1# This file contains auto-generated functions for sampling
2# inside finite element solutions for various mesh types.
3# To see how the code generation works in detail, see
4# yt/utilities/mesh_code_generation.py.
5
6
7cimport cython
8from libc.math cimport pow
9
10
11@cython.boundscheck(False)
12@cython.wraparound(False)
13@cython.cdivision(True)
14cdef void Q1Function3D(double* fx,
15                       double* x,
16                       double* vertices,
17                       double* phys_x) nogil:
18	fx[0] = 0.125*(1 - x[0])*(1 - x[1])*(1 - x[2])*vertices[0] + 0.125*(1 - x[0])*(1 - x[1])*(1 + x[2])*vertices[12] + 0.125*(1 - x[0])*(1 + x[1])*(1 - x[2])*vertices[9] + 0.125*(1 - x[0])*(1 + x[1])*(1 + x[2])*vertices[21] + 0.125*(1 + x[0])*(1 - x[1])*(1 - x[2])*vertices[3] + 0.125*(1 + x[0])*(1 - x[1])*(1 + x[2])*vertices[15] + 0.125*(1 + x[0])*(1 + x[1])*(1 - x[2])*vertices[6] + 0.125*(1 + x[0])*(1 + x[1])*(1 + x[2])*vertices[18] - phys_x[0];
19	fx[1] = 0.125*(1 - x[0])*(1 - x[1])*(1 - x[2])*vertices[1] + 0.125*(1 - x[0])*(1 - x[1])*(1 + x[2])*vertices[13] + 0.125*(1 - x[0])*(1 + x[1])*(1 - x[2])*vertices[10] + 0.125*(1 - x[0])*(1 + x[1])*(1 + x[2])*vertices[22] + 0.125*(1 + x[0])*(1 - x[1])*(1 - x[2])*vertices[4] + 0.125*(1 + x[0])*(1 - x[1])*(1 + x[2])*vertices[16] + 0.125*(1 + x[0])*(1 + x[1])*(1 - x[2])*vertices[7] + 0.125*(1 + x[0])*(1 + x[1])*(1 + x[2])*vertices[19] - phys_x[1];
20	fx[2] = 0.125*(1 - x[0])*(1 - x[1])*(1 - x[2])*vertices[2] + 0.125*(1 - x[0])*(1 - x[1])*(1 + x[2])*vertices[14] + 0.125*(1 - x[0])*(1 + x[1])*(1 - x[2])*vertices[11] + 0.125*(1 - x[0])*(1 + x[1])*(1 + x[2])*vertices[23] + 0.125*(1 + x[0])*(1 - x[1])*(1 - x[2])*vertices[5] + 0.125*(1 + x[0])*(1 - x[1])*(1 + x[2])*vertices[17] + 0.125*(1 + x[0])*(1 + x[1])*(1 - x[2])*vertices[8] + 0.125*(1 + x[0])*(1 + x[1])*(1 + x[2])*vertices[20] - phys_x[2];
21
22
23@cython.boundscheck(False)
24@cython.wraparound(False)
25@cython.cdivision(True)
26cdef void Q1Jacobian3D(double* rcol,
27                       double* scol,
28                       double* tcol,
29                       double* x,
30                       double* vertices,
31                       double* phys_x) nogil:
32	rcol[0] = -0.125*(1 - x[1])*(1 - x[2])*vertices[0] + 0.125*(1 - x[1])*(1 - x[2])*vertices[3] - 0.125*(1 - x[1])*(1 + x[2])*vertices[12] + 0.125*(1 - x[1])*(1 + x[2])*vertices[15] + 0.125*(1 + x[1])*(1 - x[2])*vertices[6] - 0.125*(1 + x[1])*(1 - x[2])*vertices[9] + 0.125*(1 + x[1])*(1 + x[2])*vertices[18] - 0.125*(1 + x[1])*(1 + x[2])*vertices[21];
