Here's how I'd approach the problem, in pseudo-code:
R = [] # This could be typed and pre-allocated with the proper length
for i=1:N
factors = combinations_with_replacement(Xj, i)
for f in factors
push!(R, prod(f))
end
end
The only trouble is that combinations_with_replacement function. I don't
see a Julia version anywhere at the moment. See Python's itertools
package:
https://docs.python.org/2/library/itertools.html#itertools.combinations_with_replacement
On Wednesday, May 20, 2015 at 2:22:59 PM UTC-4, Júlio Hoffimann wrote:
>
> David, thank you very much for the detailed explanation, will read through
> it.
>
> Steven, sorry for not explaining the problem clearly. My issue is
> basically trying to figure out a way to loop over all possible combinations
> of exponents (e1, e2, e3) for which the sum is less or equal to N and
> generate a vector with the terms Xj[1]^e1*Xj[2]^e2*Xj[3]^e3.
>
> The j-th column of the resulting matrix contains the terms of this
> polynomial evaluated at the j-th column of X.
>
> -Júlio
>
