# Simultaneous fitting to multiple data sets with multiple variables and para

Posted 9 years ago
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 I am trying to fit two data sets to a function model described below which share a few common parameters. Say I have two functions with some common parameter(s)f[x,y]:= aExp[-x]Sin[b*y] + c g[x,y]:= dExp[-x]Sin[b*y] + cI generated two model data sets using a functional form similar to the ones above and tried to fit the data using NonlinearModelFit. But NonlinearModelFit fails to converge within the prescribed iterations and confidence interval.I tried checking the threads (http://mathematica.stackexchange.com/questions/15905/combined-fitting-via-nonlinearmodelfit or http://forums.wolfram.com/mathgroup/archive/2011/Sep/msg00555.html or http://community.wolfram.com/groups/-/m/t/135933) on similar discussions but could not solve my problem. Any suggestions would be welcome. Thanks in advance.Arijit.
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Posted 9 years ago
 Hi Priyan, Yes there is..In fact the actual problem was difficult for me to handle. So I posted a simpler version of the problem I was encountering. I post the two data sets below:data2a={{8.10^-8, 9.56}, {1.0810^-6, 9.8675}, {2.0810^-6, 9.5225}, {3.0810^-6, 9.2775}, {4.0810^-6, 9.475}, {5.0810^-6, 8.9625}, {6.0810^-6, 9.28}, {7.0810^-6, 8.54}, {8.0810^-6, 8.235}, {9.0810^-6, 7.7225}, {0.00001008, 7.55}, {0.00001108, 7.66}, {0.00001208, 6.9075}, {0.00001308, 6.085}, {0.00001408, 5.65}, {0.00001508, 4.7625}, {0.00001608, 4.7}, {0.00001708, 4.65}, {0.00001808, 4.03}, {0.00001908, 3.48}, {0.00002008, 3.0875}, {0.00002108, 2.65}, {0.00002208, 2.275}, {0.00002308, 1.6025}, {0.00002408, 1.8825}, {0.00002508, 1.2175}, {0.00002608, 1.18}, {0.00002708, 0.975}, {0.00002808, 0.7475}, {0.00002908, 0.6175}, {0.00003008, 0.5075}, {0.00003108, 0.39}, {0.00003208, 0.775}, {0.00003308, 0.4575}, {0.00003408, 0.765}, {0.00003508, 0.9775}, {0.00003608, 1.4125}, {0.00003708, 1.825}, {0.00003808, 1.9475}, {0.00003908, 2.2525}, {0.00004008, 2.375}, {0.00004108, 2.8625}, {0.00004208, 3.515}, {0.00004308, 3.8775}, {0.00004408, 4.5625}, {0.00004508, 4.94}, {0.00004608, 6.0175}, {0.00004708, 5.845}, {0.00004808, 6.695}, {0.00004908, 6.89}, {0.00005008, 7.01}, {0.00005108, 7.3675}, {0.00005208, 7.78}, {0.00005308, 7.87}, {0.00005408, 8.0925}, {0.00005508, 8.7325}, {0.00005608, 8.5675}, {0.00005708, 8.6525}, {0.00005808, 8.62}, {0.00005908, 8.995}, {0.00006008, 8.905}, {0.00006108, 8.7975}, {0.00006208, 8.4775}, {0.00006308, 8.6225}, {0.00006408, 8.7725}, {0.00006508, 8.2575}, {0.00006608, 7.91}, {0.00006708, 