cell_hex27.C
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00001 // The libMesh Finite Element Library. 00002 // Copyright (C) 2002-2014 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner 00003 00004 // This library is free software; you can redistribute it and/or 00005 // modify it under the terms of the GNU Lesser General Public 00006 // License as published by the Free Software Foundation; either 00007 // version 2.1 of the License, or (at your option) any later version. 00008 00009 // This library is distributed in the hope that it will be useful, 00010 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00011 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00012 // Lesser General Public License for more details. 00013 00014 // You should have received a copy of the GNU Lesser General Public 00015 // License along with this library; if not, write to the Free Software 00016 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 00017 00018 00019 // C++ includes 00020 00021 // Local includes 00022 #include "libmesh/side.h" 00023 #include "libmesh/cell_hex27.h" 00024 #include "libmesh/edge_edge3.h" 00025 #include "libmesh/face_quad9.h" 00026 00027 namespace libMesh 00028 { 00029 00030 00031 00032 // ------------------------------------------------------------ 00033 // Hex27 class static member initializations 00034 const unsigned int Hex27::side_nodes_map[6][9] = 00035 { 00036 {0, 3, 2, 1, 11, 10, 9, 8, 20}, // Side 0 00037 {0, 1, 5, 4, 8, 13, 16, 12, 21}, // Side 1 00038 {1, 2, 6, 5, 9, 14, 17, 13, 22}, // Side 2 00039 {2, 3, 7, 6, 10, 15, 18, 14, 23}, // Side 3 00040 {3, 0, 4, 7, 11, 12, 19, 15, 24}, // Side 4 00041 {4, 5, 6, 7, 16, 17, 18, 19, 25} // Side 5 00042 }; 00043 00044 const unsigned int Hex27::edge_nodes_map[12][3] = 00045 { 00046 {0, 1, 8}, // Side 0 00047 {1, 2, 9}, // Side 1 00048 {2, 3, 10}, // Side 2 00049 {0, 3, 11}, // Side 3 00050 {0, 4, 12}, // Side 4 00051 {1, 5, 13}, // Side 5 00052 {2, 6, 14}, // Side 6 00053 {3, 7, 15}, // Side 7 00054 {4, 5, 16}, // Side 8 00055 {5, 6, 17}, // Side 9 00056 {6, 7, 18}, // Side 10 00057 {4, 7, 19} // Side 11 00058 }; 00059 00060 00061 00062 // ------------------------------------------------------------ 00063 // Hex27 class member functions 00064 00065 bool Hex27::is_vertex(const unsigned int i) const 00066 { 00067 if (i < 8) 00068 return true; 00069 return false; 00070 } 00071 00072 bool Hex27::is_edge(const unsigned int i) const 00073 { 00074 if (i < 8) 00075 return false; 00076 if (i > 19) 00077 return false; 00078 return true; 00079 } 00080 00081 bool Hex27::is_face(const unsigned int i) const 00082 { 00083 if (i == 26) 00084 return false; 00085 if (i > 19) 00086 return true; 00087 return false; 00088 } 00089 00090 bool Hex27::is_node_on_side(const unsigned int n, 00091 const unsigned int s) const 00092 { 00093 libmesh_assert_less (s, n_sides()); 00094 for (unsigned int i = 0; i != 9; ++i) 00095 if (side_nodes_map[s][i] == n) 00096 return true; 00097 return false; 00098 } 00099 00100 bool Hex27::is_node_on_edge(const unsigned int n, 00101 const unsigned int e) const 00102 { 00103 libmesh_assert_less (e, n_edges()); 00104 for (unsigned int i = 0; i != 3; ++i) 00105 if (edge_nodes_map[e][i] == n) 00106 return true; 00107 return false; 00108 } 00109 00110 00111 00112 bool Hex27::has_affine_map() const 00113 { 00114 // Make sure x-edge endpoints are affine 00115 Point v = this->point(1) - this->point(0); 00116 if (!v.relative_fuzzy_equals(this->point(2) - this->point(3)) || 00117 !v.relative_fuzzy_equals(this->point(5) - this->point(4)) || 00118 !v.relative_fuzzy_equals(this->point(6) - this->point(7))) 00119 return false; 00120 // Make sure x-edges are straight 00121 // and x-face and center points are centered 00122 v /= 2; 00123 if (!v.relative_fuzzy_equals(this->point(8) - this->point(0)) || 00124 !v.relative_fuzzy_equals(this->point(10) - this->point(3)) || 00125 !v.relative_fuzzy_equals(this->point(16) - this->point(4)) || 00126 !v.relative_fuzzy_equals(this->point(18) - this->point(7)) || 