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_hex27.h"
21 : #include "libmesh/edge_edge3.h"
22 : #include "libmesh/face_quad9.h"
23 : #include "libmesh/enum_io_package.h"
24 : #include "libmesh/enum_order.h"
25 :
26 : namespace libMesh
27 : {
28 :
29 :
30 :
31 : // ------------------------------------------------------------
32 : // Hex27 class static member initializations
33 : const int Hex27::num_nodes;
34 : const int Hex27::nodes_per_side;
35 : const int Hex27::nodes_per_edge;
36 :
37 : // ------------------------------------------------------------
38 : // Hex27 class member functions
39 :
40 42159051 : bool Hex27::is_vertex(const unsigned int i) const
41 : {
42 42159051 : if (i < 8)
43 12806720 : return true;
44 2152138 : return false;
45 : }
46 :
47 560848 : bool Hex27::is_edge(const unsigned int i) const
48 : {
49 560848 : if (i < 8)
50 0 : return false;
51 560848 : if (i > 19)
52 197968 : return false;
53 30240 : return true;
54 : }
55 :
56 4628244 : bool Hex27::is_face(const unsigned int i) const
57 : {
58 4628244 : if (i == 26)
59 3659 : return false;
60 4612136 : if (i > 19)
61 778676 : return true;
62 313020 : return false;
63 : }
64 :
65 2920778 : bool Hex27::is_node_on_side(const unsigned int n,
66 : const unsigned int s) const
67 : {
68 210957 : libmesh_assert_less (s, n_sides());
69 210957 : return std::find(std::begin(side_nodes_map[s]),
70 2920778 : std::end(side_nodes_map[s]),
71 2920778 : n) != std::end(side_nodes_map[s]);
72 : }
73 :
74 : std::vector<unsigned>
75 570855135 : Hex27::nodes_on_side(const unsigned int s) const
76 : {
77 44419826 : libmesh_assert_less(s, n_sides());
78 615274709 : return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
79 : }
80 :
81 : std::vector<unsigned>
82 30804 : Hex27::nodes_on_edge(const unsigned int e) const
83 : {
84 2520 : libmesh_assert_less(e, n_edges());
85 33324 : return {std::begin(edge_nodes_map[e]), std::end(edge_nodes_map[e])};
86 : }
87 :
88 3950766 : bool Hex27::is_node_on_edge(const unsigned int n,
89 : const unsigned int e) const
90 : {
91 272598 : libmesh_assert_less (e, n_edges());
92 272598 : return std::find(std::begin(edge_nodes_map[e]),
93 3950766 : std::end(edge_nodes_map[e]),
94 3950766 : n) != std::end(edge_nodes_map[e]);
95 : }
96 :
97 :
98 :
99 2935675 : bool Hex27::has_affine_map() const
100 : {
101 : // Make sure x-edge endpoints are affine
102 460712 : Point v = this->point(1) - this->point(0);
103 2907596 : if (!v.relative_fuzzy_equals(this->point(2) - this->point(3), affine_tol) ||
104 5840962 : !v.relative_fuzzy_equals(this->point(5) - this->point(4), affine_tol) ||
105 3363646 : !v.relative_fuzzy_equals(this->point(6) - this->point(7), affine_tol))
106 30436 : return false;
107 : // Make sure x-edges are straight
108 : // and x-face and center points are centered
109 228043 : v /= 2;
110 3131522 : if (!v.relative_fuzzy_equals(this->point(8) - this->point(0), affine_tol) ||
111 3130982 : !v.relative_fuzzy_equals(this->point(10) - this->point(3), affine_tol) ||
112 3130766 : !v.relative_fuzzy_equals(this->point(16) - this->point(4), affine_tol) ||
113 3130558 : !v.relative_fuzzy_equals(this->point(18) - this->point(7), affine_tol) ||
114 3130526 : !v.relative_fuzzy_equals(this->point(20) - this->point(11), affine_tol) ||
115 3130526 : !v.relative_fuzzy_equals(this->point(21) - this->point(12), affine_tol) ||
116 3130526 : !v.relative_fuzzy_equals(this->point(23) - this->point(15), affine_tol) ||
117 6263648 : !v.relative_fuzzy_equals(this->point(25) - this->point(19), affine_tol) ||
118 3130738 : !v.relative_fuzzy_equals(this->point(26) - this->point(24), affine_tol))
119 2544 : return false;
120 : // Make sure xz-faces are identical parallelograms
121 3130526 : v = this->point(4) - this->point(0);
122 2902695 : if (!v.relative_fuzzy_equals(this->point(7) - this->point(3), affine_tol))
123 0 : return false;
124 227831 : v /= 2;
125 3130526 : if (!v.relative_fuzzy_equals(this->point(12) - this->point(0), affine_tol) ||
126 3130526 : !v.relative_fuzzy_equals(this->point(13) - this->point(1), affine_tol) ||
127 3130526 : !v.relative_fuzzy_equals(this->point(14) - this->point(2), affine_tol) ||
128 3130526 : !v.relative_fuzzy_equals(this->point(15) - this->point(3), affine_tol) ||
129 6261052 : !v.relative_fuzzy_equals(this->point(22) - this->point(9), affine_tol) ||
130 3130526 : !v.relative_fuzzy_equals(this->point(24) - this->point(11), affine_tol))
131 0 : return false;
132 : // Make sure y-edges are straight
133 3130526 : v = (this->point(3) - this->point(0))/2;
134 2902695 : if (!v.relative_fuzzy_equals(this->point(11) - this->point(0), affine_tol) ||
135 3130526 : !v.relative_fuzzy_equals(this->point(9) - this->point(1), affine_tol) ||
136 6261052 : !v.relative_fuzzy_equals(this->point(17) - this->point(5), affine_tol) ||
137 3358357 : !v.relative_fuzzy_equals(this->point(19) - this->point(4), affine_tol))
138 0 : return false;
139 : // If all the above checks out, the map is affine
140 227831 : return true;
141 : }
142 :
143 :
144 :
145 136013197 : Order Hex27::default_order() const
146 : {
147 136013197 : return SECOND;
148 : }
149 :
150 :
151 :
152 0 : dof_id_type Hex27::key (const unsigned int s) const
153 : {
