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## dlaed2()

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( * ) | dlambda,
|  | 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 DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

Download DLAED2 + dependencies [TGZ] [ZIP] [TXT]

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

  [out]

  K

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

  [in]

  N

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

  [in]

  N1

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

  [in,out]

  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.
      !>

  [in,out]

  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.
      !>

  [in]

  LDQ

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

  [in,out]

  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.
      !>

  [in,out]

  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.
      !>

  [in]

  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.
      !>

  [out]

  DLAMBDA

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

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  INDX

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

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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.

Contributors:
  Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
  Modified by Francoise Tisseur, University of Tennessee