pencil.math.integration
=======================

.. py:module:: pencil.math.integration

.. autoapi-nested-parse::

   Contains methods for integrating quantities in different coordinate systems.



Functions
---------

.. autoapisummary::

   pencil.math.integration.integrate


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

.. py:function:: integrate(quantity, dx=1.0, dy=1.0, dz=1.0, x=None, y=None, z=None, coordinate_system='cartesian', axis=(0, 1, 2))

   integrate(quantity, dx=1.0, dy=1.0, dz=1.0, x=None, y=None, z=None,
             coordinate_system='cartesian', axis=[0, 1, 2])

   Integrate a field along axis 'axis' using the trapezoidal rule.
   Works for Cartesian, cylindrical and spherical coordinates.
   Works with non-uniform grids.

   :param quantity: Quantity to be integrated over of shape [nz, ny, nx].
   :type quantity: ndarray
   :param dx: Grid spacing in the three dimensions. Not needed when x, y, z
              are specified.
   :type dx: floats
   :param dy: Grid spacing in the three dimensions. Not needed when x, y, z
              are specified.
   :type dy: floats
   :param dz: Grid spacing in the three dimensions. Not needed when x, y, z
              are specified.
   :type dz: floats
   :param x: Radial (x), polar (y) and vertical (z) coordinates, 1d arrays.
             These override dx, dy and dz.
             Can be non-uniform grids.
   :type x: ndarrays
   :param y: Radial (x), polar (y) and vertical (z) coordinates, 1d arrays.
             These override dx, dy and dz.
             Can be non-uniform grids.
   :type y: ndarrays
   :param z: Radial (x), polar (y) and vertical (z) coordinates, 1d arrays.
             These override dx, dy and dz.
             Can be non-uniform grids.
   :type z: ndarrays
   :param coordinate_system: Coordinate system under which to take the divergence.
                             Takes 'cartesian', 'cylindrical' and 'spherical'.
   :type coordinate_system: string
   :param axis: Axis along which to integrate.
   :type axis: list of int