SSYRFS - 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 SSYRFS( 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( * )

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


PURPOSE

       SSYRFS 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) REAL 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 SSYTRF.

       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 SSYTRF.

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

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

       FERR    (output) REAL 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) 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    (workspace) REAL 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



PARAMETERS

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


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