~ubuntu-branches/ubuntu/maverick/dolfin/maverick : revision 3

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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 0.7.0.

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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 __POISSON3DP3_H

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#define __POISSON3DP3_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 poisson3dp3_0_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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poisson3dp3_0_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 ~poisson3dp3_0_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 "FiniteElement('Lagrange', 'tetrahedron', 3)";

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

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{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -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, 0.0066815310478106, 0.00472455591261534, 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, 0.0053239713749995, 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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{0.0288675134594813, 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, -0.0606091526731326, 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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

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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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

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{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

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{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

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{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -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, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

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{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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, -0.0992156741649221, 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, 0.0154647393532936, 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

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

473

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

474

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 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, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

476

{0.0288675134594813, 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, -0.0606091526731326, 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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

483

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

486

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

487

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -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, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

489

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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, -0.0992156741649221, 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, 0.0154647393532936, 0, 0, -0.00535714285714285}};

493

494

// Interesting (new) part

495

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

496

static const 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, 8.69482604771367, 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, 0.69282032302755, 0, 0.565685424949241, 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, 8.76356092008267, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963609, 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

static const 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, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

524

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

525

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063971, 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, -0.97979589711327, 0.282842712474621, 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, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884725, -0.740656079818042, 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, 0.534522483824851, 0.377964473009229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

533

{2.01246117974981, 2.12132034355964, -0.408248290463861, 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, 9.25820099772552, 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, 3.83405790253617, 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

static const 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, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

546

{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

547

{1.32287565553229, 0, 3.86436713231719, -0.341565025531988, 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, -0.97979589711327, 0.282842712474621, 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, 0.632455532033674, 4.38178046004133, -0.774596669241485, 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, -0.44721359549996, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

555

{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054295, 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, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

558

{1.27279220613578, -6.26099033699941, 0, 3.83405790253617, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

559

{0.734846922834953, 0, -6.26099033699942, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

560

{5.71576766497729, 0, 0, -4.69574275274956, 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

static const 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

static const 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

static const 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 poisson3dp3_0_finite_element_0();

839

}

840

841

};

842

843

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

844

845

class poisson3dp3_0_finite_element_1: public ufc::finite_element

846

{

847

public:

848

849

/// Constructor

850

poisson3dp3_0_finite_element_1() : ufc::finite_element()

851

{

852

// Do nothing

853

}

854

855

/// Destructor

856

virtual ~poisson3dp3_0_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 "FiniteElement('Lagrange', 'tetrahedron', 3)";

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

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

1038

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1039

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 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, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

1041

{0.0288675134594813, 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, -0.0606091526731326, 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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

1048

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

1051

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1052

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -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, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

1054

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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, -0.0992156741649221, 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, 0.0154647393532936, 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

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

1301

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

1302

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 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, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

1304

{0.0288675134594813, 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, -0.0606091526731326, 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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

1311

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

1314

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

1315

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -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, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

1317

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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, -0.0992156741649221, 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, 0.0154647393532936, 0, 0, -0.00535714285714285}};

1321

1322

// Interesting (new) part

1323

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

1324

static const 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, 8.69482604771367, 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, 0.69282032302755, 0, 0.565685424949241, 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, 8.76356092008267, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963609, 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

static const 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, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1352

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1353

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063971, 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, -0.97979589711327, 0.282842712474621, 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, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884725, -0.740656079818042, 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, 0.534522483824851, 0.377964473009229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1361

{2.01246117974981, 2.12132034355964, -0.408248290463861, 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, 9.25820099772552, 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, 3.83405790253617, 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

static const 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, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1374

{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1375

{1.32287565553229, 0, 3.86436713231719, -0.341565025531988, 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, -0.97979589711327, 0.282842712474621, 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, 0.632455532033674, 4.38178046004133, -0.774596669241485, 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, -0.44721359549996, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1383

{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054295, 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, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1386

{1.27279220613578, -6.26099033699941, 0, 3.83405790253617, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1387

{0.734846922834953, 0, -6.26099033699942, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

1388

{5.71576766497729, 0, 0, -4.69574275274956, 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

static const 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

static const 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

static const 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 poisson3dp3_0_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 poisson3dp3_0_dof_map_0: public ufc::dof_map

1675

{

1676

private:

1677

1678

unsigned int __global_dimension;

1679

1680

public:

1681

1682

/// Constructor

1683

poisson3dp3_0_dof_map_0() : ufc::dof_map()

1684

{

1685

__global_dimension = 0;

1686

}

1687

1688

/// Destructor

1689

virtual ~poisson3dp3_0_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 FiniteElement('Lagrange', 'tetrahedron', 3)";

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 for a cell

1748

virtual unsigned int local_dimension(const ufc::cell& c) const

1749

{

1750

return 20;

1751

}

1752

1753

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

1754

virtual unsigned int max_local_dimension() const

1755

{

1756

return 20;

1757

}

1758

1759

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

1760

virtual unsigned int geometric_dimension() const

1761

{

1762

return 3;

1763

}

1764

1765

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

1766

virtual unsigned int num_facet_dofs() const

1767

{

1768

return 10;

1769

}

1770

1771

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

1772

virtual unsigned int num_entity_dofs(unsigned int d) const

1773

{

1774

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

1775

}

1776

1777

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

1778

virtual void tabulate_dofs(unsigned int* dofs,

1779

const ufc::mesh& m,

1780

const ufc::cell& c) const

1781

{

1782

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

1783

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

1784

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

1785

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

1786

unsigned int offset = m.num_entities[0];

1787

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

1788

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

1789

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

1790

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

1791

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

1792

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

1793

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

1794

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

1795

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

1796

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

1797

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

1798

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

1799

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

1800

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

1801

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

1802

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

1803

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

1804

}

1805

1806

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

1807

virtual void tabulate_facet_dofs(unsigned int* dofs,

1808

unsigned int facet) const

1809

{

1810

switch ( facet )

1811

{

1812

case 0:

1813

dofs[0] = 1;

1814

dofs[1] = 2;

1815

dofs[2] = 3;

1816

dofs[3] = 4;

1817

dofs[4] = 5;

1818

dofs[5] = 6;

1819

dofs[6] = 7;

1820

dofs[7] = 8;

1821

dofs[8] = 9;

1822

dofs[9] = 16;

1823

break;

1824

case 1:

1825

dofs[0] = 0;

1826

dofs[1] = 2;

1827

dofs[2] = 3;

1828

dofs[3] = 4;

1829

dofs[4] = 5;

1830

dofs[5] = 10;

1831

dofs[6] = 11;

1832

dofs[7] = 12;

1833

dofs[8] = 13;

1834

dofs[9] = 17;

1835

break;

1836

case 2:

1837

dofs[0] = 0;

1838

dofs[1] = 1;

1839

dofs[2] = 3;

1840

dofs[3] = 6;

1841

dofs[4] = 7;

1842

dofs[5] = 10;

1843

dofs[6] = 11;

1844

dofs[7] = 14;

1845

dofs[8] = 15;

1846

dofs[9] = 18;

1847

break;

1848

case 3:

1849

dofs[0] = 0;

1850

dofs[1] = 1;

1851

dofs[2] = 2;

1852

dofs[3] = 8;

1853

dofs[4] = 9;

1854

dofs[5] = 12;

1855

dofs[6] = 13;

1856

dofs[7] = 14;

1857

dofs[8] = 15;

1858

dofs[9] = 19;

1859

break;

1860

}

1861

}

1862

1863

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

1864

virtual void tabulate_entity_dofs(unsigned int* dofs,

1865

unsigned int d, unsigned int i) const

1866

{

1867

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

1868

}

1869

1870

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

1871

virtual void tabulate_coordinates(double** coordinates,

1872

const ufc::cell& c) const

1873

{

1874

const double * const * x = c.coordinates;

1875

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

1876

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

1877

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

1878

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

1879

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

1880

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

1881

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

1882

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

1883

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

1884

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

1885

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

1886

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

1887

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

1888

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

1889

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

1890

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

1891

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

1892

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

1893

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

1894

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

1895

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

1896

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

1897

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

1898

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

1899

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

1900

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

1901

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

1902

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

1903

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

1904

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

1905

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

1906

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

1907

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

1908

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

1909

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

1910

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

1911

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

1912

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

1913

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

1914

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

1915

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

1916

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

1917

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

1918

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

1919

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

1920

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

1921

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

1922

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

1923

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

1924

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

1925

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

1926

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

1927

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

1928

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

1929

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

1930

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

1931

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

1932

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

1933

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

1934

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

1935

}

1936

1937

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

1938

virtual unsigned int num_sub_dof_maps() const

1939

{

1940

return 1;

1941

}

1942

1943

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

1944

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

1945

{

1946

return new poisson3dp3_0_dof_map_0();

1947

}

1948

1949

};

1950

1951

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

1952

/// degrees of freedom (dofs).

1953

1954

class poisson3dp3_0_dof_map_1: public ufc::dof_map

1955

{

1956

private:

1957

1958

unsigned int __global_dimension;

1959

1960

public:

1961

1962

/// Constructor

1963

poisson3dp3_0_dof_map_1() : ufc::dof_map()

1964

{

1965

__global_dimension = 0;

1966

}

1967

1968

/// Destructor

1969

virtual ~poisson3dp3_0_dof_map_1()

1970

{

1971

// Do nothing

1972

}

1973

1974

/// Return a string identifying the dof map

1975

virtual const char* signature() const

1976

{

1977

return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 3)";

1978

}

1979

1980

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

1981

virtual bool needs_mesh_entities(unsigned int d) const

1982

{

1983

switch ( d )

1984

{

1985

case 0:

1986

return true;

1987

break;

1988

case 1:

1989

return true;

1990

break;

1991

case 2:

1992

return true;

1993

break;

1994

case 3:

1995

return false;

1996

break;

1997

}

1998

return false;

1999

}

2000

2001

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

2002

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

2003

{

2004

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

2005

return false;

2006

}

2007

2008

/// Initialize dof map for given cell

2009

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

2010

const ufc::cell& c)

2011

{

2012

// Do nothing

2013

}

2014

2015

/// Finish initialization of dof map for cells

2016

virtual void init_cell_finalize()

2017

{

2018

// Do nothing

2019

}

2020

2021

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

2022

virtual unsigned int global_dimension() const

2023

{

2024

return __global_dimension;

2025

}

2026

2027

/// Return the dimension of the local finite element function space for a cell

2028

virtual unsigned int local_dimension(const ufc::cell& c) const

2029

{

2030

return 20;

2031

}

2032

2033

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

2034

virtual unsigned int max_local_dimension() const

2035

{

2036

return 20;

2037

}

2038

2039

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

2040

virtual unsigned int geometric_dimension() const

2041

{

2042

return 3;

2043

}

2044

2045

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

2046

virtual unsigned int num_facet_dofs() const

2047

{

2048

return 10;

2049

}

2050

2051

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

2052

virtual unsigned int num_entity_dofs(unsigned int d) const

2053

{

2054

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

2055

}

2056

2057

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

2058

virtual void tabulate_dofs(unsigned int* dofs,

2059

const ufc::mesh& m,

2060

const ufc::cell& c) const

2061

{

2062

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

2063

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

2064

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

2065

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

2066

unsigned int offset = m.num_entities[0];

2067

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

2068

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

2069

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

2070

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

2071

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

2072

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

2073

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

2074

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

2075

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

2076

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

2077

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

2078

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

2079

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

2080

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

2081

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

2082

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

2083

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

2084

}

2085

2086

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

2087

virtual void tabulate_facet_dofs(unsigned int* dofs,

2088

unsigned int facet) const

2089

{

2090

switch ( facet )

2091

{

2092

case 0:

2093

dofs[0] = 1;

2094

dofs[1] = 2;

2095

dofs[2] = 3;

2096

dofs[3] = 4;

2097

dofs[4] = 5;

2098

dofs[5] = 6;

2099

dofs[6] = 7;

2100

dofs[7] = 8;

2101

dofs[8] = 9;

2102

dofs[9] = 16;

2103

break;

2104

case 1:

2105

dofs[0] = 0;

2106

dofs[1] = 2;

2107

dofs[2] = 3;

2108

dofs[3] = 4;

2109

dofs[4] = 5;

2110

dofs[5] = 10;

2111

dofs[6] = 11;

2112

dofs[7] = 12;

2113

dofs[8] = 13;

2114

dofs[9] = 17;

2115

break;

2116

case 2:

2117

dofs[0] = 0;

2118

dofs[1] = 1;

2119

dofs[2] = 3;

2120

dofs[3] = 6;

2121

dofs[4] = 7;

2122

dofs[5] = 10;

2123

dofs[6] = 11;

2124

dofs[7] = 14;

2125

dofs[8] = 15;

2126

dofs[9] = 18;

2127

break;

2128

case 3:

2129

dofs[0] = 0;

2130

dofs[1] = 1;

2131

dofs[2] = 2;

2132

dofs[3] = 8;

2133

dofs[4] = 9;

2134

dofs[5] = 12;

2135

dofs[6] = 13;

2136

dofs[7] = 14;

2137

dofs[8] = 15;

2138

dofs[9] = 19;

2139

break;

2140

}

2141

}

2142

2143

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

2144

virtual void tabulate_entity_dofs(unsigned int* dofs,

2145

unsigned int d, unsigned int i) const

2146

{

2147

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

2148

}

2149

2150

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

2151

virtual void tabulate_coordinates(double** coordinates,

2152

const ufc::cell& c) const

2153

{

2154

const double * const * x = c.coordinates;

2155

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

2156

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

2157

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

2158

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

2159

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

2160

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

2161

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

2162

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

2163

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

2164

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

2165

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

2166

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

2167

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

2168

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

2169

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

2170

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

2171

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

2172

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

2173

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

2174

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

2175

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

2176

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

2177

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

2178

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

2179

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

2180

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

2181

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

2182

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

2183

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

2184

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

2185

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

2186

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

2187

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

2188

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

2189

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

2190

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

2191

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

2192

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

2193

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

2194

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

2195

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

2196

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

2197

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

2198

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

2199

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

2200

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

2201

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

2202

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

2203

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

2204

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

2205

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

2206

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

2207

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

2208

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

2209

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

2210

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

2211

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

2212

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

2213

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

2214

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

2215

}

2216

2217

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

2218

virtual unsigned int num_sub_dof_maps() const

2219

{

2220

return 1;

2221

}

2222

2223

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

2224

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

2225

{

2226

return new poisson3dp3_0_dof_map_1();

2227

}

2228

2229

};

2230

2231

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

2232

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

2233

/// the integral over a cell.

2234

2235

class poisson3dp3_0_cell_integral_0_quadrature: public ufc::cell_integral

2236

{

2237

public:

2238

2239

/// Constructor

2240

poisson3dp3_0_cell_integral_0_quadrature() : ufc::cell_integral()

2241

{

2242

// Do nothing

2243

}

2244

2245

/// Destructor

2246

virtual ~poisson3dp3_0_cell_integral_0_quadrature()

2247

{

2248

// Do nothing

2249

}

2250

2251

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

2252

virtual void tabulate_tensor(double* A,

2253

const double * const * w,

2254

const ufc::cell& c) const

2255

{

2256

// Extract vertex coordinates

2257

const double * const * x = c.coordinates;

2258

2259

// Compute Jacobian of affine map from reference cell

2260

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

2261

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

2262

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

2263

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

2264

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

2265

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

2266

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

2267

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

2268

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

2269

2270

// Compute sub determinants

2271

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

2272

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

2273

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

2274

2275

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

2276

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

2277

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

2278

2279

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

2280

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

2281

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

2282

2283

// Compute determinant of Jacobian

2284

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

2285

2286

// Compute inverse of Jacobian

2287

const double Jinv_00 = d_00 / detJ;

2288

const double Jinv_01 = d_10 / detJ;

2289

const double Jinv_02 = d_20 / detJ;

2290

const double Jinv_10 = d_01 / detJ;

2291

const double Jinv_11 = d_11 / detJ;

2292

const double Jinv_12 = d_21 / detJ;

2293

const double Jinv_20 = d_02 / detJ;

2294

const double Jinv_21 = d_12 / detJ;

2295

const double Jinv_22 = d_22 / detJ;

2296

2297

// Set scale factor

2298

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

2299

2300

2301

// Array of quadrature weights

2302

static const double W64[64] = {0.0026134590075074, 0.00338108957856492, 0.00161758872343451, 0.000243985421620605, 0.00392412678076307, 0.00507672939399183, 0.00242882065938497, 0.000366345798555432, 0.00250430944300902, 0.0032398803788146, 0.00155003109035391, 0.000233795515279108, 0.000601372928720174, 0.000778009425931694, 0.000372217075256263, 5.6142540266951e-05, 0.00489961445988875, 0.00633873932658916, 0.00303259438036939, 0.00045741467393993, 0.00735680500908296, 0.00951766095289489, 0.00455346144286727, 0.000686811297504771, 0.00469498496963441, 0.00607400564032183, 0.00290593987575818, 0.000438311021534327, 0.00112743130421366, 0.00145858275269461, 0.000697818545806259, 0.000105253918778391, 0.00489961445988875, 0.00633873932658916, 0.00303259438036939, 0.00045741467393993, 0.00735680500908296, 0.00951766095289489, 0.00455346144286727, 0.000686811297504771, 0.00469498496963441, 0.00607400564032183, 0.00290593987575818, 0.000438311021534327, 0.00112743130421366, 0.00145858275269461, 0.000697818545806259, 0.000105253918778391, 0.0026134590075074, 0.00338108957856492, 0.00161758872343451, 0.000243985421620605, 0.00392412678076307, 0.00507672939399183, 0.00242882065938497, 0.000366345798555432, 0.00250430944300902, 0.0032398803788146, 0.00155003109035391, 0.000233795515279108, 0.000601372928720174, 0.000778009425931694, 0.000372217075256263, 5.6142540266951e-05};

2303

// Quadrature points on the UFC reference element: (0.0622918093484527, 0.0543346112272345, 0.0485005494469973), (0.0498465213688842, 0.0434790928042876, 0.238600737551862), (0.0316174621017319, 0.027578625974397, 0.517047295104368), (0.0133649941129659, 0.0116577406689234, 0.795851417896773), (0.0477749046478169, 0.263415975366112, 0.0485005494469973), (0.0382299507805671, 0.210788066397987, 0.238600737551862), (0.024249114818074, 0.13370208226799, 0.517047295104368), (0.0102503254608295, 0.0565171086994073, 0.795851417896773), (0.0275098322538483, 0.555285975747014, 0.0485005494469973), (0.0220136396042882, 0.444345324777483, 0.238600737551862), (0.013963169280339, 0.28184657786378, 0.517047295104368), (0.00590236100005809, 0.119139159297124, 0.795851417896773), (0.00923314621657362, 0.818518016420533, 0.0485005494469973), (0.007388454838612, 0.654986204816931, 0.238600737551862), (0.00468646927478461, 0.415455300374957, 0.517047295104368), (0.00198101397470041, 0.175616803962505, 0.795851417896773), (0.296072900492077, 0.0543346112272345, 0.0485005494469973), (0.236920460578858, 0.0434790928042876, 0.238600737551862), (0.150277762174051, 0.027578625974397, 0.517047295104368), (0.063523802141471, 0.0116577406689234, 0.795851417896773), (0.227074068609678, 0.263415975366112, 0.0485005494469973), (0.181706913503757, 0.210788066397987, 0.238600737551862), (0.115256015737018, 0.13370208226799, 0.517047295104368), (0.0487197855050096, 0.0565171086994073, 0.795851417896773), (0.130754202079533, 0.555285975747014, 0.0485005494469973), (0.104630804534349, 0.444345324777483, 0.238600737551862), (0.0663669280461273, 0.28184657786378, 0.517047295104368), (0.0280539152629691, 0.119139159297124, 0.795851417896773), (0.0438851336893508, 0.818518016420533, 0.0485005494469973), (0.0351173176233467, 0.654986204816931, 0.238600737551862), (0.0222747832462335, 0.415455300374957, 0.517047295104368), (0.00941575721655391, 0.175616803962505, 0.795851417896773), (0.601091938833691, 0.0543346112272345, 0.0485005494469973), (0.480999709064992, 0.0434790928042876, 0.238600737551862), (0.305096316747185, 0.027578625974397, 0.517047295104368), (0.128967039292833, 0.0116577406689234, 0.795851417896773), (0.461009406577212, 0.263415975366112, 0.0485005494469973), (0.368904282546393, 0.210788066397987, 0.238600737551862), (0.233994606890624, 0.13370208226799, 0.517047295104368), (0.0989116878988102, 0.0565171086994073, 0.795851417896773), (0.265459272726456, 0.555285975747014, 0.0485005494469973), (0.212423133136306, 0.444345324777483, 0.238600737551862), (0.134739198985725, 0.28184657786378, 0.517047295104368), (0.0569555075431344, 0.119139159297124, 0.795851417896773), (0.0890963004431186, 0.818518016420533, 0.0485005494469973), (0.0712957400078597, 0.654986204816931, 0.238600737551862), (0.045222621274442, 0.415455300374957, 0.517047295104368), (0.0191160209241683, 0.175616803962505, 0.795851417896773), (0.834873029977315, 0.0543346112272345, 0.0485005494469973), (0.668073648274966, 0.0434790928042876, 0.238600737551862), (0.423756616819504, 0.027578625974397, 0.517047295104368), (0.179125847321338, 0.0116577406689234, 0.795851417896773), (0.640308570539073, 0.263415975366112, 0.0485005494469973), (0.512381245269583, 0.210788066397987, 0.238600737551862), (0.325001507809568, 0.13370208226799, 0.517047295104368), (0.13738114794299, 0.0565171086994073, 0.795851417896773), (0.368703642552141, 0.555285975747014, 0.0485005494469973), (0.295040298066366, 0.444345324777483, 0.238600737551862), (0.187142957751513, 0.28184657786378, 0.517047295104368), (0.0791070618060454, 0.119139159297124, 0.795851417896773), (0.123748287915896, 0.818518016420533, 0.0485005494469973), (0.0990246027925943, 0.654986204816931, 0.238600737551862), (0.0628109352458909, 0.415455300374957, 0.517047295104368), (0.0265507641660218, 0.175616803962505, 0.795851417896773)

2304

2305

// Value of basis functions at quadrature points.

2306

static const double FE0_D001[64][16] = \

2307

{{-2.89581790868146, 0.595251149481942, -0.204650375830157, -0.173353771062787, -0.227929503657332, -0.198741093622954, 4.77772039793662, -2.47715363873711, -0.980281790191305, 0.204650375830158, -1.12384215149678, 0.227929503657333, 0.091384233576906, 1.15363556125409, 1.32258324511974, -0.091384233576906},

2308

{-1.01268955903752, -0.37884742650281, -0.170135092219663, 0.0844459598828055, -0.190766224310168, 0.0968129064413029, -0.211153065610757, 1.60269005115108, -0.588619458523755, 0.170135092219663, -0.674821633227638, 0.190766224310167, 0.0585166012713517, 0.504173498640949, 0.578008726786336, -0.0585166012713515},

2309

{0.389619002348325, -0.0443639333802776, -0.113835978641205, 0.260901440109651, -0.12878311667611, 0.29910994850187, -3.07176113643667, 2.72650606746862, -0.19143506458012, 0.113835978641205, -0.219470357403725, 0.128783116676109, 0.023543086362208, -0.0694663755295311, -0.079639591098143, -0.0235430863622075},

2310

{0.178970691981112, 2.38796021040115, -0.0506251436238552, 0.198041561892404, -0.0577310620952115, 0.227044363396273, -0.640627106961096, -1.92630379542116, -0.0039216392195247, 0.0506251436238544, -0.00449595565475535, 0.0577310620952113, 0.00420675215608439, -0.194119922672882, -0.222548407741519, -0.00420675215608366},

2311

{-0.772156249476526, 0.595251149481943, -0.248634212093421, -0.84042476161143, -0.184174110474718, -0.152425124534857, 2.03330371727115, -1.85639861727657, -3.36865079023594, 0.248634212093422, -0.610961313457298, 0.184174110474718, 0.339786173857347, 4.20907555184737, 0.763386437992154, -0.339786173857347},

2312

{0.0672149106221295, -0.37884742650281, -0.348719578157611, 0.409396780170706, -0.15230413516731, 0.0742509717134456, -0.988668649710359, 1.30030116559104, -1.9675577038312, 0.348719578157612, -0.356849585751078, 0.15230413516731, 0.2175772698952, 1.5581609236605, 0.282598614037633, -0.217577269895201},

2313

{0.49906283922646, -0.0443639333802784, -0.360330038368204, 1.26485872942917, -0.101182752493622, 0.229403342403398, -2.24695429009376, 1.79225538424758, -0.57158184482219, 0.360330038368204, -0.103665953049545, 0.101182752493621, 0.0875382428969645, -0.693276884606977, -0.125737389353853, -0.0875382428969649},

2314

{-0.0183629959498944, 2.38796021040115, -0.211205510874836, 0.9601119803866, -0.0447080307510176, 0.174132408827691, 0.265865044895522, -2.63546225934677, 0.044688586815663, 0.211205510874836, 0.00810502465158773, 0.0447080307510176, 0.0156416064733958, -1.00480056720226, -0.18223743347928, -0.0156416064733952},

2315

{0.48311070654784, 0.595251149481943, 1.66383705976616, -1.77163166791512, -0.113577568388746, -0.0877697116956461, -0.0885147322176989, -0.989847123812084, -3.02908408087161, -1.66383705976616, -0.150066089523472, 0.113577568388746, 0.4124472492343, 4.80071574878674, 0.237835801219117, -0.412447249234301},

2316

{0.480204186575578, -0.37884742650281, 0.665923401798019, 0.863016338431318, -0.0925192737828253, 0.0427553292168731, -0.979534009899769, 0.878177249827001, -1.54014001930344, -0.665923401798019, -0.0763012131208204, 0.0925192737828252, 0.264104761666552, 0.677123680872123, 0.0335458839039475, -0.264104761666553},

2317

{0.211483050177826, -0.0443639333802788, -0.195903438764438, 2.66634668902302, -0.0602021654607812, 0.132095448740534, -0.655194435114137, 0.48807531831659, -0.155821659379379, 0.195903438764438, -0.00771967580358115, 0.0602021654607807, 0.106257729900498, -2.51052502964364, -0.124375772936954, -0.106257729900498},

2318

{-0.372518461317996, 2.38796021040115, -0.344505336583714, 2.02393464221137, -0.0260903133176974, 0.10026923951228, 1.60998000277298, -3.62542175185613, 0.281657998210035, 0.344505336583714, 0.0139538267165683, 0.0260903133176976, 0.0189864628402054, -2.3055926404214, -0.114223066228851, -0.0189864628402044},

2319

{-0.0929995320454971, 0.595251149481942, 5.36128745937516, -2.61146958861852, -0.0403982696223155, -0.0294582160296172, -0.293930918661733, -0.208320698774712, 0.948495588562795, -5.36128745937517, 0.0106993349923761, 0.0403982696223156, 0.20405240621579, 1.66297400005573, 0.0187588810372401, -0.204052406215793},

2320

{-0.241157846302772, -0.37884742650281, 2.84415561308039, 1.27212725032541, -0.032511091697572, 0.0143500041205054, 0.12253360977631, 0.497471663029272, 1.19622470497731, -2.84415561308039, 0.0134937990213529, 0.0325110916975708, 0.130662071843505, -2.46835195530272, -0.0278438031418584, -0.130662071843505},

2321

{-0.48796196620424, -0.0443639333802785, 0.460593087542911, 3.93032220929508, -0.0207926113139715, 0.0443352973406311, 1.22046595014009, -0.688140050555571, 1.16498018051314, -0.460593087542912, 0.0131413507464737, 0.0207926113139701, 0.0525694995068508, -5.09530238980823, -0.057476648087106, -0.0525694995068486},

2322

{-0.770559854056101, 2.38796021040115, -0.373918583072206, 2.98337620805032, -0.00886158326518219, 0.0336534421910924, 2.90084716402885, -4.5182475203739, 0.664381088500103, 0.373918583072207, 0.00749443214515569, 0.00886158326518224, 0.00939328225673307, -3.64775729655043, -0.0411478743362511, -0.00939328225673128},

2323

{-0.4678780560632, 0.595251149481942, -0.204650375830157, -0.173353771062788, -0.148929359736164, -0.944616196758085, 1.60390544218324, -1.73127853560198, -0.637316863302983, 0.204650375830158, -3.47278186019387, 0.148929359736165, 0.434349160465227, 0.810670634365771, 4.41739805695196, -0.434349160465228},

2324

{0.205627659956735, -0.378847426502809, -0.170135092219662, 0.0844459598828058, -0.308369459952734, 0.460151636546686, -1.06613155449962, 1.2393513210457, -0.369006719091053, 0.170135092219663, -2.01074208786445, 0.308369459952734, 0.278129340704052, 0.284560759208247, 1.55059045131777, -0.278129340704052},

