def test_lstsq_returns_expected_values(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.wide(m_sb))
cond_bs = np.linalg.cond(m_bs).max()
cond_sb = np.linalg.cond(m_sb).max()
# overconstrained
x_sb = gfl.lstsq(m_bs, m_bb)
m_bst = la.dagger(m_bs)
# with self.subTest(msg='lstsq(over)'):
self.assertArrayAllClose(m_bst @ m_bs @ x_sb,
m_bst @ m_bb,
cond=cond_bs)
x_bs = gfl.rlstsq(m_bb, m_sb)
m_sbt = la.dagger(m_sb)
# with self.subTest(msg='rlstsq(over)'):
self.assertArrayAllClose(x_bs @ m_sb @ m_sbt,
m_bb @ m_sbt,
cond=cond_sb)
# underconstrained
x_bs = gfl.lstsq(m_sb, m_ss)
# with self.subTest(msg='lstsq(under)'):
self.assertArrayAllClose(m_sb @ x_bs, m_ss, cond=cond_sb)
x_sb = gfl.rlstsq(m_ss, m_bs)
# with self.subTest(msg='rlstsq(under)'):
self.assertArrayAllClose(x_sb @ m_bs, m_ss, cond=cond_bs)
def test_rlstsq_flexible_signature_with_vectors_mv(self, arrays):
m_sb, m_bs = arrays[:-2]
v_s, v_b = hn.core_only(*arrays[-2:], dims=1)
wide, tall = [arr.shape for arr in arrays[:-2]]
hy.assume(hn.wide(m_sb))
self.assertArrayShape(gfl.rlstsq(m_sb, v_b), wide[:-1])
self.assertArrayShape(gfl.rlstsq(m_bs, v_s), tall[:-1])
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlstsq(m_bs, v_b)
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_rlstsq_flexible_signature_with_vectors_vm(self, arrays):
m_sb, m_bs = arrays[:-2]
v_s, v_b = hn.core_only(*arrays[-2:], dims=1)
wide, tall = [arr.shape for arr in arrays[:-2]]
hy.assume(hn.wide(m_sb))
off_b, y_one = utn.make_off_by_one(m_sb, m_bs)
self.assertArrayShape(gfl.rlstsq(v_b, m_sb), wide[:-1])
self.assertArrayShape(gfl.rlstsq(v_s, m_bs), tall[:-1])
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlstsq(v_b, m_bs)
with self.assertRaisesRegex(*utn.core_dim_err):
# This would succeed/broadcast error if interpreted as vM:
gfl.rlstsq(m_bs[y_one], m_sb[off_b])
def test_rlstsq_qr_returns_expected_values_with_wide(self, arrays, fun):
m_ss, m_sb, m_bb = arrays
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb))
cond = np.linalg.cond(m_sb).max()
# overconstrained
x0_bs = gfl.rlstsq(m_bb, m_sb)
# overconstrained
x_bs, x_f, tau = fun(m_bb, m_sb)
# with self.subTest('rlstsq_qr(under,' + suffix):
self.assertArrayAllClose(x_bs, x0_bs, cond=cond)
# overconstrained
xx_bs = gfl.rqr_lstsq(m_bb, x_f, tau)
# with self.subTest('rqr_rlstsq(under,' + suffix):
self.assertArrayAllClose(xx_bs, x0_bs, cond=cond)
# underconstrained
y_bs = gfl.qr_lstsq(x_f, tau, m_ss)
# with self.subTest('qr_rlstsq(over,' + suffix):
self.assertArrayAllClose(m_sb @ y_bs, m_ss, cond=cond)
def test_rlstsq_flexible_signature_with_vectors_vv(self, v_s, v_b):
hy.assume(len(v_s) != len(v_b))
self.assertArrayShape(gfl.rlstsq(v_s, v_s), ())
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlstsq(v_s, v_b)