fem_tools.h

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/** \file fem_tools.h
 * \brief Loose implementation of some useful functions
 *
 * FIXME: Implementation here is very unstructured, need cleaning and pruning
 *
 */

/*
 * MoFEM is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>
*/

#ifndef __FEM_H__
#define __FEM_H__

#include<petscsys.h>

#ifdef __cplusplus
extern "C" {
#endif
  #include <cblas.h>
  #include <lapack_wrap.h>
#ifdef __cplusplus
}
#endif

#define LAMBDA(E,NU) (E*NU/((1.+NU)*(1.-2.*NU)))
#define MU(E,NU) (0.5*E/(1.+NU))
#define DELTA(NU_P,NU_PZ,E_P,E_Z) (((1+NU_P)*(1-NU_P-2*NU_PZ*(NU_PZ*E_Z/E_P)))/(E_P*E_P*E_Z))

#define N_MBTET0(x, y, z) ( 1.-x-y-z )          ///< tetrahedral shape function
#define N_MBTET1(x, y, z) ( x )                 ///< tetrahedral shape function
#define N_MBTET2(x, y, z) ( y )                 ///< tetrahedral shape function
#define N_MBTET3(x, y, z) ( z )                 ///< tetrahedral shape function
#define diffN_MBTET0x ( -1. )                   ///< derivative of tetrahedral shape function
#define diffN_MBTET0y ( -1. )                   ///< derivative of tetrahedral shape function
#define diffN_MBTET0z ( -1. )                   ///< derivative of tetrahedral shape function
#define diffN_MBTET1x ( 1. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET1y ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET1z ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET2x ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET2y ( 1. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET2z ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET3x ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET3y ( 0. )                    ///< derivative of tetrahedral shape function
#define diffN_MBTET3z ( 1. )                    ///< derivative of tetrahedral shape function

//MBTRI
#define N_MBTRI0(x, y) ( 1.-x-y )               ///< triangle shape function
#define N_MBTRI1(x, y) ( x )                    ///< triangle shape function
#define N_MBTRI2(x, y) ( y )                    ///< triangle shape function
#define diffN_MBTRI0x ( -1. )                   ///< derivative of triangle shape function
#define diffN_MBTRI0y ( -1. )                   ///< derivative of triangle shape function
#define diffN_MBTRI1x ( 1. )                    ///< derivative of triangle shape function
#define diffN_MBTRI1y ( 0. )                    ///< derivative of triangle shape function
#define diffN_MBTRI2x ( 0. )                    ///< derivative of triangle shape function
#define diffN_MBTRI2y ( 1. )                    ///< derivative of triangle shape function

//MBQUAD
#define N_MBQUAD0(x, y) ( (1.-x)*(1.-y) ) ///< quad shape function
#define N_MBQUAD1(x, y) ( x*(1-y) )       ///< quad shape function
#define N_MBQUAD2(x, y) ( x*y )           ///< quad shape function
#define N_MBQUAD3(x, y) ( (1.-x)*(y) )    ///< quad shape function
#define diffN_MBQUAD0x(y) ( -(1.-y) )
#define diffN_MBQUAD0y(x) ( -(1.-x) )
#define diffN_MBQUAD1x(y) ( (1.-y) )
#define diffN_MBQUAD1y(x) ( -x )
#define diffN_MBQUAD2x(y) ( y )
#define diffN_MBQUAD2y(x) ( x )
#define diffN_MBQUAD3x(y) ( -y )
#define diffN_MBQUAD3y(x) ( (1.-x) )

//MBEDGE
#define N_MBEDGE0(x) ( 1.-(x) )                 ///< edge shape function
#define N_MBEDGE1(x) ( x )                      ///< edge shape function
#define diffN_MBEDGE0 ( -1. )                   ///< derivative of edge shape function
#define diffN_MBEDGE1 ( 1. )                    ///< derivative of edge shape function

//MBTRIQ
#define N_MBTRIQ0(x, y) ( (1.-x-y)*(2*(1.-x-y)-1.) )
#define N_MBTRIQ1(x, y) ( x*(2.*x-1.) )
#define N_MBTRIQ2(x, y) ( y*(2.*y-1.) )
#define N_MBTRIQ3(x, y) ( 4.*(1.-x-y)*x )
#define N_MBTRIQ4(x, y) ( 4.*x*y )
#define N_MBTRIQ5(x, y) ( 4.*(1.-x-y)*y )
#define diffN_MBTRIQ0x(x, y) ( x+y-3.*(1.-x-y) )
#define diffN_MBTRIQ0y(x, y) ( x+y-3.*(1.-x-y) )
#define diffN_MBTRIQ1x(x, y) ( -1.+4.*x )
#define diffN_MBTRIQ1y(x, y) ( 0. )
#define diffN_MBTRIQ2x(x, y) ( 0. )
#define diffN_MBTRIQ2y(x, y) ( -1.+4.*y )
#define diffN_MBTRIQ3x(x, y) ( 4.*((1.-x-y)-x) )
#define diffN_MBTRIQ3y(x, y) ( -4.*x )
#define diffN_MBTRIQ4x(x, y) ( 4.*y )
#define diffN_MBTRIQ4y(x, y) ( 4.*x )
#define diffN_MBTRIQ5x(x, y) ( -4.*y )
#define diffN_MBTRIQ5y(x, y) ( 4.*((1.-x-y)-y) )

#ifdef __cplusplus
extern "C" {
#endif

/// print matric M
void print_mat(double *M,int m,int n);
/// print upper part of the symmetric matrix
void print_mat_sym_upper(double *M,int m,int n);
/// priint complex matrix
void print_mat_complex(__CLPK_doublecomplex *M,int m,int n);

/// \brief calculate shape functions on triangle
/// \param N shape function array
/// \param X array of Gauss X coordinates
/// \param Y array of Gauss Y coordinates
/// \param G_DIM number of Gauss points
PetscErrorCode ShapeMBTRI(double *N,const double *X,const double *Y,const int G_DIM);
/// calculate derivatives of shape functions
PetscErrorCode ShapeDiffMBTRI(double *diffN);

