Line data Source code
1 : // The libMesh Finite Element Library.
2 : // Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3 :
4 : // This library is free software; you can redistribute it and/or
5 : // modify it under the terms of the GNU Lesser General Public
6 : // License as published by the Free Software Foundation; either
7 : // version 2.1 of the License, or (at your option) any later version.
8 :
9 : // This library is distributed in the hope that it will be useful,
10 : // but WITHOUT ANY WARRANTY; without even the implied warranty of
11 : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 : // Lesser General Public License for more details.
13 :
14 : // You should have received a copy of the GNU Lesser General Public
15 : // License along with this library; if not, write to the Free Software
16 : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 :
18 :
19 : // Local includes
20 : #include "libmesh/cell_hex20.h"
21 : #include "libmesh/fe_reference_element_traits.h"
22 : #include "libmesh/edge_edge3.h"
23 : #include "libmesh/face_quad8.h"
24 : #include "libmesh/enum_io_package.h"
25 : #include "libmesh/enum_order.h"
26 :
27 : namespace libMesh
28 : {
29 :
30 :
31 :
32 : // ------------------------------------------------------------
33 : // Hex20 class static member initializations
34 : const int Hex20::num_nodes;
35 : const int Hex20::nodes_per_side;
36 : const int Hex20::nodes_per_edge;
37 :
38 : const ReferenceElementTable<Hex20::num_sides, Hex20::nodes_per_side>
39 : Hex20::side_nodes_map = build_side_nodes<Hex20::num_sides, Hex20::nodes_per_side>(HEX20);
40 :
41 : const ReferenceElementTable<Hex20::num_edges, Hex20::nodes_per_edge>
42 : Hex20::edge_nodes_map = hex_edge_nodes();
43 :
44 : // ------------------------------------------------------------
45 : // Hex20 class member functions
46 :
47 361728 : bool Hex20::is_vertex(const unsigned int i) const
48 : {
49 361728 : if (i < 8)
50 158784 : return true;
51 57408 : return false;
52 : }
53 :
54 2304 : bool Hex20::is_edge(const unsigned int i) const
55 : {
56 2304 : if (i > 7)
57 2304 : return true;
58 0 : return false;
59 : }
60 :
61 0 : bool Hex20::is_face(const unsigned int) const
62 : {
63 0 : return false;
64 : }
65 :
66 10088 : bool Hex20::is_node_on_side(const unsigned int n,
67 : const unsigned int s) const
68 : {
69 2552 : libmesh_assert_less (s, n_sides());
70 2552 : return std::find(std::begin(side_nodes_map[s]),
71 2552 : std::end(side_nodes_map[s]),
72 10088 : n) != std::end(side_nodes_map[s]);
73 : }
74 :
75 : std::vector<unsigned>
76 14886 : Hex20::nodes_on_side(const unsigned int s) const
77 : {
78 3924 : libmesh_assert_less(s, n_sides());
79 14886 : return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
80 : }
81 :
82 : std::vector<unsigned>
83 2772 : Hex20::nodes_on_edge(const unsigned int e) const
84 : {
85 696 : libmesh_assert_less(e, n_edges());
86 2772 : return {std::begin(edge_nodes_map[e]), std::end(edge_nodes_map[e])};
87 : }
88 :
89 81936 : bool Hex20::is_node_on_edge(const unsigned int n,
90 : const unsigned int e) const
91 : {
92 22464 : libmesh_assert_less (e, n_edges());
93 22464 : return std::find(std::begin(edge_nodes_map[e]),
94 22464 : std::end(edge_nodes_map[e]),
95 81936 : n) != std::end(edge_nodes_map[e]);
96 : }
97 :
98 :
99 :
100 134234 : bool Hex20::has_affine_map() const
101 : {
102 : // Make sure x-edge endpoints are affine
103 67900 : Point v = this->point(1) - this->point(0);
