How to use special method in Django Test Plus

Best Python code snippet using django-test-plus_python

pokemon.ts

Source:pokemon.ts

1/​/​ Next.js API route support: https:/​/​nextjs.org/​docs/​api-routes/​introduction2import type { NextApiRequest, NextApiResponse } from 'next'3export default function handler(req: NextApiRequest, res: NextApiResponse) {4 res.status(200).json([5 {6 id: 1,7 name: 'Bulbasaur',8 type: ['Grass', 'Poison'],9 hp: 45,10 attack: 49,11 defense: 49,12 special_attack: 65,13 special_defense: 65,14 speed: 45,15 },16 {17 id: 2,18 name: 'Ivysaur',19 type: ['Grass', 'Poison'],20 hp: 60,21 attack: 62,22 defense: 63,23 special_attack: 80,24 special_defense: 80,25 speed: 60,26 },27 {28 id: 3,29 name: 'Venusaur',30 type: ['Grass', 'Poison'],31 hp: 80,32 attack: 82,33 defense: 83,34 special_attack: 100,35 special_defense: 100,36 speed: 80,37 },38 {39 id: 4,40 name: 'Charmander',41 type: ['Fire'],42 hp: 39,43 attack: 52,44 defense: 43,45 special_attack: 60,46 special_defense: 50,47 speed: 65,48 },49 {50 id: 5,51 name: 'Charmeleon',52 type: ['Fire'],53 hp: 58,54 attack: 64,55 defense: 58,56 special_attack: 80,57 special_defense: 65,58 speed: 80,59 },60 {61 id: 6,62 name: 'Charizard',63 type: ['Fire', 'Flying'],64 hp: 78,65 attack: 84,66 defense: 78,67 special_attack: 109,68 special_defense: 85,69 speed: 100,70 },71 {72 id: 7,73 name: 'Squirtle',74 type: ['Water'],75 hp: 44,76 attack: 48,77 defense: 65,78 special_attack: 50,79 special_defense: 64,80 speed: 43,81 },82 {83 id: 8,84 name: 'Wartortle',85 type: ['Water'],86 hp: 59,87 attack: 63,88 defense: 80,89 special_attack: 65,90 special_defense: 80,91 speed: 58,92 },93 {94 id: 9,95 name: 'Blastoise',96 type: ['Water'],97 hp: 79,98 attack: 83,99 defense: 100,100 special_attack: 85,101 special_defense: 105,102 speed: 78,103 },104 {105 id: 10,106 name: 'Caterpie',107 type: ['Bug'],108 hp: 45,109 attack: 30,110 defense: 35,111 special_attack: 20,112 special_defense: 20,113 speed: 45,114 },115 {116 id: 11,117 name: 'Metapod',118 type: ['Bug'],119 hp: 50,120 attack: 20,121 defense: 55,122 special_attack: 25,123 special_defense: 25,124 speed: 30,125 },126 {127 id: 12,128 name: 'Butterfree',129 type: ['Bug', 'Flying'],130 hp: 60,131 attack: 45,132 defense: 50,133 special_attack: 90,134 special_defense: 80,135 speed: 70,136 },137 {138 id: 13,139 name: 'Weedle',140 type: ['Bug', 'Poison'],141 hp: 40,142 attack: 35,143 defense: 30,144 special_attack: 20,145 special_defense: 20,146 speed: 50,147 },148 {149 id: 14,150 name: 'Kakuna',151 type: ['Bug', 'Poison'],152 hp: 45,153 attack: 25,154 defense: 50,155 special_attack: 25,156 special_defense: 25,157 speed: 35,158 },159 {160 id: 15,161 name: 'Beedrill',162 type: ['Bug', 'Poison'],163 hp: 65,164 attack: 90,165 defense: 40,166 special_attack: 45,167 special_defense: 80,168 speed: 75,169 },170 {171 id: 16,172 name: 'Pidgey',173 type: ['Normal', 'Flying'],174 hp: 40,175 attack: 45,176 defense: 40,177 special_attack: 35,178 special_defense: 35,179 speed: 56,180 },181 {182 id: 17,183 name: 'Pidgeotto',184 type: ['Normal', 'Flying'],185 hp: 63,186 attack: 60,187 defense: 55,188 special_attack: 50,189 special_defense: 50,190 speed: 71,191 },192 {193 id: 18,194 name: 'Pidgeot',195 type: ['Normal', 'Flying'],196 hp: 83,197 attack: 80,198 defense: 75,199 special_attack: 70,200 special_defense: 70,201 speed: 101,202 },203 {204 id: 19,205 name: 'Rattata',206 type: ['Normal'],207 hp: 30,208 attack: 56,209 defense: 35,210 special_attack: 25,211 special_defense: 35,212 speed: 72,213 },214 {215 id: 20,216 name: 'Raticate',217 type: ['Normal'],218 hp: 55,219 attack: 81,220 defense: 60,221 special_attack: 50,222 special_defense: 70,223 speed: 97,224 },225 {226 id: 21,227 name: 'Spearow',228 type: ['Normal', 'Flying'],229 hp: 40,230 attack: 60,231 defense: 30,232 special_attack: 31,233 special_defense: 31,234 speed: 70,235 },236 {237 id: 22,238 name: 'Fearow',239 type: ['Normal', 'Flying'],240 hp: 65,241 attack: 90,242 defense: 65,243 special_attack: 61,244 special_defense: 61,245 speed: 100,246 },247 {248 id: 23,249 name: 'Ekans',250 type: ['Poison'],251 hp: 35,252 attack: 60,253 defense: 44,254 special_attack: 40,255 special_defense: 54,256 speed: 55,257 },258 {259 id: 24,260 name: 'Arbok',261 type: ['Poison'],262 hp: 60,263 attack: 95,264 defense: 69,265 special_attack: 65,266 special_defense: 79,267 speed: 80,268 },269 {270 id: 25,271 name: 'Pikachu',272 type: ['Electric'],273 hp: 35,274 attack: 55,275 defense: 40,276 special_attack: 50,277 special_defense: 50,278 speed: 90,279 },280 {281 id: 26,282 name: 'Raichu',283 type: ['Electric'],284 hp: 60,285 attack: 90,286 defense: 55,287 special_attack: 90,288 special_defense: 80,289 speed: 110,290 },291 {292 id: 27,293 name: 'Sandshrew',294 type: ['Ground'],295 hp: 50,296 attack: 75,297 defense: 85,298 special_attack: 20,299 special_defense: 30,300 speed: 40,301 },302 {303 id: 28,304 name: 'Sandslash',305 type: ['Ground'],306 hp: 75,307 attack: 100,308 defense: 110,309 special_attack: 45,310 special_defense: 55,311 speed: 65,312 },313 {314 id: 29,315 name: 'Nidoran♀',316 type: ['Poison'],317 hp: 55,318 attack: 47,319 defense: 52,320 special_attack: 40,321 special_defense: 40,322 speed: 41,323 },324 {325 id: 30,326 name: 'Nidorina',327 type: ['Poison'],328 hp: 70,329 attack: 62,330 defense: 67,331 special_attack: 55,332 special_defense: 55,333 speed: 56,334 },335 {336 id: 31,337 name: 'Nidoqueen',338 type: ['Poison', 'Ground'],339 hp: 90,340 attack: 92,341 defense: 87,342 special_attack: 75,343 special_defense: 85,344 speed: 76,345 },346 {347 id: 32,348 name: 'Nidoran♂',349 type: ['Poison'],350 hp: 46,351 attack: 57,352 defense: 40,353 special_attack: 40,354 special_defense: 40,355 speed: 50,356 },357 {358 id: 33,359 name: 'Nidorino',360 type: ['Poison'],361 hp: 61,362 attack: 72,363 defense: 57,364 special_attack: 55,365 special_defense: 55,366 speed: 65,367 },368 {369 id: 34,370 name: 'Nidoking',371 type: ['Poison', 'Ground'],372 hp: 81,373 attack: 102,374 defense: 77,375 special_attack: 85,376 special_defense: 75,377 speed: 85,378 },379 {380 id: 35,381 name: 'Clefairy',382 type: ['Fairy'],383 hp: 70,384 attack: 45,385 defense: 48,386 special_attack: 60,387 special_defense: 65,388 speed: 35,389 },390 {391 id: 36,392 name: 'Clefable',393 type: ['Fairy'],394 hp: 95,395 attack: 70,396 defense: 73,397 special_attack: 95,398 special_defense: 90,399 speed: 60,400 },401 {402 id: 37,403 name: 'Vulpix',404 type: ['Fire'],405 hp: 38,406 attack: 41,407 defense: 40,408 special_attack: 50,409 special_defense: 65,410 speed: 65,411 },412 {413 id: 38,414 name: 'Ninetales',415 type: ['Fire'],416 hp: 73,417 attack: 76,418 defense: 75,419 special_attack: 81,420 special_defense: 100,421 speed: 100,422 },423 {424 id: 39,425 name: 'Jigglypuff',426 type: ['Normal', 'Fairy'],427 hp: 115,428 attack: 45,429 defense: 20,430 special_attack: 45,431 special_defense: 25,432 speed: 20,433 },434 {435 id: 40,436 name: 'Wigglytuff',437 type: ['Normal', 'Fairy'],438 hp: 140,439 attack: 70,440 defense: 45,441 special_attack: 85,442 special_defense: 50,443 speed: 45,444 },445 {446 id: 41,447 name: 'Zubat',448 type: ['Poison', 'Flying'],449 hp: 40,450 attack: 45,451 defense: 35,452 special_attack: 30,453 special_defense: 40,454 speed: 55,455 },456 {457 id: 42,458 name: 'Golbat',459 type: ['Poison', 'Flying'],460 hp: 75,461 attack: 80,462 defense: 70,463 special_attack: 65,464 special_defense: 75,465 speed: 90,466 },467 {468 id: 43,469 name: 'Oddish',470 type: ['Grass', 'Poison'],471 hp: 45,472 attack: 50,473 defense: 55,474 special_attack: 75,475 special_defense: 65,476 speed: 30,477 },478 {479 id: 44,480 name: 'Gloom',481 type: ['Grass', 'Poison'],482 hp: 60,483 attack: 65,484 defense: 70,485 special_attack: 85,486 special_defense: 75,487 speed: 40,488 },489 {490 id: 45,491 name: 'Vileplume',492 type: ['Grass', 'Poison'],493 hp: 75,494 attack: 80,495 defense: 85,496 special_attack: 110,497 special_defense: 90,498 speed: 50,499 },500 {501 id: 46,502 name: 'Paras',503 type: ['Bug', 'Grass'],504 hp: 35,505 attack: 70,506 defense: 55,507 special_attack: 45,508 special_defense: 55,509 speed: 25,510 },511 {512 id: 47,513 name: 'Parasect',514 type: ['Bug', 'Grass'],515 hp: 60,516 attack: 95,517 defense: 80,518 special_attack: 60,519 special_defense: 80,520 speed: 30,521 },522 {523 id: 48,524 name: 'Venonat',525 type: ['Bug', 'Poison'],526 hp: 60,527 attack: 55,528 defense: 50,529 special_attack: 40,530 special_defense: 55,531 speed: 45,532 },533 {534 id: 49,535 name: 'Venomoth',536 type: ['Bug', 'Poison'],537 hp: 70,538 attack: 65,539 defense: 60,540 special_attack: 90,541 special_defense: 75,542 speed: 90,543 },544 {545 id: 50,546 name: 'Diglett',547 type: ['Ground'],548 hp: 10,549 attack: 55,550 defense: 25,551 special_attack: 35,552 special_defense: 45,553 speed: 95,554 },555 {556 id: 51,557 name: 'Dugtrio',558 type: ['Ground'],559 hp: 35,560 attack: 100,561 defense: 50,562 special_attack: 50,563 special_defense: 70,564 speed: 120,565 },566 {567 id: 52,568 name: 'Meowth',569 type: ['Normal'],570 hp: 40,571 attack: 45,572 defense: 35,573 special_attack: 40,574 special_defense: 40,575 speed: 90,576 },577 {578 id: 53,579 name: 'Persian',580 type: ['Normal'],581 hp: 65,582 attack: 70,583 defense: 60,584 special_attack: 65,585 special_defense: 65,586 speed: 115,587 },588 {589 id: 54,590 name: 'Psyduck',591 type: ['Water'],592 hp: 50,593 attack: 52,594 defense: 48,595 special_attack: 65,596 special_defense: 50,597 speed: 55,598 },599 {600 id: 55,601 name: 'Golduck',602 type: ['Water'],603 hp: 80,604 attack: 82,605 defense: 78,606 special_attack: 95,607 special_defense: 80,608 speed: 85,609 },610 {611 id: 56,612 name: 'Mankey',613 type: ['Fighting'],614 hp: 40,615 attack: 80,616 defense: 35,617 special_attack: 35,618 special_defense: 45,619 speed: 70,620 },621 {622 id: 57,623 name: 'Primeape',624 type: ['Fighting'],625 hp: 65,626 attack: 105,627 defense: 60,628 special_attack: 60,629 special_defense: 70,630 speed: 95,631 },632 {633 id: 58,634 name: 'Growlithe',635 type: ['Fire'],636 hp: 55,637 attack: 70,638 defense: 45,639 special_attack: 70,640 special_defense: 50,641 speed: 60,642 },643 {644 id: 59,645 name: 'Arcanine',646 type: ['Fire'],647 hp: 90,648 attack: 110,649 defense: 80,650 special_attack: 100,651 special_defense: 80,652 speed: 95,653 },654 {655 id: 60,656 name: 'Poliwag',657 type: ['Water'],658 hp: 40,659 attack: 50,660 defense: 40,661 special_attack: 40,662 special_defense: 40,663 speed: 90,664 },665 {666 id: 61,667 name: 'Poliwhirl',668 type: ['Water'],669 hp: 65,670 attack: 65,671 defense: 65,672 special_attack: 50,673 special_defense: 50,674 speed: 90,675 },676 {677 id: 62,678 name: 'Poliwrath',679 type: ['Water', 'Fighting'],680 hp: 90,681 attack: 95,682 defense: 95,683 special_attack: 70,684 special_defense: 90,685 speed: 70,686 },687 {688 id: 63,689 name: 'Abra',690 type: ['Psychic'],691 hp: 25,692 attack: 20,693 defense: 15,694 special_attack: 105,695 special_defense: 55,696 speed: 90,697 },698 {699 id: 64,700 name: 'Kadabra',701 type: ['Psychic'],702 hp: 40,703 attack: 35,704 defense: 30,705 special_attack: 120,706 special_defense: 70,707 speed: 105,708 },709 {710 id: 65,711 name: 'Alakazam',712 type: ['Psychic'],713 hp: 55,714 attack: 50,715 defense: 45,716 special_attack: 135,717 special_defense: 95,718 speed: 120,719 },720 {721 id: 66,722 name: 'Machop',723 type: ['Fighting'],724 hp: 70,725 attack: 80,726 defense: 50,727 special_attack: 35,728 special_defense: 35,729 speed: 35,730 },731 {732 id: 67,733 name: 'Machoke',734 type: ['Fighting'],735 hp: 80,736 attack: 100,737 defense: 70,738 special_attack: 50,739 special_defense: 60,740 speed: 45,741 },742 {743 id: 68,744 name: 'Machamp',745 type: ['Fighting'],746 hp: 90,747 attack: 130,748 defense: 80,749 special_attack: 65,750 special_defense: 85,751 speed: 55,752 },753 {754 id: 69,755 name: 'Bellsprout',756 type: ['Grass', 'Poison'],757 hp: 50,758 attack: 75,759 defense: 35,760 special_attack: 70,761 special_defense: 30,762 speed: 40,763 },764 {765 id: 70,766 name: 'Weepinbell',767 type: ['Grass', 'Poison'],768 hp: 65,769 attack: 90,770 defense: 50,771 special_attack: 85,772 special_defense: 45,773 speed: 55,774 },775 {776 id: 71,777 name: 'Victreebel',778 type: ['Grass', 'Poison'],779 hp: 80,780 attack: 105,781 defense: 65,782 special_attack: 100,783 special_defense: 70,784 speed: 70,785 },786 {787 id: 72,788 name: 'Tentacool',789 type: ['Water', 'Poison'],790 hp: 40,791 attack: 40,792 defense: 35,793 special_attack: 50,794 special_defense: 100,795 speed: 70,796 },797 {798 id: 73,799 name: 'Tentacruel',800 type: ['Water', 'Poison'],801 hp: 80,802 attack: 70,803 defense: 65,804 special_attack: 80,805 special_defense: 120,806 speed: 100,807 },808 {809 id: 74,810 name: 'Geodude',811 type: ['Rock', 'Ground'],812 hp: 40,813 attack: 80,814 defense: 100,815 special_attack: 30,816 special_defense: 30,817 speed: 20,818 },819 {820 id: 75,821 name: 'Graveler',822 type: ['Rock', 'Ground'],823 hp: 55,824 attack: 95,825 defense: 115,826 special_attack: 45,827 special_defense: 45,828 speed: 35,829 },830 {831 id: 76,832 name: 'Golem',833 type: ['Rock', 'Ground'],834 hp: 80,835 attack: 120,836 defense: 130,837 special_attack: 55,838 special_defense: 65,839 speed: 45,840 },841 {842 id: 77,843 name: 'Ponyta',844 type: ['Fire'],845 hp: 50,846 attack: 85,847 defense: 55,848 special_attack: 65,849 special_defense: 65,850 speed: 90,851 },852 {853 id: 78,854 name: 'Rapidash',855 type: ['Fire'],856 hp: 65,857 attack: 100,858 defense: 70,859 special_attack: 80,860 special_defense: 80,861 speed: 105,862 },863 {864 id: 79,865 name: 'Slowpoke',866 type: ['Water', 'Psychic'],867 hp: 90,868 attack: 65,869 defense: 65,870 special_attack: 40,871 special_defense: 40,872 speed: 15,873 },874 {875 id: 80,876 name: 'Slowbro',877 type: ['Water', 'Psychic'],878 hp: 95,879 attack: 75,880 defense: 110,881 special_attack: 100,882 special_defense: 80,883 speed: 30,884 },885 {886 id: 81,887 name: 'Magnemite',888 type: ['Electric', 'Steel'],889 hp: 25,890 attack: 35,891 defense: 70,892 special_attack: 95,893 special_defense: 55,894 speed: 45,895 },896 {897 id: 82,898 name: 'Magneton',899 type: ['Electric', 'Steel'],900 hp: 50,901 attack: 60,902 defense: 95,903 special_attack: 120,904 special_defense: 70,905 speed: 70,906 },907 {908 id: 83,909 name: "Farfetch'd",910 type: ['Normal', 'Flying'],911 hp: 52,912 attack: 90,913 defense: 55,914 special_attack: 58,915 special_defense: 62,916 speed: 60,917 },918 {919 id: 84,920 name: 'Doduo',921 type: ['Normal', 'Flying'],922 hp: 35,923 attack: 85,924 defense: 45,925 special_attack: 35,926 special_defense: 35,927 speed: 75,928 },929 {930 id: 85,931 name: 'Dodrio',932 type: ['Normal', 'Flying'],933 hp: 60,934 attack: 110,935 defense: 70,936 special_attack: 60,937 special_defense: 60,938 speed: 110,939 },940 {941 id: 86,942 name: 'Seel',943 type: ['Water'],944 hp: 65,945 attack: 45,946 defense: 55,947 special_attack: 45,948 special_defense: 70,949 speed: 45,950 },951 {952 id: 87,953 name: 'Dewgong',954 type: ['Water', 'Ice'],955 hp: 90,956 attack: 70,957 defense: 80,958 special_attack: 70,959 special_defense: 95,960 speed: 70,961 },962 {963 id: 88,964 name: 'Grimer',965 type: ['Poison'],966 hp: 80,967 attack: 80,968 defense: 50,969 special_attack: 40,970 special_defense: 50,971 speed: 25,972 },973 {974 id: 89,975 name: 'Muk',976 type: ['Poison'],977 hp: 105,978 attack: 105,979 defense: 75,980 special_attack: 65,981 special_defense: 100,982 speed: 50,983 },984 {985 id: 90,986 name: 'Shellder',987 type: ['Water'],988 hp: 30,989 attack: 65,990 defense: 100,991 special_attack: 45,992 special_defense: 25,993 speed: 40,994 },995 {996 id: 91,997 name: 'Cloyster',998 type: ['Water', 'Ice'],999 hp: 50,1000 attack: 95,1001 defense: 180,1002 special_attack: 85,1003 special_defense: 45,1004 speed: 70,1005 },1006 {1007 id: 92,1008 name: 'Gastly',1009 type: ['Ghost', 'Poison'],1010 hp: 30,1011 attack: 35,1012 defense: 30,1013 special_attack: 100,1014 special_defense: 35,1015 speed: 80,1016 },1017 {1018 id: 93,1019 name: 'Haunter',1020 type: ['Ghost', 'Poison'],1021 hp: 45,1022 attack: 50,1023 defense: 45,1024 special_attack: 115,1025 special_defense: 55,1026 speed: 95,1027 },1028 {1029 id: 94,1030 name: 'Gengar',1031 type: ['Ghost', 'Poison'],1032 hp: 60,1033 attack: 65,1034 defense: 60,1035 special_attack: 130,1036 special_defense: 75,1037 speed: 110,1038 },1039 {1040 id: 95,1041 name: 'Onix',1042 type: ['Rock', 'Ground'],1043 hp: 35,1044 attack: 45,1045 defense: 160,1046 special_attack: 30,1047 special_defense: 45,1048 speed: 70,1049 },1050 {1051 id: 96,1052 name: 'Drowzee',1053 type: ['Psychic'],1054 hp: 60,1055 attack: 48,1056 defense: 45,1057 special_attack: 43,1058 special_defense: 90,1059 speed: 42,1060 },1061 {1062 id: 97,1063 name: 'Hypno',1064 type: ['Psychic'],1065 hp: 85,1066 attack: 73,1067 defense: 70,1068 special_attack: 73,1069 special_defense: 115,1070 speed: 67,1071 },1072 {1073 id: 98,1074 name: 'Krabby',1075 type: ['Water'],1076 hp: 30,1077 attack: 105,1078 defense: 90,1079 special_attack: 25,1080 special_defense: 25,1081 speed: 50,1082 },1083 {1084 id: 99,1085 name: 'Kingler',1086 type: ['Water'],1087 hp: 55,1088 attack: 130,1089 defense: 115,1090 special_attack: 50,1091 special_defense: 50,1092 speed: 75,1093 },1094 {1095 id: 100,1096 name: 'Voltorb',1097 type: ['Electric'],1098 hp: 40,1099 attack: 30,1100 defense: 50,1101 special_attack: 55,1102 special_defense: 55,1103 speed: 100,1104 },1105 {1106 id: 101,1107 name: 'Electrode',1108 type: ['Electric'],1109 hp: 60,1110 attack: 50,1111 defense: 70,1112 special_attack: 80,1113 special_defense: 80,1114 speed: 150,1115 },1116 {1117 id: 102,1118 name: 'Exeggcute',1119 type: ['Grass', 'Psychic'],1120 hp: 60,1121 attack: 40,1122 defense: 80,1123 special_attack: 60,1124 special_defense: 45,1125 speed: 40,1126 },1127 {1128 id: 103,1129 name: 'Exeggutor',1130 type: ['Grass', 'Psychic'],1131 hp: 95,1132 attack: 95,1133 defense: 85,1134 special_attack: 125,1135 special_defense: 75,1136 speed: 55,1137 },1138 {1139 id: 104,1140 name: 'Cubone',1141 type: ['Ground'],1142 hp: 50,1143 attack: 50,1144 defense: 95,1145 special_attack: 40,1146 special_defense: 50,1147 speed: 35,1148 },1149 {1150 id: 105,1151 name: 'Marowak',1152 type: ['Ground'],1153 hp: 60,1154 attack: 80,1155 defense: 110,1156 special_attack: 50,1157 special_defense: 80,1158 speed: 45,1159 },1160 {1161 id: 106,1162 name: 'Hitmonlee',1163 type: ['Fighting'],1164 hp: 50,1165 attack: 120,1166 defense: 53,1167 special_attack: 35,1168 special_defense: 110,1169 speed: 87,1170 },1171 {1172 id: 107,1173 name: 'Hitmonchan',1174 type: ['Fighting'],1175 hp: 50,1176 attack: 105,1177 defense: 79,1178 special_attack: 35,1179 special_defense: 110,1180 speed: 76,1181 },1182 {1183 id: 108,1184 name: 'Lickitung',1185 type: ['Normal'],1186 hp: 90,1187 attack: 55,1188 defense: 75,1189 special_attack: 60,1190 special_defense: 75,1191 speed: 30,1192 },1193 {1194 id: 109,1195 name: 'Koffing',1196 type: ['Poison'],1197 hp: 40,1198 attack: 65,1199 defense: 95,1200 special_attack: 60,1201 special_defense: 45,1202 speed: 35,1203 },1204 {1205 id: 110,1206 name: 'Weezing',1207 type: ['Poison'],1208 hp: 65,1209 attack: 90,1210 defense: 120,1211 special_attack: 85,1212 special_defense: 70,1213 speed: 60,1214 },1215 {1216 id: 111,1217 name: 'Rhyhorn',1218 type: ['Ground', 'Rock'],1219 hp: 80,1220 attack: 85,1221 defense: 95,1222 special_attack: 30,1223 special_defense: 30,1224 speed: 25,1225 },1226 {1227 id: 112,1228 name: 'Rhydon',1229 type: ['Ground', 'Rock'],1230 hp: 105,1231 attack: 130,1232 defense: 120,1233 special_attack: 45,1234 special_defense: 45,1235 speed: 40,1236 },1237 {1238 id: 113,1239 name: 'Chansey',1240 type: ['Normal'],1241 hp: 250,1242 attack: 5,1243 defense: 5,1244 special_attack: 35,1245 special_defense: 105,1246 speed: 50,1247 },1248 {1249 id: 114,1250 name: 'Tangela',1251 type: ['Grass'],1252 hp: 65,1253 attack: 55,1254 defense: 115,1255 special_attack: 100,1256 special_defense: 40,1257 speed: 60,1258 },1259 {1260 id: 115,1261 name: 'Kangaskhan',1262 type: ['Normal'],1263 hp: 105,1264 attack: 95,1265 defense: 80,1266 special_attack: 40,1267 special_defense: 80,1268 speed: 90,1269 },1270 {1271 id: 116,1272 name: 'Horsea',1273 type: ['Water'],1274 hp: 30,1275 attack: 40,1276 defense: 70,1277 special_attack: 70,1278 special_defense: 25,1279 speed: 60,1280 },1281 {1282 id: 117,1283 name: 'Seadra',1284 type: ['Water'],1285 hp: 55,1286 attack: 65,1287 defense: 95,1288 special_attack: 95,1289 special_defense: 45,1290 speed: 85,1291 },1292 {1293 id: 118,1294 name: 'Goldeen',1295 type: ['Water'],1296 hp: 45,1297 attack: 67,1298 defense: 60,1299 special_attack: 35,1300 special_defense: 50,1301 speed: 63,1302 },1303 {1304 id: 119,1305 name: 'Seaking',1306 type: ['Water'],1307 hp: 80,1308 attack: 92,1309 defense: 65,1310 special_attack: 65,1311 special_defense: 80,1312 speed: 68,1313 },1314 {1315 id: 120,1316 name: 'Staryu',1317 type: ['Water'],1318 hp: 30,1319 attack: 45,1320 defense: 55,1321 special_attack: 70,1322 special_defense: 55,1323 speed: 85,1324 },1325 {1326 id: 121,1327 name: 'Starmie',1328 type: ['Water', 'Psychic'],1329 hp: 60,1330 attack: 75,1331 defense: 85,1332 special_attack: 100,1333 special_defense: 85,1334 speed: 115,1335 },1336 {1337 id: 122,1338 name: 'Mr. Mime',1339 type: ['Psychic', 'Fairy'],1340 hp: 40,1341 attack: 45,1342 defense: 65,1343 special_attack: 100,1344 special_defense: 120,1345 speed: 90,1346 },1347 {1348 id: 123,1349 name: 'Scyther',1350 type: ['Bug', 'Flying'],1351 hp: 70,1352 attack: 110,1353 defense: 80,1354 special_attack: 55,1355 special_defense: 80,1356 speed: 105,1357 },1358 {1359 id: 124,1360 name: 'Jynx',1361 type: ['Ice', 'Psychic'],1362 hp: 65,1363 attack: 50,1364 defense: 35,1365 special_attack: 115,1366 special_defense: 95,1367 speed: 95,1368 },1369 {1370 id: 125,1371 name: 'Electabuzz',1372 type: ['Electric'],1373 hp: 65,1374 attack: 83,1375 defense: 57,1376 special_attack: 95,1377 special_defense: 85,1378 speed: 105,1379 },1380 {1381 id: 126,1382 name: 'Magmar',1383 type: ['Fire'],1384 hp: 65,1385 attack: 95,1386 defense: 57,1387 special_attack: 100,1388 special_defense: 85,1389 speed: 93,1390 },1391 {1392 id: 127,1393 name: 'Pinsir',1394 type: ['Bug'],1395 hp: 65,1396 attack: 125,1397 defense: 100,1398 special_attack: 55,1399 special_defense: 70,1400 speed: 85,1401 },1402 {1403 id: 128,1404 name: 'Tauros',1405 type: ['Normal'],1406 hp: 75,1407 attack: 100,1408 defense: 95,1409 special_attack: 40,1410 special_defense: 70,1411 speed: 110,1412 },1413 {1414 id: 129,1415 name: 'Magikarp',1416 type: ['Water'],1417 hp: 20,1418 attack: 10,1419 defense: 55,1420 special_attack: 15,1421 special_defense: 20,1422 speed: 80,1423 },1424 {1425 id: 130,1426 name: 'Gyarados',1427 type: ['Water', 'Flying'],1428 hp: 95,1429 attack: 125,1430 defense: 79,1431 special_attack: 60,1432 special_defense: 100,1433 speed: 81,1434 },1435 {1436 id: 131,1437 name: 'Lapras',1438 type: ['Water', 'Ice'],1439 hp: 130,1440 attack: 85,1441 defense: 80,1442 special_attack: 85,1443 special_defense: 95,1444 speed: 60,1445 },1446 {1447 id: 132,1448 name: 'Ditto',1449 type: ['Normal'],1450 hp: 48,1451 attack: 48,1452 defense: 48,1453 special_attack: 48,1454 special_defense: 48,1455 speed: 48,1456 },1457 {1458 id: 133,1459 name: 'Eevee',1460 type: ['Normal'],1461 hp: 55,1462 attack: 55,1463 defense: 50,1464 special_attack: 45,1465 special_defense: 65,1466 speed: 55,1467 },1468 {1469 id: 134,1470 name: 'Vaporeon',1471 type: ['Water'],1472 hp: 130,1473 attack: 65,1474 defense: 60,1475 special_attack: 110,1476 special_defense: 95,1477 speed: 65,1478 },1479 {1480 id: 135,1481 name: 'Jolteon',1482 type: ['Electric'],1483 hp: 65,1484 attack: 65,1485 defense: 60,1486 special_attack: 110,1487 special_defense: 95,1488 speed: 130,1489 },1490 {1491 id: 136,1492 name: 'Flareon',1493 type: ['Fire'],1494 hp: 65,1495 attack: 130,1496 defense: 60,1497 special_attack: 95,1498 special_defense: 110,1499 speed: 65,1500 },1501 {1502 id: 137,1503 name: 'Porygon',1504 type: ['Normal'],1505 hp: 65,1506 attack: 60,1507 defense: 70,1508 special_attack: 85,1509 special_defense: 75,1510 speed: 40,1511 },1512 {1513 id: 138,1514 name: 'Omanyte',1515 type: ['Rock', 'Water'],1516 hp: 35,1517 attack: 40,1518 defense: 100,1519 special_attack: 90,1520 special_defense: 55,1521 speed: 35,1522 },1523 {1524 id: 139,1525 name: 'Omastar',1526 type: ['Rock', 'Water'],1527 hp: 70,1528 attack: 60,1529 defense: 125,1530 special_attack: 115,1531 special_defense: 70,1532 speed: 55,1533 },1534 {1535 id: 140,1536 name: 'Kabuto',1537 type: ['Rock', 'Water'],1538 hp: 30,1539 attack: 80,1540 defense: 90,1541 special_attack: 55,1542 special_defense: 45,1543 speed: 55,1544 },1545 {1546 id: 141,1547 name: 'Kabutops',1548 type: ['Rock', 'Water'],1549 hp: 60,1550 attack: 115,1551 defense: 105,1552 special_attack: 65,1553 special_defense: 70,1554 speed: 80,1555 },1556 {1557 id: 142,1558 name: 'Aerodactyl',1559 type: ['Rock', 'Flying'],1560 hp: 80,1561 attack: 105,1562 defense: 65,1563 special_attack: 60,1564 special_defense: 75,1565 speed: 130,1566 },1567 {1568 id: 143,1569 name: 'Snorlax',1570 type: ['Normal'],1571 hp: 160,1572 attack: 110,1573 defense: 65,1574 special_attack: 65,1575 special_defense: 110,1576 speed: 30,1577 },1578 {1579 id: 144,1580 name: 'Articuno',1581 type: ['Ice', 'Flying'],1582 hp: 90,1583 attack: 85,1584 defense: 100,1585 special_attack: 95,1586 special_defense: 125,1587 speed: 85,1588 },1589 {1590 id: 145,1591 name: 'Zapdos',1592 type: ['Electric', 'Flying'],1593 hp: 90,1594 attack: 90,1595 defense: 85,1596 special_attack: 125,1597 special_defense: 90,1598 speed: 100,1599 },1600 {1601 id: 146,1602 name: 'Moltres',1603 type: ['Fire', 'Flying'],1604 hp: 90,1605 attack: 100,1606 defense: 90,1607 special_attack: 125,1608 special_defense: 85,1609 speed: 90,1610 },1611 {1612 id: 147,1613 name: 'Dratini',1614 type: ['Dragon'],1615 hp: 41,1616 attack: 64,1617 defense: 45,1618 special_attack: 50,1619 special_defense: 50,1620 speed: 50,1621 },1622 {1623 id: 148,1624 name: 'Dragonair',1625 type: ['Dragon'],1626 hp: 61,1627 attack: 84,1628 defense: 65,1629 special_attack: 70,1630 special_defense: 70,1631 speed: 70,1632 },1633 {1634 id: 149,1635 name: 'Dragonite',1636 type: ['Dragon', 'Flying'],1637 hp: 91,1638 attack: 134,1639 defense: 95,1640 special_attack: 100,1641 special_defense: 100,1642 speed: 80,1643 },1644 {1645 id: 150,1646 name: 'Mewtwo',1647 type: ['Psychic'],1648 hp: 106,1649 attack: 110,1650 defense: 90,1651 special_attack: 154,1652 special_defense: 90,1653 speed: 130,1654 },1655 {1656 id: 151,1657 name: 'Mew',1658 type: ['Psychic'],1659 hp: 100,1660 attack: 100,1661 defense: 100,1662 special_attack: 100,1663 special_defense: 100,1664 speed: 100,1665 },1666 {1667 id: 152,1668 name: 'Chikorita',1669 type: ['Grass'],1670 hp: 45,1671 attack: 49,1672 defense: 65,1673 special_attack: 49,1674 special_defense: 65,1675 speed: 45,1676 },1677 {1678 id: 153,1679 name: 'Bayleef',1680 type: ['Grass'],1681 hp: 60,1682 attack: 62,1683 defense: 80,1684 special_attack: 63,1685 special_defense: 80,1686 speed: 60,1687 },1688 {1689 id: 154,1690 name: 'Meganium',1691 type: ['Grass'],1692 hp: 80,1693 attack: 82,1694 defense: 100,1695 special_attack: 83,1696 special_defense: 100,1697 speed: 80,1698 },1699 {1700 id: 155,1701 name: 'Cyndaquil',1702 type: ['Fire'],1703 hp: 39,1704 attack: 52,1705 defense: 43,1706 special_attack: 60,1707 special_defense: 50,1708 speed: 65,1709 },1710 {1711 id: 156,1712 name: 'Quilava',1713 type: ['Fire'],1714 hp: 58,1715 attack: 64,1716 defense: 58,1717 special_attack: 80,1718 special_defense: 65,1719 speed: 80,1720 },1721 {1722 id: 157,1723 name: 'Typhlosion',1724 type: ['Fire'],1725 hp: 78,1726 attack: 84,1727 defense: 78,1728 special_attack: 109,1729 special_defense: 85,1730 speed: 100,1731 },1732 {1733 id: 158,1734 name: 'Totodile',1735 type: ['Water'],1736 hp: 50,1737 attack: 65,1738 defense: 64,1739 special_attack: 44,1740 special_defense: 48,1741 speed: 43,1742 },1743 {1744 id: 159,1745 name: 'Croconaw',1746 type: ['Water'],1747 hp: 65,1748 attack: 80,1749 defense: 80,1750 special_attack: 59,1751 special_defense: 63,1752 speed: 58,1753 },1754 {1755 id: 160,1756 name: 'Feraligatr',1757 type: ['Water'],1758 hp: 85,1759 attack: 105,1760 defense: 100,1761 special_attack: 79,1762 special_defense: 83,1763 speed: 78,1764 },1765 {1766 id: 161,1767 name: 'Sentret',1768 type: ['Normal'],1769 hp: 35,1770 attack: 46,1771 defense: 34,1772 special_attack: 35,1773 special_defense: 45,1774 speed: 20,1775 },1776 {1777 id: 162,1778 name: 'Furret',1779 type: ['Normal'],1780 hp: 85,1781 attack: 76,1782 defense: 64,1783 special_attack: 45,1784 special_defense: 55,1785 speed: 90,1786 },1787 {1788 id: 163,1789 name: 'Hoothoot',1790 type: ['Normal', 'Flying'],1791 hp: 60,1792 attack: 30,1793 defense: 30,1794 special_attack: 36,1795 special_defense: 56,1796 speed: 50,1797 },1798 {1799 id: 164,1800 name: 'Noctowl',1801 type: ['Normal', 'Flying'],1802 hp: 100,1803 attack: 50,1804 defense: 50,1805 special_attack: 86,1806 special_defense: 96,1807 speed: 70,1808 },1809 {1810 id: 165,1811 name: 'Ledyba',1812 type: ['Bug', 'Flying'],1813 hp: 40,1814 attack: 20,1815 defense: 30,1816 special_attack: 40,1817 special_defense: 80,1818 speed: 55,1819 },1820 {1821 id: 166,1822 name: 'Ledian',1823 type: ['Bug', 'Flying'],1824 hp: 55,1825 attack: 35,1826 defense: 50,1827 special_attack: 55,1828 special_defense: 110,1829 speed: 85,1830 },1831 {1832 id: 167,1833 name: 'Spinarak',1834 type: ['Bug', 'Poison'],1835 hp: 40,1836 attack: 60,1837 defense: 40,1838 special_attack: 40,1839 special_defense: 40,1840 speed: 30,1841 },1842 {1843 id: 168,1844 name: 'Ariados',1845 type: ['Bug', 'Poison'],1846 hp: 70,1847 attack: 90,1848 defense: 70,1849 special_attack: 60,1850 special_defense: 70,1851 speed: 40,1852 },1853 {1854 id: 169,1855 name: 'Crobat',1856 type: ['Poison', 'Flying'],1857 hp: 85,1858 attack: 90,1859 defense: 80,1860 special_attack: 70,1861 special_defense: 80,1862 speed: 130,1863 },1864 {1865 id: 170,1866 name: 'Chinchou',1867 type: ['Water', 'Electric'],1868 hp: 75,1869 attack: 38,1870 defense: 38,1871 special_attack: 56,1872 special_defense: 56,1873 speed: 67,1874 },1875 {1876 id: 171,1877 name: 'Lanturn',1878 type: ['Water', 'Electric'],1879 hp: 125,1880 attack: 58,1881 defense: 58,1882 special_attack: 76,1883 special_defense: 76,1884 speed: 67,1885 },1886 {1887 id: 172,1888 name: 'Pichu',1889 type: ['Electric'],1890 hp: 20,1891 attack: 40,1892 defense: 15,1893 special_attack: 35,1894 special_defense: 35,1895 speed: 60,1896 },1897 {1898 id: 173,1899 name: 'Cleffa',1900 type: ['Fairy'],1901 hp: 50,1902 attack: 25,1903 defense: 28,1904 special_attack: 45,1905 special_defense: 55,1906 speed: 15,1907 },1908 {1909 id: 174,1910 name: 'Igglybuff',1911 type: ['Normal', 'Fairy'],1912 hp: 90,1913 attack: 30,1914 defense: 15,1915 special_attack: 40,1916 special_defense: 20,1917 speed: 15,1918 },1919 {1920 id: 175,1921 name: 'Togepi',1922 type: ['Fairy'],1923 hp: 35,1924 attack: 20,1925 defense: 65,1926 special_attack: 40,1927 special_defense: 65,1928 speed: 20,1929 },1930 {1931 id: 176,1932 name: 'Togetic',1933 type: ['Fairy', 'Flying'],1934 hp: 55,1935 attack: 40,1936 defense: 85,1937 special_attack: 80,1938 special_defense: 105,1939 speed: 40,1940 },1941 {1942 id: 177,1943 name: 'Natu',1944 type: ['Psychic', 'Flying'],1945 hp: 40,1946 attack: 50,1947 defense: 45,1948 special_attack: 70,1949 special_defense: 45,1950 speed: 70,1951 },1952 {1953 id: 178,1954 name: 'Xatu',1955 type: ['Psychic', 'Flying'],1956 hp: 65,1957 attack: 75,1958 defense: 70,1959 special_attack: 95,1960 special_defense: 70,1961 speed: 95,1962 },1963 {1964 id: 179,1965 name: 'Mareep',1966 type: ['Electric'],1967 hp: 55,1968 attack: 40,1969 defense: 40,1970 special_attack: 65,1971 special_defense: 45,1972 speed: 35,1973 },1974 {1975 id: 180,1976 name: 'Flaaffy',1977 type: ['Electric'],1978 hp: 70,1979 attack: 55,1980 defense: 55,1981 special_attack: 80,1982 special_defense: 60,1983 speed: 45,1984 },1985 {1986 id: 181,1987 name: 'Ampharos',1988 type: ['Electric'],1989 hp: 90,1990 attack: 75,1991 defense: 85,1992 special_attack: 115,1993 special_defense: 90,1994 speed: 55,1995 },1996 {1997 id: 182,1998 name: 'Bellossom',1999 type: ['Grass'],2000 hp: 75,2001 attack: 80,2002 defense: 95,2003 special_attack: 90,2004 special_defense: 100,2005 speed: 50,2006 },2007 {2008 id: 183,2009 name: 'Marill',2010 type: ['Water', 'Fairy'],2011 hp: 70,2012 attack: 20,2013 defense: 50,2014 special_attack: 20,2015 special_defense: 50,2016 speed: 40,2017 },2018 {2019 id: 184,2020 name: 'Azumarill',2021 type: ['Water', 'Fairy'],2022 hp: 100,2023 attack: 50,2024 defense: 80,2025 special_attack: 60,2026 special_defense: 80,2027 speed: 50,2028 },2029 {2030 id: 185,2031 name: 'Sudowoodo',2032 type: ['Rock'],2033 hp: 70,2034 attack: 100,2035 defense: 115,2036 special_attack: 30,2037 special_defense: 65,2038 speed: 30,2039 },2040 {2041 id: 186,2042 name: 'Politoed',2043 type: ['Water'],2044 hp: 90,2045 attack: 75,2046 defense: 75,2047 special_attack: 90,2048 special_defense: 100,2049 speed: 70,2050 },2051 {2052 id: 187,2053 name: 'Hoppip',2054 type: ['Grass', 'Flying'],2055 hp: 35,2056 attack: 35,2057 defense: 40,2058 special_attack: 35,2059 special_defense: 55,2060 speed: 50,2061 },2062 {2063 id: 188,2064 name: 'Skiploom',2065 type: ['Grass', 'Flying'],2066 hp: 55,2067 attack: 45,2068 defense: 50,2069 special_attack: 45,2070 special_defense: 65,2071 speed: 80,2072 },2073 {2074 id: 189,2075 name: 'Jumpluff',2076 type: ['Grass', 'Flying'],2077 hp: 75,2078 attack: 55,2079 defense: 70,2080 special_attack: 55,2081 special_defense: 95,2082 speed: 110,2083 },2084 {2085 id: 190,2086 name: 'Aipom',2087 type: ['Normal'],2088 hp: 55,2089 attack: 70,2090 defense: 55,2091 special_attack: 40,2092 special_defense: 55,2093 speed: 85,2094 },2095 {2096 id: 191,2097 name: 'Sunkern',2098 type: ['Grass'],2099 hp: 30,2100 attack: 30,2101 defense: 30,2102 special_attack: 30,2103 special_defense: 30,2104 speed: 30,2105 },2106 {2107 id: 192,2108 name: 'Sunflora',2109 type: ['Grass'],2110 hp: 75,2111 attack: 75,2112 defense: 55,2113 special_attack: 105,2114 special_defense: 85,2115 speed: 30,2116 },2117 {2118 id: 193,2119 name: 'Yanma',2120 type: ['Bug', 'Flying'],2121 hp: 65,2122 attack: 65,2123 defense: 45,2124 special_attack: 75,2125 special_defense: 45,2126 speed: 95,2127 },2128 {2129 id: 194,2130 name: 'Wooper',2131 type: ['Water', 'Ground'],2132 hp: 55,2133 attack: 45,2134 defense: 45,2135 special_attack: 25,2136 special_defense: 25,2137 speed: 15,2138 },2139 {2140 id: 195,2141 name: 'Quagsire',2142 type: ['Water', 'Ground'],2143 hp: 95,2144 attack: 85,2145 defense: 85,2146 special_attack: 65,2147 special_defense: 65,2148 speed: 35,2149 },2150 {2151 id: 196,2152 name: 'Espeon',2153 type: ['Psychic'],2154 hp: 65,2155 attack: 65,2156 defense: 60,2157 special_attack: 130,2158 special_defense: 95,2159 speed: 110,2160 },2161 {2162 id: 197,2163 name: 'Umbreon',2164 type: ['Dark'],2165 hp: 95,2166 attack: 65,2167 defense: 110,2168 special_attack: 60,2169 special_defense: 130,2170 speed: 65,2171 },2172 {2173 id: 198,2174 name: 'Murkrow',2175 type: ['Dark', 'Flying'],2176 hp: 60,2177 attack: 85,2178 defense: 42,2179 special_attack: 85,2180 special_defense: 42,2181 speed: 91,2182 },2183 {2184 id: 199,2185 name: 'Slowking',2186 type: ['Water', 'Psychic'],2187 hp: 95,2188 attack: 75,2189 defense: 80,2190 special_attack: 100,2191 special_defense: 110,2192 speed: 30,2193 },2194 {2195 id: 200,2196 name: 'Misdreavus',2197 type: ['Ghost'],2198 hp: 60,2199 attack: 60,2200 defense: 60,2201 special_attack: 85,2202 special_defense: 85,2203 speed: 85,2204 },2205 {2206 id: 201,2207 name: 'Unown',2208 type: ['Psychic'],2209 hp: 48,2210 attack: 72,2211 defense: 48,2212 special_attack: 72,2213 special_defense: 48,2214 speed: 48,2215 },2216 {2217 id: 202,2218 name: 'Wobbuffet',2219 type: ['Psychic'],2220 hp: 190,2221 attack: 33,2222 defense: 58,2223 special_attack: 33,2224 special_defense: 58,2225 speed: 33,2226 },2227 {2228 id: 203,2229 name: 'Girafarig',2230 type: ['Normal', 'Psychic'],2231 hp: 70,2232 attack: 80,2233 defense: 65,2234 special_attack: 90,2235 special_defense: 65,2236 speed: 85,2237 },2238 {2239 id: 204,2240 name: 'Pineco',2241 type: ['Bug'],2242 hp: 50,2243 attack: 65,2244 defense: 90,2245 special_attack: 35,2246 special_defense: 35,2247 speed: 15,2248 },2249 {2250 id: 205,2251 name: 'Forretress',2252 type: ['Bug', 'Steel'],2253 hp: 75,2254 attack: 90,2255 defense: 140,2256 special_attack: 60,2257 special_defense: 60,2258 speed: 40,2259 },2260 {2261 id: 206,2262 name: 'Dunsparce',2263 type: ['Normal'],2264 hp: 100,2265 attack: 70,2266 defense: 70,2267 special_attack: 65,2268 special_defense: 65,2269 speed: 45,2270 },2271 {2272 id: 207,2273 name: 'Gligar',2274 type: ['Ground', 'Flying'],2275 