7.58}, {0.00006808, 7.05}, {0.00006908, 6.7925}, {0.00007008, 6.635}, {0.00007108, 6.3625}, {0.00007208, 5.755}, {0.00007308, 5.455}, {0.00007408, 4.8875}, {0.00007508, 4.33}, {0.00007608, 3.5775}, {0.00007708, 4.03}, {0.00007808, 3.115}, {0.00007908, 2.6275}, {0.00008008, 2.4025}, {0.00008108, 2.92}, {0.00008208, 2.49}, {0.00008308, 2}, {0.00008408, 1.7725}, {0.00008508, 1.625}, {0.00008608, 1.655}, {0.00008708, 1.7125}, {0.00008808, 1.6075}, {0.00008908, 1.7475}, {0.00009008, 1.4125}, {0.00009108, 1.6525}, {0.00009208, 1.565}, {0.00009308, 1.6875}, {0.00009408, 2.13}, {0.00009508, 2.0475}, {0.00009608, 2.445}, {0.00009708, 2.9875}, {0.00009808, 3.035}, {0.00009908, 3.065}, {0.00010008, 3.48}, {0.00010108, 3.7725}, {0.00010208, 4.2325}, {0.00010308, 4.62}, {0.00010408, 4.805}, {0.00010508, 5.745}, {0.00010608, 5.9}, {0.00010708, 6.3675}, {0.00010808, 6.4725}, {0.00010908, 6.4275}, {0.00011008, 7.0125}, {0.00011108, 7.9575}, {0.00011208, 7.155}, {0.00011308, 7.49}, {0.00011408, 7.86}, {0.00011508, 7.9}, {0.00011608, 8.1775}, {0.00011708, 8.065}, {0.00011808, 8.2275}, {0.00011908, 8.4825}, {0.00012008, 8.3275}, {0.00012108, 8.5}, {0.00012208, 7.91}, {0.00012308, 7.2325}, {0.00012408, 7.83}, {0.00012508, 7.1625}, {0.00012608, 6.82}, {0.00012708, 7.2325}, {0.00012808, 6.415}, {0.00012908, 6.03}, {0.00013008, 5.8725}, {0.00013108, 5.78}, {0.00013208, 5.16}, {0.00013308, 5.1725}, {0.00013408, 5.0575}, {0.00013508, 4.4825}, {0.00013608, 3.8575}, {0.00013708, 4.3225}, {0.00013808, 3.925}, {0.00013908, 3.615}, {0.00014008, 3.315}, {0.00014108, 2.915}, {0.00014208, 2.5075}, {0.00014308, 2.4275}, {0.00014408, 2.06}, {0.00014508, 2.3625}, {0.00014608, 1.9525}, {0.00014708, 2.2325}, {0.00014808, 2.2575}, {0.00014908, 1.8575}, {0.00015008, 2.0475}, {0.00015108, 2.7325}, {0.00015208, 2.375}, {0.00015308, 2.59}, {0.00015408, 2.785}, {0.00015508, 2.9675}, {0.00015608, 3.515}, {0.00015708, 3.715}, {0.00015808, 3.66}, {0.00015908, 4.1925}, {0.00016008, 3.8875}, {0.00016108, 4.0925}, {0.00016208, 4.6275}, {0.00016308, 5.2725}, {0.00016408, 5.2275}, {0.00016508, 5.1775}, {0.00016608, 5.27}, {0.00016708, 5.59}, {0.00016808, 6.46}, {0.00016908, 6.72}, {0.00017008, 7.4625}, {0.00017108, 7.225}, {0.00017208, 7.4325}, {0.00017308, 6.78}, {0.00017408, 7.18}, {0.00017508, 7.5675}, {0.00017608, 7.8125}, {0.00017708, 7.74}, {0.00017808, 7.0225}, {0.00017908, 8.0475}, {0.00018008, 7.705}, {0.00018108, 7.555}, {0.00018208, 7.2525}, {0.00018308, 6.8675}, {0.00018408, 6.9925}, {0.00018508, 6.8375}, {0.00018608, 6.5275}, {0.00018708, 6.2025}, {0.00018808, 5.8425}, {0.00018908, 5.585}, {0.00019008, 5.725}, {0.00019108, 5.1875}, {0.00019208, 