104 133850 : if (!v.relative_fuzzy_equals(this->point(2) - this->point(3), affine_tol) ||
105 267956 : !v.relative_fuzzy_equals(this->point(5) - this->point(4), affine_tol) ||
106 201494 : !v.relative_fuzzy_equals(this->point(6) - this->point(7), affine_tol))
107 512 : return false;
108 : // Make sure x-edges are straight
109 33822 : v /= 2;
110 167484 : if (!v.relative_fuzzy_equals(this->point(8) - this->point(0), affine_tol) ||
111 167432 : !v.relative_fuzzy_equals(this->point(10) - this->point(3), affine_tol) ||
112 334932 : !v.relative_fuzzy_equals(this->point(16) - this->point(4), affine_tol) ||
113 167424 : !v.relative_fuzzy_equals(this->point(18) - this->point(7), affine_tol))
114 128 : return false;
115 : // Make sure xz-faces are identical parallelograms
116 167384 : v = this->point(4) - this->point(0);
117 133594 : if (!v.relative_fuzzy_equals(this->point(7) - this->point(3), affine_tol))
118 0 : return false;
119 33790 : v /= 2;
120 167384 : if (!v.relative_fuzzy_equals(this->point(12) - this->point(0), affine_tol) ||
121 167384 : !v.relative_fuzzy_equals(this->point(13) - this->point(1), affine_tol) ||
122 334768 : !v.relative_fuzzy_equals(this->point(14) - this->point(2), affine_tol) ||
123 167384 : !v.relative_fuzzy_equals(this->point(15) - this->point(3), affine_tol))
124 0 : return false;
125 : // Make sure y-edges are straight
126 167384 : v = (this->point(3) - this->point(0))/2;
127 133594 : if (!v.relative_fuzzy_equals(this->point(11) - this->point(0), affine_tol) ||
128 167384 : !v.relative_fuzzy_equals(this->point(9) - this->point(1), affine_tol) ||
129 334768 : !v.relative_fuzzy_equals(this->point(17) - this->point(5), affine_tol) ||
130 201174 : !v.relative_fuzzy_equals(this->point(19) - this->point(4), affine_tol))
131 0 : return false;
132 : // If all the above checks out, the map is affine
133 33790 : return true;
134 : }
135 :
136 :
137 :
138 3082158 : Order Hex20::default_order() const
139 : {
140 3082158 : return SECOND;
141 : }
142 :
143 :
144 :
145 35055 : std::unique_ptr<Elem> Hex20::build_side_ptr (const unsigned int i)
146 : {
147 35055 : return this->simple_build_side_ptr<Quad8, Hex20>(i);
148 : }
149 :
150 :
151 :
152 42883 : void Hex20::build_side_ptr (std::unique_ptr<Elem> & side,
153 : const unsigned int i)
154 : {
155 42883 : this->simple_build_side_ptr<Hex20>(side, i, QUAD8);
156 42883 : }
157 :
158 :
159 :
160 12960 : unsigned int Hex20::local_side_node(unsigned int side,
161 : unsigned int side_node) const
162 : {
163 3648 : libmesh_assert_less (side, this->n_sides());
164 3648 : libmesh_assert_less (side_node, Hex20::nodes_per_side);
165 :
166 12960 : return Hex20::side_nodes_map[side][side_node];
167 : }
168 :
169 :
170 :
171 544320 : unsigned int Hex20::local_edge_node(unsigned int edge,
172 : unsigned int edge_node) const
173 : {
174 151776 : libmesh_assert_less (edge, this->n_edges());
175 151776 : libmesh_assert_less (edge_node, Hex20::nodes_per_edge);
176 :
177 544320 : return Hex20::edge_nodes_map[edge][edge_node];
178 : }
179 :
180 :
181 :
182 172967 : std::unique_ptr<Elem> Hex20::build_edge_ptr (const unsigned int i)
183 : {
184 172967 : return this->simple_build_edge_ptr<Edge3,Hex20>(i);
185 : }
186 :
187 :
188 :
189 936 : void Hex20::build_edge_ptr (std::unique_ptr<Elem> & edge, const unsigned int i)
190 : {
191 936 : this->simple_build_edge_ptr<Hex20>(edge, i, EDGE3);
192 936 : }
193 :
194 :
195 :
