lsf.py

import numpy as np
import matplotlib.pyplot as plt

# fitting equation: y = (a-d)/(1+(x/c)^b)+d

# genrate the data set
a,b,c,d = 1,2,3,4
x = np.arange(0,10,0.01)
y = (a-d)/(1+(x/c)**b)+d + 0.1*np.random.random(len(x))

fuc = lambda a,b,c,d,x:(a-d)/(1+(x/c)**b)+d
err_fuc = lambda a,b,c,d,x,y: np.linalg.norm(fuc(a,b,c,d,x) - y)
# initialize parameters
a,b,c,d = np.random.random((4,))
error = err_fuc(a,b,c,d,x,y)
eta = 0.001
for iter in range(1000):
    eps = 1e-6
    par_a = (err_fuc(a+eps,b,c,d,x,y)-error)/eps
    par_b = (err_fuc(a,b+eps,c,d,x,y)-error)/eps
    par_c = (err_fuc(a,b,c+eps,d,x,y)-error)/eps
    par_d = (err_fuc(a,b,c,d+eps,x,y)-error)/eps
    a,b,c,d = a-eta*par_a,b-eta*par_b,c-eta*par_c,d-eta*par_d #gradient descent algorithm
    error = err_fuc(a,b,c,d,x,y)
print(a,b,c,d)