~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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//

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// Warning: This code was generated with the option '-l dolfin'

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// and contains DOLFIN-specific wrappers that depend on DOLFIN.

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#ifndef __POISSON3D_3_H

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#define __POISSON3D_3_H

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#include <cmath>

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#include <stdexcept>

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#include <fstream>

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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 UFC_Poisson3D_3BilinearForm_finite_element_0: public ufc::finite_element

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{

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public:

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/// Constructor

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UFC_Poisson3D_3BilinearForm_finite_element_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 ~UFC_Poisson3D_3BilinearForm_finite_element_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 "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, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

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{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

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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, -0.00535714285714286},

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{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

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{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

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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, 0.0978075995544939, -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, -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, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

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{0, -0.0978075995544939, -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, 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, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

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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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

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{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

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{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

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{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

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{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

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{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

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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, -0.00535714285714285}};

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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];

248

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

249

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

250

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

251

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

252

253

// Compute value(s)

254

*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;

255

}

256

257

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

258

virtual void evaluate_basis_all(double* values,

259

const double* coordinates,

260

const ufc::cell& c) const

261

{

262

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

263

}

264

265

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

266

virtual void evaluate_basis_derivatives(unsigned int i,

267

unsigned int n,

268

double* values,

269

const double* coordinates,

270

const ufc::cell& c) const

271

{

272

// Extract vertex coordinates

273

const double * const * element_coordinates = c.coordinates;

274

275

// Compute Jacobian of affine map from reference cell

276

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

277

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

278

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

279

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

280

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

281

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

282

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

283

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

284

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

285

286

// Compute sub determinants

287

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

288

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

289

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

290

291

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

292

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

293

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

294

295

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

296

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

297

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

298

299

// Compute determinant of Jacobian

300

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

301

302

// Compute inverse of Jacobian

303

304

// Compute constants

305

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

306

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

307

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

308

309

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

310

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

311

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

312

313

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

314

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

315

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

316

317

// Get coordinates and map to the UFC reference element

318

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

319

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

320

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

321

322

// Map coordinates to the reference cube

323

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

324

x = 1.0;

325

else

326

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

327

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

328

y = -1.0;

329

else

330

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

331

z = 2.0 * z - 1.0;

332

333

// Compute number of derivatives

334

unsigned int num_derivatives = 1;

335

336

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

337

num_derivatives *= 3;

338

339

340

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

341

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

342

343

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

344

{

345

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

346

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

347

combinations[j][k] = 0;

348

}

349

350

// Generate combinations of derivatives

351

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

352

{

353

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

354

{

355

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

356

{

357

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

358

combinations[row][col] = 0;

359

else

360

{

361

combinations[row][col] += 1;

362

break;

363

}

364

}

365

}

366

}

367

368

// Compute inverse of Jacobian

369

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

370

371

// Declare transformation matrix

372

// Declare pointer to two dimensional array and initialise

373

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

374

375

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

376

{

377

transform[j] = new double [num_derivatives];

378

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

379

transform[j][k] = 1;

380

}

381

382

// Construct transformation matrix

383

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

384

{

385

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

386

{

387

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

388

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

389

}

390

}

391

392

// Reset values

393

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

394

values[j] = 0;

395

396

// Map degree of freedom to element degree of freedom

397

const unsigned int dof = i;

398

399

// Generate scalings

400

const double scalings_y_0 = 1;

401

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

402

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

403

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

404

const double scalings_z_0 = 1;

405

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

406

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

407

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

408

409

// Compute psitilde_a

410

const double psitilde_a_0 = 1;

411

const double psitilde_a_1 = x;

412

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

413

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

414

415

// Compute psitilde_bs

416

const double psitilde_bs_0_0 = 1;

417

const double psitilde_bs_0_1 = 1.5*y + 0.5;

418

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;

419

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;

420

const double psitilde_bs_1_0 = 1;

421

const double psitilde_bs_1_1 = 2.5*y + 1.5;

422

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;

423

const double psitilde_bs_2_0 = 1;

424

const double psitilde_bs_2_1 = 3.5*y + 2.5;

425

const double psitilde_bs_3_0 = 1;

426

427

// Compute psitilde_cs

428

const double psitilde_cs_00_0 = 1;

429

const double psitilde_cs_00_1 = 2*z + 1;

430

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;

431

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;

432

const double psitilde_cs_01_0 = 1;

433

const double psitilde_cs_01_1 = 3*z + 2;

434

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;

435

const double psitilde_cs_02_0 = 1;

436

const double psitilde_cs_02_1 = 4*z + 3;

437

const double psitilde_cs_03_0 = 1;

438

const double psitilde_cs_10_0 = 1;

439

const double psitilde_cs_10_1 = 3*z + 2;

440

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;

441

const double psitilde_cs_11_0 = 1;

442

const double psitilde_cs_11_1 = 4*z + 3;

443

const double psitilde_cs_12_0 = 1;

444

const double psitilde_cs_20_0 = 1;

445

const double psitilde_cs_20_1 = 4*z + 3;

446

const double psitilde_cs_21_0 = 1;

447

const double psitilde_cs_30_0 = 1;

448

449

// Compute basisvalues

450

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

451

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

452

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

453

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

454

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

455

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

456

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

457

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

458

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

459

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

460

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

461

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

462

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

463

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

464

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

465

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

466

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

467

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

468

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

469

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

470

471

// Table(s) of coefficients

472

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

473

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

474

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

475

{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, -0.00535714285714286},

476

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

477

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

478

{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},

479

{0, 0.0978075995544939, -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},

480

{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},

481

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

482

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

483

{0, -0.0978075995544939, -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},

484

{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},

485

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

486

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

487

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

488

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

489

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

490

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

491

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

492

{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, -0.00535714285714285}};

493

494

// Interesting (new) part

495

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

496

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

497

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

498

{6.32455532033676, 0, 0, 0, 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

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

501

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

502

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

503

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

504

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

505

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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

{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},

508

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

509

{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},

510

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

511

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

512

{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},

513

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

514

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

515

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

516

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

517

518

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

519

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

520

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

521

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

522

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

523

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

524

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

525

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

526

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

527

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

528

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

529

{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},

530

{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},

531

{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},

532

{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},

533

{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},

534

{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},

535

{-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},

536

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

537

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

538

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

539

540

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

541

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

542

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

543

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

544

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

545

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

546

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

547

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

548

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

549

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

550

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

551

{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},

552

{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},

553

{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},

554

{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},

555

{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},

556

{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},

557

{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},

558

{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},

559

{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},

560

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

561

562

// Compute reference derivatives

563

// Declare pointer to array of derivatives on FIAT element

564

double *derivatives = new double [num_derivatives];

565

566

// Declare coefficients

567

double coeff0_0 = 0;

568

double coeff0_1 = 0;

569

double coeff0_2 = 0;

570

double coeff0_3 = 0;

571

double coeff0_4 = 0;

572

double coeff0_5 = 0;

573

double coeff0_6 = 0;

574

double coeff0_7 = 0;

575

double coeff0_8 = 0;

576

double coeff0_9 = 0;

577

double coeff0_10 = 0;

578

double coeff0_11 = 0;

579

double coeff0_12 = 0;

580

double coeff0_13 = 0;

581

double coeff0_14 = 0;

582

double coeff0_15 = 0;

583

double coeff0_16 = 0;

584

double coeff0_17 = 0;

585

double coeff0_18 = 0;

586

double coeff0_19 = 0;

587

588

// Declare new coefficients

589

double new_coeff0_0 = 0;

590

double new_coeff0_1 = 0;

591

double new_coeff0_2 = 0;

592

double new_coeff0_3 = 0;

593

double new_coeff0_4 = 0;

594

double new_coeff0_5 = 0;

595

double new_coeff0_6 = 0;

596

double new_coeff0_7 = 0;

597

double new_coeff0_8 = 0;

598

double new_coeff0_9 = 0;

599

double new_coeff0_10 = 0;

600

double new_coeff0_11 = 0;

601

double new_coeff0_12 = 0;

602

double new_coeff0_13 = 0;

603

double new_coeff0_14 = 0;

604

double new_coeff0_15 = 0;

605

double new_coeff0_16 = 0;

606

double new_coeff0_17 = 0;

607

double new_coeff0_18 = 0;

608

double new_coeff0_19 = 0;

609

610

// Loop possible derivatives

611

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

612

{

613

// Get values from coefficients array

614

new_coeff0_0 = coefficients0[dof][0];

615

new_coeff0_1 = coefficients0[dof][1];

616

new_coeff0_2 = coefficients0[dof][2];

617

new_coeff0_3 = coefficients0[dof][3];

618

new_coeff0_4 = coefficients0[dof][4];

619

new_coeff0_5 = coefficients0[dof][5];

620

new_coeff0_6 = coefficients0[dof][6];

621

new_coeff0_7 = coefficients0[dof][7];

622

new_coeff0_8 = coefficients0[dof][8];

623

new_coeff0_9 = coefficients0[dof][9];

624

new_coeff0_10 = coefficients0[dof][10];

625

new_coeff0_11 = coefficients0[dof][11];

626

new_coeff0_12 = coefficients0[dof][12];

627

new_coeff0_13 = coefficients0[dof][13];

628

new_coeff0_14 = coefficients0[dof][14];

629

new_coeff0_15 = coefficients0[dof][15];

630

new_coeff0_16 = coefficients0[dof][16];

631

new_coeff0_17 = coefficients0[dof][17];

632

new_coeff0_18 = coefficients0[dof][18];

633

new_coeff0_19 = coefficients0[dof][19];

634

635

// Loop derivative order

636

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

637

{

638

// Update old coefficients

639

coeff0_0 = new_coeff0_0;

640

coeff0_1 = new_coeff0_1;

641

coeff0_2 = new_coeff0_2;

642

coeff0_3 = new_coeff0_3;

643

coeff0_4 = new_coeff0_4;

644

coeff0_5 = new_coeff0_5;

645

coeff0_6 = new_coeff0_6;

646

coeff0_7 = new_coeff0_7;

647

coeff0_8 = new_coeff0_8;

648

coeff0_9 = new_coeff0_9;

649

coeff0_10 = new_coeff0_10;

650

coeff0_11 = new_coeff0_11;

651

coeff0_12 = new_coeff0_12;

652

coeff0_13 = new_coeff0_13;

653

coeff0_14 = new_coeff0_14;

654

coeff0_15 = new_coeff0_15;

655

coeff0_16 = new_coeff0_16;

656

coeff0_17 = new_coeff0_17;

657

coeff0_18 = new_coeff0_18;

658

coeff0_19 = new_coeff0_19;

659

660

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

661

{

662

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];

663

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];

664

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];

665

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];

666

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];

667

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];

668

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];

669

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];

670

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];

671

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];

672

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];

673

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];

674

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];

675

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];

676

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];

677

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];

678

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];

679

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];

680

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];

681

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];

682

}

683

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

684

{

685

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];

686

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];

687

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];

688

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];

689

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];

690

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];

691

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];

692

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];

693

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];

694

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];

695

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];

696

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];

697

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];

698

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];

699

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];

700

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];

701

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];

702

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];

703

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];

704

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];

705

}

706

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

707

{

708

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];

709

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];

710

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];

711

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];

712

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];

713

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];

714

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];

715

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];

716

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];

717

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];

718

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];

719

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];

720

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];

721

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];

722

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];

723

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];

724

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];

725

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];

726

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];

727

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];

728

}

729

730

}

731

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

732

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;

733

}

734

735

// Transform derivatives back to physical element

736

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

737

{

738

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

739

{

740

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

741

}

742

}

743

// Delete pointer to array of derivatives on FIAT element

744

delete [] derivatives;

745

746

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

747

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

748

{

749

delete [] combinations[row];

750

delete [] transform[row];

751

}

752

753

delete [] combinations;

754

delete [] transform;

755

}

756

757

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

758

virtual void evaluate_basis_derivatives_all(unsigned int n,

759

double* values,

760

const double* coordinates,

761

const ufc::cell& c) const

762

{

763

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

764

}

765

766

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

767

virtual double evaluate_dof(unsigned int i,

768

const ufc::function& f,

769

const ufc::cell& c) const

770

{

771

// The reference points, direction and weights:

772

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

773

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}};

774

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}}};

775

776

const double * const * x = c.coordinates;

777

double result = 0.0;

778

// Iterate over the points:

779

// Evaluate basis functions for affine mapping

780

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

781

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

782

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

783

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

784

785

// Compute affine mapping y = F(X)

786

double y[3];

787

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

788

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

789

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

790

791

// Evaluate function at physical points

792

double values[1];

793

f.evaluate(values, y, c);

794

795

// Map function values using appropriate mapping

796

// Affine map: Do nothing

797

798

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

799

800

// Take directional components

801

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

802

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

803

// Multiply by weights

804

result *= W[i][0];

805

806

return result;

807

}

808

809

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

810

virtual void evaluate_dofs(double* values,

811

const ufc::function& f,

812

const ufc::cell& c) const

813

{

814

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

815

}

816

817

/// Interpolate vertex values from dof values

818

virtual void interpolate_vertex_values(double* vertex_values,

819

const double* dof_values,

820

const ufc::cell& c) const

821

{

822

// Evaluate at vertices and use affine mapping

823

vertex_values[0] = dof_values[0];

824

vertex_values[1] = dof_values[1];

825

vertex_values[2] = dof_values[2];

826

vertex_values[3] = dof_values[3];

827

}

828

829

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

830

virtual unsigned int num_sub_elements() const

831

{

832

return 1;

833

}

834

835

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

836

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

837

{

838

return new UFC_Poisson3D_3BilinearForm_finite_element_0();

839

}

840

841

};

842

843

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

844

845

class UFC_Poisson3D_3BilinearForm_finite_element_1: public ufc::finite_element

846

{

847

public:

848

849

/// Constructor

850

UFC_Poisson3D_3BilinearForm_finite_element_1() : ufc::finite_element()

851

{

852

// Do nothing

853

}

854

855

/// Destructor

856

virtual ~UFC_Poisson3D_3BilinearForm_finite_element_1()

857

{

858

// Do nothing

859

}

860

861

/// Return a string identifying the finite element

862

virtual const char* signature() const

863

{

864

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

865

}

866

867

/// Return the cell shape

868

virtual ufc::shape cell_shape() const

869

{

870

return ufc::tetrahedron;

871

}

872

873

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

874

virtual unsigned int space_dimension() const

875

{

876

return 20;

877

}

878

879

/// Return the rank of the value space

880

virtual unsigned int value_rank() const

881

{

882

return 0;

883

}

884

885

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

886

virtual unsigned int value_dimension(unsigned int i) const

887

{

888

return 1;

889

}

890

891

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

892

virtual void evaluate_basis(unsigned int i,

893

double* values,

894

const double* coordinates,

895

const ufc::cell& c) const

896

{

897

// Extract vertex coordinates

898

const double * const * element_coordinates = c.coordinates;

899

900

// Compute Jacobian of affine map from reference cell

901

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

902

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

903

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

904

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

905

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

906

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

907

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

908

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

909

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

910

911

// Compute sub determinants

912

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

913

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

914

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

915

916

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

917

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

918

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

919

920

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

921

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

922

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

923

924

// Compute determinant of Jacobian

925

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

926

927

// Compute inverse of Jacobian

928

929

// Compute constants

930

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

931

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

932

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

933

934

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

935

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

936

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

937

938

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

939

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

940

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

941

942

// Get coordinates and map to the UFC reference element

943

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

944

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

945

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

946

947

// Map coordinates to the reference cube

948

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

949

x = 1.0;

950

else

951

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

952

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

953

y = -1.0;

954

else

955

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

956

z = 2.0 * z - 1.0;

957

958

// Reset values

959

*values = 0;

960

961

// Map degree of freedom to element degree of freedom

962

const unsigned int dof = i;

963

964

// Generate scalings

965

const double scalings_y_0 = 1;

966

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

967

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

968

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

969

const double scalings_z_0 = 1;

970

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

971

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

972

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

973

974

// Compute psitilde_a

975

const double psitilde_a_0 = 1;

976

const double psitilde_a_1 = x;

977

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

978

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

979

980

// Compute psitilde_bs

981

const double psitilde_bs_0_0 = 1;

982

const double psitilde_bs_0_1 = 1.5*y + 0.5;

983

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;

984

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;

985

const double psitilde_bs_1_0 = 1;

986

const double psitilde_bs_1_1 = 2.5*y + 1.5;

987

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;

988

const double psitilde_bs_2_0 = 1;

989

const double psitilde_bs_2_1 = 3.5*y + 2.5;

990

const double psitilde_bs_3_0 = 1;

991

992

// Compute psitilde_cs

993

const double psitilde_cs_00_0 = 1;

994

const double psitilde_cs_00_1 = 2*z + 1;

995

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;

996

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;

997

const double psitilde_cs_01_0 = 1;

998

const double psitilde_cs_01_1 = 3*z + 2;

999

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;

1000

const double psitilde_cs_02_0 = 1;

1001

const double psitilde_cs_02_1 = 4*z + 3;

1002

const double psitilde_cs_03_0 = 1;

1003

const double psitilde_cs_10_0 = 1;

1004

const double psitilde_cs_10_1 = 3*z + 2;

1005

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;

1006

const double psitilde_cs_11_0 = 1;

1007

const double psitilde_cs_11_1 = 4*z + 3;

1008

const double psitilde_cs_12_0 = 1;

1009

const double psitilde_cs_20_0 = 1;

1010

const double psitilde_cs_20_1 = 4*z + 3;

1011

const double psitilde_cs_21_0 = 1;

1012

const double psitilde_cs_30_0 = 1;

1013

1014

// Compute basisvalues

1015

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

1016

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

1017

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

1018

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

1019

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

1020

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

1021

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

1022

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

1023

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

1024

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

1025

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

1026

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

1027

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

1028

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

1029

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

1030

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

1031

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

1032

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

1033

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

1034

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

1035

1036

// Table(s) of coefficients

1037

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

1038

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1039

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

1040

{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, -0.00535714285714286},

1041

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

1042

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

1043

{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},

1044

{0, 0.0978075995544939, -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},

1045

{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},

1046

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

1047

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1048

{0, -0.0978075995544939, -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},

1049

{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},

1050

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

1051

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1052

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

1053

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

1054

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1055

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1056

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

1057

{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, -0.00535714285714285}};

1058

1059

// Extract relevant coefficients

1060

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

1061

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

1062

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

1063

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

1064

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

1065

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

1066

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

1067

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

1068

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

1069

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

1070

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

1071

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

1072

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

1073

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

1074

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

1075

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

1076

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

1077

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

1078

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

1079

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

1080

1081

// Compute value(s)

1082

*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;

1083

}

1084

1085

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

1086

virtual void evaluate_basis_all(double* values,

1087

const double* coordinates,

1088

const ufc::cell& c) const

1089

{

1090

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

1091

}

1092

1093

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

1094

virtual void evaluate_basis_derivatives(unsigned int i,

1095

unsigned int n,

1096

double* values,

1097

const double* coordinates,

1098

const ufc::cell& c) const

1099

{

1100

// Extract vertex coordinates

1101

const double * const * element_coordinates = c.coordinates;

1102

1103

// Compute Jacobian of affine map from reference cell

1104

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

1105

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

1106

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

1107

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

1108

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

1109

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

1110

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

1111

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

1112

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

1113

1114

// Compute sub determinants

1115

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

1116

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

1117

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

1118

1119

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

1120

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

1121

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

1122

1123

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

1124

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

1125

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

1126

1127

// Compute determinant of Jacobian

1128

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

1129

1130

// Compute inverse of Jacobian

1131

1132

// Compute constants

1133

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

1134

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

1135

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

1136

1137

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

1138

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

1139

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

1140

1141

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

1142

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

1143

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

1144

1145

// Get coordinates and map to the UFC reference element

1146

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

1147

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

1148

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

1149

1150

// Map coordinates to the reference cube

1151

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

1152

x = 1.0;

1153

else

1154

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

1155

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

1156

y = -1.0;

1157

else

1158

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

1159

z = 2.0 * z - 1.0;

1160

1161

// Compute number of derivatives

1162

unsigned int num_derivatives = 1;

1163

1164

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

1165

num_derivatives *= 3;

1166

1167

1168

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

1169

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

1170

1171

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

1172

{

1173

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

1174

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

1175

combinations[j][k] = 0;

1176

}

1177

1178

// Generate combinations of derivatives

1179

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

1180

{

1181

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

1182

{

1183

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

1184

{

1185

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

1186

combinations[row][col] = 0;

1187

else

1188

{

1189

combinations[row][col] += 1;

1190

break;

1191

}

1192

}

1193

}

1194

}

1195

1196

// Compute inverse of Jacobian

1197

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

1198

1199

// Declare transformation matrix

1200

// Declare pointer to two dimensional array and initialise

1201

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

1202

1203

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

1204

{

1205

transform[j] = new double [num_derivatives];

1206

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

1207

transform[j][k] = 1;

1208

}

1209

1210

// Construct transformation matrix

1211

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

1212

{

1213

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

1214

{

1215

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

1216

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

1217

}

1218

}

1219

1220

// Reset values

1221

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

1222

values[j] = 0;

1223

1224

// Map degree of freedom to element degree of freedom

1225

const unsigned int dof = i;

1226

1227

// Generate scalings

1228

const double scalings_y_0 = 1;

1229

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

1230

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

1231

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

1232

const double scalings_z_0 = 1;

1233

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

1234

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

1235

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

1236

1237

// Compute psitilde_a

1238

const double psitilde_a_0 = 1;

1239

const double psitilde_a_1 = x;

1240

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

1241

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

1242

1243

// Compute psitilde_bs

1244

const double psitilde_bs_0_0 = 1;

1245

const double psitilde_bs_0_1 = 1.5*y + 0.5;

1246

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;

1247

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;

1248

const double psitilde_bs_1_0 = 1;

1249

const double psitilde_bs_1_1 = 2.5*y + 1.5;

1250

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;

1251

const double psitilde_bs_2_0 = 1;

1252

const double psitilde_bs_2_1 = 3.5*y + 2.5;

1253

const double psitilde_bs_3_0 = 1;

1254

1255

// Compute psitilde_cs

1256

const double psitilde_cs_00_0 = 1;

1257

const double psitilde_cs_00_1 = 2*z + 1;

1258

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;

1259

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;

1260

const double psitilde_cs_01_0 = 1;

1261

const double psitilde_cs_01_1 = 3*z + 2;

1262

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;

1263

const double psitilde_cs_02_0 = 1;

1264

const double psitilde_cs_02_1 = 4*z + 3;

1265

const double psitilde_cs_03_0 = 1;

1266

const double psitilde_cs_10_0 = 1;

1267

const double psitilde_cs_10_1 = 3*z + 2;

1268

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;

1269

const double psitilde_cs_11_0 = 1;

1270

const double psitilde_cs_11_1 = 4*z + 3;

1271

const double psitilde_cs_12_0 = 1;

1272

const double psitilde_cs_20_0 = 1;

1273

const double psitilde_cs_20_1 = 4*z + 3;

1274

const double psitilde_cs_21_0 = 1;

1275

const double psitilde_cs_30_0 = 1;

1276

1277

// Compute basisvalues

1278

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

1279

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

1280

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

1281

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

1282

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

1283

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

1284

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

1285

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

1286

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

1287

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

1288

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

1289

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

1290

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

1291

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

1292

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

1293

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

1294

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

1295

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

1296

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

1297

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

1298

1299

// Table(s) of coefficients

1300

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

1301

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1302

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

1303

{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, -0.00535714285714286},

1304

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

1305

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

1306

{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},

1307

{0, 0.0978075995544939, -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},

1308

{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},

1309

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

1310

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1311

{0, -0.0978075995544939, -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},

1312

{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},

1313

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

1314

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1315

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

1316

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

1317

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1318

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

1319

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

1320

{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, -0.00535714285714285}};

1321

1322

// Interesting (new) part

1323

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

1324

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

1325

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

1326

{6.32455532033676, 0, 0, 0, 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

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

1329

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

1330

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

1331

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

1332

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

1333

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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

{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},

1336

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

1337

{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},

1338

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

1339

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

1340

{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},

1341

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

1342

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

1343

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

1344

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

1345

1346

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

1347

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

1348

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

1349

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

1350

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

1351

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

1352

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

1353

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

1354

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

1355

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

1356

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

1357

{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},

1358

{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},

1359

{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},

1360

{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},

1361

{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},

1362

{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},

1363

{-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},

1364

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

1365

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

1366

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

1367

1368

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

1369

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

1370

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

1371

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

1372

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

1373

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

1374

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

1375

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

1376

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

1377

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

1378

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

1379

{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},

1380

{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},

1381

{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},

1382

{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},

1383

{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},

1384

{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},

1385

{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},

1386

{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},

1387

{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},

1388

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

1389

1390

// Compute reference derivatives

1391

// Declare pointer to array of derivatives on FIAT element

1392

double *derivatives = new double [num_derivatives];

1393

1394

// Declare coefficients

1395

double coeff0_0 = 0;

1396

double coeff0_1 = 0;

1397

double coeff0_2 = 0;

1398

double coeff0_3 = 0;

1399

double coeff0_4 = 0;

1400

double coeff0_5 = 0;

1401

double coeff0_6 = 0;

1402

double coeff0_7 = 0;

1403

double coeff0_8 = 0;

1404

double coeff0_9 = 0;

1405

double coeff0_10 = 0;

1406

double coeff0_11 = 0;

1407

double coeff0_12 = 0;

1408

double coeff0_13 = 0;

1409

double coeff0_14 = 0;

1410

double coeff0_15 = 0;

1411

double coeff0_16 = 0;

1412

double coeff0_17 = 0;

1413

double coeff0_18 = 0;

1414

double coeff0_19 = 0;

1415

1416

// Declare new coefficients

1417

double new_coeff0_0 = 0;

1418

double new_coeff0_1 = 0;

1419

double new_coeff0_2 = 0;

1420

double new_coeff0_3 = 0;

1421

double new_coeff0_4 = 0;

1422

double new_coeff0_5 = 0;

1423

double new_coeff0_6 = 0;

1424

double new_coeff0_7 = 0;

1425

double new_coeff0_8 = 0;

1426

double new_coeff0_9 = 0;

1427

double new_coeff0_10 = 0;

1428

double new_coeff0_11 = 0;

1429

double new_coeff0_12 = 0;

1430

double new_coeff0_13 = 0;

