/
diff.html
229 lines (178 loc) · 12.5 KB
/
diff.html
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
215
216
217
218
219
220
221
222
223
224
225
226
227
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Lagged and Iterated Differences — diff,Expression-method • CVXR</title>
<!-- favicons -->
<link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png">
<link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png">
<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png" />
<link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png" />
<link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png" />
<link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png" />
<!-- jquery -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script>
<!-- bootstrap-toc -->
<link rel="stylesheet" href="../bootstrap-toc.css">
<script src="../bootstrap-toc.js"></script>
<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous" />
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script>
<!-- headroom.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script>
<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>
<meta property="og:title" content="Lagged and Iterated Differences — diff,Expression-method" />
<meta property="og:description" content="The lagged and iterated differences of a vector.
If x is length n, this function returns a length \(n-k\) vector of the \(k\)th order difference between the lagged terms.
diff(x) returns the vector of differences between adjacent elements in the vector, i.e. [x[2] - x[1], x[3] - x[2], ...].
diff(x,1,2) is the second-order differences vector, equivalently diff(diff(x)). diff(x,1,0) returns the vector x unchanged.
diff(x,2) returns the vector of differences [x[3] - x[1], x[4] - x[2], ...], equivalent to x[(1+lag):n] - x[1:(n-lag)]." />
<meta property="og:image" content="https://www.cvxgrp.org/CVXR/logo.svg" />
<!-- mathjax -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script>
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body data-spy="scroll" data-target="#toc">
<div class="container template-reference-topic">
<header>
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">CVXR</a>
<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.0-9</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../index.html">
<span class="fas fa fas fa-home fa-lg"></span>
</a>
</li>
<li>
<a href="../reference/index.html">Reference</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="../articles/cvxr_intro.html">Disciplined Convex Optimization in R</a>
</li>
<li>
<a href="../articles/version1.html">Version 1.0</a>
</li>
</ul>
</li>
<li>
<a href="../news/index.html">Changelog</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/cvxgrp/CVXR/">
<span class="fab fa fab fa-github fa-lg"></span>
</a>
</li>
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
</header>
<div class="row">
<div class="col-md-9 contents">
<div class="page-header">
<h1>Lagged and Iterated Differences</h1>
<small class="dont-index">Source: <a href='https://github.com/cvxgrp/CVXR/blob/master/R/exports.R'><code>R/exports.R</code></a></small>
<div class="hidden name"><code>diff.Rd</code></div>
</div>
<div class="ref-description">
<p>The lagged and iterated differences of a vector.
If <code>x</code> is length <code>n</code>, this function returns a length \(n-k\) vector of the \(k\)th order difference between the lagged terms.
<code>diff(x)</code> returns the vector of differences between adjacent elements in the vector, i.e. [x[2] - x[1], x[3] - x[2], ...].
<code>diff(x,1,2)</code> is the second-order differences vector, equivalently diff(diff(x)). <code>diff(x,1,0)</code> returns the vector x unchanged.
<code>diff(x,2)</code> returns the vector of differences [x[3] - x[1], x[4] - x[2], ...], equivalent to <code>x[(1+lag):n] - x[1:(n-lag)]</code>.</p>
</div>
<pre class="usage"><span class='co'># S4 method for Expression</span>
<span class='fu'>diff</span>(<span class='no'>x</span>, <span class='kw'>lag</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>differences</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='no'>...</span>)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>x</th>
<td><p>An <a href='Expression-class.html'>Expression</a>.</p></td>
</tr>
<tr>
<th>lag</th>
<td><p>An integer indicating which lag to use.</p></td>
</tr>
<tr>
<th>differences</th>
<td><p>An integer indicating the order of the difference.</p></td>
</tr>
<tr>
<th>...</th>
<td><p>(Optional) Addition <code>axis</code> argument, specifying the dimension across which to apply the function: <code>1</code> indicates rows, <code>2</code> indicates columns, and <code>NA</code> indicates rows and columns. The default is <code>axis = 1</code>.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>An <a href='Expression-class.html'>Expression</a> representing the <code>k</code>th order difference.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'>## Problem data</span>
<span class='no'>m</span> <span class='kw'><-</span> <span class='fl'>101</span>
<span class='no'>L</span> <span class='kw'><-</span> <span class='fl'>2</span>
<span class='no'>h</span> <span class='kw'><-</span> <span class='no'>L</span>/(<span class='no'>m</span>-<span class='fl'>1</span>)
<span class='co'>## Form objective and constraints</span>
<span class='no'>x</span> <span class='kw'><-</span> <span class='fu'><a href='Variable-class.html'>Variable</a></span>(<span class='no'>m</span>)
<span class='no'>y</span> <span class='kw'><-</span> <span class='fu'><a href='Variable-class.html'>Variable</a></span>(<span class='no'>m</span>)
<span class='no'>obj</span> <span class='kw'><-</span> <span class='fu'><a href='sum_entries.html'>sum</a></span>(<span class='no'>y</span>)
<span class='no'>constr</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='no'>x</span>[<span class='fl'>1</span>] <span class='kw'>==</span> <span class='fl'>0</span>, <span class='no'>y</span>[<span class='fl'>1</span>] <span class='kw'>==</span> <span class='fl'>1</span>, <span class='no'>x</span>[<span class='no'>m</span>] <span class='kw'>==</span> <span class='fl'>1</span>, <span class='no'>y</span>[<span class='no'>m</span>] <span class='kw'>==</span> <span class='fl'>1</span>, <span class='fu'>diff</span>(<span class='no'>x</span>)^<span class='fl'>2</span> + <span class='fu'>diff</span>(<span class='no'>y</span>)^<span class='fl'>2</span> <span class='kw'><=</span> <span class='no'>h</span>^<span class='fl'>2</span>)
<span class='co'>## Solve the catenary problem</span>
<span class='no'>prob</span> <span class='kw'><-</span> <span class='fu'><a href='Problem-class.html'>Problem</a></span>(<span class='fu'><a href='Minimize-class.html'>Minimize</a></span>(<span class='no'>obj</span>), <span class='no'>constr</span>)
<span class='no'>result</span> <span class='kw'><-</span> <span class='fu'><a href='psolve.html'>solve</a></span>(<span class='no'>prob</span>)
<span class='co'>## Plot and compare with ideal catenary</span>
<span class='no'>xs</span> <span class='kw'><-</span> <span class='no'>result</span>$<span class='fu'>getValue</span>(<span class='no'>x</span>)
<span class='no'>ys</span> <span class='kw'><-</span> <span class='no'>result</span>$<span class='fu'>getValue</span>(<span class='no'>y</span>)
<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>), <span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>'n'</span>, <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"x"</span>, <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"y"</span>)</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/lines.html'>lines</a></span>(<span class='no'>xs</span>, <span class='no'>ys</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='st'>"blue"</span>, <span class='kw'>lwd</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/grid.html'>grid</a></span>()</div><div class='img'><img src='diff-1.png' alt='' width='700' height='433' /></div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc" class="sticky-top">
<h2 data-toc-skip>Contents</h2>
</nav>
</div>
</div>
<footer>
<div class="copyright">
<p>Developed by <a href='https://web.stanford.edu/~anqif/'>Anqi Fu</a>, <a href='https://web.stanford.edu/~naras'>Balasubramanian Narasimhan</a>, David W Kang, <a href='https://web.stanford.edu/~stevend2/'>Steven Diamond</a>, <a href='https://people.eecs.berkeley.edu/~miller_john/'>John Miller</a>.</p>
</div>
<div class="pkgdown">
<p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
</div>
</footer>
</div>
</body>
</html>