PDLAED1(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDLAED1(3)



NAME
       PDLAED1  -  compute  the updated eigensystem of a diagonal matrix after
       modification by a rank-one symmetric matrix,

SYNOPSIS
       SUBROUTINE PDLAED1( N, N1, D, ID, Q, IQ, JQ, DESCQ, RHO,  WORK,  IWORK,
                           INFO )

           INTEGER         ID, INFO, IQ, JQ, N, N1

           DOUBLE          PRECISION RHO

           INTEGER         DESCQ( * ), IWORK( * )

           DOUBLE          PRECISION D( * ), Q( * ), WORK( * )

PURPOSE
       PDLAED1  computes  the  updated  eigensystem of a diagonal matrix after
       modification by a rank-one symmetric matrix, in parallel.

         T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)

          where Z = Q'u, u is a vector of length N with ones in the
          N1 and N1 + 1 th elements and zeros elsewhere.

          The eigenvectors of the original matrix are stored in Q, and the
          eigenvalues are in D.  The algorithm consists of three stages:

             The first stage consists of deflating the size of the problem
             when there are multiple eigenvalues or if there is a zero in
             the Z vector.  For each such occurence the dimension of the
             secular equation problem is reduced by one.  This stage is
             performed by the routine PDLAED2.

             The second stage consists of calculating the updated
             eigenvalues. This is done by finding the roots of the secular
             equation via the routine SLAED4 (as called by PDLAED3).
             This routine also calculates the eigenvectors of the current
             problem.

             The final stage consists of computing the updated eigenvectors
             directly using the updated eigenvalues.  The eigenvectors for
             the current problem are multiplied with the eigenvectors from
             the overall problem.


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

       N1      (input) INTEGER
               The location of the last eigenvalue in the leading  sub-matrix.
               min(1,N) <= N1 <= N.

       D       (global input/output) DOUBLE PRECISION array, dimension (N)
               On  entry,the  eigenvalues  of the rank-1-perturbed matrix.  On
               exit, the eigenvalues of the repaired matrix.

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

       Q       (local output) DOUBLE PRECISION array,
               global dimension (N, N), local dimension ( LLD_Q, LOCc(JQ+N-1))
               Q  contains  the  orthonormal  eigenvectors  of  the  symmetric
               tridiagonal matrix.

       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.

       RHO    (input) DOUBLE PRECISION
              The subdiagonal entry used to create the rank-1 modification.

       WORK    (local workspace/output) DOUBLE PRECISION array,
               dimension 6*N + 2*NP*NQ

       IWORK   (local workspace/output) INTEGER array,
               dimension 7*N + 8*NPCOL + 2

       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 ith eigenvalue.



ScaLAPACK routine               31 October 2017                     PDLAED1(3)