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<center><b><big><big>Second Partials Reverse Driver: 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 in empty namespace
// bool RevTwoCases&lt;VectorBase, VectorSize_t&gt;(void)
template &lt;class VectorBase, class VectorSize_t&gt; 
bool RevTwoCases()
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	using CppAD::exp;
	using CppAD::sin;
	using CppAD::cos;

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

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

	// a calculation between the domain and range values
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; Square = X[0] * X[0];

	// range space vector
	size_t m = 3;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;)  Y(m);
	Y[0] = Square * exp( X[1] );
	Y[1] = Square * sin( X[1] );
	Y[2] = Square * cos( X[1] );

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

	// new value for the independent variable vector
	VectorBase x(n);
	x[0] = 2.;
	x[1] = 1.;

	// set i and j to compute specific second partials of y
	size_t p = 2;
	VectorSize_t i(p);
	VectorSize_t j(p);
	i[0] = 0; j[0] = 0; // for partials y[0] w.r.t x[0] and x[k]
	i[1] = 1; j[1] = 1; // for partials y[1] w.r.t x[1] and x[k]

	// compute the second partials
	VectorBase ddw(n * p);
	ddw = f.RevTwo(x, i, j);

	// partials of y[0] w.r.t x[0] is 2 * x[0] * exp(x[1])
	// check partials of y[0] w.r.t x[0] and x[k] for k = 0, 1 
	ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(      2.*exp(x[1]), ddw[0*p+0], 1e-10, 1e-10 );
	ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>( 2.*x[0]*exp(x[1]), ddw[1*p+0], 1e-10, 1e-10 );

	// partials of y[1] w.r.t x[1] is x[0] * x[0] * cos(x[1])
	// check partials of F_1 w.r.t x[1] and x[k] for k = 0, 1 
	ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(    2.*x[0]*cos(x[1]), ddw[0*p+1], 1e-10, 1e-10 );
	ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>( -x[0]*x[0]*sin(x[1]), ddw[1*p+1], 1e-10, 1e-10 );

	return ok;
}
} // End empty namespace 
# include &lt;vector&gt;
# include &lt;valarray&gt;
bool RevTwo(void)
{	bool ok = true;
        // Run with VectorBase equal to three different cases
        // all of which are Simple Vectors with elements of type double.
	ok &amp;= RevTwoCases&lt; CppAD::vector &lt;double&gt;, std::vector&lt;size_t&gt; &gt;();
	ok &amp;= RevTwoCases&lt; std::vector   &lt;double&gt;, std::vector&lt;size_t&gt; &gt;();
	ok &amp;= RevTwoCases&lt; std::valarray &lt;double&gt;, std::vector&lt;size_t&gt; &gt;();

        // Run with VectorSize_t equal to two other cases
        // which are Simple Vectors with elements of type size_t.
	ok &amp;= RevTwoCases&lt; std::vector &lt;double&gt;, CppAD::vector&lt;size_t&gt; &gt;();
	ok &amp;= RevTwoCases&lt; std::vector &lt;double&gt;, std::valarray&lt;size_t&gt; &gt;();

	return ok;
}
</pre>

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

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