[英]Creating a Smooth Line based on Points
I have the following dataset: 我有以下数据集:
x = [1, 6, 11, 21, 101]
y = [5, 4, 3, 2, 1]
and my goal is to create a smooth curve that looks like this: 我的目标是创建一个如下所示的平滑曲线:
Is there a way to do it in Python? 有没有办法在Python中做到这一点?
I have attempted using the method shown in here , and here is the code: 我试过使用这里显示的方法,这里是代码:
from scipy.interpolate import spline
import matplotlib.pyplot as plt
import numpy as np
x = [1, 6, 11, 21, 101]
y = [5, 4, 3, 2, 1]
xnew = np.linspace(min(x), max(x), 100)
y_smooth = spline(x, y, xnew)
plt.plot(xnew, y_smooth)
plt.show()
First, interpolate.spline()
has been deprecated , so you should probably not use that. 首先, 不推荐使用 interpolate.spline()
,因此您可能不应该使用它。 Instead use interpolate.splrep()
and interpolate.splev()
. 而是使用interpolate.splrep()
和interpolate.splev()
。 It's not a difficult conversion: 这不是一个困难的转换:
y_smooth = interpolate.spline(x, y, xnew)
becomes 变
tck = interpolate.splrep(x, y)
y_smooth = interpolate.splev(xnew, tck)
But, that's not really the issue here. 但是,这不是真正的问题。 By default, scipy
tries to fit a polynomial of degree 3 to your data, which doesn't really fit your data. 默认情况下, scipy
尝试将3度多项式拟合到您的数据中,这与您的数据不scipy
。 But since there's so few points, it can fit your data fairly well even though it's a non-intuitive approximation. 但由于点数太少,它可以很好地适应您的数据,即使它是非直观的近似值。 You can set the degree of polynomial that it tries to fit with a k=...
argument to splrep()
. 您可以设置它尝试与splrep()
的k=...
参数拟合的多项式的次数。 But the same is true even of a polynomial of degree 2; 但即使是2阶多项式也是如此; it's trying to fit a parabola, and your data could possibly fit a parabola where there is a bow in the middle (which is what it does now, since the slope is so steep at the beginning and there's no datapoints in the middle). 它试图拟合抛物线,你的数据可能适合抛物线,中间有一个弓(这就是它现在所做的,因为斜率在开始时是如此陡峭,中间没有数据点)。
In your case, your data is much more accurately represented as an exponential, so it'd be best to fit an exponential. 在您的情况下,您的数据更准确地表示为指数,因此最好拟合指数。 I'd recommend using scipy.optimize.curve_fit()
. 我建议使用scipy.optimize.curve_fit()
。 It lets you specify your own fitting function which contains parameters and it'll fit the parameters for you: 它允许您指定自己的拟合函数,其中包含参数,它将适合您的参数:
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import numpy as np
x = [1, 6, 11, 21, 101]
y = [5, 4, 3, 2, 1]
xnew = np.linspace(min(x), max(x), 100)
def expfunc(x, a, b, c):
return a * np.exp(-b * x) + c
popt, pcov = curve_fit(expfunc, x, y)
plt.plot(xnew, expfunc(xnew, *popt))
plt.show()
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