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

sparse_hes_fun.hpp

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Source: sparse_hes_fun

# ifndef CPPAD_SPARSE_HES_FUN_HPP

# define CPPAD_SPARSE_HES_FUN_HPP

# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_numeric_type.hpp>
# include <cppad/utility/vector.hpp>

// following needed by gcc under fedora 17 so that exp(double) is defined
# include <cppad/base_require.hpp>

namespace CppAD {
   template <class Float, class FloatVector>
   void sparse_hes_fun(
      size_t                       n    ,
      const FloatVector&           x    ,
      const CppAD::vector<size_t>& row  ,
      const CppAD::vector<size_t>& col  ,
      size_t                       p    ,
      FloatVector&                fp    )
   {
      // check numeric type specifications
      CheckNumericType<Float>();

      // check value of p
      CPPAD_ASSERT_KNOWN(
         p == 0 || p == 2,
         "sparse_hes_fun: p != 0 and p != 2"
      );

      size_t K = row.size();
      size_t i, j, k;
      if( p == 0 )
         fp[0] = Float(0);
      else
      {  for(k = 0; k < K; k++)
            fp[k] = Float(0);
      }

      // determine which diagonal entries are present in row[k], col[k]
      CppAD::vector<size_t> diagonal(n);
      for(i = 0; i < n; i++)
         diagonal[i] = K;   // no diagonal entry for this row
      for(k = 0; k < K; k++)
      {  if( row[k] == col[k] )
         {  CPPAD_ASSERT_UNKNOWN( diagonal[row[k]] == K );
            // index of the diagonal entry
            diagonal[ row[k] ] = k;
         }
      }

      // determine which entries must be multiplied by a factor of two
      CppAD::vector<Float> factor(K);
      for(k = 0; k < K; k++)
      {  factor[k] = Float(1);
         for(size_t k1 = 0; k1 < K; k1++)
         {  bool reflected = true;
            reflected &= k != k1;
            reflected &= row[k] != col[k];
            reflected &= row[k] == col[k1];
            reflected &= col[k] == row[k1];
            if( reflected )
               factor[k] = Float(2);
         }
      }

      Float t;
      for(k = 0; k < K; k++)
      {  i    = row[k];
         j    = col[k];
         t    = exp( x[i] * x[j] );
         switch(p)
         {
            case 0:
            fp[0] += t;
            break;

            case 2:
            if( i == j )
            {  // second partial of t w.r.t. x[i], x[i]
               fp[k] += ( Float(2) + Float(4) * x[i] * x[i] ) * t;
            }
            else // (i != j)
            {  //
               // second partial of t w.r.t x[i], x[j]
               fp[k] += factor[k] * ( Float(1) + x[i] * x[j] ) * t;
               if( diagonal[i] != K )
               {  // second partial of t w.r.t x[i], x[i]
                  size_t ki = diagonal[i];
                  fp[ki] += x[j] * x[j] * t;
               }
               if( diagonal[j] != K )
               {  // second partial of t w.r.t x[j], x[j]
                  size_t kj = diagonal[j];
                  fp[kj] += x[i] * x[i] * t;
               }
            }
            break;
         }
      }

   }
}

# endif