| Diploma Thesis Percolation Simulation C++ Sourcecode Documentation |
00001 // constants.h 00002 // for the clustercounter 00003 // 00004 // a) the critical fillingfactors 00005 // b) the optimal cuts for the algorithm 00006 // 00007 // (c) 2000 Andreas Krueger (cpp__at__AndreasKrueger__dot__de) 00008 // version 1.0 last change: 10.1.2001 00009 00010 #ifndef LOADED_CONSTANTS 00011 #define LOADED_CONSTANTS 00012 #endif 00013 00014 const int MAXDIM=11; // maximal number of dimensions, e.g. 20 00015 #define MAXNUMBER 320001 00016 00017 00018 REAL critical_fillingfactor(int dim, NUMBER N); 00019 REAL saturating_fillingfactor(int dim, NUMBER N); 00020 REAL fillingfactor_noc1percent(int dim, NUMBER N); 00021 COUNTER choose_optimal_cuts_ffc (int dim, NUMBER N); 00022 COUNTER choose_optimal_cuts_ffs (int dim, NUMBER N); 00023 00024 // Critical fillingfactor 00025 00026 // The following are approximate results for 00027 // the critical fillingfactor fitted by ffc= a+ b* N^c 00028 // 00029 // a= FFC_N_LIMIT for the limit N->infinity 00030 // b= FFC_N_FACTOR 00031 // c= FFC_N_EXPONENT 00032 00033 const int DEFDIM=11; 00034 00035 const REAL FFC_N_LIMIT[DEFDIM+1]={-1, 00036 33.18634, 1.1282, 0.3416 , 0.13, 0.0543, // 5dim 00037 0.02346, 0.0105, 0.00481, 0.00227, 0.00106, // 10dim 00038 0.000505}; //,0.0002};//,-1,-1,-1,-1,-1,-1,-1,-1,-1}; 00039 // -1 if not known, Gandolfo: 2dim: 1.16, 3dim: 0.35 00040 00041 const REAL FFC_N_FACTOR[DEFDIM+1]={0, 00042 -34.26936, 1.96, 0.738, 0.614, 0.433, // 5dim 00043 0.235, 0.122, 0.0714, 0.0489, 0.0273, // 10dim 00044 0.0161}; 00045 00046 const REAL FFC_N_EXPONENT[DEFDIM+1]={0, 00047 -0.04169, -0.734, -0.462, -0.520, -0.560, // 5dim 00048 -0.534, -0.519, -0.524, -0.564, -0.567, // 10dim 00049 -0.588}; 00050 00051 00052 REAL critical_fillingfactor(int dim, NUMBER N){ 00053 if (dim==1) return saturating_fillingfactor(dim, N); 00054 REAL a,b,c; 00055 a=FFC_N_LIMIT[dim]; 00056 b=FFC_N_FACTOR[dim]; 00057 c=FFC_N_EXPONENT[dim]; 00058 if (a==-1) return -1; 00059 return (a + b* pow((REAL)N,c)); 00060 } 00061 00062 // Saturation fillingfactor 00063 00064 // The following are approximate results (4.12.2001) for 00065 // the saturating fillingfactor fitted by ffs = b + m * Log10(N) 00066 // valid for dim = {1,2} 00067 // b= FFS_B_OFFSET 00068 // m= FFS_M_FACTOR 00069 const REAL FFS_B_OFFSET[3]={0, 0.4886, 1.18622}; 00070 const REAL FFS_M_FACTOR[3]={0, 2.31157, 0.46472}; 00071 00072 // For dim >= 3, the saturating fillingfactor can be fitted by 00073 // ffs(N,dim) = c^dim (d + e * Log10(N)) 00074 // c= 00075 // d= 00076 // e= 00077 const REAL FFS_C_DIMBASIS=0.74046; 00078 const REAL FFS_D_OFFSET=1.91307; 00079 const REAL FFS_E_LOGFACTOR=0.69157; 00080 00081 REAL saturating_fillingfactor(int dim, NUMBER N){ 00082 REAL result; 00083 if (dim==1 || dim==2){ 00084 result=FFS_B_OFFSET[dim] + FFS_M_FACTOR[dim]*log10(N); 00085 return result; 00086 } 00087 if (dim>=3){ 00088 result=pow(FFS_C_DIMBASIS,dim)*(FFS_D_OFFSET+FFS_E_LOGFACTOR*log10(N)); 00089 return result; 00090 } 00091 return -1; 00092 } 00093 00094 // The almost-all fillingfactor (99% clustering) 00095 00096 // The following numerical results are (not quite satisfying) 00097 // attempts to fit the position of the fillingfactor ffnoc1% 00098 // - the ff, at which the