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HADAMALS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HADAMALS
* 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 entries are plus or minus one.
* Source: A suggestion by Alan Edelman (MIT).
* SIF input: Nick Gould, Nov 1993.
* classification OBR2-RN-V-V
* The dimension of the matrix (=> N**2 variables).
*IE N 2 $-PARAMETER original value
*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
*IE N 18 $-PARAMETER
IE N 20 $-PARAMETER
*IE N 32 $-PARAMETER
*IE N 64 $-PARAMETER
*IE N 128 $-PARAMETER
*IE N 256 $-PARAMETER
*IE N 428 $-PARAMETER
* other parameter definitions
IE 1 1
IE 2 2
RI RN N
I/ N/2 N 2
IA N/2+1 N/2 1
VARIABLES
* Define the largest entry in absolute value.
DO J 1 N
DO I 1 N
* Define the orthogonal matrix
X Q(I,J)
ND
GROUPS
* Introduce the orthogonality-equations Q(T) Q - sqrt(N) I = 0.
DO J 1 N
DO I 1 J
XN O(I,J)
ND
* Introduce the restrictions that each entry is + 1 or - 1.
DO J 1 N
DO I 2 N
XN S(I,J)
ND
CONSTANTS
DO J 1 N
Z HADAMALS O(J,J) RN
ND
DO J 1 N
DO I 2 N
X HADAMALS S(I,J) 1.0
ND
BOUNDS
LO HADAMALS 'DEFAULT' -1.0
UP HADAMALS 'DEFAULT' 1.0
DO I 1 N/2
XX HADAMALS Q(I,1) 1.0
ND
DO I N/2+1 N
XX HADAMALS Q(I,1) -1.0
ND
START POINT
DO J 1 N
DO I 1 N/2
XV HADAMALS Q(I,J) 0.9
OD I
DO I N/2+1 N
XV HADAMALS Q(I,J) -0.9
OD I
ND
ELEMENT TYPE
EV SQR Q1
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
DO J 1 N
DO I 2 N
XT S(I,J) SQR
ZV S(I,J) Q1 Q(I,J)
ND
GROUP TYPE
GV L2 GVAR
GV LARGEL2 GVAR
GROUP USES
DO J 1 N
DO I 1 J
XT O(I,J) L2
DO K 1 N
XE O(I,J) O(I,J,K)
ND
DO J 1 N
DO I 2 N
XT S(I,J) LARGEL2
XE S(I,J) S(I,J)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HADAMALS
INDIVIDUALS
T SQR
F Q1 * Q1
G Q1 Q1 + Q1
H Q1 Q1 2.0D+0
T 2PROD
F Q1 * Q2
G Q1 Q2
G Q2 Q1
H Q1 Q2 1.0D+0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HADAMALS
TEMPORARIES
R FACTOR
GLOBALS
A FACTOR 1.0D+0
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0D+0
T LARGEL2
F FACTOR * GVAR * GVAR
G 2.0D+0 * FACTOR * GVAR
H 2.0D+0 * FACTOR
ENDATA