CXML
        	    
LAPACK version 3.0
zhbtrd(3)

PURPOSE
  ZHBTRD - reduce a complex Hermitian band matrix A to real symmetric
  tridiagonal form T by a unitary similarity transformation

SYNTAX
  SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )

      CHARACTER	     UPLO, VECT

      INTEGER	     INFO, KD, LDAB, LDQ, N

      DOUBLE	     PRECISION D( * ), E( * )

      COMPLEX*16     AB( LDAB, * ), Q( LDQ, * ), WORK( * )

DESCRIPTION
  ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
  tridiagonal form T by a unitary similarity transformation: Q**H * A * Q =
  T.

ARGUMENTS
  VECT	  (input) CHARACTER*1
	  = 'N':  do not form Q;
	  = 'V':  form Q;
	  = 'U':  update a matrix X, by forming X*Q.

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangle of A is stored;
	  = 'L':  Lower triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  KD	  (input) INTEGER
	  The number of superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 KD >= 0.

  AB	  (input/output) COMPLEX*16 array, dimension (LDAB,N)
	  On entry, the upper or lower triangle of the Hermitian 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).  On exit, the
	  diagonal elements of AB are overwritten by the diagonal elements of
	  the tridiagonal matrix T; if KD > 0, the elements on the first
	  superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO =
	  'L') are overwritten by the off-diagonal elements of T; the rest of
	  AB is overwritten by values generated during the reduction.

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

  D	  (output) DOUBLE PRECISION array, dimension (N)
	  The diagonal elements of the tridiagonal matrix T.

  E	  (output) DOUBLE PRECISION array, dimension (N-1)
	  The off-diagonal elements of the tridiagonal matrix T: E(i) =
	  T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

  Q	  (input/output) COMPLEX*16 array, dimension (LDQ,N)
	  On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if
	  VECT = 'N' or 'V', then Q need not be set.

	  On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if
	  VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q
	  is not referenced.

  LDQ	  (input) INTEGER
	  The leading dimension of the array Q.	 LDQ >= 1, and LDQ >= N if
	  VECT = 'V' or 'U'.

  WORK	  (workspace) COMPLEX*16 array, dimension (N)

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

FURTHER DETAILS
  Modified by Linda Kaufman, Bell Labs.