2325

{0.489236057073233, -0.0443639333802778, -0.113835978641205, 0.260901440109652, -0.371373951428681, 1.42166925227039, -2.04881888739305, 1.6039467637001, -0.103077887670107, 0.113835978641205, -0.561678246881204, 0.371373951428681, 0.111900263272222, -0.157823552439546, -0.859991005389186, -0.111900263272221},

2326

{-0.0638353588879535, 2.38796021040115, -0.0506251436238554, 0.198041561892405, -0.23138091821675, 1.07914160648444, 0.454276186996138, -2.77840103850933, 0.0118662969394588, 0.0506251436238547, 0.0646602390927712, 0.231380918216751, 0.0199946883150681, -0.209907858831866, -1.14380184557721, -0.0199946883150676},

2327

{0.279934074333821, 0.595251149481942, -0.248634212093421, -0.840424761611429, -0.325737768171688, -0.72447644723972, 0.409162070755938, -1.2843472945717, -2.0934336579877, 0.248634212093422, -1.80461529496461, 0.325737768171689, 1.61500330610559, 2.93385841959913, 2.52909174220433, -1.61500330610559},

2328

{0.482918552223106, -0.37884742650281, -0.348719578157611, 0.409396780170706, -0.371946178163572, 0.352914785900354, -1.12570847712443, 1.02163735140413, -1.15099045211411, 0.348719578157612, -0.992195270348315, 0.371946178163572, 1.03414452161229, 0.741593671943407, 0.639280484447962, -1.03414452161229},

2329

{0.366779535287998, -0.0443639333802783, -0.360330038368204, 1.26485872942917, -0.339318757108362, 1.09035383107937, -1.25372049747933, 0.931304895571607, -0.243050916674464, 0.360330038368204, -0.209518653725823, 0.339318757108362, 0.416069171044691, -1.0218078127547, -0.880835177353546, -0.416069171044691},

2330

{-0.241872355951096, 2.38796021040115, -0.211205510874836, 0.9601119803866, -0.187195198527211, 0.827651145319748, 1.14289314138878, -3.28898099583883, 0.103391518498623, 0.211205510874836, 0.0891272168765957, 0.187195198527212, 0.0743445381563563, -1.06350349888522, -0.916778362196345, -0.0743445381563559},

2331

{0.437807010605908, 0.595251149481942, 1.66383705976616, -1.77163166791512, -0.357588980978252, -0.417169341987151, -0.372610666567272, -0.660447493520578, -1.48117001361751, -1.66383705976616, -0.348773806171044, 0.357588980978252, 1.96036131648841, 3.25280168153263, 0.765943148158195, -1.96036131648841},

2332

{0.302639767092249, -0.37884742650281, 0.665923401798019, 0.863016338431317, -0.32304594942825, 0.20321603217402, -0.641508887459292, 0.717716546869853, -0.548955142761289, -0.665923401798019, -0.129263469282916, 0.32304594942825, 1.2552896382087, -0.314061195670028, -0.073952562891104, -1.2552896382087},

2333

{-0.0324350076632249, -0.0443639333802785, -0.195903438764438, 2.66634668902302, -0.239189492840794, 0.627849520819607, 0.0844776948059878, -0.00767875376248435, 0.242963482654707, 0.195903438764438, 0.057211054657456, 0.239189492840794, 0.505042871934584, -2.90931017167773, -0.685060575477064, -0.505042871934584},

2334

{-0.531193484944987, 2.38796021040115, -0.344505336583714, 2.02393464221137, -0.115617819502004, 0.476579583785566, 2.14496537067326, -4.00173209612941, 0.352914172114247, 0.344505336583714, 0.0831013441592525, 0.115617819502005, 0.0902426367444173, -2.37684881432562, -0.559680927944821, -0.0902426367444164},

2335

{-0.305298331172714, 0.595251149481941, 5.36128745937516, -2.61146958861852, -0.171483384656493, -0.14001486799689, -0.192188771501789, -0.097764046807439, 1.71430404194646, -5.36128745937517, 0.0919130190854158, 0.171483384656494, 0.969860859599452, 0.897165546672069, 0.0481018489114732, -0.969860859599455},

2336

{-0.426959954263386, -0.378847426502809, 2.84415561308039, 1.27212725032541, -0.141379378344762, 0.0682055536108254, 0.362191267227245, 0.443616113538951, 1.68659931515741, -2.84415561308039, 0.0904276203347779, 0.14137937834476, 0.621036682023601, -2.95872656548282, -0.158633173945604, -0.6210366820236},

2337

{-0.6206050624416, -0.0443639333802783, 0.460593087542911, 3.93032220929508, -0.0935382840310485, 0.210725618907479, 1.5194993679443, -0.85453037212242, 1.36227345364377, -0.460593087542912, 0.0730387742667559, 0.0935382840310472, 0.24986277263748, -5.29259566293886, -0.283764393174236, -0.249862772637477},

2338

{-0.832889012138125, 2.38796021040115, -0.373918583072206, 2.98337620805032, -0.0411740449410156, 0.159954773272396, 3.08947765319218, -4.6445488514552, 0.699634066353339, 0.373918583072207, 0.0375111285513463, 0.0411740449410158, 0.0446462601099692, -3.68301027440366, -0.197465901823745, -0.0446462601099674},

2339

{0.48125741195051, 0.595251149481943, -0.204650375830157, -0.173353771062788, 2.17279178081481, -1.91777491360855, -0.318388742680938, -0.758119818751515, -0.189843409942675, 0.204650375830158, -2.10019618765661, -2.17279178081481, 0.881822613825533, 0.363197181005464, 4.01797110126516, -0.881822613825535},

2340

{0.374511532557597, -0.37884742650281, -0.170135092219662, 0.0844459598828063, 0.958871030835726, 0.93420721352627, -0.760959850120903, 0.765295744066115, -0.0824734230847603, 0.170135092219663, -0.912385469676855, -0.958871030835727, 0.564662636710344, -0.00197253679804641, -0.021821743849414, -0.564662636710344},

2341

{0.0476238812119082, -0.0443639333802784, -0.113835978641206, 0.260901440109653, -0.116302631710901, 2.88629565828948, -0.142580305512644, 0.139320357681015, 0.0122035536125633, 0.113835978641205, 0.135005248697902, 0.1163026317109, 0.227181704554891, -0.273104993722217, -3.02130090698738, -0.227181704554891},

2342

{-0.482761972146629, 2.38796021040115, -0.0506251436238558, 0.198041561892405, -0.355812964294298, 2.1908905524273, 1.98495174619767, -3.89014998445218, 0.0324651446950859, 0.0506251436238551, 0.359154806273899, 0.355812964294299, 0.0405935360706954, -0.230506706587493, -2.5500453587012, -0.0405935360706952},

2343

{0.347571076915241, 0.595251149481942, -0.248634212093421, -0.840424761611429, 0.794608255263633, -1.47084367257827, -0.404842157164035, -0.537980069233149, -0.429631416958082, 0.248634212093422, -0.751906274110712, -0.794608255263634, 3.2788055471352, 1.27005617856951, 2.22274994668898, -3.2788055471352},

2344

{0.189627288930479, -0.37884742650281, -0.348719578157611, 0.409396780170706, 0.177150719235663, 0.716493243884701, -0.468838755847452, 0.658058893419783, -0.0855982228213465, 0.348719578157612, -0.149807109656454, -0.177150719235664, 2.09953675090505, -0.323798557349359, -0.566686134228247, -2.09953675090506},

2345

{-0.142029172075058, -0.0443639333802782, -0.360330038368205, 1.26485872942917, -0.313803804280188, 2.21365379016098, 0.378388168965344, -0.191995063510007, 0.185590199161266, 0.360330038368204, 0.324805006465407, 0.313803804280189, 0.844710286880421, -1.45044892859043, -2.53845879662639, -0.844710286880421},

2346

{-0.593565766700245, 2.38796021040115, -0.211205510874836, 0.9601119803866, -0.313025048504257, 1.6803105950978, 2.34724600191598, -4.14164044561688, 0.179982450990976, 0.211205510874836, 0.314990777648698, 0.313025048504258, 0.15093547064871, -1.14009443137758, -1.9953013727465, -0.15093547064871},

2347

{-0.0540171096638481, 0.595251149481941, 1.66383705976616, -1.77163166791512, -0.243240283336858, -0.846943871527147, -0.310561075837515, -0.23067296398058, 0.538425574373153, -1.66383705976617, 0.257399011740106, 0.243240283336858, 3.97995690447907, 1.23320609354197, 0.589544859787042, -3.97995690447907},

2348

{-0.20611543016718, -0.378847426502809, 0.665923401798019, 0.863016338431317, -0.346735667978872, 0.412572439350424, 0.076602716976541, 0.508360139693449, 0.744264323289971, -0.665923401798019, 0.35580200942589, 0.346735667978872, 2.54850910425996, -1.60728066172129, -0.768374448776314, -2.54850910425996},

2349

{-0.462159330951633, -0.0443639333802781, -0.195903438764438, 2.66634668902302, -0.361238596901012, 1.27467014082689, 1.16102263810168, -0.654499373769769, 0.763266728452429, 0.195903438764438, 0.364886273885646, 0.361238596901012, 1.02534611773231, -3.42961341747545, -1.63955641471254, -1.02534611773231},

2350

{-0.758139561814633, 2.38796021040115, -0.344505336583714, 2.02393464221137, -0.212506731110906, 0.96755949480721, 2.86289135856455, -4.49271200715106, 0.44588358009264, 0.344505336583715, 0.213158509419996, 0.212506731110907, 0.18321204472281, -2.46981822230401, -1.18071800422721, -0.18321204472281},

2351

{-0.631033513741427, 0.595251149481941, 5.36128745937516, -2.61146958861852, -0.293768316833253, -0.28426042481401, -0.0106991457501968, 0.0464815100096822, 2.71347021429296, -5.36128745937517, 0.29536326947737, 0.293768316833253, 1.96902703194595, -0.102000625674433, -0.0111028446633603, -1.96902703194596},

2352

{-0.700592692350177, -0.378847426502809, 2.84415561308039, 1.27212725032541, -0.252209215701245, 0.138472006019522, 0.706090457722733, 0.373349661130254, 2.3264012396526, -2.84415561308039, 0.253230521065085, 0.252209215701244, 1.26083860651879, -3.59852848997801, -0.391702527084608, -1.26083860651879},

2353

{-0.8062251913609, -0.044363933380278, 0.460593087542911, 3.93032220929508, -0.17589314182341, 0.427818522466956, 1.92221240042307, -1.0716232756819, 1.61968607904983, -0.460593087542912, 0.176304045393694, 0.175893141823409, 0.507275398043541, -5.55000828834492, -0.60412256786065, -0.507275398043538},

2354

{-0.91645504758449, 2.38796021040115, -0.373918583072206, 2.98337620805032, -0.0810888937031161, 0.324742739481423, 3.33783165484757, -4.80933681766423, 0.745629357721306, 0.373918583072207, 0.0811623152356107, 0.0810888937031163, 0.0906415514779366, -3.72900556577163, -0.405905054717037, -0.0906415514779348},

2355

{-0.491757354274629, 0.595251149481943, -0.204650375830157, -0.173353771062788, 5.65274654357938, -2.66365001674368, -0.0912490795909291, -0.0122447156163844, 0.153121516945649, 0.204650375830158, 2.35277334133309, -5.65274654357937, 1.22478754071386, 0.020232254117138, 0.310876675410583, -1.22478754071386},

2356

{-0.584924429529852, -0.37884742650281, -0.170135092219662, 0.0844459598828069, 3.01902097627486, 1.29754594363165, 0.56181484207193, 0.401957013960733, 0.137139316347941, 0.170135092219663, 2.10720043784973, -3.01902097627486, 0.784275376143044, -0.221585276230749, -3.40474638148138, -0.784275376143044},

2357

{-0.728938303866098, -0.0443639333802792, -0.113835978641206, 0.260901440109654, 0.517285773339441, 4.008854962058, 1.75654118333388, -0.983238946087504, 0.100560730522576, 0.113835978641206, 1.54515583882625, -0.517285773339441, 0.315538881464903, -0.36146217063223, -5.55401080088425, -0.315538881464903},

2358

{-0.882126464396442, 2.38796021040115, -0.0506251436238561, 0.198041561892406, -0.372904379035091, 3.04298779551547, 3.23641348153565, -4.74224722754035, 0.048253080854069, 0.0506251436238555, 0.74142788378292, 0.372904379035092, 0.0563814722296786, -0.246294642746477, -3.78441567929839, -0.0563814722296787},

2359

{-0.600838818610104, 0.595251149481942, -0.248634212093421, -0.840424761611429, 2.65354481690236, -2.04289499528313, -0.0284835843435508, 0.0340712534717136, 0.845585715290159, 0.248634212093422, 2.05544018305336, -2.65354481690236, 4.55402267938344, -0.00516095367872851, -0.0125451877702227, -4.55402267938344},

2360

{-0.675661086320138, -0.37884742650281, -0.348719578157611, 0.409396780170706, 1.23850069309099, 0.995157058071609, 0.675113433590073, 0.379395079232875, 0.730969028895741, 0.348719578157612, 1.77683123944949, -1.23850069309099, 2.91610400262214, -1.14036580906645, -2.7719882975211, -2.91610400262214},

2361

{-0.789696230825047, -0.0443639333802784, -0.360330038368205, 1.26485872942917, -0.0365560540834038, 3.07460427883695, 1.8870057163913, -1.05294555218598, 0.514121127308991, 0.360330038368205, 1.24971981541218, 0.0365560540834039, 1.17324121502815, -1.77897985673816, -4.32432409424913, -1.17324121502815},

2362

{-0.909165504675249, 2.38796021040115, -0.211205510874837, 0.9601119803866, -0.363421838306648, 2.33382933158985, 3.31636447638304, -4.79515918210893, 0.238685382673936, 0.211205510874836, 0.580193725821311, 0.363421838306649, 0.20963840233167, -1.19879736306054, -2.91402305741117, -0.20963840233167},

2363

{-0.762628186468936, 0.595251149481941, 1.66383705976617, -1.77163166791512, 0.176055684936793, -1.17634350181865, 0.068650370676068, 0.0987266663109265, 2.08633964162726, -1.66383705976617, 1.38530605681884, -0.176055684936793, 5.52787097173318, -0.31470797371214, -0.208962555000192, -5.52787097173318},

2364

{-0.808419347997877, -0.378847426502809, 0.665923401798019, 0.863016338431316, -0.152522845276929, 0.573033142307571, 0.839367337764386, 0.347899436736301, 1.73544919983212, -0.66592340179802, 1.15231874995853, 0.152522845276929, 3.53969398080211, -2.59846553826344, -1.7253518922661, -3.53969398080211},

2365

{-0.876963572777694, -0.0443639333802778, -0.195903438764438, 2.66634668902302, -0.369339740296016, 1.77042421290596, 2.07158095200682, -1.15025344584884, 1.16205187048651, 0.195903438764438, 0.771589372316702, 0.369339740296016, 1.42413125976639, -3.82839855950953, -2.54201358522267, -1.42413125976639},

2366

{-0.94734906218204, 2.38796021040115, -0.344505336583714, 2.02393464221137, -0.271499760554798, 1.3438698390805, 3.42841120320524, -4.86902235142434, 0.517139753996851, 0.344505336583715, 0.343374980343511, 0.271499760554799, 0.254468218627022, -2.54107439620822, -1.68724481942401, -0.254468218627022},

2367

{-0.918052572403102, 0.595251149481941, 5.36128745937516, -2.61146958861852, -0.350133172332973, -0.394817076781283, 0.165763260944205, 0.157038161976955, 3.47927866767662, -5.36128745937517, 0.526017472639324, 0.350133172332974, 2.73483548532962, -0.867809079058096, -0.131200395858042, -2.73483548532962},

2368

{-0.934240861528672, -0.378847426502809, 2.84415561308039, 1.27212725032541, -0.313231441130554, 0.192327555509842, 0.993594176391548, 0.319494111639934, 2.81677584983269, -2.84415561308039, 0.425856464814271, 0.313231441130553, 1.75121321669889, -4.0889031001581, -0.618184020324113, -1.75121321669889},

2369

{-0.958118276949497, -0.0443639333802778, 0.460593087542911, 3.93032220929508, -0.22938882518925, 0.594208844033803, 2.24049580757852, -1.23801359724875, 1.81697935218046, -0.460593087542912, 0.274701447616451, 0.229388825189249, 0.704568671174169, -5.74730156147554, -0.868910291650255, -0.704568671174167},

2370

{-0.982223853848664, 2.38796021040115, -0.373918583072206, 2.98337620805032, -0.109961707196799, 0.451044070562726, 3.52990179219305, -4.93563814874553, 0.780882335574542, 0.373918583072207, 0.118058308006101, 0.1099617071968, 0.125894529331173, -3.76425854362487, -0.569102378568831, -0.125894529331171}};

2371

2372

// Array of non-zero columns

2373

static const unsigned int nzc0[16] = {0, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19};

2374

static const double FE0_D100[64][16] = \

2375

{{-2.89581790868146, 0.491757354274631, -0.136680424066403, -0.186496378006569, -0.153121516945648, -0.204650375830158, -0.875026145642752, 0.186496378006569, -0.980281790191305, 0.204650375830158, 4.5289043920826, -2.12484383767577, 0.0711519794597668, -0.0711519794597669, 1.01170656970915, 1.13340330713695},

2376

{-1.01268955903752, 0.584924429529853, -0.752581066382098, -0.305144107519429, -0.13713931634794, -0.170135092219663, -3.23017404188562, 0.305144107519429, -0.588619458523755, 0.170135092219663, 2.34419934304722, -1.91643421353956, 0.280101877502098, -0.280101877502098, 3.98275510826772, 0.725758774871695},

2377

{0.389619002348326, 0.728938303866098, -1.88532430000999, 1.28234889458938, -0.100560730522577, -0.113835978641205, -3.58904690977611, -1.28234889458938, -0.19143506458012, 0.113835978641205, 0.297815415935717, -1.41637272215014, 0.385005256994436, -0.385005256994436, 5.4743712097861, 0.291995795102697},

2378

{0.178970691981113, 0.882126464396443, -3.29414454363086, 4.96929159093663, -0.0482530808540704, -0.0506251436238535, -0.267722727926007, -4.96929159093663, -0.00392163921952433, 0.0506251436238531, -0.377400334689846, -0.683696821687709, 0.25050139490256, -0.250501394902559, 3.56186727155687, 0.0521747200735935},

2379

{-0.772156249476526, 0.600838818610107, -0.155690526131168, -0.18649637800657, -0.845585715290158, -0.248634212093422, -0.620241099631208, 0.18649637800657, -3.36865079023594, 0.248634212093422, 2.04258350344506, -1.87126607257864, 0.344947127536074, -0.344947127536074, 0.775931625762376, 4.21423650552609},

2380

{0.0672149106221297, 0.675661086320138, -0.827417568757383, -0.305144107519429, -0.730969028895742, -0.348719578157612, -2.22716934280135, 0.305144107519429, -1.9675577038312, 0.348719578157612, 0.881651107339918, -1.62452710428219, 1.35794307896165, -1.35794307896165, 3.05458691155874, 2.69852673272694},

2381

{0.499062839226461, 0.789696230825046, -1.98818846888492, 1.28234889458937, -0.514121127308992, -0.360330038368204, -2.21039823601036, -1.28234889458938, -0.571581844822189, 0.360330038368204, -0.140222007132949, -1.14853706291856, 1.86651809963512, -1.86651809963512, 4.19858670489528, 1.08570297213118},

2382

{-0.0183629959498933, 0.90916550467525, -3.36107250713405, 4.96929159093663, -0.238685382673937, -0.211205510874835, 0.62928688320217, -4.96929159093663, 0.0446885868156633, 0.211205510874834, -0.355316813655062, -0.535485695070294, 1.21443896953393, -1.21443896953393, 2.73178562393189, 0.193996795858273},

2383

{0.48311070654784, 0.762628186468936, -0.182227939064815, -0.18649637800657, -2.08633964162726, 1.66383705976616, -0.264570417154492, 0.18649637800657, -3.02908408087161, -1.66383705976616, 0.025989595413321, -1.2717284884301, 0.727155222946436, -0.727155222946435, 0.446798356219306, 5.11542372249887},

2384

{0.480204186575578, 0.808419347997877, -0.93188661154721, -0.305144107519429, -1.73544919983212, 0.665923401798019, -0.827011164622839, 0.305144107519429, -1.54014001930344, -0.665923401798019, -0.228824058397751, -1.05979947617571, 2.86257029992999, -2.86257029992999, 1.75889777617005, 3.27558921913556},

2385

{0.211483050177827, 0.876963572777693, -2.13178311746759, 1.28234889458937, -1.16205187048651, -0.195903438764439, -0.28585469481812, -1.28234889458938, -0.155821659379379, 0.195903438764438, -0.377059416099599, -0.711387206855921, 3.93465628941003, -3.93465628941003, 2.41763781228571, 1.31787352986589},

2386

{-0.372518461317995, 0.94734906218204, -3.45450151652294, 4.96929159093662, -0.517139753996851, -0.344505336583714, 1.88147976332778, -4.96929159093663, 0.281657998210035, 0.344505336583713, -0.257545933838233, -0.317284667025813, 2.56006085904842, -2.56006085904842, 1.57302175319516, 0.235481755786815},

2387

{-0.0929995320454972, 0.918052572403102, -0.206161530566521, -0.186496378006571, -3.47927866767661, 5.36128745937517, 0.0562022536712431, 0.186496378006571, 0.948495588562793, -5.36128745937517, -0.339433837340599, -0.485619203017006, 1.07186148527388, -1.07186148527388, 0.149959276895278, 2.53078307911382},

2388

{-0.241157846302772, 0.934240861528673, -1.02610526808912, -0.305144107519429, -2.81677584983269, 2.84415561308039, 0.435765050906867, 0.305144107519428, 1.19622470497731, -2.84415561308039, -0.299737642109204, -0.393345373116698, 4.21956517200161, -4.21956517200161, 0.590340217182254, 1.62055114485538},

2389

{-0.48796196620424, 0.958118276949496, -2.26128841889249, 1.28234889458937, -1.81697935218046, 0.460593087542911, 1.44985477532934, -1.28234889458938, 1.16498018051314, -0.460593087542911, -0.21624747444278, -0.253908836302478, 5.79987106098239, -5.79987106098239, 0.811433643563148, 0.651999171667313},

2390

{-0.7705598540561, 0.982223853848664, -3.53876337545823, 4.96929159093662, -0.780882335574539, -0.373918583072206, 3.01080887122566, -4.96929159093663, 0.664381088500102, 0.373918583072206, -0.102467275051648, -0.109196724740916, 3.7736518258816, -3.7736518258816, 0.527954504232578, 0.116501247074436},

2391

{-0.467878056063201, -0.481257411950509, 0.169459382944773, -0.18649637800657, 0.189843409942674, -0.204650375830158, -0.568886338631576, 0.18649637800657, -0.637316863302983, 0.204650375830158, -1.29999007937906, 2.24912554739277, 0.0711519794597661, -0.0711519794597664, 0.399426955686803, 0.447473453360309},

2392

{0.205627659956735, -0.374511532557597, 0.452590390168168, -0.305144107519429, 0.0824734230847601, -0.170135092219663, -2.02500258533535, 0.305144107519429, -0.369006719091053, 0.170135092219663, -1.05187105702873, 1.22075492962959, 0.280101877502098, -0.280101877502099, 1.57241219516718, 0.286533296006293},

2393

{0.489236057073233, -0.0476238812119084, -0.228793645916036, 1.28234889458938, -0.0122035536125636, -0.113835978641205, -1.93251625568215, -1.28234889458938, -0.103077887670106, 0.113835978641205, -0.677980878592105, 0.23636870273078, 0.385005256994437, -0.385005256994437, 2.16130990159819, 0.11528144128267},

2394

{-0.0638353588879527, 0.48276197214663, -2.21633266441442, 4.96929159093663, -0.032465144695087, -0.0506251436238537, 0.810089151290436, -4.96929159093663, 0.011866296939459, 0.0506251436238534, -0.291152725201528, -0.127773888057149, 0.250501394902561, -0.250501394902559, 1.40624351312398, 0.020598847755627},

2395

{0.279934074333821, -0.347571076915241, 0.0791043889923453, -0.18649637800657, 0.429631416958082, -0.248634212093422, -0.385446184507694, 0.18649637800657, -2.0934336579877, 0.248634212093422, -1.01000703970098, 1.0776440422824, 0.344947127536074, -0.344947127536074, 0.306341795515349, 1.66380224102961},

2396

{0.482918552223106, -0.189627288930479, 0.0968925776838803, -0.305144107519429, 0.085598222821346, -0.348719578157612, -1.30285919636009, 0.305144107519429, -1.15099045211411, 0.348719578157612, -0.815044551112652, 0.521753287820025, 1.35794307896165, -1.35794307896165, 1.20596661867621, 1.06539222929277},

2397

{0.366779535287999, 0.142029172075058, -0.717706926073704, 1.28234889458938, -0.185590199161266, -0.360330038368204, -0.939916693199137, -1.28234889458938, -0.243050916674464, 0.360330038368204, -0.523322458006013, 0.0145137506429557, 1.86651809963512, -1.86651809963512, 1.65762361927284, 0.428641115835729},

2398

{-0.241872355951095, 0.593565766700245, -2.53444120044319, 4.96929159093663, -0.179982450990977, -0.211205510874835, 1.45591818989304, -4.96929159093663, 0.103391518498623, 0.211205510874835, -0.223897831627663, -0.127795579121487, 1.21443896953393, -1.21443896953393, 1.07852301055015, 0.0765909324923525},

2399

{0.437807010605908, 0.054017109663848, -0.0470279051407378, -0.18649637800657, -0.538425574373153, 1.66383705976617, -0.129370383230415, 0.18649637800657, -1.48117001361751, -1.66383705976616, -0.592014089507902, 0.100189969238147, 0.727155222946437, -0.727155222946436, 0.176398288371152, 2.01959558799066},

2400

{0.302639767092249, 0.20611543016718, -0.399648666404791, -0.305144107519429, -0.744264323289971, 0.665923401798019, -0.294773219480419, 0.305144107519429, -0.548955142761289, -0.665923401798019, -0.47599913726179, -0.0327560599976398, 2.86257029992999, -2.86257029992999, 0.694421885885211, 1.29321946605126},

2401

{-0.0324350076632244, 0.462159330951632, -1.40021213094247, 1.28234889458937, -0.763266728452427, -0.195903438764439, 0.445716291707001, -1.28234889458938, 0.242963482654706, 0.195903438764438, -0.304027542243558, -0.125696781044851, 3.93465628941003, -3.93465628941003, 0.954495839235472, 0.520303245797721},

2402

{-0.531193484944986, 0.758139561814633, -2.97850917806655, 4.96929159093662, -0.445883580092639, -0.344505336583714, 2.35747210178416, -4.96929159093663, 0.352914172114247, 0.344505336583713, -0.129405386951656, -0.0975406899179906, 2.56006085904842, -2.56006085904842, 0.621037076282388, 0.0929694079783913},

2403

{-0.305298331172714, 0.631033513741428, -0.160784238906297, -0.186496378006571, -2.71347021429295, 5.36128745937517, 0.101579545331467, 0.186496378006571, 1.71430404194646, -5.36128745937517, -0.20185529774784, -0.123879884820874, 1.07186148527388, -1.07186148527388, 0.0592046935748301, 0.999166172346498},

2404

{-0.426959954263386, 0.700592692350177, -0.847469836067494, -0.305144107519429, -2.32640123965259, 2.84415561308039, 0.614400482928493, 0.305144107519428, 1.6865993151574, -2.84415561308039, -0.16178159536647, -0.111851142720322, 4.21956517200161, -4.21956517200161, 0.233069353139002, 0.639801924495189},

2405

{-0.6206050624416, 0.806225191360899, -2.01575068445412, 1.28234889458937, -1.61968607904983, 0.460593087542911, 1.69539250976771, -1.28234889458938, 1.36227345364377, -0.460593087542911, -0.102854367556658, -0.0827657613626429, 5.79987106098239, -5.79987106098239, 0.320358174686412, 0.257412625406057},

2406

{-0.832889012138124, 0.91645504758449, -3.37900569978859, 4.96929159093662, -0.745629357721303, -0.373918583072206, 3.1705665468953, -4.96929159093663, 0.699634066353338, 0.373918583072206, -0.0435777651517734, -0.039988270294592, 3.7736518258816, -3.7736518258816, 0.20843915289329, 0.0459952913679643},

2407

{0.481257411950509, 0.467878056063201, 0.568886338631574, -0.18649637800657, 0.637316863302981, -0.204650375830157, -0.169459382944775, 0.18649637800657, -0.189843409942675, 0.204650375830158, -2.24912554739277, 1.29999007937906, 0.0711519794597647, -0.0711519794597651, -0.399426955686799, -0.447473453360305},

