SPORFS(3)      LAPACK routine of NEC Numeric Library Collection      SPORFS(3)



NAME
       SPORFS

SYNOPSIS
       SUBROUTINE SPORFS (UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
           FERR, BERR, WORK, IWORK, INFO)



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)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrices B and X.  NRHS >= 0.

           A         (input)
                     A is 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           AF        (input)
                     AF is 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)
                     LDAF is INTEGER
                     The leading dimension of the array AF.  LDAF >= max(1,N).

           B         (input)
                     B is REAL array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           X         (input/output)
                     X is REAL array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by SPOTRS.
                     On exit, the improved solution matrix X.

           LDX       (input)
                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           FERR      (output)
                     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.

           BERR      (output)
                     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).

           WORK      (output)
                     WORK is REAL array, dimension (3*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                      SPORFS(3)