main2.py - constains larger user-input of size N, matrix a and vector b.

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.

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())

np.dot() is simply the manual way of accessing the operator in python.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.

Python automatically manages your memory creation and removal (no need to create empty lists of zeros).

Although it can be helpful at times, python does not require you to carve out your space in memory before creating objects.

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:

Python code for gauss seidel method