2408

{0.374511532557597, -0.205627659956735, 2.02500258533535, -0.305144107519429, 0.369006719091052, -0.170135092219663, -0.452590390168168, 0.305144107519429, -0.0824734230847598, 0.170135092219663, -1.22075492962959, 1.05187105702873, 0.280101877502098, -0.280101877502099, -1.57241219516718, -0.286533296006292},

2409

{0.0476238812119085, -0.489236057073233, 1.93251625568215, 1.28234889458938, 0.103077887670105, -0.113835978641205, 0.228793645916037, -1.28234889458938, 0.0122035536125635, 0.113835978641205, -0.236368702730779, 0.677980878592104, 0.385005256994438, -0.385005256994439, -2.16130990159819, -0.115281441282669},

2410

{-0.482761972146629, 0.0638353588879532, -0.810089151290436, 4.96929159093663, -0.01186629693946, -0.050625143623854, 2.21633266441442, -4.96929159093663, 0.0324651446950859, 0.0506251436238538, 0.127773888057148, 0.291152725201528, 0.250501394902561, -0.25050139490256, -1.40624351312398, -0.0205988477556269},

2411

{0.347571076915241, -0.27993407433382, 0.385446184507694, -0.18649637800657, 2.09343365798769, -0.248634212093422, -0.0791043889923458, 0.18649637800657, -0.429631416958082, 0.248634212093422, -1.0776440422824, 1.01000703970098, 0.344947127536074, -0.344947127536075, -0.306341795515348, -1.66380224102961},

2412

{0.189627288930479, -0.482918552223106, 1.30285919636009, -0.305144107519429, 1.15099045211411, -0.348719578157612, -0.0968925776838802, 0.305144107519429, -0.0855982228213463, 0.348719578157612, -0.521753287820026, 0.815044551112652, 1.35794307896165, -1.35794307896165, -1.20596661867621, -1.06539222929277},

2413

{-0.142029172075058, -0.366779535287999, 0.939916693199139, 1.28234889458938, 0.243050916674464, -0.360330038368204, 0.717706926073706, -1.28234889458938, 0.185590199161266, 0.360330038368204, -0.0145137506429555, 0.523322458006012, 1.86651809963512, -1.86651809963512, -1.65762361927284, -0.428641115835729},

2414

{-0.593565766700244, 0.241872355951096, -1.45591818989304, 4.96929159093663, -0.103391518498624, -0.211205510874835, 2.53444120044319, -4.96929159093663, 0.179982450990976, 0.211205510874835, 0.127795579121486, 0.223897831627663, 1.21443896953393, -1.21443896953393, -1.07852301055015, -0.0765909324923536},

2415

{-0.0540171096638479, -0.437807010605908, 0.129370383230415, -0.18649637800657, 1.48117001361751, 1.66383705976617, 0.0470279051407378, 0.186496378006571, 0.538425574373154, -1.66383705976617, -0.100189969238147, 0.592014089507902, 0.727155222946438, -0.727155222946438, -0.176398288371152, -2.01959558799066},

2416

{-0.20611543016718, -0.302639767092249, 0.29477321948042, -0.305144107519429, 0.548955142761289, 0.66592340179802, 0.399648666404792, 0.305144107519428, 0.744264323289971, -0.665923401798019, 0.0327560599976389, 0.47599913726179, 2.86257029992999, -2.86257029992999, -0.694421885885211, -1.29321946605126},

2417

{-0.462159330951633, 0.0324350076632237, -0.445716291706998, 1.28234889458937, -0.242963482654704, -0.195903438764438, 1.40021213094248, -1.28234889458938, 0.763266728452429, 0.195903438764438, 0.125696781044851, 0.304027542243558, 3.93465628941003, -3.93465628941003, -0.954495839235477, -0.520303245797725},

2418

{-0.758139561814633, 0.531193484944987, -2.35747210178416, 4.96929159093662, -0.352914172114246, -0.344505336583714, 2.97850917806655, -4.96929159093663, 0.445883580092639, 0.344505336583713, 0.0975406899179897, 0.129405386951656, 2.56006085904842, -2.56006085904842, -0.621037076282388, -0.0929694079783943},

2419

{-0.631033513741427, 0.305298331172715, -0.101579545331464, -0.186496378006572, -1.71430404194645, 5.36128745937517, 0.160784238906301, 0.186496378006572, 2.71347021429296, -5.36128745937517, 0.123879884820873, 0.201855297747839, 1.07186148527388, -1.07186148527388, -0.0592046935748368, -0.999166172346504},

2420

{-0.700592692350177, 0.426959954263386, -0.614400482928489, -0.305144107519429, -1.6865993151574, 2.84415561308039, 0.847469836067498, 0.305144107519428, 2.3264012396526, -2.84415561308039, 0.111851142720321, 0.161781595366469, 4.21956517200161, -4.21956517200161, -0.233069353139008, -0.639801924495196},

2421

{-0.8062251913609, 0.620605062441599, -1.69539250976771, 1.28234889458937, -1.36227345364377, 0.460593087542911, 2.01575068445413, -1.28234889458938, 1.61968607904983, -0.460593087542911, 0.0827657613626421, 0.102854367556657, 5.79987106098239, -5.79987106098239, -0.320358174686418, -0.257412625406065},

2422

{-0.916455047584489, 0.832889012138124, -3.1705665468953, 4.96929159093662, -0.699634066353336, -0.373918583072207, 3.37900569978859, -4.96929159093663, 0.745629357721305, 0.373918583072206, 0.0399882702945916, 0.0435777651517732, 3.7736518258816, -3.7736518258816, -0.208439152893294, -0.0459952913679701},

2423

{-0.49175735427463, 2.89581790868146, 0.875026145642751, -0.186496378006569, 0.980281790191304, -0.204650375830158, 0.136680424066403, 0.186496378006569, 0.15312151694565, 0.204650375830158, 2.12484383767576, -4.52890439208259, 0.0711519794597628, -0.0711519794597634, -1.01170656970915, -1.13340330713695},

2424

{-0.584924429529852, 1.01268955903751, 3.23017404188562, -0.305144107519429, 0.588619458523752, -0.170135092219663, 0.752581066382098, 0.305144107519429, 0.137139316347942, 0.170135092219663, 1.91643421353956, -2.34419934304722, 0.280101877502098, -0.280101877502099, -3.98275510826771, -0.725758774871694},

2425

{-0.728938303866097, -0.389619002348326, 3.58904690977611, 1.28234889458938, 0.191435064580118, -0.113835978641205, 1.88532430000999, -1.28234889458937, 0.100560730522576, 0.113835978641206, 1.41637272215014, -0.297815415935717, 0.385005256994438, -0.38500525699444, -5.4743712097861, -0.291995795102694},

2426

{-0.882126464396441, -0.178970691981113, 0.267722727926007, 4.96929159093663, 0.00392163921952302, -0.0506251436238542, 3.29414454363086, -4.96929159093663, 0.0482530808540689, 0.0506251436238541, 0.683696821687708, 0.377400334689847, 0.250501394902562, -0.250501394902561, -3.56186727155686, -0.0521747200735929},

2427

{-0.600838818610105, 0.772156249476524, 0.620241099631208, -0.18649637800657, 3.36865079023593, -0.248634212093422, 0.155690526131168, 0.18649637800657, 0.845585715290158, 0.248634212093422, 1.87126607257864, -2.04258350344506, 0.344947127536075, -0.344947127536075, -0.775931625762377, -4.21423650552609},

2428

{-0.675661086320137, -0.0672149106221305, 2.22716934280135, -0.305144107519429, 1.9675577038312, -0.348719578157611, 0.827417568757383, 0.305144107519429, 0.730969028895741, 0.348719578157612, 1.62452710428218, -0.881651107339915, 1.35794307896165, -1.35794307896165, -3.05458691155874, -2.69852673272694},

2429

{-0.789696230825046, -0.499062839226461, 2.21039823601036, 1.28234889458938, 0.571581844822189, -0.360330038368205, 1.98818846888492, -1.28234889458938, 0.514121127308991, 0.360330038368205, 1.14853706291856, 0.140222007132949, 1.86651809963512, -1.86651809963512, -4.19858670489528, -1.08570297213118},

2430

{-0.909165504675249, 0.0183629959498933, -0.629286883202169, 4.96929159093663, -0.0446885868156636, -0.211205510874835, 3.36107250713406, -4.96929159093663, 0.238685382673936, 0.211205510874835, 0.535485695070293, 0.355316813655063, 1.21443896953393, -1.21443896953393, -2.73178562393189, -0.193996795858273},

2431

{-0.762628186468936, -0.48311070654784, 0.264570417154492, -0.186496378006571, 3.02908408087161, 1.66383705976617, 0.182227939064815, 0.186496378006571, 2.08633964162726, -1.66383705976617, 1.2717284884301, -0.0259895954133212, 0.72715522294644, -0.72715522294644, -0.446798356219307, -5.11542372249888},

2432

{-0.808419347997877, -0.480204186575578, 0.82701116462284, -0.305144107519429, 1.54014001930344, 0.66592340179802, 0.931886611547211, 0.305144107519429, 1.73544919983212, -0.66592340179802, 1.0597994761757, 0.228824058397751, 2.86257029992999, -2.86257029992999, -1.75889777617005, -3.27558921913556},

2433

{-0.876963572777694, -0.211483050177827, 0.285854694818123, 1.28234889458937, 0.155821659379381, -0.195903438764438, 2.1317831174676, -1.28234889458938, 1.16205187048651, 0.195903438764438, 0.711387206855922, 0.3770594160996, 3.93465628941003, -3.93465628941003, -2.41763781228572, -1.3178735298659},

2434

{-0.947349062182039, 0.372518461317995, -1.88147976332778, 4.96929159093662, -0.281657998210034, -0.344505336583714, 3.45450151652294, -4.96929159093663, 0.517139753996851, 0.344505336583713, 0.317284667025811, 0.257545933838233, 2.56006085904842, -2.56006085904842, -1.57302175319516, -0.235481755786817},

2435

{-0.918052572403101, 0.0929995320454974, -0.0562022536712399, -0.186496378006572, -0.948495588562792, 5.36128745937517, 0.206161530566525, 0.186496378006572, 3.47927866767662, -5.36128745937517, 0.485619203017004, 0.3394338373406, 1.07186148527388, -1.07186148527388, -0.149959276895285, -2.53078307911383},

2436

{-0.934240861528672, 0.241157846302772, -0.435765050906863, -0.305144107519429, -1.19622470497731, 2.84415561308039, 1.02610526808912, 0.305144107519428, 2.81677584983269, -2.84415561308039, 0.393345373116696, 0.299737642109204, 4.21956517200161, -4.21956517200161, -0.590340217182259, -1.62055114485539},

2437

{-0.958118276949497, 0.48796196620424, -1.44985477532934, 1.28234889458937, -1.16498018051314, 0.460593087542911, 2.26128841889249, -1.28234889458938, 1.81697935218046, -0.460593087542911, 0.253908836302477, 0.21624747444278, 5.79987106098239, -5.79987106098239, -0.811433643563154, -0.651999171667321},

2438

{-0.982223853848664, 0.7705598540561, -3.01080887122565, 4.96929159093662, -0.6643810885001, -0.373918583072207, 3.53876337545824, -4.96929159093663, 0.780882335574541, 0.373918583072206, 0.109196724740916, 0.102467275051648, 3.7736518258816, -3.7736518258816, -0.527954504232582, -0.116501247074442}};

2439

2440

// Array of non-zero columns

2441

static const unsigned int nzc1[16] = {0, 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19};

2442

static const double FE0[64][20] = \

2443

{{0.316942646270776, 0.0459182870838374, 0.0417713284261773, 0.0384285806226176, -0.00992565567229704, -0.0101332081942744, -0.011054706162562, -0.0116171968229622, -0.0123844609684378, -0.0127480421943013, 0.274161313248215, -0.155700796186139, 0.307139785811479, -0.170857079355319, 0.352119809987772, -0.190292195339624, 0.00443218553927295, 0.0594028686804588, 0.0681023032468037, 0.076294231978508},

2444

{0.00141590232956291, 0.0392228167323023, 0.0353420251164078, 0.0435405986330707, -0.0405943584870655, -0.0132673889695188, -0.04551696182039, -0.0152103722760563, -0.00829434237070532, -0.00848064250992449, 0.720340631623725, -0.203858737160113, 0.131264293205546, -0.113662771758787, 0.150487693606995, -0.127445887442534, 0.0139621042223731, 0.187128683191495, 0.214533314837614, 0.0390933992960042},

2445

{-0.0418846376623705, 0.0272612052688519, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, -0.066586962132492, 0.0405446175758774, -0.00355166140662744, -0.00359920474050182, 0.267461209901129, 0.543403829153424, 0.0142660308648051, -0.0482387491813342, 0.0163552633343248, -0.0545726978261391, 0.0121728891219892, 0.163148525161687, 0.187041309311128, 0.00997653862633955},

2446

{0.0606020354974101, 0.0125719331417011, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.0459453476251609, 0.0664145528584789, -0.000673013750447378, -0.000676604746500841, -0.296776478794994, 0.890128566813322, -0.00434722254509705, -0.00906827174738709, -0.00498386483050325, -0.0103411254145656, 0.00334794966816241, 0.044871274617098, 0.051442585500075, 0.000753538044430032},

2447

{-0.0233141297875962, 0.0379946132499842, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, -0.00893254555193576, -0.00890984667642712, -0.048514402947884, -0.0118784757749483, 0.128698381601996, -0.119415229212101, 0.698986096122026, -0.159202616932648, 0.126772850606219, -0.117928261408372, 0.0164798161265746, 0.220872602144184, 0.0400589504569247, 0.21756799927154},

2448

{-0.0636942004447079, 0.0319045035068057, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, -0.0363398789831187, -0.0116656442114478, -0.0321038941563349, -0.0133315323091856, 0.295507178830004, -0.156350117797481, 0.261061166329218, -0.178677371706281, 0.047347820538567, -0.0780377824367332, 0.0519140970715157, 0.695784565803582, 0.12619219939295, 0.111482512491259},

2449

{0.00416331000853175, 0.0216671920487514, 0.0640143830484231, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.0523162684880416, 0.031095825581728, -0.0135283446980037, -0.00873768447279164, -0.0189012088835134, 0.41676532427948, -0.00488762055045253, -0.117107805778746, -0.000886451952764201, -0.0328845471247492, 0.0452614117080655, 0.606621196735265, 0.110020927132805, 0.0284500609325142},

2450

{0.0641179720678825, 0.00978236065603381, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.0355809496645704, 0.0509368561168637, -0.00252676863369164, -0.00216492522558783, -0.289229785310999, 0.682686983226322, -0.0205395515393154, -0.0290156555358705, -0.00372519212221613, -0.0061420405868454, 0.0124483946900372, 0.166841019741274, 0.0302594168725173, 0.00214886185298794},

2451

{-0.0174860280987736, 0.0241979596905522, -0.0617731070981597, 0.0384285806226176, 0.0806970115889356, -0.103558823234662, -0.00550857447170805, -0.00513048407491107, -0.0630680308857183, 0.0457718784119034, 0.00853879745270188, -0.0687618938938031, 0.0977612527959358, 0.613462784549029, 0.00484326235994762, -0.0418764631771457, 0.0200039182057663, 0.268104779401166, 0.0132823767030295, 0.152070803153297},

2452

{0.018893837039617, 0.019880943301904, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.022075166962345, -0.00671733241030488, -0.0411105067572066, 0.0146593977712432, -0.036392063376584, -0.0900298084357277, -0.0677728132205631, 0.196474238955856, -0.00335758294734686, -0.0272969141137686, 0.0630155909245982, 0.844573594527272, 0.0418416436327583, 0.077921547602846},

2453

{0.0590357207055018, 0.0130980546488276, 0.0251291929007073, -0.0639547452440237, -0.101291343114797, 0.361425647567417, -0.0311273668109228, 0.017905654691607, -0.0169677743151103, -0.00273543287806846, -0.190966113694605, 0.239982565002839, -0.10409714187153, -0.0366619489640695, -0.00515715331570969, -0.0112664113073766, 0.0549402718289831, 0.736343215735788, 0.0364797225770017, 0.0198853858575406},

2454

{0.0531740973437773, 0.00574651592133119, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.0207640128472617, 0.029330552884261, -0.00310837799446909, -0.00203339486296364, -0.216073469396172, 0.393106057016485, -0.0323462532218693, -0.0272528049536403, -0.00160248959822376, -0.00206392802816228, 0.0151104033722227, 0.202518892603982, 0.0100331378912924, 0.00150196328937838},

2455

{0.0633645780899607, 0.00885305887263062, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.00195933827339023, -0.00172194832699608, -0.0330667115180807, 0.0495015510214934, -0.0169816512377694, -0.0230786074808287, -0.286590309701014, 0.663450144122639, -0.00323283077542312, -0.00499921670052641, 0.00989665381744754, 0.132641023685632, 0.00149623336497991, 0.0252511359143223},

2456

{0.0592677805711995, 0.00714461813298492, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.00775717045765741, -0.00225454345767584, -0.0212943165654493, 0.0210139153012292, -0.0747372528781832, -0.0302167740416121, -0.20516227285544, 0.281641379865613, -0.00231429635682643, -0.00321939794170582, 0.031176066711914, 0.417840765114924, 0.00471337808350589, 0.0129387597643601},

2457

{0.0461725856048027, 0.00458809898063897, -0.0385687396087239, -0.0639547452440237, 0.238148410057832, 0.532758645187123, -0.0107507634380464, 0.00600968869404704, -0.00863840057902653, 0.00215855535294798, -0.118604871591271, 0.0805455333806929, -0.0953008032716591, 0.0289302825963627, -0.00107502368122833, -0.00130600336283491, 0.0271809175250065, 0.364295325645881, 0.00410936832204637, 0.0033019394294335},

2458

{0.0234627458142642, 0.00196338908550111, 0.0612042229600472, 0.213985565988335, -0.297583634515967, 0.872691107158041, -0.00705250360640732, 0.00984423608600665, -0.00155624293107923, -0.000740737938466264, -0.0875131805869248, 0.131938489103154, -0.0193111235761632, -0.00992782411644321, -0.000217835678638767, -0.000235281807411464, 0.00747565700272528, 0.10019333967366, 0.00113021306382384, 0.000249398821943363},

2459

{-0.0474934098882189, 0.0183974307728652, 0.0417713284261773, 0.0384285806226176, -0.00992565567229704, -0.0101332081942744, -0.00722315577599345, -0.0552165235676718, -0.00809201886158537, -0.0605914303588281, 0.105381595203438, -0.11210146944143, 0.118057796688303, -0.123013691190792, 0.643304764711186, -0.0895202375930712, 0.0210661729344058, 0.0427688812853259, 0.233050470905012, 0.261083778994831},

2460

{-0.0593435556758836, 0.044173535162678, 0.0353420251164078, 0.0435405986330707, -0.0405943584870655, -0.0132673889695187, -0.0735771805831919, -0.0722948824964278, -0.0134076243672929, -0.0403084844093089, 0.228787335174519, -0.146774226939742, 0.0416908425370495, -0.081834929859403, 0.227176166261325, -0.148325620521794, 0.0663618658268005, 0.134728921587068, 0.734146830049622, 0.133780131961088},

2461

{0.0140171944147558, 0.0639244626451169, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, -0.19201789705842, 0.192708522205259, -0.0102419833030854, -0.0171070161250932, -0.0601339611396411, 0.391239924524043, -0.00320746677979301, -0.0347309377967427, -0.0174776992284671, -0.113304824716738, 0.0578577284463695, 0.117463685837307, 0.640067415277826, 0.0341403581673956},

2462

{0.0637734994386082, 0.0465185832699072, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.184144831837059, 0.315668295805934, -0.00269737874030819, -0.00321590160694519, -0.283174252139673, 0.640874823865867, -0.00414797526438387, -0.00652897488694275, -0.0226025923432014, -0.0298405119712715, 0.0159128010459527, 0.0323064232393078, 0.176039843056651, 0.0025786557535776},

2463

{-0.0544723188739935, 0.0477306372652925, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, -0.0157984607319655, -0.0423484913349203, -0.0858045319165257, -0.056458382135615, 0.0385389369754061, -0.0859765845536079, 0.209312508594235, -0.114622710571981, 0.180434929473551, -0.150168175204615, 0.0783285477048384, 0.15902387056592, 0.137084310263545, 0.744531715767973},

2464

{-0.0175829401694107, 0.0601263089173645, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, -0.0887466324394246, -0.0554467939512141, -0.0784018156992204, -0.0633647582253519, 0.0422682922674721, -0.112568968057714, 0.0373412575686983, -0.128644145790115, 0.0321895104172831, -0.137212538001305, 0.24674764559191, 0.500951017283187, 0.431837839411788, 0.381500342794664},

2465

{0.0452580461211559, 0.0623679922432538, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.175443845541055, 0.14779842437514, -0.0453676243779744, -0.041530204572686, -0.162251408196532, 0.300062725486068, -0.0419562220558782, -0.0843152856788516, -0.0361677762044535, -0.0793987591801864, 0.215127439464974, 0.436755168978356, 0.376498703498837, 0.0973579421179106},

2466

{0.0592405099224476, 0.0385588963661094, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.14897956417135, 0.24210282042228, -0.0105797313831695, -0.0102898871872979, -0.249121428689321, 0.491521018920905, -0.0176912706919525, -0.0208906935741604, -0.0152505132208227, -0.0185157930528795, 0.0591672061046181, 0.120122208326693, 0.103549674757618, 0.00735354375510284},

2467

{0.0325299333929531, 0.0638787973684188, -0.0617731070981597, 0.0384285806226176, 0.0806970115889355, -0.103558823234662, -0.017343262053637, -0.0243851850969721, -0.198564146218889, 0.217553687140082, -0.0117972873894809, -0.0495071928717421, -0.135067918073687, 0.44168097582085, -0.0318046891613103, -0.094925310825481, 0.0950786009643269, 0.193030096642605, 0.0454531491271413, 0.52039608935609},

2468

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2469

{0.0640509106927241, 0.0478617966777029, 0.0251291929007073, -0.0639547452440237, -0.101291343114797, 0.361425647567417, -0.123672280290719, 0.0851055568172439, -0.0674147400181511, -0.0130015094244685, -0.186777439414966, 0.172782662877202, -0.101813862328864, -0.0263958724176695, -0.0239742959680135, -0.0322282006711705, 0.261131050845518, 0.530152436719253, 0.124835961777158, 0.0680490720179158},

2470

{0.043189241782395, 0.0246116712744907, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.0920146055848046, 0.139408085209121, -0.0137746098152355, -0.00966472352016019, -0.169123783267225, 0.283028524691626, -0.0253178732895336, -0.0196214762964438, -0.00596164582739598, -0.00658507159076726, 0.0718197304077884, 0.145809565568416, 0.0343340444998879, 0.00513981517780901},

2471

{0.0565572914460857, 0.0355988950588367, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.00831703837687068, -0.00818441848139805, -0.140362239858113, 0.235280816901719, -0.0142479247765323, -0.0166161373264267, -0.240454659981553, 0.477670878242413, -0.0128920618579229, -0.0152785351603578, 0.0470387845777104, 0.0954988929253688, 0.00512020700722333, 0.0864110145348935},

2472

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2473

{0.0364359152038298, 0.0200917703395614, -0.0385687396087239, -0.0639547452440237, 0.238148410057832, 0.532758645187123, -0.0483637167469587, 0.0285640436730254, -0.0388609758886781, 0.0102596111897318, -0.0909450732072041, 0.0579911784017145, -0.0730757380701406, 0.0208292267595789, -0.00391798160861548, -0.00423004639339734, 0.129190870739485, 0.262285372431402, 0.0140625232468916, 0.0112994495375666},

2474

{0.0175030551599998, 0.00902055949440797, 0.0612042229600472, 0.213985565988335, -0.297583634515967, 0.872691107158041, -0.0327684220468546, 0.0467896431585221, -0.00723085417875004, -0.00352072659696579, -0.0645347110293077, 0.0949930820306381, -0.014240572348997, -0.0071478354579437, -0.000763513336067498, -0.000787083904625139, 0.0355317894123066, 0.0721372072640786, 0.00386766194665403, 0.000853458842447994},

2475

{0.0183974307728653, -0.0474934098882189, 0.0417713284261773, 0.0384285806226176, -0.00992565567229703, -0.0101332081942744, 0.105381595203438, -0.11210146944143, 0.118057796688303, -0.123013691190792, -0.00722315577599352, -0.0552165235676718, -0.00809201886158544, -0.0605914303588281, -0.0895202375930713, 0.643304764711186, 0.0427688812853259, 0.0210661729344057, 0.233050470905012, 0.261083778994831},

2476

{0.0441735351626781, -0.0593435556758837, 0.0353420251164078, 0.0435405986330707, -0.0405943584870654, -0.0132673889695187, 0.228787335174519, -0.146774226939742, 0.0416908425370495, -0.081834929859403, -0.073577180583192, -0.0722948824964278, -0.013407624367293, -0.0403084844093089, -0.148325620521794, 0.227176166261325, 0.134728921587068, 0.0663618658268004, 0.734146830049622, 0.133780131961088},

2477

{0.0639244626451169, 0.0140171944147557, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, -0.0601339611396408, 0.391239924524043, -0.00320746677979297, -0.0347309377967428, -0.19201789705842, 0.192708522205259, -0.0102419833030855, -0.0171070161250932, -0.113304824716739, -0.017477699228467, 0.117463685837307, 0.0578577284463694, 0.640067415277826, 0.0341403581673956},

2478

{0.0465185832699073, 0.0637734994386082, 0.0110533069845139, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.283174252139672, 0.640874823865867, -0.00414797526438382, -0.00652897488694276, -0.184144831837059, 0.315668295805934, -0.00269737874030827, -0.0032159016069452, -0.0298405119712715, -0.0226025923432015, 0.0323064232393079, 0.0159128010459527, 0.176039843056651, 0.00257865575357757},

2479

{0.0477306372652926, -0.0544723188739936, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, 0.0385389369754061, -0.085976584553608, 0.209312508594235, -0.114622710571981, -0.0157984607319655, -0.0423484913349203, -0.0858045319165258, -0.0564583821356151, -0.150168175204615, 0.180434929473551, 0.15902387056592, 0.0783285477048383, 0.137084310263545, 0.744531715767973},

2480

{0.0601263089173645, -0.0175829401694107, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, 0.0422682922674721, -0.112568968057714, 0.0373412575686983, -0.128644145790115, -0.0887466324394247, -0.0554467939512141, -0.0784018156992205, -0.0633647582253519, -0.137212538001305, 0.0321895104172831, 0.500951017283187, 0.24674764559191, 0.431837839411788, 0.381500342794665},

2481

{0.0623679922432539, 0.0452580461211558, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.162251408196532, 0.300062725486068, -0.0419562220558781, -0.0843152856788517, -0.175443845541055, 0.14779842437514, -0.0453676243779745, -0.041530204572686, -0.0793987591801865, -0.0361677762044535, 0.436755168978356, 0.215127439464974, 0.376498703498837, 0.0973579421179105},

2482

{0.0385588963661094, 0.0592405099224476, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.24912142868932, 0.491521018920905, -0.0176912706919524, -0.0208906935741604, -0.14897956417135, 0.24210282042228, -0.0105797313831696, -0.0102898871872979, -0.0185157930528794, -0.0152505132208228, 0.120122208326693, 0.0591672061046181, 0.103549674757618, 0.00735354375510282},

2483

{0.0638787973684189, 0.032529933392953, -0.0617731070981598, 0.0384285806226176, 0.0806970115889355, -0.103558823234662, -0.0117972873894808, -0.0495071928717421, -0.135067918073687, 0.44168097582085, -0.0173432620536371, -0.024385185096972, -0.198564146218889, 0.217553687140082, -0.0949253108254811, -0.0318046891613103, 0.193030096642606, 0.0950786009643268, 0.0454531491271413, 0.52039608935609},

2484

{0.0605211362317534, 0.0525008116745777, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.0827313861152966, -0.0648196673773589, -0.15407037300001, 0.141457535438722, -0.0770790017967223, -0.0319274734686737, -0.143543957316746, 0.0696761012883772, -0.0686224327245416, -0.0362792319013842, 0.608076151934063, 0.299513033517807, 0.143184801205848, 0.266652557941832},

2485

{0.0478617966777029, 0.0640509106927241, 0.0251291929007073, -0.0639547452440237, -0.101291343114797, 0.361425647567417, -0.186777439414966, 0.172782662877202, -0.101813862328864, -0.0263958724176696, -0.123672280290718, 0.0851055568172438, -0.0674147400181512, -0.0130015094244684, -0.0322282006711705, -0.0239742959680135, 0.530152436719253, 0.261131050845517, 0.124835961777158, 0.0680490720179158},