5.3}, {0.00019308, 4.4225}, {0.00019408, 4.655}, {0.00019508, 4.0325}, {0.00019608, 4.0225}, {0.00019708, 3.4675}, {0.00019808, 4.045}, {0.00019908, 3.1425}, {0.00020008, 3.245}, {0.00020108, 3.395}, {0.00020208, 2.965}, {0.00020308, 2.6425}, {0.00020408, 2.815}, {0.00020508, 3.0525}, {0.00020608, 2.6775}, {0.00020708, 2.8825}, {0.00020808, 3.1425}, {0.00020908, 3.155}, {0.00021008, 3.275}, {0.00021108, 3.445}, {0.00021208, 3.2725}, {0.00021308, 3.995}, {0.00021408, 3.655}, {0.00021508, 4.6575}, {0.00021608, 4.8375}, {0.00021708, 4.86}, {0.00021808, 4.445}, {0.00021908, 4.33}, {0.00022008, 3.8275}, {0.00022108, 4.365}, {0.00022208, 4.64}, {0.00022308, 4.5825}, {0.00022408, 4.75}, {0.00022508, 5.5}, {0.00022608, 5.7175}, {0.00022708, 6.435}, {0.00022808, 6.23}, {0.00022908, 6.865}, {0.00023008, 6.5075}, {0.00023108, 6.9775}, {0.00023208, 6.765}, {0.00023308, 6.725}, {0.00023408, 7.0325}, {0.00023508, 6.6475}, {0.00023608, 6.2625}, {0.00023708, 6.205}, {0.00023808, 6.2075}, {0.00023908, 6.1275}, {0.00024008, 5.575}, {0.00024108, 5.695}, {0.00024208, 6.785}, {0.00024308, 6.0725}, {0.00024408, 6.6775}, {0.00024508, 5.7825}, {0.00024608, 5.8925}, {0.00024708, 4.07}, {0.00024808, 3.8625}, {0.00024908, 3.6275}, {0.00025008, 4.3}, {0.00025108, 3.665}, {0.00025208, 3.78}};data2b={{8.10^-8, 7.9525}, {1.0810^-6, 8.22}, {2.0810^-6, 7.875}, {3.0810^-6, 7.605}, {4.0810^-6, 7.335}, {5.0810^-6, 6.835}, {6.0810^-6, 6.3425}, {7.0810^-6, 5.4625}, {8.0810^-6, 4.195}, {9.0810^-6, 3.8275}, {0.00001008, 2.7175}, {0.00001108, 1.8625}, {0.00001208, 1.7075}, {0.00001308, 1.09}, {0.00001408, 0.525}, {0.00001508, 0.375}, {0.00001608, 0.3525}, {0.00001708, 0.5775}, {0.00001808, 0.7775}, {0.00001908, 1.0825}, {0.00002008, 1.66}, {0.00002108, 2.4525}, {0.00002208, 2.565}, {0.00002308, 3.5425}, {0.00002408, 4.5925}, {0.00002508, 4.89}, {0.00002608, 5.7225}, {0.00002708, 6.6975}, {0.00002808, 6.775}, {0.00002908, 7.2125}, {0.00003008, 7.39}, {0.00003108, 8.1675}, {0.00003208, 7.71}, {0.00003308, 7.765}, {0.00003408, 7.1675}, {0.00003508, 6.96}, {0.00003608, 6.57}, {0.00003708, 5.805}, {0.00003808, 4.92}, {0.00003908, 4.535}, {0.00004008, 3.8625}, {0.00004108, 3.3425}, {0.00004208, 1.9825}, {0.00004308, 1.4825}, {0.00004408, 1.3925}, {0.00004508, 0.94}, {0.00004608, 0.69}, {0.00004708, 0.68}, {0.00004808, 0.725}, {0.00004908, 1.0425}, {0.00005008, 1.1225}, {0.00005108, 1.5425}, {0.00005208, 2.4125}, {0.00005308, 2.76}, {0.00005408, 4.1325}, {0.00005508, 4.18}, {0.00005608, 5.22}, {0.00005708, 5.9575}, {0.00005808, 6.1725}, {0.00005908, 6.6675}, {0.00006008, 6.9075}, {0.00006108, 7.015}, {0.00006208, 7.6125}, {0.00006308, 7.26}, {0.00006408, 