~njansson/dolfin/hpc : revision 2359

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// This code conforms with the UFC specification version 1.0

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// and was automatically generated by FFC version 0.4.3.

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#ifndef __FFC_25_H

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#define __FFC_25_H

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#include <cmath>

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#include <stdexcept>

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#include <ufc.h>

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

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class ffc_25_finite_element_0_0: public ufc::finite_element

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{

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public:

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/// Constructor

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ffc_25_finite_element_0_0() : ufc::finite_element()

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{

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// Do nothing

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}

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/// Destructor

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virtual ~ffc_25_finite_element_0_0()

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{

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// Do nothing

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}

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/// Return a string identifying the finite element

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virtual const char* signature() const

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{

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return "Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

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}

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/// Return the cell shape

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virtual ufc::shape cell_shape() const

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{

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return ufc::tetrahedron;

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}

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/// Return the dimension of the finite element function space

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virtual unsigned int space_dimension() const

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{

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return 20;

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}

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/// Return the rank of the value space

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virtual unsigned int value_rank() const

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{

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return 0;

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}

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/// Return the dimension of the value space for axis i

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virtual unsigned int value_dimension(unsigned int i) const

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{

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return 1;

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}

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/// Evaluate basis function i at given point in cell

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virtual void evaluate_basis(unsigned int i,

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double* values,

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const double* coordinates,

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const ufc::cell& c) const

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{

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// Extract vertex coordinates

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const double * const * element_coordinates = c.coordinates;

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// Compute Jacobian of affine map from reference cell

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const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

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const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

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const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

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const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

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const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

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const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

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const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

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const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

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const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

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// Compute sub determinants

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const double d00 = J_11*J_22 - J_12*J_21;

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const double d01 = J_12*J_20 - J_10*J_22;

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const double d02 = J_10*J_21 - J_11*J_20;

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const double d10 = J_02*J_21 - J_01*J_22;

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const double d11 = J_00*J_22 - J_02*J_20;

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const double d12 = J_01*J_20 - J_00*J_21;

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const double d20 = J_01*J_12 - J_02*J_11;

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const double d21 = J_02*J_10 - J_00*J_12;

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const double d22 = J_00*J_11 - J_01*J_10;

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// Compute determinant of Jacobian

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double detJ = J_00*d00 + J_10*d10 + J_20*d20;

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// Compute inverse of Jacobian

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// Compute constants

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const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

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+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

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+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

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const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

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+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

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+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

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const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

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+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

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+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

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// Get coordinates and map to the UFC reference element

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double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

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double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

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double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

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// Map coordinates to the reference cube

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if (std::abs(y + z - 1.0) < 1e-14)

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x = 1.0;

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else

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x = -2.0 * x/(y + z - 1.0) - 1.0;

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if (std::abs(z - 1.0) < 1e-14)

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y = -1.0;

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else

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y = 2.0 * y/(1.0 - z) - 1.0;

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z = 2.0 * z - 1.0;

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// Reset values

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*values = 0;

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// Map degree of freedom to element degree of freedom

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const unsigned int dof = i;

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// Generate scalings

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const double scalings_y_0 = 1;

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const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

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const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

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const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

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const double scalings_z_0 = 1;

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const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

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const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

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const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

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// Compute psitilde_a

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const double psitilde_a_0 = 1;

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const double psitilde_a_1 = x;

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const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

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const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

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// Compute psitilde_bs

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const double psitilde_bs_0_0 = 1;

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const double psitilde_bs_0_1 = 1.5*y + 0.5;

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const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

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const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

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const double psitilde_bs_1_0 = 1;

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const double psitilde_bs_1_1 = 2.5*y + 1.5;

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const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

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const double psitilde_bs_2_0 = 1;

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const double psitilde_bs_2_1 = 3.5*y + 2.5;

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const double psitilde_bs_3_0 = 1;

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// Compute psitilde_cs

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const double psitilde_cs_00_0 = 1;

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const double psitilde_cs_00_1 = 2*z + 1;

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const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

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const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

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const double psitilde_cs_01_0 = 1;

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const double psitilde_cs_01_1 = 3*z + 2;

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const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

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const double psitilde_cs_02_0 = 1;

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const double psitilde_cs_02_1 = 4*z + 3;

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const double psitilde_cs_03_0 = 1;

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const double psitilde_cs_10_0 = 1;

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const double psitilde_cs_10_1 = 3*z + 2;

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const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

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const double psitilde_cs_11_0 = 1;

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const double psitilde_cs_11_1 = 4*z + 3;

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const double psitilde_cs_12_0 = 1;

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const double psitilde_cs_20_0 = 1;

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const double psitilde_cs_20_1 = 4*z + 3;

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const double psitilde_cs_21_0 = 1;

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const double psitilde_cs_30_0 = 1;

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// Compute basisvalues

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const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

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const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

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const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

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const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

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const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

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const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

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const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

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const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

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const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

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const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

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const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

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const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

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const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

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const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

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const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

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const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

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const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

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const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

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const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

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const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

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// Table(s) of coefficients

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const static double coefficients0[20][20] = \

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{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

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{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

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{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

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{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

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{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

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{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

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{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

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{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

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{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

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{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

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{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

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{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

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{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

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{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

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{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

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{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

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{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

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{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

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{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

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{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

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// Extract relevant coefficients

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const double coeff0_0 = coefficients0[dof][0];

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const double coeff0_1 = coefficients0[dof][1];

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const double coeff0_2 = coefficients0[dof][2];

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const double coeff0_3 = coefficients0[dof][3];

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const double coeff0_4 = coefficients0[dof][4];

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const double coeff0_5 = coefficients0[dof][5];

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const double coeff0_6 = coefficients0[dof][6];

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const double coeff0_7 = coefficients0[dof][7];

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const double coeff0_8 = coefficients0[dof][8];

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const double coeff0_9 = coefficients0[dof][9];

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const double coeff0_10 = coefficients0[dof][10];

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const double coeff0_11 = coefficients0[dof][11];

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const double coeff0_12 = coefficients0[dof][12];

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const double coeff0_13 = coefficients0[dof][13];

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const double coeff0_14 = coefficients0[dof][14];

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const double coeff0_15 = coefficients0[dof][15];

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const double coeff0_16 = coefficients0[dof][16];

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const double coeff0_17 = coefficients0[dof][17];

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const double coeff0_18 = coefficients0[dof][18];

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const double coeff0_19 = coefficients0[dof][19];

248

249

// Compute value(s)

250

*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

251

}

252

253

/// Evaluate all basis functions at given point in cell

254

virtual void evaluate_basis_all(double* values,

255

const double* coordinates,

256

const ufc::cell& c) const

257

{

258

throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");

259

}

260

261

/// Evaluate order n derivatives of basis function i at given point in cell

262

virtual void evaluate_basis_derivatives(unsigned int i,

263

unsigned int n,

264

double* values,

265

const double* coordinates,

266

const ufc::cell& c) const

267

{

268

// Extract vertex coordinates

269

const double * const * element_coordinates = c.coordinates;

270

271

// Compute Jacobian of affine map from reference cell

272

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

273

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

274

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

275

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

276

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

277

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

278

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

279

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

280

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

281

282

// Compute sub determinants

283

const double d00 = J_11*J_22 - J_12*J_21;

284

const double d01 = J_12*J_20 - J_10*J_22;

285

const double d02 = J_10*J_21 - J_11*J_20;

286

287

const double d10 = J_02*J_21 - J_01*J_22;

288

const double d11 = J_00*J_22 - J_02*J_20;

289

const double d12 = J_01*J_20 - J_00*J_21;

290

291

const double d20 = J_01*J_12 - J_02*J_11;

292

const double d21 = J_02*J_10 - J_00*J_12;

293

const double d22 = J_00*J_11 - J_01*J_10;

294

295

// Compute determinant of Jacobian

296

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

297

298

// Compute inverse of Jacobian

299

300

// Compute constants

301

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

302

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

303

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

304

305

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

306

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

307

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

308

309

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

310

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

311

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

312

313

// Get coordinates and map to the UFC reference element

314

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

315

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

316

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

317

318

// Map coordinates to the reference cube

319

if (std::abs(y + z - 1.0) < 1e-14)

320

x = 1.0;

321

else

322

x = -2.0 * x/(y + z - 1.0) - 1.0;

323

if (std::abs(z - 1.0) < 1e-14)

324

y = -1.0;

325

else

326

y = 2.0 * y/(1.0 - z) - 1.0;

327

z = 2.0 * z - 1.0;

328

329

// Compute number of derivatives

330

unsigned int num_derivatives = 1;

331

332

for (unsigned int j = 0; j < n; j++)

333

num_derivatives *= 3;

334

335

336

// Declare pointer to two dimensional array that holds combinations of derivatives and initialise

337

unsigned int **combinations = new unsigned int *[num_derivatives];

338

339

for (unsigned int j = 0; j < num_derivatives; j++)

340

{

341

combinations[j] = new unsigned int [n];

342

for (unsigned int k = 0; k < n; k++)

343

combinations[j][k] = 0;

344

}

345

346

// Generate combinations of derivatives

347

for (unsigned int row = 1; row < num_derivatives; row++)

348

{

349

for (unsigned int num = 0; num < row; num++)

350

{

351

for (unsigned int col = n-1; col+1 > 0; col--)

352

{

353

if (combinations[row][col] + 1 > 2)

354

combinations[row][col] = 0;

355

else

356

{

357

combinations[row][col] += 1;

358

break;

359

}

360

}

361

}

362

}

363

364

// Compute inverse of Jacobian

365

const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};

366

367

// Declare transformation matrix

368

// Declare pointer to two dimensional array and initialise

369

double **transform = new double *[num_derivatives];

370

371

for (unsigned int j = 0; j < num_derivatives; j++)

372

{

373

transform[j] = new double [num_derivatives];

374

for (unsigned int k = 0; k < num_derivatives; k++)

375

transform[j][k] = 1;

376

}

377

378

// Construct transformation matrix

379

for (unsigned int row = 0; row < num_derivatives; row++)

380

{

381

for (unsigned int col = 0; col < num_derivatives; col++)

382

{

383

for (unsigned int k = 0; k < n; k++)

384

transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];

385

}

386

}

387

388

// Reset values

389

for (unsigned int j = 0; j < 1*num_derivatives; j++)

390

values[j] = 0;

391

392

// Map degree of freedom to element degree of freedom

393

const unsigned int dof = i;

394

395

// Generate scalings

396

const double scalings_y_0 = 1;

397

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

398

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

399

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

400

const double scalings_z_0 = 1;

401

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

402

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

403

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

404

405

// Compute psitilde_a

406

const double psitilde_a_0 = 1;

407

const double psitilde_a_1 = x;

408

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

409

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

410

411

// Compute psitilde_bs

412

const double psitilde_bs_0_0 = 1;

413

const double psitilde_bs_0_1 = 1.5*y + 0.5;

414

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

415

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

416

const double psitilde_bs_1_0 = 1;

417

const double psitilde_bs_1_1 = 2.5*y + 1.5;

418

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

419

const double psitilde_bs_2_0 = 1;

420

const double psitilde_bs_2_1 = 3.5*y + 2.5;

421

const double psitilde_bs_3_0 = 1;

422

423

// Compute psitilde_cs

424

const double psitilde_cs_00_0 = 1;

425

const double psitilde_cs_00_1 = 2*z + 1;

426

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

427

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

428

const double psitilde_cs_01_0 = 1;

429

const double psitilde_cs_01_1 = 3*z + 2;

430

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

431

const double psitilde_cs_02_0 = 1;

432

const double psitilde_cs_02_1 = 4*z + 3;

433

const double psitilde_cs_03_0 = 1;

434

const double psitilde_cs_10_0 = 1;

435

const double psitilde_cs_10_1 = 3*z + 2;

436

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

437

const double psitilde_cs_11_0 = 1;

438

const double psitilde_cs_11_1 = 4*z + 3;

439

const double psitilde_cs_12_0 = 1;

440

const double psitilde_cs_20_0 = 1;

441

const double psitilde_cs_20_1 = 4*z + 3;

442

const double psitilde_cs_21_0 = 1;

443

const double psitilde_cs_30_0 = 1;

444

445

// Compute basisvalues

446

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

447

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

448

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

449

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

450

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

451

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

452

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

453

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

454

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

455

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

456

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

457

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

458

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

459

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

460

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

461

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

462

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

463

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

464

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

465

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

466

467

// Table(s) of coefficients

468

const static double coefficients0[20][20] = \

469

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

470

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

471

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

472

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

473

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

474

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

475

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

476

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

477

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

478

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

479

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

480

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

481

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

482

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

483

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

484

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

485

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

486

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

487

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

488

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

489

490

// Interesting (new) part

491

// Tables of derivatives of the polynomial base (transpose)

492

const static double dmats0[20][20] = \

493

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

494

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

495

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

496

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

497

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

498

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

499

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

500

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

501

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

502

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

503

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

504

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

505

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

506

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

507

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

508

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

509

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

510

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

511

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

512

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

513

514

const static double dmats1[20][20] = \

515

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

516

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

517

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

518

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

519

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

520

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

521

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

522

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

523

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

524

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

525

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

526

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

527

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

528

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

529

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

530

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

531

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

532

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

533

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

534

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

535

536

const static double dmats2[20][20] = \

537

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

538

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

539

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

540

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

541

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

542

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

543

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

544

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

545

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

546

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

547

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

548

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

549

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

550

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

551

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

552

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

553

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

554

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

555

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

556

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

557

558

// Compute reference derivatives

559

// Declare pointer to array of derivatives on FIAT element

560

double *derivatives = new double [num_derivatives];

561

562

// Declare coefficients

563

double coeff0_0 = 0;

564

double coeff0_1 = 0;

565

double coeff0_2 = 0;

566

double coeff0_3 = 0;

567

double coeff0_4 = 0;

568

double coeff0_5 = 0;

569

double coeff0_6 = 0;

570

double coeff0_7 = 0;

571

double coeff0_8 = 0;

572

double coeff0_9 = 0;

573

double coeff0_10 = 0;

574

double coeff0_11 = 0;

575

double coeff0_12 = 0;

576

double coeff0_13 = 0;

577

double coeff0_14 = 0;

578

double coeff0_15 = 0;

579

double coeff0_16 = 0;

580

double coeff0_17 = 0;

581

double coeff0_18 = 0;

582

double coeff0_19 = 0;

583

584

// Declare new coefficients

585

double new_coeff0_0 = 0;

586

double new_coeff0_1 = 0;

587

double new_coeff0_2 = 0;

588

double new_coeff0_3 = 0;

589

double new_coeff0_4 = 0;

590

double new_coeff0_5 = 0;

591

double new_coeff0_6 = 0;

592

double new_coeff0_7 = 0;

593

double new_coeff0_8 = 0;

594

double new_coeff0_9 = 0;

595

double new_coeff0_10 = 0;

596

double new_coeff0_11 = 0;

597

double new_coeff0_12 = 0;

598

double new_coeff0_13 = 0;

599

double new_coeff0_14 = 0;

600

double new_coeff0_15 = 0;

601

double new_coeff0_16 = 0;

602

double new_coeff0_17 = 0;

603

double new_coeff0_18 = 0;

604

double new_coeff0_19 = 0;

605

606

// Loop possible derivatives

607

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

608

{

609

// Get values from coefficients array

610

new_coeff0_0 = coefficients0[dof][0];

611

new_coeff0_1 = coefficients0[dof][1];

612

new_coeff0_2 = coefficients0[dof][2];

613

new_coeff0_3 = coefficients0[dof][3];

614

new_coeff0_4 = coefficients0[dof][4];

615

new_coeff0_5 = coefficients0[dof][5];

616

new_coeff0_6 = coefficients0[dof][6];

617

new_coeff0_7 = coefficients0[dof][7];

618

new_coeff0_8 = coefficients0[dof][8];

619

new_coeff0_9 = coefficients0[dof][9];

620

new_coeff0_10 = coefficients0[dof][10];

621

new_coeff0_11 = coefficients0[dof][11];

622

new_coeff0_12 = coefficients0[dof][12];

623

new_coeff0_13 = coefficients0[dof][13];

624

new_coeff0_14 = coefficients0[dof][14];

625

new_coeff0_15 = coefficients0[dof][15];

626

new_coeff0_16 = coefficients0[dof][16];

627

new_coeff0_17 = coefficients0[dof][17];

628

new_coeff0_18 = coefficients0[dof][18];

629

new_coeff0_19 = coefficients0[dof][19];

630

631

// Loop derivative order

632

for (unsigned int j = 0; j < n; j++)

633

{

634

// Update old coefficients

635

coeff0_0 = new_coeff0_0;

636

coeff0_1 = new_coeff0_1;

637

coeff0_2 = new_coeff0_2;

638

coeff0_3 = new_coeff0_3;

639

coeff0_4 = new_coeff0_4;

640

coeff0_5 = new_coeff0_5;

641

coeff0_6 = new_coeff0_6;

642

coeff0_7 = new_coeff0_7;

643

coeff0_8 = new_coeff0_8;

644

coeff0_9 = new_coeff0_9;

645

coeff0_10 = new_coeff0_10;

646

coeff0_11 = new_coeff0_11;

647

coeff0_12 = new_coeff0_12;

648

coeff0_13 = new_coeff0_13;

649

coeff0_14 = new_coeff0_14;

650

coeff0_15 = new_coeff0_15;

651

coeff0_16 = new_coeff0_16;

652

coeff0_17 = new_coeff0_17;

653

coeff0_18 = new_coeff0_18;

654

coeff0_19 = new_coeff0_19;

655

656

if(combinations[deriv_num][j] == 0)

657

{

658

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

659

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

660

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

661

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

662

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

663

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

664

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

665

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

666

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

667

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

668

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

669

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

670

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

671

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

672

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

673

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

674

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

675

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

676

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

677

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

678

}

679

if(combinations[deriv_num][j] == 1)

680

{

681

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

682

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

683

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

684

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

685

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

686

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

687

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

688

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

689

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

690

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

691

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

692

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

693

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

694

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

695

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

696

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

697

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

698

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

699

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

700

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

701

}

702

if(combinations[deriv_num][j] == 2)

703

{

704

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

705

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

706

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

707

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

708

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

709

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

710

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

711

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

712

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

713

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

714

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

715

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

716

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

717

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

718

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

719

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

720

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

721

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

722

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

723

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

724

}

725

726

}

727

// Compute derivatives on reference element as dot product of coefficients and basisvalues

728

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

729

}

730

731

// Transform derivatives back to physical element

732

for (unsigned int row = 0; row < num_derivatives; row++)

733

{

734

for (unsigned int col = 0; col < num_derivatives; col++)

735

{

736

values[row] += transform[row][col]*derivatives[col];

737

}

738

}

739

// Delete pointer to array of derivatives on FIAT element

740

delete [] derivatives;

741

742

// Delete pointer to array of combinations of derivatives and transform

743

for (unsigned int row = 0; row < num_derivatives; row++)

744

{

745

delete [] combinations[row];

746

delete [] transform[row];

747

}

748

749

delete [] combinations;

750

delete [] transform;

751

}

752

753

/// Evaluate order n derivatives of all basis functions at given point in cell

754

virtual void evaluate_basis_derivatives_all(unsigned int n,

755

double* values,

756

const double* coordinates,

757

const ufc::cell& c) const

758

{

759

throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");

760

}

761

762

/// Evaluate linear functional for dof i on the function f

763

virtual double evaluate_dof(unsigned int i,

764

const ufc::function& f,

765

const ufc::cell& c) const

766

{

767

// The reference points, direction and weights:

768

const static double X[20][1][3] = {{{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}};

769

const static double W[20][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};

770

const static double D[20][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};

771

772

const double * const * x = c.coordinates;

773

double result = 0.0;

774

// Iterate over the points:

775

// Evaluate basis functions for affine mapping

776

const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];

777

const double w1 = X[i][0][0];

778

const double w2 = X[i][0][1];

779

const double w3 = X[i][0][2];

780

781

// Compute affine mapping y = F(X)

782

double y[3];

783

y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];

784

y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];

785

y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];

786

787

// Evaluate function at physical points

788

double values[1];

789

f.evaluate(values, y, c);

790

791

// Map function values using appropriate mapping

792

// Affine map: Do nothing

793

794

// Note that we do not map the weights (yet).

