Coverage for src\pqlattice\lattice\_lattice.py: 95%
42 statements
« prev ^ index » next coverage.py v7.11.0, created at 2026-01-11 23:45 +0100
1import math
2from functools import reduce
4import numpy as np
6from .._utils import as_integer
7from ..linalg._linalg import det
8from ..linalg._utils import norm2, per_row_norm
9from ..typing import SquareMatrix, Vector, validate_aliases
12@validate_aliases
13def volume(lattice_basis: SquareMatrix) -> int:
14 """_summary_
16 Parameters
17 ----------
18 lattice_basis : SquareMatrix
19 _description_
21 Returns
22 -------
23 int
24 _description_
25 """
26 return abs(det(lattice_basis))
29@validate_aliases
30def rank(lattice_basis: SquareMatrix) -> int:
31 """_summary_
33 Parameters
34 ----------
35 lattice_basis : SquareMatrix
36 _description_
38 Returns
39 -------
40 int
41 _description_
42 """
43 return lattice_basis.shape[0]
46@validate_aliases
47def discriminant(lattice_basis: SquareMatrix) -> int:
48 """_summary_
50 Parameters
51 ----------
52 lattice_basis : SquareMatrix
53 _description_
55 Returns
56 -------
57 int
58 _description_
59 """
60 v = volume(lattice_basis)
61 return v * v
64@validate_aliases
65def hadamard_ratio(lattice_basis: SquareMatrix) -> float:
66 """_summary_
68 Parameters
69 ----------
70 lattice_basis : SquareMatrix
71 _description_
73 Returns
74 -------
75 float
76 _description_
77 """
78 return (volume(lattice_basis) / reduce(lambda a, b: a * b, per_row_norm(lattice_basis))) ** (1 / rank(lattice_basis))
81@validate_aliases
82def gaussian_heuristic(lattice_basis: SquareMatrix) -> float:
83 """_summary_
85 Parameters
86 ----------
87 lattice_basis : SquareMatrix
88 _description_
90 Returns
91 -------
92 float
93 _description_
94 """
95 n = rank(lattice_basis)
96 return math.sqrt(n / (2 * math.pi * math.e)) * (volume(lattice_basis) ** (1 / n))
99@validate_aliases
100def glr_2dim(lattice_basis: SquareMatrix) -> SquareMatrix:
101 """_summary_
103 Parameters
104 ----------
105 lattice_basis : SquareMatrix
106 _description_
108 Returns
109 -------
110 SquareMatrix
111 _description_
113 Raises
114 ------
115 ValueError
116 _description_
117 """
118 if lattice_basis.shape != (2, 2):
119 raise ValueError("Lattice has to have rank 2 for gaussian reduction")
121 w1: Vector = lattice_basis[0]
122 w2: Vector = lattice_basis[1]
124 v1 = w1.astype(float)
125 v2 = w2.astype(float)
126 if norm2(v1) > norm2(v2):
127 v1, v2 = v2, v1
129 while norm2(v2) > norm2(v1):
130 m = np.rint(np.dot(v1, v2) / np.dot(v1, v1))
131 if m == 0:
132 return as_integer([v1, v2])
133 v2 = v2 - m * v1
134 if norm2(v1) > norm2(v2):
135 v1, v2 = v2, v1
137 return np.array([v1, v2])