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<a name="Set-Operations"></a>
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Up: <a rel="up" accesskey="u" href="Sets.html#Sets">Sets</a>
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<h3 class="section">26.1 Set Operations</h3>
<p>Octave supports the basic set operations. That is, Octave can compute
the union, intersection, complement, and difference of two sets.
Octave also supports the <em>Exclusive Or</em> set operation, and
membership determination. The functions for set operations all work in
pretty much the same way. As an example, assume that <code>x</code> and
<code>y</code> contains two sets, then
<pre class="example"> union(x, y)
</pre>
<p class="noindent">computes the union of the two sets.
<!-- ./set/ismember.m -->
<p><a name="doc_002dismember"></a>
<div class="defun">
— Function File: [<var>tf</var> = <b>ismember</b> (<var>A, S</var>)<var><a name="index-ismember-2006"></a></var><br>
— Function File: [<var>tf</var>, <var>S_idx</var>] = <b>ismember</b> (<var>A, S</var>)<var><a name="index-ismember-2007"></a></var><br>
— Function File: [<var>tf</var>, <var>S_idx</var>] = <b>ismember</b> (<var>A, S, "rows"</var>)<var><a name="index-ismember-2008"></a></var><br>
<blockquote><p>Return a matrix <var>tf</var> with the same shape as <var>A</var> which has a 1 if
<code>A(i,j)</code> is in <var>S</var> and 0 if it is not. If a second output argument
is requested, the index into <var>S</var> of each of the matching elements is
also returned.
<pre class="example"> a = [3, 10, 1];
s = [0:9];
[tf, s_idx] = ismember (a, s);
⇒ tf = [1, 0, 1]
⇒ s_idx = [4, 0, 2]
</pre>
<p>The inputs, <var>A</var> and <var>S</var>, may also be cell arrays.
<pre class="example"> a = {'abc'};
s = {'abc', 'def'};
[tf, s_idx] = ismember (a, s);
⇒ tf = [1, 0]
⇒ s_idx = [1, 0]
</pre>
<p>With the optional third argument <code>"rows"</code>, and matrices
<var>A</var> and <var>S</var> with the same number of columns, compare rows in
<var>A</var> with the rows in <var>S</var>.
<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, 'rows');
⇒ tf = logical ([1; 0; 1])
⇒ s_idx = [2; 0; 5];
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dunique.html#doc_002dunique">unique</a>, <a href="doc_002dunion.html#doc_002dunion">union</a>, <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dsetxor.html#doc_002dsetxor">setxor</a>, <a href="doc_002dsetdiff.html#doc_002dsetdiff">setdiff</a>.
</p></blockquote></div>
<!-- ./set/union.m -->
<p><a name="doc_002dunion"></a>
<div class="defun">
— Function File: <b>union</b> (<var>a, b</var>)<var><a name="index-union-2009"></a></var><br>
— Function File: <b>union</b> (<var>a, b, "rows"</var>)<var><a name="index-union-2010"></a></var><br>
<blockquote><p>Return the set of elements that are in either of the sets <var>a</var> and
<var>b</var>. For example,
<pre class="example"> union ([1, 2, 4], [2, 3, 5])
⇒ [1, 2, 3, 4, 5]
</pre>
<p>If the optional third input argument is the string "rows" each row of
the matrices <var>a</var> and <var>b</var> will be considered an element of sets.
For example,
<pre class="example"> union([1, 2; 2, 3], [1, 2; 3, 4], "rows")
⇒ 1 2
2 3
3 4
</pre>
— Function File: [<var>c</var>, <var>ia</var>, <var>ib</var>] = <b>union</b> (<var>a, b</var>)<var><a name="index-union-2011"></a></var><br>
<blockquote>
<p>Return index vectors <var>ia</var> and <var>ib</var> such that <code>a == c(ia)</code> and
<code>b == c(ib)</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dcomplement.html#doc_002dcomplement">complement</a>, <a href="doc_002dunique.html#doc_002dunique">unique</a>.
