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<a name="Set-Operations"></a>
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<p>
Up: <a href="Sets.html#Sets" accesskey="u" rel="up">Sets</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Set-Operations-1"></a>
<h3 class="section">27.1 Set Operations</h3>

<p>Octave supports several basic set operations.  Octave can compute the union,
intersection, and difference of two sets.  Octave also supports the
<em>Exclusive Or</em> set operation.
</p>
<p>The functions for set operations all work in the same way by accepting two
input sets and returning a third set.  As an example, assume that <code>a</code> and
<code>b</code> contains two sets, then
</p>
<div class="example">
<pre class="example">union (a, b)
</pre></div>

<p>computes the union of the two sets.
</p>
<p>Finally, determining whether elements belong to a set can be done with the
<code>ismember</code> function.  Because sets are ordered this operation is very
efficient and is of order O(log2(n)) which is preferable to the <code>find</code>
function which is of order O(n).
</p>
<a name="XREFintersect"></a><dl>
<dt><a name="index-intersect"></a><em><var>c</var> =</em> <strong>intersect</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-intersect-1"></a><em><var>c</var> =</em> <strong>intersect</strong> <em>(<var>a</var>, <var>b</var>, &quot;rows&quot;)</em></dt>
<dt><a name="index-intersect-2"></a><em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>intersect</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Return the unique elements common to both <var>a</var> and <var>b</var> sorted in
ascending order.
</p>
<p>If <var>a</var> and <var>b</var> are both row vectors then return a row vector;
Otherwise, return a column vector.  The inputs may also be cell arrays of
strings.
</p>
<p>If the optional input <code>&quot;rows&quot;</code> is given then return the common rows of
<var>a</var> and <var>b</var>.  The inputs must be 2-D matrices to use this option.
</p>
<p>If requested, return index vectors <var>ia</var> and <var>ib</var> such that
<code><var>c</var> = <var>a</var>(<var>ia</var>)</code> and <code><var>c</var> = <var>b</var>(<var>ib</var>)</code>.
</p>

<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>


<a name="XREFunion"></a><dl>
<dt><a name="index-union"></a><em><var>c</var> =</em> <strong>union</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-union-1"></a><em><var>c</var> =</em> <strong>union</strong> <em>(<var>a</var>, <var>b</var>, &quot;rows&quot;)</em></dt>
<dt><a name="index-union-2"></a><em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>union</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Return the unique elements that are in either <var>a</var> or <var>b</var> sorted in
ascending order.
</p>
<p>If <var>a</var> and <var>b</var> are both row vectors then return a row vector;
Otherwise, return a column vector.  The inputs may also be cell arrays of
strings.
</p>
<p>If the optional input <code>&quot;rows&quot;</code> is given then return rows that are in
either <var>a</var> or <var>b</var>.  The inputs must be 2-D matrices to use this
option.
</p>
<p>The optional outputs <var>ia</var> and <var>ib</var> are index vectors such that
<code><var>a</var>(<var>ia</var>)</code> and <code><var>b</var>(<var>ib</var>)</code> are disjoint sets
whose union is <var>c</var>.
</p>

<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFintersect">intersect</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>


<a name="XREFsetdiff"></a><dl>
<dt><a name="index-setdiff"></a><em><var>c</var> =</em> <strong>setdiff</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-setdiff-1"></a><em><var>c</var> =</em> <strong>setdiff</strong> <em>(<var>a</var>, <var>b</var>, &quot;rows&quot;)</em></dt>
<dt><a name="index-setdiff-2"></a><em>[<var>c</var>, <var>ia</var>] =</em> <strong>setdiff</strong> <em>(&hellip;)</em></dt>
<dd><p>Return the unique elements in <var>a</var> that are not in <var>b</var> sorted in
ascending order.
</p>
<p>If <var>a</var> is a row vector return a row vector; Otherwise, return a
column vector.  The inputs may also be cell arrays of strings.
</p>
<p>If the optional input <code>&quot;rows&quot;</code> is given then return the rows in
<var>a</var> that are not in <var>b</var>.  The inputs must be 2-D matrices to use
this option.
</p>
<p>If requested, return the index vector <var>ia</var> such that
<code><var>c</var> = <var>a</var>(<var>ia</var>)</code>.
</p>
<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFintersect">intersect</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>