/// calculate face normal
/// \param diffN derivatives of shape functions
/// \param coords is position of the nodes
/// \param normal vector
PetscErrorCode ShapeFaceNormalMBTRI(double *diffN,const double *coords,double *normal);
PetscErrorCode ShapeFaceBaseMBTRI(
  double *diffN,const double *coords,
  double *normal,double *s1,double *s2);

/// calculate derivative of normal in respect to nodal positions
PetscErrorCode ShapeFaceDiffNormalMBTRI(double *diffN,const double *coords,double *diff_normal);
/// calculate jacobioan
void ShapeJacMBTRI(double *diffN,const double *coords,double *Jac);
/// calculate derivatives of shape functions in space
void ShapeDiffMBTRIinvJ(double *diffN,double *invJac,double *diffNinvJac);
/// calculate shape functions
PetscErrorCode ShapeMBTET(double *N,const double *G_X,const double *G_Y,const double *G_Z,int DIM);
/// calculate derivatives of shape functions
PetscErrorCode ShapeDiffMBTET(double *diffN);
/// determined of jacobian
double ShapeDetJacVolume(double *jac);
/// calculate jacobian
PetscErrorCode ShapeJacMBTET(double *diffN,const double *coords,double *jac);
// calculate inverse of jacobian
PetscErrorCode ShapeInvJacVolume(double *jac);
/// calculate TET volume
double ShapeVolumeMBTET(double *diffN,const double *coords);
/// calculate shape functions derivatives in space
PetscErrorCode ShapeDiffMBTETinvJ(double *diffN,double *invJac,double *diffNinvJac);

/// calculate spin matrix from vector
// \param spinOmega is a spin matrix
// \param vecOmega is a spin vector
PetscErrorCode Spin(double *spinOmega,double *vecOmega);

/// Compose complex matrix (3x3) from two real matrices
PetscErrorCode make_complex_matrix(double *reA,double *imA,__CLPK_doublecomplex *xA);
/// Complex normal
PetscErrorCode Normal_hierarchical(
  int order_approx,int *order_edge_approx,
  int order,int *order_edge,
  double *diffN,double *diffN_face,double *diffN_edge[],
  double *dofs,double *dofs_edge[],double *dofs_face,
  double *idofs,double *idofs_edge[],double *idofs_face,
    __CLPK_doublecomplex *xnormal,
    __CLPK_doublecomplex *s1,
    __CLPK_doublecomplex *s2,
    int gg);
PetscErrorCode Base_scale(
  __CLPK_doublecomplex *xnormal,__CLPK_doublecomplex *xs1,__CLPK_doublecomplex *xs2);

/**
 * \brief calculate local coordinates for given global coordinates
 *
 * new version for multiple points need to be implemented
 */
PetscErrorCode ShapeMBTET_inverse(
  double *N,double *diffN,const double *elem_coords,const double *glob_coords,double *loc_coords
);

/**
 * \brief calculate local coordinates of triangle element for given global coordinates in 2D (Assume e.g. z=0)
 \f[
 \left[\begin{array}{cc}
\frac{\partial N_{1}}{\partial\xi}x_{N_{1}}+\frac{\partial N_{2}}{\partial\xi}x_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}x_{N_{3}} & \frac{\partial N_{1}}{\partial\eta}x_{N_{1}}+\frac{\partial N_{2}}{\partial\eta}x_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}x_{N_{3}}\\
\frac{\partial N_{1}}{\partial\xi}y_{N_{1}}+\frac{\partial N_{2}}{\partial\xi}y_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}y_{N_{3}} & \frac{\partial N_{1}}{\partial\eta}y_{N_{1}}+\frac{\partial N_{2}}{\partial\eta}y_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}y_{N_{3}}
\end{array}\right]\left\{ \begin{array}{c}
\xi\\
\eta
\end{array}\right\} =\left\{ \begin{array}{c}
x_{gp}-\left(N_{1}x_{N_{1}}+N_{2}x_{N_{2}}+N_{3}x_{N_{3}}\right)\\
y_{gp}-\left(N_{1}y_{N_{1}}+N_{2}y_{N_{2}}+N_{3}y_{N_{3}}\right)
\end{array}\right\}
 \f]

 /// \param N shape function array
 /// \param diffN array of shape function derivative w.r.t to local coordinates
 /// \param elem_coords global coordinates of element
 /// \param glob_coords global coordinates of required point
 /// \param loc_coords  local coordinates of required point
 */
PetscErrorCode ShapeMBTRI_inverse(
  double *N,double *diffN,const double *elem_coords,const double *glob_coords,double *loc_coords
);

/// calculate gradient of deformation
PetscErrorCode GradientOfDeformation(double *diffN,double *dofs,double *F);

//2 Node edge
PetscErrorCode ShapeMBEDGE(double *N,const double *G_X,int DIM);
PetscErrorCode ShapeDiffMBEDGE(double *diffN);

//10 Node Tet
PetscErrorCode ShapeMBTRIQ(double *N,const double *X,const double *Y,const int G_DIM);
PetscErrorCode ShapeDiffMBTRIQ(double *diffN,const double *X,const double *Y,const int G_DIM);
PetscErrorCode ShapeMBTETQ(double *N,const double x,const double y,const double z);
PetscErrorCode ShapeDiffMBTETQ(double *diffN,const double x,const double y,const double z);
PetscErrorCode ShapeMBTETQ_GAUSS(double *N,const double *X,const double *Y,const double *Z,const int G_DIM);
PetscErrorCode ShapeDiffMBTETQ_GAUSS(double *diffN,const double *X,const double *Y,const double *Z,const int G_DIM);
PetscErrorCode ShapeJacMBTETQ(const double *diffN,const double *coords,double *Jac);
PetscErrorCode ShapeMBTETQ_detJac_at_Gauss_Points(double *detJac_at_Gauss_Points,const double *diffN,const double *coords,int G_DIM);
double ShapeVolumeMBTETQ(const double *diffN,const double *coords,int G_DIM,double *G_TET_W);
PetscErrorCode ShapeMBTETQ_inverse(
  double *N,double *diffN,const double *elem_coords,const double *glob_coords,double *loc_coords,const double eps
);

