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 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