795

796

// Take directional components

797

for(int k = 0; k < 1; k++)

798

result += values[k]*D[i][0][k];

799

// Multiply by weights

800

result *= W[i][0];

801

802

return result;

803

}

804

805

/// Evaluate linear functionals for all dofs on the function f

806

virtual void evaluate_dofs(double* values,

807

const ufc::function& f,

808

const ufc::cell& c) const

809

{

810

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

811

}

812

813

/// Interpolate vertex values from dof values

814

virtual void interpolate_vertex_values(double* vertex_values,

815

const double* dof_values,

816

const ufc::cell& c) const

817

{

818

// Evaluate at vertices and use affine mapping

819

vertex_values[0] = dof_values[0];

820

vertex_values[1] = dof_values[3];

821

vertex_values[2] = dof_values[9];

822

vertex_values[3] = dof_values[19];

823

}

824

825

/// Return the number of sub elements (for a mixed element)

826

virtual unsigned int num_sub_elements() const

827

{

828

return 1;

829

}

830

831

/// Create a new finite element for sub element i (for a mixed element)

832

virtual ufc::finite_element* create_sub_element(unsigned int i) const

833

{

834

return new ffc_25_finite_element_0_0();

835

}

836

837

};

838

839

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

840

841

class ffc_25_finite_element_0_1: public ufc::finite_element

842

{

843

public:

844

845

/// Constructor

846

ffc_25_finite_element_0_1() : ufc::finite_element()

847

{

848

// Do nothing

849

}

850

851

/// Destructor

852

virtual ~ffc_25_finite_element_0_1()

853

{

854

// Do nothing

855

}

856

857

/// Return a string identifying the finite element

858

virtual const char* signature() const

859

{

860

return "Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

861

}

862

863

/// Return the cell shape

864

virtual ufc::shape cell_shape() const

865

{

866

return ufc::tetrahedron;

867

}

868

869

/// Return the dimension of the finite element function space

870

virtual unsigned int space_dimension() const

871

{

872

return 20;

873

}

874

875

/// Return the rank of the value space

876

virtual unsigned int value_rank() const

877

{

878

return 0;

879

}

880

881

/// Return the dimension of the value space for axis i

882

virtual unsigned int value_dimension(unsigned int i) const

883

{

884

return 1;

885

}

886

887

/// Evaluate basis function i at given point in cell

888

virtual void evaluate_basis(unsigned int i,

889

double* values,

890

const double* coordinates,

891

const ufc::cell& c) const

892

{

893

// Extract vertex coordinates

894

const double * const * element_coordinates = c.coordinates;

895

896

// Compute Jacobian of affine map from reference cell

897

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

898

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

899

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

900

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

901

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

902

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

903

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

904

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

905

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

906

907

// Compute sub determinants

908

const double d00 = J_11*J_22 - J_12*J_21;

909

const double d01 = J_12*J_20 - J_10*J_22;

910

const double d02 = J_10*J_21 - J_11*J_20;

911

912

const double d10 = J_02*J_21 - J_01*J_22;

913

const double d11 = J_00*J_22 - J_02*J_20;

914

const double d12 = J_01*J_20 - J_00*J_21;

915

916

const double d20 = J_01*J_12 - J_02*J_11;

917

const double d21 = J_02*J_10 - J_00*J_12;

918

const double d22 = J_00*J_11 - J_01*J_10;

919

920

// Compute determinant of Jacobian

921

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

922

923

// Compute inverse of Jacobian

924

925

// Compute constants

926

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

927

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

928

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

929

930

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

931

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

932

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

933

934

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

935

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

936

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

937

938

// Get coordinates and map to the UFC reference element

939

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

940

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

941

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

942

943

// Map coordinates to the reference cube

944

if (std::abs(y + z - 1.0) < 1e-14)

945

x = 1.0;

946

else

947

x = -2.0 * x/(y + z - 1.0) - 1.0;

948

if (std::abs(z - 1.0) < 1e-14)

949

y = -1.0;

950

else

951

y = 2.0 * y/(1.0 - z) - 1.0;

952

z = 2.0 * z - 1.0;

953

954

// Reset values

955

*values = 0;

956

957

// Map degree of freedom to element degree of freedom

958

const unsigned int dof = i;

959

960

// Generate scalings

961

const double scalings_y_0 = 1;

962

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

963

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

964

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

965

const double scalings_z_0 = 1;

966

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

967

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

968

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

969

970

// Compute psitilde_a

971

const double psitilde_a_0 = 1;

972

const double psitilde_a_1 = x;

973

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

974

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

975

976

// Compute psitilde_bs

977

const double psitilde_bs_0_0 = 1;

978

const double psitilde_bs_0_1 = 1.5*y + 0.5;

979

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

980

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

981

const double psitilde_bs_1_0 = 1;

982

const double psitilde_bs_1_1 = 2.5*y + 1.5;

983

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

984

const double psitilde_bs_2_0 = 1;

985

const double psitilde_bs_2_1 = 3.5*y + 2.5;

986

const double psitilde_bs_3_0 = 1;

987

988

// Compute psitilde_cs

989

const double psitilde_cs_00_0 = 1;

990

const double psitilde_cs_00_1 = 2*z + 1;

991

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

992

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

993

const double psitilde_cs_01_0 = 1;

994

const double psitilde_cs_01_1 = 3*z + 2;

995

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

996

const double psitilde_cs_02_0 = 1;

997

const double psitilde_cs_02_1 = 4*z + 3;

998

const double psitilde_cs_03_0 = 1;

999

const double psitilde_cs_10_0 = 1;

1000

const double psitilde_cs_10_1 = 3*z + 2;

1001

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

1002

const double psitilde_cs_11_0 = 1;

1003

const double psitilde_cs_11_1 = 4*z + 3;

1004

const double psitilde_cs_12_0 = 1;

1005

const double psitilde_cs_20_0 = 1;

1006

const double psitilde_cs_20_1 = 4*z + 3;

1007

const double psitilde_cs_21_0 = 1;

1008

const double psitilde_cs_30_0 = 1;

1009

1010

// Compute basisvalues

1011

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

1012

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

1013

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

1014

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

1015

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

1016

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

1017

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

1018

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

1019

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

1020

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

1021

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

1022

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

1023

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

1024

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

1025

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

1026

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

1027

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

1028

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

1029

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

1030

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

1031

1032

// Table(s) of coefficients

1033

const static double coefficients0[20][20] = \

1034

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

1035

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

1036

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

1037

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1038

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

1039

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

1040

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

1041

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

1042

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

1043

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

1044

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1045

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

1046

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1047

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

1048

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1049

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

1050

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

1051

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

1052

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

1053

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

1054

1055

// Extract relevant coefficients

1056

const double coeff0_0 = coefficients0[dof][0];

1057

const double coeff0_1 = coefficients0[dof][1];

1058

const double coeff0_2 = coefficients0[dof][2];

1059

const double coeff0_3 = coefficients0[dof][3];

1060

const double coeff0_4 = coefficients0[dof][4];

1061

const double coeff0_5 = coefficients0[dof][5];

1062

const double coeff0_6 = coefficients0[dof][6];

1063

const double coeff0_7 = coefficients0[dof][7];

1064

const double coeff0_8 = coefficients0[dof][8];

1065

const double coeff0_9 = coefficients0[dof][9];

1066

const double coeff0_10 = coefficients0[dof][10];

1067

const double coeff0_11 = coefficients0[dof][11];

1068

const double coeff0_12 = coefficients0[dof][12];

1069

const double coeff0_13 = coefficients0[dof][13];

1070

const double coeff0_14 = coefficients0[dof][14];

1071

const double coeff0_15 = coefficients0[dof][15];

1072

const double coeff0_16 = coefficients0[dof][16];

1073

const double coeff0_17 = coefficients0[dof][17];

1074

const double coeff0_18 = coefficients0[dof][18];

1075

const double coeff0_19 = coefficients0[dof][19];

1076

1077

// Compute value(s)

1078

*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

1079

}

1080

1081

/// Evaluate all basis functions at given point in cell

1082

virtual void evaluate_basis_all(double* values,

1083

const double* coordinates,

1084

const ufc::cell& c) const

1085

{

1086

throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");

1087

}

1088

1089

/// Evaluate order n derivatives of basis function i at given point in cell

1090

virtual void evaluate_basis_derivatives(unsigned int i,

1091

unsigned int n,

1092

double* values,

1093

const double* coordinates,

1094

const ufc::cell& c) const

1095

{

1096

// Extract vertex coordinates

1097

const double * const * element_coordinates = c.coordinates;

1098

1099

// Compute Jacobian of affine map from reference cell

1100

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

1101

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

1102

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

1103

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

1104

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

1105

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

1106

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

1107

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

1108

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

1109

1110

// Compute sub determinants

1111

const double d00 = J_11*J_22 - J_12*J_21;

1112

const double d01 = J_12*J_20 - J_10*J_22;

1113

const double d02 = J_10*J_21 - J_11*J_20;

1114

1115

const double d10 = J_02*J_21 - J_01*J_22;

1116

const double d11 = J_00*J_22 - J_02*J_20;

1117

const double d12 = J_01*J_20 - J_00*J_21;

1118

1119

const double d20 = J_01*J_12 - J_02*J_11;

1120

const double d21 = J_02*J_10 - J_00*J_12;

1121

const double d22 = J_00*J_11 - J_01*J_10;

1122

1123

// Compute determinant of Jacobian

1124

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

1125

1126

// Compute inverse of Jacobian

1127

1128

// Compute constants

1129

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

1130

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

1131

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

1132

1133

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

1134

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

1135

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

1136

1137

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

1138

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

1139

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

1140

1141

// Get coordinates and map to the UFC reference element

1142

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

1143

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

1144

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

1145

1146

// Map coordinates to the reference cube

1147

if (std::abs(y + z - 1.0) < 1e-14)

1148

x = 1.0;

1149

else

1150

x = -2.0 * x/(y + z - 1.0) - 1.0;

1151

if (std::abs(z - 1.0) < 1e-14)

1152

y = -1.0;

1153

else

1154

y = 2.0 * y/(1.0 - z) - 1.0;

1155

z = 2.0 * z - 1.0;

1156

1157

// Compute number of derivatives

1158

unsigned int num_derivatives = 1;

1159

1160

for (unsigned int j = 0; j < n; j++)

1161

num_derivatives *= 3;

1162

1163

1164

// Declare pointer to two dimensional array that holds combinations of derivatives and initialise

1165

unsigned int **combinations = new unsigned int *[num_derivatives];

1166

1167

for (unsigned int j = 0; j < num_derivatives; j++)

1168

{

1169

combinations[j] = new unsigned int [n];

1170

for (unsigned int k = 0; k < n; k++)

1171

combinations[j][k] = 0;

1172

}

1173

1174

// Generate combinations of derivatives

1175

for (unsigned int row = 1; row < num_derivatives; row++)

1176

{

1177

for (unsigned int num = 0; num < row; num++)

1178

{

1179

for (unsigned int col = n-1; col+1 > 0; col--)

1180

{

1181

if (combinations[row][col] + 1 > 2)

1182

combinations[row][col] = 0;

1183

else

1184

{

1185

combinations[row][col] += 1;

1186

break;

1187

}

1188

}

1189

}

1190

}

1191

1192

// Compute inverse of Jacobian

1193

const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};

1194

1195

// Declare transformation matrix

1196

// Declare pointer to two dimensional array and initialise

1197

double **transform = new double *[num_derivatives];

1198

1199

for (unsigned int j = 0; j < num_derivatives; j++)

1200

{

1201

transform[j] = new double [num_derivatives];

1202

for (unsigned int k = 0; k < num_derivatives; k++)

1203

transform[j][k] = 1;

1204

}

1205

1206

// Construct transformation matrix

1207

for (unsigned int row = 0; row < num_derivatives; row++)

1208

{

1209

for (unsigned int col = 0; col < num_derivatives; col++)

1210

{

1211

for (unsigned int k = 0; k < n; k++)

1212

transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];

1213

}

1214

}

1215

1216

// Reset values

1217

for (unsigned int j = 0; j < 1*num_derivatives; j++)

1218

values[j] = 0;

1219

1220

// Map degree of freedom to element degree of freedom

1221

const unsigned int dof = i;

1222

1223

// Generate scalings

1224

const double scalings_y_0 = 1;

1225

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

1226

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

1227

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

1228

const double scalings_z_0 = 1;

1229

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

1230

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

1231

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

1232

1233

// Compute psitilde_a

1234

const double psitilde_a_0 = 1;

1235

const double psitilde_a_1 = x;

1236

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

1237

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

1238

1239

// Compute psitilde_bs

1240

const double psitilde_bs_0_0 = 1;

1241

const double psitilde_bs_0_1 = 1.5*y + 0.5;

1242

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

1243

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

1244

const double psitilde_bs_1_0 = 1;

1245

const double psitilde_bs_1_1 = 2.5*y + 1.5;

1246

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

1247

const double psitilde_bs_2_0 = 1;

1248

const double psitilde_bs_2_1 = 3.5*y + 2.5;

1249

const double psitilde_bs_3_0 = 1;

1250

1251

// Compute psitilde_cs

1252

const double psitilde_cs_00_0 = 1;

1253

const double psitilde_cs_00_1 = 2*z + 1;

1254

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

1255

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

1256

const double psitilde_cs_01_0 = 1;

1257

const double psitilde_cs_01_1 = 3*z + 2;

1258

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

1259

const double psitilde_cs_02_0 = 1;

1260

const double psitilde_cs_02_1 = 4*z + 3;

1261

const double psitilde_cs_03_0 = 1;

1262

const double psitilde_cs_10_0 = 1;

1263

const double psitilde_cs_10_1 = 3*z + 2;

1264

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

1265

const double psitilde_cs_11_0 = 1;

1266

const double psitilde_cs_11_1 = 4*z + 3;

1267

const double psitilde_cs_12_0 = 1;

1268

const double psitilde_cs_20_0 = 1;

1269

const double psitilde_cs_20_1 = 4*z + 3;

1270

const double psitilde_cs_21_0 = 1;

1271

const double psitilde_cs_30_0 = 1;

1272

1273

// Compute basisvalues

1274

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

1275

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

1276

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

1277

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

1278

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

1279

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

1280

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

1281

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

1282

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

1283

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

1284

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

1285

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

1286

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

1287

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

1288

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

1289

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

1290

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

1291

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

1292

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

1293

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

1294

1295

// Table(s) of coefficients

1296

const static double coefficients0[20][20] = \

1297

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

1298

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

1299

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

1300

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1301

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

1302

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

1303

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

1304

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

1305

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

1306

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

1307

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1308

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

1309

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1310

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

1311

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1312

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

1313

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

1314

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

1315

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

1316

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

1317

1318

// Interesting (new) part

1319

// Tables of derivatives of the polynomial base (transpose)

1320

const static double dmats0[20][20] = \

1321

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1322

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1323

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1324

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1325

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1326

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1327

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1328

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1329

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1330

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1331

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1332

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1333

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1334

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1335

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1336

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1337

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1338

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1339

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1340

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

1341

1342

const static double dmats1[20][20] = \

1343

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1344

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1345

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1346

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1347

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1348

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1349

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1350

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1351

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1352

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1353

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1354

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1355

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1356

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1357

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1358

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1359

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1360

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1361

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1362

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

1363

1364

const static double dmats2[20][20] = \

1365

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1366

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1367

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1368

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1369

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1370

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1371

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1372

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1373

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1374

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1375

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1376

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1377

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1378

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1379

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1380

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1381

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1382

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1383

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1384

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

1385

1386

// Compute reference derivatives

1387

// Declare pointer to array of derivatives on FIAT element

1388

double *derivatives = new double [num_derivatives];

1389

1390

// Declare coefficients

1391

double coeff0_0 = 0;

1392

double coeff0_1 = 0;

1393

double coeff0_2 = 0;

1394

double coeff0_3 = 0;

1395

double coeff0_4 = 0;

1396

double coeff0_5 = 0;

1397

double coeff0_6 = 0;

1398

double coeff0_7 = 0;

1399

double coeff0_8 = 0;

1400

double coeff0_9 = 0;

1401

double coeff0_10 = 0;

1402

double coeff0_11 = 0;

1403

double coeff0_12 = 0;

1404

double coeff0_13 = 0;

1405

double coeff0_14 = 0;

1406

double coeff0_15 = 0;

1407

double coeff0_16 = 0;

1408

double coeff0_17 = 0;

1409

double coeff0_18 = 0;

1410

double coeff0_19 = 0;

1411

1412

// Declare new coefficients

1413

double new_coeff0_0 = 0;

1414

double new_coeff0_1 = 0;

1415

double new_coeff0_2 = 0;

1416

double new_coeff0_3 = 0;

1417

double new_coeff0_4 = 0;

1418

double new_coeff0_5 = 0;

1419

double new_coeff0_6 = 0;

1420

double new_coeff0_7 = 0;

1421

double new_coeff0_8 = 0;

1422

double new_coeff0_9 = 0;

1423

double new_coeff0_10 = 0;

1424

double new_coeff0_11 = 0;

1425

double new_coeff0_12 = 0;

1426

double new_coeff0_13 = 0;

1427

double new_coeff0_14 = 0;

1428

double new_coeff0_15 = 0;

1429

double new_coeff0_16 = 0;

1430

double new_coeff0_17 = 0;

1431

double new_coeff0_18 = 0;

1432

double new_coeff0_19 = 0;

1433

1434

// Loop possible derivatives

1435

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

1436

{

1437

// Get values from coefficients array

1438

new_coeff0_0 = coefficients0[dof][0];

1439

new_coeff0_1 = coefficients0[dof][1];

1440

new_coeff0_2 = coefficients0[dof][2];

1441

new_coeff0_3 = coefficients0[dof][3];

1442

new_coeff0_4 = coefficients0[dof][4];

1443

new_coeff0_5 = coefficients0[dof][5];

1444

new_coeff0_6 = coefficients0[dof][6];

1445

new_coeff0_7 = coefficients0[dof][7];

1446

new_coeff0_8 = coefficients0[dof][8];

1447

new_coeff0_9 = coefficients0[dof][9];

1448

new_coeff0_10 = coefficients0[dof][10];

1449

new_coeff0_11 = coefficients0[dof][11];

1450

new_coeff0_12 = coefficients0[dof][12];

1451

new_coeff0_13 = coefficients0[dof][13];

1452

new_coeff0_14 = coefficients0[dof][14];

1453

new_coeff0_15 = coefficients0[dof][15];

1454

new_coeff0_16 = coefficients0[dof][16];

1455

new_coeff0_17 = coefficients0[dof][17];

1456

new_coeff0_18 = coefficients0[dof][18];

1457

new_coeff0_19 = coefficients0[dof][19];

1458

1459

// Loop derivative order

1460

for (unsigned int j = 0; j < n; j++)

1461

{

1462

// Update old coefficients

1463

coeff0_0 = new_coeff0_0;

1464

coeff0_1 = new_coeff0_1;

1465

coeff0_2 = new_coeff0_2;

