LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slaed8()

subroutine slaed8 ( integer icompq,
integer k,
integer n,
integer qsiz,
real, dimension( * ) d,
real, dimension( ldq, * ) q,
integer ldq,
integer, dimension( * ) indxq,
real rho,
integer cutpnt,
real, dimension( * ) z,
real, dimension( * ) dlambda,
real, dimension( ldq2, * ) q2,
integer ldq2,
real, dimension( * ) w,
integer, dimension( * ) perm,
integer givptr,
integer, dimension( 2, * ) givcol,
real, dimension( 2, * ) givnum,
integer, dimension( * ) indxp,
integer, dimension( * ) indx,
integer info )

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

Download SLAED8 + dependencies [TGZ] [ZIP] [TXT]

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
[in]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.
!>
[out]K
!>          K is INTEGER
!>         The number of non-deflated eigenvalues, and 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 orthogonal matrix used to reduce
!>         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
!>
[in,out]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.
!>
[in,out]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.
!>
[in]LDQ
!>          LDQ is INTEGER
!>         The leading dimension of the array Q.  LDQ >= max(1,N).
!>
[in]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.
!>
[in,out]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.
!>
[in]CUTPNT
!>          CUTPNT is INTEGER
!>         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 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.
!>
[out]DLAMBDA
!>          DLAMBDA is REAL array, dimension (N)
!>         A copy of the first K eigenvalues which will be used by
!>         SLAED3 to form the secular equation.
!>
[out]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.
!>
[in]LDQ2
!>          LDQ2 is INTEGER
!>         The leading dimension of the array Q2.  LDQ2 >= max(1,N).
!>
[out]W
!>          W is REAL array, dimension (N)
!>         The first k values of the final deflation-altered z-vector and
!>         will be passed to SLAED3.
!>
[out]PERM
!>          PERM is INTEGER array, dimension (N)
!>         The permutations (from deflation and sorting) to be applied
!>         to each eigenblock.
!>
[out]GIVPTR
!>          GIVPTR is INTEGER
!>         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]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.
!>
[out]INDX
!>          INDX is INTEGER array, dimension (N)
!>         The permutation used to sort the contents of D into ascending
!>         order.
!>
[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.
Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA