ZSTEIN  -  compute  the  eigenvectors  of a real symmetric
       tridiagonal matrix T corresponding to specified  eigenval­
       ues, 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 eigenval­
       ues, using inverse iteration.  The maximum number of iter­
       ations  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

               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  corre­
               sponding  eigenvalues  in W; IBLOCK(i)=1 if eigen­
               value 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


               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.


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