适合python中的数据的多个高斯-fitmultiplegaussianstothedatainpython

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This requires a non-linear fit. A good tool for this is scipy's curve_fit function.

这需要非线性拟合。一个很好的工具是scipy的curve_fit函数。

To use curve_fit, we need a model function, call it func, that takes x and our (guessed) parameters as arguments and returns the corresponding values for y. As our model, we use a sum of gaussians:

要使用curve_fit,我们需要一个模型函数,称之为func,它将x和我们的(猜测的)参数作为参数,并返回y的相应值。作为我们的模型,我们使用一个高斯的总和:

from scipy.optimize import curve_fit
import numpy as np

def func(x, *params):
    y = np.zeros_like(x)
    for i in range(0, len(params), 3):
        ctr = params[i]
        amp = params[i+1]
        wid = params[i+2]
        y = y + amp * np.exp( -((x - ctr)/wid)**2)
    return y

Now, let's create an initial guess for our parameters. This guess starts with peaks at x=0 and x=1,000 with amplitude 60,000 and e-folding widths of 80. Then, we add candidate peaks at x=60, 140, 220, ... with amplitude 46,000 and width of 25:

现在,让我们为我们的参数创建一个初始猜测。这个猜测从x = 0和x = 1,000处的峰值开始,幅度为60,000,电子折叠宽度为80.然后,我们在x = 60,140,​​220 ......处添加候选峰值,幅度为46,000,宽度为25:

guess = [0, 60000, 80, 1000, 60000, 80]
for i in range(12):
    guess += [60+80*i, 46000, 25]

Now, we are ready to perform the fit:

现在,我们已准备好执行拟合:

popt, pcov = curve_fit(func, x, y, p0=guess)
fit = func(x, *popt)

To see how well we did, let's plot the actual y values (solid black curve) and the fit (dashed red curve) against x:

为了看看我们做得多好,让我们绘制实际y值(纯黑色曲线)和拟合(虚线红色曲线)对x:

As you can see, the fit is fairly good.

正如你所看到的,合适性非常好。

Complete working code

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

data = np.loadtxt('data.txt', delimiter=',')
x, y = data

plt.plot(x,y)
plt.show()

def func(x, *params):
    y = np.zeros_like(x)
    for i in range(0, len(params), 3):
        ctr = params[i]
        amp = params[i+1]
        wid = params[i+2]
        y = y + amp * np.exp( -((x - ctr)/wid)**2)
    return y

guess = [0, 60000, 80, 1000, 60000, 80]
for i in range(12):
    guess += [60+80*i, 46000, 25]   

popt, pcov = curve_fit(func, x, y, p0=guess)
print popt
fit = func(x, *popt)

plt.plot(x, y)
plt.plot(x, fit , 'r-')
plt.show()