Reverse Mode Jacobian Sparsity: Example and Test
Keywords: reverse mode jacobian sparsity: example test Revsparsejac sparsity

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Reverse Mode Jacobian Sparsity: Example and Test
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    # include <cppad/cppad.hpp>
    namespace { // -------------------------------------------------------------
    // define the template function BoolCases<Vector>
    template <typename Vector>  // vector class, elements of type bool
    bool BoolCases(void)
    {	bool ok = true;
    	using CppAD::AD;

    	// domain space vector
    	size_t n = 2;
    	CPPAD_TESTVECTOR(AD<double>) ax(n);
    	ax[0] = 0.;
    	ax[1] = 1.;

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

    	// range space vector
    	size_t m = 3;
    	CPPAD_TESTVECTOR(AD<double>) ay(m);
    	ay[0] = ax[0];
    	ay[1] = ax[0] * ax[1];
    	ay[2] = ax[1];

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

    	// sparsity pattern for the identity matrix
    	Vector r(m * m);
    	size_t i, j;
    	for(i = 0; i < m; i++)
    	{	for(j = 0; j < m; j++)
    			r[ i * m + j ] = (i == j);
    	}

    	// sparsity pattern for F'(x)
    	Vector s(m * n);
    	s = f.RevSparseJac(m, r);

    	// check values
    	ok &= (s[ 0 * n + 0 ] == true);  // y[0] does     depend on x[0]
    	ok &= (s[ 0 * n + 1 ] == false); // y[0] does not depend on x[1]
    	ok &= (s[ 1 * n + 0 ] == true);  // y[1] does     depend on x[0]
    	ok &= (s[ 1 * n + 1 ] == true);  // y[1] does     depend on x[1]
    	ok &= (s[ 2 * n + 0 ] == false); // y[2] does not depend on x[0]
    	ok &= (s[ 2 * n + 1 ] == true);  // y[2] does     depend on x[1]

    	// sparsity pattern for F'(x)^T, note R is the identity, so R^T = R
    	bool transpose = true;
    	Vector st(n * m);
    	st = f.RevSparseJac(m, r, transpose);

    	// check values
    	ok &= (st[ 0 * m + 0 ] == true);  // y[0] does     depend on x[0]
    	ok &= (st[ 1 * m + 0 ] == false); // y[0] does not depend on x[1]
    	ok &= (st[ 0 * m + 1 ] == true);  // y[1] does     depend on x[0]
    	ok &= (st[ 1 * m + 1 ] == true);  // y[1] does     depend on x[1]
    	ok &= (st[ 0 * m + 2 ] == false); // y[2] does not depend on x[0]
    	ok &= (st[ 1 * m + 2 ] == true);  // y[2] does     depend on x[1]

    	return ok;
    }
    // define the template function SetCases<Vector>
    template <typename Vector>  // vector class, elements of type std::set<size_t>
    bool SetCases(void)
    {	bool ok = true;
    	using CppAD::AD;

    	// domain space vector
    	size_t n = 2;
    	CPPAD_TESTVECTOR(AD<double>) ax(n);
    	ax[0] = 0.;
    	ax[1] = 1.;

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

    	// range space vector
    	size_t m = 3;
    	CPPAD_TESTVECTOR(AD<double>) ay(m);
    	ay[0] = ax[0];
    	ay[1] = ax[0] * ax[1];
    	ay[2] = ax[1];

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

    	// sparsity pattern for the identity matrix
    	Vector r(m);
    	size_t i;
    	for(i = 0; i < m; i++)
    	{	assert( r[i].empty() );
    		r[i].insert(i);
    	}

    	// sparsity pattern for F'(x)
    	Vector s(m);
    	s = f.RevSparseJac(m, r);

    	// check values
    	bool found;

    	// y[0] does     depend on x[0]
    	found = s[0].find(0) != s[0].end();  ok &= (found == true);
    	// y[0] does not depend on x[1]
    	found = s[0].find(1) != s[0].end();  ok &= (found == false);
    	// y[1] does     depend on x[0]
    	found = s[1].find(0) != s[1].end();  ok &= (found == true);
    	// y[1] does     depend on x[1]
    	found = s[1].find(1) != s[1].end();  ok &= (found == true);
    	// y[2] does not depend on x[0]
    	found = s[2].find(0) != s[2].end();  ok &= (found == false);
    	// y[2] does     depend on x[1]
    	found = s[2].find(1) != s[2].end();  ok &= (found == true);

    	// sparsity pattern for F'(x)^T
    	bool transpose = true;
    	Vector st(n);
    	st = f.RevSparseJac(m, r, transpose);

    	// y[0] does     depend on x[0]
    	found = st[0].find(0) != st[0].end();  ok &= (found == true);
    	// y[0] does not depend on x[1]
    	found = st[1].find(0) != st[1].end();  ok &= (found == false);
    	// y[1] does     depend on x[0]
    	found = st[0].find(1) != st[0].end();  ok &= (found == true);
    	// y[1] does     depend on x[1]
    	found = st[1].find(1) != st[1].end();  ok &= (found == true);
    	// y[2] does not depend on x[0]
    	found = st[0].find(2) != st[0].end();  ok &= (found == false);
    	// y[2] does     depend on x[1]
    	found = st[1].find(2) != st[1].end();  ok &= (found == true);

    	return ok;
    }
    } // End empty namespace
    # include <vector>
    # include <valarray>
    bool RevSparseJac(void)
    {	bool ok = true;
    	// Run with Vector equal to four different cases
    	// all of which are Simple Vectors with elements of type bool.
    	ok &= BoolCases< CppAD::vectorBool     >();
    	ok &= BoolCases< CppAD::vector  <bool> >();
    	ok &= BoolCases< std::vector    <bool> >();
    	ok &= BoolCases< std::valarray  <bool> >();

    	// Run with Vector equal to two different cases both of which are
    	// Simple Vectors with elements of type std::set<size_t>
    	typedef std::set<size_t> set;
    	ok &= SetCases< CppAD::vector  <set> >();
    	ok &= SetCases< std::vector    <set> >();

    	// Do not use valarray because its element access in the const case
    	// returns a copy instead of a reference
    	// ok &= SetCases< std::valarray  <set> >();

    	return ok;
    }

`

Input File: example/rev_sparse_jac.cpp