minimization in scipy, algorithm to find all local minima of a N dimensional scalar function

Question

Does anybody know about a powerful routine/algorithm (preferrably in scipy/python) to localise "all" the local minima for a scalar real function of N variables in a defined ("rectangular") region of N-dimensional vector space ?

the constrained and unconstrained minimization algorithms in scipy all return only a single minimum (global or local)

Answer 1

Scipy's basinhopping has a callback argument that can be used to save all found minima.

For instance:

all_minima = []
def save_minima(x, f, accepted):
    all_minima.append(x)

basinhopping(func, x0, callback=save_minima)

Obviously, this doesn't return all local minima necessarily. But it does return all that it finds.