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 deflationadjusted updating vector.
 S (output) REAL 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 ith argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
FURTHER DETAILS
Based on contributions byJeff Rutter, Computer Science Division, University of California
at Berkeley, USA