拟合数据集的指数曲线

Question

import numpy as np
import matplotlib.pyplot as plt

points = np.array([
 (333, 195.3267),
 (500, 223.0235),
 (1000, 264.5914),
 (2000, 294.8728),
 (5000, 328.3523),
 (10000, 345.4688)
])

# get x and y vectors
x = points[:,0]
y = points[:,1]

为了创建适合图表的指数曲线，我接下来的步骤是什么？

Answer 1

这是一个将数据拟合到对数二次方程的示例，该对数二次方程对数据的拟合比指数要好一些，并根据原始数据的散点图绘制拟合曲线。代码不是最优的，例如它重复获取 X 的日志，而不是只做一次。直接使用线性拟合方法也可以更有效地拟合 log(x) 数据，但是在这里您可以用更少的代码更改更轻松地用指数替换拟合方程。

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

points = numpy.array([(333, 195.3267), (500, 223.0235), (1000, 264.5914), (2000, 294.8728
), (5000, 328.3523), (10000, 345.4688)])
# get x and y vectors
xData = points[:,0]
yData = points[:,1]

# function to be fitted
def LogQuadratic(x, a, b, c):
    return a + b*numpy.log(x) + c*numpy.power(numpy.log(x), 2.0)


# some initial parameter values
initialParameters = numpy.array([1.0, 1.0, 1.0])

fittedParameters, pcov = curve_fit(LogQuadratic, xData, yData, initialParameters)

# values for display of fitted function
a, b, c = fittedParameters

# for plotting the fitting results
xPlotData = numpy.linspace(min(xData), max(xData), 50)
y_plot = LogQuadratic(xPlotData, a, b, c)

plt.plot(xData, yData, 'D') # plot the raw data as a scatterplot
plt.plot(xPlotData, y_plot) # plot the equation using the fitted parameters
plt.show()

print('fitted parameters:', fittedParameters)