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<h3 class="section" id="Statistics-on-Sliding-Windows-of-Data-1"><span>26.2 Statistics on Sliding Windows of Data<a class="copiable-link" href="#Statistics-on-Sliding-Windows-of-Data-1"> ¶</a></span></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 class="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 class="code">movmean</code>), are already
provided.
</p>
<a class="anchor" id="XREFmovfun"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movfun"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movfun</strong> <code class="def-code-arguments">(<var class="var">fcn</var>, <var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movfun"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movfun-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movfun</strong> <code class="def-code-arguments">(<var class="var">fcn</var>, <var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movfun-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movfun-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movfun</strong> <code class="def-code-arguments">(…, "<var class="var">property</var>", <var class="var">value</var>)</code><a class="copiable-link" href="#index-movfun-2"> ¶</a></span></dt>
<dd>
<p>Apply function <var class="var">fcn</var> to a moving window of length <var class="var">wlen</var> on data
<var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>During calculations the data input <var class="var">x</var> is reshaped into a 2-dimensional
<var class="var">wlen</var>-by-<var class="var">N</var> matrix and <var class="var">fcn</var> is called on this new matrix.
Therefore, <var class="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 class="var">n</var> columns,
<var class="var">fcn</var> may return a result in either of two formats: Format 1)<!-- /@w --> an
array of size 1-by-<var class="var">n</var>-by-<var class="var">dim3</var>-by-…-by-<var class="var">dimN</var>. This
is the typical output format from Octave core functions. Type
<code class="code">demo ("movfun", 5)</code> for an example of this use case.
Format 2)<!-- /@w --> a row vector of length
<code class="code"><var class="var">n</var> * <var class="var">numel_higher_dims</var></code> where <var class="var">numel_higher_dims</var> is
<code class="code">prod (size (<var class="var">x</var>)(3:end))</code><!-- /@w -->. The output of <var class="var">fcn</var> for the
i-th input column must be found in the output at indices
<code class="code">i:<var class="var">n</var>:(<var class="var">n</var>*<var class="var">numel_higher_dims</var>)</code><!-- /@w -->.
This format is useful when concatenating functions into arrays, or when
using <code class="code">nthargout</code>. Type <code class="code">demo ("movfun", 6)</code> for an example of
this case.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are
</p>
<dl class="table">
<dt><code class="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 class="code">"SamplePoints"</code></dt>
<dd>
<p>This property specifies a sorted, numeric vector of unique coordinate
positions of the data points in <var class="var">x</var>. The default value is the vector
<code class="code">[1 : <var class="var">numel (x)</var>]</code><!-- /@w -->. When a non-default SamplePoints vector
is specified, the moving window length <var class="var">wlen</var> is measured
against the SamplePoints positions to determine which points are
included in each window slice. SamplePoints need not be uniformly spaced.
This can result in window slices containing different numbers of points.
</p>
</dd>
<dt><code class="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 class="table">
<dt><code class="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 class="code"><var class="var">y</var>(1) = <var class="var">fcn</var> (<var class="var">x</var>(1:2))</code>, and
<code class="code"><var class="var">y</var>(end) = <var class="var">fcn</var> (<var class="var">x</var>(end-1:end))</code>.
</p>
</dd>
<dt><code class="code">"discard"</code></dt>
<dd><p>Any <var class="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 class="code">[0, 1, 2]</code><!-- /@w --> and is therefore discarded. The last element would
require calculating the function over indices <code class="code">[9, 10, 11]</code><!-- /@w --> and is
therefore discarded.
</p>
</dd>
<dt><code class="code">"fill"</code></dt>
<dd><p>Any window elements outside the data array are replaced by <code class="code">NaN</code>. For
example, with a window of length 3,
<code class="code"><var class="var">y</var>(1) = <var class="var">fcn</var> ([NaN, <var class="var">x</var>(1:2)])</code>, and
<code class="code"><var class="var">y</var>(end) = <var class="var">fcn</var> ([<var class="var">x</var>(end-1:end), NaN])</code>.
This option usually results in <var class="var">y</var> having <code class="code">NaN</code> values at the
boundaries, although it is influenced by how <var class="var">fcn</var> handles <code class="code">NaN</code>,
and also by the property <code class="code">"nancond"</code>.
