Matrix/Matrix.py at master · sham-404/Matrix · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
import math
import numpy as np


def construct_name(matrix):
    size = len(matrix)
    name = ""
    for i in range(size):
        for j in range(size):
            name += str(matrix[i][j]) + ","
    return name


def mat_printer(matrix, fsize):
    size = len(matrix)
    for i in range(size):
        print("|", end="")
        for j in range(size):
            print(f"{round(matrix[i][j], 3):> {fsize}}", end="")
        print("|")


def minor(matrix, n, m):
    size = len(matrix)
    sub_mat = []
    for i in range(size):
        if i == n:
            continue
        row = []
        for j in range(len(matrix[0])):
            if j == m:
                continue
            row.append(matrix[i][j])
        sub_mat.append(row)
    return sub_mat


def determinant(matrix, hash_map={}):
    name = construct_name(matrix)
    if name in hash_map:
        return hash_map[name]

    size = len(matrix)
    if size == 2:
        return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
    det = 0
    for i in range(size):
        det += ((-1) ** i) * matrix[0][i] * determinant(minor(matrix, 0, i))

    hash_map[name] = det
    return det


def inverse(matrix):
    det = determinant(matrix)
    adj = adjugate(matrix)
    return [[adj[i][j] / det for j in range(len(matrix))] for i in range(len(matrix))]


def adjugate(matrix):
    size = len(matrix)
    adj = []
    for i in range(size):
        row = []
        for j in range(size):
            # Cofactor = (-1)^(i+j) * determinant(minor)
            cof = ((-1) ** (i + j)) * determinant(minor(matrix, j, i))
            # Notice (j, i) here instead of (i, j) → transpose done inline
            row.append(cof)
        adj.append(row)
    return adj


def inv_printer(inv, matrix):
    size = len(inv)
    det = determinant(matrix)
    a = int(math.ceil(abs((math.log10(abs(det))))))
    fsize = a * 2 + 3
    space = a + 9
    det_place = size // 2

    for i in range(size):
        if i == det_place:
            print(f"{'1 / ' + str(round(det, 3)):>{space}}", end="")

        else:
            print(" " * space, end="")
        print("|", end="")

        for j in range(size):
            print(f"{round(inv[i][j] * det, 3):> {fsize}}", end="")
        print("|")


n = int(input("Enter the order of the matrix: "))
print()
matrix = np.zeros((n, n), dtype=float)
max_value = float("-inf")
for i in range(n):
    for j in range(n):
        while True:
            try:
                x = float(input(f"Enter element [{i+1}][{j+1}] -> "))
            except ValueError:
                print("Invalid input")
                continue
            break

        x = int(x)
        if abs(x) > max_value:
            max_value = abs(x)
        matrix[i, j] = x

max_val_len = int(math.ceil(math.log10(abs(max_value)))) + 6
print("\nThe entered matrix is: \n")
mat_printer(matrix, max_val_len)

det = determinant(matrix)
print(f"\nDeterminant of the matrix is {det}")

adj_mat = adjugate(matrix)
print("\nThe adjugate (adjoint) matrix is:\n")
mat_printer(adj_mat, max_val_len + 5)
# print(adj_mat)

if det == 0:
    print("\nInverse doesn't exist\n")

else:
    inv_mat = inverse(matrix)
    print("\nThe inverse matrix is:\n")
    mat_printer(inv_mat, max_val_len + 2)
    # print(inv_mat)

    print("\nInverse matrix in divided form:\n")
    inv_printer(inv_mat, matrix)