【解方程】scipy.optimize.solve.

fsolve求方程的解

如果要求解方程：

⎧⎩⎨⎪⎪f1(u1,u2,u3)=0f2(u1,u2,u3)=0f3(u1,u2,u3)=0

那么func这么定义：

def func(x):
  u1,u2,u3=x
  return [f1(u1,u2,u3),f2(u1,u2,u3),f3(u1,u2,u3)]

代码案例1：

import scipy.optimize as opt
import numpy as np
def f(x):
    x0,x1,x2=x
    return np.array([5*x1+3,4*x0*x0-2*np.sin(x1*x2),x1*x2-1.5])

result=opt.fsolve(f,[1,1,1])
print(result)
print(f(result))

代码案例2：

如果给了Jacobian矩阵，那么迭代速度更快
Jacobian矩阵的定义是：

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢∂f1∂u1∂f2∂u1∂f3∂u1∂f1∂u2∂f2∂u2∂f3∂u2∂f1∂u2∂f2∂u2∂f3∂u2⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

import scipy.optimize as opt
import numpy as np
def obj_func(x):
    x0,x1,x2=x
    return [5*x1+3,4*x0*x0-2*np.sin(x1*x2),x1*x2-1.5]

def jacobian(x):
    x0, x1, x2 = x
    return [
        [0,5,0],
        [8*x0,-2*x2*np.cos(x1*x2),-2*x1*np.cos(x1*x2)],
        [0,x2,x1]
    ]
result=opt.fsolve(obj_func,[1,1,1],fprime=jacobian)
print(result)
print(obj_func(result))