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RedHat 9 (Linux i386) - man page for zstein (redhat section l)

ZSTEIN(l)					)					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 eigenvectors 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.

LAPACK version 3.0			   15 June 2000 				ZSTEIN(l)


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