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NAME
     dlaed1 - compute  the  updated  eigensystem  of  a  diagonal
     matrix after modification by a rank-one symmetric matrix

SYNOPSIS
     SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO,  CUTPNT,  WORK,
               IWORK, INFO )

     INTEGER CUTPNT, INFO, LDQ, N

     DOUBLE PRECISION RHO

     INTEGER INDXQ( * ), IWORK( * )

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



     #include <sunperf.h>

     void dlaed1(int n,  double  *d,  double  *q,  int  ldq,  int
               *indxq, double drho, int cutpnt, int *info) ;

PURPOSE
     DLAED1 computes the updated eigensystem of a diagonal matrix
     after  modification  by  a  rank-one symmetric matrix.  This
     routine is used only for the eigenproblem which requires all
     eigenvalues   and  eigenvectors  of  a  tridiagonal  matrix.
     DLAED7 handles the case in which eigenvalues only or  eigen-
     values  and  eigenvectors  of a full symmetric matrix (which
     was reduced to tridiagonal form) are desired.

       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
        CUTPNT and CUTPNT + 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 DLAED2.
           The second stage consists of calculating the updated
           eigenvalues. This is done by finding the roots of  the
     secular
           equation via the routine DLAED4 (as called by SLAED3).
           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 eigenvec-
     tors for
           the current problem are multiplied with the  eigenvec-
     tors from
           the overall problem.


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

     D         (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.

     Q         (input/output) DOUBLE PRECISION  array,  dimension
               (LDQ,N)
               On entry, the eigenvectors of the rank-1-perturbed
               matrix.  On exit, the eigenvectors of the repaired
               tridiagonal matrix.

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

     INDXQ     (input/output) INTEGER array, dimension (N)
               On entry, the permutation which  separately  sorts
               the two subproblems in D into ascending order.  On
               exit, the permutation which will  reintegrate  the
               subproblems back into sorted order, i.e. D( INDXQ(
               I = 1, N ) ) will be in ascending order.

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

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

     WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
               (3*N+2*N**2)

     IWORK     (workspace) INTEGER array, dimension (4*N)

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.
               > 0:  if INFO = 1, an eigenvalue did not converge

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