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HADAMARD.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HADAMARD
* Problem :
* --------
* An attempt to find Hadamard matrices of order N.
* The problem is to find an N by N orthonormal matrix Q,
* with column norms N, whose largest entry is as small
* as possible in absolute value.
* Source: A suggestion by Alan Edelman (MIT).
* SIF input: Nick Gould, Nov 1993.
* classification LQR2-RN-V-V
* The dimension of the matrix.
*IE N 2 $-PARAMETER
*IE N 4 $-PARAMETER
*IE N 6 $-PARAMETER
*IE N 8 $-PARAMETER
*IE N 10 $-PARAMETER
*IE N 12 $-PARAMETER
*IE N 14 $-PARAMETER
*IE N 16 $-PARAMETER original value
*IE N 18 $-PARAMETER
IE N 20 $-PARAMETER
*IE N 100 $-PARAMETER
* other parameter definitions
IE 1 1
RI RN N
VARIABLES
* Define the largest entry in absolute value.
X MAXABSQ
DO J 1 N
DO I 1 N
* Define the orthogonal matrix
X Q(I,J)
ND
GROUPS
N OBJECTIVE MAXABSQ 1.0
* Introduce the orthogonality-equations Q(T) Q - sqrt(N) I = 0.
DO J 1 N
DO I 1 J
XE O(I,J)
ND
* Introduce the restrictions that |Qij| is bounded by the the
* largest such value.
DO J 1 N
DO I 1 N
XG L(I,J) MAXABSQ 1.0 Q(I,J) 1.0
XG U(I,J) MAXABSQ 1.0 Q(I,J) -1.0
ND
CONSTANTS
DO J 1 N
Z HADAMARD O(J,J) RN
ND
BOUNDS
FR HADAMARD 'DEFAULT'
LO HADAMARD MAXABSQ 0.0
START POINT
XV HADAMARD MAXABSQ 0.0
DO I 1 N
DO J 1 N
XV HADAMARD Q(I,J) 1.0
ND
ELEMENT TYPE
EV 2PROD Q1 Q2
ELEMENT USES
DO J 1 N
DO I 1 J
DO K 1 N
XT O(I,J,K) 2PROD
ZV O(I,J,K) Q1 Q(K,I)
ZV O(I,J,K) Q2 Q(K,J)
ND
GROUP USES
DO J 1 N
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 HADAMARD
INDIVIDUALS
T 2PROD
F Q1 * Q2
G Q1 Q2
G Q2 Q1
H Q1 Q2 1.0D+0
ENDATA