dtrrfs man page on IRIX

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DTRRFS(3F)							    DTRRFS(3F)

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

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

	 CHARACTER	DIAG, TRANS, UPLO

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

	 INTEGER	IWORK( * )

	 DOUBLE		PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR( *
			), WORK( * ), X( LDX, * )

PURPOSE
     DTRRFS 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 computed by DTRTRS or some other means
     before entering this routine.  DTRRFS 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 = 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.

									Page 1

DTRRFS(3F)							    DTRRFS(3F)

     A	     (input) DOUBLE PRECISION 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 triangular part of A is not
	     referenced.  If UPLO = 'L', the leading N-by-N lower triangular
	     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 elements 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) 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
	     The 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 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) 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

									Page 2

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