CXML
        	    
LAPACK version 3.0
dgerfs(3)

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

SYNTAX
  SUBROUTINE DGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX,
		     FERR, BERR, WORK, IWORK, INFO )

      CHARACTER	     TRANS

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

      INTEGER	     IPIV( * ), IWORK( * )

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

DESCRIPTION
  DGERFS 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 = 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAF,N)
	  The factors L and U from the factorization A = P*L*U as computed by
	  DGETRF.

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

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

  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 DGETRS.  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 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 illegal value

PARAMETERS
  ITMAX is the maximum number of steps of iterative refinement.