%feature("docstring") OT::ConditionalDistribution
"Conditional distribution.

Helper class for defining the distribution of :math:`\vect{X}` such that
:math:`\vect{X}|\vect{\Theta}` follows the distribution :math:`\mathcal{L}_{\vect{X}|\vect{\Theta}}`,
with :math:`\vect{\Theta}=g(\vect{Y})`, :math:`\vect{Y}` follows the distribution
:math:`\mathcal{L}_{\vect{Y}}` and :math:`g` is a given function of input
dimension the dimension of :math:`\mathcal{L}_{\vect{Y}}` and output dimension the
dimension of :math:`\vect{\Theta}`.

Available constructors:
   ConditionalDistribution(*conditionedDist, conditioningDist, linkFunction*)

   ConditionalDistribution(*conditionedDist, conditioningDist*)

   ConditionalDistribution()

Parameters
----------

conditionedDist : :class:`~openturns.Distribution`, the distribution of
    :math:`\vect{X}|\vect{\Theta}`, whose parameters will be overwritten by
    :math:`g(\vect{Y})`.
    In the `ConditionalDistribution()` constructor, `conditionedDist` is taken equal to :math:`\vect{X} | \vect{\Theta} \sim` :class:`~openturns.Uniform` :math:`(\vect{\Theta})`.

conditioningDist : :class:`~openturns.Distribution`, the distribution of
    :math:`\vect{Y}`, specified with its parameters.
    In the `ConditionalDistribution()` constructor,  `conditioningDist` is taken
    equal to :math:`\vect{Y} \sim` :class:`~openturns.Uniform`:math:`(-1,1)`.

linkFunction : :class:`~openturns.Function`, the function
    :math:`g: \Rset^p \rightarrow \Rset^q`, where :math:`p` is the dimension of
    `conditioningDist` and :math:`q` is the dimension of :math:`\vect{\Theta}`.
    In the `ConditionalDistribution()` constructor, `linkFunction`  is taken equal
    to :math:`g: \Rset \rightarrow \Rset^2` with :math:`g(y)=(y,y+1)`.

    In the `ConditionalDistribution(conditionedDist, conditioningDist)` constructor, we need :math:`p=q` and `linkFunction`  is taken equal to  :math:`g(\vect{y})=\vect{y}`.


Notes
-----
Its probability density function is defined as:

.. math::

    f_{\vect{X}}(\vect{x}) = \int f_{\vect{X}|\vect{\Theta}=g(\vect{y})}(\vect{x}|g(\vect{y})) f_{\vect{Y}}(\vect{y})\di{\vect{y}}

with  :math:`f_{\vect{X}|\vect{\Theta}=g(\vect{y})}` the PDF of the distribution
of :math:`\vect{X}|\vect{\Theta}`, where :math:`\vect{\Theta}` has been replaced
by :math:`g(\vect{y})`, :math:`f_{\vect{Y}}` the PDF of :math:`\vect{Y}` and
:math:`g` the linking function.

With the default constructor, the resulting random variable :math:`X` follows a
trapezoidal distribution parametered by :math:`(-1, 0, 1, 2)`.

Note that a :class:`~openturns.ConditionalDistribution` can be obtained as the
first marginal distribution of a :class:`~openturns.BayesDistribution`.

The continuous part of the conditioning distribution is discretized using a
:class:`~openturns.WeightedExperiment` which can be modified using
'ConditionalDistribution-ContinuousDiscretizationMethod' in
:class:`~openturns.ResourceMap` (can be 'GaussProduct', 'QMC' or 'MC'), in
conjunction with 'ConditionalDistribution-MarginalIntegrationNodesNumber' and
'ConditionalDistribution-MaximumIntegrationNodesNumber'. The default is
'GaussProduct', well adapted if the conditioned model is *regular*, meaning that
its range does not depend on the parameters (e.g. a :class:`~openturns.Normal`
distribution). Otherwise, one of the other discretization methods is to be
preferred (e.g. for a :class:`~openturns.Uniform` distribution).

Examples
--------
Create a distribution:

>>> import openturns as ot
>>> conditioningDist = ot.Normal(0.0, 1.0)
>>> g = ot.SymbolicFunction(['y'], ['y', '0.1+y^2'])
>>> conditionedDist = ot.Normal()
>>> finalDist = ot.ConditionalDistribution(conditionedDist, conditioningDist, g)

Draw a sample:

>>> sample = finalDist.getSample(5)
"

// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::getConditionedDistribution
"Accessor to the distribution's conditioned distribution parameter `conditionedDistribution`.

Returns
-------
conditionedDistribution : :class:`~openturns.Distribution`, the distribution of
:math:`\vect{X}|\vect{\Theta}`, whose parameters will be overwritten by
      :math:`g(\vect{Y})`.
"

// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::getConditioningDistribution
"Accessor to the distribution's conditioned distribution parameter `conditioningDistribution`.

Returns
-------
conditioningDistribution : :class:`~openturns.Distribution`, the distribution of
:math:`\vect{Y}`, specified with its parameters.
"
// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::getLinkFunction
"Accessor to the distribution's conditioned distribution parameter `linkFunction`.

Returns
-------
linkFunction : :class:`~openturns.Function`, the function
      :math:`g: \Rset^p \rightarrow \Rset^q`, where :math:`p` is the dimension of
      `conditioningDist` and :math:`q` is the dimension of :math:`\vect{\Theta}`.
"

// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::setConditionedDistribution
"Accessor to the distribution's conditioned distribution parameter `conditionedDistribution`.

Parameters
----------
conditionedDistribution : :class:`~openturns.Distribution`, the distribution of
    :math:`\vect{X}|\vect{\Theta}`, whose parameters will be overwritten by
    :math:`g(\vect{Y})`.
"

// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::setConditioningDistribution
"Accessor to the distribution's conditioned distribution parameter `conditioningDistribution`.

Parameters
----------
conditioningDistribution : :class:`~openturns.Distribution`, the distribution of
    :math:`\vect{Y}`, specified with its parameters.
"
// ---------------------------------------------------------------------

%feature("docstring") OT::ConditionalDistribution::setLinkFunction
"Accessor to the distribution's conditioned distribution parameter `linkFunction`.

Parameters
----------
linkFunction : :class:`~openturns.Function`, the function
    :math:`g: \Rset^p \rightarrow \Rset^q`, where :math:`p` is the dimension of
    `conditioningDist` and :math:`q` is the dimension of :math:`\vect{\Theta}`.
"