pencil.math.derivatives.der_nonequi
===================================

.. py:module:: pencil.math.derivatives.der_nonequi


Functions
---------

.. autoapisummary::

   pencil.math.derivatives.der_nonequi.der_6th
   pencil.math.derivatives.der_nonequi.der2_6th
   pencil.math.derivatives.der_nonequi.der6_2nd
   pencil.math.derivatives.der_nonequi.xder_6th
   pencil.math.derivatives.der_nonequi.yder_6th
   pencil.math.derivatives.der_nonequi.zder_6th
   pencil.math.derivatives.der_nonequi.xder2_6th
   pencil.math.derivatives.der_nonequi.yder2_6th
   pencil.math.derivatives.der_nonequi.zder2_6th
   pencil.math.derivatives.der_nonequi.xder6_2nd
   pencil.math.derivatives.der_nonequi.yder6_2nd
   pencil.math.derivatives.der_nonequi.zder6_2nd


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

.. py:function:: der_6th(f, dx_1, axis)

   der_6th(f, dx_1, axis)

   Compute the 1st order derivative, 6th order accurate in x. Adapted from der2_main in deriv.f90.
   This supports nonequidistant grids.

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx_1: grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.
   :type dx_1: 1D array
   :param axis: Axis of f along which the derivative should be taken.
   :type axis: int


.. py:function:: der2_6th(f, dx_1, dx_tilde, axis)

   der2_6th(f, dx_1, dx_tilde, axis)

   Compute the 2nd order derivative, 6th order accurate in x. Adapted from der2_main in deriv.f90.
   This supports nonequidistant grids.

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx_1: grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.
   :type dx_1: 1D array
   :param dx_tilde: grid.dx_tilde (or dy_tilde or dz_tilde). Is just zero for equidistant grids.
   :type dx_tilde: 1D array
   :param axis: Axis of f along which the derivative should be taken.
   :type axis: int


.. py:function:: der6_2nd(f, dx_1, axis)

   der6_2nd(f, dx_1, axis)

   Compute the 6th order derivative, with 2nd order error in x. Adapted from der6_main in deriv.f90.
   This supports nonequidistant grids.

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx_1: grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.
   :type dx_1: 1D array
   :param axis: Axis of f along which the derivative should be taken.
   :type axis: int


.. py:function:: xder_6th(f, dx=None, dx_1=None)

   xder_6th(f, dx=None, dx_1=None)

   Compute the 1st order derivative, 6th order accurate in x.

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx: Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 argument is ignored.
   :type dx: float
   :param dx_1: Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant
   :type dx_1: ndarray


.. py:function:: yder_6th(f, dy=None, dy_1=None)

   Same as xder_6th, but for y axis


.. py:function:: zder_6th(f, dz=None, dz_1=None)

   Same as xder_6th, but for z axis


.. py:function:: xder2_6th(f, dx=None, dx_1=None, dx_tilde=None)

   xder2_6th(f, dx=None, dx_1=None)

   Compute the 2nd order derivative, 6th order accurate in x.

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx: Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 and dx_tilde arguments are ignored.
   :type dx: float
   :param dx_1: Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant
   :type dx_1: ndarray
   :param dx_tilde: grid.dx_tilde (or dy_tilde or dz_tilde). Is just zero for equidistant grids.
   :type dx_tilde: 1D array


.. py:function:: yder2_6th(f, dy=None, dy_1=None, dy_tilde=None)

   Same as xder2_6th, but for y axis


.. py:function:: zder2_6th(f, dz=None, dz_1=None, dz_tilde=None)

   Same as xder2_6th, but for z axis


.. py:function:: xder6_2nd(f, dx=None, dx_1=None)

   xder6_2nd(f, dx=None, dx_1=None)

   Compute the 6th order derivative, with 2nd order error in x

   :param f: Array for which to compute the derivative.
   :type f: ndarray
   :param dx: Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 argument is ignored.
   :type dx: float
   :param dx_1: Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant
   :type dx_1: ndarray


.. py:function:: yder6_2nd(f, dy=None, dy_1=None)

   Same as xder6_2nd, but for y axis


.. py:function:: zder6_2nd(f, dz=None, dz_1=None)

   Same as xder6_2nd, but for z axis