DLAED9(3) finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP

## SYNOPSIS

SUBROUTINE DLAED9(
K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO )

INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N

DOUBLE PRECISION RHO

DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), W( * )

## PURPOSE

DLAED9 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 DLAED4 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 DLAED4. 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) DOUBLE PRECISION array, dimension (N)
D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
Q (workspace) DOUBLE PRECISION array, dimension (LDQ,N)
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
RHO (input) DOUBLE PRECISION
The value of the parameter in the rank one update equation. RHO >= 0 required.
DLAMDA (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components of the deflation-adjusted updating vector.
S (output) DOUBLE PRECISION array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which will be stored for subsequent Z vector 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 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