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_lqr(self, arrays): m_sb, m_bs = arrays hy.assume(hn.wide(m_sb)) hy.assume(hn.all_well_behaved(m_sb, m_bs)) box = np.s_[..., :m_sb.shape[-2], :] cond_sb = np.linalg.cond(m_sb).max() cond_bs = np.linalg.cond(m_bs).max() # with self.subTest("reduced"): unitary, right = la.lqr(m_bs, 'reduced') self.assertArrayAllClose(unitary @ right, m_bs, cond=cond_bs) left, unitary = la.lqr(m_sb, 'reduced') self.assertArrayAllClose(left @ unitary, m_sb, cond=cond_sb) # with self.subTest("complete"): unitary, right = la.lqr(m_bs, 'complete') self.assertArrayAllClose(unitary @ right, m_bs, cond=cond_bs) left, unitary = la.lqr(m_sb, 'complete') self.assertArrayAllClose(left @ unitary, m_sb, cond=cond_sb) # with self.subTest("r/l/raw"): right = la.lqr(m_bs, 'r') hhold, _ = la.lqr(m_bs, 'raw') self.assertArrayAllClose(right, np.triu(la.transpose(hhold))[box], cond=cond_bs) left = la.lqr(m_sb, 'r') hhold, _ = la.lqr(m_sb, 'raw') self.assertArrayAllClose(left, np.tril(la.transpose(hhold))[box[:-1]], cond=cond_sb)
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_lu(self, arrays): m_ss, m_sb, m_bs = arrays box = np.s_[..., :m_sb.shape[-2], :] hy.assume(hn.wide(m_sb)) # with self.subTest("square"): cond = np.linalg.cond(m_ss).max() lower, upper, piv = la.lu(m_ss, 'separate') luf, piv = la.lu(m_ss, 'raw') luf = la.transpose(luf) self.assertArrayAllClose(lower @ upper, gf.pivot(m_ss, piv), cond=cond) self.assertArrayAllClose(tril(lower), tril(luf), cond=cond) self.assertArrayAllClose(upper, np.triu(luf), cond=cond) # with self.subTest("wide"): cond = np.linalg.cond(m_bs).max() lower, upper, piv = la.lu(m_bs, 'separate') luf, piv = la.lu(m_bs, 'raw') luf = la.transpose(luf) self.assertArrayAllClose(tril(lower), tril(luf), cond=cond) self.assertArrayAllClose(upper, np.triu(luf)[box], cond=cond) # with self.subTest("wide"): cond = np.linalg.cond(m_sb).max() lower, upper, piv = la.lu(m_sb, 'separate') luf, piv = la.lu(m_sb, 'raw') luf = la.transpose(luf) self.assertArrayAllClose(tril(lower), tril(luf)[box[:-1]], cond=cond) self.assertArrayAllClose(upper, np.triu(luf), cond=cond)
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_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_lu_raw_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_rawm(m_bb), (big, big[:-1])) # with self.subTest(msg="wide"): self.assertArrayShapesAre(gfl.lu_rawm(m_sb), (utn.trnsp(wide), wide[:-1])) # with self.subTest(msg="tall"): self.assertArrayShapesAre(gfl.lu_rawn(m_bs), (utn.trnsp(tall), utn.drop(tall)))
def test_lq_returns_expected_values_with_wide(self, m_sb): hy.assume(hn.wide(m_sb)) hy.assume(hn.all_well_behaved(m_sb)) cond = np.linalg.cond(m_sb).max() left, unitary = gfl.lq_m(m_sb) wide = left @ unitary eye = unitary @ la.dagger(unitary) id_s = np.identity(m_sb.shape[-2], m_sb.dtype) # with self.subTest(msg='lq'): self.assertArrayAllClose(wide, m_sb, cond=cond) # with self.subTest(msg='Q Q^T'): self.assertArrayAllClose(id_s, eye, cond=cond)
