cell_hex27.C
Go to the documentation of this file.00001 // The libMesh Finite Element Library. 00002 // Copyright (C) 2002-2012 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 00196 // We'll never get here. 00197 libmesh_error(); 00198 return 0; 00199 } 00200 00201 00202 00203 AutoPtr<Elem> Hex27::build_side (const unsigned int i, 00204 bool proxy) const 00205 { 00206 libmesh_assert_less (i, this->n_sides()); 00207 00208 if (proxy) 00209 { 00210 AutoPtr<Elem> ap(new Side<Quad9,Hex27>(this,i)); 00211 return ap; 00212 } 00213 00214 else 00215 { 00216 AutoPtr<Elem> face(new Quad9); 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 00233 return face; 00234 } 00235 case 1: // the face at y = 0 00236 { 00237 face->set_node(0) = this->get_node(0); 00238 face->set_node(1) = this->get_node(1); 00239 face->set_node(2) = this->get_node(5); 00240 face->set_node(3) = this->get_node(4); 00241 face->set_node(4) = this->get_node(8); 00242 face->set_node(5) = this->get_node(13); 00243 face->set_node(6) = this->get_node(16); 00244 face->set_node(7) = this->get_node(12); 00245 face->set_node(8) = this->get_node(21); 00246 00247 return face; 00248 } 00249 case 2: // the face at x=1 00250 { 00251 face->set_node(0) = this->get_node(1); 00252 face->set_node(1) = this->get_node(2); 00253 face->set_node(2) = this->get_node(6); 00254 face->set_node(3) = this->get_node(5); 00255 face->set_node(4) = this->get_node(9); 00256 face->set_node(5) = this->get_node(14); 00257 face->set_node(6) = this->get_node(17); 00258 face->set_node(7) = this->get_node(13); 00259 face->set_node(8) = this->get_node(22); 00260 00261 return face; 00262 } 00263 case 3: // the face at y=1 00264 { 00265 face->set_node(0) = this->get_node(2); 00266 face->set_node(1) = this->get_node(3); 00267 face->set_node(2) = this->get_node(7); 00268 face->set_node(3) = this->get_node(6); 00269 face->set_node(4) = this->get_node(10); 00270 face->set_node(5) = this->get_node(15); 00271 face->set_node(6) = this->get_node(18); 00272 face->set_node(7) = this->get_node(14); 00273 face->set_node(8) = this->get_node(23); 00274 00275 return face; 00276 } 00277 case 4: // the face at x=0 00278 { 00279 face->set_node(0) = this->get_node(3); 00280 face->set_node(1) = this->get_node(0); 00281 face->set_node(2) = this->get_node(4); 00282 face->set_node(3) = this->get_node(7); 00283 face->set_node(4) = this->get_node(11); 00284 face->set_node(5) = this->get_node(12); 00285 face->set_node(6) = this->get_node(19); 00286 face->set_node(7) = this->get_node(15); 00287 face->set_node(8) = this->get_node(24); 00288 00289 return face; 00290 } 00291 case 5: // the face at z=1 00292 { 00293 face->set_node(0) = this->get_node(4); 00294 face->set_node(1) = this->get_node(5); 00295 face->set_node(2) = this->get_node(6); 00296 face->set_node(3) = this->get_node(7); 00297 face->set_node(4) = this->get_node(16); 00298 face->set_node(5) = this->get_node(17); 00299 face->set_node(6) = this->get_node(18); 00300 face->set_node(7) = this->get_node(19); 00301 face->set_node(8) = this->get_node(25); 00302 00303 return face; 00304 } 00305 default: 00306 { 00307 libmesh_error(); 00308 return face; 00309 } 00310 } 00311 } 00312 00313 // We'll never get here. 00314 libmesh_error(); 00315 AutoPtr<Elem> ap(NULL); return ap; 00316 } 00317 00318 00319 00320 AutoPtr<Elem> Hex27::build_edge (const unsigned int i) const 00321 { 00322 libmesh_assert_less (i, this->n_edges()); 00323 00324 return AutoPtr<Elem>(new SideEdge<Edge3,Hex27>(this,i)); 00325 } 00326 00327 00328 00329 void Hex27::connectivity(const unsigned int sc, 00330 const IOPackage iop, 00331 std::vector<dof_id_type>& conn) const 00332 { 00333 libmesh_assert(_nodes); 00334 libmesh_assert_less (sc, this->n_sub_elem()); 00335 libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE); 00336 00337 conn.resize(8); 00338 00339 switch (iop) 00340 { 00341 case TECPLOT: 00342 { 00343 switch (sc) 00344 { 00345 case 0: 00346 00347 conn[0] = this->node(0)+1; 00348 conn[1] = this->node(8)+1; 00349 conn[2] = this->node(20)+1; 00350 conn[3] = this->node(11)+1; 00351 conn[4] = this->node(12)+1; 00352 conn[5] = this->node(21)+1; 00353 conn[6] = this->node(26)+1; 00354 