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_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_rmatmul_flexible_signature_with_vectors(self, arrays): m_ss, m_sb, m_bb, m_bs = arrays[:-2] v_s, v_b = hn.core_only(*arrays[-2:], dims=1) smol, wide, big, tall = [arr.shape for arr in arrays[:-2]] hy.assume(hn.nonsquare(m_sb)) off_b, y_one = utn.make_off_by_one(m_sb, m_sb) # with self.subTest('matrix-vector'): self.assertArrayShape(self.gfm.rmatmul(v_s, m_bs), tall[:-1]) self.assertArrayShape(self.gfm.rmatmul(v_b, m_sb), wide[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): self.gfm.rmatmul(v_b, m_bs) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as Mv: self.gfm.rmatmul(m_sb[y_one], m_sb[off_b]) # w\ith self.subTest('vector-matrix'): self.assertArrayShape(self.gfm.rmatmul(m_ss, v_s), smol[:-1]) self.assertArrayShape(self.gfm.rmatmul(m_bb, v_b), big[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): self.gfm.rmatmul(m_bs, v_s) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as vM: self.gfm.rmatmul(m_sb[off_b], m_sb[y_one]) # with self.subTest('vector-vector'): self.assertArrayShape(self.gfm.rmatmul(v_b, v_b), ()) with self.assertRaisesRegex(*utn.core_dim_err): self.gfm.rmatmul(v_b, v_s)
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_lstsq_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.nonsquare(m_sb)) self.assertArrayShape(gfl.lstsq(v_s, m_sb), utn.drop(wide)) self.assertArrayShape(gfl.lstsq(v_b, m_bs), utn.drop(tall)) with self.assertRaisesRegex(*utn.core_dim_err): gfl.lstsq(v_s, m_bs)
def test_rlstsq_qr_flexible_signature_with_vectors_mv(self, arrays, fun): m_sb, m_bs = arrays[:-1] wide = m_sb.shape v_b = hn.core_only(arrays[-1], dims=1) hy.assume(hn.wide(m_sb)) hy.assume(la.norm(v_b) > 0.) tau = m_sb.shape[:-2] + tau_len_vec(v_b, fun) self.assertArrayShapesAre(fun(m_sb, v_b), (wide[:-1], utn.drop(wide), tau)) with self.assertRaisesRegex(*utn.core_dim_err): fun(m_bs, v_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_functions_solve(self, arrays): m_ss, m_sb, m_bs = arrays[:-1] v_s = hn.core_only(arrays[-1], dims=1) smol, wide, tall = [arr.shape for arr in arrays[:-1]] hy.assume(hn.all_well_behaved(m_ss)) # with self.subTest('solve'): expect = gf.return_shape('(a,b),(b,c)->(a,c)', smol, wide) self.assertArrayShape(la.solve(m_ss, m_sb), expect) self.assertArrayShape(la.solve(m_ss, v_s), smol[:-1]) # with self.subTest('rsolve'): expect = gf.return_shape('(a,b),(b,c)->(a,c)', tall, smol) self.assertArrayShape(la.rsolve(m_bs, m_ss), expect) self.assertArrayShape(la.rsolve(v_s, m_ss), smol[:-1])
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_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))
def test_lu_solve_flexible_signature_with_vectors(self, arrays): m_ss = arrays[0] v_s, v_b = hn.core_only(*arrays[1:], dims=1) hy.assume(len(v_s) != len(v_b)) hy.assume(hn.all_well_behaved(m_ss)) # with self.subTest('lu_solve'): _, x_f, i_p = gfl.solve_lu(m_ss, v_s) self.assertArrayShape(gfl.lu_solve(x_f, i_p, v_s), m_ss.shape[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): gfl.lu_solve(x_f, i_p, v_b) # with self.subTest('rlu_solve'): self.assertArrayShape(gfl.rlu_solve(v_s, x_f, i_p), m_ss.shape[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): gfl.rlu_solve(v_b, x_f, i_p)
