def test_lu(self, arrays):
m_ss, m_sb, m_bs = arrays
box = np.s_[..., :m_sb.shape[-2], :]
hy.assume(hn.wide(m_sb))
# with self.subTest("square"):
cond = np.linalg.cond(m_ss).max()
lower, upper, piv = la.lu(m_ss, 'separate')
luf, piv = la.lu(m_ss, 'raw')
luf = la.transpose(luf)
self.assertArrayAllClose(lower @ upper, gf.pivot(m_ss, piv), cond=cond)
self.assertArrayAllClose(tril(lower), tril(luf), cond=cond)
self.assertArrayAllClose(upper, np.triu(luf), cond=cond)
# with self.subTest("wide"):
cond = np.linalg.cond(m_bs).max()
lower, upper, piv = la.lu(m_bs, 'separate')
luf, piv = la.lu(m_bs, 'raw')
luf = la.transpose(luf)
self.assertArrayAllClose(tril(lower), tril(luf), cond=cond)
self.assertArrayAllClose(upper, np.triu(luf)[box], cond=cond)
# with self.subTest("wide"):
cond = np.linalg.cond(m_sb).max()
lower, upper, piv = la.lu(m_sb, 'separate')
luf, piv = la.lu(m_sb, 'raw')
luf = la.transpose(luf)
self.assertArrayAllClose(tril(lower), tril(luf)[box[:-1]], cond=cond)
self.assertArrayAllClose(upper, np.triu(luf), cond=cond)
def test_lqr(self, arrays):
m_sb, m_bs = arrays
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb, m_bs))
box = np.s_[..., :m_sb.shape[-2], :]
cond_sb = np.linalg.cond(m_sb).max()
cond_bs = np.linalg.cond(m_bs).max()
# with self.subTest("reduced"):
unitary, right = la.lqr(m_bs, 'reduced')
self.assertArrayAllClose(unitary @ right, m_bs, cond=cond_bs)
left, unitary = la.lqr(m_sb, 'reduced')
self.assertArrayAllClose(left @ unitary, m_sb, cond=cond_sb)
# with self.subTest("complete"):
unitary, right = la.lqr(m_bs, 'complete')
self.assertArrayAllClose(unitary @ right, m_bs, cond=cond_bs)
left, unitary = la.lqr(m_sb, 'complete')
self.assertArrayAllClose(left @ unitary, m_sb, cond=cond_sb)
# with self.subTest("r/l/raw"):
right = la.lqr(m_bs, 'r')
hhold, _ = la.lqr(m_bs, 'raw')
self.assertArrayAllClose(right,
np.triu(la.transpose(hhold))[box],
cond=cond_bs)
left = la.lqr(m_sb, 'r')
hhold, _ = la.lqr(m_sb, 'raw')
self.assertArrayAllClose(left,
np.tril(la.transpose(hhold))[box[:-1]],
cond=cond_sb)
def test_rlstsq_returns_expected_shape(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.wide(m_sb))
# with self.subTest('underconstrained'):
expect = utn.array_return_shape('(m,n),(p,n)->(m,p)', m_ss, m_bs)
self.assertArrayShape(gfl.rlstsq(m_ss, m_bs), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlstsq(m_sb, m_bs)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.rlstsq(*utn.make_bad_broadcast(m_ss, la.transpose(m_sb)))
# with self.subTest('overconstrained'):
expect = utn.array_return_shape('(m,n),(p,n)->(m,p)', m_bb, m_sb)
self.assertArrayShape(gfl.rlstsq(m_bb, m_sb), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlstsq(m_bs, m_sb)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.rlstsq(*utn.make_bad_broadcast(m_bb, la.transpose(m_bs)))
def test_lu_raw_returns_expected_values_square(self, m_bb):
sq_l, sq_u, sq_ip0 = gfl.lu_m(m_bb)
sq_f, sq_ip = gfl.lu_rawm(m_bb)
sq_f = la.transpose(sq_f)
linds = (..., ) + np.tril_indices(m_bb.shape[-1], -1)
uinds = (..., ) + np.triu_indices(m_bb.shape[-1], 0)
# with self.subTest(msg="square"):
cond = np.linalg.cond(m_bb).max()
self.assertArrayAllClose(sq_f[linds], sq_l[linds], cond=cond)
