Get every possible combination of an array

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)

[kanav prashar]

I meant repeating combinations sorry!

Answer 1

[Benjamin Großmann]

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.

[kanav prashar]

thanks! this works great! I guess I'll just have to stick to a purely random scenario for the higher end bitnumbers and just do as many possible combinations as plausible, but this will be great for the lower ends!

[Steven Lord]

If you describe the underlying problem you were hoping to solve using this exhaustive set of permutations of elements of the array, we may be able to offer an alternative approach that avoids creating the whole (extremely large) set. Brute force works given enough resources (particularly memory and time) but it's often not the optimal approach.

[Benjamin Großmann]

You are welcome! As Steven said, the brute force method is mostly not optimal to solve a specific task. I am also interested in the underlying problem. Furthermore, I would propose to use a logical array, since you have "bitnumbers" and then solve the task using bit-operations.

[kanav prashar]

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.