00127 !v.relative_fuzzy_equals(this->point(20) - this->point(11)) || 00128 !v.relative_fuzzy_equals(this->point(21) - this->point(12)) || 00129 !v.relative_fuzzy_equals(this->point(23) - this->point(15)) || 00130 !v.relative_fuzzy_equals(this->point(25) - this->point(19)) || 00131 !v.relative_fuzzy_equals(this->point(26) - this->point(24))) 00132 return false; 00133 // Make sure xz-faces are identical parallelograms 00134 v = this->point(4) - this->point(0); 00135 if (!v.relative_fuzzy_equals(this->point(7) - this->point(3))) 00136 return false; 00137 v /= 2; 00138 if (!v.relative_fuzzy_equals(this->point(12) - this->point(0)) || 00139 !v.relative_fuzzy_equals(this->point(13) - this->point(1)) || 00140 !v.relative_fuzzy_equals(this->point(14) - this->point(2)) || 00141 !v.relative_fuzzy_equals(this->point(15) - this->point(3)) || 00142 !v.relative_fuzzy_equals(this->point(22) - this->point(9)) || 00143 !v.relative_fuzzy_equals(this->point(24) - this->point(11))) 00144 return false; 00145 // Make sure y-edges are straight 00146 v = (this->point(3) - this->point(0))/2; 00147 if (!v.relative_fuzzy_equals(this->point(11) - this->point(0)) || 00148 !v.relative_fuzzy_equals(this->point(9) - this->point(1)) || 00149 !v.relative_fuzzy_equals(this->point(17) - this->point(5)) || 00150 !v.relative_fuzzy_equals(this->point(19) - this->point(4))) 00151 return false; 00152 // If all the above checks out, the map is affine 00153 return true; 00154 } 00155 00156 00157 00158 dof_id_type Hex27::key (const unsigned int s) const 00159 { 00160 libmesh_assert_less (s, this->n_sides()); 00161 00162 // Think of a unit cube: (-1,1) x (-1,1) x (1,1) 00163 switch (s) 00164 { 00165 case 0: // the face at z=0 00166 00167 return 00168 this->compute_key (this->node(20)); 00169 00170 case 1: // the face at y = 0 00171 00172 return 00173 this->compute_key (this->node(21)); 00174 00175 case 2: // the face at x=1 00176 00177 return 00178 this->compute_key (this->node(22)); 00179 00180 case 3: // the face at y=1 00181 00182 return 00183 this->compute_key (this->node(23)); 00184 00185 case 4: // the face at x=0 00186 00187 return 00188 this->compute_key (this->node(24)); 00189 00190 case 5: // the face at z=1 00191 00192 return 00193 this->compute_key (this->node(25)); 00194 00195 default: 00196 libmesh_error_msg("Invalid side " << s); 00197 } 00198 00199 libmesh_error_msg("We'll never get here!"); 00200 return 0; 00201 } 00202 00203 00204 00205 UniquePtr<Elem> Hex27::build_side (const unsigned int i, 00206 bool proxy) const 00207 { 00208 libmesh_assert_less (i, this->n_sides()); 00209 00210 if (proxy) 00211 return UniquePtr<Elem>(new Side<Quad9,Hex27>(this,i)); 00212 00213 else 00214 { 00215 Elem* face = new Quad9; 00216 face->subdomain_id() = this->subdomain_id(); 00217 00218 // Think of a unit cube: (-1,1) x (-1,1) x (1,1) 00219 switch (i) 00220 { 00221 case 0: // the face at z=0 00222 { 00223 face->set_node(0) = this->get_node(0); 00224 face->set_node(1) = this->get_node(3); 00225 face->set_node(2) = this->get_node(2); 00226 face->set_node(3) = this->get_node(1); 00227 face->set_node(4) = this->get_node(11); 00228 face->set_node(5) = this->get_node(10); 00229 face->set_node(6) = this->get_node(9); 00230 face->set_node(7) = this->get_node(8); 00231 face->set_node(8) = this->get_node(20); 00232 break; 00233 } 00234 case 1: // the face at y = 0 00235 { 00236 face->set_node(0) = this->get_node(0); 00237 face->set_node(1) = this->get_node(1); 00238 face->set_node(2) = this->get_node(5); 00239 face->set_node(3) = this->get_node(4); 00240 face->set_node(4) = this->get_node(8); 00241 face->set_node(5) = this->get_node(13); 00242 face->set_node(6) = this->get_node(16); 00243 face->set_node(7) = this->get_node(12); 00244 face->set_node(8) = this->get_node(21); 00245 break; 00246 } 00247 case 2: // the face at x=1 00248 { 00249 face->set_node(0) = this->get_node(1); 00250 face->set_node(1) = this->get_node(2); 00251 face->set_node(2) = this->get_node(6); 00252 face->set_node(3) = this->get_node(5); 