CSYRFS(l)								 )								 CSYRFS(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	  UPLO

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

	   INTEGER	  IPIV( * )

	   REAL 	  BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX	  A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       CSYRFS improves the computed solution to a system of linear 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) COMPLEX array, dimension (LDA,N)
	       The  symmetric  matrix  A.   If UPLO = 'U', the leading 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 triangular 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) COMPLEX 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 factorization A = U*D*U**T or A = L*D*L**T as computed by CSYTRF.

       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 structure of D as determined by CSYTRF.

       B       (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by CSYTRS.	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 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    (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) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 CSYRFS(l)