1466

coeff0_3 = new_coeff0_3;

1467

coeff0_4 = new_coeff0_4;

1468

coeff0_5 = new_coeff0_5;

1469

coeff0_6 = new_coeff0_6;

1470

coeff0_7 = new_coeff0_7;

1471

coeff0_8 = new_coeff0_8;

1472

coeff0_9 = new_coeff0_9;

1473

coeff0_10 = new_coeff0_10;

1474

coeff0_11 = new_coeff0_11;

1475

coeff0_12 = new_coeff0_12;

1476

coeff0_13 = new_coeff0_13;

1477

coeff0_14 = new_coeff0_14;

1478

coeff0_15 = new_coeff0_15;

1479

coeff0_16 = new_coeff0_16;

1480

coeff0_17 = new_coeff0_17;

1481

coeff0_18 = new_coeff0_18;

1482

coeff0_19 = new_coeff0_19;

1483

1484

if(combinations[deriv_num][j] == 0)

1485

{

1486

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

1487

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

1488

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

1489

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

1490

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

1491

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

1492

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

1493

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

1494

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

1495

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

1496

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

1497

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

1498

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

1499

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

1500

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

1501

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

1502

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

1503

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

1504

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

1505

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

1506

}

1507

if(combinations[deriv_num][j] == 1)

1508

{

1509

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

1510

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

1511

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

1512

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

1513

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

1514

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

1515

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

1516

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

1517

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

1518

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

1519

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

1520

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

1521

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

1522

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

1523

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

1524

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

1525

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

1526

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

1527

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

1528

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

1529

}

1530

if(combinations[deriv_num][j] == 2)

1531

{

1532

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

1533

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

1534

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

1535

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

1536

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

1537

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

1538

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

1539

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

1540

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

1541

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

1542

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

1543

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

1544

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

1545

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

1546

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

1547

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

1548

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

1549

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

1550

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

1551

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

1552

}

1553

1554

}

1555

// Compute derivatives on reference element as dot product of coefficients and basisvalues

1556

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

1557

}

1558

1559

// Transform derivatives back to physical element

1560

for (unsigned int row = 0; row < num_derivatives; row++)

1561

{

1562

for (unsigned int col = 0; col < num_derivatives; col++)

1563

{

1564

values[row] += transform[row][col]*derivatives[col];

1565

}

1566

}

1567

// Delete pointer to array of derivatives on FIAT element

1568

delete [] derivatives;

1569

1570

// Delete pointer to array of combinations of derivatives and transform

1571

for (unsigned int row = 0; row < num_derivatives; row++)

1572

{

1573

delete [] combinations[row];

1574

delete [] transform[row];

1575

}

1576

1577

delete [] combinations;

1578

delete [] transform;

1579

}

1580

1581

/// Evaluate order n derivatives of all basis functions at given point in cell

1582

virtual void evaluate_basis_derivatives_all(unsigned int n,

1583

double* values,

1584

const double* coordinates,

1585

const ufc::cell& c) const

1586

{

1587

throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");

1588

}

1589

1590

/// Evaluate linear functional for dof i on the function f

1591

virtual double evaluate_dof(unsigned int i,

1592

const ufc::function& f,

1593

const ufc::cell& c) const

1594

{

1595

// The reference points, direction and weights:

1596

const static double X[20][1][3] = {{{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}};

1597

const static double W[20][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};

1598

const static double D[20][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};

1599

1600

const double * const * x = c.coordinates;

1601

double result = 0.0;

1602

// Iterate over the points:

1603

// Evaluate basis functions for affine mapping

1604

const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];

1605

const double w1 = X[i][0][0];

1606

const double w2 = X[i][0][1];

1607

const double w3 = X[i][0][2];

1608

1609

// Compute affine mapping y = F(X)

1610

double y[3];

1611

y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];

1612

y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];

1613

y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];

1614

1615

// Evaluate function at physical points

1616

double values[1];

1617

f.evaluate(values, y, c);

1618

1619

// Map function values using appropriate mapping

1620

// Affine map: Do nothing

1621

1622

// Note that we do not map the weights (yet).

1623

1624

// Take directional components

1625

for(int k = 0; k < 1; k++)

1626

result += values[k]*D[i][0][k];

1627

// Multiply by weights

1628

result *= W[i][0];

1629

1630

return result;

1631

}

1632

1633

/// Evaluate linear functionals for all dofs on the function f

1634

virtual void evaluate_dofs(double* values,

1635

const ufc::function& f,

1636

const ufc::cell& c) const

1637

{

1638

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

1639

}

1640

1641

/// Interpolate vertex values from dof values

1642

virtual void interpolate_vertex_values(double* vertex_values,

1643

const double* dof_values,

1644

const ufc::cell& c) const

1645

{

1646

// Evaluate at vertices and use affine mapping

1647

vertex_values[0] = dof_values[0];

1648

vertex_values[1] = dof_values[3];

1649

vertex_values[2] = dof_values[9];

1650

vertex_values[3] = dof_values[19];

1651

}

1652

1653

/// Return the number of sub elements (for a mixed element)

1654

virtual unsigned int num_sub_elements() const

1655

{

1656

return 1;

1657

}

1658

1659

/// Create a new finite element for sub element i (for a mixed element)

1660

virtual ufc::finite_element* create_sub_element(unsigned int i) const

1661

{

1662

return new ffc_25_finite_element_0_1();

1663

}

1664

1665

};

1666

1667

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

1668

1669

class ffc_25_finite_element_0_2: public ufc::finite_element

1670

{

1671

public:

1672

1673

/// Constructor

1674

ffc_25_finite_element_0_2() : ufc::finite_element()

1675

{

1676

// Do nothing

1677

}

1678

1679

/// Destructor

1680

virtual ~ffc_25_finite_element_0_2()

1681

{

1682

// Do nothing

1683

}

1684

1685

/// Return a string identifying the finite element

1686

virtual const char* signature() const

1687

{

1688

return "Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

1689

}

1690

1691

/// Return the cell shape

1692

virtual ufc::shape cell_shape() const

1693

{

1694

return ufc::tetrahedron;

1695

}

1696

1697

/// Return the dimension of the finite element function space

1698

virtual unsigned int space_dimension() const

1699

{

1700

return 20;

1701

}

1702

1703

/// Return the rank of the value space

1704

virtual unsigned int value_rank() const

1705

{

1706

return 0;

1707

}

1708

1709

/// Return the dimension of the value space for axis i

1710

virtual unsigned int value_dimension(unsigned int i) const

1711

{

1712

return 1;

1713

}

1714

1715

/// Evaluate basis function i at given point in cell

1716

virtual void evaluate_basis(unsigned int i,

1717

double* values,

1718

const double* coordinates,

1719

const ufc::cell& c) const

1720

{

1721

// Extract vertex coordinates

1722

const double * const * element_coordinates = c.coordinates;

1723

1724

// Compute Jacobian of affine map from reference cell

1725

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

1726

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

1727

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

1728

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

1729

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

1730

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

1731

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

1732

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

1733

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

1734

1735

// Compute sub determinants

1736

const double d00 = J_11*J_22 - J_12*J_21;

1737

const double d01 = J_12*J_20 - J_10*J_22;

1738

const double d02 = J_10*J_21 - J_11*J_20;

1739

1740

const double d10 = J_02*J_21 - J_01*J_22;

1741

const double d11 = J_00*J_22 - J_02*J_20;

1742

const double d12 = J_01*J_20 - J_00*J_21;

1743

1744

const double d20 = J_01*J_12 - J_02*J_11;

1745

const double d21 = J_02*J_10 - J_00*J_12;

1746

const double d22 = J_00*J_11 - J_01*J_10;

1747

1748

// Compute determinant of Jacobian

1749

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

1750

1751

// Compute inverse of Jacobian

1752

1753

// Compute constants

1754

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

1755

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

1756

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

1757

1758

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

1759

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

1760

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

1761

1762

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

1763

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

1764

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

1765

1766

// Get coordinates and map to the UFC reference element

1767

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

1768

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

1769

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

1770

1771

// Map coordinates to the reference cube

1772

if (std::abs(y + z - 1.0) < 1e-14)

1773

x = 1.0;

1774

else

1775

x = -2.0 * x/(y + z - 1.0) - 1.0;

1776

if (std::abs(z - 1.0) < 1e-14)

1777

y = -1.0;

1778

else

1779

y = 2.0 * y/(1.0 - z) - 1.0;

1780

z = 2.0 * z - 1.0;

1781

1782

// Reset values

1783

*values = 0;

1784

1785

// Map degree of freedom to element degree of freedom

1786

const unsigned int dof = i;

1787

1788

// Generate scalings

1789

const double scalings_y_0 = 1;

1790

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

1791

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

1792

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

1793

const double scalings_z_0 = 1;

1794

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

1795

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

1796

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

1797

1798

// Compute psitilde_a

1799

const double psitilde_a_0 = 1;

1800

const double psitilde_a_1 = x;

1801

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

1802

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

1803

1804

// Compute psitilde_bs

1805

const double psitilde_bs_0_0 = 1;

1806

const double psitilde_bs_0_1 = 1.5*y + 0.5;

1807

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

1808

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

1809

const double psitilde_bs_1_0 = 1;

1810

const double psitilde_bs_1_1 = 2.5*y + 1.5;

1811

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

1812

const double psitilde_bs_2_0 = 1;

1813

const double psitilde_bs_2_1 = 3.5*y + 2.5;

1814

const double psitilde_bs_3_0 = 1;

1815

1816

// Compute psitilde_cs

1817

const double psitilde_cs_00_0 = 1;

1818

const double psitilde_cs_00_1 = 2*z + 1;

1819

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

1820

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

1821

const double psitilde_cs_01_0 = 1;

1822

const double psitilde_cs_01_1 = 3*z + 2;

1823

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

1824

const double psitilde_cs_02_0 = 1;

1825

const double psitilde_cs_02_1 = 4*z + 3;

1826

const double psitilde_cs_03_0 = 1;

1827

const double psitilde_cs_10_0 = 1;

1828

const double psitilde_cs_10_1 = 3*z + 2;

1829

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

1830

const double psitilde_cs_11_0 = 1;

1831

const double psitilde_cs_11_1 = 4*z + 3;

1832

const double psitilde_cs_12_0 = 1;

1833

const double psitilde_cs_20_0 = 1;

1834

const double psitilde_cs_20_1 = 4*z + 3;

1835

const double psitilde_cs_21_0 = 1;

1836

const double psitilde_cs_30_0 = 1;

1837

1838

// Compute basisvalues

1839

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

1840

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

1841

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

1842

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

1843

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

1844

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

1845

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

1846

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

1847

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

1848

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

1849

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

1850

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

1851

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

1852

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

1853

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

1854

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

1855

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

1856

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

1857

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

1858

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

1859

1860

// Table(s) of coefficients

1861

const static double coefficients0[20][20] = \

1862

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

1863

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

1864

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

1865

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1866

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

1867

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

1868

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

1869

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

1870

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

1871

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

1872

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1873

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

1874

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

1875

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

1876

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1877

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

1878

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

1879

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

1880

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

1881

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

1882

1883

// Extract relevant coefficients

1884

const double coeff0_0 = coefficients0[dof][0];

1885

const double coeff0_1 = coefficients0[dof][1];

1886

const double coeff0_2 = coefficients0[dof][2];

1887

const double coeff0_3 = coefficients0[dof][3];

1888

const double coeff0_4 = coefficients0[dof][4];

1889

const double coeff0_5 = coefficients0[dof][5];

1890

const double coeff0_6 = coefficients0[dof][6];

1891

const double coeff0_7 = coefficients0[dof][7];

1892

const double coeff0_8 = coefficients0[dof][8];

1893

const double coeff0_9 = coefficients0[dof][9];

1894

const double coeff0_10 = coefficients0[dof][10];

1895

const double coeff0_11 = coefficients0[dof][11];

1896

const double coeff0_12 = coefficients0[dof][12];

1897

const double coeff0_13 = coefficients0[dof][13];

1898

const double coeff0_14 = coefficients0[dof][14];

1899

const double coeff0_15 = coefficients0[dof][15];

1900

const double coeff0_16 = coefficients0[dof][16];

1901

const double coeff0_17 = coefficients0[dof][17];

1902

const double coeff0_18 = coefficients0[dof][18];

1903

const double coeff0_19 = coefficients0[dof][19];

1904

1905

// Compute value(s)

1906

*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

1907

}

1908

1909

/// Evaluate all basis functions at given point in cell

1910

virtual void evaluate_basis_all(double* values,

1911

const double* coordinates,

1912

const ufc::cell& c) const

1913

{

1914

throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");

1915

}

1916

1917

/// Evaluate order n derivatives of basis function i at given point in cell

1918

virtual void evaluate_basis_derivatives(unsigned int i,

1919

unsigned int n,

1920

double* values,

1921

const double* coordinates,

1922

const ufc::cell& c) const

1923

{

1924

// Extract vertex coordinates

1925

const double * const * element_coordinates = c.coordinates;

1926

1927

// Compute Jacobian of affine map from reference cell

1928

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

1929

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

1930

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

1931

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

1932

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

1933

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

1934

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

1935

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

1936

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

1937

1938

// Compute sub determinants

1939

const double d00 = J_11*J_22 - J_12*J_21;

1940

const double d01 = J_12*J_20 - J_10*J_22;

1941

const double d02 = J_10*J_21 - J_11*J_20;

1942

1943

const double d10 = J_02*J_21 - J_01*J_22;

1944

const double d11 = J_00*J_22 - J_02*J_20;

1945

const double d12 = J_01*J_20 - J_00*J_21;

1946

1947

const double d20 = J_01*J_12 - J_02*J_11;

1948

const double d21 = J_02*J_10 - J_00*J_12;

1949

const double d22 = J_00*J_11 - J_01*J_10;

1950

1951

// Compute determinant of Jacobian

1952

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

1953

1954

// Compute inverse of Jacobian

1955

1956

// Compute constants

1957

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

1958

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

1959

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

1960

1961

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

1962

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

1963

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

1964

1965

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

1966

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

1967

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

1968

1969

// Get coordinates and map to the UFC reference element

1970

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

1971

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

1972

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

1973

1974

// Map coordinates to the reference cube

1975

if (std::abs(y + z - 1.0) < 1e-14)

1976

x = 1.0;

1977

else

1978

x = -2.0 * x/(y + z - 1.0) - 1.0;

1979

if (std::abs(z - 1.0) < 1e-14)

1980

y = -1.0;

1981

else

1982

y = 2.0 * y/(1.0 - z) - 1.0;

1983

z = 2.0 * z - 1.0;

1984

1985

// Compute number of derivatives

1986

unsigned int num_derivatives = 1;

1987

1988

for (unsigned int j = 0; j < n; j++)

1989

num_derivatives *= 3;

1990

1991

1992

// Declare pointer to two dimensional array that holds combinations of derivatives and initialise

1993

unsigned int **combinations = new unsigned int *[num_derivatives];

1994

1995

for (unsigned int j = 0; j < num_derivatives; j++)

1996

{

1997

combinations[j] = new unsigned int [n];

1998

for (unsigned int k = 0; k < n; k++)

1999

combinations[j][k] = 0;

2000

}

2001

2002

// Generate combinations of derivatives

2003

for (unsigned int row = 1; row < num_derivatives; row++)

2004

{

2005

for (unsigned int num = 0; num < row; num++)

2006

{

2007

for (unsigned int col = n-1; col+1 > 0; col--)

2008

{

2009

if (combinations[row][col] + 1 > 2)

2010

combinations[row][col] = 0;

2011

else

2012

{

2013

combinations[row][col] += 1;

2014

break;

2015

}

2016

}

2017

}

2018

}

2019

2020

// Compute inverse of Jacobian

2021

const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};

2022

2023

// Declare transformation matrix

2024

// Declare pointer to two dimensional array and initialise

2025

double **transform = new double *[num_derivatives];

2026

2027

for (unsigned int j = 0; j < num_derivatives; j++)

2028

{

2029

transform[j] = new double [num_derivatives];

2030

for (unsigned int k = 0; k < num_derivatives; k++)

2031

transform[j][k] = 1;

2032

}

2033

2034

// Construct transformation matrix

2035

for (unsigned int row = 0; row < num_derivatives; row++)

2036

{

2037

for (unsigned int col = 0; col < num_derivatives; col++)

2038

{

2039

for (unsigned int k = 0; k < n; k++)

2040

transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];

2041

}

2042

}

2043

2044

// Reset values

2045

for (unsigned int j = 0; j < 1*num_derivatives; j++)

2046

values[j] = 0;

2047

2048

// Map degree of freedom to element degree of freedom

2049

const unsigned int dof = i;

2050

2051

// Generate scalings

2052

const double scalings_y_0 = 1;

2053

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

2054

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

2055

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

2056

const double scalings_z_0 = 1;

2057

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

2058

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

2059

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

2060

2061

// Compute psitilde_a

2062

const double psitilde_a_0 = 1;

2063

const double psitilde_a_1 = x;

2064

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

2065

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

2066

2067

// Compute psitilde_bs

2068

const double psitilde_bs_0_0 = 1;

2069

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2070

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

2071

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

2072

const double psitilde_bs_1_0 = 1;

2073

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2074

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

2075

const double psitilde_bs_2_0 = 1;

2076

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2077

const double psitilde_bs_3_0 = 1;

2078

2079

// Compute psitilde_cs

2080

const double psitilde_cs_00_0 = 1;

2081

const double psitilde_cs_00_1 = 2*z + 1;

2082

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

2083

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

2084

const double psitilde_cs_01_0 = 1;

2085

const double psitilde_cs_01_1 = 3*z + 2;

2086

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

2087

const double psitilde_cs_02_0 = 1;

2088

const double psitilde_cs_02_1 = 4*z + 3;

2089

const double psitilde_cs_03_0 = 1;

2090

const double psitilde_cs_10_0 = 1;

2091

const double psitilde_cs_10_1 = 3*z + 2;

2092

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

2093

const double psitilde_cs_11_0 = 1;

2094

const double psitilde_cs_11_1 = 4*z + 3;

2095

const double psitilde_cs_12_0 = 1;

2096

const double psitilde_cs_20_0 = 1;

2097

const double psitilde_cs_20_1 = 4*z + 3;

2098

const double psitilde_cs_21_0 = 1;

2099

const double psitilde_cs_30_0 = 1;

2100

2101

// Compute basisvalues

2102

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

2103

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

2104

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

2105

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

2106

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

2107

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

2108

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

2109

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

2110

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

2111

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

2112

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

2113

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

2114

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

2115

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

2116

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

2117

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

2118

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

2119

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

2120

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

2121

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

2122

2123

// Table(s) of coefficients

2124

const static double coefficients0[20][20] = \

2125

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

2126

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

2127

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

2128

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

2129

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

2130

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

2131

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

2132

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

2133

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

2134

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

2135

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2136

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

2137

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2138

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

2139

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

2140

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

2141

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

2142

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

2143

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

2144

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

2145

2146

// Interesting (new) part

2147

// Tables of derivatives of the polynomial base (transpose)

2148

const static double dmats0[20][20] = \

2149

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2150

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2151

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2152

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2153

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2154

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2155

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2156

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2157

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2158

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2159

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2160

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2161

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2162

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2163

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2164

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2165

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2166

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2167

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2168

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

2169

2170

const static double dmats1[20][20] = \

2171

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2172

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2173

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2174

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2175

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2176

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2177

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2178

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2179

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2180

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2181

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2182

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2183

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2184

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2185

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2186

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2187

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2188

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2189

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2190

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

2191

2192

const static double dmats2[20][20] = \

2193

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2194

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2195

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2196

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2197

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2198

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2199

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2200

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2201

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2202

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2203

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2204

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2205

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2206

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2207

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2208

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2209

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2210

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2211

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

2212

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

2213

2214

// Compute reference derivatives

2215

// Declare pointer to array of derivatives on FIAT element

2216

double *derivatives = new double [num_derivatives];

