DLAED2(1) LAPACK routine (version 3.2) DLAED2(1)NAME
DLAED2 - merges the two sets of eigenvalues together into a single
sorted set
SYNOPSIS
SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
INDX, INDXC, INDXP, COLTYP, INFO )
INTEGER INFO, K, LDQ, N, N1
DOUBLE PRECISION RHO
INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
INDXQ( * )
DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
W( * ), Z( * )
PURPOSE
DLAED2 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 problem 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) 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.
Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two submatrices 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 col‐
umns.
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 elements in the second half of
this permutation must first have N1 added to their values.
Destroyed on exit.
RHO (input/output) DOUBLE PRECISION
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 DLAED3.
Z (input) DOUBLE PRECISION 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) DOUBLE PRE‐
CISION array, dimension (N) A copy of the first K eigenvalues
which will be used by DLAED3 to form the secular equation.
W (output) DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered z-vector which
will be passed to DLAED3.
Q2 (output) DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
A copy of the first K eigenvectors which will be used by DLAED3
in a matrix multiply (DGEMM) to solve for the new eigenvectors.
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of DLAMDA into ascend‐
ing 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 ele‐
ments 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 nondeflated D-values
and INDXP(K+1:N) points to the deflated eigenvalues. COLTYP
(workspace/output) INTEGER array, dimension (N) During execu‐
tion, 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 illegal 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.
LAPACK routine (version 3.2) November 2008 DLAED2(1)
