Codebase list cppad / upstream/2015.00.00.7 doc / pow.cpp.xml
upstream/2015.00.00.7

Tree @upstream/2015.00.00.7 (Download .tar.gz)

pow.cpp.xml @upstream/2015.00.00.7 — raw · history · blame 

  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
<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>The AD Power Function: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="The AD Power Function: Example and Test"/>
<meta name="keywords" id="keywords" content=" the ad power function: example and test pow Ad "/>
<style type='text/css'>
body { color : black }
body { background-color : white }
A:link { color : blue }
A:visited { color : purple }
A:active { color : purple }
</style>
<script type='text/javascript' language='JavaScript' src='_pow.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
<a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a>
</td>
<td><a href="pow.xml" target="_top">Prev</a>
</td><td><a href="limits.xml" target="_top">Next</a>
</td><td>
<select onchange='choose_across0(this)'>
<option>Index-&gt;</option>
<option>contents</option>
<option>reference</option>
<option>index</option>
<option>search</option>
<option>external</option>
</select>
</td>
<td>
<select onchange='choose_up0(this)'>
<option>Up-&gt;</option>
<option>CppAD</option>
<option>AD</option>
<option>ADValued</option>
<option>MathOther</option>
<option>pow</option>
<option>pow.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>ADValued-&gt;</option>
<option>Arithmetic</option>
<option>std_math_ad</option>
<option>MathOther</option>
<option>CondExp</option>
<option>Discrete</option>
<option>atomic</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>MathOther-&gt;</option>
<option>abs</option>
<option>sign</option>
<option>atan2</option>
<option>erf</option>
<option>pow</option>
<option>limits</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>pow-&gt;</option>
<option>pow.cpp</option>
</select>
</td>
<td>pow.cpp</td>
<td>Headings</td>
</tr></table><br/>



<center><b><big><big>The AD Power Function: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/cppad.hpp&gt;
# include &lt;cmath&gt;

bool Pow(void)
{	bool ok = true;

	using CppAD::AD;
	using CppAD::NearEqual;

	// domain space vector
	size_t n  = 2;
	double x = 0.5;
	double y = 2.;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) XY(n);
	XY[0]      = x;
	XY[1]      = y;

	// declare independent variables and start tape recording
	CppAD::<a href="independent.xml" target="_top">Independent</a>(XY);

	// range space vector 
	size_t m = 3;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) Z(m);
	Z[0] = CppAD::pow(XY[0], XY[1]);  // pow(variable, variable)
	Z[1] = CppAD::pow(XY[0], y);      // pow(variable, parameter)
	Z[2] = CppAD::pow(x,     XY[1]);  // pow(parameter, variable)

	// create f: XY -&gt; Z and stop tape recording
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f(XY, Z); 

	// check value 
	double check = std::pow(x, y);
	size_t i;
	for(i = 0; i &lt; m; i++)
		ok &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(Z[i] , check,  1e-10 , 1e-10);

	// forward computation of first partial w.r.t. x
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dxy(n);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dz(m);
	dxy[0] = 1.;
	dxy[1] = 0.;
	dz    = f.<a href="forward.xml" target="_top">Forward</a>(1, dxy);
	check = y * std::pow(x, y-1.);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[0], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[1], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[2],    0., 1e-10, 1e-10);

	// forward computation of first partial w.r.t. y
	dxy[0] = 0.;
	dxy[1] = 1.;
	dz    = f.<a href="forward.xml" target="_top">Forward</a>(1, dxy);
	check = std::log(x) * std::pow(x, y);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[0], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[1],    0., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[2], check, 1e-10, 1e-10);

	// reverse computation of derivative of z[0] + z[1] + z[2]
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double)  w(m);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dw(n);
	w[0]  = 1.;
	w[1]  = 1.;
	w[2]  = 1.;
	dw    = f.<a href="reverse.xml" target="_top">Reverse</a>(1, w);
	check = y * std::pow(x, y-1.);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0], 2. * check, 1e-10, 1e-10);
	check = std::log(x) * std::pow(x, y);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[1], 2. * check, 1e-10, 1e-10);

	// use a VecAD&lt;Base&gt;::reference object with pow
	CppAD::VecAD&lt;double&gt; v(2);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; zero(0);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; one(1);
	v[zero]           = XY[0];
	v[one]            = XY[1];
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; result = CppAD::pow(v[zero], v[one]);
	ok               &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(result, Z[0], 1e-10, 1e-10);

	return ok;
}

</pre>

</font></code>


<hr/>Input File: example/pow.cpp

</body>
</html>