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小书园

至尊木虫 (著名写手)

应助: 89 (初中生)
金币: 15083.9
散金: 3282
红花: 38
帖子: 2694
在线: 750.2小时
虫号: 2352574
注册: 2013-03-16
性别: GG
专业: 光学

[求助] 求助一个1stopt拟合，可追加金币已有1人参与

有理论公式，有数据点，但是拟合对初值太敏感，听说1stopt可以无初值拟合，求帮助拟合并告知初值。。

需要拟合的参数：gama_1, gama_2, k, g
变量：delta=0.01;
w1=.69;
w2=w1+delta
公式：X(w)=(w-w2+i*gama_2/2)/((w-w1+i*gama_1/2)*(w-w2+i*gama_2/2)-k^2);
X_imag(w)=i*(X(w));
T_func(w)=Real(1-g*X_imag(w));

数据点对应(w,T_func)
数据点：
w T

0.3 0.94557
0.30301 0.94409
0.30602 0.94264
0.30903 0.94114
0.31204 0.93957
0.31505 0.93803
0.31806 0.93639
0.32107 0.93474
0.32408 0.93307
0.32709 0.93131
0.3301 0.92957
0.33311 0.92774
0.33612 0.92588
0.33913 0.924
0.34214 0.92202
0.34515 0.92005
0.34816 0.918
0.35117 0.91589
0.35418 0.91378
0.35719 0.91155
0.3602 0.90931
0.36321 0.90701
0.36622 0.90462
0.36923 0.90222
0.37224 0.89971
0.37525 0.89716
0.37826 0.89456
0.38127 0.89185
0.38428 0.88912
0.38729 0.88628
0.3903 0.88336
0.39331 0.88041
0.39632 0.87731
0.39933 0.87419
0.40234 0.87096
0.40535 0.86762
0.40836 0.86424
0.41137 0.8607
0.41438 0.8571
0.41739 0.8534
0.4204 0.84955
0.42341 0.84565
0.42642 0.84158
0.42943 0.83741
0.43244 0.83313
0.43545 0.82867
0.43846 0.82414
0.44147 0.81941
0.44448 0.81454
0.44749 0.80955
0.4505 0.80435
0.45351 0.79902
0.45652 0.79348
0.45953 0.78775
0.46254 0.78186
0.46555 0.77571
0.46856 0.76939
0.47157 0.76282
0.47458 0.75599
0.47759 0.74896
0.4806 0.7416
0.48361 0.734
0.48662 0.7261
0.48963 0.71785
0.49264 0.70932
0.49565 0.70039
0.49866 0.6911
0.50167 0.68143
0.50468 0.6713
0.50769 0.66077
0.5107 0.64973
0.51371 0.63818
0.51672 0.62612
0.51973 0.61343
0.52274 0.60018
0.52575 0.58624
0.52876 0.57158
0.53177 0.55622
0.53478 0.53999
0.53779 0.52295
0.5408 0.50497
0.54381 0.48599
0.54682 0.46602
0.54983 0.44488
0.55284 0.42259
0.55585 0.39908
0.55886 0.37423
0.56187 0.34809
0.56488 0.32054
0.56789 0.29164
0.5709 0.26145
0.57391 0.23002
0.57692 0.19764
0.57993 0.16458
0.58294 0.13141
0.58595 0.09892
0.58896 0.06815
0.59197 0.04069
0.59498 0.01848
0.59799 0.00406
0.601 4.18529E-4
0.60401 0.01078
0.60702 0.03822
0.61003 0.08497
0.61304 0.1516
0.61605 0.23639
0.61906 0.33508
0.62207 0.44136
0.62508 0.54816
0.62809 0.64872
0.6311 0.73801
0.63411 0.81302
0.63712 0.87254
0.64013 0.91711
0.64314 0.94786
0.64615 0.96665
0.64916 0.97531
0.65217 0.97542
0.65518 0.96872
0.65819 0.95624
0.6612 0.93914
0.66421 0.91826
0.66722 0.89405
0.67023 0.86727
0.67324 0.83804
0.67625 0.80674
0.67926 0.77366
0.68227 0.73869
0.68528 0.70227
0.68829 0.66422
0.6913 0.62468
0.69431 0.58387
0.69732 0.54153
0.70033 0.49811
0.70334 0.45345
0.70635 0.40766
0.70937 0.36119
0.71237 0.31383
0.71539 0.26649
0.7184 0.21948
0.7214 0.17187
0.72442 0.12657
0.72742 0.08336
0.73043 0.04947
0.73345 0.07342
0.73645 0.14342
0.73947 0.19313
0.74248 0.22468
0.74548 0.24574
0.7485 0.26155
0.7515 0.2762
0.75452 0.29013
0.75753 0.30464
0.76053 0.31982
0.76355 0.3352
0.76655 0.35128
0.76957 0.3672
0.77258 0.38314
0.77558 0.39893
0.7786 0.4141