33	scol[0] = -0.125*(1 - x[0])*(1 - x[2])*vertices[0] + 0.125*(1 - x[0])*(1 - x[2])*vertices[9] - 0.125*(1 - x[0])*(1 + x[2])*vertices[12] + 0.125*(1 - x[0])*(1 + x[2])*vertices[21] - 0.125*(1 + x[0])*(1 - x[2])*vertices[3] + 0.125*(1 + x[0])*(1 - x[2])*vertices[6] - 0.125*(1 + x[0])*(1 + x[2])*vertices[15] + 0.125*(1 + x[0])*(1 + x[2])*vertices[18];
34	tcol[0] = -0.125*(1 - x[0])*(1 - x[1])*vertices[0] + 0.125*(1 - x[0])*(1 - x[1])*vertices[12] - 0.125*(1 - x[0])*(1 + x[1])*vertices[9] + 0.125*(1 - x[0])*(1 + x[1])*vertices[21] - 0.125*(1 + x[0])*(1 - x[1])*vertices[3] + 0.125*(1 + x[0])*(1 - x[1])*vertices[15] - 0.125*(1 + x[0])*(1 + x[1])*vertices[6] + 0.125*(1 + x[0])*(1 + x[1])*vertices[18];
35	rcol[1] = -0.125*(1 - x[1])*(1 - x[2])*vertices[1] + 0.125*(1 - x[1])*(1 - x[2])*vertices[4] - 0.125*(1 - x[1])*(1 + x[2])*vertices[13] + 0.125*(1 - x[1])*(1 + x[2])*vertices[16] + 0.125*(1 + x[1])*(1 - x[2])*vertices[7] - 0.125*(1 + x[1])*(1 - x[2])*vertices[10] + 0.125*(1 + x[1])*(1 + x[2])*vertices[19] - 0.125*(1 + x[1])*(1 + x[2])*vertices[22];
36	scol[1] = -0.125*(1 - x[0])*(1 - x[2])*vertices[1] + 0.125*(1 - x[0])*(1 - x[2])*vertices[10] - 0.125*(1 - x[0])*(1 + x[2])*vertices[13] + 0.125*(1 - x[0])*(1 + x[2])*vertices[22] - 0.125*(1 + x[0])*(1 - x[2])*vertices[4] + 0.125*(1 + x[0])*(1 - x[2])*vertices[7] - 0.125*(1 + x[0])*(1 + x[2])*vertices[16] + 0.125*(1 + x[0])*(1 + x[2])*vertices[19];
37	tcol[1] = -0.125*(1 - x[0])*(1 - x[1])*vertices[1] + 0.125*(1 - x[0])*(1 - x[1])*vertices[13] - 0.125*(1 - x[0])*(1 + x[1])*vertices[10] + 0.125*(1 - x[0])*(1 + x[1])*vertices[22] - 0.125*(1 + x[0])*(1 - x[1])*vertices[4] + 0.125*(1 + x[0])*(1 - x[1])*vertices[16] - 0.125*(1 + x[0])*(1 + x[1])*vertices[7] + 0.125*(1 + x[0])*(1 + x[1])*vertices[19];
38	rcol[2] = -0.125*(1 - x[1])*(1 - x[2])*vertices[2] + 0.125*(1 - x[1])*(1 - x[2])*vertices[5] - 0.125*(1 - x[1])*(1 + x[2])*vertices[14] + 0.125*(1 - x[1])*(1 + x[2])*vertices[17] + 0.125*(1 + x[1])*(1 - x[2])*vertices[8] - 0.125*(1 + x[1])*(1 - x[2])*vertices[11] + 0.125*(1 + x[1])*(1 + x[2])*vertices[20] - 0.125*(1 + x[1])*(1 + x[2])*vertices[23];
39	scol[2] = -0.125*(1 - x[0])*(1 - x[2])*vertices[2] + 0.125*(1 - x[0])*(1 - x[2])*vertices[11] - 0.125*(1 - x[0])*(1 + x[2])*vertices[14] + 0.125*(1 - x[0])*(1 + x[2])*vertices[23] - 0.125*(1 + x[0])*(1 - x[2])*vertices[5] + 0.125*(1 + x[0])*(1 - x[2])*vertices[8] - 0.125*(1 + x[0])*(1 + x[2])*vertices[17] + 0.125*(1 + x[0])*(1 + x[2])*vertices[20];
40	tcol[2] = -0.125*(1 - x[0])*(1 - x[1])*vertices[2] + 0.125*(1 - x[0])*(1 - x[1])*vertices[14] - 0.125*(1 - x[0])*(1 + x[1])*vertices[11] + 0.125*(1 - x[0])*(1 + x[1])*vertices[23] - 0.125*(1 + x[0])*(1 - x[1])*vertices[5] + 0.125*(1 + x[0])*(1 - x[1])*vertices[17] - 0.125*(1 + x[0])*(1 + x[1])*vertices[8] + 0.125*(1 + x[0])*(1 + x[1])*vertices[20];