154 0 : libmesh_assert_less (s, this->n_sides());
155 :
156 : // Think of a unit cube: (-1,1) x (-1,1) x (1,1)
157 0 : switch (s)
158 : {
159 0 : case 0: // the face at z=0
160 :
161 : return
162 0 : this->compute_key (this->node_id(20));
163 :
164 0 : case 1: // the face at y = 0
165 :
166 : return
167 0 : this->compute_key (this->node_id(21));
168 :
169 0 : case 2: // the face at x=1
170 :
171 : return
172 0 : this->compute_key (this->node_id(22));
173 :
174 0 : case 3: // the face at y=1
175 :
176 : return
177 0 : this->compute_key (this->node_id(23));
178 :
179 0 : case 4: // the face at x=0
180 :
181 : return
182 0 : this->compute_key (this->node_id(24));
183 :
184 0 : case 5: // the face at z=1
185 :
186 : return
187 0 : this->compute_key (this->node_id(25));
188 :
189 0 : default:
190 0 : libmesh_error_msg("Invalid side " << s);
191 : }
192 : }
193 :
194 :
195 :
196 1171146402 : unsigned int Hex27::local_side_node(unsigned int side,
197 : unsigned int side_node) const
198 : {
199 96668676 : libmesh_assert_less (side, this->n_sides());
200 96668676 : libmesh_assert_less (side_node, Hex27::nodes_per_side);
201 :
202 1171146402 : return Hex27::side_nodes_map[side][side_node];
203 : }
204 :
205 :
206 :
207 696748416 : unsigned int Hex27::local_edge_node(unsigned int edge,
208 : unsigned int edge_node) const
209 : {
210 57249684 : libmesh_assert_less (edge, this->n_edges());
211 57249684 : libmesh_assert_less (edge_node, Hex27::nodes_per_edge);
212 :
213 696748416 : return Hex27::edge_nodes_map[edge][edge_node];
214 : }
215 :
216 :
217 :
218 90765165 : std::unique_ptr<Elem> Hex27::build_side_ptr (const unsigned int i)
219 : {
220 90765165 : return this->simple_build_side_ptr<Quad9, Hex27>(i);
221 : }
222 :
223 :
224 :
225 8330409 : void Hex27::build_side_ptr (std::unique_ptr<Elem> & side,
226 : const unsigned int i)
227 : {
228 8330409 : this->simple_build_side_ptr<Hex27>(side, i, QUAD9);
229 8330409 : }
230 :
231 :
232 :
233 602573 : std::unique_ptr<Elem> Hex27::build_edge_ptr (const unsigned int i)
234 : {
235 602573 : return this->simple_build_edge_ptr<Edge3,Hex27>(i);
236 : }
237 :
238 :
239 :
240 28056 : void Hex27::build_edge_ptr (std::unique_ptr<Elem> & edge, const unsigned int i)
241 : {
242 28056 : this->simple_build_edge_ptr<Hex27>(edge, i, EDGE3);
243 28056 : }
244 :
245 :
246 :
247 0 : void Hex27::connectivity(const unsigned int sc,
248 : const IOPackage iop,
249 : std::vector<dof_id_type> & conn) const
250 : {
251 0 : libmesh_assert(_nodes);
252 0 : libmesh_assert_less (sc, this->n_sub_elem());
253 0 : libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
254 :
255 0 : conn.resize(8);
256 :
257 0 : switch (iop)
258 : {
259 0 : case TECPLOT:
260 : {
261 0 : switch (sc)
262 : {
263 0 : case 0:
264 :
265 0 : conn[0] = this->node_id(0)+1;
266 0 : conn[1] = this->node_id(8)+1;
267 0 : conn[2] = this->node_id(20)+1;
268 0 : conn[3] = this->node_id(11)+1;
269 0 : conn[4] = this->node_id(12)+1;
270 0 : conn[5] = this->node_id(21)+1;
271 0 : conn[6] = this->node_id(26)+1;
272 0 : conn[7] = this->node_id(24)+1;
273 :
274 0 : return;
275 :
276 0 : case 1:
277 :
278 0 : conn[0] = this->node_id(8)+1;
279 0 : conn[1] = this->node_id(1)+1;
280 0 : conn[2] = this->node_id(9)+1;
281 0 : conn[3] = this->node_id(20)+1;
282 0 : conn[4] = this->node_id(21)+1;
283 0 : conn[5] = this->node_id(13)+1;
284 0 : conn[6] = this->node_id(22)+1;
285 0 : conn[7] = this->node_id(26)+1;
286 :
287 0 : return;
288 :
289 0 : case 2:
290 :
291 0 : conn[0] = this->node_id(11)+1;
292 0 : conn[1] = this->node_id(20)+1;
293 0 : conn[2] = this->node_id(10)+1;
294 0 : conn[3] = this->node_id(3)+1;
295 0 : conn[4] = this->node_id(24)+1;
296 0 : conn[5] = this->node_id(26)+1;
297 0 : conn[6] = this->node_id(23)+1;
298 0 : conn[7] = this->node_id(15)+1;
299 :
300 0 : return;
301 :
302 0 : case 3:
303 :
304 0 : conn[0] = this->node_id(20)+1;
305 0 : conn[1] = this->node_id(9)+1;
306 0 : conn[2] = this->node_id(2)+1;
307 0 : conn[3] = this->node_id(10)+1;
308 0 : conn[4] = this->node_id(26)+1;
309 0 : conn[5] = this->node_id(22)+1;
310 0 : conn[6] = this->node_id(14)+1;
311 0 : conn[7] = this->node_id(23)+1;
312 :
313 0 : return;
314 :
315 0 : case 4:
316 :
317 0 : conn[0] = this->node_id(12)+1;
318 0 : conn[1] = this->node_id(21)+1;
319 0 : conn[2] = this->node_id(26)+1;
320 0 : conn[3] = this->node_id(24)+1;
321 0 : conn[4] = this->node_id(4)+1;
322 0 : conn[5] = this->node_id(16)+1;
323 0 : conn[6] = this->node_id(25)+1;
324 0 : conn[7] = this->node_id(19)+1;
325 :
326 0 : return;
327 :
328 0 : case 5:
329 :
330 0 : conn[0] = this->node_id(21)+1;
331 0 : conn[1] = this->node_id(13)+1;
332 0 : conn[2] = this->node_id(22)+1;
333 0 : conn[3] = this->node_id(26)+1;
334 0 : conn[4] = this->node_id(16)+1;
335 0 : conn[5] = this->node_id(5)+1;
336 0 : conn[6] = this->node_id(17)+1;
337 0 : conn[7] = this->node_id(25)+1;
338 :
339 0 : return;
340 :
341 0 : case 6:
342 :
343 0 : conn[0] = this->node_id(24)+1;
344 0 : conn[1] = this->node_id(26)+1;
345 0 : conn[2] = this->node_id(23)+1;
346 0 : conn[3] = this->node_id(15)+1;
347 0 : conn[4] = this->node_id(19)+1;
348 0 : conn[5] = this->node_id(25)+1;
349 0 : conn[6] = this->node_id(18)+1;
350 0 : conn[7] = this->node_id(7)+1;
351 :
352 0 : return;