1431

double new_coeff0_14 = 0;

1432

double new_coeff0_15 = 0;

1433

double new_coeff0_16 = 0;

1434

double new_coeff0_17 = 0;

1435

double new_coeff0_18 = 0;

1436

double new_coeff0_19 = 0;

1437

1438

// Loop possible derivatives

1439

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

1440

{

1441

// Get values from coefficients array

1442

new_coeff0_0 = coefficients0[dof][0];

1443

new_coeff0_1 = coefficients0[dof][1];

1444

new_coeff0_2 = coefficients0[dof][2];

1445

new_coeff0_3 = coefficients0[dof][3];

1446

new_coeff0_4 = coefficients0[dof][4];

1447

new_coeff0_5 = coefficients0[dof][5];

1448

new_coeff0_6 = coefficients0[dof][6];

1449

new_coeff0_7 = coefficients0[dof][7];

1450

new_coeff0_8 = coefficients0[dof][8];

1451

new_coeff0_9 = coefficients0[dof][9];

1452

new_coeff0_10 = coefficients0[dof][10];

1453

new_coeff0_11 = coefficients0[dof][11];

1454

new_coeff0_12 = coefficients0[dof][12];

1455

new_coeff0_13 = coefficients0[dof][13];

1456

new_coeff0_14 = coefficients0[dof][14];

1457

new_coeff0_15 = coefficients0[dof][15];

1458

new_coeff0_16 = coefficients0[dof][16];

1459

new_coeff0_17 = coefficients0[dof][17];

1460

new_coeff0_18 = coefficients0[dof][18];

1461

new_coeff0_19 = coefficients0[dof][19];

1462

1463

// Loop derivative order

1464

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

1465

{

1466

// Update old coefficients

1467

coeff0_0 = new_coeff0_0;

1468

coeff0_1 = new_coeff0_1;

1469

coeff0_2 = new_coeff0_2;

1470

coeff0_3 = new_coeff0_3;

1471

coeff0_4 = new_coeff0_4;

1472

coeff0_5 = new_coeff0_5;

1473

coeff0_6 = new_coeff0_6;

1474

coeff0_7 = new_coeff0_7;

1475

coeff0_8 = new_coeff0_8;

1476

coeff0_9 = new_coeff0_9;

1477

coeff0_10 = new_coeff0_10;

1478

coeff0_11 = new_coeff0_11;

1479

coeff0_12 = new_coeff0_12;

1480

coeff0_13 = new_coeff0_13;

1481

coeff0_14 = new_coeff0_14;

1482

coeff0_15 = new_coeff0_15;

1483

coeff0_16 = new_coeff0_16;

1484

coeff0_17 = new_coeff0_17;

1485

coeff0_18 = new_coeff0_18;

1486

coeff0_19 = new_coeff0_19;

1487

1488

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

1489

{

1490

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];

1491

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];

1492

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];

1493

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];

1494

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];

1495

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];

1496

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];

1497

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];

1498

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];

1499

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];

1500

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];

1501

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];

1502

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];

1503

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];

1504

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];

1505

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];

1506

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];

1507

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];

1508

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];

1509

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];

1510

}

1511

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

1512

{

1513

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];

1514

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];

1515

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];

1516

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];

1517

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];

1518

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];

1519

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];

1520

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];

1521

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];

1522

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];

1523

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];

1524

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];

1525

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];

1526

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];

1527

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];

1528

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];

1529

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];

1530

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];

1531

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];

1532

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];

1533

}

1534

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

1535

{

1536

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];

1537

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];

1538

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];

1539

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];

1540

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];

1541

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];

1542

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];

1543

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];

1544

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];

1545

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];

1546

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];

1547

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];

1548

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];

1549

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];

1550

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];

1551

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];

1552

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];

1553

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];

1554

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];

1555

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];

1556

}

1557

1558

}

1559

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

1560

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;

1561

}

1562

1563

// Transform derivatives back to physical element

1564

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

1565

{

1566

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

1567

{

1568

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

1569

}

1570

}

1571

// Delete pointer to array of derivatives on FIAT element

1572

delete [] derivatives;

1573

1574

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

1575

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

1576

{

1577

delete [] combinations[row];

1578

delete [] transform[row];

1579

}

1580

1581

delete [] combinations;

1582

delete [] transform;

1583

}

1584

1585

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

1586

virtual void evaluate_basis_derivatives_all(unsigned int n,

1587

double* values,

1588

const double* coordinates,

1589

const ufc::cell& c) const

1590

{

1591

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

1592

}

1593

1594

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

1595

virtual double evaluate_dof(unsigned int i,

1596

const ufc::function& f,

1597

const ufc::cell& c) const

1598

{

1599

// The reference points, direction and weights:

1600

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

1601

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}};

1602

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}}};

1603

1604

const double * const * x = c.coordinates;

1605

double result = 0.0;

1606

// Iterate over the points:

1607

// Evaluate basis functions for affine mapping

1608

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

1609

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

1610

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

1611

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

1612

1613

// Compute affine mapping y = F(X)

1614

double y[3];

1615

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

1616

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

1617

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

1618

1619

// Evaluate function at physical points

1620

double values[1];

1621

f.evaluate(values, y, c);

1622

1623

// Map function values using appropriate mapping

1624

// Affine map: Do nothing

1625

1626

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

1627

1628

// Take directional components

1629

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

1630

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

1631

// Multiply by weights

1632

result *= W[i][0];

1633

1634

return result;

1635

}

1636

1637

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

1638

virtual void evaluate_dofs(double* values,

1639

const ufc::function& f,

1640

const ufc::cell& c) const

1641

{

1642

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

1643

}

1644

1645

/// Interpolate vertex values from dof values

1646

virtual void interpolate_vertex_values(double* vertex_values,

1647

const double* dof_values,

1648

const ufc::cell& c) const

1649

{

1650

// Evaluate at vertices and use affine mapping

1651

vertex_values[0] = dof_values[0];

1652

vertex_values[1] = dof_values[1];

1653

vertex_values[2] = dof_values[2];

1654

vertex_values[3] = dof_values[3];

1655

}

1656

1657

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

1658

virtual unsigned int num_sub_elements() const

1659

{

1660

return 1;

1661

}

1662

1663

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

1664

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

1665

{

1666

return new UFC_Poisson3D_3BilinearForm_finite_element_1();

1667

}

1668

1669

};

1670

1671

/// This class defines the interface for a local-to-global mapping of

1672

/// degrees of freedom (dofs).

1673

1674

class UFC_Poisson3D_3BilinearForm_dof_map_0: public ufc::dof_map

1675

{

1676

private:

1677

1678

unsigned int __global_dimension;

1679

1680

public:

1681

1682

/// Constructor

1683

UFC_Poisson3D_3BilinearForm_dof_map_0() : ufc::dof_map()

1684

{

1685

__global_dimension = 0;

1686

}

1687

1688

/// Destructor

1689

virtual ~UFC_Poisson3D_3BilinearForm_dof_map_0()

1690

{

1691

// Do nothing

1692

}

1693

1694

/// Return a string identifying the dof map

1695

virtual const char* signature() const

1696

{

1697

return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";

1698

}

1699

1700

/// Return true iff mesh entities of topological dimension d are needed

1701

virtual bool needs_mesh_entities(unsigned int d) const

1702

{

1703

switch ( d )

1704

{

1705

case 0:

1706

return true;

1707

break;

1708

case 1:

1709

return true;

1710

break;

1711

case 2:

1712

return true;

1713

break;

1714

case 3:

1715

return false;

1716

break;

1717

}

1718

return false;

1719

}

1720

1721

/// Initialize dof map for mesh (return true iff init_cell() is needed)

1722

virtual bool init_mesh(const ufc::mesh& m)

1723

{

1724

__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];

1725

return false;

1726

}

1727

1728

/// Initialize dof map for given cell

1729

virtual void init_cell(const ufc::mesh& m,

1730

const ufc::cell& c)

1731

{

1732

// Do nothing

1733

}

1734

1735

/// Finish initialization of dof map for cells

1736

virtual void init_cell_finalize()

1737

{

1738

// Do nothing

1739

}

1740

1741

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

1742

virtual unsigned int global_dimension() const

1743

{

1744

return __global_dimension;

1745

}

1746

1747

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

1748

virtual unsigned int local_dimension() const

1749

{

1750

return 20;

1751

}

1752

1753

// Return the geometric dimension of the coordinates this dof map provides

1754

virtual unsigned int geometric_dimension() const

1755

{

1756

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

1757

}

1758

1759

/// Return the number of dofs on each cell facet

1760

virtual unsigned int num_facet_dofs() const

1761

{

1762

return 10;

1763

}

1764

1765

/// Return the number of dofs associated with each cell entity of dimension d

1766

virtual unsigned int num_entity_dofs(unsigned int d) const

1767

{

1768

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

1769

}

1770

1771

/// Tabulate the local-to-global mapping of dofs on a cell

1772

virtual void tabulate_dofs(unsigned int* dofs,

1773

const ufc::mesh& m,

1774

const ufc::cell& c) const

1775

{

1776

dofs[0] = c.entity_indices[0][0];

1777

dofs[1] = c.entity_indices[0][1];

1778

dofs[2] = c.entity_indices[0][2];

1779

dofs[3] = c.entity_indices[0][3];

1780

unsigned int offset = m.num_entities[0];

1781

dofs[4] = offset + 2*c.entity_indices[1][0];

1782

dofs[5] = offset + 2*c.entity_indices[1][0] + 1;

1783

dofs[6] = offset + 2*c.entity_indices[1][1];

1784

dofs[7] = offset + 2*c.entity_indices[1][1] + 1;

1785

dofs[8] = offset + 2*c.entity_indices[1][2];

1786

dofs[9] = offset + 2*c.entity_indices[1][2] + 1;

1787

dofs[10] = offset + 2*c.entity_indices[1][3];

1788

dofs[11] = offset + 2*c.entity_indices[1][3] + 1;

1789

dofs[12] = offset + 2*c.entity_indices[1][4];

1790

dofs[13] = offset + 2*c.entity_indices[1][4] + 1;

1791

dofs[14] = offset + 2*c.entity_indices[1][5];

1792

dofs[15] = offset + 2*c.entity_indices[1][5] + 1;

1793

offset = offset + 2*m.num_entities[1];

1794

dofs[16] = offset + c.entity_indices[2][0];

1795

dofs[17] = offset + c.entity_indices[2][1];

1796

dofs[18] = offset + c.entity_indices[2][2];

1797

dofs[19] = offset + c.entity_indices[2][3];

1798

}

1799

1800

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

1801

virtual void tabulate_facet_dofs(unsigned int* dofs,

1802

unsigned int facet) const

1803

{

1804

switch ( facet )

1805

{

1806

case 0:

1807

dofs[0] = 1;

1808

dofs[1] = 2;

1809

dofs[2] = 3;

1810

dofs[3] = 4;

1811

dofs[4] = 5;

1812

dofs[5] = 6;

1813

dofs[6] = 7;

1814

dofs[7] = 8;

1815

dofs[8] = 9;

1816

dofs[9] = 16;

1817

break;

1818

case 1:

1819

dofs[0] = 0;

1820

dofs[1] = 2;

1821

dofs[2] = 3;

1822

dofs[3] = 4;

1823

dofs[4] = 5;

1824

dofs[5] = 10;

1825

dofs[6] = 11;

1826

dofs[7] = 12;

1827

dofs[8] = 13;

1828

dofs[9] = 17;

1829

break;

1830

case 2:

1831

dofs[0] = 0;

1832

dofs[1] = 1;

1833

dofs[2] = 3;

1834

dofs[3] = 6;

1835

dofs[4] = 7;

1836

dofs[5] = 10;

1837

dofs[6] = 11;

1838

dofs[7] = 14;

1839

dofs[8] = 15;

1840

dofs[9] = 18;

1841

break;

1842

case 3:

1843

dofs[0] = 0;

1844

dofs[1] = 1;

1845

dofs[2] = 2;

1846

dofs[3] = 8;

1847

dofs[4] = 9;

1848

dofs[5] = 12;

1849

dofs[6] = 13;

1850

dofs[7] = 14;

1851

dofs[8] = 15;

1852

dofs[9] = 19;

1853

break;

1854

}

1855

}

1856

1857

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

1858

virtual void tabulate_entity_dofs(unsigned int* dofs,

1859

unsigned int d, unsigned int i) const

1860

{

1861

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

1862

}

1863

1864

/// Tabulate the coordinates of all dofs on a cell

1865

virtual void tabulate_coordinates(double** coordinates,

1866

const ufc::cell& c) const

1867

{

1868

const double * const * x = c.coordinates;

1869

coordinates[0][0] = x[0][0];

1870

coordinates[0][1] = x[0][1];

1871

coordinates[0][2] = x[0][2];

1872

coordinates[1][0] = x[1][0];

1873

coordinates[1][1] = x[1][1];

1874

coordinates[1][2] = x[1][2];

1875

coordinates[2][0] = x[2][0];

1876

coordinates[2][1] = x[2][1];

1877

coordinates[2][2] = x[2][2];

1878

coordinates[3][0] = x[3][0];

1879

coordinates[3][1] = x[3][1];

1880

coordinates[3][2] = x[3][2];

1881

coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

1882

coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

1883

coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

1884

coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

1885

coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

1886

coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

1887

coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

1888

coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

1889

coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

1890

coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

1891

coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

1892

coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

1893

coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];

1894

coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];

1895

coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];

1896

coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

1897

coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

1898

coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

1899

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

1900

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

1901

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

1902

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

1903

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

1904

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

1905

coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

1906

coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

1907

coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

1908

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

1909

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

1910

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

1911

coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

1912

coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

1913

coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

1914

coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

1915

coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

1916

coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

1917

coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

1918

coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

1919

coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

1920

coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

1921

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

1922

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

1923

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

1924

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

1925

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

1926

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

1927

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

1928

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

1929

}

1930

1931

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

1932

virtual unsigned int num_sub_dof_maps() const

1933

{

1934

return 1;

1935

}

1936

1937

/// Create a new dof_map for sub dof map i (for a mixed element)

1938

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

1939

{

1940

return new UFC_Poisson3D_3BilinearForm_dof_map_0();

1941

}

1942

1943

};

1944

1945

/// This class defines the interface for a local-to-global mapping of

1946

/// degrees of freedom (dofs).

1947

1948

class UFC_Poisson3D_3BilinearForm_dof_map_1: public ufc::dof_map

1949

{

1950

private:

1951

1952

unsigned int __global_dimension;

1953

1954

public:

1955

1956

/// Constructor

1957

UFC_Poisson3D_3BilinearForm_dof_map_1() : ufc::dof_map()

1958

{

1959

__global_dimension = 0;

1960

}

1961

1962

/// Destructor

1963

virtual ~UFC_Poisson3D_3BilinearForm_dof_map_1()

1964

{

1965

// Do nothing

1966

}

1967

1968

/// Return a string identifying the dof map

1969

virtual const char* signature() const

1970

{

1971

return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";

1972

}

1973

1974

/// Return true iff mesh entities of topological dimension d are needed

1975

virtual bool needs_mesh_entities(unsigned int d) const

1976

{

1977

switch ( d )

1978

{

1979

case 0:

1980

return true;

1981

break;

1982

case 1:

1983

return true;

1984

break;

1985

case 2:

1986

return true;

1987

break;

1988

case 3:

1989

return false;

1990

break;

1991

}

1992

return false;

1993

}

1994

1995

/// Initialize dof map for mesh (return true iff init_cell() is needed)

1996

virtual bool init_mesh(const ufc::mesh& m)

1997

{

1998

__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];

1999

return false;

2000

}

2001

2002

/// Initialize dof map for given cell

2003

virtual void init_cell(const ufc::mesh& m,

2004

const ufc::cell& c)

2005

{

2006

// Do nothing

2007

}

2008

2009

/// Finish initialization of dof map for cells

2010

virtual void init_cell_finalize()

2011

{

2012

// Do nothing

2013

}

2014

2015

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

2016

virtual unsigned int global_dimension() const

2017

{

2018

return __global_dimension;

2019

}

2020

2021

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

2022

virtual unsigned int local_dimension() const

2023

{

2024

return 20;

2025

}

2026

2027

// Return the geometric dimension of the coordinates this dof map provides

2028

virtual unsigned int geometric_dimension() const

2029

{

2030

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

2031

}

2032

2033

/// Return the number of dofs on each cell facet

2034

virtual unsigned int num_facet_dofs() const

2035

{

2036

return 10;

2037

}

2038

2039

/// Return the number of dofs associated with each cell entity of dimension d

2040

virtual unsigned int num_entity_dofs(unsigned int d) const

2041

{

2042

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

2043

}

2044

2045

/// Tabulate the local-to-global mapping of dofs on a cell

2046

virtual void tabulate_dofs(unsigned int* dofs,

2047

const ufc::mesh& m,

2048

const ufc::cell& c) const

2049

{

2050

dofs[0] = c.entity_indices[0][0];

2051

dofs[1] = c.entity_indices[0][1];

2052

dofs[2] = c.entity_indices[0][2];

2053

dofs[3] = c.entity_indices[0][3];

2054

unsigned int offset = m.num_entities[0];

2055

dofs[4] = offset + 2*c.entity_indices[1][0];

2056

dofs[5] = offset + 2*c.entity_indices[1][0] + 1;

2057

dofs[6] = offset + 2*c.entity_indices[1][1];

2058

dofs[7] = offset + 2*c.entity_indices[1][1] + 1;

2059

dofs[8] = offset + 2*c.entity_indices[1][2];

2060

dofs[9] = offset + 2*c.entity_indices[1][2] + 1;

2061

dofs[10] = offset + 2*c.entity_indices[1][3];

2062

dofs[11] = offset + 2*c.entity_indices[1][3] + 1;

2063

dofs[12] = offset + 2*c.entity_indices[1][4];

2064

dofs[13] = offset + 2*c.entity_indices[1][4] + 1;

2065

dofs[14] = offset + 2*c.entity_indices[1][5];

2066

dofs[15] = offset + 2*c.entity_indices[1][5] + 1;

2067

offset = offset + 2*m.num_entities[1];

2068

dofs[16] = offset + c.entity_indices[2][0];

2069

dofs[17] = offset + c.entity_indices[2][1];

2070

dofs[18] = offset + c.entity_indices[2][2];

2071

dofs[19] = offset + c.entity_indices[2][3];

2072

}

2073

2074

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

2075

virtual void tabulate_facet_dofs(unsigned int* dofs,

2076

unsigned int facet) const

2077

{

2078

switch ( facet )

2079

{

2080

case 0:

2081

dofs[0] = 1;

2082

dofs[1] = 2;

2083

dofs[2] = 3;

2084

dofs[3] = 4;

2085

dofs[4] = 5;

2086

dofs[5] = 6;

2087

dofs[6] = 7;

2088

dofs[7] = 8;

2089

dofs[8] = 9;

2090

dofs[9] = 16;

2091

break;

2092

case 1:

2093

dofs[0] = 0;

2094

dofs[1] = 2;

2095

dofs[2] = 3;

2096

dofs[3] = 4;

2097

dofs[4] = 5;

2098

dofs[5] = 10;

2099

dofs[6] = 11;

2100

dofs[7] = 12;

2101

dofs[8] = 13;

2102

dofs[9] = 17;

2103

break;

2104

case 2:

2105

dofs[0] = 0;

2106

dofs[1] = 1;

2107

dofs[2] = 3;

2108

dofs[3] = 6;

2109

dofs[4] = 7;

2110

dofs[5] = 10;

2111

dofs[6] = 11;

2112

dofs[7] = 14;

2113

dofs[8] = 15;

2114

dofs[9] = 18;

2115

break;

2116

case 3:

2117

dofs[0] = 0;

2118

dofs[1] = 1;

2119

dofs[2] = 2;

2120

dofs[3] = 8;

2121

dofs[4] = 9;

2122

dofs[5] = 12;

2123

dofs[6] = 13;

2124

dofs[7] = 14;

2125

dofs[8] = 15;

2126

dofs[9] = 19;

2127

break;

2128

}

2129

}

2130

2131

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

2132

virtual void tabulate_entity_dofs(unsigned int* dofs,

2133

unsigned int d, unsigned int i) const

2134

{

2135

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

2136

}

2137

2138

/// Tabulate the coordinates of all dofs on a cell

2139

virtual void tabulate_coordinates(double** coordinates,

2140

const ufc::cell& c) const

2141

{

2142

const double * const * x = c.coordinates;

2143

coordinates[0][0] = x[0][0];

2144

coordinates[0][1] = x[0][1];

2145

coordinates[0][2] = x[0][2];

2146

coordinates[1][0] = x[1][0];

2147

coordinates[1][1] = x[1][1];

2148

coordinates[1][2] = x[1][2];

2149

coordinates[2][0] = x[2][0];

2150

coordinates[2][1] = x[2][1];

2151

coordinates[2][2] = x[2][2];

2152

coordinates[3][0] = x[3][0];

2153

coordinates[3][1] = x[3][1];

2154

coordinates[3][2] = x[3][2];

2155

coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

2156

coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

2157

coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

2158

coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

2159

coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

2160

coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

2161

coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

2162

coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

2163

coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

2164

coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

2165

coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

2166

coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

2167

coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];

2168

coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];

2169

coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];

2170

coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

2171

coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

2172

coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

2173

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

2174

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

2175

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

2176

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

2177

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

2178

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

2179

coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

2180

coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

2181

coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

2182

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

2183

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

2184

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

2185

coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

2186

coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

2187

coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

2188

coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

2189

coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

2190

coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

2191

coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

2192

coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

2193

coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

2194

coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

2195

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

2196

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

2197

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

2198

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

2199

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

2200

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

2201

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

2202

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

2203

}

2204

2205

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

2206

virtual unsigned int num_sub_dof_maps() const

2207

{

2208

return 1;

2209

}

2210

2211

/// Create a new dof_map for sub dof map i (for a mixed element)

2212

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

2213

{

2214

return new UFC_Poisson3D_3BilinearForm_dof_map_1();

2215

}

2216

2217

};

2218

2219

/// This class defines the interface for the tabulation of the cell

2220

/// tensor corresponding to the local contribution to a form from

2221

/// the integral over a cell.

2222

2223

class UFC_Poisson3D_3BilinearForm_cell_integral_0: public ufc::cell_integral

2224

{

2225

public:

2226

2227

/// Constructor

2228

UFC_Poisson3D_3BilinearForm_cell_integral_0() : ufc::cell_integral()

2229

{

2230

// Do nothing

2231

}

2232

2233

/// Destructor

2234

virtual ~UFC_Poisson3D_3BilinearForm_cell_integral_0()

2235

{

2236

// Do nothing

2237

}

2238

2239

/// Tabulate the tensor for the contribution from a local cell

2240

virtual void tabulate_tensor(double* A,

2241

const double * const * w,

2242

const ufc::cell& c) const

2243

{

2244

// Extract vertex coordinates

2245

const double * const * x = c.coordinates;

2246

2247

// Compute Jacobian of affine map from reference cell

2248

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

2249

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

2250

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

2251

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

2252

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

2253

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

2254

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

2255

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

2256

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

2257

2258

// Compute sub determinants

2259

const double d_00 = J_11*J_22 - J_12*J_21;

2260

const double d_01 = J_12*J_20 - J_10*J_22;

2261

const double d_02 = J_10*J_21 - J_11*J_20;

2262

2263

const double d_10 = J_02*J_21 - J_01*J_22;

2264

const double d_11 = J_00*J_22 - J_02*J_20;

2265

const double d_12 = J_01*J_20 - J_00*J_21;

2266

2267

const double d_20 = J_01*J_12 - J_02*J_11;

2268

const double d_21 = J_02*J_10 - J_00*J_12;

2269

const double d_22 = J_00*J_11 - J_01*J_10;

2270

2271

// Compute determinant of Jacobian

2272

double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;

2273

2274

// Compute inverse of Jacobian

2275

const double Jinv_00 = d_00 / detJ;

2276

const double Jinv_01 = d_10 / detJ;

2277

const double Jinv_02 = d_20 / detJ;

2278

const double Jinv_10 = d_01 / detJ;

2279

const double Jinv_11 = d_11 / detJ;

2280

const double Jinv_12 = d_21 / detJ;

2281

const double Jinv_20 = d_02 / detJ;

2282

const double Jinv_21 = d_12 / detJ;

2283

const double Jinv_22 = d_22 / detJ;

2284

2285

// Set scale factor

2286

const double det = std::abs(detJ);

2287

2288

// Compute geometry tensors

2289

const double G0_0_0 = det*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);

2290

const double G0_0_1 = det*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);

2291

const double G0_0_2 = det*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);

2292

const double G0_1_0 = det*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);

2293

const double G0_1_1 = det*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);

2294

const double G0_1_2 = det*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);

2295

const double G0_2_0 = det*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);

2296

const double G0_2_1 = det*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);

2297

const double G0_2_2 = det*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);

2298

2299

// Compute element tensor

2300

A[0] = 0.0595238095238095*G0_0_0 + 0.0595238095238095*G0_0_1 + 0.0595238095238095*G0_0_2 + 0.0595238095238095*G0_1_0 + 0.0595238095238095*G0_1_1 + 0.0595238095238095*G0_1_2 + 0.0595238095238094*G0_2_0 + 0.0595238095238095*G0_2_1 + 0.0595238095238094*G0_2_2;

2301

A[1] = -0.0113095238095238*G0_0_0 - 0.0113095238095238*G0_1_0 - 0.0113095238095238*G0_2_0;

2302

A[2] = -0.0113095238095238*G0_0_1 - 0.0113095238095238*G0_1_1 - 0.0113095238095238*G0_2_1;

2303

A[3] = -0.0113095238095238*G0_0_2 - 0.0113095238095238*G0_1_2 - 0.0113095238095238*G0_2_2;

2304

A[4] = -0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_0_2 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_1_2 - 0.0133928571428572*G0_2_1 - 0.0133928571428572*G0_2_2;

2305

A[5] = -0.0133928571428571*G0_0_1 - 0.0133928571428571*G0_0_2 - 0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_1_2 - 0.0133928571428571*G0_2_1 - 0.0133928571428571*G0_2_2;

2306

A[6] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_2 - 0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_2 - 0.0133928571428572*G0_2_0 - 0.0133928571428572*G0_2_2;

2307

A[7] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_0_2 - 0.0133928571428571*G0_1_0 - 0.0133928571428571*G0_1_2 - 0.0133928571428571*G0_2_0 - 0.0133928571428571*G0_2_2;

