zlaed8.f - Man Page

subroutine zlaed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO)
ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

ZLAED8 used by sstedc. 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.

DLAMDA

          DLAMDA 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.

Date:

December 2016

Definition at line 230 of file zlaed8.f.