Line data Source code
1 : // The libMesh Finite Element Library.
2 : // Copyright (C) 2002-2025 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/edge_edge3.h"
22 : #include "libmesh/face_quad8.h"
23 : #include "libmesh/enum_io_package.h"
24 : #include "libmesh/enum_order.h"
25 :
26 : namespace libMesh
27 : {
28 :
29 :
30 :
31 : // ------------------------------------------------------------
32 : // Hex20 class static member initializations
33 : const int Hex20::num_nodes;
34 : const int Hex20::nodes_per_side;
35 : const int Hex20::nodes_per_edge;
36 :
37 : const unsigned int Hex20::side_nodes_map[Hex20::num_sides][Hex20::nodes_per_side] =
38 : {
39 : {0, 3, 2, 1, 11, 10, 9, 8}, // Side 0
40 : {0, 1, 5, 4, 8, 13, 16, 12}, // Side 1
41 : {1, 2, 6, 5, 9, 14, 17, 13}, // Side 2
42 : {2, 3, 7, 6, 10, 15, 18, 14}, // Side 3
43 : {3, 0, 4, 7, 11, 12, 19, 15}, // Side 4
44 : {4, 5, 6, 7, 16, 17, 18, 19} // Side 5
45 : };
46 :
47 : const unsigned int Hex20::edge_nodes_map[Hex20::num_edges][Hex20::nodes_per_edge] =
48 : {
49 : {0, 1, 8}, // Edge 0
50 : {1, 2, 9}, // Edge 1
51 : {2, 3, 10}, // Edge 2
52 : {0, 3, 11}, // Edge 3
53 : {0, 4, 12}, // Edge 4
54 : {1, 5, 13}, // Edge 5
55 : {2, 6, 14}, // Edge 6
56 : {3, 7, 15}, // Edge 7
57 : {4, 5, 16}, // Edge 8
58 : {5, 6, 17}, // Edge 9
59 : {6, 7, 18}, // Edge 10
60 : {4, 7, 19} // Edge 11
61 : };
62 :
63 : // ------------------------------------------------------------
64 : // Hex20 class member functions
65 :
66 1525068 : bool Hex20::is_vertex(const unsigned int i) const
67 : {
68 1525068 : if (i < 8)
69 601239 : return true;
70 50736 : return false;
71 : }
72 :
73 6912 : bool Hex20::is_edge(const unsigned int i) const
74 : {
75 6912 : if (i > 7)
76 6912 : return true;
77 0 : return false;
78 : }
79 :
80 0 : bool Hex20::is_face(const unsigned int) const
81 : {
82 0 : return false;
83 : }
84 :
85 640225 : bool Hex20::is_node_on_side(const unsigned int n,
86 : const unsigned int s) const
87 : {
88 18670 : libmesh_assert_less (s, n_sides());
89 18670 : return std::find(std::begin(side_nodes_map[s]),
90 640225 : std::end(side_nodes_map[s]),
91 640225 : n) != std::end(side_nodes_map[s]);
92 : }
93 :
94 : std::vector<unsigned>
95 254184 : Hex20::nodes_on_side(const unsigned int s) const
96 : {
97 9120 : libmesh_assert_less(s, n_sides());
98 272424 : return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
99 : }
100 :
101 : std::vector<unsigned>
102 7764 : Hex20::nodes_on_edge(const unsigned int e) const
103 : {
104 600 : libmesh_assert_less(e, n_edges());
105 8364 : return {std::begin(edge_nodes_map[e]), std::end(edge_nodes_map[e])};
106 : }
107 :
108 1491900 : bool Hex20::is_node_on_edge(const unsigned int n,
109 : const unsigned int e) const
110 : {
111 42216 : libmesh_assert_less (e, n_edges());
112 42216 : return std::find(std::begin(edge_nodes_map[e]),
113 1491900 : std::end(edge_nodes_map[e]),
114 1491900 : n) != std::end(edge_nodes_map[e]);
115 : }
116 :
117 :
118 :
119 430844 : bool Hex20::has_affine_map() const
120 : {
121 : // Make sure x-edge endpoints are affine
122 71244 : Point v = this->point(1) - this->point(0);
123 411968 : if (!v.relative_fuzzy_equals(this->point(2) - this->point(3), affine_tol) ||
124 840904 : !v.relative_fuzzy_equals(this->point(5) - this->point(4), affine_tol) ||
