CXML
        	    
LAPACK version 3.0
ztbrfs(3)

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

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

      CHARACTER	     DIAG, TRANS, UPLO

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

      DOUBLE	     PRECISION BERR( * ), FERR( * ), RWORK( * )

      COMPLEX*16     AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

DESCRIPTION
  ZTBRFS 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 ZTBTRS or some other means before
  entering this routine.  ZTBRFS 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.

  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) COMPLEX*16 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) COMPLEX*16 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*16 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) COMPLEX*16 array, dimension (2*N)

  RWORK	  (workspace) DOUBLE PRECISION array, dimension (N)

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value