Exponential regression function Python

问题

I am trying to implement a exponential regression function. sp stands for sympy. I use numpy and sympy. Firstly, in func_exp I tried to use np.exp but it generated an error (attribute error), so I decided to use sympy instead. Well, this is the code

import numpy as np
from numpy.linalg import matrix_rank
import scipy 
import scipy.integrate

import random 

import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D

from sympy import integrate
import sympy as sp

x, y = sp.symbols('x, y')

sp.init_printing(use_unicode=True,use_latex='mathjax')
def exponential_regression (x_data, y_data):
   def func_exp(x, a, b):
       return a*sp.exp(b*x)
   popt, pcov = scipy.optimize.curve_fit(func_exp, x_data, y_data)
   a = popt[0] # componente a, Parámetro ÓPTimo (popt).
   b = popt[1] # componente b, Parámetro ÓPTimo (popt).
   plt.figure()
   puntos = plt.plot(x_data, y_data, 'x', color='xkcd:maroon')
   curva_regresion = plt.plot(x_data, func_exp(x_data, a, b),    color='xkcd:teal')
   plt.show(puntos, curva_regresion)
   return func_exp(x, a, b)

I try to execute:

  x_data = np.arange(0, 51) # Crea un array de 0 a 50.
  y_data = np.array([0.001, 0.199, 0.394, 0.556, 0.797, 0.891, 1.171, 1.128, 1.437, 
          1.525, 1.720, 1.703, 1.895, 2.003, 2.108, 2.408, 2.424,2.537, 
          2.647, 2.740, 2.957, 2.58, 3.156, 3.051, 3.043, 3.353, 3.400, 
          3.606, 3.659, 3.671, 3.750, 3.827, 3.902, 3.976, 4.048, 4.018, 
          4.286, 4.353, 4.418, 4.382, 4.444, 4.485, 4.465, 4.600, 4.681, 
          4.737, 4.792, 4.845, 4.909, 4.919, 5.100])
  exponential_regression(x_data, y_data)

And I get:

exponential_regression(x_data, y_data)
TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'

Traceback (most recent call last):

File "<ipython-input-122-ee7c243ae4b0>", line 1, in <module>
exponential_regression(x_data, y_data)

 File "/Volumes/TOSHIBA/spline.py", line 35, in exponential_regression
popt, pcov = scipy.optimize.curve_fit(func_exp, x_data, y_data)

 File "/Applications/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py", line 742, in curve_fit
res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)

 File "/Applications/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py", line 387, in leastsq
gtol, maxfev, epsfcn, factor, diag)

 error: Result from function call is not a proper array of floats.

What is wrong? Thanks in advance!

回答1:

Here is a minimal example for your fit function as close as possible to your code but removing all unnecessary elements. You can easily remove c to adhere to your requirements:

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def func_exp(x, a, b, c):
        #c = 0
        return a * np.exp(b * x) + c

def exponential_regression (x_data, y_data):
    popt, pcov = curve_fit(func_exp, x_data, y_data, p0 = (-1, 0.01, 1))
    print(popt)
    puntos = plt.plot(x_data, y_data, 'x', color='xkcd:maroon', label = "data")
    curva_regresion = plt.plot(x_data, func_exp(x_data, *popt), color='xkcd:teal', label = "fit: {:.3f}, {:.3f}, {:.3f}".format(*popt))
    plt.legend()
    plt.show()
    return func_exp(x_data, *popt)

x_data = np.arange(0, 51) 
y_data = np.array([0.001, 0.199, 0.394, 0.556, 0.797, 0.891, 1.171, 1.128, 1.437, 
        1.525, 1.720, 1.703, 1.895, 2.003, 2.108, 2.408, 2.424,2.537, 
        2.647, 2.740, 2.957, 2.58, 3.156, 3.051, 3.043, 3.353, 3.400, 
        3.606, 3.659, 3.671, 3.750, 3.827, 3.902, 3.976, 4.048, 4.018, 
        4.286, 4.353, 4.418, 4.382, 4.444, 4.485, 4.465, 4.600, 4.681, 
        4.737, 4.792, 4.845, 4.909, 4.919, 5.100])
exponential_regression(x_data, y_data)

Output with c = 0:

Output with c != 0:

Main changes explained:

Removed sympy - it has nothing to do with the fitting procedure.
The definition of the exponential fit function is placed outside exponential_regression, so it can be accessed from other parts of the script. It uses np.exp because you work with numpy arrays in scipy.
Added the parameter p0 which contains the initial guesses for the parameters. Fit functions are often sensitive to this initial guess because of local extrema.
Unpack variables with *popt to make it more flexible for different numbers of variables. a = popt[0], b = popt[1], etc.
Removed unnecessary imports. Keep your namespace free from clutter.

来源：https://stackoverflow.com/questions/50706092/exponential-regression-function-python

标签

python

numpy

regression

sympy

exponential