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use num_traits::Inv;
use num_traits::Zero;
use crate::MMul;
use crate::Adj;
use crate::Det;
use crate::SquareMatrix;
pub trait MInv: SquareMatrix
where
Self::Output: SquareMatrix
{
type Output;
/// Returns the inverted matrix if the matrix is non-singular
///
/// A⁻¹
///
/// # Examples
///
/// ```rust
/// // Returns none if matrix is singular
/// let a = [
/// [1.0, 2.0],
/// [2.0, 4.0]
/// ];
/// assert_eq!(a.inv(), None);
///
/// // Otherwise equals adjunct matrix divided by determinant
/// let a = [
/// [1.0, 2.0],
/// [3.0, 4.0]
/// ];
/// let ai = a.adj().dot(a.det().recip());
/// assert_eq!(a.inv(), Some(ai));
/// ```
fn inv(&self) -> Option<Self::Output>;
}
impl<F, M> MInv for M
where
F: Inv<Output = F> + Zero,
Self: Adj + Det<Output = F>,
<Self as Adj>::Output: MMul<F>,
<<Self as Adj>::Output as MMul<F>>::Output: SquareMatrix
{
type Output = <<Self as Adj>::Output as MMul<F>>::Output;
fn inv(&self) -> Option<Self::Output>
{
let det = self.det();
if det.is_zero()
{
None
}
else
{
Some(self.adj().mul(det.inv()))
}
}
}