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 (integer K, integer N, integer N1, double precision, dimension( * ) D,
       double precision, dimension( ldq, * ) Q, integer LDQ, integer, dimension( * ) INDXQ,
       double precision RHO, 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, integer INFO)
       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

Author

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