python解非线性方程组_python scipy求解非线性方程的方法(fsolve/root)

使用scipy.optimize模块的root和fsolve函数进行数值求解线性及非线性方程，下面直接贴上代码，代码很简单

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,[0,0,0])

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()

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