2308

A[8] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_2_0 - 0.0133928571428572*G0_2_1;

2309

A[9] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_2_0 - 0.0133928571428572*G0_2_1;

2310

A[10] = -0.0348214285714286*G0_0_0 - 0.0348214285714286*G0_0_1 - 0.0964285714285713*G0_0_2 - 0.0348214285714286*G0_1_0 - 0.0348214285714286*G0_1_1 - 0.0964285714285713*G0_1_2 - 0.0348214285714286*G0_2_0 - 0.0348214285714286*G0_2_1 - 0.0964285714285713*G0_2_2;

2311

A[11] = 0.0133928571428571*G0_0_0 + 0.0133928571428571*G0_0_1 + 0.0482142857142856*G0_0_2 + 0.0133928571428571*G0_1_0 + 0.0133928571428571*G0_1_1 + 0.0482142857142856*G0_1_2 + 0.0133928571428571*G0_2_0 + 0.0133928571428571*G0_2_1 + 0.0482142857142856*G0_2_2;

2312

A[12] = -0.0348214285714286*G0_0_0 - 0.0964285714285713*G0_0_1 - 0.0348214285714286*G0_0_2 - 0.0348214285714286*G0_1_0 - 0.0964285714285713*G0_1_1 - 0.0348214285714286*G0_1_2 - 0.0348214285714286*G0_2_0 - 0.0964285714285713*G0_2_1 - 0.0348214285714286*G0_2_2;

2313

A[13] = 0.0133928571428572*G0_0_0 + 0.0482142857142856*G0_0_1 + 0.0133928571428572*G0_0_2 + 0.0133928571428572*G0_1_0 + 0.0482142857142856*G0_1_1 + 0.0133928571428572*G0_1_2 + 0.0133928571428572*G0_2_0 + 0.0482142857142856*G0_2_1 + 0.0133928571428572*G0_2_2;

2314

A[14] = -0.0964285714285713*G0_0_0 - 0.0348214285714287*G0_0_1 - 0.0348214285714287*G0_0_2 - 0.0964285714285714*G0_1_0 - 0.0348214285714287*G0_1_1 - 0.0348214285714287*G0_1_2 - 0.0964285714285713*G0_2_0 - 0.0348214285714287*G0_2_1 - 0.0348214285714287*G0_2_2;

2315

A[15] = 0.0482142857142857*G0_0_0 + 0.0133928571428572*G0_0_1 + 0.0133928571428572*G0_0_2 + 0.0482142857142857*G0_1_0 + 0.0133928571428572*G0_1_1 + 0.0133928571428572*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0133928571428572*G0_2_1 + 0.0133928571428572*G0_2_2;

2316

A[16] = -0.0321428571428572*G0_0_0 - 0.0321428571428572*G0_0_1 - 0.0321428571428573*G0_0_2 - 0.0321428571428572*G0_1_0 - 0.0321428571428572*G0_1_1 - 0.0321428571428573*G0_1_2 - 0.0321428571428572*G0_2_0 - 0.0321428571428572*G0_2_1 - 0.0321428571428573*G0_2_2;

2317

A[17] = 0.0321428571428572*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0321428571428572*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0482142857142857*G0_1_2 + 0.0321428571428572*G0_2_0 + 0.0482142857142858*G0_2_1 + 0.0482142857142857*G0_2_2;

2318

A[18] = 0.0482142857142858*G0_0_0 + 0.0321428571428572*G0_0_1 + 0.0482142857142858*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0321428571428572*G0_1_1 + 0.0482142857142858*G0_1_2 + 0.0482142857142858*G0_2_0 + 0.0321428571428572*G0_2_1 + 0.0482142857142858*G0_2_2;

2319

A[19] = 0.0482142857142858*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0321428571428573*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0321428571428573*G0_1_2 + 0.0482142857142858*G0_2_0 + 0.0482142857142858*G0_2_1 + 0.0321428571428573*G0_2_2;

2320

A[20] = -0.0113095238095238*G0_0_0 - 0.0113095238095238*G0_0_1 - 0.0113095238095238*G0_0_2;

2321

A[21] = 0.0595238095238094*G0_0_0;

2322

A[22] = 0.0113095238095238*G0_0_1;

2323

A[23] = 0.0113095238095238*G0_0_2;

2324

A[24] = 0.0133928571428571*G0_0_1 + 0.0133928571428571*G0_0_2;

2325

A[25] = 0.0133928571428571*G0_0_1 + 0.0133928571428571*G0_0_2;

2326

A[26] = -0.0348214285714285*G0_0_0 + 0.0616071428571428*G0_0_2;

2327

A[27] = 0.0133928571428571*G0_0_0 - 0.0348214285714285*G0_0_2;

2328

A[28] = -0.0348214285714285*G0_0_0 + 0.0616071428571428*G0_0_1;

2329

A[29] = 0.0133928571428571*G0_0_0 - 0.0348214285714285*G0_0_1;

2330

A[30] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_0_1;

2331

A[31] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_0_1;

2332

A[32] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_0_2;

2333

A[33] = -0.0133928571428572*G0_0_0 - 0.0133928571428571*G0_0_2;

2334

A[34] = 0.0482142857142857*G0_0_0 + 0.0348214285714286*G0_0_1 + 0.0348214285714286*G0_0_2;

2335

A[35] = -0.0964285714285713*G0_0_0 - 0.0616071428571428*G0_0_1 - 0.0616071428571428*G0_0_2;

2336

A[36] = 0.0321428571428571*G0_0_0 - 0.0160714285714285*G0_0_1 - 0.0160714285714285*G0_0_2;

2337

A[37] = -0.0321428571428571*G0_0_0;

2338

A[38] = 0.0482142857142856*G0_0_0 + 0.0160714285714285*G0_0_1;

2339

A[39] = 0.0482142857142856*G0_0_0 + 0.0160714285714285*G0_0_2;

2340

A[40] = -0.0113095238095238*G0_1_0 - 0.0113095238095238*G0_1_1 - 0.0113095238095238*G0_1_2;

2341

A[41] = 0.0113095238095238*G0_1_0;

2342

A[42] = 0.0595238095238094*G0_1_1;

2343

A[43] = 0.0113095238095238*G0_1_2;

2344

A[44] = -0.0348214285714285*G0_1_1 + 0.0616071428571428*G0_1_2;

2345

A[45] = 0.0133928571428571*G0_1_1 - 0.0348214285714285*G0_1_2;

2346

A[46] = 0.0133928571428571*G0_1_0 + 0.0133928571428571*G0_1_2;

2347

A[47] = 0.0133928571428572*G0_1_0 + 0.0133928571428571*G0_1_2;

2348

A[48] = -0.0348214285714286*G0_1_0 + 0.0133928571428571*G0_1_1;

2349

A[49] = 0.0616071428571428*G0_1_0 - 0.0348214285714285*G0_1_1;

2350

A[50] = -0.0133928571428571*G0_1_0 - 0.0133928571428571*G0_1_1;

2351

A[51] = -0.0133928571428571*G0_1_0 - 0.0133928571428572*G0_1_1;

2352

A[52] = 0.0348214285714286*G0_1_0 + 0.0482142857142856*G0_1_1 + 0.0348214285714286*G0_1_2;

2353

A[53] = -0.0616071428571428*G0_1_0 - 0.0964285714285713*G0_1_1 - 0.0616071428571428*G0_1_2;

2354

A[54] = -0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_1_2;

2355

A[55] = -0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_1_2;

2356

A[56] = -0.0160714285714285*G0_1_0 + 0.032142857142857*G0_1_1 - 0.0160714285714286*G0_1_2;

2357

A[57] = 0.0160714285714286*G0_1_0 + 0.0482142857142856*G0_1_1;

2358

A[58] = -0.032142857142857*G0_1_1;

2359

A[59] = 0.0482142857142856*G0_1_1 + 0.0160714285714286*G0_1_2;

2360

A[60] = -0.0113095238095238*G0_2_0 - 0.0113095238095238*G0_2_1 - 0.0113095238095238*G0_2_2;

2361

A[61] = 0.0113095238095238*G0_2_0;

2362

A[62] = 0.0113095238095238*G0_2_1;

2363

A[63] = 0.0595238095238094*G0_2_2;

2364

A[64] = -0.0348214285714286*G0_2_1 + 0.0133928571428571*G0_2_2;

2365

A[65] = 0.0616071428571428*G0_2_1 - 0.0348214285714284*G0_2_2;

2366

A[66] = -0.0348214285714285*G0_2_0 + 0.0133928571428571*G0_2_2;

2367

A[67] = 0.0616071428571428*G0_2_0 - 0.0348214285714284*G0_2_2;

2368

A[68] = 0.0133928571428571*G0_2_0 + 0.0133928571428571*G0_2_1;

2369

A[69] = 0.0133928571428571*G0_2_0 + 0.0133928571428571*G0_2_1;

2370

A[70] = 0.0348214285714285*G0_2_0 + 0.0348214285714285*G0_2_1 + 0.0482142857142856*G0_2_2;

2371

A[71] = -0.0616071428571428*G0_2_0 - 0.0616071428571428*G0_2_1 - 0.0964285714285712*G0_2_2;

2372

A[72] = -0.0133928571428571*G0_2_0 - 0.0133928571428571*G0_2_2;

2373

A[73] = -0.0133928571428571*G0_2_0 - 0.0133928571428571*G0_2_2;

2374

A[74] = -0.0133928571428571*G0_2_1 - 0.0133928571428571*G0_2_2;

2375

A[75] = -0.0133928571428571*G0_2_1 - 0.0133928571428571*G0_2_2;

2376

A[76] = -0.0160714285714285*G0_2_0 - 0.0160714285714285*G0_2_1 + 0.032142857142857*G0_2_2;

2377

A[77] = 0.0160714285714285*G0_2_0 + 0.0482142857142855*G0_2_2;

2378

A[78] = 0.0160714285714285*G0_2_1 + 0.0482142857142855*G0_2_2;

2379

A[79] = -0.032142857142857*G0_2_2;

2380

A[80] = -0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_1_2 - 0.0133928571428572*G0_2_0 - 0.0133928571428572*G0_2_1 - 0.0133928571428572*G0_2_2;

2381

A[81] = 0.0133928571428571*G0_1_0 + 0.0133928571428571*G0_2_0;

2382

A[82] = -0.0348214285714285*G0_1_1 + 0.0616071428571428*G0_2_1;

2383

A[83] = -0.0348214285714286*G0_1_2 + 0.0133928571428571*G0_2_2;

2384

A[84] = 0.241071428571428*G0_1_1 + 0.0964285714285714*G0_1_2 + 0.0964285714285714*G0_2_1 + 0.192857142857143*G0_2_2;

2385

A[85] = -0.0723214285714286*G0_1_1 + 0.0723214285714284*G0_1_2 - 0.0241071428571429*G0_2_1 - 0.0723214285714285*G0_2_2;

2386

A[86] = -0.0482142857142856*G0_1_0 - 0.0241071428571428*G0_1_2 - 0.0241071428571428*G0_2_0 - 0.0241071428571428*G0_2_2;

2387

A[87] = -0.0723214285714286*G0_1_0 - 0.0482142857142857*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_2;

2388

A[88] = -0.0482142857142856*G0_1_0 - 0.0241071428571428*G0_1_1 - 0.0723214285714285*G0_2_0 - 0.0241071428571428*G0_2_1;

2389

A[89] = 0.0964285714285714*G0_1_0 + 0.120535714285714*G0_1_1 + 0.192857142857143*G0_2_0 + 0.0964285714285714*G0_2_1;

2390

A[90] = 0.0482142857142857*G0_1_0 + 0.0482142857142857*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_1;

2391

A[91] = 0.0723214285714286*G0_1_0 + 0.0723214285714286*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_1;

2392

A[92] = 0.0482142857142858*G0_1_0 + 0.0241071428571429*G0_1_1 + 0.0482142857142858*G0_1_2 + 0.0723214285714286*G0_2_0 + 0.0482142857142858*G0_2_1 + 0.0723214285714287*G0_2_2;

2393

A[93] = -0.0964285714285714*G0_1_0 + 0.0241071428571427*G0_1_1 - 0.0964285714285714*G0_1_2 - 0.192857142857143*G0_2_0 - 0.0964285714285714*G0_2_1 - 0.192857142857143*G0_2_2;

2394

A[94] = 0.0241071428571429*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_1 + 0.0241071428571429*G0_2_2;

2395

A[95] = 0.0241071428571428*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0241071428571428*G0_2_2;

2396

A[96] = 0.241071428571428*G0_1_0 - 0.0482142857142856*G0_1_1 + 0.120535714285714*G0_1_2 + 0.0964285714285713*G0_2_0 - 0.0241071428571429*G0_2_1 + 0.0964285714285713*G0_2_2;

2397

A[97] = -0.241071428571428*G0_1_0 - 0.289285714285714*G0_1_1 - 0.120535714285714*G0_1_2 - 0.0964285714285712*G0_2_0 - 0.120535714285714*G0_2_1;

2398

A[98] = 0.0482142857142856*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571429*G0_2_1;

2399

A[99] = -0.144642857142857*G0_1_1 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1 - 0.0964285714285713*G0_2_2;

2400

A[100] = -0.0133928571428571*G0_1_0 - 0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_1_2 - 0.0133928571428571*G0_2_0 - 0.0133928571428571*G0_2_1 - 0.0133928571428571*G0_2_2;

2401

A[101] = 0.0133928571428571*G0_1_0 + 0.0133928571428571*G0_2_0;

2402

A[102] = 0.0133928571428571*G0_1_1 - 0.0348214285714285*G0_2_1;

2403

A[103] = 0.0616071428571428*G0_1_2 - 0.0348214285714284*G0_2_2;

2404

A[104] = -0.0723214285714286*G0_1_1 - 0.0241071428571429*G0_1_2 + 0.0723214285714284*G0_2_1 - 0.0723214285714285*G0_2_2;

2405

A[105] = 0.192857142857143*G0_1_1 + 0.0964285714285713*G0_1_2 + 0.0964285714285713*G0_2_1 + 0.241071428571428*G0_2_2;

2406

A[106] = -0.0723214285714285*G0_1_0 - 0.0241071428571428*G0_1_2 - 0.0482142857142857*G0_2_0 - 0.0241071428571428*G0_2_2;

2407

A[107] = 0.192857142857143*G0_1_0 + 0.0964285714285713*G0_1_2 + 0.0964285714285713*G0_2_0 + 0.120535714285714*G0_2_2;

2408

A[108] = -0.0241071428571429*G0_1_0 - 0.0241071428571428*G0_1_1 - 0.0482142857142856*G0_2_0 - 0.0241071428571428*G0_2_1;

2409

A[109] = -0.0241071428571428*G0_1_0 - 0.0241071428571428*G0_1_1 - 0.0723214285714284*G0_2_0 - 0.0482142857142856*G0_2_1;

2410

A[110] = 0.0723214285714285*G0_1_0 + 0.0723214285714285*G0_1_1 + 0.0482142857142857*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0482142857142857*G0_2_1 + 0.0241071428571429*G0_2_2;

2411

A[111] = -0.192857142857143*G0_1_0 - 0.192857142857143*G0_1_1 - 0.0964285714285713*G0_1_2 - 0.0964285714285713*G0_2_0 - 0.0964285714285713*G0_2_1 + 0.0241071428571428*G0_2_2;

2412

A[112] = 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_2 + 0.0482142857142856*G0_2_0 + 0.0241071428571427*G0_2_1 + 0.0482142857142856*G0_2_2;

2413

A[113] = 0.0241071428571428*G0_1_0 + 0.0241071428571428*G0_1_2 + 0.0723214285714284*G0_2_0 + 0.0241071428571429*G0_2_1 + 0.0723214285714284*G0_2_2;

2414

A[114] = 0.0241071428571429*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0241071428571428*G0_2_2;

2415

A[115] = 0.0241071428571428*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0241071428571428*G0_2_2;

2416

A[116] = 0.0964285714285713*G0_1_0 + 0.0964285714285713*G0_1_1 - 0.0241071428571429*G0_1_2 + 0.241071428571428*G0_2_0 + 0.120535714285714*G0_2_1 - 0.0482142857142855*G0_2_2;

2417

A[117] = -0.0964285714285713*G0_1_0 - 0.120535714285714*G0_1_2 - 0.241071428571428*G0_2_0 - 0.120535714285714*G0_2_1 - 0.289285714285714*G0_2_2;

2418

A[118] = -0.0964285714285713*G0_1_1 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1 - 0.144642857142857*G0_2_2;

2419

A[119] = 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0482142857142855*G0_2_2;

2420

A[120] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_0_2 - 0.0133928571428572*G0_2_0 - 0.0133928571428572*G0_2_1 - 0.0133928571428572*G0_2_2;

2421

A[121] = -0.0348214285714285*G0_0_0 + 0.0616071428571428*G0_2_0;

2422

A[122] = 0.0133928571428571*G0_0_1 + 0.0133928571428571*G0_2_1;

2423

A[123] = -0.0348214285714285*G0_0_2 + 0.0133928571428571*G0_2_2;

2424

A[124] = -0.0482142857142856*G0_0_1 - 0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_2_1 - 0.0241071428571428*G0_2_2;

2425

A[125] = -0.0723214285714285*G0_0_1 - 0.0482142857142857*G0_0_2 - 0.0241071428571428*G0_2_1 - 0.0241071428571428*G0_2_2;

2426

A[126] = 0.241071428571428*G0_0_0 + 0.0964285714285713*G0_0_2 + 0.0964285714285713*G0_2_0 + 0.192857142857143*G0_2_2;

2427

A[127] = -0.0723214285714285*G0_0_0 + 0.0723214285714285*G0_0_2 - 0.0241071428571428*G0_2_0 - 0.0723214285714284*G0_2_2;

2428

A[128] = 0.120535714285714*G0_0_0 + 0.0964285714285714*G0_0_1 + 0.0964285714285714*G0_2_0 + 0.192857142857143*G0_2_1;

2429

A[129] = -0.0241071428571429*G0_0_0 - 0.0482142857142856*G0_0_1 - 0.0241071428571428*G0_2_0 - 0.0723214285714284*G0_2_1;

2430

A[130] = 0.0482142857142857*G0_0_0 + 0.0482142857142856*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_1;

2431

A[131] = 0.0723214285714285*G0_0_0 + 0.0723214285714285*G0_0_1 + 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571428*G0_2_1;

2432

A[132] = 0.0241071428571429*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_2;

2433

A[133] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_2;

2434

A[134] = 0.024107142857143*G0_0_0 + 0.0482142857142857*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0482142857142859*G0_2_0 + 0.0723214285714286*G0_2_1 + 0.0723214285714287*G0_2_2;

2435

A[135] = 0.0241071428571427*G0_0_0 - 0.0964285714285714*G0_0_1 - 0.0964285714285714*G0_0_2 - 0.0964285714285714*G0_2_0 - 0.192857142857143*G0_2_1 - 0.192857142857143*G0_2_2;

2436

A[136] = -0.0482142857142857*G0_0_0 + 0.241071428571428*G0_0_1 + 0.120535714285714*G0_0_2 - 0.0241071428571428*G0_2_0 + 0.0964285714285714*G0_2_1 + 0.0964285714285714*G0_2_2;

2437

A[137] = 0.0482142857142856*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0241071428571428*G0_2_0;

2438

A[138] = -0.289285714285714*G0_0_0 - 0.241071428571428*G0_0_1 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.0964285714285714*G0_2_1;

2439

A[139] = -0.144642857142857*G0_0_0 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.0964285714285715*G0_2_2;

2440

A[140] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_0_1 - 0.0133928571428571*G0_0_2 - 0.0133928571428571*G0_2_0 - 0.0133928571428571*G0_2_1 - 0.0133928571428571*G0_2_2;

2441

A[141] = 0.0133928571428571*G0_0_0 - 0.0348214285714285*G0_2_0;

2442

A[142] = 0.0133928571428571*G0_0_1 + 0.0133928571428571*G0_2_1;

2443

A[143] = 0.0616071428571428*G0_0_2 - 0.0348214285714285*G0_2_2;

2444

A[144] = -0.0723214285714286*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0482142857142857*G0_2_1 - 0.0241071428571429*G0_2_2;

2445

A[145] = 0.192857142857143*G0_0_1 + 0.0964285714285713*G0_0_2 + 0.0964285714285713*G0_2_1 + 0.120535714285714*G0_2_2;

2446

A[146] = -0.0723214285714285*G0_0_0 - 0.0241071428571428*G0_0_2 + 0.0723214285714285*G0_2_0 - 0.0723214285714283*G0_2_2;

2447

A[147] = 0.192857142857143*G0_0_0 + 0.0964285714285713*G0_0_2 + 0.0964285714285713*G0_2_0 + 0.241071428571428*G0_2_2;

2448

A[148] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_1 - 0.0482142857142856*G0_2_0 - 0.0723214285714284*G0_2_1;

2449

A[149] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_1 - 0.0241071428571428*G0_2_0 - 0.0482142857142857*G0_2_1;

2450

A[150] = 0.0723214285714285*G0_0_0 + 0.0723214285714285*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0482142857142857*G0_2_0 + 0.0482142857142856*G0_2_1 + 0.0241071428571429*G0_2_2;

2451

A[151] = -0.192857142857143*G0_0_0 - 0.192857142857143*G0_0_1 - 0.0964285714285713*G0_0_2 - 0.0964285714285712*G0_2_0 - 0.0964285714285713*G0_2_1 + 0.0241071428571428*G0_2_2;

2452

A[152] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571428*G0_2_2;

2453

A[153] = 0.0241071428571428*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571428*G0_2_2;

2454

A[154] = 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0482142857142856*G0_2_1 + 0.0482142857142857*G0_2_2;

2455

A[155] = 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0723214285714283*G0_2_1 + 0.0723214285714283*G0_2_2;

2456

A[156] = 0.0964285714285713*G0_0_0 + 0.0964285714285714*G0_0_1 - 0.0241071428571429*G0_0_2 + 0.120535714285714*G0_2_0 + 0.241071428571428*G0_2_1 - 0.0482142857142855*G0_2_2;

2457

A[157] = -0.0964285714285713*G0_0_0 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.144642857142857*G0_2_2;

2458

A[158] = -0.0964285714285713*G0_0_1 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.241071428571428*G0_2_1 - 0.289285714285714*G0_2_2;

2459

A[159] = 0.0241071428571429*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0482142857142856*G0_2_2;

2460

A[160] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_0_2 - 0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_1_2;

2461

A[161] = -0.0348214285714285*G0_0_0 + 0.0616071428571428*G0_1_0;

2462

A[162] = -0.0348214285714286*G0_0_1 + 0.0133928571428571*G0_1_1;

2463

A[163] = 0.0133928571428571*G0_0_2 + 0.0133928571428571*G0_1_2;

2464

A[164] = -0.0482142857142856*G0_0_1 - 0.0723214285714285*G0_0_2 - 0.0241071428571428*G0_1_1 - 0.0241071428571428*G0_1_2;

2465

A[165] = -0.0241071428571429*G0_0_1 - 0.0482142857142856*G0_0_2 - 0.0241071428571429*G0_1_1 - 0.0241071428571428*G0_1_2;

2466

A[166] = 0.120535714285714*G0_0_0 + 0.0964285714285714*G0_0_2 + 0.0964285714285714*G0_1_0 + 0.192857142857143*G0_1_2;

2467

A[167] = -0.0241071428571428*G0_0_0 - 0.0482142857142856*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0723214285714284*G0_1_2;

2468

A[168] = 0.241071428571428*G0_0_0 + 0.0964285714285715*G0_0_1 + 0.0964285714285715*G0_1_0 + 0.192857142857143*G0_1_1;

2469

A[169] = -0.0723214285714286*G0_0_0 + 0.0723214285714286*G0_0_1 - 0.0241071428571428*G0_1_0 - 0.0723214285714284*G0_1_1;

2470

A[170] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_1;

2471

A[171] = 0.0241071428571429*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571428*G0_1_1;

2472

A[172] = 0.0482142857142858*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_2;

2473

A[173] = 0.0723214285714286*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0723214285714286*G0_0_2 + 0.0241071428571428*G0_1_0 + 0.0241071428571429*G0_1_2;

2474

A[174] = 0.024107142857143*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0482142857142858*G0_0_2 + 0.0482142857142859*G0_1_0 + 0.0723214285714286*G0_1_1 + 0.0723214285714286*G0_1_2;

2475

A[175] = 0.0241071428571427*G0_0_0 - 0.0964285714285715*G0_0_1 - 0.0964285714285715*G0_0_2 - 0.0964285714285714*G0_1_0 - 0.192857142857143*G0_1_1 - 0.192857142857143*G0_1_2;

2476

A[176] = -0.0482142857142856*G0_0_0 + 0.120535714285714*G0_0_1 + 0.241071428571428*G0_0_2 - 0.0241071428571428*G0_1_0 + 0.0964285714285715*G0_1_1 + 0.0964285714285715*G0_1_2;

2477

A[177] = 0.0482142857142856*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0241071428571427*G0_1_0;

2478

A[178] = -0.144642857142857*G0_0_0 - 0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.0964285714285715*G0_1_1;

2479

A[179] = -0.289285714285714*G0_0_0 - 0.120535714285714*G0_0_1 - 0.241071428571429*G0_0_2 - 0.120535714285714*G0_1_0 - 0.0964285714285716*G0_1_2;

2480

A[180] = -0.0133928571428572*G0_0_0 - 0.0133928571428572*G0_0_1 - 0.0133928571428572*G0_0_2 - 0.0133928571428572*G0_1_0 - 0.0133928571428572*G0_1_1 - 0.0133928571428572*G0_1_2;

2481

A[181] = 0.0133928571428571*G0_0_0 - 0.0348214285714285*G0_1_0;

2482

A[182] = 0.0616071428571428*G0_0_1 - 0.0348214285714285*G0_1_1;

2483

A[183] = 0.0133928571428571*G0_0_2 + 0.0133928571428571*G0_1_2;

2484

A[184] = 0.0964285714285714*G0_0_1 + 0.192857142857143*G0_0_2 + 0.120535714285714*G0_1_1 + 0.0964285714285714*G0_1_2;

2485

A[185] = -0.0241071428571428*G0_0_1 - 0.0723214285714284*G0_0_2 - 0.0241071428571428*G0_1_1 - 0.0482142857142856*G0_1_2;