353 :
354 0 : case 7:
355 :
356 0 : conn[0] = this->node_id(26)+1;
357 0 : conn[1] = this->node_id(22)+1;
358 0 : conn[2] = this->node_id(14)+1;
359 0 : conn[3] = this->node_id(23)+1;
360 0 : conn[4] = this->node_id(25)+1;
361 0 : conn[5] = this->node_id(17)+1;
362 0 : conn[6] = this->node_id(6)+1;
363 0 : conn[7] = this->node_id(18)+1;
364 :
365 0 : return;
366 :
367 0 : default:
368 0 : libmesh_error_msg("Invalid sc = " << sc);
369 : }
370 : }
371 :
372 0 : case VTK:
373 : {
374 : // VTK now supports VTK_TRIQUADRATIC_HEXAHEDRON directly
375 0 : conn.resize(27);
376 :
377 0 : conn[0] = this->node_id(0);
378 0 : conn[1] = this->node_id(1);
379 0 : conn[2] = this->node_id(2);
380 0 : conn[3] = this->node_id(3);
381 0 : conn[4] = this->node_id(4);
382 0 : conn[5] = this->node_id(5);
383 0 : conn[6] = this->node_id(6);
384 0 : conn[7] = this->node_id(7);
385 0 : conn[8] = this->node_id(8);
386 0 : conn[9] = this->node_id(9);
387 0 : conn[10] = this->node_id(10);
388 0 : conn[11] = this->node_id(11);
389 0 : conn[12] = this->node_id(16);
390 0 : conn[13] = this->node_id(17);
391 0 : conn[14] = this->node_id(18);
392 0 : conn[15] = this->node_id(19);
393 0 : conn[16] = this->node_id(12);
394 0 : conn[17] = this->node_id(13);
395 0 : conn[18] = this->node_id(14);
396 0 : conn[19] = this->node_id(15);
397 0 : conn[20] = this->node_id(24);
398 0 : conn[21] = this->node_id(22);
399 0 : conn[22] = this->node_id(21);
400 0 : conn[23] = this->node_id(23);
401 0 : conn[24] = this->node_id(20);
402 0 : conn[25] = this->node_id(25);
403 0 : conn[26] = this->node_id(26);
404 :
405 0 : return;
406 : }
407 :
408 0 : default:
409 0 : libmesh_error_msg("Unsupported IO package " << iop);
410 : }
411 : }
412 :
413 :
414 :
415 :
416 :
417 2954151 : unsigned int Hex27::n_second_order_adjacent_vertices (const unsigned int n) const
418 : {
419 168808 : switch (n)
420 : {
421 105760 : case 8:
422 : case 9:
423 : case 10:
424 : case 11:
425 : case 12:
426 : case 13:
427 : case 14:
428 : case 15:
429 : case 16:
430 : case 17:
431 : case 18:
432 : case 19:
433 105760 : return 2;
434 :
435 53896 : case 20:
436 : case 21:
437 : case 22:
438 : case 23:
439 : case 24:
440 : case 25:
441 53896 : return 4;
442 :
443 9152 : case 26:
444 9152 : return 8;
445 :
446 0 : default:
447 0 : libmesh_error_msg("Invalid node number n = " << n);
448 : }
449 : }
450 :
451 :
452 :
453 8753900 : unsigned short int Hex27::second_order_adjacent_vertex (const unsigned int n,
454 : const unsigned int v) const
455 : {
456 500320 : libmesh_assert_greater_equal (n, this->n_vertices());
457 500320 : libmesh_assert_less (n, this->n_nodes());
458 :
459 8753900 : switch (n)
460 : {
461 : /*
462 : * these are all nodes that are unique to Hex27,
463 : * use our _remaining.... matrix
464 : */
465 3771268 : case 20:
466 : case 21:
467 : case 22:
468 : case 23:
469 : case 24:
470 : case 25:
471 : {
472 215584 : libmesh_assert_less (v, 4);
473 3771268 : return _remaining_second_order_adjacent_vertices[n-20][v];
474 : }
475 :
476 : /*
477 : * for the bubble node the return value is simply v.
478 : * Why? -- the user asks for the v-th adjacent vertex,
479 : * from \p n_second_order_adjacent_vertices() there
480 : * are 8 adjacent vertices, and these happen to be
481 : * 0..7
482 : */
483 1279952 : case 26:
484 : {
485 73216 : libmesh_assert_less (v, 8);
486 1279952 : return static_cast<unsigned short int>(v);
487 : }
488 :
489 : /*
490 : * nodes 8..19:
491 : * these are all nodes that are identical for
492 : * Hex20 and Hex27. Therefore use the
493 : * matrix stored in cell_hex.C
494 : */
495 3702680 : default:
496 : {
497 211520 : libmesh_assert_less (v, 2);
498 3702680 : return _second_order_adjacent_vertices[n-this->n_vertices()][v];
499 : }
500 : }
501 : }
502 :
503 :
504 :
505 : const unsigned short int Hex27::_remaining_second_order_adjacent_vertices[6][4] =
506 : {
507 : { 0, 1, 2, 3}, // vertices adjacent to node 20 face nodes
508 : { 0, 1, 4, 5}, // vertices adjacent to node 21
509 : { 1, 2, 5, 6}, // vertices adjacent to node 22
510 : { 2, 3, 6, 7}, // vertices adjacent to node 23
511 : { 0, 3, 4, 7}, // vertices adjacent to node 24
512 : { 4, 5, 6, 7}, // vertices adjacent to node 25
513 : };
514 :
515 :
516 :
517 : std::pair<unsigned short int, unsigned short int>
518 0 : Hex27::second_order_child_vertex (const unsigned int n) const
519 : {
520 0 : libmesh_assert_greater_equal (n, this->n_vertices());
521 0 : libmesh_assert_less (n, this->n_nodes());
522 : /*
523 : * the _second_order_vertex_child_* vectors are
524 : * stored in cell_hex.C, since they are identical
525 : * for Hex20 and Hex27 (for the first 12 higher-order nodes)
526 : */
527 0 : return std::pair<unsigned short int, unsigned short int>
528 0 : (_second_order_vertex_child_number[n],
529 0 : _second_order_vertex_child_index[n]);
530 : }
531 :
532 :
533 :
534 19959 : Real Hex27::volume () const
535 : {
536 : // This specialization is good for Lagrange mappings only in general
537 19959 : if (this->mapping_type() != LAGRANGE_MAP)
538 932 : return this->Elem::volume();
539 :
540 : // Make copies of our points. It makes the subsequent calculations a bit
541 : // shorter and avoids dereferencing the same pointer multiple times.