196 0 : void Hex20::connectivity(const unsigned int sc,
197 : const IOPackage iop,
198 : std::vector<dof_id_type> & conn) const
199 : {
200 0 : libmesh_assert(_nodes);
201 0 : libmesh_assert_less (sc, this->n_sub_elem());
202 0 : libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
203 :
204 :
205 0 : switch (iop)
206 : {
207 0 : case TECPLOT:
208 : {
209 0 : switch (sc)
210 : {
211 0 : case 0:
212 0 : conn.resize(8);
213 0 : conn[0] = this->node_id(0)+1;
214 0 : conn[1] = this->node_id(1)+1;
215 0 : conn[2] = this->node_id(2)+1;
216 0 : conn[3] = this->node_id(3)+1;
217 0 : conn[4] = this->node_id(4)+1;
218 0 : conn[5] = this->node_id(5)+1;
219 0 : conn[6] = this->node_id(6)+1;
220 0 : conn[7] = this->node_id(7)+1;
221 :
222 0 : return;
223 :
224 0 : default:
225 0 : libmesh_error_msg("Unknown sc = " << sc);
226 : }
227 : }
228 :
229 0 : case VTK:
230 : {
231 0 : switch (sc)
232 : {
233 0 : case 0:
234 0 : conn.resize(20);
235 0 : conn[0] = this->node_id(0);
236 0 : conn[1] = this->node_id(1);
237 0 : conn[2] = this->node_id(2);
238 0 : conn[3] = this->node_id(3);
239 0 : conn[4] = this->node_id(4);
240 0 : conn[5] = this->node_id(5);
241 0 : conn[6] = this->node_id(6);
242 0 : conn[7] = this->node_id(7);
243 0 : conn[8] = this->node_id(8);
244 0 : conn[9] = this->node_id(9);
245 0 : conn[10] = this->node_id(10);
246 0 : conn[11] = this->node_id(11);
247 0 : conn[12] = this->node_id(16);
248 0 : conn[13] = this->node_id(17);
249 0 : conn[14] = this->node_id(18);
250 0 : conn[15] = this->node_id(19);
251 0 : conn[16] = this->node_id(12);
252 0 : conn[17] = this->node_id(13);
253 0 : conn[18] = this->node_id(14);
254 0 : conn[19] = this->node_id(15);
255 0 : return;
256 :
257 0 : default:
258 0 : libmesh_error_msg("Unknown sc = " << sc);
259 : }
260 : }
261 :
262 0 : default:
263 0 : libmesh_error_msg("Unsupported IO package " << iop);
264 : }
265 : }
266 :
267 :
268 :
269 :
270 0 : unsigned short int Hex20::second_order_adjacent_vertex (const unsigned int n,
271 : const unsigned int v) const
272 : {
273 0 : libmesh_assert_greater_equal (n, this->n_vertices());
274 0 : libmesh_assert_less (n, this->n_nodes());
275 0 : libmesh_assert_less (v, 2);
276 : /*
277 : * the _second_order_adjacent_vertices matrix is
278 : * stored in cell_hex.C, since this matrix is identical
279 : * for Hex20 and Hex27 (for the first 12 higher-order nodes)
280 : */
281 0 : return _second_order_adjacent_vertices[n-this->n_vertices()][v];
282 : }
283 :
284 :
285 :
286 : std::pair<unsigned short int, unsigned short int>
287 0 : Hex20::second_order_child_vertex (const unsigned int n) const
288 : {
289 0 : libmesh_assert_greater_equal (n, this->n_vertices());
290 0 : libmesh_assert_less (n, this->n_nodes());
291 : /*
292 : * the _second_order_vertex_child_* vectors are
293 : * stored in cell_hex.C, since they are identical
294 : * for Hex20 and Hex27 (for the first 12 higher-order nodes)
295 : */
296 0 : return std::pair<unsigned short int, unsigned short int>
297 0 : (_second_order_vertex_child_number[n],
298 0 : _second_order_vertex_child_index[n]);
299 : }
300 :
301 :
302 :
303 63 : Real Hex20::volume () const
304 : {
305 : // This specialization is good for Lagrange mappings only in general
306 63 : if (this->mapping_type() != LAGRANGE_MAP)
307 14 : return this->Elem::volume();
308 :
309 : // Make copies of our points. It makes the subsequent calculations a bit
310 : // shorter and avoids dereferencing the same pointer multiple times.
