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<html lang="en">
<head>
<title>Set Operations - GNU Octave</title>
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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">27.1 Set Operations</h3>
<p>Octave supports the basic set operations. That is, Octave can compute
the union, intersection, 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.
<!-- ismember scripts/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-2684"></a></var><br>
— Function File: [<var>tf</var>, <var>S_idx</var>] = <b>ismember</b> (<var>A, s</var>)<var><a name="index-ismember-2685"></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-2686"></a></var><br>
<blockquote><p>Return a logical matrix <var>tf</var> with the same shape as <var>A</var> which is
true (1) if <code>A(i,j)</code> is in <var>s</var> and false (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>
<!-- union scripts/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-2687"></a></var><br>
— Function File: <b>union</b> (<var>a, b, "rows"</var>)<var><a name="index-union-2688"></a></var><br>
<blockquote><p>Return the set of elements that are in either of the sets <var>a</var> and
<var>b</var>. <var>a</var>, <var>b</var> may be cell arrays of string(s).
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-2689"></a></var><br>
<blockquote>
<p>Return index vectors <var>ia</var> and <var>ib</var> such that <code>a(ia)</code> and
<code>b(ib)</code> are disjoint sets whose union is <var>c</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dintersect.html#doc_002dintersect">intersect</a>, <a href="doc_002dsetdiff.html#doc_002dsetdiff">setdiff</a>, <a href="doc_002dunique.html#doc_002dunique">unique</a>.
</p></blockquote></div>
<!-- intersect scripts/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-2690"></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-2691"></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.
<var>a</var>, <var>b</var> may be cell arrays of string(s).
<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>.
<!-- setdiff scripts/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-2692"></a></var><br>
— Function File: <b>setdiff</b> (<var>a, b, "rows"</var>)<var><a name="index-setdiff-2693"></a></var><br>
— Function File: [<var>c</var>, <var>i</var>] = <b>setdiff</b> (<var>a, b</var>)<var><a name="index-setdiff-2694"></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.
<var>a</var>, <var>b</var> may be cell arrays of string(s).
<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>
<!-- setxor scripts/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-2695"></a></var><br>
— Function File: <b>setxor</b> (<var>a, b, 'rows'</var>)<var><a name="index-setxor-2696"></a></var><br>
— Function File: [<var>c</var>, <var>ia</var>, <var>ib</var>] = <b>setxor</b> (<var>a, b</var>)<var><a name="index-setxor-2697"></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.
<var>a</var>, <var>b</var> may be cell arrays of string(s).
<p>With three output arguments, return index vectors <var>ia</var> and <var>ib</var>
such that <code>a(ia)</code> and <code>b(ib)</code> are disjoint sets whose union
is <var>c</var>.
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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>
<!-- powerset scripts/set/powerset.m -->
<p><a name="doc_002dpowerset"></a>
<div class="defun">
— Function File: <b>powerset</b> (<var>a</var>)<var><a name="index-powerset-2698"></a></var><br>
— Function File: <b>powerset</b> (<var>a, "rows"</var>)<var><a name="index-powerset-2699"></a></var><br>
<blockquote>
<p>Return a cell array containing all subsets of the set <var>a</var>.
</blockquote></div>
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<!-- @sp 1 -->
<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>.
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