542 : Point
543 32941 : x0 = point(0), x1 = point(1), x2 = point(2), x3 = point(3), x4 = point(4), x5 = point(5), x6 = point(6), x7 = point(7), x8 = point(8),
544 31395 : x9 = point(9), x10 = point(10), x11 = point(11), x12 = point(12), x13 = point(13), x14 = point(14), x15 = point(15), x16 = point(16), x17 = point(17),
545 31395 : x18 = point(18), x19 = point(19), x20 = point(20), x21 = point(21), x22 = point(22), x23 = point(23), x24 = point(24), x25 = point(25), x26 = point(26);
546 :
547 : // The constant components of the dx/dxi vector,
548 : // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
549 : // All of the xi^2 terms are zero.
550 : // These were copied directly from the output of a Python script.
551 : Point dx_dxi[3][3][3] =
552 : {
553 : {
554 : {
555 1968 : x22/2 - x24/2, // 0, 0, 0
556 1968 : x11/4 + x17/4 - x19/4 - x9/4, // 0, 0, 1
557 1968 : -x11/4 + x17/4 - x19/4 - x22/2 + x24/2 + x9/4 // 0, 0, 2
558 : },
559 :
560 : {
561 1968 : x12/4 - x13/4 + x14/4 - x15/4, // 0, 1, 0
562 1968 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 0, 1, 1
563 1968 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8 // 0, 1, 2
564 : },
565 :
566 : {
567 1968 : -x12/4 + x13/4 + x14/4 - x15/4 - x22/2 + x24/2, // 0, 2, 0
568 1968 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4, // 0, 2, 1
569 1968 : -x0/8 + x1/8 + x11/4 + x12/4 - x13/4 - x14/4 + x15/4 - x17/4 + x19/4 + x2/8 + x22/2 - x24/2 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8 - x9/4 // 0, 2, 2
570 : }
571 : },
572 : {
573 : {
574 1968 : x22 + x24 - 2*x26, // 1, 0, 0
575 1968 : -x11/2 + x17/2 + x19/2 + x20 - x25 - x9/2, // 1, 0, 1
576 1968 : x11/2 + x17/2 + x19/2 - x20 - x22 - x24 - x25 + 2*x26 + x9/2 // 1, 0, 2
577 : },
578 :
579 : {
580 1968 : -x12/2 - x13/2 + x14/2 + x15/2 + x21 - x23, // 1, 1, 0
581 1968 : x0/4 + x1/4 + x10/2 + x16/2 - x18/2 - x2/4 - x3/4 - x4/4 - x5/4 + x6/4 + x7/4 - x8/2, // 1, 1, 1
582 1968 : -x0/4 - x1/4 - x10/2 + x12/2 + x13/2 - x14/2 - x15/2 + x16/2 - x18/2 + x2/4 - x21 + x23 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2 // 1, 1, 2
583 : },
584 :
585 : {
586 1968 : x12/2 + x13/2 + x14/2 + x15/2 - x21 - x22 - x23 - x24 + 2*x26, // 1, 2, 0
587 1968 : -x0/4 - x1/4 + x10/2 + x11/2 - x16/2 - x17/2 - x18/2 - x19/2 - x2/4 - x20 + x25 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2 + x9/2, // 1, 2, 1
588 1968 : x0/4 + x1/4 - x10/2 - x11/2 - x12/2 - x13/2 - x14/2 - x15/2 - x16/2 - x17/2 - x18/2 - x19/2 + x2/4 + x20 + x21 + x22 + x23 + x24 + x25 - 2*x26 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2 - x9/2 // 1, 2, 2
589 : }
590 : },
591 : {
592 : {Point(0,0,0), Point(0,0,0), Point(0,0,0)},
593 : {Point(0,0,0), Point(0,0,0), Point(0,0,0)},
594 : {Point(0,0,0), Point(0,0,0), Point(0,0,0)}
595 : }
596 37392 : };
597 :
598 :
599 :
600 : // The constant components of the dx/deta vector, all of the eta^2
601 : // terms are zero. These were copied directly from the output of a
602 : // Python script.
603 : Point dx_deta[3][3][3] =
604 : {
605 : {
606 : {
607 1968 : -x21/2 + x23/2, // 0, 0, 0
608 1968 : -x10/4 - x16/4 + x18/4 + x8/4, // 0, 0, 1
609 1968 : x10/4 - x16/4 + x18/4 + x21/2 - x23/2 - x8/4 // 0, 0, 2
610 : },
611 : {
612 1968 : x21 + x23 - 2*x26, // 0, 1, 0
613 1968 : -x10/2 + x16/2 + x18/2 + x20 - x25 - x8/2, // 0, 1, 1
614 1968 : x10/2 + x16/2 + x18/2 - x20 - x21 - x23 - x25 + 2*x26 + x8/2 // 0, 1, 2
615 : },
616 : {
617 : Point(0,0,0), // 0, 2, 0
618 : Point(0,0,0), // 0, 2, 1
619 : Point(0,0,0) // 0, 2, 2
620 : }
621 : },
622 :
623 : {
624 : {
625 1968 : x12/4 - x13/4 + x14/4 - x15/4, // 1, 0, 0
626 1968 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 1, 0, 1
627 1968 : x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8 // 1, 0, 2
628 : },
629 : {
630 1968 : -x12/2 + x13/2 + x14/2 - x15/2 - x22 + x24, // 1, 1, 0
631 1968 : x0/4 - x1/4 - x11/2 - x17/2 + x19/2 - x2/4 + x3/4 - x4/4 + x5/4 + x6/4 - x7/4 + x9/2, // 1, 1, 1
632 1968 : -x0/4 + x1/4 + x11/2 + x12/2 - x13/2 - x14/2 + x15/2 - x17/2 + x19/2 + x2/4 + x22 - x24 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2 // 1, 1, 2
633 : },
634 : {
635 : Point(0,0,0), // 1, 2, 0
636 : Point(0,0,0), // 1, 2, 1
637 : Point(0,0,0) // 1, 2, 2
638 : }
639 : },
640 :
641 : {
642 : {
643 1968 : -x12/4 - x13/4 + x14/4 + x15/4 + x21/2 - x23/2, // 2, 0, 0
644 1968 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4, // 2, 0, 1
645 1968 : -x0/8 - x1/8 - x10/4 + x12/4 + x13/4 - x14/4 - x15/4 + x16/4 - x18/4 + x2/8 - x21/2 + x23/2 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8 + x8/4, // 2, 0, 2
646 : },
647 : {
648 1968 : x12/2 + x13/2 + x14/2 + x15/2 - x21 - x22 - x23 - x24 + 2*x26, // 2, 1, 0
649 1968 : -x0/4 - x1/4 + x10/2 + x11/2 - x16/2 - x17/2 - x18/2 - x19/2 - x2/4 - x20 + x25 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2 + x9/2, // 2, 1, 1
650 1968 : x0/4 + x1/4 - x10/2 - x11/2 - x12/2 - x13/2 - x14/2 - x15/2 - x16/2 - x17/2 - x18/2 - x19/2 + x2/4 + x20 + x21 + x22 + x23 + x24 + x25 - 2*x26 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2 - x9/2 // 2, 1, 2
651 : },
652 : {
653 : Point(0,0,0), // 2, 2, 0
654 : Point(0,0,0), // 2, 2, 1
655 : Point(0,0,0) // 2, 2, 2
656 : }
657 : }
658 37392 : };
659 :
660 :
661 :
662 : // The constant components of the dx/dzeta vector, all of the zeta^2
663 : // terms are zero. These were copied directly from the output of a
664 : // Python script.
