SLAED9 - find the roots of the secular equation, as
defined by the values in D, Z, and RHO, between KSTART and
KSTOP
SYNOPSIS
SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO,
DLAMDA, W, S, LDS, INFO )
INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N
REAL RHO
REAL D( * ), DLAMDA( * ), Q( LDQ, * ), S(
LDS, * ), W( * )
PURPOSE
SLAED9 finds the roots of the secular equation, as defined
by the values in D, Z, and RHO, between KSTART and KSTOP.
It makes the appropriate calls to SLAED4 and then stores
the new matrix of eigenvectors for use in calculating the
next level of Z vectors.
ARGUMENTS
K (input) INTEGER
The number of terms in the rational function to be
solved by SLAED4. K >= 0.
KSTART (input) INTEGER
KSTOP (input) INTEGER The updated eigenvalues
Lambda(I), KSTART <= I <= KSTOP are to be com
puted. 1 <= KSTART <= KSTOP <= K.
N (input) INTEGER
The number of rows and columns in the Q matrix. N
>= K (delation may result in N > K).
D (output) REAL array, dimension (N)
D(I) contains the updated eigenvalues for KSTART
<= I <= KSTOP.
Q (workspace) REAL array, dimension (LDQ,N)
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) REAL array, dimension (K)
The first K elements of this array contain the old
the poles of the secular equation.
W (input) REAL array, dimension (K)
The first K elements of this array contain the
components of the deflation-adjusted updating vec
tor.
S (output) REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired
matrix which will be stored for subsequent Z vec
tor calculation and 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
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA
Man(1) output converted with
man2html