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_lq_complete_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() left, unitary = gfl.lq_n(m_sb) wide = left @ unitary eye = unitary @ la.dagger(unitary) eyet = la.dagger(unitary) @ unitary id_b = np.identity(m_sb.shape[-1], 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_b, eye, cond=cond) # with self.subTest(msg='Q^T Q'): self.assertArrayAllClose(id_b, eyet, cond=cond)
def test_lq_returns_expected_values_with_tall(self, m_bs): hy.assume(hn.tall(m_bs)) hy.assume(hn.all_well_behaved(m_bs)) cond = np.linalg.cond(m_bs).max() left, unitary = gfl.lq_n(m_bs) tall = left @ unitary eye = unitary @ la.dagger(unitary) eyet = la.dagger(unitary) @ unitary id_s = np.identity(m_bs.shape[-1], m_bs.dtype) # with self.subTest(msg='lq'): self.assertArrayAllClose(tall, m_bs, cond=cond) # with self.subTest(msg='Q Q^T'): self.assertArrayAllClose(id_s, eye, cond=cond) # with self.subTest(msg='Q^T Q'): self.assertArrayAllClose(id_s, eyet, cond=cond)
def test_qr_complete_returns_expected_values(self, m_bs): hy.assume(hn.tall(m_bs)) hy.assume(hn.all_well_behaved(m_bs)) cond = np.linalg.cond(m_bs).max() unitary, right = gfl.qr_m(m_bs) tall = unitary @ right eye = la.dagger(unitary) @ unitary eyet = unitary @ la.dagger(unitary) id_b = np.identity(m_bs.shape[-2], m_bs.dtype) # with self.subTest(msg='qr'): self.assertArrayAllClose(tall, m_bs, cond=cond) # with self.subTest(msg='Q^T Q'): self.assertArrayAllClose(id_b, eye, cond=cond) # with self.subTest(msg='Q Q^T'): self.assertArrayAllClose(id_b, eyet, cond=cond)
def test_qr_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() unitary, right = gfl.qr_m(m_sb) wide = unitary @ right eye = la.dagger(unitary) @ unitary eyet = unitary @ la.dagger(unitary) id_s = np.identity(m_sb.shape[-2], m_sb.dtype) # with self.subTest(msg='qr'): self.assertArrayAllClose(wide, m_sb, cond=cond) # with self.subTest(msg='Q^T Q'): self.assertArrayAllClose(id_s, eye, cond=cond) # with self.subTest(msg='Q Q^T'): self.assertArrayAllClose(id_s, eyet, cond=cond)
def test_rlstsq_qr_returns_expected_values_with_tall(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_bs)) cond = np.linalg.cond(m_bs).max() # underconstrained x0_sb = gfl.rlstsq(m_ss, m_bs) # underconstrained x_sb, x_f, tau = fun(m_ss, m_bs) # with self.subTest('rlstsq_qr(over,' + suffix): self.assertArrayAllClose(x_sb, x0_sb, cond=cond) # underconstrained xx_sb = gfl.rqr_lstsq(m_ss, x_f, tau) # with self.subTest('rqr_rlstsq(over,' + suffix): self.assertArrayAllClose(xx_sb, x0_sb, cond=cond) # overconstrained y_sb = gfl.qr_lstsq(x_f, tau, m_bb) m_bst = la.dagger(m_bs) # with self.subTest('qr_rlstsq(under,' + suffix): self.assertArrayAllClose(m_bst @ m_bs @ y_sb, m_bst @ m_bb, cond=cond)
def test_qr_rawn_returns_expected_values(self, m_bs): hy.assume(hn.tall(m_bs)) hy.assume(hn.all_well_behaved(m_bs)) cond = np.linalg.cond(m_bs).max() rrr = gfl.qr_n(m_bs)[1] num = rrr.shape[-1] ht_bs, tau = gfl.qr_rawn(m_bs) h_bs = la.transpose(ht_bs) vecs = np.tril(h_bs, -1) vecs[(..., ) + np.diag_indices(num)] = 1 vnorm = gfb.norm(la.row(tau) * vecs, axis=-2)**2 right = np.triu(h_bs) # with self.subTest(msg='raw_n'): self.assertArrayAllClose(right[..., :num, :], 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_n'): self.assertArrayAllClose(right, m_bs, cond=cond)
def test_lq_rawn_returns_expected_values(self, m_bs): hy.assume(hn.tall(m_bs)) hy.assume(hn.all_well_behaved(m_bs)) cond = np.linalg.cond(m_bs).max() llo = gfl.lq_n(m_bs)[0] num = llo.shape[-1] ht_bs, tau = gfl.lq_rawn(m_bs) h_bs = la.transpose(ht_bs) vecs = np.triu(h_bs, 1) vecs[(..., ) + np.diag_indices(num)] = 1 vnorm = gfb.norm(la.col(tau) * vecs[..., :num, :], axis=-1)**2 left = np.tril(h_bs) # with self.subTest(msg='raw_n'): self.assertArrayAllClose(left, llo, cond=cond) # with self.subTest(msg='tau_n'): 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]) left -= ttt.conj() * (left @ la.dagger(vvv)) * vvv # with self.subTest(msg='h_n'): self.assertArrayAllClose(left, m_bs, cond=cond)