SLAED2 - merge the two sets of eigenvalues together into a
single sorted set
SYNOPSIS
SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z,
DLAMDA, W, Q2, INDX, INDXC, INDXP,
COLTYP, INFO )
INTEGER INFO, K, LDQ, N, N1
REAL RHO
INTEGER COLTYP( * ), INDX( * ), INDXC( * ),
INDXP( * ), INDXQ( * )
REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( *
), W( * ), Z( * )
PURPOSE
SLAED2 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 entry in the Z vector. For each such
occurrence the order of the related secular equation prob
lem is reduced by one.
ARGUMENTS
K (output) INTEGER
The number of non-deflated eigenvalues, and the
order of the related secular equation. 0 <= K <=N.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix.
N >= 0.
N1 (input) INTEGER
The location of the last eigenvalue in the leading
sub-matrix. min(1,N) <= N1 <= N/2.
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 (N-K) updated eigenvalues (those which
were deflated) sorted into increasing order.
Q (input/output) REAL array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two subma
trices in the two square blocks with corners at
(1,1), (N1,N1) and (N1+1, N1+1), (N,N). On exit, Q
contains the trailing (N-K) updated eigenvectors
(those which were deflated) in its last N-K
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >=
max(1,N).
INDXQ (input/output) INTEGER array, dimension (N)
The permutation which separately sorts the two sub-
problems in D into ascending order. Note that ele
ments in the second half of this permutation must
first have N1 added to their values. Destroyed on
exit.
RHO (input/output) REAL
On entry, the off-diagonal element associated with
the rank-1 cut which originally split the two sub
matrices which are now being recombined. On exit,
RHO has been modified to the value required by
SLAED3.
Z (input) 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 have been destroyed by
the updating process.
DLAMDA (output) REAL array, dimension (N) A copy of
the first K eigenvalues which will be used by
SLAED3 to form the secular equation.
W (output) REAL array, dimension (N)
The first k values of the final deflation-altered
z-vector which will be passed to SLAED3.
Q2 (output) REAL array, dimension (N1**2+(N-N1)**2)
A copy of the first K eigenvectors which will be
used by SLAED3 in a matrix multiply (SGEMM) to
solve for the new eigenvectors.
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of DLAMDA
into ascending order.
INDXC (output) INTEGER array, dimension (N)
The permutation used to arrange the columns of the
deflated Q matrix into three groups: the first
group contains non-zero elements only at and above
N1, the second contains non-zero elements only
below N1, and the third is dense.
INDXP (workspace) 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
and INDXP(K+1:N) points to the deflated eigenval
ues.
COLTYP (workspace/output) INTEGER array, dimension
(N) During execution, a label which will indicate
which of the following types a column in the Q2
matrix is:
1 : non-zero in the upper half only;
2 : dense;
3 : non-zero in the lower half only;
4 : deflated. On exit, COLTYP(i) is the number of
columns of type i, for i=1 to 4 only.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
Man(1) output converted with
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