00253 face->set_node(4) = this->get_node(9); 00254 face->set_node(5) = this->get_node(14); 00255 face->set_node(6) = this->get_node(17); 00256 face->set_node(7) = this->get_node(13); 00257 face->set_node(8) = this->get_node(22); 00258 break; 00259 } 00260 case 3: // the face at y=1 00261 { 00262 face->set_node(0) = this->get_node(2); 00263 face->set_node(1) = this->get_node(3); 00264 face->set_node(2) = this->get_node(7); 00265 face->set_node(3) = this->get_node(6); 00266 face->set_node(4) = this->get_node(10); 00267 face->set_node(5) = this->get_node(15); 00268 face->set_node(6) = this->get_node(18); 00269 face->set_node(7) = this->get_node(14); 00270 face->set_node(8) = this->get_node(23); 00271 break; 00272 } 00273 case 4: // the face at x=0 00274 { 00275 face->set_node(0) = this->get_node(3); 00276 face->set_node(1) = this->get_node(0); 00277 face->set_node(2) = this->get_node(4); 00278 face->set_node(3) = this->get_node(7); 00279 face->set_node(4) = this->get_node(11); 00280 face->set_node(5) = this->get_node(12); 00281 face->set_node(6) = this->get_node(19); 00282 face->set_node(7) = this->get_node(15); 00283 face->set_node(8) = this->get_node(24); 00284 break; 00285 } 00286 case 5: // the face at z=1 00287 { 00288 face->set_node(0) = this->get_node(4); 00289 face->set_node(1) = this->get_node(5); 00290 face->set_node(2) = this->get_node(6); 00291 face->set_node(3) = this->get_node(7); 00292 face->set_node(4) = this->get_node(16); 00293 face->set_node(5) = this->get_node(17); 00294 face->set_node(6) = this->get_node(18); 00295 face->set_node(7) = this->get_node(19); 00296 face->set_node(8) = this->get_node(25); 00297 break; 00298 } 00299 default: 00300 libmesh_error_msg("Invalid side i = " << i); 00301 } 00302 00303 return UniquePtr<Elem>(face); 00304 } 00305 00306 libmesh_error_msg("We'll never get here!"); 00307 return UniquePtr<Elem>(); 00308 } 00309 00310 00311 00312 UniquePtr<Elem> Hex27::build_edge (const unsigned int i) const 00313 { 00314 libmesh_assert_less (i, this->n_edges()); 00315 00316 return UniquePtr<Elem>(new SideEdge<Edge3,Hex27>(this,i)); 00317 } 00318 00319 00320 00321 void Hex27::connectivity(const unsigned int sc, 00322 const IOPackage iop, 00323 std::vector<dof_id_type>& conn) const 00324 { 00325 libmesh_assert(_nodes); 00326 libmesh_assert_less (sc, this->n_sub_elem()); 00327 libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE); 00328 00329 conn.resize(8); 00330 00331 switch (iop) 00332 { 00333 case TECPLOT: 00334 { 00335 switch (sc) 00336 { 00337 case 0: 00338 00339 conn[0] = this->node(0)+1; 00340 conn[1] = this->node(8)+1; 00341 conn[2] = this->node(20)+1; 00342 conn[3] = this->node(11)+1; 00343 conn[4] = this->node(12)+1; 00344 conn[5] = this->node(21)+1; 00345 conn[6] = this->node(26)+1; 00346 conn[7] = this->node(24)+1; 00347 00348 return; 00349 00350 case 1: 00351 00352 conn[0] = this->node(8)+1; 00353 conn[1] = this->node(1)+1; 00354 conn[2] = this->node(9)+1; 00355 conn[3] = this->node(20)+1; 00356 conn[4] = this->node(21)+1; 00357 conn[5] = this->node(13)+1; 00358 conn[6] = this->node(22)+1; 00359 conn[7] = this->node(26)+1; 00360 00361 return; 00362 00363 case 2: 00364 00365 conn[0] = this->node(11)+1; 00366 conn[1] = this->node(20)+1; 00367 conn[2] = this->node(10)+1; 00368 conn[3] = this->node(3)+1; 00369 conn[4] = this->node(24)+1; 00370 conn[5] = this->node(26)+1; 00371 conn[6] = this->node(23)+1; 00372 conn[7] = this->node(15)+1; 00373 00374 return; 00375 00376 case 3: 00377 00378 conn[0] = this->node(20)+1; 00379 conn[1] = this->node(9)+1; 00380 conn[2] = this->node(2)+1; 00381 conn[3] = this->node(10)+1; 00382 conn[4] = this->node(26)+1; 00383 conn[5] = this->node(22)+1; 00384 conn[6] = this->node(14)+1; 00385 conn[7] = this->node(23)+1; 00386 00387 return; 00388 00389 case 4: 00390 00391 conn[0] = this->node(12)+1; 00392 conn[1] = this->node(21)+1; 00393 conn[2] = this->node(26)+1; 00394 conn[3] = this->node(24)+1; 00395 conn[4] = this->node(4)+1; 00396 conn[5] = this->node(16)+1; 00397 conn[6] = this->node(25)+1; 