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PDSTEDC(l)                             )                            PDSTEDC(l)


NAME

       PDSTEDC - tridiagonal matrix in parallel, using the divide and conquer
       algorithm


SYNOPSIS

       SUBROUTINE PDSTEDC( COMPZ, N, D, E, Q, IQ, JQ, DESCQ, WORK, LWORK,
                           IWORK, LIWORK, INFO )
           CHARACTER COMPZ
           INTEGER INFO, IQ, JQ, LIWORK, LWORK, N
           INTEGER DESCQ( * ), IWORK( * )
           DOUBLE PRECISION D( * ), E( * ), Q( * ), WORK( * )


PURPOSE

       symmetric tridiagonal matrix in parallel, using the divide and conquer
       algorithm.  This code makes very mild assumptions about floating point
       arithmetic. It will work on machines with a guard digit in
       add/subtract, or on those binary machines without guard digits which
       subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.  It could
       conceivably fail on hexadecimal or decimal machines without guard
       digits, but we know of none.  See DLAED3 for details.


ARGUMENTS

       COMPZ   (input) CHARACTER*1
               = 'N':  Compute eigenvalues only.    (NOT IMPLEMENTED YET)
               = 'I':  Compute eigenvectors of tridiagonal matrix also.
               = 'V':  Compute eigenvectors of original dense symmetric matrix
               also.  On entry, Z contains the orthogonal matrix used to
               reduce the original matrix to tridiagonal form.            (NOT
               IMPLEMENTED YET)

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

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

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

       Q       (local output) DOUBLE PRECISION array,
               local dimension ( LLD_Q, LOCc(JQ+N-1)) Q  contains the
               orthonormal eigenvectors of the symmetric tridiagonal matrix.
               On output, Q is distributed across the P processes in block
               cyclic format.

       IQ      (global input) INTEGER
               Q's global row index, which points to the beginning of the
               submatrix which is to be operated on.

       JQ      (global input) INTEGER
               Q's global column index, which points to the beginning of the
               submatrix which is to be operated on.

       DESCQ   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix Z.

       WORK    (local workspace/output) DOUBLE PRECISION array,
               dimension (LWORK) On output, WORK(1) returns the workspace
               needed.

       LWORK   (local input/output) INTEGER,
               the dimension of the array WORK.  LWORK = 6*N + 2*NP*NQ NP =
               NUMROC( N, NB, MYROW, DESCQ( RSRC_ ), NPROW ) NQ = NUMROC( N,
               NB, MYCOL, DESCQ( CSRC_ ), NPCOL )

               If LWORK = -1, the LWORK is global input and a workspace query
               is assumed; the routine only calculates the minimum size for
               the WORK array.  The required workspace is returned as the
               first element of WORK and no error message is issued by
               PXERBLA.

       IWORK   (local workspace/output) INTEGER array, dimension (LIWORK)
               On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

       LIWORK  (input) INTEGER
               The dimension of the array IWORK.  LIWORK = 2 + 7*N + 8*NPCOL

       INFO    (global output) INTEGER
               = 0:  successful exit
               < 0:  If the i-th argument is an array and the j-entry had an
               illegal value, then INFO = -(i*100+j), if the i-th argument is
               a scalar and had an illegal value, then INFO = -i.  > 0:  The
               algorithm failed to compute the INFO/(N+1) th eigenvalue while
               working on the submatrix lying in global rows and columns
               mod(INFO,N+1).


FURTHER DETAILS

       Contributed by Francoise Tisseur, University of Manchester.

       Reference:  F. Tisseur and J. Dongarra, "A Parallel Divide and
                   Conquer Algorithm for the Symmetric Eigenvalue Problem
                   on Distributed Memory Architectures",
                   SIAM J. Sci. Comput., 6:20 (1999), pp. 2223--2236.
                   (see also LAPACK Working Note 132)
                     http://www.netlib.org/lapack/lawns/lawn132.ps

ScaLAPACK version 1.7           13 August 2001                      PDSTEDC(l)

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