slaed2.f(3)

NAME
slaed2.f -

SYNOPSIS

  Functions/Subroutines
subroutine slaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO)
SLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation

  subroutine slaed2 (integerK, integerN, integerN1, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, realRHO, real, dimension( * )Z, real, dimension( * )DLAMDA, real, dimension( * )W, real, dimension( * )Q2, integer, dimension( * )INDX, integer, dimension( * )INDXC, integer, dimension( * )INDXP, integer, dimension( * )COLTYP, integerINFO)

SLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

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.

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 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

              Q is 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

              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 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

              Z is 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

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

    W

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

    Q2

              Q2 is 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

              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 slaed2.f.

Author

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