2217

2218

// Declare coefficients

2219

double coeff0_0 = 0;

2220

double coeff0_1 = 0;

2221

double coeff0_2 = 0;

2222

double coeff0_3 = 0;

2223

double coeff0_4 = 0;

2224

double coeff0_5 = 0;

2225

double coeff0_6 = 0;

2226

double coeff0_7 = 0;

2227

double coeff0_8 = 0;

2228

double coeff0_9 = 0;

2229

double coeff0_10 = 0;

2230

double coeff0_11 = 0;

2231

double coeff0_12 = 0;

2232

double coeff0_13 = 0;

2233

double coeff0_14 = 0;

2234

double coeff0_15 = 0;

2235

double coeff0_16 = 0;

2236

double coeff0_17 = 0;

2237

double coeff0_18 = 0;

2238

double coeff0_19 = 0;

2239

2240

// Declare new coefficients

2241

double new_coeff0_0 = 0;

2242

double new_coeff0_1 = 0;

2243

double new_coeff0_2 = 0;

2244

double new_coeff0_3 = 0;

2245

double new_coeff0_4 = 0;

2246

double new_coeff0_5 = 0;

2247

double new_coeff0_6 = 0;

2248

double new_coeff0_7 = 0;

2249

double new_coeff0_8 = 0;

2250

double new_coeff0_9 = 0;

2251

double new_coeff0_10 = 0;

2252

double new_coeff0_11 = 0;

2253

double new_coeff0_12 = 0;

2254

double new_coeff0_13 = 0;

2255

double new_coeff0_14 = 0;

2256

double new_coeff0_15 = 0;

2257

double new_coeff0_16 = 0;

2258

double new_coeff0_17 = 0;

2259

double new_coeff0_18 = 0;

2260

double new_coeff0_19 = 0;

2261

2262

// Loop possible derivatives

2263

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

2264

{

2265

// Get values from coefficients array

2266

new_coeff0_0 = coefficients0[dof][0];

2267

new_coeff0_1 = coefficients0[dof][1];

2268

new_coeff0_2 = coefficients0[dof][2];

2269

new_coeff0_3 = coefficients0[dof][3];

2270

new_coeff0_4 = coefficients0[dof][4];

2271

new_coeff0_5 = coefficients0[dof][5];

2272

new_coeff0_6 = coefficients0[dof][6];

2273

new_coeff0_7 = coefficients0[dof][7];

2274

new_coeff0_8 = coefficients0[dof][8];

2275

new_coeff0_9 = coefficients0[dof][9];

2276

new_coeff0_10 = coefficients0[dof][10];

2277

new_coeff0_11 = coefficients0[dof][11];

2278

new_coeff0_12 = coefficients0[dof][12];

2279

new_coeff0_13 = coefficients0[dof][13];

2280

new_coeff0_14 = coefficients0[dof][14];

2281

new_coeff0_15 = coefficients0[dof][15];

2282

new_coeff0_16 = coefficients0[dof][16];

2283

new_coeff0_17 = coefficients0[dof][17];

2284

new_coeff0_18 = coefficients0[dof][18];

2285

new_coeff0_19 = coefficients0[dof][19];

2286

2287

// Loop derivative order

2288

for (unsigned int j = 0; j < n; j++)

2289

{

2290

// Update old coefficients

2291

coeff0_0 = new_coeff0_0;

2292

coeff0_1 = new_coeff0_1;

2293

coeff0_2 = new_coeff0_2;

2294

coeff0_3 = new_coeff0_3;

2295

coeff0_4 = new_coeff0_4;

2296

coeff0_5 = new_coeff0_5;

2297

coeff0_6 = new_coeff0_6;

2298

coeff0_7 = new_coeff0_7;

2299

coeff0_8 = new_coeff0_8;

2300

coeff0_9 = new_coeff0_9;

2301

coeff0_10 = new_coeff0_10;

2302

coeff0_11 = new_coeff0_11;

2303

coeff0_12 = new_coeff0_12;

2304

coeff0_13 = new_coeff0_13;

2305

coeff0_14 = new_coeff0_14;

2306

coeff0_15 = new_coeff0_15;

2307

coeff0_16 = new_coeff0_16;

2308

coeff0_17 = new_coeff0_17;

2309

coeff0_18 = new_coeff0_18;

2310

coeff0_19 = new_coeff0_19;

2311

2312

if(combinations[deriv_num][j] == 0)

2313

{

2314

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

2315

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

2316

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

2317

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

2318

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

2319

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

2320

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

2321

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

2322

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

2323

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

2324

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

2325

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

2326

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

2327

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

2328

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

2329

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

2330

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

2331

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

2332

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

2333

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

2334

}

2335

if(combinations[deriv_num][j] == 1)

2336

{

2337

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

2338

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

2339

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

2340

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

2341

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

2342

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

2343

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

2344

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

2345

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

2346

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

2347

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

2348

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

2349

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

2350

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

2351

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

2352

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

2353

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

2354

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

2355

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

2356

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

2357

}

2358

if(combinations[deriv_num][j] == 2)

2359

{

2360

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

2361

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

2362

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

2363

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

2364

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

2365

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

2366

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

2367

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

2368

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

2369

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

2370

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

2371

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

2372

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

2373

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

2374

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

2375

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

2376

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

2377

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

2378

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

2379

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

2380

}

2381

2382

}

2383

// Compute derivatives on reference element as dot product of coefficients and basisvalues

2384

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

2385

}

2386

2387

// Transform derivatives back to physical element

2388

for (unsigned int row = 0; row < num_derivatives; row++)

2389

{

2390

for (unsigned int col = 0; col < num_derivatives; col++)

2391

{

2392

values[row] += transform[row][col]*derivatives[col];

2393

}

2394

}

2395

// Delete pointer to array of derivatives on FIAT element

2396

delete [] derivatives;

2397

2398

// Delete pointer to array of combinations of derivatives and transform

2399

for (unsigned int row = 0; row < num_derivatives; row++)

2400

{

2401

delete [] combinations[row];

2402

delete [] transform[row];

2403

}

2404

2405

delete [] combinations;

2406

delete [] transform;

2407

}

2408

2409

/// Evaluate order n derivatives of all basis functions at given point in cell

2410

virtual void evaluate_basis_derivatives_all(unsigned int n,

2411

double* values,

2412

const double* coordinates,

2413

const ufc::cell& c) const

2414

{

2415

throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");

2416

}

2417

2418

/// Evaluate linear functional for dof i on the function f

2419

virtual double evaluate_dof(unsigned int i,

2420

const ufc::function& f,

2421

const ufc::cell& c) const

2422

{

2423

// The reference points, direction and weights:

2424

const static double X[20][1][3] = {{{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}};

2425

const static double W[20][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};

2426

const static double D[20][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};

2427

2428

const double * const * x = c.coordinates;

2429

double result = 0.0;

2430

// Iterate over the points:

2431

// Evaluate basis functions for affine mapping

2432

const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];

2433

const double w1 = X[i][0][0];

2434

const double w2 = X[i][0][1];

2435

const double w3 = X[i][0][2];

2436

2437

// Compute affine mapping y = F(X)

2438

double y[3];

2439

y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];

2440

y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];

2441

y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];

2442

2443

// Evaluate function at physical points

2444

double values[1];

2445

f.evaluate(values, y, c);

2446

2447

// Map function values using appropriate mapping

2448

// Affine map: Do nothing

2449

2450

// Note that we do not map the weights (yet).

2451

2452

// Take directional components

2453

for(int k = 0; k < 1; k++)

2454

result += values[k]*D[i][0][k];

2455

// Multiply by weights

2456

result *= W[i][0];

2457

2458

return result;

2459

}

2460

2461

/// Evaluate linear functionals for all dofs on the function f

2462

virtual void evaluate_dofs(double* values,

2463

const ufc::function& f,

2464

const ufc::cell& c) const

2465

{

2466

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

2467

}

2468

2469

/// Interpolate vertex values from dof values

2470

virtual void interpolate_vertex_values(double* vertex_values,

2471

const double* dof_values,

2472

const ufc::cell& c) const

2473

{

2474

// Evaluate at vertices and use affine mapping

2475

vertex_values[0] = dof_values[0];

2476

vertex_values[1] = dof_values[3];

2477

vertex_values[2] = dof_values[9];

2478

vertex_values[3] = dof_values[19];

2479

}

2480

2481

/// Return the number of sub elements (for a mixed element)

2482

virtual unsigned int num_sub_elements() const

2483

{

2484

return 1;

2485

}

2486

2487

/// Create a new finite element for sub element i (for a mixed element)

2488

virtual ufc::finite_element* create_sub_element(unsigned int i) const

2489

{

2490

return new ffc_25_finite_element_0_2();

2491

}

2492

2493

};

2494

2495

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

2496

2497

class ffc_25_finite_element_0: public ufc::finite_element

2498

{

2499

public:

2500

2501

/// Constructor

2502

ffc_25_finite_element_0() : ufc::finite_element()

2503

{

2504

// Do nothing

2505

}

2506

2507

/// Destructor

2508

virtual ~ffc_25_finite_element_0()

2509

{

2510

// Do nothing

2511

}

2512

2513

/// Return a string identifying the finite element

2514

virtual const char* signature() const

2515

{

2516

return "Mixed finite element: [Discontinuous Lagrange finite element of degree 3 on a tetrahedron, Discontinuous Lagrange finite element of degree 3 on a tetrahedron, Discontinuous Lagrange finite element of degree 3 on a tetrahedron]";

2517

}

2518

2519

/// Return the cell shape

2520

virtual ufc::shape cell_shape() const

2521

{

2522

return ufc::tetrahedron;

2523

}

2524

2525

/// Return the dimension of the finite element function space

2526

virtual unsigned int space_dimension() const

2527

{

2528

return 60;

2529

}

2530

2531

/// Return the rank of the value space

2532

virtual unsigned int value_rank() const

2533

{

2534

return 1;

2535

}

2536

2537

/// Return the dimension of the value space for axis i

2538

virtual unsigned int value_dimension(unsigned int i) const

2539

{

2540

return 3;

2541

}

2542

2543

/// Evaluate basis function i at given point in cell

2544

virtual void evaluate_basis(unsigned int i,

2545

double* values,

2546

const double* coordinates,

2547

const ufc::cell& c) const

2548

{

2549

// Extract vertex coordinates

2550

const double * const * element_coordinates = c.coordinates;

2551

2552

// Compute Jacobian of affine map from reference cell

2553

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

2554

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

2555

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

2556

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

2557

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

2558

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

2559

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

2560

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

2561

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

2562

2563

// Compute sub determinants

2564

const double d00 = J_11*J_22 - J_12*J_21;

2565

const double d01 = J_12*J_20 - J_10*J_22;

2566

const double d02 = J_10*J_21 - J_11*J_20;

2567

2568

const double d10 = J_02*J_21 - J_01*J_22;

2569

const double d11 = J_00*J_22 - J_02*J_20;

2570

const double d12 = J_01*J_20 - J_00*J_21;

2571

2572

const double d20 = J_01*J_12 - J_02*J_11;

2573

const double d21 = J_02*J_10 - J_00*J_12;

2574

const double d22 = J_00*J_11 - J_01*J_10;

2575

2576

// Compute determinant of Jacobian

2577

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

2578

2579

// Compute inverse of Jacobian

2580

2581

// Compute constants

2582

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

2583

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

2584

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

2585

2586

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

2587

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

2588

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

2589

2590

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

2591

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

2592

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

2593

2594

// Get coordinates and map to the UFC reference element

2595

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

2596

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

2597

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

2598

2599

// Map coordinates to the reference cube

2600

if (std::abs(y + z - 1.0) < 1e-14)

2601

x = 1.0;

2602

else

2603

x = -2.0 * x/(y + z - 1.0) - 1.0;

2604

if (std::abs(z - 1.0) < 1e-14)

2605

y = -1.0;

2606

else

2607

y = 2.0 * y/(1.0 - z) - 1.0;

2608

z = 2.0 * z - 1.0;

2609

2610

// Reset values

2611

values[0] = 0;

2612

values[1] = 0;

2613

values[2] = 0;

2614

2615

if (0 <= i && i <= 19)

2616

{

2617

// Map degree of freedom to element degree of freedom

2618

const unsigned int dof = i;

2619

2620

// Generate scalings

2621

const double scalings_y_0 = 1;

2622

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

2623

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

2624

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

2625

const double scalings_z_0 = 1;

2626

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

2627

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

2628

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

2629

2630

// Compute psitilde_a

2631

const double psitilde_a_0 = 1;

2632

const double psitilde_a_1 = x;

2633

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

2634

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

2635

2636

// Compute psitilde_bs

2637

const double psitilde_bs_0_0 = 1;

2638

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2639

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

2640

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

2641

const double psitilde_bs_1_0 = 1;

2642

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2643

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

2644

const double psitilde_bs_2_0 = 1;

2645

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2646

const double psitilde_bs_3_0 = 1;

2647

2648

// Compute psitilde_cs

2649

const double psitilde_cs_00_0 = 1;

2650

const double psitilde_cs_00_1 = 2*z + 1;

2651

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

2652

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

2653

const double psitilde_cs_01_0 = 1;

2654

const double psitilde_cs_01_1 = 3*z + 2;

2655

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

2656

const double psitilde_cs_02_0 = 1;

2657

const double psitilde_cs_02_1 = 4*z + 3;

2658

const double psitilde_cs_03_0 = 1;

2659

const double psitilde_cs_10_0 = 1;

2660

const double psitilde_cs_10_1 = 3*z + 2;

2661

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

2662

const double psitilde_cs_11_0 = 1;

2663

const double psitilde_cs_11_1 = 4*z + 3;

2664

const double psitilde_cs_12_0 = 1;

2665

const double psitilde_cs_20_0 = 1;

2666

const double psitilde_cs_20_1 = 4*z + 3;

2667

const double psitilde_cs_21_0 = 1;

2668

const double psitilde_cs_30_0 = 1;

2669

2670

// Compute basisvalues

2671

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

2672

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

2673

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

2674

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

2675

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

2676

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

2677

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

2678

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

2679

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

2680

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

2681

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

2682

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

2683

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

2684

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

2685

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

2686

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

2687

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

2688

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

2689

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

2690

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

2691

2692

// Table(s) of coefficients

2693

const static double coefficients0[20][20] = \

2694

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

2695

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

2696

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

2697

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

2698

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

2699

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

2700

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

2701

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

2702

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

2703

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

2704

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2705

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

2706

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2707

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

2708

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

2709

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

2710

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

2711

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

2712

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

2713

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

2714

2715

// Extract relevant coefficients

2716

const double coeff0_0 = coefficients0[dof][0];

2717

const double coeff0_1 = coefficients0[dof][1];

2718

const double coeff0_2 = coefficients0[dof][2];

2719

const double coeff0_3 = coefficients0[dof][3];

2720

const double coeff0_4 = coefficients0[dof][4];

2721

const double coeff0_5 = coefficients0[dof][5];

2722

const double coeff0_6 = coefficients0[dof][6];

2723

const double coeff0_7 = coefficients0[dof][7];

2724

const double coeff0_8 = coefficients0[dof][8];

2725

const double coeff0_9 = coefficients0[dof][9];

2726

const double coeff0_10 = coefficients0[dof][10];

2727

const double coeff0_11 = coefficients0[dof][11];

2728

const double coeff0_12 = coefficients0[dof][12];

2729

const double coeff0_13 = coefficients0[dof][13];

2730

const double coeff0_14 = coefficients0[dof][14];

2731

const double coeff0_15 = coefficients0[dof][15];

2732

const double coeff0_16 = coefficients0[dof][16];

2733

const double coeff0_17 = coefficients0[dof][17];

2734

const double coeff0_18 = coefficients0[dof][18];

2735

const double coeff0_19 = coefficients0[dof][19];

2736

2737

// Compute value(s)

2738

values[0] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

2739

}

2740

2741

if (20 <= i && i <= 39)

2742

{

2743

// Map degree of freedom to element degree of freedom

2744

const unsigned int dof = i - 20;

2745

2746

// Generate scalings

2747

const double scalings_y_0 = 1;

2748

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

2749

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

2750

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

2751

const double scalings_z_0 = 1;

2752

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

2753

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

2754

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

2755

2756

// Compute psitilde_a

2757

const double psitilde_a_0 = 1;

2758

const double psitilde_a_1 = x;

2759

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

2760

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

2761

2762

// Compute psitilde_bs

2763

const double psitilde_bs_0_0 = 1;

2764

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2765

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

2766

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

2767

const double psitilde_bs_1_0 = 1;

2768

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2769

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

2770

const double psitilde_bs_2_0 = 1;

2771

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2772

const double psitilde_bs_3_0 = 1;

2773

2774

// Compute psitilde_cs

2775

const double psitilde_cs_00_0 = 1;

2776

const double psitilde_cs_00_1 = 2*z + 1;

2777

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

2778

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

2779

const double psitilde_cs_01_0 = 1;

2780

const double psitilde_cs_01_1 = 3*z + 2;

2781

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

2782

const double psitilde_cs_02_0 = 1;

2783

const double psitilde_cs_02_1 = 4*z + 3;

2784

const double psitilde_cs_03_0 = 1;

2785

const double psitilde_cs_10_0 = 1;

2786

const double psitilde_cs_10_1 = 3*z + 2;

2787

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

2788

const double psitilde_cs_11_0 = 1;

2789

const double psitilde_cs_11_1 = 4*z + 3;

2790

const double psitilde_cs_12_0 = 1;

2791

const double psitilde_cs_20_0 = 1;

2792

const double psitilde_cs_20_1 = 4*z + 3;

2793

const double psitilde_cs_21_0 = 1;

2794

const double psitilde_cs_30_0 = 1;

2795

2796

// Compute basisvalues

2797

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

2798

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

2799

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

2800

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

2801

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

2802

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

2803

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

2804

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

2805

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

2806

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

2807

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

2808

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

2809

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

2810

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

2811

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

2812

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

2813

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

2814

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

2815

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

2816

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

2817

2818

// Table(s) of coefficients

2819

const static double coefficients0[20][20] = \

2820

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

2821

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

2822

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

2823

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

2824

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

2825

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

2826

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

2827

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

2828

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

2829

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

2830

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2831

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

2832

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2833

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

2834

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

2835

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

2836

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

2837

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

2838

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

2839

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

2840

2841

// Extract relevant coefficients

2842

const double coeff0_0 = coefficients0[dof][0];

2843

const double coeff0_1 = coefficients0[dof][1];

2844

const double coeff0_2 = coefficients0[dof][2];

2845

const double coeff0_3 = coefficients0[dof][3];

2846

const double coeff0_4 = coefficients0[dof][4];

2847

const double coeff0_5 = coefficients0[dof][5];

2848

const double coeff0_6 = coefficients0[dof][6];

2849

const double coeff0_7 = coefficients0[dof][7];

2850

const double coeff0_8 = coefficients0[dof][8];

2851

const double coeff0_9 = coefficients0[dof][9];

2852

const double coeff0_10 = coefficients0[dof][10];

2853

const double coeff0_11 = coefficients0[dof][11];

2854

const double coeff0_12 = coefficients0[dof][12];

2855

const double coeff0_13 = coefficients0[dof][13];

2856

const double coeff0_14 = coefficients0[dof][14];

2857

const double coeff0_15 = coefficients0[dof][15];

2858

const double coeff0_16 = coefficients0[dof][16];