311 : Point
312 109 : x0 = point(0), x1 = point(1), x2 = point(2), x3 = point(3), x4 = point(4),
313 97 : x5 = point(5), x6 = point(6), x7 = point(7), x8 = point(8), x9 = point(9),
314 97 : x10 = point(10), x11 = point(11), x12 = point(12), x13 = point(13), x14 = point(14),
315 97 : x15 = point(15), x16 = point(16), x17 = point(17), x18 = point(18), x19 = point(19);
316 :
317 : // The constant components of the dx/dxi vector,
318 : // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
319 : // These were copied directly from the output of a Python script.
320 : // There are at most 17 terms with total degree <=3, but only 12
321 : // of them are non-zero for each direction.
322 : Point dx_dxi[17] =
323 : {
324 14 : x0/8 - x1/8 - x11/4 - x12/4 + x13/4 + x14/4 - x15/4 + x17/4 - x19/4 - x2/8 + x3/8 + x4/8 - x5/8 - x6/8 + x7/8 + x9/4,
325 14 : x11/4 + x17/4 - x19/4 - x9/4,
326 14 : -x0/8 + x1/8 + x12/4 - x13/4 - x14/4 + x15/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8,
327 14 : x12/4 - x13/4 + x14/4 - x15/4,
328 14 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
329 14 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
330 14 : -x0/8 + x1/8 + x11/4 - x17/4 + x19/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8 - x9/4,
331 14 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
332 14 : x0/4 + x1/4 - x10/2 - x16/2 - x18/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2,
333 14 : -x0/4 - x1/4 + x10/2 - x16/2 - x18/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2,
334 : Point(0,0,0),
335 14 : -x0/4 - x1/4 - x10/2 + x16/2 - x18/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2,
336 14 : x0/4 + x1/4 + x10/2 + x16/2 - x18/2 - x2/4 - x3/4 - x4/4 - x5/4 + x6/4 + x7/4 - x8/2,
337 : Point(0,0,0),
338 : Point(0,0,0),
339 : Point(0,0,0),
340 : Point(0,0,0)
341 182 : };
342 :
343 : // The constant components of the dx/deta vector. These were copied
344 : // directly from the output of a Python script. There are at most
345 : // 17 terms with total degree <=3, but only 12 of them are non-zero
346 : // for each direction.
347 : Point dx_deta[17] =
348 : {
349 14 : x0/8 + x1/8 + x10/4 - x12/4 - x13/4 + x14/4 + x15/4 - x16/4 + x18/4 - x2/8 - x3/8 + x4/8 + x5/8 - x6/8 - x7/8 - x8/4,
350 14 : -x10/4 - x16/4 + x18/4 + x8/4,
351 14 : -x0/8 - x1/8 + x12/4 + x13/4 - x14/4 - x15/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8,
352 14 : x0/4 + x1/4 - x11/2 - x17/2 - x19/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x9/2,
353 14 : -x0/4 - x1/4 + x11/2 - x17/2 - x19/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x9/2,
354 : Point(0,0,0),
355 : Point(0,0,0),
356 : Point(0,0,0),
357 14 : x12/4 - x13/4 + x14/4 - x15/4,
358 14 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
359 14 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
360 14 : -x0/4 + x1/4 + x11/2 - x17/2 + x19/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2,
361 14 : x0/4 - x1/4 - x11/2 - x17/2 + x19/2 - x2/4 + x3/4 - x4/4 + x5/4 + x6/4 - x7/4 + x9/2,
362 : Point(0,0,0),
363 14 : -x0/8 - x1/8 - x10/4 + x16/4 - x18/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8 + x8/4,
364 14 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
365 : Point(0,0,0)
366 182 : };
367 :
368 : // The constant components of the dx/dzeta vector. These were copied
369 : // directly from the output of a Python script. There are at most
370 : // 17 terms with total degree <=3, but only 12 of them are non-zero
371 : // for each direction.
