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EIGENC2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME EIGENC2
* Problem :
* --------
* Solving symmetric eigenvalue problems as systems of
* nonlinear equations.
* The problem is, given a symmetric matrix A, to find an orthogonal
* matrix Q and diagonal matrix D such that A Q(T) = Q(T) D.
* Example C: a tridiagonal matrix suggested by J. H. Wilkinson.
* Source: An idea by Nick Gould
* Constrained Optimization version 2.
* SIF input: Nick Gould, Nov 1992.
* classification QQR2-AN-V-V
* The dimension of the matrix is 2 M + 1.
*IE M 2 $-PARAMETER
*IE M 10 $-PARAMETER original value
IE M 25 $-PARAMETER
* other parameter definitions
IA M+1 M 1
I+ N M+1 M
IE 1 1
* 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
DO J 1 N
* Define the eigenvalues
X D(J)
DO I 1 N
* Define the eigenvectors
X Q(I,J)
ND
GROUPS
DO J 1 N
DO I 1 J
* Introduce the orthogonality-equations Q(T) Q - I = 0.
ZE O(I,J)
OD I
* Introduce the eigen-equations Q(T) D - A Q(T) = 0.
DO I 1 N
DO K 1 N
AM -AIK A(I,K) -1.0
ZN E(I,J) Q(J,K) -AIK
ND
CONSTANTS
DO J 1 N
X EIGENC2 O(J,J) 1.0
ND
BOUNDS
FR EIGENC2 'DEFAULT'
START POINT
XV EIGENC2 'DEFAULT' 0.0
DO J 1 N
RI RJ J
*ZV EIGENC2 D(J) RJ
XV EIGENC2 D(J) 1.0
XV EIGENC2 Q(J,J) 1.0
ND
ELEMENT TYPE
EV 2PROD Q1 Q2
ELEMENT USES
XT 'DEFAULT' 2PROD
DO J 1 N
DO I 1 N
ZV E(I,J) Q1 Q(J,I)
ZV E(I,J) Q2 D(J)
OD I
DO I 1 J
DO K 1 N
ZV O(I,J,K) Q1 Q(K,I)
ZV O(I,J,K) Q2 Q(K,J)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO J 1 N
DO I 1 N
XT E(I,J) L2
XE E(I,J) E(I,J)
OD I
DO I 1 J
DO K 1 N
XE O(I,J) O(I,J,K)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS EIGENC2
INDIVIDUALS
T 2PROD
F Q1 * Q2
G Q1 Q2
G Q2 Q1
H Q1 Q2 1.0D+0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS EIGENC2
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0D+0
ENDATA