Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  improves  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.

 LAPACK routine (version 3.2)               April 2011                            SPORFS(3lapack)