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from __future__ import division, print_function, absolute_import
import warnings
import numpy as np
from numpy.testing import assert_raises, assert_approx_equal, \
assert_, run_module_suite, TestCase,\
assert_allclose, assert_array_equal,\
assert_array_almost_equal_nulp
from scipy import signal, fftpack
from scipy.signal import periodogram, welch, lombscargle
class TestPeriodogram(TestCase):
def test_real_onesided_even(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x)
assert_allclose(f, np.linspace(0, 0.5, 9))
q = np.ones(9)
q[0] = 0
q[-1] /= 2.0
q /= 8
assert_allclose(p, q)
def test_real_onesided_odd(self):
x = np.zeros(15)
x[0] = 1
f, p = periodogram(x)
assert_allclose(f, np.arange(8.0)/15.0)
q = np.ones(8)
q[0] = 0
q[-1] /= 2.0
q *= 2.0/15.0
assert_allclose(p, q, atol=1e-15)
def test_real_twosided(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x, return_onesided=False)
assert_allclose(f, fftpack.fftfreq(16, 1.0))
q = np.ones(16)/16.0
q[0] = 0
assert_allclose(p, q)
def test_real_spectrum(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x, scaling='spectrum')
g, q = periodogram(x, scaling='density')
assert_allclose(f, np.linspace(0, 0.5, 9))
assert_allclose(p, q/16.0)
def test_complex(self):
x = np.zeros(16, np.complex128)
x[0] = 1.0 + 2.0j
f, p = periodogram(x)
assert_allclose(f, fftpack.fftfreq(16, 1.0))
q = 5.0*np.ones(16)/16.0
q[0] = 0
assert_allclose(p, q)
def test_unk_scaling(self):
assert_raises(ValueError, periodogram, np.zeros(4, np.complex128),
scaling='foo')
def test_nd_axis_m1(self):
x = np.zeros(20, dtype=np.float64)
x = x.reshape((2,1,10))
x[:,:,0] = 1.0
f, p = periodogram(x)
assert_array_equal(p.shape, (2, 1, 6))
assert_array_almost_equal_nulp(p[0,0,:], p[1,0,:], 60)
f0, p0 = periodogram(x[0,0,:])
assert_array_almost_equal_nulp(p0[np.newaxis,:], p[1,:], 60)
def test_nd_axis_0(self):
x = np.zeros(20, dtype=np.float64)
x = x.reshape((10,2,1))
x[0,:,:] = 1.0
f, p = periodogram(x, axis=0)
assert_array_equal(p.shape, (6,2,1))
assert_array_almost_equal_nulp(p[:,0,0], p[:,1,0], 60)
f0, p0 = periodogram(x[:,0,0])
assert_array_almost_equal_nulp(p0, p[:,1,0])
def test_window_external(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x, 10, 'hanning')
win = signal.get_window('hanning', 16)
fe, pe = periodogram(x, 10, win)
assert_array_almost_equal_nulp(p, pe)
assert_array_almost_equal_nulp(f, fe)
def test_padded_fft(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x)
fp, pp = periodogram(x, nfft=32)
assert_allclose(f, fp[::2])
assert_allclose(p, pp[::2])
assert_array_equal(pp.shape, (17,))
def test_empty_input(self):
f, p = periodogram([])
assert_array_equal(f.shape, (0,))
assert_array_equal(p.shape, (0,))
for shape in [(0,), (3,0), (0,5,2)]:
f, p = periodogram(np.empty(shape))
assert_array_equal(f.shape, shape)
assert_array_equal(p.shape, shape)
def test_short_nfft(self):
x = np.zeros(18)
x[0] = 1
f, p = periodogram(x, nfft=16)
assert_allclose(f, np.linspace(0, 0.5, 9))
q = np.ones(9)
q[0] = 0
q[-1] /= 2.0
q /= 8
assert_allclose(p, q)
def test_nfft_is_xshape(self):
x = np.zeros(16)
x[0] = 1
f, p = periodogram(x, nfft=16)
assert_allclose(f, np.linspace(0, 0.5, 9))
q = np.ones(9)
q[0] = 0
q[-1] /= 2.0
q /= 8
assert_allclose(p, q)
class TestWelch(TestCase):
def test_real_onesided_even(self):
x = np.zeros(16)
x[0] = 1
x[8] = 1
f, p = welch(x, nperseg=8)
assert_allclose(f, np.linspace(0, 0.5, 5))
assert_allclose(p, np.array([0.08333333, 0.15277778, 0.22222222,
0.22222222, 0.11111111]))
def test_real_onesided_odd(self):
x = np.zeros(16)
x[0] = 1
x[8] = 1
f, p = welch(x, nperseg=9)
assert_allclose(f, np.arange(5.0)/9.0)
assert_allclose(p, np.array([0.15958226, 0.24193954, 0.24145223,
0.24100919, 0.12188675]))
def test_real_twosided(self):
x = np.zeros(16)
x[0] = 1
x[8] = 1
f, p = welch(x, nperseg=8, return_onesided=False)
assert_allclose(f, fftpack.fftfreq(8, 1.0))
assert_allclose(p, np.array([0.08333333, 0.07638889, 0.11111111,
0.11111111, 0.11111111, 0.11111111, 0.11111111, 0.07638889]))
def test_real_spectrum(self):
x = np.zeros(16)
x[0] = 1
x[8] = 1
f, p = welch(x, nperseg=8, scaling='spectrum')
assert_allclose(f, np.linspace(0, 0.5, 5))
assert_allclose(p, np.array([0.015625, 0.028645833333333332,
0.041666666666666664, 0.041666666666666664, 0.020833333333333332]))
