures

public interface solve_triangular_system

Module Procedures

private pure function solve_tri_mtx(lside, upper, trans, nounit, alpha, a, b) result(x)

Arguments

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

private pure function solve_tri_mtx_cmplx(lside, upper, trans, nounit, alpha, a, b) result(x)

Arguments

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

private pure function solve_tri_vec(upper, trans, nounit, a, b) result(x)

Arguments

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

private pure function solve_tri_vec_cmplx(upper, trans, nounit, a, b) result(x)

Arguments

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