DSYRFS - improve the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  symmetric
       indefinite,  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, * )


PURPOSE

       DSYRFS improves the computed solution to a system of  lin­
       ear  equations  when  the  coefficient matrix is symmetric
       indefinite, 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 refer­
               enced.  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  tri­
               angular part of A is not referenced.

       LDA     (input) INTEGER
               The  leading  dimension  of  the  array A.  LDA >=
               max(1,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 factor­
               ization 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  corre­
               sponding  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 reli­
               able  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)

               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


PARAMETERS

       ITMAX  is the maximum number of steps of iterative refine­
       ment.


Man(1) output converted with man2html