slaed3(3)

NAME

SLAED3 - find the roots of the secular equation, as de

fined by the values in D, W, and RHO, between 1 and K

SYNOPSIS

SUBROUTINE  SLAED3(  K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2,
INDX, CTOT, W, S, INFO )
    INTEGER        INFO, K, LDQ, N, N1
    REAL           RHO
    INTEGER        CTOT( * ), INDX( * )
    REAL           D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( *
), S( * ), W( * )

PURPOSE

SLAED3 finds the roots of the secular equation, as defined

by the values in D, W, and RHO, between 1 and K. It makes the ap

propriate calls to SLAED4 and then updates the eigenvectors by

multiplying the matrix of eigenvectors of the pair of eigensys

tems being combined by the matrix of eigenvectors of the K-by-K

system which is solved here.

This code makes very mild assumptions about floating point

arithmetic. It will work on machines with a guard digit in

add/subtract, or on those binary machines without guard digits

which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or

Cray-2. It could conceivably fail on hexadecimal or decimal ma

chines without guard digits, but we know of none.

ARGUMENTS

K (input) INTEGER

The number of terms in the rational function to be

solved by SLAED4. K >= 0.

N (input) INTEGER

The number of rows and columns in the Q matrix. N

>= K (deflation may result in N>K).

N1 (input) INTEGER

The location of the last eigenvalue in the leading

submatrix. min(1,N) <= N1 <= N/2.

D (output) REAL array, dimension (N)

D(I) contains the updated eigenvalues for 1 <= I

<= K.

Q (output) REAL array, dimension (LDQ,N)

Initially the first K columns are used as

workspace. On output the columns 1 to K contain the updated

eigenvectors.

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/output) 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. May be changed on output by having lowest

order bit set to zero on Cray X-MP, Cray Y-MP, Cray-2, or Cray

C-90, as described above.

Q2 (input) REAL array, dimension (LDQ2, N)

The first K columns of this matrix contain the

non-deflated eigenvectors for the split problem.

INDX (input) INTEGER array, dimension (N)

The permutation used to arrange the columns of the

deflated Q matrix into three groups (see SLAED2). The rows of

the eigenvectors found by SLAED4 must be likewise permuted before

the matrix multiply can take place.

CTOT (input) INTEGER array, dimension (4)

A count of the total number of the various types

of columns in Q, as described in INDX. The fourth column type is

any column which has been deflated.

W (input/output) REAL array, dimension (K)

The first K elements of this array contain the

components of the deflation-adjusted updating vector. Destroyed

on output.

S (workspace) REAL array, dimension (N1 + 1)*K

Will contain the eigenvectors of the repaired ma

trix which will be 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 ille

gal 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

Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0 15 June 2000

SLAED3(3)