<a name="XREFsetxor"></a><dl>
<dt><a name="index-setxor"></a><em><var>c</var> =</em> <strong>setxor</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-setxor-1"></a><em><var>c</var> =</em> <strong>setxor</strong> <em>(<var>a</var>, <var>b</var>, &quot;rows&quot;)</em></dt>
<dt><a name="index-setxor-2"></a><em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>setxor</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Return the unique elements exclusive to sets <var>a</var> or <var>b</var> sorted in
ascending order.
</p>
<p>If <var>a</var> and <var>b</var> are both row vectors then return a row vector;
Otherwise, return a column vector.  The inputs may also be cell arrays of
strings.
</p>
<p>If the optional input <code>&quot;rows&quot;</code> is given then return the rows exclusive
to sets <var>a</var> and <var>b</var>.  The inputs must be 2-D matrices to use this
option.
</p>
<p>If requested, return index vectors <var>ia</var> and <var>ib</var> such that
<code><var>a</var>(<var>ia</var>)</code> and <code><var>b</var>(<var>ib</var>)</code> are disjoint sets
whose union is <var>c</var>.
</p>

<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFintersect">intersect</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>


<a name="XREFismember"></a><dl>
<dt><a name="index-ismember"></a><em><var>tf</var> =</em> <strong>ismember</strong> <em>(<var>a</var>, <var>s</var>)</em></dt>
<dt><a name="index-ismember-1"></a><em><var>tf</var> =</em> <strong>ismember</strong> <em>(<var>a</var>, <var>s</var>, &quot;rows&quot;)</em></dt>
<dt><a name="index-ismember-2"></a><em>[<var>tf</var>, <var>s_idx</var>] =</em> <strong>ismember</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Return a logical matrix <var>tf</var> with the same shape as <var>a</var> which is
true (1) if the element in <var>a</var> is found in <var>s</var> and false (0) if it
is not.
</p>
<p>If a second output argument is requested then the index into <var>s</var> of each
matching element is also returned.
</p>
<div class="example">
<pre class="example">a = [3, 10, 1];
s = [0:9];
[tf, s_idx] = ismember (a, s)
     &rArr; tf = [1, 0, 1]
     &rArr; s_idx = [4, 0, 2]
</pre></div>

<p>The inputs <var>a</var> and <var>s</var> may also be cell arrays.
</p>
<div class="example">
<pre class="example">a = {&quot;abc&quot;};
s = {&quot;abc&quot;, &quot;def&quot;};
[tf, s_idx] = ismember (a, s)
     &rArr; tf = 1
     &rArr; s_idx = 1
</pre></div>

<p>If the optional third argument <code>&quot;rows&quot;</code> is given then compare rows
in <var>a</var> with rows in <var>s</var>.  The inputs must be 2-D matrices with the
same number of columns to use this option.
</p>
<div class="example">
<pre class="example">a = [1:3; 5:7; 4:6];
s = [0:2; 1:3; 2:4; 3:5; 4:6];
[tf, s_idx] = ismember (a, s, &quot;rows&quot;)
     &rArr; tf = logical ([1; 0; 1])
     &rArr; s_idx = [2; 0; 5];
</pre></div>


<p><strong>See also:</strong> <a href="Finding-Elements-and-Checking-Conditions.html#XREFlookup">lookup</a>, <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFintersect">intersect</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFsetxor">setxor</a>.
</p></dd></dl>


<a name="XREFpowerset"></a><dl>
<dt><a name="index-powerset"></a><em></em> <strong>powerset</strong> <em>(<var>a</var>)</em></dt>
<dt><a name="index-powerset-1"></a><em></em> <strong>powerset</strong> <em>(<var>a</var>, &quot;rows&quot;)</em></dt>
<dd><p>Compute the powerset (all subsets) of the set <var>a</var>.
</p>
<p>The set <var>a</var> must be a numerical matrix or a cell array of strings.  The
output will always be a cell array of either vectors or strings.
</p>
<p>With the optional argument <code>&quot;rows&quot;</code>, each row of the set <var>a</var> is
considered one element of the set.  The input must be a 2-D numeric matrix
to use this argument.
</p>

<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFintersect">intersect</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>



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