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NAME
     zstein - compute the eigenvectors of a real symmetric tridi-
     agonal  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, * )



     #include <sunperf.h>

     void zstein(int n, double *d, double *e, int m,  double  *w,
               int  *iblock,  int *isplit, doublecomplex *zz, int
               ldz, int *ifail, int *info) ;

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

     The maximum number of iterations allowed for each  eigenvec-
     tor  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  asso-
               ciated  with  the eigenvalue W(i) is stored in the
               i-th column of Z.  Any vector which fails to  con-
               verge  is  set to its current iterate after MAXITS
               iterations.  The imaginary parts of the  eigenvec-
               tors 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  ille-
               gal 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  itera-
               tions performed.

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

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