conn[7] = this->node(24)+1; 00355 00356 return; 00357 00358 case 1: 00359 00360 conn[0] = this->node(8)+1; 00361 conn[1] = this->node(1)+1; 00362 conn[2] = this->node(9)+1; 00363 conn[3] = this->node(20)+1; 00364 conn[4] = this->node(21)+1; 00365 conn[5] = this->node(13)+1; 00366 conn[6] = this->node(22)+1; 00367 conn[7] = this->node(26)+1; 00368 00369 return; 00370 00371 case 2: 00372 00373 conn[0] = this->node(11)+1; 00374 conn[1] = this->node(20)+1; 00375 conn[2] = this->node(10)+1; 00376 conn[3] = this->node(3)+1; 00377 conn[4] = this->node(24)+1; 00378 conn[5] = this->node(26)+1; 00379 conn[6] = this->node(23)+1; 00380 conn[7] = this->node(15)+1; 00381 00382 return; 00383 00384 case 3: 00385 00386 conn[0] = this->node(20)+1; 00387 conn[1] = this->node(9)+1; 00388 conn[2] = this->node(2)+1; 00389 conn[3] = this->node(10)+1; 00390 conn[4] = this->node(26)+1; 00391 conn[5] = this->node(22)+1; 00392 conn[6] = this->node(14)+1; 00393 conn[7] = this->node(23)+1; 00394 00395 return; 00396 00397 case 4: 00398 00399 conn[0] = this->node(12)+1; 00400 conn[1] = this->node(21)+1; 00401 conn[2] = this->node(26)+1; 00402 conn[3] = this->node(24)+1; 00403 conn[4] = this->node(4)+1; 00404 conn[5] = this->node(16)+1; 00405 conn[6] = this->node(25)+1; 00406 conn[7] = this->node(19)+1; 00407 00408 return; 00409 00410 case 5: 00411 00412 conn[0] = this->node(21)+1; 00413 conn[1] = this->node(13)+1; 00414 conn[2] = this->node(22)+1; 00415 conn[3] = this->node(26)+1; 00416 conn[4] = this->node(16)+1; 00417 conn[5] = this->node(5)+1; 00418 conn[6] = this->node(17)+1; 00419 conn[7] = this->node(25)+1; 00420 00421 return; 00422 00423 case 6: 00424 00425 conn[0] = this->node(24)+1; 00426 conn[1] = this->node(26)+1; 00427 conn[2] = this->node(23)+1; 00428 conn[3] = this->node(15)+1; 00429 conn[4] = this->node(19)+1; 00430 conn[5] = this->node(25)+1; 00431 conn[6] = this->node(18)+1; 00432 conn[7] = this->node(7)+1; 00433 00434 return; 00435 00436 case 7: 00437 00438 conn[0] = this->node(26)+1; 00439 conn[1] = this->node(22)+1; 00440 conn[2] = this->node(14)+1; 00441 conn[3] = this->node(23)+1; 00442 conn[4] = this->node(25)+1; 00443 conn[5] = this->node(17)+1; 00444 conn[6] = this->node(6)+1; 00445 conn[7] = this->node(18)+1; 00446 00447 return; 00448 00449 default: 00450 libmesh_error(); 00451 } 00452 } 00453 00454 case VTK: 00455 { 00456 // VTK now supports VTK_TRIQUADRATIC_HEXAHEDRON directly 00457 conn.resize(27); 00458 00459 conn[0] = this->node(0); 00460 conn[1] = this->node(1); 00461 conn[2] = this->node(2); 00462 conn[3] = this->node(3); 00463 conn[4] = this->node(4); 00464 conn[5] = this->node(5); 00465 conn[6] = this->node(6); 00466 conn[7] = this->node(7); 00467 conn[8] = this->node(8); 00468 conn[9] = this->node(9); 00469 conn[10] = this->node(10); 00470 conn[11] = this->node(11); // 00471 conn[12] = this->node(16); 00472 conn[13] = this->node(17); 00473 conn[14] = this->node(18); 00474 conn[15] = this->node(19); 00475 conn[16] = this->node(12); 00476 conn[17] = this->node(13); // 00477 conn[18] = this->node(14); 00478 conn[19] = this->node(15); 00479 conn[20] = this->node(24); 00480 conn[21] = this->node(22); 00481 conn[22] = this->node(21); 00482 conn[23] = this->node(23); 00483 conn[24] = this->node(20); 00484 conn[25] = this->node(25); 00485 conn[26] = this->node(26); 00486 00487 return; 00488 00489 /* 00490 switch (sc) 00491 { 00492 case 0: 00493 00494 conn[0] = this->node(0); 00495 conn[1] = this->node(8); 00496 conn[2] = this->node(20); 00497 conn[3] = this->node(11); 00498 conn[4] = this->node(12); 00499 conn[5] = this->node(21); 00500 conn[6] = this->node(26); 00501 conn[7] = this->node(24); 00502 00503 return; 00504 00505 case 1: 00506 00507 conn[0] = this->node(8); 00508 conn[1] = this->node(1); 00509 conn[2] = this->node(9); 00510 conn[3] = this->node(20); 00511 conn[4] = this->node(21); 00512 conn[5] = this->node(13); 00513 conn[6] = this->node(22); 00514 conn[7] = this->node(26); 00515 00516 return; 00517 00518 case 2: 00519 00520 conn[0] = this->node(11); 00521 conn[1] = this->node(20); 00522 conn[2] = this->node(10); 00523 conn[3] = this->node(3); 00524 conn[4] = this->node(24); 00525 conn[5] = this->node(26); 00526 