与`scipy.optimize.curve_fit`错误的指数拟合

Question

我试图以指数方式拟合某些数据，但似乎无法强迫scipy.optimize.curve_fit给我一个令人满意的结果。

我已经将我的代码归结为下面的示例，包括符合经验的手动拟合数据。

import matplotlib.pylab as plt
import numpy
import scipy.stats

x = [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
     43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
     61, 62, 63, 64]
y = [9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14,
     14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 21, 22, 24, 25, 27, 30, 31,
     32, 37, 37]

def fitting_function(x, a, b, c):
    return a * numpy.exp(b * x) + c

plt.plot(x, y, 'o', label='Original data')
OptimalValues, Covariance = scipy.optimize.curve_fit(fitting_function, x, y)
plt.plot(x, fitting_function(x, *OptimalValues), '-',
         label='Fitted Curve (%0.2e*e^%sx+%0.2e)' % (OptimalValues[0],
                                              OptimalValues[1],
                                              OptimalValues[2]))
ManualFit = [0.1 * numpy.exp(0.09 * i) + 8 for i in x]
plt.plot(x, ManualFit, '-', label='Manual Fit (%s*e^%sx+%s)' % (0.1, 0.09, 8))
plt.legend(loc='best')
plt.show()

根据Stack Overflow的其他答案，一个明显的解决方案是为curve_fit提供合理的初始猜测。 如果我通过将以下行放在相关位置我的代码（第16和17行），解释器会抱怨ValueError因为它以某种方式尝试将guess广播到len(x)或len(y0（即操作数无法与形状（0）（40）一起广播。

guess = (0.1, 0.1, 10)
OptimalValues, Covariance = scipy.optimize.curve_fit(fitting_function, x, y,
                                                     p0=guess)

在这种情况下，如何让scipy.optimize.curve_fit给我一个有意义的输出？

Answer 1

将您的x和y列表转换为numpy阵列，它会正常工作。我发现为了获得满意的效果，你需要包括你的初步猜测。所以，这段代码：

import matplotlib.pylab as plt
import numpy
import scipy.stats

x = numpy.array([25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
     43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
     61, 62, 63, 64])
y = numpy.array([9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14,
     14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 21, 22, 24, 25, 27, 30, 31,
     32, 37, 37])

def fitting_function(x, a, b, c):
    return a * numpy.exp(b * x) + c

plt.plot(x, y, 'o', label='Original data')

guess =(0.1,0.1,10)
OptimalValues, Covariance = scipy.optimize.curve_fit(fitting_function, x, y,
                                                     p0=guess)

plt.plot(x, fitting_function(x, *OptimalValues), '-',
         label='Fitted Curve (%0.2e*e^%sx+%0.2e)' % (OptimalValues[0],
                                              OptimalValues[1],
                                              OptimalValues[2]))
ManualFit = [0.1 * numpy.exp(0.09 * i) + 8 for i in x]
plt.plot(x, ManualFit, '-', label='Manual Fit (%s*e^%sx+%s)' % (0.1, 0.09, 8))
plt.legend(loc='best')
plt.show()

制作此情节：