fit hyperbola from data points

Question

I have experimental data points (x1, x2, ..., xn), (y1, y2, ..., yn) of turbocharger pressure map and want to get trendline equation. In result of my research it's something like:

y = (ax^5 + bx^4 + cx^3 + dx^2 + ex + f)/(x+g)    # my equation

Tell me please, are there any ready-made functions for this? I tried using np.polyfit, but it works with usual polynoms and I must guess "g" in this way:

# y*(x-g) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f
pc  = np.polyfit(x, y*(x+g), 5)
y = (pc[0]*x**5 + pc[1]*x**4 + pc[2]*x**3 + pc[3]*x**2 + pc[4]*x + pc[5])/(x + g)

It would be nice if someone could help to get coefficiens of my equation.

Answer 1

Though this will lead to a slightly different minimization, you can linearize the equation as

x y = ax^5 + bx^4 + cx^3 + dx^2 + ex + f - g y

and solve by linear least-squares.