Different computation of symmetrized conditional probabilities

[javagl]

Apologies if this is not an "issue", but rather a question that I have about the implementation (or my lack of understanding thereof).

The paper says in section 3.1 (and in the pseudocode of Algorithm 1)

set p_ij = (p_{j | i}+p_{i | j}) / 2n

The actual implementation of the symmetrization in tsne.cpp, line 112 seems to be

double sum_P = .0;
for(int i = 0; i < N * N; i++) sum_P += P[i];
for(int i = 0; i < N * N; i++) P[i] /= sum_P;

thus not dividing by 2n, but by the sum of all elements.

Which one is right?

My gut feeling is: It does not matter. Both achieve the same goal. But then, I wonder why the effort of computing the sum is undertaken.

Am I overlooking something here?

[lvdmaaten]

Both achieve the same goal, although I can imagine sum_P may be slightly different from 2n in practice because of numerical issues.

[javagl]

Well. Sure, they are different. They have different values. But although I have to admit that this is not really a satisfactory answer, it answers my question at least implicitly: There are some magic factors and guesses involved, and the implementation may have some degrees of freedom (only justified by how well they work in one or the other case).