41
42
43@cython.boundscheck(False)
44@cython.wraparound(False)
45@cython.cdivision(True)
46cdef void Q1Function2D(double* fx,
47                       double* x,
48                       double* vertices,
49                       double* phys_x) nogil:
50	fx[0] = 0.25*(1 - x[0])*(1 - x[1])*vertices[0] + 0.25*(1 - x[0])*(1 + x[1])*vertices[6] + 0.25*(1 + x[0])*(1 - x[1])*vertices[2] + 0.25*(1 + x[0])*(1 + x[1])*vertices[4] - phys_x[0];
51	fx[1] = 0.25*(1 - x[0])*(1 - x[1])*vertices[1] + 0.25*(1 - x[0])*(1 + x[1])*vertices[7] + 0.25*(1 + x[0])*(1 - x[1])*vertices[3] + 0.25*(1 + x[0])*(1 + x[1])*vertices[5] - phys_x[1];
52
53
54@cython.boundscheck(False)
55@cython.wraparound(False)
56@cython.cdivision(True)
57cdef void Q1Jacobian2D(double* rcol,
58                       double* scol,
59                       double* x,
60                       double* vertices,
61                       double* phys_x) nogil:
62	rcol[0] = -0.25*(1 - x[1])*vertices[0] + 0.25*(1 - x[1])*vertices[2] + 0.25*(1 + x[1])*vertices[4] - 0.25*(1 + x[1])*vertices[6];
63	scol[0] = -0.25*(1 - x[0])*vertices[0] + 0.25*(1 - x[0])*vertices[6] - 0.25*(1 + x[0])*vertices[2] + 0.25*(1 + x[0])*vertices[4];
64	rcol[1] = -0.25*(1 - x[1])*vertices[1] + 0.25*(1 - x[1])*vertices[3] + 0.25*(1 + x[1])*vertices[5] - 0.25*(1 + x[1])*vertices[7];
65	scol[1] = -0.25*(1 - x[0])*vertices[1] + 0.25*(1 - x[0])*vertices[7] - 0.25*(1 + x[0])*vertices[3] + 0.25*(1 + x[0])*vertices[5];
66
67
68@cython.boundscheck(False)
69@cython.wraparound(False)
70@cython.cdivision(True)
71cdef void Q2Function2D(double* fx,
72                       double* x,
73                       double* vertices,
74                       double* phys_x) nogil:
75	fx[0] = (1 + x[0])*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[16] - 0.5*(1 + x[0])*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[8] - 0.5*(1 + x[0])*(-1 + x[0])*x[1]*(1 + x[1])*vertices[12] - phys_x[0] - 0.5*x[0]*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[14] + 0.25*x[0]*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[0] + 0.25*x[0]*(-1 + x[0])*x[1]*(1 + x[1])*vertices[6] - 0.5*x[0]*(1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[10] + 0.25*x[0]*(1 + x[0])*x[1]*(-1 + x[1])*vertices[2] + 0.25*x[0]*(1 + x[0])*x[1]*(1 + x[1])*vertices[4];
