def test_entropy_nonuniform(self):
d = Dist([2, 1])
self.assertTrue(isnan(entropy(d, b=-1.0)))
self.assertTrue(isnan(entropy(d, b=-0.5)))
self.assertAlmostEqual(0.000000, entropy(d, b=0.0), places=6)
self.assertAlmostEqual(-0.918296, entropy(d, b=0.5), places=6)
self.assertAlmostEqual(1.569837, entropy(d, b=1.5), places=6)
self.assertAlmostEqual(0.918296, entropy(d, b=2), places=6)
self.assertAlmostEqual(0.579380, entropy(d, b=3), places=6)
self.assertAlmostEqual(0.459148, entropy(d, b=4), places=6)
d = Dist([1, 1, 0])
self.assertTrue(isnan(entropy(d, b=-1.0)))
self.assertTrue(isnan(entropy(d, b=-0.5)))
self.assertAlmostEqual(0.000000, entropy(d, b=0.0), places=6)
self.assertAlmostEqual(-1.000000, entropy(d, b=0.5), places=6)
self.assertAlmostEqual(1.709511, entropy(d, b=1.5), places=6)
self.assertAlmostEqual(1.000000, entropy(d, b=2), places=6)
self.assertAlmostEqual(0.630930, entropy(d, b=3), places=6)
self.assertAlmostEqual(0.500000, entropy(d, b=4), places=6)
d = Dist([2, 2, 1])
self.assertTrue(isnan(entropy(d, b=-1.0)))
self.assertTrue(isnan(entropy(d, b=-0.5)))
self.assertAlmostEqual(0.000000, entropy(d, b=0.0), places=6)
self.assertAlmostEqual(-1.521928, entropy(d, b=0.5), places=6)
self.assertAlmostEqual(2.601753, entropy(d, b=1.5), places=6)
self.assertAlmostEqual(1.521928, entropy(d, b=2), places=6)
self.assertAlmostEqual(0.960230, entropy(d, b=3), places=6)
self.assertAlmostEqual(0.760964, entropy(d, b=4), places=6)
def test_conditional_entropy_dependent(self):
joint = Dist([10, 70, 15, 5])
x = Dist([80, 20])
y = Dist([25, 75])
self.assertTrue(isnan(conditional_entropy(joint, x, b=-1.0)))
self.assertTrue(isnan(conditional_entropy(joint, x, b=-0.5)))
self.assertAlmostEqual(
0.000000, conditional_entropy(joint, x, b=0.0), places=6)
self.assertAlmostEqual(-0.597107,
conditional_entropy(joint, x, b=0.5), places=6)
self.assertAlmostEqual(
1.020761, conditional_entropy(joint, x, b=1.5), places=6)
self.assertAlmostEqual(
0.597107, conditional_entropy(joint, x, b=2), places=6)
self.assertAlmostEqual(
0.376733, conditional_entropy(joint, x, b=3), places=6)
self.assertAlmostEqual(
0.298554, conditional_entropy(joint, x, b=4), places=6)
self.assertTrue(isnan(conditional_entropy(joint, y, b=-1.0)))
self.assertTrue(isnan(conditional_entropy(joint, y, b=-0.5)))
self.assertAlmostEqual(
0.000000, conditional_entropy(joint, y, b=0.0), places=6)
self.assertAlmostEqual(-0.507757,
conditional_entropy(joint, y, b=0.5), places=6)
self.assertAlmostEqual(
0.868017, conditional_entropy(joint, y, b=1.5), places=6)
self.assertAlmostEqual(
0.507757, conditional_entropy(joint, y, b=2), places=6)
self.assertAlmostEqual(
0.320359, conditional_entropy(joint, y, b=3), places=6)
self.assertAlmostEqual(
0.253879, conditional_entropy(joint, y, b=4), places=6)
def test_relative_entropy_sizes(self):
p = Dist(5)
p.tick(0)
q = Dist(4)
p.tick(1)
self.assertTrue(isnan(relative_entropy(p, q)))
self.assertTrue(isnan(relative_entropy(q, p)))
def test_relative_entropy_invalid(self):
p = Dist(5)
q = Dist(5)
self.assertTrue(isnan(relative_entropy(p, q)))
p.tick(0)
self.assertTrue(isnan(relative_entropy(p, q)))
self.assertTrue(isnan(relative_entropy(q, p)))
def test_relative_entropy(self):
p = Dist([1, 0, 0])
q = Dist([1, 1, 1])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(log(3., b), relative_entropy(p, q, b))
p = Dist([1, 1, 0])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(log(3. / 2., b), relative_entropy(p, q, b))
p = Dist([2, 2, 1])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(
