ufsingapore.blogg.se - Gauss seidel python code

Numpy version 1.19.3 (previous to 1.19.

myMatrixTools.py - constains few basic matrix manipulation and analysis functions for usage.

In step 1.

main2.py - constains larger user-input of size N, matrix a and vector b Provided that you have to use the Gauss-Seidel method to solve the linear system of equations, I will leave that modifications for you to do.

main.py - contains basic usage demonstration of jacobi_calc() or gauss_seidel_calc(), using a 3x3 matrix, and basic arguments.

rel_diff, the relative difference between last 2.

If max_iter is None, the default value will set as 200. max_iter, the maxim number of possible iterations to receive the most exact solution.If tolerance is None, the default value will set as 1e-16. Gauss-Seidel Method, differences from key in Python. tolerance, the desired limitation of tolerance of solution's anomaly.If x is None, the initial guess will bw determined as a vector of 0's.

if b is None - the functions returns None. If a is None or NxM, where N != M - the functions returns None. a, the NxN matrix that the method is being performed on.The algorithms will terminate when the change in x is less than tolerance, or if max_iter iterations have been exceeded.įor each function: (jacobi_calc() or gauss_seidel_calc()) #LnormInf corresponds to the absolute value of the greatest element of the vector.Jacobi & Gauss-Seidel Algorithms Using Python The following methods solve the line system of equations, Ax=b,using Jacobi OR Gauss-Seidel algorithms, starting from an initial guess, x0. Mtodo de Gauss-Seidel Python (3) Publicado el 6 de Junio del 2013 por Abraham ( 21 cdigos) 32.314 visualizaciones desde el 6 de Junio del 2013 Cdigo de ejecuta el Mtodo de Gauss-Seidel para resolucin de sistemas de ecuaciones lineales de tres ecuaciones por tres variables. Print ("The solution vector in iteration", iter1, "is:", x) The Poisson Equation in Any Space Dimensions def sor_method(A, b, omega, initial_guess, tolerance, max_iterations): See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to Obviously, with higher omega values the number of iterations should decrease.Īs for a working algorithm on SOR this is what I have computed, where best convergence is reached when the optimal omega is used. Phi = sor_solver(A, b, omega, initial_guess, residual_convergence)įor an extended answer on omega and its uses please refer to my other answer SOR method as what is quoted below is not accurate. #An example case that mirrors the one in the Wikipedia article Here I have some python script, which solves the system of linear equations using Gauss-Seidel method: import numpy as np