00398 conn[7] = this->node(19)+1; 00399 00400 return; 00401 00402 case 5: 00403 00404 conn[0] = this->node(21)+1; 00405 conn[1] = this->node(13)+1; 00406 conn[2] = this->node(22)+1; 00407 conn[3] = this->node(26)+1; 00408 conn[4] = this->node(16)+1; 00409 conn[5] = this->node(5)+1; 00410 conn[6] = this->node(17)+1; 00411 conn[7] = this->node(25)+1; 00412 00413 return; 00414 00415 case 6: 00416 00417 conn[0] = this->node(24)+1; 00418 conn[1] = this->node(26)+1; 00419 conn[2] = this->node(23)+1; 00420 conn[3] = this->node(15)+1; 00421 conn[4] = this->node(19)+1; 00422 conn[5] = this->node(25)+1; 00423 conn[6] = this->node(18)+1; 00424 conn[7] = this->node(7)+1; 00425 00426 return; 00427 00428 case 7: 00429 00430 conn[0] = this->node(26)+1; 00431 conn[1] = this->node(22)+1; 00432 conn[2] = this->node(14)+1; 00433 conn[3] = this->node(23)+1; 00434 conn[4] = this->node(25)+1; 00435 conn[5] = this->node(17)+1; 00436 conn[6] = this->node(6)+1; 00437 conn[7] = this->node(18)+1; 00438 00439 return; 00440 00441 default: 00442 libmesh_error_msg("Invalid sc = " << sc); 00443 } 00444 } 00445 00446 case VTK: 00447 { 00448 // VTK now supports VTK_TRIQUADRATIC_HEXAHEDRON directly 00449 conn.resize(27); 00450 00451 conn[0] = this->node(0); 00452 conn[1] = this->node(1); 00453 conn[2] = this->node(2); 00454 conn[3] = this->node(3); 00455 conn[4] = this->node(4); 00456 conn[5] = this->node(5); 00457 conn[6] = this->node(6); 00458 conn[7] = this->node(7); 00459 conn[8] = this->node(8); 00460 conn[9] = this->node(9); 00461 conn[10] = this->node(10); 00462 conn[11] = this->node(11); // 00463 conn[12] = this->node(16); 00464 conn[13] = this->node(17); 00465 conn[14] = this->node(18); 00466 conn[15] = this->node(19); 00467 conn[16] = this->node(12); 00468 conn[17] = this->node(13); // 00469 conn[18] = this->node(14); 00470 conn[19] = this->node(15); 00471 conn[20] = this->node(24); 00472 conn[21] = this->node(22); 00473 conn[22] = this->node(21); 00474 conn[23] = this->node(23); 00475 conn[24] = this->node(20); 00476 conn[25] = this->node(25); 00477 conn[26] = this->node(26); 00478 00479 return; 00480 00481 /* 00482 switch (sc) 00483 { 00484 case 0: 00485 00486 conn[0] = this->node(0); 00487 conn[1] = this->node(8); 00488 conn[2] = this->node(20); 00489 conn[3] = this->node(11); 00490 conn[4] = this->node(12); 00491 conn[5] = this->node(21); 00492 conn[6] = this->node(26); 00493 conn[7] = this->node(24); 00494 00495 return; 00496 00497 case 1: 00498 00499 conn[0] = this->node(8); 00500 conn[1] = this->node(1); 00501 conn[2] = this->node(9); 00502 conn[3] = this->node(20); 00503 conn[4] = this->node(21); 00504 conn[5] = this->node(13); 00505 conn[6] = this->node(22); 00506 conn[7] = this->node(26); 00507 00508 return; 00509 00510 case 2: 00511 00512 conn[0] = this->node(11); 00513 conn[1] = this->node(20); 00514 conn[2] = this->node(10); 00515 conn[3] = this->node(3); 00516 conn[4] = this->node(24); 00517 conn[5] = this->node(26); 00518 conn[6] = this->node(23); 00519 conn[7] = this->node(15); 00520 00521 return; 00522 00523 case 3: 00524 00525 conn[0] = this->node(20); 00526 conn[1] = this->node(9); 00527 conn[2] = this->node(2); 00528 conn[3] = this->node(10); 00529 conn[4] = this->node(26); 00530 conn[5] = this->node(22); 00531 conn[6] = this->node(14); 00532 conn[7] = this->node(23); 00533 00534 return; 00535 00536 case 4: 00537 00538 conn[0] = this->node(12); 00539 conn[1] = this->node(21); 00540 conn[2] = this->node(26); 00541 conn[3] = this->node(24); 00542 conn[4] = this->node(4); 00543 conn[5] = this->node(16); 00544 conn[6] = this->node(25); 00545 conn[7] = this->node(19); 00546 00547 return; 00548 00549 case 5: 00550 00551 conn[0] = this->node(21); 00552 conn[1] = this->node(13); 00553 conn[2] = this->node(22); 00554 conn[3] = this->node(26); 00555 conn[4] = this->node(16); 00556 conn[5] = this->node(5); 00557 conn[6] = this->node(17); 00558 conn[7] = this->node(25); 00559 00560 return; 00561 00562 case 6: 00563 00564 conn[0] = this->node(24); 00565 conn[1] = this->node(26); 