
SPORFS(l) ) SPORFS(l)
NAME
SPORFS  improve the computed solution to a system of linear equations when the coeffi
cient matrix is symmetric positive definite,
SYNOPSIS
SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK,
IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( *
), X( LDX, * )
PURPOSE
SPORFS improves the computed solution to a system of linear equations when the coefficient
matrix is symmetric positive definite, and provides error bounds and backward error esti
mates for the solution.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrices B and
X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the leading NbyN 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 NbyN 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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) REAL array, dimension (LDAF,N)
The triangular factor U or L from the Cholesky factorization A = U**T*U or A =
L*L**T, as computed by SPOTRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPOTRS. On exit, the improved
solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j) (the jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate of the true error.
BERR (output) 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 solu
tion).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 SPORFS(l) 
