// $Id: interp_retape.cpp 3757 2015-11-30 12:03:07Z bradbell $
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin interp_retape.cpp$$
$spell
	Retaping
	retape
$$

$section Interpolation With Retaping: Example and Test$$
$mindex interpolate tape retape$$


$head See Also$$
$cref interp_onetape.cpp$$

$pre

$$
$code
$verbatim%example/interp_retape.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++
# 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 CppAD::AD<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 CppAD::AD<double> &x)
	{	size_t j = Index(x);
		return ArgumentValue[j];
	}
	double Function(const CppAD::AD<double> &x)
	{	size_t j = Index(x);
		return FunctionValue[j];
	}
	double Slope(const CppAD::AD<double> &x)
	{	size_t j  = Index(x);
		double dx = ArgumentValue[j+1] - ArgumentValue[j];
		double dy = FunctionValue[j+1] - FunctionValue[j];
		return dy / dx;
	}
}

bool interp_retape(void)
{	bool ok = true;

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

	// domain space vector
	size_t n = 1;
	CPPAD_TESTVECTOR(AD<double>) X(n);

	// loop over argument values
	size_t k;
	for(k = 0; k < TableLength - 1; k++)
	{
		X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1];

		// declare independent variables and start tape recording
		// (use a different tape for each argument value)
		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[k] and ArgumentValue[k+1]
		double delta, check;
		x[0]   = Value(X[0]);
		delta  = ArgumentValue[k+1] - ArgumentValue[k];
		check  = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta
	               + FunctionValue[k] * (ArgumentValue[k+1]-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[k+1] - FunctionValue[k])
		      / (ArgumentValue[k+1] - ArgumentValue[k]);
		ok   &= NearEqual(dy[0], check, 1e-10, 1e-10);
	}
	return ok;
}

// END C++
