libMesh
cell_hex27.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2017 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 // C++ includes
20 
21 // Local includes
22 #include "libmesh/side.h"
23 #include "libmesh/cell_hex27.h"
24 #include "libmesh/edge_edge3.h"
25 #include "libmesh/face_quad9.h"
26 
27 namespace libMesh
28 {
29 
30 
31 
32 // ------------------------------------------------------------
33 // Hex27 class static member initializations
34 const unsigned int Hex27::side_nodes_map[6][9] =
35  {
36  {0, 3, 2, 1, 11, 10, 9, 8, 20}, // Side 0
37  {0, 1, 5, 4, 8, 13, 16, 12, 21}, // Side 1
38  {1, 2, 6, 5, 9, 14, 17, 13, 22}, // Side 2
39  {2, 3, 7, 6, 10, 15, 18, 14, 23}, // Side 3
40  {3, 0, 4, 7, 11, 12, 19, 15, 24}, // Side 4
41  {4, 5, 6, 7, 16, 17, 18, 19, 25} // Side 5
42  };
43 
44 const unsigned int Hex27::edge_nodes_map[12][3] =
45  {
46  {0, 1, 8}, // Edge 0
47  {1, 2, 9}, // Edge 1
48  {2, 3, 10}, // Edge 2
49  {0, 3, 11}, // Edge 3
50  {0, 4, 12}, // Edge 4
51  {1, 5, 13}, // Edge 5
52  {2, 6, 14}, // Edge 6
53  {3, 7, 15}, // Edge 7
54  {4, 5, 16}, // Edge 8
55  {5, 6, 17}, // Edge 9
56  {6, 7, 18}, // Edge 10
57  {4, 7, 19} // Edge 11
58  };
59 
60 
61 
62 // ------------------------------------------------------------
63 // Hex27 class member functions
64 
65 bool Hex27::is_vertex(const unsigned int i) const
66 {
67  if (i < 8)
68  return true;
69  return false;
70 }
71 
72 bool Hex27::is_edge(const unsigned int i) const
73 {
74  if (i < 8)
75  return false;
76  if (i > 19)
77  return false;
78  return true;
79 }
80 
81 bool Hex27::is_face(const unsigned int i) const
82 {
83  if (i == 26)
84  return false;
85  if (i > 19)
86  return true;
87  return false;
88 }
89 
90 bool Hex27::is_node_on_side(const unsigned int n,
91  const unsigned int s) const
92 {
93  libmesh_assert_less (s, n_sides());
94  for (unsigned int i = 0; i != 9; ++i)
95  if (side_nodes_map[s][i] == n)
96  return true;
97  return false;
98 }
99 
100 bool Hex27::is_node_on_edge(const unsigned int n,
101  const unsigned int e) const
102 {
103  libmesh_assert_less (e, n_edges());
104  for (unsigned int i = 0; i != 3; ++i)
105  if (edge_nodes_map[e][i] == n)
106  return true;
107  return false;
108 }
109 
110 
111 
112 bool Hex27::has_affine_map() const
113 {
114  // Make sure x-edge endpoints are affine
115  Point v = this->point(1) - this->point(0);
116  if (!v.relative_fuzzy_equals(this->point(2) - this->point(3)) ||
117  !v.relative_fuzzy_equals(this->point(5) - this->point(4)) ||
118  !v.relative_fuzzy_equals(this->point(6) - this->point(7)))
119  return false;
120  // Make sure x-edges are straight
121  // and x-face and center points are centered
122  v /= 2;
123  if (!v.relative_fuzzy_equals(this->point(8) - this->point(0)) ||
124  !v.relative_fuzzy_equals(this->point(10) - this->point(3)) ||
125  !v.relative_fuzzy_equals(this->point(16) - this->point(4)) ||
126  !v.relative_fuzzy_equals(this->point(18) - this->point(7)) ||
127  !v.relative_fuzzy_equals(this->point(20) - this->point(11)) ||
128  !v.relative_fuzzy_equals(this->point(21) - this->point(12)) ||
129  !v.relative_fuzzy_equals(this->point(23) - this->point(15)) ||
130  !v.relative_fuzzy_equals(this->point(25) - this->point(19)) ||
131  !v.relative_fuzzy_equals(this->point(26) - this->point(24)))
132  return false;
