def test_lower_bounds_inequalities():
"""Test that the expected inequalities are verified."""
# Toy dataset
rng = np.random.RandomState(42)
n_samples_train, n_samples_test, n_timestamps = 20, 30, 60
window_size = 0.1
X_train = rng.randn(n_samples_train, n_timestamps)
X_test = rng.randn(n_samples_test, n_timestamps)
# DTW
X_dtw = pairwise_distances(X_test, X_train, dtw)
region = sakoe_chiba_band(n_timestamps, window_size=window_size)
X_dtw_window = pairwise_distances(X_test,
X_train,
dtw_sakoechiba,
window_size=window_size)
# Lower bounds
lb_yi = lower_bound_yi(X_train, X_test)
lb_kim = lower_bound_kim(X_train, X_test)
lb_keogh = lower_bound_keogh(X_train, X_test, region)
lb_improved = lower_bound_improved(X_train, X_test, region)
# Sanity check
EPS = 1e-8
np.testing.assert_array_less(lb_yi, X_dtw + EPS)
np.testing.assert_array_less(lb_kim, X_dtw + EPS)
np.testing.assert_array_less(lb_keogh, X_dtw_window + EPS)
np.testing.assert_array_less(lb_improved, X_dtw_window + EPS)
np.testing.assert_array_less(lb_keogh, lb_improved + EPS)
def plot_sakoe_chiba(n_timestamps_1, n_timestamps_2, window_size=0.5, ax=None):
"""Plot the Sakoe-Chiba band."""
region = sakoe_chiba_band(n_timestamps_1, n_timestamps_2, window_size)
scale, horizontal_shift, vertical_shift = \
_check_sakoe_chiba_params(n_timestamps_1, n_timestamps_2, window_size)
mask = np.zeros((n_timestamps_2, n_timestamps_1))
for i, (j, k) in enumerate(region.T):
mask[j:k, i] = 1.
plt.imshow(mask, origin='lower', cmap='Wistia', vmin=0, vmax=1)
sz = max(n_timestamps_1, n_timestamps_2)
x = np.arange(-1, sz + 1)
lower_bound = scale * (x - horizontal_shift) - vertical_shift
upper_bound = scale * (x + horizontal_shift) + vertical_shift
plt.plot(x, lower_bound, 'b', lw=2)
plt.plot(x, upper_bound, 'g', lw=2)
diag = (n_timestamps_2 - 1) / (n_timestamps_1 - 1) * np.arange(-1, sz + 1)
plt.plot(x, diag, 'black', lw=1)
for i in range(n_timestamps_1):
for j in range(n_timestamps_2):
plt.plot(i, j, 'o', color='green', ms=1)
ax.set_xticks(np.arange(-.5, n_timestamps_1, 1), minor=True)
ax.set_yticks(np.arange(-.5, n_timestamps_2, 1), minor=True)
plt.grid(which='minor', color='b', linestyle='--', linewidth=1)
plt.xticks(np.arange(0, n_timestamps_1, 2))
plt.yticks(np.arange(0, n_timestamps_2, 2))
plt.xlim((-0.5, n_timestamps_1 - 0.5))
plt.ylim((-0.5, n_timestamps_2 - 0.5))
def test_actual_results_sakoe_chiba_band(params, arr_desired):
"""Test that the actual results are the expected ones."""
arr_actual = sakoe_chiba_band(**params)
np.testing.assert_allclose(arr_actual, arr_desired, atol=1e-5, rtol=0.)
def test_parameter_check_sakoe_chiba_band(params, error, err_msg):
"""Test parameter validation."""
with pytest.raises(error, match=re.escape(err_msg)):
sakoe_chiba_band(**params)
plt.subplot(2, 2, 1)
plt.pcolor(timestamps_1, timestamps_2, matrix_classic,
edgecolors='k', cmap='Greys')
plt.xlabel('x', fontsize=12)
plt.ylabel('y', fontsize=12)
plt.title("{0}\nDTW(x, y) = {1:.2f}".format('classic', dtw_classic),
fontsize=14)
# Dynamic Time Warping: sakoechiba
window_size = 0.1
dtw_sakoechiba, path_sakoechiba = dtw(
x, y, dist='square', method='sakoechiba',
options={'window_size': window_size}, return_path=True
)
band = sakoe_chiba_band(n_timestamps_1, n_timestamps_2,
window_size=window_size)
matrix_sakoechiba = np.zeros((n_timestamps_1 + 1, n_timestamps_2 + 1))
for i in range(n_timestamps_1):
matrix_sakoechiba[i, np.arange(*band[:, i])] = 0.5
matrix_sakoechiba[tuple(path_sakoechiba)] = 1.
plt.subplot(2, 2, 2)
plt.pcolor(timestamps_1, timestamps_2, matrix_sakoechiba.T,
edgecolors='k', cmap='Greys')
plt.xlabel('x', fontsize=12)
plt.ylabel('y', fontsize=12)
plt.title("{0}\nDTW(x, y) = {1:.2f}".format('sakoechiba', dtw_sakoechiba),
fontsize=14)
# Dynamic Time Warping: itakura
slope = 1.2
matrix_classic,
edgecolors='k',
cmap='Greys')
plt.xlabel('x', fontsize=20, labelpad=-10)
plt.ylabel('y', fontsize=20, labelpad=-10)
plt.title("{0}\nDTW(x, y) = {1:.2f}".format('classic', dtw_classic),
fontsize=16)
# Dynamic Time Warping: sakoechiba
dtw_sakoechiba, path_sakoechiba = dtw(x,
y,
dist='square',
method='sakoechiba',
options={'window_size': 5},
return_path=True)
band = sakoe_chiba_band(n_timestamps, window_size=5)
matrix_sakoechiba = np.zeros((n_timestamps + 1, n_timestamps + 1))
for i in range(n_timestamps):
matrix_sakoechiba[i, np.arange(*band[:, i])] = 0.5
matrix_sakoechiba[tuple(path_sakoechiba)[::-1]] = 1.
plt.subplot(2, 2, 2)
plt.pcolor(timestamps,
timestamps,
matrix_sakoechiba,
edgecolors='k',
cmap='Greys')
plt.xlabel('x', fontsize=20, labelpad=-10)
plt.ylabel('y', fontsize=20, labelpad=-10)
plt.title("{0}\nDTW(x, y) = {1:.2f}".format('sakoechiba', dtw_sakoechiba),
fontsize=16)