2859

const double coeff0_17 = coefficients0[dof][17];

2860

const double coeff0_18 = coefficients0[dof][18];

2861

const double coeff0_19 = coefficients0[dof][19];

2862

2863

// Compute value(s)

2864

values[1] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

2865

}

2866

2867

if (40 <= i && i <= 59)

2868

{

2869

// Map degree of freedom to element degree of freedom

2870

const unsigned int dof = i - 40;

2871

2872

// Generate scalings

2873

const double scalings_y_0 = 1;

2874

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

2875

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

2876

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

2877

const double scalings_z_0 = 1;

2878

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

2879

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

2880

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

2881

2882

// Compute psitilde_a

2883

const double psitilde_a_0 = 1;

2884

const double psitilde_a_1 = x;

2885

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

2886

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

2887

2888

// Compute psitilde_bs

2889

const double psitilde_bs_0_0 = 1;

2890

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2891

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

2892

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

2893

const double psitilde_bs_1_0 = 1;

2894

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2895

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

2896

const double psitilde_bs_2_0 = 1;

2897

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2898

const double psitilde_bs_3_0 = 1;

2899

2900

// Compute psitilde_cs

2901

const double psitilde_cs_00_0 = 1;

2902

const double psitilde_cs_00_1 = 2*z + 1;

2903

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

2904

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

2905

const double psitilde_cs_01_0 = 1;

2906

const double psitilde_cs_01_1 = 3*z + 2;

2907

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

2908

const double psitilde_cs_02_0 = 1;

2909

const double psitilde_cs_02_1 = 4*z + 3;

2910

const double psitilde_cs_03_0 = 1;

2911

const double psitilde_cs_10_0 = 1;

2912

const double psitilde_cs_10_1 = 3*z + 2;

2913

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

2914

const double psitilde_cs_11_0 = 1;

2915

const double psitilde_cs_11_1 = 4*z + 3;

2916

const double psitilde_cs_12_0 = 1;

2917

const double psitilde_cs_20_0 = 1;

2918

const double psitilde_cs_20_1 = 4*z + 3;

2919

const double psitilde_cs_21_0 = 1;

2920

const double psitilde_cs_30_0 = 1;

2921

2922

// Compute basisvalues

2923

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

2924

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

2925

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

2926

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

2927

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

2928

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

2929

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

2930

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

2931

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

2932

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

2933

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

2934

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

2935

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

2936

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

2937

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

2938

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

2939

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

2940

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

2941

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

2942

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

2943

2944

// Table(s) of coefficients

2945

const static double coefficients0[20][20] = \

2946

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

2947

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

2948

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

2949

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

2950

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

2951

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

2952

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

2953

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

2954

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

2955

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

2956

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2957

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

2958

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

2959

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

2960

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

2961

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

2962

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

2963

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

2964

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

2965

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

2966

2967

// Extract relevant coefficients

2968

const double coeff0_0 = coefficients0[dof][0];

2969

const double coeff0_1 = coefficients0[dof][1];

2970

const double coeff0_2 = coefficients0[dof][2];

2971

const double coeff0_3 = coefficients0[dof][3];

2972

const double coeff0_4 = coefficients0[dof][4];

2973

const double coeff0_5 = coefficients0[dof][5];

2974

const double coeff0_6 = coefficients0[dof][6];

2975

const double coeff0_7 = coefficients0[dof][7];

2976

const double coeff0_8 = coefficients0[dof][8];

2977

const double coeff0_9 = coefficients0[dof][9];

2978

const double coeff0_10 = coefficients0[dof][10];

2979

const double coeff0_11 = coefficients0[dof][11];

2980

const double coeff0_12 = coefficients0[dof][12];

2981

const double coeff0_13 = coefficients0[dof][13];

2982

const double coeff0_14 = coefficients0[dof][14];

2983

const double coeff0_15 = coefficients0[dof][15];

2984

const double coeff0_16 = coefficients0[dof][16];

2985

const double coeff0_17 = coefficients0[dof][17];

2986

const double coeff0_18 = coefficients0[dof][18];

2987

const double coeff0_19 = coefficients0[dof][19];

2988

2989

// Compute value(s)

2990

values[2] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;

2991

}

2992

2993

}

2994

2995

/// Evaluate all basis functions at given point in cell

2996

virtual void evaluate_basis_all(double* values,

2997

const double* coordinates,

2998

const ufc::cell& c) const

2999

{

3000

throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");

3001

}

3002

3003

/// Evaluate order n derivatives of basis function i at given point in cell

3004

virtual void evaluate_basis_derivatives(unsigned int i,

3005

unsigned int n,

3006

double* values,

3007

const double* coordinates,

3008

const ufc::cell& c) const

3009

{

3010

// Extract vertex coordinates

3011

const double * const * element_coordinates = c.coordinates;

3012

3013

// Compute Jacobian of affine map from reference cell

3014

const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];

3015

const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];

3016

const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];

3017

const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];

3018

const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];

3019

const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];

3020

const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];

3021

const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];

3022

const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];

3023

3024

// Compute sub determinants

3025

const double d00 = J_11*J_22 - J_12*J_21;

3026

const double d01 = J_12*J_20 - J_10*J_22;

3027

const double d02 = J_10*J_21 - J_11*J_20;

3028

3029

const double d10 = J_02*J_21 - J_01*J_22;

3030

const double d11 = J_00*J_22 - J_02*J_20;

3031

const double d12 = J_01*J_20 - J_00*J_21;

3032

3033

const double d20 = J_01*J_12 - J_02*J_11;

3034

const double d21 = J_02*J_10 - J_00*J_12;

3035

const double d22 = J_00*J_11 - J_01*J_10;

3036

3037

// Compute determinant of Jacobian

3038

double detJ = J_00*d00 + J_10*d10 + J_20*d20;

3039

3040

// Compute inverse of Jacobian

3041

3042

// Compute constants

3043

const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \

3044

+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \

3045

+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);

3046

3047

const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \

3048

+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \

3049

+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);

3050

3051

const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \

3052

+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \

3053

+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);

3054

3055

// Get coordinates and map to the UFC reference element

3056

double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;

3057

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

3058

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

3059

3060

// Map coordinates to the reference cube

3061

if (std::abs(y + z - 1.0) < 1e-14)

3062

x = 1.0;

3063

else

3064

x = -2.0 * x/(y + z - 1.0) - 1.0;

3065

if (std::abs(z - 1.0) < 1e-14)

3066

y = -1.0;

3067

else

3068

y = 2.0 * y/(1.0 - z) - 1.0;

3069

z = 2.0 * z - 1.0;

3070

3071

// Compute number of derivatives

3072

unsigned int num_derivatives = 1;

3073

3074

for (unsigned int j = 0; j < n; j++)

3075

num_derivatives *= 3;

3076

3077

3078

// Declare pointer to two dimensional array that holds combinations of derivatives and initialise

3079

unsigned int **combinations = new unsigned int *[num_derivatives];

3080

3081

for (unsigned int j = 0; j < num_derivatives; j++)

3082

{

3083

combinations[j] = new unsigned int [n];

3084

for (unsigned int k = 0; k < n; k++)

3085

combinations[j][k] = 0;

3086

}

3087

3088

// Generate combinations of derivatives

3089

for (unsigned int row = 1; row < num_derivatives; row++)

3090

{

3091

for (unsigned int num = 0; num < row; num++)

3092

{

3093

for (unsigned int col = n-1; col+1 > 0; col--)

3094

{

3095

if (combinations[row][col] + 1 > 2)

3096

combinations[row][col] = 0;

3097

else

3098

{

3099

combinations[row][col] += 1;

3100

break;

3101

}

3102

}

3103

}

3104

}

3105

3106

// Compute inverse of Jacobian

3107

const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};

3108

3109

// Declare transformation matrix

3110

// Declare pointer to two dimensional array and initialise

3111

double **transform = new double *[num_derivatives];

3112

3113

for (unsigned int j = 0; j < num_derivatives; j++)

3114

{

3115

transform[j] = new double [num_derivatives];

3116

for (unsigned int k = 0; k < num_derivatives; k++)

3117

transform[j][k] = 1;

3118

}

3119

3120

// Construct transformation matrix

3121

for (unsigned int row = 0; row < num_derivatives; row++)

3122

{

3123

for (unsigned int col = 0; col < num_derivatives; col++)

3124

{

3125

for (unsigned int k = 0; k < n; k++)

3126

transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];

3127

}

3128

}

3129

3130

// Reset values

3131

for (unsigned int j = 0; j < 3*num_derivatives; j++)

3132

values[j] = 0;

3133

3134

if (0 <= i && i <= 19)

3135

{

3136

// Map degree of freedom to element degree of freedom

3137

const unsigned int dof = i;

3138

3139

// Generate scalings

3140

const double scalings_y_0 = 1;

3141

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

3142

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

3143

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

3144

const double scalings_z_0 = 1;

3145

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

3146

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

3147

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

3148

3149

// Compute psitilde_a

3150

const double psitilde_a_0 = 1;

3151

const double psitilde_a_1 = x;

3152

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

3153

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

3154

3155

// Compute psitilde_bs

3156

const double psitilde_bs_0_0 = 1;

3157

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3158

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

3159

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

3160

const double psitilde_bs_1_0 = 1;

3161

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3162

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

3163

const double psitilde_bs_2_0 = 1;

3164

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3165

const double psitilde_bs_3_0 = 1;

3166

3167

// Compute psitilde_cs

3168

const double psitilde_cs_00_0 = 1;

3169

const double psitilde_cs_00_1 = 2*z + 1;

3170

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

3171

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

3172

const double psitilde_cs_01_0 = 1;

3173

const double psitilde_cs_01_1 = 3*z + 2;

3174

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

3175

const double psitilde_cs_02_0 = 1;

3176

const double psitilde_cs_02_1 = 4*z + 3;

3177

const double psitilde_cs_03_0 = 1;

3178

const double psitilde_cs_10_0 = 1;

3179

const double psitilde_cs_10_1 = 3*z + 2;

3180

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

3181

const double psitilde_cs_11_0 = 1;

3182

const double psitilde_cs_11_1 = 4*z + 3;

3183

const double psitilde_cs_12_0 = 1;

3184

const double psitilde_cs_20_0 = 1;

3185

const double psitilde_cs_20_1 = 4*z + 3;

3186

const double psitilde_cs_21_0 = 1;

3187

const double psitilde_cs_30_0 = 1;

3188

3189

// Compute basisvalues

3190

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

3191

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

3192

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

3193

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

3194

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

3195

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

3196

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

3197

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

3198

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

3199

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

3200

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

3201

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

3202

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

3203

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

3204

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

3205

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

3206

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

3207

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

3208

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

3209

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

3210

3211

// Table(s) of coefficients

3212

const static double coefficients0[20][20] = \

3213

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3214

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

3215

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

3216

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3217

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

3218

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

3219

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

3220

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

3221

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

3222

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

3223

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3224

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3225

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3226

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

3227

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3228

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3229

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

3230

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

3231

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

3232

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

3233

3234

// Interesting (new) part

3235

// Tables of derivatives of the polynomial base (transpose)

3236

const static double dmats0[20][20] = \

3237

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3238

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3239

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3240

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3241

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3242

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3243

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3244

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3245

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3246

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3247

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3248

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3249

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3250

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3251

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3252

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3253

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3254

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3255

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3256

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3257

3258

const static double dmats1[20][20] = \

3259

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3260

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3261

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3262

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3263

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3264

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3265

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3266

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3267

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3268

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3269

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3270

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3271

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3272

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3273

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3274

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3275

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3276

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3277

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3278

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3279

3280

const static double dmats2[20][20] = \

3281

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3282

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3283

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3284

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3285

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3286

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3287

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3288

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3289

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3290

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3291

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3292

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3293

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3294

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3295

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3296

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3297

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3298

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3299

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3300

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3301

3302

// Compute reference derivatives

3303

// Declare pointer to array of derivatives on FIAT element

3304

double *derivatives = new double [num_derivatives];

3305

3306

// Declare coefficients

3307

double coeff0_0 = 0;

3308

double coeff0_1 = 0;

3309

double coeff0_2 = 0;

3310

double coeff0_3 = 0;

3311

double coeff0_4 = 0;

3312

double coeff0_5 = 0;

3313

double coeff0_6 = 0;

3314

double coeff0_7 = 0;

3315

double coeff0_8 = 0;

3316

double coeff0_9 = 0;

3317

double coeff0_10 = 0;

3318

double coeff0_11 = 0;

3319

double coeff0_12 = 0;

3320

double coeff0_13 = 0;

3321

double coeff0_14 = 0;

3322

double coeff0_15 = 0;

3323

double coeff0_16 = 0;

3324

double coeff0_17 = 0;

3325

double coeff0_18 = 0;

3326

double coeff0_19 = 0;

3327

3328

// Declare new coefficients

3329

double new_coeff0_0 = 0;

3330

double new_coeff0_1 = 0;

3331

double new_coeff0_2 = 0;

3332

double new_coeff0_3 = 0;

3333

double new_coeff0_4 = 0;

3334

double new_coeff0_5 = 0;

3335

double new_coeff0_6 = 0;

3336

double new_coeff0_7 = 0;

3337

double new_coeff0_8 = 0;

3338

double new_coeff0_9 = 0;

3339

double new_coeff0_10 = 0;

3340

double new_coeff0_11 = 0;

3341

double new_coeff0_12 = 0;

3342

double new_coeff0_13 = 0;

3343

double new_coeff0_14 = 0;

3344

double new_coeff0_15 = 0;

3345

double new_coeff0_16 = 0;

3346

double new_coeff0_17 = 0;

3347

double new_coeff0_18 = 0;

3348

double new_coeff0_19 = 0;

3349

3350

// Loop possible derivatives

3351

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

3352

{

3353

// Get values from coefficients array

3354

new_coeff0_0 = coefficients0[dof][0];

3355

new_coeff0_1 = coefficients0[dof][1];

3356

new_coeff0_2 = coefficients0[dof][2];

3357

new_coeff0_3 = coefficients0[dof][3];

3358

new_coeff0_4 = coefficients0[dof][4];

3359

new_coeff0_5 = coefficients0[dof][5];

3360

new_coeff0_6 = coefficients0[dof][6];

3361

new_coeff0_7 = coefficients0[dof][7];

3362

new_coeff0_8 = coefficients0[dof][8];

3363

new_coeff0_9 = coefficients0[dof][9];

3364

new_coeff0_10 = coefficients0[dof][10];

3365

new_coeff0_11 = coefficients0[dof][11];

3366

new_coeff0_12 = coefficients0[dof][12];

3367

new_coeff0_13 = coefficients0[dof][13];

3368

new_coeff0_14 = coefficients0[dof][14];

3369

new_coeff0_15 = coefficients0[dof][15];

3370

new_coeff0_16 = coefficients0[dof][16];

3371

new_coeff0_17 = coefficients0[dof][17];

3372

new_coeff0_18 = coefficients0[dof][18];

3373

new_coeff0_19 = coefficients0[dof][19];

3374

3375

// Loop derivative order

3376

for (unsigned int j = 0; j < n; j++)

3377

{

3378

// Update old coefficients

3379

coeff0_0 = new_coeff0_0;

3380

coeff0_1 = new_coeff0_1;

3381

coeff0_2 = new_coeff0_2;

3382

coeff0_3 = new_coeff0_3;

3383

coeff0_4 = new_coeff0_4;

3384

coeff0_5 = new_coeff0_5;

3385

coeff0_6 = new_coeff0_6;

3386

coeff0_7 = new_coeff0_7;

3387

coeff0_8 = new_coeff0_8;

3388

coeff0_9 = new_coeff0_9;

3389

coeff0_10 = new_coeff0_10;

3390

coeff0_11 = new_coeff0_11;

3391

coeff0_12 = new_coeff0_12;

3392

coeff0_13 = new_coeff0_13;

3393

coeff0_14 = new_coeff0_14;

3394

coeff0_15 = new_coeff0_15;

3395

coeff0_16 = new_coeff0_16;

3396

coeff0_17 = new_coeff0_17;

3397

coeff0_18 = new_coeff0_18;

3398

coeff0_19 = new_coeff0_19;

3399

3400

if(combinations[deriv_num][j] == 0)

3401

{

3402

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

3403

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

3404

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

3405

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

3406

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

3407

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

3408

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

3409

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

3410

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

3411

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

3412

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

3413

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

3414

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

3415

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

3416

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

3417

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

3418

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

3419

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

3420

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

3421

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

3422

}

3423

if(combinations[deriv_num][j] == 1)

3424

{

3425

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

3426

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

3427

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

3428

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

3429

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

3430

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

3431

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

3432

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

3433

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

3434

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

3435

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

3436

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

3437

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

3438

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

3439

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

3440

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

3441

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

3442

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

3443

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

3444

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

3445

}

3446

if(combinations[deriv_num][j] == 2)

3447

{

3448

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

3449

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

3450

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

3451

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

3452

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

3453

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

3454

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

3455

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

3456

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

3457

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

3458

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

3459

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

3460

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

3461

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

3462

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

3463

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

3464

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

3465

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

3466

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

3467

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

3468

}

3469

3470

}

3471

// Compute derivatives on reference element as dot product of coefficients and basisvalues

3472

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

3473

}

3474

3475

// Transform derivatives back to physical element

3476

for (unsigned int row = 0; row < num_derivatives; row++)

3477

{

3478

for (unsigned int col = 0; col < num_derivatives; col++)

3479

{

3480

values[row] += transform[row][col]*derivatives[col];

3481

}

3482

}

3483

// Delete pointer to array of derivatives on FIAT element

3484

delete [] derivatives;

3485

3486

// Delete pointer to array of combinations of derivatives and transform

3487

for (unsigned int row = 0; row < num_derivatives; row++)

3488

{

3489

delete [] combinations[row];

3490

delete [] transform[row];

3491

}

3492

3493

delete [] combinations;

3494

delete [] transform;

3495

}

3496

3497

if (20 <= i && i <= 39)

3498

{

3499

// Map degree of freedom to element degree of freedom

3500

const unsigned int dof = i - 20;

3501

3502

// Generate scalings

3503

const double scalings_y_0 = 1;

3504

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

3505

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

3506

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

3507

const double scalings_z_0 = 1;

3508

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

3509

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

3510

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

3511

3512

// Compute psitilde_a

3513

const double psitilde_a_0 = 1;

3514

const double psitilde_a_1 = x;

3515

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

3516

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

3517

3518

// Compute psitilde_bs

3519

const double psitilde_bs_0_0 = 1;

3520

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3521

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

3522

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

3523

const double psitilde_bs_1_0 = 1;

3524

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3525

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

3526

const double psitilde_bs_2_0 = 1;

3527

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3528

const double psitilde_bs_3_0 = 1;

3529

3530

// Compute psitilde_cs

3531

const double psitilde_cs_00_0 = 1;

3532

const double psitilde_cs_00_1 = 2*z + 1;

3533

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

3534

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

3535

const double psitilde_cs_01_0 = 1;

3536

const double psitilde_cs_01_1 = 3*z + 2;

3537

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

3538

const double psitilde_cs_02_0 = 1;

3539

const double psitilde_cs_02_1 = 4*z + 3;

3540

const double psitilde_cs_03_0 = 1;

3541

const double psitilde_cs_10_0 = 1;

3542

const double psitilde_cs_10_1 = 3*z + 2;

3543

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

3544

const double psitilde_cs_11_0 = 1;

3545

const double psitilde_cs_11_1 = 4*z + 3;

3546

const double psitilde_cs_12_0 = 1;

3547

const double psitilde_cs_20_0 = 1;

3548

const double psitilde_cs_20_1 = 4*z + 3;

