7void q_0_basis_grad_value_2d(
const int local_index,
const Eigen::MatrixXd &uv, Eigen::MatrixXd &
val){
9auto x=uv.col(0).array();
10auto y=uv.col(1).array();
12val.resize(uv.rows(), uv.cols());
13 Eigen::ArrayXd result_0(uv.rows());
15 case 0: {{result_0.setZero();
val.col(0) = result_0; }{result_0.setZero();
val.col(1) = result_0; }}
break;
16 default: assert(
false);
19void q_1_basis_grad_value_2d(
const int local_index,
const Eigen::MatrixXd &uv, Eigen::MatrixXd &
val){
21auto x=uv.col(0).array();
22auto y=uv.col(1).array();
24val.resize(uv.rows(), uv.cols());
25 Eigen::ArrayXd result_0(uv.rows());
27 case 0: {{result_0 = 1.0*(
y - 1);
val.col(0) = result_0; }{result_0 = 1.0*(
x - 1);
val.col(1) = result_0; }}
break;
28 case 1: {{result_0 = 1.0*(1 -
y);
val.col(0) = result_0; }{result_0 = -1.0*
x;
val.col(1) = result_0; }}
break;
29 case 2: {{result_0 = 1.0*
y;
val.col(0) = result_0; }{result_0 = 1.0*
x;
val.col(1) = result_0; }}
break;
30 case 3: {{result_0 = -1.0*
y;
val.col(0) = result_0; }{result_0 = 1.0*(1 -
x);
val.col(1) = result_0; }}
break;
31 default: assert(
false);
34void q_2_basis_grad_value_2d(
const int local_index,
const Eigen::MatrixXd &uv, Eigen::MatrixXd &
val){
36auto x=uv.col(0).array();
37auto y=uv.col(1).array();
39val.resize(uv.rows(), uv.cols());
40 Eigen::ArrayXd result_0(uv.rows());
42 case 0: {{result_0 = (4.0*
x - 3.0)*(
y - 1)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 = (
x - 1)*(2.0*
x - 1.0)*(4.0*
y - 3.0);
val.col(1) = result_0; }}
break;
43 case 1: {{result_0 = (4.0*
x - 1.0)*(
y - 1)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 =
x*(2.0*
x - 1.0)*(4.0*
y - 3.0);
val.col(1) = result_0; }}
break;
44 case 2: {{result_0 =
y*(4.0*
x - 1.0)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 =
x*(2.0*
x - 1.0)*(4.0*
y - 1.0);
val.col(1) = result_0; }}
break;
45 case 3: {{result_0 =
y*(4.0*
x - 3.0)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 = (
x - 1)*(2.0*
x - 1.0)*(4.0*
y - 1.0);
val.col(1) = result_0; }}
break;
46 case 4: {{result_0 = -4.0*(2*
x - 1)*(
y - 1)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 = -
x*(
x - 1)*(16.0*
y - 12.0);
val.col(1) = result_0; }}
break;
47 case 5: {{result_0 = -
y*(16.0*
x - 4.0)*(
y - 1);
val.col(0) = result_0; }{result_0 = -4.0*
x*(2.0*
x - 1.0)*(2*
y - 1);
val.col(1) = result_0; }}
break;
48 case 6: {{result_0 = -4.0*
y*(2*
x - 1)*(2.0*
y - 1.0);
val.col(0) = result_0; }{result_0 = -
x*(
x - 1)*(16.0*
y - 4.0);
val.col(1) = result_0; }}
break;
49 case 7: {{result_0 = -
y*(16.0*
x - 12.0)*(
y - 1);
val.col(0) = result_0; }{result_0 = -4.0*(
x - 1)*(2.0*
x - 1.0)*(2*
y - 1);
val.col(1) = result_0; }}
break;
50 case 8: {{result_0 = 16.0*
y*(2*
x - 1)*(
y - 1);
val.col(0) = result_0; }{result_0 = 16.0*
x*(
x - 1)*(2*
y - 1);
val.col(1) = result_0; }}
break;
51 default: assert(
false);
54void q_3_basis_grad_value_2d(
const int local_index,
const Eigen::MatrixXd &uv, Eigen::MatrixXd &
val){
56auto x=uv.col(0).array();
57auto y=uv.col(1).array();
59val.resize(uv.rows(), uv.cols());
60 Eigen::ArrayXd result_0(uv.rows());
62 case 0: {{
const auto helper_0 =
x - 1;
63const auto helper_1 = 1.5*
x - 1.0;
64const auto helper_2 = 3.0*
x - 1.0;
65result_0 = (
y - 1)*(1.5*
y - 1.0)*(3.0*
y - 1.0)*(3.0*helper_0*helper_1 + 1.5*helper_0*helper_2 + 1.0*helper_1*helper_2);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
66const auto helper_1 = 1.5*
y - 1.0;
67const auto helper_2 = 3.0*
y - 1.0;
68result_0 = (
x - 1)*(1.5*
