zstein()

subroutine zstein	(	integer	n,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e,
		integer	m,
		double precision, dimension( * )	w,
		integer, dimension( * )	iblock,
		integer, dimension( * )	isplit,
		complex*16, dimension( ldz, * )	z,
		integer	ldz,
		double precision, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer, dimension( * )	ifail,
		integer	info )

ZSTEIN

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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.
!>
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix. N >= 0. !>
[in]	D	!> D is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the tridiagonal matrix T. !>
[in]	E	!> E is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) subdiagonal elements of the tridiagonal matrix !> T, stored in elements 1 to N-1. !>
[in]	M	!> M is INTEGER !> The number of eigenvectors to be found. 0 <= M <= N. !>
[in]	W	!> W is 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. ) !>
[in]	IBLOCK	!> IBLOCK is 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. ) !>
[in]	ISPLIT	!> ISPLIT is 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. ) !>
[out]	Z	!> Z is 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. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= max(1,N). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (5*N) !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N) !>
[out]	IFAIL	!> IFAIL is 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. !>
[out]	INFO	!> INFO is 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. !>

Internal 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.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.