665 : Point dx_dzeta[3][3][3] =
666 : {
667 : {
668 : {
669 1968 : -x20/2 + x25/2, // 0, 0, 0
670 1968 : x20 + x25 - 2*x26, // 0, 0, 1
671 : Point(0,0,0) // 0, 0, 2
672 : },
673 : {
674 1968 : -x10/4 - x16/4 + x18/4 + x8/4, // 0, 1, 0
675 1968 : x10/2 - x16/2 + x18/2 + x21 - x23 - x8/2, // 0, 1, 1
676 : Point(0,0,0) // 0, 1, 2
677 : },
678 : {
679 1968 : -x10/4 + x16/4 + x18/4 + x20/2 - x25/2 - x8/4, // 0, 2, 0
680 1968 : x10/2 + x16/2 + x18/2 - x20 - x21 - x23 - x25 + 2*x26 + x8/2, // 0, 2, 1
681 : Point(0,0,0) // 0, 2, 2
682 : }
683 : },
684 : {
685 : {
686 1968 : x11/4 + x17/4 - x19/4 - x9/4, // 1, 0, 0
687 1968 : -x11/2 + x17/2 - x19/2 - x22 + x24 + x9/2, // 1, 0, 1
688 : Point(0,0,0) // 1, 0, 2
689 : },
690 : {
691 1968 : -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 1, 1, 0
692 1968 : x0/4 - x1/4 - x12/2 + x13/2 - x14/2 + x15/2 + x2/4 - x3/4 + x4/4 - x5/4 + x6/4 - x7/4, // 1, 1, 1
693 : Point(0,0,0) // 1, 1, 2
694 : },
695 : {
696 1968 : x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4, // 1, 2, 0
697 1968 : -x0/4 + x1/4 + x11/2 + x12/2 - x13/2 - x14/2 + x15/2 - x17/2 + x19/2 + x2/4 + x22 - x24 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2, // 1, 2, 1
698 : Point(0,0,0) // 1, 2, 2
699 : }
700 : },
701 : {
702 : {
703 1968 : -x11/4 + x17/4 + x19/4 + x20/2 - x25/2 - x9/4, // 2, 0, 0
704 1968 : x11/2 + x17/2 + x19/2 - x20 - x22 - x24 - x25 + 2*x26 + x9/2, // 2, 0, 1
705 : Point(0,0,0) // 2, 0, 2
706 : },
707 : {
708 1968 : x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4, // 2, 1, 0
709 1968 : -x0/4 - x1/4 - x10/2 + x12/2 + x13/2 - x14/2 - x15/2 + x16/2 - x18/2 + x2/4 - x21 + x23 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2, // 2, 1, 1
710 : Point(0,0,0) // 2, 1, 2
711 : },
712 : {
713 1968 : -x0/8 - x1/8 + x10/4 + x11/4 - x16/4 - x17/4 - x18/4 - x19/4 - x2/8 - x20/2 + x25/2 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x8/4 + x9/4, // 2, 2, 0
714 1968 : x0/4 + x1/4 - x10/2 - x11/2 - x12/2 - x13/2 - x14/2 - x15/2 - x16/2 - x17/2 - x18/2 - x19/2 + x2/4 + x20 + x21 + x22 + x23 + x24 + x25 - 2*x26 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2 - x9/2, // 2, 2, 1
715 : Point(0,0,0) // 2, 2, 2
716 : }
717 : }
718 37392 : };
719 :
720 : // 3x3 quadrature, exact for bi-quintics
721 1968 : const int N = 3;
722 19027 : const Real w[N] = {5./9, 8./9, 5./9};
723 :
724 : // Quadrature point locations raised to powers. q[0][2] is
725 : // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
726 : // first power, etc.
727 19027 : const Real q[N][N] =
728 : {
729 : //^0 ^1 ^2
730 : { 1., -std::sqrt(15)/5., 15./25},
731 : { 1., 0., 0.},
732 : { 1., std::sqrt(15)/5., 15./25}
733 : };
734 :
735 1968 : Real vol = 0.;
736 76108 : for (int i=0; i<N; ++i)
737 228324 : for (int j=0; j<N; ++j)
738 684972 : for (int k=0; k<N; ++k)
739 : {
740 : // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
741 53136 : Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
742 2054916 : for (int ii=0; ii<N; ++ii)
743 6164748 : for (int jj=0; jj<N; ++jj)
744 18494244 : for (int kk=0; kk<N; ++kk)
745 : {
746 13870683 : Real coeff = q[i][ii] * q[j][jj] * q[k][kk];
747 :
748 1434672 : dx_dxi_q += coeff * dx_dxi[ii][jj][kk];
749 1434672 : dx_deta_q += coeff * dx_deta[ii][jj][kk];
750 1434672 : dx_dzeta_q += coeff * dx_dzeta[ii][jj][kk];
751 : }
752 :
753 : // Compute scalar triple product, multiply by weight, and accumulate volume.