//complex part
void ShapeDiffMBTETinvJ_complex(double *diffN,__CLPK_doublecomplex *invJac,__CLPK_doublecomplex *diffNinvJac,const enum CBLAS_TRANSPOSE Trans);
PetscErrorCode ShapeFaceNormalMBTRI_complex(double *diffN,__CLPK_doublecomplex *xcoords,__CLPK_doublecomplex *xnormal);
PetscErrorCode MakeComplexTensor(double *reA,double *imA,__CLPK_doublecomplex *xA);
PetscErrorCode InvertComplexGradient(__CLPK_doublecomplex *xF);
PetscErrorCode DeterminantComplexGradient(__CLPK_doublecomplex *xF,__CLPK_doublecomplex *det_xF);

//integration
///Compute weights and integration points for edge using Grundmann_Moeller rule
PetscErrorCode Grundmann_Moeller_integration_points_1D_EDGE(int rule,double *G_TRI_X,double *G_TRI_W);
///Compute weights and integration points for 2D Triangle using Grundmann_Moeller rule
PetscErrorCode Grundmann_Moeller_integration_points_2D_TRI(int rule,double *G_TRI_X,double *G_TRI_Y,double *G_TRI_W);
///Compute weights and integration points for 3D Tet using Grundmann_Moeller rule
PetscErrorCode Grundmann_Moeller_integration_points_3D_TET(int rule,double *G_TET_X,double *G_TET_Y,double *G_TET_Z, double *G_TET_W);

//http://people.sc.fsu.edu/~jburkardt/datasets/quadrature_rules_tet/quadrature_rules_tet.html
//TRI
static const double G_TRI_X1[] = {
3.3333333333333331e-01
};
static const double G_TRI_Y1[] = {
3.3333333333333331e-01
};
static const double G_TRI_W1[] = {
1.
};
static const double G_TRI_X3[] = {
0.5, 0., 0.5
};
static const double G_TRI_Y3[] = {
0., 0.5, 0.5
};
static const double G_TRI_W3[] = {
3.3333333333333331e-01, 3.3333333333333331e-01, 3.3333333333333331e-01
};
static const double G_TRI_X4[] = {
7.503111022260811058e-02, 1.785587282636164064e-01,
2.800199154990741235e-01, 6.663902460147014262e-01
};
static const double G_TRI_Y4[] = {
2.800199154990741235e-01, 6.663902460147014262e-01,
7.503111022260811058e-02, 1.785587282636164064e-01
};
static const double G_TRI_W4[] = {
1.8195861825602258066e-01, 3.1804138174397683647e-01,
1.8195861825602258066e-01, 3.1804138174397683647e-01
};
static const double G_TRI_X7[] = {
0.333333333333333, 0.736712498968435, 0.736712498968435,
0.237932366472434, 0.237932366472434, 0.025355134551932,
0.025355134551932
};
static const double G_TRI_Y7[] = {
0.333333333333333, 0.237932366472434, 0.025355134551932,
0.736712498968435, 0.025355134551932, 0.736712498968435,
0.237932366472434
};
static const double G_TRI_W7[] = {
  0.375000000000000, 0.104166666666667, 0.104166666666667, 0.104166666666667, 0.104166666666667, 0.104166666666667, 0.104166666666667
};
static const double G_TRI_X13[] = {
0.333333333333333, 0.479308067841923, 0.260345966079038, 0.260345966079038, 0.869739794195568,
0.065130102902216, 0.065130102902216, 0.638444188569809, 0.638444188569809, 0.312865496004875,
0.312865496004875, 0.048690315425316, 0.048690315425316
};
static const double G_TRI_Y13[] = {
0.333333333333333, 0.260345966079038, 0.479308067841923, 0.260345966079038, 0.065130102902216,
0.869739794195568, 0.065130102902216, 0.312865496004875, 0.048690315425316, 0.638444188569809,
0.048690315425316, 0.638444188569809, 0.312865496004875
};
static const double G_TRI_W13[] = {
 -0.149570044467670, 0.175615257433204, 0.175615257433204, 0.175615257433204, 0.053347235608839,
  0.053347235608839, 0.053347235608839, 0.077113760890257, 0.077113760890257, 0.077113760890257,
  0.077113760890257, 0.077113760890257, 0.077113760890257 };

static const double G_TRI_X19[] = {
0.333333333333333, 0.797426985353087, 0.101286507323456, 0.101286507323456, 0.059715871789770,
0.470142064105115, 0.470142064105115, 0.535795346449899, 0.232102326775050, 0.232102326775050,
0.941038278231121, 0.029480860884440, 0.029480860884440, 0.738416812340510, 0.738416812340510,
0.232102326775050, 0.232102326775050, 0.029480860884440, 0.029480860884440};
static const double G_TRI_Y19[] = {
0.333333333333333, 0.101286507323456, 0.797426985353087, 0.101286507323456, 0.470142064105115,
0.059715871789770, 0.470142064105115, 0.232102326775050, 0.535795346449899, 0.232102326775050,
0.029480860884440, 0.941038278231121, 0.029480860884440, 0.232102326775050, 0.029480860884440,
0.738416812340510, 0.029480860884440, 0.738416812340510, 0.232102326775050};
static const double G_TRI_W19[] = {
9.71357962827961025E-002, 3.13347002271398278E-002, 3.13347002271398278E-002, 3.13347002271398278E-002, 7.78275410047754301E-002,
7.78275410047754301E-002, 7.78275410047754301E-002, 7.96477389272090969E-002, 7.96477389272090969E-002, 7.96477389272090969E-002,
2.55776756586981006E-002, 2.55776756586981006E-002, 2.55776756586981006E-002, 4.32835393772893970E-002, 4.32835393772893970E-002,
4.32835393772893970E-002, 4.32835393772893970E-002, 4.32835393772893970E-002, 4.32835393772893970E-002};

