PL_Programing_Languages_Project/matalgo.py at main · KfirCohen-PyLab/PL_Programing_Languages_Project · 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
137
138
139
140
141
142
143
144
145
146
147
148
149
150
import numpy as np
import time

EPSILON = 1e-10

def swap_rows(matrix, row1, row2):
    if row1 != row2:
        matrix[[row1, row2]] = matrix[[row2, row1]]

def my_abs(x):
    return x if x >= 0 else -x

def pivot_index(mat, col, start):
    col_slice = mat[start:, col]
    max_idx = 0
    max_val = my_abs(col_slice[0])
    for i in range(1, len(col_slice)):
        v = my_abs(col_slice[i])
        if v > max_val:
            max_val = v
            max_idx = i
    return start + max_idx


def row_has_nonzero(row):
    for v in row:
        if my_abs(v) > EPSILON:
            return True
    return False

def rank(mat):

    m, n = mat.shape
    row  = 0

    start = time.perf_counter()

    for j in range(n):
        if row >= m:
            break

        pivot_row_index = pivot_index(mat, j, row)
        if my_abs(mat[pivot_row_index, j]) < EPSILON:
            continue

        swap_rows(mat, row, pivot_row_index)
        mat[row, :] /= mat[row, j]

        if row + 1 < m:
            factors = mat[row+1:, j:j+1]
            mat[row+1:, :] -= factors * mat[row:row+1, :]

        row += 1

    elapsed = time.perf_counter() - start
    print(f"rank() finished in {elapsed:.6f} s")

    return row


def det(A):

    U = A.copy().astype(np.float64)
    n = U.shape[0]

    sign = 1.0
    prod_diag = 1.0

    start = time.perf_counter()

    for k in range(n):

        abs_col = []
        for i in range(k, n):
            abs_col.append(my_abs(U[i, k]))

        pivot_off = 0
        pivot_val = abs_col[0]

        for i in range(1, len(abs_col)):
            v = abs_col[i]
            if v > pivot_val:
                pivot_off = i
                pivot_val = v
        p = k + pivot_off

        if abs(U[p, k]) < EPSILON:
            return 0.0

        if p != k:
            U[[k, p]] = U[[p, k]]
            sign = -sign

        pivot = U[k, k]
        prod_diag *= pivot

        if k + 1 == n:
            break

        f = U[k + 1:, k] / pivot
        U[k + 1:, k + 1:] -= f[:, None] * U[k, k + 1:]
        U[k + 1:, k] = 0.0

    elapsed = time.perf_counter() - start
    print(f"det() finished in {elapsed:.6f} s")

    return sign * prod_diag


def inverse(mat):
    n = mat.shape[0]
    aug = np.hstack((mat.copy().astype(np.float64), np.eye(n)))

    start = time.perf_counter()

    for k in range(n):
        p = pivot_index(aug, k, k)

        if my_abs(aug[p, k]) < EPSILON:
            raise ValueError("Matrix is singular")

        swap_rows(aug, k, p)
        aug[k, :] /= aug[k, k]
        factors = aug[k + 1:, k:k + 1]
        aug[k + 1:, :] -= factors * aug[k:k + 1, :]

    for k in range(n - 1, -1, -1):
        factors = aug[:k, k:k + 1]
        aug[:k, :] -= factors * aug[k:k + 1, :]

    elapsed = time.perf_counter() - start
    print(f"inverse() finished in {elapsed:.6f} s")

    return aug[:, n:]


A = np.loadtxt(r"C:\Users\kfirn\Desktop\PL_Proj_Echelon\rank_data.txt")
B = np.loadtxt(r"C:\Users\kfirn\Desktop\PL_Proj_Echelon\det_data.txt")
C = np.loadtxt(r"C:\Users\kfirn\Desktop\PL_Proj_Echelon\inv_data.txt")
matrix_copy = A.copy()
demat = B.copy()
inmat = C.copy()
r = rank(matrix_copy)
d = det(demat)
inve = inverse(inmat)
inve1 = np.linalg.inv(inmat)
print(np.linalg.norm(inve - inve1))
print("matrix rank =", r)
print("determinant =", d)