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求大佬用1stopt 跑下程序 我运行总是出错 不知道哪里错了已有1人参与
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求大佬用1stopt 跑下程序 我运行总是出错 不知道哪里错了 Parameters p1,p2; Variable t,y,x; ODEFunction y'=p1*y+p2*x; Data; 0 1.25664E-07 0 0.0001 0.000788493 0.003141591 0.0002 0.002423513 0.006283175 0.0003 0.004449871 0.009424743 0.0004 0.006657071 0.012566288 0.0005 0.00894778 0.015707802 0.0006 0.011276971 0.018849277 0.0007 0.013623798 0.021990705 0.0008 0.015978593 0.02513208 0.0009 0.018336855 0.028273392 0.001 0.020696472 0.031414635 0.0011 0.023056434 0.0345558 0.0012 0.025416244 0.037696879 0.0013 0.027775639 0.040837866 0.0014 0.030134467 0.043978752 0.0015 0.032492625 0.04711953 0.0016 0.034850035 0.050260191 0.0017 0.037206627 0.053400728 0.0018 0.03956234 0.056541134 0.0019 0.041917112 0.059681399 0.002 0.044270884 0.062821518 0.0021 0.046623598 0.065961482 0.0022 0.048975195 0.069101283 0.0023 0.051325618 0.072240913 0.0024 0.053674808 0.075380365 0.0025 0.056022709 0.078519632 0.0026 0.058369262 0.081658704 0.0027 0.060714413 0.084797575 0.0028 0.063058102 0.087936237 0.0029 0.065400276 0.091074681 0.003 0.067740876 0.094212901 0.0031 0.070079848 0.097350889 0.0032 0.072417136 0.100488636 0.0033 0.074752685 0.103626136 0.0034 0.07708644 0.10676338 0.0035 0.079418346 0.10990036 0.0036 0.081748349 0.113037069 0.0037 0.084076395 0.116173499 0.0038 0.086402432 0.119309643 0.0039 0.088726405 0.122445492 0.004 0.091048262 0.125581039 0.0041 0.09336795 0.128716276 0.0042 0.095685418 0.131851196 0.0043 0.098000614 0.13498579 0.0044 0.100313486 0.138120051 0.0045 0.102623984 0.141253972 0.0046 0.104932058 0.144387544 0.0047 0.107237657 0.147520759 0.0048 0.109540732 0.150653611 0.0049 0.111841233 0.153786091 0.005 0.114139113 0.156918191 0.0051 0.116434323 0.160049905 0.0052 0.118726815 0.163181223 0.0053 0.121016541 0.166312139 0.0054 0.123303456 0.169442644 0.0055 0.125587512 0.172572732 0.0056 0.127868664 0.175702393 0.0057 0.130146866 0.178831621 0.0058 0.132422074 0.181960408 0.0059 0.134694243 0.185088746 0.006 0.136963329 0.188216627 0.0061 0.139229288 0.191344043 0.0062 0.141492078 0.194470988 0.0063 0.143751656 0.197597453 0.0064 0.146007981 0.20072343 0.0065 0.14826101 0.203848912 0.0066 0.150510703 0.206973891 0.0067 0.15275702 0.210098359 0.0068 0.154999921 0.213222309 0.0069 0.157239367 0.216345732 0.007 0.159475318 0.219468622 0.0071 0.161707736 0.222590971 0.0072 0.163936584 0.22571277 0.0073 0.166161825 0.228834012 0.0074 0.168383421 0.23195469 0.0075 0.170601337 0.235074795 0.0076 0.172815537 0.23819432 0.0077 0.175025986 0.241313258 0.0078 0.177232649 0.2444316 0.0079 0.179435493 0.247549339 0.008 0.181634484 0.250666467 0.0081 0.183829589 0.253782977 0.0082 0.186020776 0.25689886 0.0083 0.188208013 0.26001411 0.0084 0.190391269 0.263128718 0.0085 0.192570512 0.266242677 0.0086 0.194745713 0.269355979 0.0087 0.196916843 0.272468616 0.0088 0.199083871 0.275580581 0.0089 0.201246769 0.278691866 0.009 