self.assertArrayAllClose(sq_f[uinds], sq_u[uinds], cond=cond)
self.assertEqual(sq_ip, sq_ip0)
def test_lu_raw_returns_expected_values_tall(self, m_bs):
tall = m_bs.shape
hy.assume(hn.tall(m_bs))
cond = np.linalg.cond(m_bs).max()
tl_l, tl_u, tl_ip0 = gfl.lu_n(m_bs)
tl_f, tl_ip = gfl.lu_rawn(m_bs)
tl_f = la.transpose(tl_f)
linds = (..., ) + np.tril_indices(tall[-2], -1, tall[-1])
uinds = (..., ) + np.triu_indices(tall[-2], 0, tall[-1])
# with self.subTest(msg="tall"):
self.assertArrayAllClose(tl_f[linds], tl_l[linds], cond=cond)
self.assertArrayAllClose(tl_f[uinds], tl_u[uinds], cond=cond)
self.assertEqual(tl_ip, tl_ip0)
def test_lu_raw_returns_expected_values_wide(self, m_sb):
wide = m_sb.shape
hy.assume(hn.wide(m_sb))
cond = np.linalg.cond(m_sb).max()
wd_l, wd_u, wd_ip0 = gfl.lu_m(m_sb)
wd_f, wd_ip = gfl.lu_rawm(m_sb)
wd_f = la.transpose(wd_f)
linds = (..., ) + np.tril_indices(wide[-2], -1, wide[-1])
uinds = (..., ) + np.triu_indices(wide[-2], 0, wide[-1])
# with self.subTest(msg="wide"):
self.assertArrayAllClose(wd_f[linds], wd_l[linds], cond=cond)
self.assertArrayAllClose(wd_f[uinds], wd_u[uinds], cond=cond)
self.assertEqual(wd_ip, wd_ip0)
def test_rlstsq_qr_returns_expected_shape_wide(self, arrays, fun):
_, m_sb, m_bb, m_bs = arrays
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb))
wide = m_sb.shape
expect = utn.array_return_shape('(m,n),(p,n)->(m,p),(n,p)', m_bb, m_sb)
tau = expect[1][:-2] + tau_len(m_sb, fun)
result = fun(m_bb, m_sb)
self.assertArrayShapesAre(result, expect + (tau, ))
self.assertArrayShapesAre(unbroadcast_factors(m_sb, *result[1:]),
(utn.trnsp(wide), wide[:-2] + tau[-1:]))
with self.assertRaisesRegex(*utn.core_dim_err):
fun(m_bs, m_sb)
with self.assertRaisesRegex(*utn.broadcast_err):
fun(*utn.make_bad_broadcast(m_bb, la.transpose(m_bs)))
def test_qr_rawn_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()
rrr = gfl.qr_n(m_bs)[1]
num = rrr.shape[-1]
ht_bs, tau = gfl.qr_rawn(m_bs)
h_bs = la.transpose(ht_bs)
vecs = np.tril(h_bs, -1)
vecs[(..., ) + np.diag_indices(num)] = 1
vnorm = gfb.norm(la.row(tau) * vecs, axis=-2)**2
right = np.triu(h_bs)
# with self.subTest(msg='raw_n'):
self.assertArrayAllClose(right[..., :num, :], 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_n'):
self.assertArrayAllClose(right, m_bs, cond=cond)
def test_lq_rawn_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()
llo = gfl.lq_n(m_bs)[0]
num = llo.shape[-1]
ht_bs, tau = gfl.lq_rawn(m_bs)
h_bs = la.transpose(ht_bs)
vecs = np.triu(h_bs, 1)
vecs[(..., ) + np.diag_indices(num)] = 1
vnorm = gfb.norm(la.col(tau) * vecs[..., :num, :], axis=-1)**2
left = np.tril(h_bs)
# with self.subTest(msg='raw_n'):
self.assertArrayAllClose(left, llo, cond=cond)
# with self.subTest(msg='tau_n'):
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])
left -= ttt.conj() * (left @ la.dagger(vvv)) * vvv
# with self.subTest(msg='h_n'):
self.assertArrayAllClose(left, m_bs, cond=cond)
def test_functions_shape(self, array):
shape = array.shape
self.assertArrayShape(la.transpose(array), utn.trnsp(shape))
self.assertArrayShape(la.row(array), shape[:-1] + (1, ) + shape[-1:])
self.assertArrayShape(la.col(array), shape + (1, ))
self.assertArrayShape(la.scalar(array), shape + (1, 1))