Error non-linear-regression python curve-fit

Question

Hello guys i want to make non-linear regression in python with curve fit this is my code:

#fit a fourth degree polynomial to the economic data
from numpy import arange
from scipy.optimize import curve_fit
from matplotlib import pyplot
import math

x = [17.47,20.71,21.08,18.08,17.12,14.16,14.06,12.44,11.86,11.19,10.65]
y = [5,35,65,95,125,155,185,215,245,275,305]

# define the true objective function
def objective(x, a, b, c, d, e):
    return ((a)-((b)*(x/3-5)))+((c)*(x/305)**2)-((d)*(math.log(305))-math.log(x))+((e)*(math.log(305)-(math.log(x))**2))

popt, _ = curve_fit(objective, x, y)
# summarize the parameter values
a, b, c, d, e = popt
# plot input vs output
pyplot.scatter(x, y)
# define a sequence of inputs between the smallest and largest known inputs
x_line = arange(min(x), max(x), 1)
# calculate the output for the range
y_line = objective(x_line, a, b, c, d, e)
# create a line plot for the mapping function
pyplot.plot(x_line, y_line, '--', color='red')
pyplot.show()

this is my error:

Traceback (most recent call last): File "C:\Users\Fahmi\PycharmProjects\pythonProject\main.py", line 16, in popt, _ = curve_fit(objective, x, y) File "C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py", line 784, in curve_fit res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs) File "C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py", line 410, in leastsq shape, dtype = _check_func('leastsq', 'func', func, x0, args, n) File "C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py", line 24, in _check_func res = atleast_1d(thefunc( ((x0[:numinputs],) + args))) File "C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py", line 484, in func_wrapped return func(xdata, params) - ydata File "C:\Users\Fahmi\PycharmProjects\pythonProject\main.py", line 13, in objective return ((a)-((b) (x/3-5)))+((c) (x/305)**2)-((d) (math.l og(305))-math.log(x))+((e) (math.log(305)-(math.log(x))**2)) TypeError: only size-1 arrays can be converted to Python scalars

thanks before

Answer 1

This is a known problem with the math library. Simply use numpy and your problem should be fixed as numpy functions have support for scalars and arrays.

#fit a fourth degree polynomial to the economic data
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

x = [17.47,20.71,21.08,18.08,17.12,14.16,14.06,12.44,11.86,11.19,10.65]
y = [5,35,65,95,125,155,185,215,245,275,305]

# define the true objective function
def objective(x, a, b, c, d, e):
    return ((a)-((b)*(x/3-5)))+((c)*(x/305)**2)-((d)*(np.log(305))-np.log(x))+((e)*(np.log(305)-(np.log(x))**2))

popt, _ = curve_fit(objective, x, y)
# summarize the parameter values
a, b, c, d, e = popt
# plot input vs output
plt.scatter(x, y)
# define a sequence of inputs between the smallest and largest known inputs
x_line = np.arange(np.min(x), np.max(x), 1)
# calculate the output for the range
y_line = objective(x_line, a, b, c, d, e)
# create a line plot for the mapping function
plt.plot(x_line, y_line, '--', color='red')
plt.show()