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<center><b><big><big>First Order Reverse Mode: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
# include &lt;cppad/cppad.hpp&gt;
namespace { // ----------------------------------------------------------
// define the template function reverse_one_cases&lt;Vector&gt; in empty namespace
template &lt;typename Vector&gt; 
bool reverse_one_cases(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;

	// domain space vector
	size_t n = 2;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) X(n);
	X[0] = 0.; 
	X[1] = 1.;

	// declare independent variables and start recording
	CppAD::<a href="independent.xml" target="_top">Independent</a>(X);

	// range space vector
	size_t m = 1;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) Y(m);
	Y[0] = X[0] * X[0] * X[1];

	// create f : X -&gt; Y and stop recording
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f(X, Y);

	// use first order reverse mode to evaluate derivative of y[0]
	// and use the values in X for the independent variables.
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) w(m), dw(n);
	w[0] = 1.;
	dw   = f.<a href="reverse.xml" target="_top">Reverse</a>(1, w);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0] , 2.*X[0]*X[1], 1e-10, 1e-10);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[1] ,    X[0]*X[0], 1e-10, 1e-10);

	// use zero order forward mode to evaluate y at x = (3, 4)
	// and use the template parameter Vector for the vector type
	Vector x(n), y(m);
	x[0]    = 3.;
	x[1]    = 4.;
	y       = f.<a href="forward.xml" target="_top">Forward</a>(0, x);
	ok     &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y[0] , x[0]*x[0]*x[1], 1e-10, 1e-10);

	// use first order reverse mode to evaluate derivative of y[0]
	// and using the values in x for the independent variables.
	w[0] = 1.;
	dw   = f.<a href="reverse.xml" target="_top">Reverse</a>(1, w);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0] , 2.*x[0]*x[1], 1e-10, 1e-10);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[1] ,    x[0]*x[0], 1e-10, 1e-10);

	return ok;
}
} // End empty namespace 
# include &lt;vector&gt;
# include &lt;valarray&gt;
bool reverse_one(void)
{	bool ok = true;
	// Run with Vector equal to three different cases
	// all of which are Simple Vectors with elements of type double.
	ok &amp;= reverse_one_cases&lt; CppAD::vector  &lt;double&gt; &gt;();
	ok &amp;= reverse_one_cases&lt; std::vector    &lt;double&gt; &gt;();
	ok &amp;= reverse_one_cases&lt; std::valarray  &lt;double&gt; &gt;();
	return ok;
}
</pre>

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<hr/>Input File: example/reverse_one.cpp

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