SLAED9(3f)

NAME
SLAED9 - 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 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