Question

我在为数据拟合高斯时遇到了一些麻烦。我认为问题是大多数元素接近于零，实际上没有多少要点。但无论如何，我认为他们制作了一个很好的数据集，而且我没有得到令人困惑的python。这是程序，我还添加了一行来绘制数据，这样你就可以看到我想要的东西

#Gaussian function
def gauss_function(x, a, x0, sigma):
    return a*np.exp(-(x-x0)**2/(2*sigma**2))

# program
from scipy.optimize import curve_fit
x = np.arange(0,21.,0.2)
# sorry about these data!
y = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.2888599818864958e-275, 1.0099964933708256e-225, 4.9869496866403137e-184, 4.4182929795060327e-149, 7.2953754336628778e-120, 1.6214815763354974e-95, 2.5845990267696154e-75, 1.2195550372375896e-58, 5.6756631456872126e-45, 7.2520963306599953e-34, 6.0926453402093181e-25, 7.1075523112494745e-18, 2.1895584709541657e-12, 3.1040093615952226e-08, 3.2818874974043519e-05, 0.0039462011337049593, 0.077653596114448178, 0.33645159419151383, 0.40139213808285212, 0.15616093582013874, 0.0228751827752081, 0.0014423440677009125, 4.4400754532288282e-05, 7.4939123408714068e-07, 7.698340466102054e-09, 5.2805658851032628e-11, 2.6233358880470556e-13, 1.0131613609937094e-15, 3.234727006243684e-18, 9.0031014316344088e-21, 2.2867065482392331e-23, 5.5126221075296919e-26, 1.3045106781768978e-28, 3.1185031969890313e-31, 7.7170036365830092e-34, 2.0179753504732056e-36, 5.6739187799428708e-39, 1.7403776988666581e-41, 5.8939645426573027e-44, 2.2255784749636281e-46, 9.4448944519959299e-49, 4.5331936383388069e-51, 2.4727435506007072e-53, 1.5385048936078214e-55, 1.094651071873419e-57, 8.9211199390945735e-60, 8.3347561634783632e-62, 8.928140776588251e-64, 1.0960564546383266e-65, 1.5406342485015278e-67, 2.4760905399114866e-69, 4.5423744881977258e-71, 9.4921949220625905e-73, 2.2543765002199549e-74, 6.0698995872666723e-76, 1.8478996852922248e-77, 6.3431644488676084e-79, 0.0, 0.0, 0.0, 0.0]

plot(x,y) #Plot the curve, the gaussian is quite clear
plot(x,y,'ok') #Overplot the dots

# Try to fit the result
popt, pcov = curve_fit(gauss_function, x, y)

问题是popt的结果是

print popt
array([  7.39717176e-10,   1.00000000e+00,   1.00000000e+00])

有关为何会发生这种情况的任何提示？

谢谢！

Answer 1

你的问题在于curve_fit的初始参数。默认情况下，如果没有给出其他信息，它将以1的数组开头，但这显然会导致严重错误的结果。这可以通过给出合理的起始向量来简单地纠正。为此，我从数据集的估计平均值和标准差开始

#estimate mean and standard deviation
meam = sum(x * y)
sigma = sum(y * (x - m)**2)
#do the fit!
popt, pcov = curve_fit(gauss_function, x, y, p0 = [1, mean, sigma])
#plot the fit results
plot(x,gauss_function(x, *popt))
#confront with the given data
plot(x,y,'ok')

这将完全接近您的结果。请记住，除非从一个好点开始（在汇聚盆地内部，要清楚），否则曲线拟合通常不起作用，这不依赖于实施。当你可以运用你的知识时，千万不要盲目适应！

高斯适合python中的scipy.optimize.curve_fit，结果错误

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