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<center><b><big><big>Reverse Mode Jacobian Sparsity: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'>
# 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;
<a href="test_vector.xml" target="_top">CPPAD_TEST_VECTOR</a>< <a href="ad.xml" target="_top">AD</a><double> > X(n);
X[0] = 0.;
X[1] = 1.;
// declare independent variables and start recording
CppAD::<a href="independent.xml" target="_top">Independent</a>(X);
// range space vector
size_t m = 3;
<a href="test_vector.xml" target="_top">CPPAD_TEST_VECTOR</a>< <a href="ad.xml" target="_top">AD</a><double> > Y(m);
Y[0] = X[0];
Y[1] = X[0] * X[1];
Y[2] = X[1];
// create f: X -> Y and stop tape recording
CppAD::<a href="funconstruct.xml" target="_top">ADFun</a><double> f(X, Y);
// sparsity pattern for the identity matrix
Vector s(m * m);
size_t i, j;
for(i = 0; i < m; i++)
{ for(j = 0; j < m; j++)
s[ i * m + j ] = (i == j);
}
// sparsity pattern for F'(x)
Vector r(m * n);
r = f.RevSparseJac(m, s);
// check values
ok &= (r[ 0 * n + 0 ] == true); // Y[0] does depend on X[0]
ok &= (r[ 0 * n + 1 ] == false); // Y[0] does not depend on X[1]
ok &= (r[ 1 * n + 0 ] == true); // Y[1] does depend on X[0]
ok &= (r[ 1 * n + 1 ] == true); // Y[1] does depend on X[1]
ok &= (r[ 2 * n + 0 ] == false); // Y[2] does not depend on X[0]
ok &= (r[ 2 * n + 1 ] == 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;
<a href="test_vector.xml" target="_top">CPPAD_TEST_VECTOR</a>< <a href="ad.xml" target="_top">AD</a><double> > X(n);
X[0] = 0.;
X[1] = 1.;
// declare independent variables and start recording
CppAD::<a href="independent.xml" target="_top">Independent</a>(X);
// range space vector
size_t m = 3;
<a href="test_vector.xml" target="_top">CPPAD_TEST_VECTOR</a>< <a href="ad.xml" target="_top">AD</a><double> > Y(m);
Y[0] = X[0];
Y[1] = X[0] * X[1];
Y[2] = X[1];
// create f: X -> Y and stop tape recording
CppAD::<a href="funconstruct.xml" target="_top">ADFun</a><double> f(X, Y);
// sparsity pattern for the identity matrix
Vector s(m);
size_t i;
for(i = 0; i < m; i++)
{ assert( s[i].empty() );
s[i].insert(i);
}
// sparsity pattern for F'(x)
Vector r(m);
r = f.RevSparseJac(m, s);
// check values
bool found;
// Y[0] does depend on X[0]
found = r[0].find(0) != r[0].end(); ok &= (found == true);
// Y[0] does not depend on X[1]
found = r[0].find(1) != r[0].end(); ok &= (found == false);
// Y[1] does depend on X[0]
found = r[1].find(0) != r[1].end(); ok &= (found == true);
// Y[1] does depend on X[1]
found = r[1].find(1) != r[1].end(); ok &= (found == true);
// Y[2] does not depend on X[0]
found = r[2].find(0) != r[2].end(); ok &= (found == false);
// Y[2] does depend on X[1]
found = r[2].find(1) != r[2].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;
}
</pre>
</font></code>
<hr/>Input File: example/rev_sparse_jac.cpp
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