hp: 65,2276 attack: 75,2277 defense: 105,2278 special_attack: 35,2279 special_defense: 65,2280 speed: 85,2281 },2282 {2283 id: 208,2284 name: 'Steelix',2285 type: ['Steel', 'Ground'],2286 hp: 75,2287 attack: 85,2288 defense: 200,2289 special_attack: 55,2290 special_defense: 65,2291 speed: 30,2292 },2293 {2294 id: 209,2295 name: 'Snubbull',2296 type: ['Fairy'],2297 hp: 60,2298 attack: 80,2299 defense: 50,2300 special_attack: 40,2301 special_defense: 40,2302 speed: 30,2303 },2304 {2305 id: 210,2306 name: 'Granbull',2307 type: ['Fairy'],2308 hp: 90,2309 attack: 120,2310 defense: 75,2311 special_attack: 60,2312 special_defense: 60,2313 speed: 45,2314 },2315 {2316 id: 211,2317 name: 'Qwilfish',2318 type: ['Water', 'Poison'],2319 hp: 65,2320 attack: 95,2321 defense: 85,2322 special_attack: 55,2323 special_defense: 55,2324 speed: 85,2325 },2326 {2327 id: 212,2328 name: 'Scizor',2329 type: ['Bug', 'Steel'],2330 hp: 70,2331 attack: 130,2332 defense: 100,2333 special_attack: 55,2334 special_defense: 80,2335 speed: 65,2336 },2337 {2338 id: 213,2339 name: 'Shuckle',2340 type: ['Bug', 'Rock'],2341 hp: 20,2342 attack: 10,2343 defense: 230,2344 special_attack: 10,2345 special_defense: 230,2346 speed: 5,2347 },2348 {2349 id: 214,2350 name: 'Heracross',2351 type: ['Bug', 'Fighting'],2352 hp: 80,2353 attack: 125,2354 defense: 75,2355 special_attack: 40,2356 special_defense: 95,2357 speed: 85,2358 },2359 {2360 id: 215,2361 name: 'Sneasel',2362 type: ['Dark', 'Ice'],2363 hp: 55,2364 attack: 95,2365 defense: 55,2366 special_attack: 35,2367 special_defense: 75,2368 speed: 115,2369 },2370 {2371 id: 216,2372 name: 'Teddiursa',2373 type: ['Normal'],2374 hp: 60,2375 attack: 80,2376 defense: 50,2377 special_attack: 50,2378 special_defense: 50,2379 speed: 40,2380 },2381 {2382 id: 217,2383 name: 'Ursaring',2384 type: ['Normal'],2385 hp: 90,2386 attack: 130,2387 defense: 75,2388 special_attack: 75,2389 special_defense: 75,2390 speed: 55,2391 },2392 {2393 id: 218,2394 name: 'Slugma',2395 type: ['Fire'],2396 hp: 40,2397 attack: 40,2398 defense: 40,2399 special_attack: 70,2400 special_defense: 40,2401 speed: 20,2402 },2403 {2404 id: 219,2405 name: 'Magcargo',2406 type: ['Fire', 'Rock'],2407 hp: 60,2408 attack: 50,2409 defense: 120,2410 special_attack: 90,2411 special_defense: 80,2412 speed: 30,2413 },2414 {2415 id: 220,2416 name: 'Swinub',2417 type: ['Ice', 'Ground'],2418 hp: 50,2419 attack: 50,2420 defense: 40,2421 special_attack: 30,2422 special_defense: 30,2423 speed: 50,2424 },2425 {2426 id: 221,2427 name: 'Piloswine',2428 type: ['Ice', 'Ground'],2429 hp: 100,2430 attack: 100,2431 defense: 80,2432 special_attack: 60,2433 special_defense: 60,2434 speed: 50,2435 },2436 {2437 id: 222,2438 name: 'Corsola',2439 type: ['Water', 'Rock'],2440 hp: 65,2441 attack: 55,2442 defense: 95,2443 special_attack: 65,2444 special_defense: 95,2445 speed: 35,2446 },2447 {2448 id: 223,2449 name: 'Remoraid',2450 type: ['Water'],2451 hp: 35,2452 attack: 65,2453 defense: 35,2454 special_attack: 65,2455 special_defense: 35,2456 speed: 65,2457 },2458 {2459 id: 224,2460 name: 'Octillery',2461 type: ['Water'],2462 hp: 75,2463 attack: 105,2464 defense: 75,2465 special_attack: 105,2466 special_defense: 75,2467 speed: 45,2468 },2469 {2470 id: 225,2471 name: 'Delibird',2472 type: ['Ice', 'Flying'],2473 hp: 45,2474 attack: 55,2475 defense: 45,2476 special_attack: 65,2477 special_defense: 45,2478 speed: 75,2479 },2480 {2481 id: 226,2482 name: 'Mantine',2483 type: ['Water', 'Flying'],2484 hp: 85,2485 attack: 40,2486 defense: 70,2487 special_attack: 80,2488 special_defense: 140,2489 speed: 70,2490 },2491 {2492 id: 227,2493 name: 'Skarmory',2494 type: ['Steel', 'Flying'],2495 hp: 65,2496 attack: 80,2497 defense: 140,2498 special_attack: 40,2499 special_defense: 70,2500 speed: 70,2501 },2502 {2503 id: 228,2504 name: 'Houndour',2505 type: ['Dark', 'Fire'],2506 hp: 45,2507 attack: 60,2508 defense: 30,2509 special_attack: 80,2510 special_defense: 50,2511 speed: 65,2512 },2513 {2514 id: 229,2515 name: 'Houndoom',2516 type: ['Dark', 'Fire'],2517 hp: 75,2518 attack: 90,2519 defense: 50,2520 special_attack: 110,2521 special_defense: 80,2522 speed: 95,2523 },2524 {2525 id: 230,2526 name: 'Kingdra',2527 type: ['Water', 'Dragon'],2528 hp: 75,2529 attack: 95,2530 defense: 95,2531 special_attack: 95,2532 special_defense: 95,2533 speed: 85,2534 },2535 {2536 id: 231,2537 name: 'Phanpy',2538 type: ['Ground'],2539 hp: 90,2540 attack: 60,2541 defense: 60,2542 special_attack: 40,2543 special_defense: 40,2544 speed: 40,2545 },2546 {2547 id: 232,2548 name: 'Donphan',2549 type: ['Ground'],2550 hp: 90,2551 attack: 120,2552 defense: 120,2553 special_attack: 60,2554 special_defense: 60,2555 speed: 50,2556 },2557 {2558 id: 233,2559 name: 'Porygon2',2560 type: ['Normal'],2561 hp: 85,2562 attack: 80,2563 defense: 90,2564 special_attack: 105,2565 special_defense: 95,2566 speed: 60,2567 },2568 {2569 id: 234,2570 name: 'Stantler',2571 type: ['Normal'],2572 hp: 73,2573 attack: 95,2574 defense: 62,2575 special_attack: 85,2576 special_defense: 65,2577 speed: 85,2578 },2579 {2580 id: 235,2581 name: 'Smeargle',2582 type: ['Normal'],2583 hp: 55,2584 attack: 20,2585 defense: 35,2586 special_attack: 20,2587 special_defense: 45,2588 speed: 75,2589 },2590 {2591 id: 236,2592 name: 'Tyrogue',2593 type: ['Fighting'],2594 hp: 35,2595 attack: 35,2596 defense: 35,2597 special_attack: 35,2598 special_defense: 35,2599 speed: 35,2600 },2601 {2602 id: 237,2603 name: 'Hitmontop',2604 type: ['Fighting'],2605 hp: 50,2606 attack: 95,2607 defense: 95,2608 special_attack: 35,2609 special_defense: 110,2610 speed: 70,2611 },2612 {2613 id: 238,2614 name: 'Smoochum',2615 type: ['Ice', 'Psychic'],2616 hp: 45,2617 attack: 30,2618 defense: 15,2619 special_attack: 85,2620 special_defense: 65,2621 speed: 65,2622 },2623 {2624 id: 239,2625 name: 'Elekid',2626 type: ['Electric'],2627 hp: 45,2628 attack: 63,2629 defense: 37,2630 special_attack: 65,2631 special_defense: 55,2632 speed: 95,2633 },2634 {2635 id: 240,2636 name: 'Magby',2637 type: ['Fire'],2638 hp: 45,2639 attack: 75,2640 defense: 37,2641 special_attack: 70,2642 special_defense: 55,2643 speed: 83,2644 },2645 {2646 id: 241,2647 name: 'Miltank',2648 type: ['Normal'],2649 hp: 95,2650 attack: 80,2651 defense: 105,2652 special_attack: 40,2653 special_defense: 70,2654 speed: 100,2655 },2656 {2657 id: 242,2658 name: 'Blissey',2659 type: ['Normal'],2660 hp: 255,2661 attack: 10,2662 defense: 10,2663 special_attack: 75,2664 special_defense: 135,2665 speed: 55,2666 },2667 {2668 id: 243,2669 name: 'Raikou',2670 type: ['Electric'],2671 hp: 90,2672 attack: 85,2673 defense: 75,2674 special_attack: 115,2675 special_defense: 100,2676 speed: 115,2677 },2678 {2679 id: 244,2680 name: 'Entei',2681 type: ['Fire'],2682 hp: 115,2683 attack: 115,2684 defense: 85,2685 special_attack: 90,2686 special_defense: 75,2687 speed: 100,2688 },2689 {2690 id: 245,2691 name: 'Suicune',2692 type: ['Water'],2693 hp: 100,2694 attack: 75,2695 defense: 115,2696 special_attack: 90,2697 special_defense: 115,2698 speed: 85,2699 },2700 {2701 id: 246,2702 name: 'Larvitar',2703 type: ['Rock', 'Ground'],2704 hp: 50,2705 attack: 64,2706 defense: 50,2707 special_attack: 45,2708 special_defense: 50,2709 speed: 41,2710 },2711 {2712 id: 247,2713 name: 'Pupitar',2714 type: ['Rock', 'Ground'],2715 hp: 70,2716 attack: 84,2717 defense: 70,2718 special_attack: 65,2719 special_defense: 70,2720 speed: 51,2721 },2722 {2723 id: 248,2724 name: 'Tyranitar',2725 type: ['Rock', 'Dark'],2726 hp: 100,2727 attack: 134,2728 defense: 110,2729 special_attack: 95,2730 special_defense: 100,2731 speed: 61,2732 },2733 {2734 id: 249,2735 name: 'Lugia',2736 type: ['Psychic', 'Flying'],2737 hp: 106,2738 attack: 90,2739 defense: 130,2740 special_attack: 90,2741 special_defense: 154,2742 speed: 110,2743 },2744 {2745 id: 250,2746 name: 'Ho-Oh',2747 type: ['Fire', 'Flying'],2748 hp: 106,2749 attack: 130,2750 defense: 90,2751 special_attack: 110,2752 special_defense: 154,2753 speed: 90,2754 },2755 {2756 id: 251,2757 name: 'Celebi',2758 type: ['Psychic', 'Grass'],2759 hp: 100,2760 attack: 100,2761 defense: 100,2762 special_attack: 100,2763 special_defense: 100,2764 speed: 100,2765 },2766 {2767 id: 252,2768 name: 'Treecko',2769 type: ['Grass'],2770 hp: 40,2771 attack: 45,2772 defense: 35,2773 special_attack: 65,2774 special_defense: 55,2775 speed: 70,2776 },2777 {2778 id: 253,2779 name: 'Grovyle',2780 type: ['Grass'],2781 hp: 50,2782 attack: 65,2783 defense: 45,2784 special_attack: 85,2785 special_defense: 65,2786 speed: 95,2787 },2788 {2789 id: 254,2790 name: 'Sceptile',2791 type: ['Grass'],2792 hp: 70,2793 attack: 85,2794 defense: 65,2795 special_attack: 105,2796 special_defense: 85,2797 speed: 120,2798 },2799 {2800 id: 255,2801 name: 'Torchic',2802 type: ['Fire'],2803 hp: 45,2804 attack: 60,2805 defense: 40,2806 special_attack: 70,2807 special_defense: 50,2808 speed: 45,2809 },2810 {2811 id: 256,2812 name: 'Combusken',2813 type: ['Fire', 'Fighting'],2814 hp: 60,2815 attack: 85,2816 defense: 60,2817 special_attack: 85,2818 special_defense: 60,2819 speed: 55,2820 },2821 {2822 id: 257,2823 name: 'Blaziken',2824 type: ['Fire', 'Fighting'],2825 hp: 80,2826 attack: 120,2827 defense: 70,2828 special_attack: 110,2829 special_defense: 70,2830 speed: 80,2831 },2832 {2833 id: 258,2834 name: 'Mudkip',2835 type: ['Water'],2836 hp: 50,2837 attack: 70,2838 defense: 50,2839 special_attack: 50,2840 special_defense: 50,2841 speed: 40,2842 },2843 {2844 id: 259,2845 name: 'Marshtomp',2846 type: ['Water', 'Ground'],2847 hp: 70,2848 attack: 85,2849 defense: 70,2850 special_attack: 60,2851 special_defense: 70,2852 speed: 50,2853 },2854 {2855 id: 260,2856 name: 'Swampert',2857 type: ['Water', 'Ground'],2858 hp: 100,2859 attack: 110,2860 defense: 90,2861 special_attack: 85,2862 special_defense: 90,2863 speed: 60,2864 },2865 {2866 id: 261,2867 name: 'Poochyena',2868 type: ['Dark'],2869 hp: 35,2870 attack: 55,2871 defense: 35,2872 special_attack: 30,2873 special_defense: 30,2874 speed: 35,2875 },2876 {2877 id: 262,2878 name: 'Mightyena',2879 type: ['Dark'],2880 hp: 70,2881 attack: 90,2882 defense: 70,2883 special_attack: 60,2884 special_defense: 60,2885 speed: 70,2886 },2887 {2888 id: 263,2889 name: 'Zigzagoon',2890 type: ['Normal'],2891 hp: 38,2892 attack: 30,2893 defense: 41,2894 special_attack: 30,2895 special_defense: 41,2896 speed: 60,2897 },2898 {2899 id: 264,2900 name: 'Linoone',2901 type: ['Normal'],2902 hp: 78,2903 attack: 70,2904 defense: 61,2905 special_attack: 50,2906 special_defense: 61,2907 speed: 100,2908 },2909 {2910 id: 265,2911 name: 'Wurmple',2912 type: ['Bug'],2913 hp: 45,2914 attack: 45,2915 defense: 35,2916 special_attack: 20,2917 special_defense: 30,2918 speed: 20,2919 },2920 {2921 id: 266,2922 name: 'Silcoon',2923 type: ['Bug'],2924 hp: 50,2925 attack: 35,2926 defense: 55,2927 special_attack: 25,2928 special_defense: 25,2929 speed: 15,2930 },2931 {2932 id: 267,2933 name: 'Beautifly',2934 type: ['Bug', 'Flying'],2935 hp: 60,2936 attack: 70,2937 defense: 50,2938 special_attack: 100,2939 special_defense: 50,2940 speed: 65,2941 },2942 {2943 id: 268,2944 name: 'Cascoon',2945 type: ['Bug'],2946 hp: 50,2947 attack: 35,2948 defense: 55,2949 special_attack: 25,2950 special_defense: 25,2951 speed: 15,2952 },2953 {2954 id: 269,2955 name: 'Dustox',2956 type: ['Bug', 'Poison'],2957 hp: 60,2958 attack: 50,2959 defense: 70,2960 special_attack: 50,2961 special_defense: 90,2962 speed: 65,2963 },2964 {2965 id: 270,2966 name: 'Lotad',2967 type: ['Water', 'Grass'],2968 hp: 40,2969 attack: 30,2970 defense: 30,2971 special_attack: 40,2972 special_defense: 50,2973 speed: 30,2974 },2975 {2976 id: 271,2977 name: 'Lombre',2978 type: ['Water', 'Grass'],2979 hp: 60,2980 attack: 50,2981 defense: 50,2982 special_attack: 60,2983 special_defense: 70,2984 speed: 50,2985 },2986 {2987 id: 272,2988 name: 'Ludicolo',2989 type: ['Water', 'Grass'],2990 hp: 80,2991 attack: 70,2992 defense: 70,2993 special_attack: 90,2994 special_defense: 100,2995 speed: 70,2996 },2997 {2998 id: 273,2999 name: 'Seedot',3000 type: ['Grass'],3001 hp: 40,3002 attack: 40,3003 defense: 50,3004 special_attack: 30,3005 special_defense: 30,3006 speed: 30,3007 },3008 {3009 id: 274,3010 name: 'Nuzleaf',3011 type: ['Grass', 'Dark'],3012 hp: 70,3013 attack: 70,3014 defense: 40,3015 special_attack: 60,3016 special_defense: 40,3017 speed: 60,3018 },3019 {3020 id: 275,3021 name: 'Shiftry',3022 type: ['Grass', 'Dark'],3023 hp: 90,3024 attack: 100,3025 defense: 60,3026 special_attack: 90,3027 special_defense: 60,3028 speed: 80,3029 },3030 {3031 id: 276,3032 name: 'Taillow',3033 type: ['Normal', 'Flying'],3034 hp: 40,3035 attack: 55,3036 defense: 30,3037 special_attack: 30,3038 special_defense: 30,3039 speed: 85,3040 },3041 {3042 id: 277,3043 name: 'Swellow',3044 type: ['Normal', 'Flying'],3045 hp: 60,3046 attack: 85,3047 defense: 60,3048 special_attack: 75,3049 special_defense: 50,3050 speed: 125,3051 },3052 {3053 id: 278,3054 name: 'Wingull',3055 type: ['Water', 'Flying'],3056 hp: 40,3057 attack: 30,3058 defense: 30,3059 special_attack: 55,3060 special_defense: 30,3061 speed: 85,3062 },3063 {3064 id: 279,3065 name: 'Pelipper',3066 type: ['Water', 'Flying'],3067 hp: 60,3068 attack: 50,3069 defense: 100,3070 special_attack: 95,3071 special_defense: 70,3072 speed: 65,3073 },3074 {3075 id: 280,3076 name: 'Ralts',3077 type: ['Psychic', 'Fairy'],3078 hp: 28,3079 attack: 25,3080 defense: 25,3081 special_attack: 45,3082 special_defense: 35,3083 speed: 40,3084 },3085 {3086 id: 281,3087 name: 'Kirlia',3088 type: ['Psychic', 'Fairy'],3089 hp: 38,3090 attack: 35,3091 defense: 35,3092 special_attack: 65,3093 special_defense: 55,3094 speed: 50,3095 },3096 {3097 id: 282,3098 name: 'Gardevoir',3099 type: ['Psychic', 'Fairy'],3100 hp: 68,3101 attack: 65,3102 defense: 65,3103 special_attack: 125,3104 special_defense: 115,3105 speed: 80,3106 },3107 {3108 id: 283,3109 name: 'Surskit',3110 type: ['Bug', 'Water'],3111 hp: 40,3112 attack: 30,3113 defense: 32,3114 special_attack: 50,3115 special_defense: 52,3116 speed: 65,3117 },3118 {3119 id: 284,3120 name: 'Masquerain',3121 type: ['Bug', 'Flying'],3122 hp: 70,3123 attack: 60,3124 defense: 62,3125 special_attack: 100,3126 special_defense: 82,3127 speed: 80,3128 },3129 {3130 id: 285,3131 name: 'Shroomish',3132 type: ['Grass'],3133 hp: 60,3134 attack: 40,3135 defense: 60,3136 special_attack: 40,3137 special_defense: 60,3138 speed: 35,3139 },3140 {3141 id: 286,3142 name: 'Breloom',3143 type: ['Grass', 'Fighting'],3144 hp: 60,3145 attack: 130,3146 defense: 80,3147 special_attack: 60,3148 special_defense: 60,3149 speed: 70,3150 },3151 {3152 id: 287,3153 name: 'Slakoth',3154 type: ['Normal'],3155 hp: 60,3156 attack: 60,3157 defense: 60,3158 special_attack: 35,3159 special_defense: 35,3160 speed: 30,3161 },3162 {3163 id: 288,3164 name: 'Vigoroth',3165 type: ['Normal'],3166 hp: 80,3167 attack: 80,3168 defense: 80,3169 special_attack: 55,3170 special_defense: 55,3171 speed: 90,3172 },3173 {3174 id: 289,3175 name: 'Slaking',3176 type: ['Normal'],3177 hp: 150,3178 attack: 160,3179 defense: 100,3180 special_attack: 95,3181 special_defense: 65,3182 speed: 100,3183 },3184 {3185 id: 290,3186 name: 'Nincada',3187 type: ['Bug', 'Ground'],3188 hp: 31,3189 attack: 45,3190 defense: 90,3191 special_attack: 30,3192 special_defense: 30,3193 speed: 40,3194 },3195 {3196 id: 291,3197 name: 'Ninjask',3198 type: ['Bug', 'Flying'],3199 hp: 61,3200 attack: 90,3201 defense: 45,3202 special_attack: 50,3203 special_defense: 50,3204 speed: 160,3205 },3206 {3207 id: 292,3208 name: 'Shedinja',3209 type: ['Bug', 'Ghost'],3210 hp: 1,3211 attack: 90,3212 defense: 45,3213 special_attack: 30,3214 special_defense: 30,3215 speed: 40,3216 },3217 {3218 id: 293,3219 name: 'Whismur',3220 type: ['Normal'],3221 hp: 64,3222 attack: 51,3223 defense: 23,3224 special_attack: 51,3225 special_defense: 23,3226 speed: 28,3227 },3228 {3229 id: 294,3230 name: 'Loudred',3231 type: ['Normal'],3232 hp: 84,3233 attack: 71,3234 defense: 43,3235 special_attack: 71,3236 special_defense: 43,3237 speed: 48,3238 },3239 {3240 id: 295,3241 name: 'Exploud',3242 type: ['Normal'],3243 hp: 104,3244 attack: 91,3245 defense: 63,3246 special_attack: 91,3247 special_defense: 73,3248 speed: 68,3249 },3250 {3251 id: 296,3252 name: 'Makuhita',3253 type: ['Fighting'],3254 hp: 72,3255 attack: 60,3256 defense: 30,3257 special_attack: 20,3258 special_defense: 30,3259 speed: 25,3260 },3261 {3262 id: 297,3263 name: 'Hariyama',3264 type: ['Fighting'],3265 hp: 144,3266 attack: 120,3267 defense: 60,3268 special_attack: 40,3269 special_defense: 60,3270 speed: 50,3271 },3272 {3273 id: 298,3274 name: 'Azurill',3275 type: ['Normal', 'Fairy'],3276 hp: 50,3277 attack: 20,3278 defense: 40,3279 special_attack: 20,3280 special_defense: 40,3281 speed: 20,3282 },3283 {3284 id: 299,3285 name: 'Nosepass',3286 type: ['Rock'],3287 hp: 30,3288 attack: 45,3289 defense: 135,3290 special_attack: 45,3291 special_defense: 90,3292 speed: 30,3293 },3294 {3295 id: 300,3296 name: 'Skitty',3297 type: ['Normal'],3298 hp: 50,3299 attack: 45,3300 defense: 45,3301 special_attack: 35,3302 special_defense: 35,3303 speed: 50,3304 },3305 {3306 id: 301,3307 name: 'Delcatty',3308 type: ['Normal'],3309 hp: 70,3310 attack: 65,3311 defense: 65,3312 special_attack: 55,3313 special_defense: 55,3314 speed: 90,3315 },3316 {3317 id: 302,3318 name: 'Sableye',3319 type: ['Dark', 'Ghost'],3320 hp: 50,3321 attack: 75,3322 defense: 75,3323 special_attack: 65,3324 special_defense: 65,3325 speed: 50,3326 },3327 {3328 id: 303,3329 name: 'Mawile',3330 type: ['Steel', 'Fairy'],3331 hp: 50,3332 attack: 85,3333 defense: 85,3334 special_attack: 55,3335 special_defense: 55,3336 speed: 50,3337 },3338 {3339 id: 304,3340 name: 'Aron',3341 type: ['Steel', 'Rock'],3342 hp: 50,3343 attack: 70,3344 defense: 100,3345 special_attack: 40,3346 special_defense: 40,3347 speed: 30,3348 },3349 {3350 id: 305,3351 name: 'Lairon',3352 type: ['Steel', 'Rock'],3353 hp: 60,3354 attack: 90,3355 defense: 140,3356 special_attack: 50,3357 special_defense: 50,3358 speed: 40,3359 },3360 {3361 id: 306,3362 name: 'Aggron',3363 type: ['Steel', 'Rock'],3364 hp: 70,3365 attack: 110,3366 defense: 180,3367 special_attack: 60,3368 special_defense: 60,3369 speed: 50,3370 },3371 {3372 id: 307,3373 name: 'Meditite',3374 type: ['Fighting', 'Psychic'],3375 hp: 30,3376 attack: 40,3377 defense: 55,3378 special_attack: 40,3379 special_defense: 55,3380 speed: 60,3381 },3382 {3383 id: 308,3384 name: 'Medicham',3385 type: ['Fighting', 'Psychic'],3386 hp: 60,3387 attack: 60,3388 defense: 75,3389 special_attack: 60,3390 special_defense: 75,3391 speed: 80,3392 },3393 {3394 id: 309,3395 name: 'Electrike',3396 type: ['Electric'],3397 hp: 40,3398 attack: 45,3399 defense: 40,3400 special_attack: 65,3401 special_defense: 40,3402 speed: 65,3403 },3404 {3405 id: 310,3406 name: 'Manectric',3407 type: ['Electric'],3408 hp: 70,3409 attack: 75,3410 defense: 60,3411 special_attack: 105,3412 special_defense: 60,3413 speed: 105,3414 },3415 {3416 id: 311,3417 name: 'Plusle',3418 type: ['Electric'],3419 hp: 60,3420 attack: 50,3421 defense: 40,3422 special_attack: 85,3423 special_defense: 75,3424 speed: 95,3425 },3426 {3427 id: 312,3428 name: 'Minun',3429 type: ['Electric'],3430 hp: 60,3431 attack: 40,3432 defense: 50,3433 special_attack: 75,3434 special_defense: 85,3435 speed: 95,3436 },3437 {3438 id: 313,3439 name: 'Volbeat',3440 type: ['Bug'],3441 hp: 65,3442 attack: 73,3443 defense: 75,3444 special_attack: 47,3445 special_defense: 85,3446 speed: 85,3447 },3448 {3449 id: 314,3450 name: 'Illumise',3451 type: ['Bug'],3452 hp: 65,3453 attack: 47,3454 defense: 75,3455 special_attack: 73,3456 special_defense: 85,3457 speed: 85,3458 },3459 {3460 id: 315,3461 name: 'Roselia',3462 type: ['Grass', 'Poison'],3463 hp: 50,3464 attack: 60,3465 defense: 45,3466 special_attack: 100,3467 special_defense: 80,3468 speed: 65,3469 },3470 {3471 id: 316,3472 name: 'Gulpin',3473 type: ['Poison'],3474 hp: 70,3475 attack: 43,3476 defense: 53,3477 special_attack: 43,3478 special_defense: 53,3479 speed: 40,3480 },3481 {3482 id: 317,3483 name: 'Swalot',3484 type: ['Poison'],3485 hp: 100,3486 attack: 73,3487 defense: 83,3488 special_attack: 73,3489 special_defense: 83,3490 speed: 55,3491 },3492 {3493 id: 318,3494 name: 'Carvanha',3495 type: ['Water', 'Dark'],3496 hp: 45,3497 attack: 90,3498 defense: 20,3499 special_attack: 65,3500 special_defense: 20,3501 speed: 65,3502 },3503 {3504 id: 319,3505 name: 'Sharpedo',3506 type: ['Water', 'Dark'],3507 hp: 70,3508 attack: 120,3509 defense: 40,3510 special_attack: 95,3511 special_defense: 40,3512 speed: 95,3513 },3514 {3515 id: 320,3516 name: 'Wailmer',3517 type: ['Water'],3518 hp: 130,3519 attack: 70,3520 defense: 35,3521 special_attack: 70,3522 special_defense: 35,3523 speed: 60,3524 },3525 {3526 id: 321,3527 name: 'Wailord',3528 type: ['Water'],3529 hp: 170,3530 attack: 90,3531 defense: 45,3532 special_attack: 90,3533 special_defense: 45,3534 speed: 60,3535 },3536 {3537 id: 322,3538 name: 'Numel',3539 type: ['Fire', 'Ground'],3540 hp: 60,3541 attack: 60,3542 defense: 40,3543 special_attack: 65,3544 special_defense: 45,3545 speed: 35,3546 },3547 {3548 id: 323,3549 name: 'Camerupt',3550 type: ['Fire', 'Ground'],3551 hp: 70,3552 attack: 100,3553 defense: 70,3554 special_attack: 105,3555 special_defense: 75,3556 speed: 40,3557 },3558 {3559 id: 324,3560 name: 'Torkoal',3561 type: ['Fire'],3562 hp: 70,3563 attack: 85,3564 defense: 140,3565 special_attack: 85,3566 special_defense: 70,3567 speed: 20,3568 },3569 {3570 id: 325,3571 name: 'Spoink',3572 type: ['Psychic'],3573 hp: 60,3574 attack: 25,3575 defense: 35,3576 special_attack: 70,3577 special_defense: 80,3578 speed: 60,3579 },3580 {3581 id: 326,3582 name: 'Grumpig',3583 type: ['Psychic'],3584 hp: 80,3585 attack: 45,3586 defense: 65,3587 special_attack: 90,3588 special_defense: 110,3589 speed: 80,3590 },3591 {3592 id: 327,3593 name: 'Spinda',3594 type: ['Normal'],3595 hp: 60,3596 attack: 60,3597 defense: 60,3598 special_attack: 60,3599 special_defense: 60,3600 speed: 60,3601 },3602 {3603 id: 328,3604 name: 'Trapinch',3605 type: ['Ground'],3606 hp: 45,3607 attack: 100,3608 defense: 45,3609 special_attack: 45,3610 special_defense: 45,3611 speed: 10,3612 },3613 {3614 id: 329,3615 name: 'Vibrava',3616 type: ['Ground', 'Dragon'],3617 hp: 50,3618 attack: 70,3619 defense: 50,3620 special_attack: 50,3621 special_defense: 50,3622 speed: 70,3623 },3624 {3625 id: 330,3626 name: 'Flygon',3627 type: ['Ground', 'Dragon'],3628 hp: 80,3629 attack: 100,3630 defense: 80,3631 special_attack: 80,3632 special_defense: 80,3633 speed: 100,3634 },3635 {3636 id: 331,3637 name: 'Cacnea',3638 type: ['Grass'],3639 hp: 50,3640 attack: 85,3641 defense: 40,3642 special_attack: 85,3643 special_defense: 40,3644 speed: 35,3645 },3646 {3647 id: 332,3648 name: 'Cacturne',3649 type: ['Grass', 'Dark'],3650 hp: 70,3651 attack: 115,3652 defense: 60,3653 special_attack: 115,3654 special_defense: 60,3655 speed: 55,3656 },3657 {3658 id: 333,3659 name: 'Swablu',3660 type: ['Normal', 'Flying'],3661 hp: 45,3662 attack: 40,3663 defense: 60,3664 special_attack: 40,3665 special_defense: 75,3666 speed: 50,3667 },3668 {3669 id: 334,3670 name: 'Altaria',3671 type: ['Dragon', 'Flying'],3672 hp: 75,3673 attack: 70,3674 defense: 90,3675 special_attack: 70,3676 special_defense: 105,3677 speed: 80,3678 },3679 {3680 id: 335,3681 name: 'Zangoose',3682 type: ['Normal'],3683 hp: 73,3684 attack: 115,3685 defense: 60,3686 special_attack: 60,3687 special_defense: 60,3688 speed: 90,3689 },3690 {3691 id: 336,3692 name: 'Seviper',3693 type: ['Poison'],3694 hp: 73,3695 attack: 100,3696 defense: 60,3697 special_attack: 100,3698 special_defense: 60,3699 speed: 65,3700 },3701 {3702 id: 337,3703 name: 'Lunatone',3704 type: ['Rock', 'Psychic'],3705 hp: 90,3706 attack: 55,3707 defense: 65,3708 special_attack: 95,3709 special_defense: 85,3710 speed: 70,3711 },3712 {3713 id: 338,3714 name: 'Solrock',3715 type: ['Rock', 'Psychic'],3716 hp: 90,3717 attack: 95,3718 defense: 85,3719 special_attack: 55,3720 special_defense: 65,3721 speed: 70,3722 },3723 {3724 id: 339,3725 name: 'Barboach',3726 type: ['Water', 'Ground'],3727 hp: 50,3728 attack: 48,3729 defense: 43,3730 special_attack: 46,3731 special_defense: 41,3732 speed: 60,3733 },3734 {3735 id: 340,3736 name: 'Whiscash',3737 type: ['Water', 'Ground'],3738 hp: 110,3739 attack: 78,3740 defense: 73,3741 special_attack: 76,3742 special_defense: 71,3743 speed: 60,3744 },3745 {3746 id: 341,3747 name: 'Corphish',3748 type: ['Water'],3749 hp: 43,3750 attack: 80,3751 defense: 65,3752 special_attack: 50,3753 special_defense: 35,3754 speed: 35,3755 },3756 {3757 id: 342,3758 name: 'Crawdaunt',3759 type: ['Water', 'Dark'],3760 hp: 63,3761 attack: 120,3762 defense: 85,3763 special_attack: 90,3764 special_defense: 55,3765 speed: 55,3766 },3767 {3768 id: 343,3769 name: 'Baltoy',3770 type: ['Ground', 'Psychic'],3771 hp: 40,3772 attack: 40,3773 defense: 55,3774 special_attack: 40,3775 special_defense: 70,3776 speed: 55,3777 },3778 {3779 id: 344,3780 name: 'Claydol',3781 type: ['Ground', 'Psychic'],3782 hp: 60,3783 attack: 70,3784 defense: 105,3785 special_attack: 70,3786 special_defense: 120,3787 speed: 75,3788 },3789 {3790 id: 345,3791 name: 'Lileep',3792 type: ['Rock', 'Grass'],3793 hp: 66,3794 attack: 41,3795 defense: 77,3796 special_attack: 61,3797 special_defense: 87,3798 speed: 23,3799 },3800 {3801 id: 346,3802 name: 'Cradily',3803 type: ['Rock', 'Grass'],3804 hp: 86,3805 attack: 81,3806 defense: 97,3807 special_attack: 81,3808 special_defense: 107,3809 speed: 43,3810 },3811 {3812 id: 347,3813 name: 'Anorith',3814 type: ['Rock', 'Bug'],3815 hp: 45,3816 attack: 95,3817 defense: 50,3818 special_attack: 40,3819 special_defense: 50,3820 speed: 75,3821 },3822 {3823 id: 348,3824 name: 'Armaldo',3825 type: ['Rock', 'Bug'],3826 hp: 75,3827 attack: 125,3828 defense: 100,3829 special_attack: 70,3830 special_defense: 80,3831 speed: 45,3832 },3833 {3834 id: 349,3835 name: 'Feebas',3836 type: ['Water'],3837 hp: 20,3838 attack: 15,3839 defense: 20,3840 special_attack: 10,3841 special_defense: 55,3842 speed: 80,3843 },3844 {3845 id: 350,3846 name: 'Milotic',3847 type: ['Water'],3848 hp: 95,3849 attack: 60,3850 defense: 79,3851 special_attack: 100,3852 special_defense: 125,3853 speed: 81,3854 },3855 {3856 id: 351,3857 name: 'Castform',3858 type: ['Normal'],3859 hp: 70,3860 attack: 70,3861 defense: 70,3862 special_attack: 70,3863 special_defense: 70,3864 speed: 70,3865 },3866 {3867 id: 352,3868 name: 'Kecleon',3869 type: ['Normal'],3870 hp: 60,3871 attack: 90,3872 defense: 70,3873 special_attack: 60,3874 special_defense: 120,3875 speed: 40,3876 },3877 {3878 id: 353,3879 name: 'Shuppet',3880 type: ['Ghost'],3881 hp: 44,3882 attack: 75,3883 defense: 35,3884 special_attack: 63,3885 special_defense: 33,3886 speed: 45,3887 },3888 {3889 id: 354,3890 name: 'Banette',3891 type: ['Ghost'],3892 hp: 64,3893 attack: 115,3894 defense: 65,3895 special_attack: 83,3896 special_defense: 63,3897 speed: 65,3898 },3899 {3900 id: 355,3901 name: 'Duskull',3902 type: ['Ghost'],3903 hp: 20,3904 attack: 40,3905 defense: 90,3906 special_attack: 30,3907 special_defense: 90,3908 speed: 25,3909 },3910 {3911 id: 356,3912 name: 'Dusclops',3913 type: ['Ghost'],3914 hp: 40,3915 attack: 70,3916 defense: 130,3917 special_attack: 60,3918 special_defense: 130,3919 speed: 25,3920 },3921 {3922 id: 357,3923 name: 'Tropius',3924 type: ['Grass', 'Flying'],3925 hp: 99,3926 attack: 68,3927 defense: 83,3928 special_attack: 72,3929 special_defense: 87,3930 speed: 51,3931 },3932 {3933 id: 358,3934 name: 'Chimecho',3935 type: ['Psychic'],3936 hp: 75,3937 attack: 50,3938 defense: 80,3939 special_attack: 95,3940 special_defense: 90,3941 speed: 65,3942 },3943 {3944 id: 359,3945 name: 'Absol',3946 type: ['Dark'],3947 hp: 65,3948 attack: 130,3949 defense: 60,3950 special_attack: 75,3951 special_defense: 60,3952 speed: 75,3953 },3954 {3955 id: 360,3956 name: 'Wynaut',3957 type: ['Psychic'],3958 hp: 95,3959 attack: 23,3960 defense: 48,3961 special_attack: 23,3962 special_defense: 48,3963 speed: 23,3964 },3965 {3966 id: 361,3967 name: 'Snorunt',3968 type: ['Ice'],3969 hp: 50,3970 attack: 50,3971 defense: 50,3972 special_attack: 50,3973 special_defense: 50,3974 speed: 50,3975 },3976 {3977 id: 362,3978 name: 'Glalie',3979 type: ['Ice'],3980 hp: 80,3981 attack: 80,3982 defense: 80,3983 special_attack: 80,3984 special_defense: 80,3985 speed: 80,3986 },3987 {3988 id: 363,3989 name: 'Spheal',3990 type: ['Ice', 'Water'],3991 hp: 70,3992 attack: 40,3993 defense: 50,3994 special_attack: 55,3995 special_defense: 50,3996 speed: 25,3997 },3998 {3999 id: 364,4000 name: 'Sealeo',4001 type: ['Ice', 'Water'],4002 hp: 90,4003 attack: 60,4004 defense: 70,4005 special_attack: 75,4006 special_defense: 70,4007 speed: 45,4008 },4009 {4010 id: 365,4011 name: 'Walrein',4012 type: ['Ice', 'Water'],4013 hp: 110,4014 attack: 80,4015 defense: 90,4016 special_attack: 95,4017 special_defense: 90,4018 speed: 65,4019 },4020 {4021 id: 366,4022 name: 'Clamperl',4023 type: ['Water'],4024 hp: 35,4025 attack: 64,4026 defense: 85,4027 special_attack: 74,4028 special_defense: 55,4029 speed: 32,4030 },4031 {4032 id: 367,4033 name: 'Huntail',4034 type: ['Water'],4035 hp: 55,4036 attack: 104,4037 defense: 105,4038 special_attack: 94,4039 special_defense: 75,4040 speed: 52,4041 },4042 {4043 id: 368,4044 name: 'Gorebyss',4045 type: ['Water'],4046 hp: 55,4047 attack: 84,4048 defense: 105,4049 special_attack: 114,4050 special_defense: 75,4051 speed: 52,4052 },4053 {4054 id: 369,4055 name: 'Relicanth',4056 type: ['Water', 'Rock'],4057 hp: 100,4058 attack: 90,4059 defense: 130,4060 special_attack: 45,4061 special_defense: 65,4062 speed: 55,4063 },4064 {4065 id: 370,4066 name: 'Luvdisc',4067 type: ['Water'],4068 hp: 43,4069 attack: 30,4070 defense: 55,4071 special_attack: 40,4072 special_defense: 65,4073 speed: 97,4074 },4075 {4076 id: 371,4077 name: 'Bagon',4078 type: ['Dragon'],4079 hp: 45,4080 attack: 75,4081 defense: 60,4082 special_attack: 40,4083 special_defense: 30,4084 speed: 50,4085 },4086 {4087 id: 372,4088 name: 'Shelgon',4089 type: ['Dragon'],4090 hp: 65,4091 attack: 95,4092 defense: 100,4093 special_attack: 60,4094 special_defense: 50,4095 speed: 50,4096 },4097 {4098 id: 373,4099 name: 'Salamence',4100 type: ['Dragon', 'Flying'],4101 hp: 95,4102 attack: 135,4103 defense: 80,4104 special_attack: 110,4105 special_defense: 80,4106 speed: 100,4107 },4108 {4109 id: 374,4110 name: 'Beldum',4111 type: ['Steel', 'Psychic'],4112 hp: 40,4113 attack: 55,4114 defense: 80,4115 special_attack: 35,4116 special_defense: 60,4117 speed: 30,4118 },4119 {4120 id: 375,4121 name: 'Metang',4122 type: ['Steel', 'Psychic'],4123 hp: 60,4124 attack: 75,4125 defense: 100,4126 special_attack: 55,4127 special_defense: 80,4128 speed: 50,4129 },4130 {4131 id: 376,4132 name: 'Metagross',4133 type: ['Steel', 'Psychic'],4134 hp: 80,4135 attack: 135,4136 defense: 130,4137 special_attack: 95,4138 special_defense: 90,4139 speed: 70,4140 },4141 {4142 id: 377,4143 name: 'Regirock',4144 type: ['Rock'],4145 hp: 80,4146 attack: 100,4147 defense: 200,4148 special_attack: 50,4149 special_defense: 100,4150 speed: 50,4151 },4152 {4153 id: 378,4154 name: 'Regice',4155 type: ['Ice'],4156 hp: 80,4157 attack: 50,4158 defense: 100,4159 special_attack: 100,4160 special_defense: 200,4161 speed: 50,4162 },4163 {4164 id: 379,4165 name: 'Registeel',4166 type: ['Steel'],4167 hp: 80,4168 attack: 75,4169 defense: 150,4170 special_attack: 75,4171 special_defense: 150,4172 speed: 50,4173 },4174 {4175 id: 380,4176 name: 'Latias',4177 type: ['Dragon', 'Psychic'],4178 hp: 80,4179 attack: 80,4180 defense: 90,4181 special_attack: 110,4182 special_defense: 130,4183 speed: 110,4184 },4185 {4186 id: 381,4187 name: 'Latios',4188 type: ['Dragon', 'Psychic'],4189 hp: 80,4190 attack: 90,4191 defense: 80,4192 special_attack: 130,4193 special_defense: 110,4194 speed: 110,4195 },4196 {4197 id: 382,4198 name: 'Kyogre',4199 type: ['Water'],4200 hp: 100,4201 attack: 100,4202 defense: 90,4203 special_attack: 150,4204 special_defense: 140,4205 speed: 90,4206 },4207 {4208 id: 383,4209 name: 'Groudon',4210 type: ['Ground'],4211 hp: 100,4212 attack: 150,4213 defense: 140,4214 special_attack: 100,4215 special_defense: 90,4216 speed: 90,4217 },4218 {4219 id: 384,4220 name: 'Rayquaza',4221 type: ['Dragon', 'Flying'],4222 hp: 105,4223 attack: 150,4224 defense: 90,4225 special_attack: 150,4226 special_defense: 90,4227 speed: 95,4228 },4229 {4230 id: 385,4231 name: 'Jirachi',4232 type: ['Steel', 'Psychic'],4233 hp: 100,4234 attack: 100,4235 defense: 100,4236 special_attack: 100,4237 special_defense: 100,4238 speed: 100,4239 },4240 {4241 id: 386,4242 name: 'Deoxys',4243 type: ['Psychic'],4244 hp: 50,4245 attack: 150,4246 defense: 50,4247 special_attack: 150,4248 special_defense: 50,4249 speed: 150,4250 },4251 {4252 id: 387,4253 name: 'Turtwig',4254 type: ['Grass'],4255 hp: 55,4256 attack: 68,4257 defense: 64,4258 special_attack: 45,4259 special_defense: 55,4260 speed: 31,4261 },4262 {4263 id: 388,4264 name: 'Grotle',4265 type: ['Grass'],4266 hp: 75,4267 attack: 89,4268 defense: 85,4269 special_attack: 55,4270 special_defense: 65,4271 speed: 36,4272 },4273 {4274 id: 389,4275 name: 'Torterra',4276 type: ['Grass', 'Ground'],4277 hp: 95,4278 attack: 109,4279 defense: 105,4280 special_attack: 75,4281 special_defense: 85,4282 speed: 56,4283 },4284 {4285 id: 390,4286 name: 'Chimchar',4287 type: ['Fire'],4288 hp: 44,4289 attack: 58,4290 defense: 44,4291 special_attack: 58,4292 special_defense: 44,4293 speed: 61,4294 },4295 {4296 id: 391,4297 name: 'Monferno',4298 type: ['Fire', 'Fighting'],4299 hp: 64,4300 attack: 78,4301 defense: 52,4302 special_attack: 78,4303 special_defense: 52,4304 speed: 81,4305 },4306 {4307 id: 392,4308 name: 'Infernape',4309 type: ['Fire', 'Fighting'],4310 hp: 76,4311 attack: 104,4312 defense: 71,4313 special_attack: 104,4314 special_defense: 71,4315 speed: 108,4316 },4317 {4318 id: 393,4319 name: 'Piplup',4320 type: ['Water'],4321 hp: 53,4322 attack: 51,4323 defense: 53,4324 special_attack: 61,4325 special_defense: 56,4326 speed: 40,4327 },4328 {4329 id: 394,4330 name: 'Prinplup',4331 type: ['Water'],4332 hp: 64,4333 attack: 66,4334 defense: 68,4335 special_attack: 81,4336 special_defense: 76,4337 speed: 50,4338 },4339 {4340 id: 395,4341 name: 'Empoleon',4342 type: ['Water', 'Steel'],4343 hp: 84,4344 attack: 86,4345 defense: 88,4346 special_attack: 111,4347 special_defense: 101,4348 speed: 60,4349 },4350 {4351 id: 396,4352 name: 'Starly',4353 type: ['Normal', 'Flying'],4354 hp: 40,4355 attack: 55,4356 defense: 30,4357 special_attack: 30,4358 special_defense: 30,4359 speed: 60,4360 },4361 {4362 id: 397,4363 name: 'Staravia',4364 type: ['Normal', 'Flying'],4365 hp: 55,4366 attack: 75,4367 defense: 50,4368 special_attack: 40,4369 special_defense: 40,4370 speed: 80,4371 },4372 {4373 id: 398,4374 name: 'Staraptor',4375 type: ['Normal', 'Flying'],4376 hp: 85,4377 attack: 120,4378 defense: 70,4379 special_attack: 50,4380 special_defense: 60,4381 speed: 100,4382 },4383 {4384 id: 399,4385 name: 'Bidoof',4386 type: ['Normal'],4387 hp: 59,4388 attack: 45,4389 defense: 40,4390 special_attack: 35,4391 special_defense: 40,4392 speed: 31,4393 },4394 {4395 id: 400,4396 name: 'Bibarel',4397 type: ['Normal', 'Water'],4398 hp: 79,4399 attack: 85,4400 defense: 60,4401 special_attack: 55,4402 special_defense: 60,4403 speed: 71,4404 },4405 {4406 id: 401,4407 name: 'Kricketot',4408 type: ['Bug'],4409 hp: 37,4410 attack: 25,4411 defense: 41,4412 special_attack: 25,4413 special_defense: 41,4414 speed: 25,4415 },4416 {4417 id: 402,4418 name: 'Kricketune',4419 type: ['Bug'],4420 hp: 77,4421 attack: 85,4422 defense: 51,4423 special_attack: 55,4424 special_defense: 51,4425 speed: 65,4426 },4427 {4428 id: 403,4429 name: 'Shinx',4430 type: ['Electric'],4431 hp: 45,4432 attack: 65,4433 defense: 34,4434 special_attack: 40,4435 special_defense: 34,4436 speed: 45,4437 },4438 {4439 id: 404,4440 name: 'Luxio',4441 type: ['Electric'],4442 hp: 60,4443 attack: 85,4444 defense: 49,4445 special_attack: 60,4446 special_defense: 49,4447 speed: 60,4448 },4449 {4450 id: 405,4451 name: 'Luxray',4452 type: ['Electric'],4453 hp: 80,4454 attack: 120,4455 defense: 79,4456 special_attack: 95,4457 special_defense: 79,4458 speed: 70,4459 },4460 {4461 id: 406,4462 name: 'Budew',4463 type: ['Grass', 'Poison'],4464 hp: 40,4465 attack: 30,4466 defense: 35,4467 special_attack: 50,4468 special_defense: 70,4469 speed: 55,4470 },4471 {4472 id: 407,4473 name: 'Roserade',4474 type: ['Grass', 'Poison'],4475 hp: 60,4476 attack: 70,4477 defense: 65,4478 special_attack: 125,4479 special_defense: 105,4480 speed: 90,4481 },4482 {4483 id: 408,4484 name: 'Cranidos',4485 type: ['Rock'],4486 hp: 67,4487 attack: 125,4488 defense: 40,4489 special_attack: 30,4490 special_defense: 30,4491 speed: 58,4492 },4493 {4494 id: 409,4495 name: 