def test_detrend(show=False):
"""Test detrending."""
# basic
x = np.arange(100)[:, None]
x = x + np.random.randn(*x.shape)
y, _, _ = detrend(x, 1)
assert y.shape == x.shape
# detrend biased random walk
x = np.cumsum(np.random.randn(1000, 1) + 0.1)
y, _, _ = detrend(x, 3)
assert y.shape == x.shape
# weights
trend = np.linspace(0, 100, 1000)[:, None]
data = 3 * np.random.randn(*trend.shape)
x = trend + data
x[:100, :] = 100
w = np.ones(x.shape)
w[:100, :] = 0
y, _, _ = detrend(x, 3, None, show=show)
yy, _, _ = detrend(x, 3, w, show=show)
assert y.shape == x.shape
assert yy.shape == x.shape
def test_detrend(show=False):
"""Test detrending."""
# basic
x = np.arange(100)[:, None] # trend
source = np.random.randn(*x.shape)
x = x + source
y, _, _ = detrend(x, 1)
assert y.shape == x.shape
# detrend biased random walk
x = np.cumsum(np.random.randn(1000, 1) + 0.1)
y, _, _ = detrend(x, 3)
assert y.shape == x.shape
# test weights
trend = np.linspace(0, 100, 1000)[:, None]
data = 3 * np.random.randn(*trend.shape)
data[:100, :] = 100
x = trend + data
w = np.ones(x.shape)
w[:100, :] = 0
# Without weights – detrending fails
y, _, _ = detrend(x, 3, None, show=show)
# With weights – detrending works
yy, _, _ = detrend(x, 3, w, show=show)
assert y.shape == x.shape
assert yy.shape == x.shape
assert np.all(np.abs(yy[100:] - data[100:]) < 1.)
# detrend higher-dimensional data
x = np.cumsum(np.random.randn(1000, 16) + 0.1, axis=0)
y, _, _ = detrend(x, 1, show=False)
# detrend higher-dimensional data with order 3 polynomial
x = np.cumsum(np.random.randn(1000, 16) + 0.1, axis=0)
y, _, _ = detrend(x, 3, basis='polynomials', show=True)
# detrend with sinusoids
x = np.random.randn(1000, 2)
x += 2 * np.sin(2 * np.pi * np.arange(1000) / 200)[:, None]
y, _, _ = detrend(x, 5, basis='sinusoids', show=True)
plt.figure(4)
plt.plot(x, label='data', color='C0')
plt.plot(y, ls=':', label='fit', color='C1')
plt.title('Channel-wise regression')
plt.legend()
###############################################################################
# Detrending
# =============================================================================
###############################################################################
# Basic example with a linear trend
# -----------------------------------------------------------------------------
x = np.arange(100)[:, None]
x = x + np.random.randn(*x.shape)
y, _, _ = detrend(x, 1)
plt.figure(5)
plt.plot(x, label='original')
plt.plot(y, label='detrended')
plt.legend()
###############################################################################
# Detrend biased random walk with a third-order polynomial
# -----------------------------------------------------------------------------
x = np.cumsum(np.random.randn(1000, 1) + 0.1)
y, _, _ = detrend(x, 3)
plt.figure(6)
plt.plot(x, label='original')
plt.plot(y, label='detrended')