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cholesky.rs
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cholesky.rs
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use ndarray::*;
use ndarray_linalg::*;
macro_rules! cholesky {
($elem:ty, $rtol:expr) => {
paste::item! {
#[test]
fn [<cholesky_ $elem>]() {
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);
let a_orig: Array2<$elem> = random_hpd_using(3, &mut rng);
println!("a = \n{:?}", a_orig);
let upper = a_orig.cholesky(UPLO::Upper).unwrap();
assert_close_l2!(
&upper.t().mapv(|elem| elem.conj()).dot(&upper.view()),
&a_orig,
$rtol
);
let lower = a_orig.cholesky(UPLO::Lower).unwrap();
assert_close_l2!(
&lower.dot(&lower.t().mapv(|elem| elem.conj())),
&a_orig,
$rtol
);
let a: Array2<$elem> = replicate(&a_orig);
let upper = a.cholesky_into(UPLO::Upper).unwrap();
assert_close_l2!(
&upper.t().mapv(|elem| elem.conj()).dot(&upper.view()),
&a_orig,
$rtol
);
let a: Array2<$elem> = replicate(&a_orig);
let lower = a.cholesky_into(UPLO::Lower).unwrap();
assert_close_l2!(
&lower.dot(&lower.t().mapv(|elem| elem.conj())),
&a_orig,
$rtol
);
let mut a: Array2<$elem> = replicate(&a_orig);
{
let upper = a.cholesky_inplace(UPLO::Upper).unwrap();
assert_close_l2!(
&upper.t().mapv(|elem| elem.conj()).dot(&upper.view()),
&a_orig,
$rtol
);
}
assert_close_l2!(
&a.t().mapv(|elem| elem.conj()).dot(&upper.view()),
&a_orig,
$rtol
);
let mut a: Array2<$elem> = replicate(&a_orig);
{
let lower = a.cholesky_inplace(UPLO::Lower).unwrap();
assert_close_l2!(
&lower.dot(&lower.t().mapv(|elem| elem.conj())),
&a_orig,
$rtol
);
}
assert_close_l2!(&a.dot(&lower.t().mapv(|elem| elem.conj())), &a_orig, $rtol);
}
} // paste::item
};
}
cholesky!(f64, 1e-9);
cholesky!(f32, 1e-5);
cholesky!(c64, 1e-9);
cholesky!(c32, 1e-5);
macro_rules! cholesky_into_lower_upper {
($elem:ty, $rtol:expr) => {
paste::item! {
#[test]
fn [<cholesky_into_lower_upper_ $elem>]() {
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);
let a: Array2<$elem> = random_hpd_using(3, &mut rng);
println!("a = \n{:?}", a);
let upper = a.cholesky(UPLO::Upper).unwrap();
let fac_upper = a.factorizec(UPLO::Upper).unwrap();
let fac_lower = a.factorizec(UPLO::Lower).unwrap();
assert_close_l2!(&upper, &fac_lower.into_upper(), $rtol);
assert_close_l2!(&upper, &fac_upper.into_upper(), $rtol);
let lower = a.cholesky(UPLO::Lower).unwrap();
let fac_upper = a.factorizec(UPLO::Upper).unwrap();
let fac_lower = a.factorizec(UPLO::Lower).unwrap();
assert_close_l2!(&lower, &fac_lower.into_lower(), $rtol);
assert_close_l2!(&lower, &fac_upper.into_lower(), $rtol);
}
}
};
}
cholesky_into_lower_upper!(f64, 1e-9);
cholesky_into_lower_upper!(f32, 1e-5);
cholesky_into_lower_upper!(c64, 1e-9);
cholesky_into_lower_upper!(c32, 1e-5);
macro_rules! cholesky_into_inverse {
($elem:ty, $rtol:expr) => {
paste::item! {
#[test]
fn [<cholesky_inverse_ $elem>]() {
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);
let a: Array2<$elem> = random_hpd_using(3, &mut rng);
println!("a = \n{:?}", a);
let inv = a.invc().unwrap();
assert_close_l2!(&a.dot(&inv), &Array2::eye(3), $rtol);
