// This code conforms with the UFC specification version 1.5.0
// and was automatically generated by FFC version 1.5.0.
//
// This code was generated with the option '-l dolfin' and
// contains DOLFIN-specific wrappers that depend on DOLFIN.
// 
// This code was generated with the following parameters:
// 
//   cache_dir:                      ''
//   convert_exceptions_to_warnings: False
//   cpp_optimize:                   True
//   cpp_optimize_flags:             '-O2'
//   epsilon:                        1e-14
//   error_control:                  False
//   form_postfix:                   True
//   format:                         'dolfin'
//   log_level:                      20
//   log_prefix:                     ''
//   optimize:                       True
//   output_dir:                     '.'
//   precision:                      15
//   quadrature_degree:              'auto'
//   quadrature_rule:                'auto'
//   representation:                 'auto'
//   restrict_keyword:               ''
//   split:                          False

#ifndef __MTH_H
#define __MTH_H

#include <cmath>
#include <stdexcept>
#include <fstream>
#include <ufc.h>

/// This class defines the interface for a finite element.

class mth_finite_element_0: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_0() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_0()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None)";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 3;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 0;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    return 1;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    *values = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values = 0.0;
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 3; r++)
    {
      _evaluate_basis(r, &dof_values, x, vertex_coordinates, cell_orientation);
      values[r] = dof_values;
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[2][1];
    for (unsigned int row = 0; row < 2; row++)
    {
      for (unsigned int col = 0; col < 1; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[2][2];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 3; r++)
    {
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[2];
    for (unsigned int r = 0; r < 2; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 3; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0];
    vertex_values[1] = dof_values[1];
    vertex_values[2] = dof_values[2];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 0;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_0();
  }

};

/// This class defines the interface for a finite element.

class mth_finite_element_1: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_1() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_1()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "VectorElement('Lagrange', Domain(Cell('triangle', 2)), 1, 2, None)";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 6;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 1;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return 2;
        break;
      }
    }
    
    return 0;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    values[0] = 0.0;
    values[1] = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values[2] = {0.0, 0.0};
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 6; r++)
    {
      _evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 2; s++)
      {
        values[r*2 + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < 2*num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[2][1];
    for (unsigned int row = 0; row < 2; row++)
    {
      for (unsigned int col = 0; col < 1; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[2][2];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 6; r++)
    {
      for (unsigned int s = 0; s < 2*num_derivatives; s++)
      {
        values[r*2*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[4];
    for (unsigned int r = 0; r < 4; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 6; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 2*num_derivatives; s++)
      {
        values[r*2*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[2];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 3:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 4:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 5:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[2];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[3] = vals[1];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[4] = vals[1];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[5] = vals[1];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0];
    vertex_values[2] = dof_values[1];
    vertex_values[4] = dof_values[2];
    // Evaluate function and change variables
    vertex_values[1] = dof_values[3];
    vertex_values[3] = dof_values[4];
    vertex_values[5] = dof_values[5];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 2;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_finite_element_0();
        break;
      }
    case 1:
      {
        return new mth_finite_element_0();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_1();
  }

};

/// This class defines the interface for a finite element.

class mth_finite_element_2: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_2() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_2()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 2, None)";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 6;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 0;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    return 1;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    *values = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values = 0.0;
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 6; r++)
    {
      _evaluate_basis(r, &dof_values, x, vertex_coordinates, cell_orientation);
      values[r] = dof_values;
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[4][2];
    for (unsigned int row = 0; row < 4; row++)
    {
      for (unsigned int col = 0; col < 2; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[4][4];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 6; r++)
    {
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[4];
    for (unsigned int r = 0; r < 4; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 6; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 3:
      {
        y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 4:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 5:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
    y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[3] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[4] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[5] = vals[0];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0];
    vertex_values[1] = dof_values[1];
    vertex_values[2] = dof_values[2];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 0;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_2();
  }

};

/// This class defines the interface for a finite element.

class mth_finite_element_3: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_3() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_3()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "VectorElement('Lagrange', Domain(Cell('triangle', 2)), 2, 2, None)";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 12;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 1;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return 2;
        break;
      }
    }
    
    return 0;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    values[0] = 0.0;
    values[1] = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 6:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 7:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 8:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 9:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 10:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 11:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values[2] = {0.0, 0.0};
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 12; r++)
    {
      _evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 2; s++)
      {
        values[r*2 + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < 2*num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[4][2];
    for (unsigned int row = 0; row < 4; row++)
    {
      for (unsigned int col = 0; col < 2; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[4][4];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 6:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 7:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 8:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 9:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 10:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 11:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 12; r++)
    {
      for (unsigned int s = 0; s < 2*num_derivatives; s++)
      {
        values[r*2*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[8];
    for (unsigned int r = 0; r < 8; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 12; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 2*num_derivatives; s++)
      {
        values[r*2*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[2];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 3:
      {
        y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 4:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 5:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 6:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 7:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 8:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 9:
      {
        y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 10:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 11:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[2];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
    y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[3] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[4] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[5] = vals[0];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[6] = vals[1];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[7] = vals[1];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[8] = vals[1];
    y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[9] = vals[1];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[10] = vals[1];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[11] = vals[1];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0];
    vertex_values[2] = dof_values[1];
    vertex_values[4] = dof_values[2];
    // Evaluate function and change variables
    vertex_values[1] = dof_values[6];
    vertex_values[3] = dof_values[7];
    vertex_values[5] = dof_values[8];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 2;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_finite_element_2();
        break;
      }
    case 1:
      {
        return new mth_finite_element_2();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_3();
  }

};

/// This class defines the interface for a finite element.

class mth_finite_element_4: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_4() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_4()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "EnrichedElement(FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None), FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2)), 0, None))";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 4;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 0;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    return 1;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    *values = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[1] = {0.0};
      
      // Declare helper variables
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      
      // Table(s) of coefficients
      static const double coefficients0[1] = \
      {1.0};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 1; r++)
      {
        *values += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values = 0.0;
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 4; r++)
    {
      _evaluate_basis(r, &dof_values, x, vertex_coordinates, cell_orientation);
      values[r] = dof_values;
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[2][1];
    for (unsigned int row = 0; row < 2; row++)
    {
      for (unsigned int col = 0; col < 1; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[2][2];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[1] = {0.0};
      
      // Declare helper variables
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      
      // Table(s) of coefficients
      static const double coefficients0[1] = \
      {1.0};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[1][1] = \
      {{0.0}};
      
      static const double dmats1[1][1] = \
      {{0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[2];
      for (unsigned int r = 0; r < 2; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[1][1] = \
      {{1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[1][1] = \
      {{1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 1; t++)
        {
          for (unsigned int u = 0; u < 1; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              for (unsigned int tu = 0; tu < 1; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              for (unsigned int tu = 0; tu < 1; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 1; s++)
        {
          for (unsigned int t = 0; t < 1; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 4; r++)
    {
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 1)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[2];
    for (unsigned int r = 0; r < 2; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 4; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < num_derivatives; s++)
      {
        values[r*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 3:
      {
        y[0] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
      y[1] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[1];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
    y[0] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
    y[1] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[3] = vals[0];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0] + dof_values[3];
    vertex_values[1] = dof_values[1] + dof_values[3];
    vertex_values[2] = dof_values[2] + dof_values[3];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 0;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_4();
  }

};

/// This class defines the interface for a finite element.

class mth_finite_element_5: public ufc::finite_element
{
public:

  /// Constructor
  mth_finite_element_5() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_finite_element_5()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "MixedElement(VectorElement('Lagrange', Domain(Cell('triangle', 2)), 2, 2, None), EnrichedElement(FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None), FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2)), 0, None)), **{'value_shape': (3,) })";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the topological dimension of the cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the finite element function space
  virtual std::size_t space_dimension() const
  {
    return 16;
  }

  /// Return the rank of the value space
  virtual std::size_t value_rank() const
  {
    return 1;
  }

  /// Return the dimension of the value space for axis i
  virtual std::size_t value_dimension(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return 3;
        break;
      }
    }
    
    return 0;
  }

  /// Evaluate basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation)
  {
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Reset values
    values[0] = 0.0;
    values[1] = 0.0;
    values[2] = 0.0;
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[0] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 6:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 7:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 8:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 9:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 10:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 11:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 6; r++)
      {
        values[1] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 12:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[2] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 13:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[2] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 14:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 3; r++)
      {
        values[2] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    case 15:
      {
        
      // Array of basisvalues
      double basisvalues[1] = {0.0};
      
      // Declare helper variables
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      
      // Table(s) of coefficients
      static const double coefficients0[1] = \
      {1.0};
      
      // Compute value(s)
      for (unsigned int r = 0; r < 1; r++)
      {
        values[2] += coefficients0[r]*basisvalues[r];
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis(std::size_t i,
                              double* values,
                              const double* x,
                              const double* vertex_coordinates,
                              int cell_orientation) const
  {
    _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation)
  {
    // Helper variable to hold values of a single dof.
    double dof_values[3] = {0.0, 0.0, 0.0};
    
    // Loop dofs and call evaluate_basis
    for (unsigned int r = 0; r < 16; r++)
    {
      _evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 3; s++)
      {
        values[r*3 + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_all(double* values,
                                  const double* x,
                                  const double* vertex_coordinates,
                                  int cell_orientation) const
  {
    _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation)
  {
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Reset values. Assuming that values is always an array.
    for (unsigned int r = 0; r < 3*num_derivatives; r++)
    {
      values[r] = 0.0;
    } // end loop over 'r'
    
    // Call evaluate_basis if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis(i, values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
    return ;
    }
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    
    // Compute constants
    const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
    const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
    
    // Get coordinates and map to the reference (FIAT) element
    double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
    double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
    
