agedi.utils.truncated_normal
============================

.. py:module:: agedi.utils.truncated_normal

.. autoapi-nested-parse::

   BSD 3-Clause License

   Copyright (c) 2020, Anton Obukhov
   All rights reserved.

   https://github.com/toshas/torch_truncnorm



Attributes
----------

.. autoapisummary::

   agedi.utils.truncated_normal.CONST_SQRT_2
   agedi.utils.truncated_normal.CONST_INV_SQRT_2PI
   agedi.utils.truncated_normal.CONST_INV_SQRT_2
   agedi.utils.truncated_normal.CONST_LOG_INV_SQRT_2PI
   agedi.utils.truncated_normal.CONST_LOG_SQRT_2PI_E


Classes
-------

.. autoapisummary::

   agedi.utils.truncated_normal.TruncatedStandardNormal
   agedi.utils.truncated_normal.TruncatedNormal


Module Contents
---------------

.. py:data:: CONST_SQRT_2

.. py:data:: CONST_INV_SQRT_2PI

.. py:data:: CONST_INV_SQRT_2

.. py:data:: CONST_LOG_INV_SQRT_2PI

.. py:data:: CONST_LOG_SQRT_2PI_E

.. py:class:: TruncatedStandardNormal(a: Union[numbers.Number, torch.Tensor], b: Union[numbers.Number, torch.Tensor], validate_args: Optional[bool] = None)

   Bases: :py:obj:`torch.distributions.Distribution`


   Truncated Standard Normal distribution
   https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf


   .. py:attribute:: arg_constraints


   .. py:attribute:: has_rsample
      :value: True



   .. py:attribute:: _dtype_min_gt_0


   .. py:attribute:: _dtype_max_lt_1


   .. py:attribute:: _little_phi_a


   .. py:attribute:: _little_phi_b


   .. py:attribute:: _big_phi_a


   .. py:attribute:: _big_phi_b


   .. py:attribute:: _Z


   .. py:attribute:: _log_Z


   .. py:attribute:: _lpbb_m_lpaa_d_Z


   .. py:attribute:: _mean


   .. py:attribute:: _variance


   .. py:attribute:: _entropy


   .. py:method:: support()

      Return the support interval ``[a, b]``.



   .. py:property:: mean
      :type: torch.Tensor


      Mean of the truncated standard normal distribution.


   .. py:property:: variance
      :type: torch.Tensor


      Variance of the truncated standard normal distribution.


   .. py:property:: entropy
      :type: torch.Tensor


      Differential entropy of the truncated standard normal distribution.


   .. py:property:: auc
      :type: torch.Tensor


      Normalisation constant Z = Φ(b) − Φ(a).


   .. py:method:: _little_phi(x: torch.Tensor) -> torch.Tensor
      :staticmethod:


      Standard normal probability density function φ(x).



   .. py:method:: _big_phi(x: torch.Tensor) -> torch.Tensor
      :staticmethod:


      Standard normal cumulative distribution function Φ(x).



   .. py:method:: _inv_big_phi(x: torch.Tensor) -> torch.Tensor
      :staticmethod:


      Inverse of the standard normal CDF Φ⁻¹(x).



   .. py:method:: cdf(value: torch.Tensor) -> torch.Tensor

      Cumulative distribution function evaluated at *value*.



   .. py:method:: icdf(value: torch.Tensor) -> torch.Tensor

      Inverse CDF (quantile function) evaluated at *value*.



   .. py:method:: log_prob(value: torch.Tensor) -> torch.Tensor

      Log probability density evaluated at *value*.



   .. py:method:: rsample(sample_shape: torch.Size = torch.Size()) -> torch.Tensor

      Draw a re-parameterised sample of the given shape.



.. py:class:: TruncatedNormal(loc: Union[numbers.Number, torch.Tensor], scale: Union[numbers.Number, torch.Tensor], a: Union[numbers.Number, torch.Tensor], b: Union[numbers.Number, torch.Tensor], validate_args: Optional[bool] = None)

   Bases: :py:obj:`TruncatedStandardNormal`


   Truncated Normal distribution
   https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf


   .. py:attribute:: has_rsample
      :value: True



   .. py:attribute:: _log_scale


   .. py:attribute:: _mean


   .. py:attribute:: _variance


   .. py:method:: _to_std_rv(value: torch.Tensor) -> torch.Tensor

      Standardise *value* to the standard (zero-mean, unit-variance) domain.



   .. py:method:: _from_std_rv(value: torch.Tensor) -> torch.Tensor

      Map *value* from the standard domain back to the original (loc/scale) domain.



   .. py:method:: cdf(value: torch.Tensor) -> torch.Tensor

      Cumulative distribution function evaluated at *value*.



   .. py:method:: icdf(value: torch.Tensor) -> torch.Tensor

      Inverse CDF (quantile function) evaluated at *value*.



   .. py:method:: log_prob(value: torch.Tensor) -> torch.Tensor

      Log probability density evaluated at *value*.