def test_fit_eval2(self):
"""Polynomial1DFit: Basic fitting and evaluation (non-zero-mean)."""
interp = Polynomial1DFit(2)
interp.fit(self.x2, self.y2)
y2 = interp(self.x2)
assert_almost_equal(interp.poly, self.poly, decimal=10)
assert_almost_equal(y2, self.y2, decimal=10)
def test_randomised_polyfit(self):
"""Randomise: Randomise the fit of a polynomial fitter."""
interp = Polynomial1DFit(2)
# Perfect fit (no noise)
interp.fit(self.x, self.y)
random_interp = randomise(interp, self.x, self.y, 'unknown')
y = random_interp(self.x)
assert_almost_equal(random_interp.poly, self.poly, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
random_interp = randomise(interp, self.x, self.y, 'shuffle')
y = random_interp(self.x)
assert_almost_equal(random_interp.poly, self.poly, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
# Fit polynomials to a set of noisy samples
noisy_poly = []
for yn in self.y_noisy:
interp.fit(self.x, yn)
noisy_poly.append(interp.poly)
noisy_poly = np.array(noisy_poly)
# Randomise polynomial fit to first noisy sample in various ways
# pylint: disable-msg=W0612
shuffle_poly = np.array([randomise(interp, self.x, self.y_noisy[0], 'shuffle').poly
for n in range(self.num_runs)])
assert_almost_equal(shuffle_poly.mean(axis=0), noisy_poly[0], decimal=2)
assert_almost_equal(shuffle_poly.std(axis=0), noisy_poly.std(axis=0), decimal=2)
normal_poly = np.array([randomise(interp, self.x, self.y_noisy[0], 'normal').poly
for n in range(self.num_runs)])
assert_almost_equal(normal_poly.mean(axis=0), noisy_poly[0], decimal=2)
assert_almost_equal(normal_poly.std(axis=0), noisy_poly.std(axis=0), decimal=2)
boot_poly = np.array([randomise(interp, self.x, self.y_noisy[0], 'bootstrap').poly
for n in range(self.num_runs)])
assert_almost_equal(boot_poly.mean(axis=0), noisy_poly[0], decimal=2)
assert_almost_equal(boot_poly.std(axis=0), noisy_poly.std(axis=0), decimal=2)
def test_fit_eval(self):
"""Polynomial1DFit: Basic function fitting + evaluation (zero-mean)."""
interp = Polynomial1DFit(2)
self.assertRaises(NotFittedError, interp, self.x)
interp.fit(self.x, self.y)
y = interp(self.x)
self.assertAlmostEqual(interp._mean, 0.0, places=10)
assert_almost_equal(interp.poly, self.poly, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
def test_vs_numpy(self):
"""Polynomial1DFit: Compare fitter to np.polyfit and np.polyval."""
x, p = self.randx, self.randp
y = p[0] * (x**3) + p[1] * (x**2) + p[2] * x + p[3]
interp = Polynomial1DFit(3)
interp.fit(x, y)
interp_y = interp(x)
np_poly = np.polyfit(x, y, 3)
np_y = np.polyval(np_poly, x)
self.assertAlmostEqual(interp._mean, self.randx.mean(), places=10)
assert_almost_equal(interp.poly, np_poly, decimal=10)
assert_almost_equal(interp_y, np_y, decimal=10)
def test_fit_eval(self):
"""Independent1DFit: Basic function fitting and evaluation using data from a known function."""
interp = Independent1DFit(Polynomial1DFit(2), self.axis)
self.assertRaises(NotFittedError, interp, self.x)
self.assertRaises(ValueError, interp.fit, self.x, self.y_too_low_dim)
self.assertRaises(ValueError, interp.fit, self.x, self.y_wrong_size)
interp.fit(self.x, self.y)
y = interp(self.x)
self.assertEqual(interp._axis, self.axis)
self.assertEqual(interp._interps.shape, (2, 3))
assert_almost_equal(interp._interps[0, 0].poly, self.poly1, decimal=10)
assert_almost_equal(interp._interps[0, 1].poly, self.poly2, decimal=10)
assert_almost_equal(interp._interps[0, 2].poly, self.poly1, decimal=10)
assert_almost_equal(interp._interps[1, 0].poly, self.poly2, decimal=10)
assert_almost_equal(interp._interps[1, 1].poly, self.poly1, decimal=10)
assert_almost_equal(interp._interps[1, 2].poly, self.poly2, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
def test_cov_params(self):
"""Polynomial1DFit: Compare parameter stats to covariance matrix."""
interp = Polynomial1DFit(2)
std_y = 1.3
M = 200
poly_set = np.zeros((len(self.poly), M))
for n in range(M):
yn = self.y2 + std_y * np.random.randn(len(self.y2))
interp.fit(self.x2, yn, std_y)
poly_set[:, n] = interp.poly
mean_poly = poly_set.mean(axis=1)
norm_poly = poly_set - mean_poly[:, np.newaxis]
cov_poly = np.dot(norm_poly, norm_poly.T) / M
std_poly = np.sqrt(np.diag(interp.cov_poly))
self.assertTrue(
(np.abs(mean_poly - self.poly) / std_poly < 0.5).all(),
"Sample mean coefficient vector differs too much from true value")
self.assertTrue(
(np.abs(cov_poly - interp.cov_poly) / np.abs(interp.cov_poly) <
0.5).all(),
"Sample coefficient covariance matrix differs too much")
def test_reduce_degree(self):
"""Polynomial1DFit: Reduce polynomial degree if too few data points."""
interp = Polynomial1DFit(2)
interp.fit([1.0], [1.0])
assert_almost_equal(interp.poly, [1.0], decimal=10)