PSSTEDC(3)    ScaLAPACK routine of NEC Numeric Library Collection   PSSTEDC(3)



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

SYNOPSIS
       SUBROUTINE PSSTEDC( 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( * )

           REAL            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/sub-
       tract, 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 conceiv-
       ably fail on hexadecimal or decimal machines without guard digits,  but
       we know of none.  See SLAED3 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) REAL 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) REAL array, dimension (N-1)
               On  entry,  the subdiagonal elements of the tridiagonal matrix.
               On exit, E has been destroyed.

       Q       (local output) REAL 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 sub-
               matrix 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) REAL 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 routine               31 October 2017                     PSSTEDC(3)