3549

const double psitilde_cs_21_0 = 1;

3550

const double psitilde_cs_30_0 = 1;

3551

3552

// Compute basisvalues

3553

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

3554

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

3555

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

3556

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

3557

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

3558

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

3559

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

3560

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

3561

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

3562

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

3563

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

3564

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

3565

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

3566

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

3567

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

3568

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

3569

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

3570

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

3571

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

3572

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

3573

3574

// Table(s) of coefficients

3575

const static double coefficients0[20][20] = \

3576

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3577

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

3578

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

3579

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3580

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

3581

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

3582

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

3583

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

3584

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

3585

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

3586

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3587

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3588

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3589

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

3590

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3591

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3592

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

3593

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

3594

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

3595

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

3596

3597

// Interesting (new) part

3598

// Tables of derivatives of the polynomial base (transpose)

3599

const static double dmats0[20][20] = \

3600

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3601

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3602

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3603

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3604

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3605

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3606

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3607

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3608

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3609

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3610

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3611

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3612

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3613

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3614

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3615

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3616

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3617

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3618

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3619

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3620

3621

const static double dmats1[20][20] = \

3622

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3623

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3624

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3625

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3626

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3627

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3628

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3629

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3630

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3631

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3632

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3633

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3634

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3635

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3636

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3637

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3638

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3639

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3640

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3641

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3642

3643

const static double dmats2[20][20] = \

3644

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3645

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3646

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3647

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3648

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3649

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3650

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3651

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3652

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3653

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3654

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3655

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3656

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3657

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3658

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3659

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3660

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3661

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3662

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3663

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3664

3665

// Compute reference derivatives

3666

// Declare pointer to array of derivatives on FIAT element

3667

double *derivatives = new double [num_derivatives];

3668

3669

// Declare coefficients

3670

double coeff0_0 = 0;

3671

double coeff0_1 = 0;

3672

double coeff0_2 = 0;

3673

double coeff0_3 = 0;

3674

double coeff0_4 = 0;

3675

double coeff0_5 = 0;

3676

double coeff0_6 = 0;

3677

double coeff0_7 = 0;

3678

double coeff0_8 = 0;

3679

double coeff0_9 = 0;

3680

double coeff0_10 = 0;

3681

double coeff0_11 = 0;

3682

double coeff0_12 = 0;

3683

double coeff0_13 = 0;

3684

double coeff0_14 = 0;

3685

double coeff0_15 = 0;

3686

double coeff0_16 = 0;

3687

double coeff0_17 = 0;

3688

double coeff0_18 = 0;

3689

double coeff0_19 = 0;

3690

3691

// Declare new coefficients

3692

double new_coeff0_0 = 0;

3693

double new_coeff0_1 = 0;

3694

double new_coeff0_2 = 0;

3695

double new_coeff0_3 = 0;

3696

double new_coeff0_4 = 0;

3697

double new_coeff0_5 = 0;

3698

double new_coeff0_6 = 0;

3699

double new_coeff0_7 = 0;

3700

double new_coeff0_8 = 0;

3701

double new_coeff0_9 = 0;

3702

double new_coeff0_10 = 0;

3703

double new_coeff0_11 = 0;

3704

double new_coeff0_12 = 0;

3705

double new_coeff0_13 = 0;

3706

double new_coeff0_14 = 0;

3707

double new_coeff0_15 = 0;

3708

double new_coeff0_16 = 0;

3709

double new_coeff0_17 = 0;

3710

double new_coeff0_18 = 0;

3711

double new_coeff0_19 = 0;

3712

3713

// Loop possible derivatives

3714

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

3715

{

3716

// Get values from coefficients array

3717

new_coeff0_0 = coefficients0[dof][0];

3718

new_coeff0_1 = coefficients0[dof][1];

3719

new_coeff0_2 = coefficients0[dof][2];

3720

new_coeff0_3 = coefficients0[dof][3];

3721

new_coeff0_4 = coefficients0[dof][4];

3722

new_coeff0_5 = coefficients0[dof][5];

3723

new_coeff0_6 = coefficients0[dof][6];

3724

new_coeff0_7 = coefficients0[dof][7];

3725

new_coeff0_8 = coefficients0[dof][8];

3726

new_coeff0_9 = coefficients0[dof][9];

3727

new_coeff0_10 = coefficients0[dof][10];

3728

new_coeff0_11 = coefficients0[dof][11];

3729

new_coeff0_12 = coefficients0[dof][12];

3730

new_coeff0_13 = coefficients0[dof][13];

3731

new_coeff0_14 = coefficients0[dof][14];

3732

new_coeff0_15 = coefficients0[dof][15];

3733

new_coeff0_16 = coefficients0[dof][16];

3734

new_coeff0_17 = coefficients0[dof][17];

3735

new_coeff0_18 = coefficients0[dof][18];

3736

new_coeff0_19 = coefficients0[dof][19];

3737

3738

// Loop derivative order

3739

for (unsigned int j = 0; j < n; j++)

3740

{

3741

// Update old coefficients

3742

coeff0_0 = new_coeff0_0;

3743

coeff0_1 = new_coeff0_1;

3744

coeff0_2 = new_coeff0_2;

3745

coeff0_3 = new_coeff0_3;

3746

coeff0_4 = new_coeff0_4;

3747

coeff0_5 = new_coeff0_5;

3748

coeff0_6 = new_coeff0_6;

3749

coeff0_7 = new_coeff0_7;

3750

coeff0_8 = new_coeff0_8;

3751

coeff0_9 = new_coeff0_9;

3752

coeff0_10 = new_coeff0_10;

3753

coeff0_11 = new_coeff0_11;

3754

coeff0_12 = new_coeff0_12;

3755

coeff0_13 = new_coeff0_13;

3756

coeff0_14 = new_coeff0_14;

3757

coeff0_15 = new_coeff0_15;

3758

coeff0_16 = new_coeff0_16;

3759

coeff0_17 = new_coeff0_17;

3760

coeff0_18 = new_coeff0_18;

3761

coeff0_19 = new_coeff0_19;

3762

3763

if(combinations[deriv_num][j] == 0)

3764

{

3765

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

3766

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

3767

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

3768

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

3769

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

3770

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

3771

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

3772

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

3773

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

3774

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

3775

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

3776

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

3777

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

3778

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

3779

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

3780

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

3781

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

3782

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

3783

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

3784

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

3785

}

3786

if(combinations[deriv_num][j] == 1)

3787

{

3788

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

3789

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

3790

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

3791

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

3792

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

3793

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

3794

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

3795

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

3796

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

3797

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

3798

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

3799

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

3800

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

3801

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

3802

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

3803

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

3804

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

3805

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

3806

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

3807

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

3808

}

3809

if(combinations[deriv_num][j] == 2)

3810

{

3811

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

3812

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

3813

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

3814

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

3815

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

3816

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

3817

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

3818

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

3819

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

3820

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

3821

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

3822

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

3823

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

3824

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

3825

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

3826

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

3827

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

3828

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

3829

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

3830

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

3831

}

3832

3833

}

3834

// Compute derivatives on reference element as dot product of coefficients and basisvalues

3835

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

3836

}

3837

3838

// Transform derivatives back to physical element

3839

for (unsigned int row = 0; row < num_derivatives; row++)

3840

{

3841

for (unsigned int col = 0; col < num_derivatives; col++)

3842

{

3843

values[num_derivatives + row] += transform[row][col]*derivatives[col];

3844

}

3845

}

3846

// Delete pointer to array of derivatives on FIAT element

3847

delete [] derivatives;

3848

3849

// Delete pointer to array of combinations of derivatives and transform

3850

for (unsigned int row = 0; row < num_derivatives; row++)

3851

{

3852

delete [] combinations[row];

3853

delete [] transform[row];

3854

}

3855

3856

delete [] combinations;

3857

delete [] transform;

3858

}

3859

3860

if (40 <= i && i <= 59)

3861

{

3862

// Map degree of freedom to element degree of freedom

3863

const unsigned int dof = i - 40;

3864

3865

// Generate scalings

3866

const double scalings_y_0 = 1;

3867

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

3868

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

3869

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

3870

const double scalings_z_0 = 1;

3871

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

3872

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

3873

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

3874

3875

// Compute psitilde_a

3876

const double psitilde_a_0 = 1;

3877

const double psitilde_a_1 = x;

3878

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

3879

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

3880

3881

// Compute psitilde_bs

3882

const double psitilde_bs_0_0 = 1;

3883

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3884

const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;

3885

const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;

3886

const double psitilde_bs_1_0 = 1;

3887

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3888

const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;

3889

const double psitilde_bs_2_0 = 1;

3890

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3891

const double psitilde_bs_3_0 = 1;

3892

3893

// Compute psitilde_cs

3894

const double psitilde_cs_00_0 = 1;

3895

const double psitilde_cs_00_1 = 2*z + 1;

3896

const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;

3897

const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;

3898

const double psitilde_cs_01_0 = 1;

3899

const double psitilde_cs_01_1 = 3*z + 2;

3900

const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;

3901

const double psitilde_cs_02_0 = 1;

3902

const double psitilde_cs_02_1 = 4*z + 3;

3903

const double psitilde_cs_03_0 = 1;

3904

const double psitilde_cs_10_0 = 1;

3905

const double psitilde_cs_10_1 = 3*z + 2;

3906

const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;

3907

const double psitilde_cs_11_0 = 1;

3908

const double psitilde_cs_11_1 = 4*z + 3;

3909

const double psitilde_cs_12_0 = 1;

3910

const double psitilde_cs_20_0 = 1;

3911

const double psitilde_cs_20_1 = 4*z + 3;

3912

const double psitilde_cs_21_0 = 1;

3913

const double psitilde_cs_30_0 = 1;

3914

3915

// Compute basisvalues

3916

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

3917

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

3918

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

3919

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

3920

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

3921

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

3922

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

3923

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

3924

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

3925

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

3926

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

3927

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

3928

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

3929

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

3930

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

3931

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

3932

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

3933

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

3934

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

3935

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

3936

3937

// Table(s) of coefficients

3938

const static double coefficients0[20][20] = \

3939

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421041, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.0081831708838497, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197614, -0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3940

{0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.0182981263677849, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131743, -0.0107142857142857, 0.0207481250689683, -0.00535714285714288, -0.00927884361197612, -0.00437408882639854, -0.00757614408414157, -0.00535714285714285},

3941

{0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.0182981263677851, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131743, -0.0107142857142857, 0.0207481250689683, 0.00535714285714288, -0.00927884361197614, 0.00437408882639855, -0.0075761440841416, -0.00535714285714286},

3942

{0.0288675134594813, -0.0130410132739325, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384971, -0.0115727512471569, 0.00668153104781061, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197612, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3943

{0, -0.0978075995544939, -0.0790569415042094, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532936, -0.00874817765279706, 0, -0.00535714285714285},

3944

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286},

3945

{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.0141736677378461, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},

3946

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.0092788436119761, -0.00437408882639853, 0.00757614408414159, -0.00535714285714286},

3947

{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414157, -0.00535714285714285},

3948

{0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},

3949

{0, -0.0978075995544939, -0.0564692439315782, -0.0638876564999939, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3950

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515492, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551855, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3951

{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3952

{0.259807621135332, -0.117369119465393, 0.0677630927178937, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546475, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682831, 0.0267857142857143},

3953

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3954

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546475, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3955

{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714285},

3956

{0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},

3957

{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},

3958

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286}};

3959

3960

// Interesting (new) part

3961

// Tables of derivatives of the polynomial base (transpose)

3962

const static double dmats0[20][20] = \

3963

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3964

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3965

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3966

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3967

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3968

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3969

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3970

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3971

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3972

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3973

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027551, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3974

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3975

{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3976

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3977

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3978

{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3979

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3980

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3981

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3982

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3983

3984

const static double dmats1[20][20] = \

3985

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3986

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3987

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3988

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3989

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3990

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3991

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3992

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3993

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3994

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3995

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3996

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3997

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818041, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3998

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.37796447300923, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3999

{2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4000

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4001

{-1.8, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4002

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4003

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4004

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4005

4006

const static double dmats2[20][20] = \

4007

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4008

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4009

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4010

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4011

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4012

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4013

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4014

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4015

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4016

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4017

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474619, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4018

{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4019

{1.8, 0.632455532033675, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4020

{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4021

{2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4022

{1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4023

{0.900000000000001, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755175, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4024

{1.27279220613578, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4025

{0.734846922834954, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4026

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4027

4028

// Compute reference derivatives

4029

// Declare pointer to array of derivatives on FIAT element

4030

double *derivatives = new double [num_derivatives];

4031

4032

// Declare coefficients

4033

double coeff0_0 = 0;

4034

double coeff0_1 = 0;

4035

double coeff0_2 = 0;

4036

double coeff0_3 = 0;

4037

double coeff0_4 = 0;

4038

double coeff0_5 = 0;

4039

double coeff0_6 = 0;

4040

double coeff0_7 = 0;

4041

double coeff0_8 = 0;

4042

double coeff0_9 = 0;

4043

double coeff0_10 = 0;

4044

double coeff0_11 = 0;

4045

double coeff0_12 = 0;

4046

double coeff0_13 = 0;

4047

double coeff0_14 = 0;

4048

double coeff0_15 = 0;

4049

double coeff0_16 = 0;

4050

double coeff0_17 = 0;

4051

double coeff0_18 = 0;

4052

double coeff0_19 = 0;

4053

4054

// Declare new coefficients

4055

double new_coeff0_0 = 0;

4056

double new_coeff0_1 = 0;

4057

double new_coeff0_2 = 0;

4058

double new_coeff0_3 = 0;

4059

double new_coeff0_4 = 0;

4060

double new_coeff0_5 = 0;

4061

double new_coeff0_6 = 0;

4062

double new_coeff0_7 = 0;

4063

double new_coeff0_8 = 0;

4064

double new_coeff0_9 = 0;

4065

double new_coeff0_10 = 0;

4066

double new_coeff0_11 = 0;

4067

double new_coeff0_12 = 0;

4068

double new_coeff0_13 = 0;

4069

double new_coeff0_14 = 0;

4070

double new_coeff0_15 = 0;

4071

double new_coeff0_16 = 0;

4072

double new_coeff0_17 = 0;

4073

double new_coeff0_18 = 0;

4074

double new_coeff0_19 = 0;

4075

4076

// Loop possible derivatives

4077

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

4078

{

4079

// Get values from coefficients array

4080

new_coeff0_0 = coefficients0[dof][0];

4081

new_coeff0_1 = coefficients0[dof][1];

4082

new_coeff0_2 = coefficients0[dof][2];

4083

new_coeff0_3 = coefficients0[dof][3];

4084

new_coeff0_4 = coefficients0[dof][4];

4085

new_coeff0_5 = coefficients0[dof][5];

4086

new_coeff0_6 = coefficients0[dof][6];

4087

new_coeff0_7 = coefficients0[dof][7];

4088

new_coeff0_8 = coefficients0[dof][8];

4089

new_coeff0_9 = coefficients0[dof][9];

4090

new_coeff0_10 = coefficients0[dof][10];

4091

new_coeff0_11 = coefficients0[dof][11];

4092

new_coeff0_12 = coefficients0[dof][12];

4093

new_coeff0_13 = coefficients0[dof][13];

4094

new_coeff0_14 = coefficients0[dof][14];

4095

new_coeff0_15 = coefficients0[dof][15];

4096

new_coeff0_16 = coefficients0[dof][16];

4097

new_coeff0_17 = coefficients0[dof][17];

4098

new_coeff0_18 = coefficients0[dof][18];

4099

new_coeff0_19 = coefficients0[dof][19];

4100

4101

// Loop derivative order

4102

for (unsigned int j = 0; j < n; j++)

4103

{

4104

// Update old coefficients

4105

coeff0_0 = new_coeff0_0;

4106

coeff0_1 = new_coeff0_1;

4107

coeff0_2 = new_coeff0_2;

4108

coeff0_3 = new_coeff0_3;

4109

coeff0_4 = new_coeff0_4;

4110

coeff0_5 = new_coeff0_5;

4111

coeff0_6 = new_coeff0_6;

4112

coeff0_7 = new_coeff0_7;

4113

coeff0_8 = new_coeff0_8;

4114

coeff0_9 = new_coeff0_9;

4115

coeff0_10 = new_coeff0_10;

4116

coeff0_11 = new_coeff0_11;

4117

coeff0_12 = new_coeff0_12;

4118

coeff0_13 = new_coeff0_13;

4119

coeff0_14 = new_coeff0_14;

4120

coeff0_15 = new_coeff0_15;

4121

coeff0_16 = new_coeff0_16;

4122

coeff0_17 = new_coeff0_17;

4123

coeff0_18 = new_coeff0_18;

4124

coeff0_19 = new_coeff0_19;

4125

4126

if(combinations[deriv_num][j] == 0)

4127

{

4128

new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];

4129

new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];

4130

new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];

4131

new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];

4132

new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];

4133

new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];

4134

new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];

4135

new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];

4136

new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];

4137

new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];

4138

new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];

4139

new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];

4140

new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];

4141

new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];

4142

new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];

4143

new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];

4144

new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];

4145

new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];

4146

new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];

4147

new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];

4148

}

4149

if(combinations[deriv_num][j] == 1)

4150

{

4151

new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];

4152

new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];

4153

new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];

4154

new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];

4155

new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];

4156

new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];

4157

new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];

4158

new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];

4159

new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];

4160

new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];

4161

new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];

4162

new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];

4163

new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];

4164

new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];

4165

new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];

4166

new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];

4167

new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];

4168

new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];

4169

new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];

4170

new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];

4171

}

4172

if(combinations[deriv_num][j] == 2)

4173

{

4174

new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];

4175

new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];

4176

new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];

4177

new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];

4178

new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];

4179

new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];

4180

new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];

4181

new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];

4182

new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];

4183

new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];

4184

new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];

4185

new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];

4186

new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];

4187

new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];

4188

new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];

4189

new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];

4190

new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];

4191

new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];

4192

new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];

4193

new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];

4194

}

4195

4196

}

4197

// Compute derivatives on reference element as dot product of coefficients and basisvalues

4198

derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;

4199

}

4200

4201

// Transform derivatives back to physical element

4202

for (unsigned int row = 0; row < num_derivatives; row++)

4203

{

4204

for (unsigned int col = 0; col < num_derivatives; col++)

4205

{

4206

values[2*num_derivatives + row] += transform[row][col]*derivatives[col];

4207

}

4208

}

4209

// Delete pointer to array of derivatives on FIAT element

4210

delete [] derivatives;

4211

4212

// Delete pointer to array of combinations of derivatives and transform

4213

for (unsigned int row = 0; row < num_derivatives; row++)

4214

{

4215

delete [] combinations[row];

4216

delete [] transform[row];

4217

}

4218

4219

delete [] combinations;

4220

delete [] transform;

4221

}

4222

4223

}

4224

4225

/// Evaluate order n derivatives of all basis functions at given point in cell

4226

virtual void evaluate_basis_derivatives_all(unsigned int n,

4227

double* values,

4228

const double* coordinates,

4229

const ufc::cell& c) const

4230

{

4231

throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");

4232

}

4233

4234

/// Evaluate linear functional for dof i on the function f

4235

virtual double evaluate_dof(unsigned int i,

4236

const ufc::function& f,

4237

const ufc::cell& c) const

4238

{

4239

// The reference points, direction and weights:

4240

const static double X[60][1][3] = {{{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}, {{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}, {{0, 0, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{1, 0, 0}}, {{0, 0.333333333333333, 0}}, {{0.333333333333333, 0.333333333333333, 0}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 1, 0}}, {{0, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0, 0, 1}}};

4241

const static double W[60][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};

4242

const static double D[60][1][3] = {{{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}, {{0, 0, 1}}};

4243

4244

const double * const * x = c.coordinates;

4245

double result = 0.0;

4246

// Iterate over the points:

4247

// Evaluate basis functions for affine mapping

4248

const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];

4249

const double w1 = X[i][0][0];

4250

const double w2 = X[i][0][1];

4251

const double w3 = X[i][0][2];

4252

4253

// Compute affine mapping y = F(X)

4254

double y[3];

4255

y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];

4256

y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];

4257

y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];

4258

4259

// Evaluate function at physical points

4260

double values[3];

4261

f.evaluate(values, y, c);

4262

4263

// Map function values using appropriate mapping

4264

// Affine map: Do nothing

4265

4266

// Note that we do not map the weights (yet).

