如何拟合三条不同参数的指数衰减曲线？

Question

我不太熟悉Python，但一直在尝试曲线拟合经典谐振子的三种不同的能量曲线。我发现了一个方法，这是不是最有效的，如果我想曲线拟合更多

import numpy as np import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy import optimize import sympy as sy dU=np.zeros(2) def oscil(U,t): dU[0]=U[1] dU[1]=-U[0]-b*U[1] return dU ic = [0,1] #initial condition t = np.linspace(0,100,1000) #time #4 different graphs with different beta, B, values; B=[0,0.1,0.5,1] b=0 soln1 = odeint(oscil, ic, t) b=0.1 soln2 = odeint(oscil, ic, t) b=0.5 soln3 = odeint(oscil, ic, t) b=1 soln4 = odeint(oscil, ic, t) #Create 4 subplbots fig, ( (plt1,plt2), (plt3,plt4) ) = plt.subplots(2,2) fig.subplots_adjust(wspace=0.4, hspace=0.8) plt1.plot(t, soln1[:,0], label='position') plt1.plot(t, soln1[:,1], label='velocity') plt1.set_title('Undamped Harmonic Oscillator') plt1.set_xlim(-1,4*np.pi) plt1.set_xlabel('Time') plt2.plot(t, soln2[:,0], label='position') plt2.plot(t, soln2[:,1], label='velocity') plt2.set_title('Damped HO for B=0.1') plt2.set_xlabel('Time') plt3.plot(t, soln3[:,0], label='position') plt3.plot(t, soln3[:,1], label='velocity') plt3.set_title('Damped HO for B=0.5') plt3.set_xlim(-1,50) plt3.set_xlabel('Time') plt4.plot(t, soln4[:,0], label='position') plt4.plot(t, soln4[:,1], label='velocity') plt4.set_title('Damped HO for B=1') plt4.set_xlim(-1,20) plt4.set_xlabel('Time') plt.title('HMO with Driving Force') plt.legend(loc='best') plt.show() # Energy = x^2 + dxdt^2 Energy1 = soln1[:,0]**2+soln1[:,1]**2 Energy2 = soln2[:,0]**2+soln2[:,1]**2 Energy3 = soln3[:,0]**2+soln3[:,1]**2 Energy4 = soln4[:,0]**2+soln4[:,1]**2 # curve fit x=t y2=Energy2 y3=Energy3 y4=Energy4 def mod2(x, xshift, steepness, yshift): ###estimated function return xshift*np.exp(-steepness*x) + yshift init_vals2 = [1.11913923, 0.11376818, 0.0826447 ] init_vals3 = [1.21244276, 0.57442609, 0.07596321 ] init_vals4 = [1.04292458, 0.90770071, 0.06833576] fitParams2, fitCovariances = optimize.curve_fit(mod2, x, y2, p0=init_vals2) fitParams3, fitCovariances = optimize.curve_fit(mod2, x, y3, p0=init_vals3) fitParams4, fitCovariances = optimize.curve_fit(mod2, x, y4, p0=init_vals4) plt.plot(t,y2, t,y3, t,y4) plt.plot(t,mod2(x,*fitParams2), 'k' ) plt.plot(t,mod2(x,*fitParams3), 'k' ) plt.plot(t,mod2(x,*fitParams4), 'k' ) plt.title('Energy') plt.xlabel('t') plt.show()