76	fx[1] = (1 + x[0])*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[17] - 0.5*(1 + x[0])*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[9] - 0.5*(1 + x[0])*(-1 + x[0])*x[1]*(1 + x[1])*vertices[13] - phys_x[1] - 0.5*x[0]*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[15] + 0.25*x[0]*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[1] + 0.25*x[0]*(-1 + x[0])*x[1]*(1 + x[1])*vertices[7] - 0.5*x[0]*(1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[11] + 0.25*x[0]*(1 + x[0])*x[1]*(-1 + x[1])*vertices[3] + 0.25*x[0]*(1 + x[0])*x[1]*(1 + x[1])*vertices[5];
77
78
79@cython.boundscheck(False)
80@cython.wraparound(False)
81@cython.cdivision(True)
82cdef void Q2Jacobian2D(double* rcol,
83                       double* scol,
84                       double* x,
85                       double* vertices,
86                       double* phys_x) nogil:
87	rcol[0] = -0.5*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[14] + (-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[16] + 0.25*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[0] - 0.5*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[8] + 0.25*(-1 + x[0])*x[1]*(1 + x[1])*vertices[6] - 0.5*(-1 + x[0])*x[1]*(1 + x[1])*vertices[12] - 0.5*(1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[10] + (1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[16] + 0.25*(1 + x[0])*x[1]*(-1 + x[1])*vertices[2] - 0.5*(1 + x[0])*x[1]*(-1 + x[1])*vertices[8] + 0.25*(1 + x[0])*x[1]*(1 + x[1])*vertices[4] - 0.5*(1 + x[0])*x[1]*(1 + x[1])*vertices[12] - 0.5*x[0]*(1 + x[1])*(-1 + x[1])*vertices[10] - 0.5*x[0]*(1 + x[1])*(-1 + x[1])*vertices[14] + 0.25*x[0]*x[1]*(-1 + x[1])*vertices[0] + 0.25*x[0]*x[1]*(-1 + x[1])*vertices[2] + 0.25*x[0]*x[1]*(1 + x[1])*vertices[4] + 0.25*x[0]*x[1]*(1 + x[1])*vertices[6];
88	scol[0] = -0.5*(-1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[8] + (-1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[16] + 0.25*(-1 + x[1])*x[0]*(-1 + x[0])*vertices[0] - 0.5*(-1 + x[1])*x[0]*(-1 + x[0])*vertices[14] + 0.25*(-1 + x[1])*x[0]*(1 + x[0])*vertices[2] - 0.5*(-1 + x[1])*x[0]*(1 + x[0])*vertices[10] - 0.5*(1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[12] + (1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[16] + 0.25*(1 + x[1])*x[0]*(-1 + x[0])*vertices[6] - 0.5*(1 + x[1])*x[0]*(-1 + x[0])*vertices[14] + 0.25*(1 + x[1])*x[0]*(1 + x[0])*vertices[4] - 0.5*(1 + x[1])*x[0]*(1 + x[0])*vertices[10] - 0.5*x[1]*(1 + x[0])*(-1 + x[0])*vertices[8] - 0.5*x[1]*(1 + x[0])*(-1 + x[0])*vertices[12] + 0.25*x[1]*x[0]*(-1 + x[0])*vertices[0] + 0.25*x[1]*x[0]*(-1 + x[0])*vertices[6] + 0.25*x[1]*x[0]*(1 + x[0])*vertices[2] + 0.25*x[1]*x[0]*(1 + x[0])*vertices[4];
