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_nterms_methods(method, center_data, fit_mean, errors,
nterms, normalization, data):
t, y, dy = data
frequency = 0.8 + 0.01 * np.arange(40)
if errors == 'none':
dy = None
elif errors == 'partial':
dy = dy[0]
elif errors == 'full':
pass
else:
raise ValueError("Unrecognized error type: '{0}'".format(errors))
ls = LombScargle(t, y, dy, center_data=center_data,
fit_mean=fit_mean, nterms=nterms,
normalization=normalization)
if nterms == 0 and not fit_mean:
with pytest.raises(ValueError) as err:
ls.power(frequency, method=method)
assert 'nterms' in str(err.value) and 'bias' in str(err.value)
else:
P_expected = ls.power(frequency)
# don't use fast fft approximations here
kwds = {}
if 'fast' in method:
kwds['method_kwds'] = dict(use_fft=False)
P_method = ls.power(frequency, method=method, **kwds)
assert_allclose(P_expected, P_method, rtol=1E-7, atol=1E-25)
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_model_units_match(data, t_unit, frequency_unit, y_unit):
t, y, dy = data
t_fit = t[:5]
frequency = 1.0
t = t * t_unit
t_fit = t_fit * t_unit
y = y * y_unit
dy = dy * y_unit
frequency = frequency * frequency_unit
ls = LombScargle(t, y, dy)
y_fit = ls.model(t_fit, frequency)
assert y_fit.unit == y_unit
def test_false_alarm_equivalence(method, normalization, use_errs, units):
# 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, fmax = make_data(units=units)
if not use_errs:
dy = None
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_model(fit_mean, with_units, freq):
rand = np.random.RandomState(0)
t = 10 * rand.rand(40)
params = 10 * rand.rand(3)
y = np.zeros_like(t)
if fit_mean:
y += params[0]
y += params[1] * np.sin(2 * np.pi * freq * (t - params[2]))
if with_units:
t = t * u.day
y = y * u.mag
freq = freq / u.day
ls = LombScargle(t, y, center_data=False, fit_mean=fit_mean)
y_fit = ls.model(t, freq)
assert_quantity_allclose(y_fit, y)
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_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)
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)
def test_all_methods(data, method, center_data, fit_mean,
errors, with_units, normalization):
if method == 'scipy' and (fit_mean or errors != 'none'):
return
t, y, dy = data
frequency = 0.8 + 0.01 * np.arange(40)
if with_units:
t = t * u.day
y = y * u.mag
dy = dy * u.mag
frequency = frequency / t.unit
if errors == 'none':
dy = None
elif errors == 'partial':
dy = dy[0]
elif errors == 'full':
pass
else:
raise ValueError("Unrecognized error type: '{0}'".format(errors))
kwds = {}
ls = LombScargle(t, y, dy, center_data=center_data, fit_mean=fit_mean,
normalization=normalization)
P_expected = ls.power(frequency)
# don't use the fft approximation here; we'll test this elsewhere
if method in FAST_METHODS:
kwds['method_kwds'] = dict(use_fft=False)
P_method = ls.power(frequency, method=method, **kwds)
if with_units:
if normalization == 'psd' and errors == 'none':
assert P_method.unit == y.unit ** 2
else:
assert P_method.unit == u.dimensionless_unscaled
else:
assert not hasattr(P_method, 'unit')
assert_quantity_allclose(P_expected, P_method)
def test_false_alarm_smoketest(method, normalization, units):
if not HAS_SCIPY and method in ['baluev', 'davies']:
pytest.skip("SciPy required")
kwds = METHOD_KWDS.get(method, None)
t, y, dy, fmax = make_data(units=units)
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_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)
def test_distribution(normalization, with_errors, units):
t, y, dy, fmax = null_data(units=units)
if not with_errors:
dy = None
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)
if isinstance(dz, u.Quantity):
dz = dz.value
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, density=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 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)
def test_model_parameters(data, nterms, fit_mean, center_data,
errors, with_units):
if nterms == 0 and not fit_mean:
return
t, y, dy = data
frequency = 1.5
if with_units:
t = t * u.day
y = y * u.mag
dy = dy * u.mag
frequency = frequency / t.unit
if errors == 'none':
