# Obtain a multiple variable Nonlinear fit using NonlinearModelFit?

GROUPS:
 I am trying to make a Nonlinear fit of the following efvc functional, where I want to vary parameters from alpha and gamma equations. I kept trying the way I thought it would work, but I always get an the error FindFit::fitd: "First argument in FindFit is not a list or a rectangular array". Clear[n, m, u, w, bint, beta, g, dg, bb, dbb, gama, dgama, fvc, defvc] {beta[0.] = 2, beta[Infinity] = 1} {2, 1} beta bint[u_?NumericQ] := If[u != 0, NIntegrate[BesselJ[0, x] BesselJ[1, x]/(x + x Exp[u x/2]), {x, 0, Infinity}]] beta[u_?NumericQ] := x /. FindRoot[(x/Pi) Sin[Pi/x] == 2 bint[u], {x, 1, 0, 2}] efvc bb[n_, m_, u_] := beta[u]^alpha[n, m, u] alpha[n_, m_, u_] := ((n^2 - m^2)/n^(A))^CubeRoot[u] gamma[n_, m_, u_] := 2 Exp[(Sqrt[u])/(1 - (m/n)^(3/2))] ClearAll[efvc] efvc[n_, m_, u_] /; n == 0 := 0 efvc[n_, m_, u_] /; n == m := -(2/Pi)*Sin[Pi*n] efvc[n_, m_, u_] := -(((2 bb[n, m, u])/Pi)) (Sin[(Pi*n)/(bb[n, m, u])]) (Cos[(Pi*m)/ gamma[n, m, u]]) data = Import["C:\\Users\\caioa\\Documents\\Pasta1.xls"] {{{0.508224, 4.52*10^-7, 0.2}, {0.500808, 7.99*10^-6, 0.5}, {0.502848, 0.000143831, 1.}, {0.50025, 0.000845692, 1.5}, {0.504386, 0.000448702, 2.}, {0.512548, 0.000124658, 2.5}, {0.509866, 0.0000426, 3.}, {0.509804, 0.000045, 3.5}, {0.511647, 0.000148473, 4.}, {0.50246, 0.000047, 4.5}, {0.507061, 0.0030538, 5.}, {0.500444, 0.0000483, 5.5}, {0.506678, 0.0000495, 6.}, {0.501696, 0.000669212, 6.5}, {0.508953, 0.0000503, 7.}, {0.505067, 0.0000501, 7.5}, {0.501641, 0.000498973, 8.}, {0.509878, 0.00529143, 8.5}, {0.507094, 0.0000507, 9.}, {0.504594, 0.00433331, 9.5}, {0.502338, 0.0000504, 10.}}} NonlinearModelFit[data, (efvc), {A}, {n, m, u}] NonlinearModelFit::fitd: First argument {{{0.508224,4.52*10^-7,0.2},{0.500808,7.99*10^-6,0.5},{0.502848,0.000143831,1.},{0.50025,0.000845692,1.5},{0.504386,0.000448702,2.},{0.512548,0.000124658,2.5},<<9>>,{0.505067,0.0000501,7.5},{0.501641,0.000498973,8.},{0.509878,0.00529143,8.5},{0.507094,0.0000507,9.},{0.504594,0.00433331,9.5},{0.502338,0.0000504,10.}}} in NonlinearModelFit is not a list or a rectangular array.  Attachments:
17 days ago
6 Replies
 John Doty 2 Votes Your data isn't a rectangular array: it's a list containing a single element, and that single element is a rectangular array. Use data[[1]].
17 days ago
 Now it returned: NonlinearModelFit::fitc: Number of coordinates (2) is not equal to the number of variables (3). 
17 days ago
 John Doty 1 Vote It means what it says. Your data items contain three numbers, which it interprets as two independent variables and a quantity derived from them. Your list of variables is {n, m, u}. Three independent variables. I have no idea what you mean by your parameter A or how you expect to inform your function evfc of its value, or of the values of the independent variables.
 I called A just a little bit of the equation so I could test if I could achieve what I am looking for. I want to improve the form of efvc, but I can change some bits of it, because the overall form has a physical meaning behind it. I don't how to make it possible. I need the three variables {n, m, u} without fixing one of them, so I can obtain a efvc form that works well in all regimes.I made some changes, where now my table is {n, m, u, f}, here calling fjust to say it's the solution of the equation. Getting now another error that seems to be caused because I am using roots, I don't know. Attachments:
 John Doty 1 Vote If you wish to get advice, post your code.Remember that Mathematica is an expression rewriting language. Consider your code: NonlinearModelFit[data, (efvc), {A}, {n, m, u}] NonlinearModelfit works by substituting values for the variables and parameters into the given formula. The formula here is (efvc). It contains none of A, n, m, u. The fact that you've told Mathematica how to rewrite expressions of the form evfc[_,_,_] is irrelevant: you have no such expression here. The pattern names in your definition of evfc have no connection to names of variables and parameters elsewhere.