00566 conn[2] = this->node(23); 00567 conn[3] = this->node(15); 00568 conn[4] = this->node(19); 00569 conn[5] = this->node(25); 00570 conn[6] = this->node(18); 00571 conn[7] = this->node(7); 00572 00573 return; 00574 00575 case 7: 00576 00577 conn[0] = this->node(26); 00578 conn[1] = this->node(22); 00579 conn[2] = this->node(14); 00580 conn[3] = this->node(23); 00581 conn[4] = this->node(25); 00582 conn[5] = this->node(17); 00583 conn[6] = this->node(6); 00584 conn[7] = this->node(18); 00585 00586 return; 00587 00588 default: 00589 libmesh_error_msg("Invalid sc = " << sc); 00590 } 00591 */ 00592 } 00593 00594 default: 00595 libmesh_error_msg("Unsupported IO package " << iop); 00596 } 00597 } 00598 00599 00600 00601 00602 00603 unsigned int Hex27::n_second_order_adjacent_vertices (const unsigned int n) const 00604 { 00605 switch (n) 00606 { 00607 case 8: 00608 case 9: 00609 case 10: 00610 case 11: 00611 case 12: 00612 case 13: 00613 case 14: 00614 case 15: 00615 case 16: 00616 case 17: 00617 case 18: 00618 case 19: 00619 return 2; 00620 00621 case 20: 00622 case 21: 00623 case 22: 00624 case 23: 00625 case 24: 00626 case 25: 00627 return 4; 00628 00629 case 26: 00630 return 8; 00631 00632 default: 00633 libmesh_error_msg("Invalid node number n = " << n); 00634 } 00635 00636 libmesh_error_msg("We'll never get here!"); 00637 return libMesh::invalid_uint; 00638 } 00639 00640 00641 00642 unsigned short int Hex27::second_order_adjacent_vertex (const unsigned int n, 00643 const unsigned int v) const 00644 { 00645 libmesh_assert_greater_equal (n, this->n_vertices()); 00646 libmesh_assert_less (n, this->n_nodes()); 00647 00648 switch (n) 00649 { 00650 /* 00651 * these are all nodes that are unique to Hex27, 00652 * use our _remaining.... matrix 00653 */ 00654 case 20: 00655 case 21: 00656 case 22: 00657 case 23: 00658 case 24: 00659 case 25: 00660 { 00661 libmesh_assert_less (v, 4); 00662 return _remaining_second_order_adjacent_vertices[n-20][v]; 00663 } 00664 00665 /* 00666 * for the bubble node the return value is simply v. 00667 * Why? -- the user asks for the v-th adjacent vertex, 00668 * from \p n_second_order_adjacent_vertices() there 00669 * are 8 adjacent vertices, and these happen to be 00670 * 0..7 00671 */ 00672 case 26: 00673 { 00674 libmesh_assert_less (v, 8); 00675 return static_cast<unsigned short int>(v); 00676 } 00677 00678 /* 00679 * nodes 8..19: 00680 * these are all nodes that are identical for 00681 * Hex20 and Hex27. Therefore use the 00682 * matrix stored in cell_hex.C 00683 */ 00684 default: 00685 { 00686 libmesh_assert_less (v, 2); 00687 return _second_order_adjacent_vertices[n-this->n_vertices()][v]; 00688 } 00689 } 00690 } 00691 00692 00693 00694 const unsigned short int Hex27::_remaining_second_order_adjacent_vertices[6][4] = 00695 { 00696 { 0, 1, 2, 3}, // vertices adjacent to node 20 face nodes 00697 { 0, 1, 4, 5}, // vertices adjacent to node 21 00698 { 1, 2, 5, 6}, // vertices adjacent to node 22 00699 { 2, 3, 6, 7}, // vertices adjacent to node 23 00700 { 0, 3, 4, 7}, // vertices adjacent to node 24 00701 { 4, 5, 6, 7}, // vertices adjacent to node 25 00702 }; 00703 00704 00705 00706 std::pair<unsigned short int, unsigned short int> 00707 Hex27::second_order_child_vertex (const unsigned int n) const 00708 { 00709 libmesh_assert_greater_equal (n, this->n_vertices()); 00710 libmesh_assert_less (n, this->n_nodes()); 00711 /* 00712 * the _second_order_vertex_child_* vectors are 00713 * stored in cell_hex.C, since they are identical 00714 * for Hex20 and Hex27 (for the first 12 higher-order nodes) 00715 */ 00716 return std::pair<unsigned short int, unsigned short int> 00717 (_second_order_vertex_child_number[n], 00718 _second_order_vertex_child_index[n]); 00719 } 00720 00721 00722 00723 00724 00725 00726 00727 #ifdef LIBMESH_ENABLE_AMR 00728 00729 const float Hex27::_embedding_matrix[8][27][27] = 00730 { 00731 // embedding matrix for child 0 00732 { 00733 // 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 00734 { 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 