def test_time_delaying_fast_calc():
"""Test time delaying and fast calculations."""
X = np.array([[1, 2, 3], [5, 7, 11]]).T
# all negative
smin, smax = 1, 2
X_del = _delay_time_series(X, smin, smax, 1.)
# (n_times, n_features, n_delays) -> (n_times, n_features * n_delays)
X_del.shape = (X.shape[0], -1)
expected = np.array([[0, 1, 2], [0, 0, 1], [0, 5, 7], [0, 0, 5]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[5, 2, 19, 10], [2, 1, 7, 5], [19, 7, 74, 35], [10, 5, 35, 25]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# all positive
smin, smax = -2, -1
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[3, 0, 0], [2, 3, 0], [11, 0, 0], [7, 11, 0]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[9, 6, 33, 21], [6, 13, 22, 47], [33, 22, 121, 77],
[21, 47, 77, 170]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# both sides
smin, smax = -1, 1
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[2, 3, 0], [1, 2, 3], [0, 1, 2], [7, 11, 0],
[5, 7, 11], [0, 5, 7]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[13, 8, 3, 47, 31, 15], [8, 14, 8, 29, 52, 31],
[3, 8, 5, 11, 29, 19], [47, 29, 11, 170, 112, 55],
[31, 52, 29, 112, 195, 112], [15, 31, 19, 55, 112, 74]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# slightly harder to get the non-Toeplitz correction correct
X = np.array([[1, 2, 3, 5]]).T
smin, smax = 0, 3
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[1, 2, 3, 5], [0, 1, 2, 3], [0, 0, 1, 2],
[0, 0, 0, 1]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[39, 23, 13, 5], [23, 14, 8, 3], [13, 8, 5, 2], [5, 3, 2, 1]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# even worse
X = np.array([[1, 2, 3], [5, 7, 11]]).T
smin, smax = 0, 2
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[1, 2, 3], [0, 1, 2], [0, 0, 1], [5, 7, 11],
[0, 5, 7], [0, 0, 5]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = np.array([[14, 8, 3, 52, 31, 15], [8, 5, 2, 29, 19, 10],
[3, 2, 1, 11, 7, 5], [52, 29, 11, 195, 112, 55],
[31, 19, 7, 112, 74, 35], [15, 10, 5, 55, 35, 25]])
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# And a bunch of random ones for good measure
rng = np.random.RandomState(0)
X = rng.randn(25, 3)
y = np.empty((25, 2))
vals = (0, -1, 1, -2, 2, -11, 11)
for smax in vals:
for smin in vals:
if smin > smax:
continue
for ii in range(X.shape[1]):
kernel = rng.randn(smax - smin + 1)
kernel -= np.mean(kernel)
y[:, ii % y.shape[-1]] = np.convolve(X[:, ii], kernel, 'same')
x_xt, x_yt, n_ch_x = _compute_corrs(X, y, smin, smax + 1)
X_del = _delay_time_series(X, smin, smax, 1., fill_mean=False)
x_yt_true = einsum('tfd,to->ofd', X_del, y)
x_yt_true = np.reshape(x_yt_true, (x_yt_true.shape[0], -1)).T
assert_allclose(x_yt, x_yt_true, atol=1e-7, err_msg=(smin, smax))
X_del.shape = (X.shape[0], -1)
x_xt_true = np.dot(X_del.T, X_del).T
assert_allclose(x_xt, x_xt_true, atol=1e-7, err_msg=(smin, smax))
def test_time_delaying_fast_calc(n_jobs):
"""Test time delaying and fast calculations."""
X = np.array([[1, 2, 3], [5, 7, 11]]).T
# all negative
smin, smax = 1, 2
X_del = _delay_time_series(X, smin, smax, 1.)
# (n_times, n_features, n_delays) -> (n_times, n_features * n_delays)
X_del.shape = (X.shape[0], -1)
expected = np.array([[0, 1, 2], [0, 0, 1], [0, 5, 7], [0, 0, 5]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[5, 2, 19, 10], [2, 1, 7, 5], [19, 7, 74, 35], [10, 5, 35, 25]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# all positive
smin, smax = -2, -1
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[3, 0, 0], [2, 3, 0], [11, 0, 0], [7, 11, 0]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[9, 6, 33, 21], [6, 13, 22, 47],
[33, 22, 121, 77], [21, 47, 77, 170]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# both sides
smin, smax = -1, 1
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[2, 3, 0], [1, 2, 3], [0, 1, 2],
[7, 11, 0], [5, 7, 11], [0, 5, 7]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[13, 8, 3, 47, 31, 15],
[8, 14, 8, 29, 52, 31],
[3, 8, 5, 11, 29, 19],
[47, 29, 11, 170, 112, 55],
[31, 52, 29, 112, 195, 112],
[15, 31, 19, 55, 112, 74]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# slightly harder to get the non-Toeplitz correction correct
X = np.array([[1, 2, 3, 5]]).T
smin, smax = 0, 3
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[1, 2, 3, 5], [0, 1, 2, 3],
[0, 0, 1, 2], [0, 0, 0, 1]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = [[39, 23, 13, 5], [23, 14, 8, 3], [13, 8, 5, 2], [5, 3, 2, 1]]
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# even worse
X = np.array([[1, 2, 3], [5, 7, 11]]).T
smin, smax = 0, 2
X_del = _delay_time_series(X, smin, smax, 1.)
X_del.shape = (X.shape[0], -1)
expected = np.array([[1, 2, 3], [0, 1, 2], [0, 0, 1],
[5, 7, 11], [0, 5, 7], [0, 0, 5]]).T
assert_allclose(X_del, expected)
Xt_X = np.dot(X_del.T, X_del)
expected = np.array([[14, 8, 3, 52, 31, 15],
[8, 5, 2, 29, 19, 10],
[3, 2, 1, 11, 7, 5],
[52, 29, 11, 195, 112, 55],
[31, 19, 7, 112, 74, 35],
[15, 10, 5, 55, 35, 25]])
assert_allclose(Xt_X, expected)
x_xt = _compute_corrs(X, np.zeros((X.shape[0], 1)), smin, smax + 1)[0]
assert_allclose(x_xt, expected)
# And a bunch of random ones for good measure
rng = np.random.RandomState(0)
X = rng.randn(25, 3)
y = np.empty((25, 2))
vals = (0, -1, 1, -2, 2, -11, 11)
for smax in vals:
for smin in vals:
if smin > smax:
continue
for ii in range(X.shape[1]):
kernel = rng.randn(smax - smin + 1)
kernel -= np.mean(kernel)
y[:, ii % y.shape[-1]] = np.convolve(X[:, ii], kernel, 'same')
x_xt, x_yt, n_ch_x, _, _ = _compute_corrs(X, y, smin, smax + 1)
X_del = _delay_time_series(X, smin, smax, 1., fill_mean=False)
x_yt_true = einsum('tfd,to->ofd', X_del, y)
x_yt_true = np.reshape(x_yt_true, (x_yt_true.shape[0], -1)).T
assert_allclose(x_yt, x_yt_true, atol=1e-7, err_msg=(smin, smax))
X_del.shape = (X.shape[0], -1)
x_xt_true = np.dot(X_del.T, X_del).T
assert_allclose(x_xt, x_xt_true, atol=1e-7, err_msg=(smin, smax))
