How can I generate a Matrix (4x4) with random different figures from 1 to 4 ?
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Hello, How can I generate a Matrix (size 4x4) with random different figures from 1 to 4 ? Figures must be different in the lines and the columns. in example:
A=[1 2 3 4; 2 1 4 3; 3 4 1 2; 4 3 2 1]
thank you.
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Jan
2013-4-10
编辑:Jan
2013-4-10
You can start with a valid matrix:
A = [1:4; 1:4, 1:4, 1:4];
Then perform only operations, which do not destroy the validity: Interchange rows and columns in pairs:
for k = 1:1000
index = randperm(4, 2); % older Matlab versions accept 1 input only
A(index(1), :) = A(index(2), :);
index = randperm(4, 2);
A(:, index(1)) = A(:, index(2));
end
Or a constructive method which rejects not matching input:
A = zeros(4, 4);
A(1, :) = randperm(4, 4);
index = 2;
while index <= 4
newRow = randperm(4, 4);
match = bsxfun(@ne, A(1:index - 1, :), newRow);
if all(match(:))
A(index, :) = newRow;
index = index + 1;
end
end
Actually trivial ideas with just some tricks in the implementation.
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Andrei Bobrov
2013-4-10
编辑:Andrei Bobrov
2013-4-17
n = 4;
A = rem(bsxfun(@plus,1:n,(0:n-1)')-1,n)+1;
or [EDIT]
A = hankel(1:n,[n 1:n-1]);
A = A(randperm(n),:);
A = A(:,rendperm(n));
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