zporfs()

subroutine zporfs	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldaf, * )	af,
		integer	ldaf,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( ldx, * )	x,
		integer	ldx,
		double precision, dimension( * )	ferr,
		double precision, dimension( * )	berr,
		complex*16, dimension( * )	work,
		double precision, dimension( * )	rwork,
		integer	info )

ZPORFS

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Purpose:

!>
!> ZPORFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is Hermitian positive definite,
!> 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]	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]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> The Hermitian matrix A. If UPLO = 'U', the leading N-by-N !> upper triangular part of A contains the upper triangular part !> of the matrix A, and the strictly lower triangular part of A !> is not referenced. If UPLO = 'L', the leading N-by-N lower !> triangular part of A contains the lower triangular part of !> the matrix A, and the strictly upper triangular part of A is !> not referenced. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	AF	!> AF is COMPLEX*16 array, dimension (LDAF,N) !> The triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by ZPOTRF. !>
[in]	LDAF	!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
[in]	B	!> B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by ZPOTRS. !> 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 COMPLEX*16 array, dimension (2*N) !>
[out]	RWORK	!> RWORK is DOUBLE PRECISION 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.