</p>
</dd>
<dt><var class="var">user_value</var></dt>
<dd><p>Any window elements outside the data array are replaced by the specified
value <var class="var">user_value</var> which must be a numeric scalar. For example, with a
window of length 3,
<code class="code"><var class="var">y</var>(1) = <var class="var">fcn</var> ([<var class="var">user_value</var>, <var class="var">x</var>(1:2)])</code>, and
<code class="code"><var class="var">y</var>(end) = <var class="var">fcn</var> ([<var class="var">x</var>(end-1:end), <var class="var">user_value</var>])</code>.
A common choice for <var class="var">user_value</var> is 0.
</p>
</dd>
<dt><code class="code">"same"</code></dt>
<dd><p>Any window elements outside the data array are replaced by the value of
<var class="var">x</var> at the boundary. For example, with a window of length 3,
<code class="code"><var class="var">y</var>(1) = <var class="var">fcn</var> ([<var class="var">x</var>(1), <var class="var">x</var>(1:2)])</code>, and
<code class="code"><var class="var">y</var>(end) = <var class="var">fcn</var> ([<var class="var">x</var>(end-1:end), <var class="var">x</var>(end)])</code>.
</p>
</dd>
<dt><code class="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 class="code"><var class="var">y</var>(1) = <var class="var">fcn</var> ([<var class="var">x</var>(end), <var class="var">x</var>(1:2)])</code>, and
<code class="code"><var class="var">y</var>(end) = <var class="var">fcn</var> ([<var class="var">x</var>(end-1:end), <var class="var">x</var>(1)])</code>.
</p>
</dd>
</dl>
<p>Note 1: For non-uniform SamplePoint spacing, the only permitted value for
<code class="code">"EndPoints"</code> is <code class="code">"shrink"</code>.
</p>
<p>Note 2: For some <code class="code">"Endpoints"</code> options, the window size at the
boundaries may not be the same as for the central part, and <var class="var">fcn</var> must
work in these cases.
</p>
</dd>
<dt><code class="code">"nancond"</code></dt>
<dd><p>Controls haw <code class="code">NaN</code> and <code class="code">NA</code> values affect the output of
<code class="code">"movfun"</code>. The value <code class="code">"includenan"</code> (default) causes
<code class="code">NaN</code> and <code class="code">NA</code> values to be included in the moving window, and any
window slice containing <code class="code">NaN</code> or <code class="code">NA</code> values will return
<code class="code">NaN</code> for that element. The value <code class="code">"omitnan"</code> causes
<code class="code">"movfun"</code> to ignore any <code class="code">NaN</code> or <code class="code">NA</code> values resulting
in fewer elements being used to calculate the result for that window
slice. If <code class="code">"omitnan"</code> is specified and a window slice contains all
<code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movfun"</code> returns the value
specified by the <code class="code">"nanval"</code> property for that element. The values
<code class="code">"includemissing"</code> and <code class="code">"omitmissing"</code> may be used
synonymously with <code class="code">"includenan"</code> and <code class="code">"omitnan"</code>,
respectively.
</p>
</dd>
<dt><code class="code">"nanval"</code></dt>
<dd><p>Specifies the value to return when <code class="code">"nancond"</code> is set to
<code class="code">"omitnan"</code> or <code class="code">"omitmissing"</code> and all elements in a window
are <code class="code">NaN</code> or <code class="code">NA</code>. <code class="code">"nanval"</code> must be a numeric scalar
value or <code class="code">NaN</code> (default).
</p>
</dd>
<dt><code class="code">"outdim"</code></dt>
<dd><p>A row vector that selects which dimensions of the calculation will appear
in the output <var class="var">y</var>. This is only useful when <var class="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 class="code">"outdim"</code> can be used to save memory
when the output of <var class="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 class="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 class="code">basefcn</code>
is a function returning a <var class="var">K</var>-dimensional row output, and only
dimension <var class="var">D</var> is desired, then the following wrapper could be used.
