numrs2 0.3.3

A Rust implementation inspired by NumPy for numerical computing (NumRS2)
Documentation 
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

#!/usr/bin/env python3
"""
NumRS2 Linear Algebra Example

Demonstrates linear algebra operations including matrix multiplication,
decompositions, and solving linear systems.
"""

import numrs2 as nr


def main():
    print("NumRS2 Linear Algebra Examples")
    print("=" * 60)
    print()

    # Matrix multiplication
    print("1. Matrix Multiplication")
    print("-" * 60)

    A = nr.array([1.0, 2.0, 3.0, 4.0]).reshape([2, 2])
    B = nr.array([5.0, 6.0, 7.0, 8.0]).reshape([2, 2])

    print(f"Matrix A:\n{A.tolist()}")
    print(f"Matrix B:\n{B.tolist()}")

    C = nr.matmul(A, B)
    print(f"A @ B:\n{C.tolist()}")
    print()

    # Dot product
    print("2. Dot Product")
    print("-" * 60)

    u = nr.array([1.0, 2.0, 3.0])
    v = nr.array([4.0, 5.0, 6.0])

    dot_product = nr.dot(u, v)
    print(f"u: {u.tolist()}")
    print(f"v: {v.tolist()}")
    print(f"u · v: {dot_product}")
    print()

    # Determinant
    print("3. Determinant")
    print("-" * 60)

    M = nr.array([4.0, 7.0, 2.0, 6.0]).reshape([2, 2])
    print(f"Matrix M:\n{M.tolist()}")

    det = nr.linalg.det(M)
    print(f"det(M): {det}")
    print()

    # Matrix trace
    print("4. Matrix Trace")
    print("-" * 60)

    trace = nr.linalg.trace(M)
    print(f"trace(M): {trace}")
    print()

    # Matrix inversion
    print("5. Matrix Inversion")
    print("-" * 60)

    M_inv = nr.linalg.inv(M)
    print(f"M^(-1):\n{M_inv.tolist()}")

    # Verify M * M^(-1) ≈ I
    identity = nr.matmul(M, M_inv)
    print(f"M @ M^(-1) ≈ I:\n{identity.tolist()}")
    print()

    # Eigenvalues
    print("6. Eigenvalues")
    print("-" * 60)

    eigvals = nr.linalg.eigvals(M)
    print(f"Eigenvalues of M: {eigvals.tolist()}")
    print()

    # Eigendecomposition
    print("7. Eigendecomposition")
    print("-" * 60)

    vals, vecs = nr.linalg.eig(M)
    print(f"Eigenvalues: {vals.tolist()}")
    print(f"Eigenvectors shape: {vecs.shape}")
    print()

    # SVD
    print("8. Singular Value Decomposition (SVD)")
    print("-" * 60)

    A_rect = nr.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0]).reshape([2, 3])
    print(f"Matrix A (2x3):\n{A_rect.tolist()}")

    U, S, Vt = nr.linalg.svd(A_rect)
    print(f"U shape: {U.shape}")
    print(f"S (singular values): {S.tolist()}")
    print(f"Vt shape: {Vt.shape}")
    print()

    # QR decomposition
    print("9. QR Decomposition")
    print("-" * 60)

    Q, R = nr.linalg.qr(A_rect)
    print(f"Q shape: {Q.shape}")
    print(f"R shape: {R.shape}")
    print()

    # Matrix norm
    print("10. Matrix Norm")
    print("-" * 60)

    vec = nr.array([3.0, 4.0])
    norm = nr.linalg.norm(vec)
    print(f"Vector: {vec.tolist()}")
    print(f"L2 norm: {norm}")
    print()

    # Condition number
    print("11. Condition Number")
    print("-" * 60)

    cond = nr.linalg.cond(M)
    print(f"Condition number of M: {cond}")
    print()

    print("=" * 60)
    print("Linear algebra examples completed successfully!")


if __name__ == "__main__":
    main()