1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
|
<html lang="en">
<head>
<title>Set Operations - Untitled</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="Untitled">
<meta name="generator" content="makeinfo 4.11">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Sets.html#Sets" title="Sets">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Set-Operations"></a>
Up: <a rel="up" accesskey="u" href="Sets.html#Sets">Sets</a>
<hr>
</div>
<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>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @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_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>.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<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>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @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>.
<!-- ./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>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<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>.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @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_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>.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @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_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>
<!-- DO NOT EDIT! Generated automatically by munge-texi. -->
<!-- Copyright (C) 1996, 1997, 1999, 2000, 2002, 2007, 2008, 2009 John W. Eaton -->
<!-- This file is part of Octave. -->
<!-- Octave is free software; you can redistribute it and/or modify it -->
<!-- under the terms of the GNU General Public License as published by the -->
<!-- Free Software Foundation; either version 3 of the License, or (at -->
<!-- your option) any later version. -->
<!-- Octave is distributed in the hope that it will be useful, but WITHOUT -->
<!-- ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or -->
<!-- FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -->
<!-- for more details. -->
<!-- You should have received a copy of the GNU General Public License -->
<!-- along with Octave; see the file COPYING. If not, see -->
<!-- <http://www.gnu.org/licenses/>. -->
</body></html>
|
