cgerfs man page on IRIX

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CGERFS(3F)							    CGERFS(3F)

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

SYNOPSIS
     SUBROUTINE CGERFS( 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( * )

	 REAL		BERR( * ), FERR( * ), RWORK( * )

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

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

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

									Page 1

CGERFS(3F)							    CGERFS(3F)

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

     B	     (input) COMPLEX 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 array, dimension (LDX,NRHS)
	     On entry, the solution matrix X, as computed by CGETRS.  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
	     estimate is as reliable as the estimate for RCOND, and is almost
	     always a slight overestimate 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 solution).

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

     RWORK   (workspace) REAL 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.

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