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NAME
dlaed2 - merge the two sets of eigenvalues together into a
single sorted set
SYNOPSIS
SUBROUTINE DLAED2( K, N, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
DLAMDA, Q2, LDQ2, INDXC, W, INDXP, INDX, COLTYP,
INFO )
INTEGER CUTPNT, INFO, K, LDQ, LDQ2, N
DOUBLE PRECISION RHO
INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
INDXQ( * )
DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2,
* ), W( * ), Z( * )
#include <sunperf.h>
void dlaed2(int *k, int n, double *d, double *q, int ldq,
int *indxq, double *drho, int cutpnt, double *dz,
double *dlamda, double *q2, int ldq2, int *indxc,
double *w, int *indxp, int *indx, int *coltyp, int
*info) ;
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.
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 eigenvalues (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 sub-
matrices in the two square blocks with corners at
(1,1), (CUTPNT,CUTPNT) and (CUTPNT+1, CUTPNT+1),
(N,N). 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).
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 CUTPNT added to their values. Des-
troyed on exit.
RHO (input/output) DOUBLE PRECISION
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
DLAED3.
CUTPNT (input) INTEGER The location of the last
eigenvalue in the leading sub-matrix. min(1,N) <=
CUTPNT <= N.
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 PRECISION array, dimension
(N) A copy of the first K eigenvalues which will
be used by DLAED3 to form the secular equation.
Q2 (output) DOUBLE PRECISION array, dimension (LDQ2,
N)
A copy of the first K eigenvectors which will be
used by DLAED3 in a matrix multiply (DGEMM) to
solve for the new eigenvectors. Q2 is arranged
into three blocks. The first block contains non-
zero elements only at and above CUTPNT, the second
contains non-zero elements only below CUTPNT, and
the third is dense.
LDQ2 (input) INTEGER
The leading dimension of the array Q2. LDQ2 >=
max(1,N).
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
CUTPNT, the second contains non-zero elements only
below CUTPNT, and the third is dense.
W (output) DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered
z-vector which will be passed to DLAED3.
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 eigen-
values.
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of D
into ascending order.
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 : non-zero in the lower half only;
3 : dense;
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.
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