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DGERFS(1)		 LAPACK routine (version 3.2)		     DGERFS(1)

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

SYNOPSIS
       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, * )

PURPOSE
       DGERFS improves the computed solution to a system of  linear  equations
       and  provides  error  bounds and backward error estimates for the solu‐
       tion.

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 com‐
	       puted 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 vec‐
	       tor  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.

 LAPACK routine (version 3.2)	 November 2008			     DGERFS(1)
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