


SPORFS(3f)         LAPACK routine (version 3.1)        SPORFS(3f)


NAME
       SPORFS - 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 pro-
       vides 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 trian-
               gular  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).




 LAPACK routine (version 3November 2006                         1





SPORFS(3f)         LAPACK routine (version 3.1)        SPORFS(3f)


       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 vec-
               tor 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.




















 LAPACK routine (version 3November 2006                         2