(4. * log(6. / 5., b) + log(3. / 5., b)) / 5., relative_entropy(p, q, b))
q = Dist([1, 2, 2])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(log(2., b) / 5., relative_entropy(p, q, b))
p = Dist([1, 0, 0])
q = Dist([4, 1, 0])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(log(5. / 4., b), relative_entropy(p, q, b))
q = Dist([1, 4, 0])
for b in np.arange(2.0, 4.0, 0.5):
self.assertAlmostEqual(log(5., b), relative_entropy(p, q, b))
def test_tick_bounds_error(self):
d = Dist(2)
with self.assertRaises(IndexError):
d.tick(-1)
with self.assertRaises(IndexError):
d.tick(3)
def test_set_negative(self):
d = Dist(2)
d[0] = 5
self.assertEqual(5, d[0])
d[0] = -1
self.assertEqual(0, d[0])
def test_tick(self):
d = Dist(2)
self.assertEqual(1, d.tick(0))
self.assertEqual(2, d.tick(0))
self.assertEqual(2, d.counts())
self.assertTrue(d.valid())
def test_set_bounds_error(self):
d = Dist(2)
with self.assertRaises(IndexError):
d[-1] = 3
with self.assertRaises(IndexError):
d[3] = 1
def test_alloc_list_copies(self):
lst = [0, 0, 0, 0]
d = Dist(lst)
for i in range(len(d)):
d[i] = i
self.assertEqual(d[i], i)
self.assertEqual(lst[i], 0)
def test_alloc_array_copies(self):
arr = np.array([0, 0, 0, 0], dtype=np.uint32)
d = Dist(arr)
for i in range(len(d)):
d[i] = i
self.assertEqual(d[i], i)
self.assertEqual(arr[i], 0)
def test_probabilify_bounds_error(self):
d = Dist(2)
d[0] = 1
with self.assertRaises(IndexError):
d.probability(-1)
with self.assertRaises(IndexError):
d.probability(3)
def test_dump(self):
d = Dist(5)
for i in range(1, len(d)):
d[i] = i + 1
self.assertEqual(14, d.counts())
probs = d.dump()
self.assertTrue(
(probs == np.array([0., 2. / 14, 3. / 14, 4. / 14, 5. / 14])).all())
def test_entropy_delta_function(self):
d = Dist([0, 1, 0, 0, 0])
self.assertTrue(isnan(entropy(d, b=-1.0)))
self.assertTrue(isnan(entropy(d, b=-0.5)))
self.assertAlmostEqual(0.000000, entropy(d, b=0.0), places=6)
self.assertAlmostEqual(0.000000, entropy(d, b=0.5), places=6)
self.assertAlmostEqual(0.000000, entropy(d, b=1.5), places=6)
self.assertAlmostEqual(0.000000, entropy(d, b=2), places=6)
self.assertAlmostEqual(0.000000, entropy(d, b=3), places=6)
self.assertAlmostEqual(0.000000, entropy(d, b=4), places=6)
def test_relative_entropy_same_dist(self):
p = Dist(np.random.randint(0, 100, 20))
self.assertTrue(isnan(relative_entropy(p, p, -1.0)))
self.assertTrue(isnan(relative_entropy(p, p, -0.5)))
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 0.0), 1e-6)
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 0.5), 1e-6)
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 1.5), 1e-6)
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 2.0), 1e-6)
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 3.0), 1e-6)
self.assertAlmostEqual(0.000000, relative_entropy(p, p, 4.0), 1e-6)
def test_entropy_uniform(self):
d = Dist([1, 1, 1, 1, 1])
self.assertTrue(isnan(entropy(d, b=-1.0)))
self.assertTrue(isnan(entropy(d, b=-0.5)))
self.assertAlmostEqual(0.000000, entropy(d, b=0.0), places=6)
self.assertAlmostEqual(-2.321928, entropy(d, b=0.5), places=6)
self.assertAlmostEqual(3.969362, entropy(d, b=1.5), places=6)
self.assertAlmostEqual(2.321928, entropy(d, b=2), places=6)
self.assertAlmostEqual(1.464974, entropy(d, b=3), places=6)
self.assertAlmostEqual(1.160964, entropy(d, b=4), places=6)
def test_valid(self):
d = Dist(2)
self.assertFalse(d.valid())
d[0] = 2
self.assertTrue(d.valid())
d[1] = 2
self.assertTrue(d.valid())
d[0] = 0
self.assertTrue(d.valid())
d[1] = 0
self.assertFalse(d.valid())
def test_get_and_set(self):
d = Dist(2)
self.assertEqual(0, d[0])
