gaussianeliminationpivoting.py

import numpy as np

def custom_pivoting(a, n, i):
    min_index = i
    for index in range(i + 1, n):
        if abs(a[index][i]) < abs(a[min_index][i]):
            min_index = index
    return min_index

def custom_gauss_elimination_pivoting(a, b, n):
    result = []
    for i in range(n - 1):
        new_index = custom_pivoting(a, n, i)
        a[i], a[new_index] = a[new_index], a[i]
        b[i], b[new_index] = b[new_index], b[i]
        pivot = a[i][i]
        for j in range(i + 1, n):
            m = -1 * a[j][i] / pivot
            for k in range(0, n):
                a[j][k] += m * a[i][k]
            b[j] += m * b[i]

    for p in range(n - 1, -1, -1):
        result.append(b[p] / a[p][p])
        for q in range(p - 1, -1, -1):
            b[q] = b[q] - result[n - p - 1] * a[q][p]
    return result

# Example usage:
# n_size = 3
# a_matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=float)
# b_vector = np.array([10, 11, 12], dtype=float)

# solution = custom_gauss_elimination_pivoting(a_matrix, b_vector, n_size)
# print("Solution:", solution)


#URL that points to Wikipedia or another similar explanation.
#>>>>>>URL:https://courses.engr.illinois.edu/cs357/su2013/lectures/lecture07.pdf<<<<<#