133  // Make sure xz-faces are identical parallelograms
134  v = this->point(4) - this->point(0);
135  if (!v.relative_fuzzy_equals(this->point(7) - this->point(3)))
136  return false;
137  v /= 2;
138  if (!v.relative_fuzzy_equals(this->point(12) - this->point(0)) ||
139  !v.relative_fuzzy_equals(this->point(13) - this->point(1)) ||
140  !v.relative_fuzzy_equals(this->point(14) - this->point(2)) ||
141  !v.relative_fuzzy_equals(this->point(15) - this->point(3)) ||
142  !v.relative_fuzzy_equals(this->point(22) - this->point(9)) ||
143  !v.relative_fuzzy_equals(this->point(24) - this->point(11)))
144  return false;
145  // Make sure y-edges are straight
146  v = (this->point(3) - this->point(0))/2;
147  if (!v.relative_fuzzy_equals(this->point(11) - this->point(0)) ||
148  !v.relative_fuzzy_equals(this->point(9) - this->point(1)) ||
149  !v.relative_fuzzy_equals(this->point(17) - this->point(5)) ||
150  !v.relative_fuzzy_equals(this->point(19) - this->point(4)))
151  return false;
152  // If all the above checks out, the map is affine
153  return true;
154 }
155 
156 
157 
158 dof_id_type Hex27::key (const unsigned int s) const
159 {
160  libmesh_assert_less (s, this->n_sides());
161 
162  // Think of a unit cube: (-1,1) x (-1,1) x (1,1)
163  switch (s)
164  {
165  case 0: // the face at z=0
166 
167  return
168  this->compute_key (this->node_id(20));
169 
170  case 1: // the face at y = 0
171 
172  return
173  this->compute_key (this->node_id(21));
174 
175  case 2: // the face at x=1
176 
177  return
178  this->compute_key (this->node_id(22));
179 
180  case 3: // the face at y=1
181 
182  return
183  this->compute_key (this->node_id(23));
184 
185  case 4: // the face at x=0
186 
187  return
188  this->compute_key (this->node_id(24));
189 
190  case 5: // the face at z=1
191 
192  return
193  this->compute_key (this->node_id(25));
194 
195  default:
196  libmesh_error_msg("Invalid side " << s);
197  }
198 
199  libmesh_error_msg("We'll never get here!");
200  return 0;
201 }
202 
203 
204 
205 unsigned int Hex27::which_node_am_i(unsigned int side,
206  unsigned int side_node) const
207 {
208  libmesh_assert_less (side, this->n_sides());
209  libmesh_assert_less (side_node, 9);
210 
211  return Hex27::side_nodes_map[side][side_node];
212 }
213 
214 
215 
216 UniquePtr<Elem> Hex27::build_side_ptr (const unsigned int i,
217  bool proxy)
218 {
219  libmesh_assert_less (i, this->n_sides());
220 
221  if (proxy)
222  return UniquePtr<Elem>(new Side<Quad9,Hex27>(this,i));
223 
224  else
225  {
226  Elem * face = new Quad9;
227  face->subdomain_id() = this->subdomain_id();
228 
229  for (unsigned n=0; n<face->n_nodes(); ++n)
230  face->set_node(n) = this->node_ptr(Hex27::side_nodes_map[i][n]);
231 
232  return UniquePtr<Elem>(face);
233  }
234 
235  libmesh_error_msg("We'll never get here!");
236  return UniquePtr<Elem>();
237 }
238 
239 
240 
241 UniquePtr<Elem> Hex27::build_edge_ptr (const unsigned int i)
242 {
243  libmesh_assert_less (i, this->n_edges());
244 
245  return UniquePtr<Elem>(new SideEdge<Edge3,Hex27>(this,i));
246 }
247 
248 
249 
250 void Hex27::connectivity(const unsigned int sc,
251  const IOPackage iop,
252  std::vector<dof_id_type> & conn) const
253 {
254  libmesh_assert(_nodes);
255  libmesh_assert_less (sc, this->n_sub_elem());
256  libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
257 
258  conn.resize(8);
