Hint: All you need to do is generate the set of exponents. For example, here column 1 of uv might represent the exponent of a, column 2 the exponent of b.
[u,v] = meshgrid(0:3);
uv = [u(:),v(:)]
uv =
0 0
0 1
0 2
0 3
1 0
1 1
1 2
1 3
2 0
2 1
2 2
2 3
3 0
3 1
3 2
3 3
If you don't wish a constant term, then delete the first row. You state that the polynomial order should be no greater than 3, but you included a term in there for a*b^3, which would have a total order of 4. So I'm not sure if you were careful in your example.
But if you do not wish to have terms in the model with total order greater than 3, that is trivially done:
uv(sum(uv,2)>3,:) = []
uv =
0 0
0 1
0 2
0 3
1 0
1 1
1 2
2 0
2 1
3 0
Dropping the constant term, we get:
uv(sum(uv,2) == 0,:) = []
uv =
0 1
0 2
0 3
1 0
1 1
1 2
2 0
2 1
3 0
I'm not sure what you mean by non-integer orders of the polynomials, but the above example does not require the exponents to be integers. As well, I don't see any issue with the fact that you must delete some terms. The memory involved is trivial. Finally, actual computation of the polynomial is as trivial as:
syms a b
sum(a.^uv(:,1).*b.^uv(:,2))
ans =
a^3 + a^2*b + a^2 + a*b^2 + a*b + a + b^3 + b^2 + b
Higher orders?
help ndgrid
help meshgrid
