Re: Nonlinear Fit with complex model

*To*: mathgroup at smc.vnet.net*Subject*: [mg19637] Re: Nonlinear Fit with complex model*From*: "Kevin J. McCann" <kevinmccann at Home.com>*Date*: Tue, 7 Sep 1999 00:28:35 -0400*Organization*: @Home Network*References*: <7qsfre$159@smc.vnet.net> <7qvttf$4nq@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul, I noticed in the fragment you enclosed that upon execution the term in the numerator: deltaz(Es - I eta omega) did not get magnitude squared as it should. I converted the original expression to Normal form rather than Traditional and noted that this term had square brackets, viz. deltaz[Es - I eta omega] seems that Mathematica got confused !? Kevin Paul Abbott <paul at physics.uwa.edu.au> wrote in message news:7qvttf$4nq at smc.vnet.net... > mtir at my-deja.com wrote: > > > Hi, > > > > I am trying to fit a data set of real values with > > a model that involves complex numbers, i.e. > > model[a,b,c,d]=Abs[<complex expression in > > a,b,c,d>]^2 > > > > When I am using NonlinearRegress (or > > NonlinearFit) Mathematica complains that "One or > > more derivatives of the model with respect to > > parameters did not evaluate" and does not return a > > result. > > > > I suspect that the reason for this is that Abs[], > > Re[], Im[] etc. are not evaluated if the argument > > is an expression rather than a number. > > > > Does anyone know a way round this? > > > > Thanks! > > Sebastian > > > > (For those interested: I am trying to calculate > > the complex refractive index of a thin film from > > reflectance measurements as a function of angle) > > In the Notebook fragment below, I show a simple trick for computing the > complex conjugate of complex expressions with real variables. The basic > > idea is to compute the conjugate using the replacement > > Complex[a_, b_] :> Complex[a, -b] > > actually implemented using the built-in SuperStar function (so that you > can compute conjugates by raising them to the power *): > > SuperStar[x_] := x /. Complex[a_, b_] :> Complex[a, -b] > > The point then is that Abs[z]^2 = SuperStar[z] z which enables you to > quickly and efficiently compute the type of expression you want. > > Notebook[{ > Cell[BoxData[ > \(TraditionalForm > \`\(exp = > \(b0\ \[CapitalDelta]z\ > \((Es - \[ImaginaryI]\ \[Eta]\ \[Omega])\)\)\/\(\(-m\)\ > \[Omega]\^2 + m\ \[Omega] - > \[ImaginaryI]\ m\ \[Gamma]\ \[Omega] + > b0\ \((Es - \[ImaginaryI]\ \[Eta]\ \[Omega])\)\); \)\)], > "Input"], > > Cell[BoxData[ > \(TraditionalForm > \`\(x_\^*\) := x /. Complex(a_, b_) \[RuleDelayed] Complex(a, > \(-b\))\)], > "Input"], > > Cell[CellGroupData[{ > > Cell[BoxData[ > \(TraditionalForm\`\(\(exp\^*\) exp // ExpandAll\) // Simplify\)], > "Input"], > > Cell[BoxData[ > \(TraditionalForm > \`\(b0\^2\ \[CapitalDelta]z\^2\ > \((Es\^2 + \[Eta]\^2\ \[Omega]\^2) > \)\)\/\(\((Es\^2 + \[Eta]\^2\ \[Omega]\^2)\)\ b0\^2 + > 2\ m\ \[Omega]\ > \((\(-\[Omega]\)\ Es + Es + \[Gamma]\ \[Eta]\ \[Omega])\)\ b0 > + > m\^2\ \((\[Gamma]\^2 + \((\[Omega] - 1)\)\^2)\)\ > \[Omega]\^2\)\)], > "Output"] > }, Open ]] > } > ] > > ____________________________________________________________________ > Paul Abbott Phone: +61-8-9380-2734 > Department of Physics Fax: +61-8-9380-1014 > The University of Western Australia > Nedlands WA 6907 mailto:paul at physics.uwa.edu.au > AUSTRALIA http://physics.uwa.edu.au/~paul > > God IS a weakly left-handed dice player > ____________________________________________________________________ > > >