slaed2(3F)

NAME
     SLAED2 - merge the two sets of eigenvalues together into a single sorted
     set

SYNOPSIS
     SUBROUTINE SLAED2( K, N, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2,
                        LDQ2, INDXC, W, INDXP, INDX, COLTYP, INFO )

         INTEGER        CUTPNT, INFO, K, LDQ, LDQ2, N

         REAL           RHO

         INTEGER        COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), INDXQ(
                        * )

         REAL           D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2, * ), W( *
                        ), Z( * )

PURPOSE
     SLAED2 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.


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

     N      (input) INTEGER
            The dimension of the symmetric tridiagonal matrix.  N >= 0.

     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
            eigenvalues (those which were deflated) sorted into increasing
            order.

     Q      (input/output) REAL array, dimension (LDQ, N)
            On entry, Q contains the eigenvectors of two submatrices in the
            two square blocks with corners at (1,1), (CUTPNT,CUTPNT) and
            (CUTPNT+1, CUTPNT+1), (N,N).  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).
     INDXQ  (input/output) 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.
            Destroyed on exit.

     RHO    (input/output) REAL
            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 SLAED3.

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

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

     Q2     (output) REAL array, dimension (LDQ2, N)
            A copy of the first K eigenvectors which will be used by SLAED3 in
            a matrix multiply (SGEMM) to solve for the new eigenvectors.   Q2
            is arranged into three blocks.  The first block contains non-zero
            elements only at and above CUTPNT, the second contains non-zero
            elements only below CUTPNT, and the third is dense.

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

     INDXC  (output) 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 CUTPNT, the second contains non-zero
            elements only below CUTPNT, and the third is dense.

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

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

            COLTYP (workspace/output) 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 : non-zero in the lower half only;
            3 : dense;
            4 : deflated.  On exit, COLTYP(i) is the number of columns of type
            i, for i=1 to 4 only.

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