def test_rsvd_adaptive(self, dtype, shape, q, p):
X = rand_rank(*shape, 10, dtype=dtype)
U, s, V = qu.rsvd(X, 1e-5, q=q, p=p, k_start=10)
k = s.size
assert 10 <= k <= 20
assert U.dtype == dtype
assert V.dtype == dtype
assert_allclose(U.conj().T @ U, np.eye(k), rtol=1e-6, atol=1e-6)
assert_allclose(V @ V.conj().T, np.eye(k), rtol=1e-6, atol=1e-6)
Ue, se, Ve = qu.svds(X, k)
act_err = qu.norm(X - usv2dense(U, s, V), 'fro')
assert act_err < 1e-4
assert_allclose(s[:k // 2], se[:k // 2], rtol=0.1)
def test_rsvd(self, dtype, shape, sparse, q, p):
X = rand_rect(*shape, dtype=dtype, sparse=sparse)
k = 15
U, s, V = qu.rsvd(X, k, q=q, p=p)
assert U.shape == (shape[0], k)
assert s.shape == (k, )
assert V.shape == (k, shape[1])
assert U.dtype == dtype
assert V.dtype == dtype
assert_allclose(U.conj().T @ U, np.eye(k), rtol=1e-5, atol=1e-5)
assert_allclose(V @ V.conj().T, np.eye(k), rtol=1e-5, atol=1e-5)
Ue, se, Ve = qu.svds(X, k)
opt_err = qu.norm(X.A - usv2dense(Ue, se, Ve), 'fro')
act_err = qu.norm(X.A - usv2dense(U, s, V), 'fro')
assert act_err < 1.2 * opt_err
assert_allclose(s[:k // 2], se[:k // 2], rtol=0.05)