def test_return_array_types(self, arrays):
m_sb_n, m_bs_n = arrays[:2]
m_sb, m_bs, m_ss, m_bb = view_as(*arrays)
m_bs_m, m_ss_m, m_bb_m = hn.core_only(m_bs, m_ss, m_bb)
hy.assume(hn.all_well_behaved(m_ss, m_bb))
hy.assume(m_sb.ndim != m_ss.ndim - 1) # np..solve's broadcasting issue
self.assertIsInstance(m_sb @ m_bs, la.lnarray)
self.assertIsInstance(m_sb_n @ m_bs, la.lnarray)
expect = utn.array_return_shape('(a,b),(b,c)->(a,c)', m_bs, m_sb)
tw_o = np.empty(expect, m_bs.dtype)
tw_r = la.matmul(m_bs, m_sb_n, tw_o)
self.assertIsInstance(tw_r, np.ndarray)
self.assertIsInstance(tw_o, np.ndarray)
self.assertIsInstance(np.matmul(m_bs, m_sb_n), np.ndarray)
self.assertIsInstance(la.solve(m_ss, m_sb_n), la.lnarray)
self.assertIsInstance(nl.solve(m_ss, m_sb_n), np.ndarray)
self.assertIsInstance(la.lstsq(m_bs, m_bb), la.lnarray)
self.assertIsInstance(
nl.lstsq(m_bs_m, m_bb_m, rcond=None)[0], np.ndarray)
self.assertIsInstance(la.lu(m_ss)[0], la.lnarray)
self.assertIsInstance(la.lu(m_bs_n)[0], np.ndarray)
self.assertIsInstance(la.qr(m_ss)[0], la.lnarray)
self.assertIsInstance(la.qr(m_bs_n)[0], np.ndarray)
self.assertIsInstance(la.lq(m_ss)[0], la.lnarray)
self.assertIsInstance(la.lq(m_bs_n)[0], np.ndarray)
self.assertIsInstance(la.lqr(m_ss)[0], la.lnarray)
self.assertIsInstance(la.lqr(m_bs_n)[0], np.ndarray)
self.assertIsInstance(nl.qr(m_ss_m)[0], np.ndarray)
def test_functions_lstsq(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays[:-1]
v_b = hn.core_only(arrays[-1], dims=1)
hy.assume(hn.wide(m_sb))
cond_sb = np.linalg.cond(m_sb).max()
cond_bs = np.linalg.cond(m_bs).max()
# with self.subTest('lstsq'):
self.assertArrayAllClose(la.lstsq(m_bs, m_bb),
gf.lstsq(m_bs, m_bb),
cond=cond_bs)
self.assertArrayAllClose(la.lstsq(m_sb, m_ss),
gf.lstsq(m_sb, m_ss),
cond=cond_sb)
lsq_sh = utn.array_return_shape('(a,b),(a,c)->(b,c)', m_bs, m_bb)
lsq_out = np.empty(lsq_sh, m_bs.dtype)
lsq_r = la.lstsq(m_bs, m_bb, out=lsq_out)
self.assertArrayAllClose(lsq_out, lsq_r)
# with self.subTest('rlstsq'):
self.assertArrayAllClose(la.rlstsq(m_ss, m_bs),
gf.rlstsq(m_ss, m_bs),
cond=cond_bs)
self.assertArrayAllClose(la.rlstsq(v_b, m_sb),
gf.rlstsq(v_b, m_sb),
cond=cond_sb)
def test_rtrue_divide_returns_expected_shapes(self, arrays):
a_bs, m_bs = arrays
a_bs[np.abs(a_bs) < 1e-5] += 1.