'Rampardos',4496 type: ['Rock'],4497 hp: 97,4498 attack: 165,4499 defense: 60,4500 special_attack: 65,4501 special_defense: 50,4502 speed: 58,4503 },4504 {4505 id: 410,4506 name: 'Shieldon',4507 type: ['Rock', 'Steel'],4508 hp: 30,4509 attack: 42,4510 defense: 118,4511 special_attack: 42,4512 special_defense: 88,4513 speed: 30,4514 },4515 {4516 id: 411,4517 name: 'Bastiodon',4518 type: ['Rock', 'Steel'],4519 hp: 60,4520 attack: 52,4521 defense: 168,4522 special_attack: 47,4523 special_defense: 138,4524 speed: 30,4525 },4526 {4527 id: 412,4528 name: 'Burmy',4529 type: ['Bug'],4530 hp: 40,4531 attack: 29,4532 defense: 45,4533 special_attack: 29,4534 special_defense: 45,4535 speed: 36,4536 },4537 {4538 id: 413,4539 name: 'Wormadam',4540 type: ['Bug', 'Grass'],4541 hp: 60,4542 attack: 59,4543 defense: 85,4544 special_attack: 79,4545 special_defense: 105,4546 speed: 36,4547 },4548 {4549 id: 414,4550 name: 'Mothim',4551 type: ['Bug', 'Flying'],4552 hp: 70,4553 attack: 94,4554 defense: 50,4555 special_attack: 94,4556 special_defense: 50,4557 speed: 66,4558 },4559 {4560 id: 415,4561 name: 'Combee',4562 type: ['Bug', 'Flying'],4563 hp: 30,4564 attack: 30,4565 defense: 42,4566 special_attack: 30,4567 special_defense: 42,4568 speed: 70,4569 },4570 {4571 id: 416,4572 name: 'Vespiquen',4573 type: ['Bug', 'Flying'],4574 hp: 70,4575 attack: 80,4576 defense: 102,4577 special_attack: 80,4578 special_defense: 102,4579 speed: 40,4580 },4581 {4582 id: 417,4583 name: 'Pachirisu',4584 type: ['Electric'],4585 hp: 60,4586 attack: 45,4587 defense: 70,4588 special_attack: 45,4589 special_defense: 90,4590 speed: 95,4591 },4592 {4593 id: 418,4594 name: 'Buizel',4595 type: ['Water'],4596 hp: 55,4597 attack: 65,4598 defense: 35,4599 special_attack: 60,4600 special_defense: 30,4601 speed: 85,4602 },4603 {4604 id: 419,4605 name: 'Floatzel',4606 type: ['Water'],4607 hp: 85,4608 attack: 105,4609 defense: 55,4610 special_attack: 85,4611 special_defense: 50,4612 speed: 115,4613 },4614 {4615 id: 420,4616 name: 'Cherubi',4617 type: ['Grass'],4618 hp: 45,4619 attack: 35,4620 defense: 45,4621 special_attack: 62,4622 special_defense: 53,4623 speed: 35,4624 },4625 {4626 id: 421,4627 name: 'Cherrim',4628 type: ['Grass'],4629 hp: 70,4630 attack: 60,4631 defense: 70,4632 special_attack: 87,4633 special_defense: 78,4634 speed: 85,4635 },4636 {4637 id: 422,4638 name: 'Shellos',4639 type: ['Water'],4640 hp: 76,4641 attack: 48,4642 defense: 48,4643 special_attack: 57,4644 special_defense: 62,4645 speed: 34,4646 },4647 {4648 id: 423,4649 name: 'Gastrodon',4650 type: ['Water', 'Ground'],4651 hp: 111,4652 attack: 83,4653 defense: 68,4654 special_attack: 92,4655 special_defense: 82,4656 speed: 39,4657 },4658 {4659 id: 424,4660 name: 'Ambipom',4661 type: ['Normal'],4662 hp: 75,4663 attack: 100,4664 defense: 66,4665 special_attack: 60,4666 special_defense: 66,4667 speed: 115,4668 },4669 {4670 id: 425,4671 name: 'Drifloon',4672 type: ['Ghost', 'Flying'],4673 hp: 90,4674 attack: 50,4675 defense: 34,4676 special_attack: 60,4677 special_defense: 44,4678 speed: 70,4679 },4680 {4681 id: 426,4682 name: 'Drifblim',4683 type: ['Ghost', 'Flying'],4684 hp: 150,4685 attack: 80,4686 defense: 44,4687 special_attack: 90,4688 special_defense: 54,4689 speed: 80,4690 },4691 {4692 id: 427,4693 name: 'Buneary',4694 type: ['Normal'],4695 hp: 55,4696 attack: 66,4697 defense: 44,4698 special_attack: 44,4699 special_defense: 56,4700 speed: 85,4701 },4702 {4703 id: 428,4704 name: 'Lopunny',4705 type: ['Normal'],4706 hp: 65,4707 attack: 76,4708 defense: 84,4709 special_attack: 54,4710 special_defense: 96,4711 speed: 105,4712 },4713 {4714 id: 429,4715 name: 'Mismagius',4716 type: ['Ghost'],4717 hp: 60,4718 attack: 60,4719 defense: 60,4720 special_attack: 105,4721 special_defense: 105,4722 speed: 105,4723 },4724 {4725 id: 430,4726 name: 'Honchkrow',4727 type: ['Dark', 'Flying'],4728 hp: 100,4729 attack: 125,4730 defense: 52,4731 special_attack: 105,4732 special_defense: 52,4733 speed: 71,4734 },4735 {4736 id: 431,4737 name: 'Glameow',4738 type: ['Normal'],4739 hp: 49,4740 attack: 55,4741 defense: 42,4742 special_attack: 42,4743 special_defense: 37,4744 speed: 85,4745 },4746 {4747 id: 432,4748 name: 'Purugly',4749 type: ['Normal'],4750 hp: 71,4751 attack: 82,4752 defense: 64,4753 special_attack: 64,4754 special_defense: 59,4755 speed: 112,4756 },4757 {4758 id: 433,4759 name: 'Chingling',4760 type: ['Psychic'],4761 hp: 45,4762 attack: 30,4763 defense: 50,4764 special_attack: 65,4765 special_defense: 50,4766 speed: 45,4767 },4768 {4769 id: 434,4770 name: 'Stunky',4771 type: ['Poison', 'Dark'],4772 hp: 63,4773 attack: 63,4774 defense: 47,4775 special_attack: 41,4776 special_defense: 41,4777 speed: 74,4778 },4779 {4780 id: 435,4781 name: 'Skuntank',4782 type: ['Poison', 'Dark'],4783 hp: 103,4784 attack: 93,4785 defense: 67,4786 special_attack: 71,4787 special_defense: 61,4788 speed: 84,4789 },4790 {4791 id: 436,4792 name: 'Bronzor',4793 type: ['Steel', 'Psychic'],4794 hp: 57,4795 attack: 24,4796 defense: 86,4797 special_attack: 24,4798 special_defense: 86,4799 speed: 23,4800 },4801 {4802 id: 437,4803 name: 'Bronzong',4804 type: ['Steel', 'Psychic'],4805 hp: 67,4806 attack: 89,4807 defense: 116,4808 special_attack: 79,4809 special_defense: 116,4810 speed: 33,4811 },4812 {4813 id: 438,4814 name: 'Bonsly',4815 type: ['Rock'],4816 hp: 50,4817 attack: 80,4818 defense: 95,4819 special_attack: 10,4820 special_defense: 45,4821 speed: 10,4822 },4823 {4824 id: 439,4825 name: 'Mime Jr.',4826 type: ['Psychic', 'Fairy'],4827 hp: 20,4828 attack: 25,4829 defense: 45,4830 special_attack: 70,4831 special_defense: 90,4832 speed: 60,4833 },4834 {4835 id: 440,4836 name: 'Happiny',4837 type: ['Normal'],4838 hp: 100,4839 attack: 5,4840 defense: 5,4841 special_attack: 15,4842 special_defense: 65,4843 speed: 30,4844 },4845 {4846 id: 441,4847 name: 'Chatot',4848 type: ['Normal', 'Flying'],4849 hp: 76,4850 attack: 65,4851 defense: 45,4852 special_attack: 92,4853 special_defense: 42,4854 speed: 91,4855 },4856 {4857 id: 442,4858 name: 'Spiritomb',4859 type: ['Ghost', 'Dark'],4860 hp: 50,4861 attack: 92,4862 defense: 108,4863 special_attack: 92,4864 special_defense: 108,4865 speed: 35,4866 },4867 {4868 id: 443,4869 name: 'Gible',4870 type: ['Dragon', 'Ground'],4871 hp: 58,4872 attack: 70,4873 defense: 45,4874 special_attack: 40,4875 special_defense: 45,4876 speed: 42,4877 },4878 {4879 id: 444,4880 name: 'Gabite',4881 type: ['Dragon', 'Ground'],4882 hp: 68,4883 attack: 90,4884 defense: 65,4885 special_attack: 50,4886 special_defense: 55,4887 speed: 82,4888 },4889 {4890 id: 445,4891 name: 'Garchomp',4892 type: ['Dragon', 'Ground'],4893 hp: 108,4894 attack: 130,4895 defense: 95,4896 special_attack: 80,4897 special_defense: 85,4898 speed: 102,4899 },4900 {4901 id: 446,4902 name: 'Munchlax',4903 type: ['Normal'],4904 hp: 135,4905 attack: 85,4906 defense: 40,4907 special_attack: 40,4908 special_defense: 85,4909 speed: 5,4910 },4911 {4912 id: 447,4913 name: 'Riolu',4914 type: ['Fighting'],4915 hp: 40,4916 attack: 70,4917 defense: 40,4918 special_attack: 35,4919 special_defense: 40,4920 speed: 60,4921 },4922 {4923 id: 448,4924 name: 'Lucario',4925 type: ['Fighting', 'Steel'],4926 hp: 70,4927 attack: 110,4928 defense: 70,4929 special_attack: 115,4930 special_defense: 70,4931 speed: 90,4932 },4933 {4934 id: 449,4935 name: 'Hippopotas',4936 type: ['Ground'],4937 hp: 68,4938 attack: 72,4939 defense: 78,4940 special_attack: 38,4941 special_defense: 42,4942 speed: 32,4943 },4944 {4945 id: 450,4946 name: 'Hippowdon',4947 type: ['Ground'],4948 hp: 108,4949 attack: 112,4950 defense: 118,4951 special_attack: 68,4952 special_defense: 72,4953 speed: 47,4954 },4955 {4956 id: 451,4957 name: 'Skorupi',4958 type: ['Poison', 'Bug'],4959 hp: 40,4960 attack: 50,4961 defense: 90,4962 special_attack: 30,4963 special_defense: 55,4964 speed: 65,4965 },4966 {4967 id: 452,4968 name: 'Drapion',4969 type: ['Poison', 'Dark'],4970 hp: 70,4971 attack: 90,4972 defense: 110,4973 special_attack: 60,4974 special_defense: 75,4975 speed: 95,4976 },4977 {4978 id: 453,4979 name: 'Croagunk',4980 type: ['Poison', 'Fighting'],4981 hp: 48,4982 attack: 61,4983 defense: 40,4984 special_attack: 61,4985 special_defense: 40,4986 speed: 50,4987 },4988 {4989 id: 454,4990 name: 'Toxicroak',4991 type: ['Poison', 'Fighting'],4992 hp: 83,4993 attack: 106,4994 defense: 65,4995 special_attack: 86,4996 special_defense: 65,4997 speed: 85,4998 },4999 {5000 id: 455,5001 name: 'Carnivine',5002 type: ['Grass'],5003 hp: 74,5004 attack: 100,5005 defense: 72,5006 special_attack: 90,5007 special_defense: 72,5008 speed: 46,5009 },5010 {5011 id: 456,5012 name: 'Finneon',5013 type: ['Water'],5014 hp: 49,5015 attack: 49,5016 defense: 56,5017 special_attack: 49,5018 special_defense: 61,5019 speed: 66,5020 },5021 {5022 id: 457,5023 name: 'Lumineon',5024 type: ['Water'],5025 hp: 69,5026 attack: 69,5027 defense: 76,5028 special_attack: 69,5029 special_defense: 86,5030 speed: 91,5031 },5032 {5033 id: 458,5034 name: 'Mantyke',5035 type: ['Water', 'Flying'],5036 hp: 45,5037 attack: 20,5038 defense: 50,5039 special_attack: 60,5040 special_defense: 120,5041 speed: 50,5042 },5043 {5044 id: 459,5045 name: 'Snover',5046 type: ['Grass', 'Ice'],5047 hp: 60,5048 attack: 62,5049 defense: 50,5050 special_attack: 62,5051 special_defense: 60,5052 speed: 40,5053 },5054 {5055 id: 460,5056 name: 'Abomasnow',5057 type: ['Grass', 'Ice'],5058 hp: 90,5059 attack: 92,5060 defense: 75,5061 special_attack: 92,5062 special_defense: 85,5063 speed: 60,5064 },5065 {5066 id: 461,5067 name: 'Weavile',5068 type: ['Dark', 'Ice'],5069 hp: 70,5070 attack: 120,5071 defense: 65,5072 special_attack: 45,5073 special_defense: 85,5074 speed: 125,5075 },5076 {5077 id: 462,5078 name: 'Magnezone',5079 type: ['Electric', 'Steel'],5080 hp: 70,5081 attack: 70,5082 defense: 115,5083 special_attack: 130,5084 special_defense: 90,5085 speed: 60,5086 },5087 {5088 id: 463,5089 name: 'Lickilicky',5090 type: ['Normal'],5091 hp: 110,5092 attack: 85,5093 defense: 95,5094 special_attack: 80,5095 special_defense: 95,5096 speed: 50,5097 },5098 {5099 id: 464,5100 name: 'Rhyperior',5101 type: ['Ground', 'Rock'],5102 hp: 115,5103 attack: 140,5104 defense: 130,5105 special_attack: 55,5106 special_defense: 55,5107 speed: 40,5108 },5109 {5110 id: 465,5111 name: 'Tangrowth',5112 type: ['Grass'],5113 hp: 100,5114 attack: 100,5115 defense: 125,5116 special_attack: 110,5117 special_defense: 50,5118 speed: 50,5119 },5120 {5121 id: 466,5122 name: 'Electivire',5123 type: ['Electric'],5124 hp: 75,5125 attack: 123,5126 defense: 67,5127 special_attack: 95,5128 special_defense: 85,5129 speed: 95,5130 },5131 {5132 id: 467,5133 name: 'Magmortar',5134 type: ['Fire'],5135 hp: 75,5136 attack: 95,5137 defense: 67,5138 special_attack: 125,5139 special_defense: 95,5140 speed: 83,5141 },5142 {5143 id: 468,5144 name: 'Togekiss',5145 type: ['Fairy', 'Flying'],5146 hp: 85,5147 attack: 50,5148 defense: 95,5149 special_attack: 120,5150 special_defense: 115,5151 speed: 80,5152 },5153 {5154 id: 469,5155 name: 'Yanmega',5156 type: ['Bug', 'Flying'],5157 hp: 86,5158 attack: 76,5159 defense: 86,5160 special_attack: 116,5161 special_defense: 56,5162 speed: 95,5163 },5164 {5165 id: 470,5166 name: 'Leafeon',5167 type: ['Grass'],5168 hp: 65,5169 attack: 110,5170 defense: 130,5171 special_attack: 60,5172 special_defense: 65,5173 speed: 95,5174 },5175 {5176 id: 471,5177 name: 'Glaceon',5178 type: ['Ice'],5179 hp: 65,5180 attack: 60,5181 defense: 110,5182 special_attack: 130,5183 special_defense: 95,5184 speed: 65,5185 },5186 {5187 id: 472,5188 name: 'Gliscor',5189 type: ['Ground', 'Flying'],5190 hp: 75,5191 attack: 95,5192 defense: 125,5193 special_attack: 45,5194 special_defense: 75,5195 speed: 95,5196 },5197 {5198 id: 473,5199 name: 'Mamoswine',5200 type: ['Ice', 'Ground'],5201 hp: 110,5202 attack: 130,5203 defense: 80,5204 special_attack: 70,5205 special_defense: 60,5206 speed: 80,5207 },5208 {5209 id: 474,5210 name: 'Porygon-Z',5211 type: ['Normal'],5212 hp: 85,5213 attack: 80,5214 defense: 70,5215 special_attack: 135,5216 special_defense: 75,5217 speed: 90,5218 },5219 {5220 id: 475,5221 name: 'Gallade',5222 type: ['Psychic', 'Fighting'],5223 hp: 68,5224 attack: 125,5225 defense: 65,5226 special_attack: 65,5227 special_defense: 115,5228 speed: 80,5229 },5230 {5231 id: 476,5232 name: 'Probopass',5233 type: ['Rock', 'Steel'],5234 hp: 60,5235 attack: 55,5236 defense: 145,5237 special_attack: 75,5238 special_defense: 150,5239 speed: 40,5240 },5241 {5242 id: 477,5243 name: 'Dusknoir',5244 type: ['Ghost'],5245 hp: 45,5246 attack: 100,5247 defense: 135,5248 special_attack: 65,5249 special_defense: 135,5250 speed: 45,5251 },5252 {5253 id: 478,5254 name: 'Froslass',5255 type: ['Ice', 'Ghost'],5256 hp: 70,5257 attack: 80,5258 defense: 70,5259 special_attack: 80,5260 special_defense: 70,5261 speed: 110,5262 },5263 {5264 id: 479,5265 name: 'Rotom',5266 type: ['Electric', 'Ghost'],5267 hp: 50,5268 attack: 50,5269 defense: 77,5270 special_attack: 95,5271 special_defense: 77,5272 speed: 91,5273 },5274 {5275 id: 480,5276 name: 'Uxie',5277 type: ['Psychic'],5278 hp: 75,5279 attack: 75,5280 defense: 130,5281 special_attack: 75,5282 special_defense: 130,5283 speed: 95,5284 },5285 {5286 id: 481,5287 name: 'Mesprit',5288 type: ['Psychic'],5289 hp: 80,5290 attack: 105,5291 defense: 105,5292 special_attack: 105,5293 special_defense: 105,5294 speed: 80,5295 },5296 {5297 id: 482,5298 name: 'Azelf',5299 type: ['Psychic'],5300 hp: 75,5301 attack: 125,5302 defense: 70,5303 special_attack: 125,5304 special_defense: 70,5305 speed: 115,5306 },5307 {5308 id: 483,5309 name: 'Dialga',5310 type: ['Steel', 'Dragon'],5311 hp: 100,5312 attack: 120,5313 defense: 120,5314 special_attack: 150,5315 special_defense: 100,5316 speed: 90,5317 },5318 {5319 id: 484,5320 name: 'Palkia',5321 type: ['Water', 'Dragon'],5322 hp: 90,5323 attack: 120,5324 defense: 100,5325 special_attack: 150,5326 special_defense: 120,5327 speed: 100,5328 },5329 {5330 id: 485,5331 name: 'Heatran',5332 type: ['Fire', 'Steel'],5333 hp: 91,5334 attack: 90,5335 defense: 106,5336 special_attack: 130,5337 special_defense: 106,5338 speed: 77,5339 },5340 {5341 id: 486,5342 name: 'Regigigas',5343 type: ['Normal'],5344 hp: 110,5345 attack: 160,5346 defense: 110,5347 special_attack: 80,5348 special_defense: 110,5349 speed: 100,5350 },5351 {5352 id: 487,5353 name: 'Giratina',5354 type: ['Ghost', 'Dragon'],5355 hp: 150,5356 attack: 100,5357 defense: 120,5358 special_attack: 100,5359 special_defense: 120,5360 speed: 90,5361 },5362 {5363 id: 488,5364 name: 'Cresselia',5365 type: ['Psychic'],5366 hp: 120,5367 attack: 70,5368 defense: 120,5369 special_attack: 75,5370 special_defense: 130,5371 speed: 85,5372 },5373 {5374 id: 489,5375 name: 'Phione',5376 type: ['Water'],5377 hp: 80,5378 attack: 80,5379 defense: 80,5380 special_attack: 80,5381 special_defense: 80,5382 speed: 80,5383 },5384 {5385 id: 490,5386 name: 'Manaphy',5387 type: ['Water'],5388 hp: 100,5389 attack: 100,5390 defense: 100,5391 special_attack: 100,5392 special_defense: 100,5393 speed: 100,5394 },5395 {5396 id: 491,5397 name: 'Darkrai',5398 type: ['Dark'],5399 hp: 70,5400 attack: 90,5401 defense: 90,5402 special_attack: 135,5403 special_defense: 90,5404 speed: 125,5405 },5406 {5407 id: 492,5408 name: 'Shaymin',5409 type: ['Grass'],5410 hp: 100,5411 attack: 100,5412 defense: 100,5413 special_attack: 100,5414 special_defense: 100,5415 speed: 100,5416 },5417 {5418 id: 493,5419 name: 'Arceus',5420 type: ['Normal'],5421 hp: 120,5422 attack: 120,5423 defense: 120,5424 special_attack: 120,5425 special_defense: 120,5426 speed: 120,5427 },5428 {5429 id: 494,5430 name: 'Victini',5431 type: ['Psychic', 'Fire'],5432 hp: 100,5433 attack: 100,5434 defense: 100,5435 special_attack: 100,5436 special_defense: 100,5437 speed: 100,5438 },5439 {5440 id: 495,5441 name: 'Snivy',5442 type: ['Grass'],5443 hp: 45,5444 attack: 45,5445 defense: 55,5446 special_attack: 45,5447 special_defense: 55,5448 speed: 63,5449 },5450 {5451 id: 496,5452 name: 'Servine',5453 type: ['Grass'],5454 hp: 60,5455 attack: 60,5456 defense: 75,5457 special_attack: 60,5458 special_defense: 75,5459 speed: 83,5460 },5461 {5462 id: 497,5463 name: 'Serperior',5464 type: ['Grass'],5465 hp: 75,5466 attack: 75,5467 defense: 95,5468 special_attack: 75,5469 special_defense: 95,5470 speed: 113,5471 },5472 {5473 id: 498,5474 name: 'Tepig',5475 type: ['Fire'],5476 hp: 65,5477 attack: 63,5478 defense: 45,5479 special_attack: 45,5480 special_defense: 45,5481 speed: 45,5482 },5483 {5484 id: 499,5485 name: 'Pignite',5486 type: ['Fire', 'Fighting'],5487 hp: 90,5488 attack: 93,5489 defense: 55,5490 special_attack: 70,5491 special_defense: 55,5492 speed: 55,5493 },5494 {5495 id: 500,5496 name: 'Emboar',5497 type: ['Fire', 'Fighting'],5498 hp: 110,5499 attack: 123,5500 defense: 65,5501 special_attack: 100,5502 special_defense: 65,5503 speed: 65,5504 },5505 {5506 id: 501,5507 name: 'Oshawott',5508 type: ['Water'],5509 hp: 55,5510 attack: 55,5511 defense: 45,5512 special_attack: 63,5513 special_defense: 45,5514 speed: 45,5515 },5516 {5517 id: 502,5518 name: 'Dewott',5519 type: ['Water'],5520 hp: 75,5521 attack: 75,5522 defense: 60,5523 special_attack: 83,5524 special_defense: 60,5525 speed: 60,5526 },5527 {5528 id: 503,5529 name: 'Samurott',5530 type: ['Water'],5531 hp: 95,5532 attack: 100,5533 defense: 85,5534 special_attack: 108,5535 special_defense: 70,5536 speed: 70,5537 },5538 {5539 id: 504,5540 name: 'Patrat',5541 type: ['Normal'],5542 hp: 45,5543 attack: 55,5544 defense: 39,5545 special_attack: 35,5546 special_defense: 39,5547 speed: 42,5548 },5549 {5550 id: 505,5551 name: 'Watchog',5552 type: ['Normal'],5553 hp: 60,5554 attack: 85,5555 defense: 69,5556 special_attack: 60,5557 special_defense: 69,5558 speed: 77,5559 },5560 {5561 id: 506,5562 name: 'Lillipup',5563 type: ['Normal'],5564 hp: 45,5565 attack: 60,5566 defense: 45,5567 special_attack: 25,5568 special_defense: 45,5569 speed: 55,5570 },5571 {5572 id: 507,5573 name: 'Herdier',5574 type: ['Normal'],5575 hp: 65,5576 attack: 80,5577 defense: 65,5578 special_attack: 35,5579 special_defense: 65,5580 speed: 60,5581 },5582 {5583 id: 508,5584 name: 'Stoutland',5585 type: ['Normal'],5586 hp: 85,5587 attack: 110,5588 defense: 90,5589 special_attack: 45,5590 special_defense: 90,5591 speed: 80,5592 },5593 {5594 id: 509,5595 name: 'Purrloin',5596 type: ['Dark'],5597 hp: 41,5598 attack: 50,5599 defense: 37,5600 special_attack: 50,5601 special_defense: 37,5602 speed: 66,5603 },5604 {5605 id: 510,5606 name: 'Liepard',5607 type: ['Dark'],5608 hp: 64,5609 attack: 88,5610 defense: 50,5611 special_attack: 88,5612 special_defense: 50,5613 speed: 106,5614 },5615 {5616 id: 511,5617 name: 'Pansage',5618 type: ['Grass'],5619 hp: 50,5620 attack: 53,5621 defense: 48,5622 special_attack: 53,5623 special_defense: 48,5624 speed: 64,5625 },5626 {5627 id: 512,5628 name: 'Simisage',5629 type: ['Grass'],5630 hp: 75,5631 attack: 98,5632 defense: 63,5633 special_attack: 98,5634 special_defense: 63,5635 speed: 101,5636 },5637 {5638 id: 513,5639 name: 'Pansear',5640 type: ['Fire'],5641 hp: 50,5642 attack: 53,5643 defense: 48,5644 special_attack: 53,5645 special_defense: 48,5646 speed: 64,5647 },5648 {5649 id: 514,5650 name: 'Simisear',5651 type: ['Fire'],5652 hp: 75,5653 attack: 98,5654 defense: 63,5655 special_attack: 98,5656 special_defense: 63,5657 speed: 101,5658 },5659 {5660 id: 515,5661 name: 'Panpour',5662 type: ['Water'],5663 hp: 50,5664 attack: 53,5665 defense: 48,5666 special_attack: 53,5667 special_defense: 48,5668 speed: 64,5669 },5670 {5671 id: 516,5672 name: 'Simipour',5673 type: ['Water'],5674 hp: 75,5675 attack: 98,5676 defense: 63,5677 special_attack: 98,5678 special_defense: 63,5679 speed: 101,5680 },5681 {5682 id: 517,5683 name: 'Munna',5684 type: ['Psychic'],5685 hp: 76,5686 attack: 25,5687 defense: 45,5688 special_attack: 67,5689 special_defense: 55,5690 speed: 24,5691 },5692 {5693 id: 518,5694 name: 'Musharna',5695 type: ['Psychic'],5696 hp: 116,5697 attack: 55,5698 defense: 85,5699 special_attack: 107,5700 special_defense: 95,5701 speed: 29,5702 },5703 {5704 id: 519,5705 name: 'Pidove',5706 type: ['Normal', 'Flying'],5707 hp: 50,5708 attack: 55,5709 defense: 50,5710 special_attack: 36,5711 special_defense: 30,5712 speed: 43,5713 },5714 {5715 id: 520,5716 name: 'Tranquill',5717 type: ['Normal', 'Flying'],5718 hp: 62,5719 attack: 77,5720 defense: 62,5721 special_attack: 50,5722 special_defense: 42,5723 speed: 65,5724 },5725 {5726 id: 521,5727 name: 'Unfezant',5728 type: ['Normal', 'Flying'],5729 hp: 80,5730 attack: 115,5731 defense: 80,5732 special_attack: 65,5733 special_defense: 55,5734 speed: 93,5735 },5736 {5737 id: 522,5738 name: 'Blitzle',5739 type: ['Electric'],5740 hp: 45,5741 attack: 60,5742 defense: 32,5743 special_attack: 50,5744 special_defense: 32,5745 speed: 76,5746 },5747 {5748 id: 523,5749 name: 'Zebstrika',5750 type: ['Electric'],5751 hp: 75,5752 attack: 100,5753 defense: 63,5754 special_attack: 80,5755 special_defense: 63,5756 speed: 116,5757 },5758 {5759 id: 524,5760 name: 'Roggenrola',5761 type: ['Rock'],5762 hp: 55,5763 attack: 75,5764 defense: 85,5765 special_attack: 25,5766 special_defense: 25,5767 speed: 15,5768 },5769 {5770 id: 525,5771 name: 'Boldore',5772 type: ['Rock'],5773 hp: 70,5774 attack: 105,5775 defense: 105,5776 special_attack: 50,5777 special_defense: 40,5778 speed: 20,5779 },5780 {5781 id: 526,5782 name: 'Gigalith',5783 type: ['Rock'],5784 hp: 85,5785 attack: 135,5786 defense: 130,5787 special_attack: 60,5788 special_defense: 80,5789 speed: 25,5790 },5791 {5792 id: 527,5793 name: 'Woobat',5794 type: ['Psychic', 'Flying'],5795 hp: 65,5796 attack: 45,5797 defense: 43,5798 special_attack: 55,5799 special_defense: 43,5800 speed: 72,5801 },5802 {5803 id: 528,5804 name: 'Swoobat',5805 type: ['Psychic', 'Flying'],5806 hp: 67,5807 attack: 57,5808 defense: 55,5809 special_attack: 77,5810 special_defense: 55,5811 speed: 114,5812 },5813 {5814 id: 529,5815 name: 'Drilbur',5816 type: ['Ground'],5817 hp: 60,5818 attack: 85,5819 defense: 40,5820 special_attack: 30,5821 special_defense: 45,5822 speed: 68,5823 },5824 {5825 id: 530,5826 name: 'Excadrill',5827 type: ['Ground', 'Steel'],5828 hp: 110,5829 attack: 135,5830 defense: 60,5831 special_attack: 50,5832 special_defense: 65,5833 speed: 88,5834 },5835 {5836 id: 531,5837 name: 'Audino',5838 type: ['Normal'],5839 hp: 103,5840 attack: 60,5841 defense: 86,5842 special_attack: 60,5843 special_defense: 86,5844 speed: 50,5845 },5846 {5847 id: 532,5848 name: 'Timburr',5849 type: ['Fighting'],5850 hp: 75,5851 attack: 80,5852 defense: 55,5853 special_attack: 25,5854 special_defense: 35,5855 speed: 35,5856 },5857 {5858 id: 533,5859 name: 'Gurdurr',5860 type: ['Fighting'],5861 hp: 85,5862 attack: 105,5863 defense: 85,5864 special_attack: 40,5865 special_defense: 50,5866 speed: 40,5867 },5868 {5869 id: 534,5870 name: 'Conkeldurr',5871 type: ['Fighting'],5872 hp: 105,5873 attack: 140,5874 defense: 95,5875 special_attack: 55,5876 special_defense: 65,5877 speed: 45,5878 },5879 {5880 id: 535,5881 name: 'Tympole',5882 type: ['Water'],5883 hp: 50,5884 attack: 50,5885 defense: 40,5886 special_attack: 50,5887 special_defense: 40,5888 speed: 64,5889 },5890 {5891 id: 536,5892 name: 'Palpitoad',5893 type: ['Water', 'Ground'],5894 hp: 75,5895 attack: 65,5896 defense: 55,5897 special_attack: 65,5898 special_defense: 55,5899 speed: 69,5900 },5901 {5902 id: 537,5903 name: 'Seismitoad',5904 type: ['Water', 'Ground'],5905 hp: 105,5906 attack: 95,5907 defense: 75,5908 special_attack: 85,5909 special_defense: 75,5910 speed: 74,5911 },5912 {5913 id: 538,5914 name: 'Throh',5915 type: ['Fighting'],5916 hp: 120,5917 attack: 100,5918 defense: 85,5919 special_attack: 30,5920 special_defense: 85,5921 speed: 45,5922 },5923 {5924 id: 539,5925 name: 'Sawk',5926 type: ['Fighting'],5927 hp: 75,5928 attack: 125,5929 defense: 75,5930 special_attack: 30,5931 special_defense: 75,5932 speed: 85,5933 },5934 {5935 id: 540,5936 name: 'Sewaddle',5937 type: ['Bug', 'Grass'],5938 hp: 45,5939 attack: 53,5940 defense: 70,5941 special_attack: 40,5942 special_defense: 60,5943 speed: 42,5944 },5945 {5946 id: 541,5947 name: 'Swadloon',5948 type: ['Bug', 'Grass'],5949 hp: 55,5950 attack: 63,5951 defense: 90,5952 special_attack: 50,5953 special_defense: 80,5954 speed: 42,5955 },5956 {5957 id: 542,5958 name: 'Leavanny',5959 type: ['Bug', 'Grass'],5960 hp: 75,5961 attack: 103,5962 defense: 80,5963 special_attack: 70,5964 special_defense: 80,5965 speed: 92,5966 },5967 {5968 id: 543,5969 name: 'Venipede',5970 type: ['Bug', 'Poison'],5971 hp: 30,5972 attack: 45,5973 defense: 59,5974 special_attack: 30,5975 special_defense: 39,5976 speed: 57,5977 },5978 {5979 id: 544,5980 name: 'Whirlipede',5981 type: ['Bug', 'Poison'],5982 hp: 40,5983 attack: 55,5984 defense: 99,5985 special_attack: 40,5986 special_defense: 79,5987 speed: 47,5988 },5989 {5990 id: 545,5991 name: 'Scolipede',5992 type: ['Bug', 'Poison'],5993 hp: 60,5994 attack: 100,5995 defense: 89,5996 special_attack: 55,5997 special_defense: 69,5998 speed: 112,5999 },6000 {6001 id: 546,6002 name: 'Cottonee',6003 type: ['Grass', 'Fairy'],6004 hp: 40,6005 attack: 27,6006 defense: 60,6007 special_attack: 37,6008 special_defense: 50,6009 speed: 66,6010 },6011 {6012 id: 547,6013 name: 'Whimsicott',6014 type: ['Grass', 'Fairy'],6015 hp: 60,6016 attack: 67,6017 defense: 85,6018 special_attack: 77,6019 special_defense: 75,6020 speed: 116,6021 },6022 {6023 id: 548,6024 name: 'Petilil',6025 type: ['Grass'],6026 hp: 45,6027 attack: 35,6028 defense: 50,6029 special_attack: 70,6030 special_defense: 50,6031 speed: 30,6032 },6033 {6034 id: 549,6035 name: 'Lilligant',6036 type: ['Grass'],6037 hp: 70,6038 attack: 60,6039 defense: 75,6040 special_attack: 110,6041 special_defense: 75,6042 speed: 90,6043 },6044 {6045 id: 550,6046 name: 'Basculin',6047 type: ['Water'],6048 hp: 70,6049 attack: 92,6050 defense: 65,6051 special_attack: 80,6052 special_defense: 55,6053 speed: 98,6054 },6055 {6056 id: 551,6057 name: 'Sandile',6058 type: ['Ground', 'Dark'],6059 hp: 50,6060 attack: 72,6061 defense: 35,6062 special_attack: 35,6063 special_defense: 35,6064 speed: 65,6065 },6066 {6067 id: 552,6068 name: 'Krokorok',6069 type: ['Ground', 'Dark'],6070 hp: 60,6071 attack: 82,6072 defense: 45,6073 special_attack: 45,6074 special_defense: 45,6075 speed: 74,6076 },6077 {6078 id: 553,6079 name: 'Krookodile',6080 type: ['Ground', 'Dark'],6081 hp: 95,6082 attack: 117,6083 defense: 80,6084 special_attack: 65,6085 special_defense: 70,6086 speed: 92,6087 },6088 {6089 id: 554,6090 name: 'Darumaka',6091 type: ['Fire'],6092 hp: 70,6093 attack: 90,6094 defense: 45,6095 special_attack: 15,6096 special_defense: 45,6097 speed: 50,6098 },6099 {6100 id: 555,6101 name: 'Darmanitan',6102 type: ['Fire'],6103 hp: 105,6104 attack: 140,6105 defense: 55,6106 special_attack: 30,6107 special_defense: 55,6108 speed: 95,6109 },6110 {6111 id: 556,6112 name: 'Maractus',6113 type: ['Grass'],6114 hp: 75,6115 attack: 86,6116 defense: 67,6117 special_attack: 106,6118 special_defense: 67,6119 speed: 60,6120 },6121 {6122 id: 557,6123 name: 'Dwebble',6124 type: ['Bug', 'Rock'],6125 hp: 50,6126 attack: 65,6127 defense: 85,6128 special_attack: 35,6129 special_defense: 35,6130 speed: 55,6131 },6132 {6133 id: 558,6134 name: 'Crustle',6135 type: ['Bug', 'Rock'],6136 hp: 70,6137 attack: 105,6138 defense: 125,6139 special_attack: 65,6140 special_defense: 75,6141 speed: 45,6142 },6143 {6144 id: 559,6145 name: 'Scraggy',6146 type: ['Dark', 'Fighting'],6147 hp: 50,6148 attack: 75,6149 defense: 70,6150 special_attack: 35,6151 special_defense: 70,6152 speed: 48,6153 },6154 {6155 id: 560,6156 name: 'Scrafty',6157 type: ['Dark', 'Fighting'],6158 hp: 65,6159 attack: 90,6160 defense: 115,6161 special_attack: 45,6162 special_defense: 115,6163 speed: 58,6164 },6165 {6166 id: 561,6167 name: 'Sigilyph',6168 type: ['Psychic', 'Flying'],6169 hp: 72,6170 attack: 58,6171 defense: 80,6172 special_attack: 103,6173 special_defense: 80,6174 speed: 97,6175 },6176 {6177 id: 562,6178 name: 'Yamask',6179 type: ['Ghost'],6180 hp: 38,6181 attack: 30,6182 defense: 85,6183 special_attack: 55,6184 special_defense: 65,6185 speed: 30,6186 },6187 {6188 id: 563,6189 name: 'Cofagrigus',6190 type: ['Ghost'],6191 hp: 58,6192 attack: 50,6193 defense: 145,6194 special_attack: 95,6195 special_defense: 105,6196 speed: 30,6197 },6198 {6199 id: 564,6200 name: 'Tirtouga',6201 type: ['Water', 'Rock'],6202 hp: 54,6203 attack: 78,6204 defense: 103,6205 special_attack: 53,6206 special_defense: 45,6207 speed: 22,6208 },6209 {6210 id: 565,6211 name: 'Carracosta',6212 type: ['Water', 'Rock'],6213 hp: 74,6214 attack: 108,6215 defense: 133,6216 special_attack: 83,6217 special_defense: 65,6218 speed: 32,6219 },6220 {6221 id: 566,6222 name: 'Archen',6223 type: ['Rock', 'Flying'],6224 hp: 55,6225 attack: 112,6226 defense: 45,6227 special_attack: 74,6228 special_defense: 45,6229 speed: 70,6230 },6231 {6232 id: 567,6233 name: 'Archeops',6234 type: ['Rock', 'Flying'],6235 hp: 75,6236 attack: 140,6237 defense: 65,6238 special_attack: 112,6239 special_defense: 65,6240 speed: 110,6241 },6242 {6243 id: 568,6244 name: 'Trubbish',6245 type: ['Poison'],6246 hp: 50,6247 attack: 50,6248 defense: 62,6249 special_attack: 40,6250 special_defense: 62,6251 speed: 65,6252 },6253 {6254 id: 569,6255 name: 'Garbodor',6256 type: ['Poison'],6257 hp: 80,6258 attack: 95,6259 defense: 82,6260 special_attack: 60,6261 special_defense: 82,6262 speed: 75,6263 },6264 {6265 id: 570,6266 name: 'Zorua',6267 type: ['Dark'],6268 hp: 40,6269 attack: 65,6270 defense: 40,6271 special_attack: 80,6272 special_defense: 40,6273 speed: 65,6274 },6275 {6276 id: 571,6277 name: 'Zoroark',6278 type: ['Dark'],6279 hp: 60,6280 attack: 105,6281 defense: 60,6282 special_attack: 120,6283 special_defense: 60,6284 speed: 105,6285 },6286 {6287 id: 572,6288 name: 'Minccino',6289 type: ['Normal'],6290 hp: 55,6291 attack: 50,6292 defense: 40,6293 special_attack: 40,6294 special_defense: 40,6295 speed: 75,6296 },6297 {6298 id: 573,6299 name: 'Cinccino',6300 type: ['Normal'],6301 hp: 75,6302 attack: 95,6303 defense: 60,6304 special_attack: 65,6305 special_defense: 60,6306 speed: 115,6307 },6308 {6309 id: 574,6310 name: 'Gothita',6311 type: ['Psychic'],6312 hp: 45,6313 attack: 30,6314 defense: 50,6315 special_attack: 55,6316 special_defense: 65,6317 speed: 45,6318 },6319 {6320 id: 575,6321 name: 'Gothorita',6322 type: ['Psychic'],6323 hp: 60,6324 attack: 45,6325 defense: 70,6326 special_attack: 75,6327 special_defense: 85,6328 speed: 55,6329 },6330 {6331 id: 576,6332 name: 'Gothitelle',6333 type: ['Psychic'],6334 hp: 70,6335 attack: 55,6336 defense: 95,6337 special_attack: 95,6338 special_defense: 110,6339 speed: 65,6340 },6341 {6342 id: 577,6343 name: 'Solosis',6344 type: ['Psychic'],6345 hp: 45,6346 attack: 30,6347 defense: 40,6348 special_attack: 105,6349 special_defense: 50,6350 speed: 20,6351 },6352 {6353 id: 578,6354 name: 'Duosion',6355 type: ['Psychic'],6356 hp: 65,6357 attack: 40,6358 defense: 50,6359 special_attack: 125,6360 special_defense: 60,6361 speed: 30,6362 },6363 {6364 id: 579,6365 name: 'Reuniclus',6366 type: ['Psychic'],6367 hp: 110,6368 attack: 65,6369 defense: 75,6370 special_attack: 125,6371 special_defense: 85,6372 speed: 30,6373 },6374 {6375 id: 580,6376 name: 'Ducklett',6377 type: ['Water', 'Flying'],6378 hp: 62,6379 attack: 44,6380 defense: 50,6381 special_attack: 44,6382 special_defense: 50,6383 speed: 55,6384 },6385 {6386 id: 581,6387 name: 'Swanna',6388 type: ['Water', 'Flying'],6389 hp: 75,6390 attack: 87,6391 defense: 63,6392 special_attack: 87,6393 special_defense: 63,6394 speed: 98,6395 },6396 {6397 id: 582,6398 name: 'Vanillite',6399 type: ['Ice'],6400 hp: 36,6401 attack: 50,6402 defense: 50,6403 special_attack: 65,6404 special_defense: 60,6405 speed: 44,6406 },6407 {6408 id: 583,6409 name: 'Vanillish',6410 type: ['Ice'],6411 hp: 51,6412 attack: 65,6413 defense: 65,6414 special_attack: 80,6415 special_defense: 75,6416 speed: 59,6417 },6418 {6419 id: 584,6420 name: 'Vanilluxe',6421 type: ['Ice'],6422 hp: 71,6423 attack: 95,6424 defense: 85,6425 special_attack: 110,6426 special_defense: 95,6427 speed: 79,6428 },6429 {6430 id: 585,6431 name: 'Deerling',6432 type: ['Normal', 'Grass'],6433 hp: 60,6434 attack: 60,6435 defense: 50,6436 special_attack: 40,6437 special_defense: 50,6438 speed: 75,6439 },6440 {6441 id: 586,6442 name: 'Sawsbuck',6443 type: ['Normal', 'Grass'],6444 hp: 80,6445 attack: 100,6446 defense: 70,6447 special_attack: 60,6448 special_defense: 70,6449 speed: 95,6450 },6451 {6452 id: 587,6453 name: 'Emolga',6454 type: ['Electric', 'Flying'],6455 hp: 55,6456 attack: 75,6457 defense: 60,6458 special_attack: 75,6459 special_defense: 60,6460 speed: 103,6461 },6462 {6463 id: 588,6464 name: 'Karrablast',6465 type: ['Bug'],6466 hp: 50,6467 attack: 75,6468 defense: 45,6469 special_attack: 40,6470 special_defense: 45,6471 speed: 60,6472 },6473 {6474 id: 589,6475 name: 'Escavalier',6476 type: ['Bug', 'Steel'],6477 hp: 70,6478 attack: 135,6479 defense: 105,6480 special_attack: 60,6481 special_defense: 105,6482 speed: 20,6483 },6484 {6485 id: 590,6486 name: 'Foongus',6487 type: ['Grass', 'Poison'],6488 hp: 69,6489 attack: 55,6490 defense: 45,6491 special_attack: 55,6492 special_defense: 55,6493 speed: 15,6494 },6495 {6496 id: 591,6497 name: 'Amoonguss',6498 type: ['Grass', 'Poison'],6499 hp: 114,6500 attack: 85,6501 defense: 70,6502 special_attack: 85,6503 special_defense: 80,6504 speed: 30,6505 },6506 {6507 id: 592,6508 name: 'Frillish',6509 type: ['Water', 'Ghost'],6510 hp: 55,6511 attack: 40,6512 defense: 50,6513 special_attack: 65,6514 special_defense: 85,6515 speed: 40,6516 },6517 {6518 id: 593,6519 name: 'Jellicent',6520 type: ['Water', 'Ghost'],6521 hp: 100,6522 attack: 60,6523 defense: 70,6524 special_attack: 85,6525 special_defense: 105,6526 speed: 60,6527 },6528 {6529 id: 594,6530 name: 'Alomomola',6531 type: ['Water'],6532 hp: 165,6533 attack: 75,6534 defense: 80,6535 special_attack: 40,6536 special_defense: 45,6537 speed: 65,6538 },6539 {6540 id: 595,6541 name: 'Joltik',6542 type: ['Bug', 'Electric'],6543 hp: 50,6544 attack: 47,6545 defense: 50,6546 special_attack: 57,6547 special_defense: 50,6548 speed: 65,6549 },6550 {6551 id: 596,6552 name: 'Galvantula',6553 type: ['Bug', 'Electric'],6554 hp: 70,6555 attack: 77,6556 defense: 60,6557 special_attack: 97,6558 special_defense: 60,6559 speed: 108,6560 },6561 {6562 id: 597,6563 name: 'Ferroseed',6564 type: ['Grass', 'Steel'],6565 hp: 44,6566 attack: 50,6567 defense: 91,6568 special_attack: 24,6569 special_defense: 86,6570 speed: 10,6571 },6572 {6573 id: 598,6574 name: 'Ferrothorn',6575 type: ['Grass', 'Steel'],6576 hp: 74,6577 attack: 94,6578 defense: 131,6579 special_attack: 54,6580 special_defense: 116,6581 speed: 20,6582 },6583 {6584 id: 599,6585 name: 'Klink',6586 type: ['Steel'],6587 hp: 40,6588 attack: 55,6589 defense: 70,6590 special_attack: 45,6591 special_defense: 60,6592 speed: 30,6593 },6594 {6595 id: 600,6596 name: 'Klang',6597 type: ['Steel'],6598 hp: 60,6599 attack: 80,6600 defense: 95,6601 special_attack: 70,6602 special_defense: 85,6603 speed: 50,6604 },6605 {6606 id: 601,6607 name: 'Klinklang',6608 type: ['Steel'],6609 hp: 60,6610 attack: 100,6611 defense: 115,6612 special_attack: 70,6613 special_defense: 85,6614 speed: 90,6615 },6616 {6617 id: 602,6618 name: 'Tynamo',6619 type: ['Electric'],6620 hp: 35,6621 attack: 55,6622 defense: 40,6623 special_attack: 45,6624 special_defense: 40,6625 speed: 60,6626 },6627 {6628 id: 603,6629 name: 'Eelektrik',6630 type: ['Electric'],6631 hp: 65,6632 attack: 85,6633 defense: 70,6634 special_attack: 75,6635 special_defense: 70,6636 speed: 40,6637 },6638 {6639 id: 604,6640 name: 'Eelektross',6641 type: ['Electric'],6642 hp: 85,6643 attack: 115,6644 defense: 80,6645 special_attack: 105,6646 special_defense: 80,6647 speed: 50,6648 },6649 {6650 id: 605,6651 name: 'Elgyem',6652 type: ['Psychic'],6653 hp: 55,6654 attack: 55,6655 defense: 55,6656 special_attack: 85,6657 special_defense: 55,6658 speed: 30,6659 },6660 {6661 id: 606,6662 name: 'Beheeyem',6663 type: ['Psychic'],6664 hp: 75,6665 attack: 75,6666 defense: 75,6667 special_attack: 125,6668 special_defense: 95,6669 speed: 40,6670 },6671 {6672 id: 607,6673 name: 'Litwick',6674 type: ['Ghost', 'Fire'],6675 hp: 50,6676 attack: 30,6677 defense: 55,6678 special_attack: 65,6679 special_defense: 55,6680 speed: 20,6681 },6682 {6683 id: 608,6684 name: 'Lampent',6685 type: ['Ghost', 'Fire'],6686 hp: 60,6687 attack: 40,6688 defense: 60,6689 special_attack: 95,6690 special_defense: 60,6691 speed: 55,6692 },6693 {6694 id: 609,6695 name: 'Chandelure',6696 type: ['Ghost', 'Fire'],6697 hp: 60,6698 attack: 55,6699 defense: 90,6700 special_attack: 145,6701 special_defense: 90,6702 speed: 80,6703 },6704 {6705 id: 610,6706 name: 'Axew',6707 type: ['Dragon'],6708 hp: 46,6709 attack: 87,6710 defense: 