number-of-clusters = 1% * number-of-spheres 00099 // 00100 // The fit is ffnoc1% (N,dim) = a + b * ( N - N0) ^ c 00101 // with a, b, N0, c functions of dim 00102 // so that the resulting fitfunction is 00103 // 00104 // ffnoc1% (N, dim) = d*e^dim + (f*g^dim) * (N-k-l*dim)^(m+dim^n) 00105 // 00106 // The deviations are mostly < 10 % 00107 // but for 1dim and >10dim up to 50% 00108 // 00109 // This is then used in ff:ffnoc_guessed 00110 00111 const REAL noc1_d=6.25188; 00112 const REAL noc1_e=0.46828; 00113 const REAL noc1_f=8.40778; 00114 const REAL noc1_g=0.70916; 00115 const REAL noc1_k=115.74947; 00116 const REAL noc1_l=3.10626; 00117 const REAL noc1_m=-1.53707; 00118 const REAL noc1_n=0.13135; 00119 00120 #include <iostream> // for cout 00121 using std::cout; 00122 REAL fillingfactor_noc1percent(int dim, NUMBER N){ 00123 std::cout <<"fillingfactor_noc1percent ACCESSED\n"; 00124 REAL a=noc1_d*pow(noc1_e,dim); 00125 REAL b=noc1_f*pow(noc1_g,dim); 00126 REAL N0=noc1_k+noc1_l*dim; 00127 REAL c=noc1_m+pow(dim, noc1_n); 00128 return a+b*pow((N-N0),c); 00129 } 00130 00131 00132 COUNTER choose_optimal_cuts_ffc (int dim, NUMBER N) { 00133 00134 switch(dim) { 00135 case 1: switch (N) { // not tested! 00136 case 39: return 0; 00137 case 78: return 0; // not tested 00138 case 156: return 0; // not tested 00139 case 312: return 2; // ?? 00140 case 625: return 4; // ?? 00141 case 1250: return 5; // ?? 00142 case 2500: return 5; // ?? 00143 case 5000: return 6; // ?? 00144 case 10000: return 7; // ?? 00145 case 20000: return 7; // ?? 00146 case 40000: return 9; // ?? 00147 case 80000: return 9; // ?? 00148 case 160000: return 11; // ?? 00149 case 320000: return 11; // ?? 00150 case 480000: return 11; // ?? 00151 default: return 8; // ?? 00152 } 00153 00154 case 2: switch (N) { // for maxdim=4: 00155 case 39: return 0; 00156 // tested on pc_uni 00157 case 78: return 0; // not tested 00158 case 156: return 0; // not tested 00159 case 312: return 2; 00160 case 625: return 4; 00161 case 1250: return 5; 00162 case 2500: return 5; 00163 case 5000: return 6; 00164 case 10000: return 7; 00165 case 20000: return 7; 00166 case 40000: return 9; 00167 case 80000: return 9; 00168 case 160000: return 11; 00169 case 320000: return 11; 00170 case 480000: return 11; 00171 default: return 8; 00172 } 00173 00174 case 3: switch (N) { // for maxdim=4: 00175 case 39: return 0; 00176 case 78: return 0; // not tested 00177 case 156: return 0; // not tested 00178 // tested on pc_uni 00179 case 312: return 3; 00180 case 625: return 4; 00181 case 1250: return 5; 00182 case 2500: return 5; 00183 case 5000: return 6; 00184 case 10000: return 7; 00185 case 20000: return 7; 00186 case 40000: return 8; 00187 case 80000: return 8; 00188 case 160000: return 8; 00189 case 320000: return 8; 00190 case 480000: return 8; // ?? evtl. niedriger 00191 default: return 7; 00192 00193 } 00194 case 4: switch (N) { // for maxdim=4: 00195 case 39: return 0; 00196 case 78: return 0; // not tested 00197 case 156: return 0; // not tested 00198 // tested on pc_uni 00199 case 312: return 2; 00200 case 625: return 4; 00201 case 1250: return 4; 00202 case 2500: return 5; 00203 case 5000: return 5; 00204 case 10000: return 6; 00205 case 20000: return 6; 00206 case 40000: return 6; 00207 case 80000: return 6; 