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">fcn</var> = @(x) basefcn (x)(:,columns(x) * (<var class="var">D</var>-1) + (1:columns(x)));
<var class="var">y</var> = movfun (@fcn, ...);
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="Rearranging-Matrices.html#XREFprepad">prepad</a>, <a class="ref" href="Rearranging-Matrices.html#XREFpostpad">postpad</a>, <a class="ref" href="Rearranging-Matrices.html#XREFpermute">permute</a>, <a class="ref" href="Rearranging-Matrices.html#XREFreshape">reshape</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovslice"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movslice"><span><code class="def-type"><var class="var">slcidx</var> =</code> <strong class="def-name">movslice</strong> <code class="def-code-arguments">(<var class="var">N</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movslice"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movslice-1"><span><code class="def-type"><var class="var">slcidx</var> =</code> <strong class="def-name">movslice</strong> <code class="def-code-arguments">(<var class="var">N</var>, <var class="var">wlen</var>, <var class="var">samplepoints</var>)</code><a class="copiable-link" href="#index-movslice-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movslice-2"><span><code class="def-type">[<var class="var">slcidx</var>, <var class="var">C</var>, <var class="var">Cpre</var>, <var class="var">Cpost</var>, <var class="var">win</var>, <var class="var">wlen</var>, <var class="var">scalar_wlen</var>] =</code> <strong class="def-name">movslice</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-movslice-2"> ¶</a></span></dt>
<dd><p>Generate indices to slice a vector of length <var class="var">N</var> into windows of length
<var class="var">wlen</var>.
</p>
<p>The input <var class="var">N</var> must be a positive integer.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array. The elements included in the moving window
will depend on the size and value of <var class="var">wlen</var> as well as whether the
<var class="var">samplepoints</var> input was specified.
</p>
<p>The optional input <var class="var">samplepoints</var> is a sorted, numeric vector of unique
positions of the <var class="var">N</var> data points. The default value is the vector
<code class="code">[1 : <var class="var">N</var>]</code>. When a non-default <var class="var">samplepoints</var> vector is
specified, the moving window length <var class="var">wlen</var> is measured
against the <var class="var">samplepoints</var> positions to determine which points are
included in each window slice. It should be noted that <var class="var">samplepoints</var>
need not be uniformly spaced which can result in window slices containing
different numbers of points. Because of this, as specified below the
shape and content of some <code class="code">movslice</code> outputs will be different when
a non-default <var class="var">samplepoints</var> is used.
</p>
<p>The moving window size and included elements will be defined as follows:
</p>
<ul class="itemize mark-bullet">
<li>If <var class="var">samplepoints</var> has the default value of <code class="code">1:<var class="var">N</var></code> (or has
not been specified):
<ul class="itemize mark-bullet">
<li>For integer-valued <var class="var">wlen</var>:
<ul class="itemize mark-bullet">
<li>For odd, integer-valued, scalar <var class="var">wlen</var> the window is symmetric and
includes <code class="code">(<var class="var">wlen</var> - 1) / 2</code><!-- /@w --> elements on either side of the
central element. For example, the window slice at index 5 with a window
length of 3 will include the elements <code class="code">[4, 5, 6]</code><!-- /@w -->.
</li><li>For even, integer-valued, scalar <var class="var">wlen</var> the window is asymmetric and
has <code class="code"><var class="var">wlen</var>/2</code><!-- /@w --> elements to the left of the central element
and <code class="code"><var class="var">wlen</var>/2 - 1</code><!-- /@w --> elements to the right of the central
element. For example, the window slice at index 5 with a window length of
4 will include the elements <code class="code">[3, 4, 5, 6]</code><!-- /@w -->.
</li><li>For integer-valued vector <var class="var">wlen</var> of the form
<code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w --> where <var class="var">nb</var> and <var class="var">na</var> are integer
valued the window includes <var class="var">nb</var> elements to the left of the central
element and <var class="var">na</var> elements to the right of the central element. For
example, given <code class="code"><var class="var">wlen</var> = [3, 1]</code><!-- /@w -->, the window slice at index 5
will include the elements <code class="code">[2, 3, 4, 5, 6]</code><!-- /@w -->.