6.87}, {0.00006508, 7.1275}, {0.00006608, 6.9375}, {0.00006708, 6.11}, {0.00006808, 5.46}, {0.00006908, 4.26}, {0.00007008, 4.0625}, {0.00007108, 3.545}, {0.00007208, 3.1575}, {0.00007308, 2.3625}, {0.00007408, 1.665}, {0.00007508, 1.53}, {0.00007608, 1.195}, {0.00007708, 1.1325}, {0.00007808, 1.0975}, {0.00007908, 1.22}, {0.00008008, 1.28}, {0.00008108, 1.4925}, {0.00008208, 2.43}, {0.00008308, 2.415}, {0.00008408, 3.0875}, {0.00008508, 3.7575}, {0.00008608, 4.2325}, {0.00008708, 5.0875}, {0.00008808, 5.7975}, {0.00008908, 5.7275}, {0.00009008, 6.38}, {0.00009108, 6.98}, {0.00009208, 6.8775}, {0.00009308, 6.6775}, {0.00009408, 6.7225}, {0.00009508, 6.7725}, {0.00009608, 6.5775}, {0.00009708, 5.8525}, {0.00009808, 5.55}, {0.00009908, 5.215}, {0.00010008, 4.81}, {0.00010108, 3.9125}, {0.00010208, 3.6525}, {0.00010308, 2.955}, {0.00010408, 2.9575}, {0.00010508, 1.8325}, {0.00010608, 1.68}, {0.00010708, 1.55}, {0.00010808, 1.575}, {0.00010908, 1.7625}, {0.00011008, 1.63}, {0.00011108, 1.7075}, {0.00011208, 2.25}, {0.00011308, 2.4425}, {0.00011408, 3.135}, {0.00011508, 3.2725}, {0.00011608, 4.2325}, {0.00011708, 4.3775}, {0.00011808, 4.4025}, {0.00011908, 5.59}, {0.00012008, 5.78}, {0.00012108, 6.0325}, {0.00012208, 6.2575}, {0.00012308, 6.54}, {0.00012408, 6.545}, {0.00012508, 6.28}, {0.00012608, 6.2225}, {0.00012708, 6.37}, {0.00012808, 5.875}, {0.00012908, 5.225}, {0.00013008, 4.8025}, {0.00013108, 4.3425}, {0.00013208, 3.7825}, {0.00013308, 3.055}, {0.00013408, 2.71}, {0.00013508, 2.575}, {0.00013608, 2.3925}, {0.00013708, 2.1775}, {0.00013808, 2.4}, {0.00013908, 1.9525}, {0.00014008, 2.05}, {0.00014108, 2.135}, {0.00014208, 3.1175}, {0.00014308, 3.2675}, {0.00014408, 3.355}, {0.00014508, 3.9775}, {0.00014608, 3.81}};My functional form is f[t, n, offset, Pitime, a, t[Phi], [Tau]_] := offset + a*1/ 2 (1 + Exp[-t/[Tau]]*(1/(n + 1)) (( Cos[2[CapitalOmega]R[Pitime](t + t[Phi])](1 - x[n]Cos[ 2[CapitalOmega]R[Pitime](t + t[Phi])*[Eta]LD^2]) + x[n]Sin[2[CapitalOmega]R[Pitime](t + t[Phi])] Sin[2[CapitalOmega]R[Pitime](t + t[Phi])*[Eta]LD^2])/( 1 + x[n]^2 - 2x[n]Cos[ 2[CapitalOmega]R[Pitime](t + t[Phi])*[Eta]LD^2])));where [Eta]LD = 0.02786;x[n_] := ( n/(n + 1));[CapitalOmega]R[Pitime_] := [Pi]/(2*Pitime);Here offset, Pitime, a, t[Phi] are the free parameters for both data sets. n and [Tau] are the fixed parameters for both data sets. t is the time over which the data has been recorded.Hope this gives you the complete picture of the problem I am trying to address. If there is any other information you may need, kindly inform me.Cheers, Arijit.
Posted 9 years ago
 Arijit, do you have any sample data and code?