#ifndef _1D_LAGRANGIAN_CC
#define _1D_LAGRANGIAN_CC

// the degree of the Lagrangian elements.
#define DEGREE 4

//mapping from a reference element to a given FE
double map_to_FE(double x, int ele)
{
   return ((ele+x)*h);
}

//mapping from a a given FE to a reference element
double map_from_FE(double x, int ele)
{
   return ((x-ele*h)/h);
}

// the number of local degrees of freedom
int dofs_per_element()
{
   return DEGREE+1;
}

// the mapping of local to global degrees of freedom
void fill_element_dofs(int* array, int ele)
{
   for (int i=0; i<=DEGREE; i++)
      array[i] = DEGREE*ele+i;
}

//the i-th shape function on the reference element
double reference_shape_funct(int index, double x)
{
   double step = 1.0/DEGREE;
   double result = 1;
   for (int i=0; i<=DEGREE; i++)
      if (i!=index)
         result *= (x-i*step)/(index*step-i*step);

   return result;
}

//the x-derivative of the i-th shape function on the reference element
double reference_shape_funct_x(int index, double x)
{
   double step = 1.0/DEGREE;
   double result = 0;
   for (int i=0; i<=DEGREE; i++)
   {
      double prod = 1;
      if (i==index) continue;
      for (int j=0; j<=DEGREE; j++)
         if ((j!=index) && (j!=i))
         prod *= (x-j*step)/(index*step-j*step);
      result += prod / (index*step-i*step);
   }

   return result;
}

// the jacobian of the transformation
//   (i.e. the change of variables in the integral over an element
//      to the reference elemen (unit interval))
double jacobian(double q_point, int ele)
{
   return h;
}


/*********
          NOTE
**********/          
// The following two functions are not needed in general,
//   since we are only working on the reference element.
// I've included them here for clarity.
double shape_funct(double x, int ele, int index)
{
   return reference_shape_funct(index, map_from_FE(x,ele));
}

double shape_funct_x(double x, int ele, int index)
{
   // (1.0/h) = (map_from_FE)' <------------ TODO
   return reference_shape_funct_x(index, map_from_FE(x,ele))*(1.0/h);
}

#endif