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<span id="Statistics-on-Sliding-Windows-of-Data"></span><div class="header">
<p>
Next: <a href="Basic-Statistical-Functions.html" accesskey="n" rel="next">Basic Statistical Functions</a>, Previous: <a href="Descriptive-Statistics.html" accesskey="p" rel="prev">Descriptive Statistics</a>, Up: <a href="Statistics.html" accesskey="u" rel="up">Statistics</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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<hr>
<span id="Statistics-on-Sliding-Windows-of-Data-1"></span><h3 class="section">26.2 Statistics on Sliding Windows of Data</h3>
<p>It is often useful to calculate descriptive statistics over a subsection
(i.e., window) of a full dataset. Octave provides the function <code>movfun</code>
which will call an arbitrary function handle with windows of data and
accumulate the results. Many of the most commonly desired functions, such as
the moving average over a window of data (<code>movmean</code>), are already
provided.
</p>
<span id="XREFmovfun"></span><dl>
<dt id="index-movfun">: <em><var>y</var> =</em> <strong>movfun</strong> <em>(<var>fcn</var>, <var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movfun-1">: <em><var>y</var> =</em> <strong>movfun</strong> <em>(<var>fcn</var>, <var>x</var>, <var>[<var>nb</var>, <var>na</var></var>])</em></dt>
<dt id="index-movfun-2">: <em><var>y</var> =</em> <strong>movfun</strong> <em>(…, "<var>property</var>", <var>value</var>)</em></dt>
<dd>
<p>Apply function <var>fcn</var> to a moving window of length <var>wlen</var> on data
<var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <var>fcn</var> is applied to a moving
window of length <var>wlen</var>. When <var>wlen</var> is an odd number the window is
symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on either
side of the central element. For example, when calculating the output at
index 5 with a window length of 3, <code>movfun</code> uses data elements
<code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window is
asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movfun</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>During calculations the data input <var>x</var> is reshaped into a 2-dimensional
<var>wlen</var>-by-<var>N</var> matrix and <var>fcn</var> is called on this new matrix.
Therefore, <var>fcn</var> must accept an array input argument and apply the
computation along dimension 1, i.e., down the columns of the array.
</p>
<p>When applied to an array (possibly multi-dimensional) with <var>n</var> columns,
<var>fcn</var> may return a result in either of two formats: Format 1)<!-- /@w -->
an array of size 1-by-<var>n</var>-by-<var>dim3</var>-by-…-by-<var>dimN</var>. This
is the typical output format from Octave core functions. Type
<code>demo ("movfun", 5)</code> for an example of this use case.
Format 2)<!-- /@w --> a row vector of length
<code><var>n</var> * <var>numel_higher_dims</var></code> where <var>numel_higher_dims</var> is
<code>prod (size (<var>x</var>)(3:end))</code><!-- /@w -->. The output of <var>fcn</var> for the
i-th input column must be found in the output at indices
<code>i:<var>n</var>:(<var>n</var>*<var><span class="nolinebreak">numel_higher_dims</span></var>)</code><!-- /@w -->.
This format is useful when concatenating functions into arrays, or when
using <code>nthargout</code>. Type <code>demo ("movfun", 6)</code> for an example of
this case.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"dim"</code></dt>
<dd><p>Operate along the dimension specified, rather than the default of the first
non-singleton dimension.
</p>
</dd>
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = <var>fcn</var> (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = <var>fcn</var> (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = <var>fcn</var> ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = <var>fcn</var> ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <var>fcn</var> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = <var>fcn</var> ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = <var>fcn</var> ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = <var>fcn</var> ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = <var>fcn</var> ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = <var>fcn</var> ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = <var>fcn</var> ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
<p>Note that for some of these choices, the window size at the boundaries is
not the same as for the central part, and <var>fcn</var> must work in these
cases.
</p>
</dd>
<dt><code>"nancond"</code></dt>
<dd><p>Controls whether <code>NaN</code> and <code>NA</code> values should be included (value:
<code>"includenan"</code>), or excluded (value: <code>"omitnan"</code>), from the data
passed to <var>fcn</var>. The default is <code>"includenan"</code>. Caution:
The <code>"omitnan"</code> option is not yet implemented.
</p>
</dd>
<dt><code>"outdim"</code></dt>
<dd><p>A row vector that selects which dimensions of the calculation will appear
in the output <var>y</var>. This is only useful when <var>fcn</var> returns an
N-dimensional array in Format 1<!-- /@w -->. The default is to return all output
dimensions.