89	rcol[1] = -0.5*(-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[15] + (-1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[17] + 0.25*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[1] - 0.5*(-1 + x[0])*x[1]*(-1 + x[1])*vertices[9] + 0.25*(-1 + x[0])*x[1]*(1 + x[1])*vertices[7] - 0.5*(-1 + x[0])*x[1]*(1 + x[1])*vertices[13] - 0.5*(1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[11] + (1 + x[0])*(1 + x[1])*(-1 + x[1])*vertices[17] + 0.25*(1 + x[0])*x[1]*(-1 + x[1])*vertices[3] - 0.5*(1 + x[0])*x[1]*(-1 + x[1])*vertices[9] + 0.25*(1 + x[0])*x[1]*(1 + x[1])*vertices[5] - 0.5*(1 + x[0])*x[1]*(1 + x[1])*vertices[13] - 0.5*x[0]*(1 + x[1])*(-1 + x[1])*vertices[11] - 0.5*x[0]*(1 + x[1])*(-1 + x[1])*vertices[15] + 0.25*x[0]*x[1]*(-1 + x[1])*vertices[1] + 0.25*x[0]*x[1]*(-1 + x[1])*vertices[3] + 0.25*x[0]*x[1]*(1 + x[1])*vertices[5] + 0.25*x[0]*x[1]*(1 + x[1])*vertices[7];
90	scol[1] = -0.5*(-1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[9] + (-1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[17] + 0.25*(-1 + x[1])*x[0]*(-1 + x[0])*vertices[1] - 0.5*(-1 + x[1])*x[0]*(-1 + x[0])*vertices[15] + 0.25*(-1 + x[1])*x[0]*(1 + x[0])*vertices[3] - 0.5*(-1 + x[1])*x[0]*(1 + x[0])*vertices[11] - 0.5*(1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[13] + (1 + x[1])*(1 + x[0])*(-1 + x[0])*vertices[17] + 0.25*(1 + x[1])*x[0]*(-1 + x[0])*vertices[7] - 0.5*(1 + x[1])*x[0]*(-1 + x[0])*vertices[15] + 0.25*(1 + x[1])*x[0]*(1 + x[0])*vertices[5] - 0.5*(1 + x[1])*x[0]*(1 + x[0])*vertices[11] - 0.5*x[1]*(1 + x[0])*(-1 + x[0])*vertices[9] - 0.5*x[1]*(1 + x[0])*(-1 + x[0])*vertices[13] + 0.25*x[1]*x[0]*(-1 + x[0])*vertices[1] + 0.25*x[1]*x[0]*(-1 + x[0])*vertices[7] + 0.25*x[1]*x[0]*(1 + x[0])*vertices[3] + 0.25*x[1]*x[0]*(1 + x[0])*vertices[5];
91
92
93@cython.boundscheck(False)
94@cython.wraparound(False)
95@cython.cdivision(True)
96cdef void Tet2Function3D(double* fx,
97                       double* x,
98                       double* vertices,
99                       double* phys_x) nogil:
100	fx[0] = (-x[0] + 2*pow(x[0], 2))*vertices[3] + (-x[1] + 2*pow(x[1], 2))*vertices[6] + (-x[2] + 2*pow(x[2], 2))*vertices[9] + (4*x[0] - 4*x[0]*x[1] - 4*x[0]*x[2] - 4*pow(x[0], 2))*vertices[12] + (4*x[1] - 4*x[1]*x[0] - 4*x[1]*x[2] - 4*pow(x[1], 2))*vertices[18] + (4*x[2] - 4*x[2]*x[0] - 4*x[2]*x[1] - 4*pow(x[2], 2))*vertices[21] + (1 - 3*x[0] + 4*x[0]*x[1] + 4*x[0]*x[2] + 2*pow(x[0], 2) - 3*x[1] + 4*x[1]*x[2] + 2*pow(x[1], 2) - 3*x[2] + 2*pow(x[2], 2))*vertices[0] - phys_x[0] + 4*x[0]*x[1]*vertices[15] + 4*x[0]*x[2]*vertices[24] + 4*x[1]*x[2]*vertices[27];
