def test_reconstruction_freq():
"""In principle one can reconstruct the input data from the
wavelet transform.
Check within 10% when computing with frequency representation of
wavelet.
"""
wa = WaveletAnalysis(anomaly_sst, frequency=True)
rdata = wa.reconstruction()
err = wa.data - rdata
assert (np.abs(err.mean()) < 0.02)
def test_multi_dim():
data = np.random.random((10, 100))
wa = WaveletAnalysis(data, frequency=True)
ns = len(wa.scales)
assert (wa.wavelet_transform.shape == (ns, 10, 100))
wan = WaveletAnalysis(data[0], frequency=True)
assert (wan.wavelet_transform.shape == (ns, 100))
npt.assert_array_almost_equal(wa.wavelet_transform[:, 0, :],
wan.wavelet_transform[:, :],
decimal=13)
def test_reconstruction_freq():
"""In principle one can reconstruct the input data from the
wavelet transform.
Check within 10% when computing with frequency representation of
wavelet.
"""
wa = WaveletAnalysis(anomaly_sst, frequency=True)
rdata = wa.reconstruction()
err = wa.data - rdata
assert(np.abs(err.mean()) < 0.02)
def test_multi_dim_axis_nd_time():
data = np.random.random((3, 4, 100, 5))
wa = WaveletAnalysis(data, frequency=False, axis=2)
ns = len(wa.scales)
print(wa.wavelet_transform.shape)
print(ns)
assert (wa.wavelet_transform.shape == (ns, 3, 4, 100, 5))
wan = WaveletAnalysis(data[0, 0, :, 0], frequency=False)
print(wan.wavelet_transform.shape)
assert (wan.wavelet_transform.shape == (ns, 100))
npt.assert_array_almost_equal(wa.wavelet_transform[:, 0, 0, :, 0],
wan.wavelet_transform[:, :],
decimal=13)
def compare_morlet(N=2000):
"""Compare scipy morlet with my morlet (same, but correct
argument order).
"""
data = np.random.random(N)
wave_anal = WaveletAnalysis(data, wavelet='ricker')
scales = wave_anal.scales[::-1]
cwt = wavelets.cwt
cwt_sp = cwt(data, scipy.signal.morlet, scales)
cwt_me = cwt(data, wavelets.Morlet(), scales)
cwt_ri = cwt(data, scipy.signal.ricker, scales)
t = np.indices(data.shape)
T, S = np.meshgrid(t, scales)
fig, ax = plt.subplots(nrows=3)
ax[0].set_title('Scipy morlet')
ax[0].contourf(T, S, cwt_sp, 100)
ax[1].set_title('My morlet')
ax[1].contourf(T, S, cwt_me, 100)
ax[2].set_title('Scipy Ricker')
ax[2].contourf(T, S, cwt_ri, 100)
fig.tight_layout()
return fig
def analyse_song():
"""Compute the wavelet transform of a song."""
fs, song = wavfile.read('alarma.wav')
# select first part of one channel
stride = 1
# time step is inverse sample rate * stride
dt = stride / fs
# number of seconds of song to analyse
t_s = 1
n_s = fs * t_s
# sub sample song on a single channel
sub_song = song[:n_s:stride, 0]
wa = WaveletAnalysis(sub_song, dt=dt)
fig, ax = plt.subplots()
T, F = np.meshgrid(wa.time, wa.fourier_periods)
freqs = 1 / F
ax.contourf(T, freqs, wa.wavelet_power, 100)
ax.set_yscale('log')
ax.set_ylabel('frequency (Hz)')
ax.set_xlabel('time (s)')
ax.set_ylim(100, 10000)
fig.savefig('alarma_wavelet.png')
def test_var_freq():
"""The wavelet transform conserves total energy, i.e. variance.
The variance of the data should be the same as the variance of
the wavelet.
Check that they are within 1%% for the frequency representation.
N.B. the performance of this test does depend on the input data.
If e.g. np.random.random is used for the input, the variance
difference is larger.
