在python中将多个gaussian拟合到数据

Question

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个峰值，提取半高宽，并确定半高宽在x值上的位置。复杂的方法是分离峰，拟合数据，提取半峰宽。

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

任何建议都非常感谢。谢谢。

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'

Answer 1

@john1024的答案很好，但需要手动生成初始猜测。这里有一个简单的方法自动开始猜测。将john1024的相关3行代码替换为以下代码：

    import scipy.signal
    i_pk = scipy.signal.find_peaks_cwt(y, widths=range(3,len(x)//Npks))
    DX = (np.max(x)-np.min(x))/float(Npks) # starting guess for component width
    guess = np.ravel([[x[i], y[i], DX] for i in i_pk]) # starting guess for (x, amp, width) for each component

Answer 2

这需要非线性拟合。一个很好的工具是scipy的curve_fit函数。

要使用curve_fit，我们需要一个模型函数，调用它func，它接受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

现在，让我们为参数创建一个初始猜测。这一猜测从振幅为60000、e折叠宽度为80的x=0和x=1,000处的峰值开始。然后，我们在x=60, 140, 220, ...处添加振幅为46000、宽度为25的候选峰：

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

现在，我们准备好进行调整：

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

为了了解我们做得有多好，让我们绘制实际的y值（实心黑色曲线）和fit（红色虚线曲线）与x：

如你所见，合身性相当好。

完整工作代码

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()