LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ claed8()

subroutine claed8 ( integer k,
integer n,
integer qsiz,
complex, dimension( ldq, * ) q,
integer ldq,
real, dimension( * ) d,
real rho,
integer cutpnt,
real, dimension( * ) z,
real, dimension( * ) dlambda,
complex, dimension( ldq2, * ) q2,
integer ldq2,
real, dimension( * ) w,
integer, dimension( * ) indxp,
integer, dimension( * ) indx,
integer, dimension( * ) indxq,
integer, dimension( * ) perm,
integer givptr,
integer, dimension( 2, * ) givcol,
real, dimension( 2, * ) givnum,
integer info )

CLAED8 used by CSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Download CLAED8 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> CLAED8 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
[out]K
!>          K is INTEGER
!>         Contains the number of non-deflated eigenvalues.
!>         This is the order of the related secular equation.
!>
[in]N
!>          N is INTEGER
!>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
!>
[in]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.
!>
[in,out]Q
!>          Q is COMPLEX 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.
!>
[in]LDQ
!>          LDQ is INTEGER
!>         The leading dimension of the array Q.  LDQ >= max( 1, N ).
!>
[in,out]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.
!>
[in,out]RHO
!>          RHO is REAL
!>         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 SLAED3.
!>
[in]CUTPNT
!>          CUTPNT is INTEGER
!>         Contains the location of the last eigenvalue in the leading
!>         sub-matrix.  MIN(1,N) <= CUTPNT <= N.
!>
[in]Z
!>          Z is REAL 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.
!>
[out]DLAMBDA
!>          DLAMBDA is REAL array, dimension (N)
!>         Contains a copy of the first K eigenvalues which will be used
!>         by SLAED3 to form the secular equation.
!>
[out]Q2
!>          Q2 is COMPLEX 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 SLAED7 in a matrix multiply (SGEMM) to update the new
!>         eigenvectors.
!>
[in]LDQ2
!>          LDQ2 is INTEGER
!>         The leading dimension of the array Q2.  LDQ2 >= max( 1, N ).
!>
[out]W
!>          W is REAL array, dimension (N)
!>         This will hold the first k values of the final
!>         deflation-altered z-vector and will be passed to SLAED3.
!>
[out]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.
!>
[out]INDX
!>          INDX is INTEGER array, dimension (N)
!>         This will contain the permutation used to sort the contents of
!>         D into ascending order.
!>
[in]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.
!>
[out]PERM
!>          PERM is INTEGER array, dimension (N)
!>         Contains the permutations (from deflation and sorting) to be
!>         applied to each eigenblock.
!>
[out]GIVPTR
!>          GIVPTR is INTEGER
!>         Contains the number of Givens rotations which took place in
!>         this subproblem.
!>
[out]GIVCOL
!>          GIVCOL is INTEGER array, dimension (2, N)
!>         Each pair of numbers indicates a pair of columns to take place
!>         in a Givens rotation.
!>
[out]GIVNUM
!>          GIVNUM is REAL array, dimension (2, N)
!>         Each number indicates the S value to be used in the
!>         corresponding Givens rotation.
!>
[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.