</p>
</dd>
</dl>
<p>Programming Note: The property <code>"outdim"</code> can be used to save memory
when the output of <var>fcn</var> has many dimensions, or when a wrapper to the
base function that selects the desired outputs is too costly. When memory
is not an issue, the easiest way to select output dimensions is to first
calculate the complete result with <code>movfun</code> and then filter that result
with indexing. If code complexity is not an issue then a wrapper can be
created using anonymous functions. For example, if <code>basefcn</code>
is a function returning a <var>K</var>-dimensional row output, and only
dimension <var>D</var> is desired, then the following wrapper could be used.
</p>
<div class="example">
<pre class="example"><var>fcn</var> = @(x) basefcn (x)(:,size(x,2) * (<var>D</var>-1) + (1:size(x,2)));
<var>y</var> = movfun (@fcn, …);
</pre></div>
<p><strong>See also:</strong> <a href="#XREFmovslice">movslice</a>, <a href="Rearranging-Matrices.html#XREFprepad">prepad</a>, <a href="Rearranging-Matrices.html#XREFpostpad">postpad</a>, <a href="Rearranging-Matrices.html#XREFpermute">permute</a>, <a href="Rearranging-Matrices.html#XREFreshape">reshape</a>.
</p></dd></dl>
<span id="XREFmovslice"></span><dl>
<dt id="index-movslice">: <em><var>slcidx</var> =</em> <strong>movslice</strong> <em>(<var>N</var>, <var>wlen</var>)</em></dt>
<dt id="index-movslice-1">: <em>[<var>slcidx</var>, <var>C</var>, <var>Cpre</var>, <var>Cpost</var>, <var>win</var>] =</em> <strong>movslice</strong> <em>(…)</em></dt>
<dd><p>Generate indices to slice a vector of length <var>N</var> in to windows
of length <var>wlen</var>.
</p>
<p>FIXME: Document inputs N, wlen
</p>
<p>FIXME: Document outputs slcidx, C, Cpre, Cpost, win.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>.
</p></dd></dl>
<span id="XREFmovmad"></span><dl>
<dt id="index-movmad">: <em><var>y</var> =</em> <strong>movmad</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movmad-1">: <em><var>y</var> =</em> <strong>movmad</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movmad-2">: <em><var>y</var> =</em> <strong>movmad</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movmad-3">: <em><var>y</var> =</em> <strong>movmad</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movmad-4">: <em><var>y</var> =</em> <strong>movmad</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving mean absolute deviation over a sliding window of length
<var>wlen</var> on data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>mad</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movmad</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movmad</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>mad</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = mad (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = mad (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = mad ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mad ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>mad</code> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = mad ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mad ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = mad ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mad ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = mad ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mad ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovmax"></span><dl>
<dt id="index-movmax">: <em><var>y</var> =</em> <strong>movmax</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movmax-1">: <em><var>y</var> =</em> <strong>movmax</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movmax-2">: <em><var>y</var> =</em> <strong>movmax</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movmax-3">: <em><var>y</var> =</em> <strong>movmax</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movmax-4">: <em><var>y</var> =</em> <strong>movmax</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving maximum over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>max</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movmax</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movmax</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>max</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = max (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = max (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = max ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = max ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>max</code> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = max ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = max ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = max ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = max ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = max ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = max ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovmean"></span><dl>
<dt id="index-movmean">: <em><var>y</var> =</em> <strong>movmean</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movmean-1">: <em><var>y</var> =</em> <strong>movmean</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movmean-2">: <em><var>y</var> =</em> <strong>movmean</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movmean-3">: <em><var>y</var> =</em> <strong>movmean</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movmean-4">: <em><var>y</var> =</em> <strong>movmean</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving average over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>mean</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movmean</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movmean</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>mean</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = mean (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = mean (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = mean ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mean ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>mean</code> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = mean ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mean ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = mean ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mean ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = mean ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = mean ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovmedian"></span><dl>
<dt id="index-movmedian">: <em><var>y</var> =</em> <strong>movmedian</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movmedian-1">: <em><var>y</var> =</em> <strong>movmedian</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movmedian-2">: <em><var>y</var> =</em> <strong>movmedian</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movmedian-3">: <em><var>y</var> =</em> <strong>movmedian</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movmedian-4">: <em><var>y</var> =</em> <strong>movmedian</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving median over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>movmedian</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movmedian</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movmedian</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to
<code>movmedian</code>. The default is <code>"includenan"</code>. Caution: the
<code>"omitnan"</code> option is not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = movmedian (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = movmedian (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = movmedian ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movmedian ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>movmedian</code> handles
<code>NaN</code>, and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = movmedian ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movmedian ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = movmedian ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movmedian ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = movmedian ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movmedian ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovmin"></span><dl>
<dt id="index-movmin">: <em><var>y</var> =</em> <strong>movmin</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movmin-1">: <em><var>y</var> =</em> <strong>movmin</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movmin-2">: <em><var>y</var> =</em> <strong>movmin</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movmin-3">: <em><var>y</var> =</em> <strong>movmin</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movmin-4">: <em><var>y</var> =</em> <strong>movmin</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving minimum over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>min</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movmin</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movmin</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>min</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = min (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = min (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = min ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = min ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>min</code> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = min ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = min ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = min ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = min ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = min ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = min ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovprod"></span><dl>
<dt id="index-movprod">: <em><var>y</var> =</em> <strong>movprod</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movprod-1">: <em><var>y</var> =</em> <strong>movprod</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movprod-2">: <em><var>y</var> =</em> <strong>movprod</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movprod-3">: <em><var>y</var> =</em> <strong>movprod</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movprod-4">: <em><var>y</var> =</em> <strong>movprod</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving product over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>movprod</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movprod</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movprod</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>movprod</code>.