2486

{0.0246116712744908, 0.0431892417823949, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.169123783267225, 0.283028524691625, -0.0253178732895334, -0.0196214762964438, -0.0920146055848049, 0.139408085209121, -0.0137746098152356, -0.00966472352016022, -0.00658507159076725, -0.00596164582739602, 0.145809565568416, 0.0718197304077886, 0.034334044499888, 0.005139815177809},

2487

{0.0355988950588367, 0.0565572914460857, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.0142479247765323, -0.0166161373264268, -0.240454659981553, 0.477670878242413, -0.00831703837687075, -0.00818441848139802, -0.140362239858113, 0.235280816901719, -0.0152785351603579, -0.0128920618579228, 0.095498892925369, 0.0470387845777103, 0.00512020700722332, 0.0864110145348935},

2488

{0.0297626847872616, 0.0500526781546473, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.060177304883694, -0.0217554749546356, -0.165193557012014, 0.202776179132074, -0.0337332239476843, -0.0107158425446524, -0.0926015424614136, 0.0998791160347682, -0.010079747400941, -0.00885691113531576, 0.300837021449246, 0.148179810377592, 0.0161294835790437, 0.0442772698168981},

2489

{0.0200917703395613, 0.0364359152038299, -0.0385687396087239, -0.0639547452440237, 0.238148410057832, 0.532758645187123, -0.0909450732072041, 0.0579911784017145, -0.0730757380701405, 0.0208292267595789, -0.0483637167469586, 0.0285640436730253, -0.0388609758886781, 0.0102596111897318, -0.00423004639339734, -0.00391798160861548, 0.262285372431403, 0.129190870739485, 0.0140625232468916, 0.0112994495375665},

2490

{0.00902055949440803, 0.0175030551599997, 0.0612042229600472, 0.213985565988335, -0.297583634515967, 0.872691107158041, -0.0645347110293075, 0.0949930820306377, -0.0142405723489969, -0.00714783545794369, -0.0327684220468548, 0.0467896431585224, -0.00723085417875017, -0.0035207265969658, -0.000787083904625131, -0.000763513336067518, 0.0721372072640785, 0.0355317894123067, 0.00386766194665405, 0.00085345884244799},

2491

{0.0459182870838375, 0.316942646270776, 0.0417713284261773, 0.0384285806226176, -0.00992565567229701, -0.0101332081942743, 0.274161313248215, -0.155700796186139, 0.307139785811479, -0.170857079355319, -0.011054706162562, -0.0116171968229622, -0.0123844609684377, -0.0127480421943014, -0.190292195339624, 0.352119809987772, 0.0594028686804587, 0.00443218553927282, 0.0681023032468037, 0.0762942319785081},

2492

{0.0392228167323025, 0.00141590232956263, 0.0353420251164078, 0.0435405986330708, -0.0405943584870654, -0.0132673889695187, 0.720340631623725, -0.203858737160113, 0.131264293205546, -0.113662771758787, -0.04551696182039, -0.0152103722760563, -0.00829434237070529, -0.0084806425099245, -0.127445887442534, 0.150487693606995, 0.187128683191495, 0.0139621042223729, 0.214533314837614, 0.0390933992960044},

2493

{0.027261205268852, -0.0418846376623705, 0.0242504041833649, -0.0639547452440238, -0.0588585848419933, 0.0353654205325618, 0.267461209901129, 0.543403829153424, 0.0142660308648051, -0.0482387491813341, -0.0665869621324919, 0.0405446175758774, -0.00355166140662746, -0.00359920474050181, -0.0545726978261391, 0.0163552633343248, 0.163148525161687, 0.012172889121989, 0.187041309311128, 0.00997653862633953},

2494

{0.0125719331417013, 0.0606020354974101, 0.0110533069845139, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.296776478794994, 0.890128566813322, -0.00434722254509705, -0.00906827174738711, -0.0459453476251611, 0.0664145528584792, -0.000673013750447483, -0.000676604746500861, -0.0103411254145656, -0.00498386483050329, 0.0448712746170982, 0.00334794966816239, 0.0514425855000751, 0.000753538044429961},

2495

{0.0379946132499844, -0.0233141297875965, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, 0.128698381601996, -0.119415229212101, 0.698986096122025, -0.159202616932648, -0.00893254555193573, -0.00890984667642714, -0.0485144029478841, -0.0118784757749484, -0.117928261408373, 0.126772850606219, 0.220872602144184, 0.0164798161265745, 0.0400589504569248, 0.21756799927154},

2496

{0.0319045035068058, -0.063694200444708, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.0643207363967599, 0.295507178830004, -0.156350117797481, 0.261061166329218, -0.178677371706281, -0.0363398789831187, -0.0116656442114479, -0.032103894156335, -0.0133315323091857, -0.0780377824367335, 0.0473478205385671, 0.695784565803581, 0.0519140970715157, 0.12619219939295, 0.11148251249126},

2497

{0.0216671920487514, 0.0041633100085317, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.0189012088835131, 0.41676532427948, -0.0048876205504524, -0.117107805778746, -0.0523162684880414, 0.031095825581728, -0.0135283446980038, -0.00873768447279162, -0.0328845471247492, -0.000886451952764223, 0.606621196735265, 0.0452614117080653, 0.110020927132805, 0.0284500609325141},

2498

{0.00978236065603392, 0.0641179720678825, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.289229785310999, 0.682686983226322, -0.0205395515393154, -0.0290156555358705, -0.0355809496645706, 0.0509368561168639, -0.00252676863369175, -0.00216492522558786, -0.0061420405868454, -0.0037251921222162, 0.166841019741274, 0.0124483946900372, 0.0302594168725175, 0.00214886185298789},

2499

{0.0241979596905522, -0.0174860280987737, -0.0617731070981598, 0.0384285806226176, 0.0806970115889355, -0.103558823234662, 0.00853879745270196, -0.0687618938938031, 0.097761252795936, 0.613462784549029, -0.00550857447170807, -0.00513048407491103, -0.0630680308857182, 0.0457718784119034, -0.0418764631771457, 0.00484326235994764, 0.268104779401166, 0.0200039182057662, 0.0132823767030295, 0.152070803153297},

2500

{0.019880943301904, 0.018893837039617, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.0363920633765839, -0.0900298084357277, -0.067772813220563, 0.196474238955856, -0.022075166962345, -0.00671733241030489, -0.0411105067572068, 0.0146593977712433, -0.0272969141137688, -0.0033575829473469, 0.844573594527272, 0.0630155909245982, 0.0418416436327584, 0.0779215476028461},

2501

{0.0130980546488274, 0.0590357207055018, 0.0251291929007073, -0.0639547452440238, -0.101291343114797, 0.361425647567417, -0.190966113694605, 0.239982565002839, -0.104097141871529, -0.0366619489640696, -0.0311273668109225, 0.0179056546916068, -0.0169677743151103, -0.00273543287806841, -0.0112664113073766, -0.00515715331570972, 0.736343215735788, 0.0549402718289825, 0.0364797225770015, 0.0198853858575404},

2502

{0.00574651592133132, 0.0531740973437773, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.216073469396172, 0.393106057016485, -0.0323462532218692, -0.0272528049536403, -0.0207640128472621, 0.0293305528842615, -0.00310837799446924, -0.00203339486296368, -0.0020639280281623, -0.00160248959822383, 0.202518892603981, 0.0151104033722229, 0.0100331378912926, 0.00150196328937837},

2503

{0.00885305887263062, 0.0633645780899607, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.0169816512377693, -0.0230786074808287, -0.286590309701014, 0.663450144122639, -0.0019593382733903, -0.00172194832699607, -0.0330667115180806, 0.0495015510214933, -0.00499921670052645, -0.00323283077542309, 0.132641023685632, 0.00989665381744747, 0.0014962333649799, 0.0252511359143222},

2504

{0.00714461813298495, 0.0592677805711995, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.0747372528781831, -0.0302167740416121, -0.20516227285544, 0.281641379865613, -0.00775717045765746, -0.00225454345767584, -0.0212943165654494, 0.0210139153012293, -0.0032193979417059, -0.00231429635682643, 0.417840765114924, 0.031176066711914, 0.00471337808350594, 0.0129387597643601},

2505

{0.00458809898063892, 0.0461725856048027, -0.0385687396087239, -0.0639547452440237, 0.238148410057832, 0.532758645187123, -0.118604871591271, 0.0805455333806929, -0.095300803271659, 0.0289302825963627, -0.0107507634380463, 0.00600968869404697, -0.00863840057902652, 0.00215855535294799, -0.00130600336283492, -0.00107502368122835, 0.364295325645881, 0.0271809175250061, 0.00410936832204636, 0.00330193942943344},

2506

{0.00196338908550119, 0.0234627458142642, 0.0612042229600472, 0.213985565988335, -0.297583634515967, 0.872691107158041, -0.0875131805869245, 0.131938489103153, -0.0193111235761631, -0.00992782411644321, -0.00705250360640757, 0.00984423608600694, -0.00155624293107936, -0.000740737938466279, -0.000235281807411467, -0.000217835678638792, 0.10019333967366, 0.00747565700272542, 0.00113021306382388, 0.000249398821943354}};

2507

2508

static const double FE0_D010[64][16] = \

2509

{{-2.89581790868146, 0.550843873647288, -0.147100493051721, -0.186496378006569, -0.227929503657332, -0.188928908491132, -0.875026145642752, 0.186496378006569, 4.67246475338807, -2.3274907183539, -1.12384215149678, 0.227929503657332, 0.0815720484450847, 1.02212663869447, -0.081572048445085, 1.31277105998792},

2510

{-1.01268955903752, 0.634208990161043, -0.793601441481282, -0.305144107519429, -0.190766224310168, -0.165792744888627, -3.23017404188562, 0.305144107519429, 2.43040151775111, -2.05192094887464, -0.674821633227638, 0.190766224310168, 0.321122252601283, 4.0237754833669, -0.321122252601281, 0.840614378116265},

2511

{0.389619002348325, 0.762060204474009, -1.94170757097522, 1.28234889458938, -0.12878311667611, -0.118735493095584, -3.58904690977611, -1.28234889458938, 0.325850708759322, -1.47752991558166, -0.219470357403724, 0.128783116676109, 0.441388527959663, 5.53075448075133, -0.441388527959662, 0.338205850499309},

2512

{0.178970691981112, 0.896915023365993, -3.33082998563292, 4.96929159093663, -0.0577310620952133, -0.0559357213522612, -0.267722727926006, -4.96929159093663, -0.376826018254617, -0.69905969709249, -0.00449595565475457, 0.0577310620952123, 0.287186836904624, 3.59855271355893, -0.287186836904623, 0.0604316770070172},

2513

{-0.772156249476526, -0.434006101240926, 0.126694655024588, -0.186496378006569, -0.184174110474718, 0.12479910294217, -0.620241099631208, 0.186496378006569, -0.715105973333578, 1.92126832405103, -0.610961313457298, 0.184174110474717, 0.0625619463803196, 0.493546444606621, -0.0625619463803203, 0.486162210515127},

2514

{0.0672149106221293, -0.297265876948554, 0.284239759978268, -0.305144107519429, -0.15230413516731, 0.0455424913826485, -2.22716934280135, 0.305144107519429, -0.729057010740207, 0.959107977066631, -0.356849585751078, 0.152304135167311, 0.246285750225997, 1.94292958282309, -0.246285750225997, 0.311307094368429},

2515

{0.49906283922646, 0.0380105914258389, -0.46019472833453, 1.28234889458938, -0.101182752493622, -0.0215827737843673, -2.21039823601036, -1.28234889458938, -0.608137898905595, 0.0710644682532944, -0.103665953049544, 0.101182752493622, 0.33852435908473, 2.67059296434489, -0.33852435908473, 0.125248726833912},

2516

{-0.0183629959498944, 0.534467499977834, -2.36689241100155, 4.96929159093663, -0.0447080307510196, -0.0304848581003364, 0.629286883202171, -4.96929159093663, -0.318733251490988, -0.197371252536953, 0.00810502465158824, 0.0447080307510188, 0.220258873401427, 1.73760552779938, -0.220258873401427, 0.0223798334487492},

2517

{0.48311070654784, 0.165050168904604, 0.508902750434951, -0.18649637800657, -0.113577568388747, 0.288653004091984, -0.264570417154491, 0.18649637800657, -2.85302839593482, 2.20486752048238, -0.150066089523472, 0.113577568388746, 0.0360245334466714, -0.24433233328046, -0.0360245334466716, -0.138586914568512},

2518

{0.480204186575578, -0.333630559700654, 1.78886698094661, -0.305144107519429, -0.0925192737828259, 0.165043383447255, -0.827011164622839, 0.305144107519429, -1.69266286458037, 1.54608923770545, -0.0763012131208206, 0.0925192737828256, 0.14181670743617, -0.96185581632377, -0.141816707436171, -0.0887421703264342},

2519

{0.211483050177827, -0.464213039151449, 1.60794346144038, 1.28234889458937, -0.0602021654607815, 0.043423468138972, -0.28585469481812, -1.28234889458937, -0.525161399675397, 0.77789138864902, -0.00771967580358129, 0.0602021654607812, 0.194929710502059, -1.32208876662226, -0.194929710502061, -0.0357037923353905},

2520

{-0.372518461317996, 0.119368446579232, -1.02127052148706, 4.96929159093662, -0.0260903133176998, -0.00757416166005619, 1.88147976332778, -4.96929159093663, 0.010158237655233, 0.242991777083531, 0.0139538267165684, 0.0260903133176989, 0.126829864012545, -0.86020924184072, -0.126829864012546, -0.00637966505651153},

2521

{-0.0929995320454974, 2.67795638548276, 0.853609012762395, -0.186496378006571, -0.0403982696223159, 0.162503248241208, 0.0562022536712438, 0.186496378006571, 0.598362416229819, -3.18331926966708, 0.010699334992376, 0.040398269622315, 0.0120909419449659, -0.909811266433639, -0.0120909419449657, -0.173202583233583},

2522

{-0.241157846302771, 0.896717691404195, 3.14586185301822, -0.305144107519429, -0.0325110916975726, 0.0974140250697482, 0.435765050906867, 0.305144107519429, 0.882993263846752, -1.53855310894818, 0.0134937990213523, 0.0325110916975708, 0.0475980508942626, -3.58162690392509, -0.0475980508942622, -0.110907824091098},

2523

{-0.48796196620424, -0.408955764144395, 3.47315823301274, 1.28234889458937, -0.0207926113139723, 0.0314803877703174, 1.44985477532934, -1.28234889458938, 0.935591355323889, -0.0386736249752544, 0.0131413507464731, 0.0207926113139706, 0.0654244090771633, -4.92301300834208, -0.0654244090771642, -0.044621738516789},

2524

{-0.7705598540561, -0.164194200903477, 0.192320445346117, 4.96929159093662, -0.008861583265185, 0.00047871937058011, 3.01080887122566, -4.96929159093663, 0.554419381303298, 0.38033467365628, 0.00749443214515546, 0.00886158326518377, 0.0425680050772475, -3.20312931657177, -0.0425680050772485, -0.00797315151573477},

2525

{-0.467878056063201, 0.550843873647288, -0.147100493051721, -0.186496378006569, -0.148929359736163, -0.897978891749118, -0.568886338631576, 0.18649637800657, 1.53547491751183, -1.61844073509592, -3.47278186019387, 0.148929359736164, 0.38771185545626, 0.715986831683297, -0.38771185545626, 4.37076075194299},

2526

{0.205627659956735, 0.634208990161044, -0.793601441481281, -0.305144107519429, -0.308369459952734, -0.78801273190081, -2.02500258533535, 0.305144107519429, 0.589864311744675, -1.42970096186245, -2.01074208786445, 0.308369459952734, 1.52629370915155, 2.81860402681663, -1.52629370915155, 2.79875481976526},

2527

{0.489236057073233, 0.762060204474009, -1.94170757097522, 1.28234889458938, -0.371373951428681, -0.564349666511006, -1.93251625568215, -1.28234889458938, -0.219380519381007, -1.03191574216624, -0.561678246881203, 0.371373951428681, 2.09791918205362, 3.87422382665737, -2.09791918205362, 1.12602791339221},

2528

{-0.0638353588879538, 0.896915023365993, -3.33082998563292, 4.96929159093663, -0.231380918216752, -0.265862421321552, 0.810089151290437, -4.96929159093663, -0.343946667354841, -0.489132997123199, 0.0646602390927717, 0.231380918216752, 1.36499871612107, 2.52074083434249, -1.36499871612107, 0.201202182228781},

2529

{0.27993407433382, -0.434006101240926, 0.126694655024588, -0.18649637800657, -0.325737768171688, 0.593169997362034, -0.385446184507694, 0.18649637800657, -1.29882540272406, 1.45289742963117, -1.80461529496461, 0.325737768171688, 0.297356861503832, 0.258751529483107, -0.297356861503832, 1.21144529760258},

2530

{0.482918552223105, -0.297265876948554, 0.284239759978268, -0.305144107519429, -0.371946178163572, 0.216463410845381, -1.30285919636009, 0.305144107519429, -0.97383973287845, 0.788187057603898, -0.992195270348315, 0.371946178163572, 1.17059589666726, 1.01861943638182, -1.17059589666726, 0.775731859502934},

2531

{0.366779535287998, 0.0380105914258388, -0.46019472833453, 1.28234889458938, -0.339318757108362, -0.102582899771889, -0.939916693199137, -1.28234889458938, -0.556854720954653, 0.152064594240816, -0.209518653725823, 0.339318757108362, 1.60900590189595, 1.40011142153367, -1.60900590189595, 0.312101553497711},

2532

{-0.241872355951096, 0.534467499977834, -2.36689241100155, 4.96929159093663, -0.187195198527213, -0.144894496616187, 1.45591818989304, -4.96929159093663, -0.209633530005636, -0.0829616140211016, 0.089127216876596, 0.187195198527213, 1.0468901800923, 0.910974221108511, -1.04689018009229, 0.0557672797395916},

2533

{0.437807010605908, 0.165050168904603, 0.508902750434952, -0.18649637800657, -0.357588980978253, 1.37196740713051, -0.129370383230414, 0.18649637800657, -1.72441029695436, 1.12155311744385, -0.348773806171044, 0.357588980978252, 0.171224567370748, -0.379532367204537, -0.171224567370748, -1.02319360095947},

2534

{0.302639767092249, -0.333630559700654, 1.78886698094661, -0.305144107519429, -0.323045949428251, 0.784451017804134, -0.294773219480419, 0.305144107519429, -0.895690810740162, 0.926681603348568, -0.129263469282916, 0.32304594942825, 0.67405465257859, -1.49409376146619, -0.67405465257859, -0.655187548521217},

2535

{-0.0324350076632246, -0.464213039151449, 1.60794346144038, 1.28234889458937, -0.239189492840795, 0.20639169572701, 0.445716291707001, -1.28234889458938, -0.118275114246308, 0.614923161060981, 0.0572110546574559, 0.239189492840794, 0.926500697027181, -2.05365975314738, -0.926500697027181, -0.263602750384466},

2536

{-0.531193484944987, 0.119368446579232, -1.02127052148706, 4.96929159093662, -0.115617819502007, -0.0359999819389442, 2.35747210178416, -4.96929159093663, 0.140407441003337, 0.271417597362419, 0.0831013441592525, 0.115617819502006, 0.602822202468931, -1.33620158029711, -0.602822202468931, -0.047101362220308},

2537

{-0.305298331172715, 2.67795638548276, 0.853609012762396, -0.186496378006571, -0.171483384656493, 0.772377757997374, 0.101579545331468, 0.186496378006571, 1.4205357251132, -3.79319377942325, 0.0919130190854158, 0.171483384656493, 0.0574682336051896, -0.955188558093863, -0.0574682336051899, -0.864290777082788},

2538

{-0.426959954263386, 0.896717691404195, 3.14586185301822, -0.305144107519429, -0.141379378344762, 0.463008752718538, 0.614400482928493, 0.305144107519429, 1.43439009945616, -1.90414783659697, 0.0904276203347775, 0.14137937834476, 0.226233482915889, -3.76026233594672, -0.226233482915888, -0.553436373053314},

2539

{-0.620605062441599, -0.408955764144395, 3.47315823301274, 1.28234889458937, -0.0935382840310493, 0.149626248029426, 1.69539250976771, -1.28234889458938, 1.18638031182036, -0.156819485234363, 0.0730387742667553, 0.0935382840310477, 0.310962143515531, -5.16855074278045, -0.310962143515532, -0.22266502229618},

2540

{-0.832889012138124, -0.164194200903477, 0.192320445346117, 4.96929159093662, -0.0411740449410185, 0.00227535263547532, 3.1705665468953, -4.96929159093663, 0.618545172650217, 0.378538040391385, 0.037511128551346, 0.0411740449410173, 0.202325680746892, -3.36288699224142, -0.202325680746893, -0.0397864811868207},

2541

{0.481257411950509, 0.550843873647289, -0.147100493051722, -0.18649637800657, 2.17279178081481, -1.82309111092608, -0.169459382944774, 0.186496378006569, -0.338772769678836, -0.693328515918961, -2.10019618765661, -2.17279178081481, 0.787138811143062, 0.316559875996497, -0.787138811143061, 3.92328729858268},

2542

{0.374511532557597, 0.634208990161044, -0.793601441481281, -0.305144107519429, 0.958871030835728, -1.59983605408212, -0.452590390168168, 0.305144107519429, -0.390842883037494, -0.617877639681148, -0.912385469676855, -0.958871030835727, 3.09870590431873, 1.24619183164945, -3.09870590431873, 2.51222152375897},

2543

{0.047623881211908, 0.762060204474009, -1.94170757097522, 1.28234889458938, -0.1163026317109, -1.14575172080744, 0.228793645916037, -1.28234889458938, -0.359170397816118, -0.4505136878698, 0.135005248697902, 0.116302631710901, 4.25922908365181, 1.71291392505918, -4.25922908365181, 1.01074647210954},

2544

{-0.48276197214663, 0.896915023365993, -3.33082998563292, 4.96929159093663, -0.3558129642943, -0.539758140747053, 2.21633266441442, -4.96929159093663, -0.198915773521666, -0.215237277697697, 0.359154806273899, 0.3558129642943, 2.77124222924505, 1.11449732121851, -2.77124222924505, 0.180603334473153},

2545

{0.347571076915241, -0.434006101240927, 0.126694655024588, -0.18649637800657, 0.794608255263633, 1.20426321753775, -0.0791043889923459, 0.18649637800657, -0.75536918512977, 0.841804209455456, -0.751906274110712, -0.794608255263634, 0.603698657019181, -0.0475902660322414, -0.603698657019181, -0.452356943427033},

2546

{0.189627288930479, -0.297265876948554, 0.284239759978268, -0.305144107519429, 0.177150719235663, 0.439467479446286, -0.0968925776838803, 0.305144107519429, -0.457544400984918, 0.565182989002993, -0.149807109656454, -0.177150719235663, 2.37656251534347, -0.187347182294387, -2.37656251534347, -0.289660369789832},

2547

{-0.142029172075059, 0.0380105914258387, -0.46019472833453, 1.28234889458938, -0.313803804280189, -0.208265444127389, 0.717706926073706, -1.28234889458938, -0.153728557947097, 0.257747138596316, 0.324805006465407, 0.313803804280189, 3.26662952116879, -0.257512197739175, -3.26662952116879, -0.116539562338018},

2548

{-0.593565766700245, 0.534467499977833, -2.36689241100155, 4.96929159093663, -0.313025048504259, -0.294167124895937, 2.53444120044319, -4.96929159093663, -0.00721274753623695, 0.0663110142586485, 0.314990777648698, 0.313025048504259, 2.12541319064245, -0.16754878944164, -2.12541319064245, -0.0208236527527615},

2549

{-0.0540171096638478, 0.165050168904603, 0.508902750434953, -0.18649637800657, -0.243240283336858, 2.78539017721002, 0.0470279051407377, 0.18649637800657, 0.1808365933949, -0.291869652635655, 0.257399011740106, 0.243240283336858, 0.3476228557419, -0.55593065557569, -0.347622855741901, -3.04278918895013},

2550

{-0.20611543016718, -0.333630559700654, 1.78886698094661, -0.305144107519429, -0.346735667978873, 1.59260500514659, 0.399648666404792, 0.305144107519429, 0.421218373861721, 0.118527616006114, 0.35580200942589, 0.346735667978872, 1.3684765384638, -2.1885156473514, -1.3684765384638, -1.94840701457248},

2551

{-0.462159330951633, -0.464213039151449, 1.60794346144038, 1.28234889458938, -0.361238596901013, 0.419019722296543, 1.40021213094248, -1.28234889458938, 0.524077235611634, 0.402295134491448, 0.364886273885646, 0.361238596901012, 1.88099653626266, -3.00815559238285, -1.88099653626266, -0.783905996182189},

2552

{-0.758139561814633, 0.119368446579232, -1.02127052148706, 4.96929159093662, -0.212506731110909, -0.0730877392212954, 2.97850917806655, -4.96929159093663, 0.330265760590632, 0.30850535464477, 0.213158509419996, 0.212506731110908, 1.22385927875132, -1.95723865657949, -1.22385927875132, -0.140070770198701},

2553

{-0.631033513741427, 2.67795638548276, 0.853609012762397, -0.186496378006571, -0.293768316833252, 1.56809367995192, 0.160784238906301, 0.186496378006571, 2.54198682963646, -4.5889097013778, 0.29536326947737, 0.293768316833252, 0.116672927180023, -1.0143932516687, -0.116672927180024, -1.86345694942929},

2554

{-0.700592692350177, 0.896717691404196, 3.14586185301822, -0.305144107519429, -0.252209215701245, 0.940007776483423, 0.847469836067498, 0.305144107519429, 2.18502186130783, -2.38114686036185, 0.253230521065085, 0.252209215701243, 0.459302836054894, -3.99333168908572, -0.459302836054893, -1.19323829754851},

2555

{-0.806225191360899, -0.408955764144395, 3.47315823301274, 1.28234889458937, -0.175893141823411, 0.303773602308549, 2.01575068445413, -1.28234889458938, 1.52614779501878, -0.310966839513486, 0.176304045393693, 0.175893141823409, 0.631320318201947, -5.48890891746686, -0.631320318201947, -0.480077647702241},

2556

{-0.91645504758449, -0.164194200903477, 0.192320445346117, 4.96929159093662, -0.0810888937031189, 0.004619457319178, 3.37900569978859, -4.96929159093663, 0.704455312780285, 0.376193935707682, 0.0811623152356104, 0.0810888937031178, 0.410764833640184, -3.57132614513471, -0.410764833640184, -0.0857817725547879},

2557

{-0.49175735427463, 0.550843873647289, -0.147100493051723, -0.186496378006569, 5.65274654357938, -2.53214109418406, 0.136680424066405, 0.186496378006569, -0.0748079867116807, 0.0157214673390227, 2.3527733413331, -5.65274654357938, 1.09327861815424, 0.0104200689853184, -1.09327861815424, 0.179367752850965},

2558

{-0.584924429529852, 0.634208990161044, -0.793601441481281, -0.305144107519429, 3.01902097627486, -2.2220560410943, 0.752581066382098, 0.305144107519429, -0.0536269079622267, 0.0043423473310342, 2.10720043784973, -3.01902097627486, 4.303877360869, 0.0410203750991849, -4.303877360869, 0.114855603244573},

2559

{-0.728938303866098, 0.762060204474009, -1.94170757097521, 1.28234889458937, 0.517285773339441, -1.59136589422286, 1.88532430000999, -1.28234889458938, -0.0282223861535331, -0.00489951445437849, 1.54515583882625, -0.517285773339441, 5.91575973774576, 0.0563832709652265, -5.91575973774576, 0.046210055396613},

2560

{-0.882126464396442, 0.896915023365992, -3.33082998563292, 4.96929159093663, -0.372904379035093, -0.749684840716344, 3.29414454363086, -4.96929159093663, -0.00947798124114361, -0.00531057772840652, 0.741427883782919, 0.372904379035093, 3.84905410846149, 0.0366854420020629, -3.84905410846149, 0.00825695693342338},

2561

{-0.600838818610105, -0.434006101240927, 0.126694655024588, -0.18649637800657, 2.65354481690235, 1.67263411195761, 0.155690526131169, 0.18649637800657, 0.661411604815439, 0.373433315035593, 2.05544018305336, -2.65354481690236, 0.838493572142695, -0.282385181155756, -0.838493572142697, -3.72807429501096},

2562

{-0.675661086320138, -0.297265876948554, 0.284239759978268, -0.305144107519429, 1.23850069309099, 0.610388398909019, 0.827417568757383, 0.305144107519429, 0.578664893728431, 0.39426206954026, 1.77683123944949, -1.23850069309099, 3.30087266178473, -1.11165732873565, -3.30087266178473, -2.38721963835851},