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_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_lq_l_returns_expected_values(self, arrays): m_sb, m_bs = arrays hy.assume(hn.all_well_behaved(m_bs, m_sb)) hy.assume(hn.wide(m_sb)) # with self.subTest(msg='l_m'): cond = np.linalg.cond(m_sb).max() left = gfl.lq_lm(m_sb) llo = gfl.lq_m(m_sb)[0] self.assertArrayAllClose(left, llo, cond=cond) # with self.subTest(msg='l_n'): cond = np.linalg.cond(m_bs).max() left = gfl.lq_ln(m_bs) llo = gfl.lq_n(m_bs)[0] self.assertArrayAllClose(left, llo, cond=cond)
def test_qr_r_returns_expected_values(self, arrays): m_sb, m_bs = arrays hy.assume(hn.all_well_behaved(m_sb, m_bs)) hy.assume(hn.wide(m_sb)) # with self.subTest(msg='r_m'): cond = np.linalg.cond(m_sb).max() right = gfl.qr_rm(m_sb) rrr = gfl.qr_m(m_sb)[1] self.assertArrayAllClose(right, rrr, cond=cond) # with self.subTest(msg='r_n'): cond = np.linalg.cond(m_bs).max() right = gfl.qr_rn(m_bs) rrr = gfl.qr_n(m_bs)[1] self.assertArrayAllClose(right, rrr, cond=cond)
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_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_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)
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_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_lu(self, arrays): m_ss, m_sb, m_bs = arrays smol, wide, tall = [arr.shape for arr in arrays] hy.assume(hn.wide(m_sb)) # with self.subTest("separate"): self.assertArrayShapesAre(la.lu(m_ss, 'separate'), (smol, smol, smol[:-1])) self.assertArrayShapesAre(la.lu(m_bs, 'separate'), (tall, utn.chop(tall), utn.drop(tall))) self.assertArrayShapesAre(la.lu(m_sb, 'separate'), (utn.chop(wide), wide, wide[:-1])) # with self.subTest("raw"): self.assertArrayShapesAre(la.lu(m_ss, 'raw'), (smol, smol[:-1])) self.assertArrayShapesAre(la.lu(m_bs, 'raw'), (utn.trnsp(tall), utn.drop(tall))) self.assertArrayShapesAre(la.lu(m_sb, 'raw'), (utn.trnsp(wide), wide[:-1]))
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_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_pinv_returns_expected_values_wide(self, m_sb): hy.assume(hn.wide(m_sb)) hy.assume(hn.all_well_behaved(m_sb)) cond = np.linalg.cond(m_sb).max() id_s = np.identity(m_sb.shape[-2], m_sb.dtype) # with self.subTest(msg='wide'): wide_p = gfl.pinv(m_sb) self.assertArrayAllClose(m_sb @ wide_p, id_s, cond=cond) # with self.subTest(msg='wide,+qr'): wide_pq, wide_f, wide_tau = gfl.pinv_qrm(m_sb) # actually want lq here qrf, tau = gfl.lq_rawm(m_sb) # qrf = la.dagger(qrf) self.assertArrayAllClose(wide_pq, wide_p, cond=cond) self.assertArrayAllClose(wide_f, qrf, cond=cond) self.assertArrayAllClose(wide_tau, tau, cond=cond) # with self.subTest(msg='wide,-qr'): wide_qp = gfl.qr_pinv(wide_f, wide_tau) self.assertArrayAllClose(wide_qp, wide_p, cond=cond)