125 479572 : !v.relative_fuzzy_equals(this->point(6) - this->point(7), affine_tol))
126 20784 : return false;
127 : // Make sure x-edges are straight
128 33890 : v /= 2;
129 443840 : if (!v.relative_fuzzy_equals(this->point(8) - this->point(0), affine_tol) ||
130 443820 : !v.relative_fuzzy_equals(this->point(10) - this->point(3), affine_tol) ||
131 887760 : !v.relative_fuzzy_equals(this->point(16) - this->point(4), affine_tol) ||
132 443830 : !v.relative_fuzzy_equals(this->point(18) - this->point(7), affine_tol))
133 120 : return false;
134 : // Make sure xz-faces are identical parallelograms
135 443820 : v = this->point(4) - this->point(0);
136 409940 : if (!v.relative_fuzzy_equals(this->point(7) - this->point(3), affine_tol))
137 0 : return false;
138 33880 : v /= 2;
139 443776 : if (!v.relative_fuzzy_equals(this->point(12) - this->point(0), affine_tol) ||
140 443768 : !v.relative_fuzzy_equals(this->point(13) - this->point(1), affine_tol) ||
141 887584 : !v.relative_fuzzy_equals(this->point(14) - this->point(2), affine_tol) ||
142 443772 : !v.relative_fuzzy_equals(this->point(15) - this->point(3), affine_tol))
143 48 : return false;
144 : // Make sure y-edges are straight
145 443768 : v = (this->point(3) - this->point(0))/2;
146 409870 : if (!v.relative_fuzzy_equals(this->point(11) - this->point(0), affine_tol) ||
147 443742 : !v.relative_fuzzy_equals(this->point(9) - this->point(1), affine_tol) ||
148 887508 : !v.relative_fuzzy_equals(this->point(17) - this->point(5), affine_tol) ||
149 477618 : !v.relative_fuzzy_equals(this->point(19) - this->point(4), affine_tol))
150 24 : return false;
151 : // If all the above checks out, the map is affine
152 33874 : return true;
153 : }
154 :
155 :
156 :
157 9462875 : Order Hex20::default_order() const
158 : {
159 9462875 : return SECOND;
160 : }
161 :
162 :
163 :
164 174008 : std::unique_ptr<Elem> Hex20::build_side_ptr (const unsigned int i)
165 : {
166 174008 : return this->simple_build_side_ptr<Quad8, Hex20>(i);
167 : }
168 :
169 :
170 :
171 389554 : void Hex20::build_side_ptr (std::unique_ptr<Elem> & side,
172 : const unsigned int i)
173 : {
174 389554 : this->simple_build_side_ptr<Hex20>(side, i, QUAD8);
175 389554 : }
176 :
177 :
178 :
179 38736 : unsigned int Hex20::local_side_node(unsigned int side,
180 : unsigned int side_node) const
181 : {
182 3168 : libmesh_assert_less (side, this->n_sides());
183 3168 : libmesh_assert_less (side_node, Hex20::nodes_per_side);
184 :
185 38736 : return Hex20::side_nodes_map[side][side_node];
186 : }
187 :
188 :
189 :
190 2378352 : unsigned int Hex20::local_edge_node(unsigned int edge,
191 : unsigned int edge_node) const
192 : {
193 151392 : libmesh_assert_less (edge, this->n_edges());
194 151392 : libmesh_assert_less (edge_node, Hex20::nodes_per_edge);
195 :
196 2378352 : return Hex20::edge_nodes_map[edge][edge_node];
197 : }
198 :
199 :
200 :
201 493722 : std::unique_ptr<Elem> Hex20::build_edge_ptr (const unsigned int i)
202 : {
203 493722 : return this->simple_build_edge_ptr<Edge3,Hex20>(i);
204 : }
205 :
206 :
207 :
208 2304 : void Hex20::build_edge_ptr (std::unique_ptr<Elem> & edge, const unsigned int i)
209 : {
210 2304 : this->simple_build_edge_ptr<Hex20>(edge, i, EDGE3);
211 2304 : }
212 :
213 :
214 :
215 0 : void Hex20::connectivity(const unsigned int sc,
216 : const IOPackage iop,
217 : std::vector<dof_id_type> & conn) const
