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NAME
     dsprfs - improve the computed solution to a system of linear
     equations  when the coefficient matrix is symmetric indefin-
     ite and packed, and provides error bounds and backward error
     estimates for the solution

SYNOPSIS
     SUBROUTINE DSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB,  X,
               LDX, FERR, BERR, WORK, IWORK, INFO )

     CHARACTER UPLO

     INTEGER INFO, LDB, LDX, N, NRHS

     INTEGER IPIV( * ), IWORK( * )

     DOUBLE PRECISION AFP( * ), AP( * ), B( LDB, * ), BERR( *  ),
               FERR( * ), WORK( * ), X( LDX, * )



     #include <sunperf.h>

     void dsprfs(char uplo, int n, int nrhs, double *dap,  double
               *afp,  int  *ipivot,  double  *db, int ldb, double
               *dx, int ldx,  double  *ferr,  double  *berr,  int
               *info);

PURPOSE
     DSPRFS improves the computed solution to a system of  linear
     equations  when the coefficient matrix is symmetric indefin-
     ite and packed, 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.

     AP        (input)   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       (input)   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 factori-
               zation A = U*D*U**T or A = L*D*L**T as computed by
               DSPTRF, stored as a packed triangular matrix.

     IPIV      (input) INTEGER array, dimension (N)
               Details of the interchanges and the  block  struc-
               ture of D as determined by DSPTRF.

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

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

     FERR      (output) DOUBLE PRECISION array, dimension (NRHS)
               The estimated forward error bound for  each  solu-
               tion  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  ele-
               ment 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) 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      (workspace)  DOUBLE  PRECISION  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 ille-
               gal value

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