static const double G_TRI_X28[] = {
0.333333333333333,   0.948021718143423,   0.025989140928288,   0.025989140928288,   0.811424994704155,
0.094287502647923,   0.094287502647923,   0.010726449965571,   0.494636775017215,   0.494636775017215,
0.585313234770972,   0.207343382614514,   0.207343382614514,   0.122184388599019,   0.438907805700491,
0.438907805700491,   0.677937654882590,   0.677937654882590,   0.044841677589131,   0.044841677589131,
0.277220667528279,   0.277220667528279,   0.858870281282636,   0.858870281282636,   0.0000000000000000,
0.0000000000000000,  0.141129718717364,   0.141129718717364};
static const double G_TRI_Y28[] = {
0.333333333333333,   0.025989140928288,   0.948021718143423,   0.025989140928288,   0.094287502647923,
0.811424994704155,   0.094287502647923,   0.494636775017215,   0.010726449965571,   0.494636775017215,
0.207343382614514,   0.585313234770972,   0.207343382614514,   0.438907805700491,   0.122184388599019,
0.438907805700491,   0.044841677589131,   0.277220667528279,   0.677937654882590 ,  0.277220667528279,
0.677937654882590,   0.044841677589131,   0.000000000000000,   0.141129718717364,   0.858870281282636,
0.141129718717364,   0.858870281282636,   0.000000000000000};
static const double G_TRI_W28[] = {
0.08797730116222190,  0.008744311553736190, 0.008744311553736190,  0.008744311553736190,  0.03808157199393533,
0.03808157199393533,  0.03808157199393533,  0.01885544805613125,   0.01885544805613125,   0.01885544805613125,
0.07215969754474100,  0.07215969754474100,  0.07215969754474100,   0.06932913870553720,   0.06932913870553720,
0.06932913870553720,  0.04105631542928860,  0.04105631542928860,   0.04105631542928860,   0.04105631542928860,
0.04105631542928860,  0.04105631542928860,  0.007362383783300573,  0.007362383783300573,  0.007362383783300573,
0.007362383783300573, 0.007362383783300573, 0.007362383783300573};

