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<hr>
<h3 class="section" id="Basic-Statistical-Functions-1"><span>26.3 Basic Statistical Functions<a class="copiable-link" href="#Basic-Statistical-Functions-1"> ¶</a></span></h3>
<p>Octave supports various helpful statistical functions. Many are useful as
initial steps to prepare a data set for further analysis. Others provide
different measures from those of the basic descriptive statistics.
</p>
<a class="anchor" id="XREFcenter"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-center"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">center</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-center"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-center-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">center</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-center-1"> ¶</a></span></dt>
<dd><p>Center data by subtracting its mean.
</p>
<p>If <var class="var">x</var> is a vector, subtract its mean.
</p>
<p>If <var class="var">x</var> is a matrix, do the above for each column.
</p>
<p>If the optional argument <var class="var">dim</var> is given, operate along this dimension.
</p>
<p>Programming Note: <code class="code">center</code> has obvious application for normalizing
statistical data. It is also useful for improving the precision of general
numerical calculations. Whenever there is a large value that is common
to a batch of data, the mean can be subtracted off, the calculation
performed, and then the mean added back to obtain the final answer.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFzscore">zscore</a>.
</p></dd></dl>
<a class="anchor" id="XREFzscore"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-zscore"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">zscore</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-zscore"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-zscore-1"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">zscore</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">opt</var>)</code><a class="copiable-link" href="#index-zscore-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-zscore-2"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">zscore</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">opt</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-zscore-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-zscore-3"><span><code class="def-type">[<var class="var">z</var>, <var class="var">mu</var>, <var class="var">sigma</var>] =</code> <strong class="def-name">zscore</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-zscore-3"> ¶</a></span></dt>
<dd><p>Compute the Z score of <var class="var">x</var>.
</p>
<p>If <var class="var">x</var> is a vector, subtract its mean and divide by its standard
deviation. If the standard deviation is zero, divide by 1 instead.
</p>
<p>The optional parameter <var class="var">opt</var> determines the normalization to use when
computing the standard deviation and has the same definition as the
corresponding parameter for <code class="code">std</code>.
</p>
<p>If <var class="var">x</var> is a matrix, calculate along the first non-singleton dimension.
If the third optional argument <var class="var">dim</var> is given, operate along this
dimension.
</p>
<p>The optional outputs <var class="var">mu</var> and <var class="var">sigma</var> contain the mean and standard
deviation.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Descriptive-Statistics.html#XREFmean">mean</a>, <a class="ref" href="Descriptive-Statistics.html#XREFstd">std</a>, <a class="ref" href="#XREFcenter">center</a>.
</p></dd></dl>
<a class="anchor" id="XREFnormalize"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-normalize"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-normalize"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-normalize-1"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-normalize-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-normalize-2"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(…, <var class="var">method</var>)</code><a class="copiable-link" href="#index-normalize-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-normalize-3"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(…, <var class="var">method</var>, <var class="var">option</var>)</code><a class="copiable-link" href="#index-normalize-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-normalize-4"><span><code class="def-type"><var class="var">z</var> =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(…, <var class="var">scale</var>, <var class="var">scaleoption</var>, <var class="var">center</var>, <var class="var">centeroption</var>)</code><a class="copiable-link" href="#index-normalize-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-normalize-5"><span><code class="def-type">[<var class="var">z</var>, <var class="var">c</var>, <var class="var">s</var>] =</code> <strong class="def-name">normalize</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-normalize-5"> ¶</a></span></dt>
<dd><p>Return a normalization of the data in <var class="var">x</var> using one of several available
scaling and centering methods.
</p>
<p><code class="code">normalize</code> by default will return the <code class="code">zscore</code> of <var class="var">x</var>,
defined as the number of standard deviations each element is from the mean
of <var class="var">x</var>. This is equivalent to centering at the mean of the data and
scaling by the standard deviation.
