test_wavelets.py
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import numpy as np
from numpy.testing import assert_equal, \
assert_array_equal, assert_array_almost_equal, assert_array_less, assert_
from scipy.signal import wavelets
class TestWavelets(object):
def test_qmf(self):
assert_array_equal(wavelets.qmf([1, 1]), [1, -1])
def test_daub(self):
for i in range(1, 15):
assert_equal(len(wavelets.daub(i)), i * 2)
def test_cascade(self):
for J in range(1, 7):
for i in range(1, 5):
lpcoef = wavelets.daub(i)
k = len(lpcoef)
x, phi, psi = wavelets.cascade(lpcoef, J)
assert_(len(x) == len(phi) == len(psi))
assert_equal(len(x), (k - 1) * 2 ** J)
def test_morlet(self):
x = wavelets.morlet(50, 4.1, complete=True)
y = wavelets.morlet(50, 4.1, complete=False)
# Test if complete and incomplete wavelet have same lengths:
assert_equal(len(x), len(y))
# Test if complete wavelet is less than incomplete wavelet:
assert_array_less(x, y)
x = wavelets.morlet(10, 50, complete=False)
y = wavelets.morlet(10, 50, complete=True)
# For large widths complete and incomplete wavelets should be
# identical within numerical precision:
assert_equal(x, y)
# miscellaneous tests:
x = np.array([1.73752399e-09 + 9.84327394e-25j,
6.49471756e-01 + 0.00000000e+00j,
1.73752399e-09 - 9.84327394e-25j])
y = wavelets.morlet(3, w=2, complete=True)
assert_array_almost_equal(x, y)
x = np.array([2.00947715e-09 + 9.84327394e-25j,
7.51125544e-01 + 0.00000000e+00j,
2.00947715e-09 - 9.84327394e-25j])
y = wavelets.morlet(3, w=2, complete=False)
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, s=4, complete=True)
y = wavelets.morlet(20000, s=8, complete=True)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, s=4, complete=False)
assert_array_almost_equal(y, x, decimal=2)
y = wavelets.morlet(20000, s=8, complete=False)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, w=3, s=5, complete=True)
y = wavelets.morlet(20000, w=3, s=10, complete=True)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, w=3, s=5, complete=False)
assert_array_almost_equal(y, x, decimal=2)
y = wavelets.morlet(20000, w=3, s=10, complete=False)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, w=7, s=10, complete=True)
y = wavelets.morlet(20000, w=7, s=20, complete=True)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
x = wavelets.morlet(10000, w=7, s=10, complete=False)
assert_array_almost_equal(x, y, decimal=2)
y = wavelets.morlet(20000, w=7, s=20, complete=False)[5000:15000]
assert_array_almost_equal(x, y, decimal=2)
def test_morlet2(self):
w = wavelets.morlet2(1.0, 0.5)
expected = (np.pi**(-0.25) * np.sqrt(1/0.5)).astype(complex)
assert_array_equal(w, expected)
lengths = [5, 11, 15, 51, 101]
for length in lengths:
w = wavelets.morlet2(length, 1.0)
assert_(len(w) == length)
max_loc = np.argmax(w)
assert_(max_loc == (length // 2))
points = 100
w = abs(wavelets.morlet2(points, 2.0))
half_vec = np.arange(0, points // 2)
assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
x = np.array([5.03701224e-09 + 2.46742437e-24j,
1.88279253e+00 + 0.00000000e+00j,
5.03701224e-09 - 2.46742437e-24j])
y = wavelets.morlet2(3, s=1/(2*np.pi), w=2)
assert_array_almost_equal(x, y)
def test_ricker(self):
w = wavelets.ricker(1.0, 1)
expected = 2 / (np.sqrt(3 * 1.0) * (np.pi ** 0.25))
assert_array_equal(w, expected)
lengths = [5, 11, 15, 51, 101]
for length in lengths:
w = wavelets.ricker(length, 1.0)
assert_(len(w) == length)
max_loc = np.argmax(w)
assert_(max_loc == (length // 2))
points = 100
w = wavelets.ricker(points, 2.0)
half_vec = np.arange(0, points // 2)
#Wavelet should be symmetric
assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
#Check zeros
aas = [5, 10, 15, 20, 30]
points = 99
for a in aas:
w = wavelets.ricker(points, a)
vec = np.arange(0, points) - (points - 1.0) / 2
exp_zero1 = np.argmin(np.abs(vec - a))
exp_zero2 = np.argmin(np.abs(vec + a))
assert_array_almost_equal(w[exp_zero1], 0)
assert_array_almost_equal(w[exp_zero2], 0)
def test_cwt(self):
widths = [1.0]
delta_wavelet = lambda s, t: np.array([1])
len_data = 100
test_data = np.sin(np.pi * np.arange(0, len_data) / 10.0)
#Test delta function input gives same data as output
cwt_dat = wavelets.cwt(test_data, delta_wavelet, widths)
assert_(cwt_dat.shape == (len(widths), len_data))
assert_array_almost_equal(test_data, cwt_dat.flatten())
#Check proper shape on output
widths = [1, 3, 4, 5, 10]
cwt_dat = wavelets.cwt(test_data, wavelets.ricker, widths)
assert_(cwt_dat.shape == (len(widths), len_data))
widths = [len_data * 10]
#Note: this wavelet isn't defined quite right, but is fine for this test
flat_wavelet = lambda l, w: np.full(w, 1 / w)
cwt_dat = wavelets.cwt(test_data, flat_wavelet, widths)
assert_array_almost_equal(cwt_dat, np.mean(test_data))