expect = utn.array_return_shape('(),()->()', a_bs, m_bs)
self.assertArrayShape(self.gfm.rtrue_divide(a_bs, m_bs), expect)
with self.assertRaisesRegex(*utn.broadcast_err):
self.gfm.rtrue_divide(*utn.make_bad_broadcast(m_bs, a_bs))
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_rmatmul_returns_expected_values(self, arrays):
m_sb, m_bs = arrays
expect = utn.array_return_shape('(a,b),(b,c)->(a,c)', m_sb, m_bs)
pout = np.empty(expect, m_sb.dtype)
pres = self.gfm.rmatmul(m_bs, m_sb, out=pout)
prod = np.matmul(m_sb, m_bs)
self.assertArrayAllClose(pres, prod)
self.assertArrayAllClose(pout, prod)
def test_rqr_lstsq_returns_expected_shape_wide(self, arrays, fun):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.wide(m_sb))
hy.assume(hn.all_well_behaved(m_sb))
_, x_f, tau = fun(m_bb, m_sb)
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_bs)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rqr_lstsq(m_bs, 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),(m,p)->(n,p)', m_sb, m_ss)
self.assertArrayShape(gfl.qr_lstsq(x_f, tau, m_ss), expect)
def test_rtrue_divide_returns_expected_values(self, arrays):
a_bs, m_bs = arrays
expect = utn.array_return_shape('(),()->()', a_bs, m_bs)
zout = np.empty(expect, m_bs.dtype)
a_bs[np.abs(a_bs) < 1e-5] += 1.
zres = self.gfm.rtrue_divide(a_bs, m_bs, out=zout)
zzz = m_bs / a_bs
self.assertArrayAllClose(zres, zzz)
self.assertArrayAllClose(zout, zzz)
def test_rmatmul_returns_expected_shapes(self, arrays):
m_sb, m_bs = arrays
hy.assume(hn.nonsquare(m_sb))
hy.assume(hn.nonsquare(m_bs))
expect = utn.array_return_shape('(a,b),(b,c)->(a,c)', m_sb, m_bs)
self.assertArrayShape(self.gfm.rmatmul(m_bs, m_sb), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
self.gfm.rmatmul(m_bs, m_bs)
with self.assertRaisesRegex(*utn.broadcast_err):
self.gfm.rmatmul(*utn.make_bad_broadcast(m_bs, m_sb))
def test_rlu_solve_returns_expected_shapes(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.nonsquare(m_sb))
hy.assume(hn.all_well_behaved(m_bb))
_, x_f, i_p = gfl.rsolve_lu(m_sb, m_bb)
expect = utn.array_return_shape('(a,b),(b,b)->(a,b)', m_sb, x_f)
self.assertArrayShape(gfl.rlu_solve(m_sb, x_f, i_p), expect)
expect = utn.array_return_shape('(a,a),(a,b)->(a,b)', x_f, m_bs)
self.assertArrayShape(gfl.lu_solve(x_f, i_p, m_bs), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rlu_solve(m_ss, x_f, i_p)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.lu_solve(x_f, i_p, m_sb)
_, x_f, i_p = gfl.rsolve_lu(m_sb, m_bb)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.rlu_solve(*utn.make_bad_broadcast(m_sb, x_f), i_p)
x_f, i_p = unbroadcast_factors(m_bb, x_f, i_p)
expect = utn.array_return_shape('(a,a),(a,b)->(a,b)', m_bb, m_bs)
self.assertArrayShape(gfl.lu_solve(x_f, i_p, m_bs), expect)
def test_rsolve_returns_expected_shapes(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.nonsquare(m_sb))
hy.assume(hn.all_well_behaved(m_bb))
expect = utn.array_return_shape('(a,b),(b,b)->(a,b)', m_sb, m_bb)
self.assertArrayShape(gfl.rsolve(m_sb, m_bb), expect)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rsolve(m_bs, m_bb)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rsolve(m_bs, m_sb)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.rsolve(*utn.make_bad_broadcast(m_bs, m_ss))
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_lstsq_qr_returns_expected_shape_tall(self, arrays, fun):
m_sb, m_bb, m_bs = arrays
