NAME

       spprfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine spprfs (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
           SPPRFS

Function/Subroutine Documentation

   subroutine spprfs (character UPLO, integer N, integer NRHS, real, dimension( * ) AP, real,
       dimension( * ) AFP, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldx, * ) X,
       integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * )
       WORK, integer, dimension( * ) IWORK, integer INFO)
       SPPRFS

       Purpose:

            SPPRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is symmetric positive definite
            and packed, and provides error bounds and backward error estimates
            for the solution.

       Parameters:
           UPLO

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

           N

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

           NRHS

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

           AP

                     AP is REAL array, dimension (N*(N+1)/2)
                     The upper or lower triangle of the symmetric matrix A, packed
                     columnwise in a linear array.  The j-th column of A is stored
                     in the array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

           AFP

                     AFP is REAL array, dimension (N*(N+1)/2)
                     The triangular factor U or L from the Cholesky factorization
                     A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF,
                     packed columnwise in a linear array in the same format as A
                     (see AP).

           B

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

           LDB

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

           X

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

           LDX

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

           FERR

                     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

                     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

                     WORK is REAL array, dimension (3*N)

           IWORK

                     IWORK is INTEGER array, dimension (N)

           INFO

                     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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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