Solve Equations in Python

The following tutorials are an introduction to solving linear and nonlinear equations with Python. The solution to linear equations is through matrix operations while sets of nonlinear equations require a solver to numerically find a solution.

Solve Linear Equations with Python

Source Code for Linear Solutions

import numpy as np

A = np.array([ [3,-9], [2,4] ])
b = np.array([-42,2])
z = np.linalg.solve(A,b)

M = np.array([ [1,-2,-1], [2,2,-1], [-1,-1,2] ])
c = np.array([6,1,1])
y = np.linalg.solve(M,c)

Solve Nonlinear Equations with Python

Source Code for Nonlinear Solution

from numpy import *
from scipy.optimize import *

def myFunction(z):
   x = z[0]
   y = z[1]
   w = z[2]

   F = empty((3))
   F[0] = pow(x,2)+pow(y,2)-20
   F[1] = y - pow(x,2)
   F[2] = w + 5 - x*y
   return F

zGuess = array([1,1,1])
z = fsolve(myFunction,zGuess)

Additional Tutorials

Linear and nonlinear equations can also be solved with Excel and MATLAB. Click on the appropriate link for additional information and source code.

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