ZLAED8(1) LAPACK routine (version 3.2) ZLAED8(1)NAME
ZLAED8 - merges the two sets of eigenvalues together into a single
sorted set
SYNOPSIS
SUBROUTINE ZLAED8( 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
DOUBLE PRECISION RHO
INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ( * ),
PERM( * )
DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( *
), Z( * )
COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * )
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.
ARGUMENTS
K (output) INTEGER
Contains the number of non-deflated 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*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 (input) INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
D (input/output) 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 ei‐
genvalues (those which were deflated) sorted into increasing
order.
RHO (input/output) 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 (input) INTEGER Contains the loca‐
tion of the last eigenvalue in the leading sub-matrix. MIN(1,N)
<= CUTPNT <= N.
Z (input) 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 (output) 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 (output) 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 (input) INTEGER
The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
W (output) 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 (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 D-values and INDXP(K+1:N) points to
the deflated eigenvalues.
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
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 (output) INTEGER array, dimension (N)
Contains the permutations (from deflation and sorting) to be
applied to each eigenblock. GIVPTR (output) INTEGER Contains
the number of Givens rotations which took place in this subprob‐
lem. 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) DOUBLE PRECISION array, dimension (2,
N) Each number indicates the S value to be used in the corre‐
sponding Givens rotation.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
LAPACK routine (version 3.2) November 2008 ZLAED8(1)
