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

CTRRFS(l)					)					CTRRFS(l)

NAME
       CTRRFS - provide error bounds and backward error estimates for the solution to a system of
       linear equations with a triangular coefficient matrix

SYNOPSIS
       SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR,  BERR,  WORK,
			  RWORK, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

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

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

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

PURPOSE
       CTRRFS  provides error bounds and backward error estimates for the solution to a system of
       linear equations with a triangular coefficient matrix.  The solution matrix X must be com-
       puted  by  CTRTRS  or  some  other means before entering this routine.  CTRRFS does not do
       iterative refinement because doing so cannot improve the backward error.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       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)

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

       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  triangular matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part
	       of the array A contains the upper triangular matrix, and the strictly lower trian-
	       gular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower trian-
	       gular part of the array A contains the lower triangular matrix, and  the  strictly
	       upper  triangular  part	of A is not referenced.  If DIAG = 'U', the diagonal ele-
	       ments of A are also not referenced and are assumed to be 1.

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

       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) COMPLEX array, dimension (LDX,NRHS)
	       The 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) 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

LAPACK version 3.0			   15 June 2000 				CTRRFS(l)


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