NAME

       dsprfs.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine dsprfs (character UPLO, integer N, integer NRHS, double precision, dimension( * )
       AP, double precision, dimension( * ) AFP, integer, dimension( * ) IPIV, double precision,
       dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX,
       double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double
       precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)
       DSPRFS

       Purpose:

            DSPRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is symmetric indefinite
            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 DOUBLE PRECISION 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

           AFP

                     AFP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
                     The factored form of the matrix A.  AFP contains the block
                     diagonal matrix D and the multipliers used to obtain the
                     factor U or L from the factorization A = U*D*U**T or
                     A = L*D*L**T as computed by DSPTRF, stored as a packed
                     triangular matrix.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by DSPTRF.

           B

                     B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by DSPTRS.
                     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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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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