用Python解决非线性方程组(scipy.optimize.fsolve) [英] Solve a system of non-linear equations in Python (scipy.optimize.fsolve)

问题描述

我正在尝试解决以下简单的非线性方程组(

I am trying to solve the following simple system of non-linear equations (Source(second example)):

(I) y - x^2 = 7 - 5x
(II) 4y - 8x = -21

应该只有一个解(x = 3.5，y = 1.75).

which should have only one solution (x=3.5, y=1.75).

我当前使用 scipy 堆栈如下:

from scipy.optimize import fsolve

def equations(p):
    x, y = p
    return (y - x**2 -7 + 5*x, 4*y - 8*x + 21)

x, y =  fsolve(equations, (5, 5))

print(equations((x, y)))

并产生以下结果(不是结果):

and yields the following (which is not the result):

(0.0, 0.0)

我已经尝试了不同的初始估计，但是它没有提供正确的解决方案.

I have already tried different starting estimates but it doesn't deliver the right solution.

我的方法有什么问题?我想念什么吗?

What's wrong with my approach? Am I missing something?

提前谢谢！

推荐答案

这工作得很好:

In [1]: %paste
from scipy.optimize import fsolve

def equations(p):
    x, y = p
    return (y - x**2 -7 + 5*x, 4*y - 8*x + 21)

x, y =  fsolve(equations, (5, 5))

print(equations((x, y)))

## -- End pasted text --
(0.0, 0.0)

In [2]: x
Out[2]: 3.5000000414181831

In [3]: y
Out[3]: 1.7500000828363667

equations(x, y)为(0, 0)表示y - x**2 -7 + 5*x和4*y - 8*x + 21均为0.

也许您感到困惑并且打算使用print(x, y)而不是print(equations(x, y))吗?

Maybe you got confused and meant to print(x, y) instead of print(equations(x, y)) ?

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