00208 case 160000: return 7; // evtl. lower 00209 case 320000: return 7; // evtl. lower 00210 case 480000: return 7; //evtl. 10 00211 default: return 6; 00212 } 00213 00214 case 5: switch (N) { // for maxdim=6; 00215 case 39: return 0; 00216 case 78: return 0; // not tested 00217 case 156: return 0; // not tested 00218 // tested on pc_uni 00219 case 312: return 2; 00220 case 625: return 3; 00221 case 1250: return 4; 00222 case 2500: return 5; 00223 case 5000: return 5; 00224 case 10000: return 6; 00225 case 20000: return 6; 00226 case 40000: return 6; // ?? 00227 case 80000: return 6; // ?? 00228 case 160000: return 7; // ?? 00229 case 320000: return 7; // ?? 00230 case 480000: return 7; // ?? 00231 default: return 6; 00232 } 00233 00234 case 6: switch (N) { // for maxdim=6; 00235 case 39: return 0; 00236 case 78: return 0; // not tested 00237 case 156: return 0; // not tested 00238 // tested on pc_uni 00239 case 312: return 0; 00240 case 625: return 1; 00241 case 1250: return 3; 00242 case 2500: return 5; 00243 case 5000: return 5; 00244 case 10000: return 6; 00245 case 20000: return 6; 00246 case 40000: return 6; 00247 case 80000: return 7; 00248 case 160000: return 7; 00249 case 320000: return 7; // ?? 00250 case 480000: return 7; // ?? 00251 default: return 6; 00252 } 00253 00254 case 7: switch (N) { // tested on PC_uni for maxdim=11 00255 case 39: return 0; 00256 case 78: return 0; // not tested 00257 case 156: return 0; // not tested 00258 case 312: return 0; 00259 case 625: return 0; 00260 case 1250: return 1; 00261 case 2500: return 6; 00262 case 5000: return 5; 00263 case 10000: return 6; 00264 case 20000: return 7; 00265 case 40000: return 7; 00266 case 80000: return 7; 00267 case 160000: return 7; // ?? 00268 case 320000: return 7; // ?? 00269 case 480000: return 7; // ?? 00270 default: return 6; 00271 } 00272 case 8: switch (N) { // tested on PC_uni for maxdim=11 00273 case 39: return 0; 00274 case 78: return 0; // not tested 00275 case 156: return 0; // not tested 00276 case 312: return 0; 00277 case 625: return 0; 00278 case 1250: return 1; 00279 case 2500: return 3; 00280 case 5000: return 4; 00281 case 10000: return 5; 00282 case 20000: return 7; 00283 case 40000: return 7; 00284 case 80000: return 7; 00285 case 160000: return 7; // ?? 00286 case 320000: return 7; // ?? 00287 case 480000: return 7; // ?? 00288 default: return 6; 00289 } 00290 case 9: switch (N) { // tested on PC_uni for maxdim=11 00291 case 39: return 0; 00292 case 78: return 0; // not tested 00293 case 156: return 0; // not tested 00294 00295 case 312: return 0; 00296 case 625: return 0; 00297 case 1250: return 1; 00298 case 2500: return 3; 00299 case 5000: return 4; 00300 case 10000: return 8; 00301 case 20000: return 8; 00302 case 40000: return 8; 00303 case 80000: return 8; 00304 case 160000: return 8; // ?? 00305 case 320000: return 8; // ?? 00306 case 480000: return 8; // ?? 00307 default: return 6; 00308 } 00309 case 10: switch (N) { // tested on PC_uni for maxdim=11 00310 case 39: return 0; 00311 case 78: return 0; // not tested 00312 case 156: return 0; // not tested 00313 00314 case 312: return 0; 00315 case 625: return 0; 00316 case 1250: return 1; 00317 case 2500: return 3; 00318 case 5000: return 3; 00319 case 10000: return 4; 00320 case 20000: return 4; 00321 case 40000: return 5; 00322 case 80000: return 6; 00323 case 160000: return 6; // ?? 