CODEWITHSUNDEEP
pythonequation
Camila Fonseca Amorim da Silva
Camila Fonseca Amorim da Silva

Reputation: 35

How can I solve a system with multiple non-linear equations using Python?

I have 12 non-linear equations and 7 variables to solve in Python. I tried to run the code below, but it seems that it has a error, I'm not sure if it is because the system results in multiple solutions. Is there another way to proceed? I'd like to know the value of each variable and the result of each equation. Thanks.

from scipy.optimize import fsolve
from math import exp

def equations(vars):
  a, b, c, d, e, f, g = vars
  eq1=a*c*f-0.17142857
  eq2=a*c*g-0.296922996
  eq3=a*d*f-0.514285714
  eq4=a*d*g-0.890768987
  eq5=a*e*f-1.542857143
  eq6=a*e*g-2.67230696
  eq7=b*c*f-4.628571429
  eq8=b*c*g-8.016920881
  eq9=b*d*f-13.88571429
  eq10=b*d*g-24.05076264
  eq11=b*e*f-41.65714286
  eq12=b*e*g-72.15228793
  return [eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12]


a, b, c, d, e, f, g =  fsolve(equations, (1, 1, 1, 1, 1, 1, 1))


print(a, b, c, d, e, f, g)
print(eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12)

Upvotes: 0

Views: 162

Answers (1)

Nin17
Nin17

Reputation: 3472

I think this (changing to 12 variables and 12 equations) solves your error:

from scipy.optimize import fsolve
from math import exp

def equations(vars):
  a, b, c, d, e, f, g, h, i, j, k, l = vars
  eq1=a*c*f-0.17142857
  eq2=a*c*g-0.296922996
  eq3=a*d*f-0.514285714
  eq4=a*d*g-0.890768987
  eq5=a*e*f-1.542857143
  eq6=a*e*g-2.67230696
  eq7=b*c*f-4.628571429
  eq8=b*c*g-8.016920881
  eq9=b*d*f-13.88571429
  eq10=b*d*g-24.05076264
  eq11=b*e*f-41.65714286
  eq12=b*e*g-72.15228793
  return [eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12]


a, b, c, d, e, f, g, h, i, j, k, l =  fsolve(equations, (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1))


print(a, b, c, d, e, f, g, h, i, j, k, l)
print(equations([a, b, c, d, e, f, g, h, i, j, k, l]))

Output

0.09788651653637173 2.64293594672212 -0.44472893008448783 -1.334186790203708 -4.002560370786989 -3.9379024240750766 -6.820647073325204 10473726.450237518 -9311686.344387261 -2218712.0864749462 2072840.8309073711 -2892329.2634591246

[1.4286000160623757e-09, -4.3506231950374286e-10, 2.6662094754215104e-10, -3.384060809352718e-10, -1.3234724427491074e-10, 1.0219736168437521e-10, -7.342570995660935e-12, -1.84297022087776e-11, -3.5398635134242795e-09, 2.0477912698879663e-09, 1.210743505453138e-09, -6.863842827442568e-10]

Just ignore the output for the last 5 variables

Upvotes: 1

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