</li></ul>
</li><li>For non-integer-valued scalar <var class="var">wlen</var>:
<ul class="itemize mark-bullet">
<li>Non-integer-valued scalar <var class="var">wlen</var> will be converted to
two-element vector form with
<code class="code"><var class="var">nb</var> = <var class="var">na</var> = fix (<var class="var">wlen</var> / 2)</code><!-- /@w -->, and then processed
as stated above for integer-valued vectors. For example, the window slice
at index 5 with <code class="code"><var class="var">wlen</var> = 2.5</code><!-- /@w --> will include the elements
<code class="code">[3, 4, 5, 6, 7]</code><!-- /@w -->.
</li><li>Non-integer-valued vector <var class="var">wlen</var> will be truncated to integer values
with <code class="code"><var class="var">wlen</var> = fix (<var class="var">wlen</var>)</code><!-- /@w --> and then processed as
stated above for integer-valued vectors. For example, the window slice
at index 5 with <code class="code"><var class="var">wlen</var> = [1.2, 2.3]</code><!-- /@w --> will include the
elements <code class="code">[4, 5, 6, 7]</code><!-- /@w -->.
</li></ul>
</li></ul>
</li><li>If <var class="var">samplepoints</var> has been specified with a non-default vector:
<ul class="itemize mark-bullet">
<li>For vector <var class="var">wlen</var> specified as <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->, the
window will include all points within a distance less than or equal to
<var class="var">nb</var> before and <var class="var">na</var> after the central element’s position, with
point positions defined by the elements of <var class="var">samplepoints</var>. For
example, at index 5 with <code class="code"><var class="var">wlen</var> = [2, 3]</code><!-- /@w --> and the 3rd-8th
elements of <var class="var">samplepoints</var> being <code class="code">[1, 3, 5, 7, 8 ,9]</code><!-- /@w -->, the
window slice will include the elements <code class="code">[4, 5, 6, 7]</code><!-- /@w --> corresponding to <var class="var">samplepoints</var> <code class="code">[3, 5, 7, 8]</code><!-- /@w -->.
</li><li>Scalar <var class="var">wlen</var> will be converted to two-element vector form with
<code class="code"><var class="var">nb</var> = <var class="var">na</var> = <var class="var">wlen</var> / 2</code><!-- /@w -->. The window will then
include all points within a distance of less than or equal to <var class="var">nb</var>
before and less than, but not equal to, <var class="var">na</var> after the central
element’s position, <code class="code">[<var class="var">nb</var>, <var class="var">na</var>)</code><!-- /@w -->. For example, at
index 5 with <code class="code"><var class="var">wlen</var> = [2, 3]</code><!-- /@w --> and the 3rd-8th elements of
<var class="var">samplepoints</var> being <code class="code">[1, 3, 5, 7, 8 ,9]</code><!-- /@w -->, the window slice
will include the elements <code class="code">[4, 5, 6]</code><!-- /@w --> corresponding to
<var class="var">samplepoints</var> <code class="code">[3, 5, 7]</code><!-- /@w -->.
</li></ul>
</li></ul>
<p>The output <var class="var">slcidx</var> is an array of indices of the slices of the vector.
</p>
<ul class="itemize mark-bullet">
<li>If <var class="var">samplepoints</var> is default or unspecified, <var class="var">slcidx</var> will contain
only the indices of the slices that fit fully within the vector. Each
column will be the indices of one slice as the window moves from left to
right. The slices will have <code class="code">fix (<var class="var">wlen</var>)</code><!-- /@w --> elements for
scalar <var class="var">wlen</var>, or <code class="code"><var class="var">nb</var> + <var class="var">na</var> + 1</code><!-- /@w --> elements for array
valued <var class="var">wlen</var>.
</li><li>If a non-default <var class="var">samplepoints</var> has been specified, <var class="var">slcidx</var> will
be a 2x<var class="var">N</var> array with the first and second rows containing the first
and last elements of each slice, respectively.
</li></ul>
<p>Optional output <var class="var">C</var> is a row vector of window center positions where
the window stays fully within the vector.
</p>
<p>Optional outputs <var class="var">Cpre</var> and <var class="var">Cpost</var> contain the vector elements at
the start and end of the vector, respectively, that result in the window
extending beyond the ends of the vector.
