:orphan:

:mod:`atsim.potentials._util`
=============================

.. py:module:: atsim.potentials._util


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


Functions
~~~~~~~~~

.. autoapisummary::

   atsim.potentials._util.deriv
   atsim.potentials._util.num_deriv
   atsim.potentials._util.gradient


.. function:: deriv(r, func, h=1e-06)

   Evaluates the derivative of a unary callable, `func` at a value of `r`.

   If the object `func` has a unary method `deriv(r)`, this will be used to evauluate
   the derivative (allowing analytical derivatives to be used). 

   If `func` does not have a specific `deriv(r)` method then its numerical-derivative of
   will be taken by calling num_deriv()

   :param r: Value at which derivative of `func` should be evaluated.
   :param func: Function whose derivative is to be evaluated.
   :param h: Step size used when performing numerical differentiation.
   :return: Derivative of func at `r`.


.. function:: num_deriv(r, func, h=1e-06)

   Returns numerical derivative of the callable `func`

   :param r: Value at which derivative of `func` should be evaluated.
   :param func: Function whose gradient is to be evaluated.
   :param h: Step size used when performing numerical differentiation.
   :return: Numerical derivative of func at `r`.


.. function:: gradient(func, h=1e-06)

   Function wrapper that returns derivative of func.

   If the callable, `func` provides a `.deriv(r)` method this will be used
   to evaluate the derivative of the function, if not the returned function
   will use num_deriv() in gradient evaluation.

   If the callable additionally provides a `.deriv2(r)` method, representing
   its second derivative, the function returned by this routine will have a `deriv()`
   method which will delegate to func.deriv2() when called.

   By providing .deriv() and .deriv2() on the `func` callable analytical descriptions
   of a potential's first and second derivatives may be specified.

   :param func: Function to be wrapped
   :param h: Step size used when performing numerical differentiation
   :return: Function that returns derivative of func