pyuncertainnumber.propagation.taylor_expansion
==============================================

.. py:module:: pyuncertainnumber.propagation.taylor_expansion


Functions
---------

.. autoapisummary::

   pyuncertainnumber.propagation.taylor_expansion.taylor_expansion_method
   pyuncertainnumber.propagation.taylor_expansion.taylor_expansion_method_scalar
   pyuncertainnumber.propagation.taylor_expansion.taylor_expansion_method_vector


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

.. py:function:: taylor_expansion_method(func, mean, *, var=None, cov=None) -> tuple

   Performs uncertainty propagation using the Taylor expansion method.

   :param func: function to propagate uncertainty through. Expecting a iterable-signature function.
   :param mean: mean of the input random variable (scalar or vector)
   :type mean: Jax array
   :param var: variance of the input random variable (scalar only)
   :type var: Jax array
   :param cov: covariance matrix of the input random vector (vector only)
   :type cov: Jax array

   :returns: mean of the output random variable through the function
             var_f: variance of the output random variable through the function
   :rtype: mu_f

   .. note::

      Currently it only supports scalar-output functions. Also, for multivariate function, the
      calling signature is assumed to be func(x) where x is a 1D array, i.e. func: R^n -> R, the vec style.
      For best compatibility to work with derivatives, the `func` is better written in jax.numpy.

   .. rubric:: Example

   >>> import jax.numpy as jnp
   >>> from pyuncertainnumber import taylor_expansion_method
   >>> MEAN= jnp.array([3., 2.5])
   >>> COV = jnp.array([[4, 0.3], [0.3, 0.25]])
   >>> def bar(x): return x[0]**2 + x[1] + 3
   >>> mu_, var_ = taylor_expansion_method(func=bar, mean=MEAN, cov=COV)


.. py:function:: taylor_expansion_method_scalar(func, mean, var) -> tuple

   For scalar random variable only


.. py:function:: taylor_expansion_method_vector(func, mean, cov) -> tuple

   For random vector only