let inv_into: Array2<$elem> = replicate(&a).invc_into().unwrap();
assert_close_l2!(&a.dot(&inv_into), &Array2::eye(3), $rtol);
let inv_upper = a.factorizec(UPLO::Upper).unwrap().invc().unwrap();
assert_close_l2!(&a.dot(&inv_upper), &Array2::eye(3), $rtol);
let inv_upper_into = a.factorizec(UPLO::Upper).unwrap().invc_into().unwrap();
assert_close_l2!(&a.dot(&inv_upper_into), &Array2::eye(3), $rtol);
let inv_lower = a.factorizec(UPLO::Lower).unwrap().invc().unwrap();
assert_close_l2!(&a.dot(&inv_lower), &Array2::eye(3), $rtol);
let inv_lower_into = a.factorizec(UPLO::Lower).unwrap().invc_into().unwrap();
assert_close_l2!(&a.dot(&inv_lower_into), &Array2::eye(3), $rtol);
}
}
};
}
cholesky_into_inverse!(f64, 1e-9);
cholesky_into_inverse!(f32, 1e-3);
cholesky_into_inverse!(c64, 1e-9);
cholesky_into_inverse!(c32, 1e-3);
macro_rules! cholesky_det {
($elem:ty, $atol:expr) => {
paste::item! {
#[test]
fn [<cholesky_det_ $elem>]() {
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);
let a: Array2<$elem> = random_hpd_using(3, &mut rng);
println!("a = \n{:?}", a);
let ln_det = a
.eigvalsh(UPLO::Upper)
.unwrap()
.mapv(|elem| elem.ln())
.sum();
let det = ln_det.exp();
assert_aclose!(a.factorizec(UPLO::Upper).unwrap().detc(), det, $atol);
assert_aclose!(a.factorizec(UPLO::Upper).unwrap().ln_detc(), ln_det, $atol);
assert_aclose!(a.factorizec(UPLO::Lower).unwrap().detc_into(), det, $atol);
assert_aclose!(
a.factorizec(UPLO::Lower).unwrap().ln_detc_into(),
ln_det,
$atol
);
assert_aclose!(a.detc().unwrap(), det, $atol);
assert_aclose!(a.ln_detc().unwrap(), ln_det, $atol);
assert_aclose!(a.clone().detc_into().unwrap(), det, $atol);
assert_aclose!(a.ln_detc_into().unwrap(), ln_det, $atol);
}
}
};
}
cholesky_det!(f64, 1e-9);
cholesky_det!(f32, 1e-3);
cholesky_det!(c64, 1e-9);
cholesky_det!(c32, 1e-3);
macro_rules! cholesky_solve {
($elem:ty, $rtol:expr) => {
paste::item! {
#[test]
fn [<cholesky_solve_ $elem>]() {
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);
let a: Array2<$elem> = random_hpd_using(3, &mut rng);
let x: Array1<$elem> = random_using(3, &mut rng);
let b = a.dot(&x);
println!("a = \n{:?}", a);
println!("x = \n{:?}", x);
assert_close_l2!(&a.solvec(&b).unwrap(), &x, $rtol);
assert_close_l2!(&a.solvec_into(b.clone()).unwrap(), &x, $rtol);
assert_close_l2!(&a.solvec_inplace(&mut b.clone()).unwrap(), &x, $rtol);
assert_close_l2!(
&a.factorizec(UPLO::Upper).unwrap().solvec(&b).unwrap(),
&x,
$rtol
);
assert_close_l2!(
&a.factorizec(UPLO::Lower).unwrap().solvec(&b).unwrap(),
&x,
$rtol
);
assert_close_l2!(
&a.factorizec(UPLO::Upper)
.unwrap()
.solvec_into(b.clone())
.unwrap(),
&x,
$rtol
);
assert_close_l2!(
&a.factorizec(UPLO::Lower)
.unwrap()
.solvec_into(b.clone())
.unwrap(),
&x,
$rtol
);
assert_close_l2!(
&a.factorizec(UPLO::Upper)
.unwrap()
.solvec_inplace(&mut b.clone())
.unwrap(),
&x,
$rtol
);
assert_close_l2!(
&a.factorizec(UPLO::Lower)
.unwrap()
.solvec_inplace(&mut b.clone())
.unwrap(),
&x,
$rtol
);
}
}
};
}
cholesky_solve!(f64, 1e-9);
cholesky_solve!(f32, 1e-3);
cholesky_solve!(c64, 1e-9);
cholesky_solve!(c32, 1e-3);