1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
// Copyright © 2023 Marcel Luca Schmidt
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
//! This module includes functionality to compute the dot product of two polynomials.
use crate::error::MathError;
use crate::rational::{PolyOverQ, Q};
use flint_sys::fmpq::{fmpq_add, fmpq_mul};
use flint_sys::fmpq_poly::fmpq_poly_get_coeff_fmpq;
impl PolyOverQ {
/// Returns the dot product of two polynomials of type [`PolyOverQ`].
/// The dot product for polynomials is obtained by treating the coefficients
/// of the polynomials as vectors and then applying the standard dot product operation.
///
/// Parameters:
/// - `other`: specifies the other polynomial the dot product is calculated over
///
/// Returns the resulting `dot_product` as a [`PolyOverQ`].
///
/// # Examples
/// ```
/// use qfall_math::rational::PolyOverQ;
/// use std::str::FromStr;
///
/// let poly_1 = PolyOverQ::from_str("4 -1/2 0 7/8 1").unwrap();
/// let poly_2 = PolyOverQ::from_str("1 5/42").unwrap();
///
/// let dot_prod = poly_1.dot_product(&poly_2).unwrap();
/// ```
pub fn dot_product(&self, other: &Self) -> Result<Q, MathError> {
let self_degree = self.get_degree();
let other_degree = other.get_degree();
let mut smaller_degree = self_degree;
if smaller_degree > other_degree {
smaller_degree = other_degree;
}
// calculate dot product of polynomials
let mut result = Q::default();
let mut temp = Q::default();
for i in 0..=smaller_degree {
// sets result = result + coefficient_1 * coefficient_2
unsafe {
let mut coefficient_1 = Q::default();
let mut coefficient_2 = Q::default();
fmpq_poly_get_coeff_fmpq(&mut coefficient_1.value, &self.poly, i);
fmpq_poly_get_coeff_fmpq(&mut coefficient_2.value, &other.poly, i);
fmpq_mul(&mut temp.value, &coefficient_1.value, &coefficient_2.value);
fmpq_add(&mut result.value, &result.value, &temp.value)
}
}
Ok(result)
}
}
#[cfg(test)]
mod test_dot_product {
use crate::rational::{PolyOverQ, Q};
use std::str::FromStr;
/// Check whether the dot product is calculated correctly
#[test]
fn dot_product_correct() {
let poly_1 = PolyOverQ::from_str("2 1/2 1").unwrap();
let poly_2 = PolyOverQ::from_str("2 3 4/2").unwrap();
let cmp = Q::from((7, 2));
let dot_prod = poly_1.dot_product(&poly_2).unwrap();
assert_eq!(dot_prod, cmp);
}
/// Check whether the dot product is calculated correctly with large numbers.
#[test]
fn large_numbers() {
let poly_1 = PolyOverQ::from_str("3 6 2 2").unwrap();
let poly_2 = PolyOverQ::from_str(&format!("3 1 2 {}", i64::MAX / 3)).unwrap();
let cmp = Q::from(10 + 2 * (i64::MAX / 3));
let dot_prod = poly_1.dot_product(&poly_2).unwrap();
assert_eq!(dot_prod, cmp);
}
/// Check whether the dot product calculation on
/// polynomials of different lengths works.
#[test]
fn different_lengths_work() {
let poly_1 = PolyOverQ::from_str("3 1 2 3/7").unwrap();
let poly_2 = PolyOverQ::from_str("2 3 4").unwrap();
let cmp = Q::from(11);
let dot_prod = poly_1.dot_product(&poly_2).unwrap();
assert_eq!(dot_prod, cmp);
}
/// Check whether the dot product calculation on
/// polynomials with length 0 works.
#[test]
fn zero_length_works() {
let poly_1 = PolyOverQ::from_str("3 1 2/11 3").unwrap();
let poly_2 = PolyOverQ::from_str("0").unwrap();
let cmp = Q::ZERO;
let dot_prod = poly_1.dot_product(&poly_2).unwrap();
assert_eq!(dot_prod, cmp);
}
}