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Cholesky decomposition: Proper check for positive definiteness #1574

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Cholesky decomposition: Proper check for positive definiteness #1574

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6d8dd09
check sqrt for real + strictly positive value
PaulXiCao Nov 9, 2025
80b2c6b
test: cholesky_check_positive_definiteness
PaulXiCao Nov 9, 2025
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10 changes: 8 additions & 2 deletions src/linalg/cholesky.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -235,10 +235,16 @@ where
}

let sqrt_denom = |v: T| {
if v.is_zero() {
// positive definiteness requires the diagonal to be real and strictly positive
if !v.clone().imaginary().is_zero() {
return None;
}
v.try_sqrt()
let re = v.real();
if re <= T::RealField::zero() {
return None;
}
Comment on lines +239 to +245
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@alexhroom alexhroom Nov 23, 2025

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it would be clearer to write this as something like

let re = v.real();
let im = v.imaginary();

if re <= T::RealField::zero() || !im.is_zero() {
    return None;
}

// fixme: could be improved by sqrt on real, e.g. `T::from_real(re.sqrt())`
Some(T::from_real(re).sqrt())
};

let diag = unsafe { matrix.get_unchecked((j, j)).clone() };
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14 changes: 14 additions & 0 deletions tests/linalg/cholesky.rs
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Expand Up @@ -11,6 +11,20 @@ fn cholesky_with_substitute() {
assert!(na::Cholesky::new_with_substitute(m, 1e-8).is_some());
}

// 2x2 matrix filled with -1 is not positive definite and should not return a Cholesky
// decomposition (regardless of element type).
// See https://github.com/dimforge/nalgebra/issues/1536 .
#[test]
fn cholesky_check_positive_definiteness() {
let x = -1.0;
let m = na::Matrix2::new(x, x, x, x);
assert!(nalgebra::Cholesky::new(m).is_none());

let x = na::Complex::new(-1.0, 0.0);
let m = na::Matrix2::new(x, x, x, x);
assert!(nalgebra::Cholesky::new(m).is_none());
}

macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
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