754 555471 : vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
755 : }
756 :
757 1968 : return vol;
758 : }
759 :
760 :
761 :
762 :
763 :
764 :
765 :
766 : #ifdef LIBMESH_ENABLE_AMR
767 :
768 : const Real Hex27::_embedding_matrix[Hex27::num_children][Hex27::num_nodes][Hex27::num_nodes] =
769 : {
770 : // embedding matrix for child 0
771 : {
772 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
773 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
774 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
775 : { 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, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
776 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
777 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
778 : { 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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
779 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 6
780 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 7
781 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
782 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 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, 0.00000, 0.00000, 0.00000 }, // 9
783 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 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 }, // 10
784 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
785 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
786 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
787 : { 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, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.750000 }, // 14
788 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 15
789 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -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 }, // 16
790 : { 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, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 17
791 : { 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, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 18
792 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 19
793 : { 0.140625, -0.0468750, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, -0.0937500, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 20
794 : { 0.140625, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 21
795 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.281250, 0.281250, 0.00000, -0.0937500, 0.00000, -0.0937500, 0.562500 }, // 22
796 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.281250, 0.00000, -0.0937500, 0.00000, 0.281250, -0.0937500, 0.562500 }, // 23
797 : { 0.140625, 0.00000, 0.00000, -0.0468750, -0.0468750, 0.00000, 0.00000, 0.0156250, 0.00000, 0.00000, 0.00000, 0.281250, 0.281250, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000 }, // 24
798 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, -0.0468750, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, -0.0937500, 0.281250, 0.00000, 0.562500 }, // 25
799 : { 0.052734375, -0.017578125, 0.005859375, -0.017578125, -0.017578125, 0.005859375, -0.001953125, 0.005859375, 0.10546875, -0.03515625, -0.03515625, 0.10546875, 0.10546875, -0.03515625, 0.01171875, -0.03515625, -0.03515625, 0.01171875, 0.01171875, -0.03515625, 0.2109375, 0.2109375, -0.0703125, -0.0703125, 0.2109375, -0.0703125, 0.421875 } // 26
800 : },
801 :
802 : // embedding matrix for child 1
803 : {
804 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
805 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
806 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
807 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
808 : { 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, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
809 : { 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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
810 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
811 : { 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, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
812 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 7
813 : { -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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
814 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
815 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 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 }, // 10
816 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 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, 0.00000, 0.00000, 0.00000 }, // 11
817 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
818 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
819 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
820 : { 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, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.750000 }, // 15
821 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 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 }, // 16
822 : { 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, 0.375000, -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 }, // 17
823 : { 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, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.750000 }, // 18
824 : { 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, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 19
825 : { -0.0468750, 0.140625, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, 0.281250, -0.0937500, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 20
826 : { -0.0468750, 0.140625, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 21
827 : { 0.00000, 0.140625, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000 }, // 22
828 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.281250, 0.00000, 0.281250, 0.00000, -0.0937500, -0.0937500, 0.562500 }, // 23
829 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.281250, 0.281250, 0.00000, -0.0937500, 0.00000, -0.0937500, 0.562500 }, // 24
830 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.140625, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, 0.281250, -0.0937500, -0.0937500, 0.00000, 0.562500 }, // 25
831 : { -0.017578125, 0.052734375, -0.017578125, 0.005859375, 0.005859375, -0.017578125, 0.005859375, -0.001953125, 0.10546875, 0.10546875, -0.03515625, -0.03515625, -0.03515625, 0.10546875, -0.03515625, 0.01171875, -0.03515625, -0.03515625, 0.01171875, 0.01171875, 0.2109375, 0.2109375, 0.2109375, -0.0703125, -0.0703125, -0.0703125, 0.421875 } // 26
832 :
833 : },
834 :
835 : // embedding matrix for child 2
836 : {
837 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
838 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
839 : { 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, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
840 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
841 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
842 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 4
843 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 5
844 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 6
845 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
846 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 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 }, // 8
847 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 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, 0.00000, 0.00000, 0.00000 }, // 9
848 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
849 : { -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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
850 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 12
851 : { 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, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.750000 }, // 13
852 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 14
853 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
854 : { 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, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 16
855 : { 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, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.750000 }, // 17
856 : { 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, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 18
857 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 19
858 : { -0.0468750, 0.0156250, -0.0468750, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, -0.0937500, 0.281250, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 20
859 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.281250, 0.00000, -0.0937500, 0.00000, 0.281250, -0.0937500, 0.562500 }, // 21
860 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.281250, -0.0937500, 0.00000, 0.281250, 0.00000, -0.0937500, 0.562500 }, // 22
861 : { 0.00000, 0.00000, -0.0468750, 0.140625, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000 }, // 23
862 : { -0.0468750, 0.00000, 0.00000, 0.140625, 0.0156250, 0.00000, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000 }, // 24
863 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.0156250, -0.0468750, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, -0.0937500, 0.281250, 0.281250, 0.00000, 0.562500 }, // 25
864 : { -0.017578125, 0.005859375, -0.017578125, 0.052734375, 0.005859375, -0.001953125, 0.005859375, -0.017578125, -0.03515625, -0.03515625, 0.10546875, 0.10546875, -0.03515625, 0.01171875, -0.03515625, 0.10546875, 0.01171875, 0.01171875, -0.03515625, -0.03515625, 0.2109375, -0.0703125, -0.0703125, 0.2109375, 0.2109375, -0.0703125, 0.421875 } // 26
865 : },
866 :
867 : // embedding matrix for child 3
868 : {
869 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
870 : { 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, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
