We shouldn't pass a one-rank OT matrix as initialization

[othmanesebbouh]

ott/src/ott/problems/quadratic/quadratic_problem.py

Line 225 in 2f5242b

def init_transport(self) -> jnp.ndarray:

[michalk8]

Hi @othmanesebbouh , do you suggest a different initialization or just a way to supply custom initializer in this case (for better flexibility)?

[marcocuturi]

othmane was discussing with me as we spotted this. the generic GW initializer materializes a rank 1 matrix (product of marginals) to then have this taken as a product with Cx on the left and Cy on the right. It would be more effective to save this cubic operation by computing instead (Cx a) (Cy^T b)^T using two apply and then materialize that cost. here everything remains quadratic.