60,6711 special_attack: 30,6712 special_defense: 40,6713 speed: 57,6714 },6715 {6716 id: 611,6717 name: 'Fraxure',6718 type: ['Dragon'],6719 hp: 66,6720 attack: 117,6721 defense: 70,6722 special_attack: 40,6723 special_defense: 50,6724 speed: 67,6725 },6726 {6727 id: 612,6728 name: 'Haxorus',6729 type: ['Dragon'],6730 hp: 76,6731 attack: 147,6732 defense: 90,6733 special_attack: 60,6734 special_defense: 70,6735 speed: 97,6736 },6737 {6738 id: 613,6739 name: 'Cubchoo',6740 type: ['Ice'],6741 hp: 55,6742 attack: 70,6743 defense: 40,6744 special_attack: 60,6745 special_defense: 40,6746 speed: 40,6747 },6748 {6749 id: 614,6750 name: 'Beartic',6751 type: ['Ice'],6752 hp: 95,6753 attack: 130,6754 defense: 80,6755 special_attack: 70,6756 special_defense: 80,6757 speed: 50,6758 },6759 {6760 id: 615,6761 name: 'Cryogonal',6762 type: ['Ice'],6763 hp: 80,6764 attack: 50,6765 defense: 50,6766 special_attack: 95,6767 special_defense: 135,6768 speed: 105,6769 },6770 {6771 id: 616,6772 name: 'Shelmet',6773 type: ['Bug'],6774 hp: 50,6775 attack: 40,6776 defense: 85,6777 special_attack: 40,6778 special_defense: 65,6779 speed: 25,6780 },6781 {6782 id: 617,6783 name: 'Accelgor',6784 type: ['Bug'],6785 hp: 80,6786 attack: 70,6787 defense: 40,6788 special_attack: 100,6789 special_defense: 60,6790 speed: 145,6791 },6792 {6793 id: 618,6794 name: 'Stunfisk',6795 type: ['Ground', 'Electric'],6796 hp: 109,6797 attack: 66,6798 defense: 84,6799 special_attack: 81,6800 special_defense: 99,6801 speed: 32,6802 },6803 {6804 id: 619,6805 name: 'Mienfoo',6806 type: ['Fighting'],6807 hp: 45,6808 attack: 85,6809 defense: 50,6810 special_attack: 55,6811 special_defense: 50,6812 speed: 65,6813 },6814 {6815 id: 620,6816 name: 'Mienshao',6817 type: ['Fighting'],6818 hp: 65,6819 attack: 125,6820 defense: 60,6821 special_attack: 95,6822 special_defense: 60,6823 speed: 105,6824 },6825 {6826 id: 621,6827 name: 'Druddigon',6828 type: ['Dragon'],6829 hp: 77,6830 attack: 120,6831 defense: 90,6832 special_attack: 60,6833 special_defense: 90,6834 speed: 48,6835 },6836 {6837 id: 622,6838 name: 'Golett',6839 type: ['Ground', 'Ghost'],6840 hp: 59,6841 attack: 74,6842 defense: 50,6843 special_attack: 35,6844 special_defense: 50,6845 speed: 35,6846 },6847 {6848 id: 623,6849 name: 'Golurk',6850 type: ['Ground', 'Ghost'],6851 hp: 89,6852 attack: 124,6853 defense: 80,6854 special_attack: 55,6855 special_defense: 80,6856 speed: 55,6857 },6858 {6859 id: 624,6860 name: 'Pawniard',6861 type: ['Dark', 'Steel'],6862 hp: 45,6863 attack: 85,6864 defense: 70,6865 special_attack: 40,6866 special_defense: 40,6867 speed: 60,6868 },6869 {6870 id: 625,6871 name: 'Bisharp',6872 type: ['Dark', 'Steel'],6873 hp: 65,6874 attack: 125,6875 defense: 100,6876 special_attack: 60,6877 special_defense: 70,6878 speed: 70,6879 },6880 {6881 id: 626,6882 name: 'Bouffalant',6883 type: ['Normal'],6884 hp: 95,6885 attack: 110,6886 defense: 95,6887 special_attack: 40,6888 special_defense: 95,6889 speed: 55,6890 },6891 {6892 id: 627,6893 name: 'Rufflet',6894 type: ['Normal', 'Flying'],6895 hp: 70,6896 attack: 83,6897 defense: 50,6898 special_attack: 37,6899 special_defense: 50,6900 speed: 60,6901 },6902 {6903 id: 628,6904 name: 'Braviary',6905 type: ['Normal', 'Flying'],6906 hp: 100,6907 attack: 123,6908 defense: 75,6909 special_attack: 57,6910 special_defense: 75,6911 speed: 80,6912 },6913 {6914 id: 629,6915 name: 'Vullaby',6916 type: ['Dark', 'Flying'],6917 hp: 70,6918 attack: 55,6919 defense: 75,6920 special_attack: 45,6921 special_defense: 65,6922 speed: 60,6923 },6924 {6925 id: 630,6926 name: 'Mandibuzz',6927 type: ['Dark', 'Flying'],6928 hp: 110,6929 attack: 65,6930 defense: 105,6931 special_attack: 55,6932 special_defense: 95,6933 speed: 80,6934 },6935 {6936 id: 631,6937 name: 'Heatmor',6938 type: ['Fire'],6939 hp: 85,6940 attack: 97,6941 defense: 66,6942 special_attack: 105,6943 special_defense: 66,6944 speed: 65,6945 },6946 {6947 id: 632,6948 name: 'Durant',6949 type: ['Bug', 'Steel'],6950 hp: 58,6951 attack: 109,6952 defense: 112,6953 special_attack: 48,6954 special_defense: 48,6955 speed: 109,6956 },6957 {6958 id: 633,6959 name: 'Deino',6960 type: ['Dark', 'Dragon'],6961 hp: 52,6962 attack: 65,6963 defense: 50,6964 special_attack: 45,6965 special_defense: 50,6966 speed: 38,6967 },6968 {6969 id: 634,6970 name: 'Zweilous',6971 type: ['Dark', 'Dragon'],6972 hp: 72,6973 attack: 85,6974 defense: 70,6975 special_attack: 65,6976 special_defense: 70,6977 speed: 58,6978 },6979 {6980 id: 635,6981 name: 'Hydreigon',6982 type: ['Dark', 'Dragon'],6983 hp: 92,6984 attack: 105,6985 defense: 90,6986 special_attack: 125,6987 special_defense: 90,6988 speed: 98,6989 },6990 {6991 id: 636,6992 name: 'Larvesta',6993 type: ['Bug', 'Fire'],6994 hp: 55,6995 attack: 85,6996 defense: 55,6997 special_attack: 50,6998 special_defense: 55,6999 speed: 60,7000 },7001 {7002 id: 637,7003 name: 'Volcarona',7004 type: ['Bug', 'Fire'],7005 hp: 85,7006 attack: 60,7007 defense: 65,7008 special_attack: 135,7009 special_defense: 105,7010 speed: 100,7011 },7012 {7013 id: 638,7014 name: 'Cobalion',7015 type: ['Steel', 'Fighting'],7016 hp: 91,7017 attack: 90,7018 defense: 129,7019 special_attack: 90,7020 special_defense: 72,7021 speed: 108,7022 },7023 {7024 id: 639,7025 name: 'Terrakion',7026 type: ['Rock', 'Fighting'],7027 hp: 91,7028 attack: 129,7029 defense: 90,7030 special_attack: 72,7031 special_defense: 90,7032 speed: 108,7033 },7034 {7035 id: 640,7036 name: 'Virizion',7037 type: ['Grass', 'Fighting'],7038 hp: 91,7039 attack: 90,7040 defense: 72,7041 special_attack: 90,7042 special_defense: 129,7043 speed: 108,7044 },7045 {7046 id: 641,7047 name: 'Tornadus',7048 type: ['Flying'],7049 hp: 79,7050 attack: 115,7051 defense: 70,7052 special_attack: 125,7053 special_defense: 80,7054 speed: 111,7055 },7056 {7057 id: 642,7058 name: 'Thundurus',7059 type: ['Electric', 'Flying'],7060 hp: 79,7061 attack: 115,7062 defense: 70,7063 special_attack: 125,7064 special_defense: 80,7065 speed: 111,7066 },7067 {7068 id: 643,7069 name: 'Reshiram',7070 type: ['Dragon', 'Fire'],7071 hp: 100,7072 attack: 120,7073 defense: 100,7074 special_attack: 150,7075 special_defense: 120,7076 speed: 90,7077 },7078 {7079 id: 644,7080 name: 'Zekrom',7081 type: ['Dragon', 'Electric'],7082 hp: 100,7083 attack: 150,7084 defense: 120,7085 special_attack: 120,7086 special_defense: 100,7087 speed: 90,7088 },7089 {7090 id: 645,7091 name: 'Landorus',7092 type: ['Ground', 'Flying'],7093 hp: 89,7094 attack: 125,7095 defense: 90,7096 special_attack: 115,7097 special_defense: 80,7098 speed: 101,7099 },7100 {7101 id: 646,7102 name: 'Kyurem',7103 type: ['Dragon', 'Ice'],7104 hp: 125,7105 attack: 130,7106 defense: 90,7107 special_attack: 130,7108 special_defense: 90,7109 speed: 95,7110 },7111 {7112 id: 647,7113 name: 'Keldeo',7114 type: ['Water', 'Fighting'],7115 hp: 91,7116 attack: 72,7117 defense: 90,7118 special_attack: 129,7119 special_defense: 90,7120 speed: 108,7121 },7122 {7123 id: 648,7124 name: 'Meloetta',7125 type: ['Normal', 'Psychic'],7126 hp: 100,7127 attack: 77,7128 defense: 77,7129 special_attack: 128,7130 special_defense: 128,7131 speed: 90,7132 },7133 {7134 id: 649,7135 name: 'Genesect',7136 type: ['Bug', 'Steel'],7137 hp: 71,7138 attack: 120,7139 defense: 95,7140 special_attack: 120,7141 special_defense: 95,7142 speed: 99,7143 },7144 {7145 id: 650,7146 name: 'Chespin',7147 type: ['Grass'],7148 hp: 56,7149 attack: 61,7150 defense: 65,7151 special_attack: 48,7152 special_defense: 45,7153 speed: 38,7154 },7155 {7156 id: 651,7157 name: 'Quilladin',7158 type: ['Grass'],7159 hp: 61,7160 attack: 78,7161 defense: 95,7162 special_attack: 56,7163 special_defense: 58,7164 speed: 57,7165 },7166 {7167 id: 652,7168 name: 'Chesnaught',7169 type: ['Grass', 'Fighting'],7170 hp: 88,7171 attack: 107,7172 defense: 122,7173 special_attack: 74,7174 special_defense: 75,7175 speed: 64,7176 },7177 {7178 id: 653,7179 name: 'Fennekin',7180 type: ['Fire'],7181 hp: 40,7182 attack: 45,7183 defense: 40,7184 special_attack: 62,7185 special_defense: 60,7186 speed: 60,7187 },7188 {7189 id: 654,7190 name: 'Braixen',7191 type: ['Fire'],7192 hp: 59,7193 attack: 59,7194 defense: 58,7195 special_attack: 90,7196 special_defense: 70,7197 speed: 73,7198 },7199 {7200 id: 655,7201 name: 'Delphox',7202 type: ['Fire', 'Psychic'],7203 hp: 75,7204 attack: 69,7205 defense: 72,7206 special_attack: 114,7207 special_defense: 100,7208 speed: 104,7209 },7210 {7211 id: 656,7212 name: 'Froakie',7213 type: ['Water'],7214 hp: 41,7215 attack: 56,7216 defense: 40,7217 special_attack: 62,7218 special_defense: 44,7219 speed: 71,7220 },7221 {7222 id: 657,7223 name: 'Frogadier',7224 type: ['Water'],7225 hp: 54,7226 attack: 63,7227 defense: 52,7228 special_attack: 83,7229 special_defense: 56,7230 speed: 97,7231 },7232 {7233 id: 658,7234 name: 'Greninja',7235 type: ['Water', 'Dark'],7236 hp: 72,7237 attack: 95,7238 defense: 67,7239 special_attack: 103,7240 special_defense: 71,7241 speed: 122,7242 },7243 {7244 id: 659,7245 name: 'Bunnelby',7246 type: ['Normal'],7247 hp: 38,7248 attack: 36,7249 defense: 38,7250 special_attack: 32,7251 special_defense: 36,7252 speed: 57,7253 },7254 {7255 id: 660,7256 name: 'Diggersby',7257 type: ['Normal', 'Ground'],7258 hp: 85,7259 attack: 56,7260 defense: 77,7261 special_attack: 50,7262 special_defense: 77,7263 speed: 78,7264 },7265 {7266 id: 661,7267 name: 'Fletchling',7268 type: ['Normal', 'Flying'],7269 hp: 45,7270 attack: 50,7271 defense: 43,7272 special_attack: 40,7273 special_defense: 38,7274 speed: 62,7275 },7276 {7277 id: 662,7278 name: 'Fletchinder',7279 type: ['Fire', 'Flying'],7280 hp: 62,7281 attack: 73,7282 defense: 55,7283 special_attack: 56,7284 special_defense: 52,7285 speed: 84,7286 },7287 {7288 id: 663,7289 name: 'Talonflame',7290 type: ['Fire', 'Flying'],7291 hp: 78,7292 attack: 81,7293 defense: 71,7294 special_attack: 74,7295 special_defense: 69,7296 speed: 126,7297 },7298 {7299 id: 664,7300 name: 'Scatterbug',7301 type: ['Bug'],7302 hp: 38,7303 attack: 35,7304 defense: 40,7305 special_attack: 27,7306 special_defense: 25,7307 speed: 35,7308 },7309 {7310 id: 665,7311 name: 'Spewpa',7312 type: ['Bug'],7313 hp: 45,7314 attack: 22,7315 defense: 60,7316 special_attack: 27,7317 special_defense: 30,7318 speed: 29,7319 },7320 {7321 id: 666,7322 name: 'Vivillon',7323 type: ['Bug', 'Flying'],7324 hp: 80,7325 attack: 52,7326 defense: 50,7327 special_attack: 90,7328 special_defense: 50,7329 speed: 89,7330 },7331 {7332 id: 667,7333 name: 'Litleo',7334 type: ['Fire', 'Normal'],7335 hp: 62,7336 attack: 50,7337 defense: 58,7338 special_attack: 73,7339 special_defense: 54,7340 speed: 72,7341 },7342 {7343 id: 668,7344 name: 'Pyroar',7345 type: ['Fire', 'Normal'],7346 hp: 86,7347 attack: 68,7348 defense: 72,7349 special_attack: 109,7350 special_defense: 66,7351 speed: 106,7352 },7353 {7354 id: 669,7355 name: 'Flabébé',7356 type: ['Fairy'],7357 hp: 44,7358 attack: 38,7359 defense: 39,7360 special_attack: 61,7361 special_defense: 79,7362 speed: 42,7363 },7364 {7365 id: 670,7366 name: 'Floette',7367 type: ['Fairy'],7368 hp: 54,7369 attack: 45,7370 defense: 47,7371 special_attack: 75,7372 special_defense: 98,7373 speed: 52,7374 },7375 {7376 id: 671,7377 name: 'Florges',7378 type: ['Fairy'],7379 hp: 78,7380 attack: 65,7381 defense: 68,7382 special_attack: 112,7383 special_defense: 154,7384 speed: 75,7385 },7386 {7387 id: 672,7388 name: 'Skiddo',7389 type: ['Grass'],7390 hp: 66,7391 attack: 65,7392 defense: 48,7393 special_attack: 62,7394 special_defense: 57,7395 speed: 52,7396 },7397 {7398 id: 673,7399 name: 'Gogoat',7400 type: ['Grass'],7401 hp: 123,7402 attack: 100,7403 defense: 62,7404 special_attack: 97,7405 special_defense: 81,7406 speed: 68,7407 },7408 {7409 id: 674,7410 name: 'Pancham',7411 type: ['Fighting'],7412 hp: 67,7413 attack: 82,7414 defense: 62,7415 special_attack: 46,7416 special_defense: 48,7417 speed: 43,7418 },7419 {7420 id: 675,7421 name: 'Pangoro',7422 type: ['Fighting', 'Dark'],7423 hp: 95,7424 attack: 124,7425 defense: 78,7426 special_attack: 69,7427 special_defense: 71,7428 speed: 58,7429 },7430 {7431 id: 676,7432 name: 'Furfrou',7433 type: ['Normal'],7434 hp: 75,7435 attack: 80,7436 defense: 60,7437 special_attack: 65,7438 special_defense: 90,7439 speed: 102,7440 },7441 {7442 id: 677,7443 name: 'Espurr',7444 type: ['Psychic'],7445 hp: 62,7446 attack: 48,7447 defense: 54,7448 special_attack: 63,7449 special_defense: 60,7450 speed: 68,7451 },7452 {7453 id: 678,7454 name: 'Meowstic',7455 type: ['Psychic'],7456 hp: 74,7457 attack: 48,7458 defense: 76,7459 special_attack: 83,7460 special_defense: 81,7461 speed: 104,7462 },7463 {7464 id: 679,7465 name: 'Honedge',7466 type: ['Steel', 'Ghost'],7467 hp: 45,7468 attack: 80,7469 defense: 100,7470 special_attack: 35,7471 special_defense: 37,7472 speed: 28,7473 },7474 {7475 id: 680,7476 name: 'Doublade',7477 type: ['Steel', 'Ghost'],7478 hp: 59,7479 attack: 110,7480 defense: 150,7481 special_attack: 45,7482 special_defense: 49,7483 speed: 35,7484 },7485 {7486 id: 681,7487 name: 'Aegislash',7488 type: ['Steel', 'Ghost'],7489 hp: 60,7490 attack: 50,7491 defense: 150,7492 special_attack: 50,7493 special_defense: 150,7494 speed: 60,7495 },7496 {7497 id: 682,7498 name: 'Spritzee',7499 type: ['Fairy'],7500 hp: 78,7501 attack: 52,7502 defense: 60,7503 special_attack: 63,7504 special_defense: 65,7505 speed: 23,7506 },7507 {7508 id: 683,7509 name: 'Aromatisse',7510 type: ['Fairy'],7511 hp: 101,7512 attack: 72,7513 defense: 72,7514 special_attack: 99,7515 special_defense: 89,7516 speed: 29,7517 },7518 {7519 id: 684,7520 name: 'Swirlix',7521 type: ['Fairy'],7522 hp: 62,7523 attack: 48,7524 defense: 66,7525 special_attack: 59,7526 special_defense: 57,7527 speed: 49,7528 },7529 {7530 id: 685,7531 name: 'Slurpuff',7532 type: ['Fairy'],7533 hp: 82,7534 attack: 80,7535 defense: 86,7536 special_attack: 85,7537 special_defense: 75,7538 speed: 72,7539 },7540 {7541 id: 686,7542 name: 'Inkay',7543 type: ['Dark', 'Psychic'],7544 hp: 53,7545 attack: 54,7546 defense: 53,7547 special_attack: 37,7548 special_defense: 46,7549 speed: 45,7550 },7551 {7552 id: 687,7553 name: 'Malamar',7554 type: ['Dark', 'Psychic'],7555 hp: 86,7556 attack: 92,7557 defense: 88,7558 special_attack: 68,7559 special_defense: 75,7560 speed: 73,7561 },7562 {7563 id: 688,7564 name: 'Binacle',7565 type: ['Rock', 'Water'],7566 hp: 42,7567 attack: 52,7568 defense: 67,7569 special_attack: 39,7570 special_defense: 56,7571 speed: 50,7572 },7573 {7574 id: 689,7575 name: 'Barbaracle',7576 type: ['Rock', 'Water'],7577 hp: 72,7578 attack: 105,7579 defense: 115,7580 special_attack: 54,7581 special_defense: 86,7582 speed: 68,7583 },7584 {7585 id: 690,7586 name: 'Skrelp',7587 type: ['Poison', 'Water'],7588 hp: 50,7589 attack: 60,7590 defense: 60,7591 special_attack: 60,7592 special_defense: 60,7593 speed: 30,7594 },7595 {7596 id: 691,7597 name: 'Dragalge',7598 type: ['Poison', 'Dragon'],7599 hp: 65,7600 attack: 75,7601 defense: 90,7602 special_attack: 97,7603 special_defense: 123,7604 speed: 44,7605 },7606 {7607 id: 692,7608 name: 'Clauncher',7609 type: ['Water'],7610 hp: 50,7611 attack: 53,7612 defense: 62,7613 special_attack: 58,7614 special_defense: 63,7615 speed: 44,7616 },7617 {7618 id: 693,7619 name: 'Clawitzer',7620 type: ['Water'],7621 hp: 71,7622 attack: 73,7623 defense: 88,7624 special_attack: 120,7625 special_defense: 89,7626 speed: 59,7627 },7628 {7629 id: 694,7630 name: 'Helioptile',7631 type: ['Electric', 'Normal'],7632 hp: 44,7633 attack: 38,7634 defense: 33,7635 special_attack: 61,7636 special_defense: 43,7637 speed: 70,7638 },7639 {7640 id: 695,7641 name: 'Heliolisk',7642 type: ['Electric', 'Normal'],7643 hp: 62,7644 attack: 55,7645 defense: 52,7646 special_attack: 109,7647 special_defense: 94,7648 speed: 109,7649 },7650 {7651 id: 696,7652 name: 'Tyrunt',7653 type: ['Rock', 'Dragon'],7654 hp: 58,7655 attack: 89,7656 defense: 77,7657 special_attack: 45,7658 special_defense: 45,7659 speed: 48,7660 },7661 {7662 id: 697,7663 name: 'Tyrantrum',7664 type: ['Rock', 'Dragon'],7665 hp: 82,7666 attack: 121,7667 defense: 119,7668 special_attack: 69,7669 special_defense: 59,7670 speed: 71,7671 },7672 {7673 id: 698,7674 name: 'Amaura',7675 type: ['Rock', 'Ice'],7676 hp: 77,7677 attack: 59,7678 defense: 50,7679 special_attack: 67,7680 special_defense: 63,7681 speed: 46,7682 },7683 {7684 id: 699,7685 name: 'Aurorus',7686 type: ['Rock', 'Ice'],7687 hp: 123,7688 attack: 77,7689 defense: 72,7690 special_attack: 99,7691 special_defense: 92,7692 speed: 58,7693 },7694 {7695 id: 700,7696 name: 'Sylveon',7697 type: ['Fairy'],7698 hp: 95,7699 attack: 65,7700 defense: 65,7701 special_attack: 110,7702 special_defense: 130,7703 speed: 60,7704 },7705 {7706 id: 701,7707 name: 'Hawlucha',7708 type: ['Fighting', 'Flying'],7709 hp: 78,7710 attack: 92,7711 defense: 75,7712 special_attack: 74,7713 special_defense: 63,7714 speed: 118,7715 },7716 {7717 id: 702,7718 name: 'Dedenne',7719 type: ['Electric', 'Fairy'],7720 hp: 67,7721 attack: 58,7722 defense: 57,7723 special_attack: 81,7724 special_defense: 67,7725 speed: 101,7726 },7727 {7728 id: 703,7729 name: 'Carbink',7730 type: ['Rock', 'Fairy'],7731 hp: 50,7732 attack: 50,7733 defense: 150,7734 special_attack: 50,7735 special_defense: 150,7736 speed: 50,7737 },7738 {7739 id: 704,7740 name: 'Goomy',7741 type: ['Dragon'],7742 hp: 45,7743 attack: 50,7744 defense: 35,7745 special_attack: 55,7746 special_defense: 75,7747 speed: 40,7748 },7749 {7750 id: 705,7751 name: 'Sliggoo',7752 type: ['Dragon'],7753 hp: 68,7754 attack: 75,7755 defense: 53,7756 special_attack: 83,7757 special_defense: 113,7758 speed: 60,7759 },7760 {7761 id: 706,7762 name: 'Goodra',7763 type: ['Dragon'],7764 hp: 90,7765 attack: 100,7766 defense: 70,7767 special_attack: 110,7768 special_defense: 150,7769 speed: 80,7770 },7771 {7772 id: 707,7773 name: 'Klefki',7774 type: ['Steel', 'Fairy'],7775 hp: 57,7776 attack: 80,7777 defense: 91,7778 special_attack: 80,7779 special_defense: 87,7780 speed: 75,7781 },7782 {7783 id: 708,7784 name: 'Phantump',7785 type: ['Ghost', 'Grass'],7786 hp: 43,7787 attack: 70,7788 defense: 48,7789 special_attack: 50,7790 special_defense: 60,7791 speed: 38,7792 },7793 {7794 id: 709,7795 name: 'Trevenant',7796 type: ['Ghost', 'Grass'],7797 hp: 85,7798 attack: 110,7799 defense: 76,7800 special_attack: 65,7801 special_defense: 82,7802 speed: 56,7803 },7804 {7805 id: 710,7806 name: 'Pumpkaboo',7807 type: ['Ghost', 'Grass'],7808 hp: 59,7809 attack: 66,7810 defense: 70,7811 special_attack: 44,7812 special_defense: 55,7813 speed: 41,7814 },7815 {7816 id: 711,7817 name: 'Gourgeist',7818 type: ['Ghost', 'Grass'],7819 hp: 85,7820 attack: 100,7821 defense: 122,7822 special_attack: 58,7823 special_defense: 75,7824 speed: 54,7825 },7826 {7827 id: 712,7828 name: 'Bergmite',7829 type: ['Ice'],7830 hp: 55,7831 attack: 69,7832 defense: 85,7833 special_attack: 32,7834 special_defense: 35,7835 speed: 28,7836 },7837 {7838 id: 713,7839 name: 'Avalugg',7840 type: ['Ice'],7841 hp: 95,7842 attack: 117,7843 defense: 184,7844 special_attack: 44,7845 special_defense: 46,7846 speed: 28,7847 },7848 {7849 id: 714,7850 name: 'Noibat',7851 type: ['Flying', 'Dragon'],7852 hp: 40,7853 attack: 30,7854 defense: 35,7855 special_attack: 45,7856 special_defense: 40,7857 speed: 55,7858 },7859 {7860 id: 715,7861 name: 'Noivern',7862 type: ['Flying', 'Dragon'],7863 hp: 85,7864 attack: 70,7865 defense: 80,7866 special_attack: 97,7867 special_defense: 80,7868 speed: 123,7869 },7870 {7871 id: 716,7872 name: 'Xerneas',7873 type: ['Fairy'],7874 hp: 126,7875 attack: 131,7876 defense: 95,7877 special_attack: 131,7878 special_defense: 98,7879 speed: 99,7880 },7881 {7882 id: 717,7883 name: 'Yveltal',7884 type: ['Dark', 'Flying'],7885 hp: 126,7886 attack: 131,7887 defense: 95,7888 special_attack: 131,7889 special_defense: 98,7890 speed: 99,7891 },7892 {7893 id: 718,7894 name: 'Zygarde',7895 type: ['Dragon', 'Ground'],7896 hp: 108,7897 attack: 100,7898 defense: 121,7899 special_attack: 81,7900 special_defense: 95,7901 speed: 95,7902 },7903 {7904 id: 719,7905 name: 'Diancie',7906 type: ['Rock', 'Fairy'],7907 hp: 50,7908 attack: 100,7909 defense: 150,7910 special_attack: 100,7911 special_defense: 150,7912 speed: 50,7913 },7914 {7915 id: 720,7916 name: 'Hoopa',7917 type: ['Psychic', 'Ghost'],7918 hp: 80,7919 attack: 110,7920 defense: 60,7921 special_attack: 150,7922 special_defense: 130,7923 speed: 70,7924 },7925 {7926 id: 721,7927 name: 'Volcanion',7928 type: ['Fire', 'Water'],7929 hp: 80,7930 attack: 110,7931 defense: 120,7932 special_attack: 130,7933 special_defense: 90,7934 speed: 70,7935 },7936 {7937 id: 722,7938 name: 'Rowlet',7939 type: ['Grass', 'Flying'],7940 hp: 68,7941 attack: 55,7942 defense: 55,7943 special_attack: 50,7944 special_defense: 50,7945 speed: 42,7946 },7947 {7948 id: 723,7949 name: 'Dartrix',7950 type: ['Grass', 'Flying'],7951 hp: 78,7952 attack: 75,7953 defense: 75,7954 special_attack: 70,7955 special_defense: 70,7956 speed: 52,7957 },7958 {7959 id: 724,7960 name: 'Decidueye',7961 type: ['Grass', 'Ghost'],7962 hp: 78,7963 attack: 107,7964 defense: 75,7965 special_attack: 100,7966 special_defense: 100,7967 speed: 70,7968 },7969 {7970 id: 725,7971 name: 'Litten',7972 type: ['Fire'],7973 hp: 45,7974 attack: 65,7975 defense: 40,7976 special_attack: 60,7977 special_defense: 40,7978 speed: 70,7979 },7980 {7981 id: 726,7982 name: 'Torracat',7983 type: ['Fire'],7984 hp: 65,7985 attack: 85,7986 defense: 50,7987 special_attack: 80,7988 special_defense: 50,7989 speed: 90,7990 },7991 {7992 id: 727,7993 name: 'Incineroar',7994 type: ['Fire', 'Dark'],7995 hp: 95,7996 attack: 115,7997 defense: 90,7998 special_attack: 80,7999 special_defense: 90,8000 speed: 60,8001 },8002 {8003 id: 728,8004 name: 'Popplio',8005 type: ['Water'],8006 hp: 50,8007 attack: 54,8008 defense: 54,8009 special_attack: 66,8010 special_defense: 56,8011 speed: 40,8012 },8013 {8014 id: 729,8015 name: 'Brionne',8016 type: ['Water'],8017 hp: 60,8018 attack: 69,8019 defense: 69,8020 special_attack: 91,8021 special_defense: 81,8022 speed: 50,8023 },8024 {8025 id: 730,8026 name: 'Primarina',8027 type: ['Water', 'Fairy'],8028 hp: 80,8029 attack: 74,8030 defense: 74,8031 special_attack: 126,8032 special_defense: 116,8033 speed: 60,8034 },8035 {8036 id: 731,8037 name: 'Pikipek',8038 type: ['Normal', 'Flying'],8039 hp: 35,8040 attack: 75,8041 defense: 30,8042 special_attack: 30,8043 special_defense: 30,8044 speed: 65,8045 },8046 {8047 id: 732,8048 name: 'Trumbeak',8049 type: ['Normal', 'Flying'],8050 hp: 55,8051 attack: 85,8052 defense: 50,8053 special_attack: 40,8054 special_defense: 50,8055 speed: 75,8056 },8057 {8058 id: 733,8059 name: 'Toucannon',8060 type: ['Normal', 'Flying'],8061 hp: 80,8062 attack: 120,8063 defense: 75,8064 special_attack: 75,8065 special_defense: 75,8066 speed: 60,8067 },8068 {8069 id: 734,8070 name: 'Yungoos',8071 type: ['Normal'],8072 hp: 48,8073 attack: 70,8074 defense: 30,8075 special_attack: 30,8076 special_defense: 30,8077 speed: 45,8078 },8079 {8080 id: 735,8081 name: 'Gumshoos',8082 type: ['Normal'],8083 hp: 88,8084 attack: 110,8085 defense: 60,8086 special_attack: 55,8087 special_defense: 60,8088 speed: 45,8089 },8090 {8091 id: 736,8092 name: 'Grubbin',8093 type: ['Bug'],8094 hp: 47,8095 attack: 62,8096 defense: 45,8097 special_attack: 55,8098 special_defense: 45,8099 speed: 46,8100 },8101 {8102 id: 737,8103 name: 'Charjabug',8104 type: ['Bug', 'Electric'],8105 hp: 57,8106 attack: 82,8107 defense: 95,8108 special_attack: 55,8109 special_defense: 75,8110 speed: 36,8111 },8112 {8113 id: 738,8114 name: 'Vikavolt',8115 type: ['Bug', 'Electric'],8116 hp: 77,8117 attack: 70,8118 defense: 90,8119 special_attack: 145,8120 special_defense: 75,8121 speed: 43,8122 },8123 {8124 id: 739,8125 name: 'Crabrawler',8126 type: ['Fighting'],8127 hp: 47,8128 attack: 82,8129 defense: 57,8130 special_attack: 42,8131 special_defense: 47,8132 speed: 63,8133 },8134 {8135 id: 740,8136 name: 'Crabominable',8137 type: ['Fighting', 'Ice'],8138 hp: 97,8139 attack: 132,8140 defense: 77,8141 special_attack: 62,8142 special_defense: 67,8143 speed: 43,8144 },8145 {8146 id: 741,8147 name: 'Oricorio',8148 type: ['Fire', 'Flying'],8149 hp: 75,8150 attack: 70,8151 defense: 70,8152 special_attack: 98,8153 special_defense: 70,8154 speed: 93,8155 },8156 {8157 id: 742,8158 name: 'Cutiefly',8159 type: ['Bug', 'Fairy'],8160 hp: 40,8161 attack: 45,8162 defense: 40,8163 special_attack: 55,8164 special_defense: 40,8165 speed: 84,8166 },8167 {8168 id: 743,8169 name: 'Ribombee',8170 type: ['Bug', 'Fairy'],8171 hp: 60,8172 attack: 55,8173 defense: 60,8174 special_attack: 95,8175 special_defense: 70,8176 speed: 124,8177 },8178 {8179 id: 744,8180 name: 'Rockruff',8181 type: ['Rock'],8182 hp: 45,8183 attack: 65,8184 defense: 40,8185 special_attack: 30,8186 special_defense: 40,8187 speed: 60,8188 },8189 {8190 id: 745,8191 name: 'Lycanroc',8192 type: ['Rock'],8193 hp: 75,8194 attack: 115,8195 defense: 65,8196 special_attack: 55,8197 special_defense: 65,8198 speed: 112,8199 },8200 {8201 id: 746,8202 name: 'Wishiwashi',8203 type: ['Water'],8204 hp: 45,8205 attack: 20,8206 defense: 20,8207 special_attack: 25,8208 special_defense: 25,8209 speed: 40,8210 },8211 {8212 id: 747,8213 name: 'Mareanie',8214 type: ['Poison', 'Water'],8215 hp: 50,8216 attack: 53,8217 defense: 62,8218 special_attack: 43,8219 special_defense: 52,8220 speed: 45,8221 },8222 {8223 id: 748,8224 name: 'Toxapex',8225 type: ['Poison', 'Water'],8226 hp: 50,8227 attack: 63,8228 defense: 152,8229 special_attack: 53,8230 special_defense: 142,8231 speed: 35,8232 },8233 {8234 id: 749,8235 name: 'Mudbray',8236 type: ['Ground'],8237 hp: 70,8238 attack: 100,8239 defense: 70,8240 special_attack: 45,8241 special_defense: 55,8242 speed: 45,8243 },8244 {8245 id: 750,8246 name: 'Mudsdale',8247 type: ['Ground'],8248 hp: 100,8249 attack: 125,8250 defense: 100,8251 special_attack: 55,8252 special_defense: 85,8253 speed: 35,8254 },8255 {8256 id: 751,8257 name: 'Dewpider',8258 type: ['Water', 'Bug'],8259 hp: 38,8260 attack: 40,8261 defense: 52,8262 special_attack: 40,8263 special_defense: 72,8264 speed: 27,8265 },8266 {8267 id: 752,8268 name: 'Araquanid',8269 type: ['Water', 'Bug'],8270 hp: 68,8271 attack: 70,8272 defense: 92,8273 special_attack: 50,8274 special_defense: 132,8275 speed: 42,8276 },8277 {8278 id: 753,8279 name: 'Fomantis',8280 type: ['Grass'],8281 hp: 40,8282 attack: 55,8283 defense: 35,8284 special_attack: 50,8285 special_defense: 35,8286 speed: 35,8287 },8288 {8289 id: 754,8290 name: 'Lurantis',8291 type: ['Grass'],8292 hp: 70,8293 attack: 105,8294 defense: 90,8295 special_attack: 80,8296 special_defense: 90,8297 speed: 45,8298 },8299 {8300 id: 755,8301 name: 'Morelull',8302 type: ['Grass', 'Fairy'],8303 hp: 40,8304 attack: 35,8305 defense: 55,8306 special_attack: 65,8307 special_defense: 75,8308 speed: 15,8309 },8310 {8311 id: 756,8312 name: 'Shiinotic',8313 type: ['Grass', 'Fairy'],8314 hp: 60,8315 attack: 45,8316 defense: 80,8317 special_attack: 90,8318 special_defense: 100,8319 speed: 30,8320 },8321 {8322 id: 757,8323 name: 'Salandit',8324 type: ['Poison', 'Fire'],8325 hp: 48,8326 attack: 44,8327 defense: 40,8328 special_attack: 71,8329 special_defense: 40,8330 speed: 77,8331 },8332 {8333 id: 758,8334 name: 'Salazzle',8335 type: ['Poison', 'Fire'],8336 hp: 68,8337 attack: 64,8338 defense: 60,8339 special_attack: 111,8340 special_defense: 60,8341 speed: 117,8342 },8343 {8344 id: 759,8345 name: 'Stufful',8346 type: ['Normal', 'Fighting'],8347 hp: 70,8348 attack: 75,8349 defense: 50,8350 special_attack: 45,8351 special_defense: 50,8352 speed: 50,8353 },8354 {8355 id: 760,8356 name: 'Bewear',8357 type: ['Normal', 'Fighting'],8358 hp: 120,8359 attack: 125,8360 defense: 80,8361 special_attack: 55,8362 special_defense: 60,8363 speed: 60,8364 },8365 {8366 id: 761,8367 name: 'Bounsweet',8368 type: ['Grass'],8369 hp: 42,8370 attack: 30,8371 defense: 38,8372 special_attack: 30,8373 special_defense: 38,8374 speed: 32,8375 },8376 {8377 id: 762,8378 name: 'Steenee',8379 type: ['Grass'],8380 hp: 52,8381 attack: 40,8382 defense: 48,8383 special_attack: 40,8384 special_defense: 48,8385 speed: 62,8386 },8387 {8388 id: 763,8389 name: 'Tsareena',8390 type: ['Grass'],8391 hp: 72,8392 attack: 120,8393 defense: 98,8394 special_attack: 50,8395 special_defense: 98,8396 speed: 72,8397 },8398 {8399 id: 764,8400 name: 'Comfey',8401 type: ['Fairy'],8402 hp: 51,8403 attack: 52,8404 defense: 90,8405 special_attack: 82,8406 special_defense: 110,8407 speed: 100,8408 },8409 {8410 id: 765,8411 name: 'Oranguru',8412 type: ['Normal', 'Psychic'],8413 hp: 90,8414 attack: 60,8415 defense: 80,8416 special_attack: 90,8417 special_defense: 110,8418 speed: 60,8419 },8420 {8421 id: 766,8422 name: 'Passimian',8423 type: ['Fighting'],8424 hp: 100,8425 attack: 120,8426 defense: 90,8427 special_attack: 40,8428 special_defense: 60,8429 speed: 80,8430 },8431 {8432 id: 767,8433 name: 'Wimpod',8434 type: ['Bug', 'Water'],8435 hp: 25,8436 attack: 35,8437 defense: 40,8438 special_attack: 20,8439 special_defense: 30,8440 speed: 80,8441 },8442 {8443 id: 768,8444 name: 'Golisopod',8445 type: ['Bug', 'Water'],8446 hp: 75,8447 attack: 125,8448 defense: 140,8449 special_attack: 60,8450 special_defense: 90,8451 speed: 40,8452 },8453 {8454 id: 769,8455 name: 'Sandygast',8456 type: ['Ghost', 'Ground'],8457 hp: 55,8458 attack: 55,8459 defense: 80,8460 special_attack: 70,8461 special_defense: 45,8462 speed: 15,8463 },8464 {8465 id: 770,8466 name: 'Palossand',8467 type: ['Ghost', 'Ground'],8468 hp: 85,8469 attack: 75,8470 defense: 110,8471 special_attack: 100,8472 special_defense: 75,8473 speed: 35,8474 },8475 {8476 id: 771,8477 name: 'Pyukumuku',8478 type: ['Water'],8479 hp: 55,8480 attack: 60,8481 defense: 130,8482 special_attack: 30,8483 special_defense: 130,8484 speed: 5,8485 },8486 {8487 id: 772,8488 name: 'Type: Null',8489 type: ['Normal'],8490 hp: 95,8491 attack: 95,8492 defense: 95,8493 special_attack: 95,8494 special_defense: 95,8495 speed: 59,8496 },8497 {8498 id: 773,8499 name: 'Silvally',8500 type: ['Normal'],8501 hp: 95,8502 attack: 95,8503 defense: 95,8504 special_attack: 95,8505 special_defense: 95,8506 speed: 95,8507 },8508 {8509 id: 774,8510 name: 'Minior',8511 type: ['Rock', 'Flying'],8512 hp: 60,8513 attack: 60,8514 defense: 100,8515 special_attack: 60,8516 special_defense: 100,8517 speed: 60,8518 },8519 {8520 id: 775,8521 name: 'Komala',8522 type: ['Normal'],8523 hp: 65,8524 attack: 115,8525 defense: 65,8526 special_attack: 75,8527 special_defense: 95,8528 speed: 65,8529 },8530 {8531 id: 776,8532 name: 'Turtonator',8533 type: ['Fire', 'Dragon'],8534 hp: 60,8535 attack: 78,8536 defense: 135,8537 special_attack: 91,8538 special_defense: 85,8539 speed: 36,8540 },8541 {8542 id: 777,8543 name: 'Togedemaru',8544 type: ['Electric', 'Steel'],8545 hp: 65,8546 attack: 98,8547 defense: 63,8548 special_attack: 40,8549 special_defense: 73,8550 speed: 96,8551 },8552 {8553 id: 778,8554 name: 'Mimikyu',8555 type: ['Ghost', 'Fairy'],8556 hp: 55,8557 attack: 90,8558 defense: 80,8559 special_attack: 50,8560 special_defense: 105,8561 speed: 96,8562 },8563 {8564 id: 779,8565 name: 'Bruxish',8566 type: ['Water', 'Psychic'],8567 hp: 68,8568 attack: 105,8569 defense: 70,8570 special_attack: 70,8571 special_defense: 70,8572 speed: 92,8573 },8574 {8575 id: 780,8576 name: 'Drampa',8577 type: ['Normal', 'Dragon'],8578 hp: 78,8579 attack: 60,8580 defense: 85,8581 special_attack: 135,8582 special_defense: 91,8583 speed: 36,8584 },8585 {8586 id: 781,8587 name: 'Dhelmise',8588 type: ['Ghost', 'Grass'],8589 hp: 70,8590 attack: 131,8591 defense: 100,8592 special_attack: 86,8593 special_defense: 90,8594 speed: 40,8595 },8596 {8597 id: 782,8598 name: 'Jangmo-o',8599 type: ['Dragon'],8600 hp: 45,8601 attack: 55,8602 defense: 65,8603 special_attack: 45,8604 special_defense: 45,8605 speed: 45,8606 },8607 {8608 id: 783,8609 name: 'Hakamo-o',8610 type: ['Dragon', 'Fighting'],8611 hp: 55,8612 attack: 75,8613 defense: 90,8614 special_attack: 65,8615 special_defense: 70,8616 speed: 65,8617 },8618 {8619 id: 784,8620 name: 'Kommo-o',8621 type: ['Dragon', 'Fighting'],8622 hp: 75,8623 attack: 110,8624 defense: 125,8625 special_attack: 100,8626 special_defense: 105,8627 speed: 85,8628 },8629 {8630 id: 785,8631 name: 'Tapu Koko',8632 type: ['Electric', 'Fairy'],8633 hp: 70,8634 attack: 115,8635 defense: 85,8636 special_attack: 95,8637 special_defense: 75,8638 speed: 130,8639 },8640 {8641 id: 786,8642 name: 'Tapu Lele',8643 type: ['Psychic', 'Fairy'],8644 hp: 70,8645 attack: 85,8646 defense: 75,8647 special_attack: 130,8648 special_defense: 115,8649 speed: 95,8650 },8651 {8652 id: 787,8653 name: 'Tapu Bulu',8654 type: ['Grass', 'Fairy'],8655 hp: 70,8656 attack: 130,8657 defense: 115,8658 special_attack: 85,8659 special_defense: 95,8660 speed: 75,8661 },8662 {8663 id: 788,8664 name: 'Tapu Fini',8665 type: ['Water', 'Fairy'],8666 hp: 70,8667 attack: 75,8668 defense: 115,8669 special_attack: 95,8670 special_defense: 130,8671 speed: 85,8672 },8673 {8674 id: 789,8675 name: 'Cosmog',8676 type: ['Psychic'],8677 hp: 43,8678 attack: 29,8679 defense: 31,8680 special_attack: 29,8681 special_defense: 31,8682 speed: 37,8683 },8684 {8685 id: 790,8686 name: 'Cosmoem',8687 type: ['Psychic'],8688 hp: 43,8689 attack: 29,8690 defense: 131,8691 special_attack: 29,8692 special_defense: 131,8693 speed: 37,8694 },8695 {8696 id: 791,8697 name: 'Solgaleo',8698 type: ['Psychic', 'Steel'],8699 hp: 137,8700 attack: 137,8701 defense: 107,8702 special_attack: 113,8703 special_defense: 89,8704 speed: 97,8705 },8706 {8707 id: 792,8708 name: 'Lunala',8709 type: ['Psychic', 'Ghost'],8710 hp: 137,8711 attack: 113,8712 defense: 89,8713 special_attack: 137,8714 special_defense: 107,8715 speed: 97,8716 },8717 {8718 id: 793,8719 name: 'Nihilego',8720 type: ['Rock', 'Poison'],8721 hp: 109,8722 attack: 53,8723 defense: 47,8724 special_attack: 127,8725 special_defense: 131,8726 speed: 103,8727 },8728 {8729 id: 794,8730 name: 'Buzzwole',8731 type: ['Bug', 'Fighting'],8732 hp: 107,8733 attack: 139,8734 defense: 139,8735 special_attack: 53,8736 special_defense: 53,8737 speed: 79,8738 },8739 {8740 id: 795,8741 name: 'Pheromosa',8742 type: ['Bug', 'Fighting'],8743 hp: 71,8744 attack: 137,8745 defense: 37,8746 special_attack: 137,8747 special_defense: 37,8748 speed: 151,8749 },8750 {8751 id: 796,8752 name: 'Xurkitree',8753 type: ['Electric'],8754 hp: 83,8755 attack: 89,8756 defense: 71,8757 special_attack: 173,8758 special_defense: 71,8759 speed: 83,8760 },8761 {8762 id: 797,8763 name: 'Celesteela',8764 type: ['Steel', 'Flying'],8765 hp: 97,8766 attack: 101,8767 defense: 103,8768 special_attack: 107,8769 special_defense: 101,8770 speed: 61,8771 },8772 {8773 id: 798,8774 name: 'Kartana',8775 type: ['Grass', 'Steel'],8776 hp: 59,8777 attack: 181,8778 defense: 131,8779 special_attack: 59,8780 special_defense: 31,8781 speed: 109,8782 },8783 {8784 id: 799,8785 name: 'Guzzlord',8786 type: ['Dark', 'Dragon'],8787 hp: 223,8788 attack: 101,8789 defense: 53,8790 special_attack: 97,8791 special_defense: 53,8792 speed: 43,8793 },8794 {8795 id: 800,8796 name: 'Necrozma',8797 type: ['Psychic'],8798 hp: 97,8799 attack: 107,8800 defense: 101,8801 special_attack: 127,8802 special_defense: 89,8803 speed: 79,8804 },8805 {8806 id: 801,8807 name: 'Magearna',8808 type: ['Steel', 'Fairy'],8809 hp: 80,8810 attack: 95,8811 defense: 115,8812 special_attack: 130,8813 special_defense: 115,8814 speed: 65,8815 },8816 {8817 id: 802,8818 name: 'Marshadow',8819 type: ['Fighting', 'Ghost'],8820 hp: 90,8821 attack: 125,8822 defense: 80,8823 special_attack: 90,8824 special_defense: 90,8825 speed: 125,8826 },8827 {8828 id: 803,8829 name: 'Poipole',8830 type: ['Poison'],8831 hp: 67,8832 attack: 73,8833 defense: 67,8834 special_attack: 73,8835 special_defense: 67,8836 speed: 73,8837 },8838 {8839 id: 804,8840 name: 'Naganadel',8841 type: ['Poison', 'Dragon'],8842 hp: 73,8843 attack: 73,8844 defense: 73,8845 special_attack: 127,8846 special_defense: 73,8847 speed: 121,8848 },8849 {8850 id: 805,8851 name: 'Stakataka',8852 type: ['Rock', 'Steel'],8853 hp: 61,8854 attack: 131,8855 defense: 211,8856 special_attack: 53,8857 special_defense: 101,8858 speed: 13,8859 },8860 {8861 id: 806,8862 name: 'Blacephalon',8863 type: ['Fire', 'Ghost'],8864 hp: 53,8865 attack: 127,8866 defense: 53,8867 special_attack: 151,8868 special_defense: 79,8869 speed: 107,8870 },8871 {8872 id: 807,8873 name: 'Zeraora',8874 type: ['Electric'],8875 hp: 88,8876 attack: 112,8877 defense: 75,8878 special_attack: 102,8879 special_defense: 80,8880 speed: 143,8881 },8882 {8883 id: 808,8884 name: 'Meltan',8885 type: ['Steel'],8886 hp: 46,8887 attack: 65,8888 defense: 65,8889 special_attack: 55,8890 special_defense: 35,8891 speed: 34,8892 },8893 {8894 id: 809,8895 name: 'Melmetal',8896 type: ['Steel'],8897 hp: 135,8898 attack: 143,8899 defense: 143,8900 special_attack: 80,8901 special_defense: 65,8902 speed: 34,8903 },8904 ])...