871 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
872 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
873 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
874 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 4
875 : { 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, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
876 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
877 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 7
878 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 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 }, // 8
879 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
880 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
881 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 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, 0.00000, 0.00000, 0.00000 }, // 11
882 : { 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, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.750000 }, // 12
883 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
884 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
885 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 15
886 : { 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, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.750000 }, // 16
887 : { 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, -0.125000, 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 }, // 17
888 : { 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, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 18
889 : { 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, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.750000 }, // 19
890 : { 0.0156250, -0.0468750, 0.140625, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.281250, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 20
891 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.281250, 0.00000, 0.281250, 0.00000, -0.0937500, -0.0937500, 0.562500 }, // 21
892 : { 0.00000, -0.0468750, 0.140625, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000 }, // 22
893 : { 0.00000, 0.00000, 0.140625, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000 }, // 23
894 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.281250, -0.0937500, 0.00000, 0.281250, 0.00000, -0.0937500, 0.562500 }, // 24
895 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.140625, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.281250, -0.0937500, 0.00000, 0.562500 }, // 25
896 : { 0.005859375, -0.017578125, 0.052734375, -0.017578125, -0.001953125, 0.005859375, -0.017578125, 0.005859375, -0.03515625, 0.10546875, 0.10546875, -0.03515625, 0.01171875, -0.03515625, 0.10546875, -0.03515625, 0.01171875, -0.03515625, -0.03515625, 0.01171875, 0.2109375, -0.0703125, 0.2109375, 0.2109375, -0.0703125, -0.0703125, 0.421875 } // 26
897 : },
898 :
899 : // embedding matrix for child 4
900 : {
901 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
902 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
903 : { 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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
904 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 2
905 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 3
906 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
907 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
908 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 6
909 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
910 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -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 }, // 8
911 : { 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, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 9
912 : { 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, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 10
913 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 11
914 : { -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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
915 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
916 : { 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, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000 }, // 14
917 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 15
918 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 16
919 : { 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, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 17
920 : { 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, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
921 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 19
922 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, -0.0468750, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, -0.0937500, 0.281250, 0.00000, 0.562500 }, // 20
923 : { -0.0468750, 0.0156250, 0.00000, 0.00000, 0.140625, -0.0468750, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 21
924 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, -0.0937500, 0.281250, 0.00000, -0.0937500, 0.00000, 0.281250, 0.562500 }, // 22
925 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, -0.0937500, 0.00000, -0.0937500, 0.00000, 0.281250, 0.281250, 0.562500 }, // 23
926 : { -0.0468750, 0.00000, 0.00000, 0.0156250, 0.140625, 0.00000, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000 }, // 24
927 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, -0.0468750, 0.0156250, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, -0.0937500, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000 }, // 25
928 : { -0.017578125, 0.005859375, -0.001953125, 0.005859375, 0.052734375, -0.017578125, 0.005859375, -0.017578125, -0.03515625, 0.01171875, 0.01171875, -0.03515625, 0.10546875, -0.03515625, 0.01171875, -0.03515625, 0.10546875, -0.03515625, -0.03515625, 0.10546875, -0.0703125, 0.2109375, -0.0703125, -0.0703125, 0.2109375, 0.2109375, 0.421875 } // 26
929 : },
930 :
931 : // embedding matrix for child 5
932 : {
933 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
934 : { 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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
935 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
936 : { 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, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
937 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 3
938 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
939 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
940 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
941 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 7
942 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 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 }, // 8
943 : { 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, 0.375000, -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 }, // 9
944 : { 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, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.750000 }, // 10
945 : { 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, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 11
946 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
947 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
948 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
949 : { 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, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000 }, // 15
950 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 16
951 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 17
952 : { 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, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
953 : { 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, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 19
954 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.140625, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, 0.281250, -0.0937500, -0.0937500, 0.00000, 0.562500 }, // 20
955 : { 0.0156250, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.140625, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 21
956 : { 0.00000, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.140625, -0.0468750, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000 }, // 22
957 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, -0.0937500, 0.00000, 0.281250, 0.00000, -0.0937500, 0.281250, 0.562500 }, // 23
958 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, 0.00000, -0.0937500, 0.281250, 0.00000, -0.0937500, 0.00000, 0.281250, 0.562500 }, // 24
959 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.140625, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.281250, 0.281250, -0.0937500, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000 }, // 25
960 : { 0.005859375, -0.017578125, 0.005859375, -0.001953125, -0.017578125, 0.052734375, -0.017578125, 0.005859375, -0.03515625, -0.03515625, 0.01171875, 0.01171875, -0.03515625, 0.10546875, -0.03515625, 0.01171875, 0.10546875, 0.10546875, -0.03515625, -0.03515625, -0.0703125, 0.2109375, 0.2109375, -0.0703125, -0.0703125, 0.2109375, 0.421875 } // 26
961 : },
962 :
963 : // embedding matrix for child 6
964 : {
965 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
966 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 0
967 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 1
968 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 2
969 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
970 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
971 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 5
972 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
973 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
