Get every possible combination of an array

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I have an array that contains n number of 1s and -1s for example:
[1 -1 1 -1 1 1 1 -1]
I'd like every possible combination of this array (like [1 - 1-1 1 1 1 1 -1] ect...)
I tried using perms, but perms has a limit of size 10 and I need to be able to do upto 32. Another thing about perms is I'll have repeating numbers (which I can remove with ease)

Accepted Answer

Benjamin Großmann
Benjamin Großmann on 26 Feb 2020
Edited: Benjamin Großmann on 26 Feb 2020
This could be a starting point:
clearvars, close all
clc
arr = [-1 1 -1 1 1 1 1 1 -1];
num_arr_elements = numel(arr);
% find the number of -1
num_minus_one = sum(arr == -1);
% get all possible positions of -1
idx = nchoosek(1:num_arr_elements, num_minus_one);
% Initialize the matrix of combinations with ones
out = ones(size(idx,1), num_arr_elements);
% Place the -1s on the idx position
for ii = 1:size(idx,1)
out(ii,idx(ii,:)) = -1;
end
Two more aspects:
  • We have to get rid of this for loop
  • Number of possible combinations is with n: array length, s1: number of 1s and s2: number of -1s; for n = 32 and (worst case) s1=s2=16, we have an output array of size 9 x 601.080.390. Optimization is heavily needed or buy a lot of RAM.
  4 Comments
kanav prashar
kanav prashar on 26 Feb 2020
I'm doing some simulations on pseudo-random sequences in non-destructive testing, I found that depending on sequence size you get sidelobe images at a certain level (dB) and these sidelobes are based on the "randomness" of these signals (the 1s and -1s). I want to see how changing the size effects the range of these sidelobes, ideally I'd test every possible combination, however realistically thinking about data size now I understand thats not possible. I already know the worst case scenario happens when there is no randomness in the signal i.e. there is a repeating period -1,1,-1,1,-1... etc is one of these bad responses. I want to also identify the best response, I'll probably just stick to a large data set maybe 300 - 400 per codelength and do 1 forced test on the bad cases and hopefully see a trend.

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