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1、例子：拟合一种函数Func，此处为一个指数函数。
出处：
SciPy v1.1.0 Reference Guide
#Headerimport numpy as npimport matplotlib.pyplot as pltfrom scipy.optimize import curve_fit#Define a function(here a exponential function is used)def func(x, a, b, c): return a * np.exp(-b * x) + c#Create the data to be fit with some noisexdata = np.linspace(0, 4, 50)y = func(xdata, 2.5, 1.3, 0.5)np.random.seed(1729)y_noise = 0.2 * np.random.normal(size=xdata.size)ydata = y + y_noiseplt.plot(xdata, ydata, 'bo', label='data')#Fit for the parameters a, b, c of the function func:popt, pcov = curve_fit(func, xdata, ydata)popt #output: array([ 2.55423706, 1.35190947, 0.47450618])plt.plot(xdata, func(xdata, *popt), 'r-', label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))#In the case of parameters a,b,c need be constrainted#Constrain the optimization to the region of #0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5]))popt #output: array([ 2.43708906, 1. , 0.35015434])plt.plot(xdata, func(xdata, *popt), 'g--', label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))#Labelsplt.title("Exponential Function Fitting")plt.xlabel('x coordinate')plt.ylabel('y coordinate')plt.legend()leg = plt.legend() # remove the frame of Legend, personal choiceleg.get_frame().set_linewidth(0.0) # remove the frame of Legend, personal choice#leg.get_frame().set_edgecolor('b') # change the color of Legend frame#plt.show()#Export figure#plt.savefig('fit1.eps', format='eps', dpi=1000)plt.savefig('fit1.pdf', format='pdf', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')plt.savefig('fit1.jpg', format='jpg', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')上面一段代码可以直接在spyder中运行。得到的JPG导出图如下：
2. 例子：拟合一个Gaussian函数
出处：LMFIT: Non-Linear Least-Squares Minimization and Curve-Fitting for Python
#Headerimport numpy as npimport matplotlib.pyplot as pltfrom numpy import exp, linspace, randomfrom scipy.optimize import curve_fit#Define the Gaussian functiondef gaussian(x, amp, cen, wid): return amp * exp(-(x-cen)**2 / wid)#Create the data to be fittedx = linspace(-10, 10, 101)y = gaussian(x, 2.33, 0.21, 1.51) + random.normal(0, 0.2, len(x))np.savetxt ('data.dat',[x,y]) #[x,y] is is saved as a matrix of 2 lines#Set the initial(init) values of parameters need to optimize(best)init_vals = [1, 0, 1] # for [amp, cen, wid]#Define the optimized values of parametersbest_vals, covar = curve_fit(gaussian, x, y, p0=init_vals)print(best_vals) # output: array [2.27317256 0.20682276 1.64512305]#Plot the curve with initial parameters and optimized parametersy1 = gaussian(x, *best_vals) #best_vals, '*'is used to read-out the values in the arrayy2 = gaussian(x, *init_vals) #init_valsplt.plot(x, y, 'bo',label='raw data')plt.plot(x, y1, 'r-',label='best_vals')plt.plot(x, y2, 'k--',label='init_vals')#plt.show()#Labelsplt.title("Gaussian Function Fitting")plt.xlabel('x coordinate')plt.ylabel('y coordinate')plt.legend()leg = plt.legend() # remove the frame of Legend, personal choiceleg.get_frame().set_linewidth(0.0) # remove the frame of Legend, personal choice#leg.get_frame().set_edgecolor('b') # change the color of Legend frame#plt.show()#Export figure#plt.savefig('fit2.eps', format='eps', dpi=1000)plt.savefig('fit2.pdf', format='pdf', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')plt.savefig('fit2.jpg', format='jpg', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')上面一段代码可以直接在spyder中运行。得到的JPG导出图如下：
3. 用一个lmfit的包来实现2中的Gaussian函数拟合
需要下载lmfit这个包，下载地址：
https://pypi.org/project/lmfit/#files
下载下来的文件是.tar.gz格式，在MacOS及Linux命令行中解压，指令：
将其中的lmfit文件夹复制到当前project目录下。
上述例子2中生成了data.dat，用来作为接下来的方法中的原始数据。
出处：
Modeling Data and Curve Fitting
#Headerimport numpy as npimport matplotlib.pyplot as pltfrom numpy import exp, loadtxt, pi, sqrtfrom lmfit import Model#Import the data and define x, y and the functiondata = loadtxt('data.dat')x = data[0, :]y = data[1, :]def gaussian1(x, amp, cen, wid): return (amp / (sqrt(2*pi) * wid)) * exp(-(x-cen)**2 / (2*wid**2))#Fittinggmodel = Model(gaussian1)result = gmodel.fit(y, x=x, amp=5, cen=5, wid=1) #Fit from initial values (5,5,1)print(result.fit_report())#Plotplt.plot(x, y, 'bo',label='raw data')plt.plot(x, result.init_fit, 'k--',label='init_fit')plt.plot(x, result.best_fit, 'r-',label='best_fit')#plt.show()#Labelsplt.title("Gaussian Function Fitting")plt.xlabel('x coordinate')plt.ylabel('y coordinate')plt.legend()leg = plt.legend() # remove the frame of Legend, personal choiceleg.get_frame().set_linewidth(0.0) # remove the frame of Legend, personal choice#leg.get_frame().set_edgecolor('b') # change the color of Legend frame#plt.show()#Export figure#plt.savefig('fit3.eps', format='eps', dpi=1000)plt.savefig('fit3.pdf', format='pdf', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')plt.savefig('fit3.jpg', format='jpg', dpi=1000, figsize=(8, 6), facecolor='w', edgecolor='k')上面这一段代码需要按指示下载lmfit包，并且读取例子2中生成的data.dat。
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