2563

{-0.789696230825047, 0.0380105914258387, -0.46019472833453, 1.28234889458937, -0.0365560540834043, -0.28926557011491, 1.98818846888492, -1.28234889458938, 0.41293837481537, 0.338747264583837, 1.24971981541218, 0.0365560540834042, 4.53711106398001, -1.52799374055039, -4.53711106398001, -0.960454245297269},

2564

{-0.909165504675249, 0.534467499977833, -2.36689241100155, 4.96929159093663, -0.363421838306651, -0.408576763411788, 3.36107250713406, -4.96929159093663, 0.193977351922917, 0.180720652774499, 0.580193725821311, 0.36342183830665, 2.95204449733331, -0.994180096132508, -2.95204449733331, -0.171616962409524},

2565

{-0.762628186468936, 0.165050168904603, 0.508902750434954, -0.186496378006571, 0.176055684936792, 3.86870458024855, 0.182227939064815, 0.186496378006571, 1.97276207323851, -1.37518405567418, 1.38530605681884, -0.176055684936793, 0.482822889665977, -0.691130689499767, -0.48282288966598, -5.25401063706739},

2566

{-0.808419347997877, -0.333630559700654, 1.78886698094661, -0.305144107519429, -0.15252284527693, 2.21201263950347, 0.931886611547211, 0.305144107519429, 1.6429299260493, -0.500880018350764, 1.15231874995853, 0.152522845276929, 1.90071448360622, -2.72075359249382, -1.90071448360622, -3.364331389462},

2567

{-0.876963572777694, -0.464213039151449, 1.60794346144038, 1.28234889458938, -0.369339740296017, 0.581987949884581, 2.1317831174676, -1.28234889458938, 1.10184970502573, 0.23932690690341, 0.771589372316702, 0.369339740296016, 2.61256752278778, -3.73972657890797, -2.61256752278778, -1.35357732220128},

2568

{-0.94734906218204, 0.119368446579231, -1.02127052148706, 4.96929159093662, -0.271499760554801, -0.101513559500183, 3.45450151652294, -4.96929159093663, 0.49104944067915, 0.336931174923658, 0.34337498034351, 0.2714997605548, 1.6998516172077, -2.43323099503588, -1.6998516172077, -0.241861420843327},

2569

{-0.918052572403102, 2.67795638548276, 0.853609012762397, -0.186496378006572, -0.350133172332972, 2.17796818970809, 0.206161530566525, 0.186496378006572, 3.4388803980543, -5.19878421113396, 0.526017472639324, 0.350133172332973, 0.162050218840247, -1.05977054332892, -0.162050218840248, -2.70398566234741},

2570

{-0.934240861528672, 0.896717691404196, 3.14586185301822, -0.305144107519429, -0.313231441130554, 1.30560250413221, 1.02610526808912, 0.305144107519429, 2.78426475813512, -2.74674158801064, 0.425856464814271, 0.313231441130552, 0.637938268076519, -4.17196712110735, -0.637938268076519, -1.73145896894648},

2571

{-0.958118276949496, -0.408955764144395, 3.47315823301274, 1.28234889458937, -0.229388825189251, 0.421919462567658, 2.26128841889249, -1.28234889458938, 1.79618674086649, -0.429112699772595, 0.27470144761645, 0.229388825189249, 0.876858052640315, -5.73444665190523, -0.876858052640315, -0.696620910184106},

2572

{-0.982223853848664, -0.164194200903477, 0.192320445346116, 4.96929159093662, -0.109961707196802, 0.00641609058407321, 3.53876337545824, -4.96929159093663, 0.772020752309354, 0.374397302442787, 0.118058308006101, 0.109961707196801, 0.570522509309828, -3.73108382080435, -0.570522509309828, -0.124474398590174}};

2573

2574

// Array of non-zero columns

2575

static const unsigned int nzc2[16] = {0, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19};

2576

2577

// Number of operations to compute geometry constants: 36

2578

const double G0 = det*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);

2579

const double G1 = det*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);

2580

const double G2 = det*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);

2581

const double G3 = det*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);

2582

const double G4 = det*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);

2583

const double G5 = det*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);

2584

2585

// Compute element tensor using UFL quadrature representation

2586

// Optimisations: ('simplify expressions', True), ('ignore zero tables', True), ('non zero columns', True), ('remove zero terms', True), ('ignore ones', True)

2587

// Total number of operations to compute element tensor: 519652

2588

2589

// Loop quadrature points for integral

2590

// Number of operations to compute element tensor for following IP loop = 519616

2591

for (unsigned int ip = 0; ip < 64; ip++)

2592

{

2593

2594

// Number of operations to compute ip constants: 7

2595

// Number of operations: 1

2596

const double Gip0 = G0*W64[ip];

2597

2598

// Number of operations: 1

2599

const double Gip1 = G1*W64[ip];

2600

2601

// Number of operations: 1

2602

const double Gip2 = W64[ip]*det;

2603

2604

// Number of operations: 1

2605

const double Gip3 = G2*W64[ip];

2606

2607

// Number of operations: 1

2608

const double Gip4 = G3*W64[ip];

2609

2610

// Number of operations: 1

2611

const double Gip5 = G4*W64[ip];

2612

2613

// Number of operations: 1

2614

const double Gip6 = G5*W64[ip];

2615

2616

2617

// Number of operations for primary indices = 6912

2618

for (unsigned int j = 0; j < 16; j++)

2619

{

2620

for (unsigned int k = 0; k < 16; k++)

2621

{

2622

// Number of operations to compute entry = 3

2623

A[nzc1[j]*20 + nzc2[k]] += FE0_D010[ip][k]*FE0_D100[ip][j]*Gip0;

2624

// Number of operations to compute entry = 3

2625

A[nzc1[j]*20 + nzc0[k]] += FE0_D001[ip][k]*FE0_D100[ip][j]*Gip1;

2626

// Number of operations to compute entry = 3

2627

A[nzc1[j]*20 + nzc1[k]] += FE0_D100[ip][j]*FE0_D100[ip][k]*Gip3;

2628

// Number of operations to compute entry = 3

2629

A[nzc0[j]*20 + nzc2[k]] += FE0_D001[ip][j]*FE0_D010[ip][k]*Gip4;

2630

// Number of operations to compute entry = 3

2631

A[nzc2[j]*20 + nzc1[k]] += FE0_D010[ip][j]*FE0_D100[ip][k]*Gip0;

2632

// Number of operations to compute entry = 3

2633

A[nzc0[j]*20 + nzc0[k]] += FE0_D001[ip][j]*FE0_D001[ip][k]*Gip5;

2634

// Number of operations to compute entry = 3

2635

A[nzc2[j]*20 + nzc2[k]] += FE0_D010[ip][j]*FE0_D010[ip][k]*Gip6;

2636

// Number of operations to compute entry = 3

2637

A[nzc0[j]*20 + nzc1[k]] += FE0_D001[ip][j]*FE0_D100[ip][k]*Gip1;

2638

// Number of operations to compute entry = 3

2639

A[nzc2[j]*20 + nzc0[k]] += FE0_D001[ip][k]*FE0_D010[ip][j]*Gip4;

2640

}// end loop over 'k'

2641

}// end loop over 'j'

2642

2643

// Number of operations for primary indices = 1200

2644

for (unsigned int j = 0; j < 20; j++)

2645

{

2646

for (unsigned int k = 0; k < 20; k++)

2647

{

2648

// Number of operations to compute entry = 3

2649

A[j*20 + k] += FE0[ip][j]*FE0[ip][k]*Gip2;

2650

}// end loop over 'k'

2651

}// end loop over 'j'

2652

}// end loop over 'ip'

2653

}

2654

2655

};

2656

2657

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

2658

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

2659

/// the integral over a cell.

2660

2661

class poisson3dp3_0_cell_integral_0: public ufc::cell_integral

2662

{

2663

private:

2664

2665

poisson3dp3_0_cell_integral_0_quadrature integral_0_quadrature;

2666

2667

public:

2668

2669

/// Constructor

2670

poisson3dp3_0_cell_integral_0() : ufc::cell_integral()

2671

{

2672

// Do nothing

2673

}

2674

2675

/// Destructor

2676

virtual ~poisson3dp3_0_cell_integral_0()

2677

{

2678

// Do nothing

2679

}

2680

2681

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

2682

virtual void tabulate_tensor(double* A,

2683

const double * const * w,

2684

const ufc::cell& c) const

2685

{

2686

// Reset values of the element tensor block

2687

for (unsigned int j = 0; j < 400; j++)

2688

A[j] = 0;

2689

2690

// Add all contributions to element tensor

2691

integral_0_quadrature.tabulate_tensor(A, w, c);

2692

}

2693

2694

};

2695

2696

/// This class defines the interface for the assembly of the global

2697

/// tensor corresponding to a form with r + n arguments, that is, a

2698

/// mapping

2699

///

2700

/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R

2701

///

2702

/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r

2703

/// global tensor A is defined by

2704

///

2705

/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),

2706

///

2707

/// where each argument Vj represents the application to the

2708

/// sequence of basis functions of Vj and w1, w2, ..., wn are given

2709

/// fixed functions (coefficients).

2710

2711

class poisson3dp3_form_0: public ufc::form

2712

{

2713

public:

2714

2715

/// Constructor

2716

poisson3dp3_form_0() : ufc::form()

2717

{

2718

// Do nothing

2719

}

2720

2721

/// Destructor

2722

virtual ~poisson3dp3_form_0()

2723

{

2724

// Do nothing

2725

}

2726

2727

/// Return a string identifying the form

2728

virtual const char* signature() const

2729

{

2730

return "Form([Integral(Sum(IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 0), MultiIndex((Index(0),), {Index(0): 3})), MultiIndex((Index(0),), {Index(0): 3})), MultiIndex((Index(1),), {Index(1): 3})), Indexed(ComponentTensor(SpatialDerivative(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 1), MultiIndex((Index(2),), {Index(2): 3})), MultiIndex((Index(2),), {Index(2): 3})), MultiIndex((Index(1),), {Index(1): 3}))), MultiIndex((Index(1),), {Index(1): 3})), Product(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 0), BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 1))), Measure('cell', 0, None))])";

2731

}

2732

2733

/// Return the rank of the global tensor (r)

2734

virtual unsigned int rank() const

2735

{

2736

return 2;

2737

}

2738

2739

/// Return the number of coefficients (n)

2740

virtual unsigned int num_coefficients() const

2741

{

2742

return 0;

2743

}

2744

2745

/// Return the number of cell integrals

2746

virtual unsigned int num_cell_integrals() const

2747

{

2748

return 1;

2749

}

2750

2751

/// Return the number of exterior facet integrals

2752

virtual unsigned int num_exterior_facet_integrals() const

2753

{

2754

return 0;

2755

}

2756

2757

/// Return the number of interior facet integrals

2758

virtual unsigned int num_interior_facet_integrals() const

2759

{

2760

return 0;

2761

}

2762

2763

/// Create a new finite element for argument function i

2764

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

2765

{

2766

switch ( i )

2767

{

2768

case 0:

2769

return new poisson3dp3_0_finite_element_0();

2770

break;

2771

case 1:

2772

return new poisson3dp3_0_finite_element_1();

2773

break;

2774

}

2775

return 0;

2776

}

2777

2778

/// Create a new dof map for argument function i

2779

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

2780

{

2781

switch ( i )

2782

{

2783

case 0:

2784

return new poisson3dp3_0_dof_map_0();

2785

break;

2786

case 1:

2787

return new poisson3dp3_0_dof_map_1();

2788

break;

2789

}

2790

return 0;

2791

}

2792

2793

/// Create a new cell integral on sub domain i

2794

virtual ufc::cell_integral* create_cell_integral(unsigned int i) const

2795

{

2796

return new poisson3dp3_0_cell_integral_0();

2797

}

2798

2799

/// Create a new exterior facet integral on sub domain i

2800

virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const

2801

{

2802

return 0;

2803

}

2804

2805

/// Create a new interior facet integral on sub domain i

2806

virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const

2807

{

2808

return 0;

2809

}

2810

2811

};

2812

2813

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

2814

2815

class poisson3dp3_1_finite_element_0: public ufc::finite_element

2816

{

2817

public:

2818

2819

/// Constructor

2820

poisson3dp3_1_finite_element_0() : ufc::finite_element()

2821

{

2822

// Do nothing

2823

}

2824

2825

/// Destructor

2826

virtual ~poisson3dp3_1_finite_element_0()

2827

{

2828

// Do nothing

2829

}

2830

2831

/// Return a string identifying the finite element

2832

virtual const char* signature() const

2833

{

2834

return "FiniteElement('Lagrange', 'tetrahedron', 3)";

2835

}

2836

2837

/// Return the cell shape

2838

virtual ufc::shape cell_shape() const

2839

{

2840

return ufc::tetrahedron;

2841

}

2842

2843

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

2844

virtual unsigned int space_dimension() const

2845

{

2846

return 20;

2847

}

2848

2849

/// Return the rank of the value space

2850

virtual unsigned int value_rank() const

2851

{

2852

return 0;

2853

}

2854

2855

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

2856

virtual unsigned int value_dimension(unsigned int i) const

2857

{

2858

return 1;

2859

}

2860

2861

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

2862

virtual void evaluate_basis(unsigned int i,

2863

double* values,

2864

const double* coordinates,

2865

const ufc::cell& c) const

2866

{

2867

// Extract vertex coordinates

2868

const double * const * element_coordinates = c.coordinates;

2869

2870

// Compute Jacobian of affine map from reference cell

2871

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

2872

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

2873

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

2874

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

2875

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

2876

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

2877

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

2878

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

2879

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

2880

2881

// Compute sub determinants

2882

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

2883

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

2884

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

2885

2886

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

2887

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

2888

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

2889

2890

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

2891

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

2892

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

2893

2894

// Compute determinant of Jacobian

2895

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

2896

2897

// Compute inverse of Jacobian

2898

2899

// Compute constants

2900

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

2901

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

2902

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

2903

2904

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

2905

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

2906

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

2907

2908

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

2909

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

2910

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

2911

2912

// Get coordinates and map to the UFC reference element

2913

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

2914

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

2915

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

2916

2917

// Map coordinates to the reference cube

2918

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

2919

x = 1.0;

2920

else

2921

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

2922

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

2923

y = -1.0;

2924

else

2925

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

2926

z = 2.0 * z - 1.0;

2927

2928

// Reset values

2929

*values = 0;

2930

2931

// Map degree of freedom to element degree of freedom

2932

const unsigned int dof = i;

2933

2934

// Generate scalings

2935

const double scalings_y_0 = 1;

2936

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

2937

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

2938

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

2939

const double scalings_z_0 = 1;

2940

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

2941

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

2942

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

2943

2944

// Compute psitilde_a

2945

const double psitilde_a_0 = 1;

2946

const double psitilde_a_1 = x;

2947

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

2948

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

2949

2950

// Compute psitilde_bs

2951

const double psitilde_bs_0_0 = 1;

2952

const double psitilde_bs_0_1 = 1.5*y + 0.5;

2953

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;

2954

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;

2955

const double psitilde_bs_1_0 = 1;

2956

const double psitilde_bs_1_1 = 2.5*y + 1.5;

2957

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;

2958

const double psitilde_bs_2_0 = 1;

2959

const double psitilde_bs_2_1 = 3.5*y + 2.5;

2960

const double psitilde_bs_3_0 = 1;

2961

2962

// Compute psitilde_cs

2963

const double psitilde_cs_00_0 = 1;

2964

const double psitilde_cs_00_1 = 2*z + 1;

2965

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;

2966

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;

2967

const double psitilde_cs_01_0 = 1;

2968

const double psitilde_cs_01_1 = 3*z + 2;

2969

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;

2970

const double psitilde_cs_02_0 = 1;

2971

const double psitilde_cs_02_1 = 4*z + 3;

2972

const double psitilde_cs_03_0 = 1;

2973

const double psitilde_cs_10_0 = 1;

2974

const double psitilde_cs_10_1 = 3*z + 2;

2975

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;

2976

const double psitilde_cs_11_0 = 1;

2977

const double psitilde_cs_11_1 = 4*z + 3;

2978

const double psitilde_cs_12_0 = 1;

2979

const double psitilde_cs_20_0 = 1;

2980

const double psitilde_cs_20_1 = 4*z + 3;

2981

const double psitilde_cs_21_0 = 1;

2982

const double psitilde_cs_30_0 = 1;

2983

2984

// Compute basisvalues

2985

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

2986

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

2987

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

2988

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

2989

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

2990

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

2991

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

2992

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

2993

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

2994

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

2995

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

2996

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

2997

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

2998

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

2999

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

3000

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

3001

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

3002

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

3003

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

3004

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

3005

3006

// Table(s) of coefficients

3007

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

3008

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3009

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3010

{0.0288675134594813, 0, -0.0150584650484208, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

3011

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3012

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731326, 0.0267857142857143},

3013

{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},

3014

{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},

3015

{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},

3016

{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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

3017

{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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

3018

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3019

{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},

3020

{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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

3021

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3022

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -0.00757614408414158, -0.00535714285714286},

3023

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

3024

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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},

3025

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3026

{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},

3027

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532936, 0, 0, -0.00535714285714285}};

3028

3029

// Extract relevant coefficients

3030

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

3031

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

3032

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

3033

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

3034

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

3035

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

3036

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

3037

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

3038

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

3039

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

3040

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

3041

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

3042

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

3043

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

3044

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

3045

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

3046

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

3047

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

3048

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

3049

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

3050

3051

// Compute value(s)

3052

*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;

3053

}

3054

3055

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

3056

virtual void evaluate_basis_all(double* values,

3057

const double* coordinates,

3058

const ufc::cell& c) const

3059

{

3060

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

3061

}

3062

3063

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

3064

virtual void evaluate_basis_derivatives(unsigned int i,

3065

unsigned int n,

3066

double* values,

3067

const double* coordinates,

3068

const ufc::cell& c) const

3069

{

3070

// Extract vertex coordinates

3071

const double * const * element_coordinates = c.coordinates;

3072

3073

// Compute Jacobian of affine map from reference cell

3074

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

3075

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

3076

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

3077

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

3078

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

3079

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

3080

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

3081

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

3082

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

3083

3084

// Compute sub determinants

3085

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

3086

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

3087

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

3088

3089

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

3090

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

3091

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

3092

3093

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

3094

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

3095

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

3096

3097

// Compute determinant of Jacobian

3098

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

3099

3100

// Compute inverse of Jacobian

3101

3102

// Compute constants

3103

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

3104

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

3105

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

3106

3107

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

3108

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

3109

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

3110

3111

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

3112

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

3113

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

3114

3115

// Get coordinates and map to the UFC reference element

3116

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

3117

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

3118

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

3119

3120

// Map coordinates to the reference cube

3121

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

3122

x = 1.0;

3123

else

3124

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

3125

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

3126

y = -1.0;

3127

else

3128

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

3129

z = 2.0 * z - 1.0;

3130

3131

// Compute number of derivatives

3132

unsigned int num_derivatives = 1;

3133

3134

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

3135

num_derivatives *= 3;

3136

3137

3138

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

3139

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

3140

3141

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

3142

{

3143

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

3144

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

3145

combinations[j][k] = 0;

3146

}

3147

3148

// Generate combinations of derivatives

3149

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

3150

{

3151

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

3152

{

3153

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

3154

{

3155

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

3156

combinations[row][col] = 0;

3157

else

3158

{

3159

combinations[row][col] += 1;

3160

break;

3161

}

3162

}

3163

}

3164

}

3165

3166

// Compute inverse of Jacobian

3167

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

3168

3169

// Declare transformation matrix

3170

// Declare pointer to two dimensional array and initialise

3171

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

3172

3173

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

3174

{

3175

transform[j] = new double [num_derivatives];

3176

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

3177

transform[j][k] = 1;

3178

}

3179

3180

// Construct transformation matrix

3181

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

3182

{

3183

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

3184

{

3185

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

3186

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

3187

}

3188

}

3189

3190

// Reset values

3191

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

3192

values[j] = 0;

3193

3194

// Map degree of freedom to element degree of freedom

3195

const unsigned int dof = i;

3196

3197

// Generate scalings

3198

const double scalings_y_0 = 1;

3199

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

3200

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

3201

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

3202

const double scalings_z_0 = 1;

3203

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

3204

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

3205

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

3206

3207

// Compute psitilde_a

3208

const double psitilde_a_0 = 1;

3209

const double psitilde_a_1 = x;

3210

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

3211

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

3212

3213

// Compute psitilde_bs

3214

const double psitilde_bs_0_0 = 1;

3215

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3216

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;

3217

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;

3218

const double psitilde_bs_1_0 = 1;

3219

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3220

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;

3221

const double psitilde_bs_2_0 = 1;

3222

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3223

const double psitilde_bs_3_0 = 1;

3224

3225

// Compute psitilde_cs

3226

const double psitilde_cs_00_0 = 1;

3227

const double psitilde_cs_00_1 = 2*z + 1;

3228

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;

3229

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;

3230

const double psitilde_cs_01_0 = 1;

3231

const double psitilde_cs_01_1 = 3*z + 2;

3232

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;

3233

const double psitilde_cs_02_0 = 1;

3234

const double psitilde_cs_02_1 = 4*z + 3;

3235

const double psitilde_cs_03_0 = 1;

3236

const double psitilde_cs_10_0 = 1;

3237

const double psitilde_cs_10_1 = 3*z + 2;

3238

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;

3239

const double psitilde_cs_11_0 = 1;

3240

const double psitilde_cs_11_1 = 4*z + 3;

3241

const double psitilde_cs_12_0 = 1;

3242

const double psitilde_cs_20_0 = 1;

3243

const double psitilde_cs_20_1 = 4*z + 3;

3244

const double psitilde_cs_21_0 = 1;

3245

const double psitilde_cs_30_0 = 1;

3246

3247

// Compute basisvalues

3248

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

3249

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

3250

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

3251

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

3252

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

3253

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

3254

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

3255

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

3256

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

3257

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

3258

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

3259

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

3260

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

3261

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

3262

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

3263

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

3264

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

3265

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

3266

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

3267

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

3268

3269

// Table(s) of coefficients

3270

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

3271

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3272

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3273

{0.0288675134594813, 0, -0.0150584650484208, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

3274

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3275

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731326, 0.0267857142857143},

3276

{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},

3277

{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},

3278

{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},

3279

{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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

3280

{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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

3281

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3282

{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},

3283

{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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

3284

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3285

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -0.00757614408414158, -0.00535714285714286},

3286

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

3287

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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},

3288

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3289

{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},

3290

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532936, 0, 0, -0.00535714285714285}};

3291

3292

// Interesting (new) part

3293

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

3294

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

3295

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

3296

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

3297

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

3298

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

3299

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

3300

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

3301

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

3302

{3.74165738677394, 0, 0, 8.69482604771367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3303

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

3304

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

3305

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.69282032302755, 0, 0.565685424949241, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3306

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

3307

{3.6, 0, 8.76356092008267, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963609, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3308

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

3309

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

3310

{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},

3311

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

3312

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

3313

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

3314

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

3315

3316

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

3317

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

3318

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

3319

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

3320

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

3321

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3322

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3323

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063971, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3324

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

3325

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

3326

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

3327

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.97979589711327, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3328

{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},

3329

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884725, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3330

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824851, 0.377964473009229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3331

{2.01246117974981, 2.12132034355964, -0.408248290463861, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3332

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772552, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3333

{-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},

3334

{1.27279220613579, 0, 0, 3.83405790253617, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3335

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

3336

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

3337

3338

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

3339

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

3340

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

3341

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

3342

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

3343

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3344

{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3345

{1.32287565553229, 0, 3.86436713231719, -0.341565025531988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3346

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

3347

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

3348

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

3349

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.97979589711327, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3350

{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},

3351

{1.8, 0.632455532033674, 4.38178046004133, -0.774596669241485, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3352

{1.03923048454133, 0, 3.16227766016838, -0.44721359549996, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3353

{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054295, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3354

{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},

3355

{0.900000000000001, 0, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3356

{1.27279220613578, -6.26099033699941, 0, 3.83405790253617, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3357

{0.734846922834953, 0, -6.26099033699942, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

3358

{5.71576766497729, 0, 0, -4.69574275274956, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

3359

3360

// Compute reference derivatives

3361

// Declare pointer to array of derivatives on FIAT element

3362

double *derivatives = new double [num_derivatives];

3363

3364

// Declare coefficients

3365

double coeff0_0 = 0;

3366

double coeff0_1 = 0;

3367

double coeff0_2 = 0;

3368

double coeff0_3 = 0;

3369

double coeff0_4 = 0;

3370

double coeff0_5 = 0;

3371

double coeff0_6 = 0;

3372

double coeff0_7 = 0;

3373

double coeff0_8 = 0;

3374

double coeff0_9 = 0;

3375

double coeff0_10 = 0;

3376

double coeff0_11 = 0;

3377

double coeff0_12 = 0;

3378

double coeff0_13 = 0;

3379

double coeff0_14 = 0;

3380

double coeff0_15 = 0;

3381

double coeff0_16 = 0;

3382

double coeff0_17 = 0;

3383

double coeff0_18 = 0;

3384

double coeff0_19 = 0;

3385

3386

// Declare new coefficients

3387

double new_coeff0_0 = 0;

3388

double new_coeff0_1 = 0;

3389

double new_coeff0_2 = 0;

3390

double new_coeff0_3 = 0;

3391

double new_coeff0_4 = 0;

3392

double new_coeff0_5 = 0;

3393

double new_coeff0_6 = 0;

3394

double new_coeff0_7 = 0;

3395

double new_coeff0_8 = 0;

3396

double new_coeff0_9 = 0;

3397

double new_coeff0_10 = 0;

3398

double new_coeff0_11 = 0;

3399

double new_coeff0_12 = 0;

3400

double new_coeff0_13 = 0;

3401

double new_coeff0_14 = 0;

3402

double new_coeff0_15 = 0;

3403

double new_coeff0_16 = 0;

3404

double new_coeff0_17 = 0;

3405

double new_coeff0_18 = 0;

3406

double new_coeff0_19 = 0;

3407

3408

// Loop possible derivatives

3409

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

3410

{

3411

// Get values from coefficients array

3412

new_coeff0_0 = coefficients0[dof][0];

3413

new_coeff0_1 = coefficients0[dof][1];

3414

new_coeff0_2 = coefficients0[dof][2];

3415

new_coeff0_3 = coefficients0[dof][3];

3416

new_coeff0_4 = coefficients0[dof][4];

3417

new_coeff0_5 = coefficients0[dof][5];

3418

new_coeff0_6 = coefficients0[dof][6];

3419

new_coeff0_7 = coefficients0[dof][7];

3420

new_coeff0_8 = coefficients0[dof][8];

3421

new_coeff0_9 = coefficients0[dof][9];

3422

new_coeff0_10 = coefficients0[dof][10];

3423

new_coeff0_11 = coefficients0[dof][11];

3424

new_coeff0_12 = coefficients0[dof][12];

3425

new_coeff0_13 = coefficients0[dof][13];

3426

new_coeff0_14 = coefficients0[dof][14];

3427

new_coeff0_15 = coefficients0[dof][15];

3428

new_coeff0_16 = coefficients0[dof][16];

3429

new_coeff0_17 = coefficients0[dof][17];

3430

new_coeff0_18 = coefficients0[dof][18];

3431

new_coeff0_19 = coefficients0[dof][19];

3432

3433

// Loop derivative order

3434

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

3435

{

3436

// Update old coefficients

3437

coeff0_0 = new_coeff0_0;

3438

coeff0_1 = new_coeff0_1;

3439

coeff0_2 = new_coeff0_2;

3440

coeff0_3 = new_coeff0_3;

3441

coeff0_4 = new_coeff0_4;

3442

coeff0_5 = new_coeff0_5;

3443

coeff0_6 = new_coeff0_6;

3444

coeff0_7 = new_coeff0_7;

3445

coeff0_8 = new_coeff0_8;

3446

coeff0_9 = new_coeff0_9;

3447

coeff0_10 = new_coeff0_10;

3448

coeff0_11 = new_coeff0_11;

3449

coeff0_12 = new_coeff0_12;

3450

coeff0_13 = new_coeff0_13;

3451

coeff0_14 = new_coeff0_14;

3452

coeff0_15 = new_coeff0_15;

3453

coeff0_16 = new_coeff0_16;

3454

coeff0_17 = new_coeff0_17;

3455

coeff0_18 = new_coeff0_18;

3456

coeff0_19 = new_coeff0_19;

3457

3458

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

3459

{

3460

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];

3461

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];

3462

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];

3463

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];

3464

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];

3465

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];

3466

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];

3467

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];

3468

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];

3469

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];

3470

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];

3471

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];

3472

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];

3473

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];

3474

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];

3475

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];

3476

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];

3477

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];

3478

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];

3479

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];

3480

}

3481

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

3482

{

3483

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];

3484

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];

3485

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];

3486

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];

3487

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];

3488

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];

3489

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];

3490

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];

3491

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];

3492

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];

3493

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];

3494

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];