    // Declare two dimensional array that holds combinations of derivatives and initialise
    unsigned int combinations[4][2];
    for (unsigned int row = 0; row < 4; row++)
    {
      for (unsigned int col = 0; col < 2; col++)
        combinations[row][col] = 0;
    }
    
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double transform[4][4];
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    switch (i)
    {
    case 0:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 1:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 2:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 3:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 4:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 5:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 6:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, -0.173205080756888, -0.1, 0.121716123890037, 0.0942809041582064, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 7:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.173205080756888, -0.1, 0.121716123890037, -0.0942809041582063, 0.0544331053951818};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 8:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.0, 0.0, 0.2, 0.0, 0.0, 0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 9:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.23094010767585, 0.133333333333333, 0.0, 0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 10:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791031, -0.23094010767585, 0.133333333333333, 0.0, -0.188561808316413, -0.163299316185545};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 11:
      {
        
      // Array of basisvalues
      double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      double tmp1 = (1.0 - Y)/2.0;
      double tmp2 = tmp1*tmp1;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
      basisvalues[5] = basisvalues[2]*(0.111111111111111 + Y*1.66666666666667) - basisvalues[0]*0.555555555555556;
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[5] *= std::sqrt(1.5);
      basisvalues[1] *= std::sqrt(3.0);
      basisvalues[4] *= std::sqrt(4.5);
      basisvalues[3] *= std::sqrt(7.5);
      
      // Table(s) of coefficients
      static const double coefficients0[6] = \
      {0.471404520791032, 0.0, -0.266666666666667, -0.243432247780074, 0.0, 0.0544331053951817};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 9.48683298050515, 0.0, 0.0, 0.0, 0.0},
      {3.99999999999999, 0.0, 7.07106781186547, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}};
      
      static const double dmats1[6][6] = \
      {{0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0, 0.0, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0, 0.0, 0.0, 0.0},
      {2.58198889747162, 4.74341649025257, -0.912870929175279, 0.0, 0.0, 0.0},
      {1.99999999999991, 6.12372435695794, 3.53553390593273, 0.0, 0.0, 0.0},
      {-2.30940107675849, 0.0, 8.16496580927727, 0.0, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[6][6] = \
      {{1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
      {0.0, 0.0, 0.0, 0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 6; t++)
        {
          for (unsigned int u = 0; u < 6; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 6; t++)
          {
            for (unsigned int u = 0; u < 6; u++)
            {
              for (unsigned int tu = 0; tu < 6; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 6; s++)
        {
          for (unsigned int t = 0; t < 6; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 12:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, -0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 13:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.288675134594813, -0.166666666666667};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 14:
      {
        
      // Array of basisvalues
      double basisvalues[3] = {0.0, 0.0, 0.0};
      
      // Declare helper variables
      double tmp0 = (1.0 + Y + 2.0*X)/2.0;
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      basisvalues[1] = tmp0;
      basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
      basisvalues[0] *= std::sqrt(0.5);
      basisvalues[2] *= std::sqrt(1.0);
      basisvalues[1] *= std::sqrt(3.0);
      
      // Table(s) of coefficients
      static const double coefficients0[3] = \
      {0.471404520791032, 0.0, 0.333333333333333};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[3][3] = \
      {{0.0, 0.0, 0.0},
      {4.89897948556635, 0.0, 0.0},
      {0.0, 0.0, 0.0}};
      
      static const double dmats1[3][3] = \
      {{0.0, 0.0, 0.0},
      {2.44948974278318, 0.0, 0.0},
      {4.24264068711928, 0.0, 0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[3][3] = \
      {{1.0, 0.0, 0.0},
      {0.0, 1.0, 0.0},
      {0.0, 0.0, 1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 3; t++)
        {
          for (unsigned int u = 0; u < 3; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 3; t++)
          {
            for (unsigned int u = 0; u < 3; u++)
            {
              for (unsigned int tu = 0; tu < 3; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 3; s++)
        {
          for (unsigned int t = 0; t < 3; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    case 15:
      {
        
      // Array of basisvalues
      double basisvalues[1] = {0.0};
      
      // Declare helper variables
      
      // Compute basisvalues
      basisvalues[0] = 1.0;
      
      // Table(s) of coefficients
      static const double coefficients0[1] = \
      {1.0};
      
      // Tables of derivatives of the polynomial base (transpose).
      static const double dmats0[1][1] = \
      {{0.0}};
      
      static const double dmats1[1][1] = \
      {{0.0}};
      
      // Compute reference derivatives.
      // Declare array of derivatives on FIAT element.
      double derivatives[4];
      for (unsigned int r = 0; r < 4; r++)
      {
        derivatives[r] = 0.0;
      } // end loop over 'r'
      
      // Declare derivative matrix (of polynomial basis).
      double dmats[1][1] = \
      {{1.0}};
      
      // Declare (auxiliary) derivative matrix (of polynomial basis).
      double dmats_old[1][1] = \
      {{1.0}};
      
      // Loop possible derivatives.
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        // Resetting dmats values to compute next derivative.
        for (unsigned int t = 0; t < 1; t++)
        {
          for (unsigned int u = 0; u < 1; u++)
          {
            dmats[t][u] = 0.0;
            if (t == u)
            {
            dmats[t][u] = 1.0;
            }
            
          } // end loop over 'u'
        } // end loop over 't'
        
        // Looping derivative order to generate dmats.
        for (unsigned int s = 0; s < n; s++)
        {
          // Updating dmats_old with new values and resetting dmats.
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              dmats_old[t][u] = dmats[t][u];
              dmats[t][u] = 0.0;
            } // end loop over 'u'
          } // end loop over 't'
          
          // Update dmats using an inner product.
          if (combinations[r][s] == 0)
          {
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              for (unsigned int tu = 0; tu < 1; tu++)
              {
                dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
          if (combinations[r][s] == 1)
          {
          for (unsigned int t = 0; t < 1; t++)
          {
            for (unsigned int u = 0; u < 1; u++)
            {
              for (unsigned int tu = 0; tu < 1; tu++)
              {
                dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
              } // end loop over 'tu'
            } // end loop over 'u'
          } // end loop over 't'
          }
          
        } // end loop over 's'
        for (unsigned int s = 0; s < 1; s++)
        {
          for (unsigned int t = 0; t < 1; t++)
          {
            derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
          } // end loop over 't'
        } // end loop over 's'
      } // end loop over 'r'
      
      // Transform derivatives back to physical element
      for (unsigned int r = 0; r < num_derivatives; r++)
      {
        for (unsigned int s = 0; s < num_derivatives; s++)
        {
          values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
        } // end loop over 's'
      } // end loop over 'r'
        break;
      }
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives(std::size_t i,
                                          std::size_t n,
                                          double* values,
                                          const double* x,
                                          const double* vertex_coordinates,
                                          int cell_orientation) const
  {
    _evaluate_basis_derivatives(i, n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (actual implementation)
  static void _evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation)
  {
    // Call evaluate_basis_all if order of derivatives is equal to zero.
    if (n == 0)
    {
      _evaluate_basis_all(values, x, vertex_coordinates, cell_orientation);
      return ;
    }
    
    // Compute number of derivatives.
    unsigned int num_derivatives = 1;
    for (unsigned int r = 0; r < n; r++)
    {
      num_derivatives *= 2;
    } // end loop over 'r'
    
    // Set values equal to zero.
    for (unsigned int r = 0; r < 16; r++)
    {
      for (unsigned int s = 0; s < 3*num_derivatives; s++)
      {
        values[r*3*num_derivatives + s] = 0.0;
      } // end loop over 's'
    } // end loop over 'r'
    
    // If order of derivatives is greater than the maximum polynomial degree, return zeros.
    if (n > 2)
    {
      return ;
    }
    
    // Helper variable to hold values of a single dof.
    double dof_values[12];
    for (unsigned int r = 0; r < 12; r++)
    {
      dof_values[r] = 0.0;
    } // end loop over 'r'
    
    // Loop dofs and call evaluate_basis_derivatives.
    for (unsigned int r = 0; r < 16; r++)
    {
      _evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
      for (unsigned int s = 0; s < 3*num_derivatives; s++)
      {
        values[r*3*num_derivatives + s] = dof_values[s];
      } // end loop over 's'
    } // end loop over 'r'
  }

  /// Evaluate order n derivatives of all basis functions at given point x in cell (non-static member function)
  virtual void evaluate_basis_derivatives_all(std::size_t n,
                                              double* values,
                                              const double* x,
                                              const double* vertex_coordinates,
                                              int cell_orientation) const
  {
    _evaluate_basis_derivatives_all(n, values, x, vertex_coordinates, cell_orientation);
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(std::size_t i,
                              const ufc::function& f,
                              const double* vertex_coordinates,
                              int cell_orientation,
                              const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[3];
    
    // Declare variable for physical coordinates
    double y[2];
    switch (i)
    {
    case 0:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 1:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 2:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 3:
      {
        y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 4:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 5:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[0];
        break;
      }
    case 6:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 7:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 8:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 9:
      {
        y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 10:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 11:
      {
        y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
      y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[1];
        break;
      }
    case 12:
      {
        y[0] = vertex_coordinates[0];
      y[1] = vertex_coordinates[1];
      f.evaluate(vals, y, c);
      return vals[2];
        break;
      }
    case 13:
      {
        y[0] = vertex_coordinates[2];
      y[1] = vertex_coordinates[3];
      f.evaluate(vals, y, c);
      return vals[2];
        break;
      }
    case 14:
      {
        y[0] = vertex_coordinates[4];
      y[1] = vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[2];
        break;
      }
    case 15:
      {
        y[0] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
      y[1] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
      f.evaluate(vals, y, c);
      return vals[2];
        break;
      }
    }
    
    return 0.0;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const double* vertex_coordinates,
                             int cell_orientation,
                             const ufc::cell& c) const
  {
    // Declare variables for result of evaluation
    double vals[3];
    
