nalgebra/linalg/
determinant.rs

1use simba::scalar::ComplexField;
2
3use crate::base::allocator::Allocator;
4use crate::base::dimension::DimMin;
5use crate::base::storage::Storage;
6use crate::base::{DefaultAllocator, SquareMatrix};
7
8use crate::linalg::LU;
9
10impl<T: ComplexField, D: DimMin<D, Output = D>, S: Storage<T, D, D>> SquareMatrix<T, D, S> {
11    /// Computes the matrix determinant.
12    ///
13    /// If the matrix has a dimension larger than 3, an LU decomposition is used.
14    #[inline]
15    #[must_use]
16    pub fn determinant(&self) -> T
17    where
18        DefaultAllocator: Allocator<D, D> + Allocator<D>,
19    {
20        assert!(
21            self.is_square(),
22            "Unable to compute the determinant of a non-square matrix."
23        );
24        let dim = self.shape().0;
25
26        unsafe {
27            match dim {
28                0 => T::one(),
29                1 => self.get_unchecked((0, 0)).clone(),
30                2 => {
31                    let m11 = self.get_unchecked((0, 0)).clone();
32                    let m12 = self.get_unchecked((0, 1)).clone();
33                    let m21 = self.get_unchecked((1, 0)).clone();
34                    let m22 = self.get_unchecked((1, 1)).clone();
35
36                    m11 * m22 - m21 * m12
37                }
38                3 => {
39                    let m11 = self.get_unchecked((0, 0)).clone();
40                    let m12 = self.get_unchecked((0, 1)).clone();
41                    let m13 = self.get_unchecked((0, 2)).clone();
42
43                    let m21 = self.get_unchecked((1, 0)).clone();
44                    let m22 = self.get_unchecked((1, 1)).clone();
45                    let m23 = self.get_unchecked((1, 2)).clone();
46
47                    let m31 = self.get_unchecked((2, 0)).clone();
48                    let m32 = self.get_unchecked((2, 1)).clone();
49                    let m33 = self.get_unchecked((2, 2)).clone();
50
51                    let minor_m12_m23 = m22.clone() * m33.clone() - m32.clone() * m23.clone();
52                    let minor_m11_m23 = m21.clone() * m33 - m31.clone() * m23;
53                    let minor_m11_m22 = m21 * m32 - m31 * m22;
54
55                    m11 * minor_m12_m23 - m12 * minor_m11_m23 + m13 * minor_m11_m22
56                }
57                _ => LU::new(self.clone_owned()).determinant(),
58            }
59        }
60    }
61}
nalgebra/linalg/determinant.rs

nalgebra/linalg/
determinant.rs