conn[6] = this->node(23); 00527 conn[7] = this->node(15); 00528 00529 return; 00530 00531 case 3: 00532 00533 conn[0] = this->node(20); 00534 conn[1] = this->node(9); 00535 conn[2] = this->node(2); 00536 conn[3] = this->node(10); 00537 conn[4] = this->node(26); 00538 conn[5] = this->node(22); 00539 conn[6] = this->node(14); 00540 conn[7] = this->node(23); 00541 00542 return; 00543 00544 case 4: 00545 00546 conn[0] = this->node(12); 00547 conn[1] = this->node(21); 00548 conn[2] = this->node(26); 00549 conn[3] = this->node(24); 00550 conn[4] = this->node(4); 00551 conn[5] = this->node(16); 00552 conn[6] = this->node(25); 00553 conn[7] = this->node(19); 00554 00555 return; 00556 00557 case 5: 00558 00559 conn[0] = this->node(21); 00560 conn[1] = this->node(13); 00561 conn[2] = this->node(22); 00562 conn[3] = this->node(26); 00563 conn[4] = this->node(16); 00564 conn[5] = this->node(5); 00565 conn[6] = this->node(17); 00566 conn[7] = this->node(25); 00567 00568 return; 00569 00570 case 6: 00571 00572 conn[0] = this->node(24); 00573 conn[1] = this->node(26); 00574 conn[2] = this->node(23); 00575 conn[3] = this->node(15); 00576 conn[4] = this->node(19); 00577 conn[5] = this->node(25); 00578 conn[6] = this->node(18); 00579 conn[7] = this->node(7); 00580 00581 return; 00582 00583 case 7: 00584 00585 conn[0] = this->node(26); 00586 conn[1] = this->node(22); 00587 conn[2] = this->node(14); 00588 conn[3] = this->node(23); 00589 conn[4] = this->node(25); 00590 conn[5] = this->node(17); 00591 conn[6] = this->node(6); 00592 conn[7] = this->node(18); 00593 00594 return; 00595 00596 default: 00597 libmesh_error(); 00598 } 00599 */ 00600 } 00601 00602 default: 00603 libmesh_error(); 00604 } 00605 00606 libmesh_error(); 00607 } 00608 00609 00610 00611 00612 00613 unsigned int Hex27::n_second_order_adjacent_vertices (const unsigned int n) const 00614 { 00615 switch (n) 00616 { 00617 case 8: 00618 case 9: 00619 case 10: 00620 case 11: 00621 case 12: 00622 case 13: 00623 case 14: 00624 case 15: 00625 case 16: 00626 case 17: 00627 case 18: 00628 case 19: 00629 return 2; 00630 00631 case 20: 00632 case 21: 00633 case 22: 00634 case 23: 00635 case 24: 00636 case 25: 00637 return 4; 00638 00639 case 26: 00640 return 8; 00641 00642 default: 00643 libmesh_error(); 00644 } 00645 00646 libmesh_error(); 00647 return libMesh::invalid_uint; 00648 } 00649 00650 00651 00652 unsigned short int Hex27::second_order_adjacent_vertex (const unsigned int n, 00653 const unsigned int v) const 00654 { 00655 libmesh_assert_greater_equal (n, this->n_vertices()); 00656 libmesh_assert_less (n, this->n_nodes()); 00657 00658 switch (n) 00659 { 00660 /* 00661 * these are all nodes that are unique to Hex27, 00662 * use our _remaining.... matrix 00663 */ 00664 case 20: 00665 case 21: 00666 case 22: 00667 case 23: 00668 case 24: 00669 case 25: 00670 { 00671 libmesh_assert_less (v, 4); 00672 return _remaining_second_order_adjacent_vertices[n-20][v]; 00673 } 00674 00675 /* 00676 * for the bubble node the return value is simply v. 00677 * Why? -- the user asks for the v-th adjacent vertex, 00678 * from \p n_second_order_adjacent_vertices() there 00679 * are 8 adjacent vertices, and these happen to be 00680 * 0..7 00681 */ 00682 case 26: 00683 { 00684 libmesh_assert_less (v, 8); 00685 return static_cast<unsigned short int>(v); 00686 } 00687 00688 /* 00689 * nodes 8..19: 00690 * these are all nodes that are identical for 00691 * Hex20 and Hex27. Therefore use the 00692 * matrix stored in cell_hex.C 00693 */ 00694 default: 00695 { 00696 libmesh_assert_less (v, 2); 00697 return _second_order_adjacent_vertices[n-this->n_vertices()][v]; 00698 } 00699 } 00700 } 00701 00702 00703 00704 const unsigned short int Hex27::_remaining_second_order_adjacent_vertices[6][4] = 00705 { 00706 { 0, 1, 2, 3}, // vertices adjacent to node 20 face nodes 00707 { 0, 1, 4, 5}, // vertices adjacent to node 21 00708 { 1, 2, 5, 6}, // vertices adjacent to node 22 00709 { 2, 3, 6, 7}, // vertices adjacent to node 23 00710 { 0, 3, 4, 7}, // vertices adjacent to node 24 00711 { 4, 5, 6, 7}, // vertices adjacent to node 25 00712 }; 00713 00714 00715 00716 std::pair<unsigned short int, unsigned short int> 00717 