def test_qr_returns_expected_shapes(self, arrays):
m_sb, m_bs = arrays
wide, tall = [arr.shape for arr in arrays]
hy.assume(hn.wide(m_sb))
# with self.subTest(msg='wide'):
self.assertArrayShapesAre(gfl.qr_m(m_sb), (utn.chop(wide), wide))
self.assertArrayShape(gfl.qr_rm(m_sb), wide)
with self.assertRaisesRegex(*utn.invalid_err):
gfl.qr_n(m_sb)
# with self.subTest(msg='tall'):
self.assertArrayShapesAre(gfl.qr_n(m_bs), (tall, utn.chop(tall)))
self.assertArrayShape(gfl.qr_rn(m_bs), utn.chop(tall))
# with self.subTest(msg='complete'):
self.assertArrayShapesAre(gfl.qr_m(m_bs), (utn.grow(tall), tall))
# with self.subTest(msg='raw'):
self.assertArrayShapesAre(gfl.qr_rawm(m_sb),
(utn.trnsp(wide), wide[:-1]))
self.assertArrayShapesAre(gfl.qr_rawn(m_bs),
(utn.trnsp(tall), utn.drop(tall)))
def test_qr_r_returns_expected_values(self, arrays):
m_sb, m_bs = arrays
hy.assume(hn.all_well_behaved(m_sb, m_bs))
hy.assume(hn.wide(m_sb))
# with self.subTest(msg='r_m'):
cond = np.linalg.cond(m_sb).max()
right = gfl.qr_rm(m_sb)
rrr = gfl.qr_m(m_sb)[1]
self.assertArrayAllClose(right, rrr, cond=cond)
# with self.subTest(msg='r_n'):
cond = np.linalg.cond(m_bs).max()
right = gfl.qr_rn(m_bs)
rrr = gfl.qr_n(m_bs)[1]
self.assertArrayAllClose(right, rrr, cond=cond)
def test_qr_complete_returns_expected_values(self, m_bs):
hy.assume(hn.tall(m_bs))
hy.assume(hn.all_well_behaved(m_bs))
cond = np.linalg.cond(m_bs).max()
unitary, right = gfl.qr_m(m_bs)
tall = unitary @ right
eye = la.dagger(unitary) @ unitary
eyet = unitary @ la.dagger(unitary)
id_b = np.identity(m_bs.shape[-2], m_bs.dtype)
# with self.subTest(msg='qr'):
self.assertArrayAllClose(tall, m_bs, cond=cond)
# with self.subTest(msg='Q^T Q'):
self.assertArrayAllClose(id_b, eye, cond=cond)
# with self.subTest(msg='Q Q^T'):
self.assertArrayAllClose(id_b, eyet, cond=cond)
def test_qr_returns_expected_values_with_wide(self, m_sb):
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb))
cond = np.linalg.cond(m_sb).max()
unitary, right = gfl.qr_m(m_sb)
wide = unitary @ right
eye = la.dagger(unitary) @ unitary
eyet = unitary @ la.dagger(unitary)
id_s = np.identity(m_sb.shape[-2], m_sb.dtype)
# with self.subTest(msg='qr'):
self.assertArrayAllClose(wide, m_sb, cond=cond)
# with self.subTest(msg='Q^T Q'):
self.assertArrayAllClose(id_s, eye, cond=cond)
# with self.subTest(msg='Q Q^T'):
self.assertArrayAllClose(id_s, eyet, cond=cond)
def test_qr_rawm_returns_expected_values(self, m_sb):
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb))
cond = np.linalg.cond(m_sb).max()
rrr = gfl.qr_m(m_sb)[1]
num = rrr.shape[-2]
ht_sb, tau = gfl.qr_rawm(m_sb)
h_sb = la.transpose(ht_sb)
vecs = np.tril(h_sb, -1)
vecs[(..., ) + np.diag_indices(num)] = 1
vnorm = gfb.norm(la.row(tau) * vecs[..., :num], axis=-2)**2
right = np.triu(h_sb)
# with self.subTest(msg='raw_m'):
self.assertArrayAllClose(right, rrr, cond=cond)
self.assertArrayAllClose(vnorm, 2 * tau.real, cond=cond)
for k in range(num):
vvv = vecs[..., num - k - 1:num - k]
ttt = la.scalar(tau[..., -k - 1])
right -= ttt * vvv * (la.dagger(vvv) @ right)
# with self.subTest(msg='h_m'):
self.assertArrayAllClose(right, m_sb, cond=cond)