Generating all possible pairs of polynomial?

Basically what I want to do is similar to here https://uk.mathworks.com/matlabcentral/answers/267009-generating-all-possible-pairs-of-polynomial-interaction-combinations i.e. I want to generate all possible power polinomial witch each term less than a certain number. My code is here

clear all
clc
%%input;

mu=7;
my=7;
me=7;
delay=1;
degree=2;

totalD=my+mu+me;

A = cell(totalD,1);
[A{1:totalD}] = ndgrid([0:degree]);

for k=1:totalD
polyPow(:,k)=reshape(A{k},[],1);
end

polyPow(sum(polyPow,2)>degree,:) = [];

The problem I am facing now. If the inputs mu,my, and me (also degree) are a bit big, the matrix A becomes very large and I got error "Requested 3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3 (77.9GB) array exceeds maximum array size preference". Anyone has a better idea for my purpose?

Thank you

[Rik]

Shouldn't you expect a 7x7x7x3 array? Otherwise I don't understand your explanation.

[Husni Rois Ali]

Hi Rik

Thank for your response and sorry for the confusion . The code above working fine for a small value of mu, my, me, and degree. The problem now is if those values are a bit big (as in the code above), the cell A becomes very large. I just to ask if anyone has a better idea than mine?

Answer 1

[Rik]

The big problem is that you are throwing out most of your array. The method I use below does that as well, but much less so, making it faster (except for small cases) and more memory-efficient. There are probably way to make this code better, and it is sorely lacking in comments explaining what I'm doing, but it's getting late. If you need some explanation, just comment below this question and I'll edit in comments.

%~ shared setup ~%
clc,clearvars%better than clear all, better still is to use functions
mu=7;
my=7;
me=7;
delay=1;
degree=2;
totalD=my+mu+me;
%~ my code ~%
v=sort(repmat(1:(totalD+1),1,degree+1))-1;
selection=unique(nchoosek(v,degree+1),'rows');
polyPow=zeros(size(selection,1),totalD);
for row=1:size(selection,1)
    for col=1:size(selection,2)
        if selection(row,col)~=0
            c=selection(row,col);
            polyPow(row,c)=polyPow(row,c)+1;
        end
    end
end
polyPow(sum(polyPow,2)>degree,:) = [];
polyPow=unique(polyPow,'rows');
try
    %~ your code ~%
    A = cell(totalD,1);
    [A{1:totalD}] = ndgrid([0:degree]);
    polyPow_old=[];
    for k=1:totalD
        polyPow_old(:,k)=reshape(A{k},[],1);
    end
    polyPow_old(sum(polyPow_old,2)>degree,:) = [];
catch
    polyPow_old=[];
end
%~ check equivalence ~%
if ~isequal(sortrows(polyPow),sortrows(polyPow_old))
    if ~isempty(polyPow_old)
        error('oops')
    end
end

[Husni Rois Ali]

Dear Rik

Thank you so much. It does exactly what i wanted.

I was also aware that most of my array are omitted, but just cannot find a way around

Thank you