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ZGERFS(l)					)					ZGERFS(l)

NAME
       ZGERFS  - improve the computed solution to a system of linear equations and provides error
       bounds and backward error estimates for the solution

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

	   CHARACTER	  TRANS

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

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX*16	  A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       ZGERFS  improves  the computed solution to a system of linear equations and provides error
       bounds and backward error estimates for the solution.

ARGUMENTS
       TRANS   (input) CHARACTER*1
	       Specifies the form of the system of equations:
	       = 'N':  A * X = B     (No transpose)
	       = 'T':  A**T * X = B  (Transpose)
	       = 'C':  A**H * X = B  (Conjugate transpose)

       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*16 array, dimension (LDA,N)
	       The original N-by-N matrix A.

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

       AF      (input) COMPLEX*16 array, dimension (LDAF,N)
	       The factors L and U from the factorization A = P*L*U as computed by ZGETRF.

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

       IPIV    (input) INTEGER array, dimension (N)
	       The  pivot  indices from ZGETRF; for 1<=i<=N, row i of the matrix was interchanged
	       with row IPIV(i).

       B       (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by ZGETRS.	 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 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 esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate 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 solu-
	       tion).

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION 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 				ZGERFS(l)
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