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<center><b><big><big>AD Unary Minus Operator</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'>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'>x</span></font></i></code>



<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Computes the negative of 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
.

<br/>
<br/>
<b><big><a name="Base" id="Base">Base</a></big></b>
<br/>
The operation in the syntax above must be supported for the case where
the operand is a <code><font color="blue">const</font></code> 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 object.

<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 one of the following prototypes

<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;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#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/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;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&#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 result 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 has 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'>y</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is equal to the negative of the operand 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
.

<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="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>

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

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

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

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

contains an example and test of this operation.


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

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