I want to fit data with my custom function to calculate parameters of the model. Data of x and y are attached at the end. The custom function is:
y=a+(-((4/3)*3.14*((60e-10)^3-((60e-10)-x).^3).*b*(c-1096)/c+4*3.14*(60e-10)^2.*(d.*((60e-10)-x).^2/(60e-10)^2+e+(f-e-d.*((60e-10)-x).^2/(60e-10)^2).*exp(-x./g)))/(1e3*1.38e-23*1090))
and parameters have constraints and initials:
-inf<a<inf, a=2e4
1e11<b<1e12, b=7.8e11
1120<c<1300, c=1200
70<d<130, d=127
300<e<700, e=680
400<f<900, f=850
1e-10<g<3e-10, g=2.5e-10
However, I both tried matlab and rigin to fit data with the model, but they all failed to find a good fit. I am appreciate if you can provide any suggestions. In fact, I understand there are too many parameters, and I also tried to fix parameter b, d, e and g while free others, but still no good results.
x=[3.70400000000000e-10
3.80400000000000e-10
3.90400000000000e-10
4.00400000000000e-10
4.10400000000000e-10
4.20400000000000e-10
4.30400000000000e-10
4.40400000000000e-10
4.50400000000000e-10
4.60400000000000e-10
4.70400000000000e-10
4.80400000000000e-10
4.90400000000000e-10
5.00400000000000e-10
5.10400000000000e-10
5.20400000000000e-10
5.30400000000000e-10
5.40400000000000e-10
5.50400000000000e-10
5.60400000000000e-10
5.70400000000000e-10
5.80400000000000e-10
5.90400000000000e-10
6.00400000000000e-10
6.10400000000000e-10
6.20400000000000e-10
6.30400000000000e-10
6.40400000000000e-10
6.50400000000000e-10
6.60400000000000e-10
6.70400000000000e-10
6.80400000000000e-10
6.90400000000000e-10
7.00400000000000e-10
7.10400000000000e-10
7.20400000000000e-10
7.30400000000000e-10
7.40400000000000e-10
7.50400000000000e-10
7.60400000000000e-10
7.70400000000000e-10
7.80400000000000e-10
7.90400000000000e-10
8.00400000000000e-10
8.10400000000000e-10
8.20400000000000e-10
8.30400000000000e-10
8.40400000000000e-10
8.50400000000000e-10
8.60400000000000e-10
8.70400000000000e-10
8.80400000000000e-10
8.90400000000000e-10
9.00400000000000e-10
9.10400000000000e-10
9.20400000000000e-10
9.30400000000000e-10
9.40400000000000e-10
9.50400000000000e-10
9.60400000000000e-10
9.70400000000000e-10
9.80400000000000e-10
9.90400000000000e-10
1.00040000000000e-09
1.01040000000000e-09
1.02040000000000e-09
1.03040000000000e-09
1.04040000000000e-09
1.05040000000000e-09
1.06040000000000e-09
1.07040000000000e-09
1.08040000000000e-09
1.09040000000000e-09
1.10040000000000e-09
1.11040000000000e-09
1.12040000000000e-09
1.13040000000000e-09
1.14040000000000e-09
1.15040000000000e-09
1.16040000000000e-09
1.17040000000000e-09
1.18040000000000e-09
1.19040000000000e-09
1.20040000000000e-09
1.21040000000000e-09
1.22040000000000e-09
1.23040000000000e-09
1.24040000000000e-09
1.25040000000000e-09
1.26040000000000e-09
1.27040000000000e-09
1.28040000000000e-09
1.29040000000000e-09
1.30040000000000e-09
1.31040000000000e-09
1.32040000000000e-09
1.33040000000000e-09
1.34040000000000e-09
1.35040000000000e-09
1.36040000000000e-09
1.37040000000000e-09
1.38040000000000e-09
1.39040000000000e-09
1.40040000000000e-09
1.41040000000000e-09
1.42040000000000e-09
1.43040000000000e-09
1.44040000000000e-09
1.45040000000000e-09
1.46040000000000e-09
1.47040000000000e-09
1.48040000000000e-09
1.49040000000000e-09
1.50040000000000e-09
1.51040000000000e-09
1.52040000000000e-09
1.53040000000000e-09
1.54040000000000e-09
1.55040000000000e-09
1.56040000000000e-09
1.57040000000000e-09
1.58040000000000e-09
1.59040000000000e-09
