pencil.math.transform
=====================

.. py:module:: pencil.math.transform

.. autoapi-nested-parse::

   Routines to transform coordinates and fields.



Functions
---------

.. autoapisummary::

   pencil.math.transform.coordinate_transformation
   pencil.math.transform.vector_field_transformation
   pencil.math.transform.pospolar2cart
   pencil.math.transform.velpolar2cart


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

.. py:function:: coordinate_transformation(x, y, z, xyz_from='', xyz_to='')

   coordinate_transformation(x, y, z, xyz_from='', xyz_to='')

   Tranform coordinates between coordinate systems.
   Returns a tuple (x, y, z).

   :param x: Input coordinates.
   :type x: 1d ndarray
   :param y: Input coordinates.
   :type y: 1d ndarray
   :param z: Input coordinates.
   :type z: 1d ndarray
   :param xyz_from: Origin coordinate system: 'cartesian', 'cylindrical' and 'spherical'.
   :type xyz_from: string
   :param xyz_to: Destination coordinate system: 'cartesian', 'cylindrical' and 'spherical'.
   :type xyz_to: string

   :rtype: Tuple of 3 ndarrays containing the transformed coordinates.


.. py:function:: vector_field_transformation(field, x, y, z, xyz_from='', xyz_to='')

   vector_field_transformation(field, x, y, z, xyz_from='', xyz_to='')

   Transform a vector field from one coordinate system to another.

   :param field: Vector field.
   :type field: 4d ndarray
   :param x: Input coordinates of the 'from' system.
   :type x: 1d ndarrays
   :param y: Input coordinates of the 'from' system.
   :type y: 1d ndarrays
   :param z: Input coordinates of the 'from' system.
   :type z: 1d ndarrays
   :param xyz_from: Origin coordinate system: 'cartesian', 'cylindrical' and 'spherical'.
   :type xyz_from: string
   :param xyz_to: Destination coordinate system: 'cartesian', 'cylindrical' and 'spherical'.
   :type xyz_to: string

   :rtype: ndarray with the transformed vector field.


.. py:function:: pospolar2cart(r, th)

   Transform from polar to cartesian coordinates


.. py:function:: velpolar2cart(vr, vth, r, th, zcoord=0)

   Transform from polar velocities to cartesian velocities

   call signature:

   velpolar2cart(vr, vth, r, th, zcoord=0)

   Keyword arguments:

   *vr*:
     3D array of velocities in radial direction

   *vth*:
     3D array of velocities in theta direction

   *r*
     coordinates in radial direction

   *th*
     coordinates in theta direction

   *zcoord*
     plane in z-dir