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_lq_returns_expected_shapes(self, arrays): m_sb, m_bs = arrays wide, tall = [arr.shape for arr in arrays] hy.assume(hn.wide(m_sb)) # with self.subTest(msg='wide'): self.assertArrayShapesAre(gfl.lq_m(m_sb), (utn.chop(wide), wide)) self.assertArrayShape(gfl.lq_lm(m_sb), utn.chop(wide)) # with self.subTest(msg='tall'): self.assertArrayShapesAre(gfl.lq_n(m_bs), (tall, utn.chop(tall))) self.assertArrayShape(gfl.lq_ln(m_bs), tall) with self.assertRaisesRegex(*utn.invalid_err): gfl.lq_m(m_bs) # with self.subTest(msg='complete'): self.assertArrayShapesAre(gfl.lq_n(m_sb), (wide, utn.grow(wide))) # with self.subTest(msg='raw'): self.assertArrayShapesAre(gfl.lq_rawm(m_sb), (utn.trnsp(wide), wide[:-1])) self.assertArrayShapesAre(gfl.lq_rawn(m_bs), (utn.trnsp(tall), utn.drop(tall)))
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])
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_lq(self, arrays): m_sb, m_bs = arrays wide, tall = [arr.shape for arr in arrays] hy.assume(hn.wide(m_sb)) # with self.subTest("reduced"): self.assertArrayShapesAre(la.lq(m_bs, 'reduced'), (tall, utn.chop(tall))) self.assertArrayShapesAre(la.lq(m_sb, 'reduced'), (utn.chop(wide), wide)) # with self.subTest("complete"): self.assertArrayShapesAre(la.lq(m_bs, 'complete'), (tall, utn.chop(tall))) self.assertArrayShapesAre(la.lq(m_sb, 'complete'), (wide, utn.grow(wide))) # with self.subTest("l/raw"): self.assertArrayShape(la.lq(m_bs, 'l'), tall) self.assertArrayShape(la.lq(m_sb, 'l'), utn.chop(wide)) self.assertArrayShapesAre(la.lq(m_bs, 'raw'), (utn.trnsp(tall), utn.drop(tall))) self.assertArrayShapesAre(la.lq(m_sb, 'raw'), (utn.trnsp(wide), wide[:-1]))
def test_qr_rawm_returns_expected_values(self, m_sb): hy.assume(hn.wide(m_sb)) hy.assume(hn.all_well_behaved(m_sb)) cond = np.linalg.cond(m_sb).max() rrr = gfl.qr_m(m_sb)[1] num = rrr.shape[-2] ht_sb, tau = gfl.qr_rawm(m_sb) h_sb = la.transpose(ht_sb) vecs = np.tril(h_sb, -1) vecs[(..., ) + np.diag_indices(num)] = 1 vnorm = gfb.norm(la.row(tau) * vecs[..., :num], axis=-2)**2 right = np.triu(h_sb) # with self.subTest(msg='raw_m'): self.assertArrayAllClose(right, rrr, cond=cond) self.assertArrayAllClose(vnorm, 2 * tau.real, cond=cond) for k in range(num): vvv = vecs[..., num - k - 1:num - k] ttt = la.scalar(tau[..., -k - 1]) right -= ttt * vvv * (la.dagger(vvv) @ right) # with self.subTest(msg='h_m'): self.assertArrayAllClose(right, m_sb, cond=cond)
def test_pinv_returns_expected_shapes(self, arrays): m_sb, m_bs = arrays wide, tall = [arr.shape for arr in arrays] hy.assume(hn.wide(m_sb)) hy.assume(hn.all_well_behaved(m_bs, m_sb)) # with self.subTest(msg='wide'): self.assertArrayShape(gfl.pinv(m_sb), utn.trnsp(wide)) # with self.subTest(msg='tall'): self.assertArrayShape(gfl.pinv(m_bs), utn.trnsp(tall)) # with self.subTest(msg='wide,+qr'): self.assertArrayShapesAre( gfl.pinv_qrm(m_sb), (utn.trnsp(wide), utn.trnsp(wide), wide[:-1])) # with self.subTest(msg='tall,+qr'): self.assertArrayShapesAre( gfl.pinv_qrn(m_bs), (utn.trnsp(tall), utn.trnsp(tall), utn.drop(tall))) # with self.subTest(msg='wide,-qr'): _, m_sb_f, m_sb_tau = gfl.pinv_qrm(m_sb) self.assertArrayShape(gfl.qr_pinv(m_sb_f, m_sb_tau), utn.trnsp(wide)) # with self.subTest(msg='tall,-qr'): _, m_bs_f, m_bs_tau = gfl.pinv_qrn(m_bs) self.assertArrayShape(gfl.qr_pinv(m_bs_f, m_bs_tau), utn.trnsp(tall))