    // Declare variable for physical coordinates
    double y[2];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[0] = vals[0];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[1] = vals[0];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[2] = vals[0];
    y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[3] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[4] = vals[0];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[5] = vals[0];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[6] = vals[1];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[7] = vals[1];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[8] = vals[1];
    y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[9] = vals[1];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[10] = vals[1];
    y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[11] = vals[1];
    y[0] = vertex_coordinates[0];
    y[1] = vertex_coordinates[1];
    f.evaluate(vals, y, c);
    values[12] = vals[2];
    y[0] = vertex_coordinates[2];
    y[1] = vertex_coordinates[3];
    f.evaluate(vals, y, c);
    values[13] = vals[2];
    y[0] = vertex_coordinates[4];
    y[1] = vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[14] = vals[2];
    y[0] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
    y[1] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
    f.evaluate(vals, y, c);
    values[15] = vals[2];
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const double* vertex_coordinates,
                                         int cell_orientation,
                                         const ufc::cell& c) const
  {
    // Evaluate function and change variables
    vertex_values[0] = dof_values[0];
    vertex_values[3] = dof_values[1];
    vertex_values[6] = dof_values[2];
    // Evaluate function and change variables
    vertex_values[1] = dof_values[6];
    vertex_values[4] = dof_values[7];
    vertex_values[7] = dof_values[8];
    // Evaluate function and change variables
    vertex_values[2] = dof_values[12] + dof_values[15];
    vertex_values[5] = dof_values[13] + dof_values[15];
    vertex_values[8] = dof_values[14] + dof_values[15];
  }

  /// Map coordinate xhat from reference cell to coordinate x in cell
  virtual void map_from_reference_cell(double* x,
                                       const double* xhat,
                                       const ufc::cell& c) const
  {
    throw std::runtime_error("map_from_reference_cell not yet implemented.");
  }

  /// Map from coordinate x in cell to coordinate xhat in reference cell
  virtual void map_to_reference_cell(double* xhat,
                                     const double* x,
                                     const ufc::cell& c) const
  {
    throw std::runtime_error("map_to_reference_cell not yet implemented.");
  }

  /// Return the number of sub elements (for a mixed element)
  virtual std::size_t num_sub_elements() const
  {
    return 2;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_finite_element_3();
        break;
      }
    case 1:
      {
        return new mth_finite_element_4();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::finite_element* create() const
  {
    return new mth_finite_element_5();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_0: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_0() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_0()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None)";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return false;
        break;
      }
    case 2:
      {
        return false;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return num_global_entities[0];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 3;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 2;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 1;
        break;
      }
    case 1:
      {
        return 0;
        break;
      }
    case 2:
      {
        return 0;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    dofs[0] = c.entity_indices[0][0];
    dofs[1] = c.entity_indices[0][1];
    dofs[2] = c.entity_indices[0][2];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        
        break;
      }
    case 2:
      {
        
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 0;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_0();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_1: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_1() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_1()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for VectorElement('Lagrange', Domain(Cell('triangle', 2)), 1, 2, None)";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return false;
        break;
      }
    case 2:
      {
        return false;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return 2*num_global_entities[0];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 6;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 4;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 2;
        break;
      }
    case 1:
      {
        return 0;
        break;
      }
    case 2:
      {
        return 0;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    unsigned int offset = 0;
    dofs[0] = offset + c.entity_indices[0][0];
    dofs[1] = offset + c.entity_indices[0][1];
    dofs[2] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[3] = offset + c.entity_indices[0][0];
    dofs[4] = offset + c.entity_indices[0][1];
    dofs[5] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
      dofs[2] = 4;
      dofs[3] = 5;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
      dofs[2] = 3;
      dofs[3] = 5;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 3;
      dofs[3] = 4;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
        dofs[1] = 3;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
        dofs[1] = 4;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
        dofs[1] = 5;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        
        break;
      }
    case 2:
      {
        
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
    dof_coordinates[6] = vertex_coordinates[0];
    dof_coordinates[7] = vertex_coordinates[1];
    dof_coordinates[8] = vertex_coordinates[2];
    dof_coordinates[9] = vertex_coordinates[3];
    dof_coordinates[10] = vertex_coordinates[4];
    dof_coordinates[11] = vertex_coordinates[5];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 2;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_dofmap_0();
        break;
      }
    case 1:
      {
        return new mth_dofmap_0();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_1();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_2: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_2() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_2()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 2, None)";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return true;
        break;
      }
    case 2:
      {
        return false;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return num_global_entities[0] + num_global_entities[1];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 6;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 3;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 1;
        break;
      }
    case 1:
      {
        return 1;
        break;
      }
    case 2:
      {
        return 0;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    unsigned int offset = 0;
    dofs[0] = offset + c.entity_indices[0][0];
    dofs[1] = offset + c.entity_indices[0][1];
    dofs[2] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[3] = offset + c.entity_indices[1][0];
    dofs[4] = offset + c.entity_indices[1][1];
    dofs[5] = offset + c.entity_indices[1][2];
    offset += num_global_entities[1];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
      dofs[2] = 3;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
      dofs[2] = 4;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 5;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 3;
          break;
        }
      case 1:
        {
          dofs[0] = 4;
          break;
        }
      case 2:
        {
          dofs[0] = 5;
          break;
        }
      }
      
        break;
      }
    case 2:
      {
        
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
    dof_coordinates[6] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    dof_coordinates[7] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    dof_coordinates[8] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    dof_coordinates[9] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    dof_coordinates[10] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    dof_coordinates[11] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 0;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_2();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_3: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_3() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_3()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for VectorElement('Lagrange', Domain(Cell('triangle', 2)), 2, 2, None)";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return true;
        break;
      }
    case 2:
      {
        return false;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return 2*num_global_entities[0] + 2*num_global_entities[1];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 12;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 6;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 2;
        break;
      }
    case 1:
      {
        return 2;
        break;
      }
    case 2:
      {
        return 0;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    unsigned int offset = 0;
    dofs[0] = offset + c.entity_indices[0][0];
    dofs[1] = offset + c.entity_indices[0][1];
    dofs[2] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[3] = offset + c.entity_indices[1][0];
    dofs[4] = offset + c.entity_indices[1][1];
    dofs[5] = offset + c.entity_indices[1][2];
    offset += num_global_entities[1];
    dofs[6] = offset + c.entity_indices[0][0];
    dofs[7] = offset + c.entity_indices[0][1];
    dofs[8] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[9] = offset + c.entity_indices[1][0];
    dofs[10] = offset + c.entity_indices[1][1];
    dofs[11] = offset + c.entity_indices[1][2];
    offset += num_global_entities[1];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
      dofs[2] = 3;
      dofs[3] = 7;
      dofs[4] = 8;
      dofs[5] = 9;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
      dofs[2] = 4;
      dofs[3] = 6;
      dofs[4] = 8;
      dofs[5] = 10;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 5;
      dofs[3] = 6;
      dofs[4] = 7;
      dofs[5] = 11;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
        dofs[1] = 6;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
        dofs[1] = 7;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
        dofs[1] = 8;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 3;
        dofs[1] = 9;
          break;
        }
      case 1:
        {
          dofs[0] = 4;
        dofs[1] = 10;
          break;
        }
      case 2:
        {
          dofs[0] = 5;
        dofs[1] = 11;
          break;
        }
      }
      
        break;
      }
    case 2:
      {
        
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
    dof_coordinates[6] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    dof_coordinates[7] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    dof_coordinates[8] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    dof_coordinates[9] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    dof_coordinates[10] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    dof_coordinates[11] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    dof_coordinates[12] = vertex_coordinates[0];
    dof_coordinates[13] = vertex_coordinates[1];
    dof_coordinates[14] = vertex_coordinates[2];
    dof_coordinates[15] = vertex_coordinates[3];
    dof_coordinates[16] = vertex_coordinates[4];
    dof_coordinates[17] = vertex_coordinates[5];
    dof_coordinates[18] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    dof_coordinates[19] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    dof_coordinates[20] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    dof_coordinates[21] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    dof_coordinates[22] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    dof_coordinates[23] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 2;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_dofmap_2();
        break;
      }
    case 1:
      {
        return new mth_dofmap_2();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_3();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_4: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_4() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_4()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for EnrichedElement(FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None), FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2)), 0, None))";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return false;
        break;
      }
    case 2:
      {
        return true;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return num_global_entities[0] + num_global_entities[2];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 4;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 2;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 1;
        break;
      }
    case 1:
      {
        return 0;
        break;
      }
    case 2:
      {
        return 1;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    unsigned int offset = 0;
    dofs[0] = offset + c.entity_indices[0][0];
    dofs[1] = offset + c.entity_indices[0][1];
    dofs[2] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[3] = offset + c.entity_indices[2][0];
    offset += num_global_entities[2];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        
        break;
      }
    case 2:
      {
        if (i > 0)
      {
      throw std::runtime_error("i is larger than number of entities (0)");
      }
      
      dofs[0] = 3;
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
    dof_coordinates[6] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
    dof_coordinates[7] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 0;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_4();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class mth_dofmap_5: public ufc::dofmap
{
public:

  /// Constructor
  mth_dofmap_5() : ufc::dofmap()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_dofmap_5()
  {
    // Do nothing
  }

  /// Return a string identifying the dofmap
  virtual const char* signature() const
  {
    return "FFC dofmap for MixedElement(VectorElement('Lagrange', Domain(Cell('triangle', 2)), 2, 2, None), EnrichedElement(FiniteElement('Lagrange', Domain(Cell('triangle', 2)), 1, None), FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2)), 0, None)), **{'value_shape': (3,) })";
  }

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return true;
        break;
      }
    case 1:
      {
        return true;
        break;
      }
    case 2:
      {
        return true;
        break;
      }
    }
    
    return false;
  }

  /// Return the topological dimension of the associated cell shape
  virtual std::size_t topological_dimension() const
  {
    return 2;
  }

