How do I get every combination of 3 vectors?

Hello!

I have 3 vectors, one is a 35x1, one is a 31x1 and the last one is a 13x1. I want to create some kind of loop that outputs a number from the first, a number from the second, and a number from a third, over and over, eventually outputting every combination.

If I am not clear, please comment.

Thanks!

-Kevin

Answer 1

[Bruno Luong]

yourvector1 = ...
yourvector2 = ...
yourvector3 = ...

Then

c = {yourvector1, yourvector2, yourvector3};
c = flip(c);
[c{:}] = ndgrid(c{:});
c = cellfun(@(x) x(:), flip(c), 'unif', 0);
c = cat(2, c{:});

check

disp(c)

[Kevin Shen]

Thanks! I will try this. Just a quick question, what is c, and if it is a matrix how would I separate individual parts to use one at a time?

[Bruno Luong]

c is an array of combination.

• Row dimension corresponds to different combination,
• Column dimension corresponds to yourvector1, yourvector2, yourvector3 values.

You have to tell us what you meant by "use one at the time", but it probably goes like this

for i=1:size(c,1)
    combi = c(i,:); % 1 x 3 vector
     % do something with it
     ...
 end

You probably need more learning of basic stuff of MATLAB/programming.

[Kevin Shen]

Thanks for the help, and yes I definately do need more learning, I'm just getting started.

Answer 2

[Matt J]

Example:

[X,Y,Z]=ndgrid(1:3,10:15,100:102);

[X(:),Y(:),Z(:)]

[Kevin Shen]

Thanks for responding!

So how does this work? What happens? What do the numbers mean? What do I plug in to it? What do I get in return? What is X, Y, Z? (I'm relatively new to MATLAB)

Again, thanks, but I am not totally clear on what to do.

-Kevin

[Matt J]

Did you try it?

[Kevin Shen]

Well I don't know how

[Matt J]

I mean did you run the code I gave you and did you inspect the result? You will see that every row of the output matrix is a combination of the inputs to ndgrid.

[Kevin Shen]

So it does work, thanks! Although it isn't the perfect solution for my current project, I will definately use this in another project I am working on for the sheer simplicity of it.

Answer 3

[Image Analyst]

Here's a for loop way to do it:

% Create 3 sample vectors, one is a 35x1, one is a 31x1 and the last one is a 13x1.
v1 = (1:35)'; % Actual values are whatever yours are - not a ramp like this.
v2 = (1:31)';
v3 = (1:13)';
% Get 3 random selection orderings:
order1 = randperm(length(v1));
order2 = randperm(length(v2));
order3 = randperm(length(v3));
% Now make 3 loops
for k1 = 1 : length(order1)
	index1 = order1(k1);
	for k2 = 1 : length(order2)
	       index2 = order2(k2);
		for k3 = 1 : length(order3)
			index3 = order3(k3);
			fprintf('Processing index %d from v1, index %d from v2, and index %d from v3.\n', index1, index2, index3);
		end
	end
end

Of course you can do it with a built-in function rather than loops like Matt showed you.

[Kevin Shen]

Thanks for answering!

However, since I am new to MATLAB, many of these functions are new to me, could you please explain what things do, or at least what to plug in and what comes out?

Again, thank you so much.

-Kevin

[Image Analyst]

v1, v2, and v3 are your existing vectors that you mentioned. I just made some because you forgot to attach yours or give us code to create them.

randperm just takes all the indexes from 1 to whatever (the length of your vector) and basically shuffles them so that they're in a scrambled, random order. Then the for loops just go taking one index from each scrambled order. For example if your order vectors were

order1 = [2,19,30, .....

order2 = [4,1,8,....

order3 = [5,7,17,.....

then in the first iteration, it would use element 2 from v1, element 4 from v2, and element 5 from v3. Then on the next iteration it would use element 19 from v1, element 1 from v2, and element 7 from v3. And so on. Once you have those you can use those elements for whatever you want to do.

[Kevin Shen]

But would that get every combination, or just the corresponding elements in each vector?

[Image Analyst]

It absolutely gets every combination. Every single element of a vector gets paired with every single other element of the other vectors at some point (one of the iterations). Do you think some might get skipped? If so, why? Every element is in the order vectors and every one of them will get used. No combination will get skipped.

[Kevin Shen]

Thank you so much, this does work! However I could only accept one answer, and the other one was the one that applied to me more directly.

I deeply appreciate your hard work helping me

-Kevin

[Image Analyst]

You're welcome. Thanks for voting for it though. Matt's answer is the more MATLAB-y, vectorized way of doing it and is probably what I would have done. I just offered the looping way of doing it because that's what you specifically asked for, and sometimes the vectorized methods use functions, which, honestly, can be more confusing to beginners than a simple, intuitive for loop.