218 : {
219 0 : libmesh_assert(_nodes);
220 0 : libmesh_assert_less (sc, this->n_sub_elem());
221 0 : libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
222 :
223 :
224 0 : switch (iop)
225 : {
226 0 : case TECPLOT:
227 : {
228 0 : switch (sc)
229 : {
230 0 : case 0:
231 0 : conn.resize(8);
232 0 : conn[0] = this->node_id(0)+1;
233 0 : conn[1] = this->node_id(1)+1;
234 0 : conn[2] = this->node_id(2)+1;
235 0 : conn[3] = this->node_id(3)+1;
236 0 : conn[4] = this->node_id(4)+1;
237 0 : conn[5] = this->node_id(5)+1;
238 0 : conn[6] = this->node_id(6)+1;
239 0 : conn[7] = this->node_id(7)+1;
240 :
241 0 : return;
242 :
243 0 : default:
244 0 : libmesh_error_msg("Unknown sc = " << sc);
245 : }
246 : }
247 :
248 0 : case VTK:
249 : {
250 0 : switch (sc)
251 : {
252 0 : case 0:
253 0 : conn.resize(20);
254 0 : conn[0] = this->node_id(0);
255 0 : conn[1] = this->node_id(1);
256 0 : conn[2] = this->node_id(2);
257 0 : conn[3] = this->node_id(3);
258 0 : conn[4] = this->node_id(4);
259 0 : conn[5] = this->node_id(5);
260 0 : conn[6] = this->node_id(6);
261 0 : conn[7] = this->node_id(7);
262 0 : conn[8] = this->node_id(8);
263 0 : conn[9] = this->node_id(9);
264 0 : conn[10] = this->node_id(10);
265 0 : conn[11] = this->node_id(11);
266 0 : conn[12] = this->node_id(16);
267 0 : conn[13] = this->node_id(17);
268 0 : conn[14] = this->node_id(18);
269 0 : conn[15] = this->node_id(19);
270 0 : conn[16] = this->node_id(12);
271 0 : conn[17] = this->node_id(13);
272 0 : conn[18] = this->node_id(14);
273 0 : conn[19] = this->node_id(15);
274 0 : return;
275 :
276 0 : default:
277 0 : libmesh_error_msg("Unknown sc = " << sc);
278 : }
279 : }
280 :
281 0 : default:
282 0 : libmesh_error_msg("Unsupported IO package " << iop);
283 : }
284 : }
285 :
286 :
287 :
288 :
289 0 : unsigned short int Hex20::second_order_adjacent_vertex (const unsigned int n,
290 : const unsigned int v) const
291 : {
292 0 : libmesh_assert_greater_equal (n, this->n_vertices());
293 0 : libmesh_assert_less (n, this->n_nodes());
294 0 : libmesh_assert_less (v, 2);
295 : /*
296 : * the _second_order_adjacent_vertices matrix is
297 : * stored in cell_hex.C, since this matrix is identical
298 : * for Hex20 and Hex27 (for the first 12 higher-order nodes)
299 : */
300 0 : return _second_order_adjacent_vertices[n-this->n_vertices()][v];
301 : }
302 :
303 :
304 :
305 : std::pair<unsigned short int, unsigned short int>
306 0 : Hex20::second_order_child_vertex (const unsigned int n) const
307 : {
308 0 : libmesh_assert_greater_equal (n, this->n_vertices());
309 0 : libmesh_assert_less (n, this->n_nodes());
310 : /*
311 : * the _second_order_vertex_child_* vectors are
312 : * stored in cell_hex.C, since they are identical
313 : * for Hex20 and Hex27 (for the first 12 higher-order nodes)
314 : */
315 0 : return std::pair<unsigned short int, unsigned short int>
316 0 : (_second_order_vertex_child_number[n],
317 0 : _second_order_vertex_child_index[n]);
318 : }
319 :
320 :
321 :
322 1573 : Real Hex20::volume () const
323 : {
324 : // This specialization is good for Lagrange mappings only
325 1573 : if (this->mapping_type() != LAGRANGE_MAP)
326 0 : return this->Elem::volume();
327 :
328 : // Make copies of our points. It makes the subsequent calculations a bit
329 : // shorter and avoids dereferencing the same pointer multiple times.
