
CLAED8(l) ) CLAED8(l)
NAME
CLAED8  merge the two sets of eigenvalues together into a single sorted set
SYNOPSIS
SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP,
INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO )
INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ
REAL RHO
INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ( * ), PERM( * )
REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), Z( * )
COMPLEX Q( LDQ, * ), Q2( LDQ2, * )
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.
ARGUMENTS
K (output) INTEGER
Contains the number of nondeflated eigenvalues. This is the order of the related
secular equation.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
QSIZ (input) INTEGER
The dimension of the unitary matrix used to reduce the dense or band matrix to
tridiagonal form. QSIZ >= N if ICOMPQ = 1.
Q (input/output) 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 (NK) updated eigenvectors (those which were
deflated) in its last NK columns.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
D (input/output) REAL array, dimension (N)
On entry, D contains the eigenvalues of the two submatrices to be combined. On
exit, D contains the trailing (NK) updated eigenvalues (those which were deflated)
sorted into increasing order.
RHO (input/output) REAL
Contains the off diagonal element associated with the rank1 cut which originally
split the two submatrices which are now being recombined. RHO is modified during
the computation to the value required by SLAED3.
CUTPNT (input) INTEGER Contains the location of the last eigenvalue in the leading
submatrix. MIN(1,N) <= CUTPNT <= N.
Z (input) 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 subeigenvector matrix). The
contents of Z are destroyed during the updating process.
DLAMDA (output) REAL array, dimension (N) Contains a copy of the first K eigenval
ues which will be used by SLAED3 to form the secular equation.
Q2 (output) 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.
LDQ2 (input) INTEGER
The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
W (output) REAL array, dimension (N)
This will hold the first k values of the final deflationaltered zvector and will
be passed to SLAED3.
INDXP (workspace) 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 Dvalues and INDXP(K+1:N) points to the deflated eigen
values.
INDX (workspace) INTEGER array, dimension (N)
This will contain the permutation used to sort the contents of D into ascending
order.
INDXQ (input) INTEGER array, dimension (N)
This contains the permutation which separately sorts the two subproblems 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 (output) INTEGER array, dimension (N)
Contains the permutations (from deflation and sorting) to be applied to each eigen
block.
GIVPTR (output) INTEGER Contains the number of Givens rotations which took place in
this subproblem.
GIVCOL (output) INTEGER array, dimension (2, N) Each pair of numbers indicates a
pair of columns to take place in a Givens rotation.
GIVNUM (output) REAL array, dimension (2, N) Each number indicates the S value to
be used in the corresponding Givens rotation.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
LAPACK version 3.0 15 June 2000 CLAED8(l) 
