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Fix Cholesky::determinant for Complex elements

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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.
This commit is contained in:
Jim Turner 2021-04-09 13:55:40 -04:00
parent 5aa6033a3b
commit cea3bdc8e5
2 changed files with 7 additions and 4 deletions
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4
src/linalg/cholesky.rs
View File

@ -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()
}
}

7
tests/linalg/cholesky.rs
View File

@ -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]