Python cartesian product and conditions?

Python 3

In Python 3 you can filter out undesirable combinations using itertools.filterfalse:

# predicate is true when need to skip the combination
predicate = (lambda (a1, a2, b1, b2): a1 <= a2 and (b1 != 0 or b2 == 5), params)
filtered_params = itertools.filterfalse(predicate, params)

Python 2

You can use list comprehension or itertools.ifilter:

filtered_params = itertools.ifilter
    (lambda (a1, a2, b1, b2): a1 <= a2 and (b1 != 0 or b2 == 5), params)

Note that both of these versions loop and filter out under the hood. If you want to avoid that, you'll need to construct an improved algorithm that creates the tuples without the undesirables.

If you have many parameters, a constraint-based approach using a module like python-constraint may be easier to work with - let it do the hard work of figuring out which combinations are valid.

This would look something like

from constraint import Problem

prob = Problem()
prob.addVariables(["a1", "a2"], range(10,41,2))
prob.addVariable("b1", [0, 2])
prob.addVariable("b2", range(5, 31, 5))
prob.addConstraint(lambda a1, a2: a2 <= a1, ["a1", "a2"])
prob.addConstraint(lambda b1, b2: b1 != 0 or b2 == 5, ["b1", "b2"])

for params in prob.getSolutionIter():
    run_sim(**params)