# Question:statistic nonlinearfit

## Question:statistic nonlinearfit

Maple

Please I need to adjust this expression (Physics) help me to find at least one other solution and thank you very much, since there are several problems (although I test it with the correct parameters but the answer was (unexpected parameters)

Amplitude=abs((.9756567752*exp(-(.1628102823*(1.+i))*sqrt(x))*(-5.084444444*10^(-21)*(5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)*(S+sqrt((6.28*i*x+1/t)/n)*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))-5.208333335*10^21*(S-1.5*10^5*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S)))*(1.+0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))/(t*((6.28*i*x+1/t)/n-1.308996939*10^5*(1.+i)^2*x))+n*(1.-0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))+(26.48148149/(t*n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))+1973.518519/(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))*(1.+414.5929793/((1.+i)*sqrt(x)))-1.405316647*10^(-23)*S*(5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)*(S+sqrt((6.28*i*x+1/t)/n)*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))-5.208333335*10^21*(S-1.5*10^5*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))+5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n))-5.208333335*10^21/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)))/((1.+i)*sqrt(x)))-1.024343225*exp((.1628102823*(1.+i))*sqrt (x))*(-5.084444444*10^(-21)*(5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)*(S+sqrt((6.28*i*x+1/t)/n)*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))-5.208333335*10^21*(S-1.5*10^5*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S)))*(1.-0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))/(t*((6.28*i*x+1/t)/n-1.308996939*10^5*(1.+i)^2*x))+n*(1.+0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))+(26.48148149/(t*n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))+1973.518519/(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))*(1.-414.5929793/((1.+i)*sqrt(x)))+1.405316647*10^(-23)*S*(5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)*(S+sqrt((6.28*i*x+1/t)/n)*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))-5.208333335*10^21*(S-1.5*10^5*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))+5.208333335*10^21*exp(- 0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n))-5.208333335*10^21/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)))/((1.+i)*sqrt(x)))-1.016888889*10^(-20)*(5.208333335*10^21*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n)-67.50)*(S+sqrt((6.28*i*x+1/t)/n)*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S))-5.208333335*10^21*(S-1.5*10^5*n)/(n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(sqrt((6.28*i*x+1/t)/n)*n-1.*S)))*(0.2434322478e-1-0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))*exp(-0.450e-3*sqrt((6.28*i*x+1/t)/n))/(t*((6.28*i*x+1/t)/n-1.308996939*10^5*(1.+i)^2*x))+2.*n*(0.2434322478e-1+0.2763953196e-2*sqrt((6.28*i*x+1/t)/n)/((1.+i)*sqrt(x)))*exp(0.450e-3*sqrt((6.28*i*x+1/t)/n))+9.686178480*10^(-30)*(26.48148149/(t*n*(2.25*10^10-(1.*(6.28*i*x+1/t))/n)*(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))+1973.518519/(2.25*10^10-1.308996939*10^5*(1.+i)^2*x))*(0.2434322478e-1-414.5929793/((1.+i)*sqrt(x))))/(.9751817626*exp(-(.1628102 823*(1.+i))*sqrt(x))-1.024841941*exp((.1628102823*(1.+i))*sqrt(x)))).

X := Vector([3.3166247903554, 3.54964786985977, 3.75499667110372, 3.92428337406972, 4.06201920231798, 4.23083916026124, 4.38178046004133, 4.56070170039655, 4.7116875957559, 4.9295030175465, 4.9295030175465, 5.05964425626941, 5.23450093132096, 5.46808924579693, 5.81377674149945, 6.04979338490167, 6.27694193059009, 6.64830805543787, 6.92098258919931, 7.3348483283569, 7.61577310586391, 7.90569415042095, 8.14248119432891, 8.40832920383116, 8.73498712076898, 9.04986187739901, 9.42867965305853, 9.91463564635635, 10.4163333279998, 10.7191417566893, 11.0589330407594, 11.3401940018679, 11.8406080924925, 12.169634341261, 12.5019998400256, 12.8062484748657, 13.1529464379659, 13.4126805672841, 13.5683455144686, 13.8130373198656, 14.0712472794703, 14.1067359796659, 14.3527000944073, 14.5945195193264, 14.7105404387466, 14.8963082674869, 15.0864177325169, 15.1986841535707, 15.4175224987674, 15.6204993518133], datatype = float);
> Y := Vector([1, .914285714285714, .828571428571429, .8, .771428571428571, .714285714285714, .685714285714286, .714285714285714, .685714285714286, .6, .628571428571428, .6, .628571428571428, .571428571428571, .542857142857143, .542857142857143, .514285714285714, .485714285714286, .457142857142857, .428571428571428, .4, .4, .4, .4, .371428571428571, .371428571428571, .371428571428571, .4, .371428571428571, .342857142857143, .371428571428571, .371428571428571, .371428571428571, .4, .371428571428571, .4, .371428571428571, .4, .4, .4, .4, .4, .314285714285714, .371428571428571, .371428571428571, .342857142857143, .371428571428571, .371428571428571, .4, .371428571428571], datatype = float);
>
>
>
> fcn := NonlinearFit(amplitude, X, Y, ff, parameterranges = [Dé = 0.1e-5 .. 0.1e-2, S = .1 .. 100, tau = 0.1e-9 .. 0.1e-5], output = [parametervalues]);

Error, (in Statistics:-NonlinearFit) abs is not differentiable at non-real arguments

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