class MarginalTests(TestCase):
def setUp(self):
self.norm = JointNormal(
mu=[0, 1, 2],
labels=['x', 'y', 'z'],
cov=[
[0, 1, 2],
[3, 4, 5],
[6, 7, 8]
], N=10)
def test_forward(self):
marg = self.norm.marginal('y', 'z')
cov_diff = marg.cov - np.matrix([[4, 5], [7, 8]])
mu_diff = marg.mu - np.matrix([[1], [2]])
self.assertAlmostEqual(cov_diff.max(), 0)
self.assertAlmostEqual(cov_diff.min(), 0)
self.assertAlmostEqual(mu_diff.min(), 0)
self.assertAlmostEqual(mu_diff.max(), 0)
self.assertEqual(marg.N, self.norm.N)
def test_backward(self):
marg = self.norm.marginal('z', 'y')
cov_diff = marg.cov - np.matrix([[8, 7], [5, 4]])
mu_diff = marg.mu - np.matrix([[2], [1]])
self.assertAlmostEqual(cov_diff.max(), 0)
self.assertAlmostEqual(cov_diff.min(), 0)
self.assertAlmostEqual(mu_diff.min(), 0)
self.assertAlmostEqual(mu_diff.max(), 0)
self.assertEqual(marg.N, self.norm.N)
def test_str(self):
p = JointNormal(labels=['x', 'y'], mu=[0, 0], cov=[[1e-19, 1e-19], [1e-19, 1e-19]])
p.ingest(self.df)
s = str(p)
self.assertTrue('N' in s)
self.assertTrue('x' in s)
self.assertTrue('x' in s)
def test_cov(self):
p = JointNormal(labels=['x', 'y'])
p.ingest(self.df)
self.assertAlmostEqual(p.cov[0, 0], self.cov[0, 0])
self.assertAlmostEqual(p.cov[1, 1], self.cov[1, 1])
self.assertAlmostEqual(p.cov[1, 0], self.cov[1, 0])
self.assertAlmostEqual(p.cov[0, 1], self.cov[0, 1])
self.assertAlmostEqual(self.N, p.N)
def setUp(self):
self.P = JointNormal(
mu=[1, 1],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
def setUp(self):
self.norm = JointNormal(
mu=[0, 1, 2],
labels=['x', 'y', 'z'],
cov=[
[0, 1, 2],
[3, 4, 5],
[6, 7, 8]
], N=10)
def test_list_input(self):
p = JointNormal(labels=['x', 'y'], mu=[0, 0], cov=[[1e-19, 1e-19], [1e-19, 1e-19]])
df = self.df[['y', 'x']]
p.ingest(df)
mu, cov, N = p.mu_cov_n
self.assertAlmostEqual(p.mu[0, 0], self.mu[0])
self.assertAlmostEqual(p.mu[1, 0], self.mu[1])
self.assertEqual(tuple(cov.shape), (2, 2))
self.assertEqual(N, len(self.df))
def test_correct_value(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 0],
[0, 1],
], N=10)
percentile_value = P.percentile(x=.75)
self.assertAlmostEqual(P.probability(x__lt=percentile_value), .75, places=12)
def test_too_many_vars(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 0],
[0, 1],
], N=10)
with self.assertRaises(ValueError):
P.percentile(x=.75, y=.2)
def test_no_limits(self):
P = JointNormal(
mu=[1, 1],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
with self.assertRaises(ValueError):
P.probability(x=2, y=2)
def test_conditional(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
mu_x, sigma_x = P.estimate('x', y=9)
self.assertAlmostEqual(mu_x, 8.91, places=2)
self.assertAlmostEqual(sigma_x, .1, places=1)
def test_full_subtract(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[1, 1], cov=[[2, 1], [1, 2]])
norm2 = JointNormal(labels=['x', 'y'], mu=[2, 2], cov=[[2, 1], [1, 2]])
normp = norm1 - norm2
mu_diff = normp.mu - (norm1.mu - norm2.mu)
cov_diff = normp.cov - (norm1.cov + norm2.cov)
self.assertAlmostEqual(mu_diff.max(), 0)
self.assertAlmostEqual(mu_diff.min(), 0)
self.assertAlmostEqual(cov_diff.max(), 0)
self.assertAlmostEqual(cov_diff.min(), 0)
def test_correct_value(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 0],
[0, 1],
], N=10)
N = stats.norm()
self.assertAlmostEqual(P.probability(x__gt=0, y=0), N.cdf(0), places=14)
self.assertAlmostEqual(P.probability(x__lt=1, y=0), N.cdf(1), places=14)
