如何用 Python 绘制 polyfit `n log n`？

Question

Below is an excerpt of my code that plots and creates a trend line based of the order that is given to the numpy.polyfit library. I'm able to plot linear, quadratic, and many other polynomial trends. However I'm not able to create trend lines for data that might fitortrends.

Any hits how to go about doing this?

import numpy as np
from matplotlib import pyplot, pylab

def plotChart(title, xlabel, ylabel, x, y, fit):
    plot1 = pyplot.plot(x, y, "o", label="runtime")
    plot2 = pyplot.plot(x, fit(x), "--", label="trendline")
    pylab.title(title)
    pylab.ylabel(ylabel)
    pylab.xlabel(xlabel)
    pyplot.legend()
    pyplot.tight_layout()
    pyplot.show()

def analyzeTimes(sampleList, timingList, order, title, xlabel, ylabel):
    x = np.array(sampleList)
    y = np.array(timingList)
    coefficients = np.polyfit(x, y, order)
    fit = np.poly1d(coefficients)

    plotChart(
        f"{title}\n {fit}", 
        xlabel, 
        ylabel,
        x,
        y,
        fit
    )

Answer 1

You can treat log(n) and nlog(n) as first order polynomials where the x values is log(n) or nlog(n). That is, you take the log(n) or nlog(n) before fitting and use that as the input to polyfit. Here's an example for log(n):

import numpy as np
from matplotlib import pyplot as plt

# Fake Data 
x = range(1,101)
y = 5 * np.log(x) + np.random.rand(len(x))

# Fit 
coefficients = np.polyfit(np.log(x),y,1) # Use log(x) as the input to polyfit.
fit = np.poly1d(coefficients) 

plt.plot(x,y,"o",label="data")
plt.plot(x,fit(np.log(x)),"--", label="fit")
plt.legend()
plt.show()

If you are using other functions that can't be simplified to polynomials you can use curvefit from the scipy library.