test_basic.py

Source:test_basic.py

1# this program corresponds to special.py2### Means test is not done yet3# E Means test is giving error (E)4# F Means test is failing (F)5# EF Means test is giving error and Failing6#! Means test is segfaulting7# 8 Means test runs forever8### test_besselpoly9### test_mathieu_a10### test_mathieu_even_coef11### test_mathieu_odd_coef12### test_modfresnelp13### test_modfresnelm14# test_pbdv_seq15### test_pbvv_seq16### test_sph_harm17from __future__ import division, print_function, absolute_import18import itertools19import numpy as np20from numpy import (array, isnan, r_, arange, finfo, pi, sin, cos, tan, exp,21 log, zeros, sqrt, asarray, inf, nan_to_num, real, arctan, float_)22import pytest23from pytest import raises as assert_raises24from numpy.testing import (assert_equal, assert_almost_equal,25 assert_array_equal, assert_array_almost_equal, assert_approx_equal,26 assert_, assert_allclose,27 assert_array_almost_equal_nulp)28from scipy import special29import scipy.special._ufuncs as cephes30from scipy.special import ellipk, zeta31from scipy.special._testutils import with_special_errors, \32 assert_func_equal, FuncData33from scipy._lib._numpy_compat import suppress_warnings34from scipy._lib._version import NumpyVersion35import math36class TestCephes(object):37 def test_airy(self):38 cephes.airy(0)39 def test_airye(self):40 cephes.airye(0)41 def test_binom(self):42 n = np.array([0.264, 4, 5.2, 17])43 k = np.array([2, 0.4, 7, 3.3])44 nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])45 ).reshape(2, -1).T46 rknown = np.array([[-0.097152, 0.9263051596159367, 0.01858423645695389,47 -0.007581020651518199],[6, 2.0214389119675666, 0, 2.9827344527963846],48 [10.92, 2.22993515861399, -0.00585728, 10.468891352063146],49 [136, 3.5252179590758828, 19448, 1024.5526916174495]])50 assert_func_equal(cephes.binom, rknown.ravel(), nk, rtol=1e-13)51 # Test branches in implementation52 np.random.seed(1234)53 n = np.r_[np.arange(-7, 30), 1000*np.random.rand(30) - 500]54 k = np.arange(0, 102)55 nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])56 ).reshape(2, -1).T57 assert_func_equal(cephes.binom,58 cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),59 nk,60 atol=1e-10, rtol=1e-10)61 def test_binom_2(self):62 # Test branches in implementation63 np.random.seed(1234)64 n = np.r_[np.logspace(1, 300, 20)]65 k = np.arange(0, 102)66 nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])67 ).reshape(2, -1).T68 assert_func_equal(cephes.binom,69 cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),70 nk,71 atol=1e-10, rtol=1e-10)72 def test_binom_exact(self):73 @np.vectorize74 def binom_int(n, k):75 n = int(n)76 k = int(k)77 num = int(1)78 den = int(1)79 for i in range(1, k+1):80 num *= i + n - k81 den *= i82 return float(num/​den)83 np.random.seed(1234)84 n = np.arange(1, 15)85 k = np.arange(0, 15)86 nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])87 ).reshape(2, -1).T88 nk = nk[nk[:,0] >= nk[:,1]]89 assert_func_equal(cephes.binom,90 binom_int(nk[:,0], nk[:,1]),91 nk,92 atol=0, rtol=0)93 def test_binom_nooverflow_8346(self):94 # Test (binom(n, k) doesn't overflow prematurely */​95 dataset = [96 (1000, 500, 2.70288240945436551e+299),97 (1002, 501, 1.08007396880791225e+300),98 (1004, 502, 4.31599279169058121e+300),99 (1006, 503, 1.72468101616263781e+301),100 (1008, 504, 6.89188009236419153e+301),101 (1010, 505, 2.75402257948335448e+302),102 (1012, 506, 1.10052048531923757e+303),103 (1014, 507, 4.39774063758732849e+303),104 (1016, 508, 1.75736486108312519e+304),105 (1018, 509, 7.02255427788423734e+304),106 (1020, 510, 2.80626776829962255e+305),107 (1022, 511, 1.12140876377061240e+306),108 (1024, 512, 4.48125455209897109e+306),109 (1026, 513, 1.79075474304149900e+307),110 (1028, 514, 7.15605105487789676e+307)111 ]112 dataset = np.asarray(dataset)113 FuncData(cephes.binom, dataset, (0, 1), 2, rtol=1e-12).check()114 def test_bdtr(self):115 assert_equal(cephes.bdtr(1,1,0.5),1.0)116 def test_bdtri(self):117 assert_equal(cephes.bdtri(1,3,0.5),0.5)118 def test_bdtrc(self):119 assert_equal(cephes.bdtrc(1,3,0.5),0.5)120 def test_bdtrin(self):121 assert_equal(cephes.bdtrin(1,0,1),5.0)122 def test_bdtrik(self):123 cephes.bdtrik(1,3,0.5)124 def test_bei(self):125 assert_equal(cephes.bei(0),0.0)126 def test_beip(self):127 assert_equal(cephes.beip(0),0.0)128 def test_ber(self):129 assert_equal(cephes.ber(0),1.0)130 def test_berp(self):131 assert_equal(cephes.berp(0),0.0)132 def test_besselpoly(self):133 assert_equal(cephes.besselpoly(0,0,0),1.0)134 def test_beta(self):135 assert_equal(cephes.beta(1,1),1.0)136 assert_allclose(cephes.beta(-100.3, 1e-200), cephes.gamma(1e-200))137 assert_allclose(cephes.beta(0.0342, 171), 24.070498359873497,138 rtol=1e-13, atol=0)139 def test_betainc(self):140 assert_equal(cephes.betainc(1,1,1),1.0)141 assert_allclose(cephes.betainc(0.0342, 171, 1e-10), 0.55269916901806648)142 def test_betaln(self):143 assert_equal(cephes.betaln(1,1),0.0)144 assert_allclose(cephes.betaln(-100.3, 1e-200), cephes.gammaln(1e-200))145 assert_allclose(cephes.betaln(0.0342, 170), 3.1811881124242447,146 rtol=1e-14, atol=0)147 def test_betaincinv(self):148 assert_equal(cephes.betaincinv(1,1,1),1.0)149 assert_allclose(cephes.betaincinv(0.0342, 171, 0.25),150 8.4231316935498957e-21, rtol=3e-12, atol=0)151 def test_beta_inf(self):152 assert_(np.isinf(special.beta(-1, 2)))153 def test_btdtr(self):154 assert_equal(cephes.btdtr(1,1,1),1.0)155 def test_btdtri(self):156 assert_equal(cephes.btdtri(1,1,1),1.0)157 def test_btdtria(self):158 assert_equal(cephes.btdtria(1,1,1),5.0)159 def test_btdtrib(self):160 assert_equal(cephes.btdtrib(1,1,1),5.0)161 def test_cbrt(self):162 assert_approx_equal(cephes.cbrt(1),1.0)163 def test_chdtr(self):164 assert_equal(cephes.chdtr(1,0),0.0)165 def test_chdtrc(self):166 assert_equal(cephes.chdtrc(1,0),1.0)167 def test_chdtri(self):168 assert_equal(cephes.chdtri(1,1),0.0)169 def test_chdtriv(self):170 assert_equal(cephes.chdtriv(0,0),5.0)171 def test_chndtr(self):172 assert_equal(cephes.chndtr(0,1,0),0.0)173 # Each row holds (x, nu, lam, expected_value)174 # These values were computed using Wolfram Alpha with175 # CDF[NoncentralChiSquareDistribution[nu, lam], x]176 values = np.array([177 [25.00, 20.0, 400, 4.1210655112396197139e-57],178 [25.00, 8.00, 250, 2.3988026526832425878e-29],179 [0.001, 8.00, 40., 5.3761806201366039084e-24],180 [0.010, 8.00, 40., 5.45396231055999457039e-20],181 [20.00, 2.00, 107, 1.39390743555819597802e-9],182 [22.50, 2.00, 107, 7.11803307138105870671e-9],183 [25.00, 2.00, 107, 3.11041244829864897313e-8],184 [3.000, 2.00, 1.0, 0.62064365321954362734],185 [350.0, 300., 10., 0.93880128006276407710],186 [100.0, 13.5, 10., 0.99999999650104210949],187 [700.0, 20.0, 400, 0.99999999925680650105],188 [150.0, 13.5, 10., 0.99999999999999983046],189 [160.0, 13.5, 10., 0.99999999999999999518], # 1.0190 ])191 cdf = cephes.chndtr(values[:, 0], values[:, 1], values[:, 2])192 assert_allclose(cdf, values[:, 3], rtol=1e-12)193 assert_almost_equal(cephes.chndtr(np.inf, np.inf, 0), 2.0)194 assert_almost_equal(cephes.chndtr(2, 1, np.inf), 0.0)195 assert_(np.isnan(cephes.chndtr(np.nan, 1, 2)))196 assert_(np.isnan(cephes.chndtr(5, np.nan, 2)))197 assert_(np.isnan(cephes.chndtr(5, 1, np.nan)))198 def test_chndtridf(self):199 assert_equal(cephes.chndtridf(0,0,1),5.0)200 def test_chndtrinc(self):201 assert_equal(cephes.chndtrinc(0,1,0),5.0)202 def test_chndtrix(self):203 assert_equal(cephes.chndtrix(0,1,0),0.0)204 def test_cosdg(self):205 assert_equal(cephes.cosdg(0),1.0)206 def test_cosm1(self):207 assert_equal(cephes.cosm1(0),0.0)208 def test_cotdg(self):209 assert_almost_equal(cephes.cotdg(45),1.0)210 def test_dawsn(self):211 assert_equal(cephes.dawsn(0),0.0)212 assert_allclose(cephes.dawsn(1.23), 0.50053727749081767)213 def test_diric(self):214 # Test behavior near multiples of 2pi. Regression test for issue215 # described in gh-4001.216 n_odd = [1, 5, 25]217 x = np.array(2*np.pi + 5e-5).astype(np.float32)218 assert_almost_equal(special.diric(x, n_odd), 1.0, decimal=7)219 x = np.array(2*np.pi + 1e-9).astype(np.float64)220 assert_almost_equal(special.diric(x, n_odd), 1.0, decimal=15)221 x = np.array(2*np.pi + 1e-15).astype(np.float64)222 assert_almost_equal(special.diric(x, n_odd), 1.0, decimal=15)223 if hasattr(np, 'float128'):224 # No float128 available in 32-bit numpy225 x = np.array(2*np.pi + 1e-12).astype(np.float128)226 assert_almost_equal(special.diric(x, n_odd), 1.0, decimal=19)227 n_even = [2, 4, 24]228 x = np.array(2*np.pi + 1e-9).astype(np.float64)229 assert_almost_equal(special.diric(x, n_even), -1.0, decimal=15)230 # Test at some values not near a multiple of pi231 x = np.arange(0.2*np.pi, 1.0*np.pi, 0.2*np.pi)232 octave_result = [0.872677996249965, 0.539344662916632,233 0.127322003750035, -0.206011329583298]234 assert_almost_equal(special.diric(x, 3), octave_result, decimal=15)235 def test_diric_broadcasting(self):236 x = np.arange(5)237 n = np.array([1, 3, 7])238 assert_(special.diric(x[:, np.newaxis], n).shape == (x.size, n.size))239 def test_ellipe(self):240 assert_equal(cephes.ellipe(1),1.0)241 def test_ellipeinc(self):242 assert_equal(cephes.ellipeinc(0,1),0.0)243 def test_ellipj(self):244 cephes.ellipj(0,1)245 def test_ellipk(self):246 assert_allclose(ellipk(0), pi/​2)247 def test_ellipkinc(self):248 assert_equal(cephes.ellipkinc(0,0),0.0)249 def test_erf(self):250 assert_equal(cephes.erf(0), 0.0)251 def test_erf_symmetry(self):252 x = 5.905732037710919253 assert_equal(cephes.erf(x) + cephes.erf(-x), 0.0)254 def test_erfc(self):255 assert_equal(cephes.erfc(0), 1.0)256 def test_exp1(self):257 cephes.exp1(1)258 def test_expi(self):259 cephes.expi(1)260 def test_expn(self):261 cephes.expn(1,1)262 def test_exp1_reg(self):263 # Regression for #834264 a = cephes.exp1(-complex(19.9999990))265 b = cephes.exp1(-complex(19.9999991))266 assert_array_almost_equal(a.imag, b.imag)267 def test_exp10(self):268 assert_approx_equal(cephes.exp10(2),100.0)269 def test_exp2(self):270 assert_equal(cephes.exp2(2),4.0)271 def test_expm1(self):272 assert_equal(cephes.expm1(0),0.0)273 assert_equal(cephes.expm1(np.inf), np.inf)274 assert_equal(cephes.expm1(-np.inf), -1)275 assert_equal(cephes.expm1(np.nan), np.nan)276 # Earlier numpy version don't guarantee that npy_cexp conforms to C99.277 @pytest.mark.skipif(NumpyVersion(np.__version__) < '1.9.0', reason='')278 def test_expm1_complex(self):279 expm1 = cephes.expm1280 assert_equal(expm1(0 + 0j), 0 + 0j)281 assert_equal(expm1(complex(np.inf, 0)), complex(np.inf, 0))282 assert_equal(expm1(complex(np.inf, 1)), complex(np.inf, np.inf))283 assert_equal(expm1(complex(np.inf, 2)), complex(-np.inf, np.inf))284 assert_equal(expm1(complex(np.inf, 4)), complex(-np.inf, -np.inf))285 assert_equal(expm1(complex(np.inf, 5)), complex(np.inf, -np.inf))286 assert_equal(expm1(complex(1, np.inf)), complex(np.nan, np.nan))287 assert_equal(expm1(complex(0, np.inf)), complex(np.nan, np.nan))288 assert_equal(expm1(complex(np.inf, np.inf)), complex(np.inf, np.nan))289 assert_equal(expm1(complex(-np.inf, np.inf)), complex(-1, 0))290 assert_equal(expm1(complex(-np.inf, np.nan)), complex(-1, 0))291 assert_equal(expm1(complex(np.inf, np.nan)), complex(np.inf, np.nan))292 assert_equal(expm1(complex(0, np.nan)), complex(np.nan, np.nan))293 assert_equal(expm1(complex(1, np.nan)), complex(np.nan, np.nan))294 assert_equal(expm1(complex(np.nan, 1)), complex(np.nan, np.nan))295 assert_equal(expm1(complex(np.nan, np.nan)), complex(np.nan, np.nan))296 @pytest.mark.xfail(reason='The real part of expm1(z) bad at these points')297 def test_expm1_complex_hard(self):298 # The real part of this function is difficult to evaluate when299 # z.real = -log(cos(z.imag)).300 y = np.array([0.1, 0.2, 0.3, 5, 11, 20])301 x = -np.log(np.cos(y))302 z = x + 1j*y303 # evaluate using mpmath.expm1 with dps=1000304 expected = np.array([-5.5507901846769623e-17+0.10033467208545054j,305 2.4289354732893695e-18+0.20271003550867248j,306 4.5235500262585768e-17+0.30933624960962319j,307 7.8234305217489006e-17-3.3805150062465863j,308 -1.3685191953697676e-16-225.95084645419513j,309 8.7175620481291045e-17+2.2371609442247422j])310 found = cephes.expm1(z)311 # this passes.312 assert_array_almost_equal_nulp(found.imag, expected.imag, 3)313 # this fails.314 assert_array_almost_equal_nulp(found.real, expected.real, 20)315 def test_fdtr(self):316 assert_equal(cephes.fdtr(1, 1, 0), 0.0)317 # Computed using Wolfram Alpha: CDF[FRatioDistribution[1e-6, 5], 10]318 assert_allclose(cephes.fdtr(1e-6, 5, 10), 0.9999940790193488,319 rtol=1e-12)320 def test_fdtrc(self):321 assert_equal(cephes.fdtrc(1, 1, 0), 1.0)322 # Computed using Wolfram Alpha:323 # 1 - CDF[FRatioDistribution[2, 1/​10], 1e10]324 assert_allclose(cephes.fdtrc(2, 0.1, 1e10), 0.27223784621293512,325 rtol=1e-12)326 def test_fdtri(self):327 assert_allclose(cephes.fdtri(1, 1, [0.499, 0.501]),328 array([0.9937365, 1.00630298]), rtol=1e-6)329 # From Wolfram Alpha:330 # CDF[FRatioDistribution[1/​10, 1], 3] = 0.8756751669632105666874...331 p = 0.8756751669632105666874332 assert_allclose(cephes.fdtri(0.1, 1, p), 3, rtol=1e-12)333 @pytest.mark.xfail(reason='Returns nan on i686.')334 def test_fdtri_mysterious_failure(self):335 assert_allclose(cephes.fdtri(1, 1, 0.5), 1)336 def test_fdtridfd(self):337 assert_equal(cephes.fdtridfd(1,0,0),5.0)338 def test_fresnel(self):339 assert_equal(cephes.fresnel(0),(0.0,0.0))340 def test_gamma(self):341 assert_equal(cephes.gamma(5),24.0)342 def test_gammainc(self):343 assert_equal(cephes.gammainc(5,0),0.0)344 def test_gammaincc(self):345 assert_equal(cephes.gammaincc(5,0),1.0)346 def test_gammainccinv(self):347 assert_equal(cephes.gammainccinv(5,1),0.0)348 def test_gammaln(self):349 cephes.gammaln(10)350 def test_gammasgn(self):351 vals = np.array([-4, -3.5, -2.3, 1, 4.2], np.float64)352 assert_array_equal(cephes.gammasgn(vals), np.sign(cephes.rgamma(vals)))353 def test_gdtr(self):354 assert_equal(cephes.gdtr(1,1,0),0.0)355 def test_gdtr_inf(self):356 assert_equal(cephes.gdtr(1,1,np.inf),1.0)357 def test_gdtrc(self):358 assert_equal(cephes.gdtrc(1,1,0),1.0)359 def test_gdtria(self):360 assert_equal(cephes.gdtria(0,1,1),0.0)361 def test_gdtrib(self):362 cephes.gdtrib(1,0,1)363 # assert_equal(cephes.gdtrib(1,0,1),5.0)364 def test_gdtrix(self):365 cephes.gdtrix(1,1,.1)366 def test_hankel1(self):367 cephes.hankel1(1,1)368 def test_hankel1e(self):369 cephes.hankel1e(1,1)370 def test_hankel2(self):371 cephes.hankel2(1,1)372 def test_hankel2e(self):373 cephes.hankel2e(1,1)374 def test_hyp1f1(self):375 assert_approx_equal(cephes.hyp1f1(1,1,1), exp(1.0))376 assert_approx_equal(cephes.hyp1f1(3,4,-6), 0.026056422099537251095)377 cephes.hyp1f1(1,1,1)378 def test_hyp2f1(self):379 assert_equal(cephes.hyp2f1(1,1,1,0),1.0)380 def test_hyperu(self):381 assert_equal(cephes.hyperu(0,1,1),1.0)382 def test_i0(self):383 assert_equal(cephes.i0(0),1.0)384 def test_i0e(self):385 assert_equal(cephes.i0e(0),1.0)386 def test_i1(self):387 assert_equal(cephes.i1(0),0.0)388 def test_i1e(self):389 assert_equal(cephes.i1e(0),0.0)390 def test_it2i0k0(self):391 cephes.it2i0k0(1)392 def test_it2j0y0(self):393 cephes.it2j0y0(1)394 def test_it2struve0(self):395 cephes.it2struve0(1)396 def test_itairy(self):397 cephes.itairy(1)398 def test_iti0k0(self):399 assert_equal(cephes.iti0k0(0),(0.0,0.0))400 def test_itj0y0(self):401 assert_equal(cephes.itj0y0(0),(0.0,0.0))402 def test_itmodstruve0(self):403 assert_equal(cephes.itmodstruve0(0),0.0)404 def test_itstruve0(self):405 assert_equal(cephes.itstruve0(0),0.0)406 def test_iv(self):407 assert_equal(cephes.iv(1,0),0.0)408 def _check_ive(self):409 assert_equal(cephes.ive(1,0),0.0)410 def test_j0(self):411 assert_equal(cephes.j0(0),1.0)412 def test_j1(self):413 assert_equal(cephes.j1(0),0.0)414 def test_jn(self):415 assert_equal(cephes.jn(0,0),1.0)416 def test_jv(self):417 assert_equal(cephes.jv(0,0),1.0)418 def _check_jve(self):419 assert_equal(cephes.jve(0,0),1.0)420 def test_k0(self):421 cephes.k0(2)422 def test_k0e(self):423 cephes.k0e(2)424 def test_k1(self):425 cephes.k1(2)426 def test_k1e(self):427 cephes.k1e(2)428 def test_kei(self):429 cephes.kei(2)430 def test_keip(self):431 assert_equal(cephes.keip(0),0.0)432 def test_ker(self):433 cephes.ker(2)434 def test_kerp(self):435 cephes.kerp(2)436 def _check_kelvin(self):437 cephes.kelvin(2)438 def test_kn(self):439 cephes.kn(1,1)440 def test_kolmogi(self):441 assert_equal(cephes.kolmogi(1),0.0)442 assert_(np.isnan(cephes.kolmogi(np.nan)))443 def test_kolmogorov(self):444 assert_equal(cephes.kolmogorov(0), 1.0)445 def test_kolmogp(self):446 assert_equal(cephes._kolmogp(0), -0.0)447 def test_kolmogc(self):448 assert_equal(cephes._kolmogc(0), 0.0)449 def test_kolmogci(self):450 assert_equal(cephes._kolmogci(0), 0.0)451 assert_(np.isnan(cephes._kolmogci(np.nan)))452 def _check_kv(self):453 cephes.kv(1,1)454 def _check_kve(self):455 cephes.kve(1,1)456 def test_log1p(self):457 log1p = cephes.log1p458 assert_equal(log1p(0), 0.0)459 assert_equal(log1p(-1), -np.inf)460 assert_equal(log1p(-2), np.nan)461 assert_equal(log1p(np.inf), np.inf)462 # earlier numpy version don't guarantee that npy_clog conforms to C99463 @pytest.mark.skipif(NumpyVersion(np.__version__) < '1.9.0', reason='')464 def test_log1p_complex(self):465 log1p = cephes.log1p466 c = complex467 assert_equal(log1p(0 + 0j), 0 + 0j)468 assert_equal(log1p(c(-1, 0)), c(-np.inf, 0))469 with suppress_warnings() as sup:470 sup.filter(RuntimeWarning, "invalid value encountered in multiply")471 assert_allclose(log1p(c(1, np.inf)), c(np.inf, np.pi/​2))472 assert_equal(log1p(c(1, np.nan)), c(np.nan, np.nan))473 assert_allclose(log1p(c(-np.inf, 1)), c(np.inf, np.pi))474 assert_equal(log1p(c(np.inf, 1)), c(np.inf, 0))475 assert_allclose(log1p(c(-np.inf, np.inf)), c(np.inf, 3*np.pi/​4))476 assert_allclose(log1p(c(np.inf, np.inf)), c(np.inf, np.pi/​4))477 assert_equal(log1p(c(np.inf, np.nan)), c(np.inf, np.nan))478 assert_equal(log1p(c(-np.inf, np.nan)), c(np.inf, np.nan))479 assert_equal(log1p(c(np.nan, np.inf)), c(np.inf, np.nan))480 assert_equal(log1p(c(np.nan, 1)), c(np.nan, np.nan))481 assert_equal(log1p(c(np.nan, np.nan)), c(np.nan, np.nan))482 def test_lpmv(self):483 assert_equal(cephes.lpmv(0,0,1),1.0)484 def test_mathieu_a(self):485 assert_equal(cephes.mathieu_a(1,0),1.0)486 def test_mathieu_b(self):487 assert_equal(cephes.mathieu_b(1,0),1.0)488 def test_mathieu_cem(self):489 assert_equal(cephes.mathieu_cem(1,0,0),(1.0,0.0))490 # Test AMS 20.2.27491 @np.vectorize492 def ce_smallq(m, q, z):493 z *= np.pi/​180494 if m == 0:495 return 2**(-0.5) * (1 - .5*q*cos(2*z)) # + O(q^2)496 elif m == 1:497 return cos(z) - q/​8 * cos(3*z) # + O(q^2)498 elif m == 2:499 return cos(2*z) - q*(cos(4*z)/​12 - 1/​4) # + O(q^2)500 else:501 return cos(m*z) - q*(cos((m+2)*z)/​(4*(m+1)) - cos((m-2)*z)/​(4*(m-1))) # + O(q^2)502 m = np.arange(0, 100)503 q = np.r_[0, np.logspace(-30, -9, 10)]504 assert_allclose(cephes.mathieu_cem(m[:,None], q[None,:], 0.123)[0],505 ce_smallq(m[:,None], q[None,:], 0.123),506 rtol=1e-14, atol=0)507 def test_mathieu_sem(self):508 assert_equal(cephes.mathieu_sem(1,0,0),(0.0,1.0))509 # Test AMS 20.2.27510 @np.vectorize511 def se_smallq(m, q, z):512 z *= np.pi/​180513 if m == 1:514 return sin(z) - q/​8 * sin(3*z) # + O(q^2)515 elif m == 2:516 return sin(2*z) - q*sin(4*z)/​12 # + O(q^2)517 else:518 return sin(m*z) - q*(sin((m+2)*z)/​(4*(m+1)) - sin((m-2)*z)/​(4*(m-1))) # + O(q^2)519 m = np.arange(1, 100)520 q = np.r_[0, np.logspace(-30, -9, 10)]521 assert_allclose(cephes.mathieu_sem(m[:,None], q[None,:], 0.123)[0],522 se_smallq(m[:,None], q[None,:], 0.123),523 rtol=1e-14, atol=0)524 def test_mathieu_modcem1(self):525 assert_equal(cephes.mathieu_modcem1(1,0,0),(0.0,0.0))526 def test_mathieu_modcem2(self):527 cephes.mathieu_modcem2(1,1,1)528 # Test reflection relation AMS 20.6.19529 m = np.arange(0, 4)[:,None,None]530 q = np.r_[np.logspace(-2, 2, 10)][None,:,None]531 z = np.linspace(0, 1, 7)[None,None,:]532 y1 = cephes.mathieu_modcem2(m, q, -z)[0]533 fr = -cephes.mathieu_modcem2(m, q, 0)[0] /​ cephes.mathieu_modcem1(m, q, 0)[0]534 y2 = -cephes.mathieu_modcem2(m, q, z)[0] - 2*fr*cephes.mathieu_modcem1(m, q, z)[0]535 assert_allclose(y1, y2, rtol=1e-10)536 def test_mathieu_modsem1(self):537 assert_equal(cephes.mathieu_modsem1(1,0,0),(0.0,0.0))538 def test_mathieu_modsem2(self):539 cephes.mathieu_modsem2(1,1,1)540 # Test reflection relation AMS 20.6.20541 m = np.arange(1, 4)[:,None,None]542 q = np.r_[np.logspace(-2, 2, 10)][None,:,None]543 z = np.linspace(0, 1, 7)[None,None,:]544 y1 = cephes.mathieu_modsem2(m, q, -z)[0]545 fr = cephes.mathieu_modsem2(m, q, 0)[1] /​ cephes.mathieu_modsem1(m, q, 0)[1]546 y2 = cephes.mathieu_modsem2(m, q, z)[0] - 2*fr*cephes.mathieu_modsem1(m, q, z)[0]547 assert_allclose(y1, y2, rtol=1e-10)548 def test_mathieu_overflow(self):549 # Check that these return NaNs instead of causing a SEGV550 assert_equal(cephes.mathieu_cem(10000, 0, 1.3), (np.nan, np.nan))551 assert_equal(cephes.mathieu_sem(10000, 0, 1.3), (np.nan, np.nan))552 assert_equal(cephes.mathieu_cem(10000, 1.5, 1.3), (np.nan, np.nan))553 assert_equal(cephes.mathieu_sem(10000, 1.5, 1.3), (np.nan, np.nan))554 assert_equal(cephes.mathieu_modcem1(10000, 1.5, 1.3), (np.nan, np.nan))555 assert_equal(cephes.mathieu_modsem1(10000, 1.5, 1.3), (np.nan, np.nan))556 assert_equal(cephes.mathieu_modcem2(10000, 1.5, 1.3), (np.nan, np.nan))557 assert_equal(cephes.mathieu_modsem2(10000, 1.5, 1.3), (np.nan, np.nan))558 def test_mathieu_ticket_1847(self):559 # Regression test --- this call had some out-of-bounds access560 # and could return nan occasionally561 for k in range(60):562 v = cephes.mathieu_modsem2(2, 100, -1)563 # Values from ACM TOMS 804 (derivate by numerical differentiation)564 assert_allclose(v[0], 0.1431742913063671074347, rtol=1e-10)565 assert_allclose(v[1], 0.9017807375832909144719, rtol=1e-4)566 def test_modfresnelm(self):567 cephes.modfresnelm(0)568 def test_modfresnelp(self):569 cephes.modfresnelp(0)570 def _check_modstruve(self):571 assert_equal(cephes.modstruve(1,0),0.0)572 def test_nbdtr(self):573 assert_equal(cephes.nbdtr(1,1,1),1.0)574 def test_nbdtrc(self):575 assert_equal(cephes.nbdtrc(1,1,1),0.0)576 def test_nbdtri(self):577 assert_equal(cephes.nbdtri(1,1,1),1.0)578 def __check_nbdtrik(self):579 cephes.nbdtrik(1,.4,.5)580 def test_nbdtrin(self):581 assert_equal(cephes.nbdtrin(1,0,0),5.0)582 def test_ncfdtr(self):583 assert_equal(cephes.ncfdtr(1,1,1,0),0.0)584 def test_ncfdtri(self):585 assert_equal(cephes.ncfdtri(1, 1, 1, 0), 0.0)586 f = [0.5, 1, 1.5]587 p = cephes.ncfdtr(2, 3, 1.5, f)588 assert_allclose(cephes.ncfdtri(2, 3, 1.5, p), f)589 def test_ncfdtridfd(self):590 dfd = [1, 2, 3]591 p = cephes.ncfdtr(2, dfd, 0.25, 15)592 assert_allclose(cephes.ncfdtridfd(2, p, 0.25, 15), dfd)593 def test_ncfdtridfn(self):594 dfn = [0.1, 1, 2, 3, 1e4]595 p = cephes.ncfdtr(dfn, 2, 0.25, 15)596 assert_allclose(cephes.ncfdtridfn(p, 2, 0.25, 15), dfn, rtol=1e-5)597 def test_ncfdtrinc(self):598 nc = [0.5, 1.5, 2.0]599 p = cephes.ncfdtr(2, 3, nc, 15)600 assert_allclose(cephes.ncfdtrinc(2, 3, p, 15), nc)601 def test_nctdtr(self):602 assert_equal(cephes.nctdtr(1,0,0),0.5)603 assert_equal(cephes.nctdtr(9, 65536, 45), 0.0)604 assert_approx_equal(cephes.nctdtr(np.inf, 1., 1.), 0.5, 5)605 assert_(np.isnan(cephes.nctdtr(2., np.inf, 10.)))606 assert_approx_equal(cephes.nctdtr(2., 1., np.inf), 1.)607 assert_(np.isnan(cephes.nctdtr(np.nan, 1., 1.)))608 assert_(np.isnan(cephes.nctdtr(2., np.nan, 1.)))609 assert_(np.isnan(cephes.nctdtr(2., 1., np.nan)))610 def __check_nctdtridf(self):611 cephes.nctdtridf(1,0.5,0)612 def test_nctdtrinc(self):613 cephes.nctdtrinc(1,0,0)614 def test_nctdtrit(self):615 cephes.nctdtrit(.1,0.2,.5)616 def test_ndtr(self):617 assert_equal(cephes.ndtr(0), 0.5)618 assert_almost_equal(cephes.ndtr(1), 0.84134474606)619 def test_ndtri(self):620 assert_equal(cephes.ndtri(0.5),0.0)621 def test_nrdtrimn(self):622 assert_approx_equal(cephes.nrdtrimn(0.5,1,1),1.0)623 def test_nrdtrisd(self):624 assert_allclose(cephes.nrdtrisd(0.5,0.5,0.5), 0.0,625 atol=0, rtol=0)626 def test_obl_ang1(self):627 cephes.obl_ang1(1,1,1,0)628 def test_obl_ang1_cv(self):629 result = cephes.obl_ang1_cv(1,1,1,1,0)630 assert_almost_equal(result[0],1.0)631 assert_almost_equal(result[1],0.0)632 def _check_obl_cv(self):633 assert_equal(cephes.obl_cv(1,1,0),2.0)634 def test_obl_rad1(self):635 cephes.obl_rad1(1,1,1,0)636 def test_obl_rad1_cv(self):637 cephes.obl_rad1_cv(1,1,1,1,0)638 def test_obl_rad2(self):639 cephes.obl_rad2(1,1,1,0)640 def test_obl_rad2_cv(self):641 cephes.obl_rad2_cv(1,1,1,1,0)642 def test_pbdv(self):643 assert_equal(cephes.pbdv(1,0),(0.0,1.0))644 def test_pbvv(self):645 cephes.pbvv(1,0)646 def test_pbwa(self):647 cephes.pbwa(1,0)648 def test_pdtr(self):649 val = cephes.pdtr(0, 1)650 assert_almost_equal(val, np.exp(-1))651 # Edge case: m = 0.652 val = cephes.pdtr([0, 1, 2], 0.0)653 assert_array_equal(val, [1, 1, 1])654 def test_pdtrc(self):655 val = cephes.pdtrc(0, 1)656 assert_almost_equal(val, 1 - np.exp(-1))657 # Edge case: m = 0.658 val = cephes.pdtrc([0, 1, 2], 0.0)659 assert_array_equal(val, [0, 0, 0])660 def test_pdtri(self):661 with suppress_warnings() as sup:662 sup.filter(RuntimeWarning, "floating point number truncated to an integer")663 cephes.pdtri(0.5,0.5)664 def test_pdtrik(self):665 k = cephes.pdtrik(0.5, 1)666 assert_almost_equal(cephes.gammaincc(k + 1, 1), 0.5)667 # Edge case: m = 0 or very small.668 k = cephes.pdtrik([[0], [0.25], [0.95]], [0, 1e-20, 1e-6])669 assert_array_equal(k, np.zeros((3, 3)))670 def test_pro_ang1(self):671 cephes.pro_ang1(1,1,1,0)672 def test_pro_ang1_cv(self):673 assert_array_almost_equal(cephes.pro_ang1_cv(1,1,1,1,0),674 array((1.0,0.0)))675 def _check_pro_cv(self):676 assert_equal(cephes.pro_cv(1,1,0),2.0)677 def test_pro_rad1(self):678 cephes.pro_rad1(1,1,1,0.1)679 def test_pro_rad1_cv(self):680 cephes.pro_rad1_cv(1,1,1,1,0)681 def test_pro_rad2(self):682 cephes.pro_rad2(1,1,1,0)683 def test_pro_rad2_cv(self):684 cephes.pro_rad2_cv(1,1,1,1,0)685 def test_psi(self):686 cephes.psi(1)687 def test_radian(self):688 assert_equal(cephes.radian(0,0,0),0)689 def test_rgamma(self):690 assert_equal(cephes.rgamma(1),1.0)691 def test_round(self):692 assert_equal(cephes.round(3.4),3.0)693 assert_equal(cephes.round(-3.4),-3.0)694 assert_equal(cephes.round(3.6),4.0)695 assert_equal(cephes.round(-3.6),-4.0)696 assert_equal(cephes.round(3.5),4.0)697 assert_equal(cephes.round(-3.5),-4.0)698 def test_shichi(self):699 cephes.shichi(1)700 def test_sici(self):701 cephes.sici(1)702 s, c = cephes.sici(np.inf)703 assert_almost_equal(s, np.pi * 0.5)704 assert_almost_equal(c, 0)705 s, c = cephes.sici(-np.inf)706 assert_almost_equal(s, -np.pi * 0.5)707 assert_(np.isnan(c), "cosine integral(-inf) is not nan")708 def test_sindg(self):709 assert_equal(cephes.sindg(90),1.0)710 def test_smirnov(self):711 assert_equal(cephes.smirnov(1,.1),0.9)712 assert_(np.isnan(cephes.smirnov(1,np.nan)))713 def test_smirnovp(self):714 assert_equal(cephes._smirnovp(1, .1), -1)715 assert_equal(cephes._smirnovp(2, 0.75), -2*(0.25)**(2-1))716 assert_equal(cephes._smirnovp(3, 0.75), -3*(0.25)**(3-1))717 assert_(np.isnan(cephes._smirnovp(1, np.nan)))718 def test_smirnovc(self):719 assert_equal(cephes._smirnovc(1,.1),0.1)720 assert_(np.isnan(cephes._smirnovc(1,np.nan)))721 x10 = np.linspace(0, 1, 11, endpoint=True)722 assert_almost_equal(cephes._smirnovc(3, x10), 1-cephes.smirnov(3, x10))723 x4 = np.linspace(0, 1, 5, endpoint=True)724 assert_almost_equal(cephes._smirnovc(4, x4), 1-cephes.smirnov(4, x4))725 def test_smirnovi(self):726 assert_almost_equal(cephes.smirnov(1,cephes.smirnovi(1,0.4)),0.4)727 assert_almost_equal(cephes.smirnov(1,cephes.smirnovi(1,0.6)),0.6)728 assert_(np.isnan(cephes.smirnovi(1,np.nan)))729 def test_smirnovci(self):730 assert_almost_equal(cephes._smirnovc(1,cephes._smirnovci(1,0.4)),0.4)731 assert_almost_equal(cephes._smirnovc(1,cephes._smirnovci(1,0.6)),0.6)732 assert_(np.isnan(cephes._smirnovci(1,np.nan)))733 def test_spence(self):734 assert_equal(cephes.spence(1),0.0)735 def test_stdtr(self):736 assert_equal(cephes.stdtr(1,0),0.5)737 assert_almost_equal(cephes.stdtr(1,1), 0.75)738 assert_almost_equal(cephes.stdtr(1,2), 0.852416382349)739 def test_stdtridf(self):740 cephes.stdtridf(0.7,1)741 def test_stdtrit(self):742 cephes.stdtrit(1,0.7)743 def test_struve(self):744 assert_equal(cephes.struve(0,0),0.0)745 def test_tandg(self):746 assert_equal(cephes.tandg(45),1.0)747 def test_tklmbda(self):748 assert_almost_equal(cephes.tklmbda(1,1),1.0)749 def test_y0(self):750 cephes.y0(1)751 def test_y1(self):752 cephes.y1(1)753 def test_yn(self):754 cephes.yn(1,1)755 def test_yv(self):756 cephes.yv(1,1)757 def _check_yve(self):758 cephes.yve(1,1)759 def test_wofz(self):760 z = [complex(624.2,-0.26123), complex(-0.4,3.), complex(0.6,2.),761 complex(-1.,1.), complex(-1.,-9.), complex(-1.,9.),762 complex(-0.0000000234545,1.1234), complex(-3.,5.1),763 complex(-53,30.1), complex(0.0,0.12345),764 complex(11,1), complex(-22,-2), complex(9,-28),765 complex(21,-33), complex(1e5,1e5), complex(1e14,1e14)766 ]767 w = [768 complex(-3.78270245518980507452677445620103199303131110e-7,769 0.000903861276433172057331093754199933411710053155),770 complex(0.1764906227004816847297495349730234591778719532788,771 -0.02146550539468457616788719893991501311573031095617),772 complex(0.2410250715772692146133539023007113781272362309451,773 0.06087579663428089745895459735240964093522265589350),774 complex(0.30474420525691259245713884106959496013413834051768,775 -0.20821893820283162728743734725471561394145872072738),776 complex(7.317131068972378096865595229600561710140617977e34,777 8.321873499714402777186848353320412813066170427e34),778 complex(0.0615698507236323685519612934241429530190806818395,779 -0.00676005783716575013073036218018565206070072304635),780 complex(0.3960793007699874918961319170187598400134746631,781 -5.593152259116644920546186222529802777409274656e-9),782 complex(0.08217199226739447943295069917990417630675021771804,783 -0.04701291087643609891018366143118110965272615832184),784 complex(0.00457246000350281640952328010227885008541748668738,785 -0.00804900791411691821818731763401840373998654987934),786 complex(0.8746342859608052666092782112565360755791467973338452,787 0.),788 complex(0.00468190164965444174367477874864366058339647648741,789 0.0510735563901306197993676329845149741675029197050),790 complex(-0.0023193175200187620902125853834909543869428763219,791 -0.025460054739731556004902057663500272721780776336),792 complex(9.11463368405637174660562096516414499772662584e304,793 3.97101807145263333769664875189354358563218932e305),794 complex(-4.4927207857715598976165541011143706155432296e281,795 -2.8019591213423077494444700357168707775769028e281),796 complex(2.820947917809305132678577516325951485807107151e-6,797 2.820947917668257736791638444590253942253354058e-6),798 complex(2.82094791773878143474039725787438662716372268e-15,799 2.82094791773878143474039725773333923127678361e-15)800 ]801 assert_func_equal(cephes.wofz, w, z, rtol=1e-13)802class TestAiry(object):803 def test_airy(self):804 # This tests the airy function to ensure 8 place accuracy in computation805 x = special.airy(.99)806 assert_array_almost_equal(x,array([0.13689066,-0.16050153,1.19815925,0.92046818]),8)807 x = special.airy(.41)808 assert_array_almost_equal(x,array([0.25238916,-.23480512,0.80686202,0.51053919]),8)809 x = special.airy(-.36)810 assert_array_almost_equal(x,array([0.44508477,-0.23186773,0.44939534,0.48105354]),8)811 def test_airye(self):812 a = special.airye(0.01)813 b = special.airy(0.01)814 b1 = [None]*4815 for n in range(2):816 b1[n] = b[n]*exp(2.0/​3.0*0.01*sqrt(0.01))817 for n in range(2,4):818 b1[n] = b[n]*exp(-abs(real(2.0/​3.0*0.01*sqrt(0.01))))819 assert_array_almost_equal(a,b1,6)820 def test_bi_zeros(self):821 bi = special.bi_zeros(2)822 bia = (array([-1.17371322, -3.2710930]),823 array([-2.29443968, -4.07315509]),824 array([-0.45494438, 0.39652284]),825 array([0.60195789, -0.76031014]))826 assert_array_almost_equal(bi,bia,4)827 bi = special.bi_zeros(5)828 assert_array_almost_equal(bi[0],array([-1.173713222709127,829 -3.271093302836352,830 -4.830737841662016,831 -6.169852128310251,832 -7.376762079367764]),11)833 assert_array_almost_equal(bi[1],array([-2.294439682614122,834 -4.073155089071828,835 -5.512395729663599,836 -6.781294445990305,837 -7.940178689168587]),10)838 assert_array_almost_equal(bi[2],array([-0.454944383639657,839 0.396522836094465,840 -0.367969161486959,841 0.349499116831805,842 -0.336026240133662]),11)843 assert_array_almost_equal(bi[3],array([0.601957887976239,844 -0.760310141492801,845 0.836991012619261,846 -0.88947990142654,847 0.929983638568022]),10)848 def test_ai_zeros(self):849 ai = special.ai_zeros(1)850 assert_array_almost_equal(ai,(array([-2.33810741]),851 array([-1.01879297]),852 array([0.5357]),853 array([0.7012])),4)854 def test_ai_zeros_big(self):855 z, zp, ai_zpx, aip_zx = special.ai_zeros(50000)856 ai_z, aip_z, _, _ = special.airy(z)857 ai_zp, aip_zp, _, _ = special.airy(zp)858 ai_envelope = 1/​abs(z)**(1./​4)859 aip_envelope = abs(zp)**(1./​4)860 # Check values861 assert_allclose(ai_zpx, ai_zp, rtol=1e-10)862 assert_allclose(aip_zx, aip_z, rtol=1e-10)863 # Check they are zeros864 assert_allclose(ai_z/​ai_envelope, 0, atol=1e-10, rtol=0)865 assert_allclose(aip_zp/​aip_envelope, 0, atol=1e-10, rtol=0)866 # Check first zeros, DLMF 9.9.1867 assert_allclose(z[:6],868 [-2.3381074105, -4.0879494441, -5.5205598281,869 -6.7867080901, -7.9441335871, -9.0226508533], rtol=1e-10)870 assert_allclose(zp[:6],871 [-1.0187929716, -3.2481975822, -4.8200992112,872 -6.1633073556, -7.3721772550, -8.4884867340], rtol=1e-10)873 def test_bi_zeros_big(self):874 z, zp, bi_zpx, bip_zx = special.bi_zeros(50000)875 _, _, bi_z, bip_z = special.airy(z)876 _, _, bi_zp, bip_zp = special.airy(zp)877 bi_envelope = 1/​abs(z)**(1./​4)878 bip_envelope = abs(zp)**(1./​4)879 # Check values880 assert_allclose(bi_zpx, bi_zp, rtol=1e-10)881 assert_allclose(bip_zx, bip_z, rtol=1e-10)882 # Check they are