The default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code>
option is not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = movprod (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = movprod (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = movprod ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movprod ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>movprod</code> handles
<code>NaN</code>, and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = movprod ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movprod ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = movprod ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movprod ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = movprod ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movprod ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovstd"></span><dl>
<dt id="index-movstd">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movstd-1">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movstd-2">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(…, <var>opt</var>)</em></dt>
<dt id="index-movstd-3">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(…, <var>opt</var>, <var>dim</var>)</em></dt>
<dt id="index-movstd-4">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movstd-5">: <em><var>y</var> =</em> <strong>movstd</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving standard deviation over a sliding window of length
<var>wlen</var> on data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>movstd</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movstd</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movstd</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>The optional argument <var>opt</var> determines the type of normalization to use.
Valid values are
</p>
<dl compact="compact">
<dt>0:</dt>
<dd><p>normalize with <em>N-1</em>, provides the square root of the best unbiased
estimator of the variance [default]
</p>
</dd>
<dt>1:</dt>
<dd><p>normalize with <em>N</em>, this provides the square root of the second
moment around the mean
</p></dd>
</dl>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
The normalization argument <var>opt</var> must be given before the dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>movstd</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = movstd (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = movstd (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = movstd ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movstd ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>movstd</code> handles
<code>NaN</code>, and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = movstd ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movstd ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = movstd ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movstd ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = movstd ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movstd ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovsum">movsum</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovsum"></span><dl>
<dt id="index-movsum">: <em><var>y</var> =</em> <strong>movsum</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movsum-1">: <em><var>y</var> =</em> <strong>movsum</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movsum-2">: <em><var>y</var> =</em> <strong>movsum</strong> <em>(…, <var>dim</var>)</em></dt>
<dt id="index-movsum-3">: <em><var>y</var> =</em> <strong>movsum</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movsum-4">: <em><var>y</var> =</em> <strong>movsum</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving sum over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>movsum</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movsum</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movsum</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>movsum</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = movsum (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = movsum (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = movsum ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movsum ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>movsum</code> handles
<code>NaN</code>, and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = movsum ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movsum ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = movsum ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movsum ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = movsum ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = movsum ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<span id="XREFmovvar"></span><dl>
<dt id="index-movvar">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(<var>x</var>, <var>wlen</var>)</em></dt>
<dt id="index-movvar-1">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(<var>x</var>, [<var>nb</var>, <var>na</var>])</em></dt>
<dt id="index-movvar-2">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(…, <var>opt</var>)</em></dt>
<dt id="index-movvar-3">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(…, <var>opt</var>, <var>dim</var>)</em></dt>
<dt id="index-movvar-4">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(…, "<var>nancond</var>")</em></dt>
<dt id="index-movvar-5">: <em><var>y</var> =</em> <strong>movvar</strong> <em>(…, <var>property</var>, <var>value</var>)</em></dt>
<dd><p>Calculate the moving variance over a sliding window of length <var>wlen</var> on
data <var>x</var>.
</p>
<p>If <var>wlen</var> is a scalar, the function <code>var</code> is applied to a
moving window of length <var>wlen</var>. When <var>wlen</var> is an odd number the
window is symmetric and includes <code>(<var>wlen</var> <span class="nolinebreak">-</span> 1) / 2</code><!-- /@w --> elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, <code>movvar</code> uses data
elements <code>[4, 5, 6]</code><!-- /@w -->. If <var>wlen</var> is an even number, the window
is asymmetric and has <code><var>wlen</var>/2</code><!-- /@w --> elements to the left of the
central element and <code><var>wlen</var>/2 <span class="nolinebreak">-</span> 1</code><!-- /@w --> elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, <code>movvar</code> uses data elements
<code>[3, 4, 5, 6]</code><!-- /@w -->.
