Question

我正在尝试实现指数回归函数。 sp代表同情。我使用numpy和sympy。首先，在func_exp中我尝试使用np.exp，但它生成了一个错误（属性错误），所以我决定改用sympy。好吧，这是代码

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)

我尝试执行：

  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)

我得到了：

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.

有什么问题？提前谢谢！

Answer 1

以下是适合函数的最小示例，尽可能接近您的代码，但删除所有不必要的元素。您可以轻松删除c以符合您的要求：

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)

以c = 0输出：

c != 0的输出：

主要变化解释：

删除sympy - 它与拟合程序无关。
指数拟合函数的定义位于exponential_regression之外，因此可以从脚本的其他部分访问它。它使用np.exp，因为你在scipy中使用numpy数组。
添加了parameter p0，其中包含参数的初始猜测。由于局部极值，拟合函数通常对这个初始猜测很敏感。
使用*popt解压缩变量，使其对不同数量的变量更加灵活。 a = popt[0]，b = popt[1]等
删除了不必要的导入。 Keep your namespace free from clutter.

指数回归函数Python

1 个答案: