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

for_jac_sparsity.cpp

View page source

Forward Mode Jacobian Sparsity: Example and Test

# include <cppad/cppad.hpp>

bool for_jac_sparsity(void)
{  bool ok = true;
   using CppAD::AD;
   typedef CPPAD_TESTVECTOR(size_t)     SizeVector;
   typedef CppAD::sparse_rc<SizeVector> sparsity;
   //
   // 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
   size_t nr     = n;
   size_t nc     = n;
   size_t nnz_in = n;
   sparsity pattern_in(nr, nc, nnz_in);
   for(size_t k = 0; k < nnz_in; k++)
   {  size_t r = k;
      size_t c = k;
      pattern_in.set(k, r, c);
   }
   //
   // Compute sparsity pattern for J(x) = F'(x)
   bool transpose       = false;
   bool dependency      = false;
   bool internal_bool   = false;
   sparsity pattern_out;
   f.for_jac_sparsity(
      pattern_in, transpose, dependency, internal_bool, pattern_out
   );
   size_t nnz = pattern_out.nnz();
   ok        &= nnz == 4;
   ok        &= pattern_out.nr() == m;
   ok        &= pattern_out.nc() == n;
   {  // check results
      const SizeVector& row( pattern_out.row() );
      const SizeVector& col( pattern_out.col() );
      SizeVector col_major = pattern_out.col_major();
      //
      ok &= row[ col_major[0] ] ==  0  && col[ col_major[0] ] ==  0;
      ok &= row[ col_major[1] ] ==  1  && col[ col_major[1] ] ==  0;
      ok &= row[ col_major[2] ] ==  1  && col[ col_major[2] ] ==  1;
      ok &= row[ col_major[3] ] ==  2  && col[ col_major[3] ] ==  1;
      //
      // check that set and not boolean values are stored
      ok &= (f.size_forward_set() > 0);
      ok &= (f.size_forward_bool() == 0);
   }
   //
   // note that the transpose of the identity is the identity
   transpose     = true;
   internal_bool = true;
   f.for_jac_sparsity(
      pattern_in, transpose, dependency, internal_bool, pattern_out
   );
   nnz  = pattern_out.nnz();
   ok  &= nnz == 4;
   ok  &= pattern_out.nr() == n;
   ok  &= pattern_out.nc() == m;
   {  // check results
      const SizeVector& row( pattern_out.row() );
      const SizeVector& col( pattern_out.col() );
      SizeVector row_major = pattern_out.row_major();
      //
      ok &= col[ row_major[0] ] ==  0  && row[ row_major[0] ] ==  0;
      ok &= col[ row_major[1] ] ==  1  && row[ row_major[1] ] ==  0;
      ok &= col[ row_major[2] ] ==  1  && row[ row_major[2] ] ==  1;
      ok &= col[ row_major[3] ] ==  2  && row[ row_major[3] ] ==  1;
      //
      // check that set and not boolean values are stored
      ok &= (f.size_forward_set() == 0);
      ok &= (f.size_forward_bool() > 0);
   }
   return ok;
}