  /// Return the geometric dimension of the associated cell shape
  virtual std::size_t geometric_dimension() const
  {
    return 2;
  }

  /// Return the dimension of the global finite element function space
  virtual std::size_t global_dimension(const std::vector<std::size_t>&
                                       num_global_entities) const
  {
    return 3*num_global_entities[0] + 2*num_global_entities[1] + num_global_entities[2];
  }

  /// Return the dimension of the local finite element function space for a cell
  virtual std::size_t local_dimension() const
  {
    return 16;
  }

  /// Return the number of dofs on each cell facet
  virtual std::size_t num_facet_dofs() const
  {
    return 8;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual std::size_t num_entity_dofs(std::size_t d) const
  {
    switch (d)
    {
    case 0:
      {
        return 3;
        break;
      }
    case 1:
      {
        return 2;
        break;
      }
    case 2:
      {
        return 1;
        break;
      }
    }
    
    return 0;
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(std::size_t* dofs,
                             const std::vector<std::size_t>& num_global_entities,
                             const ufc::cell& c) const
  {
    unsigned int offset = 0;
    dofs[0] = offset + c.entity_indices[0][0];
    dofs[1] = offset + c.entity_indices[0][1];
    dofs[2] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[3] = offset + c.entity_indices[1][0];
    dofs[4] = offset + c.entity_indices[1][1];
    dofs[5] = offset + c.entity_indices[1][2];
    offset += num_global_entities[1];
    dofs[6] = offset + c.entity_indices[0][0];
    dofs[7] = offset + c.entity_indices[0][1];
    dofs[8] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[9] = offset + c.entity_indices[1][0];
    dofs[10] = offset + c.entity_indices[1][1];
    dofs[11] = offset + c.entity_indices[1][2];
    offset += num_global_entities[1];
    dofs[12] = offset + c.entity_indices[0][0];
    dofs[13] = offset + c.entity_indices[0][1];
    dofs[14] = offset + c.entity_indices[0][2];
    offset += num_global_entities[0];
    dofs[15] = offset + c.entity_indices[2][0];
    offset += num_global_entities[2];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(std::size_t* dofs,
                                   std::size_t facet) const
  {
    switch (facet)
    {
    case 0:
      {
        dofs[0] = 1;
      dofs[1] = 2;
      dofs[2] = 3;
      dofs[3] = 7;
      dofs[4] = 8;
      dofs[5] = 9;
      dofs[6] = 13;
      dofs[7] = 14;
        break;
      }
    case 1:
      {
        dofs[0] = 0;
      dofs[1] = 2;
      dofs[2] = 4;
      dofs[3] = 6;
      dofs[4] = 8;
      dofs[5] = 10;
      dofs[6] = 12;
      dofs[7] = 14;
        break;
      }
    case 2:
      {
        dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 5;
      dofs[3] = 6;
      dofs[4] = 7;
      dofs[5] = 11;
      dofs[6] = 12;
      dofs[7] = 13;
        break;
      }
    }
    
  }

  /// Tabulate the local-to-local mapping of dofs on entity (d, i)
  virtual void tabulate_entity_dofs(std::size_t* dofs,
                                    std::size_t d, std::size_t i) const
  {
    if (d > 2)
    {
    throw std::runtime_error("d is larger than dimension (2)");
    }
    
    switch (d)
    {
    case 0:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 0;
        dofs[1] = 6;
        dofs[2] = 12;
          break;
        }
      case 1:
        {
          dofs[0] = 1;
        dofs[1] = 7;
        dofs[2] = 13;
          break;
        }
      case 2:
        {
          dofs[0] = 2;
        dofs[1] = 8;
        dofs[2] = 14;
          break;
        }
      }
      
        break;
      }
    case 1:
      {
        if (i > 2)
      {
      throw std::runtime_error("i is larger than number of entities (2)");
      }
      
      switch (i)
      {
      case 0:
        {
          dofs[0] = 3;
        dofs[1] = 9;
          break;
        }
      case 1:
        {
          dofs[0] = 4;
        dofs[1] = 10;
          break;
        }
      case 2:
        {
          dofs[0] = 5;
        dofs[1] = 11;
          break;
        }
      }
      
        break;
      }
    case 2:
      {
        if (i > 0)
      {
      throw std::runtime_error("i is larger than number of entities (0)");
      }
      
      dofs[0] = 15;
        break;
      }
    }
    
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double* dof_coordinates,
                                    const double* vertex_coordinates) const
  {
    dof_coordinates[0] = vertex_coordinates[0];
    dof_coordinates[1] = vertex_coordinates[1];
    dof_coordinates[2] = vertex_coordinates[2];
    dof_coordinates[3] = vertex_coordinates[3];
    dof_coordinates[4] = vertex_coordinates[4];
    dof_coordinates[5] = vertex_coordinates[5];
    dof_coordinates[6] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    dof_coordinates[7] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    dof_coordinates[8] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    dof_coordinates[9] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    dof_coordinates[10] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    dof_coordinates[11] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    dof_coordinates[12] = vertex_coordinates[0];
    dof_coordinates[13] = vertex_coordinates[1];
    dof_coordinates[14] = vertex_coordinates[2];
    dof_coordinates[15] = vertex_coordinates[3];
    dof_coordinates[16] = vertex_coordinates[4];
    dof_coordinates[17] = vertex_coordinates[5];
    dof_coordinates[18] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
    dof_coordinates[19] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
    dof_coordinates[20] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
    dof_coordinates[21] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
    dof_coordinates[22] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
    dof_coordinates[23] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
    dof_coordinates[24] = vertex_coordinates[0];
    dof_coordinates[25] = vertex_coordinates[1];
    dof_coordinates[26] = vertex_coordinates[2];
    dof_coordinates[27] = vertex_coordinates[3];
    dof_coordinates[28] = vertex_coordinates[4];
    dof_coordinates[29] = vertex_coordinates[5];
    dof_coordinates[30] = 0.333333333333333*vertex_coordinates[0] + 0.333333333333333*vertex_coordinates[2] + 0.333333333333333*vertex_coordinates[4];
    dof_coordinates[31] = 0.333333333333333*vertex_coordinates[1] + 0.333333333333333*vertex_coordinates[3] + 0.333333333333333*vertex_coordinates[5];
  }

  /// Return the number of sub dofmaps (for a mixed element)
  virtual std::size_t num_sub_dofmaps() const
  {
    return 2;
  }

  /// Create a new dofmap for sub dofmap i (for a mixed element)
  virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_dofmap_3();
        break;
      }
    case 1:
      {
        return new mth_dofmap_4();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new class instance
  virtual ufc::dofmap* create() const
  {
    return new mth_dofmap_5();
  }

};

/// This class defines the interface for the tabulation of the cell
/// tensor corresponding to the local contribution to a form from
/// the integral over a cell.

class mth_cell_integral_0_otherwise: public ufc::cell_integral
{
public:

  /// Constructor
  mth_cell_integral_0_otherwise() : ufc::cell_integral()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_cell_integral_0_otherwise()
  {
    // Do nothing
  }

  /// Tabulate which form coefficients are used by this integral
  virtual const std::vector<bool> & enabled_coefficients() const
  {
    static const std::vector<bool> enabled({});
    return enabled;
  }

  /// Tabulate the tensor for the contribution from a local cell
  virtual void tabulate_tensor(double*  A,
                               const double * const *  w,
                               const double*  vertex_coordinates,
                               int cell_orientation) const
  {
    // Number of operations (multiply-add pairs) for Jacobian data:      3
    // Number of operations (multiply-add pairs) for geometry tensor:    32
    // Number of operations (multiply-add pairs) for tensor contraction: 302
    // Total number of operations (multiply-add pairs):                  337
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    // Set scale factor
    const double det = std::abs(detJ);
    
    // Compute geometry tensor
    const double G0_0_0 = det*K[0]*K[0]*(1.0);
    const double G0_0_1 = det*K[0]*K[2]*(1.0);
    const double G0_1_0 = det*K[2]*K[0]*(1.0);
    const double G0_1_1 = det*K[2]*K[2]*(1.0);
    const double G1_0_0 = det*K[0]*K[0]*(1.0);
    const double G1_0_1 = det*K[0]*K[2]*(1.0);
    const double G1_1_0 = det*K[2]*K[0]*(1.0);
    const double G1_1_1 = det*K[2]*K[2]*(1.0);
    const double G2_0_0 = det*K[1]*K[1]*(1.0);
    const double G2_0_1 = det*K[1]*K[3]*(1.0);
    const double G2_1_0 = det*K[3]*K[1]*(1.0);
    const double G2_1_1 = det*K[3]*K[3]*(1.0);
    const double G3_0_0 = det*K[1]*K[1]*(1.0);
    const double G3_0_1 = det*K[1]*K[3]*(1.0);
    const double G3_1_0 = det*K[3]*K[1]*(1.0);
    const double G3_1_1 = det*K[3]*K[3]*(1.0);
    const double G4_0 = det*K[0]*(1.0);
    const double G4_1 = det*K[2]*(1.0);
    const double G5_0 = det*K[1]*(1.0);
    const double G5_1 = det*K[3]*(1.0);
    const double G6_0 = det*K[0]*(1.0);
    const double G6_1 = det*K[2]*(1.0);
    const double G7_0 = det*K[1]*(1.0);
    const double G7_1 = det*K[3]*(1.0);
    