0.20340551 0.281802464 0.0091 0.205560065 0.284912366 0.0092 0.207710408 0.288021565 0.0093 0.209856512 0.291130054 0.0094 0.211998351 0.294237824 0.0095 0.214135901 0.297344868 0.0096 0.216269135 0.300451178 0.0097 0.21839803 0.303556747 0.0098 0.220522561 0.306661567 0.0099 0.222642706 0.309765631 0.01 0.224758442 0.31286893 0.0101 0.226869746 0.315971457 0.0102 0.228976596 0.319073205 0.0103 0.231078971 0.322174165 0.0104 0.233176851 0.32527433 0.0105 0.235270215 0.328373693 0.0106 0.237359043 0.331472246 0.0107 0.239443317 0.33456998 0.0108 0.241523016 0.337666889 0.0109 0.243598124 0.340762965 0.011 0.245668621 0.343858201 0.0111 0.247734491 0.346952587 0.0112 0.249795717 0.350046118 0.0113 0.251852283 0.353138785 0.0114 0.253904172 0.356230581 0.0115 0.255951369 0.359321497 0.0116 0.257993859 0.362411527 0.0117 0.260031627 0.365500663 0.0118 0.26206466 0.368588897 0.0119 0.264092944 0.371676222 0.012 0.266116465 0.374762629 0.0121 0.268135211 0.377848112 0.0122 0.270149169 0.380932662 0.0123 0.272158329 0.384016273 0.0124 0.274162677 0.387098936 0.0125 0.276162203 0.390180644 0.0126 0.278156897 0.393261389 0.0127 0.280146748 0.396341164 0.0128 0.282131747 0.399419961 0.0129 0.284111883 0.402497772 0.013 0.286087149 0.405574591 0.0131 0.288057536 0.408650408 0.0132 0.290023034 0.411725218 0.0133 0.291983638 0.414799011 0.0134 0.293939338 0.417871781 0.0135 0.295890129 0.42094352 0.0136 0.297836003 0.42401422 0.0137 0.299776954 0.427083874 0.0138 0.301712977 0.430152474 0.0139 0.303644065 0.433220013 0.014 0.305570214 0.436286483 0.0141 0.307491418 0.439351876 0.0142 0.309407674 0.442416186 0.0143 0.311318976 0.445479403 0.0144 0.313225322 0.448541522 0.0145 0.315126707 0.451602534 0.0146 0.317023129 0.454662431 0.0147 0.318914584 0.457721207 0.0148 0.32080107 0.460778853 0.0149 0.322682586 0.463835363 0.015 0.324559128 0.466890728 0.0151 0.326430696 0.469944941 0.0152 0.328297288 0.472997994 0.0153 0.330158902 0.47604988 0.0154 0.33201554 0.479100592 0.0155 0.333867199 0.482150122 0.0156 0.335713881 0.485198462 0.0157 0.337555584 0.488245604 0.0158 0.33939231 0.491291542 0.0159 0.341224059 0.494336268 0.016 0.343050832 0.497379774 0.0161 0.34487263 0.500422053 0.0162 0.346689455 0.503463097 0.0163 0.348501309 0.506502899 0.0164 0.350308194 0.509541451 0.0165 0.352110111 0.512578746 0.0166 0.353907063 0.515614776 0.0167 0.355699053 0.518649534 0.0168 0.357486085 0.521683013 0.0169 0.35926816 0.524715204 0.017 0.361045283 0.5277461 0.0171 0.362817456 0.530775694 0.0172 0.364584685 0.533803979 0.0173 0.366346972 0.536830946 0.0174 0.368104323 0.539856589 0.0175 0.369856741 0.5428809 0.0176 0.371604232 0.545903871 0.0177 0.3733468 0.548925495 0.0178 0.375084449 0.551945765 0.0179 0.376817187 0.554964673 0.018 0.378545017 0.557982212 0.0181 0.380267945 0.560998374 0.0182 0.381985978 0.564013152 0.0183 0.38369912 0.567026538 0.0184 0.385407379 0.570038525 0.0185 0.387110761 0.573049105 0.0186 0.388809271 0.576058272 0.0187 0.390502917 0.579066017 