Hex27::second_order_child_vertex (const unsigned int n) const 00718 { 00719 libmesh_assert_greater_equal (n, this->n_vertices()); 00720 libmesh_assert_less (n, this->n_nodes()); 00721 /* 00722 * the _second_order_vertex_child_* vectors are 00723 * stored in cell_hex.C, since they are identical 00724 * for Hex20 and Hex27 (for the first 12 higher-order nodes) 00725 */ 00726 return std::pair<unsigned short int, unsigned short int> 00727 (_second_order_vertex_child_number[n], 00728 _second_order_vertex_child_index[n]); 00729 } 00730 00731 00732 00733 00734 00735 00736 00737 #ifdef LIBMESH_ENABLE_AMR 00738 00739 const float Hex27::_embedding_matrix[8][27][27] = 00740 { 00741 // embedding matrix for child 0 00742 { 00743 // 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 00744 { 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 00745 { 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 00746 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00747 { 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 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, 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 00749 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 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, 0.00000, 0.00000, 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 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, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 7 00752 { 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 00753 { 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 00754 { 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 00755 { 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 00756 { 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 00757 { 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 00758 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00759 { 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 00760 { 0.00000, 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 00761 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00762 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00763 { 0.00000, 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 00764 { 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 00765 { 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 00766 { 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 00767 { 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 00768 { 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 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, 0.140625, -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 00770 { 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 00771 }, 00772 00773 // embedding matrix for child 1 00774 { 00775 // 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 00776 { 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 00777 { 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 00778 { 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 00779 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00780 { 0.00000, 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1.00000 }, // 7 00784 { -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 00785 { 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 00786 { 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 00787 { 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, 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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 00792 { 0.00000, 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 00793 { 0.00000, 0.00000, 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 00794 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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 00795 { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 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0.00000 }, // 22 00799 { 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 00800 { 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 00801 { 0.00000, 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 00802 { -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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