Merge pull request #104 from GiovannaRMendes/feat-gauss

feat: Added Gauss Elimination

Author: king04aman

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