sgbrfs()

subroutine sgbrfs	(	character	trans,
		integer	n,
		integer	kl,
		integer	ku,
		integer	nrhs,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( ldafb, * )	afb,
		integer	ldafb,
		integer, dimension( * )	ipiv,
		real, dimension( ldb, * )	b,
		integer	ldb,
		real, dimension( ldx, * )	x,
		integer	ldx,
		real, dimension( * )	ferr,
		real, dimension( * )	berr,
		real, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info )

SGBRFS

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Purpose:

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

Parameters

[in]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the form of 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]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	KL	!> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !>
[in]	KU	!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 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 REAL array, dimension (LDAB,N) !> The original band matrix A, stored in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !>
[in]	AFB	!> AFB is REAL array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by SGBTRF. U is stored as an upper triangular band !> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and !> the multipliers used during the factorization are stored in !> rows KL+KU+2 to 2*KL+KU+1. !>
[in]	LDAFB	!> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices from SGBTRF; for 1<=i<=N, row i of the !> matrix was interchanged with row IPIV(i). !>
[in]	B	!> B is REAL 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 REAL array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by SGBTRS. !> 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 REAL 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 REAL 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 REAL 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.