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1stopt 7参数拟合求助 已有2人参与
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需要根据两个式子（一个微分方程，一个代数方程）拟合7个未知参数fac(1)~fac(7)，网上下载的软件有参数限制，想向有正版软件的朋友求助，帮忙拟合一下。写了两版，程序分别如下。完整程序和数据放在了文件里，不知为什么上传失败，只能贴一下网盘链接，麻烦大家了。 链接：https://pan.baidu.com/s/18yjg6HL9hhQ5hmjGdjFhEQ 提取码：8xmm 第一种： //title "fit"; parameter fac(1:7); variable t,lamb,pa,p,lambv; odefunction lambv'=((1/3/fac(7))*(fac(1)*((lamb/lambv)^fac(2)-(lambv/lamb)^(0.5*fac(2)))+fac(3)*((lamb/lambv)^fac(4)-(lambv/lamb)^(0.5*fac(4)))+fac(5)*((lamb/lambv)^fac(6)-(lambv/lamb)^(0.5*fac(6))))); p=(pa+fac(1)*((lamb/lambv)^fac(2)/lamb-(lambv/lamb)^(fac(2)*0.5)/lamb)+fac(3)*((lamb/lambv)^fac(4)/lamb-(lambv/lamb)^(fac(4)*0.5)/lamb)+fac(5)*((lamb/lambv).^fac(6)/lamb-(lambv/lamb)^(fac(6)*0.5)/lamb)); //根据上面两个式子拟合fac(1)~fac(7)，共计7个参数。lambv为中间变量 data; //t,lamb,pa,p 第二种： //title "fit"; parameter fac(1:7); variable t,lamb,pa,p; conststr lambvdif=((1/3/fac(7))*(fac(1)*((lamb/lambv)^fac(2)-(lambv/lamb)^(0.5*fac(2)))+fac(3)*((lamb/lambv)^fac(4)-(lambv/lamb)^(0.5*fac(4)))+fac(5)*((lamb/lambv)^fac(6)-(lambv/lamb)^(0.5*fac(6))))); function p=(pa+fac(1)*((lamb/lambv)^fac(2)/lamb-(lambv/lamb)^(fac(2)*0.5)/lamb)+fac(3)*((lamb/lambv)^fac(4)/lamb-(lambv/lamb)^(fac(4)*0.5)/lamb)+fac(5)*((lamb/lambv).^fac(6)/lamb-(lambv/lamb)^(fac(6)*0.5)/lamb)); //根据上面两个式子拟合fac(1)~fac(7)，共计7个参数。lambv为中间变量 data; //t,lamb,pa,p |
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独孤神宇
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2楼2021-07-20 22:43:35
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您好，我用微分方程组的形式写了一下程序，可以麻烦您帮我跑一下看看吗 Parameter fac(1:7); ConstStr lambdif=A*w*cos(w*t); lambvdif=((1/3/fac(7))*(fac(1)*((lamb/lambv)^fac(2)-(lambv/lamb)^(0.5*fac(2)))+fac(3)*((lamb/lambv)^fac(4)-(lambv/lamb)^(0.5*fac(4)))+fac(5)*((lamb/lambv)^fac(6)-(lambv/lamb)^(0.5*fac(6))))); Variable t,lamb,pa,p; Constant A=0.02,w=2*pi*0.1; ODEFunction p'=pa+fac(1)*((fac(2)-1)*lamb^(fac(2)-2)*lambv^(-fac(2))*lambdif-fac(2)*lamb^(fac(2)-1)*lambv^(-fac(2)-1)*lambvdif+(0.5*fac(2)+1)*lamb^(-0.5*fac(2)-2)*lambv^(0.5*fac(2))*lambdif-0.5*fac(2)*lamb^(-0.5*fac(2)-1)*lambv^(0.5*fac(2)-1)*lambvdif)+fac(3)*((fac(4)-1)*lamb^(fac(4)-2)*lambv^(-fac(4))*lambdif-fac(4)*lamb^(fac(4)-1)*lambv^(-fac(4)-1)*lambvdif+(0.5*fac(4)+1)*lamb^(-0.5*fac(4)-2)*lambv^(0.5*fac(4))*lambdif-0.5*fac(4)*lamb^(-0.5*fac(4)-1)*lambv^(0.5*fac(4)-1)*lambvdif)+fac(5)*((fac(6)-1)*lamb^(fac(6)-2)*lambv^(-fac(6))*lambdif-fac(6)*lamb^(fac(6)-1)*lambv^(-fac(6)-1)*lambvdif+(0.5*fac(6)+1)*lamb^(-0.5*fac(6)-2)*lambv^(0.5*fac(6))*lambdif-0.5*fac(6)*lamb^(-0.5*fac(6)-1)*lambv^(0.5*fac(6)-1)*lambvdif); //根据上面两个式子拟合fac(1)~fac(7)，共计7个参数。lambv为中间变量 Data; //t,lamb,pa,p 0 0.959926667213440 -0.218715993911157 -0.0609662220570843 0.0100000000000000 0.960060000419617 -0.217953308698164 -0.0601988575052841 0.0200000000000000 0.960183332761129 -0.217248055533299 -0.0586004556313694 0.0300000000000000 0.960310000181198 -0.216523956896799 -0.0598319351599084 0.0400000000000000 0.960420000155767 -0.215895323573625 -0.0592181922334017 0.0500000000000000 0.960559999942780 -0.215095494743585 -0.0577557643513868 0.0600000000000000 0.960676667292913 -0.214429178596415 -0.0563035568552177 0.0700000000000000 0.960810000101725 -0.213667918567369 -0.0562269347026404 0.0800000000000000 0.960936667521795 -0.212944948052557 -0.0564259238264651 0.0900000000000000 0.961046667098999 -0.212317295943482 -0.0537828971720869 0.100000000000000 0.961189999580383 -0.211499705156834 -0.0547939745570696 0.110000000000000 0.961310000419617 -0.210815425359240 -0.0536558808743694 0.120000000000000 0.961439999739329 -0.210074361156256 -0.0552049394966249 0.130000000000000 0.961553332805634 -0.209428498212864 -0.0533279895347856 0.140000000000000 0.961696667273839 -0.208611922930574 -0.0547945686849519 0.150000000000000 0.961800000270208 -0.208023415546762 -0.0532876594536559 0.160000000000000 0.961940000057221 -0.207226321745154 -0.0509894265270881 0.170000000000000 0.962063333988190 -0.206524344385847 -0.0501778902776873 0.180000000000000 0.962169999678930 -0.205917410019245 -0.0502746930628899 0.190000000000000 0.962316667238871 -0.205083123883024 -0.0495968417849477 0.200000000000000 0.962433333396912 -0.204419710035615 -0.0472132050693843 0.210000000000000 0.962576666275660 -0.203604919455239 -0.0484606909901491 0.220000000000000 0.962676665782928 -0.203036632647645 -0.0495768924563658 0.230000000000000 0.962816666762034 -0.202241257206550 -0.0508967558960456 0.240000000000000 0.962926666736603 -0.201616516537996 -0.0476233841843231 0.250000000000000 0.963063333431880 -0.200840559228892 -0.0468362780039746 0.260000000000000 0.963176666895549 -0.200197280019895 -0.0486882526110127 0.270000000000000 0.963316667079926 -0.199402888747258 -0.0454051383025184 0.280000000000000 0.963433334032695 -0.198741104393035 -0.0452764009626071 0.290000000000000 0.963550000190735 -0.198079514508925 -0.0448494356201968 0.300000000000000 0.963679999907811 -0.197342536339294 -0.0449833927792348 0.310000000000000 0.963783333698909 -0.196756897310271 -0.0426126775765766 0.320000000000000 0.963916666507721 -0.196001460068449 -0.0441506994685100 0.330000000000000 0.964036666949590 -0.195321772871168 -0.0425706893672636 0.340000000000000 0.964173332850138 -0.194547935703942 -0.0438506779501000 0.350000000000000 0.964290000597636 -0.193887538472069 -0.0417353759771666 0.360000000000000 0.964416666428248 -0.193170761056756 -0.0438396124512487 0.370000000000000 0.964553333918254 -0.192397635767639 -0.0429577403349063 0.380000000000000 0.964653333822886 -0.191832102284730 -0.0409461894762005 0.390000000000000 0.964793333609899 -0.191040588507138 -0.0417681424238785 0.400000000000000 0.964893333117167 -0.190475389506915 -0.0403640892202786 0.410000000000000 0.965033333698908 -0.189684336018058 -0.0395319429176814 0.420000000000000 0.965153333346049 -0.189006510522505 -0.0396276800113452 0.430000000000000 0.965280000766118 -0.188291237369717 -0.0385797461602765 0.440000000000000 0.965410000085831 -0.187557379585116 -0.0385647679180981 0.450000000000000 0.965513333479563 -0.186974219511924 -0.0377487349326589 0.460000000000000 0.965636665821075 -0.186278388275524 -0.0369432895124589 0.470000000000000 0.965739999214808 -0.185695550701227 -0.0385068828949284 0.480000000000000 0.965873333215713 -0.184943715898085 -0.0363684893042258 0.490000000000000 0.965996665954590 -0.184248493064694 -0.0350844423645908 0.500000000000000 0.966119999885559 -0.183553472396837 -0.0350422560310213 0.510000000000000 0.966236666838328 -0.182896214094321 -0.0357082890947156 0.520000000000000 0.966343333721161 -0.182295455797467 -0.0344226096619861 0.530000000000000 0.966483333508174 -0.181507199906605 -0.0344232075748849 0.540000000000000 0.966569999456406 -0.181019369758473 -0.0337612557794114 0.550000000000000 0.966713333129883 -0.180212790651351 -0.0328476531863676 0.560000000000000 0.966833333174388 -0.179537732473905 -0.0325253978559010 0.570000000000000 0.966953334013621 -0.178862866531231 -0.0332915932673917 0.580000000000000 0.967066667079926 -0.178225679580843 -0.0316902061386422 0.590000000000000 0.967166666587194 -0.177663602741103 -0.0315181295683456 0.600000000000000 0.967303333679835 -0.176895645311491 -0.0325612034572683 0.610000000000000 0.967396666606267 -0.176371336695062 -0.0309402003803836 0.620000000000000 0.967536666393280 -0.175585093835344 -0.0312076525270728 0.630000000000000 0.967653333346049 -0.174930092472352 -0.0308357845343375 0.640000000000000 0.967749999761581 -0.174387519925182 -0.0291192343976965 0.650000000000000 0.967886667251587 -0.173620644511959 -0.0285421873746685 0.660000000000000 0.967986666758855 -0.173059682888543 -0.0285225129376410 0.670000000000000 0.968120000362396 -0.172311939786930 -0.0267974070448110 0.680000000000000 0.968226666450501 -0.171713923202809 -0.0274131745724031 0.690000000000000 0.968336667617162 -0.171097370069903 -0.0267161701869239 0.700000000000000 0.968463333050410 -0.170387617041473 -0.0258419432819456 0.710000000000000 0.968573333422343 -0.169771420474682 -0.0258780128939212 0.720000000000000 0.968689999580383 -0.169118062356982 -0.0272440635226749 0.730000000000000 0.968783333698909 -0.168595501500778 -0.0253793840193742 0.740000000000000 0.968916666905085 -0.167849196856469 -0.0264425615317059 0.750000000000000 0.969016666809718 -0.167289625665833 -0.0244389879012050 0.760000000000001 0.969113333225250 -0.166748835804261 -0.0231584760478411 0.770000000000001 0.969256667693456 -0.165947198113151 -0.0226372159513464 0.780000000000001 0.969343333641688 -0.165462628897229 -0.0234939984434984 0.790000000000001 0.969470000267029 -0.164754588351801 -0.0222578608226590 0.800000000000001 0.969576666355133 -0.164158513908713 -0.0236720328297027 0.810000000000001 0.969686666329702 -0.163543968928945 -0.0237222206510110 0.820000000000001 0.969803333282471 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1.49000000000000 0.976066666841507 -0.128174463951086 -0.00567856775016018 1.50000000000000 0.976123333374659 -0.127862697050313 -0.00679508718595573 1.51000000000000 0.976206665833791 -0.127404295173509 -0.00606474724543268 1.52000000000000 0.976286667188009 -0.126964301415781 -0.00591084743659025 1.53000000000000 0.976373333136241 -0.126487746458794 -0.00515028595828926 1.54000000000000 0.976420000394185 -0.126231174577858 -0.00580364021825536 1.55000000000000 0.976506667137146 -0.125754763834189 -0.00399862953750100 1.56000000000000 0.976590000391007 -0.125296768436358 -0.00553045896313559 1.57000000000000 0.976653332710266 -0.124948756822278 -0.00525656545380120 1.58000000000000 0.976700000365575 -0.124692350624149 -0.00647749227391488 1.59000000000000 0.976790000200272 -0.124197943259200 -0.00561358559725699 1.60000000000000 0.976853334108988 -0.123850085447757 -0.00474168051791277 1.61000000000000 0.976913332939148 -0.123520592798238 -0.00422623112262671 1.62000000000000 0.976973333756129 -0.123191135376305 -0.00415277659066092 1.63000000000000 0.977050000429154 -0.122770234815717 -0.00463853748062707 1.64000000000000 0.977129999796550 -0.122331117983482 -0.00409135493502994 1.65000000000000 0.977176666657130 -0.122075001237547 -0.00440044737324113 1.66000000000000 0.977239999771118 -0.121727461439988 -0.00300569597944612 1.67000000000000 0.977296666701635 -0.121416545739723 -0.00316428837175479 1.68000000000000 0.977370000282923 -0.121014245698521 -0.00316819237219542 1.69000000000000 0.977439999977748 -0.120630299103985 -0.00333913222417426 