zeros883 assert_allclose(bi_z/​bi_envelope, 0, atol=1e-10, rtol=0)884 assert_allclose(bip_zp/​bip_envelope, 0, atol=1e-10, rtol=0)885 # Check first zeros, DLMF 9.9.2886 assert_allclose(z[:6],887 [-1.1737132227, -3.2710933028, -4.8307378417,888 -6.1698521283, -7.3767620794, -8.4919488465], rtol=1e-10)889 assert_allclose(zp[:6],890 [-2.2944396826, -4.0731550891, -5.5123957297,891 -6.7812944460, -7.9401786892, -9.0195833588], rtol=1e-10)892class TestAssocLaguerre(object):893 def test_assoc_laguerre(self):894 a1 = special.genlaguerre(11,1)895 a2 = special.assoc_laguerre(.2,11,1)896 assert_array_almost_equal(a2,a1(.2),8)897 a2 = special.assoc_laguerre(1,11,1)898 assert_array_almost_equal(a2,a1(1),8)899class TestBesselpoly(object):900 def test_besselpoly(self):901 pass902class TestKelvin(object):903 def test_bei(self):904 mbei = special.bei(2)905 assert_almost_equal(mbei, 0.9722916273066613,5) # this may not be exact906 def test_beip(self):907 mbeip = special.beip(2)908 assert_almost_equal(mbeip,0.91701361338403631,5) # this may not be exact909 def test_ber(self):910 mber = special.ber(2)911 assert_almost_equal(mber,0.75173418271380821,5) # this may not be exact912 def test_berp(self):913 mberp = special.berp(2)914 assert_almost_equal(mberp,-0.49306712470943909,5) # this may not be exact915 def test_bei_zeros(self):916 # Abramowitz & Stegun, Table 9.12917 bi = special.bei_zeros(5)918 assert_array_almost_equal(bi,array([5.02622,919 9.45541,920 13.89349,921 18.33398,922 22.77544]),4)923 def test_beip_zeros(self):924 bip = special.beip_zeros(5)925 assert_array_almost_equal(bip,array([3.772673304934953,926 8.280987849760042,927 12.742147523633703,928 17.193431752512542,929 21.641143941167325]),8)930 def test_ber_zeros(self):931 ber = special.ber_zeros(5)932 assert_array_almost_equal(ber,array([2.84892,933 7.23883,934 11.67396,935 16.11356,936 20.55463]),4)937 def test_berp_zeros(self):938 brp = special.berp_zeros(5)939 assert_array_almost_equal(brp,array([6.03871,940 10.51364,941 14.96844,942 19.41758,943 23.86430]),4)944 def test_kelvin(self):945 mkelv = special.kelvin(2)946 assert_array_almost_equal(mkelv,(special.ber(2) + special.bei(2)*1j,947 special.ker(2) + special.kei(2)*1j,948 special.berp(2) + special.beip(2)*1j,949 special.kerp(2) + special.keip(2)*1j),8)950 def test_kei(self):951 mkei = special.kei(2)952 assert_almost_equal(mkei,-0.20240006776470432,5)953 def test_keip(self):954 mkeip = special.keip(2)955 assert_almost_equal(mkeip,0.21980790991960536,5)956 def test_ker(self):957 mker = special.ker(2)958 assert_almost_equal(mker,-0.041664513991509472,5)959 def test_kerp(self):960 mkerp = special.kerp(2)961 assert_almost_equal(mkerp,-0.10660096588105264,5)962 def test_kei_zeros(self):963 kei = special.kei_zeros(5)964 assert_array_almost_equal(kei,array([3.91467,965 8.34422,966 12.78256,967 17.22314,968 21.66464]),4)969 def test_keip_zeros(self):970 keip = special.keip_zeros(5)971 assert_array_almost_equal(keip,array([4.93181,972 9.40405,973 13.85827,974 18.30717,975 22.75379]),4)976 # numbers come from 9.9 of A&S pg. 381977 def test_kelvin_zeros(self):978 tmp = special.kelvin_zeros(5)979 berz,beiz,kerz,keiz,berpz,beipz,kerpz,keipz = tmp980 assert_array_almost_equal(berz,array([2.84892,981 7.23883,982 11.67396,983 16.11356,984 20.55463]),4)985 assert_array_almost_equal(beiz,array([5.02622,986 9.45541,987 13.89349,988 18.33398,989 22.77544]),4)990 assert_array_almost_equal(kerz,array([1.71854,991 6.12728,992 10.56294,993 15.00269,994 19.44382]),4)995 assert_array_almost_equal(keiz,array([3.91467,996 8.34422,997 12.78256,998 17.22314,999 21.66464]),4)1000 assert_array_almost_equal(berpz,array([6.03871,1001 10.51364,1002 14.96844,1003 19.41758,1004 23.86430]),4)1005 assert_array_almost_equal(beipz,array([3.77267,1006 # table from 1927 had 3.773201007 # but this is more accurate1008 8.28099,1009 12.74215,1010 17.19343,1011 21.64114]),4)1012 assert_array_almost_equal(kerpz,array([2.66584,1013 7.17212,1014 11.63218,1015 16.08312,1016 20.53068]),4)1017 assert_array_almost_equal(keipz,array([4.93181,1018 9.40405,1019 13.85827,1020 18.30717,1021 22.75379]),4)1022 def test_ker_zeros(self):1023 ker = special.ker_zeros(5)1024 assert_array_almost_equal(ker,array([1.71854,1025 6.12728,1026 10.56294,1027 15.00269,1028 19.44381]),4)1029 def test_kerp_zeros(self):1030 kerp = special.kerp_zeros(5)1031 assert_array_almost_equal(kerp,array([2.66584,1032 7.17212,1033 11.63218,1034 16.08312,1035 20.53068]),4)1036class TestBernoulli(object):1037 def test_bernoulli(self):1038 brn = special.bernoulli(5)1039 assert_array_almost_equal(brn,array([1.0000,1040 -0.5000,1041 0.1667,1042 0.0000,1043 -0.0333,1044 0.0000]),4)1045class TestBeta(object):1046 def test_beta(self):1047 bet = special.beta(2,4)1048 betg = (special.gamma(2)*special.gamma(4))/​special.gamma(6)1049 assert_almost_equal(bet,betg,8)1050 def test_betaln(self):1051 betln = special.betaln(2,4)1052 bet = log(abs(special.beta(2,4)))1053 assert_almost_equal(betln,bet,8)1054 def test_betainc(self):1055 btinc = special.betainc(1,1,.2)1056 assert_almost_equal(btinc,0.2,8)1057 def test_betaincinv(self):1058 y = special.betaincinv(2,4,.5)1059 comp = special.betainc(2,4,y)1060 assert_almost_equal(comp,.5,5)1061class TestCombinatorics(object):1062 def test_comb(self):1063 assert_array_almost_equal(special.comb([10, 10], [3, 4]), [120., 210.])1064 assert_almost_equal(special.comb(10, 3), 120.)1065 assert_equal(special.comb(10, 3, exact=True), 120)1066 assert_equal(special.comb(10, 3, exact=True, repetition=True), 220)1067 assert_allclose([special.comb(20, k, exact=True) for k in range(21)],1068 special.comb(20, list(range(21))), atol=1e-15)1069 ii = np.iinfo(int).max + 11070 assert_equal(special.comb(ii, ii-1, exact=True), ii)1071 expected = 1008913445455641933348124972561072 assert_equal(special.comb(100, 50, exact=True), expected)1073 def test_comb_with_np_int64(self):1074 n = 701075 k = 301076 np_n = np.int64(n)1077 np_k = np.int64(k)1078 assert_equal(special.comb(np_n, np_k, exact=True),1079 special.comb(n, k, exact=True))1080 def test_comb_zeros(self):1081 assert_equal(special.comb(2, 3, exact=True), 0)1082 assert_equal(special.comb(-1, 3, exact=True), 0)1083 assert_equal(special.comb(2, -1, exact=True), 0)1084 assert_equal(special.comb(2, -1, exact=False), 0)1085 assert_array_almost_equal(special.comb([2, -1, 2, 10], [3, 3, -1, 3]),1086 [0., 0., 0., 120.])1087 def test_perm(self):1088 assert_array_almost_equal(special.perm([10, 10], [3, 4]), [720., 5040.])1089 assert_almost_equal(special.perm(10, 3), 720.)1090 assert_equal(special.perm(10, 3, exact=True), 720)1091 def test_perm_zeros(self):1092 assert_equal(special.perm(2, 3, exact=True), 0)1093 assert_equal(special.perm(-1, 3, exact=True), 0)1094 assert_equal(special.perm(2, -1, exact=True), 0)1095 assert_equal(special.perm(2, -1, exact=False), 0)1096 assert_array_almost_equal(special.perm([2, -1, 2, 10], [3, 3, -1, 3]),1097 [0., 0., 0., 720.])1098class TestTrigonometric(object):1099 def test_cbrt(self):1100 cb = special.cbrt(27)1101 cbrl = 27**(1.0/​3.0)1102 assert_approx_equal(cb,cbrl)1103 def test_cbrtmore(self):1104 cb1 = special.cbrt(27.9)1105 cbrl1 = 27.9**(1.0/​3.0)1106 assert_almost_equal(cb1,cbrl1,8)1107 def test_cosdg(self):1108 cdg = special.cosdg(90)1109 cdgrl = cos(pi/​2.0)1110 assert_almost_equal(cdg,cdgrl,8)1111 def test_cosdgmore(self):1112 cdgm = special.cosdg(30)1113 cdgmrl = cos(pi/​6.0)1114 assert_almost_equal(cdgm,cdgmrl,8)1115 def test_cosm1(self):1116 cs = (special.cosm1(0),special.cosm1(.3),special.cosm1(pi/​10))1117 csrl = (cos(0)-1,cos(.3)-1,cos(pi/​10)-1)1118 assert_array_almost_equal(cs,csrl,8)1119 def test_cotdg(self):1120 ct = special.cotdg(30)1121 ctrl = tan(pi/​6.0)**(-1)1122 assert_almost_equal(ct,ctrl,8)1123 def test_cotdgmore(self):1124 ct1 = special.cotdg(45)1125 ctrl1 = tan(pi/​4.0)**(-1)1126 assert_almost_equal(ct1,ctrl1,8)1127 def test_specialpoints(self):1128 assert_almost_equal(special.cotdg(45), 1.0, 14)1129 assert_almost_equal(special.cotdg(-45), -1.0, 14)1130 assert_almost_equal(special.cotdg(90), 0.0, 14)1131 assert_almost_equal(special.cotdg(-90), 0.0, 14)1132 assert_almost_equal(special.cotdg(135), -1.0, 14)1133 assert_almost_equal(special.cotdg(-135), 1.0, 14)1134 assert_almost_equal(special.cotdg(225), 1.0, 14)1135 assert_almost_equal(special.cotdg(-225), -1.0, 14)1136 assert_almost_equal(special.cotdg(270), 0.0, 14)1137 assert_almost_equal(special.cotdg(-270), 0.0, 14)1138 assert_almost_equal(special.cotdg(315), -1.0, 14)1139 assert_almost_equal(special.cotdg(-315), 1.0, 14)1140 assert_almost_equal(special.cotdg(765), 1.0, 14)1141 def test_sinc(self):1142 # the sinc implementation and more extensive sinc tests are in numpy1143 assert_array_equal(special.sinc([0]), 1)1144 assert_equal(special.sinc(0.0), 1.0)1145 def test_sindg(self):1146 sn = special.sindg(90)1147 assert_equal(sn,1.0)1148 def test_sindgmore(self):1149 snm = special.sindg(30)1150 snmrl = sin(pi/​6.0)1151 assert_almost_equal(snm,snmrl,8)1152 snm1 = special.sindg(45)1153 snmrl1 = sin(pi/​4.0)1154 assert_almost_equal(snm1,snmrl1,8)1155class TestTandg(object):1156 def test_tandg(self):1157 tn = special.tandg(30)1158 tnrl = tan(pi/​6.0)1159 assert_almost_equal(tn,tnrl,8)1160 def test_tandgmore(self):1161 tnm = special.tandg(45)1162 tnmrl = tan(pi/​4.0)1163 assert_almost_equal(tnm,tnmrl,8)1164 tnm1 = special.tandg(60)1165 tnmrl1 = tan(pi/​3.0)1166 assert_almost_equal(tnm1,tnmrl1,8)1167 def test_specialpoints(self):1168 assert_almost_equal(special.tandg(0), 0.0, 14)1169 assert_almost_equal(special.tandg(45), 1.0, 14)1170 assert_almost_equal(special.tandg(-45), -1.0, 14)1171 assert_almost_equal(special.tandg(135), -1.0, 14)1172 assert_almost_equal(special.tandg(-135), 1.0, 14)1173 assert_almost_equal(special.tandg(180), 0.0, 14)1174 assert_almost_equal(special.tandg(-180), 0.0, 14)1175 assert_almost_equal(special.tandg(225), 1.0, 14)1176 assert_almost_equal(special.tandg(-225), -1.0, 14)1177 assert_almost_equal(special.tandg(315), -1.0, 14)1178 assert_almost_equal(special.tandg(-315), 1.0, 14)1179class TestEllip(object):1180 def test_ellipj_nan(self):1181 """Regression test for #912."""1182 special.ellipj(0.5, np.nan)1183 def test_ellipj(self):1184 el = special.ellipj(0.2,0)1185 rel = [sin(0.2),cos(0.2),1.0,0.20]1186 assert_array_almost_equal(el,rel,13)1187 def test_ellipk(self):1188 elk = special.ellipk(.2)1189 assert_almost_equal(elk,1.659623598610528,11)1190 assert_equal(special.ellipkm1(0.0), np.inf)1191 assert_equal(special.ellipkm1(1.0), pi/​2)1192 assert_equal(special.ellipkm1(np.inf), 0.0)1193 assert_equal(special.ellipkm1(np.nan), np.nan)1194 assert_equal(special.ellipkm1(-1), np.nan)1195 assert_allclose(special.ellipk(-10), 0.7908718902387385)1196 def test_ellipkinc(self):1197 elkinc = special.ellipkinc(pi/​2,.2)1198 elk = special.ellipk(0.2)1199 assert_almost_equal(elkinc,elk,15)1200 alpha = 20*pi/​1801201 phi = 45*pi/​1801202 m = sin(alpha)**21203 elkinc = special.ellipkinc(phi,m)1204 assert_almost_equal(elkinc,0.79398143,8)1205 # From pg. 614 of A & S1206 assert_equal(special.ellipkinc(pi/​2, 0.0), pi/​2)1207 assert_equal(special.ellipkinc(pi/​2, 1.0), np.inf)1208 assert_equal(special.ellipkinc(pi/​2, -np.inf), 0.0)1209 assert_equal(special.ellipkinc(pi/​2, np.nan), np.nan)1210 assert_equal(special.ellipkinc(pi/​2, 2), np.nan)1211 assert_equal(special.ellipkinc(0, 0.5), 0.0)1212 assert_equal(special.ellipkinc(np.inf, 0.5), np.inf)1213 assert_equal(special.ellipkinc(-np.inf, 0.5), -np.inf)1214 assert_equal(special.ellipkinc(np.inf, np.inf), np.nan)1215 assert_equal(special.ellipkinc(np.inf, -np.inf), np.nan)1216 assert_equal(special.ellipkinc(-np.inf, -np.inf), np.nan)1217 assert_equal(special.ellipkinc(-np.inf, np.inf), np.nan)1218 assert_equal(special.ellipkinc(np.nan, 0.5), np.nan)1219 assert_equal(special.ellipkinc(np.nan, np.nan), np.nan)1220 assert_allclose(special.ellipkinc(0.38974112035318718, 1), 0.4, rtol=1e-14)1221 assert_allclose(special.ellipkinc(1.5707, -10), 0.79084284661724946)1222 def test_ellipkinc_2(self):1223 # Regression test for gh-35501224 # ellipkinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value1225 mbad = 0.683593750000000111226 phi = 0.92729521800161231227 m = np.nextafter(mbad, 0)1228 mvals = []1229 for j in range(10):1230 mvals.append(m)1231 m = np.nextafter(m, 1)1232 f = special.ellipkinc(phi, mvals)1233 assert_array_almost_equal_nulp(f, 1.0259330100195334 * np.ones_like(f), 1)1234 # this bug also appears at phi + n * pi for at least small n1235 f1 = special.ellipkinc(phi + pi, mvals)1236 assert_array_almost_equal_nulp(f1, 5.1296650500976675 * np.ones_like(f1), 2)1237 def test_ellipkinc_singular(self):1238 # ellipkinc(phi, 1) has closed form and is finite only for phi in (-pi/​2, pi/​2)1239 xlog = np.logspace(-300, -17, 25)1240 xlin = np.linspace(1e-17, 0.1, 25)1241 xlin2 = np.linspace(0.1, pi/​2, 25, endpoint=False)1242 assert_allclose(special.ellipkinc(xlog, 1), np.arcsinh(np.tan(xlog)), rtol=1e14)1243 assert_allclose(special.ellipkinc(xlin, 1), np.arcsinh(np.tan(xlin)), rtol=1e14)1244 assert_allclose(special.ellipkinc(xlin2, 1), np.arcsinh(np.tan(xlin2)), rtol=1e14)1245 assert_equal(special.ellipkinc(np.pi/​2, 1), np.inf)1246 assert_allclose(special.ellipkinc(-xlog, 1), np.arcsinh(np.tan(-xlog)), rtol=1e14)1247 assert_allclose(special.ellipkinc(-xlin, 1), np.arcsinh(np.tan(-xlin)), rtol=1e14)1248 assert_allclose(special.ellipkinc(-xlin2, 1), np.arcsinh(np.tan(-xlin2)), rtol=1e14)1249 assert_equal(special.ellipkinc(-np.pi/​2, 1), np.inf)1250 def test_ellipe(self):1251 ele = special.ellipe(.2)1252 assert_almost_equal(ele,1.4890350580958529,8)1253 assert_equal(special.ellipe(0.0), pi/​2)1254 assert_equal(special.ellipe(1.0), 1.0)1255 assert_equal(special.ellipe(-np.inf), np.inf)1256 assert_equal(special.ellipe(np.nan), np.nan)1257 assert_equal(special.ellipe(2), np.nan)1258 assert_allclose(special.ellipe(-10), 3.6391380384177689)1259 def test_ellipeinc(self):1260 eleinc = special.ellipeinc(pi/​2,.2)1261 ele = special.ellipe(0.2)1262 assert_almost_equal(eleinc,ele,14)1263 # pg 617 of A & S1264 alpha, phi = 52*pi/​180,35*pi/​1801265 m = sin(alpha)**21266 eleinc = special.ellipeinc(phi,m)1267 assert_almost_equal(eleinc, 0.58823065, 8)1268 assert_equal(special.ellipeinc(pi/​2, 0.0), pi/​2)1269 assert_equal(special.ellipeinc(pi/​2, 1.0), 1.0)1270 assert_equal(special.ellipeinc(pi/​2, -np.inf), np.inf)1271 assert_equal(special.ellipeinc(pi/​2, np.nan), np.nan)1272 assert_equal(special.ellipeinc(pi/​2, 2), np.nan)1273 assert_equal(special.ellipeinc(0, 0.5), 0.0)1274 assert_equal(special.ellipeinc(np.inf, 0.5), np.inf)1275 assert_equal(special.ellipeinc(-np.inf, 0.5), -np.inf)1276 assert_equal(special.ellipeinc(np.inf, -np.inf), np.inf)1277 assert_equal(special.ellipeinc(-np.inf, -np.inf), -np.inf)1278 assert_equal(special.ellipeinc(np.inf, np.inf), np.nan)1279 assert_equal(special.ellipeinc(-np.inf, np.inf), np.nan)1280 assert_equal(special.ellipeinc(np.nan, 0.5), np.nan)1281 assert_equal(special.ellipeinc(np.nan, np.nan), np.nan)1282 assert_allclose(special.ellipeinc(1.5707, -10), 3.6388185585822876)1283 def test_ellipeinc_2(self):1284 # Regression test for gh-35501285 # ellipeinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value1286 mbad = 0.683593750000000111287 phi = 0.92729521800161231288 m = np.nextafter(mbad, 0)1289 mvals = []1290 for j in range(10):1291 mvals.append(m)1292 m = np.nextafter(m, 1)1293 f = special.ellipeinc(phi, mvals)1294 assert_array_almost_equal_nulp(f, 0.84442884574781019 * np.ones_like(f), 2)1295 # this bug also appears at phi + n * pi for at least small n1296 f1 = special.ellipeinc(phi + pi, mvals)1297 assert_array_almost_equal_nulp(f1, 3.3471442287390509 * np.ones_like(f1), 4)1298class TestErf(object):1299 def test_erf(self):1300 er = special.erf(.25)1301 assert_almost_equal(er,0.2763263902,8)1302 def test_erf_zeros(self):1303 erz = special.erf_zeros(5)1304 erzr = array([1.45061616+1.88094300j,1305 2.24465928+2.61657514j,1306 2.83974105+3.17562810j,1307 3.33546074+3.64617438j,1308 3.76900557+4.06069723j])1309 assert_array_almost_equal(erz,erzr,4)1310 def _check_variant_func(self, func, other_func, rtol, atol=0):1311 np.random.seed(1234)1312 n = 100001313 x = np.random.pareto(0.02, n) * (2*np.random.randint(0, 2, n) - 1)1314 y = np.random.pareto(0.02, n) * (2*np.random.randint(0, 2, n) - 1)1315 z = x + 1j*y1316 old_errors = np.seterr(all='ignore')1317 try:1318 w = other_func(z)1319 w_real = other_func(x).real1320 mask = np.isfinite(w)1321 w = w[mask]1322 z = z[mask]1323 mask = np.isfinite(w_real)1324 w_real = w_real[mask]1325 x = x[mask]1326 # test both real and complex variants1327 assert_func_equal(func, w, z, rtol=rtol, atol=atol)1328 assert_func_equal(func, w_real, x, rtol=rtol, atol=atol)1329 finally:1330 np.seterr(**old_errors)1331 def test_erfc_consistent(self):1332 self._check_variant_func(1333 cephes.erfc,1334 lambda z: 1 - cephes.erf(z),1335 rtol=1e-12,1336 atol=1e-14 # <- the test function loses precision1337 )1338 def test_erfcx_consistent(self):1339 self._check_variant_func(1340 cephes.erfcx,1341 lambda z: np.exp(z*z) * cephes.erfc(z),1342 rtol=1e-121343 )1344 def test_erfi_consistent(self):1345 self._check_variant_func(1346 cephes.erfi,1347 lambda z: -1j * cephes.erf(1j*z),1348 rtol=1e-121349 )1350 def test_dawsn_consistent(self):1351 self._check_variant_func(1352 cephes.dawsn,1353 lambda z: sqrt(pi)/​2 * np.exp(-z*z) * cephes.erfi(z),1354 rtol=1e-121355 )1356 def test_erfcinv(self):1357 i = special.erfcinv(1)1358 # Use assert_array_equal instead of assert_equal, so the comparison1359 # of -0.0 and 0.0 doesn't fail.1360 assert_array_equal(i, 0)1361 def test_erfinv(self):1362 i = special.erfinv(0)1363 assert_equal(i,0)1364 def test_erf_nan_inf(self):1365 vals = [np.nan, -np.inf, np.inf]1366 expected = [np.nan, -1, 1]1367 assert_allclose(special.erf(vals), expected, rtol=1e-15)1368 def test_erfc_nan_inf(self):1369 vals = [np.nan, -np.inf, np.inf]1370 expected = [np.nan, 2, 0]1371 assert_allclose(special.erfc(vals), expected, rtol=1e-15)1372 def test_erfcx_nan_inf(self):1373 vals = [np.nan, -np.inf, np.inf]1374 expected = [np.nan, np.inf, 0]1375 assert_allclose(special.erfcx(vals), expected, rtol=1e-15)1376 def test_erfi_nan_inf(self):1377 vals = [np.nan, -np.inf, np.inf]1378 expected = [np.nan, -np.inf, np.inf]1379 assert_allclose(special.erfi(vals), expected, rtol=1e-15)1380 def test_dawsn_nan_inf(self):1381 vals = [np.nan, -np.inf, np.inf]1382 expected = [np.nan, -0.0, 0.0]1383 assert_allclose(special.dawsn(vals), expected, rtol=1e-15)1384 def test_wofz_nan_inf(self):1385 vals = [np.nan, -np.inf, np.inf]1386 expected = [np.nan + np.nan * 1.j, 0.-0.j, 0.+0.j]1387 assert_allclose(special.wofz(vals), expected, rtol=1e-15)1388class TestEuler(object):1389 def test_euler(self):1390 eu0 = special.euler(0)1391 eu1 = special.euler(1)1392 eu2 = special.euler(2) # just checking segfaults1393 assert_allclose(eu0, [1], rtol=1e-15)1394 assert_allclose(eu1, [1, 0], rtol=1e-15)1395 assert_allclose(eu2, [1, 0, -1], rtol=1e-15)1396 eu24 = special.euler(24)1397 mathworld = [1,1,5,61,1385,50521,2702765,199360981,1398 19391512145,2404879675441,1399 370371188237525,69348874393137901,1400 15514534163557086905]1401 correct = zeros((25,),'d')1402 for k in range(0,13):1403 if (k % 2):1404 correct[2*k] = -float(mathworld[k])1405 else:1406 correct[2*k] = float(mathworld[k])1407 olderr = np.seterr(all='ignore')1408 try:1409 err = nan_to_num((eu24-correct)/​correct)1410 errmax = max(err)1411 finally:1412 np.seterr(**olderr)1413 assert_almost_equal(errmax, 0.0, 14)1414class TestExp(object):1415 def test_exp2(self):1416 ex = special.exp2(2)1417 exrl = 2**21418 assert_equal(ex,exrl)1419 def test_exp2more(self):1420 exm = special.exp2(2.5)1421 exmrl = 2**(2.5)1422 assert_almost_equal(exm,exmrl,8)1423 def test_exp10(self):1424 ex = special.exp10(2)1425 exrl = 10**21426 assert_approx_equal(ex,exrl)1427 def test_exp10more(self):1428 exm = special.exp10(2.5)1429 exmrl = 10**(2.5)1430 assert_almost_equal(exm,exmrl,8)1431 def test_expm1(self):1432 ex = (special.expm1(2),special.expm1(3),special.expm1(4))1433 exrl = (exp(2)-1,exp(3)-1,exp(4)-1)1434 assert_array_almost_equal(ex,exrl,8)1435 def test_expm1more(self):1436 ex1 = (special.expm1(2),special.expm1(2.1),special.expm1(2.2))1437 exrl1 = (exp(2)-1,exp(2.1)-1,exp(2.2)-1)1438 assert_array_almost_equal(ex1,exrl1,8)1439class TestFactorialFunctions(object):1440 def test_factorial(self):1441 # Some known values, float math1442 assert_array_almost_equal(special.factorial(0), 1)1443 assert_array_almost_equal(special.factorial(1), 1)1444 assert_array_almost_equal(special.factorial(2), 2)1445 assert_array_almost_equal([6., 24., 120.],1446 special.factorial([3, 4, 5], exact=False))1447 assert_array_almost_equal(special.factorial([[5, 3], [4, 3]]),1448 [[120, 6], [24, 6]])1449 # Some known values, integer math1450 assert_equal(special.factorial(0, exact=True), 1)1451 assert_equal(special.factorial(1, exact=True), 1)1452 assert_equal(special.factorial(2, exact=True), 2)1453 assert_equal(special.factorial(5, exact=True), 120)1454 assert_equal(special.factorial(15, exact=True), 1307674368000)1455 # ndarray shape is maintained1456 assert_equal(special.factorial([7, 4, 15, 10], exact=True),1457 [5040, 24, 1307674368000, 3628800])1458 assert_equal(special.factorial([[5, 3], [4, 3]], True),1459 [[120, 6], [24, 6]])1460 # object arrays1461 assert_equal(special.factorial(np.arange(-3, 22), True),1462 special.factorial(np.arange(-3, 22), False))1463 # int64 array1464 assert_equal(special.factorial(np.arange(-3, 15), True),1465 special.factorial(np.arange(-3, 15), False))1466 # int32 array1467 assert_equal(special.factorial(np.arange(-3, 5), True),1468 special.factorial(np.arange(-3, 5), False))1469 # Consistent output for n < 01470 for exact in (True, False):1471 assert_array_equal(0, special.factorial(-3, exact))1472 assert_array_equal([1, 2, 0, 0],1473 special.factorial([1, 2, -5, -4], exact))1474 for n in range(0, 22):1475 # Compare all with math.factorial1476 correct = math.factorial(n)1477 assert_array_equal(correct, special.factorial(n, True))1478 assert_array_equal(correct, special.factorial([n], True)[0])1479 assert_allclose(float(correct), special.factorial(n, False))1480 assert_allclose(float(correct), special.factorial([n], False)[0])1481 # Compare exact=True vs False, scalar vs array1482 assert_array_equal(special.factorial(n, True),1483 special.factorial(n, False))1484 assert_array_equal(special.factorial([n], True),1485 special.factorial([n], False))1486 def test_factorial2(self):1487 assert_array_almost_equal([105., 384., 945.],1488 special.factorial2([7, 8, 9], exact=False))1489 assert_equal(special.factorial2(7, exact=True), 105)1490 def test_factorialk(self):1491 assert_equal(special.factorialk(5, 1, exact=True), 120)1492 assert_equal(special.factorialk(5, 3, exact=True), 10)1493class TestFresnel(object):1494 def test_fresnel(self):1495 frs = array(special.fresnel(.5))1496 assert_array_almost_equal(frs,array([0.064732432859999287, 0.49234422587144644]),8)1497 def test_fresnel_inf1(self):1498 frs = special.fresnel(np.inf)1499 assert_equal(frs, (0.5, 0.5))1500 def test_fresnel_inf2(self):1501 frs = special.fresnel(-np.inf)1502 assert_equal(frs, (-0.5, -0.5))1503 # values from pg 329 Table 7.11 of A & S1504 # slightly corrected in 4th decimal place1505 def test_fresnel_zeros(self):1506 szo, czo = special.fresnel_zeros(5)1507 assert_array_almost_equal(szo,1508 array([2.0093+0.2885j,1509 2.8335+0.2443j,1510 3.4675+0.2185j,1511 4.0026+0.2009j,1512 4.4742+0.1877j]),3)1513 assert_array_almost_equal(czo,1514 array([1.7437+0.3057j,1515 2.6515+0.2529j,1516 3.3204+0.2240j,1517 3.8757+0.2047j,1518 4.3611+0.1907j]),3)1519 vals1 = special.fresnel(szo)[0]1520 vals2 = special.fresnel(czo)[1]1521 assert_array_almost_equal(vals1,0,14)1522 assert_array_almost_equal(vals2,0,14)1523 def test_fresnelc_zeros(self):1524 szo, czo = special.fresnel_zeros(6)1525 frc = special.fresnelc_zeros(6)1526 assert_array_almost_equal(frc,czo,12)1527 def test_fresnels_zeros(self):1528 szo, czo = special.fresnel_zeros(5)1529 frs = special.fresnels_zeros(5)1530 assert_array_almost_equal(frs,szo,12)1531class TestGamma(object):1532 def test_gamma(self):1533 gam = special.gamma(5)1534 assert_equal(gam,24.0)1535 def test_gammaln(self):1536 gamln = special.gammaln(3)1537 lngam = log(special.gamma(3))1538 assert_almost_equal(gamln,lngam,8)1539 def test_gammainc(self):1540 gama = special.gammainc(.5,.5)1541 assert_almost_equal(gama,.7,1)1542 def test_gammaincnan(self):1543 gama = special.gammainc(-1,1)1544 assert_(isnan(gama))1545 def test_gammainczero(self):1546 # bad arg but zero integration limit1547 gama = special.gammainc(-1,0)1548 assert_equal(gama,0.0)1549 def test_gammaincinf(self):1550 gama = special.gammainc(0.5, np.inf)1551 assert_equal(gama,1.0)1552 def test_gammaincc(self):1553 gicc = special.gammaincc(.5,.5)1554 greal = 1 - special.gammainc(.5,.5)1555 assert_almost_equal(gicc,greal,8)1556 def test_gammainccnan(self):1557 gama = special.gammaincc(-1,1)1558 assert_(isnan(gama))1559 def test_gammainccinf(self):1560 gama = special.gammaincc(0.5,np.inf)1561 assert_equal(gama,0.0)1562 def test_gammainccinv(self):1563 gccinv = special.gammainccinv(.5,.5)1564 gcinv = special.gammaincinv(.5,.5)1565 assert_almost_equal(gccinv,gcinv,8)1566 @with_special_errors1567 def test_gammaincinv(self):1568 y = special.gammaincinv(.4,.4)1569 x = special.gammainc(.4,y)1570 assert_almost_equal(x,0.4,1)1571 y = special.gammainc(10, 0.05)1572 x = special.gammaincinv(10, 2.5715803516000736e-20)1573 assert_almost_equal(0.05, x, decimal=10)1574 assert_almost_equal(y, 2.5715803516000736e-20, decimal=10)1575 x = special.gammaincinv(50, 8.20754777388471303050299243573393e-18)1576 assert_almost_equal(11.0, x, decimal=10)1577 @with_special_errors1578 def test_975(self):1579 # Regression test for ticket #975 -- switch point in algorithm1580 # check that things work OK at the point, immediately next floats1581 # around it, and a bit further away1582 pts = [0.25,1583 np.nextafter(0.25, 0), 0.25 - 1e-12,1584 np.nextafter(0.25, 1), 0.25 + 1e-12]1585 for xp in pts:1586 y = special.gammaincinv(.4, xp)1587 x = special.gammainc(0.4, y)1588 assert_allclose(x, xp, rtol=1e-12)1589 def test_rgamma(self):1590 rgam = special.rgamma(8)1591 rlgam = 1/​special.gamma(8)1592 assert_almost_equal(rgam,rlgam,8)1593 def test_infinity(self):1594 assert_(np.isinf(special.gamma(-1)))1595 assert_equal(special.rgamma(-1), 0)1596class TestHankel(object):1597 def test_negv1(self):1598 assert_almost_equal(special.hankel1(-3,2), -special.hankel1(3,2), 14)1599 def test_hankel1(self):1600 hank1 = special.hankel1(1,.1)1601 hankrl = (special.jv(1,.1) + special.yv(1,.1)*1j)1602 assert_almost_equal(hank1,hankrl,8)1603 def test_negv1e(self):1604 assert_almost_equal(special.hankel1e(-3,2), -special.hankel1e(3,2), 14)1605 def test_hankel1e(self):1606 hank1e = special.hankel1e(1,.1)1607 hankrle = special.hankel1(1,.1)*exp(-.1j)1608 assert_almost_equal(hank1e,hankrle,8)1609 def test_negv2(self):1610 assert_almost_equal(special.hankel2(-3,2), -special.hankel2(3,2), 14)1611 def test_hankel2(self):1612 hank2 = special.hankel2(1,.1)1613 hankrl2 = (special.jv(1,.1) - special.yv(1,.1)*1j)1614 assert_almost_equal(hank2,hankrl2,8)1615 def test_neg2e(self):1616 assert_almost_equal(special.hankel2e(-3,2), -special.hankel2e(3,2), 14)1617 def test_hankl2e(self):1618 hank2e = special.hankel2e(1,.1)1619 hankrl2e = special.hankel2e(1,.1)1620 assert_almost_equal(hank2e,hankrl2e,8)1621class TestHyper(object):1622 def test_h1vp(self):1623 h1 = special.h1vp(1,.1)1624 h1real = (special.jvp(1,.1) + special.yvp(1,.1)*1j)1625 assert_almost_equal(h1,h1real,8)1626 def test_h2vp(self):1627 h2 = special.h2vp(1,.1)1628 h2real = (special.jvp(1,.1) - special.yvp(1,.1)*1j)1629 assert_almost_equal(h2,h2real,8)1630 def test_hyp0f1(self):1631 # scalar input1632 assert_allclose(special.hyp0f1(2.5, 0.5), 1.21482702689997, rtol=1e-12)1633 assert_allclose(special.hyp0f1(2.5, 0), 1.0, rtol=1e-15)1634 # float input, expected values match mpmath1635 x = special.hyp0f1(3.0, [-1.5, -1, 0, 1, 1.5])1636 expected = np.array([0.58493659229143, 0.70566805723127, 1.0,1637 1.37789689539747, 1.60373685288480])1638 assert_allclose(x, expected, rtol=1e-12)1639 # complex input1640 x = special.hyp0f1(3.0, np.array([-1.5, -1, 0, 1, 1.5]) + 0.j)1641 assert_allclose(x, expected.astype(complex), rtol=1e-12)1642 # test broadcasting1643 x1 = [0.5, 1.5, 2.5]1644 x2 = [0, 1, 0.5]1645 x = special.hyp0f1(x1, x2)1646 expected = [1.0, 1.8134302039235093, 1.21482702689997]1647 assert_allclose(x, expected, rtol=1e-12)1648 x = special.hyp0f1(np.row_stack([x1] * 2), x2)1649 assert_allclose(x, np.row_stack([expected] * 2), rtol=1e-12)1650 assert_raises(ValueError, special.hyp0f1,1651 np.row_stack([x1] * 3), [0, 1])1652 def test_hyp0f1_gh5764(self):1653 # Just checks the point that failed; there's a more systematic1654 # test in test_mpmath1655 res = special.hyp0f1(0.8, 0.5 + 0.5*1J)1656 # The expected value was generated using mpmath1657 assert_almost_equal(res, 1.6139719776441115 + 1J*0.80893054061790665)1658 def test_hyp1f1(self):1659 hyp1 = special.hyp1f1(.1,.1,.3)1660 assert_almost_equal(hyp1, 1.3498588075760032,7)1661 # test contributed by Moritz Deger (2008-05-29)1662 # https:/​/​github.com/​scipy/​scipy/​issues/​1186 (Trac #659)1663 # reference data obtained from mathematica [ a, b, x, m(a,b,x)]:1664 # produced with test_hyp1f1.nb1665 ref_data = array([[-8.38132975e+00, -1.28436461e+01, -2.91081397e+01, 1.04178330e+04],1666 [2.91076882e+00, -6.35234333e+00, -1.27083993e+01, 6.68132725e+00],1667 [-1.42938258e+01, 1.80869131e-01, 1.90038728e+01, 1.01385897e+05],1668 [5.84069088e+00, 1.33187908e+01, 2.91290106e+01, 1.59469411e+08],1669 [-2.70433202e+01, -1.16274873e+01, -2.89582384e+01, 1.39900152e+24],1670 [4.26344966e+00, -2.32701773e+01, 1.91635759e+01, 6.13816915e+21],1671 [1.20514340e+01, -3.40260240e+00, 7.26832235e+00, 1.17696112e+13],1672 [2.77372955e+01, -1.99424687e+00, 3.61332246e+00, 3.07419615e+13],1673 [1.50310939e+01, -2.91198675e+01, -1.53581080e+01, -3.79166033e+02],1674 [1.43995827e+01, 9.84311196e+00, 1.93204553e+01, 2.55836264e+10],1675 [-4.08759686e+00, 1.34437025e+01, -1.42072843e+01, 1.70778449e+01],1676 [8.05595738e+00, -1.31019838e+01, 1.52180721e+01, 3.06233294e+21],1677 [1.81815804e+01, -1.42908793e+01, 9.57868793e+00, -2.84771348e+20],1678 [-2.49671396e+01, 1.25082843e+01, -1.71562286e+01, 2.36290426e+07],1679 [2.67277673e+01, 1.70315414e+01, 6.12701450e+00, 7.77917232e+03],1680 [2.49565476e+01, 2.91694684e+01, 6.29622660e+00, 2.35300027e+02],1681 [6.11924542e+00, -1.59943768e+00, 9.57009289e+00, 1.32906326e+11],1682 [-1.47863653e+01, 2.41691301e+01, -1.89981821e+01, 2.73064953e+03],1683 [2.24070483e+01, -2.93647433e+00, 8.19281432e+00, -6.42000372e+17],1684 [8.04042600e-01, 1.82710085e+01, -1.97814534e+01, 5.48372441e-01],1685 [1.39590390e+01, 1.97318686e+01, 2.37606635e+00, 5.51923681e+00],1686 [-4.66640483e+00, -2.00237930e+01, 7.40365095e+00, 4.50310752e+00],1687 [2.76821999e+01, -6.36563968e+00, 1.11533984e+01, -9.28725179e+23],1688 [-2.56764457e+01, 1.24544906e+00, 1.06407572e+01, 1.25922076e+01],1689 [3.20447808e+00, 1.30874383e+01, 2.26098014e+01, 2.03202059e+04],1690 [-1.24809647e+01, 4.15137113e+00, -2.92265700e+01, 2.39621411e+08],1691 [2.14778108e+01, -2.35162960e+00, -1.13758664e+01, 4.46882152e-01],1692 [-9.85469168e+00, -3.28157680e+00, 1.67447548e+01, -1.07342390e+07],1693 [1.08122310e+01, -2.47353236e+01, -1.15622349e+01, -2.91733796e+03],1694 [-2.67933347e+01, -3.39100709e+00, 2.56006986e+01, -5.29275382e+09],1695 [-8.60066776e+00, -8.02200924e+00, 1.07231926e+01, 1.33548320e+06],1696 [-1.01724238e-01, -1.18479709e+01, -2.55407104e+01, 1.55436570e+00],1697 [-3.93356771e+00, 2.11106818e+01, -2.57598485e+01, 2.13467840e+01],1698 [3.74750503e+00, 1.55687633e+01, -2.92841720e+01, 1.43873509e-02],1699 [6.99726781e+00, 2.69855571e+01, -1.63707771e+01, 3.08098673e-02],1700 [-2.31996011e+01, 3.47631054e+00, 9.75119815e-01, 1.79971073e-02],1701 [2.38951044e+01, -2.91460190e+01, -2.50774708e+00, 9.56934814e+00],1702 [1.52730825e+01, 5.77062507e+00, 1.21922003e+01, 1.32345307e+09],1703 [1.74673917e+01, 1.89723426e+01, 4.94903250e+00, 9.90859484e+01],1704 [1.88971241e+01, 2.86255413e+01, 5.52360109e-01, 1.44165360e+00],1705 [1.02002319e+01, -1.66855152e+01, -2.55426235e+01, 6.56481554e+02],1706 [-1.79474153e+01, 1.22210200e+01, -1.84058212e+01, 8.24041812e+05],1707 [-1.36147103e+01, 1.32365492e+00, -7.22375200e+00, 9.92446491e+05],1708 [7.57407832e+00, 2.59738234e+01, -1.34139168e+01, 3.64037761e-02],1709 [2.21110169e+00, 1.28012666e+01, 1.62529102e+01, 1.33433085e+02],1710 [-2.64297569e+01, -1.63176658e+01, -1.11642006e+01, -2.44797251e+13],1711 [-2.46622944e+01, -3.02147372e+00, 8.29159315e+00, -3.21799070e+05],1712 [-1.37215095e+01, -1.96680183e+01, 2.91940118e+01, 3.21457520e+12],1713 [-5.45566105e+00, 2.81292086e+01, 1.72548215e-01, 9.66973000e-01],1714 [-1.55751298e+00, -8.65703373e+00, 2.68622026e+01, -3.17190834e+16],1715 [2.45393609e+01, -2.70571903e+01, 1.96815505e+01, 1.80708004e+37],1716 [5.77482829e+00, 1.53203143e+01, 2.50534322e+01, 1.14304242e+06],1717 [-1.02626819e+01, 2.36887658e+01, -2.32152102e+01, 7.28965646e+02],1718 [-1.30833446e+00, -1.28310210e+01, 1.87275544e+01, -9.33487904e+12],1719 [5.83024676e+00, -1.49279672e+01, 2.44957538e+01, -7.61083070e+27],1720 [-2.03130747e+01, 2.59641715e+01, -2.06174328e+01, 4.54744859e+04],1721 [1.97684551e+01, -2.21410519e+01, -2.26728740e+01, 3.53113026e+06],1722 [2.73673444e+01, 2.64491725e+01, 1.57599882e+01, 1.07385118e+07],1723 [5.73287971e+00, 1.21111904e+01, 1.33080171e+01, 2.63220467e+03],1724 [-2.82751072e+01, 2.08605881e+01, 9.09838900e+00, -6.60957033e-07],1725 [1.87270691e+01, -1.74437016e+01, 1.52413599e+01, 6.59572851e+27],1726 [6.60681457e+00, -2.69449855e+00, 9.78972047e+00, -2.38587870e+12],1727 [1.20895561e+01, -2.51355765e+01, 2.30096101e+01, 7.58739886e+32],1728 [-2.44682278e+01, 2.10673441e+01, -1.36705538e+01, 