def test_distribution_convex_combination(self):
a = statistics.Distribution({
(0, 0): 0.4,
(0, 1): 0.3,
(1, 0): 0.2,
(1, 1): 0.1
})
b = statistics.Distribution({
(0, -1): 0.1,
(0, 0): 0.2,
(0, 1): 0.3,
(0, 2): 0.4
})
tau = 0.73111
# let c be a convex combination of a and b, written in a wierd way.
# this should test scalar mult, addition, unary negation operator
# etc.
c = a * tau + b + tau * (-b)
assert len(c) == 6
assert_almost_equal(c[(0, -1)], 0.1 * (1.0 - tau))
assert_almost_equal(c[(0, 0)], 0.4 * tau + 0.2 * (1.0 - tau))
assert_almost_equal(c[(0, 1)], 0.3 * tau + 0.3 * (1.0 - tau))
assert_almost_equal(c[(1, 0)], 0.2 * tau)
assert_almost_equal(c[(1, 1)], 0.1 * tau)
assert_almost_equal(c[(0, 2)], 0.4 * (1.0 - tau))
def test_norms_and_metrics(self):
a = statistics.Distribution({
(0, 0): 0.4,
(0, 1): 0.3,
(1, 0): 0.2,
(1, 1): 0.1
})
for p in numpy.linspace(0.1, 2.5, 25):
assert_almost_equal(a.lp_distance(a, p), 0.0)
assert a.lp_norm(p) > 0.0
assert numpy.isinf(a.kl_divergence(statistics.Distribution()))
assert_almost_equal(a.kl_divergence(a), 0.0)
def test_dense_conversions(self):
p = statistics.Distribution()
p_dense = numpy.array([
[0.0, 0.2, 0.1, 0.0],
[0.3, 0.0, 0.1, 0.3],
])
p.from_dense(p_dense)
assert len(p) == 5
assert p[(0, 1)] == 0.2
assert p[(0, 2)] == 0.1
assert p[(1, 0)] == 0.3
assert p[(1, 2)] == 0.1
assert p[(1, 3)] == 0.3
p.from_dense(p_dense, origin=(-1, 3))
assert len(p) == 5
assert p[(-1, 4)] == 0.2
assert p[(-1, 5)] == 0.1
assert p[(0, 3)] == 0.3
assert p[(0, 5)] == 0.1
assert p[(0, 6)] == 0.3
def test_distribution_scalar_multiplication(self):
a = statistics.Distribution({
(0, 0): 0.4,
(0, 1): 0.3,
(1, 0): 0.2,
(1, 1): 0.1
})
b = -3.2
# left mult with scalar
c = a * b
assert len(c) == 4
assert_almost_equal(c[(0, 0)], 0.4 * b)
assert_almost_equal(c[(0, 1)], 0.3 * b)
assert_almost_equal(c[(1, 0)], 0.2 * b)
assert_almost_equal(c[(1, 1)], 0.1 * b)
# right mult with scalar
c = b * a
assert len(c) == 4
assert_almost_equal(c[(0, 0)], 0.4 * b)
assert_almost_equal(c[(0, 1)], 0.3 * b)
assert_almost_equal(c[(1, 0)], 0.2 * b)
assert_almost_equal(c[(1, 1)], 0.1 * b)
def unpack_distribution(self, p_dense, p_sparse=None):
"""
convenience routine to translate a distribution from a dense array
to a dictionary, using this state enumeration
"""
p_indices = numpy.arange(numpy.size(p_dense))
# convert from list of coordinate vectors to list of states
p_states = domain.to_iter(self.states(p_indices))
if p_sparse is None:
p_sparse = statistics.Distribution()
for index, state in zip(p_indices, p_states):
value = p_dense[index]
if value != 0.0:
p_sparse[state] = value
return p_sparse
def test_distribution_addition(self):
a = statistics.Distribution({
(0, 0): 0.4,
(0, 1): 0.3,
(1, 0): 0.2,
(1, 1): 0.1
})
b = statistics.Distribution({
(0, -1): 0.1,
(0, 0): 0.2,
(0, 1): 0.3,
(0, 2): 0.4
})
c = a + b
assert len(c) == 6
assert_almost_equal(c[(0, -1)], 0.1)
assert_almost_equal(c[(0, 0)], 0.6)
assert_almost_equal(c[(0, 1)], 0.6)
assert_almost_equal(c[(1, 0)], 0.2)
assert_almost_equal(c[(1, 1)], 0.1)
assert_almost_equal(c[(0, 2)], 0.4)
def test_distribution_subtraction(self):
a = statistics.Distribution({
(0, 0): 0.4,
(0, 1): 0.3,
(1, 0): 0.2,
(1, 1): 0.1
})
b = statistics.Distribution({
(0, -1): 0.1,
(0, 0): 0.2,
(0, 1): 0.3,
(0, 2): 0.4
})
c = b - a
assert len(c) == 6
assert_almost_equal(c[(0, -1)], 0.1)
assert_almost_equal(c[(0, 0)], -0.2)
assert_almost_equal(c[(0, 1)], 0.0)
assert_almost_equal(c[(1, 0)], -0.2)
assert_almost_equal(c[(1, 1)], -0.1)
assert_almost_equal(c[(0, 2)], 0.4)