1.70000000000000 0.977500000000000 -0.120301250283446 -0.00460603563632659 1.71000000000000 0.977553333441416 -0.120008800548805 -0.00286257019926090 1.72000000000000 0.977610000371933 -0.119698111670606 -0.00331784950939558 1.73000000000000 0.977679999272029 -0.119314383909412 -0.00272281543881660 1.74000000000000 0.977743332783381 -0.118967249068857 -0.00271987920981313 1.75000000000000 0.977786667346954 -0.118729759148057 -0.00291984239228051 1.76000000000000 0.977849999666214 -0.118382716954719 -0.00265887138358447 1.77000000000000 0.977900000015895 -0.118108766071159 -0.00304781865782646 1.78000000000000 0.977970000505447 -0.117725288324857 -0.00148861976742845 1.79000000000000 0.978019999663035 -0.117451420372089 -0.00414695289290331 1.80000000000000 0.978063333431880 -0.117214087498257 -0.00220443687694125 1.81000000000000 0.978119999567668 -0.116903771198761 -0.00244294833954917 1.82000000000000 0.978183333476385 -0.116556989029199 -0.00345659633596527 1.83000000000000 0.978249999682109 -0.116192016097293 -0.00379151467155537 1.84000000000000 0.978293333450953 -0.115954809956241 -0.00196670082839388 1.85000000000000 0.978330000638962 -0.115754114865117 -0.00343401219441312 1.86000000000000 0.978363333543142 -0.115571684543762 -0.00216514673934279 1.87000000000000 0.978426667054494 -0.115225100366517 -0.00420038864217331 1.88000000000000 0.978480000098546 -0.114933281902525 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0.979503333568573 -0.109340960272890 -0.00100693017391792 2.16000000000000 0.979539999961853 -0.109140830962900 0 2.17000000000000 0.979563333590825 -0.109013482207766 -0.00231125194412904 2.18000000000000 0.979586666822433 -0.108886142482770 -0.00178229371672884 2.19000000000000 0.979620000123978 -0.108704239870753 -0.00255076939499388 2.20000000000000 0.979636666774750 -0.108613293814128 -0.000800200785157157 2.21000000000000 0.979660000801086 -0.108485971310552 -0.000316767290521802 2.22000000000000 0.979683332840602 -0.108358666504859 -0.00268006280942534 2.23000000000000 0.979709999561310 -0.108213175330761 -0.00203133868584265 2.24000000000000 0.979729999303818 -0.108104064451914 -0.00179167301339058 2.25000000000000 0.979743333260218 -0.108031322328111 -0.00116367640768096 2.26000000000000 0.979763333797455 -0.107922215506472 -0.00156989833625272 2.27000000000000 0.979779999653498 -0.107831303865221 -0.00365339419267337 2.28000000000000 0.979806667168935 -0.107685840805742 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-0.107267704125400 -0.00789672304202340 2.68999999999999 0.979879999160767 -0.107285883574300 -0.00702927783211347 2.69999999999999 0.979856667121252 -0.107413130626981 -0.00667694024627001 2.70999999999999 0.979840000073115 -0.107504032692458 -0.00668806982554102 2.71999999999999 0.979820000727971 -0.107613113715511 -0.00945740192394345 2.72999999999999 0.979806666771571 -0.107685842973174 -0.00812179898087077 2.73999999999999 0.979789999723435 -0.107776755523851 -0.00917126175905406 2.74999999999999 0.979766666889191 -0.107904033332083 -0.00972369676888354 2.75999999999999 0.979743333260218 -0.108031322328111 -0.00978176787343009 2.76999999999999 0.979739999771118 -0.108049507649231 -0.0106328714583969 2.77999999999998 0.979706666469574 -0.108231359882885 -0.0113300882239846 2.78999999999998 0.979693333307902 -0.108304103826230 -0.00936222048583495 2.79999999999998 0.979660000403722 -0.108485973478719 -0.0117506887026474 2.80999999999998 0.979639999866486 -0.108595106323666 -0.0119864429172659 2.81999999999998 0.979606666564941 -0.108777000536710 -0.0116921036422925 2.82999999999998 0.979589999914169 -0.108867952892690 -0.0123121088826255 |