259 
260  switch (iop)
261  {
262  case TECPLOT:
263  {
264  switch (sc)
265  {
266  case 0:
267 
268  conn[0] = this->node_id(0)+1;
269  conn[1] = this->node_id(8)+1;
270  conn[2] = this->node_id(20)+1;
271  conn[3] = this->node_id(11)+1;
272  conn[4] = this->node_id(12)+1;
273  conn[5] = this->node_id(21)+1;
274  conn[6] = this->node_id(26)+1;
275  conn[7] = this->node_id(24)+1;
276 
277  return;
278 
279  case 1:
280 
281  conn[0] = this->node_id(8)+1;
282  conn[1] = this->node_id(1)+1;
283  conn[2] = this->node_id(9)+1;
284  conn[3] = this->node_id(20)+1;
285  conn[4] = this->node_id(21)+1;
286  conn[5] = this->node_id(13)+1;
287  conn[6] = this->node_id(22)+1;
288  conn[7] = this->node_id(26)+1;
289 
290  return;
291 
292  case 2:
293 
294  conn[0] = this->node_id(11)+1;
295  conn[1] = this->node_id(20)+1;
296  conn[2] = this->node_id(10)+1;
297  conn[3] = this->node_id(3)+1;
298  conn[4] = this->node_id(24)+1;
299  conn[5] = this->node_id(26)+1;
300  conn[6] = this->node_id(23)+1;
301  conn[7] = this->node_id(15)+1;
302 
303  return;
304 
305  case 3:
306 
307  conn[0] = this->node_id(20)+1;
308  conn[1] = this->node_id(9)+1;
309  conn[2] = this->node_id(2)+1;
310  conn[3] = this->node_id(10)+1;
311  conn[4] = this->node_id(26)+1;
312  conn[5] = this->node_id(22)+1;
313  conn[6] = this->node_id(14)+1;
314  conn[7] = this->node_id(23)+1;
315 
316  return;
317 
318  case 4:
319 
320  conn[0] = this->node_id(12)+1;
321  conn[1] = this->node_id(21)+1;
322  conn[2] = this->node_id(26)+1;
323  conn[3] = this->node_id(24)+1;
324  conn[4] = this->node_id(4)+1;
325  conn[5] = this->node_id(16)+1;
326  conn[6] = this->node_id(25)+1;
327  conn[7] = this->node_id(19)+1;
328 
329  return;
330 
331  case 5:
332 
333  conn[0] = this->node_id(21)+1;
334  conn[1] = this->node_id(13)+1;
335  conn[2] = this->node_id(22)+1;
336  conn[3] = this->node_id(26)+1;
337  conn[4] = this->node_id(16)+1;
338  conn[5] = this->node_id(5)+1;
339  conn[6] = this->node_id(17)+1;
340  conn[7] = this->node_id(25)+1;
341 
342  return;
343 
344  case 6:
345 
346  conn[0] = this->node_id(24)+1;
347  conn[1] = this->node_id(26)+1;
348  conn[2] = this->node_id(23)+1;
349  conn[3] = this->node_id(15)+1;
350  conn[4] = this->node_id(19)+1;
351  conn[5] = this->node_id(25)+1;
352  conn[6] = this->node_id(18)+1;
353  conn[7] = this->node_id(7)+1;
354 
355  return;
356 
357  case 7:
358 
359  conn[0] = this->node_id(26)+1;
360  conn[1] = this->node_id(22)+1;
361  conn[2] = this->node_id(14)+1;
362  conn[3] = this->node_id(23)+1;
363  conn[4] = this->node_id(25)+1;
364  conn[5] = this->node_id(17)+1;
365  conn[6] = this->node_id(6)+1;
366  conn[7] = this->node_id(18)+1;
367 
368  return;
369 
370  default:
371  libmesh_error_msg("Invalid sc = " << sc);
372  }
373  }
374 
375  case VTK:
376  {
377  // VTK now supports VTK_TRIQUADRATIC_HEXAHEDRON directly
378  conn.resize(27);
379 
380  conn[0] = this->node_id(0);
381  conn[1] = this->node_id(1);
382  conn[2] = this->node_id(2);
383  conn[3] = this->node_id(3);
384  conn[4] = this->node_id(4);
385  conn[5] = this->node_id(5);
386  conn[6] = this->node_id(6);
387  conn[7] = this->node_id(7);
388  conn[8] = this->node_id(8);
389  conn[9] = this->node_id(9);
390  conn[10] = this->node_id(10);
391  conn[11] = this->node_id(11); //
392  conn[12] = this->node_id(16);
393  conn[13] = this->node_id(17);