4.54213550e+04],1729 [-4.50665152e+00, 3.72292059e+00, -4.83403707e+00, 2.68938214e+01],1730 [-7.46540049e+00, -1.08422222e+01, -1.72203805e+01, -2.09402162e+02],1731 [-2.00307551e+01, -7.50604431e+00, -2.78640020e+01, 4.15985444e+19],1732 [1.99890876e+01, 2.20677419e+01, -2.51301778e+01, 1.23840297e-09],1733 [2.03183823e+01, -7.66942559e+00, 2.10340070e+01, 1.46285095e+31],1734 [-2.90315825e+00, -2.55785967e+01, -9.58779316e+00, 2.65714264e-01],1735 [2.73960829e+01, -1.80097203e+01, -2.03070131e+00, 2.52908999e+02],1736 [-2.11708058e+01, -2.70304032e+01, 2.48257944e+01, 3.09027527e+08],1737 [2.21959758e+01, 4.00258675e+00, -1.62853977e+01, -9.16280090e-09],1738 [1.61661840e+01, -2.26845150e+01, 2.17226940e+01, -8.24774394e+33],1739 [-3.35030306e+00, 1.32670581e+00, 9.39711214e+00, -1.47303163e+01],1740 [7.23720726e+00, -2.29763909e+01, 2.34709682e+01, -9.20711735e+29],1741 [2.71013568e+01, 1.61951087e+01, -7.11388906e-01, 2.98750911e-01],1742 [8.40057933e+00, -7.49665220e+00, 2.95587388e+01, 6.59465635e+29],1743 [-1.51603423e+01, 1.94032322e+01, -7.60044357e+00, 1.05186941e+02],1744 [-8.83788031e+00, -2.72018313e+01, 1.88269907e+00, 1.81687019e+00],1745 [-1.87283712e+01, 5.87479570e+00, -1.91210203e+01, 2.52235612e+08],1746 [-5.61338513e-01, 2.69490237e+01, 1.16660111e-01, 9.97567783e-01],1747 [-5.44354025e+00, -1.26721408e+01, -4.66831036e+00, 1.06660735e-01],1748 [-2.18846497e+00, 2.33299566e+01, 9.62564397e+00, 3.03842061e-01],1749 [6.65661299e+00, -2.39048713e+01, 1.04191807e+01, 4.73700451e+13],1750 [-2.57298921e+01, -2.60811296e+01, 2.74398110e+01, -5.32566307e+11],1751 [-1.11431826e+01, -1.59420160e+01, -1.84880553e+01, -1.01514747e+02],1752 [6.50301931e+00, 2.59859051e+01, -2.33270137e+01, 1.22760500e-02],1753 [-1.94987891e+01, -2.62123262e+01, 3.90323225e+00, 1.71658894e+01],1754 [7.26164601e+00, -1.41469402e+01, 2.81499763e+01, -2.50068329e+31],1755 [-1.52424040e+01, 2.99719005e+01, -2.85753678e+01, 1.31906693e+04],1756 [5.24149291e+00, -1.72807223e+01, 2.22129493e+01, 2.50748475e+25],1757 [3.63207230e-01, -9.54120862e-02, -2.83874044e+01, 9.43854939e-01],1758 [-2.11326457e+00, -1.25707023e+01, 1.17172130e+00, 1.20812698e+00],1759 [2.48513582e+00, 1.03652647e+01, -1.84625148e+01, 6.47910997e-02],1760 [2.65395942e+01, 2.74794672e+01, 1.29413428e+01, 2.89306132e+05],1761 [-9.49445460e+00, 1.59930921e+01, -1.49596331e+01, 3.27574841e+02],1762 [-5.89173945e+00, 9.96742426e+00, 2.60318889e+01, -3.15842908e-01],1763 [-1.15387239e+01, -2.21433107e+01, -2.17686413e+01, 1.56724718e-01],1764 [-5.30592244e+00, -2.42752190e+01, 1.29734035e+00, 1.31985534e+00]])1765 for a,b,c,expected in ref_data:1766 result = special.hyp1f1(a,b,c)1767 assert_(abs(expected - result)/​expected < 1e-4)1768 def test_hyp1f1_gh2957(self):1769 hyp1 = special.hyp1f1(0.5, 1.5, -709.7827128933)1770 hyp2 = special.hyp1f1(0.5, 1.5, -709.7827128934)1771 assert_almost_equal(hyp1, hyp2, 12)1772 def test_hyp1f1_gh2282(self):1773 hyp = special.hyp1f1(0.5, 1.5, -1000)1774 assert_almost_equal(hyp, 0.028024956081989643, 12)1775 def test_hyp2f1(self):1776 # a collection of special cases taken from AMS 551777 values = [[0.5, 1, 1.5, 0.2**2, 0.5/​0.2*log((1+0.2)/​(1-0.2))],1778 [0.5, 1, 1.5, -0.2**2, 1./​0.2*arctan(0.2)],1779 [1, 1, 2, 0.2, -1/​0.2*log(1-0.2)],1780 [3, 3.5, 1.5, 0.2**2,1781 0.5/​0.2/​(-5)*((1+0.2)**(-5)-(1-0.2)**(-5))],1782 [-3, 3, 0.5, sin(0.2)**2, cos(2*3*0.2)],1783 [3, 4, 8, 1, special.gamma(8)*special.gamma(8-4-3)/​special.gamma(8-3)/​special.gamma(8-4)],1784 [3, 2, 3-2+1, -1, 1./​2**3*sqrt(pi) *1785 special.gamma(1+3-2)/​special.gamma(1+0.5*3-2)/​special.gamma(0.5+0.5*3)],1786 [5, 2, 5-2+1, -1, 1./​2**5*sqrt(pi) *1787 special.gamma(1+5-2)/​special.gamma(1+0.5*5-2)/​special.gamma(0.5+0.5*5)],1788 [4, 0.5+4, 1.5-2*4, -1./​3, (8./​9)**(-2*4)*special.gamma(4./​3) *1789 special.gamma(1.5-2*4)/​special.gamma(3./​2)/​special.gamma(4./​3-2*4)],1790 # and some others1791 # ticket #4241792 [1.5, -0.5, 1.0, -10.0, 4.1300097765277476484],1793 # negative integer a or b, with c-a-b integer and x > 0.91794 [-2,3,1,0.95,0.715],1795 [2,-3,1,0.95,-0.007],1796 [-6,3,1,0.95,0.0000810625],1797 [2,-5,1,0.95,-0.000029375],1798 # huge negative integers1799 (10, -900, 10.5, 0.99, 1.91853705796607664803709475658e-24),1800 (10, -900, -10.5, 0.99, 3.54279200040355710199058559155e-18),1801 ]1802 for i, (a, b, c, x, v) in enumerate(values):1803 cv = special.hyp2f1(a, b, c, x)1804 assert_almost_equal(cv, v, 8, err_msg='test #%d' % i)1805 def test_hyperu(self):1806 val1 = special.hyperu(1,0.1,100)1807 assert_almost_equal(val1,0.0098153,7)1808 a,b = [0.3,0.6,1.2,-2.7],[1.5,3.2,-0.4,-3.2]1809 a,b = asarray(a), asarray(b)1810 z = 0.51811 hypu = special.hyperu(a,b,z)1812 hprl = (pi/​sin(pi*b))*(special.hyp1f1(a,b,z) /​1813 (special.gamma(1+a-b)*special.gamma(b)) -1814 z**(1-b)*special.hyp1f1(1+a-b,2-b,z)1815 /​ (special.gamma(a)*special.gamma(2-b)))1816 assert_array_almost_equal(hypu,hprl,12)1817 def test_hyperu_gh2287(self):1818 assert_almost_equal(special.hyperu(1, 1.5, 20.2),1819 0.048360918656699191, 12)1820class TestBessel(object):1821 def test_itj0y0(self):1822 it0 = array(special.itj0y0(.2))1823 assert_array_almost_equal(it0,array([0.19933433254006822, -0.34570883800412566]),8)1824 def test_it2j0y0(self):1825 it2 = array(special.it2j0y0(.2))1826 assert_array_almost_equal(it2,array([0.0049937546274601858, -0.43423067011231614]),8)1827 def test_negv_iv(self):1828 assert_equal(special.iv(3,2), special.iv(-3,2))1829 def test_j0(self):1830 oz = special.j0(.1)1831 ozr = special.jn(0,.1)1832 assert_almost_equal(oz,ozr,8)1833 def test_j1(self):1834 o1 = special.j1(.1)1835 o1r = special.jn(1,.1)1836 assert_almost_equal(o1,o1r,8)1837 def test_jn(self):1838 jnnr = special.jn(1,.2)1839 assert_almost_equal(jnnr,0.099500832639235995,8)1840 def test_negv_jv(self):1841 assert_almost_equal(special.jv(-3,2), -special.jv(3,2), 14)1842 def test_jv(self):1843 values = [[0, 0.1, 0.99750156206604002],1844 [2./​3, 1e-8, 0.3239028506761532e-5],1845 [2./​3, 1e-10, 0.1503423854873779e-6],1846 [3.1, 1e-10, 0.1711956265409013e-32],1847 [2./​3, 4.0, -0.2325440850267039],1848 ]1849 for i, (v, x, y) in enumerate(values):1850 yc = special.jv(v, x)1851 assert_almost_equal(yc, y, 8, err_msg='test #%d' % i)1852 def test_negv_jve(self):1853 assert_almost_equal(special.jve(-3,2), -special.jve(3,2), 14)1854 def test_jve(self):1855 jvexp = special.jve(1,.2)1856 assert_almost_equal(jvexp,0.099500832639235995,8)1857 jvexp1 = special.jve(1,.2+1j)1858 z = .2+1j1859 jvexpr = special.jv(1,z)*exp(-abs(z.imag))1860 assert_almost_equal(jvexp1,jvexpr,8)1861 def test_jn_zeros(self):1862 jn0 = special.jn_zeros(0,5)1863 jn1 = special.jn_zeros(1,5)1864 assert_array_almost_equal(jn0,array([2.4048255577,1865 5.5200781103,1866 8.6537279129,1867 11.7915344391,1868 14.9309177086]),4)1869 assert_array_almost_equal(jn1,array([3.83171,1870 7.01559,1871 10.17347,1872 13.32369,1873 16.47063]),4)1874 jn102 = special.jn_zeros(102,5)1875 assert_allclose(jn102, array([110.89174935992040343,1876 117.83464175788308398,1877 123.70194191713507279,1878 129.02417238949092824,1879 134.00114761868422559]), rtol=1e-13)1880 jn301 = special.jn_zeros(301,5)1881 assert_allclose(jn301, array([313.59097866698830153,1882 323.21549776096288280,1883 331.22338738656748796,1884 338.39676338872084500,1885 345.03284233056064157]), rtol=1e-13)1886 def test_jn_zeros_slow(self):1887 jn0 = special.jn_zeros(0, 300)1888 assert_allclose(jn0[260-1], 816.02884495068867280, rtol=1e-13)1889 assert_allclose(jn0[280-1], 878.86068707124422606, rtol=1e-13)1890 assert_allclose(jn0[300-1], 941.69253065317954064, rtol=1e-13)1891 jn10 = special.jn_zeros(10, 300)1892 assert_allclose(jn10[260-1], 831.67668514305631151, rtol=1e-13)1893 assert_allclose(jn10[280-1], 894.51275095371316931, rtol=1e-13)1894 assert_allclose(jn10[300-1], 957.34826370866539775, rtol=1e-13)1895 jn3010 = special.jn_zeros(3010,5)1896 assert_allclose(jn3010, array([3036.86590780927,1897 3057.06598526482,1898 3073.66360690272,1899 3088.37736494778,1900 3101.86438139042]), rtol=1e-8)1901 def test_jnjnp_zeros(self):1902 jn = special.jn1903 def jnp(n, x):1904 return (jn(n-1,x) - jn(n+1,x))/​21905 for nt in range(1, 30):1906 z, n, m, t = special.jnjnp_zeros(nt)1907 for zz, nn, tt in zip(z, n, t):1908 if tt == 0:1909 assert_allclose(jn(nn, zz), 0, atol=1e-6)1910 elif tt == 1:1911 assert_allclose(jnp(nn, zz), 0, atol=1e-6)1912 else:1913 raise AssertionError("Invalid t return for nt=%d" % nt)1914 def test_jnp_zeros(self):1915 jnp = special.jnp_zeros(1,5)1916 assert_array_almost_equal(jnp, array([1.84118,1917 5.33144,1918 8.53632,1919 11.70600,1920 14.86359]),4)1921 jnp = special.jnp_zeros(443,5)1922 assert_allclose(special.jvp(443, jnp), 0, atol=1e-15)1923 def test_jnyn_zeros(self):1924 jnz = special.jnyn_zeros(1,5)1925 assert_array_almost_equal(jnz,(array([3.83171,1926 7.01559,1927 10.17347,1928 13.32369,1929 16.47063]),1930 array([1.84118,1931 5.33144,1932 8.53632,1933 11.70600,1934 14.86359]),1935 array([2.19714,1936 5.42968,1937 8.59601,1938 11.74915,1939 14.89744]),1940 array([3.68302,1941 6.94150,1942 10.12340,1943 13.28576,1944 16.44006])),5)1945 def test_jvp(self):1946 jvprim = special.jvp(2,2)1947 jv0 = (special.jv(1,2)-special.jv(3,2))/​21948 assert_almost_equal(jvprim,jv0,10)1949 def test_k0(self):1950 ozk = special.k0(.1)1951 ozkr = special.kv(0,.1)1952 assert_almost_equal(ozk,ozkr,8)1953 def test_k0e(self):1954 ozke = special.k0e(.1)1955 ozker = special.kve(0,.1)1956 assert_almost_equal(ozke,ozker,8)1957 def test_k1(self):1958 o1k = special.k1(.1)1959 o1kr = special.kv(1,.1)1960 assert_almost_equal(o1k,o1kr,8)1961 def test_k1e(self):1962 o1ke = special.k1e(.1)1963 o1ker = special.kve(1,.1)1964 assert_almost_equal(o1ke,o1ker,8)1965 def test_jacobi(self):1966 a = 5*np.random.random() - 11967 b = 5*np.random.random() - 11968 P0 = special.jacobi(0,a,b)1969 P1 = special.jacobi(1,a,b)1970 P2 = special.jacobi(2,a,b)1971 P3 = special.jacobi(3,a,b)1972 assert_array_almost_equal(P0.c,[1],13)1973 assert_array_almost_equal(P1.c,array([a+b+2,a-b])/​2.0,13)1974 cp = [(a+b+3)*(a+b+4), 4*(a+b+3)*(a+2), 4*(a+1)*(a+2)]1975 p2c = [cp[0],cp[1]-2*cp[0],cp[2]-cp[1]+cp[0]]1976 assert_array_almost_equal(P2.c,array(p2c)/​8.0,13)1977 cp = [(a+b+4)*(a+b+5)*(a+b+6),6*(a+b+4)*(a+b+5)*(a+3),1978 12*(a+b+4)*(a+2)*(a+3),8*(a+1)*(a+2)*(a+3)]1979 p3c = [cp[0],cp[1]-3*cp[0],cp[2]-2*cp[1]+3*cp[0],cp[3]-cp[2]+cp[1]-cp[0]]1980 assert_array_almost_equal(P3.c,array(p3c)/​48.0,13)1981 def test_kn(self):1982 kn1 = special.kn(0,.2)1983 assert_almost_equal(kn1,1.7527038555281462,8)1984 def test_negv_kv(self):1985 assert_equal(special.kv(3.0, 2.2), special.kv(-3.0, 2.2))1986 def test_kv0(self):1987 kv0 = special.kv(0,.2)1988 assert_almost_equal(kv0, 1.7527038555281462, 10)1989 def test_kv1(self):1990 kv1 = special.kv(1,0.2)1991 assert_almost_equal(kv1, 4.775972543220472, 10)1992 def test_kv2(self):1993 kv2 = special.kv(2,0.2)1994 assert_almost_equal(kv2, 49.51242928773287, 10)1995 def test_kn_largeorder(self):1996 assert_allclose(special.kn(32, 1), 1.7516596664574289e+43)1997 def test_kv_largearg(self):1998 assert_equal(special.kv(0, 1e19), 0)1999 def test_negv_kve(self):2000 assert_equal(special.kve(3.0, 2.2), special.kve(-3.0, 2.2))2001 def test_kve(self):2002 kve1 = special.kve(0,.2)2003 kv1 = special.kv(0,.2)*exp(.2)2004 assert_almost_equal(kve1,kv1,8)2005 z = .2+1j2006 kve2 = special.kve(0,z)2007 kv2 = special.kv(0,z)*exp(z)2008 assert_almost_equal(kve2,kv2,8)2009 def test_kvp_v0n1(self):2010 z = 2.22011 assert_almost_equal(-special.kv(1,z), special.kvp(0,z, n=1), 10)2012 def test_kvp_n1(self):2013 v = 3.2014 z = 2.22015 xc = -special.kv(v+1,z) + v/​z*special.kv(v,z)2016 x = special.kvp(v,z, n=1)2017 assert_almost_equal(xc, x, 10) # this function (kvp) is broken2018 def test_kvp_n2(self):2019 v = 3.2020 z = 2.22021 xc = (z**2+v**2-v)/​z**2 * special.kv(v,z) + special.kv(v+1,z)/​z2022 x = special.kvp(v, z, n=2)2023 assert_almost_equal(xc, x, 10)2024 def test_y0(self):2025 oz = special.y0(.1)2026 ozr = special.yn(0,.1)2027 assert_almost_equal(oz,ozr,8)2028 def test_y1(self):2029 o1 = special.y1(.1)2030 o1r = special.yn(1,.1)2031 assert_almost_equal(o1,o1r,8)2032 def test_y0_zeros(self):2033 yo,ypo = special.y0_zeros(2)2034 zo,zpo = special.y0_zeros(2,complex=1)2035 all = r_[yo,zo]2036 allval = r_[ypo,zpo]2037 assert_array_almost_equal(abs(special.yv(0.0,all)),0.0,11)2038 assert_array_almost_equal(abs(special.yv(1,all)-allval),0.0,11)2039 def test_y1_zeros(self):2040 y1 = special.y1_zeros(1)2041 assert_array_almost_equal(y1,(array([2.19714]),array([0.52079])),5)2042 def test_y1p_zeros(self):2043 y1p = special.y1p_zeros(1,complex=1)2044 assert_array_almost_equal(y1p,(array([0.5768+0.904j]), array([-0.7635+0.5892j])),3)2045 def test_yn_zeros(self):2046 an = special.yn_zeros(4,2)2047 assert_array_almost_equal(an,array([5.64515, 9.36162]),5)2048 an = special.yn_zeros(443,5)2049 assert_allclose(an, [450.13573091578090314, 463.05692376675001542,2050 472.80651546418663566, 481.27353184725625838,2051 488.98055964441374646], rtol=1e-15)2052 def test_ynp_zeros(self):2053 ao = special.ynp_zeros(0,2)2054 assert_array_almost_equal(ao,array([2.19714133, 5.42968104]),6)2055 ao = special.ynp_zeros(43,5)2056 assert_allclose(special.yvp(43, ao), 0, atol=1e-15)2057 ao = special.ynp_zeros(443,5)2058 assert_allclose(special.yvp(443, ao), 0, atol=1e-9)2059 def test_ynp_zeros_large_order(self):2060 ao = special.ynp_zeros(443,5)2061 assert_allclose(special.yvp(443, ao), 0, atol=1e-14)2062 def test_yn(self):2063 yn2n = special.yn(1,.2)2064 assert_almost_equal(yn2n,-3.3238249881118471,8)2065 def test_negv_yv(self):2066 assert_almost_equal(special.yv(-3,2), -special.yv(3,2), 14)2067 def test_yv(self):2068 yv2 = special.yv(1,.2)2069 assert_almost_equal(yv2,-3.3238249881118471,8)2070 def test_negv_yve(self):2071 assert_almost_equal(special.yve(-3,2), -special.yve(3,2), 14)2072 def test_yve(self):2073 yve2 = special.yve(1,.2)2074 assert_almost_equal(yve2,-3.3238249881118471,8)2075 yve2r = special.yv(1,.2+1j)*exp(-1)2076 yve22 = special.yve(1,.2+1j)2077 assert_almost_equal(yve22,yve2r,8)2078 def test_yvp(self):2079 yvpr = (special.yv(1,.2) - special.yv(3,.2))/​2.02080 yvp1 = special.yvp(2,.2)2081 assert_array_almost_equal(yvp1,yvpr,10)2082 def _cephes_vs_amos_points(self):2083 """Yield points at which to compare Cephes implementation to AMOS"""2084 # check several points, including large-amplitude ones2085 for v in [-120, -100.3, -20., -10., -1., -.5,2086 0., 1., 12.49, 120., 301]:2087 for z in [-1300, -11, -10, -1, 1., 10., 200.5, 401., 600.5,2088 700.6, 1300, 10003]:2089 yield v, z2090 # check half-integers; these are problematic points at least2091 # for cephes/​iv2092 for v in 0.5 + arange(-60, 60):2093 yield v, 3.52094 def check_cephes_vs_amos(self, f1, f2, rtol=1e-11, atol=0, skip=None):2095 for v, z in self._cephes_vs_amos_points():2096 if skip is not None and skip(v, z):2097 continue2098 c1, c2, c3 = f1(v, z), f1(v,z+0j), f2(int(v), z)2099 if np.isinf(c1):2100 assert_(np.abs(c2) >= 1e300, (v, z))2101 elif np.isnan(c1):2102 assert_(c2.imag != 0, (v, z))2103 else:2104 assert_allclose(c1, c2, err_msg=(v, z), rtol=rtol, atol=atol)2105 if v == int(v):2106 assert_allclose(c3, c2, err_msg=(v, z),2107 rtol=rtol, atol=atol)2108 def test_jv_cephes_vs_amos(self):2109 self.check_cephes_vs_amos(special.jv, special.jn, rtol=1e-10, atol=1e-305)2110 def test_yv_cephes_vs_amos(self):2111 self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305)2112 def test_yv_cephes_vs_amos_only_small_orders(self):2113 skipper = lambda v, z: (abs(v) > 50)2114 self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305, skip=skipper)2115 def test_iv_cephes_vs_amos(self):2116 olderr = np.seterr(all='ignore')2117 try:2118 self.check_cephes_vs_amos(special.iv, special.iv, rtol=5e-9, atol=1e-305)2119 finally:2120 np.seterr(**olderr)2121 @pytest.mark.slow2122 def test_iv_cephes_vs_amos_mass_test(self):2123 N = 10000002124 np.random.seed(1)2125 v = np.random.pareto(0.5, N) * (-1)**np.random.randint(2, size=N)2126 x = np.random.pareto(0.2, N) * (-1)**np.random.randint(2, size=N)2127 imsk = (np.random.randint(8, size=N) == 0)2128 v[imsk] = v[imsk].astype(int)2129 old_err = np.seterr(all='ignore')2130 try:2131 c1 = special.iv(v, x)2132 c2 = special.iv(v, x+0j)2133 # deal with differences in the inf and zero cutoffs2134 c1[abs(c1) > 1e300] = np.inf2135 c2[abs(c2) > 1e300] = np.inf2136 c1[abs(c1) < 1e-300] = 02137 c2[abs(c2) < 1e-300] = 02138 dc = abs(c1/​c2 - 1)2139 dc[np.isnan(dc)] = 02140 finally:2141 np.seterr(**old_err)2142 k = np.argmax(dc)2143 # Most error apparently comes from AMOS and not our implementation;2144 # there are some problems near integer orders there2145 assert_(dc[k] < 2e-7, (v[k], x[k], special.iv(v[k], x[k]), special.iv(v[k], x[k]+0j)))2146 def test_kv_cephes_vs_amos(self):2147 self.check_cephes_vs_amos(special.kv, special.kn, rtol=1e-9, atol=1e-305)2148 self.check_cephes_vs_amos(special.kv, special.kv, rtol=1e-9, atol=1e-305)2149 def test_ticket_623(self):2150 assert_allclose(special.jv(3, 4), 0.43017147387562193)2151 assert_allclose(special.jv(301, 1300), 0.0183487151115275)2152 assert_allclose(special.jv(301, 1296.0682), -0.0224174325312048)2153 def test_ticket_853(self):2154 """Negative-order Bessels"""2155 # cephes2156 assert_allclose(special.jv(-1, 1), -0.4400505857449335)2157 assert_allclose(special.jv(-2, 1), 0.1149034849319005)2158 assert_allclose(special.yv(-1, 1), 0.7812128213002887)2159 assert_allclose(special.yv(-2, 1), -1.650682606816255)2160 assert_allclose(special.iv(-1, 1), 0.5651591039924851)2161 assert_allclose(special.iv(-2, 1), 0.1357476697670383)2162 assert_allclose(special.kv(-1, 1), 0.6019072301972347)2163 assert_allclose(special.kv(-2, 1), 1.624838898635178)2164 assert_allclose(special.jv(-0.5, 1), 0.43109886801837607952)2165 assert_allclose(special.yv(-0.5, 1), 0.6713967071418031)2166 assert_allclose(special.iv(-0.5, 1), 1.231200214592967)2167 assert_allclose(special.kv(-0.5, 1), 0.4610685044478945)2168 # amos2169 assert_allclose(special.jv(-1, 1+0j), -0.4400505857449335)2170 assert_allclose(special.jv(-2, 1+0j), 0.1149034849319005)2171 assert_allclose(special.yv(-1, 1+0j), 0.7812128213002887)2172 assert_allclose(special.yv(-2, 1+0j), -1.650682606816255)2173 assert_allclose(special.iv(-1, 1+0j), 0.5651591039924851)2174 assert_allclose(special.iv(-2, 1+0j), 0.1357476697670383)2175 assert_allclose(special.kv(-1, 1+0j), 0.6019072301972347)2176 assert_allclose(special.kv(-2, 1+0j), 1.624838898635178)2177 assert_allclose(special.jv(-0.5, 1+0j), 0.43109886801837607952)2178 assert_allclose(special.jv(-0.5, 1+1j), 0.2628946385649065-0.827050182040562j)2179 assert_allclose(special.yv(-0.5, 1+0j), 0.6713967071418031)2180 assert_allclose(special.yv(-0.5, 1+1j), 0.967901282890131+0.0602046062142816j)2181 assert_allclose(special.iv(-0.5, 1+0j), 1.231200214592967)2182 assert_allclose(special.iv(-0.5, 1+1j), 0.77070737376928+0.39891821043561j)2183 assert_allclose(special.kv(-0.5, 1+0j), 0.4610685044478945)2184 assert_allclose(special.kv(-0.5, 1+1j), 0.06868578341999-0.38157825981268j)2185 assert_allclose(special.jve(-0.5,1+0.3j), special.jv(-0.5, 1+0.3j)*exp(-0.3))2186 assert_allclose(special.yve(-0.5,1+0.3j), special.yv(-0.5, 1+0.3j)*exp(-0.3))2187 assert_allclose(special.ive(-0.5,0.3+1j), special.iv(-0.5, 0.3+1j)*exp(-0.3))2188 assert_allclose(special.kve(-0.5,0.3+1j), special.kv(-0.5, 0.3+1j)*exp(0.3+1j))2189 assert_allclose(special.hankel1(-0.5, 1+1j), special.jv(-0.5, 1+1j) + 1j*special.yv(-0.5,1+1j))2190 assert_allclose(special.hankel2(-0.5, 1+1j), special.jv(-0.5, 1+1j) - 1j*special.yv(-0.5,1+1j))2191 def test_ticket_854(self):2192 """Real-valued Bessel domains"""2193 assert_(isnan(special.jv(0.5, -1)))2194 assert_(isnan(special.iv(0.5, -1)))2195 assert_(isnan(special.yv(0.5, -1)))2196 assert_(isnan(special.yv(1, -1)))2197 assert_(isnan(special.kv(0.5, -1)))2198 assert_(isnan(special.kv(1, -1)))2199 assert_(isnan(special.jve(0.5, -1)))2200 assert_(isnan(special.ive(0.5, -1)))2201 assert_(isnan(special.yve(0.5, -1)))2202 assert_(isnan(special.yve(1, -1)))2203 assert_(isnan(special.kve(0.5, -1)))2204 assert_(isnan(special.kve(1, -1)))2205 assert_(isnan(special.airye(-1)[0:2]).all(), special.airye(-1))2206 assert_(not isnan(special.airye(-1)[2:4]).any(), special.airye(-1))2207 def test_gh_7909(self):2208 assert_(special.kv(1.5, 0) == np.inf)2209 assert_(special.kve(1.5, 0) == np.inf)2210 def test_ticket_503(self):2211 """Real-valued Bessel I overflow"""2212 assert_allclose(special.iv(1, 700), 1.528500390233901e302)2213 assert_allclose(special.iv(1000, 1120), 1.301564549405821e301)2214 def test_iv_hyperg_poles(self):2215 assert_allclose(special.iv(-0.5, 1), 1.231200214592967)2216 def iv_series(self, v, z, n=200):2217 k = arange(0, n).astype(float_)2218 r = (v+2*k)*log(.5*z) - special.gammaln(k+1) - special.gammaln(v+k+1)2219 r[isnan(r)] = inf2220 r = exp(r)2221 err = abs(r).max() * finfo(float_).eps * n + abs(r[-1])*102222 return r.sum(), err2223 def test_i0_series(self):2224 for z in [1., 10., 200.5]:2225 value, err = self.iv_series(0, z)2226 assert_allclose(special.i0(z), value, atol=err, err_msg=z)2227 def test_i1_series(self):2228 for z in [1., 10., 200.5]:2229 value, err = self.iv_series(1, z)2230 assert_allclose(special.i1(z), value, atol=err, err_msg=z)2231 def test_iv_series(self):2232 for v in [-20., -10., -1., 0., 1., 12.49, 120.]:2233 for z in [1., 10., 200.5, -1+2j]:2234 value, err = self.iv_series(v, z)2235 assert_allclose(special.iv(v, z), value, atol=err, err_msg=(v, z))2236 def test_i0(self):2237 values = [[0.0, 1.0],2238 [1e-10, 1.0],2239 [0.1, 0.9071009258],2240 [0.5, 0.6450352706],2241 [1.0, 0.4657596077],2242 [2.5, 0.2700464416],2243 [5.0, 0.1835408126],2244 [20.0, 0.0897803119],2245 ]2246 for i, (x, v) in enumerate(values):2247 cv = special.i0(x) * exp(-x)2248 assert_almost_equal(cv, v, 8, err_msg='test #%d' % i)2249 def test_i0e(self):2250 oize = special.i0e(.1)2251 oizer = special.ive(0,.1)2252 assert_almost_equal(oize,oizer,8)2253 def test_i1(self):2254 values = [[0.0, 0.0],2255 [1e-10, 0.4999999999500000e-10],2256 [0.1, 0.0452984468],2257 [0.5, 0.1564208032],2258 [1.0, 0.2079104154],2259 [5.0, 0.1639722669],2260 [20.0, 0.0875062222],2261 ]2262 for i, (x, v) in enumerate(values):2263 cv = special.i1(x) * exp(-x)2264 assert_almost_equal(cv, v, 8, err_msg='test #%d' % i)2265 def test_i1e(self):2266 oi1e = special.i1e(.1)2267 oi1er = special.ive(1,.1)2268 assert_almost_equal(oi1e,oi1er,8)2269 def test_iti0k0(self):2270 iti0 = array(special.iti0k0(5))2271 assert_array_almost_equal(iti0,array([31.848667776169801, 1.5673873907283657]),5)2272 def test_it2i0k0(self):2273 it2k = special.it2i0k0(.1)2274 assert_array_almost_equal(it2k,array([0.0012503906973464409, 3.3309450354686687]),6)2275 def test_iv(self):2276 iv1 = special.iv(0,.1)*exp(-.1)2277 assert_almost_equal(iv1,0.90710092578230106,10)2278 def test_negv_ive(self):2279 assert_equal(special.ive(3,2), special.ive(-3,2))2280 def test_ive(self):2281 ive1 = special.ive(0,.1)2282 iv1 = special.iv(0,.1)*exp(-.1)2283 assert_almost_equal(ive1,iv1,10)2284 def test_ivp0(self):2285 assert_almost_equal(special.iv(1,2), special.ivp(0,2), 10)2286 def test_ivp(self):2287 y = (special.iv(0,2) + special.iv(2,2))/​22288 x = special.ivp(1,2)2289 assert_almost_equal(x,y,10)2290class TestLaguerre(object):2291 def test_laguerre(self):2292 lag0 = special.laguerre(0)2293 lag1 = special.laguerre(1)2294 lag2 = special.laguerre(2)2295 lag3 = special.laguerre(3)2296 lag4 = special.laguerre(4)2297 lag5 = special.laguerre(5)2298 assert_array_almost_equal(lag0.c,[1],13)2299 assert_array_almost_equal(lag1.c,[-1,1],13)2300 assert_array_almost_equal(lag2.c,array([1,-4,2])/​2.0,13)2301 assert_array_almost_equal(lag3.c,array([-1,9,-18,6])/​6.0,13)2302 assert_array_almost_equal(lag4.c,array([1,-16,72,-96,24])/​24.0,13)2303 assert_array_almost_equal(lag5.c,array([-1,25,-200,600,-600,120])/​120.0,13)2304 def test_genlaguerre(self):2305 k = 5*np.random.random() - 0.92306 lag0 = special.genlaguerre(0,k)2307 lag1 = special.genlaguerre(1,k)2308 lag2 = special.genlaguerre(2,k)2309 lag3 = special.genlaguerre(3,k)2310 assert_equal(lag0.c,[1])2311 assert_equal(lag1.c,[-1,k+1])2312 assert_almost_equal(lag2.c,array([1,-2*(k+2),(k+1.)*(k+2.)])/​2.0)2313 assert_almost_equal(lag3.c,array([-1,3*(k+3),-3*(k+2)*(k+3),(k+1)*(k+2)*(k+3)])/​6.0)2314# Base polynomials come from Abrahmowitz and Stegan2315class TestLegendre(object):2316 def test_legendre(self):2317 leg0 = special.legendre(0)2318 leg1 = special.legendre(1)2319 leg2 = special.legendre(2)2320 leg3 = special.legendre(3)2321 leg4 = special.legendre(4)2322 leg5 = special.legendre(5)2323 assert_equal(leg0.c, [1])2324 assert_equal(leg1.c, [1,0])2325 assert_almost_equal(leg2.c, array([3,0,-1])/​2.0, decimal=13)2326 assert_almost_equal(leg3.c, array([5,0,-3,0])/​2.0)2327 assert_almost_equal(leg4.c, array([35,0,-30,0,3])/​8.0)2328 assert_almost_equal(leg5.c, array([63,0,-70,0,15,0])/​8.0)2329class TestLambda(object):2330 def test_lmbda(self):2331 lam = special.lmbda(1,.1)2332 lamr = (array([special.jn(0,.1), 2*special.jn(1,.1)/​.1]),2333 array([special.jvp(0,.1), -2*special.jv(1,.1)/​.01 + 2*special.jvp(1,.1)/​.1]))2334 assert_array_almost_equal(lam,lamr,8)2335class TestLog1p(object):2336 def test_log1p(self):2337 l1p = (special.log1p(10), special.log1p(11), special.log1p(12))2338 l1prl = (log(11), log(12), log(13))2339 assert_array_almost_equal(l1p,l1prl,8)2340 def test_log1pmore(self):2341 l1pm = (special.log1p(1), special.log1p(1.1), special.log1p(1.2))2342 l1pmrl = (log(2),log(2.1),log(2.2))2343 assert_array_almost_equal(l1pm,l1pmrl,8)2344class TestLegendreFunctions(object):2345 def test_clpmn(self):2346 z = 0.5+0.3j2347 clp = special.clpmn(2, 2, z, 3)2348 assert_array_almost_equal(clp,2349 (array([[1.0000, z, 0.5*(3*z*z-1)],2350 [0.0000, sqrt(z*z-1), 3*z*sqrt(z*z-1)],2351 [0.0000, 0.0000, 3*(z*z-1)]]),2352 array([[0.0000, 1.0000, 3*z],2353 [0.0000, z/​sqrt(z*z-1), 3*(2*z*z-1)/​sqrt(z*z-1)],2354 [0.0000, 0.0000, 6*z]])),2355 7)2356 def test_clpmn_close_to_real_2(self):2357 eps = 1e-102358 m = 12359 n = 32360 x = 0.52361 clp_plus = special.clpmn(m, n, x+1j*eps, 2)[0][m, n]2362 clp_minus = special.clpmn(m, n, x-1j*eps, 2)[0][m, n]2363 assert_array_almost_equal(array([clp_plus, clp_minus]),2364 array([special.lpmv(m, n, x),2365 special.lpmv(m, n, x)]),2366 7)2367 def test_clpmn_close_to_real_3(self):2368 eps = 1e-102369 m = 12370 n = 32371 x = 0.52372 clp_plus = special.clpmn(m, n, x+1j*eps, 3)[0][m, n]2373 clp_minus = special.clpmn(m, n, x-1j*eps, 3)[0][m, n]2374 assert_array_almost_equal(array([clp_plus, clp_minus]),2375 array([special.lpmv(m, n, x)*np.exp(-0.5j*m*np.pi),2376 special.lpmv(m, n, x)*np.exp(0.5j*m*np.pi)]),2377 7)2378 def test_clpmn_across_unit_circle(self):2379 eps = 1e-72380 m = 12381 n = 12382 x = 1j2383 for type in [2, 3]:2384 assert_almost_equal(special.clpmn(m, n, x+1j*eps, type)[0][m, n],2385 special.clpmn(m, n, x-1j*eps, type)[0][m, n], 6)2386 def test_inf(self):2387 for z in (1, -1):2388 for n in range(4):2389 for m in range(1, n):2390 lp = special.clpmn(m, n, z)2391 assert_(np.isinf(lp[1][1,1:]).all())2392 lp = special.lpmn(m, n, z)2393 assert_(np.isinf(lp[1][1,1:]).all())2394 def test_deriv_clpmn(self):2395 # data inside and outside of the unit circle2396 zvals = [0.5+0.5j, -0.5+0.5j, -0.5-0.5j, 0.5-0.5j,2397 1+1j, -1+1j, -1-1j, 1-1j]2398 m = 22399 n = 32400 for type in [2, 3]:2401 for z in zvals:2402 for h in [1e-3, 1e-3j]:2403 approx_derivative = (special.clpmn(m, n, z+0.5*h, type)[0]2404 - special.clpmn(m, n, z-0.5*h, type)[0])/​h2405 assert_allclose(special.clpmn(m, n, z, type)[1],2406 approx_derivative,2407 rtol=1e-4)2408 def test_lpmn(self):2409 lp = special.lpmn(0,2,.5)2410 assert_array_almost_equal(lp,(array([[1.00000,2411 0.50000,2412 -0.12500]]),2413 array([[0.00000,2414 1.00000,2415 1.50000]])),4)2416 def test_lpn(self):2417 lpnf = special.lpn(2,.5)2418 assert_array_almost_equal(lpnf,(array([1.00000,2419 0.50000,2420 -0.12500]),2421 array([0.00000,2422 1.00000,2423 1.50000])),4)2424 def test_lpmv(self):2425 lp = special.lpmv(0,2,.5)2426 assert_almost_equal(lp,-0.125,7)2427 lp = special.lpmv(0,40,.001)2428 assert_almost_equal(lp,0.1252678976534484,7)2429 # XXX: this is outside the domain of the current implementation,2430 # so ensure it returns a NaN rather than a wrong answer.2431 olderr = np.seterr(all='ignore')2432 try:2433 lp = special.lpmv(-1,-1,.001)2434 finally:2435 np.seterr(**olderr)2436 assert_(lp != 0 or np.isnan(lp))2437 def test_lqmn(self):2438 lqmnf = special.lqmn(0,2,.5)2439 lqf = special.lqn(2,.5)2440 assert_array_almost_equal(lqmnf[0][0],lqf[0],4)2441 assert_array_almost_equal(lqmnf[1][0],lqf[1],4)2442 def test_lqmn_gt1(self):2443 """algorithm for real arguments changes at 1.00012444 test against analytical result for m=2, n=12445 """2446 x0 = 1.00012447 delta = 0.000022448 for x in (x0-delta, x0+delta):2449 lq = special.lqmn(2, 1, x)[0][-1, -1]2450 expected = 2/​(x*x-1)2451 assert_almost_equal(lq, expected)2452 def test_lqmn_shape(self):2453 a, b = special.lqmn(4, 4, 1.1)2454 assert_equal(a.shape, (5, 5))2455 assert_equal(b.shape, (5, 5))2456 a, b = special.lqmn(4, 0, 1.1)2457 assert_equal(a.shape, (5, 1))2458 assert_equal(b.shape, (5, 1))2459 def test_lqn(self):2460 lqf = special.lqn(2,.5)2461 assert_array_almost_equal(lqf,(array([0.5493, -0.7253, -0.8187]),2462 array([1.3333, 1.216, -0.8427])),4)2463class TestMathieu(object):2464 def test_mathieu_a(self):2465 pass2466 def test_mathieu_even_coef(self):2467 mc = special.mathieu_even_coef(2,5)2468 # Q not defined broken and cannot figure out proper reporting order2469 def test_mathieu_odd_coef(self):2470 # same problem as above2471 pass2472class TestFresnelIntegral(object):2473 def test_modfresnelp(self):2474 pass2475 def test_modfresnelm(self):2476 pass2477class TestOblCvSeq(object):2478 def test_obl_cv_seq(self):2479 obl = special.obl_cv_seq(0,3,1)2480 assert_array_almost_equal(obl,array([-0.348602,2481 1.393206,2482 5.486800,2483 11.492120]),5)2484class TestParabolicCylinder(object):2485 def test_pbdn_seq(self):2486 pb = special.pbdn_seq(1,.1)2487 assert_array_almost_equal(pb,(array([0.9975,2488 0.0998]),2489 array([-0.0499,2490 0.9925])),4)2491 def test_pbdv(self):2492 pbv = special.pbdv(1,.2)2493 derrl = 1/​2*(.2)*special.pbdv(1,.2)[0] - special.pbdv(0,.2)[0]2494 def test_pbdv_seq(self):2495 pbn = special.pbdn_seq(1,.1)2496 pbv = special.pbdv_seq(1,.1)2497 assert_array_almost_equal(pbv,(real(pbn[0]),real(pbn[1])),4)2498 def test_pbdv_points(self):2499 # simple case2500 eta = np.linspace(-10, 10, 5)2501 z = 2**(eta/​2)*np.sqrt(np.pi)/​special.gamma(.5-.5*eta)2502 assert_allclose(special.pbdv(eta, 0.)[0], z, rtol=1e-14, atol=1e-14)2503 # some points2504 assert_allclose(special.pbdv(10.34, 20.44)[0], 1.3731383034455e-32, rtol=1e-12)2505 assert_allclose(special.pbdv(-9.53, 3.44)[0], 3.166735001119246e-8, rtol=1e-12)2506 def test_pbdv_gradient(self):2507 x = np.linspace(-4, 4, 8)[:,None]2508 eta = np.linspace(-10, 10, 5)[None,:]2509 p = special.pbdv(eta, x)2510 eps = 1e-7 + 1e-7*abs(x)2511 dp = (special.pbdv(eta, x + eps)[0] - special.pbdv(eta, x - eps)[0]) /​ eps /​ 2.2512 assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)2513 def test_pbvv_gradient(self):2514 x = np.linspace(-4, 4, 8)[:,None]2515 eta = np.linspace(-10, 10, 5)[None,:]2516 p = special.pbvv(eta, x)2517 eps = 1e-7 + 1e-7*abs(x)2518 dp = (special.pbvv(eta, x + eps)[0] - special.pbvv(eta, x - eps)[0]) /​ eps /​ 2.2519 assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)2520class TestPolygamma(object):2521 # from Table 6.2 (pg. 271) of A&S2522 def test_polygamma(self):2523 poly2 = special.polygamma(2,1)2524 poly3 = special.polygamma(3,1)2525 assert_almost_equal(poly2,-2.4041138063,10)2526 assert_almost_equal(poly3,6.4939394023,10)2527 # Test polygamma(0, x) == psi(x)2528 x = [2, 3, 1.1e14]2529 assert_almost_equal(special.polygamma(0, x), special.psi(x))2530 # Test broadcasting2531 n = [0, 1, 2]2532 x = [0.5, 1.5, 2.5]2533 expected = [-1.9635100260214238, 0.93480220054467933,2534 -0.23620405164172739]2535 assert_almost_equal(special.polygamma(n, x), expected)2536 expected = np.row_stack([expected]*2)2537 assert_almost_equal(special.polygamma(n, np.row_stack([x]*2)),2538 expected)2539 assert_almost_equal(special.polygamma(np.row_stack([n]*2), x),2540 expected)2541class TestProCvSeq(object):2542 def test_pro_cv_seq(self):2543 prol = special.pro_cv_seq(0,3,1)2544 assert_array_almost_equal(prol,array([0.319000,2545 2.593084,2546 6.533471,2547 12.514462]),5)2548class TestPsi(object):2549 def test_psi(self):2550 ps = special.psi(1)2551 assert_almost_equal(ps,-0.57721566490153287,8)2552class TestRadian(object):2553 def test_radian(self):2554 rad = special.radian(90,0,0)2555 assert_almost_equal(rad,pi/​2.0,5)2556 def test_radianmore(self):2557 rad1 = special.radian(90,1,60)2558 assert_almost_equal(rad1,pi/​2+0.0005816135199345904,5)2559class TestRiccati(object):2560 def test_riccati_jn(self):2561 N, x = 2, 0.22562 S = np.empty((N, N))2563 for n in range(N):2564 j = special.spherical_jn(n, x)2565 jp = special.spherical_jn(n, x, derivative=True)2566 S[0,n] = x*j2567 S[1,n] = x*jp + j2568 assert_array_almost_equal(S, special.riccati_jn(n, x), 8)2569 def test_riccati_yn(self):2570 N, x = 2, 0.22571 C = np.empty((N, N))2572 for n in range(N):2573 y = special.spherical_yn(n, x)2574 yp = special.spherical_yn(n, x, derivative=True)2575 C[0,n] = x*y2576 C[1,n] = x*yp + y2577 assert_array_almost_equal(C, special.riccati_yn(n, x), 8)2578class TestRound(object):2579 def test_round(self):2580 rnd = list(map(int,(special.round(10.1),special.round(10.4),special.round(10.5),special.round(10.6))))2581 # Note: According to the documentation, scipy.special.round is2582 # supposed to round to the nearest even number if the fractional2583 # part is exactly 0.5. On some platforms, this does not appear2584 # to work and thus this test may fail. However, this unit test is2585 # correctly written.2586 rndrl = (10,10,10,11)2587 assert_array_equal(rnd,rndrl)2588def test_sph_harm():2589 # Tests derived from tables in2590 # https:/​/​en.wikipedia.org/​wiki/​Table_of_spherical_harmonics2591 sh = special.sph_harm2592 pi = np.pi2593 exp = np.exp2594 sqrt = np.sqrt2595 sin = np.sin2596 cos = np.cos2597 assert_array_almost_equal(sh(0,0,0,0),2598 0.5/​sqrt(pi))2599 assert_array_almost_equal(sh(-2,2,0.,pi/​4),2600 0.25*sqrt(15./​(2.