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

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

sparse_hessian.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
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
228
229
230
231
232
233
234
235
236
237
238
<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Sparse Hessian: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Sparse Hessian: Example and Test"/>
<meta name="keywords" id="keywords" content=" sparse hessian: example and test Hessian spare "/>
<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='_sparse_hessian.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="sparse_hessian.xml" target="_top">Prev</a>
</td><td><a href="funcheck.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>ADFun</option>
<option>Drivers</option>
<option>sparse_hessian</option>
<option>sparse_hessian.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>ADFun-&gt;</option>
<option>Independent</option>
<option>FunConstruct</option>
<option>Dependent</option>
<option>abort_recording</option>
<option>seq_property</option>
<option>FunEval</option>
<option>Drivers</option>
<option>FunCheck</option>
<option>optimize</option>
<option>check_for_nan</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>Drivers-&gt;</option>
<option>Jacobian</option>
<option>ForOne</option>
<option>RevOne</option>
<option>Hessian</option>
<option>ForTwo</option>
<option>RevTwo</option>
<option>sparse_jacobian</option>
<option>sparse_hessian</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>sparse_hessian-&gt;</option>
<option>sparse_hessian.cpp</option>
</select>
</td>
<td>sparse_hessian.cpp</td>
<td>Headings</td>
</tr></table><br/>



<center><b><big><big>Sparse Hessian: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
# include &lt;cppad/cppad.hpp&gt;
bool sparse_hessian(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	size_t i, j, k, ell;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;)               a_vector;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double)                     d_vector;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(size_t)                     i_vector;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(bool)                       b_vector;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(std::set&lt;size_t&gt;)         s_vector;
	double eps = 10. * CppAD::numeric_limits&lt;double&gt;::epsilon();

	// domain space vector
	size_t n = 12;  // must be greater than or equal 3; see n_sweep below
	a_vector a_x(n);
	for(j = 0; j &lt; n; j++)
		a_x[j] = <a href="ad.xml" target="_top">AD</a>&lt;double&gt; (0);

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

	// range space vector
	size_t m = 1;
	a_vector a_y(m);
	a_y[0] = a_x[0]*a_x[1];
	for(j = 0; j &lt; n; j++)
		a_y[0] += a_x[j] * a_x[j] * a_x[j];

	// create f: x -&gt; y and stop tape recording
	// (without executing zero order forward calculation)
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f;
	f.Dependent(a_x, a_y);

	// new value for the independent variable vector, and weighting vector
	d_vector w(m), x(n);
	for(j = 0; j &lt; n; j++)
		x[j] = double(j);
	w[0] = 1.0;

	// vector used to check the value of the hessian
	d_vector check(n * n);
	for(ell = 0; ell &lt; n * n; ell++)
		check[ell] = 0.0;
	ell        = 0 * n + 1;
	check[ell] = 1.0;
	ell        = 1 * n + 0;
	check[ell] = 1.0 ;
	for(j = 0; j &lt; n; j++)
	{	ell = j * n + j;
		check[ell] = 6.0 * x[j];
	}

	// -------------------------------------------------------------------
	// second derivative of y[0] w.r.t x
	d_vector hes(n * n);
	hes = f.SparseHessian(x, w);
	for(ell = 0; ell &lt; n * n; ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// example using vectors of bools to compute sparsity pattern for Hessian
	b_vector r_bool(n * n);
	for(i = 0; i &lt; n; i++)
	{	for(j = 0; j &lt; n; j++)
			r_bool[i * n + j] = false;
		r_bool[i * n + i] = true;
	}
	f.ForSparseJac(n, r_bool);
	//
	b_vector s_bool(m);
	for(i = 0; i &lt; m; i++)
		s_bool[i] = w[i] != 0;
	b_vector p_bool = f.RevSparseHes(n, s_bool);

	hes = f.SparseHessian(x, w, p_bool);
	for(ell = 0; ell &lt; n * n; ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// example using vectors of sets to compute sparsity pattern for Hessian
	s_vector r_set(n);
	for(i = 0; i &lt; n; i++)
		r_set[i].insert(i);
	f.ForSparseJac(n, r_set);
	//
	s_vector s_set(m);
	for(i = 0; i &lt; m; i++)
		if( w[i] != 0. )
			s_set[0].insert(i);
	s_vector p_set = f.RevSparseHes(n, s_set);

	// example passing sparsity pattern to SparseHessian
	hes = f.SparseHessian(x, w, p_set);
	for(ell = 0; ell &lt; n * n; ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// use row and column indices to specify upper triangle of
	// non-zero elements of Hessian
	size_t K = n + 1;
	i_vector row(K), col(K);
	hes.resize(K);
	k = 0;
	for(j = 0; j &lt; n; j++)
	{	// diagonal of Hessian
		row[k] = j;
		col[k] = j;
		k++;
	}
	// only off diagonal non-zero elemenet in upper triangle
	row[k] = 0;
	col[k] = 1;
	k++;
	ok &amp;= k == K;
	CppAD::sparse_hessian_work work;

	// can use p_set or p_bool.
	size_t n_sweep = f.SparseHessian(x, w, p_set, row, col, hes, work);
	for(k = 0; k &lt; K; k++)
	{	ell = row[k] * n + col[k];
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(w[0] * check[ell], hes[k], eps, eps );
	}
	ok &amp;= n_sweep == 2;

	// now recompute at a different x and w (using work from previous call
	w[0]       = 2.0;
	x[1]       = 0.5;
	ell        = 1 * n + 1;
	check[ell] = 6.0 * x[1];
	n_sweep    = f.SparseHessian(x, w, p_set, row, col, hes, work);
	for(k = 0; k &lt; K; k++)
	{	ell = row[k] * n + col[k];
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(w[0] * check[ell], hes[k], eps, eps );
	}
	ok &amp;= n_sweep == 2;
	


	return ok;
}
</pre>

</font></code>


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

</body>
</html>