2486

A[186] = -0.0241071428571429*G0_0_0 - 0.0241071428571428*G0_0_2 - 0.0482142857142856*G0_1_0 - 0.0723214285714284*G0_1_2;

2487

A[187] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0482142857142857*G0_1_2;

2488

A[188] = -0.0723214285714286*G0_0_0 - 0.0241071428571428*G0_0_1 + 0.0723214285714286*G0_1_0 - 0.0723214285714284*G0_1_1;

2489

A[189] = 0.192857142857143*G0_0_0 + 0.0964285714285713*G0_0_1 + 0.0964285714285713*G0_1_0 + 0.241071428571428*G0_1_1;

2490

A[190] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_1;

2491

A[191] = 0.0241071428571428*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_1_0 + 0.0241071428571428*G0_1_1;

2492

A[192] = 0.0723214285714287*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0723214285714287*G0_0_2 + 0.0482142857142859*G0_1_0 + 0.0241071428571429*G0_1_1 + 0.0482142857142859*G0_1_2;

2493

A[193] = -0.192857142857143*G0_0_0 - 0.0964285714285714*G0_0_1 - 0.192857142857143*G0_0_2 - 0.0964285714285713*G0_1_0 + 0.0241071428571428*G0_1_1 - 0.0964285714285713*G0_1_2;

2494

A[194] = 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0241071428571429*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0482142857142858*G0_1_2;

2495

A[195] = 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_1_0 + 0.0723214285714284*G0_1_1 + 0.0723214285714283*G0_1_2;

2496

A[196] = 0.0964285714285714*G0_0_0 - 0.0241071428571428*G0_0_1 + 0.0964285714285713*G0_0_2 + 0.120535714285714*G0_1_0 - 0.0482142857142856*G0_1_1 + 0.241071428571428*G0_1_2;

2497

A[197] = -0.0964285714285713*G0_0_0 - 0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.144642857142857*G0_1_1;

2498

A[198] = 0.0241071428571429*G0_0_1 + 0.0241071428571427*G0_1_0 + 0.0482142857142856*G0_1_1;

2499

A[199] = -0.120535714285714*G0_0_1 - 0.0964285714285713*G0_0_2 - 0.120535714285714*G0_1_0 - 0.289285714285714*G0_1_1 - 0.241071428571428*G0_1_2;

2500

A[200] = -0.0348214285714286*G0_0_0 - 0.0348214285714286*G0_0_1 - 0.0348214285714286*G0_0_2 - 0.0348214285714286*G0_1_0 - 0.0348214285714286*G0_1_1 - 0.0348214285714286*G0_1_2 - 0.0964285714285713*G0_2_0 - 0.0964285714285713*G0_2_1 - 0.0964285714285713*G0_2_2;

2501

A[201] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_1_0;

2502

A[202] = -0.0133928571428571*G0_0_1 - 0.0133928571428571*G0_1_1;

2503

A[203] = 0.0348214285714285*G0_0_2 + 0.0348214285714285*G0_1_2 + 0.0482142857142856*G0_2_2;

2504

A[204] = 0.0482142857142857*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0482142857142857*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_1;

2505

A[205] = 0.0723214285714284*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0723214285714285*G0_1_1 + 0.0482142857142857*G0_1_2 + 0.0482142857142857*G0_2_1 + 0.0241071428571429*G0_2_2;

2506

A[206] = 0.0482142857142857*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0482142857142856*G0_1_0 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_0;

2507

A[207] = 0.0723214285714285*G0_0_0 + 0.0482142857142857*G0_0_2 + 0.0723214285714285*G0_1_0 + 0.0482142857142856*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0241071428571429*G0_2_2;

2508

A[208] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_1;

2509

A[209] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_1;

2510

A[210] = 0.241071428571428*G0_0_0 + 0.241071428571428*G0_0_1 + 0.144642857142857*G0_0_2 + 0.241071428571428*G0_1_0 + 0.241071428571428*G0_1_1 + 0.144642857142857*G0_1_2 + 0.144642857142857*G0_2_0 + 0.144642857142857*G0_2_1 + 0.241071428571428*G0_2_2;

2511

A[211] = -0.0723214285714284*G0_0_0 - 0.0723214285714284*G0_0_1 - 0.144642857142857*G0_0_2 - 0.0723214285714285*G0_1_0 - 0.0723214285714285*G0_1_1 - 0.144642857142857*G0_1_2 - 0.0482142857142857*G0_2_0 - 0.0482142857142857*G0_2_1 - 0.192857142857142*G0_2_2;

2512

A[212] = 0.120535714285714*G0_0_0 + 0.024107142857143*G0_0_1 + 0.120535714285714*G0_0_2 + 0.120535714285714*G0_1_0 + 0.024107142857143*G0_1_1 + 0.120535714285714*G0_1_2 + 0.024107142857143*G0_2_0 + 0.120535714285714*G0_2_1 + 0.024107142857143*G0_2_2;

2513

A[213] = -0.0241071428571429*G0_0_0 + 0.0241071428571427*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.024107142857143*G0_1_0 + 0.0241071428571427*G0_1_1 - 0.0241071428571429*G0_1_2 - 0.0241071428571428*G0_2_1;

2514

A[214] = 0.024107142857143*G0_0_0 + 0.120535714285714*G0_0_1 + 0.120535714285714*G0_0_2 + 0.024107142857143*G0_1_0 + 0.120535714285714*G0_1_1 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_0 + 0.024107142857143*G0_2_1 + 0.024107142857143*G0_2_2;

2515

A[215] = 0.0241071428571427*G0_0_0 - 0.0241071428571429*G0_0_1 - 0.0241071428571429*G0_0_2 + 0.0241071428571427*G0_1_0 - 0.0241071428571429*G0_1_1 - 0.0241071428571429*G0_1_2 - 0.0241071428571429*G0_2_0;

2516

A[216] = 0.0482142857142858*G0_0_0 + 0.0482142857142857*G0_0_1 + 0.024107142857143*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.024107142857143*G0_1_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_1;

2517

A[217] = -0.0482142857142858*G0_0_0 - 0.289285714285714*G0_0_1 - 0.16875*G0_0_2 - 0.0482142857142858*G0_1_0 - 0.289285714285714*G0_1_1 - 0.16875*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.16875*G0_2_1 - 0.0482142857142859*G0_2_2;

2518

A[218] = -0.289285714285714*G0_0_0 - 0.0482142857142857*G0_0_1 - 0.16875*G0_0_2 - 0.289285714285714*G0_1_0 - 0.0482142857142858*G0_1_1 - 0.16875*G0_1_2 - 0.16875*G0_2_0 - 0.0241071428571429*G0_2_1 - 0.0482142857142859*G0_2_2;

2519

A[219] = -0.144642857142857*G0_0_0 - 0.144642857142857*G0_0_1 - 0.024107142857143*G0_0_2 - 0.144642857142857*G0_1_0 - 0.144642857142857*G0_1_1 - 0.024107142857143*G0_1_2 - 0.024107142857143*G0_2_0 - 0.024107142857143*G0_2_1;

2520

A[220] = 0.0133928571428571*G0_0_0 + 0.0133928571428571*G0_0_1 + 0.0133928571428571*G0_0_2 + 0.0133928571428571*G0_1_0 + 0.0133928571428571*G0_1_1 + 0.0133928571428571*G0_1_2 + 0.0482142857142856*G0_2_0 + 0.0482142857142856*G0_2_1 + 0.0482142857142856*G0_2_2;

2521

A[221] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_1_0;

2522

A[222] = -0.0133928571428571*G0_0_1 - 0.0133928571428572*G0_1_1;

2523

A[223] = -0.0616071428571428*G0_0_2 - 0.0616071428571428*G0_1_2 - 0.0964285714285712*G0_2_2;

2524

A[224] = 0.0723214285714286*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0723214285714286*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_1;

2525

A[225] = -0.192857142857143*G0_0_1 - 0.0964285714285713*G0_0_2 - 0.192857142857143*G0_1_1 - 0.0964285714285713*G0_1_2 - 0.0964285714285713*G0_2_1 + 0.0241071428571428*G0_2_2;

2526

A[226] = 0.0723214285714285*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0723214285714285*G0_1_0 + 0.0241071428571428*G0_1_2 + 0.0241071428571428*G0_2_0;

2527

A[227] = -0.192857142857143*G0_0_0 - 0.0964285714285712*G0_0_2 - 0.192857142857143*G0_1_0 - 0.0964285714285713*G0_1_2 - 0.0964285714285713*G0_2_0 + 0.0241071428571428*G0_2_2;

2528

A[228] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0241071428571428*G0_1_1;

2529

A[229] = 0.0241071428571428*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_1_0 + 0.0241071428571428*G0_1_1;

2530

A[230] = -0.0723214285714284*G0_0_0 - 0.0723214285714285*G0_0_1 - 0.0482142857142857*G0_0_2 - 0.0723214285714285*G0_1_0 - 0.0723214285714285*G0_1_1 - 0.0482142857142857*G0_1_2 - 0.144642857142857*G0_2_0 - 0.144642857142857*G0_2_1 - 0.192857142857142*G0_2_2;

2531

A[231] = 0.192857142857143*G0_0_0 + 0.192857142857143*G0_0_1 + 0.0964285714285713*G0_0_2 + 0.192857142857143*G0_1_0 + 0.192857142857143*G0_1_1 + 0.0964285714285713*G0_1_2 + 0.0964285714285713*G0_2_0 + 0.0964285714285713*G0_2_1 + 0.241071428571428*G0_2_2;

2532

A[232] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_2 - 0.0241071428571429*G0_1_0 - 0.0241071428571429*G0_1_2 + 0.0241071428571427*G0_2_0 - 0.0241071428571428*G0_2_1 + 0.0241071428571427*G0_2_2;

2533

A[233] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0241071428571428*G0_1_2 - 0.0241071428571428*G0_2_1;

2534

A[234] = -0.0241071428571428*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0241071428571429*G0_1_1 - 0.0241071428571429*G0_1_2 - 0.0241071428571428*G0_2_0 + 0.0241071428571427*G0_2_1 + 0.0241071428571427*G0_2_2;

2535

A[235] = -0.0241071428571428*G0_0_1 - 0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_1 - 0.0241071428571428*G0_1_2 - 0.0241071428571428*G0_2_0;

2536

A[236] = -0.0964285714285712*G0_0_0 - 0.0964285714285713*G0_0_1 + 0.0241071428571429*G0_0_2 - 0.0964285714285713*G0_1_0 - 0.0964285714285713*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571429*G0_2_1;

2537

A[237] = 0.0964285714285712*G0_0_0 + 0.120535714285714*G0_0_2 + 0.0964285714285712*G0_1_0 + 0.120535714285714*G0_1_2 - 0.0241071428571429*G0_2_0 + 0.120535714285714*G0_2_1 - 0.0482142857142855*G0_2_2;

2538

A[238] = 0.0964285714285712*G0_0_1 + 0.120535714285714*G0_0_2 + 0.0964285714285713*G0_1_1 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_0 - 0.0241071428571428*G0_2_1 - 0.0482142857142855*G0_2_2;

2539

A[239] = -0.0241071428571429*G0_0_2 - 0.0241071428571429*G0_1_2 - 0.0241071428571428*G0_2_0 - 0.0241071428571427*G0_2_1;

2540

A[240] = -0.0348214285714286*G0_0_0 - 0.0348214285714286*G0_0_1 - 0.0348214285714286*G0_0_2 - 0.0964285714285713*G0_1_0 - 0.0964285714285713*G0_1_1 - 0.0964285714285713*G0_1_2 - 0.0348214285714286*G0_2_0 - 0.0348214285714286*G0_2_1 - 0.0348214285714286*G0_2_2;

2541

A[241] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_2_0;

2542

A[242] = 0.0348214285714286*G0_0_1 + 0.0482142857142856*G0_1_1 + 0.0348214285714286*G0_2_1;

2543

A[243] = -0.0133928571428571*G0_0_2 - 0.0133928571428571*G0_2_2;

2544

A[244] = 0.0482142857142858*G0_0_1 + 0.0723214285714286*G0_0_2 + 0.0241071428571429*G0_1_1 + 0.0482142857142858*G0_1_2 + 0.0482142857142858*G0_2_1 + 0.0723214285714287*G0_2_2;

2545

A[245] = 0.0241071428571429*G0_0_1 + 0.0482142857142856*G0_0_2 + 0.0241071428571427*G0_1_2 + 0.0241071428571429*G0_2_1 + 0.0482142857142856*G0_2_2;

2546

A[246] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571429*G0_2_2;

2547

A[247] = 0.0241071428571429*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571428*G0_2_2;

2548

A[248] = 0.0482142857142858*G0_0_0 + 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0482142857142857*G0_2_0 + 0.0241071428571429*G0_2_1;

2549

A[249] = 0.0723214285714287*G0_0_0 + 0.0482142857142859*G0_0_1 + 0.0482142857142858*G0_1_0 + 0.0241071428571429*G0_1_1 + 0.0723214285714287*G0_2_0 + 0.0482142857142859*G0_2_1;

2550

A[250] = 0.120535714285714*G0_0_0 + 0.120535714285714*G0_0_1 + 0.024107142857143*G0_0_2 + 0.024107142857143*G0_1_0 + 0.024107142857143*G0_1_1 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_0 + 0.120535714285714*G0_2_1 + 0.024107142857143*G0_2_2;

2551

A[251] = -0.0241071428571428*G0_0_0 - 0.0241071428571429*G0_0_1 + 0.0241071428571427*G0_0_2 - 0.0241071428571428*G0_1_2 - 0.0241071428571428*G0_2_0 - 0.0241071428571429*G0_2_1 + 0.0241071428571427*G0_2_2;

2552

A[252] = 0.241071428571428*G0_0_0 + 0.144642857142857*G0_0_1 + 0.241071428571428*G0_0_2 + 0.144642857142857*G0_1_0 + 0.241071428571428*G0_1_1 + 0.144642857142857*G0_1_2 + 0.241071428571428*G0_2_0 + 0.144642857142857*G0_2_1 + 0.241071428571428*G0_2_2;

2553

A[253] = -0.0723214285714287*G0_0_0 - 0.144642857142857*G0_0_1 - 0.0723214285714287*G0_0_2 - 0.0482142857142858*G0_1_0 - 0.192857142857143*G0_1_1 - 0.0482142857142858*G0_1_2 - 0.0723214285714287*G0_2_0 - 0.144642857142857*G0_2_1 - 0.0723214285714287*G0_2_2;

2554

A[254] = 0.024107142857143*G0_0_0 + 0.120535714285714*G0_0_1 + 0.120535714285714*G0_0_2 + 0.120535714285714*G0_1_0 + 0.024107142857143*G0_1_1 + 0.024107142857143*G0_1_2 + 0.024107142857143*G0_2_0 + 0.120535714285714*G0_2_1 + 0.120535714285714*G0_2_2;

2555

A[255] = 0.0241071428571427*G0_0_0 - 0.0241071428571429*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0241071428571429*G0_1_0 + 0.0241071428571427*G0_2_0 - 0.0241071428571429*G0_2_1 - 0.0241071428571429*G0_2_2;

2556

A[256] = 0.0482142857142859*G0_0_0 + 0.024107142857143*G0_0_1 + 0.0482142857142861*G0_0_2 + 0.024107142857143*G0_1_0 + 0.0241071428571432*G0_1_2 + 0.0482142857142859*G0_2_0 + 0.024107142857143*G0_2_1 + 0.0482142857142861*G0_2_2;

2557

A[257] = -0.0482142857142859*G0_0_0 - 0.16875*G0_0_1 - 0.289285714285714*G0_0_2 - 0.024107142857143*G0_1_0 - 0.0482142857142859*G0_1_1 - 0.16875*G0_1_2 - 0.0482142857142859*G0_2_0 - 0.16875*G0_2_1 - 0.289285714285714*G0_2_2;

2558

A[258] = -0.144642857142857*G0_0_0 - 0.024107142857143*G0_0_1 - 0.144642857142857*G0_0_2 - 0.024107142857143*G0_1_0 - 0.0241071428571429*G0_1_2 - 0.144642857142857*G0_2_0 - 0.024107142857143*G0_2_1 - 0.144642857142857*G0_2_2;

2559

A[259] = -0.289285714285714*G0_0_0 - 0.16875*G0_0_1 - 0.0482142857142861*G0_0_2 - 0.16875*G0_1_0 - 0.0482142857142859*G0_1_1 - 0.0241071428571432*G0_1_2 - 0.289285714285714*G0_2_0 - 0.16875*G0_2_1 - 0.0482142857142861*G0_2_2;

2560

A[260] = 0.0133928571428572*G0_0_0 + 0.0133928571428572*G0_0_1 + 0.0133928571428572*G0_0_2 + 0.0482142857142856*G0_1_0 + 0.0482142857142856*G0_1_1 + 0.0482142857142856*G0_1_2 + 0.0133928571428572*G0_2_0 + 0.0133928571428572*G0_2_1 + 0.0133928571428572*G0_2_2;

2561

A[261] = -0.0133928571428571*G0_0_0 - 0.0133928571428571*G0_2_0;

2562

A[262] = -0.0616071428571428*G0_0_1 - 0.0964285714285713*G0_1_1 - 0.0616071428571428*G0_2_1;

2563

A[263] = -0.0133928571428571*G0_0_2 - 0.0133928571428571*G0_2_2;

2564

A[264] = -0.0964285714285714*G0_0_1 - 0.192857142857143*G0_0_2 + 0.0241071428571427*G0_1_1 - 0.0964285714285714*G0_1_2 - 0.0964285714285714*G0_2_1 - 0.192857142857143*G0_2_2;

2565

A[265] = 0.0241071428571428*G0_0_1 + 0.0723214285714284*G0_0_2 + 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0723214285714285*G0_2_2;

2566

A[266] = 0.0241071428571429*G0_0_0 + 0.0241071428571429*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_2;

2567

A[267] = 0.0241071428571428*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_2_0 + 0.0241071428571428*G0_2_2;

2568

A[268] = 0.0723214285714286*G0_0_0 + 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_1_0 + 0.0723214285714286*G0_2_0 + 0.0241071428571428*G0_2_1;

2569

A[269] = -0.192857142857143*G0_0_0 - 0.0964285714285713*G0_0_1 - 0.0964285714285714*G0_1_0 + 0.0241071428571427*G0_1_1 - 0.192857142857143*G0_2_0 - 0.0964285714285713*G0_2_1;

2570

A[270] = -0.0241071428571429*G0_0_0 - 0.024107142857143*G0_0_1 + 0.0241071428571427*G0_1_0 + 0.0241071428571427*G0_1_1 - 0.0241071428571428*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_1;

2571

A[271] = -0.0241071428571428*G0_0_0 - 0.0241071428571428*G0_0_1 - 0.0241071428571428*G0_1_2 - 0.0241071428571428*G0_2_0 - 0.0241071428571428*G0_2_1;

2572

A[272] = -0.0723214285714287*G0_0_0 - 0.0482142857142858*G0_0_1 - 0.0723214285714287*G0_0_2 - 0.144642857142857*G0_1_0 - 0.192857142857143*G0_1_1 - 0.144642857142857*G0_1_2 - 0.0723214285714287*G0_2_0 - 0.0482142857142858*G0_2_1 - 0.0723214285714287*G0_2_2;

2573

A[273] = 0.192857142857143*G0_0_0 + 0.0964285714285714*G0_0_1 + 0.192857142857143*G0_0_2 + 0.0964285714285714*G0_1_0 + 0.241071428571428*G0_1_1 + 0.0964285714285714*G0_1_2 + 0.192857142857143*G0_2_0 + 0.0964285714285714*G0_2_1 + 0.192857142857143*G0_2_2;

2574

A[274] = -0.0241071428571429*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0241071428571428*G0_1_0 + 0.0241071428571428*G0_1_1 + 0.0241071428571427*G0_1_2 - 0.0241071428571429*G0_2_1 - 0.0241071428571429*G0_2_2;

2575

A[275] = -0.0241071428571429*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0241071428571429*G0_2_1 - 0.0241071428571429*G0_2_2;

2576

A[276] = -0.0964285714285714*G0_0_0 + 0.0241071428571429*G0_0_1 - 0.0964285714285713*G0_0_2 + 0.0241071428571427*G0_1_0 + 0.0241071428571427*G0_1_2 - 0.0964285714285713*G0_2_0 + 0.0241071428571429*G0_2_1 - 0.0964285714285713*G0_2_2;

2577

A[277] = 0.0964285714285713*G0_0_0 + 0.120535714285714*G0_0_1 - 0.0241071428571427*G0_1_0 - 0.0482142857142855*G0_1_1 + 0.120535714285714*G0_1_2 + 0.0964285714285713*G0_2_0 + 0.120535714285714*G0_2_1;

2578

A[278] = -0.0241071428571429*G0_0_1 - 0.0241071428571428*G0_1_0 - 0.0241071428571428*G0_1_2 - 0.0241071428571429*G0_2_1;

2579

A[279] = 0.120535714285714*G0_0_1 + 0.0964285714285713*G0_0_2 + 0.120535714285714*G0_1_0 - 0.0482142857142855*G0_1_1 - 0.0241071428571427*G0_1_2 + 0.120535714285714*G0_2_1 + 0.0964285714285713*G0_2_2;

2580

A[280] = -0.0964285714285713*G0_0_0 - 0.0964285714285714*G0_0_1 - 0.0964285714285713*G0_0_2 - 0.0348214285714287*G0_1_0 - 0.0348214285714287*G0_1_1 - 0.0348214285714287*G0_1_2 - 0.0348214285714287*G0_2_0 - 0.0348214285714287*G0_2_1 - 0.0348214285714287*G0_2_2;

2581

A[281] = 0.0482142857142857*G0_0_0 + 0.0348214285714286*G0_1_0 + 0.0348214285714286*G0_2_0;

2582

A[282] = -0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_2_1;

2583

A[283] = -0.0133928571428571*G0_1_2 - 0.0133928571428571*G0_2_2;

2584

A[284] = 0.0241071428571429*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_1 + 0.0241071428571429*G0_2_2;

2585

A[285] = 0.0241071428571429*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571429*G0_2_1 + 0.0241071428571428*G0_2_2;

2586

A[286] = 0.024107142857143*G0_0_0 + 0.0482142857142859*G0_0_2 + 0.0482142857142857*G0_1_0 + 0.0723214285714286*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0723214285714287*G0_2_2;

2587

A[287] = 0.0241071428571428*G0_0_2 + 0.0241071428571429*G0_1_0 + 0.0482142857142856*G0_1_2 + 0.0241071428571429*G0_2_0 + 0.0482142857142857*G0_2_2;

2588

A[288] = 0.024107142857143*G0_0_0 + 0.0482142857142859*G0_0_1 + 0.0482142857142858*G0_1_0 + 0.0723214285714286*G0_1_1 + 0.0482142857142858*G0_2_0 + 0.0723214285714286*G0_2_1;

2589

A[289] = 0.0241071428571429*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0241071428571429*G0_2_0 + 0.0482142857142858*G0_2_1;

2590

A[290] = 0.024107142857143*G0_0_0 + 0.024107142857143*G0_0_1 + 0.120535714285714*G0_0_2 + 0.120535714285714*G0_1_0 + 0.120535714285714*G0_1_1 + 0.024107142857143*G0_1_2 + 0.120535714285714*G0_2_0 + 0.120535714285714*G0_2_1 + 0.024107142857143*G0_2_2;

2591

A[291] = -0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0241071428571429*G0_1_1 + 0.0241071428571427*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_1 + 0.0241071428571427*G0_2_2;

2592

A[292] = 0.024107142857143*G0_0_0 + 0.120535714285714*G0_0_1 + 0.024107142857143*G0_0_2 + 0.120535714285714*G0_1_0 + 0.024107142857143*G0_1_1 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_0 + 0.024107142857143*G0_2_1 + 0.120535714285714*G0_2_2;

2593

A[293] = -0.0241071428571428*G0_0_1 - 0.0241071428571429*G0_1_0 + 0.0241071428571428*G0_1_1 - 0.0241071428571429*G0_1_2 - 0.0241071428571429*G0_2_0 + 0.0241071428571427*G0_2_1 - 0.0241071428571429*G0_2_2;

2594

A[294] = 0.241071428571428*G0_0_0 + 0.144642857142857*G0_0_1 + 0.144642857142857*G0_0_2 + 0.144642857142857*G0_1_0 + 0.241071428571428*G0_1_1 + 0.241071428571428*G0_1_2 + 0.144642857142857*G0_2_0 + 0.241071428571428*G0_2_1 + 0.241071428571428*G0_2_2;

2595

A[295] = -0.192857142857143*G0_0_0 - 0.0482142857142859*G0_0_1 - 0.0482142857142859*G0_0_2 - 0.144642857142857*G0_1_0 - 0.0723214285714287*G0_1_1 - 0.0723214285714287*G0_1_2 - 0.144642857142857*G0_2_0 - 0.0723214285714287*G0_2_1 - 0.0723214285714287*G0_2_2;

2596

A[296] = 0.024107142857143*G0_0_1 + 0.0241071428571431*G0_0_2 + 0.024107142857143*G0_1_0 + 0.0482142857142859*G0_1_1 + 0.048214285714286*G0_1_2 + 0.024107142857143*G0_2_0 + 0.0482142857142859*G0_2_1 + 0.048214285714286*G0_2_2;

2597

A[297] = -0.024107142857143*G0_0_1 - 0.024107142857143*G0_0_2 - 0.024107142857143*G0_1_0 - 0.144642857142857*G0_1_1 - 0.144642857142857*G0_1_2 - 0.024107142857143*G0_2_0 - 0.144642857142857*G0_2_1 - 0.144642857142857*G0_2_2;

2598

A[298] = -0.048214285714286*G0_0_0 - 0.024107142857143*G0_0_1 - 0.16875*G0_0_2 - 0.16875*G0_1_0 - 0.0482142857142858*G0_1_1 - 0.289285714285714*G0_1_2 - 0.16875*G0_2_0 - 0.0482142857142859*G0_2_1 - 0.289285714285714*G0_2_2;

2599

A[299] = -0.048214285714286*G0_0_0 - 0.16875*G0_0_1 - 0.0241071428571431*G0_0_2 - 0.16875*G0_1_0 - 0.289285714285714*G0_1_1 - 0.048214285714286*G0_1_2 - 0.16875*G0_2_0 - 0.289285714285714*G0_2_1 - 0.048214285714286*G0_2_2;