0.0188 0.392191706 0.582072334 0.0189 0.393875644 0.585077214 0.019 0.395554738 0.58808065 0.0191 0.397228996 0.591082636 0.0192 0.398898424 0.594083163 0.0193 0.400563032 0.597082224 0.0194 0.402222825 0.600079812 0.0195 0.403877812 0.60307592 0.0196 0.405528002 0.606070539 0.0197 0.407173401 0.609063663 0.0198 0.408814018 0.612055284 0.0199 0.410449861 0.615045395 0.02 0.41208094 0.618033989 0.0201 0.413707261 0.621021057 0.0202 0.415328835 0.624006593 0.0203 0.416945669 0.62699059 0.0204 0.418557773 0.629973039 0.0205 0.420165155 0.632953934 0.0206 0.421767825 0.635933268 0.0207 0.423365792 0.638911032 0.0208 0.424959065 0.64188722 0.0209 0.426547653 0.644861824 0.021 0.428131566 0.647834836 0.0211 0.429710814 0.650806251 0.0212 0.431285405 0.653776059 0.0213 0.432855351 0.656744255 0.0214 0.43442066 0.65971083 0.0215 0.435981343 0.662675777 0.0216 0.437537409 0.665639089 0.0217 0.439088868 0.668600759 0.0218 0.440635732 0.671560779 0.0219 0.442178009 0.674519142 0.022 0.44371571 0.67747584 0.0221 0.445248846 0.680430868 0.0222 0.446777426 0.683384216 0.0223 0.448301462 0.686335878 0.0224 0.449820963 0.689285846 0.0225 0.451335941 0.692234114 0.0226 0.452846406 0.695180674 0.0227 0.454352368 0.698125518 0.0228 0.455853839 0.70106864 0.0229 0.457350829 0.704010033 0.023 0.45884335 0.706949688 0.0231 0.460331411 0.709887598 0.0232 0.461815024 0.712823757 0.0233 0.4632942 0.715758158 0.0234 0.464768949 0.718690792 0.0235 0.466239284 0.721621653 0.0236 0.467705215 0.724550733 0.0237 0.469166753 0.727478026 0.0238 0.470623909 0.730403524 0.0239 0.472076695 0.733327219 0.024 0.473525121 0.736249105 0.0241 0.4749692 0.739169175 0.0242 0.476408942 0.74208742 0.0243 0.477844359 0.745003835 0.0244 0.479275462 0.747918411 0.0245 0.480702262 0.750831142 0.0246 0.482124772 0.753742021 0.0247 0.483543001 0.756651039 0.0248 0.484956962 0.759558191 0.0249 0.486366667 0.762463469 0.025 0.487772126 0.765366865 0.0251 0.489173351 0.768268372 0.0252 0.490570355 0.771167985 0.0253 0.491963147 0.774065694 0.0254 0.49335174 0.776961493 0.0255 0.494736146 0.779855376 0.0256 0.496116375 0.782747334 0.0257 0.49749244 0.78563736 0.0258 0.498864352 0.788525449 0.0259 0.500232123 0.791411591 0.026 0.501595764 0.794295781 0.0261 0.502955287 0.797178011 0.0262 0.504310704 0.800058274 0.0263 0.505662026 0.802936564 0.0264 0.507009264 0.805812871 0.0265 0.508352431 0.808687191 0.0266 0.509691538 0.811559515 0.0267 0.511026597 0.814429837 0.0268 0.512357619 0.817298149 0.0269 0.513684616 0.820164445 0.027 0.515007599 0.823028717 0.0271 0.516326581 0.825890959 0.0272 0.517641572 0.828751162 0.0273 0.518952585 0.831609321 0.0274 0.520259631 0.834465427 0.0275 0.521562721 0.837319475 0.0276 0.522861867 0.840171457 0.0277 0.524157081 0.843021366 0.0278 0.525448375 0.845869194 0.0279 0.526735759 0.848714936 0.028 0.528019245 0.851558583 0.0281 0.529298846 0.854400129 0.0282 0.530574572 0.857239568 0.0283 0.531846435 0.860076891 0.0284 0.533114446 0.862912091 0.0285 0.534378617 