    // Compute element tensor
    A[0] = 0.5*G0_0_0 + 0.5*G0_0_1 + 0.5*G0_1_0 + 0.5*G0_1_1 + 0.5*G2_0_0 + 0.5*G2_0_1 + 0.5*G2_1_0 + 0.5*G2_1_1;
    A[1] = 0.166666666666668*G0_0_0 + 0.166666666666666*G0_1_0 + 0.166666666666668*G2_0_0 + 0.166666666666666*G2_1_0;
    A[2] = 0.166666666666666*G0_0_1 + 0.166666666666665*G0_1_1 + 0.166666666666666*G2_0_1 + 0.166666666666665*G2_1_1;
    A[3] = 0.0;
    A[4] = -0.666666666666667*G0_0_1 - 0.666666666666667*G0_1_1 - 0.666666666666667*G2_0_1 - 0.666666666666667*G2_1_1;
    A[5] = -0.666666666666667*G0_0_0 - 0.666666666666667*G0_1_0 - 0.666666666666667*G2_0_0 - 0.666666666666667*G2_1_0;
    A[6] = 0.0;
    A[7] = 0.0;
    A[8] = 0.0;
    A[9] = 0.0;
    A[10] = 0.0;
    A[11] = 0.0;
    A[12] = 0.166666666666666*G4_0 + 0.166666666666667*G4_1;
    A[13] = 0.0;
    A[14] = 0.0;
    A[15] = 0.166666666666666*G4_0 + 0.166666666666669*G4_1;
    A[16] = 0.166666666666668*G0_0_0 + 0.166666666666666*G0_0_1 + 0.166666666666668*G2_0_0 + 0.166666666666666*G2_0_1;
    A[17] = 0.5*G0_0_0 + 0.5*G2_0_0;
    A[18] = -0.166666666666666*G0_0_1 - 0.166666666666666*G2_0_1;
    A[19] = 0.666666666666663*G0_0_1 + 0.666666666666663*G2_0_1;
    A[20] = 0.0;
    A[21] = -0.666666666666667*G0_0_0 - 0.666666666666666*G0_0_1 - 0.666666666666667*G2_0_0 - 0.666666666666666*G2_0_1;
    A[22] = 0.0;
    A[23] = 0.0;
    A[24] = 0.0;
    A[25] = 0.0;
    A[26] = 0.0;
    A[27] = 0.0;
    A[28] = 0.0;
    A[29] = -0.166666666666666*G4_0;
    A[30] = 0.0;
    A[31] = -0.166666666666666*G4_0;
    A[32] = 0.166666666666666*G0_1_0 + 0.166666666666665*G0_1_1 + 0.166666666666666*G2_1_0 + 0.166666666666665*G2_1_1;
    A[33] = -0.166666666666666*G0_1_0 - 0.166666666666666*G2_1_0;
    A[34] = 0.5*G0_1_1 + 0.5*G2_1_1;
    A[35] = 0.666666666666666*G0_1_0 + 0.666666666666666*G2_1_0;
    A[36] = -0.666666666666666*G0_1_0 - 0.666666666666665*G0_1_1 - 0.666666666666666*G2_1_0 - 0.666666666666665*G2_1_1;
    A[37] = 0.0;
    A[38] = 0.0;
    A[39] = 0.0;
    A[40] = 0.0;
    A[41] = 0.0;
    A[42] = 0.0;
    A[43] = 0.0;
    A[44] = 0.0;
    A[45] = 0.0;
    A[46] = -0.166666666666667*G4_1;
    A[47] = -0.166666666666667*G4_1;
    A[48] = 0.0;
    A[49] = 0.666666666666663*G0_1_0 + 0.666666666666663*G2_1_0;
    A[50] = 0.666666666666666*G0_0_1 + 0.666666666666666*G2_0_1;
    A[51] = 1.33333333333333*G0_0_0 + 0.666666666666656*G0_0_1 + 0.666666666666656*G0_1_0 + 1.33333333333331*G0_1_1 + 1.33333333333333*G2_0_0 + 0.666666666666656*G2_0_1 + 0.666666666666656*G2_1_0 + 1.33333333333331*G2_1_1;
    A[52] = -1.33333333333333*G0_0_0 - 0.666666666666659*G0_0_1 - 0.666666666666656*G0_1_0 - 1.33333333333333*G2_0_0 - 0.666666666666659*G2_0_1 - 0.666666666666656*G2_1_0;
    A[53] = -0.666666666666665*G0_0_1 - 0.666666666666665*G0_1_0 - 1.33333333333332*G0_1_1 - 0.666666666666665*G2_0_1 - 0.666666666666665*G2_1_0 - 1.33333333333332*G2_1_1;
    A[54] = 0.0;
    A[55] = 0.0;
    A[56] = 0.0;
    A[57] = 0.0;
    A[58] = 0.0;
    A[59] = 0.0;
    A[60] = -0.166666666666666*G4_0 - 0.166666666666665*G4_1;
    A[61] = -0.166666666666666*G4_0 - 0.333333333333331*G4_1;
    A[62] = -0.333333333333333*G4_0 - 0.166666666666664*G4_1;
    A[63] = -0.666666666666665*G4_0 - 0.66666666666666*G4_1;
    A[64] = -0.666666666666667*G0_1_0 - 0.666666666666667*G0_1_1 - 0.666666666666667*G2_1_0 - 0.666666666666667*G2_1_1;
    A[65] = 0.0;
    A[66] = -0.666666666666666*G0_0_1 - 0.666666666666665*G0_1_1 - 0.666666666666666*G2_0_1 - 0.666666666666665*G2_1_1;
    A[67] = -1.33333333333333*G0_0_0 - 0.666666666666656*G0_0_1 - 0.666666666666659*G0_1_0 - 1.33333333333333*G2_0_0 - 0.666666666666656*G2_0_1 - 0.666666666666659*G2_1_0;
    A[68] = 1.33333333333333*G0_0_0 + 0.666666666666659*G0_0_1 + 0.666666666666659*G0_1_0 + 1.33333333333333*G0_1_1 + 1.33333333333333*G2_0_0 + 0.666666666666659*G2_0_1 + 0.666666666666659*G2_1_0 + 1.33333333333333*G2_1_1;
    A[69] = 0.666666666666665*G0_0_1 + 0.666666666666665*G0_1_0 + 0.666666666666665*G2_0_1 + 0.666666666666665*G2_1_0;
    A[70] = 0.0;
    A[71] = 0.0;
    A[72] = 0.0;
    A[73] = 0.0;
    A[74] = 0.0;
    A[75] = 0.0;
    A[76] = 0.166666666666666*G4_0 - 0.166666666666668*G4_1;
    A[77] = 0.166666666666666*G4_0;
    A[78] = 0.333333333333333*G4_0 + 0.166666666666665*G4_1;
    A[79] = 0.666666666666665*G4_0;
    A[80] = -0.666666666666667*G0_0_0 - 0.666666666666667*G0_0_1 - 0.666666666666667*G2_0_0 - 0.666666666666667*G2_0_1;
    A[81] = -0.666666666666667*G0_0_0 - 0.666666666666666*G0_1_0 - 0.666666666666667*G2_0_0 - 0.666666666666666*G2_1_0;
    A[82] = 0.0;
    A[83] = -0.666666666666665*G0_0_1 - 0.666666666666665*G0_1_0 - 1.33333333333332*G0_1_1 - 0.666666666666665*G2_0_1 - 0.666666666666665*G2_1_0 - 1.33333333333332*G2_1_1;
    A[84] = 0.666666666666665*G0_0_1 + 0.666666666666665*G0_1_0 + 0.666666666666665*G2_0_1 + 0.666666666666665*G2_1_0;
    A[85] = 1.33333333333333*G0_0_0 + 0.666666666666667*G0_0_1 + 0.666666666666667*G0_1_0 + 1.33333333333333*G0_1_1 + 1.33333333333333*G2_0_0 + 0.666666666666667*G2_0_1 + 0.666666666666667*G2_1_0 + 1.33333333333333*G2_1_1;
    A[86] = 0.0;
    A[87] = 0.0;
    A[88] = 0.0;
    A[89] = 0.0;
    A[90] = 0.0;
    A[91] = 0.0;
    A[92] = -0.166666666666667*G4_0 + 0.166666666666667*G4_1;
    A[93] = 0.166666666666667*G4_0 + 0.333333333333333*G4_1;
    A[94] = 0.166666666666667*G4_1;
    A[95] = 0.666666666666667*G4_1;
    A[96] = 0.0;
    A[97] = 0.0;
    A[98] = 0.0;
    A[99] = 0.0;
    A[100] = 0.0;
    A[101] = 0.0;
    A[102] = 0.5*G1_0_0 + 0.5*G1_0_1 + 0.5*G1_1_0 + 0.5*G1_1_1 + 0.5*G3_0_0 + 0.5*G3_0_1 + 0.5*G3_1_0 + 0.5*G3_1_1;
    A[103] = 0.166666666666668*G1_0_0 + 0.166666666666666*G1_1_0 + 0.166666666666668*G3_0_0 + 0.166666666666666*G3_1_0;
    A[104] = 0.166666666666666*G1_0_1 + 0.166666666666665*G1_1_1 + 0.166666666666666*G3_0_1 + 0.166666666666665*G3_1_1;
    A[105] = 0.0;
    A[106] = -0.666666666666667*G1_0_1 - 0.666666666666667*G1_1_1 - 0.666666666666667*G3_0_1 - 0.666666666666667*G3_1_1;
    A[107] = -0.666666666666667*G1_0_0 - 0.666666666666667*G1_1_0 - 0.666666666666667*G3_0_0 - 0.666666666666667*G3_1_0;
    A[108] = 0.166666666666666*G5_0 + 0.166666666666667*G5_1;
    A[109] = 0.0;
    A[110] = 0.0;
    A[111] = 0.166666666666666*G5_0 + 0.166666666666669*G5_1;
    A[112] = 0.0;
    A[113] = 0.0;
    A[114] = 0.0;
    A[115] = 0.0;
    A[116] = 0.0;
    A[117] = 0.0;
    A[118] = 0.166666666666668*G1_0_0 + 0.166666666666666*G1_0_1 + 0.166666666666668*G3_0_0 + 0.166666666666666*G3_0_1;
    A[119] = 0.5*G1_0_0 + 0.5*G3_0_0;
    A[120] = -0.166666666666666*G1_0_1 - 0.166666666666666*G3_0_1;
