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## Problem with fitting 2 functions simultaneously

Hi, I have a big Problem, I have experimental points which can be describe by a complex function. I can get data points of the real part and of the imaginary partof the function: REAL PART: [0.1000000000e-1, 5.1328], [0.2000000000e-1, 5.1295], [0.4000000000e-1, 5.1246], [0.8000000000e-1, 5.1207], [.1600000000, 5.1135], [.3200000000, 5.1031], [.6400000000, 5.0936], [1.280000000, 5.081], [2.560000000, 5.0688], [5.120000000, 5.0582], [10.24000000, 5.0481], [20.48000000, 5.038], [40.96000000, 5.0281], [81.92000000, 5.0174], [163.8400000, 5.0051], [327.6800000, 4.9908], [655.3600000, 4.9733], [1310.700000, 4.9518], [2621.400000, 4.9254], [5242.900000, 4.8927], [10486.00000, 4.8534], [20972.00000, 4.8077], [41943.00000, 4.7539], [83886.00000, 4.6957], [167770.0000, 4.6343], [335540.0000, 4.5702], [671090.0000, 4.5076], [1342200.000, 4.4478], [2684400.000, 4.3949], [5368700.000, 4.3688], [10000000.00, 4.288] IMAGINARY PART: [[0.1e-1, 0.863e-2], [0.2e-1, 0.913e-2], [0.4e-1, 0.1037e-1], [0.8e-1, 0.1283e-1], [.16, 0.1684e-1], [.32, 0.2187e-1], [.64, 0.2379e-1], [1.28, 0.2463e-1], [2.56, 0.2553e-1], [5.12, 0.2482e-1], [10.24, 0.2426e-1], [20.48, 0.2424e-1], [40.96, 0.2579e-1], [81.92, 0.2861e-1], [163.84, 0.3307e-1], [327.68, 0.3917e-1], [655.36, 0.4723e-1], [1310.7, 0.5733e-1], [2621.4, 0.6929e-1], [5242.9, 0.8269e-1], [10486., 0.9674e-1], [20972., .11028], [41943., .12213], [83886., .13115], [167770.0000, .13663], [335540.0000, .1383], [671090.0000, .13535], [1342200.000, .12717], [2684400.000, .11686], [5368700.000, .12487], [10000000., .1531]] The respectively real and imaginary data points can be described by the following functions: REAL PART: Eu1 + (Es1 - Eu1)/(1 + x^2*tau1^2) IMAGINARY PART: (Es1 - Eu1)*x *tau1/(1 + (x^2*tau1^2) x is the variable, Eu1,Es1, tau1 are the parameters. I would like to fit the data points with the given functions simultaneously that i get the best fit parameters for the function. A possibility is to shift the imaginary part(for exemple) in the x axe, and to define a new function (with the piecewise). The problem can be difficult if there two complex functions, I mean if 10^7>x=>0, [Eu1 + (Es1 - Eu1)/(1 + x^2*tau1^2)]+ [Eu2 + (Es2 - Eu2)/(1 +x^2*tau2^2)] and if 2*10^7>x=>10^7, [(Es1 - Eu1)*x *tau1/(1 + (x^2*tau1^2)]+[(Es2 - Eu2)*x *tau2/(1 + (x^2*tau2^2)]. I get more parameters. My first problem is to define the function which is a piecewise sum of 2 functions. My second Problem is to fit with Nonlinearfit the data points, with a possibility to give a range for each parameters. If somebody have an idea, Thanks a lot , Ravi

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