d[0] = 4
self.assertEqual(4, d[0])
self.assertEqual(0, d[1])
d[1] = 2
self.assertEqual(2, d[1])
self.assertEqual(4, d[0])
def test_resize_shrink(self):
d = Dist(5)
for i in range(len(d)):
d[i] = i + 1
self.assertEqual(5, len(d))
self.assertEqual(15, d.counts())
d.resize(3)
self.assertEqual(3, len(d))
self.assertEqual(6, d.counts())
for i in range(len(d)):
self.assertEqual(i + 1, d[i])
def test_resize_grow(self):
d = Dist(3)
for i in range(len(d)):
d[i] = i + 1
self.assertEqual(3, len(d))
self.assertEqual(6, d.counts())
d.resize(5)
self.assertEqual(5, len(d))
self.assertEqual(6, d.counts())
for i in range(3):
self.assertEqual(i + 1, d[i])
for i in range(3, len(d)):
self.assertEqual(0, d[i])
def test_conditional_entropy_independent(self):
x = Dist([5, 2, 3, 5, 1, 4, 6, 2, 1, 4, 2, 4])
y = Dist([2, 4, 5, 2, 7, 3, 9, 8, 8, 7, 2, 3])
joint = Dist(len(x) * len(y))
for i in range(len(x)):
for j in range(len(y)):
joint[i * len(y) + j] = x[i] * y[j]
self.assertTrue(isnan(conditional_entropy(joint, x, b=-1.0)))
self.assertTrue(isnan(conditional_entropy(joint, x, b=-0.5)))
self.assertAlmostEqual(
0.00000, conditional_entropy(joint, x, b=0.0), places=6)
self.assertAlmostEqual(-3.391029,
conditional_entropy(joint, x, b=0.5), places=6)
self.assertAlmostEqual(
5.797002, conditional_entropy(joint, x, b=1.5), places=6)
self.assertAlmostEqual(
3.391029, conditional_entropy(joint, x, b=2), places=6)
self.assertAlmostEqual(
2.139501, conditional_entropy(joint, x, b=3), places=6)
self.assertAlmostEqual(
1.695514, conditional_entropy(joint, x, b=4), places=6)
self.assertTrue(isnan(conditional_entropy(joint, y, b=-1.0)))
self.assertTrue(isnan(conditional_entropy(joint, y, b=-0.5)))
self.assertAlmostEqual(
0.00000, conditional_entropy(joint, y, b=0.0), places=6)
self.assertAlmostEqual(-3.401199,
conditional_entropy(joint, y, b=0.5), places=6)
self.assertAlmostEqual(
5.814387, conditional_entropy(joint, y, b=1.5), places=6)
self.assertAlmostEqual(
3.401199, conditional_entropy(joint, y, b=2), places=6)
self.assertAlmostEqual(
2.145917, conditional_entropy(joint, y, b=3), places=6)
self.assertAlmostEqual(
1.700599, conditional_entropy(joint, y, b=4), places=6)
def test_copy(self):
d = Dist(5)
for i in range(len(d)):
d[i] = i + 1
self.assertEqual(5, len(d))
self.assertEqual(15, d.counts())
e = d.copy()
self.assertEqual(5, len(d))
self.assertEqual(15, d.counts())
for i in range(len(d)):
self.assertEqual(e[i], d[i])
d[0] = 5
self.assertNotEqual(e[0], d[0])
def test_counts(self):
d = Dist(2)
self.assertEqual(0, d.counts())
d[0] = 3
self.assertEqual(3, d.counts())
d[0] = 2
self.assertEqual(2, d.counts())
d[1] = 3
self.assertEqual(5, d.counts())
d[0] = 0
d[1] = 0
self.assertEqual(0, d.counts())
def test_dump_invalid(self):
d = Dist(2)
with self.assertRaises(ValueError):
d.dump()
def test_resize_zero(self):
d = Dist(3)
with self.assertRaises(ValueError):
d.resize(0)
def test_resize_negative(self):
d = Dist(3)
with self.assertRaises(ValueError):
d.resize(-1)
def test_alloc_array(self):
arr = np.array([1, 1, 2, 2], dtype=np.uint32)
d = Dist(arr)
self.assertEqual(4, len(d))
for i in range(len(arr)):
self.assertEqual(arr[i], d[i])
def test_alloc_list(self):
lst = [1, 1, 2, 2]
d = Dist(lst)
self.assertEqual(4, len(d))
for i in range(len(d)):
self.assertEqual(lst[i], d[i])
def test_alloc_size(self):
d = Dist(5)
self.assertEqual(5, d.__len__())
self.assertEqual(5, len(d))
def test_alloc_mulitdimensional(self):
with self.assertRaises(ValueError):
Dist([[1, 1, 2, 2]])
with self.assertRaises(ValueError):
Dist(np.array([[1, 1, 2, 2]]))