def test_solve_flexible_signature_with_vectors(self, arrays): m_ss, m_sb, m_bb, m_bs = arrays[:-1] v_s = hn.core_only(arrays[-1], dims=1) hy.assume(hn.nonsquare(m_sb)) hy.assume(hn.all_well_behaved(m_ss)) off_b, y_one = utn.make_off_by_one(m_bb, m_sb) # with self.subTest('solve'): self.assertArrayShape(gfl.solve(m_ss, v_s), m_ss.shape[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): gfl.solve(m_bb, v_s) with self.assertRaisesRegex(*utn.core_dim_err): gfl.solve(m_bs, v_s) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as Mv: gfl.solve(m_bb[off_b], m_sb[y_one])
def test_rsolve_lu_flexible_signature_with_vectors(self, arrays): m_ss, m_sb, m_bb = arrays[:-1] v_s = hn.core_only(arrays[-1], dims=1) hy.assume(hn.nonsquare(m_sb)) hy.assume(hn.all_well_behaved(m_ss)) # with self.subTest('rsolve_lu'): self.assertArrayShapesAre(gfl.rsolve_lu( v_s, m_ss), (m_ss.shape[:-1], m_ss.shape, m_ss.shape[:-1])) with self.assertRaisesRegex(*utn.core_dim_err): gfl.rsolve_lu(v_s, m_bb) with self.assertRaisesRegex(*utn.core_dim_err): gfl.rsolve_lu(v_s, m_sb) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as vM: gfl.rsolve_lu(m_sb, m_ss)
def test_functions_matmul(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]] # with self.subTest('matmul'): expect = gf.return_shape('(a,b),(b,c)->(a,c)', tall, wide) self.assertArrayShape(la.matmul(m_bs, m_sb), expect) self.assertArrayShape(la.matmul(m_bs, v_s), tall[:-1]) self.assertArrayShape(la.matmul(v_b, m_bs), utn.drop(tall)) self.assertArrayShape(la.matmul(v_s, v_s), ()) # with self.subTest('rmatmul'): expect = gf.return_shape('(a,b),(b,c)->(a,c)', wide, tall) self.assertArrayShape(gf.rmatmul(m_bs, m_sb), expect) self.assertArrayShape(gf.rmatmul(m_sb, v_s), utn.drop(wide)) self.assertArrayShape(gf.rmatmul(v_b, m_sb), wide[:-1]) self.assertArrayShape(gf.rmatmul(v_b, v_b), ())
def test_functions_matrdiv(self, arrays): m_ss, m_sb, m_bs = arrays[:-2] v_s, v_b = hn.core_only(*arrays[-2:], dims=1) smol, wide, tall = [arr.shape for arr in arrays[:-2]] hy.assume(hn.all_well_behaved(m_ss)) hy.assume(hn.wide(m_sb)) # with self.subTest('rsolve'): expect = gf.return_shape('(a,b),(c,b)->(a,c)', tall, smol) self.assertArrayShape(la.matrdiv(m_bs, m_ss), expect) self.assertArrayShape(la.matrdiv(v_s, m_ss), smol[:-1]) # with self.subTest('rlstsq'): expect = gf.return_shape('(a,b),(c,b)->(a,c)', smol, tall) self.assertArrayShape(la.matrdiv(m_ss, m_bs), expect) self.assertArrayShape(la.matrdiv(v_b, m_sb), wide[:-1]) self.assertArrayShape(la.matrdiv(m_ss, v_s), smol[:-1]) self.assertArrayShape(la.matrdiv(v_s, m_bs), tall[:-1])
def test_functions_matldiv(self, arrays): m_ss, m_sb, m_bb, m_bs = arrays[:-1] v_s = hn.core_only(arrays[-1], dims=1) smol, wide, big, tall = [arr.shape for arr in arrays[:-1]] hy.assume(hn.all_well_behaved(m_ss)) hy.assume(hn.wide(m_sb)) # with self.subTest('solve'): expect = gf.return_shape('(a,b),(a,c)->(b,c)', smol, wide) self.assertArrayShape(la.matldiv(m_ss, m_sb), expect) self.assertArrayShape(la.matldiv(m_ss, v_s), smol[:-1]) # with self.subTest('lstsq'): expect = gf.return_shape('(a,b),(a,c)->(b,c)', tall, big) self.assertArrayShape(la.matldiv(m_bs, m_bb), expect) expect = gf.return_shape('(a,b),(a,c)->(b,c)', wide, smol) self.assertArrayShape(la.matldiv(m_sb, m_ss), expect) self.assertArrayShape(la.matldiv(m_sb, v_s), utn.drop(wide)) self.assertArrayShape(la.matldiv(v_s, m_ss), smol[:-1])
