Fix Cholesky::determinant for Complex elements

The previous implementation was correct only for real elements. The
Cholesky decomposition is `L L^H`, so the determinant is `det(L) *
det(L^H)`. Since `L` is a triangular matrix, `det(L)` is the product
of the diagonal elements of `L`. Since `L^H` is triangular and its
diagonal elements are the conjugates of the diagonal elements of `L`,
`det(L^H)` is the conjugate of `det(L)`. So, the overall determinant
is the product of the diagonal elements of `L` times its conjugate.

src/linalg/cholesky.rs

@@ -140,13 +140,13 @@ where
     }
 
     /// Computes the determinant of the decomposed matrix.
-    pub fn determinant(&self) -> N {
+    pub fn determinant(&self) -> N::SimdRealField {
         let dim = self.chol.nrows();
         let mut prod_diag = N::one();
         for i in 0..dim {
             prod_diag *= unsafe { *self.chol.get_unchecked((i, i)) };
         }
-        prod_diag * prod_diag
+        prod_diag.simd_modulus_squared()
     }
 }
 

tests/linalg/cholesky.rs

@@ -7,6 +7,7 @@ macro_rules! gen_tests(
             use na::dimension::{U4, Dynamic};
             use na::{DMatrix, DVector, Matrix4x3, Vector4};
             use rand::random;
+            use simba::scalar::ComplexField;
             #[allow(unused_imports)]
             use crate::core::helper::{RandScalar, RandComplex};
 
@@ -83,18 +84,20 @@ macro_rules! gen_tests(
                 fn cholesky_determinant(n in PROPTEST_MATRIX_DIM) {
                     let m = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
                     let lu_det = m.clone().lu().determinant();
+                    assert_relative_eq!(lu_det.imaginary(), 0., epsilon = 1.0e-7);
                     let chol_det = m.cholesky().unwrap().determinant();
 
-                    prop_assert!(relative_eq!(lu_det, chol_det, epsilon = 1.0e-7));
+                    prop_assert!(relative_eq!(lu_det.real(), chol_det, epsilon = 1.0e-7));
                 }
 
                 #[test]
                 fn cholesky_determinant_static(_n in PROPTEST_MATRIX_DIM) {
                     let m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
                     let lu_det = m.clone().lu().determinant();
+                    assert_relative_eq!(lu_det.imaginary(), 0., epsilon = 1.0e-7);
                     let chol_det = m.cholesky().unwrap().determinant();
 
-                    prop_assert!(relative_eq!(lu_det, chol_det, epsilon = 1.0e-7));
+                    prop_assert!(relative_eq!(lu_det.real(), chol_det, epsilon = 1.0e-7));
                 }
 
                 #[test]