python scipy求解非线性方程的方法(fsolve/root)

 from scipy.integrate import odeint import numpy as np import matplotlib.pyplot as plt from scipy.optimize import root,fsolve #plt.rc('text', usetex=True) #使用latex ## 使用scipy.optimize模块的root和fsolve函数进行数值求解方程 ## 1、求解f(x)=2*sin(x)-x+1 rangex1 = np.linspace(-2,8) rangey1_1,rangey1_2 = 2*np.sin(rangex1),rangex1-1 plt.figure(1) plt.plot(rangex1,rangey1_1,'r',rangex1,rangey1_2,'b--') plt.title('$2sin(x)$ and $x-1$') def f1(x): return np.sin(x)*2-x+1 sol1_root = root(f1,[2]) sol1_fsolve = fsolve(f1,[2]) plt.scatter(sol1_fsolve,2*np.sin(sol1_fsolve),linewidths=9) plt.show() ## 2、求解线性方程组{3X1+2X2=3;X1-2X2=5} def f2(x): return np.array([3*x[0]+2*x[1]-3,x[0]-2*x[1]-5]) sol2_root = root(f2,[0,0]) sol2_fsolve = fsolve(f2,[0,0]) print(sol2_fsolve) # [2. -1.5] a = np.array([[3,2],[1,-2]]) b = np.array([3,5]) x = np.linalg.solve(a,b) print(x) # [2. -1.5] ## 3、求解非线性方程组 def f3(x): return np.array([2*x[0]**2+3*x[1]-3*x[2]**3-7, x[0]+4*x[1]**2+8*x[2]-10, x[0]-2*x[1]**3-2*x[2]**2+1]) sol3_root = root(f3,[0,0,0]) sol3_fsolve = fsolve(f3,[0,<div style="color:transparent">来源gaodai.ma#com搞##代!^码网</div>0,0]) print(sol3_fsolve) ## 4、非线性方程 def f4(x): return np.array(np.sin(2*x-np.pi)*np.exp(-x/5)-np.sin(x)) init_guess =np.array([[0],[3],[6],[9]]) sol4_root = root(f4,init_guess) sol4_fsolve = fsolve(f4,init_guess) print(sol4_fsolve) t = np.linspace(-2,12,2000) y1 = np.sin(2*t-np.pi)*np.exp(-t/5) y2 = np.sin(t) plt.figure(2) a , = plt.plot(t,y1,label='$sin(2x-\pi)e^{-x/5}$') b , = plt.plot(t,y2,label='$sin(x)$') plt.scatter(sol4_fsolve,np.sin(sol4_fsolve),linewidths=8) plt.title('$sin(2x-\pi)e^{-x/5}$ and $sin(x)$') plt.legend()