!>
!> 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.
!> 

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.
!> 

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