slaed8.f(3)

NAME
slaed8.f -

SYNOPSIS

  Functions/Subroutines
subroutine slaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
SLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

  subroutine slaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, realRHO, integerCUTPNT, real, dimension( * )Z, real, dimension( * )DLAMDA, real, dimension( ldq2, * )Q2, integerLDQ2, real, dimension( * )W, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( 2, * )GIVCOL, real, dimension( 2, * )GIVNUM, integer, dimension( * )INDXP, integer, dimension( * )INDX, integerINFO)

SLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Purpose:

     SLAED8 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:
    ICOMPQ

              ICOMPQ is INTEGER
              = 0:  Compute eigenvalues only.
              = 1:  Compute eigenvectors of original dense symmetric matrix
                    also.  On entry, Q contains the orthogonal matrix used
                    to reduce the original matrix to tridiagonal form.

    K

              K is INTEGER
             The number of non-deflated eigenvalues, and 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 orthogonal matrix used to reduce
             the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

    D

              D is REAL array, dimension (N)
             On entry, the eigenvalues of the two submatrices to be
             combined.  On exit, the trailing (N-K) updated eigenvalues
             (those which were deflated) sorted into increasing order.

    Q

              Q is REAL array, dimension (LDQ,N)
             If ICOMPQ = 0, Q is not referenced.  Otherwise,
             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).

    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 CUTPNT added to
             their values in order to be accurate.

    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.

    CUTPNT

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

    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 are 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.

    Q2

              Q2 is REAL array, dimension (LDQ2,N)
             If ICOMPQ = 0, Q2 is not referenced.  Otherwise,
             a copy of the first K eigenvectors which will be used by
             SLAED7 in a matrix multiply (SGEMM) to update the new
             eigenvectors.

    LDQ2

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

    W

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

    PERM

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

    GIVPTR

              GIVPTR is INTEGER
             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 REAL array, dimension (2, N)
             Each number indicates the S value to be used in the
             corresponding Givens rotation.

    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.

    INDX

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

    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

Definition at line 242 of file slaed8.f.

Author

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