0.865745163 0.0286 0.53563896 0.868576099 0.0287 0.536895486 0.871404891 0.0288 0.538148206 0.874231533 0.0289 0.539397131 0.877056019 0.029 0.540642274 0.87987834 0.0291 0.541883645 0.88269849 0.0292 0.543121256 0.885516462 0.0293 0.544355118 0.888332249 0.0294 0.545585243 0.891145845 0.0295 0.546811642 0.893957241 0.0296 0.548034326 0.896766432 0.0297 0.549253306 0.89957341 0.0298 0.550468594 0.902378169 0.0299 0.551680201 0.905180701 0.03 0.552888138 0.907980999 0.0301 0.554092417 0.910779058 0.0302 0.555293048 0.913574869 0.0303 0.556490042 0.916368425 0.0304 0.557683412 0.919159721 0.0305 0.558873167 0.921948749 0.0306 0.560059319 0.924735502 0.0307 0.561241879 0.927519973 0.0308 0.562420858 0.930302156 0.0309 0.563596266 0.933082043 0.031 0.564768116 0.935859629 0.0311 0.565936418 0.938634904 0.0312 0.567101182 0.941407864 0.0313 0.568262421 0.944178501 0.0314 0.569420143 0.946946809 0.0315 0.570574362 0.94971278 0.0316 0.571725086 0.952476407 0.0317 0.572872327 0.955237685 0.0318 0.574016096 0.957996605 0.0319 0.575156404 0.960753162 0.032 0.576293261 0.963507348 0.0321 0.577426677 0.966259157 0.0322 0.578556664 0.969008582 0.0323 0.579683233 0.971755615 0.0324 0.580806392 0.974500251 0.0325 0.581926155 0.977242483 0.0326 0.583042529 0.979982303 0.0327 0.584155527 0.982719706 0.0328 0.585265159 0.985454683 0.0329 0.586371435 0.988187229 0.033 0.587474366 0.990917337 0.0331 0.588573961 0.993645 0.0332 0.589670232 0.996370211 0.0333 0.590763189 0.999092963 0.0334 0.591852841 1.001813251 0.0335 0.592939199 1.004531066 0.0336 0.594022274 1.007246403 0.0337 0.595102075 1.009959255 0.0338 0.596178613 1.012669615 0.0339 0.597251898 1.015377476 0.034 0.59832194 1.018082832 0.0341 0.599388748 1.020785675 0.0342 0.600452334 1.023486 0.0343 0.601512707 1.0261838 0.0344 0.602569877 1.028879068 0.0345 0.603623853 1.031571797 0.0346 0.604674646 1.03426198 0.0347 0.605722266 1.036949612 0.0348 0.606766723 1.039634685 0.0349 0.607808026 1.042317193 0.035 0.608846185 1.044997129 0.0351 0.60988121 1.047674487 0.0352 0.61091311 1.05034926 0.0353 0.611941895 1.053021441 0.0354 0.612967576 1.055691024 0.0355 0.613990161 1.058358002 0.0356 0.615009659 1.061022369 0.0357 0.616026082 1.063684117 0.0358 0.617039437 1.066343241 0.0359 0.618049735 1.068999735 0.036 0.619056985 1.07165359 0.0361 0.620061197 1.074304801 0.0362 0.621062379 1.076953362 0.0363 0.622060541 1.079599265 0.0364 0.623055693 1.082242504 0.0365 0.624047844 1.084883073 0.0366 0.625037002 1.087520966 0.0367 0.626023178 1.090156174 0.0368 0.62700638 1.092788693 0.0369 0.627986617 1.095418516 0.037 0.628963899 1.098045636 0.0371 0.629938235 1.100670047 0.0372 0.630909634 1.103291741 0.0373 0.631878104 1.105910714 0.0374 0.632843655 1.108526957 0.0375 0.633806295 1.111140466 0.0376 0.634766035 1.113751233 0.0377 0.635722881 1.116359252 0.0378 0.636676844 1.118964516 0.0379 0.637627932 1.12156702 0.038 0.638576154 1.124166756 0.0381 0.639521519 1.126763718 0.0382 0.640464035 1.1293579 0.0383 