2600

A[300] = 0.0482142857142857*G0_0_0 + 0.0482142857142857*G0_0_1 + 0.0482142857142857*G0_0_2 + 0.0133928571428572*G0_1_0 + 0.0133928571428572*G0_1_1 + 0.0133928571428572*G0_1_2 + 0.0133928571428572*G0_2_0 + 0.0133928571428572*G0_2_1 + 0.0133928571428572*G0_2_2;

2601

A[301] = -0.0964285714285713*G0_0_0 - 0.0616071428571428*G0_1_0 - 0.0616071428571428*G0_2_0;

2602

A[302] = -0.0133928571428571*G0_1_1 - 0.0133928571428571*G0_2_1;

2603

A[303] = -0.0133928571428571*G0_1_2 - 0.0133928571428571*G0_2_2;

2604

A[304] = 0.0241071428571428*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0241071428571428*G0_2_2;

2605

A[305] = 0.0241071428571428*G0_1_1 + 0.0241071428571428*G0_1_2 + 0.0241071428571428*G0_2_1 + 0.0241071428571428*G0_2_2;

2606

A[306] = 0.0241071428571427*G0_0_0 - 0.0964285714285714*G0_0_2 - 0.0964285714285714*G0_1_0 - 0.192857142857143*G0_1_2 - 0.0964285714285714*G0_2_0 - 0.192857142857143*G0_2_2;

2607

A[307] = 0.0241071428571428*G0_0_2 + 0.0241071428571428*G0_1_0 + 0.0723214285714283*G0_1_2 + 0.0241071428571428*G0_2_0 + 0.0723214285714283*G0_2_2;

2608

A[308] = 0.0241071428571427*G0_0_0 - 0.0964285714285714*G0_0_1 - 0.0964285714285715*G0_1_0 - 0.192857142857143*G0_1_1 - 0.0964285714285715*G0_2_0 - 0.192857142857143*G0_2_1;

2609

A[309] = 0.0241071428571428*G0_0_1 + 0.0241071428571428*G0_1_0 + 0.0723214285714284*G0_1_1 + 0.0241071428571428*G0_2_0 + 0.0723214285714283*G0_2_1;

2610

A[310] = 0.0241071428571427*G0_0_0 + 0.0241071428571427*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.0241071428571429*G0_1_0 - 0.0241071428571429*G0_1_1 - 0.0241071428571429*G0_2_0 - 0.024107142857143*G0_2_1;

2611

A[311] = -0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_0 - 0.0241071428571428*G0_1_1 - 0.0241071428571428*G0_2_0 - 0.0241071428571428*G0_2_1;

2612

A[312] = 0.0241071428571427*G0_0_0 - 0.0241071428571429*G0_0_1 + 0.0241071428571427*G0_0_2 - 0.0241071428571429*G0_1_0 - 0.0241071428571429*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_2;

2613

A[313] = -0.0241071428571428*G0_0_1 - 0.0241071428571429*G0_1_0 - 0.0241071428571429*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_2;

2614

A[314] = -0.192857142857143*G0_0_0 - 0.144642857142857*G0_0_1 - 0.144642857142857*G0_0_2 - 0.0482142857142859*G0_1_0 - 0.0723214285714287*G0_1_1 - 0.0723214285714287*G0_1_2 - 0.0482142857142859*G0_2_0 - 0.0723214285714287*G0_2_1 - 0.0723214285714287*G0_2_2;

2615

A[315] = 0.241071428571428*G0_0_0 + 0.0964285714285714*G0_0_1 + 0.0964285714285714*G0_0_2 + 0.0964285714285714*G0_1_0 + 0.192857142857143*G0_1_1 + 0.192857142857143*G0_1_2 + 0.0964285714285714*G0_2_0 + 0.192857142857143*G0_2_1 + 0.192857142857143*G0_2_2;

2616

A[316] = 0.0241071428571427*G0_0_1 + 0.0241071428571427*G0_0_2 + 0.0241071428571427*G0_1_0 - 0.0964285714285715*G0_1_1 - 0.0964285714285715*G0_1_2 + 0.0241071428571427*G0_2_0 - 0.0964285714285715*G0_2_1 - 0.0964285714285716*G0_2_2;

2617

A[317] = -0.0241071428571427*G0_0_1 - 0.0241071428571427*G0_0_2 - 0.0241071428571427*G0_1_0 - 0.0241071428571427*G0_2_0;

2618

A[318] = -0.0482142857142854*G0_0_0 - 0.0241071428571427*G0_0_1 + 0.120535714285714*G0_0_2 + 0.120535714285714*G0_1_0 + 0.0964285714285716*G0_1_1 + 0.120535714285714*G0_2_0 + 0.0964285714285715*G0_2_1;

2619

A[319] = -0.0482142857142854*G0_0_0 + 0.120535714285714*G0_0_1 - 0.0241071428571427*G0_0_2 + 0.120535714285714*G0_1_0 + 0.0964285714285716*G0_1_2 + 0.120535714285714*G0_2_0 + 0.0964285714285716*G0_2_2;

2620

A[320] = -0.0321428571428572*G0_0_0 - 0.0321428571428572*G0_0_1 - 0.0321428571428572*G0_0_2 - 0.0321428571428572*G0_1_0 - 0.0321428571428572*G0_1_1 - 0.0321428571428572*G0_1_2 - 0.0321428571428573*G0_2_0 - 0.0321428571428573*G0_2_1 - 0.0321428571428573*G0_2_2;

2621

A[321] = 0.0321428571428571*G0_0_0 - 0.0160714285714285*G0_1_0 - 0.0160714285714285*G0_2_0;

2622

A[322] = -0.0160714285714286*G0_0_1 + 0.032142857142857*G0_1_1 - 0.0160714285714286*G0_2_1;

2623

A[323] = -0.0160714285714285*G0_0_2 - 0.0160714285714285*G0_1_2 + 0.032142857142857*G0_2_2;

2624

A[324] = 0.241071428571428*G0_0_1 + 0.0964285714285713*G0_0_2 - 0.0482142857142856*G0_1_1 - 0.0241071428571429*G0_1_2 + 0.120535714285714*G0_2_1 + 0.0964285714285713*G0_2_2;

2625

A[325] = 0.0964285714285713*G0_0_1 + 0.241071428571428*G0_0_2 + 0.0964285714285713*G0_1_1 + 0.120535714285714*G0_1_2 - 0.0241071428571429*G0_2_1 - 0.0482142857142855*G0_2_2;

2626

A[326] = -0.0482142857142857*G0_0_0 - 0.0241071428571428*G0_0_2 + 0.241071428571428*G0_1_0 + 0.0964285714285714*G0_1_2 + 0.120535714285714*G0_2_0 + 0.0964285714285714*G0_2_2;

2627

A[327] = 0.0964285714285713*G0_0_0 + 0.120535714285714*G0_0_2 + 0.0964285714285714*G0_1_0 + 0.241071428571428*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0482142857142855*G0_2_2;

2628

A[328] = -0.0482142857142856*G0_0_0 - 0.0241071428571428*G0_0_1 + 0.120535714285714*G0_1_0 + 0.0964285714285715*G0_1_1 + 0.241071428571428*G0_2_0 + 0.0964285714285715*G0_2_1;

2629

A[329] = 0.0964285714285714*G0_0_0 + 0.120535714285714*G0_0_1 - 0.0241071428571428*G0_1_0 - 0.0482142857142856*G0_1_1 + 0.0964285714285713*G0_2_0 + 0.241071428571428*G0_2_1;

2630

A[330] = 0.0482142857142858*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0241071428571429*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.024107142857143*G0_2_0 + 0.024107142857143*G0_2_1;

2631

A[331] = -0.0964285714285712*G0_0_0 - 0.0964285714285713*G0_0_1 + 0.0241071428571428*G0_0_2 - 0.0964285714285713*G0_1_0 - 0.0964285714285713*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571429*G0_2_0 + 0.0241071428571429*G0_2_1;

2632

A[332] = 0.0482142857142859*G0_0_0 + 0.024107142857143*G0_0_1 + 0.0482142857142859*G0_0_2 + 0.024107142857143*G0_1_0 + 0.024107142857143*G0_1_2 + 0.0482142857142861*G0_2_0 + 0.0241071428571432*G0_2_1 + 0.0482142857142861*G0_2_2;

2633

A[333] = -0.0964285714285713*G0_0_0 + 0.0241071428571427*G0_0_1 - 0.0964285714285713*G0_0_2 + 0.0241071428571429*G0_1_0 + 0.0241071428571429*G0_1_2 - 0.0964285714285713*G0_2_0 + 0.0241071428571427*G0_2_1 - 0.0964285714285713*G0_2_2;

2634

A[334] = 0.024107142857143*G0_0_1 + 0.024107142857143*G0_0_2 + 0.024107142857143*G0_1_0 + 0.0482142857142859*G0_1_1 + 0.0482142857142859*G0_1_2 + 0.0241071428571431*G0_2_0 + 0.048214285714286*G0_2_1 + 0.048214285714286*G0_2_2;

2635

A[335] = 0.0241071428571427*G0_0_1 + 0.0241071428571427*G0_0_2 + 0.0241071428571427*G0_1_0 - 0.0964285714285715*G0_1_1 - 0.0964285714285715*G0_1_2 + 0.0241071428571427*G0_2_0 - 0.0964285714285715*G0_2_1 - 0.0964285714285716*G0_2_2;

2636

A[336] = 0.578571428571427*G0_0_0 + 0.289285714285714*G0_0_1 + 0.289285714285714*G0_0_2 + 0.289285714285714*G0_1_0 + 0.578571428571428*G0_1_1 + 0.289285714285714*G0_1_2 + 0.289285714285714*G0_2_0 + 0.289285714285714*G0_2_1 + 0.578571428571428*G0_2_2;

2637

A[337] = -0.578571428571427*G0_0_0 - 0.289285714285714*G0_0_1 - 0.289285714285714*G0_0_2 - 0.289285714285714*G0_1_0 - 0.144642857142857*G0_1_2 - 0.289285714285714*G0_2_0 - 0.144642857142857*G0_2_1;

2638

A[338] = -0.289285714285714*G0_0_1 - 0.144642857142857*G0_0_2 - 0.289285714285714*G0_1_0 - 0.578571428571428*G0_1_1 - 0.289285714285714*G0_1_2 - 0.144642857142857*G0_2_0 - 0.289285714285714*G0_2_1;

2639

A[339] = -0.144642857142857*G0_0_1 - 0.289285714285714*G0_0_2 - 0.144642857142857*G0_1_0 - 0.289285714285714*G0_1_2 - 0.289285714285714*G0_2_0 - 0.289285714285714*G0_2_1 - 0.578571428571428*G0_2_2;

2640

A[340] = 0.0321428571428572*G0_0_0 + 0.0321428571428572*G0_0_1 + 0.0321428571428572*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0482142857142858*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0482142857142857*G0_2_1 + 0.0482142857142857*G0_2_2;

2641

A[341] = -0.0321428571428571*G0_0_0;

2642

A[342] = 0.0160714285714286*G0_0_1 + 0.0482142857142856*G0_1_1;

2643

A[343] = 0.0160714285714285*G0_0_2 + 0.0482142857142855*G0_2_2;

2644

A[344] = -0.241071428571428*G0_0_1 - 0.0964285714285712*G0_0_2 - 0.289285714285714*G0_1_1 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1;

2645

A[345] = -0.0964285714285713*G0_0_1 - 0.241071428571428*G0_0_2 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1 - 0.289285714285714*G0_2_2;

2646

A[346] = 0.0482142857142856*G0_0_0 + 0.0241071428571428*G0_0_2 + 0.0241071428571429*G0_2_0;

2647

A[347] = -0.0964285714285713*G0_0_0 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.144642857142857*G0_2_2;

2648

A[348] = 0.0482142857142856*G0_0_0 + 0.0241071428571427*G0_0_1 + 0.0241071428571428*G0_1_0;

2649

A[349] = -0.0964285714285713*G0_0_0 - 0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.144642857142857*G0_1_1;

2650

A[350] = -0.0482142857142858*G0_0_0 - 0.0482142857142858*G0_0_1 - 0.0241071428571429*G0_0_2 - 0.289285714285714*G0_1_0 - 0.289285714285714*G0_1_1 - 0.16875*G0_1_2 - 0.16875*G0_2_0 - 0.16875*G0_2_1 - 0.0482142857142859*G0_2_2;

2651

A[351] = 0.0964285714285712*G0_0_0 + 0.0964285714285712*G0_0_1 - 0.0241071428571428*G0_0_2 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_0 + 0.120535714285714*G0_2_1 - 0.0482142857142855*G0_2_2;

2652

A[352] = -0.0482142857142859*G0_0_0 - 0.024107142857143*G0_0_1 - 0.0482142857142859*G0_0_2 - 0.16875*G0_1_0 - 0.0482142857142859*G0_1_1 - 0.16875*G0_1_2 - 0.289285714285714*G0_2_0 - 0.16875*G0_2_1 - 0.289285714285714*G0_2_2;

2653

A[353] = 0.0964285714285713*G0_0_0 - 0.0241071428571427*G0_0_1 + 0.0964285714285713*G0_0_2 + 0.120535714285714*G0_1_0 - 0.0482142857142855*G0_1_1 + 0.120535714285714*G0_1_2 + 0.120535714285714*G0_2_1;

2654

A[354] = -0.024107142857143*G0_0_1 - 0.024107142857143*G0_0_2 - 0.024107142857143*G0_1_0 - 0.144642857142857*G0_1_1 - 0.144642857142857*G0_1_2 - 0.024107142857143*G0_2_0 - 0.144642857142857*G0_2_1 - 0.144642857142857*G0_2_2;

2655

A[355] = -0.0241071428571427*G0_0_1 - 0.0241071428571427*G0_0_2 - 0.0241071428571427*G0_1_0 - 0.0241071428571427*G0_2_0;

2656

A[356] = -0.578571428571427*G0_0_0 - 0.289285714285714*G0_0_1 - 0.289285714285714*G0_0_2 - 0.289285714285714*G0_1_0 - 0.144642857142857*G0_1_2 - 0.289285714285714*G0_2_0 - 0.144642857142857*G0_2_1;

2657

A[357] = 0.578571428571427*G0_0_0 + 0.289285714285714*G0_0_1 + 0.289285714285714*G0_0_2 + 0.289285714285714*G0_1_0 + 0.578571428571428*G0_1_1 + 0.289285714285714*G0_1_2 + 0.289285714285714*G0_2_0 + 0.289285714285714*G0_2_1 + 0.578571428571428*G0_2_2;

2658

A[358] = 0.289285714285714*G0_0_1 + 0.144642857142857*G0_0_2 + 0.289285714285714*G0_1_0 + 0.144642857142857*G0_1_2 + 0.144642857142857*G0_2_0 + 0.144642857142857*G0_2_1 + 0.289285714285714*G0_2_2;

2659

A[359] = 0.144642857142857*G0_0_1 + 0.289285714285714*G0_0_2 + 0.144642857142857*G0_1_0 + 0.289285714285714*G0_1_1 + 0.144642857142857*G0_1_2 + 0.289285714285714*G0_2_0 + 0.144642857142857*G0_2_1;

2660

A[360] = 0.0482142857142858*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0482142857142858*G0_0_2 + 0.0321428571428572*G0_1_0 + 0.0321428571428572*G0_1_1 + 0.0321428571428572*G0_1_2 + 0.0482142857142857*G0_2_0 + 0.0482142857142857*G0_2_1 + 0.0482142857142858*G0_2_2;

2661

A[361] = 0.0482142857142856*G0_0_0 + 0.0160714285714285*G0_1_0;

2662

A[362] = -0.032142857142857*G0_1_1;

2663

A[363] = 0.0160714285714285*G0_1_2 + 0.0482142857142855*G0_2_2;

2664

A[364] = 0.0482142857142856*G0_1_1 + 0.0241071428571429*G0_1_2 + 0.0241071428571428*G0_2_1;

2665

A[365] = -0.0964285714285713*G0_1_1 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1 - 0.144642857142857*G0_2_2;

2666

A[366] = -0.289285714285714*G0_0_0 - 0.120535714285714*G0_0_2 - 0.241071428571428*G0_1_0 - 0.0964285714285714*G0_1_2 - 0.120535714285714*G0_2_0;

2667

A[367] = -0.120535714285714*G0_0_2 - 0.0964285714285713*G0_1_0 - 0.241071428571428*G0_1_2 - 0.120535714285714*G0_2_0 - 0.289285714285714*G0_2_2;

2668

A[368] = -0.144642857142857*G0_0_0 - 0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.0964285714285715*G0_1_1;

2669

A[369] = 0.0241071428571427*G0_0_1 + 0.0241071428571429*G0_1_0 + 0.0482142857142856*G0_1_1;

2670

A[370] = -0.289285714285714*G0_0_0 - 0.289285714285714*G0_0_1 - 0.16875*G0_0_2 - 0.0482142857142857*G0_1_0 - 0.0482142857142858*G0_1_1 - 0.0241071428571429*G0_1_2 - 0.16875*G0_2_0 - 0.16875*G0_2_1 - 0.0482142857142859*G0_2_2;

2671

A[371] = 0.120535714285714*G0_0_2 + 0.0964285714285712*G0_1_0 + 0.0964285714285713*G0_1_1 - 0.0241071428571428*G0_1_2 + 0.120535714285714*G0_2_0 + 0.120535714285714*G0_2_1 - 0.0482142857142855*G0_2_2;

2672

A[372] = -0.144642857142857*G0_0_0 - 0.024107142857143*G0_0_1 - 0.144642857142857*G0_0_2 - 0.024107142857143*G0_1_0 - 0.024107142857143*G0_1_2 - 0.144642857142857*G0_2_0 - 0.0241071428571429*G0_2_1 - 0.144642857142857*G0_2_2;

2673

A[373] = -0.0241071428571428*G0_0_1 - 0.0241071428571429*G0_1_0 - 0.0241071428571429*G0_1_2 - 0.0241071428571428*G0_2_1;

2674

A[374] = -0.048214285714286*G0_0_0 - 0.16875*G0_0_1 - 0.16875*G0_0_2 - 0.024107142857143*G0_1_0 - 0.0482142857142859*G0_1_1 - 0.0482142857142859*G0_1_2 - 0.16875*G0_2_0 - 0.289285714285714*G0_2_1 - 0.289285714285714*G0_2_2;

2675

A[375] = -0.0482142857142854*G0_0_0 + 0.120535714285714*G0_0_1 + 0.120535714285714*G0_0_2 - 0.0241071428571427*G0_1_0 + 0.0964285714285716*G0_1_1 + 0.0964285714285715*G0_1_2 + 0.120535714285714*G0_2_0;

2676

A[376] = -0.289285714285714*G0_0_1 - 0.144642857142857*G0_0_2 - 0.289285714285714*G0_1_0 - 0.578571428571428*G0_1_1 - 0.289285714285714*G0_1_2 - 0.144642857142857*G0_2_0 - 0.289285714285714*G0_2_1;

2677

A[377] = 0.289285714285714*G0_0_1 + 0.144642857142857*G0_0_2 + 0.289285714285714*G0_1_0 + 0.144642857142857*G0_1_2 + 0.144642857142857*G0_2_0 + 0.144642857142857*G0_2_1 + 0.289285714285714*G0_2_2;

2678

A[378] = 0.578571428571428*G0_0_0 + 0.289285714285714*G0_0_1 + 0.289285714285714*G0_0_2 + 0.289285714285714*G0_1_0 + 0.578571428571428*G0_1_1 + 0.289285714285714*G0_1_2 + 0.289285714285714*G0_2_0 + 0.289285714285714*G0_2_1 + 0.578571428571428*G0_2_2;

2679

A[379] = 0.289285714285714*G0_0_0 + 0.144642857142857*G0_0_1 + 0.144642857142857*G0_0_2 + 0.144642857142857*G0_1_0 + 0.289285714285714*G0_1_2 + 0.144642857142857*G0_2_0 + 0.289285714285714*G0_2_1;

2680

A[380] = 0.0482142857142858*G0_0_0 + 0.0482142857142858*G0_0_1 + 0.0482142857142858*G0_0_2 + 0.0482142857142858*G0_1_0 + 0.0482142857142858*G0_1_1 + 0.0482142857142858*G0_1_2 + 0.0321428571428573*G0_2_0 + 0.0321428571428573*G0_2_1 + 0.0321428571428573*G0_2_2;

2681

A[381] = 0.0482142857142856*G0_0_0 + 0.0160714285714285*G0_2_0;

2682

A[382] = 0.0482142857142856*G0_1_1 + 0.0160714285714286*G0_2_1;

2683

A[383] = -0.032142857142857*G0_2_2;

2684

A[384] = -0.144642857142857*G0_1_1 - 0.120535714285714*G0_1_2 - 0.120535714285714*G0_2_1 - 0.0964285714285713*G0_2_2;

2685

A[385] = 0.0241071428571428*G0_1_2 + 0.0241071428571429*G0_2_1 + 0.0482142857142855*G0_2_2;

2686

A[386] = -0.144642857142857*G0_0_0 - 0.120535714285714*G0_0_2 - 0.120535714285714*G0_2_0 - 0.0964285714285715*G0_2_2;

2687

A[387] = 0.0241071428571428*G0_0_2 + 0.0241071428571429*G0_2_0 + 0.0482142857142856*G0_2_2;

2688

A[388] = -0.289285714285714*G0_0_0 - 0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.241071428571429*G0_2_0 - 0.0964285714285716*G0_2_1;

2689

A[389] = -0.120535714285714*G0_0_1 - 0.120535714285714*G0_1_0 - 0.289285714285714*G0_1_1 - 0.0964285714285713*G0_2_0 - 0.241071428571428*G0_2_1;

2690

A[390] = -0.144642857142857*G0_0_0 - 0.144642857142857*G0_0_1 - 0.024107142857143*G0_0_2 - 0.144642857142857*G0_1_0 - 0.144642857142857*G0_1_1 - 0.024107142857143*G0_1_2 - 0.024107142857143*G0_2_0 - 0.024107142857143*G0_2_1;

2691

A[391] = -0.0241071428571428*G0_0_2 - 0.0241071428571428*G0_1_2 - 0.0241071428571429*G0_2_0 - 0.0241071428571429*G0_2_1;

2692

A[392] = -0.289285714285714*G0_0_0 - 0.16875*G0_0_1 - 0.289285714285714*G0_0_2 - 0.16875*G0_1_0 - 0.0482142857142859*G0_1_1 - 0.16875*G0_1_2 - 0.0482142857142861*G0_2_0 - 0.0241071428571432*G0_2_1 - 0.0482142857142861*G0_2_2;

2693

A[393] = 0.120535714285714*G0_0_1 + 0.120535714285714*G0_1_0 - 0.0482142857142855*G0_1_1 + 0.120535714285714*G0_1_2 + 0.0964285714285713*G0_2_0 - 0.0241071428571427*G0_2_1 + 0.0964285714285713*G0_2_2;

2694

A[394] = -0.048214285714286*G0_0_0 - 0.16875*G0_0_1 - 0.16875*G0_0_2 - 0.16875*G0_1_0 - 0.289285714285714*G0_1_1 - 0.289285714285714*G0_1_2 - 0.0241071428571431*G0_2_0 - 0.048214285714286*G0_2_1 - 0.048214285714286*G0_2_2;

2695

A[395] = -0.0482142857142854*G0_0_0 + 0.120535714285714*G0_0_1 + 0.120535714285714*G0_0_2 + 0.120535714285714*G0_1_0 - 0.0241071428571427*G0_2_0 + 0.0964285714285716*G0_2_1 + 0.0964285714285716*G0_2_2;

2696

A[396] = -0.144642857142857*G0_0_1 - 0.289285714285714*G0_0_2 - 0.144642857142857*G0_1_0 - 0.289285714285714*G0_1_2 - 0.289285714285714*G0_2_0 - 0.289285714285714*G0_2_1 - 0.578571428571428*G0_2_2;

2697

A[397] = 0.144642857142857*G0_0_1 + 0.289285714285714*G0_0_2 + 0.144642857142857*G0_1_0 + 0.289285714285714*G0_1_1 + 0.144642857142857*G0_1_2 + 0.289285714285714*G0_2_0 + 0.144642857142857*G0_2_1;

2698

A[398] = 0.289285714285714*G0_0_0 + 0.144642857142857*G0_0_1 + 0.144642857142857*G0_0_2 + 0.144642857142857*G0_1_0 + 0.289285714285714*G0_1_2 + 0.144642857142857*G0_2_0 + 0.289285714285714*G0_2_1;

2699

A[399] = 0.578571428571428*G0_0_0 + 0.289285714285715*G0_0_1 + 0.289285714285715*G0_0_2 + 0.289285714285715*G0_1_0 + 0.578571428571428*G0_1_1 + 0.289285714285714*G0_1_2 + 0.289285714285715*G0_2_0 + 0.289285714285714*G0_2_1 + 0.578571428571429*G0_2_2;

2700

}

2701

2702

};

2703

2704

/// This class defines the interface for the assembly of the global

2705

/// tensor corresponding to a form with r + n arguments, that is, a

2706

/// mapping

2707

///

2708

/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R

2709

///

2710

/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r

2711

/// global tensor A is defined by

2712

///

2713

/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),

2714

///

2715

/// where each argument Vj represents the application to the

2716

/// sequence of basis functions of Vj and w1, w2, ..., wn are given

2717

/// fixed functions (coefficients).

