bluemira.magnetostatics._ellipk
===============================

.. py:module:: bluemira.magnetostatics._ellipk


Attributes
----------

.. autoapisummary::

   bluemira.magnetostatics._ellipk._FloatOrArray
   bluemira.magnetostatics._ellipk._P
   bluemira.magnetostatics._ellipk._Q
   bluemira.magnetostatics._ellipk._C1
   bluemira.magnetostatics._ellipk._MACHEP


Functions
---------

.. autoapisummary::

   bluemira.magnetostatics._ellipk.eval_polynomial
   bluemira.magnetostatics._ellipk._ellipk
   bluemira.magnetostatics._ellipk.ellipk_nb


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

.. py:data:: _FloatOrArray

.. py:data:: _P
   :value: (0.00013798286460627325, 0.002280257240058756, 0.007974040132204152, 0.00985821379021226,...


.. py:data:: _Q
   :value: (2.940789550485985e-05, 0.0009141847238659173, 0.005940583037531678, 0.01548505166497624,...


.. py:data:: _C1
   :value: 1.3862943611198906


.. py:data:: _MACHEP
   :value: 1.1102230246251565e-16


.. py:function:: eval_polynomial(x: float, coefs: collections.abc.Sequence[float]) -> float

   Evaluate a polynomial via Horner's method.

   :returns: The evaluation of the polynomial.


.. py:function:: _ellipk(m: float) -> float

   K(m) for m >= 0.

   :param m: Positive scalar.

   :returns: Evaluation of K(m).


.. py:function:: ellipk_nb(m: _FloatOrArray) -> _FloatOrArray

   Complete elliptic integral of the first kind, K(m).

   :param m: Parameter(s) of the elliptic integral. Values m > 1 return NaN. Can be a float or
             an NDArray. If an array, the function is executed elementwise.

   :returns: K(m).

   .. rubric:: Notes

   .. math::
       K(m) = \int_{0}^{\tfrac{\pi}{2}}{(1 - m \sin^2(t)})^{-\tfrac{1}{2}} dt

   [ellipk_1]_

   Implementation based on Scipy's XSF implementation [ellipk_3]_ of the Cephes C
   [ellipk_2]_ library (MIT licensed) - with help from Claude to translate the C
   into Python.

   .. [ellipk_1] Abramowitz, M., and I. A. Stegun. Handbook of Mathematical Functions.
                 Dover Publications, 1965.
   .. [ellipk_2] Moshier, S. L. (2000). Cephes Math Library Release 2.8.
                 http://www.netlib.org/cephes
   .. [ellipk_3] https://github.com/scipy/xsf/blob/a4e89b2aa684ed63f63e5ece79b916e1f0fe619b/include/xsf/cephes/ellpk.h