CXML
        	    
LAPACK version 3.0
dtbrfs(3)

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

SYNTAX
  SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
		     LDX, FERR, BERR, WORK, IWORK, INFO )

      CHARACTER	     DIAG, TRANS, UPLO

      INTEGER	     INFO, KD, LDAB, LDB, LDX, N, NRHS

      INTEGER	     IWORK( * )

      DOUBLE	     PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( *
		     ), WORK( * ), X( LDX, * )

DESCRIPTION
  DTBRFS provides error bounds and backward error estimates for the solution
  to a system of linear equations with a triangular band coefficient matrix.
  The solution matrix X must be computed by DTBTRS or some other means before
  entering this routine.  DTBRFS 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.

  KD	  (input) INTEGER
	  The number of superdiagonals or subdiagonals of the triangular band
	  matrix A.  KD >= 0.

  NRHS	  (input) INTEGER
	  The number of right hand sides, i.e., the number of columns of the
	  matrices B and X.  NRHS >= 0.

  AB	  (input) DOUBLE PRECISION array, dimension (LDAB,N)
	  The upper or lower triangular band matrix A, stored in the first
	  kd+1 rows of the array. The j-th column of A is stored in the j-th
	  column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) =
	  A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    =
	  A(i,j) for j<=i<=min(n,j+kd).	 If DIAG = 'U', the diagonal elements
	  of A are not referenced and are assumed to be 1.

  LDAB	  (input) INTEGER
	  The leading dimension of the array AB.  LDAB >= KD+1.

  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