372 : Point dx_dzeta[17] =
373 : {
374 14 : x0/8 + x1/8 - x10/4 - x11/4 + x16/4 + x17/4 + x18/4 + x19/4 + x2/8 + x3/8 - x4/8 - x5/8 - x6/8 - x7/8 - x8/4 - x9/4,
375 14 : x0/4 + x1/4 - x12/2 - x13/2 - x14/2 - x15/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4,
376 : Point(0,0,0),
377 14 : -x10/4 - x16/4 + x18/4 + x8/4,
378 14 : -x0/4 - x1/4 + x12/2 + x13/2 - x14/2 - x15/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4,
379 : Point(0,0,0),
380 14 : -x0/8 - x1/8 + x11/4 - x17/4 - x19/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x9/4,
381 : Point(0,0,0),
382 14 : x11/4 + x17/4 - x19/4 - x9/4,
383 14 : -x0/4 + x1/4 + x12/2 - x13/2 - x14/2 + x15/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4,
384 : Point(0,0,0),
385 14 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
386 14 : x0/4 - x1/4 - x12/2 + x13/2 - x14/2 + x15/2 + x2/4 - x3/4 + x4/4 - x5/4 + x6/4 - x7/4,
387 14 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
388 14 : -x0/8 - x1/8 + x10/4 - x16/4 - x18/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x8/4,
389 : Point(0,0,0),
390 14 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
391 182 : };
392 :
393 : // The integer exponents for each term.
394 : static const int exponents[17][3] =
395 : {
396 : {0, 0, 0},
397 : {0, 0, 1},
398 : {0, 0, 2},
399 : {0, 1, 0},
400 : {0, 1, 1},
401 : {0, 1, 2},
402 : {0, 2, 0},
403 : {0, 2, 1},
404 : {1, 0, 0},
405 : {1, 0, 1},
406 : {1, 0, 2},
407 : {1, 1, 0},
408 : {1, 1, 1},
409 : {1, 2, 0},
410 : {2, 0, 0},
411 : {2, 0, 1},
412 : {2, 1, 0}
413 : };
414 :
415 :
416 : // 3x3 quadrature, exact for bi-quintics
417 14 : const int N = 3;
418 49 : const Real w[N] = {5./9, 8./9, 5./9};
419 :
420 : // Quadrature point locations raised to powers. q[0][2] is
421 : // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
422 : // first power, etc.
423 49 : const Real q[N][N] =
424 : {
425 : //^0 ^1 ^2
426 : { 1., -std::sqrt(15)/5., 15./25},
427 : { 1., 0., 0.},
428 : { 1., std::sqrt(15)/5., 15./25}
429 : };
430 :
431 :
432 14 : Real vol = 0.;
433 196 : for (int i=0; i<N; ++i)
434 588 : for (int j=0; j<N; ++j)
435 1764 : for (int k=0; k<N; ++k)
436 : {
437 : // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
438 378 : Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
439 23814 : for (int c=0; c<17; ++c)
440 : {
441 6426 : Real coeff =
442 34425 : q[i][exponents[c][0]] *
443 34425 : q[j][exponents[c][1]] *
444 22491 : q[k][exponents[c][2]];
445 :
446 6426 : dx_dxi_q += coeff * dx_dxi[c];
447 6426 : dx_deta_q += coeff * dx_deta[c];
448 6426 : dx_dzeta_q += coeff * dx_dzeta[c];
449 : }
450 :
451 : // Compute scalar triple product, multiply by weight, and accumulate volume.
