Entry-wise domination of vectors

Question

I have several list of reals in [0,1] of identical size. For instance:

[0.33, 0.0, 0.0, 0.33, 0.33, 0.33, 0.0]
[0.0, 0.33, 0.0, 0.33, 0.33, 0.33, 0.0]
[0.0, 0.33, 0.0, 0.33, 0.0, 0.33, 0.0]

I suspect that some lists are strictly dominated by others; for instance the third list is dominated by the second; in the sense that l3[i] <= l2[i] for all i; and l3[j] < l2[j] for at least one j. I want to get rid of those; so I wrote these two functions:

        # R correspond to the original list of lists. 
        # Rp is the list where the striclty dominated lists have been removed.

        def minor_solution(r, R):
            """determines if there exists r2 in R such that r <= r2 for all value and r<r2 for at least one value"""
            for r2 in R:
                if strict_domination(r, r2):
                    return True
            return False

        def strict_domination(r1,r2):
            """return true iff r1 is stricly dominated by r2."""
            strict = False
            dom = True
            for i in range(len(r1)):
                strict = strict or (r1[i] < r2[i])
                dom = dom and (r1[i] <= r2[i])
            return dom and strict

        Rp = []
        for ri in R:
            if minor_solution(ri, R) == False:
                Rp.append(ri)

My problem is that this does not work. Some list are eventually removed; but some which should be removed remains. For instance; the third list in the example I gave was not removed. Any idea?

Answer 1

for such comparisons you don't need to loop over all your elements, it will be enough to check elements like this :

l1 = [0,2,5]
l2 = [0,2,5]

l1==l2
True

or

l1 = [0,2,5]
l2 = [0,2,10]

l1<l2
True

and python will do the element-wise work for you. Here come's my question, do you need a "survival of the fittest", the most predominant list of all or something else, because from the description you gave,it is not clear what the relation to the rest of list-elements should be. Maybe a bit more exhaustive example of what you'd like to receive will be helpful.