101	fx[1] = (-x[0] + 2*pow(x[0], 2))*vertices[4] + (-x[1] + 2*pow(x[1], 2))*vertices[7] + (-x[2] + 2*pow(x[2], 2))*vertices[10] + (4*x[0] - 4*x[0]*x[1] - 4*x[0]*x[2] - 4*pow(x[0], 2))*vertices[13] + (4*x[1] - 4*x[1]*x[0] - 4*x[1]*x[2] - 4*pow(x[1], 2))*vertices[19] + (4*x[2] - 4*x[2]*x[0] - 4*x[2]*x[1] - 4*pow(x[2], 2))*vertices[22] + (1 - 3*x[0] + 4*x[0]*x[1] + 4*x[0]*x[2] + 2*pow(x[0], 2) - 3*x[1] + 4*x[1]*x[2] + 2*pow(x[1], 2) - 3*x[2] + 2*pow(x[2], 2))*vertices[1] - phys_x[1] + 4*x[0]*x[1]*vertices[16] + 4*x[0]*x[2]*vertices[25] + 4*x[1]*x[2]*vertices[28];
102	fx[2] = (-x[0] + 2*pow(x[0], 2))*vertices[5] + (-x[1] + 2*pow(x[1], 2))*vertices[8] + (-x[2] + 2*pow(x[2], 2))*vertices[11] + (4*x[0] - 4*x[0]*x[1] - 4*x[0]*x[2] - 4*pow(x[0], 2))*vertices[14] + (4*x[1] - 4*x[1]*x[0] - 4*x[1]*x[2] - 4*pow(x[1], 2))*vertices[20] + (4*x[2] - 4*x[2]*x[0] - 4*x[2]*x[1] - 4*pow(x[2], 2))*vertices[23] + (1 - 3*x[0] + 4*x[0]*x[1] + 4*x[0]*x[2] + 2*pow(x[0], 2) - 3*x[1] + 4*x[1]*x[2] + 2*pow(x[1], 2) - 3*x[2] + 2*pow(x[2], 2))*vertices[2] - phys_x[2] + 4*x[0]*x[1]*vertices[17] + 4*x[0]*x[2]*vertices[26] + 4*x[1]*x[2]*vertices[29];
103
104
105@cython.boundscheck(False)
106@cython.wraparound(False)
107@cython.cdivision(True)
108cdef void Tet2Jacobian3D(double* rcol,
109                       double* scol,
110                       double* tcol,
111                       double* x,
112                       double* vertices,
113                       double* phys_x) nogil:
114	rcol[0] = (-1 + 4*x[0])*vertices[3] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[0] + (4 - 8*x[0] - 4*x[1] - 4*x[2])*vertices[12] + 4*x[1]*vertices[15] - 4*x[1]*vertices[18] - 4*x[2]*vertices[21] + 4*x[2]*vertices[24];
115	scol[0] = (-1 + 4*x[1])*vertices[6] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[0] + (4 - 4*x[0] - 8*x[1] - 4*x[2])*vertices[18] - 4*x[0]*vertices[12] + 4*x[0]*vertices[15] - 4*x[2]*vertices[21] + 4*x[2]*vertices[27];
116	tcol[0] = (-1 + 4*x[2])*vertices[9] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[0] + (4 - 4*x[0] - 4*x[1] - 8*x[2])*vertices[21] - 4*x[0]*vertices[12] + 4*x[0]*vertices[24] - 4*x[1]*vertices[18] + 4*x[1]*vertices[27];
117	rcol[1] = (-1 + 4*x[0])*vertices[4] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[1] + (4 - 8*x[0] - 4*x[1] - 4*x[2])*vertices[13] + 4*x[1]*vertices[16] - 4*x[1]*vertices[19] - 4*x[2]*vertices[22] + 4*x[2]*vertices[25];
118	scol[1] = (-1 + 4*x[1])*vertices[7] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[1] + (4 - 4*x[0] - 8*x[1] - 4*x[2])*vertices[19] - 4*x[0]*vertices[13] + 4*x[0]*vertices[16] - 4*x[2]*vertices[22] + 4*x[2]*vertices[28];
119	tcol[1] = (-1 + 4*x[2])*vertices[10] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[1] + (4 - 4*x[0] - 4*x[1] - 8*x[2])*vertices[22] - 4*x[0]*vertices[13] + 4*x[0]*vertices[25] - 4*x[1]*vertices[19] + 4*x[1]*vertices[28];
