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

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

sacado_poly.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
174
175
<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Sacado Speed: Second Derivative of a Polynomial</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Sacado Speed: Second Derivative of a Polynomial"/>
<meta name="keywords" id="keywords" content=" sacado speed: second derivative of a polynomial link_poly speed specifications implementation "/>
<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='_sacado_poly.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="sacado_ode.cpp.xml" target="_top">Prev</a>
</td><td><a href="sacado_sparse_hessian.cpp.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>speed</option>
<option>speed_sacado</option>
<option>sacado_poly.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>CppAD-&gt;</option>
<option>Install</option>
<option>Introduction</option>
<option>AD</option>
<option>ADFun</option>
<option>preprocessor</option>
<option>multi_thread</option>
<option>library</option>
<option>ipopt_solve</option>
<option>Example</option>
<option>speed</option>
<option>Appendix</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>speed-&gt;</option>
<option>speed_main</option>
<option>speed_utility</option>
<option>speed_double</option>
<option>speed_adolc</option>
<option>speed_cppad</option>
<option>speed_fadbad</option>
<option>speed_sacado</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>speed_sacado-&gt;</option>
<option>sacado_det_minor.cpp</option>
<option>sacado_det_lu.cpp</option>
<option>sacado_mat_mul.cpp</option>
<option>sacado_ode.cpp</option>
<option>sacado_poly.cpp</option>
<option>sacado_sparse_hessian.cpp</option>
<option>sacado_sparse_jacobian.cpp</option>
</select>
</td>
<td>sacado_poly.cpp</td>
<td>
<select onchange='choose_current0(this)'>
<option>Headings-&gt;</option>
<option>Specifications</option>
<option>Implementation</option>
</select>
</td>
</tr></table><br/>



<center><b><big><big>Sacado Speed: Second Derivative of a Polynomial</big></big></b></center>
<br/>
<b><big><a name="Specifications" id="Specifications">Specifications</a></big></b>
<br/>
See <a href="link_poly.xml" target="_top"><span style='white-space: nowrap'>link_poly</span></a>
.

<br/>
<br/>
<b><big><a name="Implementation" id="Implementation">Implementation</a></big></b>



<code><font color='blue'><pre style='display:inline'> 
# include &lt;cppad/vector.hpp&gt;
# include &lt;cppad/poly.hpp&gt;
# include &lt;cppad/speed/uniform_01.hpp&gt;
# include &lt;Sacado.hpp&gt;

// list of possible options
extern bool global_memory, global_onetape, global_atomic, global_optimize;

bool link_poly(
	size_t                     size     , 
	size_t                     repeat   , 
	CppAD::vector&lt;double&gt;     &amp;a        ,  // coefficients of polynomial
	CppAD::vector&lt;double&gt;     &amp;z        ,  // polynomial argument value
	CppAD::vector&lt;double&gt;     &amp;ddp      )  // second derivative w.r.t z  
{
	if( global_atomic )
		return false;
	if( global_memory || global_onetape || global_optimize )
		return false;
	// -----------------------------------------------------
	// setup
	typedef Sacado::Tay::Taylor&lt;double&gt;  ADScalar;
	CppAD::vector&lt;ADScalar&gt;              A(size);

	size_t i;               // temporary index     
	ADScalar   Z;           // domain space AD value
	ADScalar   P;           // range space AD value 
	unsigned int order = 2; // order of Taylor coefficients
	Z.resize(order+1, false);
	P.resize(order+1, false);

	// choose the polynomial coefficients
	CppAD::uniform_01(size, a);

	// AD copy of the polynomial coefficients
	for(i = 0; i &lt; size; i++)
		A[i] = a[i];

	// ------------------------------------------------------
	while(repeat--)
	{	// get the next argument value
		CppAD::uniform_01(1, z);

		// independent variable value
		Z.fastAccessCoeff(0)   = z[0]; // argument value
		Z.fastAccessCoeff(1)   = 1.;   // first order coefficient
		Z.fastAccessCoeff(2)   = 0.;   // second order coefficient

		// AD computation of the dependent variable
		P = CppAD::Poly(0, A, Z);

		// second derivative is twice second order Taylor coefficient
		ddp[0] = 2. * P.fastAccessCoeff(2);
	}
	// ------------------------------------------------------
	return true;
}
</pre></font></code>


<hr/>Input File: speed/sacado/poly.cpp

</body>
</html>