Gauss Elimination With Partial Pivoting In Python | Numerical Methods

[@samramzi4639]

import numpy as np def gauss_elimination(a_matrix,b_matrix): #adding some contingencies to prevent future problems if a_matrix.shape[0] != a_matrix.shape[1]: print("ERROR: Squarematrix not given!") return if b_matrix.shape[1] > 1 or b_matrix.shape[0] != a_matrix.shape[0]: print("ERROR: Constant vector incorrectly sized") return #initialization of nexessary variables n=len(b_matrix) m=n-1 i=0 j=i-1 x=np.zeros(n) new_line="/n" #create our augmented matrix throug Numpys concatenate feature augmented_matrix = np.concatenate((a_matrix, b_matrix,), axis=1, dtype=float) print(f"the initial augmented matrix is: {new_line}{augmented_matrix}") print("solving for the upper-triangular matrix:") #applying gauss elimination: while i

[@shimadabr]

That's one of the best explanations and implementations i could find of Gauss Elimination. Thanks a lot!

[@thatlilvoice]

You're saving my life here bud.

[@StudySessionYT]

Thanks for watching! Happy to hear the videos are helpful!

[@patrickegry4237]

Thank you so much for this! Keep up with the content, it is tremendously useful for a lot of students.

[@shimadabr]

For some reason my x0 = 0 when i tested your example. I gets to 0 exactly when k = 0 and j = 2. x = x - augmented_matriz[k][j] * x[j] turns into x = 1.5000000000000004 - 1 * 1.5000000000000004, so x = 0. I'm wondering if it's due to a minor floating point precision error that is causing the number to be unrepresentable (as e-16 is on the verge of underflow).

[@katheodo]

for some reason my last diagonal element isn't zero (in the A -matrix , as in Ax=b). I'm wandering if it's because i-variable stops before it reaches the n-th row.