import numpy as np import pytest from numpy.testing import assert_allclose try: import scipy except ImportError: HAS_SCIPY = False else: HAS_SCIPY = True from astropy.stats.lombscargle import LombScargle from astropy.stats.lombscargle._statistics import (cdf_single, pdf_single, fap_single, inv_fap_single, METHODS) from astropy.stats.lombscargle.utils import convert_normalization, compute_chi2_ref METHOD_KWDS = dict(bootstrap={'n_bootstraps': 20, 'random_seed': 42}) NORMALIZATIONS = ['standard', 'psd', 'log', 'model'] def make_data(N=100, period=1, theta=[10, 2, 3], dy=1, rseed=0): """Generate some data for testing""" rng = np.random.RandomState(rseed) t = 5 * period * rng.rand(N) omega = 2 * np.pi / period y = theta[0] + theta[1] * np.sin(omega * t) + theta[2] * np.cos(omega * t) dy = dy * (0.5 + rng.rand(N)) y += dy * rng.randn(N) return t, y, dy @pytest.fixture def null_data(N=1000, dy=1, rseed=0): """Generate null hypothesis data""" rng = np.random.RandomState(rseed) t = 100 * rng.rand(N) dy = 0.5 * dy * (1 + rng.rand(N)) y = dy * rng.randn(N) return t, y, dy @pytest.mark.parametrize('normalization', NORMALIZATIONS) @pytest.mark.parametrize('with_errors', [True, False]) def test_distribution(null_data, normalization, with_errors, fmax=40): t, y, dy = null_data if not with_errors: dy = None N = len(t) ls = LombScargle(t, y, dy, normalization=normalization) freq, power = ls.autopower(maximum_frequency=fmax) z = np.linspace(0, power.max(), 1000) # Test that pdf and cdf are consistent dz = z[1] - z[0] z_mid = z[:-1] + 0.5 * dz pdf = ls.distribution(z_mid) cdf = ls.distribution(z, cumulative=True) assert_allclose(pdf, np.diff(cdf) / dz, rtol=1E-5, atol=1E-8) # psd normalization without specified errors produces bad results if not (normalization == 'psd' and not with_errors): # Test that observed power is distributed according to the theoretical pdf hist, bins = np.histogram(power, 30, normed=True) midpoints = 0.5 * (bins[1:] + bins[:-1]) pdf = ls.distribution(midpoints) assert_allclose(hist, pdf, rtol=0.05, atol=0.05 * pdf[0]) @pytest.mark.parametrize('N', [10, 100, 1000]) @pytest.mark.parametrize('normalization', NORMALIZATIONS) def test_inverse_single(N, normalization): fap = np.linspace(0, 1, 100) z = inv_fap_single(fap, N, normalization) fap_out = fap_single(z, N, normalization) assert_allclose(fap, fap_out) @pytest.mark.parametrize('normalization', NORMALIZATIONS) @pytest.mark.parametrize('use_errs', [True, False]) def test_inverse_bootstrap(null_data, normalization, use_errs, fmax=5): t, y, dy = null_data if not use_errs: dy = None fap = np.linspace(0, 1, 10) method = 'bootstrap' method_kwds = METHOD_KWDS['bootstrap'] ls = LombScargle(t, y, dy, normalization=normalization) z = ls.false_alarm_level(fap, maximum_frequency=fmax, method=method, method_kwds=method_kwds) fap_out = ls.false_alarm_probability(z, maximum_frequency=fmax, method=method, method_kwds=method_kwds) # atol = 1 / n_bootstraps assert_allclose(fap, fap_out, atol=0.05) @pytest.mark.parametrize('method', sorted(set(METHODS) - {'bootstrap'})) @pytest.mark.parametrize('normalization', NORMALIZATIONS) @pytest.mark.parametrize('use_errs', [True, False]) @pytest.mark.parametrize('N', [10, 100, 1000]) def test_inverses(method, normalization, use_errs, N, T=5, fmax=5): if not HAS_SCIPY and method in ['baluev', 'davies']: pytest.skip("SciPy required") t, y, dy = make_data(N, rseed=543) if not use_errs: dy = None method_kwds = METHOD_KWDS.get(method, None) fap = np.logspace(-10, 0, 10) ls = LombScargle(t, y, dy, normalization=normalization) z = ls.false_alarm_level(fap, maximum_frequency=fmax, method=method, method_kwds=method_kwds) fap_out = ls.false_alarm_probability(z, maximum_frequency=fmax, method=method, method_kwds=method_kwds) assert_allclose(fap, fap_out) @pytest.mark.parametrize('method', sorted(METHODS)) @pytest.mark.parametrize('normalization', NORMALIZATIONS) def test_false_alarm_smoketest(method, normalization): if not HAS_SCIPY and method in ['baluev', 'davies']: pytest.skip("SciPy required") kwds = METHOD_KWDS.get(method, None) t, y, dy = make_data() fmax = 5 ls = LombScargle(t, y, dy, normalization=normalization) freq, power = ls.autopower(maximum_frequency=fmax) Z = np.linspace(power.min(), power.max(), 30) fap = ls.false_alarm_probability(Z, maximum_frequency=fmax, method=method, method_kwds=kwds) assert len(fap) == len(Z) if method != 'davies': assert np.all(fap <= 1) assert np.all(fap[:-1] >= fap[1:]) # monotonically decreasing @pytest.mark.parametrize('method', sorted(METHODS)) @pytest.mark.parametrize('use_errs', [True, False]) @pytest.mark.parametrize('normalization', sorted(set(NORMALIZATIONS) - {'psd'})) def test_false_alarm_equivalence(method, normalization, use_errs): # Note: the PSD normalization is not equivalent to the others, in that it # depends on the absolute errors rather than relative errors. Because the # scaling contributes to the distribution, it cannot be converted directly # from any of the three normalized versions. if not HAS_SCIPY and method in ['baluev', 'davies']: pytest.skip("SciPy required") kwds = METHOD_KWDS.get(method, None) t, y, dy = make_data() if not use_errs: dy = None fmax = 5 ls = LombScargle(t, y, dy, normalization=normalization) freq, power = ls.autopower(maximum_frequency=fmax) Z = np.linspace(power.min(), power.max(), 30) fap = ls.false_alarm_probability(Z, maximum_frequency=fmax, method=method, method_kwds=kwds) # Compute the equivalent Z values in the standard normalization # and check that the FAP is consistent Z_std = convert_normalization(Z, len(t), from_normalization=normalization, to_normalization='standard', chi2_ref=compute_chi2_ref(y, dy)) ls = LombScargle(t, y, dy, normalization='standard') fap_std = ls.false_alarm_probability(Z_std, maximum_frequency=fmax, method=method, method_kwds=kwds) assert_allclose(fap, fap_std, rtol=0.1)