SLAED3 - find the roots of the secular equation, as
defined by the values in D, W, and RHO, between 1 and K
SYNOPSIS
SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2,
INDX, CTOT, W, S, INFO )
INTEGER INFO, K, LDQ, N, N1
REAL RHO
INTEGER CTOT( * ), INDX( * )
REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( *
), S( * ), W( * )
PURPOSE
SLAED3 finds the roots of the secular equation, as defined
by the values in D, W, and RHO, between 1 and K. It makes
the appropriate calls to SLAED4 and then updates the
eigenvectors by multiplying the matrix of eigenvectors of
the pair of eigensystems being combined by the matrix of
eigenvectors of the K-by-K system which is solved here.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray
C-90, or Cray-2. It could conceivably fail on hexadecimal
or decimal machines without guard digits, but we know of
none.
ARGUMENTS
K (input) INTEGER
The number of terms in the rational function to be
solved by SLAED4. K >= 0.
N (input) INTEGER
The number of rows and columns in the Q matrix. N
>= K (deflation may result in N>K).
N1 (input) INTEGER
The location of the last eigenvalue in the leading
submatrix. min(1,N) <= N1 <= N/2.
D (output) REAL array, dimension (N)
D(I) contains the updated eigenvalues for 1 <= I
<= K.
Q (output) REAL array, dimension (LDQ,N)
Initially the first K columns are used as
workspace. On output the columns 1 to K contain
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >=
max(1,N).
RHO (input) REAL
The value of the parameter in the rank one update
equation. RHO >= 0 required.
DLAMDA (input/output) REAL array, dimension (K)
The first K elements of this array contain the old
roots of the deflated updating problem. These are
the poles of the secular equation. May be changed
on output by having lowest order bit set to zero
on Cray X-MP, Cray Y-MP, Cray-2, or Cray C-90, as
described above.
Q2 (input) REAL array, dimension (LDQ2, N)
The first K columns of this matrix contain the
non-deflated eigenvectors for the split problem.
INDX (input) INTEGER array, dimension (N)
The permutation used to arrange the columns of the
deflated Q matrix into three groups (see SLAED2).
The rows of the eigenvectors found by SLAED4 must
be likewise permuted before the matrix multiply
can take place.
CTOT (input) INTEGER array, dimension (4)
A count of the total number of the various types
of columns in Q, as described in INDX. The fourth
column type is any column which has been deflated.
W (input/output) REAL array, dimension (K)
The first K elements of this array contain the
components of the deflation-adjusted updating vec
tor. Destroyed on output.
S (workspace) REAL array, dimension (N1 + 1)*K
Will contain the eigenvectors of the repaired
matrix which will be multiplied by the previously
accumulated eigenvectors to update the system.
LDS (input) INTEGER
The leading dimension of S. LDS >= max(1,K).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: if INFO = 1, an eigenvalue did not converge
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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