<?xml version='1.0'?> <?xml-stylesheet type='text/xsl' href='pmathml.xsl'?> <html xmlns='http://www.w3.org/1999/xhtml'> <head> <title>AD Unary Minus Operator</title> <meta name="description" id="description" content="AD Unary Minus Operator"/> <meta name="keywords" id="keywords" content=" unary Ad minus operator - "/> <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='_unaryminus_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="unaryplus.cpp.xml" target="_top">Prev</a> </td><td><a href="unaryminus.cpp.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> 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onchange='choose_down0(this)'> <option>UnaryMinus-></option> <option>UnaryMinus.cpp</option> </select> </td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Syntax</option> <option>Purpose</option> <option>Base</option> <option>x</option> <option>y</option> <option>Operation Sequence</option> <option>Derivative</option> <option>Example</option> </select> </td> </tr></table><br/> <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><font color="blue"></font></code><i><span style='white-space: nowrap'>y</span></i><code><font color="blue"><span style='white-space: nowrap'> = - </span></font></code><i><span style='white-space: nowrap'>x</span></i> <br/> <br/> <b><big><a name="Purpose" id="Purpose">Purpose</a></big></b> <br/> Computes the negative of <i>x</i>. <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> <i>Base</i> object. <br/> <br/> <b><big><a name="x" id="x">x</a></big></b> <br/> The operand <i>x</i> has one of the following prototypes <code><font color="blue"><span style='white-space: nowrap'><br/>      const AD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>               &</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>      const VecAD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>::reference &</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><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 <i>y</i> has type <code><font color="blue"><span style='white-space: nowrap'><br/>      AD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>> </span></font></code><i><span style='white-space: nowrap'>y</span></i><code><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code>It is equal to the negative of the operand <i>x</i>. <br/> <br/> <b><big><a name="Operation Sequence" id="Operation Sequence">Operation Sequence</a></big></b> <br/> This is an AD of <i>Base</i> <a href="glossary.xml#Operation.Atomic" target="_top"><span style='white-space: nowrap'>atomic operation</span></a> and hence is part of the current AD of <i>Base</i> <a href="glossary.xml#Operation.Sequence" target="_top"><span style='white-space: nowrap'>operation 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 function</span></a> , <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mfrac><mrow><mo stretchy="false">∂</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">∂</mo> <mi mathvariant='italic'>x</mi> </mrow> </mfrac> <mo stretchy="false">=</mo> <mo stretchy="false">-</mo> <mfrac><mrow><mo stretchy="false">∂</mo> <mi mathvariant='italic'>f</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow><mo stretchy="false">∂</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="unaryminus.cpp.xml" target="_top"><span style='white-space: nowrap'>UnaryMinus.cpp</span></a> contains an example and test of this operation. <hr/>Input File: cppad/local/unary_minus.hpp </body> </html>