pencil.math.stats
=================

.. py:module:: pencil.math.stats

.. autoapi-nested-parse::

   Differential operators in different coordinate systems.



Submodules
----------

.. toctree::
   :maxdepth: 1

   /code/sourcePython/pencil/math/stats/struct/index


Functions
---------

.. autoapisummary::

   pencil.math.stats.space_struct
   pencil.math.stats.time_struct
   pencil.math.stats.fit_gaussm1
   pencil.math.stats.fit_expm1
   pencil.math.stats.fit_gauss
   pencil.math.stats.fit_exp
   pencil.math.stats.fit_power
   pencil.math.stats.fit_linear


Package Contents
----------------

.. py:function:: space_struct(arr, dims=[[], [], []], Dorder=2, dirs='zyx', lperi=(True, True, True), lplot=True, InitialGuess=[1.0, 1.0], deltay=0.0, chunksize=1000.0, figname=None, dlabel='data', quiet=True, downsample=[1, 1, 1], maxl=[-1, -1, -1], loopsample=[1, 1, 1])

   Calculate the structure function in space.

   call signature:

   space_struct(arr, dims=[[],[],[]], Dorder=2, dirs='zyx',
                lperi=(True,True,True), lplot=True,
                InitialGuess = [1.0,1.0],
                deltay=0.,
                figname = None, dlabel = 'data',
                quiet=False)

   Keyword arguments:

   *arr*:
     numpy data array of shape, e.g., [nz,ny,nz].

   *z*:
     z dimension full array to replace default empty list.

   *y*:
     y dimension full array to replace default empty list.

   *x*:
     x dimension full array to replace default empty list.

   *Dorder*:
     Order of structure function, by default 2nd.

   *lperi*:
     Flag indicates for each dimension, whether boundary is periodic.

   *lplot*
     Flag to plot the result.

   *InitialGuess*:
     Initial parameters for curve fitting, default [1.0,1.0].

   *figname*:
     String name for plot, if saving rather than only display.

   *dlabel*:
     legend label for data.

   *quiet*
     Flag for switching off output.

   :rtype: D1 Structure function, length array, fit parameters [sigma, L0].

   .. rubric:: Notes

   Must provide list of dimension arrays to match dirs required.

   .. rubric:: Examples

   >>> D,ell,fit = pc.math.stats.space_struct(var.rho, dims=[gd.z,gd.y,gd.x],
                                              dirs='zyx')
   >>> D, ell, fit
   [0, ...,], [0, 0.0041, ...], [2.5,0.04]


.. py:function:: time_struct(arr, time=[], order=2, lplot=True, InitialGuess=[1.0, 1.0], figname=None, dlabel='data', quiet=False)

   Calculate the structure function in time.

   call signature:

   time_struct(arr, time=[], order=2, lplot=True, InitialGuess = [1.0,1.0],
           figname = None, dlabel = 'data',   quiet=False)

   Keyword arguments:

   *arr*:
     numpy data array of shape [ntime,:].

   *time*:
     time series for time correlations. By default empty list.

   *Dorder*:
     Order of structure function, by default 2nd.

   *lplot*
     Flag to plot the result.

   *InitialGuess*:
     Initial parameters for curve fitting, default [1.0,1.0].

   *figname*:
     String name for plot, if saving rather than only display.

   *dlabel*:
     legend label for data.

   *quiet*
     Flag for switching off output.

   :rtype: D1 Structure function, time array, fit parameters [sigma, L0].

   .. rubric:: Notes

   Provide time series of D1 -- D3 sample sets of fixed spatial location.

   .. rubric:: Examples

   >>> Dt,t,fit = pc.math.stats.space_struct(var.rho, dims=[gd.z,gd.y,gd.x],
                                              dirs='zyx')
   >>> Dt, t, fit
   [0, ...,], [0, 0.0041, ...], [2.5,0.04]


.. py:function:: fit_gaussm1(ell, sigma, L0)

   Fit for 2nd order structure function, Eq. 6 DOI 10.3847/1538-4357/aa93e7
   correlation length = sqrt(pi/2)L0


.. py:function:: fit_expm1(t, sigma, L0)

   Fit for 2nd order structure function, Eq. 5 DOI 10.3847/1538-4357/aa93e7
   correlation length = L0


.. py:function:: fit_gauss(ell, sigma, L0)

   Fit for 2nd order structure function, Eq. 6 DOI 10.3847/1538-4357/aa93e7
   correlation length = sqrt(pi/2)L0


.. py:function:: fit_exp(t, sigma, L0)

   Fit for 2nd order structure function, Eq. 5 DOI 10.3847/1538-4357/aa93e7
   correlation length = L0


.. py:function:: fit_power(t, sigma, L0)

   Fit for 2nd order structure function, Eq. 5 DOI 10.3847/1538-4357/aa93e7
   correlation length = L0


.. py:function:: fit_linear(t, sigma, L0)

   Fit for 2nd order structure function, Eq. 5 DOI 10.3847/1538-4357/aa93e7
   correlation length = L0