ZPTEQR(l)		LAPACK routine (version	1.1)		    ZPTEQR(l)

NAME
  ZPTEQR - compute all eigenvalues and,	optionally, eigenvectors of a sym-
  metric positive definite tridiagonal matrix by first factoring the matrix
  using	DPTTRF and then	calling	ZBDSQR to compute the singular values of the
  bidiagonal factor

SYNOPSIS

  SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z,	LDZ, WORK, INFO	)

      CHARACTER	     COMPZ

      INTEGER	     INFO, LDZ,	N

      DOUBLE	     PRECISION D( * ), E( * ), WORK( * )

      COMPLEX*16     Z(	LDZ, * )

PURPOSE
  ZPTEQR computes all eigenvalues and, optionally, eigenvectors	of a sym-
  metric positive definite tridiagonal matrix by first factoring the matrix
  using	DPTTRF and then	calling	ZBDSQR to compute the singular values of the
  bidiagonal factor.

  This routine computes	the eigenvalues	of the positive	definite tridiagonal
  matrix to high relative accuracy.  This means	that if	the eigenvalues	range
  over many orders of magnitude	in size, then the small	eigenvalues and
  corresponding	eigenvectors will be computed more accurately than, for	exam-
  ple, with the	standard QR method.

  The eigenvectors of a	full or	band complex Hermitian matrix can also be
  found	if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to
  tridiagonal form.  (The reduction to tridiagonal form, however, may pre-
  clude	the possibility	of obtaining high relative accuracy in the small
  eigenvalues of the original matrix, if these eigenvalues range over many
  orders of magnitude.)

ARGUMENTS

  COMPZ	  (input) CHARACTER*1
	  = 'N':  Compute eigenvalues only.
	  = 'V':  Compute eigenvectors of original Hermitian matrix also.
	  Array	Z contains the unitary matrix used to reduce the original
	  matrix to tridiagonal	form.  = 'I':  Compute eigenvectors of tridi-
	  agonal matrix	also.

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

  D	  (input/output) DOUBLE	PRECISION array, dimension (N)
	  On entry, the	n diagonal elements of the tridiagonal matrix.	On
	  normal exit, D contains the eigenvalues, in descending order.

  E	  (input/output) DOUBLE	PRECISION array, dimension (N-1)
	  On entry, the	(n-1) subdiagonal elements of the tridiagonal matrix.
	  On exit, E has been destroyed.

  Z	  (input/output) COMPLEX*16 array, dimension (LDZ, N)
	  On entry, if COMPZ = 'V', the	unitary	matrix used in the reduction
	  to tridiagonal form.	On exit, if COMPZ = 'V', the orthonormal
	  eigenvectors of the original Hermitian matrix; if COMPZ = 'I', the
	  orthonormal eigenvectors of the tridiagonal matrix.  If INFO > 0 on
	  exit,	Z contains the eigenvectors associated with only the stored
	  eigenvalues.	If  COMPZ = 'N', then Z	is not referenced.

  LDZ	  (input) INTEGER
	  The leading dimension	of the array Z.	 LDZ >=	1, and if COMPZ	= 'V'
	  or 'I', LDZ >= max(1,N).

  WORK	  (workspace) DOUBLE PRECISION array, dimension	(max(1,4*N-4))
	  If  COMPZ = 'N', then	WORK is	not referenced.

  INFO	  (output) INTEGER
	  = 0:	successful exit.
	  < 0:	if INFO	= -i, the i-th argument	had an illegal value.
	  > 0:	if INFO	= i, and i is: <= N  the Cholesky factorization	of
	  the matrix could not be performed because the	i-th principal minor
	  was not positive definite.  >	N   the	SVD algorithm failed to	con-
	  verge; if INFO = N+i,	i off-diagonal elements	of the bidiagonal
	  factor did not converge to zero.