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NAME
     zlaed8 - merge the two sets of eigenvalues together  into  a
     single sorted set

SYNOPSIS
     SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D,  RHO,  CUTPNT,  Z,
               DLAMDA,  Q2,  LDQ2,  W,  INDXP, INDX, INDXQ, PERM,
               GIVPTR, GIVCOL, GIVNUM, INFO )

     INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ

     DOUBLE PRECISION RHO

     INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ(  *  ),
               PERM( * )

     DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ),  W(  *
               ), Z( * )

     COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * )



     #include <sunperf.h>

     void zlaed8(int *k, int n, int qsiz, doublecomplex  *q,  int
               ldq,  double  *d, double *drho, int cutpnt, double
               *dz, double *dlamda, doublecomplex *q2, int  ldq2,
               double  *w, int *indxp, int *indx, int *indxq, int
               *perm, int *givptr, int *givcol,  double  *givnum,
               int *info);

PURPOSE
     ZLAED8 merges the two sets of eigenvalues  together  into  a
     single sorted set.  Then it tries to deflate the size of the
     problem.  There are two ways in which deflation  can  occur:
     when  two or more eigenvalues are close together or if there
     is a tiny element in the Z vector.  For each such occurrence
     the order of the related secular equation problem is reduced
     by one.


ARGUMENTS
     K         (output) INTEGER
               Contains the number of  non-deflated  eigenvalues.
               This is the order of the related secular equation.

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

     QSIZ      (input) INTEGER
               The dimension of the unitary matrix used to reduce
               the  dense  or  band  matrix  to tridiagonal form.
               QSIZ >= N if ICOMPQ = 1.

     Q         (input/output) COMPLEX*16 array, dimension (LDQ,N)
               On entry, Q contains the eigenvectors of the  par-
               tially  solved  system  which  has been previously
               updated in matrix multiplies with other  partially
               solved  eigensystems.   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, N ).

     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.

     RHO       (input/output) DOUBLE PRECISION
               Contains the off diagonal element associated  with
               the rank-1 cut which originally split the two sub-
               matrices which are now being  recombined.  RHO  is
               modified  during  the  computation  to  the  value
               required by DLAED3.

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

     Z         (input) DOUBLE PRECISION array, dimension (N)
               On input this vector contains the updating  vector
               (the  last row of the first sub-eigenvector matrix
               and the first row of  the  second  sub-eigenvector
               matrix).   The  contents of Z are destroyed during
               the updating process.

               DLAMDA (output) DOUBLE PRECISION array,  dimension
               (N)  Contains  a  copy  of the first K eigenvalues
               which will be used by DLAED3 to form  the  secular
               equation.

     Q2        (output) COMPLEX*16 array, dimension (LDQ2,N)
               If ICOMPQ = 0, Q2 is not  referenced.   Otherwise,
               Contains  a copy of the first K eigenvectors which
               will be  used  by  DLAED7  in  a  matrix  multiply
               (DGEMM) to update the new eigenvectors.

     LDQ2      (input) INTEGER
               The leading dimension of the array  Q2.   LDQ2  >=
               max( 1, N ).

     W         (output) DOUBLE PRECISION array, dimension (N)
               This will hold the first k  values  of  the  final
               deflation-altered  z-vector  and will be passed to
               DLAED3.

     INDXP     (workspace) INTEGER array, dimension (N)
               This will contain the permutation  used  to  place
               deflated  values  of D at the end of the array. On
               output INDXP(1:K)
               points   to   the   nondeflated    D-values    and
               INDXP(K+1:N) points to the deflated eigenvalues.

     INDX      (workspace) INTEGER array, dimension (N)
               This will contain the permutation used to sort the
               contents of D into ascending order.

     INDXQ     (input) INTEGER array, dimension (N)
               This contains  the  permutation  which  separately
               sorts  the  two  sub-problems  in D into ascending
               order.  Note that elements in the second  half  of
               this  permutation  must first have CUTPNT added to
               their values in order to be accurate.

     PERM      (output) INTEGER array, dimension (N)
               Contains  the  permutations  (from  deflation  and
               sorting) to be applied to each eigenblock.

               GIVPTR (output) INTEGER  Contains  the  number  of
               Givens rotations which took place in this subprob-
               lem.

               GIVCOL (output) INTEGER array,  dimension  (2,  N)
               Each  pair  of numbers indicates a pair of columns
               to take place in a Givens rotation.

               GIVNUM (output) DOUBLE PRECISION array,  dimension
               (2,  N)  Each  number  indicates the S value to be
               used in the corresponding Givens rotation.

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.

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