AD Binary Multiplication: Example and Test
Keywords: ad binary multiplication: example test * multiply times

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AD Binary Multiplication: Example and Test
`

    # include <cppad/cppad.hpp>

    bool Mul(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;

    	// domain space vector
    	size_t n  = 1;
    	double x0 = .5;
    	CPPAD_TESTVECTOR(AD<double>) x(n);
    	x[0]      = x0;

    	// declare independent variables and start tape recording
    	CppAD::Independent(x);

    	// some binary multiplication operations
    	AD<double> a = x[0] * 1.; // AD<double> * double
    	AD<double> b = a    * 2;  // AD<double> * int
    	AD<double> c = 3.   * b;  // double     * AD<double>
    	AD<double> d = 4    * c;  // int        * AD<double>

    	// range space vector
    	size_t m = 1;
    	CPPAD_TESTVECTOR(AD<double>) y(m);
    	y[0] = x[0] * d;          // AD<double> * AD<double>

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

    	// check value
    	ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0,  1e-10 , 1e-10);

    	// forward computation of partials w.r.t. x[0]
    	CPPAD_TESTVECTOR(double) dx(n);
    	CPPAD_TESTVECTOR(double) dy(m);
    	dx[0] = 1.;
    	dy    = f.Forward(1, dx);
    	ok   &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);

    	// reverse computation of derivative of y[0]
    	CPPAD_TESTVECTOR(double)  w(m);
    	CPPAD_TESTVECTOR(double) dw(n);
    	w[0]  = 1.;
    	dw    = f.Reverse(1, w);
    	ok   &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);

    	// use a VecAD<Base>::reference object with multiplication
    	CppAD::VecAD<double> v(1);
    	AD<double> zero(0);
    	v[zero] = c;
    	AD<double> result = 4 * v[zero];
    	ok     &= (result == d);

    	return ok;
    }

`

Input File: example/mul.cpp