spprfs()

subroutine spprfs	(	character	uplo,
		integer	n,
		integer	nrhs,
		real, dimension( * )	ap,
		real, dimension( * )	afp,
		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 )

SPPRFS

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Purpose:

!>
!> SPPRFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is symmetric positive definite
!> and packed, 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]	AP	!> AP is REAL array, dimension (N*(N+1)/2) !> The upper or lower triangle of the symmetric matrix A, packed !> columnwise in a linear array. The j-th column of A is stored !> in the array AP as follows: !> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. !>
[in]	AFP	!> AFP is REAL array, dimension (N*(N+1)/2) !> The triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, !> packed columnwise in a linear array in the same format as A !> (see AP). !>
[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 SPPTRS. !> 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.