def setUp(self):
self.true_mean, self.true_std, self.true_height = [0, 0], 1., 0.
true_gauss = GaussianFit(self.true_mean, self.true_std,
self.true_height)
self.x = 7 * np.random.randn(2, 80)
self.y = true_gauss(self.x)
self.init_mean, self.init_std, self.init_height = [0, 0], 1, 0
def test_fit_eval_diagcov(self):
"""GaussianFit (shared stdev): Basic function fitting and evaluation using data from a known function."""
interp = GaussianFit(self.init_mean, self.init_std, self.init_height)
interp.fit(self.x, self.y)
y = interp(self.x)
assert_almost_equal(interp.mean, self.true_mean, decimal=7)
assert_almost_equal(interp.std, self.true_std, decimal=7)
assert_almost_equal(interp.height, self.true_height, decimal=7)
assert_almost_equal(y, self.y, decimal=7)
def setUp(self):
# For a more challenging fit, move the true mean away from the origin, i.e. away from the region
# being randomly sampled in self.x. Fitting a Gaussian to a segment that does not contain a clear peak
# works fine if the fit is done to the log of the data, but fails in the linear domain.
self.true_mean, self.true_std, self.true_height = [0., 0.], [3., 5.], 4.
true_gauss = GaussianFit(self.true_mean, self.true_std, self.true_height)
self.x = 7. * np.random.randn(2, 300)
self.y = true_gauss(self.x)
self.init_mean, self.init_std, self.init_height = [3., -2.], [1., 1.], 1.
def test_fit_eval_diagcov(self):
"""GaussianFit (independent stdevs): Basic fitting and evaluation."""
interp = GaussianFit(self.init_mean, self.init_std, self.init_height)
interp.fit(self.x, self.y)
y = interp(self.x)
assert_almost_equal(interp.mean, self.true_mean, decimal=7)
assert_almost_equal(interp.std, self.true_std, decimal=7)
assert_almost_equal(interp.height, self.true_height, decimal=7)
assert_almost_equal(y, self.y, decimal=7)
def setUp(self):
self.true_mean = [0, 0]
self.true_std = np.sqrt(10)
self.true_height = 4
true_gauss = GaussianFit(self.true_mean, self.true_std,
self.true_height)
self.x = 7 * np.random.randn(2, 80)
self.y = true_gauss(self.x)
self.init_mean = [3, -2]
self.init_std = 1
self.init_height = 1
def __init__(self, center, width, height):
ScatterFit.__init__(self)
if not np.isscalar(width):
width = np.atleast_1d(width)
self._interp = GaussianFit(center, fwhm_to_sigma(width), height)
self.center = self._interp.mean
self.width = sigma_to_fwhm(self._interp.std)
self.height = self._interp.height
self.expected_width = width
# Initial guess for radius of first null
# XXX: POTENTIAL TWEAK
self.radius_first_null = 1.3 * np.mean(self.expected_width)
# Beam initially unrefined and invalid
self.refined = 0
self.is_valid = False
self.std_center = self.std_width = self.std_height = None
def test_cov_params(self):
"""GaussianFit (independent stdevs): Obtain sample statistics of parameters and compare to calculated covariance matrix."""
interp = GaussianFit(self.init_mean, self.init_std, self.init_height)
true_params = np.r_[self.true_mean, self.true_height, self.true_std]
std_y = 0.1
M = 200
param_set = np.zeros((len(true_params), M))
for n in range(M):
interp.fit(self.x, self.y + std_y * np.random.randn(len(self.y)), std_y)
param_set[:, n] = np.r_[interp.mean, interp.height, interp.std]
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
estm_std_params = np.sqrt(np.diag(cov_params))
std_params = np.r_[interp.std_mean, interp.std_height, interp.std_std]
self.assertTrue((np.abs(mean_params - true_params) / std_params < 0.5).all(),
"Sample mean parameter vector differs too much from true value")
# Only check diagonal of cov matrix - the rest is probably affected by linearisation
self.assertTrue((np.abs(estm_std_params - std_params) / std_params < 0.2).all(),
"Sample parameter standard deviation differs too much from expected one")
