Determinant for refactor

Added determinant for refactor (correctly this time (hopefully))

faer/src/linalg/reductions/determinant.rs

@@ -0,0 +1,36 @@
+use crate::{assert, get_global_parallelism};
+use crate::internal_prelude::*;
+use alloc::vec;
+use dyn_stack::MemBuffer;
+
+#[math]
+pub fn determinant<T: ComplexField>(mat: MatRef<'_, T>) -> T::Canonical {
+	assert!(mat.nrows() == mat.ncols());
+
+	let par = get_global_parallelism();
+	let (m, n) = mat.shape();
+	let mut row_perm_fwd = vec![0usize; m];
+	let mut row_perm_bwd = vec![0usize; m];
+
+	let mut factors = mat.to_owned();
+	let count = linalg::lu::partial_pivoting::factor::lu_in_place(
+		factors.as_mat_mut(),
+		&mut row_perm_fwd,
+		&mut row_perm_bwd,
+		par,
+		MemStack::new(&mut MemBuffer::new(
+			linalg::lu::partial_pivoting::factor::lu_in_place_scratch::<usize, T>(m, n, par, default()),
+		)),
+		default(),
+	).0.transposition_count;
+
+	let mut det = one();
+	for i in 0..factors.nrows() {
+		det = mul(det, factors.as_mat_ref().read(i, i));
+	}
+	if count % 2 == 0 {
+		det
+	} else {
+		neg(det)
+	}
+}

faer/src/linalg/reductions/mod.rs

@@ -5,3 +5,4 @@ pub mod norm_l2;
 pub mod norm_l2_sqr;
 pub mod norm_max;
 pub mod sum;
+pub mod determinant;

faer/src/mat/matmut.rs

@@ -626,6 +626,15 @@ impl<'a, T, Rows: Shape, Cols: Shape, RStride: Stride, CStride: Stride> MatMut<'
 		self.rb().sum()
 	}
 
+	#[inline]
+	/// see [`MatRef::determinant`]
+	pub fn determinant(&self) -> T::Canonical
+	where
+		T: Conjugate,
+	{
+		self.rb().determinant()
+	}
+
 	#[track_caller]
 	#[inline]
 	/// see [`MatRef::get`]

faer/src/mat/matown.rs

@@ -955,6 +955,15 @@ impl<T, Rows: Shape, Cols: Shape> Mat<T, Rows, Cols> {
 		self.as_ref().norm_l2()
 	}
 
+	#[inline]
+	/// see [`MatRef::determinant`]
+	pub fn determinant(&self) -> T::Canonical
+	where
+		T: Conjugate,
+	{
+		self.as_ref().determinant()
+	}
+
 	#[track_caller]
 	#[inline]
 	/// see [`MatRef::get`]

faer/src/mat/matref.rs

@@ -1146,6 +1146,16 @@ impl<'a, T, Rows: Shape, Cols: Shape, RStride: Stride, CStride: Stride> MatRef<'
 		if try_const! { Conj::get::<T>().is_conj() } { conj(val) } else { val }
 	}
 
+	/// returns the determinant of `self`
+	#[inline]
+	#[math]
+	pub fn determinant(&self) -> T::Canonical
+	where
+		T: Conjugate,
+	{
+		linalg::reductions::determinant::determinant(self.canonical().as_dyn_stride().as_dyn())
+	}
+
 	/// returns references to the element at the given index, or submatrices if either `row`
 	/// or `col` is a range, with bound checks
 	///