将多个高斯拟合到python中的数据 [英] fit multiple gaussians to the data in python

问题描述

我只是想知道是否有一种简单的方法可以实现对 10 个峰值的高斯/洛伦兹拟合并提取 fwhm 并确定 fwhm 在 x 值上的位置.复杂的方法是分离峰值并拟合数据并提取fwhm.

I am just wondering if there is a easy way to implement gaussian/lorentzian fits to 10 peaks and extract fwhm and also to determine the position of fwhm on the x-values. The complicated way is to separate the peaks and fit the data and extract fwhm.

数据是 [https://drive.google.com/file/d/0B6sUnnbyNGuOT2RZb2UwYXU4dlE/view?usp=sharing].

非常感谢任何建议.谢谢.

Any advise greatly appreciated. Thanks.

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)
    print len(params)
    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)



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()



Traceback (most recent call last):
File "C:Users	est.py", line 33, in <module>
popt, pcov = curve_fit(func, x, y, p0=guess)
File "C:Python27libsite-packagesscipyoptimizeminpack.py", line 533, in curve_fit
res = leastsq(func, p0, args=args, full_output=1, **kw)
File "C:Python27libsite-packagesscipyoptimizeminpack.py", line 368, in leastsq
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
File "C:Python27libsite-packagesscipyoptimizeminpack.py", line 19, in _check_func
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
File "C:Python27libsite-packagesscipyoptimizeminpack.py", line 444, in    _ general_function
return function(xdata, *params) - ydata
TypeError: unsupported operand type(s) for -: 'NoneType' and 'float'

推荐答案

这需要非线性拟合.一个很好的工具是 scipy 的 curve_fit 函数.

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

要使用 curve_fit，我们需要一个模型函数，称为 func，它接受 x 和我们的(猜测的)参数作为参数和返回 y 的相应值.作为我们的模型，我们使用高斯总和:

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:

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

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，振幅为 60,000，e 折叠宽度为 80.然后，我们在 x= 处添加候选峰值60, 140, 220, ... 幅度为 46,000，宽度为 25:

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:

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

现在，我们准备执行拟合:

Now, we are ready to perform the fit:

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

为了看看我们做得有多好，让我们绘制实际的 y 值(黑色实线曲线)和 fit(红色虚线曲线)相对于 x:

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

如您所见，合身度相当不错.

As you can see, the fit is fairly good.

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()

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