120	rcol[2] = (-1 + 4*x[0])*vertices[5] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[2] + (4 - 8*x[0] - 4*x[1] - 4*x[2])*vertices[14] + 4*x[1]*vertices[17] - 4*x[1]*vertices[20] - 4*x[2]*vertices[23] + 4*x[2]*vertices[26];
121	scol[2] = (-1 + 4*x[1])*vertices[8] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[2] + (4 - 4*x[0] - 8*x[1] - 4*x[2])*vertices[20] - 4*x[0]*vertices[14] + 4*x[0]*vertices[17] - 4*x[2]*vertices[23] + 4*x[2]*vertices[29];
122	tcol[2] = (-1 + 4*x[2])*vertices[11] + (-3 + 4*x[0] + 4*x[1] + 4*x[2])*vertices[2] + (4 - 4*x[0] - 4*x[1] - 8*x[2])*vertices[23] - 4*x[0]*vertices[14] + 4*x[0]*vertices[26] - 4*x[1]*vertices[20] + 4*x[1]*vertices[29];
123
124
125@cython.boundscheck(False)
126@cython.wraparound(False)
127@cython.cdivision(True)
128cdef void T2Function2D(double* fx,
129                       double* x,
130                       double* vertices,
131                       double* phys_x) nogil:
132	fx[0] = (-x[0] + 2*pow(x[0], 2))*vertices[2] + (-x[1] + 2*pow(x[1], 2))*vertices[4] + (-4*x[0]*x[1] + 4*x[1] - 4*pow(x[1], 2))*vertices[10] + (4*x[0] - 4*x[0]*x[1] - 4*pow(x[0], 2))*vertices[6] + (1 - 3*x[0] + 4*x[0]*x[1] + 2*pow(x[0], 2) - 3*x[1] + 2*pow(x[1], 2))*vertices[0] - phys_x[0] + 4*x[0]*x[1]*vertices[8];
133	fx[1] = (-x[0] + 2*pow(x[0], 2))*vertices[3] + (-x[1] + 2*pow(x[1], 2))*vertices[5] + (-4*x[0]*x[1] + 4*x[1] - 4*pow(x[1], 2))*vertices[11] + (4*x[0] - 4*x[0]*x[1] - 4*pow(x[0], 2))*vertices[7] + (1 - 3*x[0] + 4*x[0]*x[1] + 2*pow(x[0], 2) - 3*x[1] + 2*pow(x[1], 2))*vertices[1] - phys_x[1] + 4*x[0]*x[1]*vertices[9];
134
135
136@cython.boundscheck(False)
137@cython.wraparound(False)
138@cython.cdivision(True)
139cdef void T2Jacobian2D(double* rcol,
140                       double* scol,
141                       double* x,
142                       double* vertices,
143                       double* phys_x) nogil:
144	rcol[0] = (-1 + 4*x[0])*vertices[2] + (-3 + 4*x[0] + 4*x[1])*vertices[0] + (4 - 8*x[0] - 4*x[1])*vertices[6] + 4*x[1]*vertices[8] - 4*x[1]*vertices[10];
145	scol[0] = (-1 + 4*x[1])*vertices[4] + (-3 + 4*x[0] + 4*x[1])*vertices[0] + (4 - 4*x[0] - 8*x[1])*vertices[10] - 4*x[0]*vertices[6] + 4*x[0]*vertices[8];
146	rcol[1] = (-1 + 4*x[0])*vertices[3] + (-3 + 4*x[0] + 4*x[1])*vertices[1] + (4 - 8*x[0] - 4*x[1])*vertices[7] + 4*x[1]*vertices[9] - 4*x[1]*vertices[11];
147	scol[1] = (-1 + 4*x[1])*vertices[5] + (-3 + 4*x[0] + 4*x[1])*vertices[1] + (4 - 4*x[0] - 8*x[1])*vertices[11] - 4*x[0]*vertices[7] + 4*x[0]*vertices[9];
148
149
150@cython.boundscheck(False)
151@cython.wraparound(False)
