Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - merges the two sets of eigenvalues together into a single sorted set

SYNOPSIS

       SUBROUTINE SLAED2( K,  N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP,
                          COLTYP, INFO )

           INTEGER        INFO, K, LDQ, N, N1

           REAL           RHO

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

           REAL           D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), 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.

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

        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), (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    (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 N1 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.

        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.

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

        Q2     (output) REAL array, dimension (N1**2+(N-N1)**2)
               A copy of the first K eigenvectors which will be used by
               SLAED3 in a matrix multiply (SGEMM) to solve for the new
               eigenvectors.

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

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

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

FURTHER DETAILS

        Based on contributions by
           Jeff Rutter, Computer Science Division, University of California
           at Berkeley, USA
        Modified by Francoise Tisseur, University of Tennessee.

 LAPACK routine (version 3.2)               April 2011                            SLAED2(3lapack)