330 : Point
331 2208 : x0 = point(0), x1 = point(1), x2 = point(2), x3 = point(3), x4 = point(4),
332 2081 : x5 = point(5), x6 = point(6), x7 = point(7), x8 = point(8), x9 = point(9),
333 2081 : x10 = point(10), x11 = point(11), x12 = point(12), x13 = point(13), x14 = point(14),
334 2081 : x15 = point(15), x16 = point(16), x17 = point(17), x18 = point(18), x19 = point(19);
335 :
336 : // The constant components of the dx/dxi vector,
337 : // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
338 : // These were copied directly from the output of a Python script.
339 : // There are at most 17 terms with total degree <=3, but only 12
340 : // of them are non-zero for each direction.
341 : Point dx_dxi[17] =
342 : {
343 129 : 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,
344 129 : x11/4 + x17/4 - x19/4 - x9/4,
345 129 : -x0/8 + x1/8 + x12/4 - x13/4 - x14/4 + x15/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8,
346 129 : x12/4 - x13/4 + x14/4 - x15/4,
347 129 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
348 129 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
349 129 : -x0/8 + x1/8 + x11/4 - x17/4 + x19/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8 - x9/4,
350 129 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
351 129 : x0/4 + x1/4 - x10/2 - x16/2 - x18/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2,
352 129 : -x0/4 - x1/4 + x10/2 - x16/2 - x18/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2,
353 : Point(0,0,0),
354 129 : -x0/4 - x1/4 - x10/2 + x16/2 - x18/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2,
355 129 : x0/4 + x1/4 + x10/2 + x16/2 - x18/2 - x2/4 - x3/4 - x4/4 - x5/4 + x6/4 + x7/4 - x8/2,
356 : Point(0,0,0),
357 : Point(0,0,0),
358 : Point(0,0,0),
359 : Point(0,0,0)
360 1677 : };
361 :
362 : // The constant components of the dx/deta vector. These were copied
363 : // directly from the output of a Python script. There are at most
364 : // 17 terms with total degree <=3, but only 12 of them are non-zero
365 : // for each direction.
366 : Point dx_deta[17] =
367 : {
368 129 : 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,
369 129 : -x10/4 - x16/4 + x18/4 + x8/4,
370 129 : -x0/8 - x1/8 + x12/4 + x13/4 - x14/4 - x15/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8,
371 129 : x0/4 + x1/4 - x11/2 - x17/2 - x19/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x9/2,
372 129 : -x0/4 - x1/4 + x11/2 - x17/2 - x19/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x9/2,
373 : Point(0,0,0),
374 : Point(0,0,0),
375 : Point(0,0,0),
376 129 : x12/4 - x13/4 + x14/4 - x15/4,
377 129 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
378 129 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
379 129 : -x0/4 + x1/4 + x11/2 - x17/2 + x19/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2,
380 129 : x0/4 - x1/4 - x11/2 - x17/2 + x19/2 - x2/4 + x3/4 - x4/4 + x5/4 + x6/4 - x7/4 + x9/2,
381 : Point(0,0,0),
382 129 : -x0/8 - x1/8 - x10/4 + x16/4 - x18/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8 + x8/4,
383 129 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
384 : Point(0,0,0)
385 1677 : };
386 :
387 : // The constant components of the dx/dzeta vector. These were copied
388 : // directly from the output of a Python script. There are at most
389 : // 17 terms with total degree <=3, but only 12 of them are non-zero
390 : // for each direction.