static const double G_TRI_X37[] = {
0.333333333333333,   0.950275662924106,   0.024862168537947,   0.024862168537947,   0.171614914923835,
0.414192542538082,   0.414192542538082,   0.539412243677190,   0.230293878161405,   0.230293878161405,
0.772160036676533,   0.113919981661734,   0.113919981661734,   0.009085399949835,   0.495457300025082,
0.495457300025082,   0.062277290305887,   0.468861354847056,   0.468861354847056,   0.022076289653624,
0.022076289653624,   0.851306504174348,   0.851306504174348,   0.126617206172027,   0.126617206172027,
0.018620522802521,   0.018620522802521,   0.689441970728591,   0.689441970728591,   0.291937506468888,
0.291937506468888,   0.096506481292159,   0.096506481292159,   0.635867859433873,   0.635867859433873,
0.267625659273968,   0.267625659273968};
static const double G_TRI_Y37[] = {
0.333333333333333,   0.024862168537947,   0.950275662924106,   0.024862168537947,   0.414192542538082,
0.171614914923835,   0.414192542538082,   0.230293878161405,   0.539412243677190,   0.230293878161405,
0.113919981661734,   0.772160036676533,   0.113919981661734,   0.495457300025082,   0.009085399949835,
0.495457300025082,   0.468861354847056,   0.062277290305887,   0.468861354847056,   0.851306504174348,
0.126617206172027,   0.022076289653624,   0.126617206172027,   0.022076289653624,   0.851306504174348,
0.689441970728591,   0.291937506468888,   0.018620522802521,   0.291937506468888,   0.018620522802521,
0.689441970728591,   0.635867859433873,   0.267625659273968,   0.096506481292159,   0.267625659273968,
0.096506481292159,   0.635867859433873};
static const double G_TRI_W37[] = {
0.051739766065744,   0.008007799555565,   0.008007799555565,   0.008007799555565,   0.046868898981822,
0.046868898981822,   0.046868898981822,   0.046590940183976,   0.046590940183976,   0.046590940183976,
0.031016943313796,   0.031016943313796,   0.031016943313796,   0.010791612736631,   0.010791612736631,
0.010791612736631,   0.032195534242432,   0.032195534242432,   0.032195534242432,   0.015445834210702,
0.015445834210702,   0.015445834210702,   0.015445834210702,   0.015445834210702,   0.015445834210702,
0.017822989923179,   0.017822989923179,   0.017822989923179,   0.017822989923179,   0.017822989923179,
0.017822989923179,   0.037038683681385,   0.037038683681385,   0.037038683681385,   0.037038683681385,
0.037038683681385,   0.037038683681385};
static const double G_TRI_X286[] = {
                0.04347826086956522,  0.1304347826086956,  0.2173913043478261,  0.3043478260869565,             0.391304347826087,  0.4782608695652174,  0.5652173913043478,  0.6521739130434783,
  0.7391304347826086,  0.8260869565217391,  0.9130434782608695, 0.04347826086956522,  0.1304347826086956,  0.2173913043478261,  0.3043478260869565,             0.391304347826087,
  0.4782608695652174,  0.5652173913043478,  0.6521739130434783,  0.7391304347826086,  0.8260869565217391,       0.04347826086956522,  0.1304347826086956,  0.2173913043478261,
  0.3043478260869565,           0.391304347826087,  0.4782608695652174,  0.5652173913043478,  0.6521739130434783,  0.7391304347826086,          0.04347826086956522,  0.1304347826086956,
  0.2173913043478261,  0.3043478260869565,      0.391304347826087,  0.4782608695652174,  0.5652173913043478,  0.6521739130434783,               0.04347826086956522,  0.1304347826086956,
  0.2173913043478261,  0.3043478260869565,      0.391304347826087,  0.4782608695652174,  0.5652173913043478,    0.04347826086956522,  0.1304347826086956,  0.2173913043478261,
  0.3043478260869565,           0.391304347826087,  0.4782608695652174,         0.04347826086956522,  0.1304347826086956,  0.2173913043478261,  0.3043478260869565,             0.391304347826087,
                0.04347826086956522,  0.1304347826086956,  0.2173913043478261,  0.3043478260869565,             0.04347826086956522,  0.1304347826086956,  0.2173913043478261,  0.04347826086956522,
  0.1304347826086956,           0.04347826086956522,            0.04761904761904762,  0.1428571428571428,  0.2380952380952381,  0.3333333333333333,  0.4285714285714285,  0.5238095238095238,
  0.6190476190476191,  0.7142857142857143,  0.8095238095238095,  0.9047619047619048,            0.04761904761904762,  0.1428571428571428,  0.2380952380952381,  0.3333333333333333,
  0.4285714285714285,  0.5238095238095238,  0.6190476190476191,  0.7142857142857143,  0.8095238095238095,       0.04761904761904762,  0.1428571428571428,  0.2380952380952381,
  0.3333333333333333,  0.4285714285714285,  0.5238095238095238,  0.6190476190476191,  0.7142857142857143,       0.04761904761904762,  0.1428571428571428,  0.2380952380952381,
  0.3333333333333333,  0.4285714285714285,  0.5238095238095238,  0.6190476190476191,            0.04761904761904762,  0.1428571428571428,  0.2380952380952381,  0.3333333333333333,
  0.4285714285714285,  0.5238095238095238,      0.04761904761904762,  0.1428571428571428,  0.2380952380952381,  0.3333333333333333,  0.4285714285714285,        0.04761904761904762,
  0.1428571428571428,  0.2380952380952381,  0.3333333333333333, 0.04761904761904762,  0.1428571428571428,  0.2380952380952381,  0.04761904761904762,  0.1428571428571428,
                0.04761904761904762,            0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,  0.4736842105263158,  0.5789473684210527,  0.6842105263157895,
  0.7894736842105263,  0.8947368421052632,      0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,  0.4736842105263158,  0.5789473684210527,
  0.6842105263157895,  0.7894736842105263,      0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,  0.4736842105263158,  0.5789473684210527,
  0.6842105263157895,           0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,  0.4736842105263158,  0.5789473684210527,   0.05263157894736842,
  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,  0.4736842105263158,            0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.3684210526315789,
                0.05263157894736842,  0.1578947368421053,  0.2631578947368421,  0.05263157894736842,  0.1578947368421053,       0.05263157894736842,            0.05882352941176471,  0.1764705882352941,
  0.2941176470588235,  0.4117647058823529,  0.5294117647058824,  0.6470588235294118,  0.7647058823529411,  0.8823529411764706,  0.05882352941176471,  0.1764705882352941,
  0.2941176470588235,  0.4117647058823529,  0.5294117647058824,  0.6470588235294118,  0.7647058823529411,       0.05882352941176471,  0.1764705882352941,  0.2941176470588235,
  0.4117647058823529,  0.5294117647058824,  0.6470588235294118, 0.05882352941176471,  0.1764705882352941,  0.2941176470588235,  0.4117647058823529,  0.5294117647058824,
                0.05882352941176471,  0.1764705882352941,  0.2941176470588235,  0.4117647058823529,             0.05882352941176471,  0.1764705882352941,  0.2941176470588235,  0.05882352941176471,
  0.1764705882352941,           0.05882352941176471,            0.06666666666666667,            0.2,  0.3333333333333333,  0.4666666666666667,  0.6,  0.7333333333333333,
  0.8666666666666667,           0.06666666666666667,            0.2,  0.3333333333333333,  0.4666666666666667,  0.6,  0.7333333333333333,       0.06666666666666667,
                0.2,  0.3333333333333333,  0.4666666666666667,  0.6,            0.06666666666666667,            0.2,  0.3333333333333333,  0.4666666666666667,
                0.06666666666666667,            0.2,  0.3333333333333333,       0.06666666666666667,            0.2,            0.06666666666666667,            0.07692307692307693,  0.2307692307692308,
  0.3846153846153846,  0.5384615384615384,  0.6923076923076923,  0.8461538461538461,            0.07692307692307693,  0.2307692307692308,  0.3846153846153846,  0.5384615384615384,
  0.6923076923076923,           0.07692307692307693,  0.2307692307692308,  0.3846153846153846,  0.5384615384615384,             0.07692307692307693,  0.2307692307692308,  0.3846153846153846,
                0.07692307692307693,  0.2307692307692308,       0.07692307692307693,            0.09090909090909091,  0.2727272727272727,  0.4545454545454545,  0.6363636363636364,  0.8181818181818182,
                0.09090909090909091,  0.2727272727272727,  0.4545454545454545,  0.6363636363636364,             0.09090909090909091,  0.2727272727272727,  0.4545454545454545,  0.09090909090909091,
  0.2727272727272727,           0.09090909090909091,  0.1111111111111111,  0.3333333333333333,  0.5555555555555556,  0.7777777777777778,  0.1111111111111111,  0.3333333333333333,
  0.5555555555555556,  0.1111111111111111,  0.3333333333333333,  0.1111111111111111,  0.1428571428571428,  0.4285714285714285,  0.7142857142857143,  0.1428571428571428,
  0.4285714285714285,  0.1428571428571428,      0.2,            0.6,            0.2,  0.3333333333333333
};
static const double G_TRI_Y286[] = {