00324 case 320000: return 6; // ?? 00325 case 480000: return 6; // ?? 00326 default: return 6; 00327 } 00328 case 11: switch (N) { // tested on PC_uni for maxdim=11 00329 case 39: return 0; 00330 case 78: return 0; // not tested 00331 case 156: return 0; // not tested 00332 case 312: return 0; 00333 case 625: return 0; 00334 case 1250: return 1; 00335 case 2500: return 3; 00336 case 5000: return 3; 00337 case 10000: return 4; 00338 case 20000: return 4; 00339 case 40000: return 4; 00340 case 80000: return 8; 00341 case 160000: return 8; // ?? 00342 case 320000: return 8; // ?? 00343 case 480000: return 8; // ?? 00344 default: return 6; 00345 } 00346 default: return 6; 00347 } 00348 } 00349 00350 00351 00352 COUNTER choose_optimal_cuts_ffs (int dim, NUMBER N) { 00353 // This is for radii around the saturation point 00354 // (all in one cluster) 00355 // for MAXDIM = 11 00356 00357 switch(dim) { 00358 case 1: switch (N) { 00359 case 39: return 0; 00360 case 78: return 0; 00361 case 156: return 0; 00362 case 312: return 3; 00363 case 625: return 3; 00364 case 1250: return 5; 00365 case 2500: return 5; 00366 case 5000: return 6; 00367 case 10000: return 7; 00368 case 20000: return 8; 00369 case 40000: return 9; 00370 case 80000: return 10; 00371 case 160000: return 11; 00372 case 320000: return 11; 00373 case 480000: return 12; 00374 default: return 5; 00375 } 00376 00377 case 2: switch (N) { 00378 case 39: return 0; 00379 case 78: return 0; 00380 case 156: return 0; 00381 case 312: return 3; 00382 case 625: return 4; 00383 case 1250: return 4; 00384 case 2500: return 5; 00385 case 5000: return 5; 00386 case 10000: return 7; 00387 case 20000: return 7; 00388 case 40000: return 9; 00389 case 80000: return 9; 00390 case 160000: return 9; 00391 case 320000: return 9; 00392 case 480000: return 9; 00393 default: return 5; 00394 } 00395 00396 case 3: switch (N) { 00397 case 39: return 0; 00398 case 78: return 0; 00399 case 156: return 0; 00400 case 312: return 3; 00401 case 625: return 3; 00402 case 1250: return 3; 00403 case 2500: return 3; //? 00404 case 5000: return 4; 00405 case 10000: return 4; //? 00406 case 20000: return 5; //? 00407 case 40000: return 5; //? 00408 case 80000: return 7; //? 00409 case 160000: return 7; 00410 case 320000: return 7; 00411 case 480000: return 7; // ? 00412 default: return 4; 00413 00414 } 00415 case 4: switch (N) { 00416 case 39: return 0; 00417 case 78: return 0; 00418 case 156: return 0; 00419 case 312: return 0; 00420 case 625: return 0; 00421 case 1250: return 0; 00422 case 2500: return 2; 00423 case 5000: return 4; 00424 case 10000: return 4; 00425 case 20000: return 4; 00426 case 40000: return 5; 00427 case 80000: return 5; 00428 case 160000: return 5; 00429 case 320000: return 6; 00430 case 480000: return 7; //? 00431 default: return 4; 00432 } 00433 00434 case 5: switch (N) { 00435 case 39: return 0; 00436 case 78: return 0; 00437 case 156: return 0; 00438 case 312: return 0; 00439 case 625: return 0; 00440 case 1250: return 0; 00441 case 2500: return 0; 00442 case 5000: return 0; 00443 case 10000: return 3; 00444 case 20000: return 4; 00445 case 40000: return 5; 00446 case 80000: return 5; 00447 case 160000: return 5; 00448 case 320000: return 6; // ?? 