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use std::ops::{Mul, Sub, Add};
use crate::SquareMatrix;
use super::Matrix;
use super::minor::Minor;
pub trait Det: SquareMatrix
{
type Output;
fn det(&self) -> Self::Output;
}
impl<F: Clone> Det for [[F; 1]; 1]
where Self: SquareMatrix
{
type Output = F;
fn det(&self) -> Self::Output
{
self[0][0].clone()
}
}
impl<F: Clone + Mul<F, Output = F> + Sub<F, Output = F>> Det for [[F; 2]; 2]
where Self: SquareMatrix
{
type Output = F;
fn det(&self) -> Self::Output
{
self[0][0].clone()*self[1][1].clone() - self[0][1].clone()*self[1][0].clone()
}
}
macro_rules! det {
($i:expr) => {
impl<F> Det for [[F; $i]; $i]
where
F: Clone + Mul<F, Output = F> + Add<F, Output = F>,
Self: SquareMatrix + Minor<Output = F, Index = (usize, usize)>
{
type Output = F;
fn det(&self) -> Self::Output
{
(0..self.length())
.map(|i| self[i][0].clone()*self.minor((i, 0)))
.reduce(|a, b| a + b)
.unwrap()
}
}
};
}
det!(3);
det!(4);
det!(5);
det!(6);
det!(7);
det!(8);
det!(9);
det!(10);
det!(11);
det!(12);
det!(13);
det!(14);
det!(15);
det!(16);