python scipy求解非线性方程的方法(fsolve/root)

from scipy.integrate import odeintimport numpy as npimport matplotlib.pyplot as pltfrom 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+1rangex1 = np.linspace(-2,8)rangey1_1,rangey1_2 = 2*np.sin(rangex1),rangex1-1plt.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+1sol1_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,[0,0,0])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()