391 : Point dx_dzeta[17] =
392 : {
393 129 : 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,
394 129 : x0/4 + x1/4 - x12/2 - x13/2 - x14/2 - x15/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4,
395 : Point(0,0,0),
396 129 : -x10/4 - x16/4 + x18/4 + x8/4,
397 129 : -x0/4 - x1/4 + x12/2 + x13/2 - x14/2 - x15/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4,
398 : Point(0,0,0),
399 129 : -x0/8 - x1/8 + x11/4 - x17/4 - x19/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x9/4,
400 : Point(0,0,0),
401 129 : x11/4 + x17/4 - x19/4 - x9/4,
402 129 : -x0/4 + x1/4 + x12/2 - x13/2 - x14/2 + x15/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4,
403 : Point(0,0,0),
404 129 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
405 129 : x0/4 - x1/4 - x12/2 + x13/2 - x14/2 + x15/2 + x2/4 - x3/4 + x4/4 - x5/4 + x6/4 - x7/4,
406 129 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
407 129 : -x0/8 - x1/8 + x10/4 - x16/4 - x18/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x8/4,
408 : Point(0,0,0),
409 129 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
410 1677 : };
411 :
412 : // The integer exponents for each term.
413 : static const int exponents[17][3] =
414 : {
415 : {0, 0, 0},
416 : {0, 0, 1},
417 : {0, 0, 2},
418 : {0, 1, 0},
419 : {0, 1, 1},
420 : {0, 1, 2},
421 : {0, 2, 0},
422 : {0, 2, 1},
423 : {1, 0, 0},
424 : {1, 0, 1},
425 : {1, 0, 2},
426 : {1, 1, 0},
427 : {1, 1, 1},
428 : {1, 2, 0},
429 : {2, 0, 0},
430 : {2, 0, 1},
431 : {2, 1, 0}
432 : };
433 :
434 :
435 : // 3x3 quadrature, exact for bi-quintics
436 129 : const int N = 3;
437 1573 : const Real w[N] = {5./9, 8./9, 5./9};
438 :
439 : // Quadrature point locations raised to powers. q[0][2] is
440 : // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
441 : // first power, etc.
442 1573 : const Real q[N][N] =
443 : {
444 : //^0 ^1 ^2
445 : { 1., -std::sqrt(15)/5., 15./25},
446 : { 1., 0., 0.},
447 : { 1., std::sqrt(15)/5., 15./25}
448 : };
449 :
450 :
451 129 : Real vol = 0.;
452 6292 : for (int i=0; i<N; ++i)
453 18876 : for (int j=0; j<N; ++j)
454 56628 : for (int k=0; k<N; ++k)
455 : {
456 : // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
457 3483 : Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
458 764478 : for (int c=0; c<17; ++c)
459 : {
460 59211 : Real coeff =
461 839511 : q[i][exponents[c][0]] *
462 839511 : q[j][exponents[c][1]] *
463 722007 : q[k][exponents[c][2]];
464 :
465 59211 : dx_dxi_q += coeff * dx_dxi[c];
466 59211 : dx_deta_q += coeff * dx_deta[c];
467 59211 : dx_dzeta_q += coeff * dx_dzeta[c];
468 : }
469 :
470 : // Compute scalar triple product, multiply by weight, and accumulate volume.