</p>
<p>If <var>wlen</var> is an array with two elements <code>[<var>nb</var>, <var>na</var>]</code><!-- /@w -->,
the function is applied to a moving window <code>-<var>nb</var>:<var>na</var></code>. This
window includes <var>nb</var> number of elements <em>before</em> the current
element and <var>na</var> number of elements <em>after</em> the current element.
The current element is always included. For example, given
<code><var>wlen</var> = [3, 0]</code><!-- /@w -->, the data used to calculate index 5 is
<code>[2, 3, 4, 5]</code><!-- /@w -->.
</p>
<p>The optional argument <var>opt</var> determines the type of normalization to use.
Valid values are
</p>
<dl compact="compact">
<dt>0:</dt>
<dd><p>normalize with <em>N-1</em>, provides the best unbiased estimator of the
variance [default]
</p>
</dd>
<dt>1:</dt>
<dd><p>normalizes with <em>N</em>, this provides the second moment around the mean
</p></dd>
</dl>
<p>If the optional argument <var>dim</var> is given, operate along this dimension.
The normalization argument <var>opt</var> must be given before the dimension.
</p>
<p>The optional string argument <code>"<var>nancond</var>"</code> controls whether
<code>NaN</code> and <code>NA</code> values should be included (<code>"includenan"</code>),
or excluded (<code>"omitnan"</code>), from the data passed to <code>var</code>. The
default is <code>"includenan"</code>. Caution: the <code>"omitnan"</code> option is
not yet implemented.
</p>
<p>The calculation can be controlled by specifying <var>property</var>/<var>value</var>
pairs. Valid properties are
</p>
<dl compact="compact">
<dt><code>"Endpoints"</code></dt>
<dd>
<p>This property controls how results are calculated at the boundaries
(endpoints<!-- /@w -->) of the window. Possible values are:
</p>
<dl compact="compact">
<dt><code>"shrink"</code> (default)</dt>
<dd><p>The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, <code><var>y</var>(1) = var (<var>x</var>(1:2))</code>, and
<code><var>y</var>(end) = var (<var>x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code>"discard"</code></dt>
<dd><p>Any <var>y</var> values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
<code>[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code>[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code>"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code>NaN</code>. For
example, with a window of length 3,
<code><var>y</var>(1) = var ([NaN, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = var ([<var>x</var>(end-1:end), NaN])</code>.
This option usually results in <var>y</var> having <code>NaN</code> values at the
boundaries, although it is influenced by how <code>var</code> handles <code>NaN</code>,
and also by the property <code>"nancond"</code>.
</p>
</dd>
<dt><var>user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var>user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code><var>y</var>(1) = var ([<var>user_value</var>, <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = var ([<var>x</var>(end-1:end), <var>user_value</var>])</code>.
A common choice for <var>user_value</var> is 0.
</p>
</dd>
<dt><code>"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var>x</var> at the boundary. For example, with a window of length 3,
<code><var>y</var>(1) = var ([<var>x</var>(1), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = var ([<var>x</var>(end-1:end), <var>x</var>(end)])</code>.
</p>
</dd>
<dt><code>"periodic"</code></dt>
<dd><p>The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
<code><var>y</var>(1) = var ([<var>x</var>(end), <var>x</var>(1:2)])</code>, and
<code><var>y</var>(end) = var ([<var>x</var>(end-1:end), <var>x</var>(1)])</code>.
</p>
</dd>
</dl>
</dd>
<dt><code>"SamplePoints"</code></dt>
<dd><p>Caution: This option is not yet implemented.
</p>
</dd>
</dl>
<p>Programming Note: This function is a wrapper which calls <code>movfun</code>.
For additional options and documentation, see <a href="#XREFmovfun">movfun</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFmovfun">movfun</a>, <a href="#XREFmovslice">movslice</a>, <a href="#XREFmovmad">movmad</a>, <a href="#XREFmovmax">movmax</a>, <a href="#XREFmovmean">movmean</a>, <a href="#XREFmovmedian">movmedian</a>, <a href="#XREFmovmin">movmin</a>, <a href="#XREFmovprod">movprod</a>, <a href="#XREFmovstd">movstd</a>, <a href="#XREFmovsum">movsum</a>.
</p></dd></dl>
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