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CLAED8(l)			       )			     CLAED8(l)

NAME
       CLAED8  -  merge	 the  two  sets	 of eigenvalues together into a single
       sorted set

SYNOPSIS
       SUBROUTINE CLAED8( 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

	   REAL		  RHO

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

	   REAL		  D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), Z( * )

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

PURPOSE
       CLAED8 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 array, dimension (LDQ,N)
	      On entry, Q contains the eigenvectors of	the  partially	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) 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 ei‐
	      genvalues (those which were  deflated)  sorted  into  increasing
	      order.

       RHO    (input/output) REAL
	      Contains the off diagonal element associated with the rank-1 cut
	      which originally split the two submatrices which are  now	 being
	      recombined.  RHO is modified during the computation to the value
	      required by SLAED3.

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

       Z      (input) REAL 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) REAL array, dimension (N) Contains a copy of the
	      first  K	eigenvalues  which  will be used by SLAED3 to form the
	      secular equation.

       Q2     (output) COMPLEX 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 SLAED7 in a
	      matrix multiply (SGEMM) to update the new eigenvectors.

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

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

       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 subproblem.

	      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)	REAL array, dimension (2, N) Each number indi‐
	      cates the S value to be used in the corresponding	 Givens	 rota‐
	      tion.

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

LAPACK version 3.0		 15 June 2000			     CLAED8(l)
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