</p></blockquote></div>
<!-- ./set/intersect.m -->
<p><a name="doc_002dintersect"></a>
<div class="defun">
— Function File: <b>intersect</b> (<var>a, b</var>)<var><a name="index-intersect-2012"></a></var><br>
— Function File: [<var>c</var>, <var>ia</var>, <var>ib</var>] = <b>intersect</b> (<var>a, b</var>)<var><a name="index-intersect-2013"></a></var><br>
<blockquote>
<p>Return the elements in both <var>a</var> and <var>b</var>, sorted in ascending
order. If <var>a</var> and <var>b</var> are both column vectors return a column
vector, otherwise return a row vector.
<p>Return index vectors <var>ia</var> and <var>ib</var> such that <code>a(ia)==c</code> and
<code>b(ib)==c</code>.
</blockquote></div>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dunique.html#doc_002dunique">unique</a>, <a href="doc_002dunion.html#doc_002dunion">union</a>, <a href="doc_002dsetxor.html#doc_002dsetxor">setxor</a>, <a href="doc_002dsetdiff.html#doc_002dsetdiff">setdiff</a>, <a href="doc_002dismember.html#doc_002dismember">ismember</a>.
<!-- ./set/complement.m -->
<p><a name="doc_002dcomplement"></a>
<div class="defun">
— Function File: <b>complement</b> (<var>x, y</var>)<var><a name="index-complement-2014"></a></var><br>
<blockquote><p>Return the elements of set <var>y</var> that are not in set <var>x</var>. For
example,
<pre class="example"> complement ([ 1, 2, 3 ], [ 2, 3, 5 ])
⇒ 5
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dunion.html#doc_002dunion">union</a>, <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dunique.html#doc_002dunique">unique</a>.
</p></blockquote></div>
<!-- ./set/setdiff.m -->
<p><a name="doc_002dsetdiff"></a>
<div class="defun">
— Function File: <b>setdiff</b> (<var>a, b</var>)<var><a name="index-setdiff-2015"></a></var><br>
— Function File: <b>setdiff</b> (<var>a, b, "rows"</var>)<var><a name="index-setdiff-2016"></a></var><br>
— Function File: [<var>c</var>, <var>i</var>] = <b>setdiff</b> (<var>a, b</var>)<var><a name="index-setdiff-2017"></a></var><br>
<blockquote><p>Return the elements in <var>a</var> that are not in <var>b</var>, sorted in
ascending order. If <var>a</var> and <var>b</var> are both column vectors
return a column vector, otherwise return a row vector.
<p>Given the optional third argument ‘<samp><span class="samp">"rows"</span></samp>’, return the rows in
<var>a</var> that are not in <var>b</var>, sorted in ascending order by rows.
<p>If requested, return <var>i</var> such that <code>c = a(i)</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dunique.html#doc_002dunique">unique</a>, <a href="doc_002dunion.html#doc_002dunion">union</a>, <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dsetxor.html#doc_002dsetxor">setxor</a>, <a href="doc_002dismember.html#doc_002dismember">ismember</a>.
</p></blockquote></div>
<!-- ./set/setxor.m -->
<p><a name="doc_002dsetxor"></a>
<div class="defun">
— Function File: <b>setxor</b> (<var>a, b</var>)<var><a name="index-setxor-2018"></a></var><br>
— Function File: <b>setxor</b> (<var>a, b, 'rows'</var>)<var><a name="index-setxor-2019"></a></var><br>
<blockquote>
<p>Return the elements exclusive to <var>a</var> or <var>b</var>, sorted in ascending
order. If <var>a</var> and <var>b</var> are both column vectors return a column
vector, otherwise return a row vector.
— Function File: [<var>c</var>, <var>ia</var>, <var>ib</var>] = <b>setxor</b> (<var>a, b</var>)<var><a name="index-setxor-2020"></a></var><br>
<blockquote>
<p>Return index vectors <var>ia</var> and <var>ib</var> such that <code>a == c(ia)</code> and
<code>b == c(ib)</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dunique.html#doc_002dunique">unique</a>, <a href="doc_002dunion.html#doc_002dunion">union</a>, <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dsetdiff.html#doc_002dsetdiff">setdiff</a>, <a href="doc_002dismember.html#doc_002dismember">ismember</a>.
</p></blockquote></div>
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