CXML
        	    
LAPACK version 3.0
strrfs(3)

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

SYNTAX
  SUBROUTINE STRRFS( 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( * )

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

DESCRIPTION
  STRRFS 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 STRTRS or some other means before
  entering this routine.  STRRFS 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.

  A	  (input) REAL 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) 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) REAL 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 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) 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