2718

2719

class UFC_Poisson3D_3BilinearForm: public ufc::form

2720

{

2721

public:

2722

2723

/// Constructor

2724

UFC_Poisson3D_3BilinearForm() : ufc::form()

2725

{

2726

// Do nothing

2727

}

2728

2729

/// Destructor

2730

virtual ~UFC_Poisson3D_3BilinearForm()

2731

{

2732

// Do nothing

2733

}

2734

2735

/// Return a string identifying the form

2736

virtual const char* signature() const

2737

{

2738

return "(dXa0/dxb0)(dXa1/dxb0) | ((d/dXa0)vi0)*((d/dXa1)vi1)*dX(0)";

2739

}

2740

2741

/// Return the rank of the global tensor (r)

2742

virtual unsigned int rank() const

2743

{

2744

return 2;

2745

}

2746

2747

/// Return the number of coefficients (n)

2748

virtual unsigned int num_coefficients() const

2749

{

2750

return 0;

2751

}

2752

2753

/// Return the number of cell integrals

2754

virtual unsigned int num_cell_integrals() const

2755

{

2756

return 1;

2757

}

2758

2759

/// Return the number of exterior facet integrals

2760

virtual unsigned int num_exterior_facet_integrals() const

2761

{

2762

return 0;

2763

}

2764

2765

/// Return the number of interior facet integrals

2766

virtual unsigned int num_interior_facet_integrals() const

2767

{

2768

return 0;

2769

}

2770

2771

/// Create a new finite element for argument function i

2772

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

2773

{

2774

switch ( i )

2775

{

2776

case 0:

2777

return new UFC_Poisson3D_3BilinearForm_finite_element_0();

2778

break;

2779

case 1:

2780

return new UFC_Poisson3D_3BilinearForm_finite_element_1();

2781

break;

2782

}

2783

return 0;

2784

}

2785

2786

/// Create a new dof map for argument function i

2787

virtual ufc::dof_map* create_dof_map(unsigned int i) const

2788

{

2789

switch ( i )

2790

{

2791

case 0:

2792

return new UFC_Poisson3D_3BilinearForm_dof_map_0();

2793

break;

2794

case 1:

2795

return new UFC_Poisson3D_3BilinearForm_dof_map_1();

2796

break;

2797

}

2798

return 0;

2799

}

2800

2801

/// Create a new cell integral on sub domain i

2802

virtual ufc::cell_integral* create_cell_integral(unsigned int i) const

2803

{

2804

return new UFC_Poisson3D_3BilinearForm_cell_integral_0();

2805

}

2806

2807

/// Create a new exterior facet integral on sub domain i

2808

virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const

2809

{

2810

return 0;

2811

}

2812

2813

/// Create a new interior facet integral on sub domain i

2814

virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const

2815

{

2816

return 0;

2817

}

2818

2819

};

2820

2821

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

2822

2823

class UFC_Poisson3D_3LinearForm_finite_element_0: public ufc::finite_element

2824

{

2825

public:

2826

2827

/// Constructor

2828

UFC_Poisson3D_3LinearForm_finite_element_0() : ufc::finite_element()

2829

{

2830

// Do nothing

2831

}

2832

2833

/// Destructor

2834

virtual ~UFC_Poisson3D_3LinearForm_finite_element_0()

2835

{

2836

// Do nothing

2837

}

2838

2839

/// Return a string identifying the finite element

2840

virtual const char* signature() const

2841

{

2842

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

2843

}

2844

2845

/// Return the cell shape

2846

virtual ufc::shape cell_shape() const

2847

{

2848

return ufc::tetrahedron;

2849

}

2850

2851

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

2852

virtual unsigned int space_dimension() const

2853

{

2854

return 20;

2855

}

2856

2857

/// Return the rank of the value space

2858

virtual unsigned int value_rank() const

2859

{

2860

return 0;

2861

}

2862

2863

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

2864

virtual unsigned int value_dimension(unsigned int i) const

2865

{

2866

return 1;

2867

}

2868

2869

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

2870

virtual void evaluate_basis(unsigned int i,

2871

double* values,

2872

const double* coordinates,

2873

const ufc::cell& c) const

2874

{

2875

// Extract vertex coordinates

2876

const double * const * element_coordinates = c.coordinates;

2877

2878

// Compute Jacobian of affine map from reference cell

2879

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

2880

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

2881

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

2882

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

2883

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

2884

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

2885

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

2886

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

2887

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

2888

2889

// Compute sub determinants

2890

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

2891

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

2892

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

2893

2894

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

2895

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

2896

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

2897

2898

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

2899

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

2900

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

2901

2902

// Compute determinant of Jacobian

2903

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

2904

2905

// Compute inverse of Jacobian

2906

2907

// Compute constants

2908

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

2909

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

2910

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

2911

2912

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

2913

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

2914

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

2915

2916

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

2917

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

2918

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

2919

2920

// Get coordinates and map to the UFC reference element

2921

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

2922

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

2923

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

2924

2925

// Map coordinates to the reference cube

2926

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

2927

x = 1.0;

2928

else

2929

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

2930

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

2931

y = -1.0;

2932

else

2933

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

2934

z = 2.0 * z - 1.0;

2935

2936

// Reset values

2937

*values = 0;

2938

2939

// Map degree of freedom to element degree of freedom

2940

const unsigned int dof = i;

2941

2942

// Generate scalings

2943

const double scalings_y_0 = 1;

2944

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

2945

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

2946

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

2947

const double scalings_z_0 = 1;

2948

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

2949

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

2950

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

2951

2952

// Compute psitilde_a

2953

const double psitilde_a_0 = 1;

2954

const double psitilde_a_1 = x;

2955

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

2956

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

2957

2958

// Compute psitilde_bs

2959

const double psitilde_bs_0_0 = 1;

2960

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2961

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;

2962

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;

2963

const double psitilde_bs_1_0 = 1;

2964

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2965

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;

2966

const double psitilde_bs_2_0 = 1;

2967

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2968

const double psitilde_bs_3_0 = 1;

2969

2970

// Compute psitilde_cs

2971

const double psitilde_cs_00_0 = 1;

2972

const double psitilde_cs_00_1 = 2*z + 1;

2973

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;

2974

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;

2975

const double psitilde_cs_01_0 = 1;

2976

const double psitilde_cs_01_1 = 3*z + 2;

2977

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;

2978

const double psitilde_cs_02_0 = 1;

2979

const double psitilde_cs_02_1 = 4*z + 3;

2980

const double psitilde_cs_03_0 = 1;

2981

const double psitilde_cs_10_0 = 1;

2982

const double psitilde_cs_10_1 = 3*z + 2;

2983

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;

2984

const double psitilde_cs_11_0 = 1;

2985

const double psitilde_cs_11_1 = 4*z + 3;

2986

const double psitilde_cs_12_0 = 1;

2987

const double psitilde_cs_20_0 = 1;

2988

const double psitilde_cs_20_1 = 4*z + 3;

2989

const double psitilde_cs_21_0 = 1;

2990

const double psitilde_cs_30_0 = 1;

2991

2992

// Compute basisvalues

2993

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

2994

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

2995

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

2996

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

2997

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

2998

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

2999

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

3000

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

3001

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

3002

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

3003

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

3004

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

3005

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

3006

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

3007

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

3008

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

3009

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

3010

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

3011

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

3012

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

3013

3014

// Table(s) of coefficients

3015

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

3016

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3017

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3018

{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, -0.00535714285714286},

3019

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3020

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3021

{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},

3022

{0, 0.0978075995544939, -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},

3023

{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},

3024

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

3025

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3026

{0, -0.0978075995544939, -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},

3027

{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},

3028

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

3029

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3030

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3031

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3032

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3033

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3034

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3035

{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, -0.00535714285714285}};

3036

3037

// Extract relevant coefficients

3038

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

3039

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

3040

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

3041

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

3042

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

3043

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

3044

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

3045

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

3046

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

3047

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

3048

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

3049

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

3050

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

3051

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

3052

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

3053

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

3054

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

3055

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

3056

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

3057

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

3058

3059

// Compute value(s)

3060

*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;

3061

}

3062

3063

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

3064

virtual void evaluate_basis_all(double* values,

3065

const double* coordinates,

3066

const ufc::cell& c) const

3067

{

3068

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

3069

}

3070

3071

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

3072

virtual void evaluate_basis_derivatives(unsigned int i,

3073

unsigned int n,

3074

double* values,

3075

const double* coordinates,

3076

const ufc::cell& c) const

3077

{

3078

// Extract vertex coordinates

3079

const double * const * element_coordinates = c.coordinates;

3080

3081

// Compute Jacobian of affine map from reference cell

3082

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

3083

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

3084

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

3085

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

3086

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

3087

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

3088

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

3089

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

3090

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

3091

3092

// Compute sub determinants

3093

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

3094

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

3095

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

3096

3097

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

3098

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

3099

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

3100

3101

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

3102

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

3103

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

3104

3105

// Compute determinant of Jacobian

3106

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

3107

3108

// Compute inverse of Jacobian

3109

3110

// Compute constants

3111

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

3112

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

3113

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

3114

3115

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

3116

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

3117

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

3118

3119

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

3120

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

3121

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

3122

3123

// Get coordinates and map to the UFC reference element

3124

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

3125

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

3126

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

3127

3128

// Map coordinates to the reference cube

3129

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

3130

x = 1.0;

3131

else

3132

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

3133

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

3134

y = -1.0;

3135

else

3136

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

3137

z = 2.0 * z - 1.0;

3138

3139

// Compute number of derivatives

3140

unsigned int num_derivatives = 1;

3141

3142

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

3143

num_derivatives *= 3;

3144

3145

3146

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

3147

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

3148

3149

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

3150

{

3151

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

3152

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

3153

combinations[j][k] = 0;

3154

}

3155

3156

// Generate combinations of derivatives

3157

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

3158

{

3159

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

3160

{

3161

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

3162

{

3163

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

3164

combinations[row][col] = 0;

3165

else

3166

{

3167

combinations[row][col] += 1;

3168

break;

3169

}

3170

}

3171

}

3172

}

3173

3174

// Compute inverse of Jacobian

3175

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

3176

3177

// Declare transformation matrix

3178

// Declare pointer to two dimensional array and initialise

3179

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

3180

3181

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

3182

{

3183

transform[j] = new double [num_derivatives];

3184

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

3185

transform[j][k] = 1;

3186

}

3187

3188

// Construct transformation matrix

3189

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

3190

{

3191

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

3192

{

3193

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

3194

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

3195

}

3196

}

3197

3198

// Reset values

3199

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

3200

values[j] = 0;

3201

3202

// Map degree of freedom to element degree of freedom

3203

const unsigned int dof = i;

3204

3205

// Generate scalings

3206

const double scalings_y_0 = 1;

3207

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

3208

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

3209

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

3210

const double scalings_z_0 = 1;

3211

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

3212

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

3213

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

3214

3215

// Compute psitilde_a

3216

const double psitilde_a_0 = 1;

3217

const double psitilde_a_1 = x;

3218

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

3219

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

3220

3221

// Compute psitilde_bs

3222

const double psitilde_bs_0_0 = 1;

3223

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3224

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;

3225

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;

3226

const double psitilde_bs_1_0 = 1;

3227

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3228

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;

3229

const double psitilde_bs_2_0 = 1;

3230

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3231

const double psitilde_bs_3_0 = 1;

3232

3233

// Compute psitilde_cs

3234

const double psitilde_cs_00_0 = 1;

3235

const double psitilde_cs_00_1 = 2*z + 1;

3236

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;

3237

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;

3238

const double psitilde_cs_01_0 = 1;

3239

const double psitilde_cs_01_1 = 3*z + 2;

3240

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;

3241

const double psitilde_cs_02_0 = 1;

3242

const double psitilde_cs_02_1 = 4*z + 3;

3243

const double psitilde_cs_03_0 = 1;

3244

const double psitilde_cs_10_0 = 1;

3245

const double psitilde_cs_10_1 = 3*z + 2;

3246

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;

3247

const double psitilde_cs_11_0 = 1;

3248

const double psitilde_cs_11_1 = 4*z + 3;

3249

const double psitilde_cs_12_0 = 1;

3250

const double psitilde_cs_20_0 = 1;

3251

const double psitilde_cs_20_1 = 4*z + 3;

3252

const double psitilde_cs_21_0 = 1;

3253

const double psitilde_cs_30_0 = 1;

3254

3255

// Compute basisvalues

3256

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

3257

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

3258

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

3259

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

3260

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

3261

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

3262

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

3263

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

3264

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

3265

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

3266

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

3267

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

3268

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

3269

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

3270

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

3271

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

3272

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

3273

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

3274

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

3275

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

3276

3277

// Table(s) of coefficients

3278

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

3279

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3280

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3281

{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, -0.00535714285714286},

3282

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3283

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3284

{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},

3285

{0, 0.0978075995544939, -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},

3286

{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},

3287

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

3288

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3289

{0, -0.0978075995544939, -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},

3290

{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},

3291

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

3292

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3293

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3294

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3295

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3296

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3297

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3298

{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, -0.00535714285714285}};

3299

3300

// Interesting (new) part

3301

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

3302

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

3303

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

3304

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

3305

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

3306

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

3307

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

3308

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

3309

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

3310

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

3311

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

3312

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

3313

{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},

3314

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

3315

{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},

3316

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

3317

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

3318

{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},

3319

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

3320

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

3321

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

3322

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

3323

3324

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

3325

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

3326

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

3327

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

3328

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

3329

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

3330

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

3331

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

3332

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

3333

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

3334

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

3335

{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},

3336

{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},

3337

{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},

3338

{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},

3339

{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},

3340

{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},

3341

{-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},

3342

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

3343

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

3344

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

3345

3346

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

3347

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

3348

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

3349

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

3350

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

3351

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

3352

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

3353

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

3354

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

3355

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

3356

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

3357

{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},

3358

{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},

3359

{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},

3360

{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},

3361

{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},

3362

{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},

3363

{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},

3364

{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},

3365

{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},

3366

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

3367

3368

// Compute reference derivatives

3369

// Declare pointer to array of derivatives on FIAT element

3370

double *derivatives = new double [num_derivatives];

3371

3372

// Declare coefficients

3373

double coeff0_0 = 0;

3374

double coeff0_1 = 0;

3375

double coeff0_2 = 0;

3376

double coeff0_3 = 0;

3377

double coeff0_4 = 0;

3378

double coeff0_5 = 0;

3379

double coeff0_6 = 0;

3380

double coeff0_7 = 0;

3381

double coeff0_8 = 0;

3382

double coeff0_9 = 0;

3383

double coeff0_10 = 0;

3384

double coeff0_11 = 0;

3385

double coeff0_12 = 0;

3386

double coeff0_13 = 0;

3387

double coeff0_14 = 0;

3388

double coeff0_15 = 0;

3389

double coeff0_16 = 0;

3390

double coeff0_17 = 0;

3391

double coeff0_18 = 0;

3392

double coeff0_19 = 0;

3393

3394

// Declare new coefficients

3395

double new_coeff0_0 = 0;

3396

double new_coeff0_1 = 0;

3397

double new_coeff0_2 = 0;

3398

double new_coeff0_3 = 0;

3399

double new_coeff0_4 = 0;

3400

double new_coeff0_5 = 0;

3401

double new_coeff0_6 = 0;

3402

double new_coeff0_7 = 0;

3403

double new_coeff0_8 = 0;

3404

double new_coeff0_9 = 0;

3405

double new_coeff0_10 = 0;

3406

double new_coeff0_11 = 0;

3407

double new_coeff0_12 = 0;

3408

double new_coeff0_13 = 0;

3409

double new_coeff0_14 = 0;

3410

double new_coeff0_15 = 0;

3411

double new_coeff0_16 = 0;

3412

double new_coeff0_17 = 0;

3413

double new_coeff0_18 = 0;

3414

double new_coeff0_19 = 0;

3415

3416

// Loop possible derivatives

3417

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

3418

{

3419

// Get values from coefficients array

3420

new_coeff0_0 = coefficients0[dof][0];

3421

new_coeff0_1 = coefficients0[dof][1];

3422

new_coeff0_2 = coefficients0[dof][2];

3423

new_coeff0_3 = coefficients0[dof][3];

3424

new_coeff0_4 = coefficients0[dof][4];

3425

new_coeff0_5 = coefficients0[dof][5];

3426

new_coeff0_6 = coefficients0[dof][6];

3427

new_coeff0_7 = coefficients0[dof][7];

3428

new_coeff0_8 = coefficients0[dof][8];

3429

new_coeff0_9 = coefficients0[dof][9];

3430

new_coeff0_10 = coefficients0[dof][10];

3431

new_coeff0_11 = coefficients0[dof][11];

3432

new_coeff0_12 = coefficients0[dof][12];

3433

new_coeff0_13 = coefficients0[dof][13];

3434

new_coeff0_14 = coefficients0[dof][14];

3435

new_coeff0_15 = coefficients0[dof][15];

3436

new_coeff0_16 = coefficients0[dof][16];

3437

new_coeff0_17 = coefficients0[dof][17];

3438

new_coeff0_18 = coefficients0[dof][18];

3439

new_coeff0_19 = coefficients0[dof][19];

3440

3441

// Loop derivative order

3442

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

3443

{

3444

// Update old coefficients

3445

coeff0_0 = new_coeff0_0;

3446

coeff0_1 = new_coeff0_1;

3447

coeff0_2 = new_coeff0_2;

3448

coeff0_3 = new_coeff0_3;

3449

coeff0_4 = new_coeff0_4;

3450

coeff0_5 = new_coeff0_5;

3451

coeff0_6 = new_coeff0_6;

3452

coeff0_7 = new_coeff0_7;

3453

coeff0_8 = new_coeff0_8;

3454

coeff0_9 = new_coeff0_9;

3455

coeff0_10 = new_coeff0_10;

3456

coeff0_11 = new_coeff0_11;

3457

coeff0_12 = new_coeff0_12;

3458

coeff0_13 = new_coeff0_13;

3459

coeff0_14 = new_coeff0_14;

3460

coeff0_15 = new_coeff0_15;

3461

coeff0_16 = new_coeff0_16;

3462

coeff0_17 = new_coeff0_17;

3463

coeff0_18 = new_coeff0_18;

3464

coeff0_19 = new_coeff0_19;

3465

3466

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

3467

{

3468

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];

3469

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];

3470

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];

3471

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];

3472

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];

3473

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];

3474

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];

3475

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];

3476

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];

3477

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];

3478

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];

3479

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];

3480

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];

3481

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];

3482

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];

3483

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];

3484

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];

3485

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];

3486

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];

3487

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];

3488

}

3489

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

3490

{

3491

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];

3492

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];

3493

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];

3494

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];

3495

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];

3496

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];

3497

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];

3498

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];

3499

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];

3500

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];

3501

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];

3502

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];

3503

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];

3504

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];

3505

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];

3506

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];

3507

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];

3508

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];

3509

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];

3510

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];

3511

}

3512

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

3513

{

3514

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];

3515

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];

3516

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];

3517

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];

3518

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];

3519

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];

3520

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];

3521

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];

3522

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];

3523

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];

3524

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];

3525

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];

3526

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];

3527

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];

3528

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];

3529

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];

3530

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];

3531

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];

3532

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];

3533

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];

3534

}

3535

3536

}

3537

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

3538

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;

3539

}

3540

3541

// Transform derivatives back to physical element

3542

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

3543

{

3544

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

3545

{

3546

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

3547

}

3548

}

3549

// Delete pointer to array of derivatives on FIAT element

3550

delete [] derivatives;

3551

3552

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

3553

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

3554

{

3555

delete [] combinations[row];

3556

delete [] transform[row];

3557

}

3558

3559

delete [] combinations;

3560

delete [] transform;

3561

}

3562

3563

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

3564

virtual void evaluate_basis_derivatives_all(unsigned int n,

3565

double* values,

3566

const double* coordinates,

3567

const ufc::cell& c) const

3568

{

3569

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

3570

}

3571

3572

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

3573

virtual double evaluate_dof(unsigned int i,

3574

const ufc::function& f,

3575

const ufc::cell& c) const

3576

{

3577

// The reference points, direction and weights:

3578

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

3579

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}};

3580

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}}};

3581

3582

const double * const * x = c.coordinates;

3583

double result = 0.0;

3584

// Iterate over the points:

3585

// Evaluate basis functions for affine mapping

3586

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

3587

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

3588

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

3589

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

3590

3591

// Compute affine mapping y = F(X)

3592

double y[3];

3593

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

3594

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

3595

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

3596

3597

// Evaluate function at physical points

3598

double values[1];

3599

f.evaluate(values, y, c);

3600

3601

// Map function values using appropriate mapping

3602

// Affine map: Do nothing

3603

3604

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

3605

3606

// Take directional components

3607

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

3608

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

3609

// Multiply by weights

3610

result *= W[i][0];

3611

3612

return result;

3613

}

3614

3615

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

3616

virtual void evaluate_dofs(double* values,

3617

const ufc::function& f,

3618

const ufc::cell& c) const

3619

{

3620

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

3621

}

3622

3623

/// Interpolate vertex values from dof values

3624

virtual void interpolate_vertex_values(double* vertex_values,

3625

const double* dof_values,

3626

const ufc::cell& c) const

3627

{

3628

// Evaluate at vertices and use affine mapping

3629

vertex_values[0] = dof_values[0];

3630

vertex_values[1] = dof_values[1];

3631

vertex_values[2] = dof_values[2];

3632

vertex_values[3] = dof_values[3];

3633

}

3634

3635

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

3636

virtual unsigned int num_sub_elements() const

3637

{

3638

return 1;

3639

}

3640

3641

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

3642

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

3643

{

3644

return new UFC_Poisson3D_3LinearForm_finite_element_0();

3645

}

3646

3647

};

3648

3649

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

3650

3651

class UFC_Poisson3D_3LinearForm_finite_element_1: public ufc::finite_element

3652

{

3653

public:

3654

3655

/// Constructor

3656

UFC_Poisson3D_3LinearForm_finite_element_1() : ufc::finite_element()

3657

{

3658

// Do nothing

3659

}

3660

3661

/// Destructor

3662

virtual ~UFC_Poisson3D_3LinearForm_finite_element_1()

3663

{

3664

// Do nothing

3665

}

3666

3667

/// Return a string identifying the finite element

3668

virtual const char* signature() const

3669

{

3670

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

3671

}

3672

3673

/// Return the cell shape

3674

virtual ufc::shape cell_shape() const

3675

{

3676

return ufc::tetrahedron;

3677

}

3678

3679

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

3680

virtual unsigned int space_dimension() const

3681

{

3682

return 20;

3683

}

3684

3685

/// Return the rank of the value space

3686

virtual unsigned int value_rank() const

3687

{

3688

return 0;

3689

}

3690

3691

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

3692

virtual unsigned int value_dimension(unsigned int i) const

3693

{

3694

return 1;

3695

}

3696

3697

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

3698

virtual void evaluate_basis(unsigned int i,

3699

double* values,

3700

const double* coordinates,

3701

const ufc::cell& c) const

3702

{

3703

// Extract vertex coordinates

3704

const double * const * element_coordinates = c.coordinates;

3705

3706

// Compute Jacobian of affine map from reference cell

3707

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

3708

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

3709

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

3710

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

3711

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

3712

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

3713

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

3714

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

3715

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

3716

3717

// Compute sub determinants

3718

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

3719

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

3720

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

3721

3722

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

3723

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

3724

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

3725

3726

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

3727

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

3728

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

3729

3730

// Compute determinant of Jacobian

3731

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

3732

3733

// Compute inverse of Jacobian

3734

3735

// Compute constants

3736

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

3737

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

3738

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

3739

3740

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

3741

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

3742

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

3743

3744

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

3745

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

3746

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

3747

3748

// Get coordinates and map to the UFC reference element

3749

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

3750

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

3751

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

3752

3753

// Map coordinates to the reference cube

3754

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

3755

x = 1.0;

3756

else

3757

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

3758

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

3759

y = -1.0;

3760

else

3761

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

3762

z = 2.0 * z - 1.0;

3763

3764

// Reset values

3765

*values = 0;

3766

3767

// Map degree of freedom to element degree of freedom

3768

const unsigned int dof = i;

3769

3770

// Generate scalings

3771

const double scalings_y_0 = 1;

3772

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

3773

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

3774

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

3775

const double scalings_z_0 = 1;

3776

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

3777

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

3778

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

3779

3780

// Compute psitilde_a

3781

const double psitilde_a_0 = 1;

3782

const double psitilde_a_1 = x;

3783

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

3784

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

3785

3786

// Compute psitilde_bs

3787

const double psitilde_bs_0_0 = 1;

3788

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3789

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;

3790

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;

3791

const double psitilde_bs_1_0 = 1;

3792

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3793

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;

3794

const double psitilde_bs_2_0 = 1;

3795

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3796

const double psitilde_bs_3_0 = 1;

3797

3798

// Compute psitilde_cs

3799

const double psitilde_cs_00_0 = 1;

3800

const double psitilde_cs_00_1 = 2*z + 1;

3801

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;

3802

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;

3803

const double psitilde_cs_01_0 = 1;

3804

const double psitilde_cs_01_1 = 3*z + 2;

3805

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;

3806

const double psitilde_cs_02_0 = 1;

3807

const double psitilde_cs_02_1 = 4*z + 3;

3808

const double psitilde_cs_03_0 = 1;

3809

const double psitilde_cs_10_0 = 1;

3810

const double psitilde_cs_10_1 = 3*z + 2;

3811

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;

3812

const double psitilde_cs_11_0 = 1;

3813

const double psitilde_cs_11_1 = 4*z + 3;

3814

const double psitilde_cs_12_0 = 1;

3815

const double psitilde_cs_20_0 = 1;

3816

const double psitilde_cs_20_1 = 4*z + 3;

3817

const double psitilde_cs_21_0 = 1;

3818

const double psitilde_cs_30_0 = 1;

3819

3820

// Compute basisvalues

3821

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

3822

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

3823

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

3824

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

3825

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

3826

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

3827

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

3828

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

3829

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

3830

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

3831

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

3832

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

3833

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

3834

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

3835

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

3836

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

3837

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

3838

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

3839

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

3840

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

3841

3842

// Table(s) of coefficients

3843

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

3844

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3845

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3846

{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, -0.00535714285714286},

3847

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3848

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

3849

{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},

3850

{0, 0.0978075995544939, -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},

3851

{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},

3852

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

3853

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3854

{0, -0.0978075995544939, -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},

3855

{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},

3856

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

3857

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3858

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3859

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

3860

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3861

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3862

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

3863

{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, -0.00535714285714285}};

3864

3865

// Extract relevant coefficients

3866

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

3867

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

3868

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

3869

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

3870

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

3871

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

3872

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

3873

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

3874

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

3875

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

3876

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

3877

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

3878

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

3879

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

3880

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

3881

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

3882

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

3883

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

3884

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

3885

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

3886

3887

// Compute value(s)

3888

*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;

3889

}

3890

3891

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

3892

virtual void evaluate_basis_all(double* values,

3893

const double* coordinates,

3894

const ufc::cell& c) const

3895

{

3896

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

3897

}

3898

3899

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

3900

virtual void evaluate_basis_derivatives(unsigned int i,

3901

unsigned int n,

3902

double* values,

3903

const double* coordinates,

3904

const ufc::cell& c) const

3905

{

3906

// Extract vertex coordinates

3907

const double * const * element_coordinates = c.coordinates;

