feat: Added Gauss Elimination

Author: GiovannaRMendes

Gauss Elimination with Partial Pivoting/README.md

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+# Implementation of Gauss Elimination with Partial Pivoting
+This implementaion is a Gauss Elimination with Partial Pivoting in Python. You can insert a number of lines of your augmented matrix and then, the numbers that compose it.
+
+# Screenshot
+Those are some examples:
+
+![Example 1](gauss_example1.jpg)
+![Example 2](gauss_example2.jpg)
+
+# Author
+[GiovannaRMendes](https://github.com/GiovannaRMendes)

Gauss Elimination with Partial Pivoting/gauss_example1.jpg

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+def gauss_partial(matrix: list, index_column: int):
+ index_max_val = index_column
+
+ for i in range(index_column, len(matrix)):
+ if matrix[index_column][index_column] < abs(matrix[i][index_column]):
+ index_max_val = i
+
+ if index_column != index_max_val:
+ matrix[index_column], matrix[index_max_val] = matrix[index_max_val], matrix[index_column]
+ 
+
+def verify_triangular(matrix: list) -> bool:
+
+ for i in range(len(matrix)):
+ for j in range(i, len(matrix)):
+
+ if (j == i and matrix[j][i] == 0) or (j != i and matrix[j][i] != 0):
+ return False
+ 
+ return True
+
+
+def gauss(matrix: list, index: int) -> list:
+ 
+ for j in range(index+1, len(matrix)):
+ coefficient = round(matrix[j][index] / matrix[index][index], 2)
+ matrix[j][index] = 0
+
+ for k in range(index+1, len(matrix)+1):
+ matrix[j][k] = round(matrix[j][k] - coefficient * matrix[index][k], 5)
+
+ return matrix
+
+
+def resolve_linear_system(matrix: list) -> list:
+ sum = 0
+ n = len(matrix)
+ results = [1] * n
+
+ for i in range(n-1, -1, -1):
+
+ for j in range(n-1, i, -1):
+ sum = sum + matrix[i][j]*results[j]
+
+ results[i] = round((matrix[i][n] - sum)/matrix[i][i], 2)
+ sum = 0
+
+ return results
+
+
+def resolve_matrix(matrix: list):
+
+ for i in range(len(matrix)):
+ gauss_partial(matrix, i)
+ matrix = gauss(matrix, i)
+
+ print('\nThe matrix after Gauss:')
+
+ for line in matrix:
+ print("[", end='')
+ print(*(f'{val}' for val in line), end='')
+ print("]")
+ 
+ if verify_triangular(matrix):
+
+ print("\nThe result of Gauss Elimination with Partial Pivoting:")
+ for i, x in enumerate(resolve_linear_system(matrix)):
+ print(f'x_{i} = {x}')
+
+ else:
+ print("It's impossible to resolve, because it's not a triangular matrix")
+ return 0
+ 
+
+def take_matrix() -> list:
+
+ line = 0
+ matrix = []
+ max_length = 0
+
+ number_lines = int(input("Please, insert the length of the your matrix: "))
+ print("Please, insert only the numbers of the your augmented matrix (separete with espace):")
+
+ for i in range(number_lines):
+ 
+ try:
+ line = list(input().split())
+ line = list(int(val) for val in line)
+ 
+ if max_length < len(line):
+ max_length = len(line)
+
+ matrix.append(line)
+ 
+ except:
+ print("This matrix don't exist!!!")
+ return 1
+ 
+ if len(matrix) == max_length - 1:
+ return matrix
+ 
+ return 0
+
+
+if __name__ == '__main__':
+
+ matrix = take_matrix()
+
+ if matrix == 0:
+ print("It's impossible to resolve")
+
+ else:
+ print('The matrix:')
+
+ for line in matrix:
+ print("[", end='')
+ print(*(f'{val}' for val in line), end='')
+ print("]")
+
+ resolve_matrix(matrix)

Gauss Elimination with Partial Pivoting/gauss_example2.jpg

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+python-3.12.6