sporfs(3F)

NAME
     SPORFS - improve the computed solution to a system of linear equations
     when the coefficient 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 estimates 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 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.

     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 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.

     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 solution).

     WORK    (workspace) REAL array, dimension (3*N)

     IWORK   (workspace) INTEGER array, dimension (N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
     ITMAX is the maximum number of steps of iterative refinement.