SGERFS(l)		LAPACK routine (version	1.1)		    SGERFS(l)

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

SYNOPSIS

  SUBROUTINE SGERFS( 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( * )

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

PURPOSE
  SGERFS 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) REAL 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) REAL array, dimension	(LDAF,N)
	  The factors L	and U from the factorization A = P*L*U as computed by
	  SGETRF.

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

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

  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 SGETRS.  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 bounds for each solution vector X(j)
	  (the j-th column of the solution matrix X).  If XTRUE	is the true
	  solution, FERR(j) bounds the magnitude of the	largest	entry in
	  (X(j)	- XTRUE) divided by the	magnitude of the largest entry in
	  X(j).	 The quality of	the error bound	depends	on the quality of the
	  estimate of norm(inv(A)) computed in the code; if the	estimate of
	  norm(inv(A)) is accurate, the	error bound is guaranteed.

  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 entry	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 illegal value

PARAMETERS

  ITMAX	is the maximum number of steps of iterative refinement.