</p>
<p>Optional output <var class="var">win</var> contains information for creating the moving
window.
</p>
<ul class="itemize mark-bullet">
<li>If <var class="var">samplepoints</var> is default or unspecified, <var class="var">win</var> is a column
vector with the same number of rows as <var class="var">slcidx</var> that contains the
moving window defined as a center relative position stencil.
</li><li>If a non-default <var class="var">samplepoints</var> has been specified, <var class="var">win</var> will
be a 2x<var class="var">N</var> array with the first and second rows containing the left and
right bounds of each window slice, respectively, using the same
coordinates as <var class="var">samplepoints</var>. These bounds may lie outside of the
position vector specified by <var class="var">samplepoints</var>.
</li></ul>
<p>Optional output <var class="var">wlen</var> returns the window length used by
<code class="code">movslice</code> in two-element <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w --> form.
</p>
<p>Optional logical output <var class="var">scalar_wlen</var> returns the scalar or vector
state of the input <var class="var">wlen</var> so that calling functions can determinine
whether the moving window should be inclusive or exclusive of the right
window endpoints. I.e., inclusive <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w --> for
vector <var class="var">wlen</var> or exclusive <code class="code">[<var class="var">nb</var>, <var class="var">na</var>)</code><!-- /@w --> for scalar
<var class="var">wlen</var>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFmovfun">movfun</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovmad"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movmad"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmad</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movmad"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmad-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmad</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movmad-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmad-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmad</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movmad-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmad-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmad</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movmad-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmad-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmad</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movmad-4"> ¶</a></span></dt>
<dd><p>Calculate the moving median or mean absolute deviation over a sliding
window of length <var class="var">wlen</var> on data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movmad"</code>. The value
<code class="code">"includenan"</code> causes <code class="code">NaN</code> and <code class="code">NA</code> values to be included
in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> (default) causes <code class="code">"movmad"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
mad for that window slice. If <code class="code">"omitnan"</code> is specified and a window
slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movmad"</code> returns
<code class="code">NaN</code> for that element. The values <code class="code">"includemissing"</code> and
<code class="code">"omitmissing"</code> may be used synonymously with <code class="code">"includenan"</code> and
<code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs:
</p>
<ul class="itemize mark-bullet">
<li>The <code class="code">"method"</code> property can take the value <code class="code">"median"</code> (default)
or <code class="code">"mean"</code> to control whether <code class="code">"movmad"</code> performs median or
mean absolute deviation calculations on the data.
</li><li>Additional valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and valid
options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</li></ul>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>. For
full documentation of inputs and options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Compatibility Note: Prior to Octave 10 this function only calculated mean
absolute deviation. For <small class="sc">MATLAB</small> compatibility, the default has been
changed to median absolute deviation. The <code class="code">"method"</code> property is now
provided to enable access to both <code class="code">"mad"</code> calculation methods. This
property should not be expected to be functional outside of Octave code.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFmad">mad</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovmax"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movmax"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmax</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movmax"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmax-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmax</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movmax-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmax-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmax</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movmax-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmax-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmax</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movmax-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmax-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmax</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movmax-4"> ¶</a></span></dt>
<dd><p>Calculate the moving maximum over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movmax"</code>. The value
<code class="code">"includenan"</code> causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> (default) causes <code class="code">"movmax"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
maximum for that window slice. If <code class="code">"omitnan"</code> is specified and a
window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movmax"</code>
returns <code class="code">NaN</code> for that element. The values <code class="code">"includemissing"</code>
and <code class="code">"omitmissing"</code> may be used synonymously with
<code class="code">"includenan"</code> and <code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Utility-Functions.html#XREFmax">max</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovmean"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movmean"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmean</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movmean"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmean-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmean</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movmean-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmean-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmean</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movmean-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmean-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmean</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movmean-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmean-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmean</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movmean-4"> ¶</a></span></dt>
<dd><p>Calculate the moving average over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movmean"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movmean"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
mean for that window slice. If <code class="code">"omitnan"</code> is specified and a window
slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movmean"</code> returns
<code class="code">NaN</code> for that element. The values <code class="code">"includemissing"</code> and
<code class="code">"omitmissing"</code> may be used synonymously with <code class="code">"includenan"</code> and
<code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFmean">mean</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovmedian"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movmedian"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmedian</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movmedian"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmedian-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmedian</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movmedian-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmedian-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmedian</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movmedian-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmedian-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmedian</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movmedian-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmedian-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmedian</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movmedian-4"> ¶</a></span></dt>
