def test_add_mpo(self):
h = MPO_ham_heis(12)
h2 = h + h
assert max(h2[6].shape) == 10
h.lower_ind_id = h.upper_ind_id
t = h ^ ...
h2.upper_ind_id = h2.lower_ind_id
t2 = h2 ^ ...
assert_allclose(2 * t, t2)
def test_adding_mpo(self):
h = MPO_ham_heis(6)
hd = h.to_dense()
assert_allclose(h @ h.H, (hd @ hd.H).tr())
h2 = h + h
assert_allclose(h2 @ h2.H, (hd @ hd.H).tr() * 4)
h2.right_compress()
assert_allclose(h2 @ h2.H, (hd @ hd.H).tr() * 4)
assert max(h2['I3'].shape) == 5
def test_mpo_site_ham_heis(self, cyclic, j, bz, n):
hh_mpo = MPO_ham_heis(n, tags=['foo'], cyclic=cyclic, j=j, bz=bz)
assert hh_mpo[0].tags == {'I0', 'foo'}
assert hh_mpo[1].tags == {'I1', 'foo'}
assert hh_mpo[-1].tags == {'I{}'.format(n - 1), 'foo'}
assert hh_mpo.shape == (2, ) * 2 * n
hh_ex = qu.ham_heis(n, cyclic=cyclic, j=j, b=bz)
assert_allclose(qu.eigvalsh(hh_ex),
qu.eigvalsh(hh_mpo.to_dense()),
atol=1e-13)
def test_expand_mpo(self):
h = MPO_ham_heis(12)
assert h.site[0].dtype == float
he = h.expand_bond_dimension(13)
assert h.site[0].dtype == float
assert max(he.site[6].shape) == 13
h.lower_ind_id = h.upper_ind_id
t = h ^ ...
he.upper_ind_id = he.lower_ind_id
te = he ^ ...
assert_allclose(t, te)
def test_expand_mpo(self, cyclic, rand_strength):
h = MPO_ham_heis(12, cyclic=cyclic)
assert h[0].dtype == float
he = h.expand_bond_dimension(13, rand_strength=rand_strength)
assert h[0].dtype == float
assert max(he[6].shape) == 13
if cyclic:
assert he.bond_size(0, -1) == 13
t = h.trace()
te = he.trace()
assert_allclose(t, te)
def test_expand_mpo(self, cyclic, rand_strength):
h = MPO_ham_heis(12, cyclic=cyclic)
assert h[0].dtype == float
he = h.expand_bond_dimension(13, rand_strength=rand_strength)
assert h[0].dtype == float
assert max(he[6].shape) == 13
if cyclic:
assert he.bond_size(0, -1) == 13
h.lower_ind_id = h.upper_ind_id
t = h ^ ...
he.upper_ind_id = he.lower_ind_id
te = he ^ ...
assert_allclose(t, te)
def test_heisenberg(self, n, l, gap):
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham)
dmrg.solve()
gl = gap // 2
gr = gap // 2 + gap % 2
m = n // 2
sysa = range(m - l - gl, m - gl)
sysb = range(m + gr, m + l + gr)
assert max(sysa) + gap + 1 == min(sysb)
ln = dmrg.state.logneg_subsys(sysa,
sysb,
approx_spectral_opts={'bsz': 16},
verbosity=2)
# exact
lne = logneg_subsys(groundstate(ham_heis(n, cyclic=False)), [2] * n,
sysa, sysb)
assert_allclose(lne, ln, rtol=0.1, atol=0.1)
def test_cyclic_solve_big_with_segmenting(self):
n = 150
ham = MPO_ham_heis(n, cyclic=True)
dmrg = DMRG2(ham, bond_dims=range(10, 30, 2))
dmrg.opts['periodic_segment_size'] = 1 / 3
assert dmrg.solve(tol=1, verbosity=2)
assert dmrg.energy == pytest.approx(heisenberg_energy(n), 1e-3)
def test_dtypes(self, dtype):
H = MPO_ham_heis(8).astype(dtype)
dmrg = DMRG2(H)
dmrg.opts['local_eig_backend'] = 'scipy'
dmrg.solve(max_sweeps=3)
res_dtype, = {t.dtype for t in dmrg.state}
assert res_dtype == dtype
def test_realistic(self):
ham = MPO_ham_heis(20)
dmrg = DMRG2(ham, bond_dims=[4, 8])
dmrg.solve()
sysa, sysb = range(3, 9), range(12, 17)