x - 1.0)*(3.0*
x - 1.0)*(3.0*helper_0*helper_1 + 1.5*helper_0*helper_2 + 1.0*helper_1*helper_2);
val.col(1) = result_0; }}
break;
69 case 1: {{
const auto helper_0 = 1.4999999999999998*
x;
70const auto helper_1 = helper_0 - 0.49999999999999989;
71const auto helper_2 = 2.9999999999999996*
x;
72const auto helper_3 = helper_2 - 1.9999999999999996;
73result_0 = -(
y - 1)*(1.5*
y - 1.0)*(3.0*
y - 1.0)*(helper_0*helper_3 + helper_1*helper_2 + 1.0*helper_1*helper_3);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
74const auto helper_1 = 1.5*
y - 1.0;
75const auto helper_2 = 3.0*
y - 1.0;
76result_0 = -
x*(1.4999999999999998*
x - 0.49999999999999989)*(2.9999999999999996*
x - 1.9999999999999996)*(3.0*helper_0*helper_1 + 1.5*helper_0*helper_2 + 1.0*helper_1*helper_2);
val.col(1) = result_0; }}
break;
77 case 2: {{
const auto helper_0 = 1.4999999999999998*
x;
78const auto helper_1 = helper_0 - 0.49999999999999989;
79const auto helper_2 = 2.9999999999999996*
x;
80const auto helper_3 = helper_2 - 1.9999999999999996;
81result_0 =
y*(1.4999999999999998*
y - 0.49999999999999989)*(2.9999999999999996*
y - 1.9999999999999996)*(helper_0*helper_3 + helper_1*helper_2 + 1.0*helper_1*helper_3);
val.col(0) = result_0; }{
const auto helper_0 = 1.4999999999999998*
y;
82const auto helper_1 = helper_0 - 0.49999999999999989;
83const auto helper_2 = 2.9999999999999996*
y;
84const auto helper_3 = helper_2 - 1.9999999999999996;
85result_0 =
x*(1.4999999999999998*
x - 0.49999999999999989)*(2.9999999999999996*
x - 1.9999999999999996)*(helper_0*helper_3 + helper_1*helper_2 + 1.0*helper_1*helper_3);
val.col(1) = result_0; }}
break;
86 case 3: {{
const auto helper_0 =
x - 1;
87const auto helper_1 = 1.5*
x - 1.0;
88const auto helper_2 = 3.0*
x - 1.0;
89result_0 = -
y*(1.4999999999999998*
y - 0.49999999999999989)*(2.9999999999999996*
y - 1.9999999999999996)*(3.0*helper_0*helper_1 + 1.5*helper_0*helper_2 + 1.0*helper_1*helper_2);
val.col(0) = result_0; }{
const auto helper_0 = 1.4999999999999998*
y;
90const auto helper_1 = helper_0 - 0.49999999999999989;
91const auto helper_2 = 2.9999999999999996*
y;
92const auto helper_3 = helper_2 - 1.9999999999999996;
93result_0 = -(
x - 1)*(1.5*
x - 1.0)*(3.0*
x - 1.0)*(helper_0*helper_3 + helper_1*helper_2 + 1.0*helper_1*helper_3);
val.col(1) = result_0; }}
break;
94 case 4: {{
const auto helper_0 =
x - 1;
95const auto helper_1 = 13.499999999999996*
x - 8.9999999999999982;
96result_0 = -(
y - 1)*(1.5*
y - 1.0)*(3.0*
y - 1.0)*(helper_0*helper_1 + 13.499999999999998*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
97const auto helper_1 = 1.5*
y - 1.0;
98const auto helper_2 = 3.0*
y - 1.0;
99result_0 = -
x*(
x - 1)*(3.0*
x - 2.0)*(13.499999999999998*helper_0*helper_1 + 6.7499999999999991*helper_0*helper_2 + 4.4999999999999991*helper_1*helper_2);
val.col(1) = result_0; }}
break;
100 case 5: {{
const auto helper_0 =
x - 1;
101const auto helper_1 = 13.499999999999996*
x - 4.4999999999999991;
102result_0 = (
y - 1)*(1.5*
y - 1.0)*(3.0*
y - 1.0)*(helper_0*helper_1 + 13.499999999999998*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
103const auto helper_1 = 1.5*
y - 1.0;
104const auto helper_2 = 3.0*
y - 1.0;
105result_0 =
x*(
x - 1)*(3.0*
x - 1.0)*(13.499999999999998*helper_0*helper_1 + 6.7499999999999991*helper_0*helper_2 + 4.4999999999999991*helper_1*helper_2);
val.col(1) = result_0; }}
break;
106 case 6: {{
const auto helper_0 = 1.4999999999999998*
x - 0.49999999999999989;
107const auto helper_1 = 2.9999999999999996*
