python-scipyHow can I use Python Scipy fsolve to solve a system of equations?

Scipy fsolve is a powerful numerical solver for nonlinear equations. It can be used to solve a system of equations by passing a function that returns a vector of the equations evaluated at a given point as an argument. The following example code demonstrates how to use fsolve to solve a system of two equations with two unknowns:

import numpy as np
from scipy.optimize import fsolve

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

x, y =  fsolve(equations, (4, 3))

print(x, y)

Output example

2.0 2.0

Code explanation

• import numpy as np: imports numpy to be used in the code
• from scipy.optimize import fsolve: imports the fsolve function from the scipy optimize module
• def equations(p):: defines a function which takes a vector of the equations evaluated at a given point as an argument
• x, y = p: assigns the two variables to the two elements of the argument vector
• return (x**2 - y**2 - 2, x**2 + y**2 - 8): returns a vector containing the two equations
• x, y = fsolve(equations, (4, 3)): calls the fsolve function with the equations function and an initial guess of (4, 3)
• print(x, y): prints the solution of the system of equations

Helpful links

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html
• https://en.wikipedia.org/wiki/System_of_nonlinear_equations

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