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<a name="Set-Operations"></a>
<div class="header">
<p>
Up: <a href="Sets.html#Sets" accesskey="u" rel="up">Sets</a> [<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>
</div>
<hr>
<a name="Set-Operations-1"></a>
<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
</p>
<div class="example">
<pre class="example">union (x, y)
</pre></div>
<p>computes the union of the two sets.
</p>
<a name="XREFismember"></a><dl>
<dt><a name="index-ismember"></a>Function File: <em><var>tf</var> =</em> <strong>ismember</strong> <em>(<var>A</var>, <var>s</var>)</em></dt>
<dt><a name="index-ismember-1"></a>Function File: <em>[<var>tf</var>, <var>S_idx</var>] =</em> <strong>ismember</strong> <em>(<var>A</var>, <var>s</var>)</em></dt>
<dt><a name="index-ismember-2"></a>Function File: <em>[<var>tf</var>, <var>S_idx</var>] =</em> <strong>ismember</strong> <em>(<var>A</var>, <var>s</var>, "rows")</em></dt>
<dd><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.
</p>
<div class="example">
<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></div>
<p>The inputs, <var>A</var> and <var>s</var>, may also be cell arrays.
</p>
<div class="example">
<pre class="example">a = {"abc"};
s = {"abc", "def"};
[tf, s_idx] = ismember (a, s)
⇒ tf = [1, 0]
⇒ s_idx = [1, 0]
</pre></div>
<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>.
</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, "rows")
⇒ tf = logical ([1; 0; 1])
⇒ s_idx = [2; 0; 5];
</pre></div>
<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="#XREFsetdiff">setdiff</a>.
</p></dd></dl>
<a name="XREFunion"></a><dl>
<dt><a name="index-union"></a>Function File: <em></em> <strong>union</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-union-1"></a>Function File: <em></em> <strong>union</strong> <em>(<var>a</var>, <var>b</var>, "rows")</em></dt>
<dt><a name="index-union-2"></a>Function File: <em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>union</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd>
<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 strings.
For example:
</p>
<div class="example">
<pre class="example">union ([1, 2, 4], [2, 3, 5])
⇒ [1, 2, 3, 4, 5]
</pre></div>
<p>If the optional third input argument is the string <code>"rows"</code> then
each row of the matrices <var>a</var> and <var>b</var> will be considered as a
single set element. For example:
</p>
<div class="example">
<pre class="example">union ([1, 2; 2, 3], [1, 2; 3, 4], "rows")
⇒ 1 2
2 3
3 4
</pre></div>
<p>The optional outputs <var>ia</var> and <var>ib</var> are index vectors such that
<code>a(ia)</code> and <code>b(ib)</code> are disjoint sets whose union is <var>c</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFintersect">intersect</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="Sets.html#XREFunique">unique</a>.
</p></dd></dl>
<a name="XREFintersect"></a><dl>
<dt><a name="index-intersect"></a>Function File: <em></em> <strong>intersect</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-intersect-1"></a>Function File: <em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>intersect</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd>
<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>
<p>Return index vectors <var>ia</var> and <var>ib</var> such that <code>a(ia)==c</code> and
<code>b(ib)==c</code>.
</p>
</dd></dl>
<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFismember">ismember</a>.
</p>
<a name="XREFsetdiff"></a><dl>
<dt><a name="index-setdiff"></a>Function File: <em></em> <strong>setdiff</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-setdiff-1"></a>Function File: <em></em> <strong>setdiff</strong> <em>(<var>a</var>, <var>b</var>, "rows")</em></dt>
<dt><a name="index-setdiff-2"></a>Function File: <em>[<var>c</var>, <var>i</var>] =</em> <strong>setdiff</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd><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>
<p>Given the optional third argument <code>"rows"</code>, return the rows in
<var>a</var> that are not in <var>b</var>, sorted in ascending order by rows.
</p>
<p>If requested, return <var>i</var> such that <code>c = a(i)</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>Function File: <em></em> <strong>setxor</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-setxor-1"></a>Function File: <em></em> <strong>setxor</strong> <em>(<var>a</var>, <var>b</var>, "rows")</em></dt>
<dt><a name="index-setxor-2"></a>Function File: <em>[<var>c</var>, <var>ia</var>, <var>ib</var>] =</em> <strong>setxor</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd>
<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>
<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>.
</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="XREFpowerset"></a><dl>
<dt><a name="index-powerset"></a>Function File: <em></em> <strong>powerset</strong> <em>(<var>a</var>)</em></dt>
<dt><a name="index-powerset-1"></a>Function File: <em></em> <strong>powerset</strong> <em>(<var>a</var>, "rows")</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 second argument <code>"rows"</code>, each row of the set <var>a</var>
is considered one element of the set. As a result, <var>a</var> must then be a
numerical 2-D matrix.
</p>
<p><strong>See also:</strong> <a href="Sets.html#XREFunique">unique</a>, <a href="#XREFunion">union</a>, <a href="#XREFsetxor">setxor</a>, <a href="#XREFsetdiff">setdiff</a>, <a href="#XREFismember">ismember</a>.
</p></dd></dl>
<hr>
<div class="header">
<p>
Up: <a href="Sets.html#Sets" accesskey="u" rel="up">Sets</a> [<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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