ZHPTRD(l)		LAPACK routine (version	1.1)		    ZHPTRD(l)

NAME
  ZHPTRD - reduce a complex Hermitian matrix A stored in packed	form to	real
  symmetric tridiagonal	form T by a unitary similarity transformation

SYNOPSIS

  SUBROUTINE ZHPTRD( UPLO, N, AP, D, E,	TAU, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, N

      DOUBLE	     PRECISION D( * ), E( * )

      COMPLEX*16     AP( * ), TAU( * )

PURPOSE
  ZHPTRD reduces a complex Hermitian matrix A stored in	packed form to real
  symmetric tridiagonal	form T by a unitary similarity transformation: Q**H *
  A * Q	= T.

ARGUMENTS

  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.

  AP	  (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
	  On entry, the	upper or lower triangle	of the Hermitian matrix	A,
	  packed columnwise in a linear	array.	The j-th column	of A is
	  stored in the	array AP as follows: if	UPLO = 'U', AP(i + (j-1)*j/2)
	  = A(i,j) for 1<=i<=j;	if UPLO	= 'L', AP(i + (j-1)*(2*n-j)/2) =
	  A(i,j) for j<=i<=n.  On exit,	if UPLO	= 'U', the diagonal and	first
	  superdiagonal	of A are overwritten by	the corresponding elements of
	  the tridiagonal matrix T, and	the elements above the first superdi-
	  agonal, with the array TAU, represent	the unitary matrix Q as	a
	  product of elementary	reflectors; if UPLO = 'L', the diagonal	and
	  first	subdiagonal of A are over- written by the corresponding	ele-
	  ments	of the tridiagonal matrix T, and the elements below the	first
	  subdiagonal, with the	array TAU, represent the unitary matrix	Q as
	  a product of elementary reflectors. See Further Details.  D
	  (output) DOUBLE PRECISION array, dimension (N) The diagonal ele-
	  ments	of the tridiagonal matrix T: D(i) = A(i,i).

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

  TAU	  (output) COMPLEX*16 array, dimension (N-1)
	  The scalar factors of	the elementary reflectors (see Further
	  Details).

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

FURTHER	DETAILS
  If UPLO = 'U', the matrix Q is represented as	a product of elementary
  reflectors

     Q = H(n-1)	. . . H(2) H(1).

  Each H(i) has	the form

     H(i) = I -	tau * v	* v'

  where	tau is a complex scalar, and v is a complex vector with	v(i+1:n) = 0
  and v(i) = 1;	v(1:i-1) is stored on exit in AP, overwriting A(1:i-1,i+1),
  and tau is stored in TAU(i).

  If UPLO = 'L', the matrix Q is represented as	a product of elementary
  reflectors

     Q = H(1) H(2) . . . H(n-1).

  Each H(i) has	the form

     H(i) = I -	tau * v	* v'

  where	tau is a complex scalar, and v is a complex vector with	v(1:i) = 0
  and v(i+1) = 1; v(i+2:n) is stored on	exit in	AP, overwriting	A(i+2:n,i),
  and tau is stored in TAU(i).