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// 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::Rational;
use crate::rational_vector::RationalVector;
use malachite_base::num::arithmetic::traits::{AbsSquared, Square};
use malachite_nz::integer_vector::IntegerVector;
use malachite_nz::natural::Natural;
// The squared norm of the vector `numerators / denominator`: the squared norm of the integer
// numerators over the square of the denominator, reduced once.
fn abs_squared_over((numerators, denominator): (IntegerVector, Natural)) -> Rational {
Rational::from_naturals(numerators.abs_squared(), denominator.square())
}
impl AbsSquared for RationalVector {
type Output = Rational;
/// Computes the squared norm of a [`RationalVector`], the sum of the squares of its elements,
/// taking the vector by value.
///
/// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
/// 0-dimensional vector is 0. The vector is written as integer numerators over a common
/// denominator, as in [`Dot`](malachite_base::num::arithmetic::traits::Dot), so that one
/// integer squared norm and one reduction suffice.
///
/// $$
/// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// the largest number of significant bits of any element.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// assert_eq!(v.abs_squared().to_string(), "25/36");
/// let v = RationalVector::from_str("()").unwrap();
/// assert_eq!(v.abs_squared(), 0);
/// ```
#[inline]
fn abs_squared(self) -> Rational {
abs_squared_over(self.into_numerators_and_denominator())
}
}
impl AbsSquared for &RationalVector {
type Output = Rational;
/// Computes the squared norm of a [`RationalVector`], the sum of the squares of its elements,
/// taking the vector by reference.
///
/// This is the dot product of the vector with itself, $\|v\|^2$. The squared norm of the
/// 0-dimensional vector is 0. The vector is written as integer numerators over a common
/// denominator, as in [`Dot`](malachite_base::num::arithmetic::traits::Dot), so that one
/// integer squared norm and one reduction suffice.
///
/// $$
/// f(v) = \|v\|^2 = \sum_{i=0}^{n-1} v_i^2,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// the largest number of significant bits of any element.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// assert_eq!((&v).abs_squared().to_string(), "25/36");
/// let v = RationalVector::from_str("()").unwrap();
/// assert_eq!((&v).abs_squared(), 0);
/// ```
#[inline]
fn abs_squared(self) -> Rational {
abs_squared_over(self.to_numerators_and_denominator())
}
}