DSTEIN  -  compute  the  eigenvectors  of a real symmetric
       tridiagonal matrix T corresponding to specified  eigenval­
       ues, using inverse iteration


SYNOPSIS

       SUBROUTINE DSTEIN( 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(
                          * ), Z( LDZ, * )


PURPOSE

       DSTEIN 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).


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, 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 corre­
               sponding eigenvalues in W; IBLOCK(i)=1  if  eigen­
               value W(i) belongs to the first submatrix from the

               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) DOUBLE PRECISION 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.

       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 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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