// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------

/*
Old example / test
@begin bool_sparsity.cpp$$
$spell
   Bool
$$

$section Using vectorBool Sparsity To Conserve Memory: Example and Test$$

$head Purpose$$
This example show how to conserve memory when computing sparsity patterns.

$srcthisfile%0%// BEGIN C++%// END C++%1%$$

@end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace {
   using CppAD::vector;
   using std::cout;
   using CppAD::vectorBool;
   using CppAD::AD;
   using CppAD::ADFun;

   // function f(x) that we are computing sparsity patterns for
   template <class Float>
   vector<Float> fun(const vector<Float>& x)
   {  size_t n  = x.size();
      vector<Float> ret(n + 1);
      for(size_t j = 0; j < n; j++)
      {  size_t k = (j + 1) % n;
         ret[j] = x[j] * x[j] * x[k];
      }
      ret[n] = 0.0;
      return ret;
   }
   // check sparsity pattern for f(x)
   bool check_jac(const vectorBool& pattern, size_t n)
   {  bool ok = true;
      for(size_t i = 0; i < n; i++)
      {  size_t k = (i + 1) % n;
         for(size_t j = 0; j < n; j++)
         {  bool non_zero = (i == j) || (j == k);
            ok &= pattern[ i * n + j] == non_zero;
         }
      }
      for(size_t j = 0; j < n; j++)
         ok &= pattern[ n * n + j] == false;
      return ok;
   }
   // check sparsity pattern for the Hessian of sum_i f_i(x)
   bool check_hes(const vectorBool& pattern, size_t n)
   {  bool ok = true;
      for(size_t i = 0; i < n; i++)
      {  size_t k1 = (i + 1) % n;
         size_t k2 = (n + i - 1) % n;
         for(size_t j = 0; j < n; j++)
         {  bool non_zero = (i == j) || (j == k1) || (j == k2);
            ok &= pattern[ i * n + j] == non_zero;
         }
      }
      return ok;
   }
   // compute sparsity for Jacobian of f(x) using forward mode
   bool for_sparse_jac(ADFun<double>& f)
   {  bool ok = true;
      size_t n = f.Domain();
      size_t m = f.Range();
      //
      // number of columns of the sparsity patter to compute at a time
      size_t n_col = vectorBool::bit_per_unit();
      vectorBool pattern(m * n), s(m * n_col), r(n * n_col);
      //
      size_t n_loop = (n - 1) / n_col + 1;
      for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
      {  size_t j_col = i_loop * n_col;

         for(size_t i = 0; i < n; i++)
         {  for(size_t j = 0; j < n_col; j++)
               r[i * n_col + j] = (i == j_col + j);
         }
         s = f.ForSparseJac(n_col, r);
         for(size_t i = 0; i < m; i++)
         {  for(size_t j = 0; j < n_col; j++)
               if( j_col + j < n )
                  pattern[ i * n + j_col + j ] = s[ i * n_col + j];
         }
      }
      ok &= check_jac(pattern, n);
      //
      return ok;
   }
   // compute sparsity for Jacobian of f(x) using reverse mode
   bool rev_sparse_jac(ADFun<double>& f)
   {  bool ok = true;
      size_t n = f.Domain();
      size_t m = f.Range();
      //
      // number of rows of the sparsity patter to compute at a time
      size_t n_row = vectorBool::bit_per_unit();
      vectorBool pattern(m * n), s(n_row * n), r(n_row * m);
      //
      size_t n_loop = (m - 1) / n_row + 1;
      for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
      {  size_t i_row = i_loop * n_row;

         for(size_t i = 0; i < n_row; i++)
         {  for(size_t j = 0; j < m; j++)
               r[i * m + j] = (i_row + i == j);
         }
         s = f.RevSparseJac(n_row, r);
         for(size_t i = 0; i < n_row; i++)
         {  for(size_t j = 0; j < n; j++)
               if( i_row + i < m )
                  pattern[ (i_row + i) * n + j ] = s[ i * n + j];
         }
      }
      ok &= check_jac(pattern, n);
      //
      return ok;
   }
   // compute sparsity for Hessian of sum_i f_i (x)
   bool rev_sparse_hes(ADFun<double>& f)
   {  bool ok = true;
      size_t n = f.Domain();
      size_t m = f.Range();
      //
      // number of columns of the sparsity patter to compute at a time
      size_t n_col = vectorBool::bit_per_unit();
      vectorBool pattern(n * n), r(n * n_col), h(n * n_col);

      // consider case where Hessian for sum of f_i(x) w.r.t i
      vectorBool s(m);
      for(size_t i = 0; i < m; i++)
         s[i] = true;
      //
      size_t n_loop = (n - 1) / n_col + 1;
      for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
      {  size_t j_col = i_loop * n_col;

         for(size_t i = 0; i < n; i++)
         {  for(size_t j = 0; j < n_col; j++)
               r[i * n_col + j] = (i == j_col + j);
         }
         //
         f.ForSparseJac(n_col, r);
         bool transpose = true;
         h = f.RevSparseHes(n_col, s, transpose);
         //
         for(size_t i = 0; i < n; i++)
         {  for(size_t j = 0; j < n_col; j++)
               if( j_col + j < n )
                  pattern[ i * n + j_col + j ] = h[ i * n_col + j];
         }
      }
      ok &= check_hes(pattern, n);
      //
      return ok;
   }
}
// driver for all of the cases above
bool bool_sparsity(void)
{  bool ok = true;
   //
   // record the funcion
   size_t n = 100;
   size_t m = n + 1;
   vector< AD<double> > x(n), y(m);
   for(size_t j = 0; j < n; j++)
      x[j] = AD<double>(j+1);
   CppAD::Independent(x);
   y = fun(x);
   ADFun<double> f(x, y);
   //
   // run the three example / tests
   ok &= for_sparse_jac(f);
   ok &= rev_sparse_jac(f);
   ok &= rev_sparse_hes(f);
   return ok;
}
// END C++