0.7816 0.42908
0.78461 0.44335
0.78763 0.45718
0.79063 0.4706
0.79365 0.48337
0.79666 0.49596
0.79967 0.50804
0.80268 0.51986
0.80569 0.53152
0.8087 0.54282
0.81171 0.55412
0.81472 0.56517
0.81773 0.57611
0.82074 0.58702
0.82375 0.59768
0.82676 0.60836
0.82977 0.61884
0.83278 0.62919
0.83579 0.63946
0.8388 0.64946
0.84181 0.65939
0.84482 0.66907
0.84783 0.67856
0.85084 0.68789
0.85385 0.69693
0.85686 0.70583
0.85987 0.71446
0.86288 0.72287
0.86589 0.73111
0.8689 0.73907
0.87191 0.74687
0.87492 0.75444
0.87793 0.7618
0.88094 0.76902
0.88395 0.77599
0.88696 0.78284
0.88997 0.78949
0.89298 0.79597
0.89599 0.80233
0.899 0.80849
0.90201 0.81455
0.90502 0.82044
0.90803 0.82618
0.91104 0.83182
0.91405 0.83728
0.91706 0.84264
0.92007 0.84786
0.92308 0.85293
0.92609 0.85789
0.9291 0.8627
0.93211 0.86739
0.93512 0.87193
0.93813 0.87634
0.94114 0.88063
0.94415 0.88476
0.94716 0.88877
0.95017 0.89264
0.95318 0.89637
0.95619 0.89997
0.9592 0.90342
0.96221 0.90674
0.96522 0.90993
0.96823 0.91298
0.97124 0.9159
0.97425 0.91867
0.97726 0.92132
0.98027 0.92383
0.98328 0.92621
0.98629 0.92845
0.9893 0.93056
0.99231 0.93254
0.99532 0.93437
0.99833 0.93608
1.00134 0.93765
1.00435 0.93908
1.00736 0.94038
1.01037 0.94152
1.01338 0.94253
1.01639 0.9434
1.0194 0.9441
1.02241 0.94467
1.02542 0.94507
1.02843 0.94532
1.03144 0.9454
1.03445 0.9453
1.03746 0.94505
1.04047 0.9446
1.04348 0.94398
1.04649 0.94316
1.0495 0.94214
1.05251 0.94093
1.05552 0.93947
1.05853 0.9378
1.06154 0.93589
1.06455 0.93371
1.06756 0.9313
1.07057 0.92855
1.07358 0.9255
1.07659 0.9221
1.0796 0.91827
1.08261 0.91404
1.08562 0.90918
1.08863 0.90361
1.09164 0.89695
1.09465 0.88805
1.09766 0.87424
1.10067 0.85748
1.10368 0.84494
1.10669 0.83366
1.1097 0.82897
1.11271 0.82571
1.11572 0.8205
1.11873 0.8138
1.12174 0.80631
1.12475 0.79869
1.12776 0.79126
1.13077 0.78433
1.13378 0.77808
1.13679 0.77241
1.1398 0.76735
1.14281 0.76265
1.14582 0.75813
1.14883 0.75368
1.15184 0.74903
1.15485 0.74423
1.15786 0.73913
1.16087 0.73375
1.16388 0.72817
1.16689 0.72232
1.1699 0.71638
1.17291 0.71031
1.17592 0.7042
1.17893 0.69816
1.18194 0.69212
1.18495 0.68625
1.18796 0.68048
1.19097 0.67485
1.19398 0.6694
1.19699 0.66402
1.2 0.65882@月只蓝@beefly

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星星之火，可以燎原。

1楼 2017-04-23 23:14:36

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

dingd

铁杆木虫 (职业作家)

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注册: 2006-10-28

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与，应助指数 +1
小书园: 金币+50, ★★★很有帮助, Thank you all the same. 2017-04-25 23:28:16

效果不是太好吧：

均方差(RMSE): 0.162665706058403
残差平方和(SSE): 7.91157944631611
相关系数(R): 0.77176499831348
相关系数之平方(R^2): 0.595621212621806
修正R平方(Adj. R^2): 0.592888923517899
确定系数(DC): 0.576685562353128
F统计(F-Statistic): 181.32287882737

参数最佳估算
-------------------- -------------
g -0.0894213923500301
gama_2 -0.131995910767894
gama_1 -0.157252595677229
k -0.0986943973329742

c44.jpg

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