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random unitary/regular matrices #140

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Merged
termoshtt merged 3 commits into from
Apr 27, 2019
Merged

random unitary/regular matrices #140

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2cd31e3
random_unitary, random_regular
termoshtt Apr 26, 2019
d6684d7
Use random_regular matrix for det test
termoshtt Apr 26, 2019
5102019
Remove *_t
termoshtt Apr 27, 2019
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28 changes: 28 additions & 0 deletions src/generate.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,7 @@ use std::ops::*;

use super::convert::*;
use super::error::*;
use super::qr::*;
use super::types::*;

/// Hermite conjugate matrix
Expand Down Expand Up @@ -34,6 +35,33 @@ where
ArrayBase::from_shape_fn(sh, |_| A::randn(&mut rng))
}

/// Generate random unitary matrix using QR decomposition
///
/// Be sure that this it **NOT** a uniform distribution. Use it only for test purpose.
pub fn random_unitary<A>(n: usize) -> Array2<A>
where
A: Scalar + RandNormal,
{
let a: Array2<A> = random((n, n));
let (q, _r) = a.qr_into().unwrap();
q
}

/// Generate random regular matrix
///
/// Be sure that this it **NOT** a uniform distribution. Use it only for test purpose.
pub fn random_regular<A>(n: usize) -> Array2<A>
where
A: Scalar + RandNormal,
{
let a: Array2<A> = random((n, n));
let (q, mut r) = a.qr_into().unwrap();
for i in 0..n {
r[(i, i)] = A::from_f64(1.0) + AssociatedReal::inject(r[(i, i)].abs());
}
q.dot(&r)
}

/// Random Hermite matrix
pub fn random_hermite<A, S>(n: usize) -> ArrayBase<S, Ix2>
where
Expand Down
78 changes: 40 additions & 38 deletions tests/det.rs
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Expand Up @@ -100,46 +100,48 @@ fn det_zero_nonsquare() {

#[test]
fn det() {
macro_rules! det {
($elem:ty, $shape:expr, $rtol:expr) => {
let a: Array2<$elem> = random($shape);
println!("a = \n{:?}", a);
let det = det_naive(&a);
let sign = det.div_real(det.abs());
let ln_det = det.abs().ln();
assert_rclose!(a.factorize().unwrap().det().unwrap(), det, $rtol);
{
let result = a.factorize().unwrap().sln_det().unwrap();
assert_rclose!(result.0, sign, $rtol);
assert_rclose!(result.1, ln_det, $rtol);
}
assert_rclose!(a.factorize().unwrap().det_into().unwrap(), det, $rtol);
{
let result = a.factorize().unwrap().sln_det_into().unwrap();
assert_rclose!(result.0, sign, $rtol);
assert_rclose!(result.1, ln_det, $rtol);
}
assert_rclose!(a.det().unwrap(), det, $rtol);
{
let result = a.sln_det().unwrap();
assert_rclose!(result.0, sign, $rtol);
assert_rclose!(result.1, ln_det, $rtol);
}
assert_rclose!(a.clone().det_into().unwrap(), det, $rtol);
{
let result = a.sln_det_into().unwrap();
assert_rclose!(result.0, sign, $rtol);
assert_rclose!(result.1, ln_det, $rtol);
}
};
fn det_impl<A, Tol>(a: Array2<A>, rtol: Tol)
where
A: Scalar<Real = Tol>,
Tol: RealScalar<Real = Tol>,
{
let det = det_naive(&a);
let sign = det.div_real(det.abs());
let ln_det = det.abs().ln();
assert_rclose!(a.factorize().unwrap().det().unwrap(), det, rtol);
{
let result = a.factorize().unwrap().sln_det().unwrap();
assert_rclose!(result.0, sign, rtol);
assert_rclose!(result.1, ln_det, rtol);
}
assert_rclose!(a.factorize().unwrap().det_into().unwrap(), det, rtol);
{
let result = a.factorize().unwrap().sln_det_into().unwrap();
assert_rclose!(result.0, sign, rtol);
assert_rclose!(result.1, ln_det, rtol);
}
assert_rclose!(a.det().unwrap(), det, rtol);
{
let result = a.sln_det().unwrap();
assert_rclose!(result.0, sign, rtol);
assert_rclose!(result.1, ln_det, rtol);
}
assert_rclose!(a.clone().det_into().unwrap(), det, rtol);
{
let result = a.sln_det_into().unwrap();
assert_rclose!(result.0, sign, rtol);
assert_rclose!(result.1, ln_det, rtol);
}
}
for rows in 1..5 {
for &shape in &[(rows, rows).into_shape(), (rows, rows).f()] {
det!(f64, shape, 1e-9);
det!(f32, shape, 1e-4);
det!(c64, shape, 1e-9);
det!(c32, shape, 1e-4);
}
det_impl(random_regular::<f64>(rows), 1e-9);
det_impl(random_regular::<f32>(rows), 1e-4);
det_impl(random_regular::<c64>(rows), 1e-9);
det_impl(random_regular::<c32>(rows), 1e-4);
det_impl(random_regular::<f64>(rows).t().to_owned(), 1e-9);
det_impl(random_regular::<f32>(rows).t().to_owned(), 1e-4);
det_impl(random_regular::<c64>(rows).t().to_owned(), 1e-9);
det_impl(random_regular::<c32>(rows).t().to_owned(), 1e-4);
}
}

Expand Down