4267

4268

// Take directional components

4269

for(int k = 0; k < 3; k++)

4270

result += values[k]*D[i][0][k];

4271

// Multiply by weights

4272

result *= W[i][0];

4273

4274

return result;

4275

}

4276

4277

/// Evaluate linear functionals for all dofs on the function f

4278

virtual void evaluate_dofs(double* values,

4279

const ufc::function& f,

4280

const ufc::cell& c) const

4281

{

4282

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4283

}

4284

4285

/// Interpolate vertex values from dof values

4286

virtual void interpolate_vertex_values(double* vertex_values,

4287

const double* dof_values,

4288

const ufc::cell& c) const

4289

{

4290

// Evaluate at vertices and use affine mapping

4291

vertex_values[0] = dof_values[0];

4292

vertex_values[1] = dof_values[3];

4293

vertex_values[2] = dof_values[9];

4294

vertex_values[3] = dof_values[19];

4295

// Evaluate at vertices and use affine mapping

4296

vertex_values[4] = dof_values[20];

4297

vertex_values[5] = dof_values[23];

4298

vertex_values[6] = dof_values[29];

4299

vertex_values[7] = dof_values[39];

4300

// Evaluate at vertices and use affine mapping

4301

vertex_values[8] = dof_values[40];

4302

vertex_values[9] = dof_values[43];

4303

vertex_values[10] = dof_values[49];

4304

vertex_values[11] = dof_values[59];

4305

}

4306

4307

/// Return the number of sub elements (for a mixed element)

4308

virtual unsigned int num_sub_elements() const

4309

{

4310

return 3;

4311

}

4312

4313

/// Create a new finite element for sub element i (for a mixed element)

4314

virtual ufc::finite_element* create_sub_element(unsigned int i) const

4315

{

4316

switch ( i )

4317

{

4318

case 0:

4319

return new ffc_25_finite_element_0_0();

4320

break;

4321

case 1:

4322

return new ffc_25_finite_element_0_1();

4323

break;

4324

case 2:

4325

return new ffc_25_finite_element_0_2();

4326

break;

4327

}

4328

return 0;

4329

}

4330

4331

};

4332

4333

/// This class defines the interface for a local-to-global mapping of

4334

/// degrees of freedom (dofs).

4335

4336

class ffc_25_dof_map_0_0: public ufc::dof_map

4337

{

4338

private:

4339

4340

unsigned int __global_dimension;

4341

4342

public:

4343

4344

/// Constructor

4345

ffc_25_dof_map_0_0() : ufc::dof_map()

4346

{

4347

__global_dimension = 0;

4348

}

4349

4350

/// Destructor

4351

virtual ~ffc_25_dof_map_0_0()

4352

{

4353

// Do nothing

4354

}

4355

4356

/// Return a string identifying the dof map

4357

virtual const char* signature() const

4358

{

4359

return "FFC dof map for Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

4360

}

4361

4362

/// Return true iff mesh entities of topological dimension d are needed

4363

virtual bool needs_mesh_entities(unsigned int d) const

4364

{

4365

switch ( d )

4366

{

4367

case 0:

4368

return false;

4369

break;

4370

case 1:

4371

return false;

4372

break;

4373

case 2:

4374

return false;

4375

break;

4376

case 3:

4377

return true;

4378

break;

4379

}

4380

return false;

4381

}

4382

4383

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4384

virtual bool init_mesh(const ufc::mesh& m)

4385

{

4386

__global_dimension = 20*m.num_entities[3];

4387

return false;

4388

}

4389

4390

/// Initialize dof map for given cell

4391

virtual void init_cell(const ufc::mesh& m,

4392

const ufc::cell& c)

4393

{

4394

// Do nothing

4395

}

4396

4397

/// Finish initialization of dof map for cells

4398

virtual void init_cell_finalize()

4399

{

4400

// Do nothing

4401

}

4402

4403

/// Return the dimension of the global finite element function space

4404

virtual unsigned int global_dimension() const

4405

{

4406

return __global_dimension;

4407

}

4408

4409

/// Return the dimension of the local finite element function space

4410

virtual unsigned int local_dimension() const

4411

{

4412

return 20;

4413

}

4414

4415

// Return the geometric dimension of the coordinates this dof map provides

4416

virtual unsigned int geometric_dimension() const

4417

{

4418

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4419

}

4420

4421

/// Return the number of dofs on each cell facet

4422

virtual unsigned int num_facet_dofs() const

4423

{

4424

return 0;

4425

}

4426

4427

/// Return the number of dofs associated with each cell entity of dimension d

4428

virtual unsigned int num_entity_dofs(unsigned int d) const

4429

{

4430

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4431

}

4432

4433

/// Tabulate the local-to-global mapping of dofs on a cell

4434

virtual void tabulate_dofs(unsigned int* dofs,

4435

const ufc::mesh& m,

4436

const ufc::cell& c) const

4437

{

4438

dofs[0] = 20*c.entity_indices[3][0];

4439

dofs[1] = 20*c.entity_indices[3][0] + 1;

4440

dofs[2] = 20*c.entity_indices[3][0] + 2;

4441

dofs[3] = 20*c.entity_indices[3][0] + 3;

4442

dofs[4] = 20*c.entity_indices[3][0] + 4;

4443

dofs[5] = 20*c.entity_indices[3][0] + 5;

4444

dofs[6] = 20*c.entity_indices[3][0] + 6;

4445

dofs[7] = 20*c.entity_indices[3][0] + 7;

4446

dofs[8] = 20*c.entity_indices[3][0] + 8;

4447

dofs[9] = 20*c.entity_indices[3][0] + 9;

4448

dofs[10] = 20*c.entity_indices[3][0] + 10;

4449

dofs[11] = 20*c.entity_indices[3][0] + 11;

4450

dofs[12] = 20*c.entity_indices[3][0] + 12;

4451

dofs[13] = 20*c.entity_indices[3][0] + 13;

4452

dofs[14] = 20*c.entity_indices[3][0] + 14;

4453

dofs[15] = 20*c.entity_indices[3][0] + 15;

4454

dofs[16] = 20*c.entity_indices[3][0] + 16;

4455

dofs[17] = 20*c.entity_indices[3][0] + 17;

4456

dofs[18] = 20*c.entity_indices[3][0] + 18;

4457

dofs[19] = 20*c.entity_indices[3][0] + 19;

4458

}

4459

4460

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4461

virtual void tabulate_facet_dofs(unsigned int* dofs,

4462

unsigned int facet) const

4463

{

4464

switch ( facet )

4465

{

4466

case 0:

4467

4468

break;

4469

case 1:

4470

4471

break;

4472

case 2:

4473

4474

break;

4475

case 3:

4476

4477

break;

4478

}

4479

}

4480

4481

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4482

virtual void tabulate_entity_dofs(unsigned int* dofs,

4483

unsigned int d, unsigned int i) const

4484

{

4485

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4486

}

4487

4488

/// Tabulate the coordinates of all dofs on a cell

4489

virtual void tabulate_coordinates(double** coordinates,

4490

const ufc::cell& c) const

4491

{

4492

const double * const * x = c.coordinates;

4493

coordinates[0][0] = x[0][0];

4494

coordinates[0][1] = x[0][1];

4495

coordinates[0][2] = x[0][2];

4496

coordinates[1][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4497

coordinates[1][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4498

coordinates[1][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4499

coordinates[2][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4500

coordinates[2][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

4501

coordinates[2][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

4502

coordinates[3][0] = x[1][0];

4503

coordinates[3][1] = x[1][1];

4504

coordinates[3][2] = x[1][2];

4505

coordinates[4][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4506

coordinates[4][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4507

coordinates[4][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4508

coordinates[5][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

4509

coordinates[5][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

4510

coordinates[5][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

4511

coordinates[6][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

4512

coordinates[6][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

4513

coordinates[6][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

4514

coordinates[7][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4515

coordinates[7][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4516

coordinates[7][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4517

coordinates[8][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4518

coordinates[8][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4519

coordinates[8][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4520

coordinates[9][0] = x[2][0];

4521

coordinates[9][1] = x[2][1];

4522

coordinates[9][2] = x[2][2];

4523

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4524

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4525

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4526

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

4527

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

4528

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

4529

coordinates[12][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

4530

coordinates[12][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

4531

coordinates[12][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

4532

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4533

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4534

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4535

coordinates[14][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4536

coordinates[14][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4537

coordinates[14][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4538

coordinates[15][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

4539

coordinates[15][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

4540

coordinates[15][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

4541

coordinates[16][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

4542

coordinates[16][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

4543

coordinates[16][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

4544

coordinates[17][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

4545

coordinates[17][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

4546

coordinates[17][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

4547

coordinates[18][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

4548

coordinates[18][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

4549

coordinates[18][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

4550

coordinates[19][0] = x[3][0];

4551

coordinates[19][1] = x[3][1];

4552

coordinates[19][2] = x[3][2];

4553

}

4554

4555

/// Return the number of sub dof maps (for a mixed element)

4556

virtual unsigned int num_sub_dof_maps() const

4557

{

4558

return 1;

4559

}

4560

4561

/// Create a new dof_map for sub dof map i (for a mixed element)

4562

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

4563

{

4564

return new ffc_25_dof_map_0_0();

4565

}

4566

4567

};

4568

4569

/// This class defines the interface for a local-to-global mapping of

4570

/// degrees of freedom (dofs).

4571

4572

class ffc_25_dof_map_0_1: public ufc::dof_map

4573

{

4574

private:

4575

4576

unsigned int __global_dimension;

4577

4578

public:

4579

4580

/// Constructor

4581

ffc_25_dof_map_0_1() : ufc::dof_map()

4582

{

4583

__global_dimension = 0;

4584

}

4585

4586

/// Destructor

4587

virtual ~ffc_25_dof_map_0_1()

4588

{

4589

// Do nothing

4590

}

4591

4592

/// Return a string identifying the dof map

4593

virtual const char* signature() const

4594

{

4595

return "FFC dof map for Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

4596

}

4597

4598

/// Return true iff mesh entities of topological dimension d are needed

4599

virtual bool needs_mesh_entities(unsigned int d) const

4600

{

4601

switch ( d )

4602

{

4603

case 0:

4604

return false;

4605

break;

4606

case 1:

4607

return false;

4608

break;

4609

case 2:

4610

return false;

4611

break;

4612

case 3:

4613

return true;

4614

break;

4615

}

4616

return false;

4617

}

4618

4619

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4620

virtual bool init_mesh(const ufc::mesh& m)

4621

{

4622

__global_dimension = 20*m.num_entities[3];

4623

return false;

4624

}

4625

4626

/// Initialize dof map for given cell

4627

virtual void init_cell(const ufc::mesh& m,

4628

const ufc::cell& c)

4629

{

4630

// Do nothing

4631

}

4632

4633

/// Finish initialization of dof map for cells

4634

virtual void init_cell_finalize()

4635

{

4636

// Do nothing

4637

}

4638

4639

/// Return the dimension of the global finite element function space

4640

virtual unsigned int global_dimension() const

4641

{

4642

return __global_dimension;

4643

}

4644

4645

/// Return the dimension of the local finite element function space

4646

virtual unsigned int local_dimension() const

4647

{

4648

return 20;

4649

}

4650

4651

// Return the geometric dimension of the coordinates this dof map provides

4652

virtual unsigned int geometric_dimension() const

4653

{

4654

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4655

}

4656

4657

/// Return the number of dofs on each cell facet

4658

virtual unsigned int num_facet_dofs() const

4659

{

4660

return 0;

4661

}

4662

4663

/// Return the number of dofs associated with each cell entity of dimension d

4664

virtual unsigned int num_entity_dofs(unsigned int d) const

4665

{

4666

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4667

}

4668

4669

/// Tabulate the local-to-global mapping of dofs on a cell

4670

virtual void tabulate_dofs(unsigned int* dofs,

4671

const ufc::mesh& m,

4672

const ufc::cell& c) const

4673

{

4674

dofs[0] = 20*c.entity_indices[3][0];

4675

dofs[1] = 20*c.entity_indices[3][0] + 1;

4676

dofs[2] = 20*c.entity_indices[3][0] + 2;

4677

dofs[3] = 20*c.entity_indices[3][0] + 3;

4678

dofs[4] = 20*c.entity_indices[3][0] + 4;

4679

dofs[5] = 20*c.entity_indices[3][0] + 5;

4680

dofs[6] = 20*c.entity_indices[3][0] + 6;

4681

dofs[7] = 20*c.entity_indices[3][0] + 7;

4682

dofs[8] = 20*c.entity_indices[3][0] + 8;

4683

dofs[9] = 20*c.entity_indices[3][0] + 9;

4684

dofs[10] = 20*c.entity_indices[3][0] + 10;

4685

dofs[11] = 20*c.entity_indices[3][0] + 11;

4686

dofs[12] = 20*c.entity_indices[3][0] + 12;

4687

dofs[13] = 20*c.entity_indices[3][0] + 13;

4688

dofs[14] = 20*c.entity_indices[3][0] + 14;

4689

dofs[15] = 20*c.entity_indices[3][0] + 15;

4690

dofs[16] = 20*c.entity_indices[3][0] + 16;

4691

dofs[17] = 20*c.entity_indices[3][0] + 17;

4692

dofs[18] = 20*c.entity_indices[3][0] + 18;

4693

dofs[19] = 20*c.entity_indices[3][0] + 19;

4694

}

4695

4696

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4697

virtual void tabulate_facet_dofs(unsigned int* dofs,

4698

unsigned int facet) const

4699

{

4700

switch ( facet )

4701

{

4702

case 0:

4703

4704

break;

4705

case 1:

4706

4707

break;

4708

case 2:

4709

4710

break;

4711

case 3:

4712

4713

break;

4714

}

4715

}

4716

4717

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4718

virtual void tabulate_entity_dofs(unsigned int* dofs,

4719

unsigned int d, unsigned int i) const

4720

{

4721

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4722

}

4723

4724

/// Tabulate the coordinates of all dofs on a cell

4725

virtual void tabulate_coordinates(double** coordinates,

4726

const ufc::cell& c) const

4727

{

4728

const double * const * x = c.coordinates;

4729

coordinates[0][0] = x[0][0];

4730

coordinates[0][1] = x[0][1];

4731

coordinates[0][2] = x[0][2];

4732

coordinates[1][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4733

coordinates[1][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4734

coordinates[1][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4735

coordinates[2][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4736

coordinates[2][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

4737

coordinates[2][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

4738

coordinates[3][0] = x[1][0];

4739

coordinates[3][1] = x[1][1];

4740

coordinates[3][2] = x[1][2];

4741

coordinates[4][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4742

coordinates[4][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4743

coordinates[4][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4744

coordinates[5][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

4745

coordinates[5][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

4746

coordinates[5][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

4747

coordinates[6][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

4748

coordinates[6][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

4749

coordinates[6][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

4750

coordinates[7][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4751

coordinates[7][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4752

coordinates[7][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4753

coordinates[8][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4754

coordinates[8][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4755

coordinates[8][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4756

coordinates[9][0] = x[2][0];

4757

coordinates[9][1] = x[2][1];

4758

coordinates[9][2] = x[2][2];

4759

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4760

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4761

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4762

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

4763

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

4764

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

4765

coordinates[12][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

4766

coordinates[12][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

4767

coordinates[12][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

4768

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4769

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4770

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4771

coordinates[14][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4772

coordinates[14][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4773

coordinates[14][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4774

coordinates[15][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

4775

coordinates[15][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

4776

coordinates[15][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

4777

coordinates[16][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

4778

coordinates[16][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

4779

coordinates[16][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

4780

coordinates[17][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

4781

coordinates[17][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

4782

coordinates[17][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

4783

coordinates[18][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

4784

coordinates[18][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

4785

coordinates[18][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

4786

coordinates[19][0] = x[3][0];

4787

coordinates[19][1] = x[3][1];

4788

coordinates[19][2] = x[3][2];

4789

}

4790

4791

/// Return the number of sub dof maps (for a mixed element)

4792

virtual unsigned int num_sub_dof_maps() const

4793

{

4794

return 1;

4795

}

4796

4797

/// Create a new dof_map for sub dof map i (for a mixed element)

4798

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

4799

{

4800

return new ffc_25_dof_map_0_1();

4801

}

4802

4803

};

4804

4805

/// This class defines the interface for a local-to-global mapping of

4806

/// degrees of freedom (dofs).

