将半高斯曲线/归一化到数据点

Question

因此，我有两个数据列表，可以将它们绘制在散点图中，如下所示：

from matplotlib import pyplot as plt
x = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
y = [22.4155688819,22.3936180362,22.3177538001,22.1924849792,21.7721194577,21.1590235248,20.6670446864,20.4996957642,20.4260953411,20.3595072628,20.3926201626,20.6023149681,21.1694961343,22.1077417713,23.8270366414,26.5355924353,31.3179807276,42.7871637946,61.9639549412,84.7710953311]

plt.scatter(degrees,RMS_one_image)

这样可以使您得到一个看起来像高斯分布的图，这应该很好，

但是，我的问题是我正在尝试使它适合高斯分布，并且由于a而惨败。 它仅是高斯的一半而不是完整的高斯，并且b。 我以前用过的只用过一堆数字。 所以像这样：

# best fit of data
num_bins = 20
(mu, sigma) = norm.fit(sixteen)

y = mlab.normpdf(num_bins, mu, sigma)

n, bins, patches = plt.hist(deg_array, num_bins, normed=1, facecolor='blue', alpha=0.5)
# add a 'best fit' line
y = mlab.normpdf(bins, mu, sigma)
plt.plot(bins, y, 'r--')

这种方法在这里根本行不通吗，还是我完全以错误的方式解决了这个问题？ 谢谢...

Answer 1

看来，通常的解决方案是直接找到数据的期望值和标准偏差，而不是使用最小二乘拟合。 这是使用scipy.optimize中的curve_fit的解决方案。

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

x = np.array([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19])
y = [22.4155688819,22.3936180362,22.3177538001,22.1924849792,21.7721194577,21.1590235248,20.6670446864,20.4996957642,20.4260953411,20.3595072628,20.3926201626,20.6023149681,21.1694961343,22.1077417713,23.8270366414,26.5355924353,31.3179807276,42.7871637946,61.9639549412,84.7710953311]

# Define a gaussian function with offset
def gaussian_func(x, a, x0, sigma,c):
    return a * np.exp(-(x-x0)**2/(2*sigma**2)) + c

initial_guess = [1,20,2,0]
popt, pcov = curve_fit(gaussian_func, x, y,p0=initial_guess)

xplot = np.linspace(0,30,1000)
plt.scatter(x,y)
plt.plot(xplot,gaussian_func(xplot,*popt))

plt.show()