def test_matches_exact(self, dense, MPO_ham):
h = MPO_ham(6)
dmrg = DMRG2(h, bond_dims=8)
assert dmrg._k.site[0].dtype == float
dmrg.opts['eff_eig_dense'] = dense
assert dmrg.solve()
# XXX: need to dispatch SLEPc seigsys on real input
# assert dmrg._k.site[0].dtype == float
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = seigsys(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(6, cyclic=False, j=(1.0, 1.0, 0.0))
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(6, cyclic=False)
actual_e, gs = seigsys(ham_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
def test_ground_state_matches(self, dense, MPO_ham):
h = MPO_ham(6)
dmrg = DMRG1(h, bond_dims=8)
dmrg.opts['eff_eig_dense'] = dense
assert dmrg.solve()
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = seigsys(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(6, cyclic=False, j=(1.0, 1.0, 0.0))
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(6, cyclic=False)
actual_e, gs = seigsys(ham_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
def test_seigsys_slepc_eigvecs(self):
h = rand_herm(100, sparse=True, density=0.2)
lks, vks = seigsys_slepc(h, k=5)
lka, vka = seigsys(h, k=5)
assert vks.shape == vka.shape
for ls, vs, la, va in zip(lks, vks.T, lka, vka.T):
assert_allclose(ls, la)
assert_allclose(expec(vs, va), 1.0)
def test_cross_equality(self, mat_herm_sparse, k, which):
_, a = mat_herm_sparse
sigma = 1 if which in {None, "TR"} else None
lks, vks = zip(*(seigsys(a, k=k, which=which, sigma=sigma, backend=b)
for b in backends))
lks, vks = tuple(lks), tuple(vks)
for i in range(len(lks) - 1):
assert_allclose(lks[i], lks[i + 1])
assert_allclose(abs(vks[i].H @ vks[i + 1]), eye(k), atol=1e-14)
def test_seigsys_sparse_wvecs(self, mat_herm_sparse, backend):
u, a = mat_herm_sparse
assert issparse(a)
lk, vk = seigsys(a, k=2, backend=backend)
assert_allclose(lk, (-3, -1))
for i, j in zip([3, 0], [0, 1]):
o = u[:, i].H @ vk[:, j]
assert_allclose(abs(o), 1.)
vk = seigvecs(a, k=2, backend=backend)
for i, j in zip([3, 0], [0, 1]):
o = u[:, i].H @ vk[:, j]
assert_allclose(abs(o), 1.)
def test_ising_and_MPS_product_state(self):
h = MPO_ham_ising(6, bx=2.0, j=0.1)
dmrg = DMRG1(h, bond_dims=8)
assert dmrg.solve()
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
# check against dense
h_dense = h.to_dense()
actual_e, gs = seigsys(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
exp_gs = MPS_product_state([plus()] * 6)
assert_allclose(abs(exp_gs.H @ mps_gs), 1.0, rtol=1e-3)