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
// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::Rational;
use crate::rational_vector::RationalVector;
use malachite_base::num::arithmetic::traits::{Abs, L1Norm};
use malachite_base::num::logic::traits::SignificantBits;
impl L1Norm for RationalVector {
type Output = Rational;
/// Returns the $\ell^1$ norm of a [`RationalVector`]: the sum of the absolute values of its
/// elements, taking the vector by reference.
///
/// The 0-dimensional vector has no elements, and its norm is 0.
///
/// $$
/// f(v) = \|v\|_1 = \sum_i |v_i|.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::L1Norm;
/// use malachite_q::rational_vector::RationalVector;
///
/// assert_eq!(
/// RationalVector::from_str("(1/2, -1/3)")
/// .unwrap()
/// .to_l1_norm()
/// .to_string(),
/// "5/6"
/// );
/// assert_eq!(RationalVector::from_str("()").unwrap().to_l1_norm(), 0);
/// ```
#[inline]
fn to_l1_norm(&self) -> Rational {
self.elements.iter().map(Abs::abs).sum()
}
/// Returns the $\ell^1$ norm of a [`RationalVector`]: the sum of the absolute values of its
/// elements, taking the vector by value.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::L1Norm;
/// use malachite_q::rational_vector::RationalVector;
///
/// assert_eq!(
/// RationalVector::from_str("(1/2, -1/3)")
/// .unwrap()
/// .into_l1_norm()
/// .to_string(),
/// "5/6"
/// );
/// assert_eq!(RationalVector::from_str("()").unwrap().into_l1_norm(), 0);
/// ```
#[inline]
fn into_l1_norm(self) -> Rational {
self.elements.into_iter().map(Abs::abs).sum()
}
/// Returns the number of significant bits of the $\ell^1$ norm of a [`RationalVector`].
///
/// As for a single [`Rational`], the count is the sum of the numbers of significant bits of the
/// norm's numerator and denominator. So a norm of 0, which is $0/1$, has 1 significant bit,
/// even for the 0-dimensional vector.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::L1Norm;
/// use malachite_q::rational_vector::RationalVector;
///
/// assert_eq!(
/// RationalVector::from_str("(1/2, -1/3)")
/// .unwrap()
/// .l1_norm_significant_bits(),
/// 6
/// );
/// assert_eq!(
/// RationalVector::from_str("()")
/// .unwrap()
/// .l1_norm_significant_bits(),
/// 1
/// );
/// ```
#[inline]
fn l1_norm_significant_bits(&self) -> u64 {
self.to_l1_norm().significant_bits()
}
}