
SLAED2(l) ) SLAED2(l)
NAME
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 problem is reduced by
one.
ARGUMENTS
K (output) INTEGER
The number of nondeflated eigenvalues, and the order of the related secular equa
tion. 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 submatrix. 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 (NK) 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 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 (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).
INDXQ (input/output) INTEGER array, dimension (N)
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
N1 added to their values. Destroyed on exit.
RHO (input/output) REAL
On entry, the offdiagonal element associated with the rank1 cut which originally
split the two submatrices 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 subeigenvector
matrix and the first row of the second subeigenvector matrix). On exit, the con
tents 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 deflationaltered zvector which will be passed to
SLAED3.
Q2 (output) REAL array, dimension (N1**2+(NN1)**2)
A copy of the first K eigenvectors which will be used by SLAED3 in a matrix multi
ply (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 nonzero elements only at and above N1, the sec
ond contains nonzero 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 nondeflated Dvalues
and INDXP(K+1:N) points to the deflated eigenvalues.
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 : nonzero in the upper half only;
2 : dense;
3 : nonzero 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 ith 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 version 3.0 15 June 2000 SLAED2(l) 