3495

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];

3496

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];

3497

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];

3498

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];

3499

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];

3500

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];

3501

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];

3502

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];

3503

}

3504

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

3505

{

3506

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];

3507

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];

3508

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];

3509

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];

3510

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];

3511

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];

3512

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];

3513

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];

3514

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];

3515

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];

3516

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];

3517

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];

3518

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];

3519

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];

3520

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];

3521

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];

3522

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];

3523

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];

3524

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];

3525

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];

3526

}

3527

3528

}

3529

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

3530

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;

3531

}

3532

3533

// Transform derivatives back to physical element

3534

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

3535

{

3536

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

3537

{

3538

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

3539

}

3540

}

3541

// Delete pointer to array of derivatives on FIAT element

3542

delete [] derivatives;

3543

3544

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

3545

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

3546

{

3547

delete [] combinations[row];

3548

delete [] transform[row];

3549

}

3550

3551

delete [] combinations;

3552

delete [] transform;

3553

}

3554

3555

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

3556

virtual void evaluate_basis_derivatives_all(unsigned int n,

3557

double* values,

3558

const double* coordinates,

3559

const ufc::cell& c) const

3560

{

3561

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

3562

}

3563

3564

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

3565

virtual double evaluate_dof(unsigned int i,

3566

const ufc::function& f,

3567

const ufc::cell& c) const

3568

{

3569

// The reference points, direction and weights:

3570

static const 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}}};

3571

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

3572

static const 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}}};

3573

3574

const double * const * x = c.coordinates;

3575

double result = 0.0;

3576

// Iterate over the points:

3577

// Evaluate basis functions for affine mapping

3578

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

3579

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

3580

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

3581

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

3582

3583

// Compute affine mapping y = F(X)

3584

double y[3];

3585

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

3586

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

3587

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

3588

3589

// Evaluate function at physical points

3590

double values[1];

3591

f.evaluate(values, y, c);

3592

3593

// Map function values using appropriate mapping

3594

// Affine map: Do nothing

3595

3596

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

3597

3598

// Take directional components

3599

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

3600

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

3601

// Multiply by weights

3602

result *= W[i][0];

3603

3604

return result;

3605

}

3606

3607

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

3608

virtual void evaluate_dofs(double* values,

3609

const ufc::function& f,

3610

const ufc::cell& c) const

3611

{

3612

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

3613

}

3614

3615

/// Interpolate vertex values from dof values

3616

virtual void interpolate_vertex_values(double* vertex_values,

3617

const double* dof_values,

3618

const ufc::cell& c) const

3619

{

3620

// Evaluate at vertices and use affine mapping

3621

vertex_values[0] = dof_values[0];

3622

vertex_values[1] = dof_values[1];

3623

vertex_values[2] = dof_values[2];

3624

vertex_values[3] = dof_values[3];

3625

}

3626

3627

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

3628

virtual unsigned int num_sub_elements() const

3629

{

3630

return 1;

3631

}

3632

3633

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

3634

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

3635

{

3636

return new poisson3dp3_1_finite_element_0();

3637

}

3638

3639

};

3640

3641

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

3642

3643

class poisson3dp3_1_finite_element_1: public ufc::finite_element

3644

{

3645

public:

3646

3647

/// Constructor

3648

poisson3dp3_1_finite_element_1() : ufc::finite_element()

3649

{

3650

// Do nothing

3651

}

3652

3653

/// Destructor

3654

virtual ~poisson3dp3_1_finite_element_1()

3655

{

3656

// Do nothing

3657

}

3658

3659

/// Return a string identifying the finite element

3660

virtual const char* signature() const

3661

{

3662

return "FiniteElement('Lagrange', 'tetrahedron', 3)";

3663

}

3664

3665

/// Return the cell shape

3666

virtual ufc::shape cell_shape() const

3667

{

3668

return ufc::tetrahedron;

3669

}

3670

3671

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

3672

virtual unsigned int space_dimension() const

3673

{

3674

return 20;

3675

}

3676

3677

/// Return the rank of the value space

3678

virtual unsigned int value_rank() const

3679

{

3680

return 0;

3681

}

3682

3683

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

3684

virtual unsigned int value_dimension(unsigned int i) const

3685

{

3686

return 1;

3687

}

3688

3689

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

3690

virtual void evaluate_basis(unsigned int i,

3691

double* values,

3692

const double* coordinates,

3693

const ufc::cell& c) const

3694

{

3695

// Extract vertex coordinates

3696

const double * const * element_coordinates = c.coordinates;

3697

3698

// Compute Jacobian of affine map from reference cell

3699

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

3700

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

3701

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

3702

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

3703

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

3704

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

3705

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

3706

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

3707

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

3708

3709

// Compute sub determinants

3710

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

3711

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

3712

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

3713

3714

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

3715

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

3716

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

3717

3718

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

3719

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

3720

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

3721

3722

// Compute determinant of Jacobian

3723

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

3724

3725

// Compute inverse of Jacobian

3726

3727

// Compute constants

3728

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

3729

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

3730

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

3731

3732

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

3733

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

3734

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

3735

3736

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

3737

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

3738

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

3739

3740

// Get coordinates and map to the UFC reference element

3741

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

3742

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

3743

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

3744

3745

// Map coordinates to the reference cube

3746

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

3747

x = 1.0;

3748

else

3749

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

3750

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

3751

y = -1.0;

3752

else

3753

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

3754

z = 2.0 * z - 1.0;

3755

3756

// Reset values

3757

*values = 0;

3758

3759

// Map degree of freedom to element degree of freedom

3760

const unsigned int dof = i;

3761

3762

// Generate scalings

3763

const double scalings_y_0 = 1;

3764

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

3765

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

3766

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

3767

const double scalings_z_0 = 1;

3768

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

3769

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

3770

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

3771

3772

// Compute psitilde_a

3773

const double psitilde_a_0 = 1;

3774

const double psitilde_a_1 = x;

3775

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

3776

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

3777

3778

// Compute psitilde_bs

3779

const double psitilde_bs_0_0 = 1;

3780

const double psitilde_bs_0_1 = 1.5*y + 0.5;

3781

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;

3782

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;

3783

const double psitilde_bs_1_0 = 1;

3784

const double psitilde_bs_1_1 = 2.5*y + 1.5;

3785

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;

3786

const double psitilde_bs_2_0 = 1;

3787

const double psitilde_bs_2_1 = 3.5*y + 2.5;

3788

const double psitilde_bs_3_0 = 1;

3789

3790

// Compute psitilde_cs

3791

const double psitilde_cs_00_0 = 1;

3792

const double psitilde_cs_00_1 = 2*z + 1;

3793

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;

3794

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;

3795

const double psitilde_cs_01_0 = 1;

3796

const double psitilde_cs_01_1 = 3*z + 2;

3797

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;

3798

const double psitilde_cs_02_0 = 1;

3799

const double psitilde_cs_02_1 = 4*z + 3;

3800

const double psitilde_cs_03_0 = 1;

3801

const double psitilde_cs_10_0 = 1;

3802

const double psitilde_cs_10_1 = 3*z + 2;

3803

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;

3804

const double psitilde_cs_11_0 = 1;

3805

const double psitilde_cs_11_1 = 4*z + 3;

3806

const double psitilde_cs_12_0 = 1;

3807

const double psitilde_cs_20_0 = 1;

3808

const double psitilde_cs_20_1 = 4*z + 3;

3809

const double psitilde_cs_21_0 = 1;

3810

const double psitilde_cs_30_0 = 1;

3811

3812

// Compute basisvalues

3813

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

3814

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

3815

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

3816

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

3817

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

3818

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

3819

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

3820

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

3821

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

3822

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

3823

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

3824

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

3825

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

3826

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

3827

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

3828

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

3829

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

3830

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

3831

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

3832

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

3833

3834

// Table(s) of coefficients

3835

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

3836

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

3837

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

3838

{0.0288675134594813, 0, -0.0150584650484208, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

3839

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

3840

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731326, 0.0267857142857143},

3841

{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},

3842

{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},

3843

{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},

3844

{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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

3845

{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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

3846

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

3847

{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},

3848

{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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

3849

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

3850

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -0.00757614408414158, -0.00535714285714286},

3851

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

3852

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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},

3853

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

3854

{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},

3855

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532936, 0, 0, -0.00535714285714285}};

3856

3857

// Extract relevant coefficients

3858

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

3859

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

3860

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

3861

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

3862

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

3863

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

3864

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

3865

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

3866

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

3867

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

3868

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

3869

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

3870

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

3871

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

3872

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

3873

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

3874

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

3875

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

3876

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

3877

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

3878

3879

// Compute value(s)

3880

*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;

3881

}

3882

3883

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

3884

virtual void evaluate_basis_all(double* values,

3885

const double* coordinates,

3886

const ufc::cell& c) const

3887

{

3888

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

3889

}

3890

3891

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

3892

virtual void evaluate_basis_derivatives(unsigned int i,

3893

unsigned int n,

3894

double* values,

3895

const double* coordinates,

3896

const ufc::cell& c) const

3897

{

3898

// Extract vertex coordinates

3899

const double * const * element_coordinates = c.coordinates;

3900

3901

// Compute Jacobian of affine map from reference cell

3902

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

3903

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

3904

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

3905

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

3906

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

3907

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

3908

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

3909

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

3910

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

3911

3912

// Compute sub determinants

3913

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

3914

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

3915

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

3916

3917

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

3918

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

3919

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

3920

3921

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

3922

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

3923

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

3924

3925

// Compute determinant of Jacobian

3926

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

3927

3928

// Compute inverse of Jacobian

3929

3930

// Compute constants

3931

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

3932

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

3933

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

3934

3935

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

3936

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

3937

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

3938

3939

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

3940

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

3941

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

3942

3943

// Get coordinates and map to the UFC reference element

3944

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

3945

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

3946

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

3947

3948

// Map coordinates to the reference cube

3949

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

3950

x = 1.0;

3951

else

3952

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

3953

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

3954

y = -1.0;

3955

else

3956

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

3957

z = 2.0 * z - 1.0;

3958

3959

// Compute number of derivatives

3960

unsigned int num_derivatives = 1;

3961

3962

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

3963

num_derivatives *= 3;

3964

3965

3966

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

3967

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

3968

3969

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

3970

{

3971

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

3972

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

3973

combinations[j][k] = 0;

3974

}

3975

3976

// Generate combinations of derivatives

3977

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

3978

{

3979

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

3980

{

3981

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

3982

{

3983

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

3984

combinations[row][col] = 0;

3985

else

3986

{

3987

combinations[row][col] += 1;

3988

break;

3989

}

3990

}

3991

}

3992

}

3993

3994

// Compute inverse of Jacobian

3995

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

3996

3997

// Declare transformation matrix

3998

// Declare pointer to two dimensional array and initialise

3999

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

4000

4001

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

4002

{

4003

transform[j] = new double [num_derivatives];

4004

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

4005

transform[j][k] = 1;

4006

}

4007

4008

// Construct transformation matrix

4009

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

4010

{

4011

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

4012

{

4013

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

4014

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

4015

}

4016

}

4017

4018

// Reset values

4019

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

4020

values[j] = 0;

4021

4022

// Map degree of freedom to element degree of freedom

4023

const unsigned int dof = i;

4024

4025

// Generate scalings

4026

const double scalings_y_0 = 1;

4027

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

4028

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

4029

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

4030

const double scalings_z_0 = 1;

4031

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

4032

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

4033

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

4034

4035

// Compute psitilde_a

4036

const double psitilde_a_0 = 1;

4037

const double psitilde_a_1 = x;

4038

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

4039

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

4040

4041

// Compute psitilde_bs

4042

const double psitilde_bs_0_0 = 1;

4043

const double psitilde_bs_0_1 = 1.5*y + 0.5;

4044

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;

4045

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;

4046

const double psitilde_bs_1_0 = 1;

4047

const double psitilde_bs_1_1 = 2.5*y + 1.5;

4048

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;

4049

const double psitilde_bs_2_0 = 1;

4050

const double psitilde_bs_2_1 = 3.5*y + 2.5;

4051

const double psitilde_bs_3_0 = 1;

4052

4053

// Compute psitilde_cs

4054

const double psitilde_cs_00_0 = 1;

4055

const double psitilde_cs_00_1 = 2*z + 1;

4056

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;

4057

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;

4058

const double psitilde_cs_01_0 = 1;

4059

const double psitilde_cs_01_1 = 3*z + 2;

4060

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;

4061

const double psitilde_cs_02_0 = 1;

4062

const double psitilde_cs_02_1 = 4*z + 3;

4063

const double psitilde_cs_03_0 = 1;

4064

const double psitilde_cs_10_0 = 1;

4065

const double psitilde_cs_10_1 = 3*z + 2;

4066

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;

4067

const double psitilde_cs_11_0 = 1;

4068

const double psitilde_cs_11_1 = 4*z + 3;

4069

const double psitilde_cs_12_0 = 1;

4070

const double psitilde_cs_20_0 = 1;

4071

const double psitilde_cs_20_1 = 4*z + 3;

4072

const double psitilde_cs_21_0 = 1;

4073

const double psitilde_cs_30_0 = 1;

4074

4075

// Compute basisvalues

4076

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

4077

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

4078

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

4079

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

4080

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

4081

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

4082

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

4083

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

4084

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

4085

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

4086

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

4087

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

4088

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

4089

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

4090

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

4091

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

4092

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

4093

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

4094

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

4095

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

4096

4097

// Table(s) of coefficients

4098

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

4099

{{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781059, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},

4100

{0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.0053239713749995, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714286},

4101

{0.0288675134594813, 0, -0.0150584650484208, 0.0053239713749995, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},

4102

{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},

4103

{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731326, 0.0267857142857143},

4104

{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},

4105

{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},

4106

{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},

4107

{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, 0.0154647393532935, 0.00874817765279705, 0, -0.00535714285714285},

4108

{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, 0.00927884361197614, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},

4109

{0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},

4110

{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},

4111

{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, 0.0154647393532936, -0.00874817765279707, 0, -0.00535714285714285},

4112

{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},

4113

{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.0334076552390531, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -0.00757614408414158, -0.00535714285714286},

4114

{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.033407655239053, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},

4115

{0.259807621135332, 0.117369119465393, 0.0677630927178939, 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},

4116

{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868637, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},

4117

{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},

4118

{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532936, 0, 0, -0.00535714285714285}};

4119

4120

// Interesting (new) part

4121

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

4122

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

4123

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

4124

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

4125

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

4126

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

4127

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

4128

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

4129

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

4130

{3.74165738677394, 0, 0, 8.69482604771367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4131

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

4132

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

4133

{5.49909083394701, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.69282032302755, 0, 0.565685424949241, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4134

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

4135

{3.6, 0, 8.76356092008267, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963609, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4136

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

4137

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

4138

{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},

4139

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

4140

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

4141

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

4142

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

4143

4144

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

4145

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

4146

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

4147

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

4148

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

4149

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4150

{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4151

{-2.64575131106459, 0, 9.66091783079296, 0.683130051063971, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4152

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

4153

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

4154

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

4155

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.97979589711327, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4156

{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},

4157

{1.8, -5.69209978830308, 4.38178046004133, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884725, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4158

{5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824851, 0.377964473009229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4159

{2.01246117974981, 2.12132034355964, -0.408248290463861, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4160

{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772552, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4161

{-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},

4162

{1.27279220613579, 0, 0, 3.83405790253617, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4163

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

4164

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

4165

4166

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

4167

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

4168

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

4169

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

4170

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

4171

{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4172

{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4173

{1.32287565553229, 0, 3.86436713231719, -0.341565025531988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4174

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

4175

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

4176

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

4177

{2.74954541697351, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.97979589711327, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4178

{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},

4179

{1.8, 0.632455532033674, 4.38178046004133, -0.774596669241485, 0, 3.14233761939829, 4.76235235991626, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4180

{1.03923048454133, 0, 3.16227766016838, -0.44721359549996, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4181

{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054295, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4182

{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},

4183

{0.900000000000001, 0, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222145, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4184

{1.27279220613578, -6.26099033699941, 0, 3.83405790253617, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4185

{0.734846922834953, 0, -6.26099033699942, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},

4186

{5.71576766497729, 0, 0, -4.69574275274956, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

4187

4188

// Compute reference derivatives

4189

// Declare pointer to array of derivatives on FIAT element

4190

double *derivatives = new double [num_derivatives];

4191

4192

// Declare coefficients

4193

double coeff0_0 = 0;

4194

double coeff0_1 = 0;

4195

double coeff0_2 = 0;

4196

double coeff0_3 = 0;

4197

double coeff0_4 = 0;

4198

double coeff0_5 = 0;

4199

double coeff0_6 = 0;

4200

double coeff0_7 = 0;

4201

double coeff0_8 = 0;

4202

double coeff0_9 = 0;

4203

double coeff0_10 = 0;

4204

double coeff0_11 = 0;

4205

double coeff0_12 = 0;

4206

double coeff0_13 = 0;

4207

double coeff0_14 = 0;

4208

double coeff0_15 = 0;

4209

double coeff0_16 = 0;

4210

double coeff0_17 = 0;

4211

double coeff0_18 = 0;

4212

double coeff0_19 = 0;

4213

4214

// Declare new coefficients

4215

double new_coeff0_0 = 0;

4216

double new_coeff0_1 = 0;

4217

double new_coeff0_2 = 0;

4218

double new_coeff0_3 = 0;

4219

double new_coeff0_4 = 0;

4220

double new_coeff0_5 = 0;

4221

double new_coeff0_6 = 0;

4222

double new_coeff0_7 = 0;

4223

double new_coeff0_8 = 0;

4224

double new_coeff0_9 = 0;

4225

double new_coeff0_10 = 0;

4226

double new_coeff0_11 = 0;

4227

double new_coeff0_12 = 0;

4228

double new_coeff0_13 = 0;

4229

double new_coeff0_14 = 0;

4230

double new_coeff0_15 = 0;

4231

double new_coeff0_16 = 0;

4232

double new_coeff0_17 = 0;

4233

double new_coeff0_18 = 0;

4234

double new_coeff0_19 = 0;

4235

4236

// Loop possible derivatives

4237

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

4238

{

4239

// Get values from coefficients array

4240

new_coeff0_0 = coefficients0[dof][0];

4241

new_coeff0_1 = coefficients0[dof][1];

4242

new_coeff0_2 = coefficients0[dof][2];

4243

new_coeff0_3 = coefficients0[dof][3];

4244

new_coeff0_4 = coefficients0[dof][4];

4245

new_coeff0_5 = coefficients0[dof][5];

4246

new_coeff0_6 = coefficients0[dof][6];

4247

new_coeff0_7 = coefficients0[dof][7];

4248

new_coeff0_8 = coefficients0[dof][8];

4249

new_coeff0_9 = coefficients0[dof][9];

4250

new_coeff0_10 = coefficients0[dof][10];

4251

new_coeff0_11 = coefficients0[dof][11];

4252

new_coeff0_12 = coefficients0[dof][12];

4253

new_coeff0_13 = coefficients0[dof][13];

4254

new_coeff0_14 = coefficients0[dof][14];

4255

new_coeff0_15 = coefficients0[dof][15];

4256

new_coeff0_16 = coefficients0[dof][16];

4257

new_coeff0_17 = coefficients0[dof][17];

4258

new_coeff0_18 = coefficients0[dof][18];

4259

new_coeff0_19 = coefficients0[dof][19];

4260

4261

// Loop derivative order

4262

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

4263

{

4264

// Update old coefficients

4265

coeff0_0 = new_coeff0_0;

4266

coeff0_1 = new_coeff0_1;

4267

coeff0_2 = new_coeff0_2;

4268

coeff0_3 = new_coeff0_3;

4269

coeff0_4 = new_coeff0_4;

4270

coeff0_5 = new_coeff0_5;

4271

coeff0_6 = new_coeff0_6;

4272

coeff0_7 = new_coeff0_7;

4273

coeff0_8 = new_coeff0_8;

4274

coeff0_9 = new_coeff0_9;

4275

coeff0_10 = new_coeff0_10;

4276

coeff0_11 = new_coeff0_11;

4277

coeff0_12 = new_coeff0_12;

4278

coeff0_13 = new_coeff0_13;

4279

coeff0_14 = new_coeff0_14;

4280

coeff0_15 = new_coeff0_15;

4281

coeff0_16 = new_coeff0_16;

4282

coeff0_17 = new_coeff0_17;

4283

coeff0_18 = new_coeff0_18;

4284

coeff0_19 = new_coeff0_19;

4285

4286

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

4287

{

4288

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];

4289

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];

4290

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];

4291

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];

4292

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];

4293

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];

4294

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];

4295

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];

4296

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];

4297

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];

4298

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];

4299

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];

4300

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];

4301

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];

4302

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];

4303

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];

4304

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];

4305

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];

4306

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];

4307

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];

4308

}

4309

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

4310

{

4311

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];

4312

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];

4313

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];

4314

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];

4315

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];

4316

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];

4317

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];

4318

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];

4319

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];

4320

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];

4321

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];

4322

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];

4323

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];

4324

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];

4325

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];

4326

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];

4327

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];

4328

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];

4329

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];

4330

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];

4331

}

4332

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

4333

{

4334

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];

4335

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];

4336

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];

4337

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];

4338

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];

4339

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];

4340

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];

4341

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];

4342

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];

4343

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];

4344

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];

4345

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];

4346

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];

4347

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];

4348

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];

4349

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];

4350

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];

4351

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];

4352

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];

4353

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];

4354

}

4355

4356

}

4357

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

4358

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;

4359

}

4360

4361

// Transform derivatives back to physical element

4362

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

4363

{

4364

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

4365

{

4366

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

4367

}

4368

}

4369

// Delete pointer to array of derivatives on FIAT element

4370

delete [] derivatives;

4371

4372

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

4373

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

4374

{

4375

delete [] combinations[row];

4376

delete [] transform[row];

4377

}

4378

4379

delete [] combinations;

4380

delete [] transform;

4381

}

4382

4383

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

4384

virtual void evaluate_basis_derivatives_all(unsigned int n,

4385

double* values,

4386

const double* coordinates,

4387

const ufc::cell& c) const

4388

{

4389

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

4390

}

4391

4392

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

4393

virtual double evaluate_dof(unsigned int i,

4394

const ufc::function& f,

4395

const ufc::cell& c) const

4396

{

4397

// The reference points, direction and weights:

4398

static const 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}}};

4399

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

4400

static const 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}}};

4401

4402

const double * const * x = c.coordinates;

4403

double result = 0.0;

4404

// Iterate over the points:

4405

// Evaluate basis functions for affine mapping

4406

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

4407

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

4408

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

4409

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

4410

4411

// Compute affine mapping y = F(X)

4412

double y[3];

4413

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

4414

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

4415

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

4416

4417

// Evaluate function at physical points

4418

double values[1];

4419

f.evaluate(values, y, c);

4420

4421

// Map function values using appropriate mapping

4422

// Affine map: Do nothing

4423

4424

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

4425

4426

// Take directional components

4427

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

4428

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

4429

// Multiply by weights

4430

result *= W[i][0];

4431

4432

return result;

4433

}

4434

4435

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

4436

virtual void evaluate_dofs(double* values,

4437

const ufc::function& f,

4438

const ufc::cell& c) const

4439

{

4440

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

4441

}

4442

4443

/// Interpolate vertex values from dof values

4444

virtual void interpolate_vertex_values(double* vertex_values,

4445

const double* dof_values,

4446

const ufc::cell& c) const

4447

{

4448

// Evaluate at vertices and use affine mapping

4449

vertex_values[0] = dof_values[0];

4450

vertex_values[1] = dof_values[1];

4451

vertex_values[2] = dof_values[2];

4452

vertex_values[3] = dof_values[3];

4453

}

4454

4455

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

4456

virtual unsigned int num_sub_elements() const

4457

{

4458

return 1;

4459

}

4460

4461

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

4462

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

4463

{

4464

return new poisson3dp3_1_finite_element_1();

4465

}

4466

4467

};

4468

4469

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

4470

/// degrees of freedom (dofs).

4471

4472

class poisson3dp3_1_dof_map_0: public ufc::dof_map

4473

{

4474

private:

4475

4476

unsigned int __global_dimension;

4477

4478

public:

4479

4480

/// Constructor

4481

poisson3dp3_1_dof_map_0() : ufc::dof_map()

4482

{

4483

__global_dimension = 0;

4484

}

4485

4486

/// Destructor

4487

virtual ~poisson3dp3_1_dof_map_0()

4488

{

4489

// Do nothing

4490

}

4491

4492

/// Return a string identifying the dof map

4493

virtual const char* signature() const

4494

{

4495

return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 3)";

4496

}

4497

4498

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

4499

virtual bool needs_mesh_entities(unsigned int d) const

4500

{

4501

switch ( d )

4502

{

4503

case 0:

4504

return true;

4505

break;

4506

case 1:

4507

return true;

4508

break;

4509

case 2:

4510

return true;

4511

break;

4512

case 3:

4513

return false;

4514

break;

4515

}

4516

return false;

4517

}

4518

4519

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

4520

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

4521

{

4522

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

4523

return false;

4524

}

4525

4526

/// Initialize dof map for given cell

4527

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

4528

const ufc::cell& c)

4529

{

4530

// Do nothing

4531

}

4532

4533

/// Finish initialization of dof map for cells

4534

virtual void init_cell_finalize()

4535

{

4536

// Do nothing

4537

}

4538

4539

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

4540

virtual unsigned int global_dimension() const

4541

{

4542

return __global_dimension;

4543

}

4544

4545

/// Return the dimension of the local finite element function space for a cell

4546

virtual unsigned int local_dimension(const ufc::cell& c) const

4547

{

4548

return 20;

4549

}

4550

4551

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

4552

virtual unsigned int max_local_dimension() const

4553

{

4554

return 20;

4555

}

4556

4557

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

4558

virtual unsigned int geometric_dimension() const

4559

{

4560

return 3;

4561

}

4562

4563

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

4564

virtual unsigned int num_facet_dofs() const

4565

{

4566

return 10;

4567

}

4568

4569

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

4570

virtual unsigned int num_entity_dofs(unsigned int d) const

4571

{

4572

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

4573

}

4574

4575

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

4576

virtual void tabulate_dofs(unsigned int* dofs,

4577

const ufc::mesh& m,

4578

const ufc::cell& c) const

4579

{

4580

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

4581

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

4582

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

4583

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

4584

unsigned int offset = m.num_entities[0];

4585

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

4586

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

4587

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

4588

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

4589

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

4590

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

4591

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

4592

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

4593

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

4594

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

4595

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

4596

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

4597

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

4598

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

4599

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

4600

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

4601

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

4602

}

4603

4604

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

4605

virtual void tabulate_facet_dofs(unsigned int* dofs,

4606

unsigned int facet) const

4607

{

4608

switch ( facet )

4609

{

4610

case 0:

4611

dofs[0] = 1;

4612

dofs[1] = 2;

4613

dofs[2] = 3;

4614

dofs[3] = 4;

4615

dofs[4] = 5;

4616

dofs[5] = 6;

4617

dofs[6] = 7;

4618

dofs[7] = 8;

4619

dofs[8] = 9;

4620

dofs[9] = 16;

4621

break;

4622

case 1:

4623

dofs[0] = 0;

4624

dofs[1] = 2;

4625

dofs[2] = 3;

4626

dofs[3] = 4;

4627

dofs[4] = 5;

4628

dofs[5] = 10;

4629

dofs[6] = 11;

4630

dofs[7] = 12;

4631

dofs[8] = 13;

4632

dofs[9] = 17;

4633

break;

4634

case 2:

4635

dofs[0] = 0;

4636

dofs[1] = 1;

4637

dofs[2] = 3;

4638

dofs[3] = 6;

4639

dofs[4] = 7;

4640

dofs[5] = 10;

4641

dofs[6] = 11;

4642

dofs[7] = 14;

4643

dofs[8] = 15;

4644

dofs[9] = 18;

4645

break;

4646

case 3:

4647

dofs[0] = 0;

4648

dofs[1] = 1;

4649

dofs[2] = 2;

4650

dofs[3] = 8;

4651

dofs[4] = 9;

4652

dofs[5] = 12;

4653

dofs[6] = 13;

4654

dofs[7] = 14;

4655

dofs[8] = 15;

4656

dofs[9] = 19;

4657

break;

4658

}

4659

}

4660

4661

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

4662

virtual void tabulate_entity_dofs(unsigned int* dofs,

4663

unsigned int d, unsigned int i) const

4664

{

4665

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

4666

}

4667

4668

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

4669

virtual void tabulate_coordinates(double** coordinates,

4670

const ufc::cell& c) const

4671

{

4672

const double * const * x = c.coordinates;

4673

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

4674

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

4675

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

4676

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

4677

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

4678

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

4679

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

4680

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

4681

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

4682

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

4683

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

4684

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

4685

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

4686

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

4687

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

4688

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

4689

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

4690

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

4691

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

4692

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

4693

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

4694

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

4695

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

4696

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

4697

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

4698

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

4699

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

4700

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

4701

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

4702

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

4703

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

4704

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

4705

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

4706

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

4707

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

4708

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

4709

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

4710

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

4711

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

4712

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

4713

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

4714

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

4715

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

4716

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

4717

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

4718

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

4719

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

4720

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

4721

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

4722

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

4723

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

4724

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

4725

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

4726

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

4727

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

4728

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

4729

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

4730

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

4731

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

4732

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

4733

}

4734

4735

/// Return the number of sub dof maps (for a mixed element)

4736

virtual unsigned int num_sub_dof_maps() const

4737

{

4738

return 1;

4739

}

4740

4741

/// Create a new dof_map for sub dof map i (for a mixed element)

4742

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

4743

{

4744

return new poisson3dp3_1_dof_map_0();

4745

}

4746

4747

};

4748

4749

/// This class defines the interface for a local-to-global mapping of

4750

/// degrees of freedom (dofs).

