python求非线性方程的解/非线性方程组的解

傷城~ 2022-06-01 09:50 556阅读 0赞

用到的是scipy.optimize中的fsolve和root这两个函数，以下是简单使用：

from scipy.optimize import root,fsolve
    import numpy as np
    from matplotlib import pyplot as plt
    #求多元非线性方程组的解
    def f1(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])
    
    sol_root = root(f1,[0,0,0])#3个0，指的的三个未知量的猜测值
    sol_fsolve = fsolve(f1,[0,0,0])
    print(sol_root)
    print(sol_fsolve)
    
    #求非线性方程的解
    def f2(x):
        return 2*np.sin(x)-x+2
    x=np.linspace(-5,5,num=100)
    y=f2(x)
    root1=fsolve(f2,[1])#其实就是方程组等于0的根
    root2=root(f2,[1])
    print(root1)
    print(root2)
    plt.plot(x,y,'r')
    plt.show()

输出如下：

fjac: array([[ 0.96686457,  0.08921948,  0.23919195],
           [ 0.07663272,  0.79230209, -0.60529731],
           [ 0.24351659, -0.60357045, -0.75921168]])
         fun: array([-1.64249059e-10, -1.37286271e-09,  1.57796576e-09])
     message: 'The solution converged.'
        nfev: 26
         qtf: array([-1.67013674e-09, -5.92841205e-08, -1.20357384e-08])
           r: array([ 6.34170416,  2.71007612, -1.39511094,  7.99929572,  1.70538181,
           -4.90041988])
      status: 1
     success: True
           x: array([1.52964909, 0.973546  , 0.58489796])
    [1.52964909 0.973546   0.58489796]
    [2.75467375]
        fjac: array([[-1.]])
         fun: array([-1.99840144e-14])
     message: 'The solution converged.'
        nfev: 14
         qtf: array([-1.24821238e-08])
           r: array([2.85214767])
      status: 1
     success: True
           x: array([2.75467375])

对了，还有个图：![SouthEast][]

还是放一下官网比较好：[root][]、[fsolve][]

[SouthEast]: /images/20220601/4456496fb3d54756bbe0919ee9387f87.png
[root]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html#scipy.optimize.root
[fsolve]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html#scipy.optimize.fsolve