Interpolation With Out Retaping: Example and Test
Keywords: interpolation with out retaping: example test interpolate tape retape see also

| Prev | Next |  |  |  |  |  | interp_onetape.cpp |

Interpolation With Out Retaping: Example and Test
See Also
interp_retape.cpp `
` `

    # include <cppad/cppad.hpp>
    # include <cassert>
    # include <cmath>

    namespace {
    	double ArgumentValue[] = {
    		.0 ,
    		.2 ,
    		.4 ,
    		.8 ,
    		1.
    	};
    	double FunctionValue[] = {
    		std::sin( ArgumentValue[0] ) ,
    		std::sin( ArgumentValue[1] ) ,
    		std::sin( ArgumentValue[2] ) ,
    		std::sin( ArgumentValue[3] ) ,
    		std::sin( ArgumentValue[4] )
    	};
    	size_t TableLength = 5;

    	size_t Index(const double &x)
    	{	// determine the index j such that x is between
    		// ArgumentValue[j] and ArgumentValue[j+1]
    		static size_t j = 0;
    		while ( x < ArgumentValue[j] && j > 0 )
    			j--;
    		while ( x > ArgumentValue[j+1] && j < TableLength - 2)
    			j++;
    		// assert conditions that must be true given logic above
    		assert( j >= 0 && j < TableLength - 1 );
    		return j;
    	}

    	double Argument(const double &x)
    	{	size_t j = Index(x);
    		return ArgumentValue[j];
    	}
    	double Function(const double &x)
    	{	size_t j = Index(x);
    		return FunctionValue[j];
    	}

    	double Slope(const double &x)
    	{	size_t j  = Index(x);
    		double dx = ArgumentValue[j+1] - ArgumentValue[j];
    		double dy = FunctionValue[j+1] - FunctionValue[j];
    		return dy / dx;
    	}
    	CPPAD_DISCRETE_FUNCTION(double, Argument)
    	CPPAD_DISCRETE_FUNCTION(double, Function)
    	CPPAD_DISCRETE_FUNCTION(double, Slope)
    }

    bool interp_onetape(void)
    {	bool ok = true;

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

    	// domain space vector
    	size_t n = 1;
    	CPPAD_TESTVECTOR(AD<double>) X(n);
    	X[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2];

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

    	// evaluate piecewise linear interpolant at X[0]
    	AD<double> A = Argument(X[0]);
    	AD<double> F = Function(X[0]);
    	AD<double> S = Slope(X[0]);
    	AD<double> I = F + (X[0] - A) * S;

    	// range space vector
    	size_t m = 1;
    	CPPAD_TESTVECTOR(AD<double>) Y(m);
    	Y[0] = I;

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

    	// vectors for arguments to the function object f
    	CPPAD_TESTVECTOR(double) x(n);   // argument values
    	CPPAD_TESTVECTOR(double) y(m);   // function values
    	CPPAD_TESTVECTOR(double) dx(n);  // differentials in x space
    	CPPAD_TESTVECTOR(double) dy(m);  // differentials in y space

    	// to check function value we use the fact that X[0] is between
    	// ArgumentValue[1] and ArgumentValue[2]
    	x[0]          = Value(X[0]);
    	double delta  = ArgumentValue[2] - ArgumentValue[1];
    	double check  = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta
    	              + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta;
    	ok  &= NearEqual(Y[0], check, 1e-10, 1e-10);

    	// evaluate f where x has different value
    	x[0]   = .7 * ArgumentValue[2] + .3 * ArgumentValue[3];
    	y      = f.Forward(0, x);

    	// check function value
    	delta  = ArgumentValue[3] - ArgumentValue[2];
    	check  = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta
    	              + FunctionValue[2] * (ArgumentValue[3] - x[0]) / delta;
    	ok  &= NearEqual(y[0], check, 1e-10, 1e-10);

    	// evaluate partials w.r.t. x[0]
    	dx[0] = 1.;
    	dy    = f.Forward(1, dx);

    	// check that the derivative is the slope
    	check = (FunctionValue[3] - FunctionValue[2])
    	      / (ArgumentValue[3] - ArgumentValue[2]);
    	ok   &= NearEqual(dy[0], check, 1e-10, 1e-10);

    	return ok;
    }

`

Input File: example/interp_onetape.cpp