4751

4752

class poisson3dp3_1_dof_map_1: public ufc::dof_map

4753

{

4754

private:

4755

4756

unsigned int __global_dimension;

4757

4758

public:

4759

4760

/// Constructor

4761

poisson3dp3_1_dof_map_1() : ufc::dof_map()

4762

{

4763

__global_dimension = 0;

4764

}

4765

4766

/// Destructor

4767

virtual ~poisson3dp3_1_dof_map_1()

4768

{

4769

// Do nothing

4770

}

4771

4772

/// Return a string identifying the dof map

4773

virtual const char* signature() const

4774

{

4775

return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 3)";

4776

}

4777

4778

/// Return true iff mesh entities of topological dimension d are needed

4779

virtual bool needs_mesh_entities(unsigned int d) const

4780

{

4781

switch ( d )

4782

{

4783

case 0:

4784

return true;

4785

break;

4786

case 1:

4787

return true;

4788

break;

4789

case 2:

4790

return true;

4791

break;

4792

case 3:

4793

return false;

4794

break;

4795

}

4796

return false;

4797

}

4798

4799

/// Initialize dof map for mesh (return true iff init_cell() is needed)

4800

virtual bool init_mesh(const ufc::mesh& m)

4801

{

4802

__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];

4803

return false;

4804

}

4805

4806

/// Initialize dof map for given cell

4807

virtual void init_cell(const ufc::mesh& m,

4808

const ufc::cell& c)

4809

{

4810

// Do nothing

4811

}

4812

4813

/// Finish initialization of dof map for cells

4814

virtual void init_cell_finalize()

4815

{

4816

// Do nothing

4817

}

4818

4819

/// Return the dimension of the global finite element function space

4820

virtual unsigned int global_dimension() const

4821

{

4822

return __global_dimension;

4823

}

4824

4825

/// Return the dimension of the local finite element function space for a cell

4826

virtual unsigned int local_dimension(const ufc::cell& c) const

4827

{

4828

return 20;

4829

}

4830

4831

/// Return the maximum dimension of the local finite element function space

4832

virtual unsigned int max_local_dimension() const

4833

{

4834

return 20;

4835

}

4836

4837

// Return the geometric dimension of the coordinates this dof map provides

4838

virtual unsigned int geometric_dimension() const

4839

{

4840

return 3;

4841

}

4842

4843

/// Return the number of dofs on each cell facet

4844

virtual unsigned int num_facet_dofs() const

4845

{

4846

return 10;

4847

}

4848

4849

/// Return the number of dofs associated with each cell entity of dimension d

4850

virtual unsigned int num_entity_dofs(unsigned int d) const

4851

{

4852

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4853

}

4854

4855

/// Tabulate the local-to-global mapping of dofs on a cell

4856

virtual void tabulate_dofs(unsigned int* dofs,

4857

const ufc::mesh& m,

4858

const ufc::cell& c) const

4859

{

4860

dofs[0] = c.entity_indices[0][0];

4861

dofs[1] = c.entity_indices[0][1];

4862

dofs[2] = c.entity_indices[0][2];

4863

dofs[3] = c.entity_indices[0][3];

4864

unsigned int offset = m.num_entities[0];

4865

dofs[4] = offset + 2*c.entity_indices[1][0];

4866

dofs[5] = offset + 2*c.entity_indices[1][0] + 1;

4867

dofs[6] = offset + 2*c.entity_indices[1][1];

4868

dofs[7] = offset + 2*c.entity_indices[1][1] + 1;

4869

dofs[8] = offset + 2*c.entity_indices[1][2];

4870

dofs[9] = offset + 2*c.entity_indices[1][2] + 1;

4871

dofs[10] = offset + 2*c.entity_indices[1][3];

4872

dofs[11] = offset + 2*c.entity_indices[1][3] + 1;

4873

dofs[12] = offset + 2*c.entity_indices[1][4];

4874

dofs[13] = offset + 2*c.entity_indices[1][4] + 1;

4875

dofs[14] = offset + 2*c.entity_indices[1][5];

4876

dofs[15] = offset + 2*c.entity_indices[1][5] + 1;

4877

offset = offset + 2*m.num_entities[1];

4878

dofs[16] = offset + c.entity_indices[2][0];

4879

dofs[17] = offset + c.entity_indices[2][1];

4880

dofs[18] = offset + c.entity_indices[2][2];

4881

dofs[19] = offset + c.entity_indices[2][3];

4882

}

4883

4884

/// Tabulate the local-to-local mapping from facet dofs to cell dofs

4885

virtual void tabulate_facet_dofs(unsigned int* dofs,

4886

unsigned int facet) const

4887

{

4888

switch ( facet )

4889

{

4890

case 0:

4891

dofs[0] = 1;

4892

dofs[1] = 2;

4893

dofs[2] = 3;

4894

dofs[3] = 4;

4895

dofs[4] = 5;

4896

dofs[5] = 6;

4897

dofs[6] = 7;

4898

dofs[7] = 8;

4899

dofs[8] = 9;

4900

dofs[9] = 16;

4901

break;

4902

case 1:

4903

dofs[0] = 0;

4904

dofs[1] = 2;

4905

dofs[2] = 3;

4906

dofs[3] = 4;

4907

dofs[4] = 5;

4908

dofs[5] = 10;

4909

dofs[6] = 11;

4910

dofs[7] = 12;

4911

dofs[8] = 13;

4912

dofs[9] = 17;

4913

break;

4914

case 2:

4915

dofs[0] = 0;

4916

dofs[1] = 1;

4917

dofs[2] = 3;

4918

dofs[3] = 6;

4919

dofs[4] = 7;

4920

dofs[5] = 10;

4921

dofs[6] = 11;

4922

dofs[7] = 14;

4923

dofs[8] = 15;

4924

dofs[9] = 18;

4925

break;

4926

case 3:

4927

dofs[0] = 0;

4928

dofs[1] = 1;

4929

dofs[2] = 2;

4930

dofs[3] = 8;

4931

dofs[4] = 9;

4932

dofs[5] = 12;

4933

dofs[6] = 13;

4934

dofs[7] = 14;

4935

dofs[8] = 15;

4936

dofs[9] = 19;

4937

break;

4938

}

4939

}

4940

4941

/// Tabulate the local-to-local mapping of dofs on entity (d, i)

4942

virtual void tabulate_entity_dofs(unsigned int* dofs,

4943

unsigned int d, unsigned int i) const

4944

{

4945

throw std::runtime_error("Not implemented (introduced in UFC v1.1).");

4946

}

4947

4948

/// Tabulate the coordinates of all dofs on a cell

4949

virtual void tabulate_coordinates(double** coordinates,

4950

const ufc::cell& c) const

4951

{

4952

const double * const * x = c.coordinates;

4953

coordinates[0][0] = x[0][0];

4954

coordinates[0][1] = x[0][1];

4955

coordinates[0][2] = x[0][2];

4956

coordinates[1][0] = x[1][0];

4957

coordinates[1][1] = x[1][1];

4958

coordinates[1][2] = x[1][2];

4959

coordinates[2][0] = x[2][0];

4960

coordinates[2][1] = x[2][1];

4961

coordinates[2][2] = x[2][2];

4962

coordinates[3][0] = x[3][0];

4963

coordinates[3][1] = x[3][1];

4964

coordinates[3][2] = x[3][2];

4965

coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];

4966

coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];

4967

coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];

4968

coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];

4969

coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];

4970

coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];

4971

coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];

4972

coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];

4973

coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];

4974

coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];

4975

coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];

4976

coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];

4977

coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];

4978

coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];

4979

coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];

4980

coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];

4981

coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];

4982

coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];

4983

coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];

4984

coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];

4985

coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];

4986

coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];

4987

coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];

4988

coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];

4989

coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];

4990

coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];

4991

coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];

4992

coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];

4993

coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];

4994

coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];

4995

coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];

4996

coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];

4997

coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];

4998

coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];

4999

coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];

5000

coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];

5001

coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5002

coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5003

coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5004

coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];

5005

coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];

5006

coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];

5007

coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];

5008

coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];

5009

coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];

5010

coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];

5011

coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];

5012

coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];

5013

}

5014

5015

/// Return the number of sub dof maps (for a mixed element)

5016

virtual unsigned int num_sub_dof_maps() const

5017

{

5018

return 1;

5019

}

5020

5021

/// Create a new dof_map for sub dof map i (for a mixed element)

5022

virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const

5023

{

5024

return new poisson3dp3_1_dof_map_1();

5025

}

5026

5027

};

5028

5029

/// This class defines the interface for the tabulation of the cell

5030

/// tensor corresponding to the local contribution to a form from

5031

/// the integral over a cell.

5032

5033

class poisson3dp3_1_cell_integral_0_quadrature: public ufc::cell_integral

5034

{

5035

public:

5036

5037

/// Constructor

5038

poisson3dp3_1_cell_integral_0_quadrature() : ufc::cell_integral()

5039

{

5040

// Do nothing

5041

}

5042

5043

/// Destructor

5044

virtual ~poisson3dp3_1_cell_integral_0_quadrature()

5045

{

5046

// Do nothing

5047

}

5048

5049

/// Tabulate the tensor for the contribution from a local cell

5050

virtual void tabulate_tensor(double* A,

5051

const double * const * w,

5052

const ufc::cell& c) const

5053

{

5054

// Extract vertex coordinates

5055

const double * const * x = c.coordinates;

5056

5057

// Compute Jacobian of affine map from reference cell

5058

const double J_00 = x[1][0] - x[0][0];

5059

const double J_01 = x[2][0] - x[0][0];

5060

const double J_02 = x[3][0] - x[0][0];

5061

const double J_10 = x[1][1] - x[0][1];

5062

const double J_11 = x[2][1] - x[0][1];

5063

const double J_12 = x[3][1] - x[0][1];

5064

const double J_20 = x[1][2] - x[0][2];

5065

const double J_21 = x[2][2] - x[0][2];

5066

const double J_22 = x[3][2] - x[0][2];

5067

5068

// Compute sub determinants

5069

const double d_00 = J_11*J_22 - J_12*J_21;

5070

5071

const double d_10 = J_02*J_21 - J_01*J_22;

5072

5073

const double d_20 = J_01*J_12 - J_02*J_11;

5074

5075

// Compute determinant of Jacobian

5076

double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;

5077

5078

// Compute inverse of Jacobian

5079

5080

// Set scale factor

5081

const double det = std::abs(detJ);

5082

5083

5084

// Array of quadrature weights

5085

static const double W64[64] = {0.0026134590075074, 0.00338108957856492, 0.00161758872343451, 0.000243985421620605, 0.00392412678076307, 0.00507672939399183, 0.00242882065938497, 0.000366345798555432, 0.00250430944300902, 0.0032398803788146, 0.00155003109035391, 0.000233795515279108, 0.000601372928720174, 0.000778009425931694, 0.000372217075256263, 5.6142540266951e-05, 0.00489961445988875, 0.00633873932658916, 0.00303259438036939, 0.00045741467393993, 0.00735680500908296, 0.00951766095289489, 0.00455346144286727, 0.000686811297504771, 0.00469498496963441, 0.00607400564032183, 0.00290593987575818, 0.000438311021534327, 0.00112743130421366, 0.00145858275269461, 0.000697818545806259, 0.000105253918778391, 0.00489961445988875, 0.00633873932658916, 0.00303259438036939, 0.00045741467393993, 0.00735680500908296, 0.00951766095289489, 0.00455346144286727, 0.000686811297504771, 0.00469498496963441, 0.00607400564032183, 0.00290593987575818, 0.000438311021534327, 0.00112743130421366, 0.00145858275269461, 0.000697818545806259, 0.000105253918778391, 0.0026134590075074, 0.00338108957856492, 0.00161758872343451, 0.000243985421620605, 0.00392412678076307, 0.00507672939399183, 0.00242882065938497, 0.000366345798555432, 0.00250430944300902, 0.0032398803788146, 0.00155003109035391, 0.000233795515279108, 0.000601372928720174, 0.000778009425931694, 0.000372217075256263, 5.6142540266951e-05};

5086

// Quadrature points on the UFC reference element: (0.0622918093484527, 0.0543346112272345, 0.0485005494469973), (0.0498465213688842, 0.0434790928042876, 0.238600737551862), (0.0316174621017319, 0.027578625974397, 0.517047295104368), (0.0133649941129659, 0.0116577406689234, 0.795851417896773), (0.0477749046478169, 0.263415975366112, 0.0485005494469973), (0.0382299507805671, 0.210788066397987, 0.238600737551862), (0.024249114818074, 0.13370208226799, 0.517047295104368), (0.0102503254608295, 0.0565171086994073, 0.795851417896773), (0.0275098322538483, 0.555285975747014, 0.0485005494469973), (0.0220136396042882, 0.444345324777483, 0.238600737551862), (0.013963169280339, 0.28184657786378, 0.517047295104368), (0.00590236100005809, 0.119139159297124, 0.795851417896773), (0.00923314621657362, 0.818518016420533, 0.0485005494469973), (0.007388454838612, 0.654986204816931, 0.238600737551862), (0.00468646927478461, 0.415455300374957, 0.517047295104368), (0.00198101397470041, 0.175616803962505, 0.795851417896773), (0.296072900492077, 0.0543346112272345, 0.0485005494469973), (0.236920460578858, 0.0434790928042876, 0.238600737551862), (0.150277762174051, 0.027578625974397, 0.517047295104368), (0.063523802141471, 0.0116577406689234, 0.795851417896773), (0.227074068609678, 0.263415975366112, 0.0485005494469973), (0.181706913503757, 0.210788066397987, 0.238600737551862), (0.115256015737018, 0.13370208226799, 0.517047295104368), (0.0487197855050096, 0.0565171086994073, 0.795851417896773), (0.130754202079533, 0.555285975747014, 0.0485005494469973), (0.104630804534349, 0.444345324777483, 0.238600737551862), (0.0663669280461273, 0.28184657786378, 0.517047295104368), (0.0280539152629691, 0.119139159297124, 0.795851417896773), (0.0438851336893508, 0.818518016420533, 0.0485005494469973), (0.0351173176233467, 0.654986204816931, 0.238600737551862), (0.0222747832462335, 0.415455300374957, 0.517047295104368), (0.00941575721655391, 0.175616803962505, 0.795851417896773), (0.601091938833691, 0.0543346112272345, 0.0485005494469973), (0.480999709064992, 0.0434790928042876, 0.238600737551862), (0.305096316747185, 0.027578625974397, 0.517047295104368), (0.128967039292833, 0.0116577406689234, 0.795851417896773), (0.461009406577212, 0.263415975366112, 0.0485005494469973), (0.368904282546393, 0.210788066397987, 0.238600737551862), (0.233994606890624, 0.13370208226799, 0.517047295104368), (0.0989116878988102, 0.0565171086994073, 0.795851417896773), (0.265459272726456, 0.555285975747014, 0.0485005494469973), (0.212423133136306, 0.444345324777483, 0.238600737551862), (0.134739198985725, 0.28184657786378, 0.517047295104368), (0.0569555075431344, 0.119139159297124, 0.795851417896773), (0.0890963004431186, 0.818518016420533, 0.0485005494469973), (0.0712957400078597, 0.654986204816931, 0.238600737551862), (0.045222621274442, 0.415455300374957, 0.517047295104368), (0.0191160209241683, 0.175616803962505, 0.795851417896773), (0.834873029977315, 0.0543346112272345, 0.0485005494469973), (0.668073648274966, 0.0434790928042876, 0.238600737551862), (0.423756616819504, 0.027578625974397, 0.517047295104368), (0.179125847321338, 0.0116577406689234, 0.795851417896773), (0.640308570539073, 0.263415975366112, 0.0485005494469973), (0.512381245269583, 0.210788066397987, 0.238600737551862), (0.325001507809568, 0.13370208226799, 0.517047295104368), (0.13738114794299, 0.0565171086994073, 0.795851417896773), (0.368703642552141, 0.555285975747014, 0.0485005494469973), (0.295040298066366, 0.444345324777483, 0.238600737551862), (0.187142957751513, 0.28184657786378, 0.517047295104368), (0.0791070618060454, 0.119139159297124, 0.795851417896773), (0.123748287915896, 0.818518016420533, 0.0485005494469973), (0.0990246027925943, 0.654986204816931, 0.238600737551862), (0.0628109352458909, 0.415455300374957, 0.517047295104368), (0.0265507641660218, 0.175616803962505, 0.795851417896773)

5087

5088

// Value of basis functions at quadrature points.

5089

static const double FE0[64][20] = \

5090

{{0.316942646270776, 0.0459182870838374, 0.0417713284261773, 0.0384285806226176, -0.00992565567229708, -0.0101332081942744, -0.011054706162562, -0.0116171968229622, -0.0123844609684378, -0.0127480421943013, 0.274161313248215, -0.155700796186139, 0.307139785811479, -0.170857079355319, 0.352119809987772, -0.190292195339624, 0.00443218553927298, 0.0594028686804588, 0.0681023032468036, 0.0762942319785079},

5091

{0.00141590232956291, 0.0392228167323023, 0.0353420251164078, 0.0435405986330707, -0.0405943584870655, -0.0132673889695188, -0.0455169618203899, -0.0152103722760564, -0.00829434237070535, -0.00848064250992449, 0.720340631623725, -0.203858737160113, 0.131264293205546, -0.113662771758787, 0.150487693606995, -0.127445887442534, 0.0139621042223731, 0.187128683191496, 0.214533314837614, 0.0390933992960042},

5092

{-0.0418846376623705, 0.0272612052688519, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, -0.066586962132492, 0.0405446175758774, -0.00355166140662748, -0.00359920474050181, 0.267461209901129, 0.543403829153424, 0.0142660308648051, -0.0482387491813342, 0.0163552633343248, -0.0545726978261391, 0.0121728891219892, 0.163148525161687, 0.187041309311128, 0.00997653862633952},

5093

{0.0606020354974101, 0.0125719331417011, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.0459453476251609, 0.0664145528584789, -0.000673013750447416, -0.000676604746500828, -0.296776478794994, 0.890128566813322, -0.004347222545097, -0.00906827174738708, -0.00498386483050322, -0.0103411254145656, 0.00334794966816241, 0.0448712746170981, 0.051442585500075, 0.000753538044429993},

5094

{-0.0233141297875962, 0.0379946132499842, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, -0.00893254555193575, -0.00890984667642714, -0.048514402947884, -0.0118784757749483, 0.128698381601996, -0.119415229212101, 0.698986096122026, -0.159202616932648, 0.126772850606219, -0.117928261408372, 0.0164798161265746, 0.220872602144184, 0.0400589504569247, 0.21756799927154},

5095

{-0.0636942004447079, 0.0319045035068057, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, -0.0363398789831187, -0.0116656442114479, -0.0321038941563349, -0.0133315323091856, 0.295507178830004, -0.156350117797481, 0.261061166329218, -0.178677371706281, 0.047347820538567, -0.0780377824367332, 0.0519140970715157, 0.695784565803582, 0.12619219939295, 0.111482512491259},

5096

{0.00416331000853175, 0.0216671920487514, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.0523162684880416, 0.031095825581728, -0.0135283446980038, -0.00873768447279163, -0.0189012088835133, 0.41676532427948, -0.00488762055045249, -0.117107805778746, -0.00088645195276417, -0.0328845471247492, 0.0452614117080655, 0.606621196735265, 0.110020927132805, 0.0284500609325142},

5097

{0.0641179720678825, 0.00978236065603381, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.0355809496645704, 0.0509368561168636, -0.00252676863369168, -0.00216492522558782, -0.289229785310999, 0.682686983226322, -0.0205395515393154, -0.0290156555358705, -0.0037251921222161, -0.00614204058684542, 0.0124483946900372, 0.166841019741274, 0.0302594168725173, 0.00214886185298791},

5098

{-0.0174860280987736, 0.0241979596905522, -0.0617731070981597, 0.0384285806226176, 0.0806970115889355, -0.103558823234662, -0.00550857447170805, -0.00513048407491109, -0.0630680308857183, 0.0457718784119034, 0.00853879745270195, -0.0687618938938031, 0.0977612527959359, 0.613462784549029, 0.00484326235994765, -0.0418764631771457, 0.0200039182057664, 0.268104779401166, 0.0132823767030295, 0.152070803153297},

5099

{0.018893837039617, 0.019880943301904, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.022075166962345, -0.00671733241030492, -0.0411105067572066, 0.0146593977712432, -0.036392063376584, -0.0900298084357277, -0.0677728132205631, 0.196474238955856, -0.00335758294734683, -0.0272969141137687, 0.0630155909245982, 0.844573594527272, 0.0418416436327583, 0.0779215476028461},

5100

{0.0590357207055018, 0.0130980546488276, 0.0251291929007073, -0.0639547452440238, -0.101291343114797, 0.361425647567417, -0.0311273668109228, 0.017905654691607, -0.0169677743151103, -0.00273543287806844, -0.190966113694605, 0.239982565002839, -0.10409714187153, -0.0366619489640695, -0.00515715331570966, -0.0112664113073766, 0.0549402718289831, 0.736343215735788, 0.0364797225770018, 0.0198853858575406},

5101

{0.0531740973437773, 0.00574651592133119, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.0207640128472617, 0.0293305528842609, -0.00310837799446912, -0.00203339486296362, -0.216073469396172, 0.393106057016485, -0.0323462532218693, -0.0272528049536403, -0.00160248959822373, -0.0020639280281623, 0.0151104033722227, 0.202518892603982, 0.0100331378912924, 0.00150196328937836},

5102

{0.0633645780899607, 0.00885305887263062, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.00195933827339019, -0.00172194832699612, -0.0330667115180807, 0.0495015510214934, -0.0169816512377693, -0.0230786074808287, -0.286590309701014, 0.663450144122639, -0.00323283077542309, -0.00499921670052643, 0.00989665381744753, 0.132641023685632, 0.00149623336497993, 0.0252511359143224},

5103

{0.0592677805711995, 0.00714461813298492, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.00775717045765738, -0.00225454345767591, -0.0212943165654494, 0.0210139153012293, -0.0747372528781831, -0.0302167740416122, -0.20516227285544, 0.281641379865613, -0.0023142963568264, -0.00321939794170585, 0.031176066711914, 0.417840765114924, 0.00471337808350592, 0.0129387597643602},

5104

{0.0461725856048027, 0.00458809898063897, -0.0385687396087239, -0.0639547452440238, 0.238148410057832, 0.532758645187123, -0.0107507634380464, 0.00600968869404698, -0.00863840057902656, 0.002158555352948, -0.118604871591271, 0.0805455333806928, -0.095300803271659, 0.0289302825963627, -0.0010750236812283, -0.00130600336283494, 0.0271809175250065, 0.364295325645881, 0.0041093683220464, 0.00330193942943354},

5105

{0.0234627458142642, 0.00196338908550111, 0.0612042229600472, 0.213985565988335, -0.297583634515968, 0.872691107158041, -0.00705250360640731, 0.00984423608600662, -0.00155624293107926, -0.000740737938466248, -0.0875131805869247, 0.131938489103154, -0.0193111235761632, -0.00992782411644321, -0.000217835678638736, -0.000235281807411492, 0.00747565700272528, 0.10019333967366, 0.00113021306382384, 0.000249398821943359},

5106

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5107

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5108

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5109

{0.0637734994386082, 0.0465185832699072, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.184144831837059, 0.315668295805934, -0.00269737874030822, -0.00321590160694518, -0.283174252139672, 0.640874823865867, -0.00414797526438382, -0.00652897488694274, -0.0226025923432014, -0.0298405119712716, 0.0159128010459527, 0.0323064232393078, 0.176039843056651, 0.00257865575357758},

5110

{-0.0544723188739935, 0.0477306372652925, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, -0.0157984607319655, -0.0423484913349203, -0.0858045319165257, -0.056458382135615, 0.0385389369754062, -0.085976584553608, 0.209312508594235, -0.114622710571981, 0.180434929473551, -0.150168175204615, 0.0783285477048384, 0.15902387056592, 0.137084310263545, 0.744531715767973},

5111

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5112

{0.0452580461211559, 0.0623679922432538, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.175443845541055, 0.14779842437514, -0.0453676243779744, -0.041530204572686, -0.162251408196532, 0.300062725486067, -0.0419562220558782, -0.0843152856788516, -0.0361677762044535, -0.0793987591801865, 0.215127439464974, 0.436755168978356, 0.376498703498837, 0.0973579421179106},

5113

{0.0592405099224476, 0.0385588963661094, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.14897956417135, 0.24210282042228, -0.0105797313831695, -0.0102898871872979, -0.24912142868932, 0.491521018920905, -0.0176912706919524, -0.0208906935741604, -0.0152505132208227, -0.0185157930528795, 0.0591672061046181, 0.120122208326693, 0.103549674757618, 0.00735354375510282},

5114

{0.0325299333929531, 0.0638787973684188, -0.0617731070981597, 0.0384285806226176, 0.0806970115889355, -0.103558823234662, -0.017343262053637, -0.0243851850969721, -0.198564146218889, 0.217553687140082, -0.0117972873894808, -0.0495071928717421, -0.135067918073687, 0.44168097582085, -0.0318046891613103, -0.0949253108254811, 0.095078600964327, 0.193030096642605, 0.0454531491271413, 0.52039608935609},

5115

{0.0525008116745778, 0.0605211362317534, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.0770790017967222, -0.0319274734686737, -0.143543957316746, 0.0696761012883771, -0.0827313861152967, -0.0648196673773589, -0.15407037300001, 0.141457535438722, -0.0362792319013842, -0.0686224327245416, 0.299513033517807, 0.608076151934063, 0.143184801205848, 0.266652557941832},

5116

{0.0640509106927241, 0.0478617966777029, 0.0251291929007073, -0.0639547452440238, -0.101291343114797, 0.361425647567417, -0.123672280290719, 0.0851055568172439, -0.0674147400181512, -0.0130015094244684, -0.186777439414966, 0.172782662877202, -0.101813862328864, -0.0263958724176695, -0.0239742959680134, -0.0322282006711705, 0.261131050845518, 0.530152436719253, 0.124835961777158, 0.0680490720179158},

5117

{0.043189241782395, 0.0246116712744907, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.0920146055848045, 0.139408085209121, -0.0137746098152355, -0.00966472352016017, -0.169123783267225, 0.283028524691626, -0.0253178732895335, -0.0196214762964438, -0.00596164582739594, -0.00658507159076729, 0.0718197304077884, 0.145809565568416, 0.0343340444998879, 0.005139815177809},

5118

{0.0565572914460857, 0.0355988950588367, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.00831703837687065, -0.00818441848139808, -0.140362239858113, 0.235280816901719, -0.0142479247765323, -0.0166161373264268, -0.240454659981553, 0.477670878242413, -0.0128920618579228, -0.0152785351603579, 0.0470387845777104, 0.0954988929253688, 0.00512020700722334, 0.0864110145348937},

5119

{0.0500526781546474, 0.0297626847872616, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.0337332239476843, -0.0107158425446525, -0.0926015424614136, 0.0998791160347683, -0.060177304883694, -0.0217554749546356, -0.165193557012014, 0.202776179132074, -0.00885691113531576, -0.010079747400941, 0.148179810377592, 0.300837021449246, 0.0161294835790437, 0.0442772698168982},

5120

{0.0364359152038298, 0.0200917703395614, -0.0385687396087239, -0.0639547452440238, 0.238148410057832, 0.532758645187123, -0.0483637167469586, 0.0285640436730253, -0.0388609758886781, 0.0102596111897318, -0.090945073207204, 0.0579911784017145, -0.0730757380701406, 0.020829226759579, -0.00391798160861545, -0.00423004639339736, 0.129190870739485, 0.262285372431402, 0.0140625232468916, 0.0112994495375666},

5121

{0.0175030551599998, 0.00902055949440797, 0.0612042229600472, 0.213985565988335, -0.297583634515968, 0.872691107158041, -0.0327684220468545, 0.0467896431585221, -0.00723085417875007, -0.00352072659696577, -0.0645347110293076, 0.094993082030638, -0.014240572348997, -0.00714783545794369, -0.000763513336067467, -0.000787083904625167, 0.0355317894123066, 0.0721372072640786, 0.00386766194665403, 0.000853458842447994},

