ZSTEIN(l)		LAPACK routine (version	1.1)		    ZSTEIN(l)

NAME
  ZSTEIN - compute the eigenvectors of a real symmetric	tridiagonal matrix T
  corresponding	to specified eigenvalues, using	inverse	iteration

SYNOPSIS

  SUBROUTINE ZSTEIN( N,	D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
		     IFAIL, INFO )

      INTEGER	     INFO, LDZ,	M, N

      INTEGER	     IBLOCK( * ), IFAIL( * ), ISPLIT( *	), IWORK( * )

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

      COMPLEX*16     Z(	LDZ, * )

PURPOSE
  ZSTEIN computes the eigenvectors of a	real symmetric tridiagonal matrix T
  corresponding	to specified eigenvalues, using	inverse	iteration.

  The maximum number of	iterations allowed for each eigenvector	is specified
  by an	internal parameter MAXITS (currently set to 5).

  Although the eigenvectors are	real, they are stored in a complex array,
  which	may be passed to ZUNMTR	or ZUPMTR for back
  transformation to the	eigenvectors of	a complex Hermitian matrix which was
  reduced to tridiagonal form.

ARGUMENTS

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

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

  E	  (input) DOUBLE PRECISION array, dimension (N)
	  The (n-1) subdiagonal	elements of the	tridiagonal matrix T, stored
	  in elements 1	to N-1;	E(N) need not be set.

  M	  (input) INTEGER
	  The number of	eigenvectors to	be found.  0 <=	M <= N.

  W	  (input) DOUBLE PRECISION array, dimension (N)
	  The first M elements of W contain the	eigenvalues for	which eigen-
	  vectors are to be computed.  The eigenvalues should be grouped by
	  split-off block and ordered from smallest to largest within the
	  block.  ( The	output array W from DSTEBZ with	ORDER =	'B' is
	  expected here. )

  IBLOCK  (input) INTEGER array, dimension (N)
	  The submatrix	indices	associated with	the corresponding eigenvalues
	  in W;	IBLOCK(i)=1 if eigenvalue W(i) belongs to the first submatrix
	  from the top,	=2 if W(i) belongs to the second submatrix, etc.  (
	  The output array IBLOCK from DSTEBZ is expected here.	)

  ISPLIT  (input) INTEGER array, dimension (N)
	  The splitting	points,	at which T breaks up into submatrices.	The
	  first	submatrix consists of rows/columns 1 to	ISPLIT(	1 ), the
	  second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc.  (
	  The output array ISPLIT from DSTEBZ is expected here.	)

  Z	  (output) COMPLEX*16 array, dimension (LDZ, M)
	  The computed eigenvectors.  The eigenvector associated with the
	  eigenvalue W(i) is stored in the i-th	column of Z.  Any vector
	  which	fails to converge is set to its	current	iterate	after MAXITS
	  iterations.  The imaginary parts of the eigenvectors are set to
	  zero.

  LDZ	  (input) INTEGER
	  The leading dimension	of the array Z.	 LDZ >=	max(1,N).

  WORK	  (workspace) DOUBLE PRECISION array, dimension	(5*N)

  IWORK	  (workspace) INTEGER array, dimension (N)

  IFAIL	  (output) INTEGER array, dimension (M)
	  On normal exit, all elements of IFAIL	are zero.  If one or more
	  eigenvectors fail to converge	after MAXITS iterations, then their
	  indices are stored in	array IFAIL.

  INFO	  (output) INTEGER
	  = 0: successful exit
	  < 0: if INFO = -i, the i-th argument had an illegal value
	  > 0: if INFO = i, then i eigenvectors	failed to converge in MAXITS
	  iterations.  Their indices are stored	in array IFAIL.

PARAMETERS

  MAXITS  INTEGER, default = 5
	  The maximum number of	iterations performed.

  EXTRA	  INTEGER, default = 2
	  The number of	iterations performed after norm	growth criterion is
	  satisfied, should be at least	1.