452 1647 : vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
453 : }
454 :
455 14 : return vol;
456 : }
457 :
458 :
459 :
460 :
461 : #ifdef LIBMESH_ENABLE_AMR
462 :
463 : const Real Hex20::_embedding_matrix[Hex20::num_children][Hex20::num_nodes][Hex20::num_nodes] =
464 : {
465 : // embedding matrix for child 0
466 : {
467 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
468 : { 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
469 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
470 : { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
471 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
472 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
473 : { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 5
474 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 6
475 : { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 7
476 : { 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
477 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
478 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
479 : { 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
480 : { 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
481 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000 }, // 13
482 : { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 14
483 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000 }, // 15
484 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 16
485 : { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 17
486 : { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 18
487 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000 } // 19
488 : },
489 :
490 : // embedding matrix for child 1
491 : {
492 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
493 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
494 : { 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
495 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
496 : { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
497 : { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 4
498 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
499 : { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 6
500 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 7
501 : { -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
502 : { 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
503 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
504 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
505 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000 }, // 12
506 : { 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
507 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000 }, // 14
508 : { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 15
509 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 16
510 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 17
511 : { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 18
512 : { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 } // 19
513 : },
514 :
515 : // embedding matrix for child 2
516 : {
517 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
518 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
519 : { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
520 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
521 : { 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
522 : { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 4
523 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 5
524 : { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 6
525 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
526 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
527 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
528 : { 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
529 : { -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
530 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000 }, // 12
531 : { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 13
532 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000 }, // 14
533 : { 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
534 : { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 16
535 : { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 17
536 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 18
537 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000 } // 19
538 : },
539 :
540 : // embedding matrix for child 3
541 : {
542 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
543 : { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
544 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
545 : { 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
546 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
547 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 4
548 : { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 5
549 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
550 : { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 7
551 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
552 : { 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
553 : { 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
554 : { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
555 : { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 12
556 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000 }, // 13
557 : { 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
558 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000 }, // 15
559 : { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 16
560 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 17
561 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 18
562 : { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 } // 19
563 : },
564 :
565 : // embedding matrix for child 4
566 : {
567 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
568 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
569 : { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 1
570 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 2
571 : { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 3
572 : { 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
573 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 5
574 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 6
575 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 7
576 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 8
577 : { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 9
578 : { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 10
579 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000 }, // 11
580 : { -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
581 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 13
582 : { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 14
583 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000 }, // 15
584 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 16
585 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000 }, // 17
586 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000 }, // 18
