Skip to main content

fitting - Need to fit curve to 5 parameters: what's a problem with NonlinearModelFit?


I have a data. The LinearModelFit works well with it. But I'm really interested to fit it to y == a 34^b x^d + e 34^f x. So, my code:


fit2 = NonlinearModelFit[data, {a 34^b x^d + e 34^f x}, {a, b, d, e, f}, {x}]

But it gives me an error:




NonlinearModelFit::nrjnum: The Jacobian is not a matrix of real numbers at {a,b,d,e,f} = {1.,1.,1.,1.,1.}.



Now I'm a bit stuck...


Update


data = {{0, 0}, {0.5`, 0.005899`}, {2.`, 0.011938`}, {5.`, 
0.016026`}, {8.`, 0.019241`}, {11.`, 0.021775`}, {14.`, 
0.023975`}, {17.`, 0.025926`}, {20.`, 0.027588`}, {23.`, 
0.029033`}, {26.`, 0.030481`}, {29.`, 0.03175`}, {32.`, 
0.032963`}, {35.`, 0.034043`}, {38.`, 0.035107`}, {44.`, 

0.036933`}, {50.`, 0.038732`}, {56.`, 0.040337`}, {62.`, 
0.041727`}, {68.`, 0.043243`}, {74.`, 0.044595`}, {80.`, 
0.045782`}, {86.`, 0.046893`}, {92.`, 0.048013`}, {98.`, 
0.04901`}, {104.`, 0.049906`}, {110.`, 0.050887`}, {116.`, 
0.051737`}, {122.`, 0.052511`}, {130.`, 0.053636`}, {142.`, 
0.056062`}, {154.`, 0.057802`}, {166.`, 0.059426`}, {178.`, 
0.060762`}, {190.`, 0.062086`}, {202.`, 0.063304`}, {214.`, 
0.064401`}, {226.`, 0.065449`}, {238.`, 0.066462`}, {250.`, 
0.067398`}, {262.`, 0.068241`}, {274.`, 0.069049`}, {286.`, 
0.069826`}, {298.`, 0.070638`}, {310.`, 0.071341`}, {322.`, 

0.071984`}, {334.`, 0.07258`}, {346.`, 0.073202`}, {358.`, 
0.073809`}, {370.`, 0.074263`}, {382.`, 0.074954`}, {394.`, 
0.075353`}, {406.`, 0.075835`}, {418.`, 0.076402`}, {430.`, 
0.076759`}, {442.`, 0.077285`}, {454.`, 0.077618`}, {466.`, 
0.077963`}, {478.`, 0.078492`}, {490.`, 0.07869`}, {502.`, 
0.079317`}, {514.`, 0.0795`}, {526.`, 0.079799`}, {538.`, 
0.080266`}, {550.`, 0.080393`}, {562.`, 0.080893`}, {574.`, 
0.081167`}, {586.`, 0.081271`}, {598.`, 0.081768`}, {610.`, 
0.082036`}, {622.`, 0.082127`}, {634.`, 0.0824`}, {646.`, 
0.082904`}, {658.`, 0.082974`}, {670.`, 0.083041`}, {682.`, 

0.083286`}, {694.`, 0.083747`}, {706.`, 0.083797`}};

Answer



Because there is a term x^d, I dropped the point {0, 0} from the data (see here).


Next, the terms a 34^b and e 34^f will be just constants - there is no point in taking them as a multiplication of two numbers - there are infinitely many ways to write them. So I changed to just a and e.


Using Manipulate:


Manipulate[
 Show[Plot[a x^d + e x, {x, 0, 700}], ListPlot@data, 
  PlotRange -> All], {a, 0, 1, 0.001}, {d, 0, 1, 0.01}, {e, 0, 1, 0.001}]

by trial-and-error I found starting values for the parameters:



fit2 = NonlinearModelFit[data, {a x^d + e x}, {{a, 0.2}, {d, 0.08}, {e, 0.}}, x]

that eventually gave


Show[Plot[Normal@fit2, {x, 0, 700}, PlotStyle -> Red], ListPlot@data]

enter image description here


being a quite good fit. The formula is


Normal@fit2



$0.00815195 x^{0.418618} - 0.0000613279 x$



Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more