00735 { 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 00736 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00737 { 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 00738 { 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 00739 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00740 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00741 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00742 { 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 00743 { 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 00744 { 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 00745 { 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 00746 { 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 00747 { 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 00748 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00749 { 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 00750 { 0.00000, 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 00751 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00752 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00753 { 0.00000, 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 00754 { 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 00755 { 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 00756 { 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 00757 { 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 00758 { 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 00759 { 0.00000, 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 00760 { 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 00761 }, 00762 00763 // embedding matrix for child 1 00764 { 00765 // 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 00766 { 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 00767 { 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 00768 { 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 00769 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00770 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00771 { 0.00000, 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 00772 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00773 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00774 { -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 00775 { 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 00776 { 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 00777 { 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 00778 { 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 00779 { 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 00780 { 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 00781 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00782 { 0.00000, 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 00783 { 0.00000, 0.00000, 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 00784 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00785 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00786 { -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 00787 { -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 00788 { 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 00789 { 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 00790 { 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 00791 { 0.00000, 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 00792 { -0.017578125, 0.052734375, -0.017578125, 0.005859375, 0.005859375, -0.017578125, 0.005859375, -0.001953125, 0.10546875, 0.10546875, -0.03515625, 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00858 }, 00859 00860 // embedding matrix for child 4 00861 { 00862 // 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 00863 { 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 00864 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00865 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00866 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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generated by
