Using ColPack: Example and Test
Keywords: using colpack: example test colpack hessian sparse

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Using ColPack: Example and Test
`

    # include <cppad/cppad.hpp>
    bool colpack_hes(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    	typedef CPPAD_TESTVECTOR(double)     d_vector;
    	typedef CppAD::vector<size_t>        i_vector;
    	size_t i, j, k, ell;
    	double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    	// domain space vector
    	size_t n = 5;
    	a_vector  a_x(n);
    	for(j = 0; j < n; j++)
    		a_x[j] = AD<double> (0);

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

    	// colpack example case where hessian is a spear head
    	// i.e, H(i, j) non zero implies i = 0, j = 0, or i = j
    	AD<double> sum = 0.0;
    	// partial_0 partial_j = x[j]
    	// partial_j partial_j = x[0]
    	for(j = 1; j < n; j++)
    		sum += a_x[0] * a_x[j] * a_x[j] / 2.0;
    	//
    	// partial_i partial_i = 2 * x[i]
    	for(i = 0; i < n; i++)
    		sum += a_x[i] * a_x[i] * a_x[i] / 3.0;

    	// declare dependent variables
    	size_t m = 1;
    	a_vector  a_y(m);
    	a_y[0] = sum;

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

    	// new value for the independent variable vector
    	d_vector x(n);
    	for(j = 0; j < n; j++)
    		x[j] = double(j + 1);

    	/*
    	      [ 2  2  3  4  5 ]
    	hes = [ 2  5  0  0  0 ]
    	      [ 3  0  7  0  0 ]
    	      [ 4  0  0  9  0 ]
    	      [ 5  0  0  0 11 ]
    	*/
    	d_vector check(n * n);
    	for(i = 0; i < n; i++)
    	{	for(j = 0; j < n; j++)
    		{	size_t index = i * n + j;
    			check[index] = 0.0;
    			if( i == 0 && 1 <= j )
    				check[index] += x[j];
    			if( 1 <= i && j == 0 )
    				check[index] += x[i];
    			if( i == j )
    			{	check[index] += 2.0 * x[i];
    				if( i != 0 )
    					check[index] += x[0];
    			}
    		}
    	}
    	// Normally one would use f.RevSparseHes to compute
    	// sparsity pattern, but for this example we extract it from check.
    	std::vector< std::set<size_t> >  p(n);
    	i_vector row, col;
    	for(i = 0; i < n; i++)
    	{	for(j = 0; j < n; j++)
    		{	ell = i * n + j;
    			if( check[ell] != 0. )
    			{	// insert this non-zero entry in sparsity pattern
    				p[i].insert(j);

    				// the Hessian is symmetric, so only upper lower triangle
    				if( j <= i )
    				{	row.push_back(i);
    					col.push_back(j);
    				}
    			}
    		}
    	}
    	size_t K = row.size();
    	d_vector hes(K);

    	// contrast and check results using both cppad and colpack
    	CppAD::sparse_hessian_work work;
    	for(size_t i_method = 0; i_method < 3; i_method++)
    	{	// empty work structure
    		ok &= work.color_method == "cppad.symmetric";
    		if( i_method == 2 )
    			work.color_method = "colpack.star";

    		// compute Hessian
    		d_vector w(m);
    		w[0] = 1.0;
    		size_t n_sweep = f.SparseHessian(x, w, p, row, col, hes, work);

    		// check result
    		for(k = 0; k < K; k++)
    		{	ell = row[k] * n + col[k];
    			ok &= NearEqual(check[ell], hes[k], eps, eps);
    		}
    		if( work.color_method != "cppad.general" )
    			ok &= n_sweep == 2;
    		else
    			ok &= n_sweep == 5;
    		//
    		// check that clear resets color_method to cppad.symmetric
    		work.clear();
    		ok &= work.color_method == "cppad.symmetric";
    	}

    	return ok;
    }

`

Input File: example/colpack_hes.cpp