152@cython.cdivision(True)
153cdef void W1Function3D(double* fx,
154                       double* x,
155                       double* vertices,
156                       double* phys_x) nogil:
157	fx[0] = 0.5*(1 - x[0] - x[1])*(1 - x[2])*vertices[0] + 0.5*(1 - x[0] - x[1])*(1 + x[2])*vertices[9] - phys_x[0] + 0.5*x[0]*(1 - x[2])*vertices[3] + 0.5*x[0]*(1 + x[2])*vertices[12] + 0.5*x[1]*(1 - x[2])*vertices[6] + 0.5*x[1]*(1 + x[2])*vertices[15];
158	fx[1] = 0.5*(1 - x[0] - x[1])*(1 - x[2])*vertices[1] + 0.5*(1 - x[0] - x[1])*(1 + x[2])*vertices[10] - phys_x[1] + 0.5*x[0]*(1 - x[2])*vertices[4] + 0.5*x[0]*(1 + x[2])*vertices[13] + 0.5*x[1]*(1 - x[2])*vertices[7] + 0.5*x[1]*(1 + x[2])*vertices[16];
159	fx[2] = 0.5*(1 - x[0] - x[1])*(1 - x[2])*vertices[2] + 0.5*(1 - x[0] - x[1])*(1 + x[2])*vertices[11] - phys_x[2] + 0.5*x[0]*(1 - x[2])*vertices[5] + 0.5*x[0]*(1 + x[2])*vertices[14] + 0.5*x[1]*(1 - x[2])*vertices[8] + 0.5*x[1]*(1 + x[2])*vertices[17];
160
161
162@cython.boundscheck(False)
163@cython.wraparound(False)
164@cython.cdivision(True)
165cdef void W1Jacobian3D(double* rcol,
166                       double* scol,
167                       double* tcol,
168                       double* x,
169                       double* vertices,
170                       double* phys_x) nogil:
171	rcol[0] = -0.5*(1 - x[2])*vertices[0] + 0.5*(1 - x[2])*vertices[3] - 0.5*(1 + x[2])*vertices[9] + 0.5*(1 + x[2])*vertices[12];
172	scol[0] = -0.5*(1 - x[2])*vertices[0] + 0.5*(1 - x[2])*vertices[6] - 0.5*(1 + x[2])*vertices[9] + 0.5*(1 + x[2])*vertices[15];
173	tcol[0] = -0.5*(1 - x[0] - x[1])*vertices[0] + 0.5*(1 - x[0] - x[1])*vertices[9] - 0.5*x[0]*vertices[3] + 0.5*x[0]*vertices[12] - 0.5*x[1]*vertices[6] + 0.5*x[1]*vertices[15];
174	rcol[1] = -0.5*(1 - x[2])*vertices[1] + 0.5*(1 - x[2])*vertices[4] - 0.5*(1 + x[2])*vertices[10] + 0.5*(1 + x[2])*vertices[13];
175	scol[1] = -0.5*(1 - x[2])*vertices[1] + 0.5*(1 - x[2])*vertices[7] - 0.5*(1 + x[2])*vertices[10] + 0.5*(1 + x[2])*vertices[16];
176	tcol[1] = -0.5*(1 - x[0] - x[1])*vertices[1] + 0.5*(1 - x[0] - x[1])*vertices[10] - 0.5*x[0]*vertices[4] + 0.5*x[0]*vertices[13] - 0.5*x[1]*vertices[7] + 0.5*x[1]*vertices[16];
177	rcol[2] = -0.5*(1 - x[2])*vertices[2] + 0.5*(1 - x[2])*vertices[5] - 0.5*(1 + x[2])*vertices[11] + 0.5*(1 + x[2])*vertices[14];
178	scol[2] = -0.5*(1 - x[2])*vertices[2] + 0.5*(1 - x[2])*vertices[8] - 0.5*(1 + x[2])*vertices[11] + 0.5*(1 + x[2])*vertices[17];
179	tcol[2] = -0.5*(1 - x[0] - x[1])*vertices[2] + 0.5*(1 - x[0] - x[1])*vertices[11] - 0.5*x[0]*vertices[5] + 0.5*x[0]*vertices[14] - 0.5*x[1]*vertices[8] + 0.5*x[1]*vertices[17];
180