x - 1.9999999999999996;
108result_0 =
y*(
y - 1)*(3.0*
y - 2.0)*(4.4999999999999991*helper_0*helper_1 + 13.499999999999995*helper_0*
x + 6.7499999999999973*helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
109const auto helper_1 = 13.499999999999996*
y - 8.9999999999999982;
110result_0 =
x*(1.4999999999999998*
x - 0.49999999999999989)*(2.9999999999999996*
x - 1.9999999999999996)*(helper_0*helper_1 + 13.499999999999998*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
111 case 7: {{
const auto helper_0 = 1.4999999999999998*
x - 0.49999999999999989;
112const auto helper_1 = 2.9999999999999996*
x - 1.9999999999999996;
113result_0 = -
y*(
y - 1)*(3.0*
y - 1.0)*(4.4999999999999991*helper_0*helper_1 + 13.499999999999995*helper_0*
x + 6.7499999999999973*helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
114const auto helper_1 = 13.499999999999996*
y - 4.4999999999999991;
115result_0 = -
x*(1.4999999999999998*
x - 0.49999999999999989)*(2.9999999999999996*
x - 1.9999999999999996)*(helper_0*helper_1 + 13.499999999999998*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
116 case 8: {{
const auto helper_0 =
x - 1;
117const auto helper_1 = 13.499999999999996*
x - 4.4999999999999991;
118result_0 = -
y*(1.4999999999999998*
y - 0.49999999999999989)*(2.9999999999999996*
y - 1.9999999999999996)*(helper_0*helper_1 + 13.499999999999998*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 = 1.4999999999999998*
y - 0.49999999999999989;
119const auto helper_1 = 2.9999999999999996*
y - 1.9999999999999996;
120result_0 = -
x*(
x - 1)*(3.0*
x - 1.0)*(4.4999999999999991*helper_0*helper_1 + 13.499999999999995*helper_0*
y + 6.7499999999999973*helper_1*
y);
val.col(1) = result_0; }}
break;
121 case 9: {{
const auto helper_0 =
x - 1;
122const auto helper_1 = 13.499999999999996*
x - 8.9999999999999982;
123result_0 =
y*(1.4999999999999998*
y - 0.49999999999999989)*(2.9999999999999996*
y - 1.9999999999999996)*(helper_0*helper_1 + 13.499999999999998*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 = 1.4999999999999998*
y - 0.49999999999999989;
124const auto helper_1 = 2.9999999999999996*
y - 1.9999999999999996;
125result_0 =
x*(
x - 1)*(3.0*
x - 2.0)*(4.4999999999999991*helper_0*helper_1 + 13.499999999999995*helper_0*
y + 6.7499999999999973*helper_1*
y);
val.col(1) = result_0; }}
break;
126 case 10: {{
const auto helper_0 =
x - 1;
127const auto helper_1 = 1.5*
x - 1.0;
128const auto helper_2 = 3.0*
x - 1.0;
129result_0 =
y*(
y - 1)*(3.0*
y - 1.0)*(13.499999999999998*helper_0*helper_1 + 6.7499999999999991*helper_0*helper_2 + 4.4999999999999991*helper_1*helper_2);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
130const auto helper_1 = 13.499999999999996*
y - 4.4999999999999991;
131result_0 = (
x - 1)*(1.5*
x - 1.0)*(3.0*
x - 1.0)*(helper_0*helper_1 + 13.499999999999998*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
132 case 11: {{
const auto helper_0 =
x - 1;
133const auto helper_1 = 1.5*
x - 1.0;
134const auto helper_2 = 3.0*
x - 1.0;
135result_0 = -
y*(
y - 1)*(3.0*
y - 2.0)*(13.499999999999998*helper_0*helper_1 + 6.7499999999999991*helper_0*helper_2 + 4.4999999999999991*helper_1*helper_2);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
136const auto helper_1 = 13.499999999999996*
y - 8.9999999999999982;
137result_0 = -(
x - 1)*(1.5*
x - 1.0)*(3.0*
x - 1.0)*(helper_0*helper_1 + 13.499999999999998*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
138 case 12: {{
const auto helper_0 =
