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NAME
     slaed2 - merge the two sets of eigenvalues together  into  a
     single sorted set

SYNOPSIS
     SUBROUTINE SLAED2( K, N, D, Q, LDQ, INDXQ, RHO,  CUTPNT,  Z,
               DLAMDA,  Q2,  LDQ2, INDXC, W, INDXP, INDX, COLTYP,
               INFO )

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

     REAL RHO

     INTEGER COLTYP( * ), INDX( * ), INDXC(  *  ),  INDXP(  *  ),
               INDXQ( * )

     REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2, * ),  W(  *
               ), Z( * )



     #include <sunperf.h>

     void slaed2(int *k, int n, float *d, float *q, int ldq,  int
               *indxq,  float *srho, int cutpnt, float *sz, float
               *dlamda, float *q2, int ldq2,  int  *indxc,  float
               *w, int *indxp, int *indx, int *coltyp, int *info)
               ;

PURPOSE
     SLAED2 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 entry in the Z vector.  For each  such  occurrence
     the order of the related secular equation problem is reduced
     by one.


ARGUMENTS
     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.

     D         (input/output) REAL 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.

     Q         (input/output) REAL array, dimension (LDQ, N)
               On entry, Q contains the eigenvectors of two  sub-
               matrices  in the two square blocks with corners at
               (1,1), (CUTPNT,CUTPNT) and  (CUTPNT+1,  CUTPNT+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,N).

     INDXQ     (input/output) INTEGER array, dimension (N)
               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. Des-
               troyed on exit.

     RHO       (input/output) REAL
               On entry, the off-diagonal element associated with
               the rank-1 cut which originally split the two sub-
               matrices which are now being recombined.  On exit,
               RHO  has  been  modified  to the value required by
               SLAED3.

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

     Z         (input) REAL 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.

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

     Q2        (output) REAL array, dimension (LDQ2, N)
               A copy of the first K eigenvectors which  will  be
               used  by  SLAED3  in  a matrix multiply (SGEMM) to
               solve for the new eigenvectors.   Q2  is  arranged
               into  three blocks.  The first block contains non-
               zero elements only at and above CUTPNT, the second
               contains  non-zero elements only below CUTPNT, and
               the third is dense.

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

     INDXC     (output) INTEGER array, dimension (N)
               The permutation used to arrange the columns of the
               deflated  Q  matrix  into three groups:  the first
               group contains non-zero elements only at and above
               CUTPNT, the second contains non-zero elements only
               below CUTPNT, and the third is dense.

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

     INDXP     (workspace) INTEGER array, dimension (N)
               The permutation used to place deflated values of D
               at the end of the array.  INDXP(1:K) points to the
               nondeflated D-values
               and INDXP(K+1:N) points  to  the  deflated  eigen-
               values.

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

               COLTYP (workspace/output) INTEGER array, dimension
               (N)  During execution, a label which will indicate
               which of the following types a column  in  the  Q2
               matrix is:
               1 : non-zero in the upper half only;
               2 : non-zero in the lower half only;
               3 : dense;
               4 : deflated.  On exit, COLTYP(i) is the number of
               columns of type i, for i=1 to 4 only.

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

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