0.641403711 1.131949296 0.0384 0.642340556 1.134537898 0.0385 0.643274578 1.137123701 0.0386 0.644205786 1.139706699 0.0387 0.645134188 1.142286884 0.0388 0.646059794 1.144864251 0.0389 0.646982611 1.147438793 0.039 0.647902648 1.150010504 0.0391 0.648819913 1.152579377 0.0392 0.649734415 1.155145407 0.0393 0.650646162 1.157708586 0.0394 0.651555162 1.160268909 0.0395 0.652461424 1.162826369 0.0396 0.653364956 1.165380959 0.0397 0.654265766 1.167932675 0.0398 0.655163863 1.170481508 0.0399 0.656059254 1.173027453 0.04 0.656951948 1.175570505 0.0401 0.657841953 1.178110655 0.0402 0.658729276 1.180647899 0.0403 0.659613926 1.183182229 0.0404 0.660495912 1.18571364 0.0405 0.66137524 1.188242126 0.0406 0.662251919 1.190767679 0.0407 0.663125956 1.193290295 0.0408 0.663997361 1.195809966 0.0409 0.664866139 1.198326687 0.041 0.6657323 1.200840451 0.0411 0.666595851 1.203351252 0.0412 0.6674568 1.205859083 0.0413 0.668315154 1.20836394 0.0414 0.669170922 1.210865815 0.0415 0.67002411 1.213364702 0.0416 0.670874727 1.215860595 0.0417 0.67172278 1.218353489 0.0418 0.672568277 1.220843376 0.0419 0.673411224 1.223330251 0.042 0.674251631 1.225814107 0.0421 0.675089504 1.228294939 0.0422 0.67592485 1.23077274 0.0423 0.676757677 1.233247505 0.0424 0.677587993 1.235719226 0.0425 0.678415805 1.238187899 0.0426 0.67924112 1.240653516 0.0427 0.680063945 1.243116072 0.0428 0.680884288 1.245575561 0.0429 0.681702156 1.248031977 0.043 0.682517556 1.250485313 0.0431 0.683330495 1.252935563 0.0432 0.684140981 1.255382723 0.0433 0.68494902 1.257826784 0.0434 0.68575462 1.260267742 0.0435 0.686557787 1.262705591 0.0436 0.68735853 1.265140324 0.0437 0.688156854 1.267571935 0.0438 0.688952767 1.270000419 0.0439 0.689746276 1.272425769 0.044 0.690537387 1.274847979 0.0441 0.691326107 1.277267044 0.0442 0.692112445 1.279682958 0.0443 0.692896405 1.282095714 0.0444 0.693677995 1.284505306 0.0445 0.694457222 1.286911729 0.0446 0.695234092 1.289314977 0.0447 0.696008613 1.291715044 0.0448 0.69678079 1.294111923 0.0449 0.697550632 1.296505609 0.045 0.698318143 1.298896097 0.0451 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1.990522804 0.0939 0.876838628 1.990825823 0.094 0.876901006 1.991123929 0.0941 0.876962357 1.991417123 0.0942 0.87702268 1.991705402 0.0943 0.877081976 1.991988768 0.0944 0.877140246 1.992267218 0.0945 0.877197489 1.992540753 0.0946 0.877253706 1.992809371 0.0947 0.877308897 1.993073073 0.0948 0.877363063 1.993331856 0.0949 0.877416204 1.993585721 0.095 0.87746832 1.993834667 0.0951 0.877519412 1.994078694 0.0952 0.877569479 1.994317801 0.0953 0.877618523 1.994551986 0.0954 0.877666543 1.99478125 0.0955 0.87771354 1.995005593 0.0956 0.877759513 1.995225013 0.0957 0.877804464 1.99543951 0.0958 0.877848393 1.995649083 0.0959 0.877891299 1.995853732 0.096 0.877933183 1.996053457 0.0961 0.877974046 1.996248256 0.0962 0.878013887 1.996438131 0.0963 0.878052707 1.996623079 0.0964 0.878090505 1.9968031 0.0965 0.878127283 1.996978195 0.0966 0.87816304 1.997148362 