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dlaed2.f(3)			    LAPACK			   dlaed2.f(3)

NAME
       dlaed2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
	   INDX, INDXC, INDXP, COLTYP, INFO)
	   DLAED2 used by sstedc. Merges eigenvalues and deflates secular
	   equation. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation
   subroutine dlaed2 (integerK, integerN, integerN1, double precision,
       dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ,
       integer, dimension( * )INDXQ, double precisionRHO, double precision,
       dimension( * )Z, double precision, dimension( * )DLAMDA, double
       precision, dimension( * )W, double precision, dimension( * )Q2,
       integer, dimension( * )INDX, integer, dimension( * )INDXC, integer,
       dimension( * )INDXP, integer, dimension( * )COLTYP, integerINFO)
       DLAED2 used by sstedc. Merges eigenvalues and deflates secular
       equation. Used when the original matrix is tridiagonal.

       Purpose:

	    DLAED2 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.

       Parameters:
	   K

		     K is INTEGER
		    The number of non-deflated eigenvalues, and the order of the
		    related secular equation. 0 <= K <=N.

	   N

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

	   N1

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

	   D

		     D is 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.

	   Q

		     Q is DOUBLE PRECISION 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

		     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 N1 added to their
		    values. Destroyed on exit.

	   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.

	   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 have been 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.

	   W

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

	   Q2

		     Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
		    A copy of the first K eigenvectors which will be used by
		    DLAED3 in a matrix multiply (DGEMM) to solve for the new
		    eigenvectors.

	   INDX

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

	   INDXC

		     INDXC is 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 second contains
		    non-zero elements only below N1, and the third is dense.

	   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.

	   COLTYP

		     COLTYP is 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

		     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
	    Modified by Francoise Tisseur, University of Tennessee

       Definition at line 212 of file dlaed2.f.

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

Version 3.4.2			Tue Sep 25 2012			   dlaed2.f(3)
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