malachite_nz/integer_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::integer_vector::IntegerVector;
10use crate::integer_vector::arithmetic::dot_general::vec_dot_general;
11use crate::natural::Natural;
12use malachite_base::num::arithmetic::traits::AbsSquared;
13
14impl AbsSquared for IntegerVector {
15    type Output = Natural;
16
17    /// Computes the squared norm of an [`IntegerVector`], the sum of the squares of its elements,
18    /// taking the vector by value.
19    ///
20    /// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
21    /// 0-dimensional vector is 0. The squared norm is non-negative, so it is returned as a
22    /// [`Natural`].
23    ///
24    /// $$
25    /// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
26    /// $$
27    ///
28    /// where $n$ is the dimension of $v$.
29    ///
30    /// # Worst-case complexity
31    /// $T(n, m) = O(nm \log m \log\log m)$
32    ///
33    /// $M(m) = O(m \log m)$
34    ///
35    /// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
36    /// the largest number of significant bits of any element.
37    ///
38    /// # Examples
39    /// ```
40    /// use core::str::FromStr;
41    /// use malachite_base::num::arithmetic::traits::AbsSquared;
42    /// use malachite_nz::integer_vector::IntegerVector;
43    ///
44    /// let v = IntegerVector::from_str("(3, -4, 12)").unwrap();
45    /// assert_eq!(v.abs_squared(), 169);
46    /// let v = IntegerVector::from_str("()").unwrap();
47    /// assert_eq!(v.abs_squared(), 0);
48    /// ```
49    ///
50    /// This is equivalent to `_fmpz_vec_dot` from `fmpz_vec/dot.c`, FLINT 3.6.0, with both vectors
51    /// the same, which squares each element instead of multiplying it by itself.
52    #[inline]
53    fn abs_squared(self) -> Natural {
54        vec_dot_general(None, false, &self.elements, &self.elements, false).abs
55    }
56}
57
58impl AbsSquared for &IntegerVector {
59    type Output = Natural;
60
61    /// Computes the squared norm of an [`IntegerVector`], the sum of the squares of its elements,
62    /// taking the vector by reference.
63    ///
64    /// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
65    /// 0-dimensional vector is 0. The squared norm is non-negative, so it is returned as a
66    /// [`Natural`].
67    ///
68    /// $$
69    /// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
70    /// $$
71    ///
72    /// where $n$ is the dimension of $v$.
73    ///
74    /// # Worst-case complexity
75    /// $T(n, m) = O(nm \log m \log\log m)$
76    ///
77    /// $M(m) = O(m \log m)$
78    ///
79    /// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
80    /// the largest number of significant bits of any element.
81    ///
82    /// # Examples
83    /// ```
84    /// use core::str::FromStr;
85    /// use malachite_base::num::arithmetic::traits::AbsSquared;
86    /// use malachite_nz::integer_vector::IntegerVector;
87    ///
88    /// let v = IntegerVector::from_str("(3, -4, 12)").unwrap();
89    /// assert_eq!((&v).abs_squared(), 169);
90    /// let v = IntegerVector::from_str("()").unwrap();
91    /// assert_eq!((&v).abs_squared(), 0);
92    /// ```
93    ///
94    /// This is equivalent to `_fmpz_vec_dot` from `fmpz_vec/dot.c`, FLINT 3.6.0, with both vectors
95    /// the same, which squares each element instead of multiplying it by itself.
96    #[inline]
97    fn abs_squared(self) -> Natural {
98        vec_dot_general(None, false, &self.elements, &self.elements, false).abs
99    }
100}
malachite_nz/integer_vector/arithmetic/abs_squared.rs

malachite_nz/integer_vector/arithmetic/
abs_squared.rs
