Lab 9

py_1.py

@@ -0,0 +1,57 @@
+import numpy as np
+import itertools
+
+print("Welcome to lab 9!")
+
+while True:
+    try:
+        dim = int(input("Set the matrix dimensions: "))
+        if dim <= 0:
+            raise ValueError("Dimension must be a positive integer.")
+        break 
+    except ValueError as exp:
+        print(exp)
+
+def random_matrix(dim):
+    """
+    Generates a dim x dim array of integers between 0 and 10.
+    """
+    return np.random.randint(10, size=(dim, dim))
+
+def permutations_matrix(dim):
+    """
+    Generates permutations of indices and their signs.
+    """
+    permutations_with_sign = []
+    for perm in itertools.permutations(range(dim)):
+        inversions = sum(1 for i in range(len(perm)) for j in range(i + 1, len(perm)) if perm[i] > perm[j])
+        sign = 1 if inversions % 2 == 0 else -1
+        permutations_with_sign.append((perm, sign))
+    return permutations_with_sign
+
+def product_matrix(matrix, perm):
+    """
+    Computes the product of matrix elements for a given permutation.
+    """
+    product = 1
+    for i in range(len(perm)):
+        product *= matrix[i, perm[i]]
+    return product
+
+def calculate_determinant(matrix):
+    """
+    Calculates the matrix determinant using permutations.
+    """
+    dim = len(matrix) 
+    permutations_with_sign = permutations_matrix(dim)
+    return sum(sign * product_matrix(matrix, perm) for perm, sign in permutations_with_sign)
+
+matrix = random_matrix(dim)
+det = calculate_determinant(matrix)
+
+print("Matrix:")
+print(matrix)
+print("Determinant of the matrix:", det)
+
+print("Done!")
+