def _likelihood_data_given_model(self, kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None,
kwargs_extinction=None, kwargs_special=None, source_marg=False, linear_prior=None,
check_positive_flux=False):
"""
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
:param source_marg: bool, performs a marginalization over the linear parameters
:param linear_prior: linear prior width in eigenvalues
:param check_positive_flux: bool, if True, checks whether the linear inversion resulted in non-negative flux
components and applies a punishment in the likelihood if so.
: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, kwargs_extinction, kwargs_special,
inv_bool=source_marg)
# compute X^2
logL = self.Data.log_likelihood(im_sim, self.likelihood_mask, model_error)
if self._pixelbased_bool is False:
if cov_matrix is not None and source_marg:
marg_const = de_lens.marginalization_new(cov_matrix, d_prior=linear_prior)
logL += marg_const
if check_positive_flux is True:
bool_ = self.check_positive_flux(kwargs_source, kwargs_lens_light, kwargs_ps)
if bool_ is False:
logL -= 10**8
return logL
def likelihood_data_given_model(self, kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None,
kwargs_extinction=None, kwargs_special=None, source_marg=False, linear_prior=None,
check_positive_flux=False):
"""
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:
:param check_positive_flux: bool, if True, checks whether the linear inversion resulted in non-negative flux
components and applies a punishment in the likelihood if so.
: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,
kwargs_extinction, kwargs_special,
inv_bool=source_marg)
# compute X^2
logL = 0
index = 0
for i in range(self._num_bands):
if self._compute_bool[i] is True:
logL += self._imageModel_list[i].Data.log_likelihood(im_sim_list[index], self._imageModel_list[i].likelihood_mask, model_error_list[index])
index += 1
if cov_matrix is not None and source_marg:
marg_const = de_lens.marginalization_new(cov_matrix, d_prior=linear_prior)
logL += marg_const
if check_positive_flux is True and self._num_bands > 0:
bool_ = self._imageModel_list[0].check_positive_flux(kwargs_source, kwargs_lens_light, kwargs_ps)
if bool_ is False:
logL -= 10 ** 5
return logL
def likelihood_data_given_model(self, kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None,
kwargs_extinction=None, kwargs_special=None, source_marg=False, linear_prior=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,
kwargs_extinction, kwargs_special,
inv_bool=source_marg)
# compute X^2
logL = 0
index = 0
for i in range(self._num_bands):
if self._compute_bool[i] is True:
logL += self._imageModel_list[i].Data.log_likelihood(im_sim_list[index], self._imageModel_list[i].likelihood_mask, model_error_list[index])
index += 1
if cov_matrix is not None and source_marg:
marg_const = de_lens.marginalization_new(cov_matrix, d_prior=linear_prior)
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)