</p>
<p>The returned value <var class="var">z</var> will have the same size as <var class="var">x</var>. The optional
return variables <var class="var">c</var> and <var class="var">s</var> are the centering and scaling factors
used in the normalization such that:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"> <code class="code"><var class="var">z</var> = (<var class="var">x</var> - <var class="var">c</var>) ./ <var class="var">s</var></code>
</pre></div></div>
<p>If <var class="var">x</var> is a vector, <code class="code">normalize</code> will operate on the data in
<var class="var">x</var>.
</p>
<p>If <var class="var">x</var> is a matrix, <code class="code">normalize</code> will operate independently on
each column in <var class="var">x</var>.
</p>
<p>If <var class="var">x</var> is an N-dimensional array, <code class="code">normalize</code> will operate
independently on the first non-singleton dimension in <var class="var">x</var>.
</p>
<p>If the optional second argument <var class="var">dim</var> is given, operate along this
dimension.
</p>
<p><code class="code">normalize</code> ignores NaN values is <var class="var">x</var> similar to the behavior of
the omitnan option in <code class="code">std</code>, <code class="code">mean</code>, and <code class="code">median</code>.
</p>
<p>The optional inputs <var class="var">method</var> and <var class="var">option</var> can be used to specify the
type of normalization performed on <var class="var">x</var>. Note that only the
<samp class="option">scale</samp> and <samp class="option">center</samp> options may be specified together using
any of the methods defined below. Valid normalization methods are:
</p>
<dl class="table">
<dt><code class="code">zscore</code></dt>
<dd><p>(Default) Normalizes the elements in <var class="var">x</var> to the scaled distance from a
central value. Valid Options:
</p>
<dl class="table">
<dt><code class="code">std</code></dt>
<dd><p>(Default) Data is centered at <code class="code">mean (<var class="var">x</var>)</code> and scaled by the
standard deviation.
</p>
</dd>
<dt><code class="code">robust</code></dt>
<dd><p>Data is centered at <code class="code">median (<var class="var">x</var>)</code> and scaled by the median
absolute deviation.
</p></dd>
</dl>
</dd>
<dt><code class="code">norm</code></dt>
<dd><p><var class="var">z</var> is the general vector norm of <var class="var">x</var>, with <var class="var">option</var> being the
normalization factor <var class="var">p</var> that determines the vector norm type according
to:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"> <code class="code"><var class="var">z</var> = [sum (abs (<var class="var">x</var>) .^ <var class="var">p</var>)] ^ (1/<var class="var">p</var>)</code>
</pre></div></div>
<p><var class="var">p</var> can be any positive scalar, specific values being:
</p>
<dl class="table">
<dt><code class="code"><var class="var">p</var> = 1</code></dt>
<dd><p><var class="var">x</var> is normalized by <code class="code">sum (abs (<var class="var">x</var>))</code>.
</p>
</dd>
<dt><code class="code"><var class="var">p</var> = 2</code></dt>
<dd><p>(Default) <var class="var">x</var> is normalized by the Euclidian norm, or vector
magnitude, of the elements.
</p>
</dd>
<dt><code class="code"><var class="var">P</var> = Inf</code></dt>
<dd><p><var class="var">x</var> is normalized by <code class="code">max (abs (<var class="var">x</var>))</code>.
</p></dd>
</dl>
</dd>
<dt><code class="code">scale</code></dt>
<dd><p><var class="var">x</var> is scaled by a factor determined by <var class="var">option</var>, which can be a
numeric scalar or one of the following:
</p>
<dl class="table">
<dt><code class="code">std</code></dt>
<dd><p>(Default) <var class="var">x</var> is scaled by its standard deviation.
</p>
</dd>
<dt><code class="code">mad</code></dt>
<dd><p><var class="var">x</var> is scaled by its median absolute deviation.
</p>
</dd>
<dt><code class="code">first</code></dt>
<dd><p><var class="var">x</var> is scaled by its first element.
</p>
</dd>
<dt><code class="code">iqr</code></dt>
<dd><p><var class="var">x</var> is scaled by its interquartile range.
