def test_marginalisation_const(self):
A = np.array([[1,2,3],[3,2,1]]).T
C_D_inv = np.array([1,1,1])
d = np.array([1,2,3])
result, cov_error, image = de_lens.get_param_WLS(A, C_D_inv, d)
logL_marg = de_lens.marginalisation_const(cov_error)
npt.assert_almost_equal(logL_marg, -2.2821740957339181, decimal=8)
M_inv = np.array([[1,0],[0,1]])
marg_const = de_lens.marginalisation_const(M_inv)
assert marg_const == 0
def likelihood_data_given_model(self,
kwargs_lens,
kwargs_source,
kwargs_lens_light,
kwargs_ps,
source_marg=False,
compute_bool=None):
"""
computes the likelihood of the data given a model
This is specified with the non-linear parameters and a linear inversion and prior marginalisation.
:param kwargs_lens: list of keyword arguments corresponding to the superposition of different lens profiles
:param kwargs_source: list of keyword arguments corresponding to the superposition of different source light profiles
:param kwargs_lens_light: list of keyword arguments corresponding to different lens light surface brightness profiles
:param kwargs_ps: keyword arguments corresponding to "other" parameters, such as external shear and point source image positions
:return: log likelihood (natural logarithm)
"""
# generate image
im_sim, model_error, cov_matrix, param = self.image_linear_solve(
kwargs_lens,
kwargs_source,
kwargs_lens_light,
kwargs_ps,
inv_bool=source_marg)
# compute X^2
logL = self.Data.log_likelihood(im_sim, self.ImageNumerics.mask,
model_error)
if cov_matrix is not None and source_marg:
marg_const = de_lens.marginalisation_const(cov_matrix)
#if marg_const + logL > 0:
#logL = np.log(np.exp(logL) + np.exp(marg_const))
logL += marg_const
return logL
def likelihood_data_given_model(self,
kwargs_lens,
kwargs_source,
kwargs_lens_light,
kwargs_ps,
source_marg=False,
compute_bool=None):
"""
computes the likelihood of the data given a model
This is specified with the non-linear parameters and a linear inversion and prior marginalisation.
:param kwargs_lens:
:param kwargs_source:
:param kwargs_lens_light:
:param kwargs_ps:
:return: log likelihood (natural logarithm) (sum of the log likelihoods of the individual images)
"""
# generate image
im_sim_list, model_error_list, cov_matrix, param = self.image_linear_solve(
kwargs_lens,
kwargs_source,
kwargs_lens_light,
kwargs_ps,
inv_bool=source_marg)
# compute X^2
logL = 0
for i in range(self._num_bands):
logL += self._imageModel_list[i].Data.log_likelihood(
im_sim_list[i], self._imageModel_list[i].ImageNumerics.mask,
model_error_list[i])
if cov_matrix is not None and source_marg:
marg_const = de_lens.marginalisation_const(cov_matrix)
logL += marg_const
return logL
def test_margnialization_new(self):
M_inv = np.array([[1, -0.5, 1], [-0.5, 3, 0], [1, 0, 2]])
d_prior = 1000
m = len(M_inv)
log_det = DeLens.marginalization_new(M_inv, d_prior=d_prior)
log_det_old = DeLens.marginalisation_const(M_inv)
npt.assert_almost_equal(log_det,
log_det_old + m / 2. * np.log(np.pi / 2.) -
m * np.log(d_prior),
decimal=9)
M_inv = np.array([[1, 1, 1], [0., 1., 0.], [1., 2., 1.]])
log_det = DeLens.marginalization_new(M_inv, d_prior=10)
log_det_old = DeLens.marginalisation_const(M_inv)
npt.assert_almost_equal(log_det, log_det_old, decimal=9)
npt.assert_almost_equal(log_det, -10**(15), decimal=10)
log_det = DeLens.marginalization_new(M_inv, d_prior=None)
log_det_old = DeLens.marginalisation_const(M_inv)
npt.assert_almost_equal(log_det, log_det_old, decimal=9)