Sparsity Patterns For a Subset of Variables: Example and Test
Keywords: sparsity patterns subset variables: example test see also forsparsejac revsparsehes

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Sparsity Patterns For a Subset of Variables: Example and Test
See Also
sparse_sub_hes.cpp , sub_sparse_hes.cpp .
ForSparseJac
The routine ForSparseJac is used to compute the sparsity for both the full Jacobian (see `s` ) and a subset of the Jacobian (see `s2` ).
RevSparseHes
The routine RevSparseHes is used to compute both sparsity for both the full Hessian (see `h` ) and a subset of the Hessian (see `h2` ). `

    # include <cppad/cppad.hpp>

    bool sparsity_sub(void)
    {	// C++ source code
    	bool ok = true;
    	//
    	using std::cout;
    	using CppAD::vector;
    	using CppAD::AD;
    	using CppAD::vectorBool;

    	size_t n = 4;
    	size_t m = n-1;
    	vector< AD<double> > ax(n), ay(m);
    	for(size_t j = 0; j < n; j++)
    		ax[j] = double(j+1);
    	CppAD::Independent(ax);
    	for(size_t i = 0; i < m; i++)
    		ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]);
    	CppAD::ADFun<double> f(ax, ay);

    	// Evaluate the full Jacobian sparsity pattern for f
    	vectorBool r(n * n), s(m * n);
    	for(size_t j = 0 ; j < n; j++)
    	{	for(size_t i = 0; i < n; i++)
    			r[i * n + j] = (i == j);
    	}
    	s = f.ForSparseJac(n, r);

    	// evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1}
    	vectorBool t(m), h(n * n);
    	for(size_t i = 0; i < m; i++)
    		t[i] = true;
    	h = f.RevSparseHes(n, t);

    	// evaluate the Jacobian sparsity pattern for first n/2 components of x
    	size_t n2 = n / 2;
    	vectorBool r2(n * n2), s2(m * n2);
    	for(size_t j = 0 ; j < n2; j++)
    	{	for(size_t i = 0; i < n; i++)
    			r2[i * n2 + j] = (i == j);
    	}
    	s2 = f.ForSparseJac(n2, r2);

    	// evaluate the sparsity for the subset of Hessian of
    	// f_0 + ... + f_{m-1} where first partial has only first n/2 components
    	vectorBool h2(n2 * n);
    	h2 = f.RevSparseHes(n2, t);

    	// check sparsity pattern for Jacobian
    	for(size_t i = 0; i < m; i++)
    	{	for(size_t j = 0; j < n2; j++)
    			ok &= s2[i * n2 + j] == s[i * n + j];
    	}

    	// check sparsity pattern for Hessian
    	for(size_t i = 0; i < n2; i++)
    	{	for(size_t j = 0; j < n; j++)
    			ok &= h2[i * n + j] == h[i * n + j];
    	}
    	return ok;
    }

`

Input File: example/sparsity_sub.cpp