                0.04347826086956522,            0.04347826086956522,            0.04347826086956522,            0.04347826086956522,            0.04347826086956522,            0.04347826086956522,            0.04347826086956522,            0.04347826086956522,
                0.04347826086956522,            0.04347826086956522,            0.04347826086956522,  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,
  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,  0.1304347826086956,  0.2173913043478261,  0.2173913043478261,  0.2173913043478261,
  0.2173913043478261,  0.2173913043478261,  0.2173913043478261,  0.2173913043478261,  0.2173913043478261,  0.2173913043478261,  0.3043478260869565,  0.3043478260869565,
  0.3043478260869565,  0.3043478260869565,  0.3043478260869565,  0.3043478260869565,  0.3043478260869565,  0.3043478260869565,  0.391304347826087,              0.391304347826087,
                0.391304347826087,              0.391304347826087,              0.391304347826087,              0.391304347826087,              0.391304347826087,  0.4782608695652174,  0.4782608695652174,  0.4782608695652174,
  0.4782608695652174,  0.4782608695652174,  0.4782608695652174,  0.5652173913043478,  0.5652173913043478,  0.5652173913043478,  0.5652173913043478,  0.5652173913043478,
  0.6521739130434783,  0.6521739130434783,  0.6521739130434783,  0.6521739130434783,  0.7391304347826086,  0.7391304347826086,  0.7391304347826086,  0.8260869565217391,
  0.8260869565217391,  0.9130434782608695,      0.04761904761904762,            0.04761904761904762,            0.04761904761904762,            0.04761904761904762,            0.04761904761904762,            0.04761904761904762,
                0.04761904761904762,            0.04761904761904762,            0.04761904761904762,            0.04761904761904762,  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,
  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,  0.2380952380952381,  0.2380952380952381,  0.2380952380952381,
  0.2380952380952381,  0.2380952380952381,  0.2380952380952381,  0.2380952380952381,  0.2380952380952381,  0.3333333333333333,  0.3333333333333333,  0.3333333333333333,
  0.3333333333333333,  0.3333333333333333,  0.3333333333333333,  0.3333333333333333,  0.4285714285714285,  0.4285714285714285,  0.4285714285714285,  0.4285714285714285,
  0.4285714285714285,  0.4285714285714285,  0.5238095238095238,  0.5238095238095238,  0.5238095238095238,  0.5238095238095238,  0.5238095238095238,  0.6190476190476191,
  0.6190476190476191,  0.6190476190476191,  0.6190476190476191,  0.7142857142857143,  0.7142857142857143,  0.7142857142857143,  0.8095238095238095,  0.8095238095238095,
  0.9047619047619048,           0.05263157894736842,            0.05263157894736842,            0.05263157894736842,            0.05263157894736842,            0.05263157894736842,            0.05263157894736842,            0.05263157894736842,
                0.05263157894736842,            0.05263157894736842,  0.1578947368421053,  0.1578947368421053,  0.1578947368421053,  0.1578947368421053,  0.1578947368421053,  0.1578947368421053,
  0.1578947368421053,  0.1578947368421053,  0.2631578947368421,  0.2631578947368421,  0.2631578947368421,  0.2631578947368421,  0.2631578947368421,  0.2631578947368421,
  0.2631578947368421,  0.3684210526315789,  0.3684210526315789,  0.3684210526315789,  0.3684210526315789,  0.3684210526315789,  0.3684210526315789,  0.4736842105263158,
  0.4736842105263158,  0.4736842105263158,  0.4736842105263158,  0.4736842105263158,  0.5789473684210527,  0.5789473684210527,  0.5789473684210527,  0.5789473684210527,
  0.6842105263157895,  0.6842105263157895,  0.6842105263157895,  0.7894736842105263,  0.7894736842105263,  0.8947368421052632,  0.05882352941176471,            0.05882352941176471,
                0.05882352941176471,            0.05882352941176471,            0.05882352941176471,            0.05882352941176471,            0.05882352941176471,            0.05882352941176471,  0.1764705882352941,  0.1764705882352941,
  0.1764705882352941,  0.1764705882352941,  0.1764705882352941,  0.1764705882352941,  0.1764705882352941,  0.2941176470588235,  0.2941176470588235,  0.2941176470588235,
  0.2941176470588235,  0.2941176470588235,  0.2941176470588235,  0.4117647058823529,  0.4117647058823529,  0.4117647058823529,  0.4117647058823529,  0.4117647058823529,
  0.5294117647058824,  0.5294117647058824,  0.5294117647058824,  0.5294117647058824,  0.6470588235294118,  0.6470588235294118,  0.6470588235294118,  0.7647058823529411,
  0.7647058823529411,  0.8823529411764706,      0.06666666666666667,            0.06666666666666667,            0.06666666666666667,            0.06666666666666667,            0.06666666666666667,            0.06666666666666667,
                0.06666666666666667,            0.2,            0.2,            0.2,            0.2,            0.2,            0.2,  0.3333333333333333,
  0.3333333333333333,  0.3333333333333333,  0.3333333333333333,  0.3333333333333333,  0.4666666666666667,  0.4666666666666667,  0.4666666666666667,  0.4666666666666667,
                0.6,            0.6,            0.6,  0.7333333333333333,  0.7333333333333333,  0.8666666666666667,             0.07692307692307693,            0.07692307692307693,
                0.07692307692307693,            0.07692307692307693,            0.07692307692307693,            0.07692307692307693,  0.2307692307692308,  0.2307692307692308,  0.2307692307692308,  0.2307692307692308,
  0.2307692307692308,  0.3846153846153846,  0.3846153846153846,  0.3846153846153846,  0.3846153846153846,  0.5384615384615384,  0.5384615384615384,  0.5384615384615384,
  0.6923076923076923,  0.6923076923076923,  0.8461538461538461, 0.09090909090909091,            0.09090909090909091,            0.09090909090909091,            0.09090909090909091,            0.09090909090909091,
  0.2727272727272727,  0.2727272727272727,  0.2727272727272727,  0.2727272727272727,  0.4545454545454545,  0.4545454545454545,  0.4545454545454545,  0.6363636363636364,
  0.6363636363636364,  0.8181818181818182,  0.1111111111111111,  0.1111111111111111,  0.1111111111111111,  0.1111111111111111,  0.3333333333333333,  0.3333333333333333,
  0.3333333333333333,  0.5555555555555556,  0.5555555555555556,  0.7777777777777778,  0.1428571428571428,  0.1428571428571428,  0.1428571428571428,  0.4285714285714285,
  0.4285714285714285,  0.7142857142857143,      0.2,            0.2,            0.6,  0.3333333333333333
};
                static const double G_TRI_W286[] = {
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668, 2.912193380035668,           2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,              2.912193380035668,
                2.912193380035668,              2.912193380035668,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,  -9.914451197589852,
  -9.914451197589852,            13.33158527957992,             13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,
                13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,
                13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,
                13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,
                13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,
                13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,              13.33158527957992,  -9.027792408986382,  -9.027792408986382,
  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,
  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,
  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,
  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,  -9.027792408986382,
  -9.027792408986382,  -9.027792408986382,      3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,
                3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,
                3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,
                3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              3.258672079964582,              -0.6133639040302452,            -0.6133639040302452,
                -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,
                -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,
                -0.6133639040302452,            -0.6133639040302452,            -0.6133639040302452,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,
                0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,            0.05511571669513555,
                0.05511571669513555,            0.05511571669513555,            -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,
                -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,          -0.001979122382447095,          2.02054621415273e-05,           2.02054621415273e-05,           2.02054621415273e-05,           2.02054621415273e-05,
                2.02054621415273e-05,           2.02054621415273e-05,           -2.874940020535803e-08,         -2.874940020535803e-08,         -2.874940020535803e-08,         8.829438425435718e-13
};

