# 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;
}