rho_ab_pt = PTPTLazyMPS(dmrg.state, sysa, sysb)
xf = approx_spectral_function(rho_ab_pt, lambda x: x, beta_tol=1e-6,
tol=0.05, verbosity=2, max_bond=20)
assert_allclose(1, xf, rtol=0.5, atol=0.1)
def test_realistic(self):
seed_rand(42)
ham = MPO_ham_heis(20)
dmrg = DMRG2(ham, bond_dims=[2, 4])
dmrg.solve()
rho_ab = dmrg.state.ptr(range(6, 14))
xf = approx_spectral_function(rho_ab, lambda x: x,
tol=0.1, verbosity=2)
assert_allclose(1.0, xf, rtol=0.6, atol=0.001)
def test_mpo_site_ham_heis(self):
hh_mpo = MPO_ham_heis(5, tags=['foo'])
assert hh_mpo.site[0].tags == {'I0', 'foo'}
assert hh_mpo.site[3].tags == {'I3', 'foo'}
assert hh_mpo.site[-1].tags == {'I4', 'foo'}
assert hh_mpo.shape == (2, ) * 10
hh_ = (hh_mpo ^ ...).fuse({
'k': ['k0', 'k1', 'k2', 'k3', 'k4'],
'b': ['b0', 'b1', 'b2', 'b3', 'b4']
})
hh = ham_heis(5, cyclic=False)
assert_allclose(hh, hh_.data)
def test_realistic_ent(self):
n = 12
sysa, sysb = range(3, 6), range(6, 8)
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham, bond_dims=[2, 4])
dmrg.solve()
rho_ab_pt = PTPTLazyMPS(dmrg.state, sysa, sysb)
psi0 = dmrg.state.to_dense()
lne = logneg_subsys(psi0, [2] * n, sysa=sysa, sysb=sysb)
lnx = log2(
approx_spectral_function(rho_ab_pt, abs, tol=0.1, verbosity=2))
assert_allclose(lne, lnx, rtol=0.5, atol=0.1)
def test_realistic_ent(self):
n = 12
sysa, sysb = range(3, 6), range(6, 8)
sysab = (*sysa, *sysb)
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham, bond_dims=[10])
dmrg.solve()
psi0 = dmrg.state.to_dense()
lne = logneg_subsys(psi0, [2] * n, sysa=sysa, sysb=sysb)
rho_ab = dmrg.state.ptr(sysab, rescale_sites=True)
rho_ab_pt = rho_ab.partial_transpose(range(3))
lnx = log2(
approx_spectral_function(rho_ab_pt, abs, tol=0.1, verbosity=2))
assert_allclose(lne, lnx, rtol=0.6, atol=0.1)
def test_single_explicit_sweep(self):
h = MPO_ham_heis(5)
dmrg = DMRG1(h, bond_dims=3)
assert dmrg._k[0].dtype == float
energy_tn = (dmrg._b | dmrg.ham | dmrg._k)
e0 = energy_tn ^ ...
assert abs(e0.imag) < 1e-13
de1 = dmrg.sweep_right()
e1 = energy_tn ^ ...
assert_allclose(de1, e1)
assert abs(e1.imag) < 1e-13
de2 = dmrg.sweep_right()
e2 = energy_tn ^ ...
assert_allclose(de2, e2)
assert abs(e2.imag) < 1e-13
# state is already left canonized after right sweep
de3 = dmrg.sweep_left(canonize=False)
e3 = energy_tn ^ ...
assert_allclose(de3, e3)
assert abs(e2.imag) < 1e-13
de4 = dmrg.sweep_left()
e4 = energy_tn ^ ...
assert_allclose(de4, e4)
assert abs(e2.imag) < 1e-13
# test still normalized
assert dmrg._k[0].dtype == float
align_TN_1D(dmrg._k, dmrg._b, inplace=True)
assert_allclose(abs(dmrg._b @ dmrg._k), 1)
assert e1.real < e0.real
assert e2.real < e1.real
assert e3.real < e2.real
assert e4.real < e3.real
def test_expand_mpo_limited(self, cyclic, rand_strength):
h = MPO_ham_heis(12, cyclic=cyclic)
he = h.expand_bond_dimension(3, rand_strength=rand_strength)
# should do nothing
assert max(he[6].shape) == 5
def test_expand_mpo_limited(self):
h = MPO_ham_heis(12)
he = h.expand_bond_dimension(3) # should do nothing
assert max(he.site[6].shape) == 5
