Cord Kaldemeyer Cord Kaldemeyer - 15 days ago 7
Python Question

Solve a system of non-linear equations in Python (scipy.optimize.fsolve)

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


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

My current approach using the scipy stack is the following:

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)))


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

(0.0, 0.0)


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

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

Thanks in advance!

Answer

This works perfectly fine:

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) being (0, 0) means that both y - x**2 -7 + 5*x and 4*y - 8*x + 21 are 0.

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