hy.assume(hn.tall(m_bs))
hy.assume(hn.all_well_behaved(m_bs))
tall = m_bs.shape
expect = utn.array_return_shape('(m,n),(m,p)->(n,p),(n,m)', m_bs, m_bb)
tau = expect[1][:-2] + tau_len(m_bs, fun)
result = fun(m_bs, m_bb)
self.assertArrayShapesAre(result, expect + (tau, ))
self.assertArrayShapesAre(unbroadcast_factors(m_bs, *result[1:]),
(utn.trnsp(tall), tall[:-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_bs, m_bb))
def test_functions_solve(self, arrays):
m_ss, m_sb, m_bs = arrays
hy.assume(hn.all_well_behaved(m_ss))
cond = np.linalg.cond(m_ss).max()
# with self.subTest('solve'):
self.assertArrayAllClose(la.solve(m_ss, m_sb),
gf.solve(m_ss, m_sb),
cond=cond)
slv_sh = utn.array_return_shape('(a,a),(a,b)->(a,b)', m_ss, m_sb)
slv_out = np.empty(slv_sh, m_ss.dtype)
slv_r = la.solve(m_ss, m_sb, out=slv_out)
self.assertArrayAllClose(slv_out, slv_r)
# with self.subTest('rsolve'):
self.assertArrayAllClose(la.rsolve(m_bs, m_ss),
gf.rsolve(m_bs, m_ss),
cond=cond)
def test_rsolve_lu_returns_expected_shapes(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.nonsquare(m_sb))
hy.assume(hn.all_well_behaved(m_bb))
expect = utn.array_return_shape('(a,b),(b,b)->(a,b)', m_sb, m_bb)
expect_f = expect[:-2] + m_bb.shape[-2:]
result = gfl.rsolve_lu(m_sb, m_bb)
self.assertArrayShapesAre(result, (expect, expect_f, expect_f[:-1]))
self.assertArrayShapesAre(unbroadcast_factors(m_bb, *result[1:]),
(m_bb.shape, m_bb.shape[:-1]))
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rsolve_lu(m_bs, m_bb)
with self.assertRaisesRegex(*utn.core_dim_err):
gfl.rsolve_lu(m_bs, m_sb)
with self.assertRaisesRegex(*utn.broadcast_err):
gfl.rsolve_lu(*utn.make_bad_broadcast(m_bs, m_ss))
def test_functions_matldiv(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.all_well_behaved(m_ss))
hy.assume(hn.wide(m_sb))
# with self.subTest('solve'):
self.assertArrayAllClose(la.matldiv(m_ss, m_sb), gf.solve(m_ss, m_sb))
slv_sh = utn.array_return_shape('(a,a),(a,b)->(a,b)', m_ss, m_sb)
slv_out = np.empty(slv_sh, m_ss.dtype)
slv_r = la.matldiv(m_ss, m_sb, out=slv_out)
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(slv_out, slv_r, cond=cond)
# with self.subTest('lstsq'):
cond = np.linalg.cond(m_bs).max()
self.assertArrayAllClose(la.matldiv(m_bs, m_bb),
gf.lstsq(m_bs, m_bb),
cond=cond)
cond = np.linalg.cond(m_sb).max()
self.assertArrayAllClose(la.matldiv(m_sb, m_ss),
gf.lstsq(m_sb, m_ss),
cond=cond)
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_lnarray_operations_return_expected_values(self, arrays):
m_bs, m_ss, vec = view_as(*arrays)
m_bs_m = hn.core_only(m_bs)
vec = hn.core_only(vec, dims=1)
hy.assume(hn.tall(m_bs))
hy.assume(m_ss.ndim != 3) # causes np..solve's broadcasting issue
hy.assume(hn.all_well_behaved(m_ss, m_bs_m))
expect = utn.array_return_shape('(a,b),(b,c)->(a,c)', m_bs, m_ss)
ts_o = np.empty(expect, m_ss.dtype)
ts_r = la.matmul(m_bs, m_ss, ts_o)
self.assertArrayAllClose(ts_r, ts_o)
self.assertArrayAllClose(m_bs @ m_ss, np.matmul(m_bs, m_ss))
self.assertArrayAllClose(m_bs @ m_ss, np.matmul(m_bs, m_ss))
self.assertArrayAllClose(m_bs @ vec, np.matmul(m_bs, vec))
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(gf.solve(m_ss, vec),
nl.solve(m_ss, vec.c).uc,
cond=cond)
cond = np.linalg.cond(m_bs_m).max()
self.assertArrayAllClose(gf.lstsq(m_bs_m.t, vec),
nl.lstsq(m_bs_m.t, vec, rcond=None)[0],
cond=cond)
self.assertArrayAllClose(gf.rmatmul(m_ss, m_bs), np.matmul(m_bs, m_ss))
