NAME

       DSTEQR2 - i a modified version of LAPACK routine DSTEQR

SYNOPSIS

       SUBROUTINE DSTEQR2( COMPZ, N, D, E, Z, LDZ, NR, WORK, INFO )

           CHARACTER       COMPZ

           INTEGER         INFO, LDZ, N, NR

           DOUBLE          PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       DSTEQR2  is a modified version of LAPACK routine DSTEQR.  DSTEQR2 computes all eigenvalues
       and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit  QL  or
       QR  method.   DSTEQR2  is  modified  from  DSTEQR  to allow each ScaLAPACK process running
       DSTEQR2 to perform updates on a distributed matrix Q.  Proper  usage  of  DSTEQR2  can  be
       gleaned from examination of ScaLAPACK's PDSYEV.

ARGUMENTS

       COMPZ   (input) CHARACTER*1
               = 'N':  Compute eigenvalues only.
               = 'I':  Compute eigenvalues and eigenvectors of the tridiagonal matrix.  Z must be
               initialized to the identity matrix by PDLASET or DLASET  prior  to  entering  this
               subroutine.

       N       (input) INTEGER
               The order of the matrix.  N >= 0.

       D       (input/output) DOUBLE PRECISION array, dimension (N)
               On  entry, the diagonal elements of the tridiagonal matrix.  On exit, if INFO = 0,
               the eigenvalues in ascending order.

       E       (input/output) DOUBLE PRECISION array, dimension (N-1)
               On entry, the (n-1) subdiagonal elements of the tridiagonal matrix.   On  exit,  E
               has been destroyed.

       Z       (local input/local output) DOUBLE PRECISION array, global
               dimension  (N,  N),  local dimension (LDZ, NR).  On entry, if  COMPZ = 'V', then Z
               contains the orthogonal matrix used in the  reduction  to  tridiagonal  form.   On
               exit,  if  INFO = 0, then if  COMPZ = 'V', Z contains the orthonormal eigenvectors
               of the original symmetric matrix, and if COMPZ = 'I', Z contains  the  orthonormal
               eigenvectors  of  the symmetric tridiagonal matrix.  If COMPZ = 'N', then Z is not
               referenced.

       LDZ     (input) INTEGER
               The leading dimension of the array Z.  LDZ >= 1, and if eigenvectors are  desired,
               then  LDZ >= max(1,N).

       NR      (input) INTEGER
               NR  = MAX(1, NUMROC( N, NB, MYPROW, 0, NPROCS ) ).  If COMPZ = 'N', then NR is not
               referenced.

       WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
               If COMPZ = 'N', then WORK is not referenced.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value
               > 0:  the algorithm has failed to find all the eigenvalues  in  a  total  of  30*N
               iterations; if INFO = i, then i elements of E have not converged to zero; on exit,
               D and  E  contain  the  elements  of  a  symmetric  tridiagonal  matrix  which  is
               orthogonally similar to the original matrix.