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dlaed8.f(3)				      LAPACK				      dlaed8.f(3)

NAME
       dlaed8.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2,
	   W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
	   DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the
	   original matrix is dense.

Function/Subroutine Documentation
   subroutine dlaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, double precision,
       dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( *
       )INDXQ, double precisionRHO, integerCUTPNT, double precision, dimension( * )Z, double
       precision, dimension( * )DLAMDA, double precision, dimension( ldq2, * )Q2, integerLDQ2,
       double precision, dimension( * )W, integer, dimension( * )PERM, integerGIVPTR, integer,
       dimension( 2, * )GIVCOL, double precision, dimension( 2, * )GIVNUM, integer, dimension( *
       )INDXP, integer, dimension( * )INDX, integerINFO)
       DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the
       original matrix is dense.

       Purpose:

	    DLAED8 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.

       Parameters:
	   ICOMPQ

		     ICOMPQ is INTEGER
		     = 0:  Compute eigenvalues only.
		     = 1:  Compute eigenvectors of original dense symmetric matrix
			   also.  On entry, Q contains the orthogonal matrix used
			   to reduce the original matrix to tridiagonal form.

	   K

		     K is INTEGER
		    The number of non-deflated eigenvalues, and the order of the
		    related secular equation.

	   N

		     N is INTEGER
		    The dimension of the symmetric tridiagonal matrix.	N >= 0.

	   QSIZ

		     QSIZ is INTEGER
		    The dimension of the orthogonal matrix used to reduce
		    the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		    On entry, the eigenvalues of the two submatrices to be
		    combined.  On exit, the trailing (N-K) updated eigenvalues
		    (those which were deflated) sorted into increasing order.

	   Q

		     Q is DOUBLE PRECISION array, dimension (LDQ,N)
		    If ICOMPQ = 0, Q is not referenced.  Otherwise,
		    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

		     LDQ is INTEGER
		    The leading dimension of the array Q.  LDQ >= max(1,N).

	   INDXQ

		     INDXQ is 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 in order to be accurate.

	   RHO

		     RHO is DOUBLE PRECISION
		    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
		    DLAED3.

	   CUTPNT

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

	   Z

		     Z is DOUBLE PRECISION 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 are destroyed by the updating
		    process.

	   DLAMDA

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

	   Q2

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

	   LDQ2

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

	   W

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

	   PERM

		     PERM is INTEGER array, dimension (N)
		    The permutations (from deflation and sorting) to be applied
		    to each eigenblock.

	   GIVPTR

		     GIVPTR is INTEGER
		    The number of Givens rotations which took place in this
		    subproblem.

	   GIVCOL

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

	   GIVNUM

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

	   INDXP

		     INDXP is 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.

	   INDX

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

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

       Definition at line 242 of file dlaed8.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlaed8.f(3)
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