5122

{0.0183974307728653, -0.0474934098882189, 0.0417713284261773, 0.0384285806226176, -0.00992565567229708, -0.0101332081942744, 0.105381595203438, -0.11210146944143, 0.118057796688303, -0.123013691190792, -0.00722315577599343, -0.0552165235676718, -0.00809201886158539, -0.0605914303588281, -0.0895202375930713, 0.643304764711186, 0.0427688812853259, 0.0210661729344057, 0.233050470905012, 0.261083778994831},

5123

{0.0441735351626781, -0.0593435556758837, 0.0353420251164078, 0.0435405986330707, -0.0405943584870655, -0.0132673889695188, 0.228787335174519, -0.146774226939742, 0.0416908425370495, -0.081834929859403, -0.0735771805831919, -0.0722948824964278, -0.0134076243672929, -0.0403084844093089, -0.148325620521794, 0.227176166261325, 0.134728921587068, 0.0663618658268004, 0.734146830049622, 0.133780131961088},

5124

{0.0639244626451169, 0.0140171944147557, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, -0.0601339611396408, 0.391239924524043, -0.003207466779793, -0.0347309377967427, -0.19201789705842, 0.192708522205259, -0.0102419833030854, -0.0171070161250932, -0.113304824716739, -0.017477699228467, 0.117463685837307, 0.0578577284463694, 0.640067415277826, 0.0341403581673955},

5125

{0.0465185832699073, 0.0637734994386082, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.283174252139672, 0.640874823865867, -0.00414797526438386, -0.00652897488694274, -0.184144831837059, 0.315668295805934, -0.00269737874030822, -0.00321590160694519, -0.0298405119712715, -0.0226025923432015, 0.0323064232393079, 0.0159128010459527, 0.176039843056651, 0.00257865575357758},

5126

{0.0477306372652926, -0.0544723188739936, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, 0.0385389369754061, -0.085976584553608, 0.209312508594235, -0.114622710571981, -0.0157984607319655, -0.0423484913349203, -0.0858045319165257, -0.0564583821356151, -0.150168175204615, 0.180434929473551, 0.15902387056592, 0.0783285477048383, 0.137084310263545, 0.744531715767973},

5127

{0.0601263089173645, -0.0175829401694107, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, 0.0422682922674721, -0.112568968057714, 0.0373412575686983, -0.128644145790115, -0.0887466324394246, -0.0554467939512141, -0.0784018156992205, -0.0633647582253519, -0.137212538001305, 0.0321895104172831, 0.500951017283187, 0.24674764559191, 0.431837839411788, 0.381500342794665},

5128

{0.0623679922432539, 0.0452580461211558, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.162251408196532, 0.300062725486068, -0.0419562220558782, -0.0843152856788516, -0.175443845541054, 0.14779842437514, -0.0453676243779745, -0.041530204572686, -0.0793987591801864, -0.0361677762044535, 0.436755168978356, 0.215127439464974, 0.376498703498837, 0.0973579421179105},

5129

{0.0385588963661094, 0.0592405099224476, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.24912142868932, 0.491521018920905, -0.0176912706919524, -0.0208906935741604, -0.14897956417135, 0.24210282042228, -0.0105797313831696, -0.0102898871872979, -0.0185157930528794, -0.0152505132208228, 0.120122208326693, 0.0591672061046181, 0.103549674757618, 0.00735354375510283},

5130

{0.0638787973684189, 0.032529933392953, -0.0617731070981597, 0.0384285806226176, 0.0806970115889354, -0.103558823234662, -0.0117972873894808, -0.0495071928717421, -0.135067918073687, 0.441680975820851, -0.017343262053637, -0.0243851850969721, -0.198564146218889, 0.217553687140082, -0.0949253108254811, -0.0318046891613103, 0.193030096642606, 0.0950786009643269, 0.0454531491271413, 0.52039608935609},

5131

{0.0605211362317534, 0.0525008116745777, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.0827313861152966, -0.0648196673773589, -0.15407037300001, 0.141457535438722, -0.0770790017967222, -0.0319274734686737, -0.143543957316746, 0.0696761012883772, -0.0686224327245416, -0.0362792319013842, 0.608076151934063, 0.299513033517807, 0.143184801205848, 0.266652557941832},

5132

{0.0478617966777029, 0.0640509106927241, 0.0251291929007073, -0.0639547452440238, -0.101291343114797, 0.361425647567417, -0.186777439414966, 0.172782662877202, -0.101813862328864, -0.0263958724176695, -0.123672280290718, 0.0851055568172437, -0.0674147400181511, -0.0130015094244684, -0.0322282006711705, -0.0239742959680135, 0.530152436719253, 0.261131050845517, 0.124835961777158, 0.0680490720179158},

5133

{0.0246116712744908, 0.0431892417823949, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.169123783267225, 0.283028524691625, -0.0253178732895335, -0.0196214762964438, -0.0920146055848049, 0.139408085209121, -0.0137746098152356, -0.00966472352016021, -0.00658507159076722, -0.00596164582739604, 0.145809565568416, 0.0718197304077886, 0.034334044499888, 0.00513981517780901},

5134

{0.0355988950588367, 0.0565572914460857, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.0142479247765322, -0.0166161373264268, -0.240454659981553, 0.477670878242413, -0.00831703837687066, -0.00818441848139806, -0.140362239858113, 0.235280816901719, -0.0152785351603578, -0.0128920618579229, 0.0954988929253689, 0.0470387845777103, 0.00512020700722334, 0.0864110145348937},

5135

{0.0297626847872616, 0.0500526781546473, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.060177304883694, -0.0217554749546356, -0.165193557012014, 0.202776179132074, -0.0337332239476842, -0.0107158425446524, -0.0926015424614135, 0.0998791160347682, -0.010079747400941, -0.00885691113531579, 0.300837021449246, 0.148179810377592, 0.0161294835790437, 0.0442772698168982},

5136

{0.0200917703395613, 0.0364359152038299, -0.0385687396087239, -0.0639547452440238, 0.238148410057832, 0.532758645187123, -0.0909450732072041, 0.0579911784017145, -0.0730757380701406, 0.020829226759579, -0.0483637167469585, 0.0285640436730253, -0.038860975888678, 0.0102596111897318, -0.00423004639339731, -0.00391798160861551, 0.262285372431403, 0.129190870739485, 0.0140625232468916, 0.0112994495375666},

5137

{0.00902055949440803, 0.0175030551599997, 0.0612042229600472, 0.213985565988335, -0.297583634515968, 0.872691107158041, -0.0645347110293074, 0.0949930820306377, -0.0142405723489969, -0.00714783545794368, -0.0327684220468547, 0.0467896431585224, -0.00723085417875015, -0.00352072659696579, -0.000787083904625099, -0.000763513336067545, 0.0721372072640785, 0.0355317894123067, 0.00386766194665405, 0.000853458842447997},

5138

{0.0459182870838375, 0.316942646270776, 0.0417713284261773, 0.0384285806226176, -0.00992565567229708, -0.0101332081942744, 0.274161313248215, -0.155700796186139, 0.307139785811479, -0.170857079355319, -0.0110547061625619, -0.0116171968229622, -0.0123844609684377, -0.0127480421943014, -0.190292195339624, 0.352119809987772, 0.0594028686804588, 0.0044321855392728, 0.0681023032468037, 0.076294231978508},

5139

{0.0392228167323025, 0.00141590232956263, 0.0353420251164078, 0.0435405986330707, -0.0405943584870655, -0.0132673889695188, 0.720340631623725, -0.203858737160113, 0.131264293205545, -0.113662771758787, -0.0455169618203899, -0.0152103722760563, -0.00829434237070526, -0.00848064250992448, -0.127445887442534, 0.150487693606995, 0.187128683191495, 0.0139621042223729, 0.214533314837614, 0.0390933992960043},

5140

{0.027261205268852, -0.0418846376623705, 0.0242504041833649, -0.0639547452440238, -0.0588585848419934, 0.0353654205325618, 0.267461209901129, 0.543403829153424, 0.014266030864805, -0.0482387491813341, -0.0665869621324919, 0.0405446175758773, -0.00355166140662741, -0.0035992047405018, -0.0545726978261391, 0.0163552633343248, 0.163148525161687, 0.012172889121989, 0.187041309311128, 0.00997653862633951},

5141

{0.0125719331417013, 0.0606020354974101, 0.0110533069845138, 0.213985565988335, -0.0402900923342712, 0.057930712675401, -0.296776478794994, 0.890128566813322, -0.00434722254509708, -0.0090682717473871, -0.045945347625161, 0.0664145528584791, -0.000673013750447433, -0.000676604746500851, -0.0103411254145655, -0.00498386483050332, 0.0448712746170982, 0.00334794966816239, 0.0514425855000752, 0.000753538044429996},

5142

{0.0379946132499844, -0.0233141297875965, 0.033420639302547, 0.0384285806226176, -0.0120588958978522, -0.0491261253148477, 0.128698381601996, -0.119415229212101, 0.698986096122025, -0.159202616932648, -0.00893254555193567, -0.00890984667642716, -0.0485144029478841, -0.0118784757749484, -0.117928261408373, 0.126772850606219, 0.220872602144184, 0.0164798161265745, 0.0400589504569248, 0.21756799927154},

5143

{0.0319045035068058, -0.063694200444708, 0.0529912643922588, 0.0435405986330707, -0.0832047485471804, -0.06432073639676, 0.295507178830004, -0.156350117797481, 0.261061166329218, -0.178677371706281, -0.0363398789831187, -0.0116656442114479, -0.032103894156335, -0.0133315323091857, -0.0780377824367335, 0.0473478205385671, 0.695784565803581, 0.0519140970715158, 0.12619219939295, 0.11148251249126},

5144

{0.0216671920487514, 0.0041633100085317, 0.064014383048423, -0.0639547452440238, -0.186307671683133, 0.171452717400655, -0.0189012088835131, 0.41676532427948, -0.00488762055045244, -0.117107805778746, -0.0523162684880414, 0.0310958255817279, -0.0135283446980038, -0.00873768447279161, -0.0328845471247491, -0.00088645195276425, 0.606621196735265, 0.0452614117080653, 0.110020927132805, 0.0284500609325141},

5145

{0.00978236065603392, 0.0641179720678825, 0.0429556497001765, 0.213985565988335, -0.168088205297349, 0.280849993004016, -0.289229785310999, 0.682686983226322, -0.0205395515393154, -0.0290156555358705, -0.0355809496645705, 0.0509368561168639, -0.0025267686336917, -0.00216492522558785, -0.00614204058684537, -0.00372519212221623, 0.166841019741274, 0.0124483946900372, 0.0302594168725175, 0.00214886185298792},

5146

{0.0241979596905522, -0.0174860280987737, -0.0617731070981597, 0.0384285806226176, 0.0806970115889354, -0.103558823234662, 0.00853879745270195, -0.0687618938938031, 0.097761252795936, 0.613462784549029, -0.00550857447170798, -0.00513048407491105, -0.0630680308857182, 0.0457718784119034, -0.0418764631771457, 0.00484326235994761, 0.268104779401166, 0.0200039182057662, 0.0132823767030295, 0.152070803153297},

5147

{0.019880943301904, 0.018893837039617, -0.0493496614277152, 0.0435405986330707, 0.158889814822053, -0.135589357559656, -0.0363920633765839, -0.0900298084357277, -0.0677728132205631, 0.196474238955856, -0.0220751669623449, -0.0067173324103049, -0.0411105067572067, 0.0146593977712433, -0.0272969141137687, -0.00335758294734693, 0.844573594527272, 0.0630155909245983, 0.0418416436327583, 0.0779215476028461},

5148

{0.0130980546488274, 0.0590357207055018, 0.0251291929007073, -0.0639547452440238, -0.101291343114797, 0.361425647567417, -0.190966113694605, 0.239982565002839, -0.10409714187153, -0.0366619489640696, -0.0311273668109224, 0.0179056546916068, -0.0169677743151102, -0.00273543287806839, -0.0112664113073766, -0.00515715331570975, 0.736343215735788, 0.0549402718289825, 0.0364797225770015, 0.0198853858575404},

5149

{0.00574651592133132, 0.0531740973437773, 0.0628753827383954, 0.213985565988335, -0.274175060593153, 0.592037222446455, -0.216073469396172, 0.393106057016485, -0.0323462532218692, -0.0272528049536403, -0.020764012847262, 0.0293305528842615, -0.00310837799446921, -0.00203339486296367, -0.00206392802816227, -0.00160248959822386, 0.202518892603981, 0.0151104033722229, 0.0100331378912926, 0.00150196328937839},

5150

{0.00885305887263062, 0.0633645780899607, 0.271372912374866, 0.0384285806226176, 0.260025387522992, -0.152650645395551, -0.0169816512377693, -0.0230786074808287, -0.286590309701014, 0.663450144122639, -0.00195933827339019, -0.0017219483269961, -0.0330667115180805, 0.0495015510214933, -0.00499921670052642, -0.00323283077542312, 0.132641023685632, 0.00989665381744741, 0.00149623336497992, 0.0252511359143223},

5151

{0.00714461813298495, 0.0592677805711995, -0.0110736837110986, 0.0435405986330707, 0.678617626993249, -0.199865180906401, -0.074737252878183, -0.0302167740416122, -0.20516227285544, 0.281641379865613, -0.00775717045765736, -0.00225454345767588, -0.0212943165654494, 0.0210139153012294, -0.00321939794170587, -0.00231429635682646, 0.417840765114924, 0.0311760667119139, 0.00471337808350592, 0.0129387597643602},

5152

{0.00458809898063892, 0.0461725856048027, -0.0385687396087239, -0.0639547452440238, 0.238148410057832, 0.532758645187123, -0.118604871591271, 0.0805455333806928, -0.0953008032716591, 0.0289302825963627, -0.0107507634380462, 0.00600968869404693, -0.00863840057902648, 0.002158555352948, -0.00130600336283489, -0.00107502368122838, 0.364295325645881, 0.0271809175250061, 0.00410936832204634, 0.0033019394294335},

5153

{0.00196338908550119, 0.0234627458142642, 0.0612042229600472, 0.213985565988335, -0.297583634515968, 0.872691107158041, -0.0875131805869245, 0.131938489103153, -0.0193111235761631, -0.0099278241164432, -0.00705250360640749, 0.00984423608600691, -0.00155624293107934, -0.00074073793846627, -0.000235281807411435, -0.000217835678638819, 0.10019333967366, 0.00747565700272542, 0.00113021306382387, 0.000249398821943366}};

5154

5155

5156

// Compute element tensor using UFL quadrature representation

5157

// Optimisations: ('simplify expressions', True), ('ignore zero tables', True), ('non zero columns', True), ('remove zero terms', True), ('ignore ones', True)

5158

// Total number of operations to compute element tensor: 5248

5159

5160

// Loop quadrature points for integral

5161

// Number of operations to compute element tensor for following IP loop = 5248

5162

for (unsigned int ip = 0; ip < 64; ip++)

5163

{

5164

5165

// Function declarations

5166

double F0 = 0;

5167

5168

// Total number of operations to compute function values = 40

5169

for (unsigned int r = 0; r < 20; r++)

5170

{

5171

F0 += FE0[ip][r]*w[0][r];

5172

}// end loop over 'r'

5173

5174

// Number of operations to compute ip constants: 2

5175

// Number of operations: 2

5176

const double Gip0 = F0*W64[ip]*det;

5177

5178

5179

// Number of operations for primary indices = 40

5180

for (unsigned int j = 0; j < 20; j++)

5181

{

5182

// Number of operations to compute entry = 2

5183

A[j] += FE0[ip][j]*Gip0;

5184

}// end loop over 'j'

5185

}// end loop over 'ip'

5186

}

5187

5188

};

5189

5190

/// This class defines the interface for the tabulation of the cell

5191

/// tensor corresponding to the local contribution to a form from

5192

/// the integral over a cell.

5193

5194

class poisson3dp3_1_cell_integral_0: public ufc::cell_integral

5195

{

5196

private:

5197

5198

poisson3dp3_1_cell_integral_0_quadrature integral_0_quadrature;

5199

5200

public:

5201

5202

/// Constructor

5203

poisson3dp3_1_cell_integral_0() : ufc::cell_integral()

5204

{

5205

// Do nothing

5206

}

5207

5208

/// Destructor

5209

virtual ~poisson3dp3_1_cell_integral_0()

5210

{

5211

// Do nothing

5212

}

5213

5214

/// Tabulate the tensor for the contribution from a local cell

5215

virtual void tabulate_tensor(double* A,

5216

const double * const * w,

5217

const ufc::cell& c) const

5218

{

5219

// Reset values of the element tensor block

5220

for (unsigned int j = 0; j < 20; j++)

5221

A[j] = 0;

5222

5223

// Add all contributions to element tensor

5224

integral_0_quadrature.tabulate_tensor(A, w, c);

5225

}

5226

5227

};

5228

5229

/// This class defines the interface for the assembly of the global

5230

/// tensor corresponding to a form with r + n arguments, that is, a

5231

/// mapping

5232

///

5233

/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R

5234

///

5235

/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r

5236

/// global tensor A is defined by

5237

///

5238

/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),

5239

///

5240

/// where each argument Vj represents the application to the

5241

/// sequence of basis functions of Vj and w1, w2, ..., wn are given

5242

/// fixed functions (coefficients).

5243

5244

class poisson3dp3_form_1: public ufc::form

5245

{

5246

public:

5247

5248

/// Constructor

5249

poisson3dp3_form_1() : ufc::form()

5250

{

5251

// Do nothing

5252

}

5253

5254

/// Destructor

5255

virtual ~poisson3dp3_form_1()

5256

{

5257

// Do nothing

5258

}

5259

5260

/// Return a string identifying the form

5261

virtual const char* signature() const

5262

{

5263

return "Form([Integral(Product(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 0), Function(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 3), 0)), Measure('cell', 0, None))])";

5264

}

5265

5266

/// Return the rank of the global tensor (r)

5267

virtual unsigned int rank() const

5268

{

5269

return 1;

5270

}

5271

5272

/// Return the number of coefficients (n)

5273

virtual unsigned int num_coefficients() const

5274

{

5275

return 1;

5276

}

5277

5278

/// Return the number of cell integrals

5279

virtual unsigned int num_cell_integrals() const

5280

{

5281

return 1;

5282

}

5283

5284

/// Return the number of exterior facet integrals

5285

virtual unsigned int num_exterior_facet_integrals() const

5286

{

5287

return 0;

5288

}

5289

5290

/// Return the number of interior facet integrals

5291

virtual unsigned int num_interior_facet_integrals() const

5292

{

5293

return 0;

5294

}

5295

5296

/// Create a new finite element for argument function i

5297

virtual ufc::finite_element* create_finite_element(unsigned int i) const

5298

{

5299

switch ( i )

5300

{

5301

case 0:

5302

return new poisson3dp3_1_finite_element_0();

5303

break;

5304

case 1:

5305

return new poisson3dp3_1_finite_element_1();

5306

break;

5307

}

5308

return 0;

5309

}

5310

5311

/// Create a new dof map for argument function i

5312

virtual ufc::dof_map* create_dof_map(unsigned int i) const

5313

{

5314

switch ( i )

5315

{

5316

case 0:

5317

return new poisson3dp3_1_dof_map_0();

5318

break;

5319

case 1:

5320

return new poisson3dp3_1_dof_map_1();

5321

break;

5322

}

5323

return 0;

5324

}

5325

5326

/// Create a new cell integral on sub domain i

5327

virtual ufc::cell_integral* create_cell_integral(unsigned int i) const

5328

{

5329

return new poisson3dp3_1_cell_integral_0();

5330

}

5331

5332

/// Create a new exterior facet integral on sub domain i

5333

virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const

5334

{

5335

return 0;

5336

}

5337

5338

/// Create a new interior facet integral on sub domain i

5339

virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const

5340

{

5341

return 0;

5342

}

5343

5344

};

5345

5346

// DOLFIN wrappers

5347

5348

// Standard library includes

5349

#include <string>

5350

5351

// DOLFIN includes

5352

#include <dolfin/common/NoDeleter.h>

5353

#include <dolfin/fem/FiniteElement.h>

5354

#include <dolfin/fem/DofMap.h>

5355

#include <dolfin/fem/Form.h>

5356

#include <dolfin/function/FunctionSpace.h>

5357

#include <dolfin/function/GenericFunction.h>

5358

#include <dolfin/function/CoefficientAssigner.h>

5359

5360

namespace Poisson3DP3

5361

{

5362

5363

class CoefficientSpace_f: public dolfin::FunctionSpace

5364

{

5365

public:

5366

5367

CoefficientSpace_f(const dolfin::Mesh& mesh):

5368

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5369

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_1()))),

5370

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))

5371

{

5372

// Do nothing

5373

}

5374

5375

CoefficientSpace_f(dolfin::Mesh& mesh):

5376

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5377

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_1()))),

5378

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))

5379

{

5380

// Do nothing

5381

}

5382

5383

CoefficientSpace_f(boost::shared_ptr<dolfin::Mesh> mesh):

5384

dolfin::FunctionSpace(mesh,

5385

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_1()))),

5386

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_1()), mesh)))

5387

{

5388

// Do nothing

5389

}

5390

5391

CoefficientSpace_f(boost::shared_ptr<const dolfin::Mesh> mesh):

5392

dolfin::FunctionSpace(mesh,

5393

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_1()))),

5394

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_1()), mesh)))

5395

{

5396

// Do nothing

5397

}

5398

5399

5400

~CoefficientSpace_f()

5401

{

5402

}

5403

5404

};

5405

5406

class Form_0_FunctionSpace_0: public dolfin::FunctionSpace

5407

{

5408

public:

5409

5410

Form_0_FunctionSpace_0(const dolfin::Mesh& mesh):

5411

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5412

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_0()))),

5413

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))

5414

{

5415

// Do nothing

5416

}

5417

5418

Form_0_FunctionSpace_0(dolfin::Mesh& mesh):

5419

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5420

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_0()))),

5421

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))

5422

{

5423

// Do nothing

5424

}

5425

5426

Form_0_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):

5427

dolfin::FunctionSpace(mesh,

5428

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_0()))),

5429

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_0()), mesh)))

5430

{

5431

// Do nothing

5432

}

5433

5434

Form_0_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):

5435

dolfin::FunctionSpace(mesh,

5436

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_0()))),

5437

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_0()), mesh)))

5438

{

5439

// Do nothing

5440

}

5441

5442

5443

~Form_0_FunctionSpace_0()

5444

{

5445

}

5446

5447

};

5448

5449

class Form_0_FunctionSpace_1: public dolfin::FunctionSpace

5450

{

5451

public:

5452

5453

Form_0_FunctionSpace_1(const dolfin::Mesh& mesh):

5454

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5455

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_1()))),

5456

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))

5457

{

5458

// Do nothing

5459

}

5460

5461

Form_0_FunctionSpace_1(dolfin::Mesh& mesh):

5462

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5463

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_1()))),

5464

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))

5465

{

5466

// Do nothing

5467

}

5468

5469

Form_0_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):

5470

dolfin::FunctionSpace(mesh,

5471

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_1()))),

5472

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_1()), mesh)))

5473

{

5474

// Do nothing

5475

}

5476

5477

Form_0_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):

5478

dolfin::FunctionSpace(mesh,

5479

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_0_finite_element_1()))),

5480

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_0_dof_map_1()), mesh)))

5481

{

5482

// Do nothing

5483

}

5484

5485

5486

~Form_0_FunctionSpace_1()

5487

{

5488

}

5489

5490

};

5491

5492

class Form_0: public dolfin::Form

5493

{

5494

public:

5495

5496

// Constructor

5497

Form_0(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):

5498

dolfin::Form(2, 0)

5499

{

5500

_function_spaces[0] = reference_to_no_delete_pointer(V0);

5501

_function_spaces[1] = reference_to_no_delete_pointer(V1);

5502

5503

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_0());

5504

}

5505

5506

// Constructor

5507

Form_0(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):

5508

dolfin::Form(2, 0)

5509

{

5510

_function_spaces[0] = V0;

5511

_function_spaces[1] = V1;

5512

5513

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_0());

5514

}

5515

5516

// Destructor

5517

~Form_0()

5518

{}

5519

5520

/// Return the number of the coefficient with this name

5521

virtual dolfin::uint coefficient_number(const std::string& name) const

5522

{

5523

5524

dolfin::error("No coefficients.");

5525

return 0;

5526

}

5527

5528

/// Return the name of the coefficient with this number

5529

virtual std::string coefficient_name(dolfin::uint i) const

5530

{

5531

5532

dolfin::error("No coefficients.");

5533

return "unnamed";

5534

}

5535

5536

// Typedefs

5537

typedef Form_0_FunctionSpace_0 TestSpace;

5538

typedef Form_0_FunctionSpace_1 TrialSpace;

5539

5540

// Coefficients

5541

};

5542

5543

class Form_1_FunctionSpace_0: public dolfin::FunctionSpace

5544

{

5545

public:

5546

5547

Form_1_FunctionSpace_0(const dolfin::Mesh& mesh):

5548

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5549

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_0()))),

5550

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))

5551

{

5552

// Do nothing

5553

}

5554

5555

Form_1_FunctionSpace_0(dolfin::Mesh& mesh):

5556

dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),

5557

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_0()))),

5558

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))

5559

{

5560

// Do nothing

5561

}

5562

5563

Form_1_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):

5564

dolfin::FunctionSpace(mesh,

5565

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_0()))),

5566

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_0()), mesh)))

5567

{

5568

// Do nothing

5569

}

5570

5571

Form_1_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):

5572

dolfin::FunctionSpace(mesh,

5573

boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3dp3_1_finite_element_0()))),

5574

boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson3dp3_1_dof_map_0()), mesh)))

5575

{

5576

// Do nothing

5577

}

5578

5579

5580

~Form_1_FunctionSpace_0()

5581

{

5582

}

5583

5584

};

5585

5586

typedef CoefficientSpace_f Form_1_FunctionSpace_1;

5587

5588

class Form_1: public dolfin::Form

5589

{

5590

public:

5591

5592

// Constructor

5593

Form_1(const dolfin::FunctionSpace& V0):

5594

dolfin::Form(1, 1), f(*this, 0)

5595

{

5596

_function_spaces[0] = reference_to_no_delete_pointer(V0);

5597

5598

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5599

}

5600

5601

// Constructor

5602

Form_1(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f):

5603

dolfin::Form(1, 1), f(*this, 0)

5604

{

5605

_function_spaces[0] = reference_to_no_delete_pointer(V0);

5606

5607

this->f = f;

5608

5609

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5610

}

5611

5612

// Constructor

5613

Form_1(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> f):

5614

dolfin::Form(1, 1), f(*this, 0)

5615

{

5616

_function_spaces[0] = reference_to_no_delete_pointer(V0);

5617

5618

this->f = *f;

5619

5620

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5621

}

5622

5623

// Constructor

5624

Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0):

5625

dolfin::Form(1, 1), f(*this, 0)

5626

{

5627

_function_spaces[0] = V0;

5628

5629

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5630

}

5631

5632

// Constructor

5633

Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f):

5634

dolfin::Form(1, 1), f(*this, 0)

5635

{

5636

_function_spaces[0] = V0;

5637

5638

this->f = f;

5639

5640

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5641

}

5642

5643

// Constructor

5644

Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> f):

5645

dolfin::Form(1, 1), f(*this, 0)

5646

{

5647

_function_spaces[0] = V0;

5648

5649

this->f = *f;

5650

5651

_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3dp3_form_1());

5652

}

5653

5654

// Destructor

5655

~Form_1()

5656

{}

5657

5658

/// Return the number of the coefficient with this name

5659

virtual dolfin::uint coefficient_number(const std::string& name) const

5660

{

5661

if (name == "f")

5662

return 0;

5663

5664

dolfin::error("Invalid coefficient.");

5665

return 0;

5666

}

5667

5668

/// Return the name of the coefficient with this number

5669

virtual std::string coefficient_name(dolfin::uint i) const

5670

{

5671

switch (i)

5672

{

5673

case 0:

5674

return "f";

5675

}

5676

5677

dolfin::error("Invalid coefficient.");

5678

return "unnamed";

5679

}

5680

5681

// Typedefs

5682

typedef Form_1_FunctionSpace_0 TestSpace;

5683

typedef Form_1_FunctionSpace_1 CoefficientSpace_f;

5684

5685

// Coefficients

5686

dolfin::CoefficientAssigner f;

5687

};

5688

5689

// Class typedefs

5690

typedef Form_0 BilinearForm;

5691

typedef Form_1 LinearForm;

5692

typedef Form_0::TestSpace FunctionSpace;

5693

5694

} // namespace Poisson3DP3

5695

5696

#endif