3908

3909

// Compute Jacobian of affine map from reference cell

3910

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

3911

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

3912

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

3913

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

3914

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

3915

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

3916

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

3917

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

3918

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

3919

3920

// Compute sub determinants

3921

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

3922

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

3923

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

3924

3925

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

3926

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

3927

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

3928

3929

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

3930

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

3931

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

3932

3933

// Compute determinant of Jacobian

3934

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

3935

3936

// Compute inverse of Jacobian

3937

3938

// Compute constants

3939

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

3940

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

3941

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

3942

3943

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

3944

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

3945

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

3946

3947

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

3948

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

3949

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

3950

3951

// Get coordinates and map to the UFC reference element

3952

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

3953

double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;

3954

double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;

3955

3956

// Map coordinates to the reference cube

3957

if (std::abs(y + z - 1.0) < 1e-14)

3958

x = 1.0;

3959

else

3960

x = -2.0 * x/(y + z - 1.0) - 1.0;

3961

if (std::abs(z - 1.0) < 1e-14)

3962

y = -1.0;

3963

else

3964

y = 2.0 * y/(1.0 - z) - 1.0;

3965

z = 2.0 * z - 1.0;

3966

3967

// Compute number of derivatives

3968

unsigned int num_derivatives = 1;

3969

3970

for (unsigned int j = 0; j < n; j++)

3971

num_derivatives *= 3;

3972

3973

3974

// Declare pointer to two dimensional array that holds combinations of derivatives and initialise

3975

unsigned int **combinations = new unsigned int *[num_derivatives];

3976

3977

for (unsigned int j = 0; j < num_derivatives; j++)

3978

{

3979

combinations[j] = new unsigned int [n];

3980

for (unsigned int k = 0; k < n; k++)

3981

combinations[j][k] = 0;

3982

}

3983

3984

// Generate combinations of derivatives

3985

for (unsigned int row = 1; row < num_derivatives; row++)

3986

{

3987

for (unsigned int num = 0; num < row; num++)

3988

{

3989

for (unsigned int col = n-1; col+1 > 0; col--)

3990

{

3991

if (combinations[row][col] + 1 > 2)

3992

combinations[row][col] = 0;

3993

else

3994

{

3995

combinations[row][col] += 1;

3996

break;

3997

}

3998

}

3999

}

4000

}

4001

4002

// Compute inverse of Jacobian

4003

const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};

4004

4005

// Declare transformation matrix

4006

// Declare pointer to two dimensional array and initialise

4007

double **transform = new double *[num_derivatives];

4008

4009

for (unsigned int j = 0; j < num_derivatives; j++)

4010

{

4011

transform[j] = new double [num_derivatives];

4012

for (unsigned int k = 0; k < num_derivatives; k++)

4013

transform[j][k] = 1;

4014

}

4015

4016

// Construct transformation matrix

4017

for (unsigned int row = 0; row < num_derivatives; row++)

4018

{

4019

for (unsigned int col = 0; col < num_derivatives; col++)

4020

{

4021

for (unsigned int k = 0; k < n; k++)

4022

transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];

4023

}

4024

}

4025

4026

// Reset values

4027

for (unsigned int j = 0; j < 1*num_derivatives; j++)

4028

values[j] = 0;

4029

4030

// Map degree of freedom to element degree of freedom

4031

const unsigned int dof = i;

4032

4033

// Generate scalings

4034

const double scalings_y_0 = 1;

4035

const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);

4036

const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);

4037

const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);

4038

const double scalings_z_0 = 1;

4039

const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);

4040

const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);

4041

const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);

4042

4043

// Compute psitilde_a

4044

const double psitilde_a_0 = 1;

4045

const double psitilde_a_1 = x;

4046

const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;

4047

const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;

4048

4049

// Compute psitilde_bs

4050

const double psitilde_bs_0_0 = 1;

4051

const double psitilde_bs_0_1 = 1.5*y + 0.5;

4052

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;

4053

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;

4054

const double psitilde_bs_1_0 = 1;

4055

const double psitilde_bs_1_1 = 2.5*y + 1.5;

4056

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;

4057

const double psitilde_bs_2_0 = 1;

4058

const double psitilde_bs_2_1 = 3.5*y + 2.5;

4059

const double psitilde_bs_3_0 = 1;

4060

4061

// Compute psitilde_cs

4062

const double psitilde_cs_00_0 = 1;

4063

const double psitilde_cs_00_1 = 2*z + 1;

4064

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;

4065

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;

4066

const double psitilde_cs_01_0 = 1;

4067

const double psitilde_cs_01_1 = 3*z + 2;

4068

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;

4069

const double psitilde_cs_02_0 = 1;

4070

const double psitilde_cs_02_1 = 4*z + 3;

4071

const double psitilde_cs_03_0 = 1;

4072

const double psitilde_cs_10_0 = 1;

4073

const double psitilde_cs_10_1 = 3*z + 2;

4074

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;

4075

const double psitilde_cs_11_0 = 1;

4076

const double psitilde_cs_11_1 = 4*z + 3;

4077

const double psitilde_cs_12_0 = 1;

4078

const double psitilde_cs_20_0 = 1;

4079

const double psitilde_cs_20_1 = 4*z + 3;

4080

const double psitilde_cs_21_0 = 1;

4081

const double psitilde_cs_30_0 = 1;

4082

4083

// Compute basisvalues

4084

const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;

4085

const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;

4086

const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;

4087

const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;

4088

const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;

4089

const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;

4090

const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;

4091

const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;

4092

const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;

4093

const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;

4094

const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;

4095

const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;

4096

const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;

4097

const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;

4098

const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;

4099

const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;

4100

const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;

4101

const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;

4102

const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;

4103

const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;

4104

4105

// Table(s) of coefficients

4106

const static double coefficients0[20][20] = \

4107

{{0.0288675134594813, 0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.0066815310478106, 0.00472455591261534, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

4108

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261535, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

4109

{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, -0.00535714285714286},

4110

{0.0288675134594812, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

4111

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},

4112

{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},

4113

{0, 0.0978075995544939, -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},

4114

{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},

4115

{0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -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},

4116

{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, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

4117

{0, -0.0978075995544939, -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},

4118

{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},

4119

{0, -0.0978075995544939, -0.0790569415042095, -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, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},

4120

{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, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

4121

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.042521003213538, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197612, -0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

4122

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197612, 0.00437408882639853, -0.00757614408414158, -0.00535714285714286},

4123

{0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

4124

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

4125

{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},

4126

{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, -0.00535714285714285}};

4127

4128

// Interesting (new) part

4129

// Tables of derivatives of the polynomial base (transpose)

4130

const static double dmats0[20][20] = \

4131

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4132

{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4133

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4134

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4135

{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4136

{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4137

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4138

{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4139

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4140

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4141

{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},

4142

{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4143

{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},

4144

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4145

{0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4146

{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},

4147

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4148

{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4149

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4150

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4151

4152

const static double dmats1[20][20] = \

4153

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4154

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4155

{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4156

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4157

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4158

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4159

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4160

{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4161

{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4162

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4163

{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},

4164

{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},

4165

{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},

4166

{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},

4167

{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},

4168

{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},

4169

{-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},

4170

{1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4171

{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4172

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4173

4174

const static double dmats2[20][20] = \

4175

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4176

{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4177

{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4178

{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4179

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4180

{2.29128784747792, 1.44913767461895, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4181

{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4182

{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4183

{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4184

{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4185

{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},

4186

{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},

4187

{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},

4188

{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},

4189

{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},

4190

{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},

4191

{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},

4192

{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},

4193

{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},

4194

{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4195

4196

// Compute reference derivatives

4197

// Declare pointer to array of derivatives on FIAT element

4198

double *derivatives = new double [num_derivatives];

4199

4200

// Declare coefficients

4201

double coeff0_0 = 0;

4202

double coeff0_1 = 0;

4203

double coeff0_2 = 0;

4204

double coeff0_3 = 0;

4205

double coeff0_4 = 0;

4206

double coeff0_5 = 0;

4207

double coeff0_6 = 0;

4208

double coeff0_7 = 0;

4209

double coeff0_8 = 0;

4210

double coeff0_9 = 0;

4211

double coeff0_10 = 0;

4212

double coeff0_11 = 0;

4213

double coeff0_12 = 0;

4214

double coeff0_13 = 0;

4215

double coeff0_14 = 0;

4216

double coeff0_15 = 0;

4217

double coeff0_16 = 0;

4218

double coeff0_17 = 0;

4219

double coeff0_18 = 0;

4220

double coeff0_19 = 0;

4221

4222

// Declare new coefficients

4223

double new_coeff0_0 = 0;

4224

double new_coeff0_1 = 0;

4225

double new_coeff0_2 = 0;

4226

double new_coeff0_3 = 0;

4227

double new_coeff0_4 = 0;

4228

double new_coeff0_5 = 0;

4229

double new_coeff0_6 = 0;

4230

double new_coeff0_7 = 0;

4231

double new_coeff0_8 = 0;

4232

double new_coeff0_9 = 0;

4233

double new_coeff0_10 = 0;

4234

double new_coeff0_11 = 0;

4235

double new_coeff0_12 = 0;

4236

double new_coeff0_13 = 0;

4237

double new_coeff0_14 = 0;

4238

double new_coeff0_15 = 0;

4239

double new_coeff0_16 = 0;

4240

double new_coeff0_17 = 0;

4241

double new_coeff0_18 = 0;

4242

double new_coeff0_19 = 0;

4243

4244

// Loop possible derivatives

4245

for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)

4246

{

4247

// Get values from coefficients array

4248

new_coeff0_0 = coefficients0[dof][0];

4249

new_coeff0_1 = coefficients0[dof][1];

4250

new_coeff0_2 = coefficients0[dof][2];

4251

new_coeff0_3 = coefficients0[dof][3];

4252

new_coeff0_4 = coefficients0[dof][4];

4253

new_coeff0_5 = coefficients0[dof][5];

4254

new_coeff0_6 = coefficients0[dof][6];

4255

new_coeff0_7 = coefficients0[dof][7];

4256

new_coeff0_8 = coefficients0[dof][8];

4257

new_coeff0_9 = coefficients0[dof][9];

4258

new_coeff0_10 = coefficients0[dof][10];

4259

new_coeff0_11 = coefficients0[dof][11];

4260

new_coeff0_12 = coefficients0[dof][12];

4261

new_coeff0_13 = coefficients0[dof][13];

4262

new_coeff0_14 = coefficients0[dof][14];

4263

new_coeff0_15 = coefficients0[dof][15];

4264

new_coeff0_16 = coefficients0[dof][16];

4265

new_coeff0_17 = coefficients0[dof][17];

4266

new_coeff0_18 = coefficients0[dof][18];

4267

new_coeff0_19 = coefficients0[dof][19];

4268

4269

// Loop derivative order

4270

for (unsigned int j = 0; j < n; j++)

4271

{

4272

// Update old coefficients

4273

coeff0_0 = new_coeff0_0;

4274

coeff0_1 = new_coeff0_1;

4275

coeff0_2 = new_coeff0_2;

4276

coeff0_3 = new_coeff0_3;

4277

coeff0_4 = new_coeff0_4;

4278

coeff0_5 = new_coeff0_5;

4279

coeff0_6 = new_coeff0_6;

4280

coeff0_7 = new_coeff0_7;

4281

coeff0_8 = new_coeff0_8;

4282

coeff0_9 = new_coeff0_9;

4283

coeff0_10 = new_coeff0_10;

4284

coeff0_11 = new_coeff0_11;

4285

coeff0_12 = new_coeff0_12;

4286

coeff0_13 = new_coeff0_13;

4287

coeff0_14 = new_coeff0_14;

4288

coeff0_15 = new_coeff0_15;

4289

coeff0_16 = new_coeff0_16;

4290

coeff0_17 = new_coeff0_17;

4291

coeff0_18 = new_coeff0_18;

4292

coeff0_19 = new_coeff0_19;

4293

4294

if(combinations[deriv_num][j] == 0)

4295

{

4296

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];

4297

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];

4298

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];

4299

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];

4300

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];

4301

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];

4302

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];

4303

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];

4304

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];

4305

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];

4306

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];

4307

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];

4308

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];

4309

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];

4310

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];

4311

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];

4312

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];

4313

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];

4314

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];

4315

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];

4316

}

4317

if(combinations[deriv_num][j] == 1)

4318

{

4319

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];

4320

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];

4321

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];

4322

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];

4323

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];

4324

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];

4325

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];

4326

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];

4327

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];

4328

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];

4329

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];

4330

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];

4331

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];

4332

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];

4333

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];

4334

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];

4335

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];

4336

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];

4337

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];

4338

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];

4339

}

4340

if(combinations[deriv_num][j] == 2)

4341

{

4342

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];

4343

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];

4344

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];

4345

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];

4346

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];

4347

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];

4348

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];

4349

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];

4350

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];

4351

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];

4352

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];

4353

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];

4354

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];

4355

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];

4356

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];

4357

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];

4358

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];

4359

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];

4360

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];

4361

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];

4362

}

4363

4364

}

4365

// Compute derivatives on reference element as dot product of coefficients and basisvalues

4366

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;

4367

}

4368

4369

// Transform derivatives back to physical element

4370

for (unsigned int row = 0; row < num_derivatives; row++)

4371

{

4372

for (unsigned int col = 0; col < num_derivatives; col++)

4373

{

4374

values[row] += transform[row][col]*derivatives[col];

4375

}

4376

}

4377

// Delete pointer to array of derivatives on FIAT element

4378

delete [] derivatives;

4379

4380

// Delete pointer to array of combinations of derivatives and transform

4381

for (unsigned int row = 0; row < num_derivatives; row++)

4382

{

4383

delete [] combinations[row];

4384

delete [] transform[row];

4385

}

4386

4387

delete [] combinations;

4388

delete [] transform;

4389

}

4390

4391

/// Evaluate order n derivatives of all basis functions at given point in cell

4392

virtual void evaluate_basis_derivatives_all(unsigned int n,

4393

double* values,

4394

const double* coordinates,

4395

const ufc::cell& c) const

4396

{

4397

throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");

4398

}

4399

4400

/// Evaluate linear functional for dof i on the function f

4401

virtual double evaluate_dof(unsigned int i,

4402

const ufc::function& f,

4403

const ufc::cell& c) const

4404

{

4405

// The reference points, direction and weights:

4406

const static double X[20][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 0, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0}}};

4407

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}};

4408

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}}};

4409

4410

const double * const * x = c.coordinates;

4411

double result = 0.0;

4412

// Iterate over the points:

4413

// Evaluate basis functions for affine mapping

4414

const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];

4415

const double w1 = X[i][0][0];

4416

const double w2 = X[i][0][1];

4417

const double w3 = X[i][0][2];

4418

4419

// Compute affine mapping y = F(X)

4420

double y[3];

4421

y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];

4422

y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];

4423

y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];

4424

4425

// Evaluate function at physical points

4426

double values[1];

4427

f.evaluate(values, y, c);

4428

4429

// Map function values using appropriate mapping

4430

// Affine map: Do nothing

4431

4432

// Note that we do not map the weights (yet).

4433

4434

// Take directional components

4435

for(int k = 0; k < 1; k++)

4436

result += values[k]*D[i][0][k];

4437

// Multiply by weights

4438

result *= W[i][0];

4439

4440

return result;

4441

}

4442

4443

/// Evaluate linear functionals for all dofs on the function f

4444

virtual void evaluate_dofs(double* values,

4445

const ufc::function& f,

4446

const ufc::cell& c) const

4447

{

4448

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4449

}

4450

4451

/// Interpolate vertex values from dof values

4452

virtual void interpolate_vertex_values(double* vertex_values,

4453

const double* dof_values,

4454

const ufc::cell& c) const

4455

{

4456

// Evaluate at vertices and use affine mapping

4457

vertex_values[0] = dof_values[0];

4458

vertex_values[1] = dof_values[1];

4459

vertex_values[2] = dof_values[2];

4460

vertex_values[3] = dof_values[3];

4461

}

4462

4463

/// Return the number of sub elements (for a mixed element)

4464

virtual unsigned int num_sub_elements() const

4465

{

4466

return 1;

4467

}

4468

4469

/// Create a new finite element for sub element i (for a mixed element)

4470

virtual ufc::finite_element* create_sub_element(unsigned int i) const

4471

{

4472

return new UFC_Poisson3D_3LinearForm_finite_element_1();

4473

}

4474

4475

};

4476

4477

/// This class defines the interface for a local-to-global mapping of

4478

/// degrees of freedom (dofs).

4479

4480

class UFC_Poisson3D_3LinearForm_dof_map_0: public ufc::dof_map

4481

{

4482

private:

4483

4484

unsigned int __global_dimension;

4485

4486

public:

4487

4488

/// Constructor

4489

UFC_Poisson3D_3LinearForm_dof_map_0() : ufc::dof_map()

4490

{

4491

__global_dimension = 0;

4492

}

4493

4494

/// Destructor

4495

virtual ~UFC_Poisson3D_3LinearForm_dof_map_0()

4496

{

4497

// Do nothing

4498

}

4499

4500

/// Return a string identifying the dof map

4501

virtual const char* signature() const

4502

{

4503

return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";

4504

}

4505

4506

/// Return true iff mesh entities of topological dimension d are needed

4507

virtual bool needs_mesh_entities(unsigned int d) const

4508

{

4509

switch ( d )

4510

{

4511

case 0:

4512

return true;

4513

break;

4514

case 1:

4515

return true;

4516

break;

4517

case 2:

4518

return true;

4519

break;

4520

case 3:

4521

return false;

4522

break;

4523

}

4524

return false;

4525

}

4526

4527

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4528

virtual bool init_mesh(const ufc::mesh& m)

4529

{

4530

__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];

4531

return false;

4532

}

4533

4534

/// Initialize dof map for given cell

4535

virtual void init_cell(const ufc::mesh& m,

4536

const ufc::cell& c)

4537

{

4538

// Do nothing

4539

}

4540

4541

/// Finish initialization of dof map for cells

4542

virtual void init_cell_finalize()

4543

{

4544

// Do nothing

4545

}

4546

4547

/// Return the dimension of the global finite element function space

4548

virtual unsigned int global_dimension() const

4549

{

4550

return __global_dimension;

4551

}

4552

4553

/// Return the dimension of the local finite element function space

4554

virtual unsigned int local_dimension() const

4555

{

4556

return 20;

4557

}

4558

4559

// Return the geometric dimension of the coordinates this dof map provides

4560

virtual unsigned int geometric_dimension() const

4561

{

4562

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4563

}

4564

4565

/// Return the number of dofs on each cell facet

4566

virtual unsigned int num_facet_dofs() const

4567

{

4568

return 10;

4569

}

4570

4571

/// Return the number of dofs associated with each cell entity of dimension d

4572

virtual unsigned int num_entity_dofs(unsigned int d) const

4573

{

4574

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4575

}

4576

4577

/// Tabulate the local-to-global mapping of dofs on a cell

4578

virtual void tabulate_dofs(unsigned int* dofs,

4579

const ufc::mesh& m,

4580

const ufc::cell& c) const

4581

{

4582

dofs[0] = c.entity_indices[0][0];

4583

dofs[1] = c.entity_indices[0][1];

4584

dofs[2] = c.entity_indices[0][2];

4585

dofs[3] = c.entity_indices[0][3];

4586

unsigned int offset = m.num_entities[0];

4587

dofs[4] = offset + 2*c.entity_indices[1][0];

4588

dofs[5] = offset + 2*c.entity_indices[1][0] + 1;

4589

dofs[6] = offset + 2*c.entity_indices[1][1];

4590

dofs[7] = offset + 2*c.entity_indices[1][1] + 1;

4591

dofs[8] = offset + 2*c.entity_indices[1][2];

4592

dofs[9] = offset + 2*c.entity_indices[1][2] + 1;

4593

dofs[10] = offset + 2*c.entity_indices[1][3];

4594

dofs[11] = offset + 2*c.entity_indices[1][3] + 1;

4595

dofs[12] = offset + 2*c.entity_indices[1][4];

4596

dofs[13] = offset + 2*c.entity_indices[1][4] + 1;

4597

dofs[14] = offset + 2*c.entity_indices[1][5];

4598

dofs[15] = offset + 2*c.entity_indices[1][5] + 1;

4599

offset = offset + 2*m.num_entities[1];

4600

dofs[16] = offset + c.entity_indices[2][0];

4601

dofs[17] = offset + c.entity_indices[2][1];

4602

dofs[18] = offset + c.entity_indices[2][2];

4603

dofs[19] = offset + c.entity_indices[2][3];

4604

}

4605

4606

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4607

virtual void tabulate_facet_dofs(unsigned int* dofs,

4608

unsigned int facet) const

4609

{

4610

switch ( facet )

4611

{

4612

case 0:

4613

dofs[0] = 1;

4614

dofs[1] = 2;

4615

dofs[2] = 3;

4616

dofs[3] = 4;

4617

dofs[4] = 5;

4618

dofs[5] = 6;

4619

dofs[6] = 7;

4620

dofs[7] = 8;

4621

dofs[8] = 9;

4622

dofs[9] = 16;

4623

break;

4624

case 1:

4625

dofs[0] = 0;

4626

dofs[1] = 2;

4627

dofs[2] = 3;

4628

dofs[3] = 4;

4629

dofs[4] = 5;

4630

dofs[5] = 10;

4631

dofs[6] = 11;

4632

dofs[7] = 12;

4633

dofs[8] = 13;

4634

dofs[9] = 17;

4635

break;

4636

case 2:

4637

dofs[0] = 0;

4638

dofs[1] = 1;

4639

dofs[2] = 3;

4640

dofs[3] = 6;

4641

dofs[4] = 7;

4642

dofs[5] = 10;

4643

dofs[6] = 11;

4644

dofs[7] = 14;

4645

dofs[8] = 15;

4646

dofs[9] = 18;

4647

break;

4648

case 3:

4649

dofs[0] = 0;

4650

dofs[1] = 1;

4651

dofs[2] = 2;

4652

dofs[3] = 8;

4653

dofs[4] = 9;

4654

dofs[5] = 12;

4655

dofs[6] = 13;

4656

dofs[7] = 14;

4657

dofs[8] = 15;

4658

dofs[9] = 19;

4659

break;

4660

}

4661

}

4662

4663

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4664

virtual void tabulate_entity_dofs(unsigned int* dofs,

4665

unsigned int d, unsigned int i) const

4666

{

4667

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4668

}

4669

4670

/// Tabulate the coordinates of all dofs on a cell

4671

virtual void tabulate_coordinates(double** coordinates,

4672

const ufc::cell& c) const

4673

{

4674

const double * const * x = c.coordinates;

4675

coordinates[0][0] = x[0][0];

4676

coordinates[0][1] = x[0][1];

4677

coordinates[0][2] = x[0][2];

4678

coordinates[1][0] = x[1][0];

4679

coordinates[1][1] = x[1][1];

4680

coordinates[1][2] = x[1][2];

4681

coordinates[2][0] = x[2][0];

4682

coordinates[2][1] = x[2][1];

4683

coordinates[2][2] = x[2][2];

4684

coordinates[3][0] = x[3][0];

4685

coordinates[3][1] = x[3][1];

4686

coordinates[3][2] = x[3][2];

4687

coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

4688

coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

4689

coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

4690

coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

4691

coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

4692

coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

4693

coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

4694

coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

4695

coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

4696

coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

4697

coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

4698

coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

4699

coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];

4700

coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];

4701

coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];

4702

coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4703

coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4704

coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4705

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4706

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4707

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4708

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

4709

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

4710

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

4711

coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4712

coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4713

coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4714

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4715

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4716

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4717

coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4718

coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4719

coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4720

coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4721

coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

4722

coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

4723

coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4724

coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4725

coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4726

coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4727

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4728

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4729

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

4730

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

4731

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

4732

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

4733

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

4734

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

4735

}

4736

4737

/// Return the number of sub dof maps (for a mixed element)

4738

virtual unsigned int num_sub_dof_maps() const

4739

{

4740

return 1;

4741

}

4742

4743

/// Create a new dof_map for sub dof map i (for a mixed element)

4744

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

4745

{

4746

return new UFC_Poisson3D_3LinearForm_dof_map_0();

4747

}

4748

4749

};

4750

4751

/// This class defines the interface for a local-to-global mapping of

4752

/// degrees of freedom (dofs).

