def logjacobian(self, **params):
r"""Returns the log of the jacobian needed to transform pdfs in the
``variable_args`` parameter space to the ``sampling_args`` parameter
space.
Let :math:`\mathbf{x}` be the set of variable parameters,
:math:`\mathbf{y} = f(\mathbf{x})` the set of sampling parameters, and
:math:`p_x(\mathbf{x})` a probability density function defined over
:math:`\mathbf{x}`.
The corresponding pdf in :math:`\mathbf{y}` is then:
.. math::
p_y(\mathbf{y}) =
p_x(\mathbf{x})\left|\mathrm{det}\,\mathbf{J}_{ij}\right|,
where :math:`\mathbf{J}_{ij}` is the Jacobian of the inverse transform
:math:`\mathbf{x} = g(\mathbf{y})`. This has elements:
.. math::
\mathbf{J}_{ij} = \frac{\partial g_i}{\partial{y_j}}
This function returns
:math:`\log \left|\mathrm{det}\,\mathbf{J}_{ij}\right|`.
Parameters
----------
\**params :
The keyword arguments should specify values for all of the variable
args and all of the sampling args.
Returns
-------
float :
The value of the jacobian.
"""
if self._sampling_transforms is None:
return 0.
else:
return numpy.log(
abs(
transforms.compute_jacobian(params,
self._sampling_transforms,
inverse=True)))
def logjacobian(self, **params):
r"""Returns the log of the jacobian needed to transform pdfs in the
``variable_params`` parameter space to the ``sampling_params``
parameter space.
Let :math:`\mathbf{x}` be the set of variable parameters,
:math:`\mathbf{y} = f(\mathbf{x})` the set of sampling parameters, and
:math:`p_x(\mathbf{x})` a probability density function defined over
:math:`\mathbf{x}`.
The corresponding pdf in :math:`\mathbf{y}` is then:
.. math::
p_y(\mathbf{y}) =
p_x(\mathbf{x})\left|\mathrm{det}\,\mathbf{J}_{ij}\right|,
where :math:`\mathbf{J}_{ij}` is the Jacobian of the inverse transform
:math:`\mathbf{x} = g(\mathbf{y})`. This has elements:
.. math::
\mathbf{J}_{ij} = \frac{\partial g_i}{\partial{y_j}}
This function returns
:math:`\log \left|\mathrm{det}\,\mathbf{J}_{ij}\right|`.
Parameters
----------
\**params :
The keyword arguments should specify values for all of the variable
args and all of the sampling args.
Returns
-------
float :
The value of the jacobian.
"""
return numpy.log(abs(transforms.compute_jacobian(
params, self.sampling_transforms, inverse=True)))