587 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000 } // 19
588 : },
589 :
590 : // embedding matrix for child 5
591 : {
592 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
593 : { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 0
594 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
595 : { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 2
596 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 3
597 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 4
598 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
599 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 6
600 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 7
601 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 8
602 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 9
603 : { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 10
604 : { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 11
605 : { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 12
606 : { 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
607 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 14
608 : { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 15
609 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 16
610 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 17
611 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000 }, // 18
612 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000 } // 19
613 : },
614 :
615 : // embedding matrix for child 6
616 : {
617 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
618 : { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 0
619 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 1
620 : { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 2
621 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
622 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 4
623 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 5
624 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 6
625 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
626 : { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 8
627 : { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 9
628 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 10
629 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000 }, // 11
630 : { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000 }, // 12
631 : { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 13
632 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 14
633 : { 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
634 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000 }, // 16
635 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000 }, // 17
636 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
637 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000 } // 19
638 : },
639 :
640 : // embedding matrix for child 7
641 : {
642 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
643 : { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 0
644 : { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 1
645 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
646 : { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 3
647 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 4
648 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 5
649 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
650 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 7
651 : { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 8
652 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 9
653 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 10
654 : { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 11
655 : { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 12
656 : { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 13
657 : { 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
658 : { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 15
659 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000 }, // 16
660 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 17
661 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
662 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000 } // 19
663 : }
664 : };
665 :
666 : #endif
667 :
668 : void
669 1328 : Hex20::permute(unsigned int perm_num)
670 : {
671 352 : libmesh_assert_less (perm_num, 24);
672 1328 : const unsigned int side = perm_num % 6;
673 1328 : const unsigned int rotate = perm_num / 6;
674 :
675 4160 : for (unsigned int i = 0; i != rotate; ++i)
676 : {
677 2832 : swap4nodes(0,1,2,3);
678 2832 : swap4nodes(4,5,6,7);
679 2832 : swap4nodes(8,9,10,11);
680 2832 : swap4nodes(12,13,14,15);
681 2832 : swap4nodes(16,17,18,19);
682 2064 : swap4neighbors(1,2,3,4);
683 : }
684 :
685 1328 : switch (side) {
686 32 : case 0:
687 32 : break;
688 128 : case 1:
689 128 : swap4nodes(3,7,4,0);
690 128 : swap4nodes(11,15,19,12);
691 128 : swap4nodes(10,18,16,8);
692 128 : swap4nodes(2,6,5,1);
693 128 : swap4nodes(9,14,17,13);
694 96 : swap4neighbors(0,3,5,1);
695 96 : break;
696 128 : case 2:
697 128 : swap4nodes(0,4,5,1);
698 128 : swap4nodes(8,12,16,13);
699 128 : swap4nodes(3,7,6,2);
700 128 : swap4nodes(10,15,18,14);
701 128 : swap4nodes(11,19,17,9);
702 96 : swap4neighbors(0,4,5,2);
703 96 : break;
704 128 : case 3:
705 128 : swap4nodes(0,4,7,3);
706 128 : swap4nodes(12,19,15,11);
707 128 : swap4nodes(8,16,18,10);
708 128 : swap4nodes(1,5,6,2);
709 128 : swap4nodes(13,17,14,9);
710 96 : swap4neighbors(0,1,5,3);
711 96 : break;
712 128 : case 4:
713 128 : swap4nodes(1,5,4,0);
714 128 : swap4nodes(8,13,16,12);
715 128 : swap4nodes(9,17,19,11);
716 128 : swap4nodes(2,6,7,3);
717 128 : swap4nodes(10,14,18,15);
718 96 : swap4neighbors(0,2,5,4);
719 96 : break;
720 688 : case 5:
721 688 : swap2nodes(0,7);
722 688 : swap2nodes(8,18);
723 688 : swap2nodes(1,6);
724 688 : swap2nodes(2,5);
725 688 : swap2nodes(10,16);
726 688 : swap2nodes(3,4);
727 688 : swap2nodes(11,19);
728 688 : swap2nodes(12,15);
729 688 : swap2nodes(9,17);
730 688 : swap2nodes(13,14);
731 192 : swap2neighbors(0,5);
732 192 : swap2neighbors(1,3);
733 192 : break;
734 0 : default:
735 0 : libmesh_error();
736 : }
737 1328 : }
738 :
739 :
740 : void
741 96 : Hex20::flip(BoundaryInfo * boundary_info)
742 : {
743 24 : libmesh_assert(boundary_info);
744 :
745 96 : swap2nodes(0,1);
746 96 : swap2nodes(2,3);
747 96 : swap2nodes(4,5);
748 96 : swap2nodes(6,7);
749 96 : swap2nodes(9,11);
750 96 : swap2nodes(12,13);
751 96 : swap2nodes(14,15);
752 96 : swap2nodes(17,19);
753 24 : swap2neighbors(2,4);
754 96 : swap2boundarysides(2,4,boundary_info);
755 96 : swap2boundaryedges(1,3,boundary_info);
756 96 : swap2boundaryedges(4,5,boundary_info);
757 96 : swap2boundaryedges(6,7,boundary_info);
758 96 : swap2boundaryedges(9,11,boundary_info);
759 96 : }
760 :
761 :
762 : ElemType
763 9108 : Hex20::side_type (const unsigned int libmesh_dbg_var(s)) const
764 : {
765 2472 : libmesh_assert_less (s, 6);
766 9108 : return QUAD8;
767 : }
768 :
769 :
770 : } // namespace libMesh
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