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
// 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 contains the implementation of the `trace` function.
use flint_sys::fmpq_mat::fmpq_mat_trace;
use super::MatQ;
use crate::{error::MathError, rational::Q, traits::MatrixDimensions};
impl MatQ {
/// Returns the trace of a matrix and an error,
/// if the matrix is not square.
///
/// # Examples
/// ```
/// use qfall_math::rational::MatQ;
/// use std::str::FromStr;
///
/// let matrix = MatQ::from_str("[[1/2, 2],[3/7, 4]]").unwrap();
/// let trace = matrix.trace().unwrap();
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type
/// [`NoSquareMatrix`](MathError::NoSquareMatrix)
/// if the matrix is not a square matrix
pub fn trace(&self) -> Result<Q, MathError> {
// check if matrix is square
if self.get_num_rows() != self.get_num_columns() {
return Err(MathError::NoSquareMatrix(self.to_string()));
}
let mut out = Q::default();
unsafe {
fmpq_mat_trace(&mut out.value, &self.matrix);
}
Ok(out)
}
}
#[cfg(test)]
mod test_trace {
use crate::rational::{MatQ, Q};
use std::str::FromStr;
/// Test whether `trace` correctly calculates the trace of a matrix
#[test]
fn trace_works() {
let mat_1 = MatQ::from_str("[[5/2, 2, 0],[2, 1/2, 0],[0, 0, 1/3]]").unwrap();
let mat_2 = MatQ::from_str("[[-1, 0],[0, 1]]").unwrap();
let trace_1 = mat_1.trace().unwrap();
let trace_2 = mat_2.trace().unwrap();
assert_eq!(Q::from((10, 3)), trace_1);
assert_eq!(Q::ZERO, trace_2);
}
/// Test whether `trace` works for large values
#[test]
fn trace_large_values() {
let mat_1 = MatQ::from_str(&format!("[[{}, 5],[1, {}]]", i64::MAX, i64::MAX)).unwrap();
let mat_2 = MatQ::from_str(&format!("[[{}]]", i64::MIN)).unwrap();
let mat_3 = MatQ::from_str(&format!("[[{}, 5],[1, 1/{}]]", i64::MIN, i64::MAX)).unwrap();
let trace_1 = mat_1.trace().unwrap();
let trace_2 = mat_2.trace().unwrap();
let trace_3 = mat_3.trace().unwrap();
assert_eq!(Q::from(2 * i64::MAX as u64), trace_1);
assert_eq!(Q::from(i64::MIN), trace_2);
assert_eq!(Q::from(i64::MIN) + Q::from((1, i64::MAX)), trace_3);
}
/// Ensure that a matrix that is not square yields an error.
#[test]
fn trace_error_not_squared() {
let mat_1 = MatQ::from_str("[[1/2, 0, 1],[0, 1/9, 1]]").unwrap();
let mat_2 = MatQ::from_str("[[2/8, 0],[0, 1],[1/7, 0]]").unwrap();
assert!(mat_1.trace().is_err());
assert!(mat_2.trace().is_err());
}
}