def test_rlu_solve_flexible_signature_with_vectors(self, arrays): m_ss, m_sb = arrays[:-2] v_s, v_b = hn.core_only(*arrays[-2:], dims=1) hy.assume(hn.nonsquare(m_sb)) hy.assume(hn.all_well_behaved(m_ss)) off_b, y_one = utn.make_off_by_one(m_ss, m_sb) # with self.subTest('rlu_solve'): _, x_f, i_p = gfl.rsolve_lu(v_s, m_ss) self.assertArrayShape(gfl.rlu_solve(v_s, x_f, i_p), m_ss.shape[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): gfl.rlu_solve(v_b, x_f, i_p) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as vM: gfl.rlu_solve(m_sb[y_one], x_f[off_b], i_p[off_b]) self.assertArrayShape(gfl.lu_solve(x_f, i_p, v_s), m_ss.shape[:-1]) with self.assertRaisesRegex(*utn.core_dim_err): gfl.lu_solve(x_f, i_p, v_b)
def test_rlstsq_qr_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_sb, m_bs)) off_b, y_one = utn.make_off_by_one(m_sb, m_bs) tau = m_sb.shape[:-2] + tau_len(m_sb, fun) self.assertArrayShapesAre(fun(v_b, m_sb), (wide[:-1], utn.trnsp(wide), tau)) tau = m_bs.shape[:-2] + tau_len(m_bs, fun) self.assertArrayShapesAre(fun(v_s, m_bs), (tall[:-1], utn.trnsp(tall), tau)) with self.assertRaisesRegex(*utn.core_dim_err): fun(v_b, m_bs) with self.assertRaisesRegex(*utn.core_dim_err): # This would succeed/broadcast error if interpreted as vM: fun(m_bs[y_one], m_sb[off_b])
def test_functions_lstsq(self, arrays): m_ss, m_sb, m_bb, m_bs = arrays[:-2] v_s, v_b = hn.core_only(*arrays[-2:], dims=1) smol, wide, big, tall = [arr.shape for arr in arrays[:-2]] # with self.subTest('lstsq'): expect = gf.return_shape('(a,b),(a,c)->(b,c)', tall, big) self.assertArrayShape(la.lstsq(m_bs, m_bb), expect) expect = gf.return_shape('(a,b),(a,c)->(b,c)', wide, smol) self.assertArrayShape(la.lstsq(m_sb, m_ss), expect) self.assertArrayShape(la.lstsq(m_sb, v_s), utn.drop(wide)) self.assertArrayShape(la.lstsq(v_s, m_ss), smol[:-1]) # with self.subTest('rlstsq'): expect = gf.return_shape('(a,b),(c,b)->(a,c)', smol, tall) self.assertArrayShape(la.rlstsq(m_ss, m_bs), expect) expect = gf.return_shape('(a,b),(c,b)->(a,c)', big, wide) self.assertArrayShape(la.rlstsq(m_bb, m_sb), expect) self.assertArrayShape(la.rlstsq(v_b, m_sb), wide[:-1]) self.assertArrayShape(la.rlstsq(m_ss, v_s), smol[:-1]) self.assertArrayShape(la.rlstsq(v_s, m_bs), tall[:-1])
def test_functions_matrdiv(self, arrays): m_ss, m_sb, m_bs = arrays[:-1] v_b = hn.core_only(arrays[-1], dims=1) hy.assume(hn.all_well_behaved(m_ss)) hy.assume(hn.wide(m_sb)) # with self.subTest('rsolve'): cond = np.linalg.cond(m_ss).max() self.assertArrayAllClose(la.matrdiv(m_bs, m_ss), gf.rsolve(m_bs, m_ss), cond=cond) # with self.subTest('rlstsq'): cond = np.linalg.cond(m_bs).max() self.assertArrayAllClose(la.matrdiv(m_ss, m_bs), gf.rlstsq(m_ss, m_bs), cond=cond) cond = np.linalg.cond(m_sb).max() self.assertArrayAllClose(la.matrdiv(v_b, m_sb), gf.rlstsq(v_b, m_sb), cond=cond)
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])