将对数曲线拟合到数据点并以numpy外推 [英] Fit a logarithmic curve to data points and extrapolate out in numpy

问题描述

我有一组数据点（代码中的x和y）。我想绘制这些点，并为其拟合一条曲线，以显示使y = 100.0（y值为百分比）需要x的值。这是我尝试的方法，但是我的曲线是3级的多项式（我知道这是错误的）。对我来说，数据看起来是对数的，但是我现在知道如何对数据进行对数曲线的拟合。

I have a set of data points (x and y in the code). I would like to plot these points, and fit a curve to them that shows what value of x would be required to make y = 100.0 (y values are percentages). Here is what I have tried, but my curve is a polynomial of degree 3 (which I know is wrong). To me, the data looks logarithmic, but I do now know how to polyfit a logarithmic curve to my data.

import numpy as np
import matplotlib.pyplot as plt

x = np.array([4,8,15,29,58,116,231,462,924,1848])
y = np.array([1.05,2.11,3.95,7.37,13.88,25.46,43.03,64.28,81.97,87.43])

for x1, y1 in zip(x,y):
    plt.plot(x1, y1, 'ro')

z = np.polyfit(x, y, 3)
f = np.poly1d(z)

for x1 in np.linspace(0, 1848, 110):
    plt.plot(x1, f(x1), 'b+')

plt.show()

推荐答案

它看起来像是绑定曲线：

def binding(x,kd,bmax):
    return (bmax*x)/(x+kd)
param=sp.optimize.curve_fit(binding, x,y)

plt.plot(x,y,'o',np.arange(2000),binding(np.arange(2000),*param[0]))

在这种情况下，严格来说，y = 100％仅会发生在x = inf

In which case, strictly speaking, y=100% will only happen at x=inf

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