malachite_q/rational_vector/arithmetic/
abs_squared.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::{AbsSquared, Square};
12use malachite_nz::integer_vector::IntegerVector;
13use malachite_nz::natural::Natural;
14
15// The squared norm of the vector `numerators / denominator`: the squared norm of the integer
16// numerators over the square of the denominator, reduced once.
17fn abs_squared_over((numerators, denominator): (IntegerVector, Natural)) -> Rational {
18    Rational::from_naturals(numerators.abs_squared(), denominator.square())
19}
20
21impl AbsSquared for RationalVector {
22    type Output = Rational;
23
24    /// Computes the squared norm of a [`RationalVector`], the sum of the squares of its elements,
25    /// taking the vector by value.
26    ///
27    /// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
28    /// 0-dimensional vector is 0. The vector is written as integer numerators over a common
29    /// denominator, as in [`Dot`](malachite_base::num::arithmetic::traits::Dot), so that one
30    /// integer squared norm and one reduction suffice.
31    ///
32    /// $$
33    /// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
34    /// $$
35    ///
36    /// where $n$ is the dimension of $v$.
37    ///
38    /// # Worst-case complexity
39    /// $T(n, m) = O(nm \log m \log\log m)$
40    ///
41    /// $M(m) = O(m \log m)$
42    ///
43    /// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
44    /// the largest number of significant bits of any element.
45    ///
46    /// # Examples
47    /// ```
48    /// use core::str::FromStr;
49    /// use malachite_base::num::arithmetic::traits::AbsSquared;
50    /// use malachite_q::rational_vector::RationalVector;
51    ///
52    /// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
53    /// assert_eq!(v.abs_squared().to_string(), "25/36");
54    /// let v = RationalVector::from_str("()").unwrap();
55    /// assert_eq!(v.abs_squared(), 0);
56    /// ```
57    #[inline]
58    fn abs_squared(self) -> Rational {
59        abs_squared_over(self.into_numerators_and_denominator())
60    }
61}
62
63impl AbsSquared for &RationalVector {
64    type Output = Rational;
65
66    /// Computes the squared norm of a [`RationalVector`], the sum of the squares of its elements,
67    /// taking the vector by reference.
68    ///
69    /// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
70    /// 0-dimensional vector is 0. The vector is written as integer numerators over a common
71    /// denominator, as in [`Dot`](malachite_base::num::arithmetic::traits::Dot), so that one
72    /// integer squared norm and one reduction suffice.
73    ///
74    /// $$
75    /// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
76    /// $$
77    ///
78    /// where $n$ is the dimension of $v$.
79    ///
80    /// # Worst-case complexity
81    /// $T(n, m) = O(nm \log m \log\log m)$
82    ///
83    /// $M(m) = O(m \log m)$
84    ///
85    /// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
86    /// the largest number of significant bits of any element.
87    ///
88    /// # Examples
89    /// ```
90    /// use core::str::FromStr;
91    /// use malachite_base::num::arithmetic::traits::AbsSquared;
92    /// use malachite_q::rational_vector::RationalVector;
93    ///
94    /// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
95    /// assert_eq!((&v).abs_squared().to_string(), "25/36");
96    /// let v = RationalVector::from_str("()").unwrap();
97    /// assert_eq!((&v).abs_squared(), 0);
98    /// ```
99    #[inline]
100    fn abs_squared(self) -> Rational {
101        abs_squared_over(self.to_numerators_and_denominator())
102    }
103}
malachite_q/rational_vector/arithmetic/abs_squared.rs

malachite_q/rational_vector/arithmetic/
abs_squared.rs