4753

4754

class UFC_Poisson3D_3LinearForm_dof_map_1: public ufc::dof_map

4755

{

4756

private:

4757

4758

unsigned int __global_dimension;

4759

4760

public:

4761

4762

/// Constructor

4763

UFC_Poisson3D_3LinearForm_dof_map_1() : ufc::dof_map()

4764

{

4765

__global_dimension = 0;

4766

}

4767

4768

/// Destructor

4769

virtual ~UFC_Poisson3D_3LinearForm_dof_map_1()

4770

{

4771

// Do nothing

4772

}

4773

4774

/// Return a string identifying the dof map

4775

virtual const char* signature() const

4776

{

4777

return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";

4778

}

4779

4780

/// Return true iff mesh entities of topological dimension d are needed

4781

virtual bool needs_mesh_entities(unsigned int d) const

4782

{

4783

switch ( d )

4784

{

4785

case 0:

4786

return true;

4787

break;

4788

case 1:

4789

return true;

4790

break;

4791

case 2:

4792

return true;

4793

break;

4794

case 3:

4795

return false;

4796

break;

4797

}

4798

return false;

4799

}

4800

4801

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4802

virtual bool init_mesh(const ufc::mesh& m)

4803

{

4804

__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];

4805

return false;

4806

}

4807

4808

/// Initialize dof map for given cell

4809

virtual void init_cell(const ufc::mesh& m,

4810

const ufc::cell& c)

4811

{

4812

// Do nothing

4813

}

4814

4815

/// Finish initialization of dof map for cells

4816

virtual void init_cell_finalize()

4817

{

4818

// Do nothing

4819

}

4820

4821

/// Return the dimension of the global finite element function space

4822

virtual unsigned int global_dimension() const

4823

{

4824

return __global_dimension;

4825

}

4826

4827

/// Return the dimension of the local finite element function space

4828

virtual unsigned int local_dimension() const

4829

{

4830

return 20;

4831

}

4832

4833

// Return the geometric dimension of the coordinates this dof map provides

4834

virtual unsigned int geometric_dimension() const

4835

{

4836

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4837

}

4838

4839

/// Return the number of dofs on each cell facet

4840

virtual unsigned int num_facet_dofs() const

4841

{

4842

return 10;

4843

}

4844

4845

/// Return the number of dofs associated with each cell entity of dimension d

4846

virtual unsigned int num_entity_dofs(unsigned int d) const

4847

{

4848

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4849

}

4850

4851

/// Tabulate the local-to-global mapping of dofs on a cell

4852

virtual void tabulate_dofs(unsigned int* dofs,

4853

const ufc::mesh& m,

4854

const ufc::cell& c) const

4855

{

4856

dofs[0] = c.entity_indices[0][0];

4857

dofs[1] = c.entity_indices[0][1];

4858

dofs[2] = c.entity_indices[0][2];

4859

dofs[3] = c.entity_indices[0][3];

4860

unsigned int offset = m.num_entities[0];

4861

dofs[4] = offset + 2*c.entity_indices[1][0];

4862

dofs[5] = offset + 2*c.entity_indices[1][0] + 1;

4863

dofs[6] = offset + 2*c.entity_indices[1][1];

4864

dofs[7] = offset + 2*c.entity_indices[1][1] + 1;

4865

dofs[8] = offset + 2*c.entity_indices[1][2];

4866

dofs[9] = offset + 2*c.entity_indices[1][2] + 1;

4867

dofs[10] = offset + 2*c.entity_indices[1][3];

4868

dofs[11] = offset + 2*c.entity_indices[1][3] + 1;

4869

dofs[12] = offset + 2*c.entity_indices[1][4];

4870

dofs[13] = offset + 2*c.entity_indices[1][4] + 1;

4871

dofs[14] = offset + 2*c.entity_indices[1][5];

4872

dofs[15] = offset + 2*c.entity_indices[1][5] + 1;

4873

offset = offset + 2*m.num_entities[1];

4874

dofs[16] = offset + c.entity_indices[2][0];

4875

dofs[17] = offset + c.entity_indices[2][1];

4876

dofs[18] = offset + c.entity_indices[2][2];

4877

dofs[19] = offset + c.entity_indices[2][3];

4878

}

4879

4880

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4881

virtual void tabulate_facet_dofs(unsigned int* dofs,

4882

unsigned int facet) const

4883

{

4884

switch ( facet )

4885

{

4886

case 0:

4887

dofs[0] = 1;

4888

dofs[1] = 2;

4889

dofs[2] = 3;

4890

dofs[3] = 4;

4891

dofs[4] = 5;

4892

dofs[5] = 6;

4893

dofs[6] = 7;

4894

dofs[7] = 8;

4895

dofs[8] = 9;

4896

dofs[9] = 16;

4897

break;

4898

case 1:

4899

dofs[0] = 0;

4900

dofs[1] = 2;

4901

dofs[2] = 3;

4902

dofs[3] = 4;

4903

dofs[4] = 5;

4904

dofs[5] = 10;

4905

dofs[6] = 11;

4906

dofs[7] = 12;

4907

dofs[8] = 13;

4908

dofs[9] = 17;

4909

break;

4910

case 2:

4911

dofs[0] = 0;

4912

dofs[1] = 1;

4913

dofs[2] = 3;

4914

dofs[3] = 6;

4915

dofs[4] = 7;

4916

dofs[5] = 10;

4917

dofs[6] = 11;

4918

dofs[7] = 14;

4919

dofs[8] = 15;

4920

dofs[9] = 18;

4921

break;

4922

case 3:

4923

dofs[0] = 0;

4924

dofs[1] = 1;

4925

dofs[2] = 2;

4926

dofs[3] = 8;

4927

dofs[4] = 9;

4928

dofs[5] = 12;

4929

dofs[6] = 13;

4930

dofs[7] = 14;

4931

dofs[8] = 15;

4932

dofs[9] = 19;

4933

break;

4934

}

4935

}

4936

4937

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4938

virtual void tabulate_entity_dofs(unsigned int* dofs,

4939

unsigned int d, unsigned int i) const

4940

{

4941

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4942

}

4943

4944

/// Tabulate the coordinates of all dofs on a cell

4945

virtual void tabulate_coordinates(double** coordinates,

4946

const ufc::cell& c) const

4947

{

4948

const double * const * x = c.coordinates;

4949

coordinates[0][0] = x[0][0];

4950

coordinates[0][1] = x[0][1];

4951

coordinates[0][2] = x[0][2];

4952

coordinates[1][0] = x[1][0];

4953

coordinates[1][1] = x[1][1];

4954

coordinates[1][2] = x[1][2];

4955

coordinates[2][0] = x[2][0];

4956

coordinates[2][1] = x[2][1];

4957

coordinates[2][2] = x[2][2];

4958

coordinates[3][0] = x[3][0];

4959

coordinates[3][1] = x[3][1];

4960

coordinates[3][2] = x[3][2];

4961

coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

4962

coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

4963

coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

4964

coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

4965

coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

4966

coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

4967

coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

4968

coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

4969

coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

4970

coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

4971

coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

4972

coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

4973

coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];

4974

coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];

4975

coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];

4976

coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4977

coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4978

coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4979

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4980

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4981

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4982

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

4983

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

4984

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

4985

coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4986

coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4987

coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4988

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4989

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4990

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4991

coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4992

coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4993

coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4994

coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4995

coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

4996

coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

4997

coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

4998

coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4999

coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5000

coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5001

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5002

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5003

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

5004

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5005

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5006

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

5007

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

5008

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

5009

}

5010

5011

/// Return the number of sub dof maps (for a mixed element)

5012

virtual unsigned int num_sub_dof_maps() const

5013

{

5014

return 1;

5015

}

5016

5017

/// Create a new dof_map for sub dof map i (for a mixed element)

5018

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

5019

{

5020

return new UFC_Poisson3D_3LinearForm_dof_map_1();

5021

}

5022

5023

};

5024

5025

/// This class defines the interface for the tabulation of the cell

5026

/// tensor corresponding to the local contribution to a form from

5027

/// the integral over a cell.

5028

5029

class UFC_Poisson3D_3LinearForm_cell_integral_0: public ufc::cell_integral

5030

{

5031

public:

5032

5033

/// Constructor

5034

UFC_Poisson3D_3LinearForm_cell_integral_0() : ufc::cell_integral()

5035

{

5036

// Do nothing

5037

}

5038

5039

/// Destructor

5040

virtual ~UFC_Poisson3D_3LinearForm_cell_integral_0()

5041

{

5042

// Do nothing

5043

}

5044

5045

/// Tabulate the tensor for the contribution from a local cell

5046

virtual void tabulate_tensor(double* A,

5047

const double * const * w,

5048

const ufc::cell& c) const

5049

{

5050

// Extract vertex coordinates

5051

const double * const * x = c.coordinates;

5052

5053

// Compute Jacobian of affine map from reference cell

5054

const double J_00 = x[1][0] - x[0][0];

5055

const double J_01 = x[2][0] - x[0][0];

5056

const double J_02 = x[3][0] - x[0][0];

5057

const double J_10 = x[1][1] - x[0][1];

5058

const double J_11 = x[2][1] - x[0][1];

5059

const double J_12 = x[3][1] - x[0][1];

5060

const double J_20 = x[1][2] - x[0][2];

5061

const double J_21 = x[2][2] - x[0][2];

5062

const double J_22 = x[3][2] - x[0][2];

5063

5064

// Compute sub determinants

5065

const double d_00 = J_11*J_22 - J_12*J_21;

5066

5067

const double d_10 = J_02*J_21 - J_01*J_22;

5068

5069

const double d_20 = J_01*J_12 - J_02*J_11;

5070

5071

// Compute determinant of Jacobian

5072

double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;

5073

5074

// Compute inverse of Jacobian

5075

5076

// Set scale factor

5077

const double det = std::abs(detJ);

5078

5079

// Compute coefficients

5080

const double c0_0_0_0 = w[0][0];

5081

const double c0_0_0_1 = w[0][1];

5082

const double c0_0_0_2 = w[0][2];

5083

const double c0_0_0_3 = w[0][3];

5084

const double c0_0_0_4 = w[0][4];

5085

const double c0_0_0_5 = w[0][5];

5086

const double c0_0_0_6 = w[0][6];

5087

const double c0_0_0_7 = w[0][7];

5088

const double c0_0_0_8 = w[0][8];

5089

const double c0_0_0_9 = w[0][9];

5090

const double c0_0_0_10 = w[0][10];

5091

const double c0_0_0_11 = w[0][11];

5092

const double c0_0_0_12 = w[0][12];

5093

const double c0_0_0_13 = w[0][13];

5094

const double c0_0_0_14 = w[0][14];

5095

const double c0_0_0_15 = w[0][15];

5096

const double c0_0_0_16 = w[0][16];

5097

const double c0_0_0_17 = w[0][17];

5098

const double c0_0_0_18 = w[0][18];

5099

const double c0_0_0_19 = w[0][19];

5100

5101

// Compute geometry tensors

5102

const double G0_0 = det*c0_0_0_0;

5103

const double G0_1 = det*c0_0_0_1;

5104

const double G0_2 = det*c0_0_0_2;

5105

const double G0_3 = det*c0_0_0_3;

5106

const double G0_4 = det*c0_0_0_4;

5107

const double G0_5 = det*c0_0_0_5;

5108

const double G0_6 = det*c0_0_0_6;

5109

const double G0_7 = det*c0_0_0_7;

5110

const double G0_8 = det*c0_0_0_8;

5111

const double G0_9 = det*c0_0_0_9;

5112

const double G0_10 = det*c0_0_0_10;

5113

const double G0_11 = det*c0_0_0_11;

5114

const double G0_12 = det*c0_0_0_12;

5115

const double G0_13 = det*c0_0_0_13;

5116

const double G0_14 = det*c0_0_0_14;

5117

const double G0_15 = det*c0_0_0_15;

5118

const double G0_16 = det*c0_0_0_16;

5119

const double G0_17 = det*c0_0_0_17;

5120

const double G0_18 = det*c0_0_0_18;

5121

const double G0_19 = det*c0_0_0_19;

5122

5123

// Compute element tensor

5124

A[0] = 0.000595238095238095*G0_0 + 7.44047619047619e-05*G0_1 + 7.44047619047618e-05*G0_2 + 7.44047619047618e-05*G0_3 + 0.000111607142857143*G0_4 + 0.000111607142857143*G0_5 + 0.000111607142857142*G0_6 + 0.000111607142857143*G0_7 + 0.000111607142857142*G0_8 + 0.000111607142857143*G0_9 - 0.000446428571428571*G0_10 + 0.000223214285714286*G0_11 - 0.000446428571428571*G0_12 + 0.000223214285714286*G0_13 - 0.000446428571428572*G0_14 + 0.000223214285714286*G0_15 + 0.00133928571428571*G0_16 + 0.000669642857142858*G0_17 + 0.000669642857142858*G0_18 + 0.000669642857142858*G0_19;

5125

A[1] = 7.44047619047619e-05*G0_0 + 0.000595238095238094*G0_1 + 7.44047619047616e-05*G0_2 + 7.44047619047616e-05*G0_3 + 0.000111607142857143*G0_4 + 0.000111607142857143*G0_5 - 0.000446428571428572*G0_6 + 0.000223214285714286*G0_7 - 0.000446428571428571*G0_8 + 0.000223214285714286*G0_9 + 0.000111607142857143*G0_10 + 0.000111607142857143*G0_11 + 0.000111607142857142*G0_12 + 0.000111607142857143*G0_13 + 0.000223214285714286*G0_14 - 0.000446428571428572*G0_15 + 0.000669642857142857*G0_16 + 0.00133928571428571*G0_17 + 0.000669642857142856*G0_18 + 0.000669642857142856*G0_19;

5126

A[2] = 7.44047619047618e-05*G0_0 + 7.44047619047616e-05*G0_1 + 0.000595238095238094*G0_2 + 7.44047619047616e-05*G0_3 - 0.000446428571428571*G0_4 + 0.000223214285714285*G0_5 + 0.000111607142857142*G0_6 + 0.000111607142857143*G0_7 + 0.000223214285714285*G0_8 - 0.00044642857142857*G0_9 + 0.000111607142857143*G0_10 + 0.000111607142857143*G0_11 + 0.000223214285714285*G0_12 - 0.00044642857142857*G0_13 + 0.000111607142857142*G0_14 + 0.000111607142857143*G0_15 + 0.000669642857142856*G0_16 + 0.000669642857142856*G0_17 + 0.00133928571428571*G0_18 + 0.000669642857142857*G0_19;

5127

A[3] = 7.44047619047618e-05*G0_0 + 7.44047619047616e-05*G0_1 + 7.44047619047616e-05*G0_2 + 0.000595238095238094*G0_3 + 0.000223214285714285*G0_4 - 0.00044642857142857*G0_5 + 0.000223214285714285*G0_6 - 0.00044642857142857*G0_7 + 0.000111607142857142*G0_8 + 0.000111607142857143*G0_9 + 0.000223214285714285*G0_10 - 0.00044642857142857*G0_11 + 0.000111607142857143*G0_12 + 0.000111607142857143*G0_13 + 0.000111607142857143*G0_14 + 0.000111607142857143*G0_15 + 0.000669642857142855*G0_16 + 0.000669642857142855*G0_17 + 0.000669642857142855*G0_18 + 0.00133928571428571*G0_19;

5128

A[4] = 0.000111607142857143*G0_0 + 0.000111607142857143*G0_1 - 0.000446428571428571*G0_2 + 0.000223214285714285*G0_3 + 0.00401785714285714*G0_4 - 0.00200892857142857*G0_5 - 0.00100446428571429*G0_7 - 0.00100446428571428*G0_8 + 0.00200892857142857*G0_9 - 0.00100446428571429*G0_11 - 0.00100446428571428*G0_12 + 0.00200892857142857*G0_13 - 0.00200892857142857*G0_18;

5129

A[5] = 0.000111607142857143*G0_0 + 0.000111607142857143*G0_1 + 0.000223214285714285*G0_2 - 0.00044642857142857*G0_3 - 0.00200892857142857*G0_4 + 0.00401785714285714*G0_5 - 0.00100446428571429*G0_6 + 0.00200892857142857*G0_7 - 0.00100446428571428*G0_9 - 0.00100446428571429*G0_10 + 0.00200892857142857*G0_11 - 0.00100446428571428*G0_13 - 0.00200892857142857*G0_19;

5130

A[6] = 0.000111607142857142*G0_0 - 0.000446428571428572*G0_1 + 0.000111607142857142*G0_2 + 0.000223214285714285*G0_3 - 0.00100446428571429*G0_5 + 0.00401785714285713*G0_6 - 0.00200892857142857*G0_7 + 0.00200892857142857*G0_8 - 0.00100446428571428*G0_9 - 0.00100446428571429*G0_11 - 0.00100446428571428*G0_14 + 0.00200892857142857*G0_15 - 0.00200892857142857*G0_17;

5131

A[7] = 0.000111607142857143*G0_0 + 0.000223214285714286*G0_1 + 0.000111607142857143*G0_2 - 0.00044642857142857*G0_3 - 0.00100446428571429*G0_4 + 0.00200892857142857*G0_5 - 0.00200892857142857*G0_6 + 0.00401785714285714*G0_7 - 0.00100446428571428*G0_8 - 0.00100446428571429*G0_10 + 0.00200892857142857*G0_11 - 0.00100446428571428*G0_15 - 0.00200892857142857*G0_19;

5132

A[8] = 0.000111607142857142*G0_0 - 0.000446428571428571*G0_1 + 0.000223214285714285*G0_2 + 0.000111607142857142*G0_3 - 0.00100446428571428*G0_4 + 0.00200892857142856*G0_6 - 0.00100446428571428*G0_7 + 0.00401785714285713*G0_8 - 0.00200892857142857*G0_9 - 0.00100446428571428*G0_13 - 0.00100446428571428*G0_14 + 0.00200892857142857*G0_15 - 0.00200892857142857*G0_17;

5133

A[9] = 0.000111607142857143*G0_0 + 0.000223214285714286*G0_1 - 0.00044642857142857*G0_2 + 0.000111607142857143*G0_3 + 0.00200892857142857*G0_4 - 0.00100446428571428*G0_5 - 0.00100446428571428*G0_6 - 0.00200892857142857*G0_8 + 0.00401785714285714*G0_9 - 0.00100446428571429*G0_12 + 0.00200892857142857*G0_13 - 0.00100446428571428*G0_15 - 0.00200892857142857*G0_18;

5134

A[10] = -0.000446428571428571*G0_0 + 0.000111607142857143*G0_1 + 0.000111607142857143*G0_2 + 0.000223214285714285*G0_3 - 0.00100446428571429*G0_5 - 0.00100446428571429*G0_7 + 0.00401785714285714*G0_10 - 0.00200892857142857*G0_11 + 0.00200892857142857*G0_12 - 0.00100446428571428*G0_13 + 0.00200892857142857*G0_14 - 0.00100446428571428*G0_15 - 0.00200892857142857*G0_16;

5135

A[11] = 0.000223214285714286*G0_0 + 0.000111607142857143*G0_1 + 0.000111607142857143*G0_2 - 0.00044642857142857*G0_3 - 0.00100446428571429*G0_4 + 0.00200892857142857*G0_5 - 0.00100446428571429*G0_6 + 0.00200892857142857*G0_7 - 0.00200892857142857*G0_10 + 0.00401785714285714*G0_11 - 0.00100446428571428*G0_12 - 0.00100446428571428*G0_14 - 0.00200892857142857*G0_19;

5136

A[12] = -0.000446428571428571*G0_0 + 0.000111607142857142*G0_1 + 0.000223214285714285*G0_2 + 0.000111607142857143*G0_3 - 0.00100446428571428*G0_4 - 0.00100446428571429*G0_9 + 0.00200892857142857*G0_10 - 0.00100446428571428*G0_11 + 0.00401785714285713*G0_12 - 0.00200892857142857*G0_13 + 0.00200892857142857*G0_14 - 0.00100446428571428*G0_15 - 0.00200892857142857*G0_16;

5137

A[13] = 0.000223214285714286*G0_0 + 0.000111607142857143*G0_1 - 0.00044642857142857*G0_2 + 0.000111607142857142*G0_3 + 0.00200892857142857*G0_4 - 0.00100446428571428*G0_5 - 0.00100446428571428*G0_8 + 0.00200892857142857*G0_9 - 0.00100446428571428*G0_10 - 0.00200892857142857*G0_12 + 0.00401785714285713*G0_13 - 0.00100446428571428*G0_14 - 0.00200892857142857*G0_18;

5138

A[14] = -0.000446428571428572*G0_0 + 0.000223214285714286*G0_1 + 0.000111607142857142*G0_2 + 0.000111607142857143*G0_3 - 0.00100446428571428*G0_6 - 0.00100446428571428*G0_8 + 0.00200892857142857*G0_10 - 0.00100446428571428*G0_11 + 0.00200892857142857*G0_12 - 0.00100446428571428*G0_13 + 0.00401785714285714*G0_14 - 0.00200892857142857*G0_15 - 0.00200892857142857*G0_16;

5139

A[15] = 0.000223214285714286*G0_0 - 0.000446428571428572*G0_1 + 0.000111607142857143*G0_2 + 0.000111607142857143*G0_3 + 0.00200892857142857*G0_6 - 0.00100446428571428*G0_7 + 0.00200892857142857*G0_8 - 0.00100446428571428*G0_9 - 0.00100446428571428*G0_10 - 0.00100446428571428*G0_12 - 0.00200892857142857*G0_14 + 0.00401785714285714*G0_15 - 0.00200892857142857*G0_17;

5140

A[16] = 0.00133928571428572*G0_0 + 0.000669642857142857*G0_1 + 0.000669642857142856*G0_2 + 0.000669642857142855*G0_3 - 0.00200892857142857*G0_10 - 0.00200892857142857*G0_12 - 0.00200892857142857*G0_14 + 0.0160714285714286*G0_16 + 0.00803571428571428*G0_17 + 0.00803571428571428*G0_18 + 0.00803571428571429*G0_19;

5141

A[17] = 0.000669642857142858*G0_0 + 0.00133928571428571*G0_1 + 0.000669642857142856*G0_2 + 0.000669642857142855*G0_3 - 0.00200892857142857*G0_6 - 0.00200892857142857*G0_8 - 0.00200892857142857*G0_15 + 0.00803571428571428*G0_16 + 0.0160714285714286*G0_17 + 0.00803571428571428*G0_18 + 0.00803571428571428*G0_19;

5142

A[18] = 0.000669642857142858*G0_0 + 0.000669642857142856*G0_1 + 0.00133928571428571*G0_2 + 0.000669642857142855*G0_3 - 0.00200892857142857*G0_4 - 0.00200892857142857*G0_9 - 0.00200892857142857*G0_13 + 0.00803571428571428*G0_16 + 0.00803571428571428*G0_17 + 0.0160714285714286*G0_18 + 0.00803571428571428*G0_19;

5143

A[19] = 0.000669642857142858*G0_0 + 0.000669642857142856*G0_1 + 0.000669642857142857*G0_2 + 0.00133928571428571*G0_3 - 0.00200892857142857*G0_5 - 0.00200892857142857*G0_7 - 0.00200892857142857*G0_11 + 0.00803571428571429*G0_16 + 0.00803571428571428*G0_17 + 0.00803571428571428*G0_18 + 0.0160714285714286*G0_19;

5144

}

5145

5146

};

5147

5148

/// This class defines the interface for the assembly of the global

5149

/// tensor corresponding to a form with r + n arguments, that is, a

5150

/// mapping

5151

///

5152

/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R

5153

///

5154

/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r

5155

/// global tensor A is defined by

5156

///

5157

/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),

5158

///

5159

/// where each argument Vj represents the application to the

5160

/// sequence of basis functions of Vj and w1, w2, ..., wn are given

5161

/// fixed functions (coefficients).

5162

5163

class UFC_Poisson3D_3LinearForm: public ufc::form

5164

{

5165

public:

5166

5167

/// Constructor

5168

UFC_Poisson3D_3LinearForm() : ufc::form()

5169

{

5170

// Do nothing

5171

}

5172

5173

/// Destructor

5174

virtual ~UFC_Poisson3D_3LinearForm()

5175

{

5176

// Do nothing

5177

}

5178

5179

/// Return a string identifying the form

5180

virtual const char* signature() const

5181

{

5182

return "w0_a0 | vi0*va0*dX(0)";

5183

}

5184

5185

/// Return the rank of the global tensor (r)

5186

virtual unsigned int rank() const

5187

{

5188

return 1;

5189

}

5190

5191

/// Return the number of coefficients (n)

5192

virtual unsigned int num_coefficients() const

5193

{

5194

return 1;

5195

}

5196

5197

/// Return the number of cell integrals

5198

virtual unsigned int num_cell_integrals() const

5199

{

5200

return 1;

5201

}

5202

5203

/// Return the number of exterior facet integrals

5204

virtual unsigned int num_exterior_facet_integrals() const

5205

{

5206

return 0;

5207

}

5208

5209

/// Return the number of interior facet integrals

5210

virtual unsigned int num_interior_facet_integrals() const

5211

{

5212

return 0;

5213

}

5214

5215

/// Create a new finite element for argument function i

5216

virtual ufc::finite_element* create_finite_element(unsigned int i) const

5217

{

5218

switch ( i )

5219

{

5220

case 0:

5221

return new UFC_Poisson3D_3LinearForm_finite_element_0();

5222

break;

5223

case 1:

5224

return new UFC_Poisson3D_3LinearForm_finite_element_1();

5225

break;

5226

}

5227

return 0;

5228

}

5229

5230

/// Create a new dof map for argument function i

5231

virtual ufc::dof_map* create_dof_map(unsigned int i) const

5232

{

5233

switch ( i )

5234

{

5235

case 0:

5236

return new UFC_Poisson3D_3LinearForm_dof_map_0();

5237

break;

5238

case 1:

5239

return new UFC_Poisson3D_3LinearForm_dof_map_1();

5240

break;

5241

}

5242

return 0;

5243

}

5244

5245

/// Create a new cell integral on sub domain i

5246

virtual ufc::cell_integral* create_cell_integral(unsigned int i) const

5247

{

5248

return new UFC_Poisson3D_3LinearForm_cell_integral_0();

5249

}

5250

5251

/// Create a new exterior facet integral on sub domain i

5252

virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const

5253

{

5254

return 0;

5255

}

5256

5257

/// Create a new interior facet integral on sub domain i

5258

virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const

5259

{

5260

return 0;

5261

}

5262

5263

};

5264

5265

// DOLFIN wrappers

5266

5267

#include <dolfin/Form.h>

5268

5269

class Poisson3D_3BilinearForm : public dolfin::Form

5270

{

5271

public:

5272

5273

Poisson3D_3BilinearForm() : dolfin::Form()

5274

{

5275

// Do nothing

5276

}

5277

5278

/// Return UFC form

5279

virtual const ufc::form& form() const

5280

{

5281

return __form;

5282

}

5283

5284

/// Return array of coefficients

5285

virtual const dolfin::Array<dolfin::Function*>& coefficients() const

5286

{

5287

return __coefficients;

5288

}

5289

5290

private:

5291

5292

// UFC form

5293

UFC_Poisson3D_3BilinearForm __form;

5294

5295

/// Array of coefficients

5296

dolfin::Array<dolfin::Function*> __coefficients;

5297

5298

};

5299

5300

class Poisson3D_3LinearForm : public dolfin::Form

5301

{

5302

public:

5303

5304

Poisson3D_3LinearForm(dolfin::Function& w0) : dolfin::Form()

5305

{

5306

__coefficients.push_back(&w0);

5307

}

5308

5309

/// Return UFC form

5310

virtual const ufc::form& form() const

5311

{

5312

return __form;

5313

}

5314

5315

/// Return array of coefficients

5316

virtual const dolfin::Array<dolfin::Function*>& coefficients() const

5317

{

5318

return __coefficients;

5319

}

5320

5321

private:

5322

5323

// UFC form

5324

UFC_Poisson3D_3LinearForm __form;

5325

5326

/// Array of coefficients

5327

dolfin::Array<dolfin::Function*> __coefficients;

5328

5329

};

5330

5331

#endif