\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

rev_sparse_jac.cpp

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Reverse Mode Jacobian Sparsity: Example and Test

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------
// define the template function BoolCases<Vector>
template <class 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 <class 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;
}