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
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>Maxima 5.47.0 Manual: Functions and Variables for cobyla</title>
<meta name="description" content="Maxima 5.47.0 Manual: Functions and Variables for cobyla">
<meta name="keywords" content="Maxima 5.47.0 Manual: Functions and Variables for cobyla">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link href="maxima_toc.html#Top" rel="start" title="Top">
<link href="maxima_423.html#Function-and-Variable-Index" rel="index" title="Function and Variable Index">
<link href="maxima_toc.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="maxima_198.html#cobyla_002dpkg" rel="up" title="cobyla-pkg">
<link href="maxima_201.html#Examples-for-cobyla" rel="next" title="Examples for cobyla">
<link href="maxima_199.html#Introduction-to-cobyla" rel="previous" title="Introduction to cobyla">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
body {color: black; background: white; margin-left: 8%; margin-right: 13%;
font-family: "FreeSans", sans-serif}
h1 {font-size: 150%; font-family: "FreeSans", sans-serif}
h2 {font-size: 125%; font-family: "FreeSans", sans-serif}
h3 {font-size: 100%; font-family: "FreeSans", sans-serif}
a[href] {color: rgb(0,0,255); text-decoration: none;}
a[href]:hover {background: rgb(220,220,220);}
div.textbox {border: solid; border-width: thin; padding-top: 1em;
padding-bottom: 1em; padding-left: 2em; padding-right: 2em}
div.titlebox {border: none; padding-top: 1em; padding-bottom: 1em;
padding-left: 2em; padding-right: 2em; background: rgb(200,255,255);
font-family: sans-serif}
div.synopsisbox {
border: none; padding-top: 1em; padding-bottom: 1em; padding-left: 2em;
padding-right: 2em; background: rgb(255,220,255);}
pre.example {border: 1px solid rgb(180,180,180); padding-top: 1em;
padding-bottom: 1em; padding-left: 1em; padding-right: 1em;
background-color: rgb(238,238,255)}
div.spacerbox {border: none; padding-top: 2em; padding-bottom: 2em}
div.image {margin: 0; padding: 1em; text-align: center}
div.categorybox {border: 1px solid gray; padding-top: 1em; padding-bottom: 1em;
padding-left: 1em; padding-right: 1em; background: rgb(247,242,220)}
img {max-width:80%; max-height: 80%; display: block; margin-left: auto; margin-right: auto}
-->
</style>
<link rel="icon" href="figures/favicon.ico">
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6>"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Functions-and-Variables-for-cobyla"></a>
<div class="header">
<p>
Next: <a href="maxima_201.html#Examples-for-cobyla" accesskey="n" rel="next">Examples for cobyla</a>, Previous: <a href="maxima_199.html#Introduction-to-cobyla" accesskey="p" rel="previous">Introduction to cobyla</a>, Up: <a href="maxima_198.html#cobyla_002dpkg" accesskey="u" rel="up">cobyla-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-cobyla-1"></a>
<h3 class="section">47.2 Functions and Variables for cobyla</h3>
<a name="fmin_005fcobyla"></a><a name="Item_003a-cobyla_002fdeffn_002ffmin_005fcobyla"></a><dl>
<dt><a name="index-fmin_005fcobyla"></a>Function: <strong>fmin_cobyla</strong> <em><br> <tt>fmin_cobyla</tt> (<var>F</var>, <var>X</var>, <var>Y</var>) <br> <tt>fmin_cobyla</tt> (<var>F</var>, <var>X</var>, <var>Y</var>, optional_args)</em></dt>
<dd>
<p>Returns an approximate minimum of the expression <var>F</var> with respect
to the variables <var>X</var>, subject to an optional set of constraints.
<var>Y</var> is a list of initial guesses for <var>X</var>.
</p>
<p><var>F</var> must be ordinary expressions, not names of functions or lambda expressions.
</p>
<p><code>optional_args</code> represents additional arguments,
specified as <code><var>symbol</var> = <var>value</var></code>.
