.. _movWindow:

Moving Window Statistics
============================

.. include:: ../replace.txt


.. index:: moving window statistics, movmean

A moving window is a contiguous subset of a vector that is used to compute
local statistics. At each step, the window advances to include one new value
and leaves off one old value.  A statistic is calculated over the values in the
window and placed at the corresponding center position of the returned data.
The resulting vector reduces some of the fluctuations that are found in the
original vector.  |M| provides functions for performing several statistical
operations on moving windows. The moving window functions are listed in
:numref:`tbl:movwind`.  These functions all use the same syntax.

::

    >> y = movmean(x,k)

Outputs
	`y` -- Result of the k-point moving mean applied to the data in x.
Inputs
	`x`	-- Array of data.

	`k`	-- Number of points in the window.

    
.. _tbl:movwind:

.. table:: Moving Window Functions

   =============  ==================================
    Function        Description
   =============  ==================================
   ``movmin``       Moving minimum
   ``movmax``       Moving maximum
   ``movsum``       Moving sum
   ``movmean``      Moving mean
   ``movmedian``    Moving median
   ``movstd``       Moving standard deviation
   ``movvar``       Moving variance
   =============  ==================================


.. .. csv-table:: Moving Window Functions
   :widths: 20 50
   :header-rows: 1

   "Function", "Description"
   "movmin", "Moving minimum"
   "movmax", "Moving maximum"
   "movsum", "Moving sum"
   "movmean", "Moving mean"
   "movmedian", "Moving median"
   "movstd", "Moving standard deviation"
   "movvar", "Moving variance"


The commands below show how the values are calculated using the
``movmean`` function with a window size of 7. Notice that the first three
values are calculated with a shortened window size. The full window size is
used beginning with the fourth term. The window advances for the first time
to not include the first data value at the fifth term. A shortened window
size is similarly used at the end of the vector.  You can change this
behavior by specifying the optional ``'Endpoints'`` argument.
A plot of the original data and the filtered data from the ``movmean``
function is shown in :numref:`fig:movWind`.

::

    >> x = linspace(0, 6, 20);
    >> y = 5*x - 0.3*x.^2 + sin(3*x);
    >> y1 = movmean(y, 7);
    >> y(1:8)
    ans =
             0  2.3609  3.9862  4.7626  5.2336  6.1471  7.8329  9.9281
    >> y1(1:5)
    ans =
        2.7774  3.2687  3.7484  4.3319  5.7502

    >> sum(y(1:4))/4
    ans =
        2.7774       % y1(1) - startup, short window
    >> sum(y(1:5))/5
    ans =
        3.2687       % y1(2) - startup, short window
    >> sum(y(1:7))/7
    ans =
        4.3319       % y1(4) - first full window mean
    >> sum(y(2:8))/7
    ans =
        5.7502       % y1(5) - window advanced

.. _fig:movWind:

.. figure:: movWind.png
   :align: center
   :width: 60%

   The moving window mean smooths the data fluctuations.

As with other statistical functions in |M|, if :math:`\bf{X}` is a matrix,
the function is applied to the columns of :math:`\bm{x}` independently. You can
change this behavior by specifying an optional dimension argument. You can also
provide an optional flag to specify how NaN values are handled.

.. note:: Now complete :ref:`TempProject`.

.. raw:: latex

    \clearpage