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RedHat 9 (Linux i386) - man page for sgerfs (redhat section l)

SGERFS(l)					)					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 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) 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  solu-
	       tion).

       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.

LAPACK version 3.0			   15 June 2000 				SGERFS(l)


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