    A[121] = 0.666666666666663*G1_0_1 + 0.666666666666663*G3_0_1;
    A[122] = 0.0;
    A[123] = -0.666666666666667*G1_0_0 - 0.666666666666666*G1_0_1 - 0.666666666666667*G3_0_0 - 0.666666666666666*G3_0_1;
    A[124] = 0.0;
    A[125] = -0.166666666666666*G5_0;
    A[126] = 0.0;
    A[127] = -0.166666666666666*G5_0;
    A[128] = 0.0;
    A[129] = 0.0;
    A[130] = 0.0;
    A[131] = 0.0;
    A[132] = 0.0;
    A[133] = 0.0;
    A[134] = 0.166666666666666*G1_1_0 + 0.166666666666665*G1_1_1 + 0.166666666666666*G3_1_0 + 0.166666666666665*G3_1_1;
    A[135] = -0.166666666666666*G1_1_0 - 0.166666666666666*G3_1_0;
    A[136] = 0.5*G1_1_1 + 0.5*G3_1_1;
    A[137] = 0.666666666666666*G1_1_0 + 0.666666666666666*G3_1_0;
    A[138] = -0.666666666666666*G1_1_0 - 0.666666666666665*G1_1_1 - 0.666666666666666*G3_1_0 - 0.666666666666665*G3_1_1;
    A[139] = 0.0;
    A[140] = 0.0;
    A[141] = 0.0;
    A[142] = -0.166666666666667*G5_1;
    A[143] = -0.166666666666667*G5_1;
    A[144] = 0.0;
    A[145] = 0.0;
    A[146] = 0.0;
    A[147] = 0.0;
    A[148] = 0.0;
    A[149] = 0.0;
    A[150] = 0.0;
    A[151] = 0.666666666666663*G1_1_0 + 0.666666666666663*G3_1_0;
    A[152] = 0.666666666666666*G1_0_1 + 0.666666666666666*G3_0_1;
    A[153] = 1.33333333333333*G1_0_0 + 0.666666666666656*G1_0_1 + 0.666666666666656*G1_1_0 + 1.33333333333331*G1_1_1 + 1.33333333333333*G3_0_0 + 0.666666666666656*G3_0_1 + 0.666666666666656*G3_1_0 + 1.33333333333331*G3_1_1;
    A[154] = -1.33333333333333*G1_0_0 - 0.666666666666659*G1_0_1 - 0.666666666666656*G1_1_0 - 1.33333333333333*G3_0_0 - 0.666666666666659*G3_0_1 - 0.666666666666656*G3_1_0;
    A[155] = -0.666666666666665*G1_0_1 - 0.666666666666665*G1_1_0 - 1.33333333333332*G1_1_1 - 0.666666666666665*G3_0_1 - 0.666666666666665*G3_1_0 - 1.33333333333332*G3_1_1;
    A[156] = -0.166666666666666*G5_0 - 0.166666666666665*G5_1;
    A[157] = -0.166666666666666*G5_0 - 0.333333333333331*G5_1;
    A[158] = -0.333333333333333*G5_0 - 0.166666666666664*G5_1;
    A[159] = -0.666666666666665*G5_0 - 0.66666666666666*G5_1;
    A[160] = 0.0;
    A[161] = 0.0;
    A[162] = 0.0;
    A[163] = 0.0;
    A[164] = 0.0;
    A[165] = 0.0;
    A[166] = -0.666666666666667*G1_1_0 - 0.666666666666667*G1_1_1 - 0.666666666666667*G3_1_0 - 0.666666666666667*G3_1_1;
    A[167] = 0.0;
    A[168] = -0.666666666666666*G1_0_1 - 0.666666666666665*G1_1_1 - 0.666666666666666*G3_0_1 - 0.666666666666665*G3_1_1;
    A[169] = -1.33333333333333*G1_0_0 - 0.666666666666656*G1_0_1 - 0.666666666666659*G1_1_0 - 1.33333333333333*G3_0_0 - 0.666666666666656*G3_0_1 - 0.666666666666659*G3_1_0;
    A[170] = 1.33333333333333*G1_0_0 + 0.666666666666659*G1_0_1 + 0.666666666666659*G1_1_0 + 1.33333333333333*G1_1_1 + 1.33333333333333*G3_0_0 + 0.666666666666659*G3_0_1 + 0.666666666666659*G3_1_0 + 1.33333333333333*G3_1_1;
    A[171] = 0.666666666666665*G1_0_1 + 0.666666666666665*G1_1_0 + 0.666666666666665*G3_0_1 + 0.666666666666665*G3_1_0;
    A[172] = 0.166666666666666*G5_0 - 0.166666666666668*G5_1;
    A[173] = 0.166666666666666*G5_0;
    A[174] = 0.333333333333333*G5_0 + 0.166666666666665*G5_1;
    A[175] = 0.666666666666665*G5_0;
    A[176] = 0.0;
    A[177] = 0.0;
    A[178] = 0.0;
    A[179] = 0.0;
    A[180] = 0.0;
    A[181] = 0.0;
    A[182] = -0.666666666666667*G1_0_0 - 0.666666666666667*G1_0_1 - 0.666666666666667*G3_0_0 - 0.666666666666667*G3_0_1;
    A[183] = -0.666666666666667*G1_0_0 - 0.666666666666666*G1_1_0 - 0.666666666666667*G3_0_0 - 0.666666666666666*G3_1_0;
    A[184] = 0.0;
    A[185] = -0.666666666666665*G1_0_1 - 0.666666666666665*G1_1_0 - 1.33333333333332*G1_1_1 - 0.666666666666665*G3_0_1 - 0.666666666666665*G3_1_0 - 1.33333333333332*G3_1_1;
    A[186] = 0.666666666666665*G1_0_1 + 0.666666666666665*G1_1_0 + 0.666666666666665*G3_0_1 + 0.666666666666665*G3_1_0;
    A[187] = 1.33333333333333*G1_0_0 + 0.666666666666667*G1_0_1 + 0.666666666666667*G1_1_0 + 1.33333333333333*G1_1_1 + 1.33333333333333*G3_0_0 + 0.666666666666667*G3_0_1 + 0.666666666666667*G3_1_0 + 1.33333333333333*G3_1_1;
    A[188] = -0.166666666666667*G5_0 + 0.166666666666667*G5_1;
    A[189] = 0.166666666666667*G5_0 + 0.333333333333333*G5_1;
    A[190] = 0.166666666666667*G5_1;
    A[191] = 0.666666666666667*G5_1;
    A[192] = -0.166666666666666*G6_0 - 0.166666666666667*G6_1;
    A[193] = 0.0;
    A[194] = 0.0;
    A[195] = 0.166666666666666*G6_0 + 0.166666666666665*G6_1;
    A[196] = -0.166666666666666*G6_0 + 0.166666666666668*G6_1;
    A[197] = 0.166666666666667*G6_0 - 0.166666666666667*G6_1;
    A[198] = -0.166666666666666*G7_0 - 0.166666666666667*G7_1;
    A[199] = 0.0;
    A[200] = 0.0;
    A[201] = 0.166666666666666*G7_0 + 0.166666666666665*G7_1;
    A[202] = -0.166666666666666*G7_0 + 0.166666666666668*G7_1;
    A[203] = 0.166666666666667*G7_0 - 0.166666666666667*G7_1;
    A[204] = 0.0;
    A[205] = 0.0;
    A[206] = 0.0;
    A[207] = 0.0;
    A[208] = 0.0;
    A[209] = 0.166666666666666*G6_0;
    A[210] = 0.0;
    A[211] = 0.166666666666666*G6_0 + 0.333333333333331*G6_1;
    A[212] = -0.166666666666666*G6_0;
    A[213] = -0.166666666666667*G6_0 - 0.333333333333333*G6_1;
    A[214] = 0.0;
    A[215] = 0.166666666666666*G7_0;
    A[216] = 0.0;
    A[217] = 0.166666666666666*G7_0 + 0.333333333333331*G7_1;
    A[218] = -0.166666666666666*G7_0;
    A[219] = -0.166666666666667*G7_0 - 0.333333333333333*G7_1;
    A[220] = 0.0;
    A[221] = 0.0;
    A[222] = 0.0;
    A[223] = 0.0;
    A[224] = 0.0;
    A[225] = 0.0;
    A[226] = 0.166666666666667*G6_1;
    A[227] = 0.333333333333333*G6_0 + 0.166666666666664*G6_1;
    A[228] = -0.333333333333333*G6_0 - 0.166666666666665*G6_1;
    A[229] = -0.166666666666667*G6_1;
    A[230] = 0.0;
    A[231] = 0.0;
    A[232] = 0.166666666666667*G7_1;
    A[233] = 0.333333333333333*G7_0 + 0.166666666666664*G7_1;
    A[234] = -0.333333333333333*G7_0 - 0.166666666666665*G7_1;
    A[235] = -0.166666666666667*G7_1;
    A[236] = 0.0;
    A[237] = 0.0;
    A[238] = 0.0;
    A[239] = 0.0;
    A[240] = -0.166666666666666*G6_0 - 0.166666666666669*G6_1;
    A[241] = 0.166666666666666*G6_0;
    A[242] = 0.166666666666667*G6_1;
    A[243] = 0.666666666666665*G6_0 + 0.66666666666666*G6_1;
    A[244] = -0.666666666666665*G6_0;
    A[245] = -0.666666666666667*G6_1;
    A[246] = -0.166666666666666*G7_0 - 0.166666666666669*G7_1;
    A[247] = 0.166666666666666*G7_0;
    A[248] = 0.166666666666667*G7_1;
    A[249] = 0.666666666666665*G7_0 + 0.66666666666666*G7_1;
    A[250] = -0.666666666666665*G7_0;
    A[251] = -0.666666666666667*G7_1;
    A[252] = 0.0;
    A[253] = 0.0;
    A[254] = 0.0;
    A[255] = 0.0;
  }

