Fit to complex-valued functions

Function DoComplexFitMC(ndat,a,b,sigma)			 // driver to demonstrate fit to complex func
	variable ndat,a,b,sigma					// uses Monte Carlo (MC) to create fake data

	make /c/d/free/n=(ndat) yw
	make /d/free/n=(2*ndat) sigw
	make /d/o/n=(2*ndat) ww2=0,yw2			// real waves for real and imag parts of yw, ww
	variable wmax=30
	ww2[0,ndat-1] = p/(ndat-1)*wmax			// linear span of frequencies  (often would be log...)
	ww2[ndat, ] = ww2[p-ndat]				// these values are not used (dummy placeholders)
	
	sigw = sigma									// wave of standard deviations
	make /d/free pars={a,b}						// pack true parameters into wave, use for fit, too
	yw = ComplexFunc(pars,ww2) 					// noiseless "core"  for fit using true a,b
	yw2[0,ndat-1] = real(yw)
	yw2[ndat, ] = imag(yw[p-ndat])				// yw20 concatenates real & imaginary responses
	yw2 += gnoise(sigma)							// add noise for fake data (to be fit)
	
	FuncFit/NTHR=0/W=2 ComplexFitAllAtOnce pars  yw2 /X=ww2 /W=sigw /I=1 /D       // does the fit
	
	//_______________	graphics stuff__________________________
	make /d/o/n=(ndat) yr,yi,w0					//  waves for nice plotting
	w0 = ww2[p]									// get first ndat points
	yr = yw2[p];		yi = yw2[p+ndat]			// get real and imag parts
	
	make /c/d/free/n=1000 fit_yc
	make /d/o/n=1000 fit_yr, fit_yi
	SetScale/I x 0,wmax,"", fit_yi,fit_yr,fit_yc
	fit_yc = ComplexFunc(pars, x)
	fit_yr=real(fit_yc);		fit_yi = imag(fit_yc)
End

Function ComplexFitAllAtOnce(pars,y2,w2) : FitFunc	// kluge for complex fits using FuncFit
	wave pars,y2,w2
	variable ndat = numpnts(w2)/2						// break between real and imag data
	make /c/d/free /n=(ndat) temp = ComplexFunc(pars,w2)				// call to complex fit func
	y2[0,ndat-1] = real(temp);	y2[ndat, ] = imag(temp[p-ndat])		// concatenates real & imag
End

Function /c ComplexFunc(pars,w)
	wave pars;  variable w
	variable a=pars[0], b=pars[1]						// unpack parameter wave
	variable /c i=cmplx(0,1)							// i = sqrt(-1)
	return exp(i*w*a) / (1-i*w*b)					// this is the function we fit!
end