</p></dd>
</dl>
</dd>
<dt><code class="code">range</code></dt>
<dd><p><var class="var">x</var> is scaled to fit the range specified by <var class="var">option</var> as a two
element scalar row vector. The default range is [0, 1].
</p>
</dd>
<dt><code class="code">center</code></dt>
<dd><p><var class="var">x</var> is shifted by an amount determined by <var class="var">option</var>, which can be a
numeric scalar or one of the following:
</p>
<dl class="table">
<dt><code class="code">mean</code></dt>
<dd><p>(Default) <var class="var">x</var> is shifted by <code class="code">mean (<var class="var">x</var>)</code>.
</p>
</dd>
<dt><code class="code">median</code></dt>
<dd><p><var class="var">x</var> is shifted by <code class="code">median (<var class="var">x</var>)</code>.
</p></dd>
</dl>
</dd>
<dt><code class="code">medianiqr</code></dt>
<dd><p><var class="var">x</var> is shifted by <code class="code">median (<var class="var">x</var>)</code> and scaled by the
interquartile range.
</p></dd>
</dl>
<p>Known <small class="sc">MATLAB</small> incompatibilities:
</p>
<ol class="enumerate">
<li> The option <samp class="option">DataVariables</samp> is not yet implemented for Table class
<var class="var">x</var> inputs.
</li></ol>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFzscore">zscore</a>, <a class="ref" href="Descriptive-Statistics.html#XREFiqr">iqr</a>, <a class="ref" href="Basic-Matrix-Functions.html#XREFnorm">norm</a>, <a class="ref" href="Simple-File-I_002fO.html#XREFrescale">rescale</a>, <a class="ref" href="Descriptive-Statistics.html#XREFstd">std</a>, <a class="ref" href="Descriptive-Statistics.html#XREFmedian">median</a>, <a class="ref" href="Descriptive-Statistics.html#XREFmean">mean</a>, <a class="ref" href="Descriptive-Statistics.html#XREFmad">mad</a>.
</p></dd></dl>
<a class="anchor" id="XREFhistc"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-histc"><span><code class="def-type"><var class="var">n</var> =</code> <strong class="def-name">histc</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">edges</var>)</code><a class="copiable-link" href="#index-histc"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-histc-1"><span><code class="def-type"><var class="var">n</var> =</code> <strong class="def-name">histc</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">edges</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-histc-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-histc-2"><span><code class="def-type">[<var class="var">n</var>, <var class="var">idx</var>] =</code> <strong class="def-name">histc</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-histc-2"> ¶</a></span></dt>
<dd><p>Compute histogram counts.
</p>
<p>When <var class="var">x</var> is a vector, the function counts the number of elements of
<var class="var">x</var> that fall in the histogram bins defined by <var class="var">edges</var>. This
must be a vector of monotonically increasing values that define the edges
of the histogram bins.
<code class="code"><var class="var">n</var>(k)</code>
contains the number of elements in <var class="var">x</var> for which
<code class="code"><var class="var">edges</var>(k) <= <var class="var">x</var> < <var class="var">edges</var>(k+1)</code>.
The final element of <var class="var">n</var> contains the number of elements of <var class="var">x</var>
exactly equal to the last element of <var class="var">edges</var>.
</p>
<p>When <var class="var">x</var> is an <em class="math">N</em>-dimensional array, the computation is carried
out along dimension <var class="var">dim</var>. If not specified <var class="var">dim</var> defaults to the
first non-singleton dimension.
</p>
<p>When a second output argument is requested an index matrix is also returned.
The <var class="var">idx</var> matrix has the same size as <var class="var">x</var>. Each element of
<var class="var">idx</var> contains the index of the histogram bin in which the
corresponding element of <var class="var">x</var> was counted.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Two_002dDimensional-Plots.html#XREFhist">hist</a>.
</p></dd></dl>
<p><code class="code">unique</code> function documented at <a class="ref" href="Sets.html#XREFunique">unique</a> is often
useful for statistics.
</p>
<a class="anchor" id="XREFnchoosek"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-nchoosek"><span><code class="def-type"><var class="var">c</var> =</code> <strong class="def-name">nchoosek</strong> <code class="def-code-arguments">(<var class="var">n</var>, <var class="var">k</var>)</code><a class="copiable-link" href="#index-nchoosek"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-nchoosek-1"><span><code class="def-type"><var class="var">c</var> =</code> <strong class="def-name">nchoosek</strong> <code class="def-code-arguments">(<var class="var">set</var>, <var class="var">k</var>)</code><a class="copiable-link" href="#index-nchoosek-1"> ¶</a></span></dt>
<dd>
<p>Compute the binomial coefficient of <var class="var">n</var> or list all possible
combinations of a <var class="var">set</var> of items.
</p>
<p>If <var class="var">n</var> is a scalar then calculate the binomial coefficient
of <var class="var">n</var> and <var class="var">k</var> which is defined as
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"> / \
| n | n (n-1) (n-2) ... (n-k+1) n!
| | = ------------------------- = ---------
| k | k! k! (n-k)!
\ /
</pre></div></div>
<p>This is the number of combinations of <var class="var">n</var> items taken in groups of
size <var class="var">k</var>.
</p>
<p>If the first argument is a vector, <var class="var">set</var>, then generate all
combinations of the elements of <var class="var">set</var>, taken <var class="var">k</var> at a time, with
one row per combination. The result <var class="var">c</var> has <var class="var">k</var> columns and
<code class="code">nchoosek (length (<var class="var">set</var>), <var class="var">k</var>)</code><!-- /@w --> rows.
</p>
<p>For example:
</p>
<p>How many ways can three items be grouped into pairs?
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">nchoosek (3, 2)
⇒ 3
</pre></div></div>
<p>What are the possible pairs?
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">nchoosek (1:3, 2)
⇒ 1 2
1 3
2 3
</pre></div></div>
<p>Programming Note: When calculating the binomial coefficient <code class="code">nchoosek</code>
works only for non-negative, integer arguments. Use <code class="code">bincoeff</code> for
non-integer and negative scalar arguments, or for computing many binomial
coefficients at once with vector inputs for <var class="var">n</var> or <var class="var">k</var>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Special-Functions.html#XREFbincoeff">bincoeff</a>, <a class="ref" href="#XREFperms">perms</a>.
</p></dd></dl>
<a class="anchor" id="XREFperms"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-perms"><span><code class="def-type"><var class="var">P</var> =</code> <strong class="def-name">perms</strong> <code class="def-code-arguments">(<var class="var">v</var>)</code><a class="copiable-link" href="#index-perms"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-perms-1"><span><code class="def-type"><var class="var">P</var> =</code> <strong class="def-name">perms</strong> <code class="def-code-arguments">(<var class="var">v</var>, "unique")</code><a class="copiable-link" href="#index-perms-1"> ¶</a></span></dt>
<dd><p>Generate all permutations of vector <var class="var">v</var> with one row per permutation.
</p>
<p>Results are returned in reverse lexicographic order if <var class="var">v</var> is in ascending
order. If <var class="var">v</var> is in a different permutation, then the result is permuted
that way too. Consequently, an input in descending order yields a result in
normal lexicographic order. The result has size
<code class="code">factorial (<var class="var">n</var>) * <var class="var">n</var></code>, where <var class="var">n</var> is the length of <var class="var">v</var>.
Any repeated elements are included in the output.
</p>
<p>If the optional argument <code class="code">"unique"</code> is given then only unique
permutations are returned, using less memory and taking less time than calling
<code class="code">unique (perms (<var class="var">v</var>), "rows")</code>.
