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

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

     CHARACTER UPLO

     INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS

     INTEGER IPIV( * ), IWORK( * )

     DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B(  LDB,  *  ),
               BERR( * ), FERR( * ), WORK( * ), X( LDX, * )



     #include <sunperf.h>

     void dsyrfs(char uplo, int n, int nrhs, double *da, int lda,
               double *af, int ldaf, int *ipivot, double *db, int
               ldb, double *dx, int  ldx,  double  *ferr,  double
               *berr, int *info) ;

PURPOSE
     DSYRFS improves the computed solution to a system of  linear
     equations  when the coefficient matrix is symmetric indefin-
     ite, 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) DOUBLE PRECISION array, dimension (LDA,N)
               The symmetric matrix A.  If UPLO = 'U', the  lead-
               ing 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 tri-
               angular 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) DOUBLE PRECISION array, dimension (LDAF,N)
               The factored form of the matrix  A.   AF  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
               DSYTRF.

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

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

     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
               DSYTRS.  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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