def test_density_gauss_2d(self):
# Arrange
mu = np.array([0, 1])
sigma = np.array([[1, 0.5], [0.5, 2]])
det_sigma = np.linalg.det(sigma)
n_bins = 100
N_points = int(10e6)
samples = np.random.multivariate_normal(mu, sigma, N_points)
p_min = np.min(samples, 0)
p_max = np.max(samples, 0)
points_linspX = np.linspace(p_min[0], p_max[0], n_bins)
points_linspY = np.linspace(p_min[1], p_max[1], n_bins)
mesh_x, mesh_y = np.meshgrid(points_linspX, points_linspY)
point_x = mesh_x.flatten()
point_y = mesh_y.flatten()
points = np.array([point_x, point_y]).T
# Act
dx_expected = (p_max - p_min) / n_bins
px_expected = 1/np.sqrt((2*np.pi)**2*det_sigma) * \
np.exp(-0.5*np.diag(np.dot((points-mu), np.dot((points-mu), np.linalg.inv(sigma)).T)))
px_expected = px_expected.reshape([n_bins, n_bins]).T
px, dx = inf.produce_P(samples, n_bins=n_bins)
# Assert
np.testing.assert_almost_equal(dx, dx_expected, decimal=3)
np.testing.assert_almost_equal(px, px_expected, decimal=2)
def test_entropy_uniform_1d(self):
# Arrange
u_min = -1
u_max = 3
N_points = int(10e6)
samples = np.random.uniform(u_min, u_max, N_points)
# Act
entropy_expected = inf.H_uniform_1d_theoretical(u_min, u_max)
entropy = inf.Entropy(*inf.produce_P(samples))
# Assert
np.testing.assert_almost_equal(entropy, entropy_expected, decimal=3)
def test_entropy_gauss_1d(self):
# Arrange
mu = 0
sigma = 1
N_points = int(10e6)
samples = np.random.randn(N_points) * sigma + mu
# Act
entropy_expected = inf.H_gaussian_1d_theoretical(mu, sigma)
entropy = inf.Entropy(*inf.produce_P(samples))
# Assert
np.testing.assert_almost_equal(entropy, entropy_expected, decimal=3)
def test_entropy_gauss_2d(self):
# Arrange
mu = np.array([0, 1])
sigma = np.array([[1, 0.5], [0.5, 2]])
N_points = int(10e6)
samples = np.random.multivariate_normal(mu, sigma, N_points)
# Act
entropy_expected = inf.H_gaussian_2d_theoretical(mu, sigma)
entropy = inf.Entropy(*inf.produce_P(samples))
# Assert
np.testing.assert_almost_equal(entropy, entropy_expected, decimal=3)
def test_entropy_uniform_2d(self):
# Arrange
u_min = np.array([-1, 2])
u_max = np.array([2, 4])
N_points = int(10e7)
samples = np.random.uniform(0, 1,
[N_points, 2]) * (u_max - u_min) + u_min
# Act
entropy_expected = inf.H_uniform_2d_theoretical(u_min, u_max)
entropy = inf.Entropy(*inf.produce_P(samples))
# Assert
np.testing.assert_almost_equal(entropy, entropy_expected, decimal=3)
def test_density_uniform_2d(self):
# Arrange
u_min = np.array([-1, 2])
u_max = np.array([2, 4])
n_bins = 100
N_points = int(10e7)
samples = np.random.uniform(0, 1,
[N_points, 2]) * (u_max - u_min) + u_min
# Act
dx_expected = (u_max - u_min) / n_bins
px_expected = np.full([n_bins, n_bins],
1 / n_bins**2 / np.prod(dx_expected))
px, dx = inf.produce_P(samples, n_bins=n_bins)
# Assert
np.testing.assert_almost_equal(dx, dx_expected, decimal=3)
np.testing.assert_almost_equal(px, px_expected, decimal=2)
def test_density_uniform_1d(self):
# Arrange
u_min = -1
u_max = 3
n_bins = 180
N_points = int(10e5)
samples = np.random.uniform(u_min, u_max, N_points)
points_linsp = np.linspace(u_min, u_max, n_bins)
# Act
dx_expected = points_linsp[1] - points_linsp[0]
px_expected = np.full(n_bins, 1 / n_bins / dx_expected)
px, dx = inf.produce_P(samples, n_bins=n_bins)
# Assert
np.testing.assert_almost_equal(dx, dx_expected, decimal=3)
np.testing.assert_almost_equal(px, px_expected, decimal=2)
def test_density_gauss_1d(self):
# Arrange
mu = 0
sigma = 1
n_bins = 180
N_points = int(10e5)
samples = np.random.randn(N_points) * sigma + mu
p_min = np.min(samples)
p_max = np.max(samples)
points_linsp = np.linspace(p_min, p_max, n_bins)
# Act
dx_expected = points_linsp[1] - points_linsp[0]
px_expected = 1 / np.sqrt(2 * np.pi * sigma**2) * np.exp(
-0.5 * (points_linsp - mu)**2 / sigma**2)
px, dx = inf.produce_P(samples, n_bins=n_bins)
# Assert
np.testing.assert_almost_equal(dx, dx_expected, decimal=3)
np.testing.assert_almost_equal(px, px_expected, decimal=2)