self.assertAlmostEqual(P.probability(x__gt=5, y=0), 1. - N.cdf(5), places=14)
def test_iterable(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 0],
[0, 1],
], N=10)
percentiles = [.25, .5, .75]
values_at_percentiles = P.percentile(x=percentiles)
new_percentiles = P.probability(x__lt=values_at_percentiles)
self.assertAlmostEqual(new_percentiles[0], percentiles[0])
self.assertAlmostEqual(new_percentiles[1], percentiles[1])
self.assertAlmostEqual(new_percentiles[2], percentiles[2])
def test_full_multiply(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[0, 0], cov=[[2, 1], [1, 2]])
norm2 = JointNormal(labels=['x', 'y'], mu=[2, 2], cov=[[2, 1], [1, 2]])
normp = norm1 * norm2
prec1 = norm1.cov.getI()
prec2 = norm2.cov.getI()
precp = normp.cov.getI()
dprec = precp - prec1 - prec2
self.assertAlmostEqual(dprec.max(), 0)
self.assertAlmostEqual(dprec.min(), 0)
self.assertAlmostEqual(normp.mu.max(), 1)
self.assertAlmostEqual(normp.mu.min(), 1)
def test_with_args(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[0, 0], cov=[[4, 1], [1, 4]])
norm2 = JointNormal(labels=['x', 'y'], mu=[2, 2], cov=[[4, 1], [1, 4]])
normp = multiply_independent_normals(norm1, norm1, norm2, norm2)
prec1 = norm1.cov.getI()
prec2 = norm2.cov.getI()
precp = normp.cov.getI()
dprec = precp - 2 * (prec1 + prec2)
self.assertAlmostEqual(dprec.max(), 0)
self.assertAlmostEqual(dprec.min(), 0)
self.assertAlmostEqual(normp.mu.max(), 1)
self.assertAlmostEqual(normp.mu.min(), 1)
def test_marginal(self):
P = JointNormal(
mu=[-1, 1],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
mu_x, sigma_x = P.estimate('x')
mu_y, sigma_y = P.estimate('y')
self.assertAlmostEqual(mu_x, -1)
self.assertAlmostEqual(mu_y, 1)
self.assertAlmostEqual(sigma_x, 1)
self.assertAlmostEqual(sigma_y, 1, places=1)
def test_with_list(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[1, 1], cov=[[4, 1], [1, 4]])
norm2 = JointNormal(labels=['x', 'y'], mu=[2, 2], cov=[[40, 1], [1, 4]])
normp = add_independent_normals([norm1, norm1, norm2, norm2])
cov1 = norm1.cov
cov2 = norm2.cov
covp = normp.cov
dcov = covp - 2 * (cov1 + cov2)
self.assertAlmostEqual(dcov.max(), 0)
self.assertAlmostEqual(dcov.min(), 0)
self.assertAlmostEqual(normp.mu.max(), 6)
self.assertAlmostEqual(normp.mu.min(), 6)
def test_sums_to_one(self):
P = JointNormal(
mu=[1, 1],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
px_gt = P.probability(x__gt=2, y=2)
px_lt = P.probability(x__lt=2, y=2)
py_gt = P.probability(y__gt=2, x=-20)
py_lt = P.probability(y__lt=2, x=-20)
self.assertAlmostEqual(sum([px_gt, px_lt]), 1, places=14)
self.assertAlmostEqual(sum([py_gt, py_lt]), 1, places=14)
def test_diag_multiply(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[1, 0], cov=[[2, 0], [0, 2]])
norm2 = JointNormal(labels=['x', 'y'], mu=[0, 1], cov=[[2, 0], [0, 2]])
normp = norm1 * norm2
V = normp.cov
mu = normp.mu
self.assertAlmostEqual(V[0, 0], 1)
self.assertAlmostEqual(V[1, 1], 1)
self.assertAlmostEqual(V[0, 1], 0)
self.assertAlmostEqual(V[1, 0], 0)
self.assertAlmostEqual(mu[0, 0], .5)
self.assertAlmostEqual(mu[1, 0], .5)
def setUp(self):
# Let R be the square root covariance matrix (lower diag)
# Then imagine a sample where measurement errors are
# e = [e_x, 0, 0].T
# Then the conditional expectation of the joint normal
# with any mu and covariance S = R * R.T
# will be X_cond = mu + R * e
# define sqrt covariance (this can be arbitrary square matrix)
self.R = np.matrix(