00449 case 480000: return 7; // ?? 00450 default: return 3; 00451 } 00452 00453 case 6: switch (N) { 00454 case 39: return 0; 00455 case 78: return 0; 00456 case 156: return 0; 00457 case 312: return 0; 00458 case 625: return 0; 00459 case 1250: return 0; 00460 case 2500: return 0; 00461 case 5000: return 0; 00462 case 10000: return 0; 00463 case 20000: return 0; 00464 case 40000: return 3; 00465 case 80000: return 5; 00466 case 160000: return 5; 00467 case 320000: return 5; // ?? 00468 case 480000: return 6; // not measured 00469 default: return 2; 00470 } 00471 00472 case 7: switch (N) { 00473 case 39: return 0; 00474 case 78: return 0; 00475 case 156: return 0; 00476 case 312: return 0; 00477 case 625: return 0; 00478 case 1250: return 0; 00479 case 2500: return 0; 00480 case 5000: return 0; 00481 case 10000: return 0; 00482 case 20000: return 0; 00483 case 40000: return 0; 00484 case 80000: return 0; 00485 case 160000: return 3; // ? 00486 case 320000: return 3; // ? 00487 case 480000: return 3; // ? 00488 default: return 0; 00489 } 00490 00491 case 8: switch (N) { 00492 case 39: return 0; 00493 case 78: return 0; 00494 case 156: return 0; 00495 case 312: return 0; 00496 case 625: return 0; 00497 case 1250: return 0; 00498 case 2500: return 0;// ? 00499 case 5000: return 1; // ? 00500 case 10000: return 1;// ? 00501 case 20000: return 2;// ? 00502 case 40000: return 2; // ? 00503 case 80000: return 3; // ? 00504 case 160000: return 3; // ? 00505 case 320000: return 3; // ? 00506 case 480000: return 3; 00507 default: return 1; 00508 } 00509 case 9: switch (N) { 00510 case 39: return 0; 00511 case 78: return 0; 00512 case 156: return 0; 00513 case 312: return 0; 00514 case 625: return 0; 00515 case 1250: return 0; 00516 case 2500: return 0; 00517 case 5000: return 1; // ?? 00518 case 10000: return 1; // ?? 00519 case 20000: return 1;// ?? 00520 case 40000: return 2;// ?? 00521 case 80000: return 2; // ?? 00522 case 160000: return 2; // ?? 00523 case 320000: return 2; // ?? 00524 case 480000: return 2; // ?? 00525 default: return 1; 00526 } 00527 case 10: switch (N) { 00528 case 39: return 0; 00529 case 78: return 0; 00530 case 156: return 0; 00531 case 312: return 0; 00532 case 625: return 0; 00533 case 1250: return 0; 00534 case 2500: return 0; 00535 case 5000: return 0; // ?? 00536 case 10000: return 1; // ?? 00537 case 20000: return 1; // ?? 00538 case 40000: return 1; // ?? 00539 case 80000: return 1; // ?? 00540 case 160000: return 2; // ?? 00541 case 320000: return 2; // ?? 00542 case 480000: return 2; // ?? 00543 default: return 1; 00544 } 00545 case 11: switch (N) { 00546 case 39: return 0; 00547 case 78: return 0; 00548 case 156: return 0; 00549 case 312: return 0; 00550 case 625: return 0; 00551 case 1250: return 0; 00552 case 2500: return 0; 00553 case 5000: return 0; // ?? 00554 case 10000: return 1; // ?? 00555 case 20000: return 1; // ?? 00556 case 40000: return 1; // ?? 00557 case 80000: return 1; // ?? 00558 case 160000: return 2; // ?? 00559 case 320000: return 2; // ?? 00560 case 480000: return 2; // ?? 00561 default: return 0; 00562 } 00563 default: return 6; 00564 } 00565 } 00566
| Diploma Thesis Sourcecode
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