x - 1;
139const auto helper_1 = 60.749999999999979*
x - 40.499999999999986;
140result_0 =
y*(
y - 1)*(3.0*
y - 2.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
141const auto helper_1 = 60.749999999999979*
y - 40.499999999999986;
142result_0 =
x*(
x - 1)*(3.0*
x - 2.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
143 case 13: {{
const auto helper_0 =
x - 1;
144const auto helper_1 = 60.749999999999979*
x - 40.499999999999986;
145result_0 = -
y*(
y - 1)*(3.0*
y - 1.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
146const auto helper_1 = 60.749999999999979*
y - 20.249999999999993;
147result_0 = -
x*(
x - 1)*(3.0*
x - 2.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
148 case 14: {{
const auto helper_0 =
x - 1;
149const auto helper_1 = 60.749999999999979*
x - 20.249999999999993;
150result_0 = -
y*(
y - 1)*(3.0*
y - 2.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
151const auto helper_1 = 60.749999999999979*
y - 40.499999999999986;
152result_0 = -
x*(
x - 1)*(3.0*
x - 1.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
153 case 15: {{
const auto helper_0 =
x - 1;
154const auto helper_1 = 60.749999999999979*
x - 20.249999999999993;
155result_0 =
y*(
y - 1)*(3.0*
y - 1.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
x + helper_1*
x);
val.col(0) = result_0; }{
const auto helper_0 =
y - 1;
156const auto helper_1 = 60.749999999999979*
y - 20.249999999999993;
157result_0 =
x*(
x - 1)*(3.0*
x - 1.0)*(helper_0*helper_1 + 60.749999999999979*helper_0*
y + helper_1*
y);
val.col(1) = result_0; }}
break;
158 default: assert(
false);
161void q_m2_basis_grad_value_2d(
const int local_index,
const Eigen::MatrixXd &uv, Eigen::MatrixXd &
val){
163auto x=uv.col(0).array();
164auto y=uv.col(1).array();
166val.resize(uv.rows(), uv.cols());
167 Eigen::ArrayXd result_0(uv.rows());
169 case 0: {{result_0 = -(
y - 1)*(4.0*
x + 2.0*
y - 3.0);
val.col(0) = result_0; }{result_0 = -(
x - 1)*(2.0*
x + 4.0*
y - 3.0);
val.col(1) = result_0; }}
break;
170 case 1: {{result_0 = (
y - 1)*(-4.0*
x + 2*
y + 1);
val.col(0) = result_0; }{result_0 = -
x*(2.0*
x - 4.0*
y + 1.0);
val.col(1) = result_0; }}
break;
171 case 2: {{result_0 =
y*(4.0*
x + 2.0*
y - 3.0);
val.col(0) = result_0; }{result_0 =
x*(2.0*
x + 4.0*
y - 3.0);
val.col(1) = result_0; }}
break;
172 case 3: {{result_0 = -
y*(-4.0*
x + 2.0*
y + 1.0);
val.col(0) = result_0; }{result_0 = (
x - 1)*(2.0*
x - 4.0*
y + 1.0);
val.col(1) = result_0; }}
break;
173 case 4: {{result_0 = 4*(2*
x - 1)*(
y - 1);
val.col(0) = result_0; }{result_0 = 4*
x*(
x - 1);
val.col(1) = result_0; }}
break;
174 case 5: {{result_0 = -4*
y*(
y - 1);
val.col(0) = result_0; }{result_0 = -4*
x*(2*
y - 1);
val.col(1) = result_0; }}
break;
175 case 6: {{result_0 = -4*
y*(2*
x - 1);
val.col(0) = result_0; }{result_0 = -4*
x*(
x - 1);
val.col(1) = result_0; }}
break;
176 case 7: {{result_0 = 4*
y*(
y - 1);
val.col(0) = result_0; }{result_0 = 4*(
x - 1)*(2*
y - 1);
val.col(1) = result_0; }}
break;
177 default: assert(
false);
184 case 0: q_0_basis_grad_value_2d(local_index, uv,
val);
break;
185 case 1: q_1_basis_grad_value_2d(local_index, uv,
val);
break;
186 case 2: q_2_basis_grad_value_2d(local_index, uv,
val);
break;
187 case 3: q_3_basis_grad_value_2d(local_index, uv,
val);
break;
188 case -2: q_m2_basis_grad_value_2d(local_index, uv,
val);
break;
189 default: assert(
false);
void q_grad_basis_value_2d(const int q, const int local_index, const Eigen::MatrixXd &uv, Eigen::MatrixXd &val)
1.9.8