Codebase list cppad / upstream/2015.00.00.7 doc / atomic_base.xml
upstream/2015.00.00.7

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

atomic_base.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
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>User Defined Atomic AD Functions</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="User Defined Atomic AD Functions"/>
<meta name="keywords" id="keywords" content=" user defined atomic ad functions function operation syntax purpose virtual examples getting started scalar vector range hessian sparsity patterns general case "/>
<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='_atomic_base_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="checkpoint.cpp.xml" target="_top">Prev</a>
</td><td><a href="atomic_ctor.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>atomic</option>
<option>atomic_base</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>AD-&gt;</option>
<option>ad_ctor</option>
<option>ad_assign</option>
<option>Convert</option>
<option>ADValued</option>
<option>BoolValued</option>
<option>VecAD</option>
<option>base_require</option>
</select>
</td>
<td>
<select onchange='choose_down2(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_down1(this)'>
<option>atomic-&gt;</option>
<option>checkpoint</option>
<option>atomic_base</option>
</select>
</td>
<td>
<select onchange='choose_down0(this)'>
<option>atomic_base-&gt;</option>
<option>atomic_ctor</option>
<option>atomic_option</option>
<option>atomic_afun</option>
<option>atomic_forward</option>
<option>atomic_reverse</option>
<option>atomic_for_sparse_jac</option>
<option>atomic_rev_sparse_jac</option>
<option>atomic_rev_sparse_hes</option>
<option>atomic_base_clear</option>
<option>atomic_get_started.cpp</option>
<option>atomic_norm_sq.cpp</option>
<option>atomic_reciprocal.cpp</option>
<option>atomic_tangent.cpp</option>
<option>atomic_hes_sparse.cpp</option>
<option>atomic_mat_mul.cpp</option>
</select>
</td>
<td>
<select onchange='choose_current0(this)'>
<option>Headings-&gt;</option>
<option>Syntax</option>
<option>Purpose</option>
<option>Virtual Functions</option>
<option>Contents</option>
<option>Examples</option>
<option>---..Getting Started</option>
<option>---..Scalar Function</option>
<option>---..Vector Range</option>
<option>---..Hessian Sparsity Patterns</option>
<option>General Case</option>
</select>
</td>
</tr></table><br/>



<center><b><big><big>User Defined Atomic AD Functions</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>


<br/>

<code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>atomic_user</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>use_set</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>user_arg_list</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>ax</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ay</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.forward(</span></font><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>vx</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>vy</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>tx</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ty</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.reverse(</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>tx</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ty</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>px</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>py</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.for_sparse_jac(</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>r</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.rev_sparse_jac(</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>r</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.rev_sparse_hes(</span></font><i><font color="black"><span style='white-space: nowrap'>vx</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>t</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>r</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>u</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>v</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
atomic_base&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;::clear()</span></font></code>


<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
In some cases, the user knows how to compute derivatives of a function 

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mi mathvariant='italic'>y</mi>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mspace width='.3em'/>
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>where</mi>
</mstyle></mrow>
<mspace width='.3em'/>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">:</mo>
<msup><mi mathvariant='italic'>B</mi>
<mi mathvariant='italic'>n</mi>
</msup>
<mo stretchy="false">&#x02192;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mi mathvariant='italic'>m</mi>
</msup>
</mrow></math>

more efficiently than by coding it using 
<code><font color="blue"><span style='white-space: nowrap'>AD&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;</span></font></code>
 
<a href="glossary.xml#Operation.Atomic" target="_top"><span style='white-space: nowrap'>atomic</span></a>
 operations
and letting CppAD do the rest.
In this case 
<code><font color="blue"><span style='white-space: nowrap'>atomic_base</span></font><i><font color="black"><span style='white-space: nowrap'>&lt;</span></font></i><font color="blue"><span style='white-space: nowrap'>Base</span></font><i><font color="black"><span style='white-space: nowrap'>&gt;</span></font></i></code>
 can use
the user code for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

, and its derivatives,
as 
<code><font color="blue"><span style='white-space: nowrap'>AD&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;</span></font></code>
 atomic operations. 

<br/>
<br/>
<b><big><a name="Virtual Functions" id="Virtual Functions">Virtual Functions</a></big></b>
<br/>
User defined derivatives are implemented by defining the
following virtual functions in the 
<code><i><font color="black"><span style='white-space: nowrap'>base_atomic</span></font></i></code>
 class:
<a href="atomic_forward.xml" target="_top"><span style='white-space: nowrap'>forward</span></a>
,
<a href="atomic_reverse.xml" target="_top"><span style='white-space: nowrap'>reverse</span></a>
,
<a href="atomic_for_sparse_jac.xml" target="_top"><span style='white-space: nowrap'>for_sparse_jac</span></a>
,
<a href="atomic_rev_sparse_jac.xml" target="_top"><span style='white-space: nowrap'>rev_sparse_jac</span></a>
, and
<a href="atomic_rev_sparse_hes.xml" target="_top"><span style='white-space: nowrap'>rev_sparse_hes</span></a>
.
These virtual functions have a default implementation
that returns 
<code><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;false</span></font></code>
.
The <code><font color="blue">forward</font></code> function, 
for the case 
<code><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;0</span></font></code>
, must be implemented.
Otherwise, only those functions
required by the your calculations need to be implemented. 
For example, 

<code><i><font color="black"><span style='white-space: nowrap'>forward</span></font></i></code>
 for the case 
<code><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;2</span></font></code>
 can just return

<code><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;false</span></font></code>
 unless you require
forward mode calculation of second derivatives.