394  conn[14] = this->node_id(18);
395  conn[15] = this->node_id(19);
396  conn[16] = this->node_id(12);
397  conn[17] = this->node_id(13); //
398  conn[18] = this->node_id(14);
399  conn[19] = this->node_id(15);
400  conn[20] = this->node_id(24);
401  conn[21] = this->node_id(22);
402  conn[22] = this->node_id(21);
403  conn[23] = this->node_id(23);
404  conn[24] = this->node_id(20);
405  conn[25] = this->node_id(25);
406  conn[26] = this->node_id(26);
407 
408  return;
409 
410  /*
411  switch (sc)
412  {
413  case 0:
414 
415  conn[0] = this->node_id(0);
416  conn[1] = this->node_id(8);
417  conn[2] = this->node_id(20);
418  conn[3] = this->node_id(11);
419  conn[4] = this->node_id(12);
420  conn[5] = this->node_id(21);
421  conn[6] = this->node_id(26);
422  conn[7] = this->node_id(24);
423 
424  return;
425 
426  case 1:
427 
428  conn[0] = this->node_id(8);
429  conn[1] = this->node_id(1);
430  conn[2] = this->node_id(9);
431  conn[3] = this->node_id(20);
432  conn[4] = this->node_id(21);
433  conn[5] = this->node_id(13);
434  conn[6] = this->node_id(22);
435  conn[7] = this->node_id(26);
436 
437  return;
438 
439  case 2:
440 
441  conn[0] = this->node_id(11);
442  conn[1] = this->node_id(20);
443  conn[2] = this->node_id(10);
444  conn[3] = this->node_id(3);
445  conn[4] = this->node_id(24);
446  conn[5] = this->node_id(26);
447  conn[6] = this->node_id(23);
448  conn[7] = this->node_id(15);
449 
450  return;
451 
452  case 3:
453 
454  conn[0] = this->node_id(20);
455  conn[1] = this->node_id(9);
456  conn[2] = this->node_id(2);
457  conn[3] = this->node_id(10);
458  conn[4] = this->node_id(26);
459  conn[5] = this->node_id(22);
460  conn[6] = this->node_id(14);
461  conn[7] = this->node_id(23);
462 
463  return;
464 
465  case 4:
466 
467  conn[0] = this->node_id(12);
468  conn[1] = this->node_id(21);
469  conn[2] = this->node_id(26);
470  conn[3] = this->node_id(24);
471  conn[4] = this->node_id(4);
472  conn[5] = this->node_id(16);
473  conn[6] = this->node_id(25);
474  conn[7] = this->node_id(19);
475 
476  return;
477 
478  case 5:
479 
480  conn[0] = this->node_id(21);
481  conn[1] = this->node_id(13);
482  conn[2] = this->node_id(22);
483  conn[3] = this->node_id(26);
484  conn[4] = this->node_id(16);
485  conn[5] = this->node_id(5);
486  conn[6] = this->node_id(17);
487  conn[7] = this->node_id(25);
488 
489  return;
490 
491  case 6:
492 
493  conn[0] = this->node_id(24);
494  conn[1] = this->node_id(26);
495  conn[2] = this->node_id(23);
496  conn[3] = this->node_id(15);
497  conn[4] = this->node_id(19);
498  conn[5] = this->node_id(25);
499  conn[6] = this->node_id(18);
500  conn[7] = this->node_id(7);
501 
502  return;
503 
504  case 7:
505 
506  conn[0] = this->node_id(26);
507  conn[1] = this->node_id(22);
508  conn[2] = this->node_id(14);
509  conn[3] = this->node_id(23);
510  conn[4] = this->node_id(25);
511  conn[5] = this->node_id(17);
512  conn[6] = this->node_id(6);
513  conn[7] = this->node_id(18);
514 
515  return;
516 
517  default:
518  libmesh_error_msg("Invalid sc = " << sc);
519  }
520  */
521  }
522 
523  default:
524  libmesh_error_msg("Unsupported IO package " << iop);
525  }
526 }
527 
528 
529 
530 
531 
532 unsigned int Hex27::n_second_order_adjacent_vertices (const unsigned int n) const
533 {
534  switch (n)
535  {
536  case 8:
537  case 9:
538  case 10:
539  case 11:
540  case 12:
541  case 13:
542  case 14:
543  case 15:
544  case 16:
545  case 17:
546  case 18:
547  case 19:
548  return 2;
549 
550  case 20:
551  case 21:
552  case 22:
553  case 23:
554  case 24:
555  case 25:
556  return 4;
557 
558  case 26:
559  return 8;
560 
561  default:
562  libmesh_error_msg("Invalid node number n = " << n);
563  }
564 
565  libmesh_error_msg("We'll never get here!");
566  return libMesh::invalid_uint;
567 }
568 
569 
570 
571 unsigned short int Hex27::second_order_adjacent_vertex (const unsigned int n,
572  const unsigned int v) const
573 {
574  libmesh_assert_greater_equal (n, this->n_vertices());
575  libmesh_assert_less (n, this->n_nodes());
576 
577  switch (n)
578  {
579  /*
580  * these are all nodes that are unique to Hex27,
581  * use our _remaining.... matrix
582  */
583  case 20:
584  case 21:
585  case 22:
586  case 23:
587  case 24:
588  case 25:
589  {
590  libmesh_assert_less (v, 4);
591  return _remaining_second_order_adjacent_vertices[n-20][v];
592  }
593 
594  /*
595  * for the bubble node the return value is simply v.
596  * Why? -- the user asks for the v-th adjacent vertex,
597  * from \p n_second_order_adjacent_vertices() there
598  * are 8 adjacent vertices, and these happen to be
599  * 0..7
600  */
601  case 26:
602  {
603  libmesh_assert_less (v, 8);
604  return static_cast<unsigned short int>(v);
605  }
606 
607  /*
608  * nodes 8..19:
609  * these are all nodes that are identical for
610  * Hex20 and Hex27. Therefore use the
611  * matrix stored in cell_hex.C
612  */
613  default:
614  {
615  libmesh_assert_less (v, 2);
616  return _second_order_adjacent_vertices[n-this->n_vertices()][v];
617  }
618  }
619 }
620 
621 
622 
623 const unsigned short int Hex27::_remaining_second_order_adjacent_vertices[6][4] =
624  {
625  { 0, 1, 2, 3}, // vertices adjacent to node 20 face nodes
626  { 0, 1, 4, 5}, // vertices adjacent to node 21
627  { 1, 2, 5, 6}, // vertices adjacent to node 22
628  { 2, 3, 6, 7}, // vertices adjacent to node 23
629  { 0, 3, 4, 7}, // vertices adjacent to node 24
630  { 4, 5, 6, 7}, // vertices adjacent to node 25
631  };
632 
633 
634 
635 std::pair<unsigned short int, unsigned short int>
636 Hex27::second_order_child_vertex (const unsigned int n) const
637 {
638  libmesh_assert_greater_equal (n, this->n_vertices());
639  libmesh_assert_less (n, this->n_nodes());
640  /*
641  * the _second_order_vertex_child_* vectors are
642  * stored in cell_hex.C, since they are identical
643  * for Hex20 and Hex27 (for the first 12 higher-order nodes)
644  */
645  return std::pair<unsigned short int, unsigned short int>
646  (_second_order_vertex_child_number[n],
647  _second_order_vertex_child_index[n]);
648 }
649 
650 
651 
652 Real Hex27::volume () const
653 {
654  // Make copies of our points. It makes the subsequent calculations a bit
655  // shorter and avoids dereferencing the same pointer multiple times.
656  Point
657  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),
658  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),
659  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);
660 
661  // The constant components of the dx/dxi vector,
662  // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
663  // All of the xi^2 terms are zero.
664  // These were copied directly from the output of a Python script.