The optional arguments recognized are:
</p>
<dl compact="compact">
<dt><code>constraints</code></dt>
<dd><p>List of inequality and equality constraints that must be satisfied by
<var>X</var>. The inequality constraints must be actual inequalities of
the form
\(g(X) \ge h(X)\) or
\(g(X) \le h(X).\) The equality constraints must be of the
form
\(g(X) = h(X).\)</p>
</dd>
<dt><code>rhobeg</code></dt>
<dd><p>Initial value of the internal <var>RHO</var> variable which controls
the size of simplex. (Defaults to 1.0)
</p></dd>
<dt><code>rhoend</code></dt>
<dd><p>The desired final value rho parameter. It is approximately
the accuracy in the variables. (Defaults to 1d-6.)
</p></dd>
<dt><code>iprint</code></dt>
<dd><p>Verbose output level. (Defaults to 0)
</p><ul>
<li> 0 - No output
</li><li> 1 - Summary at the end of the calculation
</li><li> 2 - Each new value of RHO and SIGMA is printed, including
the vector of variables, some function information when RHO is reduced.
</li><li> 3 - Like 2, but information is printed when F(X) is computed.
</li></ul>
</dd>
<dt><code>maxfun</code></dt>
<dd><p>The maximum number of function evaluations. (Defaults to 1000).
</p></dd>
</dl>
<p>On return, a vector is given:
</p><ol>
<li> The value of the variables giving the minimum. This is a list of
elements of the form <code><var>var</var> = <var>value</var></code> for each of the
variables listed in <var>X</var>.
</li><li> The minimized function value
</li><li> The number of function evaluations.
</li><li> Return code with the following meanings
<ul class="no-bullet">
<li><!-- /@w --> 0 - No errors.
</li><li><!-- /@w --> 1 - Limit on maximum number of function evaluations reached.
</li><li><!-- /@w --> 2 - Rounding errors inhibiting progress.
</li><li><!-- /@w --> -1 - <var>MAXCV</var> value exceeds <var>RHOEND</var>. This indicates that the
constraints were probably not satisfied. User should investigate
the value of the constraints.
</li></ul>
</li></ol>
<p><var>MAXCV</var> stands for “MAXimum Constraint Violation” and is the
value of <em>max(0.0, -c1(x), -c2(x),...-cm(x))</em> where <em>ck(x)</em>
denotes the k’th constraint function. (Note that maxima allows
constraints of the form <em>f(x) = g(x)</em>, which are internally
converted to <em>f(x)-g(x) >= 0</em> and <em>g(x)-f(x) >= 0</em> which is
required by COBYLA).
</p>
<p><code>load("fmin_cobyla")</code> loads this function.
</p>
</dd></dl>
<a name="bf_005ffmin_005fcobyla"></a><a name="Item_003a-cobyla_002fdeffn_002fbf_005ffmin_005fcobyla"></a><dl>
<dt><a name="index-bf_005ffmin_005fcobyla"></a>Function: <strong>bf_fmin_cobyla</strong> <em><br> <tt>bf_fmin_cobyla</tt> (<var>F</var>, <var>X</var>, <var>Y</var>) <br> <tt>bf_fmin_cobyla</tt> (<var>F</var>, <var>X</var>, <var>Y</var>, optional_args)</em></dt>
<dd>
<p>This function is identical to <code>fmin_cobyla</code>, except that bigfloat
operations are used, and the default value for <var>rhoend</var> is
<code>10^(fpprec/2)</code>.
</p>
<p>See <code><a href="#fmin_005fcobyla">fmin_cobyla</a></code> for more information.
</p>
<p><code>load("bf_fmin_cobyla")</code> loads this function.
</p>
</dd></dl>
<a name="Item_003a-cobyla_002fnode_002fExamples-for-cobyla"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_201.html#Examples-for-cobyla" accesskey="n" rel="next">Examples for cobyla</a>, Previous: <a href="maxima_199.html#Introduction-to-cobyla" accesskey="p" rel="previous">Introduction to cobyla</a>, Up: <a href="maxima_198.html#cobyla_002dpkg" accesskey="u" rel="up">cobyla-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