*pi)) *2601 (sin(pi/​4))**2.)2602 assert_array_almost_equal(sh(-2,2,0.,pi/​2),2603 0.25*sqrt(15./​(2.*pi)))2604 assert_array_almost_equal(sh(2,2,pi,pi/​2),2605 0.25*sqrt(15/​(2.*pi)) *2606 exp(0+2.*pi*1j)*sin(pi/​2.)**2.)2607 assert_array_almost_equal(sh(2,4,pi/​4.,pi/​3.),2608 (3./​8.)*sqrt(5./​(2.*pi)) *2609 exp(0+2.*pi/​4.*1j) *2610 sin(pi/​3.)**2. *2611 (7.*cos(pi/​3.)**2.-1))2612 assert_array_almost_equal(sh(4,4,pi/​8.,pi/​6.),2613 (3./​16.)*sqrt(35./​(2.*pi)) *2614 exp(0+4.*pi/​8.*1j)*sin(pi/​6.)**4.)2615def test_sph_harm_ufunc_loop_selection():2616 # see https:/​/​github.com/​scipy/​scipy/​issues/​48952617 dt = np.dtype(np.complex128)2618 assert_equal(special.sph_harm(0, 0, 0, 0).dtype, dt)2619 assert_equal(special.sph_harm([0], 0, 0, 0).dtype, dt)2620 assert_equal(special.sph_harm(0, [0], 0, 0).dtype, dt)2621 assert_equal(special.sph_harm(0, 0, [0], 0).dtype, dt)2622 assert_equal(special.sph_harm(0, 0, 0, [0]).dtype, dt)2623 assert_equal(special.sph_harm([0], [0], [0], [0]).dtype, dt)2624class TestStruve(object):2625 def _series(self, v, z, n=100):2626 """Compute Struve function & error estimate from its power series."""2627 k = arange(0, n)2628 r = (-1)**k * (.5*z)**(2*k+v+1)/​special.gamma(k+1.5)/​special.gamma(k+v+1.5)2629 err = abs(r).max() * finfo(float_).eps * n2630 return r.sum(), err2631 def test_vs_series(self):2632 """Check Struve function versus its power series"""2633 for v in [-20, -10, -7.99, -3.4, -1, 0, 1, 3.4, 12.49, 16]:2634 for z in [1, 10, 19, 21, 30]:2635 value, err = self._series(v, z)2636 assert_allclose(special.struve(v, z), value, rtol=0, atol=err), (v, z)2637 def test_some_values(self):2638 assert_allclose(special.struve(-7.99, 21), 0.0467547614113, rtol=1e-7)2639 assert_allclose(special.struve(-8.01, 21), 0.0398716951023, rtol=1e-8)2640 assert_allclose(special.struve(-3.0, 200), 0.0142134427432, rtol=1e-12)2641 assert_allclose(special.struve(-8.0, -41), 0.0192469727846, rtol=1e-11)2642 assert_equal(special.struve(-12, -41), -special.struve(-12, 41))2643 assert_equal(special.struve(+12, -41), -special.struve(+12, 41))2644 assert_equal(special.struve(-11, -41), +special.struve(-11, 41))2645 assert_equal(special.struve(+11, -41), +special.struve(+11, 41))2646 assert_(isnan(special.struve(-7.1, -1)))2647 assert_(isnan(special.struve(-10.1, -1)))2648 def test_regression_679(self):2649 """Regression test for #679"""2650 assert_allclose(special.struve(-1.0, 20 - 1e-8), special.struve(-1.0, 20 + 1e-8))2651 assert_allclose(special.struve(-2.0, 20 - 1e-8), special.struve(-2.0, 20 + 1e-8))2652 assert_allclose(special.struve(-4.3, 20 - 1e-8), special.struve(-4.3, 20 + 1e-8))2653def test_chi2_smalldf():2654 assert_almost_equal(special.chdtr(0.6,3), 0.957890536704110)2655def test_ch2_inf():2656 assert_equal(special.chdtr(0.7,np.inf), 1.0)2657def test_chi2c_smalldf():2658 assert_almost_equal(special.chdtrc(0.6,3), 1-0.957890536704110)2659def test_chi2_inv_smalldf():2660 assert_almost_equal(special.chdtri(0.6,1-0.957890536704110), 3)2661def test_agm_simple():2662 rtol = 1e-132663 # Gauss's constant2664 assert_allclose(1/​special.agm(1, np.sqrt(2)), 0.834626841674073186,2665 rtol=rtol)2666 # These values were computed using Wolfram Alpha, with the2667 # function ArithmeticGeometricMean[a, b].2668 agm13 = 1.8636167832448972669 agm15 = 2.6040081905309402670 agm35 = 3.9362355036495552671 assert_allclose(special.agm([[1], [3]], [1, 3, 5]),2672 [[1, agm13, agm15],2673 [agm13, 3, agm35]], rtol=rtol)2674 # Computed by the iteration formula using mpmath,2675 # with mpmath.mp.prec = 1000:2676 agm12 = 1.45679103104690682677 assert_allclose(special.agm(1, 2), agm12, rtol=rtol)2678 assert_allclose(special.agm(2, 1), agm12, rtol=rtol)2679 assert_allclose(special.agm(-1, -2), -agm12, rtol=rtol)2680 assert_allclose(special.agm(24, 6), 13.458171481725614, rtol=rtol)2681 assert_allclose(special.agm(13, 123456789.5), 11111458.498599306,2682 rtol=rtol)2683 assert_allclose(special.agm(1e30, 1), 2.229223055945383e+28, rtol=rtol)2684 assert_allclose(special.agm(1e-22, 1), 0.030182566420169886, rtol=rtol)2685 assert_allclose(special.agm(1e150, 1e180), 2.229223055945383e+178,2686 rtol=rtol)2687 assert_allclose(special.agm(1e180, 1e-150), 2.0634722510162677e+177,2688 rtol=rtol)2689 assert_allclose(special.agm(1e-150, 1e-170), 3.3112619670463756e-152,2690 rtol=rtol)2691 fi = np.finfo(1.0)2692 assert_allclose(special.agm(fi.tiny, fi.max), 1.9892072050015473e+305,2693 rtol=rtol)2694 assert_allclose(special.agm(0.75*fi.max, fi.max), 1.564904312298045e+308,2695 rtol=rtol)2696 assert_allclose(special.agm(fi.tiny, 3*fi.tiny), 4.1466849866735005e-308,2697 rtol=rtol)2698 # zero, nan and inf cases.2699 assert_equal(special.agm(0, 0), 0)2700 assert_equal(special.agm(99, 0), 0)2701 assert_equal(special.agm(-1, 10), np.nan)2702 assert_equal(special.agm(0, np.inf), np.nan)2703 assert_equal(special.agm(np.inf, 0), np.nan)2704 assert_equal(special.agm(0, -np.inf), np.nan)2705 assert_equal(special.agm(-np.inf, 0), np.nan)2706 assert_equal(special.agm(np.inf, -np.inf), np.nan)2707 assert_equal(special.agm(-np.inf, np.inf), np.nan)2708 assert_equal(special.agm(1, np.nan), np.nan)2709 assert_equal(special.agm(np.nan, -1), np.nan)2710 assert_equal(special.agm(1, np.inf), np.inf)2711 assert_equal(special.agm(np.inf, 1), np.inf)2712 assert_equal(special.agm(-1, -np.inf), -np.inf)2713 assert_equal(special.agm(-np.inf, -1), -np.inf)2714def test_legacy():2715 # Legacy behavior: truncating arguments to integers2716 with suppress_warnings() as sup:2717 sup.filter(RuntimeWarning, "floating point number truncated to an integer")2718 assert_equal(special.bdtrc(1, 2, 0.3), special.bdtrc(1.8, 2.8, 0.3))2719 assert_equal(special.bdtr(1, 2, 0.3), special.bdtr(1.8, 2.8, 0.3))2720 assert_equal(special.bdtri(1, 2, 0.3), special.bdtri(1.8, 2.8, 0.3))2721 assert_equal(special.expn(1, 0.3), special.expn(1.8, 0.3))2722 assert_equal(special.nbdtrc(1, 2, 0.3), special.nbdtrc(1.8, 2.8, 0.3))2723 assert_equal(special.nbdtr(1, 2, 0.3), special.nbdtr(1.8, 2.8, 0.3))2724 assert_equal(special.nbdtri(1, 2, 0.3), special.nbdtri(1.8, 2.8, 0.3))2725 assert_equal(special.pdtrc(1, 0.3), special.pdtrc(1.8, 0.3))2726 assert_equal(special.pdtr(1, 0.3), special.pdtr(1.8, 0.3))2727 assert_equal(special.pdtri(1, 0.3), special.pdtri(1.8, 0.3))2728 assert_equal(special.kn(1, 0.3), special.kn(1.8, 0.3))2729 assert_equal(special.yn(1, 0.3), special.yn(1.8, 0.3))2730 assert_equal(special.smirnov(1, 0.3), special.smirnov(1.8, 0.3))2731 assert_equal(special.smirnovi(1, 0.3), special.smirnovi(1.8, 0.3))2732@with_special_errors2733def test_error_raising():2734 assert_raises(special.SpecialFunctionError, special.iv, 1, 1e99j)2735def test_xlogy():2736 def xfunc(x, y):2737 with np.errstate(invalid='ignore'):2738 if x == 0 and not np.isnan(y):2739 return x2740 else:2741 return x*np.log(y)2742 z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0)], dtype=float)2743 z2 = np.r_[z1, [(0, 1j), (1, 1j)]]2744 w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])2745 assert_func_equal(special.xlogy, w1, z1, rtol=1e-13, atol=1e-13)2746 w2 = np.vectorize(xfunc)(z2[:,0], z2[:,1])2747 assert_func_equal(special.xlogy, w2, z2, rtol=1e-13, atol=1e-13)2748def test_xlog1py():2749 def xfunc(x, y):2750 with np.errstate(invalid='ignore'):2751 if x == 0 and not np.isnan(y):2752 return x2753 else:2754 return x * np.log1p(y)2755 z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0),2756 (1, 1e-30)], dtype=float)2757 w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])2758 assert_func_equal(special.xlog1py, w1, z1, rtol=1e-13, atol=1e-13)2759def test_entr():2760 def xfunc(x):2761 if x < 0:2762 return -np.inf2763 else:2764 return -special.xlogy(x, x)2765 values = (0, 0.5, 1.0, np.inf)2766 signs = [-1, 1]2767 arr = []2768 for sgn, v in itertools.product(signs, values):2769 arr.append(sgn * v)2770 z = np.array(arr, dtype=float)2771 w = np.vectorize(xfunc, otypes=[np.float64])(z)2772 assert_func_equal(special.entr, w, z, rtol=1e-13, atol=1e-13)2773def test_kl_div():2774 def xfunc(x, y):2775 if x < 0 or y < 0 or (y == 0 and x != 0):2776 # extension of natural domain to preserve convexity2777 return np.inf2778 elif np.isposinf(x) or np.isposinf(y):2779 # limits within the natural domain2780 return np.inf2781 elif x == 0:2782 return y2783 else:2784 return special.xlogy(x, x/​y) - x + y2785 values = (0, 0.5, 1.0)2786 signs = [-1, 1]2787 arr = []2788 for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):2789 arr.append((sgna*va, sgnb*vb))2790 z = np.array(arr, dtype=float)2791 w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])2792 assert_func_equal(special.kl_div, w, z, rtol=1e-13, atol=1e-13)2793def test_rel_entr():2794 def xfunc(x, y):2795 if x > 0 and y > 0:2796 return special.xlogy(x, x/​y)2797 elif x == 0 and y >= 0:2798 return 02799 else:2800 return np.inf2801 values = (0, 0.5, 1.0)2802 signs = [-1, 1]2803 arr = []2804 for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):2805 arr.append((sgna*va, sgnb*vb))2806 z = np.array(arr, dtype=float)2807 w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])2808 assert_func_equal(special.rel_entr, w, z, rtol=1e-13, atol=1e-13)2809def test_huber():2810 assert_equal(special.huber(-1, 1.5), np.inf)2811 assert_allclose(special.huber(2, 1.5), 0.5 * np.square(1.5))2812 assert_allclose(special.huber(2, 2.5), 2 * (2.5 - 0.5 * 2))2813 def xfunc(delta, r):2814 if delta < 0:2815 return np.inf2816 elif np.abs(r) < delta:2817 return 0.5 * np.square(r)2818 else:2819 return delta * (np.abs(r) - 0.5 * delta)2820 z = np.random.randn(10, 2)2821 w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])2822 assert_func_equal(special.huber, w, z, rtol=1e-13, atol=1e-13)2823def test_pseudo_huber():2824 def xfunc(delta, r):2825 if delta < 0:2826 return np.inf2827 elif (not delta) or (not r):2828 return 02829 else:2830 return delta**2 * (np.sqrt(1 + (r/​delta)**2) - 1)2831 z = np.array(np.random.randn(10, 2).tolist() + [[0, 0.5], [0.5, 0]])2832 w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])...

test_cython_special.py

Source:test_cython_special.py

1from __future__ import division, print_function, absolute_import2from itertools import product3from numpy.testing import assert_allclose4import pytest5from scipy import special6from scipy.special import cython_special7int_points = [-10, -1, 1, 10]8real_points = [-10.0, -1.0, 1.0, 10.0]9complex_points = [complex(*tup) for tup in product(real_points, repeat=2)]10CYTHON_SIGNATURE_MAP = {11 'f': 'float',12 'd': 'double',13 'g': 'long double',14 'F': 'float complex',15 'D': 'double complex',16 'G': 'long double complex',17 'i':'int',18 'l': 'long'19}20TEST_POINTS = {21 'f': real_points,22 'd': real_points,23 'g': real_points,24 'F': complex_points,25 'D': complex_points,26 'G': complex_points,27 'i': int_points,28 'l': int_points,29}30PARAMS = [31 (special.agm, cython_special.agm, ('dd',), None),32 (special.airy, cython_special._airy_pywrap, ('d', 'D'), None),33 (special.airye, cython_special._airye_pywrap, ('d', 'D'), None),34 (special.bdtr, cython_special.bdtr, ('lld', 'ddd'), None),35 (special.bdtrc, cython_special.bdtrc, ('lld', 'ddd'), None),36 (special.bdtri, cython_special.bdtri, ('lld', 'ddd'), None),37 (special.bdtrik, cython_special.bdtrik, ('ddd',), None),38 (special.bdtrin, cython_special.bdtrin, ('ddd',), None),39 (special.bei, cython_special.bei, ('d',), None),40 (special.beip, cython_special.beip, ('d',), None),41 (special.ber, cython_special.ber, ('d',), None),42 (special.berp, cython_special.berp, ('d',), None),43 (special.besselpoly, cython_special.besselpoly, ('ddd',), None),44 (special.beta, cython_special.beta, ('dd',), None),45 (special.betainc, cython_special.betainc, ('ddd',), None),46 (special.betaincinv, cython_special.betaincinv, ('ddd',), None),47 (special.betaln, cython_special.betaln, ('dd',), None),48 (special.binom, cython_special.binom, ('dd',), None),49 (special.boxcox, cython_special.boxcox, ('dd',), None),50 (special.boxcox1p, cython_special.boxcox1p, ('dd',), None),51 (special.btdtr, cython_special.btdtr, ('ddd',), None),52 (special.btdtri, cython_special.btdtri, ('ddd',), None),53 (special.btdtria, cython_special.btdtria, ('ddd',), None),54 (special.btdtrib, cython_special.btdtrib, ('ddd',), None),55 (special.cbrt, cython_special.cbrt, ('d',), None),56 (special.chdtr, cython_special.chdtr, ('dd',), None),57 (special.chdtrc, cython_special.chdtrc, ('dd',), None),58 (special.chdtri, cython_special.chdtri, ('dd',), None),59 (special.chdtriv, cython_special.chdtriv, ('dd',), None),60 (special.chndtr, cython_special.chndtr, ('ddd',), None),61 (special.chndtridf, cython_special.chndtridf, ('ddd',), None),62 (special.chndtrinc, cython_special.chndtrinc, ('ddd',), None),63 (special.chndtrix, cython_special.chndtrix, ('ddd',), None),64 (special.cosdg, cython_special.cosdg, ('d',), None),65 (special.cosm1, cython_special.cosm1, ('d',), None),66 (special.cotdg, cython_special.cotdg, ('d',), None),67 (special.dawsn, cython_special.dawsn, ('d', 'D'), None),68 (special.ellipe, cython_special.ellipe, ('d',), None),69 (special.ellipeinc, cython_special.ellipeinc, ('dd',), None),70 (special.ellipj, cython_special._ellipj_pywrap, ('dd',), None),71 (special.ellipkinc, cython_special.ellipkinc, ('dd',), None),72 (special.ellipkm1, cython_special.ellipkm1, ('d',), None),73 (special.entr, cython_special.entr, ('d',), None),74 (special.erf, cython_special.erf, ('d', 'D'), None),75 (special.erfc, cython_special.erfc, ('d', 'D'), None),76 (special.erfcx, cython_special.erfcx, ('d', 'D'), None),77 (special.erfi, cython_special.erfi, ('d', 'D'), None),78 (special.eval_chebyc, cython_special.eval_chebyc, ('dd', 'dD', 'ld'), None),79 (special.eval_chebys, cython_special.eval_chebys, ('dd', 'dD', 'ld'),80 'd and l differ for negative int'),81 (special.eval_chebyt, cython_special.eval_chebyt, ('dd', 'dD', 'ld'),82 'd and l differ for negative int'),83 (special.eval_chebyu, cython_special.eval_chebyu, ('dd', 'dD', 'ld'),84 'd and l differ for negative int'),85 (special.eval_gegenbauer, cython_special.eval_gegenbauer, ('ddd', 'ddD', 'ldd'),86 'd and l differ for negative int'),87 (special.eval_genlaguerre, cython_special.eval_genlaguerre, ('ddd', 'ddD', 'ldd'),88 'd and l differ for negative int'),89 (special.eval_hermite, cython_special.eval_hermite, ('ld',), None),90 (special.eval_hermitenorm, cython_special.eval_hermitenorm, ('ld',), None),91 (special.eval_jacobi, cython_special.eval_jacobi, ('dddd', 'dddD', 'lddd'),92 'd and l differ for negative int'),93 (special.eval_laguerre, cython_special.eval_laguerre, ('dd', 'dD', 'ld'),94 'd and l differ for negative int'),95 (special.eval_legendre, cython_special.eval_legendre, ('dd', 'dD', 'ld'), None),96 (special.eval_sh_chebyt, cython_special.eval_sh_chebyt, ('dd', 'dD', 'ld'), None),97 (special.eval_sh_chebyu, cython_special.eval_sh_chebyu, ('dd', 'dD', 'ld'),98 'd and l differ for negative int'),99 (special.eval_sh_jacobi, cython_special.eval_sh_jacobi, ('dddd', 'dddD', 'lddd'),100 'd and l differ for negative int'),101 (special.eval_sh_legendre, cython_special.eval_sh_legendre, ('dd', 'dD', 'ld'), None),102 (special.exp1, cython_special.exp1, ('d', 'D'), None),103 (special.exp10, cython_special.exp10, ('d',), None),104 (special.exp2, cython_special.exp2, ('d',), None),105 (special.expi, cython_special.expi, ('d', 'D'), None),106 (special.expit, cython_special.expit, ('f', 'd', 'g'), None),107 (special.expm1, cython_special.expm1, ('d', 'D'), None),108 (special.expn, cython_special.expn, ('ld', 'dd'), None),109 (special.exprel, cython_special.exprel, ('d',), None),110 (special.fdtr, cython_special.fdtr, ('ddd',), None),111 (special.fdtrc, cython_special.fdtrc, ('ddd',), None),112 (special.fdtri, cython_special.fdtri, ('ddd',), None),113 (special.fdtridfd, cython_special.fdtridfd, ('ddd',), None),114 (special.fresnel, cython_special._fresnel_pywrap, ('d', 'D'), None),115 (special.gamma, cython_special.gamma, ('d', 'D'), None),116 (special.gammainc, cython_special.gammainc, ('dd',), None),117 (special.gammaincc, cython_special.gammaincc, ('dd',), None),118 (special.gammainccinv, cython_special.gammainccinv, ('dd',), None),119 (special.gammaincinv, cython_special.gammaincinv, ('dd',), None),120 (special.gammaln, cython_special.gammaln, ('d',), None),121 (special.gammasgn, cython_special.gammasgn, ('d',), None),122 (special.gdtr, cython_special.gdtr, ('ddd',), None),123 (special.gdtrc, cython_special.gdtrc, ('ddd',), None),124 (special.gdtria, cython_special.gdtria, ('ddd',), None),125 (special.gdtrib, cython_special.gdtrib, ('ddd',), None),126 (special.gdtrix, cython_special.gdtrix, ('ddd',), None),127 (special.hankel1, cython_special.hankel1, ('dD',), None),128 (special.hankel1e, cython_special.hankel1e, ('dD',), None),129 (special.hankel2, cython_special.hankel2, ('dD',), None),130 (special.hankel2e, cython_special.hankel2e, ('dD',), None),131 (special.huber, cython_special.huber, ('dd',), None),132 (special.hyp0f1, cython_special.hyp0f1, ('dd', 'dD'), None),133 (special.hyp1f1, cython_special.hyp1f1, ('ddd', 'ddD'), None),134 (special.hyp2f1, cython_special.hyp2f1, ('dddd', 'dddD'), None),135 (special.hyperu, cython_special.hyperu, ('ddd',), None),136 (special.i0, cython_special.i0, ('d',), None),137 (special.i0e, cython_special.i0e, ('d',), None),138 (special.i1, cython_special.i1, ('d',), None),139 (special.i1e, cython_special.i1e, ('d',), None),140 (special.inv_boxcox, cython_special.inv_boxcox, ('dd',), None),141 (special.inv_boxcox1p, cython_special.inv_boxcox1p, ('dd',), None),142 (special.it2i0k0, cython_special._it2i0k0_pywrap, ('d',), None),143 (special.it2j0y0, cython_special._it2j0y0_pywrap, ('d',), None),144 (special.it2struve0, cython_special.it2struve0, ('d',), None),145 (special.itairy, cython_special._itairy_pywrap, ('d',), None),146 (special.iti0k0, cython_special._iti0k0_pywrap, ('d',), None),147 (special.itj0y0, cython_special._itj0y0_pywrap, ('d',), None),148 (special.itmodstruve0, cython_special.itmodstruve0, ('d',), None),149 (special.itstruve0, cython_special.itstruve0, ('d',), None),150 (special.iv, cython_special.iv, ('dd', 'dD'), None),151 (special.ive, cython_special.ive, ('dd', 'dD'), None),152 (special.j0, cython_special.j0, ('d',), None),153 (special.j1, cython_special.j1, ('d',), None),154 (special.jv, cython_special.jv, ('dd', 'dD'), None),155 (special.jve, cython_special.jve, ('dd', 'dD'), None),156 (special.k0, cython_special.k0, ('d',), None),157 (special.k0e, cython_special.k0e, ('d',), None),158 (special.k1, cython_special.k1, ('d',), None),159 (special.k1e, cython_special.k1e, ('d',), None),160 (special.kei, cython_special.kei, ('d',), None),161 (special.keip, cython_special.keip, ('d',), None),162 (special.kelvin, cython_special._kelvin_pywrap, ('d',), None),163 (special.ker, cython_special.ker, ('d',), None),164 (special.kerp, cython_special.kerp, ('d',), None),165 (special.kl_div, cython_special.kl_div, ('dd',), None),166 (special.kn, cython_special.kn, ('ld', 'dd'), None),167 (special.kolmogi, cython_special.kolmogi, ('d',), None),168 (special.kolmogorov, cython_special.kolmogorov, ('d',), None),169 (special.kv, cython_special.kv, ('dd', 'dD'), None),170 (special.kve, cython_special.kve, ('dd', 'dD'), None),171 (special.log1p, cython_special.log1p, ('d', 'D'), None),172 (special.log_ndtr, cython_special.log_ndtr, ('d', 'D'), None),173 (special.loggamma, cython_special.loggamma, ('D',), None),174 (special.logit, cython_special.logit, ('f', 'd', 'g'), None),175 (special.lpmv, cython_special.lpmv, ('ddd',), None),176 (special.mathieu_a, cython_special.mathieu_a, ('dd',), None),177 (special.mathieu_b, cython_special.mathieu_b, ('dd',), None),178 (special.mathieu_cem, cython_special._mathieu_cem_pywrap, ('ddd',), None),179 (special.mathieu_modcem1, cython_special._mathieu_modcem1_pywrap, ('ddd',), None),180 (special.mathieu_modcem2, cython_special._mathieu_modcem2_pywrap, ('ddd',), None),181 (special.mathieu_modsem1, cython_special._mathieu_modsem1_pywrap, ('ddd',), None),182 (special.mathieu_modsem2, cython_special._mathieu_modsem2_pywrap, ('ddd',), None),183 (special.mathieu_sem, cython_special._mathieu_sem_pywrap, ('ddd',), None),184 (special.modfresnelm, cython_special._modfresnelm_pywrap, ('d',), None),185 (special.modfresnelp, cython_special._modfresnelp_pywrap, ('d',), None),186 (special.modstruve, cython_special.modstruve, ('dd',), None),187 (special.nbdtr, cython_special.nbdtr, ('lld', 'ddd'), None),188 (special.nbdtrc, cython_special.nbdtrc, ('lld', 'ddd'), None),189 (special.nbdtri, cython_special.nbdtri, ('lld', 'ddd'), None),190 (special.nbdtrik, cython_special.nbdtrik, ('ddd',), None),191 (special.nbdtrin, cython_special.nbdtrin, ('ddd',), None),192 (special.ncfdtr, cython_special.ncfdtr, ('dddd',), None),193 (special.ncfdtri, cython_special.ncfdtri, ('dddd',), None),194 (special.ncfdtridfd, cython_special.ncfdtridfd, ('dddd',), None),195 (special.ncfdtridfn, cython_special.ncfdtridfn, ('dddd',), None),196 (special.ncfdtrinc, cython_special.ncfdtrinc, ('dddd',), None),197 (special.nctdtr, cython_special.nctdtr, ('ddd',), None),198 (special.nctdtridf, cython_special.nctdtridf, ('ddd',), None),199 (special.nctdtrinc, cython_special.nctdtrinc, ('ddd',), None),200 (special.nctdtrit, cython_special.nctdtrit, ('ddd',), None),201 (special.ndtr, cython_special.ndtr, ('d', 'D'), None),202 (special.ndtri, cython_special.ndtri, ('d',), None),203 (special.nrdtrimn, cython_special.nrdtrimn, ('ddd',), None),204 (special.nrdtrisd, cython_special.nrdtrisd, ('ddd',), None),205 (special.obl_ang1, cython_special._obl_ang1_pywrap, ('dddd',), None),206 (special.obl_ang1_cv, cython_special._obl_ang1_cv_pywrap, ('ddddd',), None),207 (special.obl_cv, cython_special.obl_cv, ('ddd',), None),208 (special.obl_rad1, cython_special._obl_rad1_pywrap, ('dddd',), "see gh-6211"),209 (special.obl_rad1_cv, cython_special._obl_rad1_cv_pywrap, ('ddddd',), "see gh-6211"),210 (special.obl_rad2, cython_special._obl_rad2_pywrap, ('dddd',), "see gh-6211"),211 (special.obl_rad2_cv, cython_special._obl_rad2_cv_pywrap, ('ddddd',), "see gh-6211"),212 (special.pbdv, cython_special._pbdv_pywrap, ('dd',), None),213 (special.pbvv, cython_special._pbvv_pywrap, ('dd',), None),214 (special.pbwa, cython_special._pbwa_pywrap, ('dd',), None),215 (special.pdtr, cython_special.pdtr, ('ld', 'dd'), None),216 (special.pdtrc, cython_special.pdtrc, ('ld', 'dd'), None),217 (special.pdtri, cython_special.pdtri, ('ld', 'dd'), None),218 (special.pdtrik, cython_special.pdtrik, ('dd',), None),219 (special.poch, cython_special.poch, ('dd',), None),220 (special.pro_ang1, cython_special._pro_ang1_pywrap, ('dddd',), None),221 (special.pro_ang1_cv, cython_special._pro_ang1_cv_pywrap, ('ddddd',), None),222 (special.pro_cv, cython_special.pro_cv, ('ddd',), None),223 (special.pro_rad1, cython_special._pro_rad1_pywrap, ('dddd',), "see gh-6211"),224 (special.pro_rad1_cv, cython_special._pro_rad1_cv_pywrap, ('ddddd',), "see gh-6211"),225 (special.pro_rad2, cython_special._pro_rad2_pywrap, ('dddd',), "see gh-6211"),226 (special.pro_rad2_cv, cython_special._pro_rad2_cv_pywrap, ('ddddd',), "see gh-6211"),227 (special.pseudo_huber, cython_special.pseudo_huber, ('dd',), None),228 (special.psi, cython_special.psi, ('d', 'D'), None),229 (special.radian, cython_special.radian, ('ddd',), None),230 (special.rel_entr, cython_special.rel_entr, ('dd',), None),231 (special.rgamma, cython_special.rgamma, ('d', 'D'), None),232 (special.round, cython_special.round, ('d',), None),233 (special.shichi, cython_special._shichi_pywrap, ('d', 'D'), None),234 (special.sici, cython_special._sici_pywrap, ('d', 'D'), None),235 (special.sindg, cython_special.sindg, ('d',), None),236 (special.smirnov, cython_special.smirnov, ('ld', 'dd'), None),237 (special.smirnovi, cython_special.smirnovi, ('ld', 'dd'), None),238 (special.spence, cython_special.spence, ('d', 'D'), None),239 (special.sph_harm, cython_special.sph_harm, ('lldd', 'dddd'), None),240 (special.stdtr, cython_special.stdtr, ('dd',), None),241 (special.stdtridf, cython_special.stdtridf, ('dd',), None),242 (special.stdtrit, cython_special.stdtrit, ('dd',), None),243 (special.struve, cython_special.struve, ('dd',), None),244 (special.tandg, cython_special.tandg, ('d',), None),245 (special.tklmbda, cython_special.tklmbda, ('dd',), None),246 (special.wofz, cython_special.wofz, ('D',), None),247 (special.wrightomega, cython_special.wrightomega, ('D',), None),248 (special.xlog1py, cython_special.xlog1py, ('dd', 'DD'), None),249 (special.xlogy, cython_special.xlogy, ('dd', 'DD'), None),250 (special.y0, cython_special.y0, ('d',), None),251 (special.y1, cython_special.y1, ('d',), None),252 (special.yn, cython_special.yn, ('ld', 'dd'), None),253 (special.yv, cython_special.yv, ('dd', 'dD'), None),254 (special.yve, cython_special.yve, ('dd', 'dD'), None),255 (special.zetac, cython_special.zetac, ('d',), None),256 (special.owens_t, cython_special.owens_t, ('dd',), None)257]258IDS = [x[0].__name__ for x in PARAMS]259def _generate_test_points(typecodes):260 axes = tuple(map(lambda x: TEST_POINTS[x], typecodes))261 pts = list(product(*axes))262 return pts263def test_cython_api_completeness():264 # Check that everything is tested265 skip = {'hyp2f0', 'hyp1f2', 'hyp3f0'}266 for name in dir(cython_special):267 func = getattr(cython_special, name)268 if callable(func) and not (name.startswith('_') or name in skip):269 for _, cyfun, _, _ in PARAMS:270 if cyfun is func:271 break272 else:273 raise RuntimeError("{} missing from tests!".format(name))274@pytest.mark.parametrize("param", PARAMS, ids=IDS)275def test_cython_api(param):276 pyfunc, cyfunc, specializations, knownfailure = param277 if knownfailure:278 pytest.xfail(reason=knownfailure)279 # Check which parameters are expected to be fused types280 values = [set() for code in specializations[0]]281 for typecodes in specializations:282 for j, v in enumerate(typecodes):283 values[j].add(v)284 seen = set()285 is_fused_code = [False] * len(values)286 for j, v in enumerate(values):287 vv = tuple(sorted(v))288 if vv in seen:289 continue290 is_fused_code[j] = (len(v) > 1)291 seen.add(vv)292 # Check results293 for typecodes in specializations:294 # Pick the correct specialized function295 signature = [CYTHON_SIGNATURE_MAP[code]296 for j, code in enumerate(typecodes)297 if is_fused_code[j]]298 if signature:299 cy_spec_func = cyfunc[tuple(signature)]300 else:301 signature = None302 cy_spec_func = cyfunc303 # Test it304 pts = _generate_test_points(typecodes)305 for pt in pts:306 pyval = pyfunc(*pt)307 cyval = cy_spec_func(*pt)...

html.js

Source:html.js

1'use strict';2var NS = exports.NAMESPACES = {3 HTML: 'http:/​/​www.w3.org/​1999/​xhtml',4 MATHML: 'http:/​/​www.w3.org/​1998/​Math/​MathML',5 SVG: 'http:/​/​www.w3.org/​2000/​svg',6 XLINK: 'http:/​/​www.w3.org/​1999/​xlink',7 XML: 'http:/​/​www.w3.org/​XML/​1998/​namespace',8 XMLNS: 'http:/​/​www.w3.org/​2000/​xmlns/​'9};10exports.ATTRS = {11 TYPE: 'type',12 ACTION: 'action',13 ENCODING: 'encoding',14 PROMPT: 'prompt',15 NAME: 'name',16 COLOR: 'color',17 FACE: 'face',18 SIZE: 'size'19};20exports.DOCUMENT_MODE = {21 NO_QUIRKS: 'no-quirks',22 QUIRKS: 'quirks',23 LIMITED_QUIRKS: 'limited-quirks'24};25var $ = exports.TAG_NAMES = {26 A: 'a',27 ADDRESS: 'address',28 ANNOTATION_XML: 'annotation-xml',29 APPLET: 'applet',30 AREA: 'area',31 ARTICLE: 'article',32 ASIDE: 'aside',33 B: 'b',34 BASE: 'base',35 BASEFONT: 'basefont',36 BGSOUND: 'bgsound',37 BIG: 'big',38 BLOCKQUOTE: 'blockquote',39 BODY: 'body',40 BR: 'br',41 BUTTON: 'button',42 CAPTION: 'caption',43 CENTER: 'center',44 CODE: 'code',45 COL: 'col',46 COLGROUP: 'colgroup',47 DD: 'dd',48 DESC: 'desc',49 DETAILS: 'details',50 DIALOG: 'dialog',51 DIR: 'dir',52 DIV: 'div',53 DL: 'dl',54 DT: 'dt',55 EM: 'em',56 EMBED: 'embed',57 FIELDSET: 'fieldset',58 FIGCAPTION: 'figcaption',59 FIGURE: 'figure',60 FONT: 'font',61 FOOTER: 'footer',62 FOREIGN_OBJECT: 'foreignObject',63 FORM: 'form',64 FRAME: 'frame',65 FRAMESET: 'frameset',66 H1: 'h1',67 H2: 'h2',68 H3: 'h3',69 H4: 'h4',70 H5: 'h5',71 H6: 'h6',72 HEAD: 'head',73 HEADER: 'header',74 HGROUP: 'hgroup',75 HR: 'hr',76 HTML: 'html',77 I: 'i',78 IMG: 'img',79 IMAGE: 'image',80 INPUT: 'input',81 IFRAME: 'iframe',82 KEYGEN: 'keygen',83 LABEL: 'label',84 LI: 'li',85 LINK: 'link',86 LISTING: 'listing',87 MAIN: 'main',88 MALIGNMARK: 'malignmark',89 MARQUEE: 'marquee',90 MATH: 'math',91 MENU: 'menu',92 MENUITEM: 'menuitem',93 META: 'meta',94 MGLYPH: 'mglyph',95 MI: 'mi',96 MO: 'mo',97 MN: 'mn',98 MS: 'ms',99 MTEXT: 'mtext',100 NAV: 'nav',101 NOBR: 'nobr',102 NOFRAMES: 'noframes',103 NOEMBED: 'noembed',104 NOSCRIPT: 'noscript',105 OBJECT: 'object',106 OL: 'ol',107 OPTGROUP: 'optgroup',108 OPTION: 'option',109 P: 'p',110 PARAM: 'param',111 PLAINTEXT: 'plaintext',112 PRE: 'pre',113 RB: 'rb',114 RP: 'rp',115 RT: 'rt',116 RTC: 'rtc',117 RUBY: 'ruby',118 S: 's',119 SCRIPT: 'script',120 SECTION: 'section',121 SELECT: 'select',122 SOURCE: 'source',123 SMALL: 'small',124 SPAN: 'span',125 STRIKE: 'strike',126 STRONG: 'strong',127 STYLE: 'style',128 SUB: 'sub',129 SUMMARY: 'summary',130 SUP: 'sup',131 TABLE: 'table',132 TBODY: 'tbody',133 TEMPLATE: 'template',134 TEXTAREA: 'textarea',135 TFOOT: 'tfoot',136 TD: 'td',137 TH: 'th',138 THEAD: 'thead',139 TITLE: 'title',140 TR: 'tr',141 TRACK: 'track',142 TT: 'tt',143 U: 'u',144 UL: 'ul',145 SVG: 'svg',146 VAR: 'var',147 WBR: 'wbr',148 XMP: 'xmp'149};150var SPECIAL_ELEMENTS = exports.SPECIAL_ELEMENTS = Object.create(null);151SPECIAL_ELEMENTS[NS.HTML] = Object.create(null);152SPECIAL_ELEMENTS[NS.HTML][$.ADDRESS] = true;153SPECIAL_ELEMENTS[NS.HTML][$.APPLET] = true;154SPECIAL_ELEMENTS[NS.HTML][$.AREA] = true;155SPECIAL_ELEMENTS[NS.HTML][$.ARTICLE] = true;156SPECIAL_ELEMENTS[NS.HTML][$.ASIDE] = true;157SPECIAL_ELEMENTS[NS.HTML][$.BASE] = true;158SPECIAL_ELEMENTS[NS.HTML][$.BASEFONT] = true;159SPECIAL_ELEMENTS[NS.HTML][$.BGSOUND] = true;160SPECIAL_ELEMENTS[NS.HTML][$.BLOCKQUOTE] = true;161SPECIAL_ELEMENTS[NS.HTML][$.BODY] = true;162SPECIAL_ELEMENTS[NS.HTML][$.BR] = true;163SPECIAL_ELEMENTS[NS.HTML][$.BUTTON] = true;164SPECIAL_ELEMENTS[NS.HTML][$.CAPTION] = true;165SPECIAL_ELEMENTS[NS.HTML][$.CENTER] = true;166SPECIAL_ELEMENTS[NS.HTML][$.COL] = true;167SPECIAL_ELEMENTS[NS.HTML][$.COLGROUP] = true;168SPECIAL_ELEMENTS[NS.HTML][$.DD] = true;169SPECIAL_ELEMENTS[NS.HTML][$.DETAILS] = true;170SPECIAL_ELEMENTS[NS.HTML][$.DIR] = true;171SPECIAL_ELEMENTS[NS.HTML][$.DIV] = true;172SPECIAL_ELEMENTS[NS.HTML][$.DL] = true;173SPECIAL_ELEMENTS[NS.HTML][$.DT] = true;174SPECIAL_ELEMENTS[NS.HTML][$.EMBED] = true;175SPECIAL_ELEMENTS[NS.HTML][$.FIELDSET] = true;176SPECIAL_ELEMENTS[NS.HTML][$.FIGCAPTION] = true;177SPECIAL_ELEMENTS[NS.HTML][$.FIGURE] = true;178SPECIAL_ELEMENTS[NS.HTML][$.FOOTER] = true;179SPECIAL_ELEMENTS[NS.HTML][$.FORM] = true;180SPECIAL_ELEMENTS[NS.HTML][$.FRAME] = true;181SPECIAL_ELEMENTS[NS.HTML][$.FRAMESET] = true;182SPECIAL_ELEMENTS[NS.HTML][$.H1] = true;183SPECIAL_ELEMENTS[NS.HTML][$.H2] = true;184SPECIAL_ELEMENTS[NS.HTML][$.H3] = true;185SPECIAL_ELEMENTS[NS.HTML][$.H4] = true;186SPECIAL_ELEMENTS[NS.HTML][$.H5] = true;187SPECIAL_ELEMENTS[NS.HTML][$.H6] = true;188SPECIAL_ELEMENTS[NS.HTML][$.HEAD] = true;189SPECIAL_ELEMENTS[NS.HTML][$.HEADER] = true;190SPECIAL_ELEMENTS[NS.HTML][$.HGROUP] = true;191SPECIAL_ELEMENTS[NS.HTML][$.HR] = true;192SPECIAL_ELEMENTS[NS.HTML][$.HTML] = true;193SPECIAL_ELEMENTS[NS.HTML][$.IFRAME] = true;194SPECIAL_ELEMENTS[NS.HTML][$.IMG] = true;195SPECIAL_ELEMENTS[NS.HTML][$.INPUT] = true;196SPECIAL_ELEMENTS[NS.HTML][$.LI] = true;197SPECIAL_ELEMENTS[NS.HTML][$.LINK] = true;198SPECIAL_ELEMENTS[NS.HTML][$.LISTING] = true;199SPECIAL_ELEMENTS[NS.HTML][$.MAIN] = true;200SPECIAL_ELEMENTS[NS.HTML][$.MARQUEE] = true;201SPECIAL_ELEMENTS[NS.HTML][$.MENU] = true;202SPECIAL_ELEMENTS[NS.HTML][$.META] = true;203SPECIAL_ELEMENTS[NS.HTML][$.NAV] = true;204SPECIAL_ELEMENTS[NS.HTML][$.NOEMBED] = true;205SPECIAL_ELEMENTS[NS.HTML][$.NOFRAMES] = true;206SPECIAL_ELEMENTS[NS.HTML][$.NOSCRIPT] = true;207SPECIAL_ELEMENTS[NS.HTML][$.OBJECT] = true;208SPECIAL_ELEMENTS[NS.HTML][$.OL] = true;209SPECIAL_ELEMENTS[NS.HTML][$.P] = true;210SPECIAL_ELEMENTS[NS.HTML][$.PARAM] = true;211SPECIAL_ELEMENTS[NS.HTML][$.PLAINTEXT] = true;212SPECIAL_ELEMENTS[NS.HTML][$.PRE] = true;213SPECIAL_ELEMENTS[NS.HTML][$.SCRIPT] = true;214SPECIAL_ELEMENTS[NS.HTML][$.SECTION] = true;215SPECIAL_ELEMENTS[NS.HTML][$.SELECT] = true;216SPECIAL_ELEMENTS[NS.HTML][$.SOURCE] = true;217SPECIAL_ELEMENTS[NS.HTML][$.STYLE] = true;218SPECIAL_ELEMENTS[NS.HTML][$.SUMMARY] = true;219SPECIAL_ELEMENTS[NS.HTML][$.TABLE] = true;220SPECIAL_ELEMENTS[NS.HTML][$.TBODY] = true;221SPECIAL_ELEMENTS[NS.HTML][$.TD] = true;222SPECIAL_ELEMENTS[NS.HTML][$.TEMPLATE] = true;223SPECIAL_ELEMENTS[NS.HTML][$.TEXTAREA] = true;224SPECIAL_ELEMENTS[NS.HTML][$.TFOOT] = true;225SPECIAL_ELEMENTS[NS.HTML][$.TH] = true;226SPECIAL_ELEMENTS[NS.HTML][$.THEAD] = true;227SPECIAL_ELEMENTS[NS.HTML][$.TITLE] = true;228SPECIAL_ELEMENTS[NS.HTML][$.TR] = true;229SPECIAL_ELEMENTS[NS.HTML][$.TRACK] = true;230SPECIAL_ELEMENTS[NS.HTML][$.UL] = true;231SPECIAL_ELEMENTS[NS.HTML][$.WBR] = true;232SPECIAL_ELEMENTS[NS.HTML][$.XMP] = true;233SPECIAL_ELEMENTS[NS.MATHML] = Object.create(null);234SPECIAL_ELEMENTS[NS.MATHML][$.MI] = true;235SPECIAL_ELEMENTS[NS.MATHML][$.MO] = true;236SPECIAL_ELEMENTS[NS.MATHML][$.MN] = true;237SPECIAL_ELEMENTS[NS.MATHML][$.MS] = true;238SPECIAL_ELEMENTS[NS.MATHML][$.MTEXT] = true;239SPECIAL_ELEMENTS[NS.MATHML][$.ANNOTATION_XML] = true;240SPECIAL_ELEMENTS[NS.SVG] = Object.create(null);241SPECIAL_ELEMENTS[NS.SVG][$.TITLE] = true;242SPECIAL_ELEMENTS[NS.SVG][$.FOREIGN_OBJECT] = true;...

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