665  Point dx_dxi[3][3][3] =
666  {
667  {
668  {
669  x22/2 - x24/2, // 0, 0, 0
670  x11/4 + x17/4 - x19/4 - x9/4, // 0, 0, 1
671  -x11/4 + x17/4 - x19/4 - x22/2 + x24/2 + x9/4 // 0, 0, 2
672  },
673 
674  {
675  x12/4 - x13/4 + x14/4 - x15/4, // 0, 1, 0
676  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 0, 1, 1
677  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
678  },
679 
680  {
681  -x12/4 + x13/4 + x14/4 - x15/4 - x22/2 + x24/2, // 0, 2, 0
682  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
683  -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
684  }
685  },
686  {
687  {
688  x22 + x24 - 2*x26, // 1, 0, 0
689  -x11/2 + x17/2 + x19/2 + x20 - x25 - x9/2, // 1, 0, 1
690  x11/2 + x17/2 + x19/2 - x20 - x22 - x24 - x25 + 2*x26 + x9/2 // 1, 0, 2
691  },
692 
693  {
694  -x12/2 - x13/2 + x14/2 + x15/2 + x21 - x23, // 1, 1, 0
695  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
696  -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
697  },
698 
699  {
700  x12/2 + x13/2 + x14/2 + x15/2 - x21 - x22 - x23 - x24 + 2*x26, // 1, 2, 0
701  -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
702  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
703  }
704  },
705  {
706  {Point(0,0,0), Point(0,0,0), Point(0,0,0)},
707  {Point(0,0,0), Point(0,0,0), Point(0,0,0)},
708  {Point(0,0,0), Point(0,0,0), Point(0,0,0)}
709  }
710  };
711 
712 
713 
714  // The constant components of the dx/deta vector, all of the eta^2
715  // terms are zero. These were copied directly from the output of a
716  // Python script.
717  Point dx_deta[3][3][3] =
718  {
719  {
720  {
721  -x21/2 + x23/2, // 0, 0, 0
722  -x10/4 - x16/4 + x18/4 + x8/4, // 0, 0, 1
723  x10/4 - x16/4 + x18/4 + x21/2 - x23/2 - x8/4 // 0, 0, 2
724  },
725  {
726  x21 + x23 - 2*x26, // 0, 1, 0
727  -x10/2 + x16/2 + x18/2 + x20 - x25 - x8/2, // 0, 1, 1
728  x10/2 + x16/2 + x18/2 - x20 - x21 - x23 - x25 + 2*x26 + x8/2 // 0, 1, 2
729  },
730  {
731  Point(0,0,0), // 0, 2, 0
732  Point(0,0,0), // 0, 2, 1
733  Point(0,0,0) // 0, 2, 2
734  }
735  },
736 
737  {
738  {
739  x12/4 - x13/4 + x14/4 - x15/4, // 1, 0, 0
740  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 1, 0, 1
741  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
742  },
743  {
744  -x12/2 + x13/2 + x14/2 - x15/2 - x22 + x24, // 1, 1, 0
745  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
746  -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
747  },
748  {
749  Point(0,0,0), // 1, 2, 0
750  Point(0,0,0), // 1, 2, 1
751  Point(0,0,0) // 1, 2, 2
752  }
753  },
754 
755  {
756  {
757  -x12/4 - x13/4 + x14/4 + x15/4 + x21/2 - x23/2, // 2, 0, 0
758  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
759  -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
760  },
761  {
762  x12/2 + x13/2 + x14/2 + x15/2 - x21 - x22 - x23 - x24 + 2*x26, // 2, 1, 0
763  -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
764  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
765  },
766  {
767  Point(0,0,0), // 2, 2, 0
768  Point(0,0,0), // 2, 2, 1
769  Point(0,0,0) // 2, 2, 2
770  }
771  }
772  };
773 
774 
775 
776  // The constant components of the dx/dzeta vector, all of the zeta^2
777  // terms are zero. These were copied directly from the output of a
778  // Python script.
