def test_error_transform_diag(N=20, rseed=0):
rng = np.random.RandomState(rseed)
X = rng.rand(N, 2)
yerr = 0.05 * (1 + rng.rand(N))
y = (X[:, 0] ** 2 + X[:, 1]) + yerr * rng.randn(N)
Sigma = np.eye(N) * yerr ** 2
X1, y1 = LinearRegression._scale_by_error(X, y, yerr)
X2, y2 = LinearRegression._scale_by_error(X, y, Sigma)
assert_allclose(X1, X2)
assert_allclose(y1, y2)
def test_error_transform_diag(N=20, rseed=0):
rng = np.random.RandomState(rseed)
X = rng.rand(N, 2)
yerr = 0.05 * (1 + rng.rand(N))
y = (X[:, 0]**2 + X[:, 1]) + yerr * rng.randn(N)
Sigma = np.eye(N) * yerr**2
X1, y1 = LinearRegression._scale_by_error(X, y, yerr)
X2, y2 = LinearRegression._scale_by_error(X, y, Sigma)
assert_allclose(X1, X2)
assert_allclose(y1, y2)
def test_error_transform_full(N=20, rseed=0):
rng = np.random.RandomState(rseed)
X = rng.rand(N, 2)
# generate a pos-definite error matrix
Sigma = 0.05 * rng.randn(N, N)
u, s, v = np.linalg.svd(Sigma)
Sigma = np.dot(u * s, u.T)
# draw y from this error distribution
y = (X[:, 0]**2 + X[:, 1])
y = rng.multivariate_normal(y, Sigma)
X2, y2 = LinearRegression._scale_by_error(X, y, Sigma)
# check that the form entering the chi^2 is correct
assert_allclose(np.dot(X2.T, X2), np.dot(X.T, np.linalg.solve(Sigma, X)))
assert_allclose(np.dot(y2, y2), np.dot(y, np.linalg.solve(Sigma, y)))
def test_error_transform_full(N=20, rseed=0):
rng = np.random.RandomState(rseed)
X = rng.rand(N, 2)
# generate a pos-definite error matrix
Sigma = 0.05 * rng.randn(N, N)
u, s, v = np.linalg.svd(Sigma)
Sigma = np.dot(u * s, u.T)
# draw y from this error distribution
y = (X[:, 0] ** 2 + X[:, 1])
y = rng.multivariate_normal(y, Sigma)
X2, y2 = LinearRegression._scale_by_error(X, y, Sigma)
# check that the form entering the chi^2 is correct
assert_allclose(np.dot(X2.T, X2),
np.dot(X.T, np.linalg.solve(Sigma, X)))
assert_allclose(np.dot(y2, y2),
np.dot(y, np.linalg.solve(Sigma, y)))
