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CHBTRD(l)			       )			     CHBTRD(l)

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

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

	   CHARACTER	  UPLO, VECT

	   INTEGER	  INFO, KD, LDAB, LDQ, N

	   REAL		  D( * ), E( * )

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

PURPOSE
       CHBTRD  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 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 overwrit‐
	       ten by values generated during the reduction.

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

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

       E       (output) REAL 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 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 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.

LAPACK version 3.0		 15 June 2000			     CHBTRD(l)
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