0.0967 0.878197777 1.997313602 0.0968 0.878231494 1.997473913 0.0969 0.878264191 1.997629296 0.097 0.878295867 1.99777975 0.0971 0.878326525 1.997925274 0.0972 0.878356163 1.998065869 0.0973 0.878384781 1.998201534 0.0974 0.87841238 1.998332269 0.0975 0.878438961 1.998458072 0.0976 0.878464523 1.998578945 0.0977 0.878489066 1.998694887 0.0978 0.87851259 1.998805897 0.0979 0.878535097 1.998911975 0.098 0.878556585 1.999013121 0.0981 0.878577055 1.999109334 0.0982 0.878596507 1.999200615 0.0983 0.878614941 1.999286963 0.0984 0.878632357 1.999368379 0.0985 0.878648756 1.99944486 0.0986 0.878664137 1.999516409 0.0987 0.878678501 1.999583024 0.0988 0.878691847 1.999644705 0.0989 0.878704176 1.999701452 0.099 0.878715488 1.999753265 0.0991 0.878725783 1.999800144 0.0992 0.878735061 1.999842088 0.0993 0.878743321 1.999879099 0.0994 0.878750565 1.999911174 0.0995 0.878756792 1.999938315 0.0996 0.878762001 1.999960522 0.0997 0.878766194 1.999977793 0.0998 0.87876937 1.99999013 0.0999 0.87877153 1.999997533 0.1 0.878772672 2 |
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【答案】应助回帖
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用OpenLu(可从www.forcal.net下载)求解。 本例的难点在于微分方程拟合时要传递参数x(中间变量),这对Lu脚本来说不是问题,gsl支持的Lu扩展数学库中求解微分方程的函数gsl_ode中提供了该功能。 进一步讨论:微分方程求解传递中间变量时,按时间t的改变量进行插值,可提高求解精度。例如,进行线性插值,需传递一个数组 x4[t0,t1,x0,x1],这样 x=x0+(x1-x0)*[(t-t0)/(t1-t0)] 。 取部分数据拟合,Lu代码: !!!using["luopt","math","win"]; //使用命名空间 f(t,y,dy,x4 : t0,t1,x0,x1,x : p1,p2)= { in[x4, 0, &t0,&t1,&x0,&x1], //取出数据 x=x0+(x1-x0)*[(t-t0)/(t1-t0)], //线性插值计算x dy=p1*y+p2*x, 0 //成功返回0 }; 目标函数(_p1,_p2 : i,s,y0,tf : tA,yA,xA,max,x4,t2,y1, p1,p2)= { p1=_p1, p2=_p2, //传递优化变量 y0=1.25664E-07, //初值 i=0, s=0, while{++i<max, SetArray{x4 : tA[i-1,0], tA[i,0], xA[i-1,0], xA[i,0]}, //准备传递数据 t2[0]=tA[i-1,0], t2[1]=tA[i,0], y1[0]=y0, //最后一个参数50表示gsl_ode函数在计算时,最多循环计算50次,这样可以提高速度 tf=gsl_ode[@f, nil, x4, t2, y1, 1e-6, 1e-6, gsl_rkf45, 1e-6,50], y0=tf(1,1), s=s+[y0-yA(i,0)]^2.0 }, s }; main(: tyArray : tA,yA,xA,max,x4,t2,y1)= { tyArray=matrix{ //存放实验数据 "0 1.25664E-07 0 0.005 0.114139113 0.156918191 0.01 0.224758442 0.31286893 0.015 0.324559128 0.466890728 0.02 0.41208094 0.618033989 0.025 0.487772126 0.765366865 0.03 0.552888138 0.907980999 0.035 0.608846185 1.044997129 0.04 0.656951948 1.175570505 0.045 0.698318143 1.298896097 0.05 0.733862018 1.414213562 0.055 0.764329017 1.520811931 0.06 0.790321332 1.618033989 0.065 0.812323879 1.705280329 0.07 0.83072574 1.782013048 0.075 0.845837104 1.847759065 0.08 0.857902342 1.902113033 0.085 0.867109907 1.944739841 0.09 0.873599694 1.975376681 0.095 0.87746832 1.993834667 0.1 0.878772672 2 " }, len[tyArray,0,&max], tA=tyArray(all:0), yA=tyArray(all:1), xA=tyArray(all:2), //用len函数取矩阵的行数,tA取矩阵的列 x4=ra1[0,0,0,0], t2=ra1[0,0], y1=ra1[0], //准备数组 Opt1[@目标函数] //Opt1函数全局优化 }; 结果: -32997.3853793671 15830.42381251212 0.1177179718140771 因模型与数据匹配不好,故效果图就不提供了,本例的意义在于微分方程拟合时如何传递中间参数。 |
2楼2021-08-10 11:18:31














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