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import pytest
import numpy as np
from numpy.testing import assert_allclose
from sklearn.linear_model import LinearRegression as skLinearRegression
from astroML.linear_model import \
LinearRegression, PolynomialRegression, BasisFunctionRegression
try:
import pymc3 as pm # noqa: F401
HAS_PYMC3 = True
except ImportError:
HAS_PYMC3 = False
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_LinearRegression_simple():
"""
Test a simple linear regression
"""
x = np.arange(10.).reshape((10, 1))
y = np.arange(10.) + 1
dy = 1
clf = LinearRegression().fit(x, y, dy)
y_true = clf.predict(x)
assert_allclose(y, y_true, atol=1E-10)
def test_LinearRegression_err():
"""
Test that errors are correctly accounted for
By comparing to scikit-learn LinearRegression
"""
np.random.seed(0)
X = np.random.random((10, 1))
y = np.random.random(10) + 1
dy = 0.1
y = np.random.normal(y, dy)
clf1 = LinearRegression().fit(X, y, dy)
clf2 = skLinearRegression().fit(X / dy, y / dy)
assert_allclose(clf1.coef_[1:], clf2.coef_)
assert_allclose(clf1.coef_[0], clf2.intercept_ * dy)
def test_LinearRegression_fit_intercept():
np.random.seed(0)
X = np.random.random((10, 1))
y = np.random.random(10)
clf1 = LinearRegression(fit_intercept=False).fit(X, y)
clf2 = skLinearRegression(fit_intercept=False).fit(X, y)
assert_allclose(clf1.coef_, clf2.coef_)
def test_PolynomialRegression_simple():
x = np.arange(10.).reshape((10, 1))
y = np.arange(10.)
dy = 1
clf = PolynomialRegression(2).fit(x, y, dy)
y_true = clf.predict(x)
assert_allclose(y, y_true, atol=1E-10)
def test_BasisfunctionRegression_simple():
x = np.arange(10.).reshape((10, 1))
y = np.arange(10.) + 1
dy = 1
mu = np.arange(11.)[:, None]
sigma = 1.0
clf = BasisFunctionRegression(mu=mu, sigma=sigma).fit(x, y, dy)
y_true = clf.predict(x)
assert_allclose(y, y_true, atol=1E-10)
@pytest.mark.skipif('not HAS_PYMC3')
def test_LinearRegressionwithErrors():
"""
Test for small errors agrees with fit with y errors only
"""
from astroML.linear_model import LinearRegressionwithErrors
np.random.seed(0)
X = np.random.random(10) + 1
dy = np.random.random(10) * 0.1
y = X * 2 + 1 + (dy - 0.05)
dx = np.random.random(10) * 0.01
X = X + (dx - 0.005)
clf1 = LinearRegression().fit(X[:, None], y, dy)
clf2 = LinearRegressionwithErrors().fit(np.atleast_2d(X), y, dy, dx)
assert_allclose(clf1.coef_, clf2.coef_, 0.2)
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