3楼2021-07-21 10:38:20
独孤神宇
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这个可能需要企业版才能计算吧。 这个是否有可能 求解x的解析解？ ，这样就可以直接带入p方程拟合 Parameter fac(1:7); Variable t,lamb,pa,p; ParVariable lambv; Constant A=0.02,w=2*pi*0.1; ConstStr lambdif=A*w*cos(w*t), lambvdif=((1/3/fac7)*(fac1*((lamb/lambv)^fac2-(lambv/lamb)^(0.5*fac2))+fac3*((lamb/lambv)^fac4 -(lambv/lamb)^(0.5*fac4))+fac5*((lamb/lambv)^fac6-(lambv/lamb)^(0.5*fac6)))); //InitialODEValue t=0,p=-0.060966222; OdeFunction p'=pa+fac1*((fac2-1)*lamb^(fac2-2)*lambv^(-fac2)*lambdif-fac2*lamb^(fac2-1)*lambv^(-fac2-1)*lambvdif +(0.5*fac2+1)*lamb^(-0.5*fac2-2)*lambv^(0.5*fac2)*lambdif-0.5*fac2*lamb^(-0.5*fac2-1)*lambv^(0.5*fac2-1)*lambvdif) +fac3*((fac4-1)*lamb^(fac4-2)*lambv^(-fac4)*lambdif-fac4*lamb^(fac4-1)*lambv^(-fac4-1)*lambvdif+(0.5*fac4+1)*lamb^(-0.5*fac4-2)*lambv^(0.5*fac4)*lambdif -0.5*fac4*lamb^(-0.5*fac4-1)*lambv^(0.5*fac4-1)*lambvdif)+fac5*((fac6-1)*lamb^(fac6-2)*lambv^(-fac6)*lambdif -fac6*lamb^(fac6-1)*lambv^(-fac6-1)*lambvdif+(0.5*fac6+1)*lamb^(-0.5*fac6-2)*lambv^(0.5*fac6)*lambdif -0.5*fac6*lamb^(-0.5*fac6-1)*lambv^(0.5*fac6-1)*lambvdif); Data; 0 0.959926667 -0.218715994 -0.060966222 0.25 0.963063333 -0.200840559 -0.046836278 0.5 0.96612 -0.183553472 -0.035042256 0.75 0.969016667 -0.167289626 -0.024438988 1 0.97171 -0.152268899 -0.01706765 1.25 0.97409 -0.139075651 -0.010939712 1.5 0.976123333 -0.127862697 -0.006795087 1.75 0.977786667 -0.118729759 -0.002919842 2 0.979000001 -0.112089924 -0.001981819 2.25 0.979743333 -0.108031322 -0.001163676 2.5 0.98001 -0.106577018 -0.003491456 2.75 0.979766667 -0.107904033 -0.009723697 |
» 本帖已获得的红花（最新10朵）
ckm08114楼2021-07-21 20:06:35
5楼2021-07-22 19:31:12
独孤神宇
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【答案】应助回帖
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可以参考一下这个结果。 数据点太多了，数据趋势明显，可以抽取部分数据拟合。 均方差(RMSE): 8.9424225760802E-18 残差平方和(SSR): 1.91920611670053E-33 相关系数(R): 0.458333333333333 相关系数之平方(R^2): 0.210069444444444 修正R平方(Adj. R^2): 0.261904761904762 确定系数(DC): 0.458333333333333 F统计(F-Statistic): -5.22814936168938E29 参数 最佳估算 -------------------- ------------- fac1 3.03402198409604 fac2 0.426767353785268 fac3 -0.162134252603988 fac4 0 fac5 0 fac6 2.21639117580836 fac7 0.00666909053919589 lambv0 -0.0642609952712269 lambv1 -0.122299617461866 lambv2 -0.179059212190809 lambv3 -0.221947016217867 lambv4 -0.260568155058273 lambv5 -0.288634667671384 lambv6 -0.316783379508389 lambv7 -0.323931620009045 lambv8 -0.33038253736283 lambv9 -0.311755103592339 lambv10 -0.262350065039908 lambv11 0 ====== 结果输出 ====== 文件: 数据文件-1 No t 目标 p 计算 p 目标 lambv 计算 lambv 1 0.25 -0.046836278 -0.046836278 0 0 2 0.5 -0.035042256 -0.035042256 0 0 3 0.75 -0.024438988 -0.024438988 0 0 4 1 -0.01706765 -0.01706765 0 0 5 1.25 -0.010939712 -0.010939712 0 0 6 1.5 -0.006795087 -0.00679508699999998 0 0 7 1.75 -0.002919842 -0.002919842 0 0 8 2 -0.001981819 -0.00198181899999999 0 0 9 2.25 -0.001163676 -0.001163676 0 0 10 2.5 -0.003491456 -0.00349145600000001 0 0 11 2.75 -0.009723697 -0.00972369699999999 0 0 |
6楼2021-07-22 21:40:44
【答案】应助回帖
