# include <cppad/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/thread_alloc.hpp>
# include <cppad/speed/sparse_evaluate.hpp>

# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/drivers/drivers.h>

bool link_sparse_hessian(
	size_t                     repeat   , 
	CppAD::vector<double>     &x_arg    ,
	CppAD::vector<size_t>     &i        ,
	CppAD::vector<size_t>     &j        ,
	CppAD::vector<double>     &h        )
{
	// -----------------------------------------------------
	// setup
	size_t k, m;
	size_t order = 0;         // derivative order corresponding to function
	size_t tag  = 0;          // tape identifier
	size_t keep = 1;          // keep forward mode results in buffer
	size_t n = x_arg.size();  // number of independent variables
	size_t ell = i.size();    // number of indices in i and j
	double f;                 // function value

	// use thread_alloc memory allocator (fast and checks for leaks)
	using CppAD::thread_alloc; // the allocator
	size_t capacity;           // capacity of an allocation

	typedef CppAD::vector<double>  DblVector;
	typedef CppAD::vector<adouble> ADVector;
	typedef CppAD::vector<size_t>  SizeVector;

	ADVector   X(n);    // AD domain space vector
	ADVector   Y(1);    // AD range space value
	DblVector tmp(2 * ell);       // double temporary vector

	// double version of domain space vector
	double* x  = thread_alloc::create_array<double>(n, capacity);
	// Hessian as computed by adolc
	double** H = thread_alloc::create_array<double*>(n, capacity);
	for(k = 0; k < n; k++)
		H[k] = thread_alloc::create_array<double>(n, capacity);

	// choose a value for x 
	CppAD::uniform_01(n, x);
	for(k = 0; k < n; k++)
		x_arg[k] = x[k];

	// ------------------------------------------------------
	while(repeat--)
	{
		// get the next set of indices
		CppAD::uniform_01(2 * ell, tmp);
		for(k = 0; k < ell; k++)
		{	i[k] = size_t( n * tmp[k] );
			i[k] = std::min(n-1, i[k]);
			//
			j[k] = size_t( n * tmp[k + ell] );
			j[k] = std::min(n-1, j[k]);
		}

		// declare independent variables
		trace_on(tag, keep);
		for(k = 0; k < n; k++)
			X[k] <<= x[k];

		// AD computation of f(x)
		CppAD::sparse_evaluate(X, i, j, order, Y);

		// create function object f : X -> Y
		Y[0] >>= f;
		trace_off();

		// evaluate and return the hessian of f
		hessian(int(tag), int(n), x, H);
	}
	for(k = 0; k < n; k++)
	{	for(m = 0; m <= k; m++)
		{	h[ k * n + m] = H[k][m];
			h[ m * n + k] = H[k][m];
		}
		thread_alloc::delete_array(H[k]);
	}
	thread_alloc::delete_array(H);
	thread_alloc::delete_array(x);
	return true;
}