dy = None
elif errors == 'partial':
dy = dy[0]
elif errors == 'full':
pass
else:
raise ValueError("Unrecognized error type: '{0}'".format(errors))
ls = LombScargle(t, y, dy,
nterms=nterms,
fit_mean=fit_mean,
center_data=center_data)
tfit = np.linspace(0, 20, 10)
if with_units:
tfit = tfit * u.day
model = ls.model(tfit, frequency)
params = ls.model_parameters(frequency)
design = ls.design_matrix(frequency, t=tfit)
offset = ls.offset()
assert len(params) == int(fit_mean) + 2 * nterms
assert_quantity_allclose(offset + design.dot(params), model)
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 test_fast_approximations(method, center_data, fit_mean,
errors, nterms, data):
t, y, dy = data
frequency = 0.8 + 0.01 * np.arange(40)
if errors == 'none':
dy = None
elif errors == 'partial':
dy = dy[0]
elif errors == 'full':
pass
else:
raise ValueError("Unrecognized error type: '{0}'".format(errors))
ls = LombScargle(t, y, dy, center_data=center_data,
fit_mean=fit_mean, nterms=nterms,
normalization='standard')
# use only standard normalization because we compare via absolute tolerance
kwds = dict(method=method)
if method == 'fast' and nterms != 1:
with pytest.raises(ValueError) as err:
ls.power(frequency, **kwds)
assert 'nterms' in str(err.value)
elif nterms == 0 and not fit_mean:
with pytest.raises(ValueError) as err:
ls.power(frequency, **kwds)
assert 'nterms' in str(err.value) and 'bias' in str(err.value)
else:
P_fast = ls.power(frequency, **kwds)
kwds['method_kwds'] = dict(use_fft=False)
P_slow = ls.power(frequency, **kwds)
assert_allclose(P_fast, P_slow, atol=0.008)
def test_absolute_times(data, timedelta):
# Make sure that we handle absolute times correctly. We also check that
# TimeDelta works properly when timedelta is True.
# The example data uses relative times
t, y, dy = data
# FIXME: There seems to be a numerical stability issue in that if we run
# the algorithm with the same values but offset in time, the transit_time
# is not offset by a fixed amount. To avoid this issue in this test, we
# make sure the first time is also the smallest so that internally the
# values of the relative time should be the same.
t[0] = 0.
# Add units
t = t * u.day
y = y * u.mag
dy = dy * u.mag
# We now construct a set of absolute times but keeping the rest the same
start = Time('2019-05-04T12:34:56')
trel = TimeDelta(t) if timedelta else t
t = trel + start
# and we set up two instances of LombScargle, one with absolute and one
# with relative times.
ls1 = LombScargle(t, y, dy)
ls2 = LombScargle(trel, y, dy)
kwargs = dict(samples_per_peak=6, nyquist_factor=2,
minimum_frequency=2 / u.day, maximum_frequency=None)
freq1 = ls1.autofrequency(**kwargs)
freq2 = ls2.autofrequency(**kwargs)
assert_quantity_allclose(freq1, freq2)
power1 = ls1.power(freq1)
power2 = ls2.power(freq2)
assert_quantity_allclose(power1, power2)
freq1, power1 = ls1.autopower(**kwargs)
freq2, power2 = ls2.autopower(**kwargs)
assert_quantity_allclose(freq1, freq2)
assert_quantity_allclose(power1, power2)
model1 = ls1.model(t, 2 / u.day)
model2 = ls2.model(trel, 2 / u.day)
assert_quantity_allclose(model1, model2)
# Check model validation
with pytest.raises(TypeError) as exc:
ls1.model(trel, 2 / u.day)
assert exc.value.args[0] == ('t was provided as a relative time but the '
'LombScargle class was initialized with '
'absolute times.')
with pytest.raises(TypeError) as exc:
ls2.model(t, 2 / u.day)
assert exc.value.args[0] == ('t was provided as an absolute time but the '
'LombScargle class was initialized with '
'relative times.')
# Check design matrix
design1 = ls1.design_matrix(2 / u.day, t=t)
design2 = ls2.design_matrix(2 / u.day, t=trel)
assert_quantity_allclose(design1, design2)
# Check design matrix validation
with pytest.raises(TypeError) as exc:
ls1.design_matrix(2 / u.day, t=trel)
assert exc.value.args[0] == ('t was provided as a relative time but the '
'LombScargle class was initialized with '
'absolute times.')
with pytest.raises(TypeError) as exc:
ls2.design_matrix(2 / u.day, t=t)
assert exc.value.args[0] == ('t was provided as an absolute time but the '
'LombScargle class was initialized with '
'relative times.')