Calculate a randomized array with some constraints.
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brainybrown
el 24 de Jun. de 2014
Hello, for a psychological experiment I have the following problem. I need to calculate an array containing 70 distinct numbers. From these 70 numbers are 20 pairs (so e.g. two 1s, two 2s, two 3s etc.), all other numbers are zeros. The constraint is now that all pairs shall have a fixed index step-size to each other (e.g. if the step-size=2 and the first 3 lays at index 2, than the second 3 must lay at index 4), but apart from that the array should be completely random. The step-size should be variable between n=2 to n=20. Whether two pairs overlap (e.g. that if the step-size=2, and the first pair lays at index 2 and 4, and the second pair lays at index 3 and 5), doesn’t matter. Also how long Matlab needs, to find such an Array does not really matter, as long it does not take more than an hour or so.
Does anyone have an idea how I can tell Matlab to output me such an array? This is what I tried so far:
myArray = [zeros(1,40),1:20,1:20]; % the array that shall be randomized,
% under the bespoken constraint.
lags = 2; % variable step-size
pairs = 20; % number of pairs
a=0;
while a==0
myArray = myArray(randperm(length(myArray))); % new randomization, new chance!
for i=1:pairs
tmp = find(myArray==i);
if tmp(1)+lags~=tmp(2); % if one pair has not the right index
%stepsize, interrupt for-loop.
break;
elseif i==pairs
a=1; % if all numbers are at their right
% place stop the while loop
end
end
However, I have to admit that this is totally bruteforce and in fact does never end (at least not within one hour ;-)).
I would be very very glad if someone could help me out with a smarter approach. Cheers.
5 comentarios
Respuesta aceptada
José-Luis
el 24 de Jun. de 2014
Editada: José-Luis
el 24 de Jun. de 2014
pairs = [1 1; 2 2; 3 3; 4 4];
your_array = zeros(1,20);
step_size = 4;
numPairs = size(pairs,1);
pos = 1:numel(your_array);
for ii = 1:numPairs
%pick a pair
idx = randi(size(pairs,1));
current_val = pairs(idx,1);
%Pick starting position
posIdx = randperm(numel(pos)-step_size,1);
your_array([pos(posIdx) pos(posIdx)+step_size]) = current_val;
%Make it so the same positions cannot be picked again
pos([posIdx posIdx+step_size]) = [];
pairs(idx,:) = [];
end
disp(your_array)
Please accept an answer once it has solved your problem.
4 comentarios
José-Luis
el 25 de Jun. de 2014
Editada: José-Luis
el 25 de Jun. de 2014
Slightly better, returns control to command prompt if all pairs cannot be placed. Note that this is more likely to happen when there are not that many zeros. Say you have 15 pairs and 30 spaces with a step of five, then the approach should be different.
pairs = (1:15)';
pairs = [pairs pairs];
your_array = zeros(1,35);
step_size = 4;
numPairs = size(pairs,1);
test_array = [your_array; circshift(your_array,[0 -step_size])];
test_array(:,end-step_size:end) = [];
for ii = 1:numPairs
%pick a pair
idx = randi(size(pairs,1));
current_val = pairs(idx,1);
%Pick starting position and check if both numbers can be saved
%Finding all possible positions for the new pair:
valid = find(sum(test_array) == 0);
if isempty(valid)
disp('Could not find a position to place pair, please try again');
return
end
%Selecting position randomly
posIdx = valid(randi(numel(valid),1));
your_array([posIdx posIdx+step_size]) = current_val;
%Make it so the same positions cannot be picked again
pairs(idx,:) = [];
test_array = [your_array; circshift(your_array,[0 -step_size])];
test_array(:,end-step_size:end) = [];
end
disp(your_array)
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