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<center><b><big><big>AD Computed Assignment Operators</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>

<br/>

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


<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Performs computed assignment operations 
where either 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 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="Op" id="Op">Op</a></big></b>
<br/>
The operator 
<code><i><font color="black"><span style='white-space: nowrap'>Op</span></font></i></code>
 is one of the following
<table><tr><td align='left'  valign='top'>

<b>Op</b>  </td><td align='left'  valign='top'>
 <b>Meaning</b> </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">+=</font></code>   </td><td align='left'  valign='top'>
 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is assigned 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 plus 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">-=</font></code>   </td><td align='left'  valign='top'>
 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is assigned 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 minus 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">*=</font></code>   </td><td align='left'  valign='top'>
 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is assigned 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 times 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">/=</font></code>   </td><td align='left'  valign='top'>
 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is assigned 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 divided by 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 
</td></tr>
</table>
<br/>
<b><big><a name="Base" id="Base">Base</a></big></b>
<br/>
The type 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 is determined by the operand 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
.

<br/>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The operand 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 has the following 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;&amp;</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>
<br/>
<b><big><a name="y" id="y">y</a></big></b>
<br/>
The operand 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 has the following 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'>Type</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&amp;</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>
where 
<code><i><font color="black"><span style='white-space: nowrap'>Type</span></font></i></code>
 is

<code><font color="blue"><span style='white-space: nowrap'>VecAD&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;::reference</span></font></code>
,

<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>
,

<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
, or
<code><font color="blue">double</font></code>.

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


<br/>
The result of this assignment 
can be used as a reference to 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
.
For example, if 
<code><i><font color="black"><span style='white-space: nowrap'>z</span></font></i></code>
 has the following type

<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'>z</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
then the syntax

<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'>z</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;+=&#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>
will compute 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 plus 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>

and then assign this value to both 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>z</span></font></i></code>
. 


<br/>
<br/>
<b><big><a name="Operation Sequence" id="Operation Sequence">Operation Sequence</a></big></b>
<br/>
This is an <a href="glossary.xml#Operation.Atomic" target="_top"><span style='white-space: nowrap'>atomic</span></a>

<a href="glossary.xml#AD of Base" target="_top"><span style='white-space: nowrap'>AD&#xA0;of&#xA0;Base</span></a>
 operation
and hence it 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="Example" id="Example">Example</a></big></b>
<br/>
The following files contain examples and tests of these functions.
Each test returns true if it succeeds and false otherwise.
<table><tr><td align='left'  valign='top'>

<a href="addeq.cpp.xml" target="_top">AddEq.cpp</a></td><td>
AD Computed Assignment Addition: Example and Test</td></tr>
<tr><td>

<a href="sub_eq.cpp.xml" target="_top">sub_eq.cpp</a></td><td>
AD Computed Assignment Subtraction: Example and Test</td></tr>
<tr><td>

<a href="mul_eq.cpp.xml" target="_top">mul_eq.cpp</a></td><td>
AD Computed Assignment Multiplication: Example and Test</td></tr>
<tr><td>

<a href="div_eq.cpp.xml" target="_top">div_eq.cpp</a></td><td>
AD Computed Assignment Division: Example and Test</td></tr>
<tr><td>

</td></tr>
</table>
<br/>
<b><big><a name="Derivative" id="Derivative">Derivative</a></big></b>
<br/>
If 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
</mrow></math>

 and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>g</mi>
</mrow></math>

 are 
<a href="glossary.xml#Base Function" target="_top"><span style='white-space: nowrap'>Base&#xA0;functions</span></a>


<br/>
<br/>
<b><a name="Derivative.Addition" id="Derivative.Addition">Addition</a></b>


<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">+</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">=</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">+</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
</mrow></math>

<br/>
<b><a name="Derivative.Subtraction" id="Derivative.Subtraction">Subtraction</a></b>


<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">-</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">=</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">-</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
</mrow></math>

<br/>
<b><a name="Derivative.Multiplication" id="Derivative.Multiplication">Multiplication</a></b>


<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">*</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">*</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">+</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">*</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
</mrow></math>

<br/>
<b><a name="Derivative.Division" id="Derivative.Division">Division</a></b>


<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">/</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">=</mo>
<mo stretchy="false">[</mo>
<mn>1</mn>
<mo stretchy="false">/</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
<mo stretchy="false">*</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
<mo stretchy="false">-</mo>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">/</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<msup><mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
<mo stretchy="false">]</mo>
<mo stretchy="false">*</mo>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>g</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
</mrow>
</mfrac>
</mrow></math>


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

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