def test_fit_eval(self):
"""LinearLeastSquaresFit: Basic function fitting and evaluation using data from a known function."""
interp = LinearLeastSquaresFit()
self.assertRaises(NotFittedError, interp, self.x)
interp.fit(self.x, self.y)
y = interp(self.x)
assert_almost_equal(interp.params, self.params, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
def test_fit_eval(self):
"""LinearLeastSquaresFit: Basic function fitting and evaluation using data from a known function."""
interp = LinearLeastSquaresFit()
self.assertRaises(NotFittedError, interp, self.x)
interp.fit(self.x, self.y)
y = interp(self.x)
assert_almost_equal(interp.params, self.params, decimal=10)
assert_almost_equal(y, self.y, decimal=10)
def test_fit_eval_linear(self):
"""NonLinearLeastSquaresFit: Compare to LinearLeastSquaresFit on a linear problem (and check use of Jacobian)."""
lin = LinearLeastSquaresFit()
lin.fit(self.x3, self.y3, std_y=2.0)
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3, func_jacobian=self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
# A correct Jacobian helps a lot...
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin.cov_params, decimal=11)
nonlin_nojac = NonLinearLeastSquaresFit(self.func3, self.init_params3)
nonlin_nojac.fit(self.x3, self.y3, std_y=0.1)
assert_almost_equal(nonlin_nojac.params, self.true_params3, decimal=6)
def test_fit_eval_linear(self):
"""NonLinearLeastSquaresFit: Do linear problem and check Jacobian."""
lin = LinearLeastSquaresFit()
lin.fit(self.x3, self.y3, std_y=2.0)
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3,
func_jacobian=self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
# A correct Jacobian helps a lot...
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin.cov_params, decimal=11)
nonlin_nojac = NonLinearLeastSquaresFit(self.func3, self.init_params3)
nonlin_nojac.fit(self.x3, self.y3, std_y=0.1)
assert_almost_equal(nonlin_nojac.params, self.true_params3, decimal=5)
def test_enabled_params(self):
"""NonLinearLeastSquaresFit: Check whether subset of parameters can be optimised."""
lin = LinearLeastSquaresFit()
lin.fit(self.x3[self.enabled_params_int, :], self.y3, std_y=2.0)
lin_cov_params = np.zeros((len(self.true_params3), len(self.true_params3)))
lin_cov_params[np.ix_(self.enabled_params_int, self.enabled_params_int)] = lin.cov_params
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3, self.enabled_params_int, self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin_cov_params, decimal=11)
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3, self.enabled_params_bool, self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin_cov_params, decimal=11)
def test_enabled_params(self):
"""NonLinearLeastSquaresFit: Check whether subset of parameters can be optimised."""
lin = LinearLeastSquaresFit()
lin.fit(self.x3[self.enabled_params_int, :], self.y3, std_y=2.0)
lin_cov_params = np.zeros(
(len(self.true_params3), len(self.true_params3)))
lin_cov_params[np.ix_(self.enabled_params_int,
self.enabled_params_int)] = lin.cov_params
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3,
self.enabled_params_int, self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin_cov_params, decimal=11)
nonlin = NonLinearLeastSquaresFit(self.func3, self.init_params3,
self.enabled_params_bool, self.jac3)
nonlin.fit(self.x3, self.y3, std_y=2.0)
assert_almost_equal(nonlin.params, self.true_params3, decimal=11)
assert_almost_equal(nonlin.cov_params, lin_cov_params, decimal=11)
def test_cov_params(self):
"""LinearLeastSquaresFit: Obtain sample statistics of parameters and compare to calculated covariance matrix."""
interp = LinearLeastSquaresFit()
std_y = 1.0
M = 200
param_set = np.zeros((len(self.params), M))
for n in range(M):
yn = self.poly_y + std_y * np.random.randn(len(self.poly_y))
interp.fit(self.poly_x, yn, std_y)
param_set[:, n] = interp.params
mean_params = param_set.mean(axis=1)
norm_params = param_set - mean_params[:, np.newaxis]
cov_params = np.dot(norm_params, norm_params.T) / M
std_params = np.sqrt(np.diag(interp.cov_params))
self.assertTrue((np.abs(mean_params - self.params) / std_params < 0.25).all(),
"Sample mean parameter vector differs too much from true value")
self.assertTrue((np.abs(cov_params - interp.cov_params) / np.abs(interp.cov_params) < 1.0).all(),
"Sample parameter covariance matrix differs too much from expected one")
def test_vs_numpy(self):
"""LinearLeastSquaresFit: Compare fitter to np.linalg.lstsq."""
