malachite_nz/integer_vector/arithmetic/
l1_norm.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::integer::Integer;
10use crate::integer_vector::IntegerVector;
11use crate::integer_vector::arithmetic::sum_max_bits::vec_sum_abs_significant_bits;
12use crate::natural::Natural;
13use malachite_base::num::arithmetic::traits::{L1Norm, UnsignedAbs};
14
15impl L1Norm for IntegerVector {
16    type Output = Natural;
17
18    /// Returns the $\ell^1$ norm of an [`IntegerVector`]: the sum of the absolute values of its
19    /// elements, taking the vector by reference.
20    ///
21    /// The 0-dimensional vector has no elements, and its norm is 0.
22    ///
23    /// $$
24    /// f(v) = \|v\|_1 = \sum_i |v_i|.
25    /// $$
26    ///
27    /// # Worst-case complexity
28    /// $T(n) = O(n)$
29    ///
30    /// $M(n) = O(n)$
31    ///
32    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
33    /// elements.
34    ///
35    /// # Examples
36    /// ```
37    /// use core::str::FromStr;
38    /// use malachite_base::num::arithmetic::traits::L1Norm;
39    /// use malachite_nz::integer_vector::IntegerVector;
40    ///
41    /// assert_eq!(
42    ///     IntegerVector::from_str("(1, -5, 2)").unwrap().to_l1_norm(),
43    ///     8
44    /// );
45    /// assert_eq!(IntegerVector::from_str("()").unwrap().to_l1_norm(), 0);
46    /// ```
47    #[inline]
48    fn to_l1_norm(&self) -> Natural {
49        self.elements.iter().map(Integer::unsigned_abs_ref).sum()
50    }
51
52    /// Returns the $\ell^1$ norm of an [`IntegerVector`]: the sum of the absolute values of its
53    /// elements, taking the vector by value.
54    ///
55    /// # Worst-case complexity
56    /// $T(n) = O(n)$
57    ///
58    /// $M(n) = O(n)$
59    ///
60    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
61    /// elements.
62    ///
63    /// # Examples
64    /// ```
65    /// use core::str::FromStr;
66    /// use malachite_base::num::arithmetic::traits::L1Norm;
67    /// use malachite_nz::integer_vector::IntegerVector;
68    ///
69    /// assert_eq!(
70    ///     IntegerVector::from_str("(1, -5, 2)")
71    ///         .unwrap()
72    ///         .into_l1_norm(),
73    ///     8
74    /// );
75    /// assert_eq!(IntegerVector::from_str("()").unwrap().into_l1_norm(), 0);
76    /// ```
77    #[inline]
78    fn into_l1_norm(self) -> Natural {
79        self.elements.into_iter().map(Integer::unsigned_abs).sum()
80    }
81
82    /// Returns the number of significant bits of the $\ell^1$ norm of an [`IntegerVector`].
83    ///
84    /// While every element fits in one limb, the absolute values are added in two limbs, so nothing
85    /// is allocated, as in FLINT's `_fmpz_vec_sum_max_bits`.
86    ///
87    /// # Worst-case complexity
88    /// $T(n) = O(n)$
89    ///
90    /// $M(n) = O(n)$
91    ///
92    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
93    /// elements.
94    ///
95    /// # Examples
96    /// ```
97    /// use core::str::FromStr;
98    /// use malachite_base::num::arithmetic::traits::L1Norm;
99    /// use malachite_nz::integer_vector::IntegerVector;
100    ///
101    /// assert_eq!(
102    ///     IntegerVector::from_str("(1, -5, 2)")
103    ///         .unwrap()
104    ///         .l1_norm_significant_bits(),
105    ///     4
106    /// );
107    /// assert_eq!(
108    ///     IntegerVector::from_str("()")
109    ///         .unwrap()
110    ///         .l1_norm_significant_bits(),
111    ///     0
112    /// );
113    /// ```
114    #[inline]
115    fn l1_norm_significant_bits(&self) -> u64 {
116        vec_sum_abs_significant_bits(&self.elements)
117    }
118}
malachite_nz/integer_vector/arithmetic/l1_norm.rs

malachite_nz/integer_vector/arithmetic/
l1_norm.rs
