
SLAED9(l) ) SLAED9(l)
NAME
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 computed. 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 roots of the deflated updating
problem. These are 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 vector.
S (output) REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which will be stored for sub
sequent Z vector calculation and multiplied by the previously accumulated eigen
vectors 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 ith argument had an illegal 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
LAPACK version 3.0 15 June 2000 SLAED9(l) 
