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rank update passed tests

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Nestor Demeure 2019-11-02 18:27:01 +01:00 committed by Sébastien Crozet
parent 96c16af66f
commit 7347d467ae
2 changed files with 25 additions and 30 deletions
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43
src/linalg/cholesky.rs
View File

@ -8,7 +8,6 @@ use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, SquareMatrix};
use crate::constraint::{SameNumberOfRows, ShapeConstraint};
use crate::dimension::{Dim, DimSub, Dynamic, U1};
use crate::storage::{Storage, StorageMut};
use crate::RealField;
/// The Cholesky decomposition of a symmetric-definite-positive matrix.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
@ -149,33 +148,35 @@ where
/// Given the Cholesky decomposition of a matrix `M`, a scalar `sigma` and a vector `v`,
/// performs a rank one update such that we end up with the decomposition of `M + sigma * v*v^*`.
/// TODO insures that code is correct for complex numbers, eigen uses abs2 and conj
/// https://eigen.tuxfamily.org/dox/LLT_8h_source.html
pub fn rank_one_update<R2: Dim, S2, N2: RealField>(
&mut self,
x: &Matrix<N, R2, U1, S2>,
sigma: N2,
) where
N: From<N2>,
pub fn rank_one_update<R2: Dim, S2>(&mut self, x: &Matrix<N, R2, U1, S2>, sigma: N::RealField)
where
S2: Storage<N, R2, U1>,
DefaultAllocator: Allocator<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let sigma = <N>::from(sigma);
// for a description of the operation, see https://en.wikipedia.org/wiki/Cholesky_decomposition#Updating_the_decomposition
// heavily inspired by Eigen's implementation https://eigen.tuxfamily.org/dox/LLT_8h_source.html
// TODO use unsafe { *matrix.get_unchecked((j, j)) }
let n = x.nrows();
let mut temp = x.clone_owned();
for k in 0..n {
let lkk = self.chol[(k, k)]; // TODO unsafe { *matrix.get_unchecked((j, j)) }
let xk = temp[k];
let r = (lkk * lkk + sigma * xk * xk).sqrt();
let c = r / lkk;
let s = xk / lkk;
self.chol[(k, k)] = r;
let mut beta = crate::one::<N::RealField>();
for j in 0..n {
let ljj = N::real(self.chol[(j, j)]);
let dj = ljj * ljj;
let wj = temp[j];
let swj2 = sigma * N::modulus_squared(wj);
let gamma = dj * beta + swj2;
let nljj = (dj + swj2 / beta).sqrt();
self.chol[(j, j)] = N::from_real(nljj);
beta += swj2 / dj;
// Update the terms of L
if k < n {
for k2 in (k + 1)..n {
self.chol[(k2, k)] = (self.chol[(k2, k)] + sigma * s * temp[k2]) / c;
temp[k2] = c * temp[k2] - s * self.chol[(k2, k)];
if j < n {
for k in (j + 1)..n {
temp[k] -= (wj / N::from_real(ljj)) * self.chol[(k, j)];
if gamma != crate::zero::<N::RealField>() {
self.chol[(k, j)] = N::from_real(nljj / ljj) * self.chol[(k, j)]
+ (N::from_real(nljj * sigma / gamma) * N::conjugate(wj)) * temp[k];
}
}
}
}

12
tests/linalg/cholesky.rs
View File

@ -79,10 +79,8 @@ macro_rules! gen_tests(
}
fn cholesky_rank_one_update(_n: usize) -> bool {
use nalgebra::dimension::U3;
use nalgebra::Vector3;
let mut m = RandomSDP::new(U3, || random::<$scalar>().0).unwrap();
let x = Vector3::<$scalar>::new_random().map(|e| e.0);
let mut m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
let x = Vector4::<$scalar>::new_random().map(|e| e.0);
// TODO this is dirty but $scalar appears to not be a scalar type in this file
let zero = random::<$scalar>().0 * 0.;
@ -96,11 +94,7 @@ macro_rules! gen_tests(
let m_chol_updated = chol.l() * chol.l().adjoint();
// updates m manually
m.ger(sigma_scalar, &x, &x, one); // m += sigma * x * x.adjoint()
println!("sigma : {}", sigma);
println!("m updated : {}", m);
println!("chol : {}", m_chol_updated);
m.gerc(sigma_scalar, &x, &x, one); // m += sigma * x * x.adjoint()
relative_eq!(m, m_chol_updated, epsilon = 1.0e-7)
}