4807

4808

class ffc_25_dof_map_0_2: public ufc::dof_map

4809

{

4810

private:

4811

4812

unsigned int __global_dimension;

4813

4814

public:

4815

4816

/// Constructor

4817

ffc_25_dof_map_0_2() : ufc::dof_map()

4818

{

4819

__global_dimension = 0;

4820

}

4821

4822

/// Destructor

4823

virtual ~ffc_25_dof_map_0_2()

4824

{

4825

// Do nothing

4826

}

4827

4828

/// Return a string identifying the dof map

4829

virtual const char* signature() const

4830

{

4831

return "FFC dof map for Discontinuous Lagrange finite element of degree 3 on a tetrahedron";

4832

}

4833

4834

/// Return true iff mesh entities of topological dimension d are needed

4835

virtual bool needs_mesh_entities(unsigned int d) const

4836

{

4837

switch ( d )

4838

{

4839

case 0:

4840

return false;

4841

break;

4842

case 1:

4843

return false;

4844

break;

4845

case 2:

4846

return false;

4847

break;

4848

case 3:

4849

return true;

4850

break;

4851

}

4852

return false;

4853

}

4854

4855

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4856

virtual bool init_mesh(const ufc::mesh& m)

4857

{

4858

__global_dimension = 20*m.num_entities[3];

4859

return false;

4860

}

4861

4862

/// Initialize dof map for given cell

4863

virtual void init_cell(const ufc::mesh& m,

4864

const ufc::cell& c)

4865

{

4866

// Do nothing

4867

}

4868

4869

/// Finish initialization of dof map for cells

4870

virtual void init_cell_finalize()

4871

{

4872

// Do nothing

4873

}

4874

4875

/// Return the dimension of the global finite element function space

4876

virtual unsigned int global_dimension() const

4877

{

4878

return __global_dimension;

4879

}

4880

4881

/// Return the dimension of the local finite element function space

4882

virtual unsigned int local_dimension() const

4883

{

4884

return 20;

4885

}

4886

4887

// Return the geometric dimension of the coordinates this dof map provides

4888

virtual unsigned int geometric_dimension() const

4889

{

4890

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4891

}

4892

4893

/// Return the number of dofs on each cell facet

4894

virtual unsigned int num_facet_dofs() const

4895

{

4896

return 0;

4897

}

4898

4899

/// Return the number of dofs associated with each cell entity of dimension d

4900

virtual unsigned int num_entity_dofs(unsigned int d) const

4901

{

4902

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4903

}

4904

4905

/// Tabulate the local-to-global mapping of dofs on a cell

4906

virtual void tabulate_dofs(unsigned int* dofs,

4907

const ufc::mesh& m,

4908

const ufc::cell& c) const

4909

{

4910

dofs[0] = 20*c.entity_indices[3][0];

4911

dofs[1] = 20*c.entity_indices[3][0] + 1;

4912

dofs[2] = 20*c.entity_indices[3][0] + 2;

4913

dofs[3] = 20*c.entity_indices[3][0] + 3;

4914

dofs[4] = 20*c.entity_indices[3][0] + 4;

4915

dofs[5] = 20*c.entity_indices[3][0] + 5;

4916

dofs[6] = 20*c.entity_indices[3][0] + 6;

4917

dofs[7] = 20*c.entity_indices[3][0] + 7;

4918

dofs[8] = 20*c.entity_indices[3][0] + 8;

4919

dofs[9] = 20*c.entity_indices[3][0] + 9;

4920

dofs[10] = 20*c.entity_indices[3][0] + 10;

4921

dofs[11] = 20*c.entity_indices[3][0] + 11;

4922

dofs[12] = 20*c.entity_indices[3][0] + 12;

4923

dofs[13] = 20*c.entity_indices[3][0] + 13;

4924

dofs[14] = 20*c.entity_indices[3][0] + 14;

4925

dofs[15] = 20*c.entity_indices[3][0] + 15;

4926

dofs[16] = 20*c.entity_indices[3][0] + 16;

4927

dofs[17] = 20*c.entity_indices[3][0] + 17;

4928

dofs[18] = 20*c.entity_indices[3][0] + 18;

4929

dofs[19] = 20*c.entity_indices[3][0] + 19;

4930

}

4931

4932

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4933

virtual void tabulate_facet_dofs(unsigned int* dofs,

4934

unsigned int facet) const

4935

{

4936

switch ( facet )

4937

{

4938

case 0:

4939

4940

break;

4941

case 1:

4942

4943

break;

4944

case 2:

4945

4946

break;

4947

case 3:

4948

4949

break;

4950

}

4951

}

4952

4953

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4954

virtual void tabulate_entity_dofs(unsigned int* dofs,

4955

unsigned int d, unsigned int i) const

4956

{

4957

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4958

}

4959

4960

/// Tabulate the coordinates of all dofs on a cell

4961

virtual void tabulate_coordinates(double** coordinates,

4962

const ufc::cell& c) const

4963

{

4964

const double * const * x = c.coordinates;

4965

coordinates[0][0] = x[0][0];

4966

coordinates[0][1] = x[0][1];

4967

coordinates[0][2] = x[0][2];

4968

coordinates[1][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4969

coordinates[1][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4970

coordinates[1][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4971

coordinates[2][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4972

coordinates[2][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

4973

coordinates[2][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

4974

coordinates[3][0] = x[1][0];

4975

coordinates[3][1] = x[1][1];

4976

coordinates[3][2] = x[1][2];

4977

coordinates[4][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4978

coordinates[4][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4979

coordinates[4][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4980

coordinates[5][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

4981

coordinates[5][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

4982

coordinates[5][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

4983

coordinates[6][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

4984

coordinates[6][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

4985

coordinates[6][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

4986

coordinates[7][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4987

coordinates[7][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4988

coordinates[7][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4989

coordinates[8][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4990

coordinates[8][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4991

coordinates[8][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4992

coordinates[9][0] = x[2][0];

4993

coordinates[9][1] = x[2][1];

4994

coordinates[9][2] = x[2][2];

4995

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4996

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4997

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4998

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

4999

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5000

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5001

coordinates[12][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

5002

coordinates[12][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

5003

coordinates[12][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

5004

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5005

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5006

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5007

coordinates[14][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5008

coordinates[14][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5009

coordinates[14][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5010

coordinates[15][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

5011

coordinates[15][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

5012

coordinates[15][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

5013

coordinates[16][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

5014

coordinates[16][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

5015

coordinates[16][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

5016

coordinates[17][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

5017

coordinates[17][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

5018

coordinates[17][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

5019

coordinates[18][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

5020

coordinates[18][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

5021

coordinates[18][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

5022

coordinates[19][0] = x[3][0];

5023

coordinates[19][1] = x[3][1];

5024

coordinates[19][2] = x[3][2];

5025

}

5026

5027

/// Return the number of sub dof maps (for a mixed element)

5028

virtual unsigned int num_sub_dof_maps() const

5029

{

5030

return 1;

5031

}

5032

5033

/// Create a new dof_map for sub dof map i (for a mixed element)

5034

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

5035

{

5036

return new ffc_25_dof_map_0_2();

5037

}

5038

5039

};

5040

5041

/// This class defines the interface for a local-to-global mapping of

5042

/// degrees of freedom (dofs).

5043

5044

class ffc_25_dof_map_0: public ufc::dof_map

5045

{

5046

private:

5047

5048

unsigned int __global_dimension;

5049

5050

public:

5051

5052

/// Constructor

5053

ffc_25_dof_map_0() : ufc::dof_map()

5054

{

5055

__global_dimension = 0;

5056

}

5057

5058

/// Destructor

5059

virtual ~ffc_25_dof_map_0()

5060

{

5061

// Do nothing

5062

}

5063

5064

/// Return a string identifying the dof map

5065

virtual const char* signature() const

5066

{

5067

return "FFC dof map for Mixed finite element: [Discontinuous Lagrange finite element of degree 3 on a tetrahedron, Discontinuous Lagrange finite element of degree 3 on a tetrahedron, Discontinuous Lagrange finite element of degree 3 on a tetrahedron]";

5068

}

5069

5070

/// Return true iff mesh entities of topological dimension d are needed

5071

virtual bool needs_mesh_entities(unsigned int d) const

5072

{

5073

switch ( d )

5074

{

5075

case 0:

5076

return false;

5077

break;

5078

case 1:

5079

return false;

5080

break;

5081

case 2:

5082

return false;

5083

break;

5084

case 3:

5085

return true;

5086

break;

5087

}

5088

return false;

5089

}

5090

5091

/// Initialize dof map for mesh (return true iff init_cell() is needed)

5092

virtual bool init_mesh(const ufc::mesh& m)

5093

{

5094

__global_dimension = 60*m.num_entities[3];

5095

return false;

5096

}

5097

5098

/// Initialize dof map for given cell

5099

virtual void init_cell(const ufc::mesh& m,

5100

const ufc::cell& c)

5101

{

5102

// Do nothing

5103

}

5104

5105

/// Finish initialization of dof map for cells

5106

virtual void init_cell_finalize()

5107

{

5108

// Do nothing

5109

}

5110

5111

/// Return the dimension of the global finite element function space

5112

virtual unsigned int global_dimension() const

5113

{

5114

return __global_dimension;

5115

}

5116

5117

/// Return the dimension of the local finite element function space

5118

virtual unsigned int local_dimension() const

5119

{

5120

return 60;

5121

}

5122

5123

// Return the geometric dimension of the coordinates this dof map provides

5124

virtual unsigned int geometric_dimension() const

5125

{

5126

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

5127

}

5128

5129

/// Return the number of dofs on each cell facet

5130

virtual unsigned int num_facet_dofs() const

5131

{

5132

return 0;

5133

}

5134

5135

/// Return the number of dofs associated with each cell entity of dimension d

5136

virtual unsigned int num_entity_dofs(unsigned int d) const

5137

{

5138

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

5139

}

5140

5141

/// Tabulate the local-to-global mapping of dofs on a cell

5142

virtual void tabulate_dofs(unsigned int* dofs,

5143

const ufc::mesh& m,

5144

const ufc::cell& c) const

5145

{

5146

dofs[0] = 20*c.entity_indices[3][0];

5147

dofs[1] = 20*c.entity_indices[3][0] + 1;

5148

dofs[2] = 20*c.entity_indices[3][0] + 2;

5149

dofs[3] = 20*c.entity_indices[3][0] + 3;

5150

dofs[4] = 20*c.entity_indices[3][0] + 4;

5151

dofs[5] = 20*c.entity_indices[3][0] + 5;

5152

dofs[6] = 20*c.entity_indices[3][0] + 6;

5153

dofs[7] = 20*c.entity_indices[3][0] + 7;

5154

dofs[8] = 20*c.entity_indices[3][0] + 8;

5155

dofs[9] = 20*c.entity_indices[3][0] + 9;

5156

dofs[10] = 20*c.entity_indices[3][0] + 10;

5157

dofs[11] = 20*c.entity_indices[3][0] + 11;

5158

dofs[12] = 20*c.entity_indices[3][0] + 12;

5159

dofs[13] = 20*c.entity_indices[3][0] + 13;

5160

dofs[14] = 20*c.entity_indices[3][0] + 14;

5161

dofs[15] = 20*c.entity_indices[3][0] + 15;

5162

dofs[16] = 20*c.entity_indices[3][0] + 16;

5163

dofs[17] = 20*c.entity_indices[3][0] + 17;

5164

dofs[18] = 20*c.entity_indices[3][0] + 18;

5165

dofs[19] = 20*c.entity_indices[3][0] + 19;

5166

unsigned int offset = 20*m.num_entities[3];

5167

dofs[20] = offset + 20*c.entity_indices[3][0];

5168

dofs[21] = offset + 20*c.entity_indices[3][0] + 1;

5169

dofs[22] = offset + 20*c.entity_indices[3][0] + 2;

5170

dofs[23] = offset + 20*c.entity_indices[3][0] + 3;

5171

dofs[24] = offset + 20*c.entity_indices[3][0] + 4;

5172

dofs[25] = offset + 20*c.entity_indices[3][0] + 5;

5173

dofs[26] = offset + 20*c.entity_indices[3][0] + 6;

5174

dofs[27] = offset + 20*c.entity_indices[3][0] + 7;

5175

dofs[28] = offset + 20*c.entity_indices[3][0] + 8;

5176

dofs[29] = offset + 20*c.entity_indices[3][0] + 9;

5177

dofs[30] = offset + 20*c.entity_indices[3][0] + 10;

5178

dofs[31] = offset + 20*c.entity_indices[3][0] + 11;

5179

dofs[32] = offset + 20*c.entity_indices[3][0] + 12;

5180

dofs[33] = offset + 20*c.entity_indices[3][0] + 13;

5181

dofs[34] = offset + 20*c.entity_indices[3][0] + 14;

5182

dofs[35] = offset + 20*c.entity_indices[3][0] + 15;

5183

dofs[36] = offset + 20*c.entity_indices[3][0] + 16;

5184

dofs[37] = offset + 20*c.entity_indices[3][0] + 17;

5185

dofs[38] = offset + 20*c.entity_indices[3][0] + 18;

5186

dofs[39] = offset + 20*c.entity_indices[3][0] + 19;

5187

offset = offset + 20*m.num_entities[3];

5188

dofs[40] = offset + 20*c.entity_indices[3][0];

5189

dofs[41] = offset + 20*c.entity_indices[3][0] + 1;

5190

dofs[42] = offset + 20*c.entity_indices[3][0] + 2;

5191

dofs[43] = offset + 20*c.entity_indices[3][0] + 3;

5192

dofs[44] = offset + 20*c.entity_indices[3][0] + 4;

5193

dofs[45] = offset + 20*c.entity_indices[3][0] + 5;

5194

dofs[46] = offset + 20*c.entity_indices[3][0] + 6;

5195

dofs[47] = offset + 20*c.entity_indices[3][0] + 7;

5196

dofs[48] = offset + 20*c.entity_indices[3][0] + 8;

5197

dofs[49] = offset + 20*c.entity_indices[3][0] + 9;

5198

dofs[50] = offset + 20*c.entity_indices[3][0] + 10;

5199

dofs[51] = offset + 20*c.entity_indices[3][0] + 11;

5200

dofs[52] = offset + 20*c.entity_indices[3][0] + 12;

5201

dofs[53] = offset + 20*c.entity_indices[3][0] + 13;

5202

dofs[54] = offset + 20*c.entity_indices[3][0] + 14;

5203

dofs[55] = offset + 20*c.entity_indices[3][0] + 15;

5204

dofs[56] = offset + 20*c.entity_indices[3][0] + 16;

5205

dofs[57] = offset + 20*c.entity_indices[3][0] + 17;

5206

dofs[58] = offset + 20*c.entity_indices[3][0] + 18;

5207

dofs[59] = offset + 20*c.entity_indices[3][0] + 19;

5208

}

5209

5210

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

5211

virtual void tabulate_facet_dofs(unsigned int* dofs,

5212

unsigned int facet) const

5213

{

5214

switch ( facet )

5215

{

5216

case 0:

5217

5218

break;

5219

case 1:

5220

5221

break;

5222

case 2:

5223

5224

break;

5225

case 3:

5226

5227

break;

5228

}

5229

}

5230

5231

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

5232

virtual void tabulate_entity_dofs(unsigned int* dofs,

5233

unsigned int d, unsigned int i) const

5234

{

5235

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

5236

}

5237

5238

/// Tabulate the coordinates of all dofs on a cell

5239

virtual void tabulate_coordinates(double** coordinates,

5240

const ufc::cell& c) const

5241

{

5242

const double * const * x = c.coordinates;

5243

coordinates[0][0] = x[0][0];

5244

coordinates[0][1] = x[0][1];

5245

coordinates[0][2] = x[0][2];

5246

coordinates[1][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

5247

coordinates[1][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

5248

coordinates[1][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

5249

coordinates[2][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

5250

coordinates[2][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

5251

coordinates[2][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

5252

coordinates[3][0] = x[1][0];

5253

coordinates[3][1] = x[1][1];

5254

coordinates[3][2] = x[1][2];

5255

coordinates[4][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

5256

coordinates[4][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

5257

coordinates[4][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

5258

coordinates[5][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

5259

coordinates[5][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

5260

coordinates[5][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

5261

coordinates[6][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

5262

coordinates[6][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

5263

coordinates[6][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

5264

coordinates[7][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

5265

coordinates[7][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

5266

coordinates[7][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

5267

coordinates[8][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

5268

coordinates[8][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

5269

coordinates[8][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

5270

coordinates[9][0] = x[2][0];

5271

coordinates[9][1] = x[2][1];

5272

coordinates[9][2] = x[2][2];

5273

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

5274

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

5275

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

5276

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

5277

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5278

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5279

coordinates[12][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

5280

coordinates[12][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

5281

coordinates[12][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

5282

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5283

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5284

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5285

coordinates[14][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5286

coordinates[14][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5287

coordinates[14][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5288

coordinates[15][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

5289

coordinates[15][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

5290

coordinates[15][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

5291

coordinates[16][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

5292

coordinates[16][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

5293

coordinates[16][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

5294

coordinates[17][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

5295

coordinates[17][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

5296

coordinates[17][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

5297

coordinates[18][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

5298

coordinates[18][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

5299

coordinates[18][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

5300

coordinates[19][0] = x[3][0];

5301

coordinates[19][1] = x[3][1];

5302

coordinates[19][2] = x[3][2];

5303

coordinates[20][0] = x[0][0];

5304

coordinates[20][1] = x[0][1];

5305

coordinates[20][2] = x[0][2];

5306

coordinates[21][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

5307

coordinates[21][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

5308

coordinates[21][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

5309

coordinates[22][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

5310

coordinates[22][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

5311

coordinates[22][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

5312

coordinates[23][0] = x[1][0];

5313

coordinates[23][1] = x[1][1];

5314

coordinates[23][2] = x[1][2];

5315

coordinates[24][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

5316

coordinates[24][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

5317

coordinates[24][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

5318

coordinates[25][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

5319

coordinates[25][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

5320

coordinates[25][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

5321

coordinates[26][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

5322

coordinates[26][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

5323

coordinates[26][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

5324

coordinates[27][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

5325

coordinates[27][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

5326

coordinates[27][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

5327

coordinates[28][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

5328

coordinates[28][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

5329

coordinates[28][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

5330

coordinates[29][0] = x[2][0];

5331

coordinates[29][1] = x[2][1];

5332

coordinates[29][2] = x[2][2];

5333

coordinates[30][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

5334

coordinates[30][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

5335

coordinates[30][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

5336

coordinates[31][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

5337

coordinates[31][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5338

coordinates[31][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5339

coordinates[32][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

5340

coordinates[32][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

5341

coordinates[32][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

5342

coordinates[33][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5343

coordinates[33][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5344

coordinates[33][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5345

coordinates[34][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5346

coordinates[34][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5347

coordinates[34][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5348

coordinates[35][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

5349

coordinates[35][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

5350

coordinates[35][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

5351

coordinates[36][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

5352

coordinates[36][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

5353

coordinates[36][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

5354

coordinates[37][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

5355

coordinates[37][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

5356

coordinates[37][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

5357

coordinates[38][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

5358

coordinates[38][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

5359

coordinates[38][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

5360

coordinates[39][0] = x[3][0];

5361

coordinates[39][1] = x[3][1];

5362

coordinates[39][2] = x[3][2];

5363

coordinates[40][0] = x[0][0];

5364

coordinates[40][1] = x[0][1];

5365

coordinates[40][2] = x[0][2];

5366

coordinates[41][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

5367

coordinates[41][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

5368

coordinates[41][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

5369

coordinates[42][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

5370

coordinates[42][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

5371

coordinates[42][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

5372

coordinates[43][0] = x[1][0];

5373

coordinates[43][1] = x[1][1];

5374

coordinates[43][2] = x[1][2];

5375

coordinates[44][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

5376

coordinates[44][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

5377

coordinates[44][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

5378

coordinates[45][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

5379

coordinates[45][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

5380

coordinates[45][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

5381

coordinates[46][0] = 0.666666666666666*x[1][0] + 0.333333333333333*x[2][0];

5382

coordinates[46][1] = 0.666666666666666*x[1][1] + 0.333333333333333*x[2][1];

5383

coordinates[46][2] = 0.666666666666666*x[1][2] + 0.333333333333333*x[2][2];

5384

coordinates[47][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

5385

coordinates[47][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

5386

coordinates[47][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

5387

coordinates[48][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

5388

coordinates[48][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

5389

coordinates[48][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

5390

coordinates[49][0] = x[2][0];

5391

coordinates[49][1] = x[2][1];

5392

coordinates[49][2] = x[2][2];

5393

coordinates[50][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

5394

coordinates[50][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

5395

coordinates[50][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

5396

coordinates[51][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

5397

coordinates[51][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5398

coordinates[51][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5399

coordinates[52][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

5400

coordinates[52][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

5401

coordinates[52][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

5402

coordinates[53][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5403

coordinates[53][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5404

coordinates[53][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5405

coordinates[54][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5406

coordinates[54][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5407

coordinates[54][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5408

coordinates[55][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

5409

coordinates[55][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

5410

coordinates[55][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

5411

coordinates[56][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

5412

coordinates[56][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

5413

coordinates[56][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

5414

coordinates[57][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

5415

coordinates[57][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

5416

coordinates[57][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

5417

coordinates[58][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

5418

coordinates[58][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

5419

coordinates[58][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

5420

coordinates[59][0] = x[3][0];

5421

coordinates[59][1] = x[3][1];

5422

coordinates[59][2] = x[3][2];

5423

}

5424

5425

/// Return the number of sub dof maps (for a mixed element)

5426

virtual unsigned int num_sub_dof_maps() const

5427

{

5428

return 3;

5429

}

5430

5431

/// Create a new dof_map for sub dof map i (for a mixed element)

5432

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

5433

{

5434

switch ( i )

5435

{

5436

case 0:

5437

return new ffc_25_dof_map_0_0();

5438

break;

5439

case 1:

5440

return new ffc_25_dof_map_0_1();

5441

break;

5442

case 2:

5443

return new ffc_25_dof_map_0_2();

5444

break;

5445

}

5446

return 0;

5447

}

5448

5449

};

5450

5451

#endif