974 : { 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, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 8
975 : { 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, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.750000 }, // 9
976 : { 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, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 10
977 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 11
978 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 12
979 : { 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, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000 }, // 13
980 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 14
981 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
982 : { 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, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 16
983 : { 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, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 17
984 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 18
985 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 19
986 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.0156250, -0.0468750, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, -0.0937500, 0.281250, 0.281250, 0.00000, 0.562500 }, // 20
987 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, -0.0937500, 0.00000, -0.0937500, 0.00000, 0.281250, 0.281250, 0.562500 }, // 21
988 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, -0.0937500, -0.0937500, 0.00000, 0.281250, 0.00000, 0.281250, 0.562500 }, // 22
989 : { 0.00000, 0.00000, 0.0156250, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.140625, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000 }, // 23
990 : { 0.0156250, 0.00000, 0.00000, -0.0468750, -0.0468750, 0.00000, 0.00000, 0.140625, 0.00000, 0.00000, 0.00000, -0.0937500, -0.0937500, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000 }, // 24
991 : { 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.0156250, -0.0468750, 0.140625, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, -0.0937500, 0.281250, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000 }, // 25
992 : { 0.005859375, -0.001953125, 0.005859375, -0.017578125, -0.017578125, 0.005859375, -0.017578125, 0.052734375, 0.01171875, 0.01171875, -0.03515625, -0.03515625, -0.03515625, 0.01171875, -0.03515625, 0.10546875, -0.03515625, -0.03515625, 0.10546875, 0.10546875, -0.0703125, -0.0703125, -0.0703125, 0.2109375, 0.2109375, 0.2109375, 0.421875 } // 26
993 : },
994 :
995 : // embedding matrix for child 7
996 : {
997 : // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
998 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 0
999 : { 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, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
1000 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
1001 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 3
1002 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 4
1003 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
1004 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
1005 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
1006 : { 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, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.750000 }, // 8
1007 : { 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, -0.125000, 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 }, // 9
1008 : { 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, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 10
1009 : { 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, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.750000 }, // 11
1010 : { 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, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000 }, // 12
1011 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
1012 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
1013 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 15
1014 : { 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, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 16
1015 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 17
1016 : { 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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 18
1017 : { 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, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 19
1018 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.140625, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.281250, -0.0937500, 0.00000, 0.562500 }, // 20
1019 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.0156250, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.140625, 0.00000, -0.0468750, -0.0937500, 0.00000, 0.281250, 0.00000, -0.0937500, 0.281250, 0.562500 }, // 21
1020 : { 0.00000, 0.0156250, -0.0468750, 0.00000, 0.00000, -0.0468750, 0.140625, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000, 0.00000 }, // 22
1021 : { 0.00000, 0.00000, -0.0468750, 0.0156250, 0.00000, 0.00000, 0.140625, -0.0468750, 0.00000, 0.00000, -0.0937500, 0.00000, 0.00000, 0.00000, 0.281250, -0.0937500, 0.00000, 0.00000, 0.281250, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000, 0.00000, 0.00000 }, // 23
1022 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, 0.00000, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0468750, 0.00000, 0.140625, 0.00000, -0.0937500, -0.0937500, 0.00000, 0.281250, 0.00000, 0.281250, 0.562500 }, // 24
1023 : { 0.00000, 0.00000, 0.00000, 0.00000, 0.0156250, -0.0468750, 0.140625, -0.0468750, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.0937500, 0.281250, 0.281250, -0.0937500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.562500, 0.00000 }, // 25
1024 : { -0.001953125, 0.005859375, -0.017578125, 0.005859375, 0.005859375, -0.017578125, 0.052734375, -0.017578125, 0.01171875, -0.03515625, -0.03515625, 0.01171875, 0.01171875, -0.03515625, 0.10546875, -0.03515625, -0.03515625, 0.10546875, 0.10546875, -0.03515625, -0.0703125, -0.0703125, 0.2109375, 0.2109375, -0.0703125, 0.2109375, 0.421875 } // 26
1025 : }
1026 : };
1027 :
1028 : #endif
1029 :
1030 :
1031 : void
1032 263334 : Hex27::permute(unsigned int perm_num)
1033 : {
1034 17676 : libmesh_assert_less (perm_num, 24);
1035 263334 : const unsigned int side = perm_num % 6;
1036 263334 : const unsigned int rotate = perm_num / 6;
1037 :
1038 662055 : for (unsigned int i = 0; i != rotate; ++i)
1039 : {
1040 398721 : swap4nodes(0,1,2,3);
1041 398721 : swap4nodes(4,5,6,7);
1042 398721 : swap4nodes(8,9,10,11);
1043 398721 : swap4nodes(12,13,14,15);
1044 398721 : swap4nodes(16,17,18,19);
1045 398721 : swap4nodes(21,22,23,24);
1046 371461 : swap4neighbors(1,2,3,4);
1047 : }
1048 :
1049 263334 : switch (side) {
1050 2786 : case 0:
1051 2786 : break;
1052 41842 : case 1:
1053 41842 : swap4nodes(3,7,4,0);
1054 41842 : swap4nodes(11,15,19,12);
1055 41842 : swap4nodes(10,18,16,8);
1056 41842 : swap4nodes(2,6,5,1);
1057 41842 : swap4nodes(9,14,17,13);
1058 41842 : swap4nodes(20,23,25,21);
1059 39008 : swap4neighbors(0,3,5,1);
1060 39008 : break;
1061 41532 : case 2:
1062 41532 : swap4nodes(0,4,5,1);
1063 41532 : swap4nodes(8,12,16,13);
1064 41532 : swap4nodes(3,7,6,2);
1065 41532 : swap4nodes(10,15,18,14);
1066 41532 : swap4nodes(11,19,17,9);
1067 41532 : swap4nodes(20,24,25,22);
1068 38768 : swap4neighbors(0,4,5,2);
1069 38768 : break;
1070 45890 : case 3:
1071 45890 : swap4nodes(0,4,7,3);
1072 45890 : swap4nodes(12,19,15,11);
1073 45890 : swap4nodes(8,16,18,10);
1074 45890 : swap4nodes(1,5,6,2);
1075 45890 : swap4nodes(13,17,14,9);
1076 45890 : swap4nodes(20,21,25,23);
1077 42894 : swap4neighbors(0,1,5,3);
1078 42894 : break;
1079 47573 : case 4:
1080 47573 : swap4nodes(1,5,4,0);
1081 47573 : swap4nodes(8,13,16,12);
1082 47573 : swap4nodes(9,17,19,11);
1083 47573 : swap4nodes(2,6,7,3);
1084 47573 : swap4nodes(10,14,18,15);
1085 47573 : swap4nodes(20,22,25,24);
1086 44473 : swap4neighbors(0,2,5,4);
1087 44473 : break;
1088 44655 : case 5:
1089 44655 : swap2nodes(0,7);
1090 44655 : swap2nodes(8,18);
1091 44655 : swap2nodes(1,6);
1092 44655 : swap2nodes(2,5);
1093 44655 : swap2nodes(10,16);
1094 44655 : swap2nodes(3,4);
1095 44655 : swap2nodes(11,19);
1096 44655 : swap2nodes(12,15);
1097 44655 : swap2nodes(9,17);
1098 44655 : swap2nodes(13,14);
1099 44655 : swap2nodes(20,25);
1100 44655 : swap2nodes(21,23);
1101 3196 : swap2neighbors(0,5);
1102 3196 : swap2neighbors(1,3);
1103 3196 : break;
1104 0 : default:
1105 0 : libmesh_error();
1106 : }
1107 263334 : }
1108 :
1109 :
1110 : void
1111 288 : Hex27::flip(BoundaryInfo * boundary_info)
1112 : {
1113 24 : libmesh_assert(boundary_info);
1114 :
1115 288 : swap2nodes(0,1);
1116 288 : swap2nodes(2,3);
1117 288 : swap2nodes(4,5);
1118 288 : swap2nodes(6,7);
1119 288 : swap2nodes(9,11);
1120 288 : swap2nodes(12,13);
1121 288 : swap2nodes(14,15);
1122 288 : swap2nodes(17,19);
1123 288 : swap2nodes(22,24);
1124 24 : swap2neighbors(2,4);
1125 288 : swap2boundarysides(2,4,boundary_info);
1126 288 : swap2boundaryedges(1,3,boundary_info);
1127 288 : swap2boundaryedges(4,5,boundary_info);
1128 288 : swap2boundaryedges(6,7,boundary_info);
1129 288 : swap2boundaryedges(9,11,boundary_info);
1130 288 : }
1131 :
1132 :
1133 576 : unsigned int Hex27::center_node_on_side(const unsigned short side) const
1134 : {
1135 48 : libmesh_assert_less (side, Hex27::num_sides);
1136 576 : return side + 20;
1137 : }
1138 :
1139 :
1140 : ElemType
1141 862908170 : Hex27::side_type (const unsigned int libmesh_dbg_var(s)) const
1142 : {
1143 68528410 : libmesh_assert_less (s, 6);
1144 862908170 : return QUAD9;
1145 : }
1146 :
1147 :
1148 : } // namespace libMesh
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