<br/>
<br/>
<b><big><a name="Contents" id="Contents">Contents</a></big></b>
<br/>
<table>
<tr><td><a href="atomic_ctor.xml" target="_top">atomic_ctor</a></td><td>Atomic&#xA0;Function&#xA0;Constructor</td></tr><tr><td><a href="atomic_option.xml" target="_top">atomic_option</a></td><td>Set&#xA0;Atomic&#xA0;Function&#xA0;Options</td></tr><tr><td><a href="atomic_afun.xml" target="_top">atomic_afun</a></td><td>Using&#xA0;AD&#xA0;Version&#xA0;of&#xA0;Atomic&#xA0;Function</td></tr><tr><td><a href="atomic_forward.xml" target="_top">atomic_forward</a></td><td>Atomic&#xA0;Forward&#xA0;Mode</td></tr><tr><td><a href="atomic_reverse.xml" target="_top">atomic_reverse</a></td><td>Atomic&#xA0;Reverse&#xA0;Mode</td></tr><tr><td><a href="atomic_for_sparse_jac.xml" target="_top">atomic_for_sparse_jac</a></td><td>Atomic&#xA0;Forward&#xA0;Jacobian&#xA0;Sparsity&#xA0;Patterns</td></tr><tr><td><a href="atomic_rev_sparse_jac.xml" target="_top">atomic_rev_sparse_jac</a></td><td>Atomic&#xA0;Reverse&#xA0;Jacobian&#xA0;Sparsity&#xA0;Patterns</td></tr><tr><td><a href="atomic_rev_sparse_hes.xml" target="_top">atomic_rev_sparse_hes</a></td><td>Atomic&#xA0;Reverse&#xA0;Hessian&#xA0;Sparsity&#xA0;Patterns</td></tr><tr><td><a href="atomic_base_clear.xml" target="_top">atomic_base_clear</a></td><td>Free&#xA0;Static&#xA0;Variables</td></tr><tr><td><a href="atomic_get_started.cpp.xml" target="_top">atomic_get_started.cpp</a></td><td>Getting&#xA0;Started&#xA0;with&#xA0;Atomic&#xA0;Operations:&#xA0;Example&#xA0;and&#xA0;Test</td></tr><tr><td><a href="atomic_norm_sq.cpp.xml" target="_top">atomic_norm_sq.cpp</a></td><td>Euclidean&#xA0;Norm&#xA0;Squared:&#xA0;Example&#xA0;and&#xA0;Test</td></tr><tr><td><a href="atomic_reciprocal.cpp.xml" target="_top">atomic_reciprocal.cpp</a></td><td>Reciprocal&#xA0;as&#xA0;an&#xA0;Atomic&#xA0;Operation:&#xA0;Example&#xA0;and&#xA0;Test</td></tr><tr><td><a href="atomic_tangent.cpp.xml" target="_top">atomic_tangent.cpp</a></td><td>Tan&#xA0;and&#xA0;Tanh&#xA0;as&#xA0;User&#xA0;Atomic&#xA0;Operations:&#xA0;Example&#xA0;and&#xA0;Test</td></tr><tr><td><a href="atomic_hes_sparse.cpp.xml" target="_top">atomic_hes_sparse.cpp</a></td><td>Atomic&#xA0;Operation&#xA0;Hessian&#xA0;Sparsity:&#xA0;Example&#xA0;and&#xA0;Test</td></tr><tr><td><a href="atomic_mat_mul.cpp.xml" target="_top">atomic_mat_mul.cpp</a></td><td>User&#xA0;Atomic&#xA0;Matrix&#xA0;Multiply:&#xA0;Example&#xA0;and&#xA0;Test</td></tr></table><br/>
<b><big><a name="Examples" id="Examples">Examples</a></big></b>


<br/>
<br/>
<b><a name="Examples.Getting Started" id="Examples.Getting Started">Getting Started</a></b>
<br/>
The file <a href="atomic_get_started.cpp.xml" target="_top"><span style='white-space: nowrap'>atomic_get_started.cpp</span></a>
 contains an example and test
that shows the minimal amount of information required to create
a user defined atomic operation.

<br/>
<br/>
<b><a name="Examples.Scalar Function" id="Examples.Scalar Function">Scalar Function</a></b>
<br/>
The file <a href="atomic_reciprocal.cpp.xml" target="_top"><span style='white-space: nowrap'>atomic_reciprocal.cpp</span></a>
 contains an example and test
where the user provides the code for computing derivatives.
This example is simple because the domain and range are scalars.

<br/>
<br/>
<b><a name="Examples.Vector Range" id="Examples.Vector Range">Vector Range</a></b>
<br/>
The file <a href="atomic_tangent.cpp.xml" target="_top"><span style='white-space: nowrap'>atomic_tangent.cpp</span></a>
 contains another example
where the user provides the code for computing derivatives.
This example is more complex because the range has two components.

<br/>
<br/>
<b><a name="Examples.Hessian Sparsity Patterns" id="Examples.Hessian Sparsity Patterns">Hessian Sparsity Patterns</a></b>
<br/>
The file <a href="atomic_hes_sparse.cpp.xml" target="_top"><span style='white-space: nowrap'>atomic_hes_sparse.cpp</span></a>
 contains an minimal example
where the user provides the code for computing Hessian sparsity patterns.

<br/>
<br/>
<b><big><a name="General Case" id="General Case">General Case</a></big></b>
<br/>
The file <a href="atomic_mat_mul.cpp.xml" target="_top"><span style='white-space: nowrap'>atomic_mat_mul.cpp</span></a>
 contains a more general example
where the user provides the code for computing derivatives.
This example is more complex because both the domain and range
dimensions are arbitrary.


<hr/>Input File: omh/atomic_base.omh

</body>
</html>