Scipy S型曲线拟合

问题描述

我有一些数据点，想找到一个拟合函数，我想一个累积的高斯S型函数就可以了，但我真的不知道如何实现。

I have some data points and would like to find a fitting function, I guess a cumulative Gaussian sigmoid function would fit, but I don't really know how to realize that.

这就是我现在拥有的：

import numpy as np
import pylab
from scipy.optimize
import curve_fit

def sigmoid(x, a, b):
     y = 1 / (1 + np.exp(-b*(x-a)))
     return y

xdata = np.array([400, 600, 800, 1000, 1200, 1400, 1600])
ydata = np.array([0, 0, 0.13, 0.35, 0.75, 0.89, 0.91])

popt, pcov = curve_fit(sigmoid, xdata, ydata)
print(popt)

x = np.linspace(-1, 2000, 50)
y = sigmoid(x, *popt)

pylab.plot(xdata, ydata, 'o', label='data')
pylab.plot(x,y, label='fit')
pylab.ylim(0, 1.05)
pylab.legend(loc='best')
pylab.show()

但我收到以下警告：

... / scipy / optimize / minpack.py：779：O ptimizeWarning：无法估计参数的协方差
category = OptimizeWarning）

有人可以帮助吗？
我也愿意尝试其他方法！我只需要以某种方式拟合此数据即可。

Can anyone help?I'm also open for any other possibilities to do it! I just need a curve fit in any way to this data.

推荐答案

您可以为参数设置一些合理的界限，例如，

You could set some reasonable bounds for parameters, for example, doing

def fsigmoid(x, a, b):
    return 1.0 / (1.0 + np.exp(-a*(x-b)))

popt, pcov = curve_fit(fsigmoid, xdata, ydata, method='dogbox', bounds=([0., 600.],[0.01, 1200.]))

我已经输出了

[7.27380294e-03 1.07431197e+03]

曲线看起来像

第一个点是（400， 0）被删除为无用。您可以添加它，尽管结果不会有太大变化...

First point at (400,0) was removed as useless. You could add it, though result won't change much...

UPDATE

请注意，被设置为[[low_a，low_b]，[high_a，high_b]），所以我要求比例尺在[0 ... 0.01]内，位置在[600 ... 1200]

Note, that bounds are set as ([low_a,low_b],[high_a,high_b]), so I asked for scale to be within [0...0.01] and location to be within [600...1200]

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