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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Discrete AD Functions</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Discrete AD Functions"/>
<meta name="keywords" id="keywords" content=" discrete ad functions Ad function syntax purpose base name x y ax ay create version Cppad_discrete_function operation sequence derivatives parallel mode example deprecated Cppadcreatediscrete "/>
<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='_discrete_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="cond_exp.cpp.xml" target="_top">Prev</a>
</td><td><a href="tape_index.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>AD</option>
<option>ADValued</option>
<option>Discrete</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>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_down1(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_down0(this)'>
<option>Discrete-&gt;</option>
<option>tape_index.cpp</option>
<option>interp_onetape.cpp</option>
<option>interp_retape.cpp</option>
</select>
</td>
<td>
<select onchange='choose_current0(this)'>
<option>Headings-&gt;</option>
<option>Syntax</option>
<option>Purpose</option>
<option>Base</option>
<option>name</option>
<option>x</option>
<option>y</option>
<option>ax</option>
<option>ay</option>
<option>Create AD Version</option>
<option>Operation Sequence</option>
<option>Derivatives</option>
<option>Parallel Mode</option>
<option>Example</option>
<option>Deprecated</option>
</select>
</td>
</tr></table><br/>



<center><b><big><big>Discrete 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'>CPPAD_DISCRETE_FUNCTION(</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>name</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>name</span></font></i><font color="blue"><span style='white-space: nowrap'>(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>ay</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>name</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'>)<br/>
</span></font></code>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Record the evaluation of a discrete function as part
of an 
<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.Sequence" target="_top"><span style='white-space: nowrap'>operation&#xA0;sequence</span></a>
.
The value of a discrete function can depend on the
<a href="glossary.xml#Tape.Independent Variable" target="_top"><span style='white-space: nowrap'>independent&#xA0;variables</span></a>
,
but its derivative is identically zero.
For example, suppose that the integer part of 
a <a href="glossary.xml#Variable" target="_top"><span style='white-space: nowrap'>variable</span></a>
 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is the 
index into an array of values. 

<br/>
<br/>
<b><big><a name="Base" id="Base">Base</a></big></b>
<br/>
This is the 
<a href="base_require.xml" target="_top"><span style='white-space: nowrap'>base&#xA0;type</span></a>

corresponding to the operations sequence;
i.e., use of the 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>
 with arguments of type

<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>
 can be recorded in an operation sequence.

<br/>
<br/>
<b><big><a name="name" id="name">name</a></big></b>
<br/>
This is the name of the function (as it is used in the source code).
The user must provide a version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>

where the argument has type 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
.
CppAD uses this to create a version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>

where the argument has type 
<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>
.

<br/>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is the value at which the user provided version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>

is to be evaluated.

<br/>
<br/>
<b><big><a name="y" id="y">y</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is the return value for the user provided version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>
.

<br/>
<br/>
<b><big><a name="ax" id="ax">ax</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>ax</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;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;&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ax</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is the value at which the CppAD provided version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>

is to be evaluated.

<br/>
<br/>
<b><big><a name="ay" id="ay">ay</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>ay</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;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;&#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></code>
It is the return value for the CppAD provided version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>
.


<br/>
<br/>
<b><big><a name="Create AD Version" id="Create AD Version">Create AD Version</a></big></b>

<br/>
The preprocessor macro invocation

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;CPPAD_DISCRETE_FUNCTION(</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>name</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>
defines the 
<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>
 version of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>
.
This can be with in a namespace (not the <code><font color="blue">CppAD</font></code> namespace) 
but must be outside of any routine.

<br/>
<br/>
<b><big><a name="Operation Sequence" id="Operation Sequence">Operation Sequence</a></big></b>
<br/>
This is an AD of 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>

<a href="glossary.xml#Operation.Atomic" target="_top"><span style='white-space: nowrap'>atomic&#xA0;operation</span></a>

and hence is part of the current
AD of 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>

<a href="glossary.xml#Operation.Sequence" target="_top"><span style='white-space: nowrap'>operation&#xA0;sequence</span></a>
.

<br/>
<br/>
<b><big><a name="Derivatives" id="Derivatives">Derivatives</a></big></b>
<br/>
During a zero order <a href="forward.xml" target="_top"><span style='white-space: nowrap'>Forward</span></a>
 operation,
an <a href="adfun.xml" target="_top"><span style='white-space: nowrap'>ADFun</span></a>
 object will compute the value of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>

using the user provided 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 version of this routine.
All the derivatives of 
<code><i><font color="black"><span style='white-space: nowrap'>name</span></font></i></code>
 will be evaluated as zero.

<br/>
<br/>
<b><big><a name="Parallel Mode" id="Parallel Mode">Parallel Mode</a></big></b>


<br/>
The first call to 

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ay</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>name</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'>)<br/>
</span></font></code>
must not be in <a href="ta_in_parallel.xml" target="_top"><span style='white-space: nowrap'>parallel</span></a>
 execution mode.
	

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

<br/>
The file
<a href="tape_index.cpp.xml" target="_top"><span style='white-space: nowrap'>tape_index.cpp</span></a>

contains an example and test that uses a discrete function 
to vary an array index during <a href="forward.xml" target="_top"><span style='white-space: nowrap'>Forward</span></a>
 mode calculations.
The file
<a href="interp_onetape.cpp.xml" target="_top"><span style='white-space: nowrap'>interp_onetape.cpp</span></a>

contains an example and test that uses discrete
functions to avoid retaping a calculation that requires interpolation.
(The file
<a href="interp_retape.cpp.xml" target="_top"><span style='white-space: nowrap'>interp_retape.cpp</span></a>

shows how interpolation can be done with retaping.)

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


<br/>
The preprocessor symbol <code><font color="blue">CppADCreateDiscrete</font></code>
is defined to be the same as <code><font color="blue">CPPAD_DISCRETE_FUNCTION</font></code>
but its use is deprecated.


<hr/>Input File: cppad/local/discrete.hpp

</body>
</html>