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<span id="Sets"></span><div class="header">
<p>
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<hr>
<span id="Sets-1"></span><h2 class="chapter">27 Sets</h2>
<p>Octave has a number of functions for managing sets of data. A set is defined
as a collection of unique elements and is typically represented by a vector of
numbers sorted in ascending order. Any vector or matrix can be converted to a
set by removing duplicates through the use of the <code>unique</code> function.
However, it isn’t necessary to explicitly create a set as all of the functions
which operate on sets will convert their input to a set before proceeding.
</p>
<span id="XREFunique"></span><dl>
<dt id="index-unique">: <em></em> <strong>unique</strong> <em>(<var>x</var>)</em></dt>
<dt id="index-unique-1">: <em></em> <strong>unique</strong> <em>(<var>x</var>, "rows")</em></dt>
<dt id="index-unique-2">: <em></em> <strong>unique</strong> <em>(…, "sorted")</em></dt>
<dt id="index-unique-3">: <em></em> <strong>unique</strong> <em>(…, "stable")</em></dt>
<dt id="index-unique-4">: <em>[<var>y</var>, <var>i</var>, <var>j</var>] =</em> <strong>unique</strong> <em>(…)</em></dt>
<dt id="index-unique-5">: <em>[<var>y</var>, <var>i</var>, <var>j</var>] =</em> <strong>unique</strong> <em>(…, "first")</em></dt>
<dt id="index-unique-6">: <em>[<var>y</var>, <var>i</var>, <var>j</var>] =</em> <strong>unique</strong> <em>(…, "last")</em></dt>
<dt id="index-unique-7">: <em>[<var>y</var>, <var>i</var>, <var>j</var>] =</em> <strong>unique</strong> <em>(…, "legacy")</em></dt>
<dd><p>Return the unique elements of <var>x</var>.
</p>
<p>If the input <var>x</var> is a column vector then return a column vector;
Otherwise, return a row vector. <var>x</var> may also be a cell array of
strings.
</p>
<p>If the optional argument <code>"rows"</code> is given then return the unique
rows of <var>x</var>. The input must be a 2-D numeric matrix to use this option.
</p>
<p>The optional argument <code>"sorted"</code>/<code>"stable"</code> controls the order
in which unique values appear in the output. The default is
<code>"sorted"</code> and values in the output are placed in ascending order.
The alternative <code>"stable"</code> preserves the order found in the input
<var>x</var>.
</p>
<p>If requested, return column index vectors <var>i</var> and <var>j</var> such that
<code><var>y</var> = <var>x</var>(<var>i</var>)</code> and <code><var>x</var> = <var>y</var>(<var>j</var>)</code>.
</p>
<p>Additionally, if <var>i</var> is a requested output then one of the flags
<code>"first"</code> or <code>"last"</code> may be given. If <code>"last"</code> is
specified, return the highest possible indices in <var>i</var>, otherwise, if
<code>"first"</code> is specified, return the lowest. The default is
<code>"first"</code>.
</p>
<p>Example 1 : sort order
</p>
<div class="example">
<pre class="example">unique ([3, 1, 1, 2])
⇒ [1, 2, 3]
unique ([3, 1, 1, 2], "stable")
⇒ [3, 1, 2]
</pre></div>
<p>Example 2 : index selection
</p>
<div class="example">
<pre class="example">[~, <var>i</var>] = unique ([3, 1, 1, 2], "first")
⇒ <var>i</var> = [2; 4; 1]
[~, <var>i</var>] = unique ([3, 1, 1, 2], "last")
⇒ <var>i</var> = [3; 4; 1]
</pre></div>
<p>Programming Notes: The input flag <code>"legacy"</code> changes the algorithm
to be compatible with <small>MATLAB</small> releases prior to R2012b. Specifically,
The index ordering flag is changed to <code>"last"</code>, and the shape of the
outputs <var>i</var>, <var>j</var> will follow the shape of the input <var>x</var> rather
than always being column vectors.
</p>
<p>The third output, <var>j</var>, has not been implemented yet when the sort
order is <code>"stable"</code>.
</p>
<p><strong>See also:</strong> <a href="Set-Operations.html#XREFunion">union</a>, <a href="Set-Operations.html#XREFintersect">intersect</a>, <a href="Set-Operations.html#XREFsetdiff">setdiff</a>, <a href="Set-Operations.html#XREFsetxor">setxor</a>, <a href="Set-Operations.html#XREFismember">ismember</a>.
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