use num::One;

use alga::general::{ClosedMul, ClosedSub, ClosedAdd};

use core::{Scalar, SquareMatrix};
use core::dimension::Dim;
use core::storage::Storage;


impl<N, D: Dim, S> SquareMatrix<N, D, S>
    where N: Scalar + One + ClosedMul + ClosedAdd + ClosedSub,
          S: Storage<N, D, D> {
    /// This matrix determinant.
    #[inline]
    pub fn determinant(&self) -> N {
        assert!(self.is_square(), "Unable to invert 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
                },
                _ => {
                    unimplemented!()
                }
            }
        }
    }
}