def test_lomb_scargle_period_folding():
"""Tests for features derived from fitting a Lomb-Scargle periodic model
and period-folding the data by the estimated period.
"""
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS)-1)))
amplitudes = np.zeros((len(WAVE_FREQS),4))
amplitudes[0,:] = [8,4,2,1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
# Folding is numerically unstable so we need to use the exact fitted frequency
freq_est = all_lomb['freq1_freq']
# Fold by 1*period
fold1ed_times = (times-times[0]) % (1./freq_est)
sort_indices = np.argsort(fold1ed_times)
fold1ed_times = fold1ed_times[sort_indices]
fold1ed_values = values[sort_indices]
# Fold by 2*period
fold2ed_times = (times-times[0]) % (2./freq_est)
sort_indices = np.argsort(fold2ed_times)
fold2ed_times = fold2ed_times[sort_indices]
fold2ed_values = values[sort_indices]
npt.assert_allclose(np.sum(np.diff(fold2ed_values)**2) /
np.sum(np.diff(values)**2), all_lomb['p2p_scatter_2praw'])
npt.assert_allclose(np.sum(np.diff(values)**2) / ((len(values) - 1) *
np.var(values)), all_lomb['p2p_ssqr_diff_over_var'])
npt.assert_allclose(np.median(np.abs(np.diff(values))) /
np.median(np.abs(values-np.median(values))),
all_lomb['p2p_scatter_over_mad'])
npt.assert_allclose(np.median(np.abs(np.diff(fold1ed_values))) /
np.median(np.abs(values-np.median(values))),
all_lomb['p2p_scatter_pfold_over_mad'])
def test_lomb_scargle_irregular_single_freq():
"""Test Lomb-Scargle model features on irregularly-sampled periodic data
with one frequency/multiple harmonics. More difficult than
regularly-sampled case, so we allow parameter estimates to be slightly
noisy.
"""
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS)-1)))
amplitudes = np.zeros((len(WAVE_FREQS),4))
amplitudes[0,:] = [8,4,2,1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
# Only test the first (true) frequency; the rest correspond to noise
npt.assert_allclose(all_lomb['freq1_freq'], frequencies[0], rtol=1e-2)
# Only test first frequency here; noise gives non-zero amplitudes for residuals
for j in range(amplitudes.shape[1]):
npt.assert_allclose(amplitudes[0,j],
all_lomb['freq1_amplitude{}'.format(j+1)], rtol=5e-2, atol=5e-2)
if j >= 1:
npt.assert_allclose(phase*j*(-1**j),
all_lomb['freq1_rel_phase{}'.format(j+1)], rtol=1e-1, atol=1e-1)
npt.assert_array_less(10., all_lomb['freq1_signif'])
# Only one frequency, so this should explain basically all the variance
npt.assert_allclose(0., all_lomb['freq_varrat'], atol=5e-3)
npt.assert_allclose(-np.mean(values), all_lomb['freq_y_offset'], rtol=5e-2)
def test_lomb_scargle_irregular_multi_freq():
"""Test Lomb-Scargle model features on irregularly-sampled periodic data
with multiple frequencies, each with a single harmonic. More difficult than
regularly-sampled case, so we allow parameter estimates to be slightly
noisy.
"""
frequencies = WAVE_FREQS
amplitudes = np.zeros((len(frequencies),4))
amplitudes[:,0] = [4,2,1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
for i, frequency in enumerate(frequencies):
npt.assert_allclose(frequency,
all_lomb['freq{}_freq'.format(i+1)], rtol=1e-2)
for (i,j), amplitude in np.ndenumerate(amplitudes):
npt.assert_allclose(amplitude,
all_lomb['freq{}_amplitude{}'.format(i+1,j+1)],
rtol=1e-1, atol=1e-1)
for i in [2,3]:
npt.assert_allclose(amplitudes[i-1,0] / amplitudes[0,0],
all_lomb['freq_amplitude_ratio_{}1'.format(i)], atol=2e-2)
npt.assert_allclose(frequencies[i-1] / frequencies[0],
all_lomb['freq_frequency_ratio_{}1'.format(i)], atol=5e-2)
npt.assert_array_less(10., all_lomb['freq1_signif'])
def test_lomb_scargle_irregular_single_freq():
"""Test Lomb-Scargle model features on irregularly-sampled periodic data
with one frequency/multiple harmonics. More difficult than
regularly-sampled case, so we allow parameter estimates to be slightly
noisy.
"""
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS) - 1)))
amplitudes = np.zeros((len(WAVE_FREQS), 4))
amplitudes[0, :] = [8, 4, 2, 1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
# Only test the first (true) frequency; the rest correspond to noise
npt.assert_allclose(all_lomb['freq1_freq'], frequencies[0], rtol=1e-2)
# Only test first frequency here; noise gives non-zero amplitudes for residuals
for j in range(amplitudes.shape[1]):
npt.assert_allclose(amplitudes[0, j],
all_lomb['freq1_amplitude{}'.format(j + 1)],
rtol=5e-2,
atol=5e-2)
if j >= 1:
npt.assert_allclose(phase * j * (-1**j),
all_lomb['freq1_rel_phase{}'.format(j + 1)],
rtol=1e-1,
atol=1e-1)
npt.assert_array_less(10., all_lomb['freq1_signif'])
# Only one frequency, so this should explain basically all the variance
npt.assert_allclose(0., all_lomb['freq_varrat'], atol=5e-3)
npt.assert_allclose(-np.mean(values), all_lomb['freq_y_offset'], rtol=5e-2)
def test_lomb_scargle_irregular_multi_freq():
"""Test Lomb-Scargle model features on irregularly-sampled periodic data
with multiple frequencies, each with a single harmonic. More difficult than
regularly-sampled case, so we allow parameter estimates to be slightly
noisy.
