def test_regress():
"""Test regression."""
# Simple regression example, no weights
# fit random walk
y = np.cumsum(np.random.randn(1000, 1), axis=0)
x = np.arange(1000)[:, None]
x = np.hstack([x, x**2, x**3])
[b, z] = regress(y, x)
# Simple regression example, with weights
y = np.cumsum(np.random.randn(1000, 1), axis=0)
w = np.random.rand(*y.shape)
[b, z] = regress(y, x, w)
# Downweight 1st half of the data
y = np.cumsum(np.random.randn(1000, 1), axis=0) + 1000
w = np.ones(y.shape[0])
w[:500] = 0
[b, z] = regress(y, x, w)
# # Multichannel regression
y = np.cumsum(np.random.randn(1000, 2), axis=0)
w = np.ones(y.shape[0])
[b, z] = regress(y, x, w)
assert z.shape == (1000, 2)
assert b.shape == (2, 1)
# Multichannel regression
y = np.cumsum(np.random.randn(1000, 2), axis=0)
w = np.ones(y.shape)
w[:, 1] == .8
[b, z] = regress(y, x, w)
assert z.shape == (1000, 2)
assert b.shape == (2, 3)
import config # plotting utils
np.random.seed(9)
###############################################################################
# Regression
# =============================================================================
###############################################################################
# Simple regression example, no weights
# -----------------------------------------------------------------------------
# We first try to fit a simple random walk process.
x = np.cumsum(np.random.randn(1000, 1), axis=0)
r = np.arange(1000)[:, None]
r = np.hstack([r, r**2, r**3])
b, y = regress(x, r)
plt.figure(1)
plt.plot(x, label='data')
plt.plot(y, label='fit')
plt.title('No weights')
plt.legend()
plt.show()
###############################################################################
# Downweight 1st half of the data
# -----------------------------------------------------------------------------
# We can also use weights for each time sample. Here we explicitly restrict the
# fit to the second half of the data by setting weights to zero for the first
# 500 samples.
x = np.cumsum(np.random.randn(1000, 1), axis=0) + 1000