nalgebra/tests/linalg/cholesky.rs

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#![cfg(all(feature = "arbitrary", feature = "debug"))]
macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
use na::debug::RandomSDP;
use na::dimension::{U4, Dynamic};
use na::{DMatrix, DVector, Matrix4x3, Vector4};
use rand::random;
#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
use std::cmp;
quickcheck! {
fn cholesky(n: usize) -> bool {
let m = RandomSDP::new(Dynamic::new(n.max(1).min(50)), || random::<$scalar>().0).unwrap();
let l = m.clone().cholesky().unwrap().unpack();
relative_eq!(m, &l * l.adjoint(), epsilon = 1.0e-7)
}
fn cholesky_static(_m: RandomSDP<f64, U4>) -> bool {
let m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
let chol = m.cholesky().unwrap();
let l = chol.unpack();
if !relative_eq!(m, &l * l.adjoint(), epsilon = 1.0e-7) {
false
}
else {
true
}
}
fn cholesky_solve(n: usize, nb: usize) -> bool {
let n = n.max(1).min(50);
let m = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let chol = m.clone().cholesky().unwrap();
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
let sol1 = chol.solve(&b1);
let sol2 = chol.solve(&b2);
relative_eq!(&m * &sol1, b1, epsilon = 1.0e-7) &&
relative_eq!(&m * &sol2, b2, epsilon = 1.0e-7)
}
fn cholesky_solve_static(_n: usize) -> bool {
let m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
let chol = m.clone().cholesky().unwrap();
let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
let sol1 = chol.solve(&b1);
let sol2 = chol.solve(&b2);
relative_eq!(m * sol1, b1, epsilon = 1.0e-7) &&
relative_eq!(m * sol2, b2, epsilon = 1.0e-7)
}
fn cholesky_inverse(n: usize) -> bool {
let m = RandomSDP::new(Dynamic::new(n.max(1).min(50)), || random::<$scalar>().0).unwrap();
let m1 = m.clone().cholesky().unwrap().inverse();
let id1 = &m * &m1;
let id2 = &m1 * &m;
id1.is_identity(1.0e-7) && id2.is_identity(1.0e-7)
}
fn cholesky_inverse_static(_n: usize) -> bool {
let m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
let m1 = m.clone().cholesky().unwrap().inverse();
let id1 = &m * &m1;
let id2 = &m1 * &m;
id1.is_identity(1.0e-7) && id2.is_identity(1.0e-7)
}
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fn cholesky_rank_one_update(_n: usize) -> bool {
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let mut m = RandomSDP::new(U4, || random::<$scalar>().0).unwrap();
let x = Vector4::<$scalar>::new_random().map(|e| e.0);
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// this is dirty but $scalar is not a scalar type (its a Rand) in this file
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let zero = random::<$scalar>().0 * 0.;
let one = zero + 1.;
let sigma = random::<f64>(); // needs to be a real
let sigma_scalar = zero + sigma;
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// updates cholesky decomposition and reconstructs m updated
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let mut chol = m.clone().cholesky().unwrap();
chol.rank_one_update(&x, sigma);
let m_chol_updated = chol.l() * chol.l().adjoint();
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// updates m manually
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m.gerc(sigma_scalar, &x, &x, one); // m += sigma * x * x.adjoint()
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relative_eq!(m, m_chol_updated, epsilon = 1.0e-7)
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}
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fn cholesky_insert_column(n: usize) -> bool {
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let n = n.max(1).min(10);
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let j = random::<usize>() % n;
let m_updated = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
// build m and col from m_updated
let col = m_updated.column(j);
let m = m_updated.clone().remove_column(j).remove_row(j);
// remove column from cholesky decomposition and rebuild m
let chol = m.clone().cholesky().unwrap().insert_column(j, &col);
let m_chol_updated = chol.l() * chol.l().adjoint();
relative_eq!(m_updated, m_chol_updated, epsilon = 1.0e-7)
}
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fn cholesky_remove_column(n: usize) -> bool {
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let n = n.max(1).min(10);
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let j = random::<usize>() % n;
let m = RandomSDP::new(Dynamic::new(n), || random::<$scalar>().0).unwrap();
// remove column from cholesky decomposition and rebuild m
let chol = m.clone().cholesky().unwrap().remove_column(j);
let m_chol_updated = chol.l() * chol.l().adjoint();
// remove column from m
let m_updated = m.remove_column(j).remove_row(j);
relative_eq!(m_updated, m_chol_updated, epsilon = 1.0e-7)
}
}
}
}
);
gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);