};

/// This class defines the interface for the tabulation of the cell
/// tensor corresponding to the local contribution to a form from
/// the integral over a cell.

class mth_cell_integral_1_otherwise: public ufc::cell_integral
{
public:

  /// Constructor
  mth_cell_integral_1_otherwise() : ufc::cell_integral()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_cell_integral_1_otherwise()
  {
    // Do nothing
  }

  /// Tabulate which form coefficients are used by this integral
  virtual const std::vector<bool> & enabled_coefficients() const
  {
    static const std::vector<bool> enabled({true});
    return enabled;
  }

  /// Tabulate the tensor for the contribution from a local cell
  virtual void tabulate_tensor(double*  A,
                               const double * const *  w,
                               const double*  vertex_coordinates,
                               int cell_orientation) const
  {
    // Number of operations (multiply-add pairs) for Jacobian data:      3
    // Number of operations (multiply-add pairs) for geometry tensor:    6
    // Number of operations (multiply-add pairs) for tensor contraction: 30
    // Total number of operations (multiply-add pairs):                  39
    
    // Compute Jacobian
    double J[4];
    compute_jacobian_triangle_2d(J, vertex_coordinates);
    
    // Compute Jacobian inverse and determinant
    double K[4];
    double detJ;
    compute_jacobian_inverse_triangle_2d(K, detJ, J);
    
    // Set scale factor
    const double det = std::abs(detJ);
    
    // Compute geometry tensor
    const double G0_0 = det*w[0][0]*(1.0);
    const double G0_1 = det*w[0][1]*(1.0);
    const double G0_2 = det*w[0][2]*(1.0);
    const double G1_3 = det*w[0][3]*(1.0);
    const double G1_4 = det*w[0][4]*(1.0);
    const double G1_5 = det*w[0][5]*(1.0);
    
    // Compute element tensor
    A[0] = 0.0166666666666666*G0_0 - 0.00833333333333332*G0_1 - 0.00833333333333332*G0_2;
    A[1] = -0.00833333333333333*G0_0 + 0.0166666666666666*G0_1 - 0.00833333333333333*G0_2;
    A[2] = -0.00833333333333332*G0_0 - 0.00833333333333332*G0_1 + 0.0166666666666666*G0_2;
    A[3] = 0.0333333333333333*G0_0 + 0.0666666666666667*G0_1 + 0.0666666666666667*G0_2;
    A[4] = 0.0666666666666667*G0_0 + 0.0333333333333333*G0_1 + 0.0666666666666667*G0_2;
    A[5] = 0.0666666666666667*G0_0 + 0.0666666666666667*G0_1 + 0.0333333333333333*G0_2;
    A[6] = 0.0166666666666666*G1_3 - 0.00833333333333332*G1_4 - 0.00833333333333332*G1_5;
    A[7] = -0.00833333333333333*G1_3 + 0.0166666666666666*G1_4 - 0.00833333333333333*G1_5;
    A[8] = -0.00833333333333332*G1_3 - 0.00833333333333332*G1_4 + 0.0166666666666666*G1_5;
    A[9] = 0.0333333333333333*G1_3 + 0.0666666666666667*G1_4 + 0.0666666666666667*G1_5;
    A[10] = 0.0666666666666667*G1_3 + 0.0333333333333333*G1_4 + 0.0666666666666667*G1_5;
    A[11] = 0.0666666666666667*G1_3 + 0.0666666666666667*G1_4 + 0.0333333333333333*G1_5;
    A[12] = 0.0;
    A[13] = 0.0;
    A[14] = 0.0;
    A[15] = 0.0;
  }

};

/// This class defines the interface for the assembly of the global
/// tensor corresponding to a form with r + n arguments, that is, a
/// mapping
///
///     a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
///
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
/// global tensor A is defined by
///
///     A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
///
/// where each argument Vj represents the application to the
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
/// fixed functions (coefficients).

class mth_form_0: public ufc::form
{
public:

  /// Constructor
  mth_form_0() : ufc::form()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_form_0()
  {
    // Do nothing
  }

  /// Return a string identifying the form
  virtual const char* signature() const
  {
    return "9ef2d602761a16cad5e071d632c15ef7219e9536d2f549d9ec63840872bec33efde8c896523f154702b672d943833fd7ead5c9c769b9bf0a601c18d4d879aa7d";
  }

  /// Return original coefficient position for each coefficient (0 <= i < n)
  virtual std::size_t original_coefficient_position(std::size_t i) const
  {
    static const std::vector<std::size_t> position({});
    return position[i];
  }

  /// Return the rank of the global tensor (r)
  virtual std::size_t rank() const
  {
    return 2;
  }

  /// Return the number of coefficients (n)
  virtual std::size_t num_coefficients() const
  {
    return 0;
  }

  /// Return the number of cell domains
  virtual std::size_t num_cell_domains() const
  {
    return 0;
  }

  /// Return the number of exterior facet domains
  virtual std::size_t num_exterior_facet_domains() const
  {
    return 0;
  }

  /// Return the number of interior facet domains
  virtual std::size_t num_interior_facet_domains() const
  {
    return 0;
  }

  /// Return the number of point domains
  virtual std::size_t num_point_domains() const
  {
    return 0;
  }

  /// Return the number of custom domains
  virtual std::size_t num_custom_domains() const
  {
    return 0;
  }

  /// Return whether the form has any cell integrals
  virtual bool has_cell_integrals() const
  {
    return true;
  }

  /// Return whether the form has any exterior facet integrals
  virtual bool has_exterior_facet_integrals() const
  {
    return false;
  }

  /// Return whether the form has any interior facet integrals
  virtual bool has_interior_facet_integrals() const
  {
    return false;
  }

  /// Return whether the form has any point integrals
  virtual bool has_point_integrals() const
  {
    return false;
  }

  /// Return whether the form has any custom integrals
  virtual bool has_custom_integrals() const
  {
    return false;
  }

  /// Create a new finite element for argument function i
  virtual ufc::finite_element* create_finite_element(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_finite_element_5();
        break;
      }
    case 1:
      {
        return new mth_finite_element_5();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new dofmap for argument function i
  virtual ufc::dofmap* create_dofmap(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_dofmap_5();
        break;
      }
    case 1:
      {
        return new mth_dofmap_5();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new cell integral on sub domain i
  virtual ufc::cell_integral* create_cell_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new exterior facet integral on sub domain i
  virtual ufc::exterior_facet_integral* create_exterior_facet_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new interior facet integral on sub domain i
  virtual ufc::interior_facet_integral* create_interior_facet_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new point integral on sub domain i
  virtual ufc::point_integral* create_point_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new custom integral on sub domain i
  virtual ufc::custom_integral* create_custom_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new cell integral on everywhere else
  virtual ufc::cell_integral* create_default_cell_integral() const
  {
    return new mth_cell_integral_0_otherwise();
  }

  /// Create a new exterior facet integral on everywhere else
  virtual ufc::exterior_facet_integral* create_default_exterior_facet_integral() const
  {
    return 0;
  }

  /// Create a new interior facet integral on everywhere else
  virtual ufc::interior_facet_integral* create_default_interior_facet_integral() const
  {
    return 0;
  }

  /// Create a new point integral on everywhere else
  virtual ufc::point_integral* create_default_point_integral() const
  {
    return 0;
  }

  /// Create a new custom integral on everywhere else
  virtual ufc::custom_integral* create_default_custom_integral() const
  {
    return 0;
  }

};

/// This class defines the interface for the assembly of the global
/// tensor corresponding to a form with r + n arguments, that is, a
/// mapping
///
///     a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
///
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
/// global tensor A is defined by
///
///     A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
///
/// where each argument Vj represents the application to the
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
/// fixed functions (coefficients).

class mth_form_1: public ufc::form
{
public:

  /// Constructor
  mth_form_1() : ufc::form()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~mth_form_1()
  {
    // Do nothing
  }

  /// Return a string identifying the form
  virtual const char* signature() const
  {
    return "dbd3357db3ff3365672af45a8254cb3daebd1d24a08f708892968b3cbb1389fa0514011ac84961c93723986c3e70d5c6fa56c66a9cbd245c6081820a6e63842f";
  }

  /// Return original coefficient position for each coefficient (0 <= i < n)
  virtual std::size_t original_coefficient_position(std::size_t i) const
  {
    static const std::vector<std::size_t> position({0});
    return position[i];
  }

  /// Return the rank of the global tensor (r)
  virtual std::size_t rank() const
  {
    return 1;
  }

  /// Return the number of coefficients (n)
  virtual std::size_t num_coefficients() const
  {
    return 1;
  }

  /// Return the number of cell domains
  virtual std::size_t num_cell_domains() const
  {
    return 0;
  }

  /// Return the number of exterior facet domains
  virtual std::size_t num_exterior_facet_domains() const
  {
    return 0;
  }

  /// Return the number of interior facet domains
  virtual std::size_t num_interior_facet_domains() const
  {
    return 0;
  }

  /// Return the number of point domains
  virtual std::size_t num_point_domains() const
  {
    return 0;
  }

  /// Return the number of custom domains
  virtual std::size_t num_custom_domains() const
  {
    return 0;
  }

  /// Return whether the form has any cell integrals
  virtual bool has_cell_integrals() const
  {
    return true;
  }

  /// Return whether the form has any exterior facet integrals
  virtual bool has_exterior_facet_integrals() const
  {
    return false;
  }

  /// Return whether the form has any interior facet integrals
  virtual bool has_interior_facet_integrals() const
  {
    return false;
  }

  /// Return whether the form has any point integrals
  virtual bool has_point_integrals() const
  {
    return false;
  }