<dd><p>Calculate the moving median over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movmedian"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movmedian"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
median for that window slice. If <code class="code">"omitnan"</code> is specified and a
window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values,
<code class="code">"movmedian"</code> returns <code class="code">NaN</code> for that element. The values
<code class="code">"includemissing"</code> and <code class="code">"omitmissing"</code> may be used
synonymously with <code class="code">"includenan"</code> and <code class="code">"omitnan"</code>,
respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFmedian">median</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovmin"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movmin"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmin</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movmin"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmin-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmin</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movmin-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmin-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmin</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movmin-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmin-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmin</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movmin-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movmin-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movmin</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movmin-4"> ¶</a></span></dt>
<dd><p>Calculate the moving minimum over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movmin"</code>. The value
<code class="code">"includenan"</code> causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> (default) causes <code class="code">"movmin"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
minimum for that window slice. If <code class="code">"omitnan"</code> is specified and a
window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movmin"</code>
returns <code class="code">NaN</code> for that element. The values <code class="code">"includemissing"</code>
and <code class="code">"omitmissing"</code> may be used synonymously with
<code class="code">"includenan"</code> and <code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Utility-Functions.html#XREFmin">min</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovprod"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movprod"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movprod</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movprod"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movprod-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movprod</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movprod-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movprod-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movprod</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movprod-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movprod-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movprod</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movprod-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movprod-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movprod</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movprod-4"> ¶</a></span></dt>
<dd><p>Calculate the moving product over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movprod"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movprod"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
product for that window slice. If <code class="code">"omitnan"</code> is specified and a
window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movprod"</code>
returns 1 for that element. The values <code class="code">"includemissing"</code> and
<code class="code">"omitmissing"</code> may be used synonymously with <code class="code">"includenan"</code> and
<code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Sums-and-Products.html#XREFprod">prod</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovstd"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movstd"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movstd"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movstd-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movstd-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movstd-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(…, <var class="var">opt</var>)</code><a class="copiable-link" href="#index-movstd-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movstd-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(…, <var class="var">opt</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movstd-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movstd-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movstd-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movstd-5"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movstd</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movstd-5"> ¶</a></span></dt>
<dd><p>Calculate the moving standard deviation over a sliding window of length
<var class="var">wlen</var> on data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>The optional argument <var class="var">opt</var> determines the type of normalization to use.
Valid values are
</p>
<dl class="table">
<dt>0:</dt>
<dd><p>normalize with <em class="math">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 class="math">N</em>, this provides the square root of the second
moment around the mean
</p></dd>
</dl>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
The normalization argument <var class="var">opt</var> must be given before the dimension.
To use the default value for <var class="var">opt</var> you may pass an empty input
argument <code class="code">[]</code>.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movstd"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movstd"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
standard deviation for that window slice. If <code class="code">"omitnan"</code> is specified
and a window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values,
<code class="code">"movstd"</code> returns <code class="code">NaN</code> for that element. The values
<code class="code">"includemissing"</code> and <code class="code">"omitmissing"</code> may be used synonymously
with <code class="code">"includenan"</code> and <code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFstd">std</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovsum">movsum</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovsum"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movsum"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movsum</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movsum"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movsum-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movsum</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movsum-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movsum-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movsum</strong> <code class="def-code-arguments">(…, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movsum-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movsum-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movsum</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movsum-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movsum-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movsum</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movsum-4"> ¶</a></span></dt>
<dd><p>Calculate the moving sum over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movsum"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movsum"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
sum for that window slice. If <code class="code">"omitnan"</code> is specified and a window
slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movsum"</code> returns
0 for that element. The values <code class="code">"includemissing"</code> and
<code class="code">"omitmissing"</code> may be used synonymously with <code class="code">"includenan"</code> and
<code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Sums-and-Products.html#XREFsum">sum</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovvar">movvar</a>.
