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
// 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::integer::Integer;
use crate::integer_vector::IntegerVector;
use crate::integer_vector::arithmetic::sum_max_bits::vec_sum_abs_significant_bits;
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{L1Norm, UnsignedAbs};
impl L1Norm for IntegerVector {
type Output = Natural;
/// Returns the $\ell^1$ norm of an [`IntegerVector`]: 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_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(1, -5, 2)").unwrap().to_l1_norm(),
/// 8
/// );
/// assert_eq!(IntegerVector::from_str("()").unwrap().to_l1_norm(), 0);
/// ```
#[inline]
fn to_l1_norm(&self) -> Natural {
self.elements.iter().map(Integer::unsigned_abs_ref).sum()
}
/// Returns the $\ell^1$ norm of an [`IntegerVector`]: 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_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(1, -5, 2)")
/// .unwrap()
/// .into_l1_norm(),
/// 8
/// );
/// assert_eq!(IntegerVector::from_str("()").unwrap().into_l1_norm(), 0);
/// ```
#[inline]
fn into_l1_norm(self) -> Natural {
self.elements.into_iter().map(Integer::unsigned_abs).sum()
}
/// Returns the number of significant bits of the $\ell^1$ norm of an [`IntegerVector`].
///
/// While every element fits in one limb, the absolute values are added in two limbs, so nothing
/// is allocated, as in FLINT's `_fmpz_vec_sum_max_bits`.
///
/// # 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_nz::integer_vector::IntegerVector;
///
/// assert_eq!(
/// IntegerVector::from_str("(1, -5, 2)")
/// .unwrap()
/// .l1_norm_significant_bits(),
/// 4
/// );
/// assert_eq!(
/// IntegerVector::from_str("()")
/// .unwrap()
/// .l1_norm_significant_bits(),
/// 0
/// );
/// ```
#[inline]
fn l1_norm_significant_bits(&self) -> u64 {
vec_sum_abs_significant_bits(&self.elements)
}
}