</p>
<p>Example 1
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">perms ([1, 2, 3])
⇒
3 2 1
3 1 2
2 3 1
2 1 3
1 3 2
1 2 3
</pre></div></div>
<p>Example 2
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">perms ([1, 1, 2, 2], "unique")
⇒
2 2 1 1
2 1 2 1
2 1 1 2
1 2 2 1
1 2 1 2
1 1 2 2
</pre></div></div>
<p>Programming Note: If the <code class="code">"unique"</code> option is not used, the length of
<var class="var">v</var> should be no more than 10-12 to limit memory consumption. Even with
<code class="code">"unique"</code>, there should be no more than 10-12 unique elements in
<var class="var">v</var>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Rearranging-Matrices.html#XREFpermute">permute</a>, <a class="ref" href="Special-Utility-Matrices.html#XREFrandperm">randperm</a>, <a class="ref" href="#XREFnchoosek">nchoosek</a>.
</p>
</dd></dl>
<a class="anchor" id="XREFranks"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ranks"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">ranks</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-ranks"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ranks-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">ranks</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-ranks-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ranks-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">ranks</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">dim</var>, <var class="var">rtype</var>)</code><a class="copiable-link" href="#index-ranks-2"> ¶</a></span></dt>
<dd><p>Return the ranks (in the sense of order statistics) of <var class="var">x</var> along the
first non-singleton dimension adjusted for ties.
</p>
<p>If the optional <var class="var">dim</var> argument is given, operate along this dimension.
</p>
<p>The optional parameter <var class="var">rtype</var> determines how ties are handled. All
examples below assume an input of <code class="code">[ 1, 2, 2, 4 ]</code>.
</p>
<dl class="table">
<dt>0 or <code class="code">"fractional"</code> (default) for fractional ranking (1, 2.5,</dt>
<dd><p>2.5, 4);
</p>
</dd>
<dt>1 or <code class="code">"competition"</code> for competition ranking (1, 2, 2, 4);</dt>
<dt>2 or <code class="code">"modified"</code> for modified competition ranking (1, 3, 3, 4);</dt>
<dt>3 or <code class="code">"ordinal"</code> for ordinal ranking (1, 2, 3, 4);</dt>
<dt>4 or <code class="code">"dense"</code> for dense ranking (1, 2, 2, 3).</dt>
</dl>
<p><strong class="strong">See also:</strong> <a class="ref" href="Correlation-and-Regression-Analysis.html#XREFspearman">spearman</a>, <a class="ref" href="Correlation-and-Regression-Analysis.html#XREFkendall">kendall</a>.
</p></dd></dl>
<a class="anchor" id="XREFrun_005fcount"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-run_005fcount"><span><code class="def-type"><var class="var">cnt</var> =</code> <strong class="def-name">run_count</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">n</var>)</code><a class="copiable-link" href="#index-run_005fcount"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-run_005fcount-1"><span><code class="def-type"><var class="var">cnt</var> =</code> <strong class="def-name">run_count</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">n</var>, <var class="var">dim</var>)</code><a class="copiable-link" href="#index-run_005fcount-1"> ¶</a></span></dt>
<dd><p>Count the upward runs along the first non-singleton dimension of <var class="var">x</var>
of length 1, 2, …, <var class="var">n</var>-1 and greater than or equal to <var class="var">n</var>.
</p>
<p>If the optional argument <var class="var">dim</var> is given then operate along this
dimension.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFrunlength">runlength</a>.
</p></dd></dl>
<a class="anchor" id="XREFrunlength"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-runlength"><span><code class="def-type">count =</code> <strong class="def-name">runlength</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-runlength"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-runlength-1"><span><code class="def-type">[count, value] =</code> <strong class="def-name">runlength</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-runlength-1"> ¶</a></span></dt>
<dd><p>Find the lengths of all sequences of common values.
</p>
<p><var class="var">count</var> is a vector with the lengths of each repeated value.
</p>
<p>The optional output <var class="var">value</var> contains the value that was repeated in
the sequence.
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1])
⇒ 2 1 3 1 4
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFrun_005fcount">run_count</a>.
</p></dd></dl>
</div>
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