[Python] Conditionally fitting

Overview

If you want to do fitting, you can do it with scipy.optimize.leastsq etc. in python.

However, when doing fitting, there are many cases where you want to condition the fitting parameters.

For example, as shown below, both parameters a and b are in the positive range to find the optimum value.

f(x, a, b)=a*x^2+b (a>0 and b>0)

This time, I will introduce such a method.

Method

When fitting, pass the difference between the fitting function and the actual data as the first argument of scipy.optimize.leastsq.

def func(param, x):
    return param[0]*x**2+param[1]
    
def fit(param, x, y):
    
    def residual(param, x, y):
        return y-func(param, x)
        
    return optimize.leastsq(residual, param, args=(x, y))

If you want to perform conditional fitting, you can minimize the function that increases the difference between the actual data and the function if the parameter does not meet the condition.

def residual(param, x, y):
    return y-func(param, x) + param_condition(param)
    
def param_condition(param):
    
    if (param meet the condition):
        return 0
    else:
        return np.inf         

※Caution

Since the objective function becomes non-differentiable, the fitting time will be considerably longer.

(I haven't looked closely at the source code, but I think we usually use the gradient of the objective function to find the optimal parameters.)