interp = LinearLeastSquaresFit()
interp.fit(self.x, self.y)
params = np.linalg.lstsq(self.x.T, self.y)[0]
assert_almost_equal(interp.params, params, decimal=10)
rcond = 1e-3
interp = LinearLeastSquaresFit(rcond)
interp.fit(self.poly_x, self.poly_y)
params = np.linalg.lstsq(self.poly_x.T, self.poly_y, rcond)[0]
assert_almost_equal(interp.params, params, decimal=10)
def test_cov_params(self):
"""LinearLeastSquaresFit: Compare param stats to covariance matrix."""
interp = LinearLeastSquaresFit()
std_y = 1.0
M = 200
param_set = np.zeros((len(self.params), M))
for n in range(M):
yn = self.poly_y + std_y * np.random.randn(len(self.poly_y))
interp.fit(self.poly_x, yn, std_y)
param_set[:, n] = interp.params
mean_params = param_set.mean(axis=1)
norm_params = param_set - mean_params[:, np.newaxis]
cov_params = np.dot(norm_params, norm_params.T) / M
std_params = np.sqrt(np.diag(interp.cov_params))
self.assertTrue(
(np.abs(mean_params - self.params) / std_params < 0.25).all(),
"Sample mean parameter vector differs too much from true value")
self.assertTrue(
(np.abs(cov_params - interp.cov_params) / np.abs(interp.cov_params)
< 1.0).all(),
"Sample parameter covariance matrix differs too much")
def test_vs_numpy(self):
"""LinearLeastSquaresFit: Compare fitter to np.linalg.lstsq."""
interp = LinearLeastSquaresFit()
interp.fit(self.x, self.y)
params = np.linalg.lstsq(self.x.T, self.y, rcond=-1)[0]
assert_almost_equal(interp.params, params, decimal=10)
rcond = 1e-3
interp = LinearLeastSquaresFit(rcond)
with warnings.catch_warnings(record=True) as warning:
interp.fit(self.poly_x, self.poly_y)
assert_equal(str(warning[0].message),
"Least-squares fit may be poorly conditioned")
params = np.linalg.lstsq(self.poly_x.T, self.poly_y, rcond)[0]
assert_almost_equal(interp.params, params, decimal=10)
def test_vs_numpy(self):
"""LinearLeastSquaresFit: Compare fitter to np.linalg.lstsq."""
interp = LinearLeastSquaresFit()
interp.fit(self.x, self.y)
params = np.linalg.lstsq(self.x.T, self.y)[0]
assert_almost_equal(interp.params, params, decimal=10)
rcond = 1e-3
interp = LinearLeastSquaresFit(rcond)
interp.fit(self.poly_x, self.poly_y)
params = np.linalg.lstsq(self.poly_x.T, self.poly_y, rcond)[0]
assert_almost_equal(interp.params, params, decimal=10)
def test_vs_numpy(self):
"""LinearLeastSquaresFit: Compare fitter to np.linalg.lstsq."""
interp = LinearLeastSquaresFit()
interp.fit(self.x, self.y)
params = np.linalg.lstsq(self.x.T, self.y, rcond=-1)[0]
assert_almost_equal(interp.params, params, decimal=10)
rcond = 1e-3
interp = LinearLeastSquaresFit(rcond)
with warnings.catch_warnings(record=True) as warning:
interp.fit(self.poly_x, self.poly_y)
assert_equal(str(warning[0].message),
"Least-squares fit may be poorly conditioned")
params = np.linalg.lstsq(self.poly_x.T, self.poly_y, rcond)[0]
assert_almost_equal(interp.params, params, decimal=10)
