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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::Dot;
use malachite_nz::integer::Integer;
use malachite_nz::integer_vector::IntegerVector;
use malachite_nz::natural::Natural;
// The dot product of two vectors, each written as integers over a common denominator: one integer
// dot product and one reduction replace a reduction per pair.
fn dot_over_denominators(
(xs, d): (IntegerVector, Natural),
(ys, e): (IntegerVector, Natural),
) -> Rational {
Rational::from_integers(xs.dot(ys), Integer::from(d * e))
}
impl Dot<Self> for RationalVector {
type Output = Rational;
/// Computes the dot product of two [`RationalVector`]s, taking the first by value and the
/// second by value.
///
/// The dot product is the sum of the products of corresponding elements, and is 0 for two
/// 0-dimensional vectors.
///
/// $$
/// f(v, w) = \sum_{i=0}^{n-1} v_iw_i,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $m$ is
/// the largest number of significant bits of the numerators the elements take over each
/// vector's common denominator.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Dot;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// let w = RationalVector::from_str("(4/5, 3/2)").unwrap();
/// assert_eq!(v.clone().dot(w.clone()).to_string(), "-3/5");
/// assert_eq!(
/// RationalVector::from_str("()")
/// .unwrap()
/// .dot(RationalVector::from_str("()").unwrap()),
/// 0
/// );
/// ```
///
/// This is equivalent to `_fmpq_vec_dot` from `fmpq_vec/dot.c`, FLINT 3.6.0.
fn dot(self, other: Self) -> Rational {
assert_eq!(
self.elements.len(),
other.elements.len(),
"the vectors must have the same dimension"
);
dot_over_denominators(
self.into_numerators_and_denominator(),
other.into_numerators_and_denominator(),
)
}
}
impl Dot<&Self> for RationalVector {
type Output = Rational;
/// Computes the dot product of two [`RationalVector`]s, taking the first by value and the
/// second by reference.
///
/// The dot product is the sum of the products of corresponding elements, and is 0 for two
/// 0-dimensional vectors.
///
/// $$
/// f(v, w) = \sum_{i=0}^{n-1} v_iw_i,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $m$ is
/// the largest number of significant bits of the numerators the elements take over each
/// vector's common denominator.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Dot;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// let w = RationalVector::from_str("(4/5, 3/2)").unwrap();
/// assert_eq!(v.clone().dot(&w).to_string(), "-3/5");
/// assert_eq!(
/// RationalVector::from_str("()")
/// .unwrap()
/// .dot(RationalVector::from_str("()").unwrap()),
/// 0
/// );
/// ```
///
/// This is equivalent to `_fmpq_vec_dot` from `fmpq_vec/dot.c`, FLINT 3.6.0.
fn dot(self, other: &Self) -> Rational {
assert_eq!(
self.elements.len(),
other.elements.len(),
"the vectors must have the same dimension"
);
dot_over_denominators(
self.into_numerators_and_denominator(),
other.to_numerators_and_denominator(),
)
}
}
impl Dot<RationalVector> for &RationalVector {
type Output = Rational;
/// Computes the dot product of two [`RationalVector`]s, taking the first by reference and the
/// second by value.
///
/// The dot product is the sum of the products of corresponding elements, and is 0 for two
/// 0-dimensional vectors.
///
/// $$
/// f(v, w) = \sum_{i=0}^{n-1} v_iw_i,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $m$ is
/// the largest number of significant bits of the numerators the elements take over each
/// vector's common denominator.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Dot;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// let w = RationalVector::from_str("(4/5, 3/2)").unwrap();
/// assert_eq!((&v).dot(w.clone()).to_string(), "-3/5");
/// assert_eq!(
/// RationalVector::from_str("()")
/// .unwrap()
/// .dot(RationalVector::from_str("()").unwrap()),
/// 0
/// );
/// ```
///
/// This is equivalent to `_fmpq_vec_dot` from `fmpq_vec/dot.c`, FLINT 3.6.0.
fn dot(self, other: RationalVector) -> Rational {
assert_eq!(
self.elements.len(),
other.elements.len(),
"the vectors must have the same dimension"
);
dot_over_denominators(
self.to_numerators_and_denominator(),
other.into_numerators_and_denominator(),
)
}
}
impl Dot<&RationalVector> for &RationalVector {
type Output = Rational;
/// Computes the dot product of two [`RationalVector`]s, taking the first by reference and the
/// second by reference.
///
/// The dot product is the sum of the products of corresponding elements, and is 0 for two
/// 0-dimensional vectors.
///
/// $$
/// f(v, w) = \sum_{i=0}^{n-1} v_iw_i,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $m$ is
/// the largest number of significant bits of the numerators the elements take over each
/// vector's common denominator.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Dot;
/// use malachite_q::rational_vector::RationalVector;
///
/// let v = RationalVector::from_str("(1/2, -2/3)").unwrap();
/// let w = RationalVector::from_str("(4/5, 3/2)").unwrap();
/// assert_eq!((&v).dot(&w).to_string(), "-3/5");
/// assert_eq!(
/// RationalVector::from_str("()")
/// .unwrap()
/// .dot(RationalVector::from_str("()").unwrap()),
/// 0
/// );
/// ```
///
/// This is equivalent to `_fmpq_vec_dot` from `fmpq_vec/dot.c`, FLINT 3.6.0.
#[inline]
fn dot(self, other: &RationalVector) -> Rational {
assert_eq!(
self.elements.len(),
other.elements.len(),
"the vectors must have the same dimension"
);
dot_over_denominators(
self.to_numerators_and_denominator(),
other.to_numerators_and_denominator(),
)
}
}