779  Point dx_dzeta[3][3][3] =
780  {
781  {
782  {
783  -x20/2 + x25/2, // 0, 0, 0
784  x20 + x25 - 2*x26, // 0, 0, 1
785  Point(0,0,0) // 0, 0, 2
786  },
787  {
788  -x10/4 - x16/4 + x18/4 + x8/4, // 0, 1, 0
789  x10/2 - x16/2 + x18/2 + x21 - x23 - x8/2, // 0, 1, 1
790  Point(0,0,0) // 0, 1, 2
791  },
792  {
793  -x10/4 + x16/4 + x18/4 + x20/2 - x25/2 - x8/4, // 0, 2, 0
794  x10/2 + x16/2 + x18/2 - x20 - x21 - x23 - x25 + 2*x26 + x8/2, // 0, 2, 1
795  Point(0,0,0) // 0, 2, 2
796  }
797  },
798  {
799  {
800  x11/4 + x17/4 - x19/4 - x9/4, // 1, 0, 0
801  -x11/2 + x17/2 - x19/2 - x22 + x24 + x9/2, // 1, 0, 1
802  Point(0,0,0) // 1, 0, 2
803  },
804  {
805  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8, // 1, 1, 0
806  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
807  Point(0,0,0) // 1, 1, 2
808  },
809  {
810  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
811  -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
812  Point(0,0,0) // 1, 2, 2
813  }
814  },
815  {
816  {
817  -x11/4 + x17/4 + x19/4 + x20/2 - x25/2 - x9/4, // 2, 0, 0
818  x11/2 + x17/2 + x19/2 - x20 - x22 - x24 - x25 + 2*x26 + x9/2, // 2, 0, 1
819  Point(0,0,0) // 2, 0, 2
820  },
821  {
822  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
823  -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
824  Point(0,0,0) // 2, 1, 2
825  },
826  {
827  -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
828  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
829  Point(0,0,0) // 2, 2, 2
830  }
831  }
832  };
833 
834  // 3x3 quadrature, exact for bi-quintics
835  const int N = 3;
836  const Real w[N] = {5./9, 8./9, 5./9};
837 
838  // Quadrature point locations raised to powers. q[0][2] is
839  // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
840  // first power, etc.
841  const Real q[N][N] =
842  {
843  //^0 ^1 ^2
844  { 1., -std::sqrt(15)/5., 15./25},
845  { 1., 0., 0.},
846  { 1., std::sqrt(15)/5., 15./25}
847  };
848 
849  Real vol = 0.;
850  for (int i=0; i<N; ++i)
851  for (int j=0; j<N; ++j)
852  for (int k=0; k<N; ++k)
853  {
854  // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
855  Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
856  for (int ii=0; ii<N; ++ii)
857  for (int jj=0; jj<N; ++jj)
858  for (int kk=0; kk<N; ++kk)
859  {
860  Real coeff = q[i][ii] * q[j][jj] * q[k][kk];
861 
862  dx_dxi_q += coeff * dx_dxi[ii][jj][kk];
863  dx_deta_q += coeff * dx_deta[ii][jj][kk];
864  dx_dzeta_q += coeff * dx_dzeta[ii][jj][kk];
865  }
866 
867  // Compute scalar triple product, multiply by weight, and accumulate volume.
868  vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
869  }
870 
871  return vol;
872 }
873 
874 
875 
876 
877 
878 
879 
880 #ifdef LIBMESH_ENABLE_AMR
881 
882 const float Hex27::_embedding_matrix[8][27][27] =
883  {
884  // embedding matrix for child 0
885  {
886  // 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
887  { 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
888  { 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
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, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
890  { 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
891  { 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
892  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
893  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
894  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
895  { 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
896  { 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
897  { 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
898  { 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
899  { 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
900  { 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
901  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
902  { 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
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, 0.375000, -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
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, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 17
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, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 18
906  { 0.00000, 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
907  { 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
908  { 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
909  { 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
910  { 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
911  { 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
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, 0.140625, -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
913  { 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
914  },
915 
916  // embedding matrix for child 1
917  {
918  // 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
919  { 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
920  { 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
921  { 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
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, 0.00000, 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
923  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
924  { 0.00000, 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
925  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
926  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
927  { -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
928  { 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
929  { 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
930  { 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
931  { 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
932  { 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
933  { 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
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, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.750000 }, // 15
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, -0.125000, 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
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, 0.375000, -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
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, 0.375000, 0.00000, -0.125000, 0.00000, 0.750000 }, // 18
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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, -0.125000, 0.00000, 0.00000, 0.750000 }, // 19
939  { -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
940  { -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
941  { 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
942  { 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
943  { 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
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, -0.0468750, 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
945  { -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
946 
947  },
948 
949  // embedding matrix for child 2
950  {
951  // 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
952  { 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
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, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
954  { 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
955  { 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
956  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
957  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
958  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
959  { 0.00000, 0.00000, 0.00000, 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
960  { 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
961  { 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
962  { 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
963  { -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
964  { 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
965  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
966  { 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
967  { 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
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, -0.125000, 0.00000, 0.375000, 0.00000, 0.750000 }, // 16
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, 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
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, -0.125000, 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
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, -0.125000, 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
972  { -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
973  { 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
974  { 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
975  { 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
976  { -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
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, -0.0468750, 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
978  { -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
979  },
980 
981  // embedding matrix for child 3
982  {
983  // 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
984  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
985  { 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
986  { 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
987  { 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
988  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
989  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
990  { 0.00000, 0.00000, 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
991  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