</p></dd></dl>
<a class="anchor" id="XREFmovvar"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-movvar"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">wlen</var>)</code><a class="copiable-link" href="#index-movvar"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movvar-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(<var class="var">x</var>, [<var class="var">nb</var>, <var class="var">na</var>])</code><a class="copiable-link" href="#index-movvar-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movvar-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(…, <var class="var">opt</var>)</code><a class="copiable-link" href="#index-movvar-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movvar-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(…, <var class="var">opt</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-movvar-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movvar-4"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(…, <var class="var">nancond</var>)</code><a class="copiable-link" href="#index-movvar-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-movvar-5"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">movvar</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-movvar-5"> ¶</a></span></dt>
<dd><p>Calculate the moving variance over a sliding window of length <var class="var">wlen</var> on
data <var class="var">x</var>.
</p>
<p>The moving window length input <var class="var">wlen</var> can either be a numeric scalar
or a 2-element numeric array <code class="code">[<var class="var">nb</var>, <var class="var">na</var>]</code><!-- /@w -->. The elements
included in the moving window depend on the size and value of <var class="var">wlen</var>
as well as whether the <code class="code">"SamplePoints"</code> option has been specified.
For full details of element inclusion,
see <a class="pxref" href="#XREFmovslice"><code class="code">movslice</code></a>.
</p>
<p>The optional argument <var class="var">opt</var> determines the type of normalization to use.
Valid values are:
</p>
<dl class="table">
<dt>0:</dt>
<dd><p>normalize with <em class="math">N-1</em>, provides the best unbiased estimator of the
variance [default]
</p>
</dd>
<dt>1:</dt>
<dd><p>normalizes with <em class="math">N</em>, this provides the second moment around the mean
</p></dd>
</dl>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
The normalization argument <var class="var">opt</var> must be given before the dimension.
To use the default value for <var class="var">opt</var> you may pass an empty input
argument <code class="code">[]</code>.
</p>
<p>The optional argument <var class="var">nancond</var> is a string that controls how <code class="code">NaN</code>
and <code class="code">NA</code> values affect the output of <code class="code">"movvar"</code>. The value
<code class="code">"includenan"</code> (default) causes <code class="code">NaN</code> and <code class="code">NA</code> values to be
included in the moving window, and any window slice containing <code class="code">NaN</code> or
<code class="code">NA</code> values will return <code class="code">NaN</code> for that element. The value
<code class="code">"omitnan"</code> causes <code class="code">"movvar"</code> to ignore any <code class="code">NaN</code>
or <code class="code">NA</code> values resulting in fewer elements being used to calculate the
variance for that window slice. If <code class="code">"omitnan"</code> is specified and a
window slice contains all <code class="code">NaN</code> or <code class="code">NA</code> values, <code class="code">"movvar"</code>
returns <code class="code">NaN</code> for that element. The values <code class="code">"includemissing"</code>
and <code class="code">"omitmissing"</code> may be used synonymously with
<code class="code">"includenan"</code> and <code class="code">"omitnan"</code>, respectively.
</p>
<p>The calculation can be controlled by specifying <var class="var">property</var>/<var class="var">value</var>
pairs. Valid properties are <code class="code">"Endpoints"</code> and
<code class="code">"SamplePoints"</code>. For full descriptions of these properties and
valid options, see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p>Programming Note: This function is a wrapper which calls <code class="code">movfun</code>.
For full documentation of inputs and options,
see <a class="pxref" href="#XREFmovfun"><code class="code">movfun</code></a>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFvar">var</a>, <a class="ref" href="#XREFmovfun">movfun</a>, <a class="ref" href="#XREFmovslice">movslice</a>, <a class="ref" href="#XREFmovmad">movmad</a>, <a class="ref" href="#XREFmovmax">movmax</a>, <a class="ref" href="#XREFmovmean">movmean</a>, <a class="ref" href="#XREFmovmedian">movmedian</a>, <a class="ref" href="#XREFmovmin">movmin</a>, <a class="ref" href="#XREFmovprod">movprod</a>, <a class="ref" href="#XREFmovstd">movstd</a>, <a class="ref" href="#XREFmovsum">movsum</a>.
</p></dd></dl>
</div>
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