1.60040000000000e-09
1.61040000000000e-09
1.62040000000000e-09
1.63040000000000e-09
1.64040000000000e-09
1.65040000000000e-09
1.66040000000000e-09
1.67040000000000e-09
1.68040000000000e-09
1.69040000000000e-09
1.70040000000000e-09
1.71040000000000e-09
1.72040000000000e-09
1.73040000000000e-09
1.74040000000000e-09
1.75040000000000e-09
1.76040000000000e-09
1.77040000000000e-09
1.78040000000000e-09
1.79040000000000e-09
1.80040000000000e-09
1.81040000000000e-09
1.82040000000000e-09
1.83040000000000e-09
1.84040000000000e-09
1.85040000000000e-09
1.86040000000000e-09
1.87040000000000e-09
1.88040000000000e-09
1.89040000000000e-09]
y=[-22.8405306447565
-22.2450287793417
-21.6577585104770
-21.0787198381626
-20.5079127623984
-19.9453372831843
-19.3909934005205
-18.8448811144068
-18.3070004248434
-17.7773513318301
-17.2559338353671
-16.7427479354542
-16.2377936320915
-15.7410709252790
-15.2525798150167
-14.7723203013046
-14.3002923841427
-13.8364960635310
-13.3809313394694
-12.9335982119581
-12.4944966809970
-12.0636267465860
-11.6409884087253
-11.2265816674147
-10.8204065226543
-10.4224629744442
-10.0327510227842
-9.65127066767441
-9.27802190911481
-8.91300474710541
-8.55621918164621
-8.20766521273719
-7.86734284037838
-7.53525206456975
-7.21139288531131
-6.89576530260307
-6.58836931644503
-6.28920492683717
-5.99827213377951
-5.71557093727205
-5.44110133731477
-5.17486333390769
-4.91685692705081
-4.66708211674411
-4.42553890298761
-4.19222728578130
-3.96714726512519
-3.75029884101927
-3.54168201346354
-3.34129678245801
-3.14914314800267
-2.96522111009752
-2.78953066874256
-2.62207182393780
-2.46284457568323
-2.31184892397886
-2.16908486882468
-2.03455241022069
-1.90825154816689
-1.79018228266329
-1.68034461370989
-1.57873854130667
-1.48536406545365
-1.40022118615082
-1.32330990339818
-1.25463021719574
-1.19418212754349
-1.14196563444144
-1.09798073788958
-1.06222743788791
-1.03470573443643
-1.01541562753515
-1.00435711718406
-1.00153020338316
-1.00693488613246
-1.02057116543195
-1.04243904128163
-1.07253851368151
-1.11086958263158
-1.15743224813184
-1.21222651018230
-1.27525236878295
-1.34650982393380
-1.42599887563483
-1.51371952388606
-1.60967176868748
-1.71385561003910
-1.82627104794091
-1.94691808239291
-2.07579671339511
-2.21290694094750
-2.35824876505008
-2.51182218570286
-2.67362720290583
-2.84366381665899
-3.02193202696235
-3.20843183381589
-3.40316323721964
-3.60612623717357
-3.81732083367770
-4.03674702673202
-4.26440481633653
-4.50029420249125
-4.74441518519615
-4.99676776445124
-5.25735194025653
-5.52616771261201
-5.80321508151769
-6.08849404697355
-6.38200460897961
-6.68374676753587
-6.99372052264231
-7.31192587429896
-7.63836282250579
-7.97303136726282
-8.31593150857004
-8.66706324642746
-9.02642658083506
-9.39402151179286
-9.76984803930086
-10.1539061633590
-10.5461958839674
-10.9467172011260
-11.3554701148348
-11.7724546250937
-12.1976707319029
-12.6311184352622
-13.0727977351718
-13.5227086316315
-13.9808511246414
-14.4472252142016
-14.9218309003119
-15.4046681829724
-15.8957370621831
-16.3950375379440
-16.9025696102550
-17.4183332791163
-17.9423285445278
-18.4745554064895
-19.0150138650013
-19.5637039200634
-20.1206255716756
-20.6857788198381
-21.2591636645507
-21.8407801058135
-22.4306281436265
-23.0287077779897
-23.6350190089032
-24.2495618363668
-24.8723362603805
-25.5033422809445
-26.1425798980587
-26.7900491117231]
