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NAME
     slaed9 - find the roots of the secular equation, as  defined
     by the values in D, Z, and RHO, between KSTART and KSTOP

SYNOPSIS
     SUBROUTINE SLAED9( K, KSTART, KSTOP,  N,  D,  Q,  LDQ,  RHO,
               DLAMDA, W, S, LDS, INFO )

     INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N

     REAL RHO

     REAL D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), W( * )



     #include <sunperf.h>

     void slaed9(int k, int kstart, int kstop, int n,  float  *d,
               float  *q,  int  ldq,  float  srho, float *dlamda,
               float *w, float *s, int lds, int *info) ;

PURPOSE
     SLAED9 finds the roots of the secular equation,  as  defined
     by  the  values  in D, Z, and RHO, between KSTART and KSTOP.
     It makes the appropriate calls to SLAED4 and then stores the
     new  matrix  of eigenvectors for use in calculating the next
     level of Z vectors.


ARGUMENTS
     K         (input) INTEGER
               The number of terms in the rational function to be
               solved by SLAED4.  K >= 0.

     KSTART    (input) INTEGER
               KSTOP   (input) INTEGER  The  updated  eigenvalues
               Lambda(I),  KSTART  <=  I  <= KSTOP are to be com-
               puted.  1 <= KSTART <= KSTOP <= K.

     N         (input) INTEGER
               The number of rows and columns in the Q matrix.  N
               >= K (delation may result in N > K).

     D         (output) REAL array, dimension (N)
               D(I) contains the updated eigenvalues  for  KSTART
               <= I <= KSTOP.

     Q         (workspace) REAL array, dimension (LDQ,N)

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

     RHO       (input) REAL
               The value of the parameter in the rank one  update
               equation.  RHO >= 0 required.

     DLAMDA    (input) REAL array, dimension (K)
               The first K elements of this array contain the old
               roots of the deflated updating problem.  These are
               the poles of the secular equation.

     W         (input) REAL array, dimension (K)
               The first K elements of  this  array  contain  the
               components of the deflation-adjusted updating vec-
               tor.

     S         (output) REAL array, dimension (LDS, K)
               Will contain  the  eigenvectors  of  the  repaired
               matrix  which will be stored for subsequent Z vec-
               tor calculation and multiplied by  the  previously
               accumulated eigenvectors to update the system.

     LDS       (input) INTEGER
               The leading dimension of S.  LDS >= max( 1, K ).

     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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