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EIGMAXC.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME EIGMAXC
* Problem :
* --------
* Find the largest eigenvalue of a symmetrix matrix.
* The problem is, given a symmetric matrix A, to find a unit vector
* q and scalar d such that A q = d q for which - d is least.
* Example C: a tridiagonal matrix suggested by J. H. Wilkinson.
* Source: An idea by Nick Gould
* SIF input: Nick Gould, Nov 1992.
* classification LQR2-AN-V-V
* The dimension of the matrix is 2 M + 1.
*IE M 2 $-PARAMETER
*IE M 10 $-PARAMETER original value
IE M 100 $-PARAMETER
* other parameter definitions
IA M+1 M 1
I+ N M+1 M
IE 1 1
RI RN N
R( ROOTN SQRT RN
RD 1/ROOTN ROOTN 1.0
* Define the whole matrix.
DO J 1 N
IA J-1 J -1
I- M+1-J M J-1
RI RM+1-J M+1-J
DO I 1 N
AE A(I,J) 0.0
OD I
AE A(J-1,J) 1.0
A= A(J,J) RM+1-J
IA J+1 J 1
AE A(J+1,J) 1.0
OD J
VARIABLES
* Define the eigenvalue
X D
DO I 1 N
* Define the eigenvector
X Q(I)
ND
GROUPS
* Define the objective
N MAXEIG D -1.0
* Introduce the normalization equation Q(T) Q - 1 = 0.
E O
* Introduce the eigen-equations D Q - A Q = 0.
DO I 1 N
DO K 1 N
AM -AIK A(I,K) -1.0
ZE E(I) Q(K) -AIK
ND
CONSTANTS
X EIGMAXC O 1.0
BOUNDS
LO EIGMAXC 'DEFAULT' -1.0
UP EIGMAXC 'DEFAULT' 1.0
START POINT
XV EIGMAXC D 1.0
DO I 1 N
ZV EIGMAXC Q(I) 1/ROOTN
ND
ELEMENT TYPE
EV 2PROD Q1 Q2
ELEMENT USES
XT 'DEFAULT' 2PROD
DO I 1 N
ZV E(I) Q1 Q(I)
ZV E(I) Q2 D
OD I
DO K 1 N
ZV O(K) Q1 Q(K)
ZV O(K) Q2 Q(K)
ND
GROUP USES
DO I 1 N
XE E(I) E(I)
ND
DO K 1 N
XE O O(K)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS EIGMAXC
INDIVIDUALS
T 2PROD
F Q1 * Q2
G Q1 Q2
G Q2 Q1
H Q1 Q2 1.0D+0
ENDATA