CXML
        	    
LAPACK version 3.0
zlaed8(3)

PURPOSE
  ZLAED8 - merge the two sets of eigenvalues together into a single sorted
  set

SYNTAX
  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, * )

DESCRIPTION
  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 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) 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 submatrices 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 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) 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 illegal value.