nalgebra/src/linalg/determinant.rs

use alga::general::Real;

use core::{DefaultAllocator, SquareMatrix};
use core::dimension::DimMin;
use core::storage::Storage;
use core::allocator::Allocator;

use linalg::LU;


impl<N: Real, D: DimMin<D, Output = D>, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
    /// Computes the matrix determinant.
    ///
    /// If the matrix has a dimension larger than 3, an LU decomposition is used.
    #[inline]
    pub fn determinant(&self) -> N
        where DefaultAllocator: Allocator<N, D, D> +
                                Allocator<(usize, usize), D> {

        assert!(self.is_square(), "Unable to compute the determinant of a non-square matrix.");
        let dim = self.shape().0;

        unsafe {
            match dim {
                0 => N::one(),
                1 => {
                    *self.get_unchecked(0, 0)
                },
                2 => {
                    let m11 = *self.get_unchecked(0, 0); let m12 = *self.get_unchecked(0, 1);
                    let m21 = *self.get_unchecked(1, 0); let m22 = *self.get_unchecked(1, 1);

                    m11 * m22 - m21 * m12
                },
                3 => {
                    let m11 = *self.get_unchecked(0, 0);
                    let m12 = *self.get_unchecked(0, 1);
                    let m13 = *self.get_unchecked(0, 2);

                    let m21 = *self.get_unchecked(1, 0);
                    let m22 = *self.get_unchecked(1, 1);
                    let m23 = *self.get_unchecked(1, 2);

                    let m31 = *self.get_unchecked(2, 0);
                    let m32 = *self.get_unchecked(2, 1);
                    let m33 = *self.get_unchecked(2, 2);

                    let minor_m12_m23 = m22 * m33 - m32 * m23;
                    let minor_m11_m23 = m21 * m33 - m31 * m23;
                    let minor_m11_m22 = m21 * m32 - m31 * m22;

                    m11 * minor_m12_m23 - m12 * minor_m11_m23 + m13 * minor_m11_m22
                },
                _ => {
                    LU::new(self.clone_owned()).determinant()
                }
            }
        }
    }
}