"""
wa = WaveletAnalysis(anomaly_sst, frequency=True)
rdiff = 1 - wa.data_variance / wa.wavelet_variance
assert_less(rdiff, 0.01)
def compare_cwt():
"""Compare the output of Scipy's cwt (using direct convolution)
and my cwt (using fft convolution).
"""
cwt = scipy.signal.cwt
fft_cwt = wavelets.cwt
data = np.random.random(2000)
wave_anal = WaveletAnalysis(data, wavelet=wavelets.Ricker())
widths = wave_anal.scales[::-1]
morlet = scipy.signal.morlet
cwt = cwt(data, morlet, widths)
fft_cwt = fft_cwt(data, morlet, widths)
npt.assert_array_almost_equal(cwt, fft_cwt, decimal=13)
def test_power_bias():
"""See if the global wavelet spectrum is biased or not.
Wavelet transform a signal of 3 distinct fourier frequencies.
The power spectrum should contain peaks at the frequencies, all
of which should be the same height.
"""
dt = 0.1
x = np.arange(5000) * dt
T1 = 20 * dt
T2 = 100 * dt
T3 = 500 * dt
w1 = 2 * np.pi / T1
w2 = 2 * np.pi / T2
w3 = 2 * np.pi / T3
signal = np.cos(w1 * x) + np.cos(w2 * x) + np.cos(w3 * x)
wa = WaveletAnalysis(signal,
dt=dt,
wavelet=wavelets.Morlet(),
unbias=False)
power_biased = wa.global_wavelet_spectrum
wa.unbias = True
power = wa.global_wavelet_spectrum
wa.mask_coi = True
power_coi = wa.global_wavelet_spectrum
freqs = wa.fourier_periods
fig, ax = plt.subplots(nrows=2)
ax_transform = ax[0]
fig_info = (r"Wavelet transform of "
r"$cos(2 \pi / {T1}) + cos(2 \pi / {T2}) + cos(2 \pi / {T3})$")
ax_transform.set_title(fig_info.format(T1=T1, T2=T2, T3=T3))
X, Y = np.meshgrid(wa.time, wa.fourier_periods)
ax_transform.set_xlabel('time')
ax_transform.set_ylabel('fourier period')
ax_transform.set_ylim(10 * dt, 1000 * dt)
ax_transform.set_yscale('log')
ax_transform.contourf(X, Y, wa.wavelet_power, 100)
# shade the region between the edge and coi
C, S = wa.coi
F = wa.fourier_period(S)
f_max = F.max()
ax_transform.fill_between(x=C, y1=F, y2=f_max, color='gray', alpha=0.3)
ax_power = ax[1]
ax_power.set_title('Global wavelet spectrum '
'(estimator for power spectrum)')
ax_power.plot(freqs, power, 'k', label=r'unbiased all domain')
ax_power.plot(freqs, power_coi, 'g', label=r'unbiased coi only')
ax_power.set_xscale('log')
ax_power.set_xlim(10 * dt, wa.time.max())
ax_power.set_xlabel('fourier period')
ax_power.set_ylabel(r'power / $\sigma^2$ (bias corrected)')
ax_power_bi = ax_power.twinx()
ax_power_bi.plot(freqs, power_biased, 'r', label='biased all domain')
ax_power_bi.set_xlim(10 * dt, wa.time.max())
ax_power_bi.set_ylabel(r'power / $\sigma^2$ (bias uncorrected)')
ax_power_bi.set_yticklabels(ax_power_bi.get_yticks(), color='r')
label = "T={0}"
for T in (T1, T2, T3):
ax_power.axvline(T)
ax_power.annotate(label.format(T), (T, 1))
ax_power.legend(fontsize='x-small', loc='lower right')
ax_power_bi.legend(fontsize='x-small', loc='upper right')
fig.tight_layout()
fig.savefig('tests/test_power_bias.png')
return fig
Value at frequency = 0 should be 0.
