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SLAED2(l)					)					SLAED2(l)

NAME
       SLAED2 - merge the two sets of eigenvalues together into a single sorted set

SYNOPSIS
       SUBROUTINE SLAED2( K,  N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP,
			  COLTYP, INFO )

	   INTEGER	  INFO, K, LDQ, N, N1

	   REAL 	  RHO

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

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

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  equa-
	      tion. 0 <= K <=N.

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

       N1     (input) INTEGER
	      The  location  of the last eigenvalue in the leading sub-matrix.	min(1,N) <= N1 <=
	      N/2.

       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 submatrices in the two  square  blocks
	      with  corners  at  (1,1), (N1,N1) and (N1+1, N1+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
	      N1 added to their values. Destroyed on exit.

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

       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  con-
	      tents 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.

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

       Q2     (output) REAL array, dimension (N1**2+(N-N1)**2)
	      A  copy of the first K eigenvectors which will be used by SLAED3 in a matrix multi-
	      ply (SGEMM) to solve for the new eigenvectors.

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

       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 N1, the sec-
	      ond contains non-zero elements only below N1, and the third is dense.

       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 eigenvalues.

	      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 : dense;
	      3 : non-zero in the lower half only;
	      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 illegal value.

FURTHER DETAILS
       Based on contributions by
	  Jeff Rutter, Computer Science Division, University of California
	  at Berkeley, USA
       Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0			   15 June 2000 				SLAED2(l)
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