我在使用scipy
中的curve_fit
时遇到问题。或者至少它没有像我期望的那样工作。在
我从一个柱状图中得到了一些数据集,x值是柱状图中一个numpy数组的大小。如果需要,我会在以后添加数据。柱状图几乎是高斯形状,我想用一个高斯函数来拟合它,只有两个自由参数,但它不起作用。在
有三个参数,代码运行良好:
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
hist=np.load('Rinnen.npy')
faktor = np.sum(hist)
norm_hist=hist/faktor # values from the histogram are normed
ref_werte = np.arange(0,1,0.001)
def gauss(x, *p):
a, b, c = p
y = a*np.exp(-0.5*((x - b)/c)**2.)
return y
p_initial = [0.1, 0.0, 0.1]
popt, pcov = curve_fit(gauss, ref_werte, norm_hist, p0=p_initial)
print(popt) #zeigen der koeffizienten
plt.figure()
plt.plot(ref_werte, norm_hist, linewidth=2.0, color='b')
plt.plot(ref_werte, gauss(ref_werte, *popt), 'b-', linewidth=2.0, color='r')
plt.xlabel('Reflektanzen')
plt.ylabel('normierte Häufigkeit')
plt.show()
但是我的目标是使用高斯函数,它是正态分布的PDF(参见wikipedia)。但是当我更改代码并使用像下面这样的函数的新定义时,它会把一切都搞乱,根本不起作用。在
^{pr2}$即使我使用与直方图非常接近的p_initial
值,也没有任何效果,我真的不明白为什么。在
如果有人能帮我,我会很高兴的。在
编辑:代码示例
hist
的一个示例数组是:
array([ 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 4,
30, 224, 2257, 3603, 2029, 2412, 1391, 2269, 3789,
8279, 9091, 6617, 7087, 5071, 2316, 2675, 2273, 3913,
2299, 3573, 1761, 2445, 2426, 3261, 5881, 8408, 11659,
15174, 21250, 19644, 32068, 25315, 19329, 23333, 17168, 15748,
15744, 15045, 14274, 11566, 13887, 10144, 8532, 10696, 8531,
9687, 9493, 9424, 10294, 8869, 9509, 8445, 7723, 8515,
7137, 7464, 8006, 6440, 6457, 4999, 5364, 4519, 4361,
3976, 3366, 3352, 2833, 2475, 2332, 1881, 1905, 1639,
1568, 1318, 1141, 1130, 1010, 907, 906, 823, 789,
745, 726, 674, 692, 630, 610, 568, 575, 589,
535, 538, 522, 511, 513, 534, 467, 446, 445,
337, 441, 454, 451, 438, 417, 388, 456, 405,
408, 399, 356, 404, 371, 412, 404, 401, 389,
354, 342, 358, 317, 306, 303, 295, 303, 294,
288, 251, 256, 226, 178, 241, 213, 196, 215,
210, 184, 165, 208, 200, 181, 171, 136, 156,
147, 137, 102, 119, 116, 89, 117, 104, 85,
77, 74, 52, 69, 34, 47, 44, 50, 32,
27, 34, 38, 24, 21, 28, 24, 22, 25,
19, 17, 15, 17, 18, 14, 11, 12, 5,
9, 9, 9, 6, 5, 5, 8, 7, 4,
4, 2, 1, 4, 0, 2, 2, 2, 3,
2, 3, 1, 1, 2, 1, 2, 2, 0,
1, 1, 2, 1, 1, 2, 0, 0, 0,
0, 0, 1, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
有了这个数组,我的代码可以处理带有三个参数的版本,结果得到[ 0.02697915 0.08060284 0.01334016]
。如果我把我的代码改成两个参数的版本,数组和一切都是一样的。。。那它就不合身了。我使用了p_initial = [0.08 , 0.02]
的另一个版本,它使用了平均值和标准推导结果根本不正确:[-1.62281493 0.53329897]
。在
正态分布是一个连续的分布,因此不能规范化直方图的和,而应该规范化积分。在
这是一个对我有用的代码版本。我唯一改变的就是用你的直方图除以箱子的宽度。它返回
[ 0.08083458 0.01470529]
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