"""
npt.assert_almost_equal(wavelets.DOG(m=2)(0), 0.867, 3)
npt.assert_almost_equal(wavelets.DOG(m=6)(0), 0.884, 3)
npt.assert_almost_equal(wavelets.DOG(m=2).frequency(0), 0, 6)
npt.assert_almost_equal(wavelets.DOG(m=6).frequency(0), 0, 6)
test_data = np.loadtxt('tests/nino3data.asc', skiprows=3)
nino_time = test_data[:, 0]
nino_dt = np.diff(nino_time).mean()
anomaly_sst = test_data[:, 2]
wa = WaveletAnalysis(anomaly_sst, time=nino_time, dt=nino_dt)
def test_N():
assert_equal(anomaly_sst.size, wa.N)
def compare_cwt():
"""Compare the output of Scipy's cwt (using direct convolution)
and my cwt (using fft convolution).
"""
cwt = scipy.signal.cwt
fft_cwt = wavelets.cwt
data = np.random.random(2000)
wave_anal = WaveletAnalysis(data, wavelet=wavelets.Ricker())
def test_power_bias():
"""See if the global wavelet spectrum is biased or not.
Wavelet transform a signal of 3 distinct fourier frequencies.
The power spectrum should contain peaks at the frequencies, all
of which should be the same height.
"""
dt = 0.1
x = np.arange(5000) * dt
T1 = 20 * dt
T2 = 100 * dt
T3 = 500 * dt
w1 = 2 * np.pi / T1
w2 = 2 * np.pi / T2
w3 = 2 * np.pi / T3
signal = np.cos(w1 * x) + np.cos(w2 * x) + np.cos(w3 * x)
wa = WaveletAnalysis(signal, dt=dt,
wavelet=wavelets.Morlet(), unbias=False)
power_biased = wa.global_wavelet_spectrum
wa.unbias = True
power = wa.global_wavelet_spectrum
wa.mask_coi = True
power_coi = wa.global_wavelet_spectrum
freqs = wa.fourier_periods
fig, ax = plt.subplots(nrows=2)
ax_transform = ax[0]
fig_info = (r"Wavelet transform of "
r"$cos(2 \pi / {T1}) + cos(2 \pi / {T2}) + cos(2 \pi / {T3})$")
ax_transform.set_title(fig_info.format(T1=T1, T2=T2, T3=T3))
X, Y = np.meshgrid(wa.time, wa.fourier_periods)
ax_transform.set_xlabel('time')
ax_transform.set_ylabel('fourier period')
ax_transform.set_ylim(10 * dt, 1000 * dt)
ax_transform.set_yscale('log')
ax_transform.contourf(X, Y, wa.wavelet_power, 100)
# shade the region between the edge and coi
C, S = wa.coi
F = wa.fourier_period(S)
f_max = F.max()
ax_transform.fill_between(x=C, y1=F, y2=f_max, color='gray', alpha=0.3)
ax_power = ax[1]
ax_power.set_title('Global wavelet spectrum '
'(estimator for power spectrum)')
ax_power.plot(freqs, power, 'k', label=r'unbiased all domain')
ax_power.plot(freqs, power_coi, 'g', label=r'unbiased coi only')
ax_power.set_xscale('log')
ax_power.set_xlim(10 * dt, wa.time.max())
ax_power.set_xlabel('fourier period')
ax_power.set_ylabel(r'power / $\sigma^2$ (bias corrected)')
ax_power_bi = ax_power.twinx()
ax_power_bi.plot(freqs, power_biased, 'r', label='biased all domain')
ax_power_bi.set_xlim(10 * dt, wa.time.max())
ax_power_bi.set_ylabel(r'power / $\sigma^2$ (bias uncorrected)')
ax_power_bi.set_yticklabels(ax_power_bi.get_yticks(), color='r')
label = "T={0}"
for T in (T1, T2, T3):
ax_power.axvline(T)
ax_power.annotate(label.format(T), (T, 1))
ax_power.legend(fontsize='x-small', loc='lower right')
ax_power_bi.legend(fontsize='x-small', loc='upper right')
fig.tight_layout()
fig.savefig('tests/test_power_bias.png')
return fig