//TET
static const double G_TET_X1[] = {
0.25
};
static const double G_TET_Y1[] = {
0.25
};
static const double G_TET_Z1[] = {
0.25
};
static const double G_TET_W1[] = {
1.
};
static const double G_TET_X4[] = {
0.1757281246520584, 0.2445310270213291,
0.5556470949048655, 0.0240937534217468
};
static const double G_TET_Y4[] = {
0.5656137776620919, 0.0501800797762026,
0.1487681308666864, 0.2354380116950194
};
static const double G_TET_Z4[] = {
0.2180665126782654, 0.5635595064952189,
0.0350112499848832, 0.1833627308416330
};
static const double G_TET_W4[] = {
0.25,0.25,0.25,0.25
};
static const double G_TET_X5[] = {
0.25000000000000000, 0.50000000000000000,
0.16666666666666667, 0.16666666666666667,
0.16666666666666667
};
static const double G_TET_Y5[] = {
0.25000000000000000, 0.16666666666666667,
0.50000000000000000, 0.16666666666666667,
0.16666666666666667
};
static const double G_TET_Z5[] = {
0.25000000000000000, 0.16666666666666667,
0.16666666666666667, 0.50000000000000000,
0.16666666666666667
};
static const double G_TET_W5[] = {
-0.80000000000000000, 0.45000000000000000,
0.45000000000000000, 0.45000000000000000,
0.45000000000000000
};
static const double G_TET_X10[] = {
  0.5684305841968444, 0.1438564719343852, 0.1438564719343852, 0.1438564719343852,
  0.0000000000000000, 0.5000000000000000, 0.5000000000000000, 0.5000000000000000,
  0.0000000000000000, 0.0000000000000000
};
static const double G_TET_Y10[] = {
  0.1438564719343852, 0.1438564719343852, 0.1438564719343852, 0.5684305841968444,
  0.5000000000000000, 0.0000000000000000, 0.5000000000000000, 0.0000000000000000,
  0.5000000000000000, 0.0000000000000000
};
static const double G_TET_Z10[] = {
  0.1438564719343852, 0.1438564719343852, 0.5684305841968444, 0.1438564719343852,
  0.5000000000000000, 0.5000000000000000, 0.0000000000000000, 0.0000000000000000,
  0.0000000000000000, 0.5000000000000000
};
static const double G_TET_W10[] = {
  0.2177650698804054, 0.2177650698804054, 0.2177650698804054, 0.2177650698804054,
  0.0214899534130631, 0.0214899534130631, 0.0214899534130631, 0.0214899534130631,
  0.0214899534130631, 0.0214899534130631
};