471 45900 : vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
472 : }
473 :
474 129 : return vol;
475 : }
476 :
477 :
478 :
479 :
480 : #ifdef LIBMESH_ENABLE_AMR
481 :
482 : const Real Hex20::_embedding_matrix[Hex20::num_children][Hex20::num_nodes][Hex20::num_nodes] =
483 : {
484 : // embedding matrix for child 0
485 : {
486 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
487 : { 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
488 : { 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
489 : { -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
490 : { 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
491 : { 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
492 : { -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
493 : { -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
494 : { -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
495 : { 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
496 : { -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
497 : { -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
498 : { 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
499 : { 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
500 : { -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
501 : { -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
502 : { -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
503 : { -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
504 : { -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
505 : { -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
506 : { -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
507 : },
508 :
509 : // embedding matrix for child 1
510 : {
511 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
512 : { 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
513 : { 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
514 : { 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
515 : { -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
516 : { -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
517 : { 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
518 : { 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
519 : { -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
520 : { -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
521 : { 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
522 : { -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
523 : { -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
524 : { -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
525 : { 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
526 : { 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
527 : { -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
528 : { -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
529 : { 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
530 : { -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
531 : { -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
532 : },
533 :
534 : // embedding matrix for child 2
535 : {
536 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
537 : { 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
538 : { -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
539 : { 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
540 : { 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
541 : { -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
542 : { -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
543 : { 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
544 : { 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
545 : { -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
546 : { -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
547 : { 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
548 : { -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
549 : { -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
550 : { -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
551 : { 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
552 : { 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
553 : { -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
554 : { -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
555 : { 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
556 : { -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
557 : },
558 :
559 : // embedding matrix for child 3
560 : {
561 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
562 : { -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
563 : { 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
564 : { 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
565 : { 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
566 : { -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
567 : { 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
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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
569 : { 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
570 : { -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
571 : { 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
572 : { 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
573 : { -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
574 : { -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
575 : { 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
576 : { 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
577 : { 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
578 : { -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
579 : { 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
580 : { 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
581 : { -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
582 : },
583 :
584 : // embedding matrix for child 4
585 : {
586 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
587 : { 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
588 : { -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
589 : { -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
590 : { -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
591 : { 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
592 : { 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
593 : { 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
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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 7
595 : { -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
596 : { -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
597 : { -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
598 : { -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
599 : { -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
600 : { -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
601 : { -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
602 : { -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
603 : { 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
604 : { 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