  /// Return whether the form has any custom integrals
  virtual bool has_custom_integrals() const
  {
    return false;
  }

  /// Create a new finite element for argument function i
  virtual ufc::finite_element* create_finite_element(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_finite_element_5();
        break;
      }
    case 1:
      {
        return new mth_finite_element_1();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new dofmap for argument function i
  virtual ufc::dofmap* create_dofmap(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      {
        return new mth_dofmap_5();
        break;
      }
    case 1:
      {
        return new mth_dofmap_1();
        break;
      }
    }
    
    return 0;
  }

  /// Create a new cell integral on sub domain i
  virtual ufc::cell_integral* create_cell_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new exterior facet integral on sub domain i
  virtual ufc::exterior_facet_integral* create_exterior_facet_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new interior facet integral on sub domain i
  virtual ufc::interior_facet_integral* create_interior_facet_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new point integral on sub domain i
  virtual ufc::point_integral* create_point_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new custom integral on sub domain i
  virtual ufc::custom_integral* create_custom_integral(std::size_t i) const
  {
    return 0;
  }

  /// Create a new cell integral on everywhere else
  virtual ufc::cell_integral* create_default_cell_integral() const
  {
    return new mth_cell_integral_1_otherwise();
  }

  /// Create a new exterior facet integral on everywhere else
  virtual ufc::exterior_facet_integral* create_default_exterior_facet_integral() const
  {
    return 0;
  }

  /// Create a new interior facet integral on everywhere else
  virtual ufc::interior_facet_integral* create_default_interior_facet_integral() const
  {
    return 0;
  }

  /// Create a new point integral on everywhere else
  virtual ufc::point_integral* create_default_point_integral() const
  {
    return 0;
  }

  /// Create a new custom integral on everywhere else
  virtual ufc::custom_integral* create_default_custom_integral() const
  {
    return 0;
  }

};

// DOLFIN wrappers

// Standard library includes
#include <string>

// DOLFIN includes
#include <dolfin/common/NoDeleter.h>
#include <dolfin/fem/FiniteElement.h>
#include <dolfin/fem/DofMap.h>
#include <dolfin/fem/Form.h>
#include <dolfin/function/FunctionSpace.h>
#include <dolfin/function/GenericFunction.h>
#include <dolfin/function/CoefficientAssigner.h>
#include <dolfin/adaptivity/ErrorControl.h>
#include <dolfin/adaptivity/GoalFunctional.h>

namespace MTH
{

class CoefficientSpace_f: public dolfin::FunctionSpace
{
public:

  //--- Constructors for standard function space, 2 different versions ---

  // Create standard function space (reference version)
  CoefficientSpace_f(const dolfin::Mesh& mesh):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_1()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_1()), mesh)))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  CoefficientSpace_f(std::shared_ptr<const dolfin::Mesh> mesh):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_1()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_1()), *mesh)))
  {
    // Do nothing
  }

  //--- Constructors for constrained function space, 2 different versions ---

  // Create standard function space (reference version)
  CoefficientSpace_f(const dolfin::Mesh& mesh, const dolfin::SubDomain& constrained_domain):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_1()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_1()), mesh,
                              dolfin::reference_to_no_delete_pointer(constrained_domain))))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  CoefficientSpace_f(std::shared_ptr<const dolfin::Mesh> mesh, std::shared_ptr<const dolfin::SubDomain> constrained_domain):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_1()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_1()), *mesh, constrained_domain)))
  {
    // Do nothing
  }

};

class Form_a_FunctionSpace_0: public dolfin::FunctionSpace
{
public:

  //--- Constructors for standard function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_a_FunctionSpace_0(const dolfin::Mesh& mesh):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh)))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_a_FunctionSpace_0(std::shared_ptr<const dolfin::Mesh> mesh):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh)))
  {
    // Do nothing
  }

  //--- Constructors for constrained function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_a_FunctionSpace_0(const dolfin::Mesh& mesh, const dolfin::SubDomain& constrained_domain):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh,
                              dolfin::reference_to_no_delete_pointer(constrained_domain))))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_a_FunctionSpace_0(std::shared_ptr<const dolfin::Mesh> mesh, std::shared_ptr<const dolfin::SubDomain> constrained_domain):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh, constrained_domain)))
  {
    // Do nothing
  }

};

class Form_a_FunctionSpace_1: public dolfin::FunctionSpace
{
public:

  //--- Constructors for standard function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_a_FunctionSpace_1(const dolfin::Mesh& mesh):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh)))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_a_FunctionSpace_1(std::shared_ptr<const dolfin::Mesh> mesh):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh)))
  {
    // Do nothing
  }

  //--- Constructors for constrained function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_a_FunctionSpace_1(const dolfin::Mesh& mesh, const dolfin::SubDomain& constrained_domain):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh,
                              dolfin::reference_to_no_delete_pointer(constrained_domain))))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_a_FunctionSpace_1(std::shared_ptr<const dolfin::Mesh> mesh, std::shared_ptr<const dolfin::SubDomain> constrained_domain):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh, constrained_domain)))
  {
    // Do nothing
  }

};

class Form_a: public dolfin::Form
{
public:

  // Constructor
  Form_a(const dolfin::FunctionSpace& V1, const dolfin::FunctionSpace& V0):
    dolfin::Form(2, 0)
  {
    _function_spaces[0] = reference_to_no_delete_pointer(V0);
    _function_spaces[1] = reference_to_no_delete_pointer(V1);

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_0());
  }

  // Constructor
  Form_a(std::shared_ptr<const dolfin::FunctionSpace> V1, std::shared_ptr<const dolfin::FunctionSpace> V0):
    dolfin::Form(2, 0)
  {
    _function_spaces[0] = V0;
    _function_spaces[1] = V1;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_0());
  }

  // Destructor
  ~Form_a()
  {}

  /// Return the number of the coefficient with this name
  virtual std::size_t coefficient_number(const std::string& name) const
  {

    dolfin::dolfin_error("generated code for class Form",
                         "access coefficient data",
                         "There are no coefficients");
    return 0;
  }

  /// Return the name of the coefficient with this number
  virtual std::string coefficient_name(std::size_t i) const
  {

    dolfin::dolfin_error("generated code for class Form",
                         "access coefficient data",
                         "There are no coefficients");
    return "unnamed";
  }

  // Typedefs
  typedef Form_a_FunctionSpace_0 TestSpace;
  typedef Form_a_FunctionSpace_1 TrialSpace;

  // Coefficients
};

class Form_L_FunctionSpace_0: public dolfin::FunctionSpace
{
public:

  //--- Constructors for standard function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_L_FunctionSpace_0(const dolfin::Mesh& mesh):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh)))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_L_FunctionSpace_0(std::shared_ptr<const dolfin::Mesh> mesh):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh)))
  {
    // Do nothing
  }

  //--- Constructors for constrained function space, 2 different versions ---

  // Create standard function space (reference version)
  Form_L_FunctionSpace_0(const dolfin::Mesh& mesh, const dolfin::SubDomain& constrained_domain):
    dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), mesh,
                              dolfin::reference_to_no_delete_pointer(constrained_domain))))
  {
    // Do nothing
  }

  // Create standard function space (shared pointer version)
  Form_L_FunctionSpace_0(std::shared_ptr<const dolfin::Mesh> mesh, std::shared_ptr<const dolfin::SubDomain> constrained_domain):
    dolfin::FunctionSpace(mesh,
                          std::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(std::shared_ptr<ufc::finite_element>(new mth_finite_element_5()))),
                          std::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(std::shared_ptr<ufc::dofmap>(new mth_dofmap_5()), *mesh, constrained_domain)))
  {
    // Do nothing
  }

};

typedef CoefficientSpace_f Form_L_FunctionSpace_1;

class Form_L: public dolfin::Form
{
public:

  // Constructor
  Form_L(const dolfin::FunctionSpace& V0):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = reference_to_no_delete_pointer(V0);

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Constructor
  Form_L(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = reference_to_no_delete_pointer(V0);

    this->f = f;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Constructor
  Form_L(const dolfin::FunctionSpace& V0, std::shared_ptr<const dolfin::GenericFunction> f):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = reference_to_no_delete_pointer(V0);

    this->f = *f;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Constructor
  Form_L(std::shared_ptr<const dolfin::FunctionSpace> V0):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = V0;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Constructor
  Form_L(std::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = V0;

    this->f = f;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Constructor
  Form_L(std::shared_ptr<const dolfin::FunctionSpace> V0, std::shared_ptr<const dolfin::GenericFunction> f):
    dolfin::Form(1, 1), f(*this, 0)
  {
    _function_spaces[0] = V0;

    this->f = *f;

    _ufc_form = std::shared_ptr<const ufc::form>(new mth_form_1());
  }

  // Destructor
  ~Form_L()
  {}

  /// Return the number of the coefficient with this name
  virtual std::size_t coefficient_number(const std::string& name) const
  {
    if (name == "f")
      return 0;

    dolfin::dolfin_error("generated code for class Form",
                         "access coefficient data",
                         "Invalid coefficient");
    return 0;
  }

  /// Return the name of the coefficient with this number
  virtual std::string coefficient_name(std::size_t i) const
  {
    switch (i)
    {
    case 0:
      return "f";
    }

    dolfin::dolfin_error("generated code for class Form",
                         "access coefficient data",
                         "Invalid coefficient");
    return "unnamed";
  }

  // Typedefs
  typedef Form_L_FunctionSpace_0 TestSpace;
  typedef Form_L_FunctionSpace_1 CoefficientSpace_f;

  // Coefficients
  dolfin::CoefficientAssigner f;
};

// Class typedefs
typedef Form_a BilinearForm;
typedef Form_a JacobianForm;
typedef Form_L LinearForm;
typedef Form_L ResidualForm;
typedef Form_a::TestSpace FunctionSpace;

}

#endif