def test_lu_basic_returns_expected_shapes(self, arrays):
m_sb, m_bb, m_bs = arrays
wide, big, tall = [arr.shape for arr in arrays]
hy.assume(hn.wide(m_sb))
# with self.subTest(msg="square"):
self.assertArrayShapesAre(gfl.lu_m(m_bb), (big, big, big[:-1]))
self.assertArrayShapesAre(gfl.lu_n(m_bb), (big, big, big[:-1]))
# with self.subTest(msg="wide"):
self.assertArrayShapesAre(gfl.lu_m(m_sb),
(utn.chop(wide), wide, wide[:-1]))
self.assertArrayShapesAre(gfl.lu_n(m_sb),
(wide, utn.grow(wide), utn.drop(wide)))
# with self.subTest(msg="tall"):
self.assertArrayShapesAre(gfl.lu_m(m_bs),
(utn.grow(tall), tall, tall[:-1]))
self.assertArrayShapesAre(gfl.lu_n(m_bs),
(tall, utn.chop(tall), utn.drop(tall)))
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_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_lu_basic_returns_expected_values_square(self, m_bb):
big = m_bb.shape
cond = np.linalg.cond(m_bb).max()
sq_l, sq_u, sq_ip = gfl.lu_m(m_bb)
squ = gfl.rpivot(sq_l @ sq_u, sq_ip)
sqp = gfl.pivot(m_bb, sq_ip)
dinds = (..., ) + np.diag_indices(big[-1], 2) # to check l
uinds = (..., ) + np.triu_indices(big[-1], 1) # to check l
linds = (..., ) + np.tril_indices(big[-1], -1) # to check u
# with self.subTest(msg="square"):
self.assertArrayAllClose(sq_l[dinds], 1.)
self.assertArrayAllClose(sq_l[uinds], 0.)
self.assertArrayAllClose(sq_u[linds], 0.)
self.assertArrayAllClose(sq_l @ sq_u, sqp, cond=cond)
self.assertArrayAllClose(squ, m_bb, cond=cond)
def test_lu_basic_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_ip = gfl.lu_m(m_sb)
wid = gfl.rpivot(wd_l @ wd_u, wd_ip)
wdp = gfl.pivot(m_sb, wd_ip)
dinds = (..., ) + np.diag_indices(wide[-2], 2) # to check l
uinds = (..., ) + np.triu_indices(wide[-2], 1, wide[-2]) # to check l
linds = (..., ) + np.tril_indices(wide[-2], -1, wide[-1]) # to check u
# with self.subTest(msg="wide"):
self.assertArrayAllClose(wd_l[dinds], 1.)
self.assertArrayAllClose(wd_l[uinds], 0.)
self.assertArrayAllClose(wd_u[linds], 0.)
self.assertArrayAllClose(wd_l @ wd_u, wdp, cond=cond)
self.assertArrayAllClose(wid, m_sb, cond=cond)