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.
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@ -140,13 +140,13 @@ where
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}
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/// Computes the determinant of the decomposed matrix.
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pub fn determinant(&self) -> N {
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pub fn determinant(&self) -> N::SimdRealField {
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let dim = self.chol.nrows();
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let mut prod_diag = N::one();
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for i in 0..dim {
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prod_diag *= unsafe { *self.chol.get_unchecked((i, i)) };
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}
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prod_diag * prod_diag
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prod_diag.simd_modulus_squared()
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}
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}
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@ -7,6 +7,7 @@ macro_rules! gen_tests(
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use na::dimension::{U4, Dynamic};
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use na::{DMatrix, DVector, Matrix4x3, Vector4};
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use rand::random;
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use simba::scalar::ComplexField;
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#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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@ -83,18 +84,20 @@ macro_rules! gen_tests(
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fn cholesky_determinant(n in PROPTEST_MATRIX_DIM) {
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let m = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
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let lu_det = m.clone().lu().determinant();
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assert_relative_eq!(lu_det.imaginary(), 0., epsilon = 1.0e-7);
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let chol_det = m.cholesky().unwrap().determinant();
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prop_assert!(relative_eq!(lu_det, chol_det, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(lu_det.real(), chol_det, epsilon = 1.0e-7));
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}
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#[test]
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fn cholesky_determinant_static(_n in PROPTEST_MATRIX_DIM) {
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let m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
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let lu_det = m.clone().lu().determinant();
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assert_relative_eq!(lu_det.imaginary(), 0., epsilon = 1.0e-7);
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let chol_det = m.cholesky().unwrap().determinant();
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prop_assert!(relative_eq!(lu_det, chol_det, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(lu_det.real(), chol_det, epsilon = 1.0e-7));
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}
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#[test]
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