malachite_q/rational_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::Rational;
10use crate::rational_vector::RationalVector;
11use malachite_base::num::arithmetic::traits::{Abs, L1Norm};
12use malachite_base::num::logic::traits::SignificantBits;
13
14impl L1Norm for RationalVector {
15    type Output = Rational;
16
17    /// Returns the $\ell^1$ norm of a [`RationalVector`]: the sum of the absolute values of its
18    /// elements, taking the vector by reference.
19    ///
20    /// The 0-dimensional vector has no elements, and its norm is 0.
21    ///
22    /// $$
23    /// f(v) = \|v\|_1 = \sum_i |v_i|.
24    /// $$
25    ///
26    /// # Worst-case complexity
27    /// $T(n) = O(n)$
28    ///
29    /// $M(n) = O(n)$
30    ///
31    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
32    /// elements.
33    ///
34    /// # Examples
35    /// ```
36    /// use core::str::FromStr;
37    /// use malachite_base::num::arithmetic::traits::L1Norm;
38    /// use malachite_q::rational_vector::RationalVector;
39    ///
40    /// assert_eq!(
41    ///     RationalVector::from_str("(1/2, -1/3)")
42    ///         .unwrap()
43    ///         .to_l1_norm()
44    ///         .to_string(),
45    ///     "5/6"
46    /// );
47    /// assert_eq!(RationalVector::from_str("()").unwrap().to_l1_norm(), 0);
48    /// ```
49    #[inline]
50    fn to_l1_norm(&self) -> Rational {
51        self.elements.iter().map(Abs::abs).sum()
52    }
53
54    /// Returns the $\ell^1$ norm of a [`RationalVector`]: the sum of the absolute values of its
55    /// elements, taking the vector by value.
56    ///
57    /// # Worst-case complexity
58    /// $T(n) = O(n)$
59    ///
60    /// $M(n) = O(n)$
61    ///
62    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
63    /// elements.
64    ///
65    /// # Examples
66    /// ```
67    /// use core::str::FromStr;
68    /// use malachite_base::num::arithmetic::traits::L1Norm;
69    /// use malachite_q::rational_vector::RationalVector;
70    ///
71    /// assert_eq!(
72    ///     RationalVector::from_str("(1/2, -1/3)")
73    ///         .unwrap()
74    ///         .into_l1_norm()
75    ///         .to_string(),
76    ///     "5/6"
77    /// );
78    /// assert_eq!(RationalVector::from_str("()").unwrap().into_l1_norm(), 0);
79    /// ```
80    #[inline]
81    fn into_l1_norm(self) -> Rational {
82        self.elements.into_iter().map(Abs::abs).sum()
83    }
84
85    /// Returns the number of significant bits of the $\ell^1$ norm of a [`RationalVector`].
86    ///
87    /// As for a single [`Rational`], the count is the sum of the numbers of significant bits of the
88    /// norm's numerator and denominator. So a norm of 0, which is $0/1$, has 1 significant bit,
89    /// even for the 0-dimensional vector.
90    ///
91    /// # Worst-case complexity
92    /// $T(n) = O(n)$
93    ///
94    /// $M(n) = O(n)$
95    ///
96    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
97    /// elements.
98    ///
99    /// # Examples
100    /// ```
101    /// use core::str::FromStr;
102    /// use malachite_base::num::arithmetic::traits::L1Norm;
103    /// use malachite_q::rational_vector::RationalVector;
104    ///
105    /// assert_eq!(
106    ///     RationalVector::from_str("(1/2, -1/3)")
107    ///         .unwrap()
108    ///         .l1_norm_significant_bits(),
109    ///     6
110    /// );
111    /// assert_eq!(
112    ///     RationalVector::from_str("()")
113    ///         .unwrap()
114    ///         .l1_norm_significant_bits(),
115    ///     1
116    /// );
117    /// ```
118    #[inline]
119    fn l1_norm_significant_bits(&self) -> u64 {
120        self.to_l1_norm().significant_bits()
121    }
122}
malachite_q/rational_vector/arithmetic/l1_norm.rs

malachite_q/rational_vector/arithmetic/
l1_norm.rs
