def test_rqr_lstsq_flexible_signature_with_vectors_vv(self, v_s, v_b, fun):
hy.assume(len(v_s) != len(v_b))
hy.assume(la.norm(v_s) > 0.)
_, x_f, tau = fun(v_s, v_s)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, v_s), ())
self.assertArrayShape(gfl.rqr_lstsq(v_s, x_f, tau), ())
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.qr_lstsq(x_f, tau, v_b)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rqr_lstsq(v_b, x_f, tau)
def test_qr_lstsq_returns_expected_shape_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))
_, x_f, tau = fun(m_sb, m_ss)
expect = utn.array_return_shape('(n,m),(m,p)->(n,p)', x_f, m_ss)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, m_ss), expect)
expect = utn.array_return_shape('(m,n),(n,p)->(m,p)', m_bb, x_f)
self.assertArrayShape(gfl.rqr_lstsq(m_bb, x_f, tau), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.qr_lstsq(x_f, tau, m_bb)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rqr_lstsq(m_ss, x_f, tau)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.qr_lstsq(x_f, *utn.make_bad_broadcast(tau, m_ss, (1, 2)))
x_f, tau = unbroadcast_factors(m_sb, x_f, tau)
expect = utn.array_return_shape('(m,n),(p,n)->(m,p)', m_bb, m_sb)
self.assertArrayShape(gfl.rqr_lstsq(m_bb, x_f, tau), expect)
def test_rqr_lstsq_flexible_signature_with_vectors_vm(self, arrays, fun):
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))
hy.assume(hn.all_well_behaved(m_bs, m_sb))
off_b, y_one = utn.make_off_by_one(m_sb, m_bs)
_, x_f, tau = fun(v_s, m_bs)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, v_b), utn.drop(tall))
self.assertArrayShape(gfl.rqr_lstsq(v_s, x_f, tau), tall[:-1])
_, x_f, tau = fun(v_b, m_sb)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, v_s), utn.drop(wide))
self.assertArrayShape(gfl.rqr_lstsq(v_b, x_f, tau), wide[:-1])
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rqr_lstsq(v_s, x_f, tau)
with self.assertRaisesRegex(*utn.core_dim_err):
# This would succeed/broadcast error if interpreted as Mv:
gfl.rqr_lstsq(m_bs[y_one], x_f[off_b], tau[off_b])
def test_rqr_lstsq_flexible_signature_with_vectors_mv(self, arrays, fun):
m_sb, m_bs = hn.core_only(*arrays[:-1])
v_s = hn.core_only(arrays[-1], dims=1)
wide, tall = [arr.shape[-2:] for arr in arrays[:-1]]
hy.assume(hn.wide(m_sb))
hy.assume(la.norm(v_s) > 0.)
_, x_f, tau = fun(m_bs, v_s)
expect = utn.array_return_shape('(m,n),(n,p)->(m,p)', m_bs, m_sb)[:-1]
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, m_sb), expect)
self.assertArrayShape(gfl.rqr_lstsq(m_bs, x_f, tau), tall[:-1])
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.qr_lstsq(x_f, tau, m_bs)
self.assertArrayShape(gfl.rqr_lstsq(v_s, x_f, tau), tall[:-2])
m_sb, m_bs = arrays[:-1]
wide, tall = [arr.shape for arr in arrays[:-1]]
_, x_f, tau = fun(m_bs, v_s)
x_f, tau = unbroadcast_factors(v_s, x_f, tau)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, m_sb), utn.drop(wide))
self.assertArrayShape(gfl.rqr_lstsq(m_bs, x_f, tau), tall[:-1])
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)