dtbtrs()

subroutine dtbtrs	(	character	uplo,
		character	trans,
		character	diag,
		integer	n,
		integer	kd,
		integer	nrhs,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		integer	info )

DTBTRS

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Purpose:

!>
!> DTBTRS solves a triangular system of the form
!>
!>    A * X = B  or  A**T * X = B,
!>
!> where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular. !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the form the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate transpose = Transpose) !>
[in]	DIAG	!> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	KD	!> KD is INTEGER !> The number of superdiagonals or subdiagonals of the !> triangular band matrix A. KD >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>
[in]	AB	!> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> The upper or lower triangular band matrix A, stored in the !> first kd+1 rows of AB. The j-th column of A is stored !> in the j-th column of the array AB as follows: !> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). !> If DIAG = 'U', the diagonal elements of A are not referenced !> and are assumed to be 1. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[in,out]	B	!> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, if INFO = 0, the solution matrix X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the i-th diagonal element of A is exactly zero, !> indicating that the matrix is singular and the !> solutions X have not been computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.