我可以将一半高斯拟合到Python中的数据集吗？

Question

I'm trying to automatically fit a Gaussian to data, but scipy can't seem to fit data that only shows half the curve. However, Scipy doesn't seem to be able to do this.

how the right side of the Gaussian curve data looks: https://i.imgur.com/LwzN2Jd.png

I have tried using the below code to fit curves. It fits fine for fully curves. But for half curves, it falls flat

'''

plotData = {}

#x = 0,2.5,5
#y = 16766,508,600.6

modelDataDf = df.loc[:,["x","y"]]
modelDataDf.sort_values(by=["x"],inplace=True)
modelData = modelDataDf.to_dict(orient="list")


def _1gaussian(x, amp1,cen1,sigma1):
        return amp1*(1/(sigma1*(np.sqrt(2*np.pi))))*(np.exp(-((x-cen1)**2)/((2*sigma1)**2)))

x_array = np.asarray(modelData["x"])
y_array_gauss = np.asarray(modelData["y"])
amp1 = 29000
sigma1 = 1
cen1 = -1

popt_gauss, pcov_gauss = scipy.optimize.curve_fit(_1gaussian, x_array, y_array_gauss, p0=[amp1, cen1, sigma1])
perr_gauss = np.sqrt(np.diag(pcov_gauss))

plotData["xGaussCurve"] = np.arange(0, 5.05, 0.05)
plotData["yGaussCurve"] = _1gaussian(plotData["xGaussCurve"],*popt_gauss)

'''

How a good fit looks: https://i.imgur.com/0gfqiRF.png

The half Gaussian it gets stuck on: https://i.imgur.com/Jsi4fzA.png

blue dots show the data, bold red line shows the fit I want it to show, red dotted line is the failed fitting.

I get the error:

RuntimeError: Optimal parameters not found: Number of calls to function has reached maxfev = 800.

When trying to fit half a gaussian.

Answer 1

As commented, you won't be able to fully fit a Gaussian with only three data points -- there are as many parameters as observations.

But if you're certain that it is "half" a Gaussian, then that implies that you know where the centroid of the Gaussian should be (perhaps at x=0 or x=-1 or something else). If that is the case, you could fix the centroid and vary the amplitude and sigma of the Gaussian. Perhaps something like

from lmfit.models import GaussianModel

modelDataDf = df.loc[:,["x","y"]]
modelDataDf.sort_values(by=["x"],inplace=True)
modelData = modelDataDf.to_dict(orient="list")

x_array = np.asarray(modelData["x"])
y_array_gauss = np.asarray(modelData["y"])

model = GaussianModel()
params = model.make_params(amplitude=29000, sigma=1, center=-1)
params['center'].vary = False  # fix the centroid at -1

result = model.fit(y_array_gauss, params, x=x_array)
print(result.fit_report())

xplot = np.linspace(0, 5, 101)
yplot = result.eval(x=xplot)