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)
def test_autopower(data):
t, y, dy = data
ls = LombScargle(t, y, dy)
kwargs = dict(samples_per_peak=6, nyquist_factor=2,
minimum_frequency=2, maximum_frequency=None)
freq1 = ls.autofrequency(**kwargs)
power1 = ls.power(freq1)
freq2, power2 = ls.autopower(**kwargs)
assert_allclose(freq1, freq2)
assert_allclose(power1, power2)
def test_autopower(data):
t, y, dy = data
ls = LombScargle(t, y, dy)
kwargs = dict(samples_per_peak=6, nyquist_factor=2,
minimum_frequency=2, maximum_frequency=None)
freq1 = ls.autofrequency(**kwargs)
power1 = ls.power(freq1)
freq2, power2 = ls.autopower(**kwargs)
assert_allclose(freq1, freq2)
assert_allclose(power1, power2)
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
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])
def bootstrapped_power():
resample = rng.randint(0, len(y), len(y)) # sample with replacement
ls_boot = LombScargle(t, y[resample], dy[resample])
freq, power = ls_boot.autopower(normalization=normalization,
maximum_frequency=fmax)
return power.max()