dpbrfs()

subroutine dpbrfs	(	character	uplo,
		integer	n,
		integer	kd,
		integer	nrhs,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( ldafb, * )	afb,
		integer	ldafb,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( ldx, * )	x,
		integer	ldx,
		double precision, dimension( * )	ferr,
		double precision, dimension( * )	berr,
		double precision, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info )

DPBRFS

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Purpose:

!>
!> DPBRFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is symmetric positive definite
!> and banded, and provides error bounds and backward error estimates
!> for the solution.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	KD	!> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrices B and X. NRHS >= 0. !>
[in]	AB	!> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> The upper or lower triangle of the symmetric band matrix A, !> stored in the first KD+1 rows of the array. 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). !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[in]	AFB	!> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) !> The triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T of the band matrix A as computed by !> DPBTRF, in the same storage format as A (see AB). !>
[in]	LDAFB	!> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= KD+1. !>
[in]	B	!> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> The right hand side matrix B. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[in,out]	X	!> X is DOUBLE PRECISION array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by DPBTRS. !> On exit, the improved solution matrix X. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N). !>
[out]	FERR	!> FERR is DOUBLE PRECISION array, dimension (NRHS) !> The estimated forward error bound for each solution vector !> X(j) (the j-th column of the solution matrix X). !> If XTRUE is the true solution corresponding to X(j), FERR(j) !> is an estimated upper bound for the magnitude of the largest !> element in (X(j) - XTRUE) divided by the magnitude of the !> largest element in X(j). The estimate is as reliable as !> the estimate for RCOND, and is almost always a slight !> overestimate of the true error. !>
[out]	BERR	!> BERR is DOUBLE PRECISION array, dimension (NRHS) !> The componentwise relative backward error of each solution !> vector X(j) (i.e., the smallest relative change in !> any element of A or B that makes X(j) an exact solution). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (3*N) !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Internal Parameters:

!>  ITMAX is the maximum number of steps of iterative refinement.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.