[
[100, 0, 0],
[20, 10, 0],
[5, 4, 3]
]
)
# compute covariance matrix
S = self.R * self.R.T
# define the mu vector
self.mu = np.matrix([2, 3, 4]).T
# create joint normal
self.N = JointNormal(mu=self.mu, labels=['x', 'y', 'z'], cov=S, N=10)
def test_iterable(self):
P = JointNormal(
mu=[0, 0],
labels=['x', 'y'],
cov=[
[1, 0],
[0, 1],
], N=10)
x0 = range(-5, 6)
p_gt = np.array(P.probability(x__gt=x0))
p_lt = np.array(P.probability(x__lt=x0, y=2))
p_sum = p_gt + p_lt
self.assertTrue(all(round(x, 2) == 1 for x in p_sum))
self.assertAlmostEqual(p_gt[5], .5)
self.assertTrue(p_gt[0] > .5)
self.assertTrue(p_lt[0] < .5)
self.assertTrue(p_gt[-1] < .5)
self.assertTrue(p_lt[-1] > .5)
def setUp(self):
self.norm = JointNormal(
mu=[0, 1, 2, 3],
labels=['a', 'b', 'c', 'd'],
cov=[
[1, 2, 3, 4],
[2, 5, 6, 7],
[3, 6, 8, 9],
[4, 7, 9, 10],
], N=10)
class RenameMeTests(TestCase):
def setUp(self):
self.P = JointNormal(
mu=[1, 1],
labels=['x', 'y'],
cov=[
[1, 1],
[1, 1.01],
], N=10)
def test_index_for_bad_labels(self):
with self.assertRaises(ValueError):
self.P._index_for(['bad', 'labels'])
def test_mu_frame(self):
df = self.P.mu_frame
self.assertEqual(list(df.columns), ['mu'])
self.assertEqual(len(df), 2)
def test_cov_frame(self):
df = self.P.cov_frame
self.assertEqual(list(df.columns), ['x', 'y'])
self.assertEqual(list(df.index), ['x', 'y'])
def test_check_args_too_big(self):
with self.assertRaises(ValueError):
self.P._check_args(free_ind=[100])
def test_check_args_overlap(self):
with self.assertRaises(ValueError):
self.P._check_args(free_ind=[1], fixed_ind=[1])
def test_check_args_dups_free(self):
with self.assertRaises(ValueError):
self.P._check_args(free_ind=[1, 1])
def test_check_args_dups_fixed(self):
with self.assertRaises(ValueError):
self.P._check_args(fixed_ind=[1, 1])
def test_set_cov(self):
p = JointNormal(labels=['x', 'y'], mu=np.array([0, 0]), cov=np.array([[1e-19, 1e-19], [1e-19, 1e-19]]))
p.cov = self.cov
self.assertAlmostEqual(p.cov[0, 0], self.cov[0, 0])
self.assertAlmostEqual(p.cov[1, 1], self.cov[1, 1])
def test_set_mu(self):
p = JointNormal(labels=['x', 'y'], mu=np.array([0, 0]), cov=np.array([[1e-19, 1e-19], [1e-19, 1e-19]]))
p.mu = self.mu
self.assertAlmostEqual(p.mu[0, 0], self.mu[0])
self.assertAlmostEqual(p.mu[1, 0], self.mu[1])
def test_array_input(self):
p = JointNormal(labels=['x', 'y'], mu=np.array([0, 0]), cov=np.array([[1e-19, 1e-19], [1e-19, 1e-19]]))
p.ingest(self.df)
self.assertAlmostEqual(p.mu[0, 0], self.mu[0])
self.assertAlmostEqual(p.mu[1, 0], self.mu[1])
def test_list_input_bad_frame(self):
p = JointNormal(labels=['a', 'b'], mu=[0, 0], cov=[[1e-19, 1e-19], [1e-19, 1e-19]])
with self.assertRaises(ValueError):
p.ingest(self.df)
def test_bad_dimensions(self):
norm1 = JointNormal(labels=['x', 'y'], mu=[1, 1], cov=[[4, 1], [1, 4]])
norm2 = JointNormal(labels=['y'], mu=[0], cov=[[2]])
with self.assertRaises(ValueError):
norm1 > norm2
def test_one_sigma_difference(self):
norm1 = JointNormal(labels=['x'], mu=[2], cov=[[2]])
norm2 = JointNormal(labels=['y'], mu=[0], cov=[[2]])
self.assertAlmostEqual(norm1 > norm2, 0.84134474606854293)
self.assertAlmostEqual(norm1 < norm2, 0.15865525393145707)
def test_5050(self):
norm1 = JointNormal(labels=['x'], mu=[1], cov=[[4]])
norm2 = JointNormal(labels=['y'], mu=[1], cov=[[4]])
self.assertAlmostEqual(norm1 > norm2, .5)
self.assertAlmostEqual(norm2 > norm1, .5)