use ndarray::*;
use ndarray_linalg::{krylov::*, *};
fn qr_full<A: Scalar + Lapack>() {
const N: usize = 5;
let rtol: A::Real = A::real(1e-9);
let a: Array2<A> = random((N, N));
let (q, r) = mgs(a.axis_iter(Axis(1)), N, rtol, Strategy::Terminate);
assert_close_l2!(&q.dot(&r), &a, rtol);
let qc: Array2<A> = conjugate(&q);
assert_close_l2!(&qc.dot(&q), &Array::eye(N), rtol);
}
#[test]
fn qr_full_real() {
qr_full::<f64>();
}
#[test]
fn qr_full_complex() {
qr_full::<c64>();
}
fn qr<A: Scalar + Lapack>() {
const N: usize = 4;
let rtol: A::Real = A::real(1e-9);
let a: Array2<A> = random((N, N / 2));
let (q, r) = mgs(a.axis_iter(Axis(1)), N, rtol, Strategy::Terminate);
assert_close_l2!(&q.dot(&r), &a, rtol);
let qc: Array2<A> = conjugate(&q);
assert_close_l2!(&qc.dot(&q), &Array::eye(N / 2), rtol);
}
#[test]
fn qr_real() {
qr::<f64>();
}
#[test]
fn qr_complex() {
qr::<c64>();
}
fn qr_over<A: Scalar + Lapack>() {
const N: usize = 4;
let rtol: A::Real = A::real(1e-9);
let a: Array2<A> = random((N, N * 2));
let (q, r) = mgs(a.axis_iter(Axis(1)), N, rtol, Strategy::Terminate);
let a_sub = a.slice(s![.., 0..N]);
assert_close_l2!(&q.dot(&r), &a_sub, rtol);
let qc: Array2<A> = conjugate(&q);
assert_close_l2!(&qc.dot(&q), &Array::eye(N), rtol);
let (q, r) = mgs(a.axis_iter(Axis(1)), N, rtol, Strategy::Skip);
let a_sub = a.slice(s![.., 0..N]);
assert_close_l2!(&q.dot(&r), &a_sub, rtol);
let qc: Array2<A> = conjugate(&q);
assert_close_l2!(&qc.dot(&q), &Array::eye(N), rtol);
let (q, r) = mgs(a.axis_iter(Axis(1)), N, rtol, Strategy::Full);
assert_close_l2!(&q.dot(&r), &a, rtol);
let qc: Array2<A> = conjugate(&q);
assert_close_l2!(&qc.dot(&q), &Array::eye(N), rtol);
}
#[test]
fn qr_over_real() {
qr_over::<f64>();
}
#[test]
fn qr_over_complex() {
qr_over::<c64>();
}