static const double G_TET_X45[] = {
0.2500000000000000, 0.6175871903000830, 0.1274709365666390, 0.1274709365666390, 0.1274709365666390,
0.9037635088221031, 0.0320788303926323, 0.0320788303926323, 0.0320788303926323, 0.4502229043567190,
0.0497770956432810, 0.0497770956432810, 0.0497770956432810, 0.4502229043567190, 0.4502229043567190,
0.3162695526014501, 0.1837304473985499, 0.1837304473985499, 0.1837304473985499, 0.3162695526014501,
0.3162695526014501, 0.0229177878448171, 0.2319010893971509, 0.2319010893971509, 0.5132800333608811,
0.2319010893971509, 0.2319010893971509, 0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
0.2319010893971509, 0.0229177878448171, 0.5132800333608811, 0.7303134278075384, 0.0379700484718286,
0.0379700484718286, 0.1937464752488044, 0.0379700484718286, 0.0379700484718286, 0.0379700484718286,
0.7303134278075384, 0.1937464752488044, 0.0379700484718286, 0.7303134278075384, 0.1937464752488044
};
static const double G_TET_Y45[] = {
0.2500000000000000, 0.1274709365666390, 0.1274709365666390, 0.1274709365666390, 0.6175871903000830,
0.0320788303926323, 0.0320788303926323, 0.0320788303926323, 0.9037635088221031, 0.0497770956432810,
0.4502229043567190, 0.0497770956432810, 0.4502229043567190, 0.0497770956432810, 0.4502229043567190,
0.1837304473985499, 0.3162695526014501, 0.1837304473985499, 0.3162695526014501, 0.1837304473985499,
0.3162695526014501, 0.2319010893971509, 0.0229177878448171, 0.2319010893971509, 0.2319010893971509,
0.5132800333608811, 0.2319010893971509, 0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
0.5132800333608811, 0.2319010893971509, 0.0229177878448171, 0.0379700484718286, 0.7303134278075384,
0.0379700484718286, 0.0379700484718286, 0.1937464752488044, 0.0379700484718286, 0.7303134278075384,
0.1937464752488044, 0.0379700484718286, 0.1937464752488044, 0.0379700484718286, 0.7303134278075384
};
static const double G_TET_Z45[] = {
0.2500000000000000, 0.1274709365666390, 0.1274709365666390, 0.6175871903000830, 0.1274709365666390,
0.0320788303926323, 0.0320788303926323, 0.9037635088221031, 0.0320788303926323, 0.0497770956432810,
0.0497770956432810, 0.4502229043567190, 0.4502229043567190, 0.4502229043567190, 0.0497770956432810,
0.1837304473985499, 0.1837304473985499, 0.3162695526014501, 0.3162695526014501, 0.3162695526014501,
0.1837304473985499, 0.2319010893971509, 0.2319010893971509, 0.0229177878448171, 0.2319010893971509,
0.2319010893971509, 0.5132800333608811, 0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
0.0229177878448171, 0.5132800333608811, 0.2319010893971509, 0.0379700484718286, 0.0379700484718286,
0.7303134278075384, 0.0379700484718286, 0.0379700484718286, 0.1937464752488044, 0.1937464752488044,
0.0379700484718286, 0.7303134278075384, 0.7303134278075384, 0.1937464752488044, 0.0379700484718286
};
static const double G_TET_W45[] = {
 -0.2359620398477557, 0.0244878963560562, 0.0244878963560562, 0.0244878963560562, 0.0244878963560562,
  0.0039485206398261, 0.0039485206398261, 0.0039485206398261, 0.0039485206398261, 0.0263055529507371,
  0.0263055529507371, 0.0263055529507371, 0.0263055529507371, 0.0263055529507371, 0.0263055529507371,
  0.0829803830550589, 0.0829803830550589, 0.0829803830550589, 0.0829803830550589, 0.0829803830550589,
  0.0829803830550589, 0.0254426245481023, 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
  0.0254426245481023, 0.0254426245481023, 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
  0.0254426245481023, 0.0254426245481023, 0.0254426245481023, 0.0134324384376852, 0.0134324384376852,
  0.0134324384376852, 0.0134324384376852, 0.0134324384376852, 0.0134324384376852, 0.0134324384376852,
  0.0134324384376852, 0.0134324384376852, 0.0134324384376852, 0.0134324384376852, 0.0134324384376852
};
static const double NC_TET_X84[] = {
  0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.7000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.6000000000000000, 0.6000000000000000, 0.6000000000000000, 0.2000000000000000,
  0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.5000000000000000, 0.5000000000000000, 0.5000000000000000, 0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
  0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.1000000000000000, 0.5000000000000000, 0.5000000000000000, 0.5000000000000000, 0.4000000000000000, 0.4000000000000000,
  0.4000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.4000000000000000, 0.4000000000000000, 0.4000000000000000,
  0.4000000000000000, 0.4000000000000000, 0.4000000000000000, 0.3000000000000000, 0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
  0.3000000000000000, 0.3000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
  0.2000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
  0.2000000000000000, 0.2000000000000000, 0.2000000000000000, 0.4000000000000000, 0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
  0.1000000000000000, 0.3000000000000000, 0.3000000000000000, 0.3000000000000000, 0.2000000000000000, 0.2000000000000000, 0.2000000000000000
};
static const double NC_TET_Y84[] = {
  0.1000000000000000, 0.1000000000000000, 0.7000000000000000, 0.1000000000000000, 0.1000000000000000, 0.1000000000000000, 0.6000000000000000,
  0.6000000000000000, 0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.1000000000000000, 0.2000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.6000000000000000, 0.1000000000000000, 0.1000000000000000, 0.5000000000000000, 0.5000000000000000, 0.3000000000000000,
  0.3000000000000000, 0.1000000000000000, 0.1000000000000000, 0.3000000000000000, 0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
  0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.1000000000000000, 0.5000000000000000, 0.5000000000000000, 0.2000000000000000,
  0.2000000000000000, 0.5000000000000000, 0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.4000000000000000, 0.4000000000000000, 0.1000000000000000, 0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
  0.2000000000000000, 0.1000000000000000, 0.1000000000000000, 0.4000000000000000, 0.4000000000000000, 0.2000000000000000, 0.2000000000000000,
  0.1000000000000000, 0.1000000000000000, 0.4000000000000000, 0.4000000000000000, 0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.4000000000000000, 0.4000000000000000, 0.3000000000000000, 0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
  0.2000000000000000, 0.2000000000000000, 0.4000000000000000, 0.2000000000000000, 0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
  0.3000000000000000, 0.3000000000000000, 0.2000000000000000, 0.2000000000000000, 0.3000000000000000, 0.3000000000000000, 0.2000000000000000
};
static const double NC_TET_Z84[] = {
  0.1000000000000000, 0.7000000000000000, 0.1000000000000000, 0.1000000000000000, 0.6000000000000000, 0.2000000000000000, 0.1000000000000000,
  0.2000000000000000, 0.1000000000000000, 0.6000000000000000, 0.1000000000000000, 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
  0.6000000000000000, 0.1000000000000000, 0.5000000000000000, 0.3000000000000000, 0.1000000000000000, 0.3000000000000000, 0.1000000000000000,
  0.5000000000000000, 0.1000000000000000, 0.3000000000000000, 0.1000000000000000, 0.1000000000000000, 0.5000000000000000, 0.1000000000000000,
  0.1000000000000000, 0.5000000000000000, 0.2000000000000000, 0.5000000000000000, 0.2000000000000000, 0.1000000000000000, 0.2000000000000000,
  0.5000000000000000, 0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.2000000000000000, 0.1000000000000000, 0.4000000000000000,
  0.1000000000000000, 0.4000000000000000, 0.1000000000000000, 0.4000000000000000, 0.2000000000000000, 0.1000000000000000, 0.3000000000000000,
  0.1000000000000000, 0.3000000000000000, 0.2000000000000000, 0.2000000000000000, 0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
  0.4000000000000000, 0.2000000000000000, 0.3000000000000000, 0.1000000000000000, 0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
  0.3000000000000000, 0.3000000000000000, 0.2000000000000000, 0.4000000000000000, 0.2000000000000000, 0.4000000000000000, 0.3000000000000000,
  0.2000000000000000, 0.4000000000000000, 0.2000000000000000, 0.2000000000000000, 0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
  0.3000000000000000, 0.2000000000000000, 0.3000000000000000, 0.2000000000000000, 0.3000000000000000, 0.2000000000000000, 0.3000000000000000
};
static const double NC_TET_W84[] = {
  0.2843915343915344, 0.2843915343915344, 0.2843915343915344, 0.2843915343915344, -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
  -0.3882275132275133, -0.3882275132275133, -0.3882275132275133, -0.3882275132275133, -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
  -0.3882275132275133, -0.3882275132275133, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027,
  0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027, 0.8776455026455027,
  0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487,
  0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487, 0.1236772486772487, -0.8584656084656085, -0.8584656084656085,
  -0.8584656084656085, -0.8584656084656085, -0.8584656084656085, -0.8584656084656085, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
  -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
  -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
  -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
  0.0145502645502645, 0.0145502645502645, 0.0145502645502645, 0.0145502645502645, 1.0165343915343916, 1.0165343915343916, 1.0165343915343916,
  1.0165343915343916, -0.0251322751322751, -0.0251322751322751, -0.0251322751322751, -0.0251322751322751, -0.0251322751322751, -0.0251322751322751
};

#ifdef __cplusplus
}
#endif

#endif