SRC/zlaed8.f(3)

NAME
SRC/zlaed8.f

SYNOPSIS

  Functions/Subroutines
subroutine zlaed8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlambda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)
ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

  subroutine zlaed8 (integer k, integer n, integer qsiz, complex*16, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) d, double precision rho, integer cutpnt, double precision, dimension( * ) z, double precision, dimension( * ) dlambda, complex*16, dimension( ldq2, * ) q2, integer ldq2, double precision, dimension( * ) w, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer, dimension( * ) indxq, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, integer info)

ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Purpose:

     ZLAED8 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 element 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
             Contains the number of non-deflated eigenvalues.
             This is the order of the related secular equation.

    N

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

    QSIZ

              QSIZ is INTEGER
             The dimension of the unitary matrix used to reduce
             the dense or band matrix to tridiagonal form.
             QSIZ >= N if ICOMPQ = 1.

    Q

              Q is COMPLEX*16 array, dimension (LDQ,N)
             On entry, Q contains the eigenvectors of the partially solved
             system which has been previously updated in matrix
             multiplies with other partially solved eigensystems.
             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 ).

    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.

    RHO

              RHO is DOUBLE PRECISION
             Contains the off diagonal element associated with the rank-1
             cut which originally split the two submatrices which are now
             being recombined. RHO is modified during the computation to
             the value required by DLAED3.

    CUTPNT

              CUTPNT is INTEGER
             Contains the location of the last eigenvalue in the leading
             sub-matrix.  MIN(1,N) <= CUTPNT <= N.

    Z

              Z is DOUBLE PRECISION array, dimension (N)
             On input this vector contains the updating vector (the last
             row of the first sub-eigenvector matrix and the first row of
             the second sub-eigenvector matrix).  The contents of Z are
             destroyed during the updating process.

    DLAMBDA

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

    Q2

              Q2 is COMPLEX*16 array, dimension (LDQ2,N)
             If ICOMPQ = 0, Q2 is not referenced.  Otherwise,
             Contains a copy of the first K eigenvectors which will be used
             by DLAED7 in a matrix multiply (DGEMM) to update the new
             eigenvectors.

    LDQ2

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

    W

              W is DOUBLE PRECISION array, dimension (N)
             This will hold the first k values of the final
             deflation-altered z-vector and will be passed to DLAED3.

    INDXP

              INDXP is INTEGER array, dimension (N)
             This will contain the permutation used to place deflated
             values of D at the end of the array. On output INDXP(1:K)
             points to the nondeflated D-values and INDXP(K+1:N)
             points to the deflated eigenvalues.

    INDX

              INDX is INTEGER array, dimension (N)
             This will contain the permutation used to sort the contents of
             D into ascending order.

    INDXQ

              INDXQ is INTEGER array, dimension (N)
             This contains 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 in order to be accurate.

    PERM

              PERM is INTEGER array, dimension (N)
             Contains the permutations (from deflation and sorting) to be
             applied to each eigenblock.

    GIVPTR

              GIVPTR is INTEGER
             Contains the number of Givens rotations which took place in
             this subproblem.

    GIVCOL

              GIVCOL is INTEGER array, dimension (2, N)
             Each pair of numbers indicates a pair of columns to take place
             in a Givens rotation.

    GIVNUM

              GIVNUM is DOUBLE PRECISION array, dimension (2, N)
             Each number indicates the S value to be used in the
             corresponding Givens rotation.

    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.

Definition at line 225 of file zlaed8.f.

Author

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