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First Order Partial Driver: Example and Test
 
# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------
// define the template function ForOneCases<Vector> in empty namespace
template <typename Vector> 
bool ForOneCases()
{	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;
	CPPAD_TEST_VECTOR< AD<double> >  X(n);
	X[0] = 1.;
	X[1] = 2.;

	// declare independent variables and starting recording
	CppAD::Independent(X);

	// range space vector
	size_t m = 3;
	CPPAD_TEST_VECTOR< AD<double> >  Y(m);
	Y[0] = X[0] * exp( X[1] );
	Y[1] = X[0] * sin( X[1] );
	Y[2] = X[0] * cos( X[1] );

	// create f: X -> Y and stop tape recording
	CppAD::ADFun<double> f(X, Y);

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

	// compute partial of y w.r.t x[0]
	Vector dy(m);
	dy  = f.ForOne(x, 0);
	ok &= NearEqual( dy[0], exp(x[1]), 1e-10, 1e-10 ); // for y[0]
	ok &= NearEqual( dy[1], sin(x[1]), 1e-10, 1e-10 ); // for y[1]
	ok &= NearEqual( dy[2], cos(x[1]), 1e-10, 1e-10 ); // for y[2]

	// compute partial of F w.r.t x[1]
	dy  = f.ForOne(x, 1);
	ok &= NearEqual( dy[0],  x[0]*exp(x[1]), 1e-10, 1e-10 );
	ok &= NearEqual( dy[1],  x[0]*cos(x[1]), 1e-10, 1e-10 );
	ok &= NearEqual( dy[2], -x[0]*sin(x[1]), 1e-10, 1e-10 );

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

Input File: example/for_one.cpp