def test_lts_regression_singular_pair():
"""
Test the lts regression with data that contains a pair
of points creating a singular matrix
"""
from ctapipe.fitting import lts_linear_regression, design_matrix, EPS
np.random.seed(1337)
true_beta = np.array([5.0, 2.0])
# make test contain data that creates a singular matrix
x = np.linspace(0, 10, 25)
x = np.repeat(x, 2)
y = np.polyval(true_beta, x)
x[:2] = 0
y[:2] = 1
X = design_matrix(x[:2])
assert np.linalg.det(X.T @ X) < EPS
beta, error = lts_linear_regression(x, y, samples=100)
assert np.allclose(true_beta, beta)
assert np.isclose(error, 0)
def test_design_matrix():
from ctapipe.fitting import design_matrix
x = np.array([1, 2, 3])
matrix = design_matrix(x)
assert np.all(matrix[:, 0] == x)
assert np.all(matrix[:, 1] == 1)
def test_linear_regression_singular():
from ctapipe.fitting import linear_regression, design_matrix
# test under-determined input
x = np.zeros(2, dtype=float)
y = np.array([2, 1], dtype=float)
X = design_matrix(x)
beta = linear_regression(X, y)
assert np.all(np.isnan(beta))
def test_linear_regression():
from ctapipe.fitting import linear_regression, design_matrix
# test without noise, should give exact result
true_beta = np.array([5.0, 2.0])
x = np.linspace(0, 10, 50)
y = np.polyval(true_beta, x)
X = design_matrix(x)
beta = linear_regression(X, y)
assert np.allclose(true_beta, beta)