"""
frequencies = WAVE_FREQS
amplitudes = np.zeros((len(frequencies), 4))
amplitudes[:, 0] = [4, 2, 1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
for i, frequency in enumerate(frequencies):
npt.assert_allclose(frequency,
all_lomb['freq{}_freq'.format(i + 1)],
rtol=1e-2)
for (i, j), amplitude in np.ndenumerate(amplitudes):
npt.assert_allclose(amplitude,
all_lomb['freq{}_amplitude{}'.format(i + 1,
j + 1)],
rtol=1e-1,
atol=1e-1)
for i in [2, 3]:
npt.assert_allclose(amplitudes[i - 1, 0] / amplitudes[0, 0],
all_lomb['freq_amplitude_ratio_{}1'.format(i)],
atol=2e-2)
npt.assert_allclose(frequencies[i - 1] / frequencies[0],
all_lomb['freq_frequency_ratio_{}1'.format(i)],
atol=5e-2)
npt.assert_array_less(10., all_lomb['freq1_signif'])
def test_lomb_scargle_fast_irregular():
"""Test gatspy's fast Lomb-Scargle period estimate on irregularly-sampled
periodic data.
Note: this model fits only a single sinusoid with no additional harmonics,
so we use only 1 frequency and 1 amplitude to generate test data.
"""
frequencies = np.array([4])
amplitudes = np.array([[1]])
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
f = generate_features(times, values, errors, ['period_fast'])
npt.assert_allclose(f['period_fast'], 1. / frequencies[0], rtol=3e-2)
def test_lomb_scargle_fast_irregular():
"""Test gatspy's fast Lomb-Scargle period estimate on irregularly-sampled
periodic data.
Note: this model fits only a single sinusoid with no additional harmonics,
so we use only 1 frequency and 1 amplitude to generate test data.
"""
frequencies = np.array([4])
amplitudes = np.array([[1]])
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
f = generate_features(times, values, errors, ['period_fast'])
npt.assert_allclose(f['period_fast'], 1. / frequencies[0], rtol=3e-2)
def test_lomb_scargle_linear_trend():
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS)-1)))
amplitudes = np.zeros((len(WAVE_FREQS),4))
amplitudes[0,:] = [8,4,2,1]
phase = 0.1
slope = 0.5
# Estimated trend should be almost exact for noiseless data
times, values, errors = regular_periodic(frequencies, amplitudes, phase)
values += slope * times
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
npt.assert_allclose(slope, all_lomb['linear_trend'], rtol=1e-3)
# Should still be close to true trend when noise is present
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
values += slope * times
values += np.random.normal(scale=1e-3, size=len(times))
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
npt.assert_allclose(slope, all_lomb['linear_trend'], rtol=1e-1)
def test_lomb_scargle_linear_trend():
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS) - 1)))
amplitudes = np.zeros((len(WAVE_FREQS), 4))
amplitudes[0, :] = [8, 4, 2, 1]
phase = 0.1
slope = 0.5
# Estimated trend should be almost exact for noiseless data
times, values, errors = regular_periodic(frequencies, amplitudes, phase)
values += slope * times
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
npt.assert_allclose(slope, all_lomb['linear_trend'], rtol=1e-3)
# Should still be close to true trend when noise is present
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
values += slope * times
values += np.random.normal(scale=1e-3, size=len(times))
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
npt.assert_allclose(slope, all_lomb['linear_trend'], rtol=1e-1)
def test_lomb_scargle_period_folding():
"""Tests for features derived from fitting a Lomb-Scargle periodic model
and period-folding the data by the estimated period.
"""
frequencies = np.hstack((WAVE_FREQS[0], np.zeros(len(WAVE_FREQS) - 1)))
amplitudes = np.zeros((len(WAVE_FREQS), 4))
amplitudes[0, :] = [8, 4, 2, 1]
phase = 0.1
times, values, errors = irregular_periodic(frequencies, amplitudes, phase)
all_lomb = generate_features(times, values, errors, LOMB_SCARGLE_FEATS)
# Folding is numerically unstable so we need to use the exact fitted frequency
freq_est = all_lomb['freq1_freq']
# Fold by 1*period
fold1ed_times = (times - times[0]) % (1. / freq_est)
sort_indices = np.argsort(fold1ed_times)
fold1ed_times = fold1ed_times[sort_indices]
fold1ed_values = values[sort_indices]
# Fold by 2*period
fold2ed_times = (times - times[0]) % (2. / freq_est)
sort_indices = np.argsort(fold2ed_times)
fold2ed_times = fold2ed_times[sort_indices]
fold2ed_values = values[sort_indices]
npt.assert_allclose(
np.sum(np.diff(fold2ed_values)**2) / np.sum(np.diff(values)**2),
all_lomb['p2p_scatter_2praw'])
npt.assert_allclose(
np.sum(np.diff(values)**2) / ((len(values) - 1) * np.var(values)),
all_lomb['p2p_ssqr_diff_over_var'])
npt.assert_allclose(
np.median(np.abs(np.diff(values))) /
np.median(np.abs(values - np.median(values))),
all_lomb['p2p_scatter_over_mad'])
npt.assert_allclose(
np.median(np.abs(np.diff(fold1ed_values))) /
np.median(np.abs(values - np.median(values))),
all_lomb['p2p_scatter_pfold_over_mad'])