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尝试用OpenLu（可从www.forcal.net下载）求解，与大家探讨。 使用 1楼 给出的第一种公式。未知中间变量lambv用解方程法求解，但不知这种方法有没有问题？ 仍类似于 4楼 使用部分数据拟合，以减少运行时间。 Lu脚本代码： !!!using["luopt","math"]; //使用命名空间 g(lambv :: fac1,fac2,fac3,fac4,fac5,fac6,fac7,lamb)= ((1.0/3/fac7)*(fac1*((lamb/lambv)^fac2-(lambv/lamb)^(0.5*fac2))+fac3*((lamb/lambv)^fac4-(lambv/lamb)^(0.5*fac4))+fac5*((lamb/lambv)^fac6-(lambv/lamb)^(0.5*fac6))))-lambv; f(t,_lamb,lambv,pp : x : fac1,fac2,fac3,fac4,fac5,fac6,fac7,lamb) = lamb=_lamb, x=lamb, if{pqrt[@g,&x,1e-6]<=0, return(1)}, //连分式法解方程，返回迭代次数，迭代次数<=0，求解失败 lambv=x, 0; //成功返回0 pp(pa,p,lamb,lambv :: fac1,fac2,fac3,fac4,fac5,fac6,fac7) = (pa+fac1*((lamb/lambv)^fac2/lamb-(lambv/lamb)^(fac2*0.5)/lamb)+fac3*((lamb/lambv)^fac4/lamb-(lambv/lamb)^(fac4*0.5)/lamb)+fac5*((lamb/lambv)^fac6/lamb-(lambv/lamb)^(fac6*0.5)/lamb)) - p; 目标函数(_fac1,_fac2,_fac3,_fac4,_fac5,_fac6,_fac7 : i,s,tf : t_A, t_lamb, t_pa, t_p, max, fac1,fac2,fac3,fac4,fac5,fac6,fac7,la)= { fac1=_fac1, fac2=_fac2, fac3=_fac3, fac4=_fac4, fac5=_fac5, fac6=_fac6, fac7=_fac7, //传递优化变量 la[0]=t_lamb[0,0], //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, 0.0, t_A, la, 1e-6, 1e-6, gsl_rkf45, 1e-6,50], i=-1, s=0, while{++i<max, s=s+pp[t_pa(i,0),t_p(i,0),t_lamb(i,0),tf(i,1)]^2.0 }, s }; main(: tArray : t_A, t_lamb, t_pa, t_p, max, la)= { tArray=matrix{ //存放实验数据//t,lamb,pa,p "0 0.959926667 -0.218715994 -0.060966222 0.25 0.963063333 -0.200840559 -0.046836278 0.5 0.96612 -0.183553472 -0.035042256 0.75 0.969016667 -0.167289626 -0.024438988 1 0.97171 -0.152268899 -0.01706765 1.25 0.97409 -0.139075651 -0.010939712 1.5 0.976123333 -0.127862697 -0.006795087 1.75 0.977786667 -0.118729759 -0.002919842 2 0.979000001 -0.112089924 -0.001981819 2.25 0.979743333 -0.108031322 -0.001163676 2.5 0.98001 -0.106577018 -0.003491456 2.75 0.979766667 -0.107904033 -0.009723697" }, len[tArray,0,&max], t_A=tArray(all:0), t_lamb=tArray(all:1), t_pa=tArray(all:2), t_p=tArray(all:3), //用len函数取矩阵的行数，t_A等取矩阵的列 la=ra1[0], //预先申请数组 Opt1[@目标函数, optwaysimdeep, optwayconfra] //Opt1函数全局优化 }; 微分方程+解方程，耗时长，未多次求解，故结果不是最优的： 1.953313036693719 -2.867510001653266e-002 -0.2767401112856916 -3.629687916321768 -0.2763230915848823 7.260677042953397 -0.3201568717886613 2.502852593689372e-002 |
7楼2021-08-09 08:09:41
【答案】应助回帖
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Lu 脚本 绘图代码，但不知道如何贴图？可以看到，第一个点没有拟合好。 !!!using["luopt","math","win"]; //使用命名空间 g(lambv :: fac1,fac2,fac3,fac4,fac5,fac6,fac7,lamb)= ((1.0/3/fac7)*(fac1*((lamb/lambv)^fac2-(lambv/lamb)^(0.5*fac2))+fac3*((lamb/lambv)^fac4-(lambv/lamb)^(0.5*fac4))+fac5*((lamb/lambv)^fac6-(lambv/lamb)^(0.5*fac6))))-lambv; f(t,_lamb,lambv,pp : x : fac1,fac2,fac3,fac4,fac5,fac6,fac7,lamb) = lamb=_lamb, x=lamb, if{pqrt[@g,&x,1e-6]<=0, return(1)}, //连分式法解方程，返回迭代次数，迭代次数<=0，求解失败 lambv=x, 0; //成功返回0 pp(pa,lamb,lambv :: fac1,fac2,fac3,fac4,fac5,fac6,fac7) = (pa+fac1*((lamb/lambv)^fac2/lamb-(lambv/lamb)^(fac2*0.5)/lamb)+fac3*((lamb/lambv)^fac4/lamb-(lambv/lamb)^(fac4*0.5)/lamb)+fac5*((lamb/lambv)^fac6/lamb-(lambv/lamb)^(fac6*0.5)/lamb)); set(_fac1,_fac2,_fac3,_fac4,_fac5,_fac6,_fac7 :: fac1,fac2,fac3,fac4,fac5,fac6,fac7)= { fac1=_fac1, fac2=_fac2, fac3=_fac3, fac4=_fac4, fac5=_fac5, fac6=_fac6, fac7=_fac7 //传递优化变量 }; init(main : tArray, tf, i, k, t_pp,t_lambv : t_A, t_lamb, t_pa, t_p, max)= { tArray=matrix{ //存放实验数据//t,lamb,pa,p "0 0.959926667 -0.218715994 -0.060966222 0.25 0.963063333 -0.200840559 -0.046836278 0.5 0.96612 -0.183553472 -0.035042256 0.75 0.969016667 -0.167289626 -0.024438988 1 0.97171 -0.152268899 -0.01706765 1.25 0.97409 -0.139075651 -0.010939712 1.5 0.976123333 -0.127862697 -0.006795087 1.75 0.977786667 -0.118729759 -0.002919842 2 0.979000001 -0.112089924 -0.001981819 2.25 0.979743333 -0.108031322 -0.001163676 2.5 0.98001 -0.106577018 -0.003491456 2.75 0.979766667 -0.107904033 -0.009723697" }, len[tArray,0,&max], t_A=tArray(all:0), t_lamb=tArray(all:1), t_pa=tArray(all:2), t_p=tArray(all:3), //用len函数取矩阵的行数，t_A等取矩阵的列 set[1.953313036693719 , -2.867510001653266e-002 , -0.2767401112856916 , -3.629687916321768 , -0.2763230915848823 , 7.260677042953397 , -0.3201568717886613 ], t_pp=new[real_s,max], t_lambv=new[real_s,max], //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, 0.0, t_A, ra1(t_lamb[0,0]), 1e-6, 1e-6, gsl_rkf45, 1e-6,50], i=-1, while{++i<max, t_pp=pp[t_pa(i,0),t_lamb(i,0),tf(i,1)], t_lambv=tf(i,1)}, t_A=reshape(t_A), o[t_lambv, t_pp], cwAttach[typeSplit], cwResizePlots(1,2,2), //左二右二分裂 k=cwAddCurve{t_A, t_p.reshape(), max, 0}, //给0子图添加曲线 cwSetScatter(k,0), //设置绘制点 cwSetDataLineSize(5, k, 0), //设置点的大小 cwAddCurve{t_A, t_pp, max, 0}, //给0子图添加曲线 cwAddCurve{t_A, t_lamb.reshape(), max, 1}, //给1子图添加曲线 cwAddCurve{t_A, t_pa.reshape(), max, 2}, //给2子图添加曲线 cwAddCurve{t_A, t_lambv, max, 3} //给3子图添加曲线 }; ChartWnd[@init]; |
8楼2021-08-09 08:16:24
9楼2021-08-09 15:37:17
【答案】应助回帖
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使用 3楼、4楼 的公式进行求解。 有两个难点： 1、微分方程求解时要传递中间变量lamb, pa。 2、lambv为未知中间变量，需要求解。 第一个难点对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：lamb=lamb0+(lamb1-lamb0)*[(t-t0)/(t1-t0)], pa=pa0+(pa1-pa0)*[(t-t0)/(t1-t0)]。 第二个难点若使用6楼的办法，当数据量大时似乎难以实现。故在这里使用幂级数逼近lambv，进行拟合的方法，需增加k0,k1,k2,k3四个拟合参数；当然拟合参数多时精度高，但耗时长。 仍使用部分数据拟合，以减少时间。 Lu脚本代码： !!!using["luopt","math"]; //使用命名空间 f(t,p,dp, i : lamb,pa, A,w,lambdif,lambvdif,lambv: t_A, t_lamb, t_pa, fac1,fac2,fac3,fac4,fac5,fac6,fac7,k0,k1,k2,k3,k4) = { lamb=t_lamb+(t_lamb[i+1]-t_lamb)*[(t-t_A)/(t_A[i+1]-t_A)], pa=t_pa+(t_pa[i+1]-t_pa)*[(t-t_A)/(t_A[i+1]-t_A)], //线性插值计算lamb,pa lambv=k0+k1*lamb+k2*lamb*lamb+k3*lamb^3+k4*lamb^4, //lambv=f(lamb,k0,k1,k2,k3,k4)，使用幂级数逼近 A=0.02,w=2*pi*0.1, lambdif=A*w*cos(w*t), lambvdif=((1.0/3/fac7)*(fac1*((lamb/lambv)^fac2-(lambv/lamb)^(0.5*fac2))+fac3*((lamb/lambv)^fac4-(lambv/lamb)^(0.5*fac4))+fac5*((lamb/lambv)^fac6-(lambv/lamb)^(0.5*fac6)))), dp=pa+fac1*((fac2-1)*lamb^(fac2-2)*lambv^(-fac2)*lambdif-fac2*lamb^(fac2-1)*lambv^(-fac2-1)*lambvdif +(0.5*fac2+1)*lamb^(-0.5*fac2-2)*lambv^(0.5*fac2)*lambdif-0.5*fac2*lamb^(-0.5*fac2-1)*lambv^(0.5*fac2-1)*lambvdif) +fac3*((fac4-1)*lamb^(fac4-2)*lambv^(-fac4)*lambdif-fac4*lamb^(fac4-1)*lambv^(-fac4-1)*lambvdif+(0.5*fac4+1)*lamb^(-0.5*fac4-2)*lambv^(0.5*fac4)*lambdif -0.5*fac4*lamb^(-0.5*fac4-1)*lambv^(0.5*fac4-1)*lambvdif)+fac5*((fac6-1)*lamb^(fac6-2)*lambv^(-fac6)*lambdif -fac6*lamb^(fac6-1)*lambv^(-fac6-1)*lambvdif+(0.5*fac6+1)*lamb^(-0.5*fac6-2)*lambv^(0.5*fac6)*lambdif -0.5*fac6*lamb^(-0.5*fac6-1)*lambv^(0.5*fac6-1)*lambvdif), 0 //必须返回0 }; 目标函数(_fac1,_fac2,_fac3,_fac4,_fac5,_fac6,_fac7,_k0,_k1,_k2,_k3,_k4 : i,s,tf: t_A, t_p, fac1,fac2,fac3,fac4,fac5,fac6,fac7,k0,k1,k2,k3,k4)= { fac1=_fac1, fac2=_fac2, fac3=_fac3, fac4=_fac4, fac5=_fac5, fac6=_fac6, fac7=_fac7, k0=_k0, k1=_k1, k2=_k2, k3=_k3, k4=_k4, //传递优化变量 //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, nil, t_A, ra1(-0.060966222), 1e-6, 1e-6, gsl_rkf45, 1e-6,50], sum{[tf(all:1).reshape()-t_p].