992  { 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
993  { 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
994  { 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
995  { 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
996  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
997  { 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
998  { 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
999  { 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
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, 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
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, -0.125000, 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
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, 0.375000, -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
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, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.375000, 0.00000, 0.00000, 0.750000 }, // 19
1004  { 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
1005  { 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
1006  { 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
1007  { 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
1008  { 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
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, 0.0156250, -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
1010  { 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
1011  },
1012 
1013  // embedding matrix for child 4
1014  {
1015  // 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
1016  { 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
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, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
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, 0.00000, 0.00000, 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
1019  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1020  { 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
1021  { 0.00000, 0.00000, 0.00000, 0.00000, 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
1022  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1023  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1024  { 0.00000, 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
1025  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1026  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1027  { 0.00000, 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
1028  { -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
1029  { 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
1030  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1031  { 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
1032  { 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
1033  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1034  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1035  { 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
1036  { 0.00000, 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
1037  { -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
1038  { 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
1039  { 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
1040  { -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
1041  { 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
1042  { -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
1043  },
1044 
1045  // embedding matrix for child 5
1046  {
1047  // 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
1048  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1049  { 0.00000, 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
1050  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1051  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1052  { 0.00000, 0.00000, 0.00000, 0.00000, 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
1053  { 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
1054  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1055  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1056  { 0.00000, 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
1057  { 0.00000, 0.00000, 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
1058  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1059  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1060  { 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
1061  { 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
1062  { 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
1063  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1064  { 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
1065  { 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
1066  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1067  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1068  { 0.00000, 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
1069  { 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
1070  { 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
1071  { 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
1072  { 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
1073  { 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
1074  { 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
1075  },
1076 
1077  // embedding matrix for child 6
1078  {
1079  // 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
1080  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1081  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1082  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1083  { 0.00000, 0.00000, 0.00000, 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
1084  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1085  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1086  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1087  { 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
1088  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1089  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1090  { 0.00000, 0.00000, 0.00000, 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
1091  { 0.00000, 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
1092  { 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
1093  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1094  { 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
1095  { 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
1096  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1097  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1098  { 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
1099  { 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
1100  { 0.00000, 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
1101  { 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
1102  { 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
1103  { 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
1104  { 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
1105  { 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
1106  { 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
1107  },
1108 
1109  // embedding matrix for child 7
1110  {
1111  // 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
1112  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1113  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1114  { 0.00000, 0.00000, 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
1115  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1116  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1117  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1118  { 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
1119  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1120  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1121  { 0.00000, 0.00000, 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
1122  { 0.00000, 0.00000, 0.00000, 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
1123  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1124  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1125  { 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
1126  { 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
1127  { 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
1128  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1129  { 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
1130  { 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
1131  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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
1132  { 0.00000, 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
1133  { 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
1134  { 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
1135  { 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
1136  { 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
1137  { 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
1138  { -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
1139  }
1140  };
1141 
1142 #endif
1143 
1144 } // namespace libMesh
const unsigned int invalid_uint
A number which is used quite often to represent an invalid or uninitialized value.
Definition: libmesh.h:184
unsigned short int side
Definition: xdr_io.C:49
The libMesh namespace provides an interface to certain functionality in the library.
libmesh_assert(j)
T triple_product(const TypeVector< T > &a, const TypeVector< T > &b, const TypeVector< T > &c)
Definition: type_vector.h:1051
const dof_id_type n_nodes
Definition: tecplot_io.C:67
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
IOPackage
libMesh interfaces with several different software packages for the purposes of creating, reading, and writing mesh files.
uint8_t dof_id_type
Definition: id_types.h:64