olzrunning.blogg.se - Python gauss seidel methos

What mistakes did I make? I think it is in TriSolve method since if I replaced it with regular LU solver such as (np.linalg.solve) it works. Here, had been heading to compose a system program code for Gauss-Seidel method in MATLAB, discuss its theoretical history, and analyze the MATLAB programs end. Below is the same implementation in MATLAB which works: function x = gSeidel(A,B,N) For some reason it is not converging even after 50000 iterations to the solution even when the matrix A is strict diagonal dominant. #O(n) per iteration, so overall O(nN), good for large SPD/SDD matricesĪ = np.array(,])Īns = is my Gauss-Seidel method in Python. The algorithms will terminate when the change in x is less than tolerance, or if maxiter default200 iterations have been exceeded.

np.dot() is simply the manual way of accessing the operator in python.From scipy.linalg import solve_triangular as triSolve Jacobi & Gauss-Seidel Algorithms Using Python The following methods solve the line system of equations, Axb,using Jacobi OR Gauss-Seidel algorithms, starting from an initial guess, x0.

Python automatically manages your memory creation and removal (no need to create empty lists of zeros). We start with an initial guess x ( 0) for the solution of Ax b.

Although it can be helpful at times, python does not require you to carve out your space in memory before creating objects. The general idea for iterative methods proceeds as follows: We write a (matrix) equation: x Tx + c in such a way that this equation is equivalent to solving Ax b.

To find L and U and then use numpy's inverse function, kindof defeats the purpose. Normally, people find L and U to manually solve for X more easily. If you were willing to use the np.linalg.inv() function, then your answer is one line, "np.linalg.inv(A) b".

It is really weird to see you manually generate the L and U matricies and then proceed to use np.linalg.inv() on the L and U.

In fact, a quick check of (A,True) reveals that you have bugs both in your L and your U.

Not really important to your code (as you may be doing this for practice), but as you may already know, lu decomposition, already exists, for example ().There is no need to include the length of your objects in python, since python automatically stores the length of it's objects, which can always be retrieved with the len() builtin.For example, you can write to and read from an entire row or column all at once. This would greatly improve your code (and make it way faster) and make it way easier to read. I notice that you import numpy, but you don't use the operations for numpy arrays.If you don't use a variable in a list comprehension, then it is customary to use an _.Python only uses to place two lines of code on the same physical line. Python doesn't need to end a line, python knows when lines end.There are many things to address in your code: