PDLAED3(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDLAED3(3)



NAME
       PDLAED3  -  find  the  roots of the secular equation, as defined by the
       values in D, W, and RHO, between 1 and K

SYNOPSIS
       SUBROUTINE PDLAED3( ICTXT, K, N, NB, D, DROW, DCOL, RHO, DLAMDA, W,  Z,
                           U,  LDU,  BUF,  INDX, INDCOL, INDROW, INDXR, INDXC,
                           CTOT, NPCOL, INFO )

           INTEGER         DCOL, DROW, ICTXT, INFO, K, LDU, N, NB, NPCOL

           DOUBLE          PRECISION RHO

           INTEGER         CTOT( 0: NPCOL-1, 4 ), INDCOL( * ),  INDROW(  *  ),
                           INDX( * ), INDXC( * ), INDXR( * )

           DOUBLE          PRECISION  BUF( * ), D( * ), DLAMDA( * ), U( LDU, *
                           ), W( * ), Z( * )

PURPOSE
       PDLAED3 finds the roots of the secular equation, as defined by the val-
       ues  in  D, W, and RHO, between 1 and K. It makes the appropriate calls
       to SLAED4

       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.


ARGUMENTS
       ICTXT  (global input) INTEGER
              The  BLACS  context handle, indicating the global context of the
              operation on the matrix. The context itself is global.

       K      (output) INTEGER
              The number of non-deflated eigenvalues, and  the  order  of  the
              related secular equation. 0 <= K <=N.

       N      (input) INTEGER
              The dimension of the symmetric tridiagonal matrix.  N >= 0.

       NB      (global input) INTEGER
               The  blocking  factor  used  to  distribute  the columns of the
               matrix. NB >= 1.

       D      (input/output) DOUBLE PRECISION array, dimension (N)
              On entry, D contains the eigenvalues of the two  submatrices  to
              be  combined.   On  exit,  D contains the trailing (N-K) updated
              eigenvalues (those which were deflated) sorted  into  increasing
              order.

       DROW   (global input) INTEGER
              The process row over which the first row of the matrix D is dis-
              tributed. 0 <= DROW < NPROW.

       DCOL   (global input) INTEGER
              The process column over which the first column of the  matrix  D
              is distributed. 0 <= DCOL < NPCOL.

       Q      (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
              On  entry, Q contains the eigenvectors of two submatrices in the
              two square blocks with corners  at  (1,1),  (N1,N1)  and  (N1+1,
              N1+1),  (N,N).   On  exit, Q contains the trailing (N-K) updated
              eigenvectors  (those  which  were  deflated)  in  its  last  N-K
              columns.

       LDQ    (input) INTEGER
              The leading dimension of the array Q.  LDQ >= max(1,NQ).

       RHO    (global input/output) DOUBLE PRECISION
              On  entry,  the  off-diagonal element associated with the rank-1
              cut which originally split the two  submatrices  which  are  now
              being  recombined.   On exit, RHO has been modified to the value
              required by PDLAED3.

              DLAMDA (global output) DOUBLE PRECISION array, dimension  (N)  A
              copy  of the first K eigenvalues which will be used by SLAED3 to
              form the secular equation.

       W      (global output) DOUBLE PRECISION array, dimension (N)
              The first k values of the final deflation-altered z-vector which
              will be passed to SLAED3.

       Z      (global input) DOUBLE PRECISION array, dimension (N)
              On  entry,  Z  contains the updating vector (the last row of the
              first sub-eigenvector matrix and the first  row  of  the  second
              sub-eigenvector  matrix).   On exit, the contents of Z have been
              destroyed by the updating process.

       U     (global output) DOUBLE PRECISION array
             global dimension (N, N), local dimension (LDU, NQ).  Q   contains
             the orthonormal eigenvectors of the symmetric tridiagonal matrix.

       LDU    (input) INTEGER
              The leading dimension of the array U.

       QBUF   (workspace) DOUBLE PRECISION array, dimension 3*N

       INDX   (workspace) INTEGER array, dimension (N)
              The permutation used to sort the contents of DLAMDA into ascend-
              ing order.

              INDCOL (workspace) INTEGER array, dimension (N)

              INDROW (workspace) INTEGER array, dimension (N)

              INDXR (workspace) INTEGER array, dimension (N)

              INDXC (workspace) INTEGER array, dimension (N)

       CTOT   (workspace) INTEGER array, dimension( NPCOL, 4)

       NPCOL   (global input) INTEGER
               The  total  number of columns over which the distributed subma-
               trix is distributed.

       INFO   (output) INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  The algorithm failed to compute the ith eigenvalue.



ScaLAPACK routine               31 October 2017                     PDLAED3(3)