Fit set of data (x,y) to function with parameter constraints?

Hi!

I'm trying to fit set of (x,y) data to y = D*sin(C*arctan{B*x-E(B*x-arctan(B*x))})

with parameter constraint function

C = 1+(1-(2/pi)*arcsin(F/D))

here B,C,D,E are the parameter constants need to find and F is the asymptote of y as x goes to infinity.

I can curve fit data with cftool for the main equation,

searched in internet but cannot find way to get an answer

How to add the constraint parameter functions ?

Thanks for the help. sorry for my knowledge, I'm new to matlab.

[Roger Stafford]

If it is assumed that B*(1-E)>0, then the asymptote of y would be

F = D*sin(C*pi/2)

which gives

C = 2/pi*asin(F/D)

rather than your formula.

In any case, such a requirement is not really a constraint. Either you vary C or you vary F in making a fit. The one determines the other.

[Shehara Perera]

Thanks Roger,

but my problem has more than 20 of coefficients like above(implicit functions).

It's hard to get one equation for all

Any suggestions ?

How to minimize (C-2/pi*asin(F/D)) ?

[Roger Stafford]

The point I was making is that you cannot regard both F and C as quantities that can be independently varied while searching for a fit. As I have said, setting one of them will determine the other. That is because as x approaches infinity, arctan(B*x-E(B*x-arctan(B*x))) will of necessity approach pi/2 assuming B*(1-E)>0, and therefore y will approach D*sin(C*pi/2). This shows that F = D*sin(C*pi/2). Therefore you can regard B, C, D, and E as your variable parameters and F will automatically be satisfied. It is not a separate constraint.