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<center><b><big><big>The AD Power Function: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/cppad.hpp&gt;
# include &lt;cmath&gt;

bool Pow(void)
{	bool ok = true;

	using CppAD::AD;
	using CppAD::NearEqual;

	// domain space vector
	size_t n  = 2;
	double x = 0.5;
	double y = 2.;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) XY(n);
	XY[0]      = x;
	XY[1]      = y;

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

	// range space vector 
	size_t m = 3;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) Z(m);
	Z[0] = CppAD::pow(XY[0], XY[1]);  // pow(variable, variable)
	Z[1] = CppAD::pow(XY[0], y);      // pow(variable, parameter)
	Z[2] = CppAD::pow(x,     XY[1]);  // pow(parameter, variable)

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

	// check value 
	double check = std::pow(x, y);
	size_t i;
	for(i = 0; i &lt; m; i++)
		ok &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(Z[i] , check,  1e-10 , 1e-10);

	// forward computation of first partial w.r.t. x
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dxy(n);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dz(m);
	dxy[0] = 1.;
	dxy[1] = 0.;
	dz    = f.<a href="forward.xml" target="_top">Forward</a>(1, dxy);
	check = y * std::pow(x, y-1.);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[0], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[1], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[2],    0., 1e-10, 1e-10);

	// forward computation of first partial w.r.t. y
	dxy[0] = 0.;
	dxy[1] = 1.;
	dz    = f.<a href="forward.xml" target="_top">Forward</a>(1, dxy);
	check = std::log(x) * std::pow(x, y);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[0], check, 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[1],    0., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dz[2], check, 1e-10, 1e-10);

	// reverse computation of derivative of z[0] + z[1] + z[2]
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double)  w(m);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dw(n);
	w[0]  = 1.;
	w[1]  = 1.;
	w[2]  = 1.;
	dw    = f.<a href="reverse.xml" target="_top">Reverse</a>(1, w);
	check = y * std::pow(x, y-1.);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0], 2. * check, 1e-10, 1e-10);
	check = std::log(x) * std::pow(x, y);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[1], 2. * check, 1e-10, 1e-10);

	// use a VecAD&lt;Base&gt;::reference object with pow
	CppAD::VecAD&lt;double&gt; v(2);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; zero(0);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; one(1);
	v[zero]           = XY[0];
	v[one]            = XY[1];
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; result = CppAD::pow(v[zero], v[one]);
	ok               &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(result, Z[0], 1e-10, 1e-10);

	return ok;
}

</pre>

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

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