^2.0} //代码矢量化加速，特别适合大数据量 }; main(: tArray : t_A, t_lamb, t_pa, t_p)= { tArray=matrix{ //存放实验数据//t,lamb,pa,p "0 0.959926667 -0.218715994 -0.060966222 0.25 0.963063333 -0.200840559 -0.046836278 0.5 0.96612 -0.183553472 -0.035042256 0.75 0.969016667 -0.167289626 -0.024438988 1 0.97171 -0.152268899 -0.01706765 1.25 0.97409 -0.139075651 -0.010939712 1.5 0.976123333 -0.127862697 -0.006795087 1.75 0.977786667 -0.118729759 -0.002919842 2 0.979000001 -0.112089924 -0.001981819 2.25 0.979743333 -0.108031322 -0.001163676 2.5 0.98001 -0.106577018 -0.003491456 2.75 0.979766667 -0.107904033 -0.009723697" }, t_A=tArray(all:0).reshape(), t_lamb=tArray(all:1).reshape(), t_pa=tArray(all:2).reshape(), t_p=tArray(all:3).reshape(), //t_A等取矩阵的列，并转为一维数组 Opt1[@目标函数, optwaysimdeep, optwayconfra] //Opt1函数全局优化 }; 结果（fac1～fac7，k0,k1,k2,k3,k4，最小值）： 17.38947868627771 0.3416680168065553 -31901.02726305072 1.871542771429994e-004 2.297270203567084e-003 8.207606707403809 -41.52220237484659 -1.705988163594953 -0.3001058349255158 2.1410790976942 4.419612473682794 -4.029380465220802 2.405714024195563e-006 绘图代码： !!!using["luopt","math","win"]; //使用命名空间 f(t,p,dp, i : lamb,pa, A,w,lambdif,lambvdif,lambv: t_A, t_lamb, t_pa, fac1,fac2,fac3,fac4,fac5,fac6,fac7,k0,k1,k2,k3,k4) = { lamb=t_lamb+(t_lamb[i+1]-t_lamb)*[(t-t_A)/(t_A[i+1]-t_A)], pa=t_pa+(t_pa[i+1]-t_pa)*[(t-t_A)/(t_A[i+1]-t_A)], //线性插值计算lamb,pa lambv=k0+k1*lamb+k2*lamb*lamb+k3*lamb^3+k4*lamb^4, //lambv=f(lamb,k0,k1,k2,k3,k4)，使用幂级数逼近 A=0.02,w=2*pi*0.1, lambdif=A*w*cos(w*t), lambvdif=((1.0/3/fac7)*(fac1*((lamb/lambv)^fac2-(lambv/lamb)^(0.5*fac2))+fac3*((lamb/lambv)^fac4-(lambv/lamb)^(0.5*fac4))+fac5*((lamb/lambv)^fac6-(lambv/lamb)^(0.5*fac6)))), dp=pa+fac1*((fac2-1)*lamb^(fac2-2)*lambv^(-fac2)*lambdif-fac2*lamb^(fac2-1)*lambv^(-fac2-1)*lambvdif +(0.5*fac2+1)*lamb^(-0.5*fac2-2)*lambv^(0.5*fac2)*lambdif-0.5*fac2*lamb^(-0.5*fac2-1)*lambv^(0.5*fac2-1)*lambvdif) +fac3*((fac4-1)*lamb^(fac4-2)*lambv^(-fac4)*lambdif-fac4*lamb^(fac4-1)*lambv^(-fac4-1)*lambvdif+(0.5*fac4+1)*lamb^(-0.5*fac4-2)*lambv^(0.5*fac4)*lambdif -0.5*fac4*lamb^(-0.5*fac4-1)*lambv^(0.5*fac4-1)*lambvdif)+fac5*((fac6-1)*lamb^(fac6-2)*lambv^(-fac6)*lambdif -fac6*lamb^(fac6-1)*lambv^(-fac6-1)*lambvdif+(0.5*fac6+1)*lamb^(-0.5*fac6-2)*lambv^(0.5*fac6)*lambdif -0.5*fac6*lamb^(-0.5*fac6-1)*lambv^(0.5*fac6-1)*lambvdif), 0 //必须返回0 }; set(_fac1,_fac2,_fac3,_fac4,_fac5,_fac6,_fac7,_k0,_k1,_k2,_k3,_k4 :: fac1,fac2,fac3,fac4,fac5,fac6,fac7,k0,k1,k2,k3,k4)= { fac1=_fac1, fac2=_fac2, fac3=_fac3, fac4=_fac4, fac5=_fac5, fac6=_fac6, fac7=_fac7, k0=_k0, k1=_k1, k2=_k2, k3=_k3, k4=_k4 //传递优化变量 }; init(init: tArray,t_lambv,i,tf,k,lamb : t_A, t_lamb, t_pa, t_p, max, fac1,fac2,fac3,fac4,fac5,fac6,fac7,k0,k1,k2,k3,k4)= { tArray=matrix{ //存放实验数据//t,lamb,pa,p "0 0.959926667 -0.218715994 -0.060966222 ... ... 数据省略 2.75 0.979766667 -0.107904033 -0.009723697" }, len[tArray,0,&max], t_A=tArray(all:0).reshape(), t_lamb=tArray(all:1).reshape(), t_pa=tArray(all:2).reshape(), t_p=tArray(all:3).reshape(), set[17.38947868627771, 0.3416680168065553, -31901.02726305072, 1.871542771429994e-004, 2.297270203567084e-003, 8.207606707403809, -41.52220237484659, -1.705988163594953, -0.3001058349255158, 2.1410790976942, 4.419612473682794, -4.029380465220802 ], t_lambv=new[real_s,max], i=-1, while{++i<max, lamb=t_lamb, t_lambv=k0+k1*lamb+k2*lamb*lamb+k3*lamb^3+k4*lamb^4}, tf=gsl_ode[@f, nil, nil, t_A, ra1(-0.060966222), 1e-6, 1e-6, gsl_rkf45, 1e-6,50], cwAttach[typeSplit], cwResizePlots(1,2,2), //左二右二分裂 k=cwAddCurve{t_A, t_p, max, 0}, //给0子图添加曲线 cwSetScatter(k,0), //设置绘制点 cwSetDataLineSize(5, k, 0), //设置点的大小 cwAddCurve{t_A, tf(all:1).reshape(), max, 0}, //给0子图添加曲线 cwAddCurve{t_A, t_lamb, max, 1}, //给1子图添加曲线 cwAddCurve{t_A, t_pa, max, 2}, //给2子图添加曲线 cwAddCurve{t_A, t_lambv, max, 3} //给3子图添加曲线 }; ChartWnd[@init]; 图形： https://blog.csdn.net/wlfc/article/details/119607664 |
» 本帖已获得的红花（最新10朵）
10楼2021-08-11 16:09:33
