How to solve nonlinear equations using a for loop in python?

问题

I am trying to solve for non linear equations in python. I have tried using the solver of the Sympy but it doesn't seem to work in a for loop statement. I am tyring to solve for the variable x over a range of inputs [N].

I have attached my code below

import numpy as np
import matplotlib.pyplot as plt
from sympy import *

f_curve_coefficients = [-7.14285714e-02, 1.96333333e+01, 6.85130952e+03]
S = [0.2122, 0, 0]

a2 = f_curve_coefficients[0]
a1 = f_curve_coefficients[1]
a0 = f_curve_coefficients[2]

s2 = S[0]
s1 = S[1]
s0 = S[2]

answer=[]
x = symbols('x')
for N in range(0,2500,5):
    solve([a2*x**2+a1*N*x+a0*N**2-s2*x**2-s1*x-s0-0])
    answer.append(x)
    
print(answer)

There could be more efficient ways of solving this problem than using sympy * any help will be much appreicated.

Note I am still new to python, after transisitioning from Matlab. I could easliy solve this problem in Matlab and could attach the code, but I am battiling with this in Python

回答1:

According to this documentation, the output of solve is the solution. Nothing is assigned to x, that's still just the symbol.

x = symbols('x')
for N in range(0,2500,5):
    result = solve(a2*x**2+a1*N*x+a0*N**2-s2*x**2-s1*x-s0-0)
    answer.append(result)

回答2:

Answering to your question "There could be more efficient ways of solving this problem than using sympy * "

you can use fsolve to find the roots of non linear equation: fsolve returns the roots of the (non-linear) equations defined by func(x) = 0 given a starting estimate https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html

below is the code:

from scipy.optimize import fsolve
import numpy as np

def f(variables) :
    (x,y) = variables
    first_eq = 2*x + y - 1
    second_eq = x**2 + y**2 - 1
    return [first_eq, second_eq]

roots = fsolve(f, (-1 , -1)) # fsolve(equations, X_0)
print(roots)

# [ 0.8  -0.6]
print(np.isclose(f(roots), [0.0, 0.0]))  # func(root) should be almost 0.0.

If you prefer sympy you can use nsolve.

>>> nsolve([x+y**2-4, exp(x)+x*y-3], [x, y], [1, 1])

[0.620344523485226] [1.83838393066159]

The first argument is a list of equations, the second is list of variables and the third is an initial guess.

Also For details, you can checkout similar question asked earlier on stack overflow regarding ways to solve Non-linear equations in python: How to solve a pair of nonlinear equations using Python?

来源：https://stackoverflow.com/questions/64096992/how-to-solve-nonlinear-equations-using-a-for-loop-in-python