def test_complex(self):
x = np.zeros(16, np.complex128)
x[0] = 1.0 + 2.0j
x[8] = 1.0 + 2.0j
f, p = welch(x, nperseg=8)
assert_allclose(f, fftpack.fftfreq(8, 1.0))
assert_allclose(p, np.array([0.41666667, 0.38194444, 0.55555556,
0.55555556, 0.55555556, 0.55555556, 0.55555556, 0.38194444]))
def test_unk_scaling(self):
assert_raises(ValueError, welch, np.zeros(4, np.complex128),
scaling='foo', nperseg=4)
def test_detrend_linear(self):
x = np.arange(10, dtype=np.float64)+0.04
f, p = welch(x, nperseg=10, detrend='linear')
assert_allclose(p, np.zeros_like(p), atol=1e-15)
def test_detrend_external(self):
x = np.arange(10, dtype=np.float64)+0.04
f, p = welch(x, nperseg=10,
detrend=lambda seg: signal.detrend(seg, type='l'))
assert_allclose(p, np.zeros_like(p), atol=1e-15)
def test_detrend_external_nd_m1(self):
x = np.arange(40, dtype=np.float64)+0.04
x = x.reshape((2,2,10))
f, p = welch(x, nperseg=10,
detrend=lambda seg: signal.detrend(seg, type='l'))
assert_allclose(p, np.zeros_like(p), atol=1e-15)
def test_detrend_external_nd_0(self):
x = np.arange(20, dtype=np.float64)+0.04
x = x.reshape((2,1,10))
x = np.rollaxis(x, 2, 0)
f, p = welch(x, nperseg=10, axis=0,
detrend=lambda seg: signal.detrend(seg, axis=0, type='l'))
assert_allclose(p, np.zeros_like(p), atol=1e-15)
def test_nd_axis_m1(self):
x = np.arange(20, dtype=np.float64)+0.04
x = x.reshape((2,1,10))
f, p = welch(x, nperseg=10)
assert_array_equal(p.shape, (2, 1, 6))
assert_allclose(p[0,0,:], p[1,0,:], atol=1e-13, rtol=1e-13)
f0, p0 = welch(x[0,0,:], nperseg=10)
assert_allclose(p0[np.newaxis,:], p[1,:], atol=1e-13, rtol=1e-13)
def test_nd_axis_0(self):
x = np.arange(20, dtype=np.float64)+0.04
x = x.reshape((10,2,1))
f, p = welch(x, nperseg=10, axis=0)
assert_array_equal(p.shape, (6,2,1))
assert_allclose(p[:,0,0], p[:,1,0], atol=1e-13, rtol=1e-13)
f0, p0 = welch(x[:,0,0], nperseg=10)
assert_allclose(p0, p[:,1,0], atol=1e-13, rtol=1e-13)
def test_window_external(self):
x = np.zeros(16)
x[0] = 1
x[8] = 1
f, p = welch(x, 10, 'hanning', 8)
win = signal.get_window('hanning', 8)
fe, pe = welch(x, 10, win, 8)
assert_array_almost_equal_nulp(p, pe)
assert_array_almost_equal_nulp(f, fe)
def test_empty_input(self):
f, p = welch([])
assert_array_equal(f.shape, (0,))
assert_array_equal(p.shape, (0,))
for shape in [(0,), (3,0), (0,5,2)]:
f, p = welch(np.empty(shape))
assert_array_equal(f.shape, shape)
assert_array_equal(p.shape, shape)
def test_short_data(self):
x = np.zeros(8)
x[0] = 1
with warnings.catch_warnings():
warnings.simplefilter('ignore', UserWarning)
f, p = welch(x)
f1, p1 = welch(x, nperseg=8)
assert_allclose(f, f1)
assert_allclose(p, p1)
def test_window_long_or_nd(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', UserWarning)
assert_raises(ValueError, welch, np.zeros(4), 1, np.array([1,1,1,1,1]))
assert_raises(ValueError, welch, np.zeros(4), 1,
np.arange(6).reshape((2,3)))
def test_nondefault_noverlap(self):
x = np.zeros(64)
x[::8] = 1
f, p = welch(x, nperseg=16, noverlap=4)
q = np.array([0, 1./12., 1./3., 1./5., 1./3., 1./5., 1./3., 1./5., 1./6.])
assert_allclose(p, q, atol=1e-12)
def test_bad_noverlap(self):
assert_raises(ValueError, welch, np.zeros(4), 1, 'hanning', 2, 7)
def test_nfft_too_short(self):
assert_raises(ValueError, welch, np.ones(12), nfft=3, nperseg=4)
class TestLombscargle:
def test_frequency(self):
"""Test if frequency location of peak corresponds to frequency of
generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
P = lombscargle(t, x, f)
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
delta = f[1] - f[0]
assert_(w - f[np.argmax(P)] < (delta/2.))
def test_amplitude(self):
"""Test if height of peak in normalized Lomb-Scargle periodogram
corresponds to amplitude of the generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f)
# Normalize
pgram = np.sqrt(4 * pgram / t.shape[0])
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
assert_approx_equal(np.max(pgram), ampl, significant=2)
def test_wrong_shape(self):
t = np.linspace(0, 1, 1)
x = np.linspace(0, 1, 2)
f = np.linspace(0, 1, 3)
assert_raises(ValueError, lombscargle, t, x, f)
def test_zero_division(self):
t = np.zeros(1)
x = np.zeros(1)
f = np.zeros(1)
assert_raises(ZeroDivisionError, lombscargle, t, x, f)
if __name__ == "__main__":
run_module_suite()
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