605 : { 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
606 : { 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
607 : },
608 :
609 : // embedding matrix for child 5
610 : {
611 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
612 : { -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
613 : { 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
614 : { 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
615 : { -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
616 : { 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
617 : { 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
618 : { 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
619 : { 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
620 : { -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
621 : { 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
622 : { -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
623 : { -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
624 : { -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
625 : { 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
626 : { 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
627 : { -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
628 : { 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
629 : { 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
630 : { 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
631 : { 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
632 : },
633 :
634 : // embedding matrix for child 6
635 : {
636 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
637 : { -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
638 : { -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
639 : { 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
640 : { 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
641 : { 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
642 : { 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
643 : { 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
644 : { 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
645 : { -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
646 : { -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
647 : { 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
648 : { -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
649 : { -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
650 : { -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
651 : { 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
652 : { 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
653 : { 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
654 : { 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
655 : { 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
656 : { 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
657 : },
658 :
659 : // embedding matrix for child 7
660 : {
661 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
662 : { -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
663 : { 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
664 : { 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
665 : { 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
666 : { 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
667 : { 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
668 : { 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
669 : { 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
670 : { -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
671 : { 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
672 : { 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
673 : { -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
674 : { -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
675 : { 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
676 : { 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
677 : { 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
678 : { 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
679 : { 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
680 : { 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
681 : { 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
682 : }
683 : };
684 :
685 : #endif
686 :
687 : void
688 3384 : Hex20::permute(unsigned int perm_num)
689 : {
690 336 : libmesh_assert_less (perm_num, 24);
691 3384 : const unsigned int side = perm_num % 6;
692 3384 : const unsigned int rotate = perm_num / 6;
693 :
694 10080 : for (unsigned int i = 0; i != rotate; ++i)
695 : {
696 6696 : swap4nodes(0,1,2,3);
697 6696 : swap4nodes(4,5,6,7);
698 6696 : swap4nodes(8,9,10,11);
699 6696 : swap4nodes(12,13,14,15);
700 6696 : swap4nodes(16,17,18,19);
701 5976 : swap4neighbors(1,2,3,4);
702 : }
703 :
704 3384 : switch (side) {
705 32 : case 0:
706 32 : break;
707 384 : case 1:
708 384 : swap4nodes(3,7,4,0);
709 384 : swap4nodes(11,15,19,12);
710 384 : swap4nodes(10,18,16,8);
711 384 : swap4nodes(2,6,5,1);
712 384 : swap4nodes(9,14,17,13);
713 352 : swap4neighbors(0,3,5,1);
714 352 : break;
715 384 : case 2:
716 384 : swap4nodes(0,4,5,1);
717 384 : swap4nodes(8,12,16,13);
718 384 : swap4nodes(3,7,6,2);
719 384 : swap4nodes(10,15,18,14);
720 384 : swap4nodes(11,19,17,9);
721 352 : swap4neighbors(0,4,5,2);
722 352 : break;
723 384 : case 3:
724 384 : swap4nodes(0,4,7,3);
725 384 : swap4nodes(12,19,15,11);
726 384 : swap4nodes(8,16,18,10);
727 384 : swap4nodes(1,5,6,2);
728 384 : swap4nodes(13,17,14,9);
729 352 : swap4neighbors(0,1,5,3);
730 352 : break;
731 384 : case 4:
732 384 : swap4nodes(1,5,4,0);
733 384 : swap4nodes(8,13,16,12);
734 384 : swap4nodes(9,17,19,11);
735 384 : swap4nodes(2,6,7,3);
736 384 : swap4nodes(10,14,18,15);
737 352 : swap4neighbors(0,2,5,4);
738 352 : break;
739 1464 : case 5:
740 1464 : swap2nodes(0,7);
741 1464 : swap2nodes(8,18);
742 1464 : swap2nodes(1,6);
743 1464 : swap2nodes(2,5);
744 1464 : swap2nodes(10,16);
745 1464 : swap2nodes(3,4);
746 1464 : swap2nodes(11,19);
747 1464 : swap2nodes(12,15);
748 1464 : swap2nodes(9,17);
749 1464 : swap2nodes(13,14);
750 176 : swap2neighbors(0,5);
751 176 : swap2neighbors(1,3);
752 176 : break;
753 0 : default:
754 0 : libmesh_error();
755 : }
756 3384 : }
757 :
758 :
759 : void
760 288 : Hex20::flip(BoundaryInfo * boundary_info)
761 : {
762 24 : libmesh_assert(boundary_info);
763 :
764 288 : swap2nodes(0,1);
765 288 : swap2nodes(2,3);
766 288 : swap2nodes(4,5);
767 288 : swap2nodes(6,7);
768 288 : swap2nodes(9,11);
769 288 : swap2nodes(12,13);
770 288 : swap2nodes(14,15);
771 288 : swap2nodes(17,19);
772 24 : swap2neighbors(2,4);
773 288 : swap2boundarysides(2,4,boundary_info);
774 288 : swap2boundaryedges(1,3,boundary_info);
775 288 : swap2boundaryedges(4,5,boundary_info);
776 288 : swap2boundaryedges(6,7,boundary_info);
777 288 : swap2boundaryedges(9,11,boundary_info);
778 288 : }
779 :
780 :
781 : ElemType
782 1728 : Hex20::side_type (const unsigned int libmesh_dbg_var(s)) const
783 : {
784 144 : libmesh_assert_less (s, 6);
785 1728 : return QUAD8;
786 : }
787 :
788 :
789 : } // namespace libMesh
|
