M-Labs/nalgebra
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UDU: d now stored in VectorN instead of MatrixN

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Signed-off-by: Christopher Rabotin <christopher.rabotin@gmail.com>
This commit is contained in:
Christopher Rabotin 2020-09-27 15:28:50 -06:00 committed by Crozet Sébastien
parent e9933e5c91
commit 7a49b9eeca
2 changed files with 21 additions and 15 deletions
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30
src/linalg/udu.rs
View File

@ -2,7 +2,7 @@
use serde::{Deserialize, Serialize};
use crate::allocator::Allocator;
use crate::base::{DefaultAllocator, MatrixN};
use crate::base::{DefaultAllocator, MatrixN, VectorN, U1};
use crate::dimension::Dim;
use simba::scalar::ComplexField;
@ -11,24 +11,25 @@ use simba::scalar::ComplexField;
#[derive(Clone, Debug)]
pub struct UDU<N: ComplexField, D: Dim>
where
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
{
/// The upper triangular matrix resulting from the factorization
pub u: MatrixN<N, D>,
/// The diagonal matrix resulting from the factorization
pub d: MatrixN<N, D>,
pub d: VectorN<N, D>,
}
impl<N: ComplexField, D: Dim> Copy for UDU<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
VectorN<N, D>: Copy,
MatrixN<N, D>: Copy,
{
}
impl<N: ComplexField, D: Dim> UDU<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
{
/// Computes the UDU^T factorization
/// NOTE: The provided matrix MUST be symmetric, and no verification is done in this regard.
@ -37,31 +38,31 @@ where
let n = p.ncols();
let n_as_dim = D::from_usize(n);
let mut d = MatrixN::<N, D>::zeros_generic(n_as_dim, n_as_dim);
let mut d = VectorN::<N, D>::zeros_generic(n_as_dim, U1);
let mut u = MatrixN::<N, D>::zeros_generic(n_as_dim, n_as_dim);
d[(n - 1, n - 1)] = p[(n - 1, n - 1)];
d[n - 1] = p[(n - 1, n - 1)];
u[(n - 1, n - 1)] = N::one();
for j in (0..n - 1).rev() {
u[(j, n - 1)] = p[(j, n - 1)] / d[(n - 1, n - 1)];
u[(j, n - 1)] = p[(j, n - 1)] / d[n - 1];
}
for j in (0..n - 1).rev() {
for k in j + 1..n {
d[(j, j)] = d[(j, j)] + d[(k, k)] * u[(j, k)].powi(2);
d[j] = d[j] + d[k] * u[(j, k)].powi(2);
}
d[(j, j)] = p[(j, j)] - d[(j, j)];
d[j] = p[(j, j)] - d[j];
for i in (0..=j).rev() {
for k in j + 1..n {
u[(i, j)] = u[(i, j)] + d[(k, k)] * u[(j, k)] * u[(i, k)];
u[(i, j)] = u[(i, j)] + d[k] * u[(j, k)] * u[(i, k)];
}
u[(i, j)] = p[(i, j)] - u[(i, j)];
u[(i, j)] /= d[(j, j)];
u[(i, j)] /= d[j];
}
u[(j, j)] = N::one();
@ -69,4 +70,9 @@ where
Self { u, d }
}
/// Returns the diagonal elements as a matrix
pub fn d_matrix(&self) -> MatrixN<N, D> {
MatrixN::from_diagonal(&self.d)
}
}

6
tests/linalg/udu.rs
View File

@ -11,7 +11,7 @@ fn udu_simple() {
let udu = UDU::new(m);
// Rebuild
let p = udu.u * udu.d * udu.u.transpose();
let p = udu.u * udu.d_matrix() * udu.u.transpose();
assert!(relative_eq!(m, p, epsilon = 3.0e-16));
}
@ -39,7 +39,7 @@ mod quickcheck_tests {
let m = m.map(|e| e.0);
let udu = UDU::new(m.clone());
let p = &udu.u * &udu.d * &udu.u.transpose();
let p = &udu.u * &udu.d_matrix() * &udu.u.transpose();
relative_eq!(m, p, epsilon = 1.0e-7)
}
@ -48,7 +48,7 @@ mod quickcheck_tests {
let m = m.map(|e| e.0);
let udu = UDU::new(m.clone());
let p = udu.u * udu.d * udu.u.transpose();
let p = udu.u * udu.d_matrix() * udu.u.transpose();
relative_eq!(m, p, epsilon = 3.0e-16)
}