使多个高斯适合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来实现高斯/洛伦兹拟合到10个峰并提取fwhm并确定fwhm在x值上的位置.复杂的方法是分离峰并拟合数据并提取分子量.

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.

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

任何忠告，不胜感激.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\test.py", line 33, in <module>
popt, pcov = curve_fit(func, x, y, p0=guess)
File "C:\Python27\lib\site-packages\scipy\optimize\minpack.py", line 533, in curve_fit
res = leastsq(func, p0, args=args, full_output=1, **kw)
File "C:\Python27\lib\site-packages\scipy\optimize\minpack.py", line 368, in leastsq
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
File "C:\Python27\lib\site-packages\scipy\optimize\minpack.py", line 19, in _check_func
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
File "C:\Python27\lib\site-packages\scipy\optimize\minpack.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. scipy的curve_fit函数是一个很好的工具.

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，将其命名为func，该函数将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，我们使用高斯的总和:

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，让我们为参数创建一个初始猜测.这个猜测从在x=0和x=1,000处的峰开始，幅度为60,000，电子折叠宽度为80.然后，在x=60, 140, 220, ...处添加候选峰，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，我们准备进行拟合:

Now, we are ready to perform the fit:

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

要了解我们做得如何，让我们针对x绘制实际的y值(黑色实线)和fit(红色虚线):

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，契合度很好.

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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