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symmetrize.m
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symmetrize.m
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% function [ks]=symmetrize(k)
% k must be a n-th dimensional array whith N<=10.
% ks is the array with N-1 NaNs points filled symmetrically where at
% least a corresponding fundamental point in k can be found among the
% permutations of their coordianates
% Copyright (C) 2006 Massimiliano Pirani
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License along
% with this program; if not, write to the Free Software Foundation, Inc.,
% 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
function [ks]=symmetrize(k)
S=size(k);
ord=length(S);
M=max(S);
switch ord
case 2
ks=tril(k)+tril(k,-1)';
case 3
ks=NaNmat(M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
P=perms([x1, x2, x3 ]);
fill=0;
for i=1:6
val=k(P(i,1),P(i,2),P(i,3));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:6
ks(P(i,1),P(i,2),P(i,3))=val;
end
end
end
end
end
case 4
ks=NaNmat(M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
P=perms([x1, x2, x3, x4]);
fill=0;
for i=1:24
val=k(P(i,1),P(i,2),P(i,3),P(i,4));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:24
ks(P(i,1),P(i,2),P(i,3),P(i,4))=val;
end
end
end
end
end
end
case 5
ks=NaNmat(M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
P=perms([x1, x2, x3, x4, x5]);
fill=0;
for i=1:120
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:120
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5))=val;
end
end
end
end
end
end
end
case 6
ks=NaNmat(M,M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
for x6=x5:M
P=perms([x1, x2, x3, x4, x5, x6]);
fill=0;
for i=1:720
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:720
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6))=val;
end
end
end
end
end
end
end
end
case 7
ks=NaNmat(M,M,M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
for x6=x5:M
for x7=x6:M
P=perms([x1, x2, x3, x4, x5, x6, x7]);
fill=0;
for i=1:5040
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:5040
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7))=val;
end
end
end
end
end
end
end
end
end
case 8
ks=NaNmat(M,M,M,M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
for x6=x5:M
for x7=x6:M
for x8=x7:M
P=perms([x1, x2, x3, x4, x5, x6, x7, x8]);
fill=0;
for i=1:40320
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:40320
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8))=val;
end
end
end
end
end
end
end
end
end
end
case 9
ks=NaNmat(M,M,M,M,M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
for x6=x5:M
for x7=x6:M
for x8=x7:M
for x9=x8:M
P=perms([x1, x2, x3, x4, x5, x6, x7, x8, x9]);
fill=0;
for i=1:362880
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8),P(i,9));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:362880
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8),P(i,9))=val;
end
end
end
end
end
end
end
end
end
end
end
case 10
ks=NaNmat(M,M,M,M,M,M,M,M,M,M);
for x1=1:M
for x2=x1:M
for x3=x2:M
for x4=x3:M
for x5=x4:M
for x6=x5:M
for x7=x6:M
for x8=x7:M
for x9=x8:M
for x10=x9:M
P=perms([x1, x2, x3, x4, x5, x6, x7, x8, x9, x10]);
fill=0;
for i=1:3628800
val=k(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8),P(i,9),P(i,10));
if ~isnan(val), fill=1; break, end
end
if fill
for i=1:3628800
ks(P(i,1),P(i,2),P(i,3),P(i,4),P(i,5),P(i,6),P(i,7),P(i,8),P(i,9),P(i,10))=val;
end
end
end
end
end
end
end
end
end
end
end
end
end