def test_thermal_state_tuple(self):
full = rand_herm(2**4)
l, v = eigsys(full)
for beta in (0, 0.5, 1, 10):
rhoth1 = thermal_state(full, beta)
rhoth2 = thermal_state((l, v), beta)
assert_allclose(rhoth1, rhoth2)
def test_eigsys(self, mat_herm_dense, bkd):
u, a = mat_herm_dense
evals, v = eigsys(a, backend=bkd)
assert(set(np.rint(evals)) == set((-1, 2, 4, -3)))
assert_allclose(evals, [-3, -1, 2, 4])
for i, j in zip([3, 0, 1, 2], range(4)):
o = u[:, i].H @ v[:, j]
assert_allclose(abs(o), 1.)
def test_exp_sparse(self):
a = rand_herm(100, sparse=True, density=0.1)
k = rand_ket(100)
out = mfn_multiply_slepc(a, k)
al, av = eigsys(a.A)
expected = av @ np.diag(np.exp(al)) @ av.conj().T @ k
assert_allclose(out, expected)
def test_1(self):
a = rand_herm(100, sparse=True)
el, ev = eigsys(a.A)
which = abs(el) < 0.2
el, ev = el[which], ev[:, which]
offset = norm(a, 'fro')
a = a + offset * sp.eye(a.shape[0])
sl, sv = seigsys_slepc(a, l_win=(-0.2 + offset, 0.2 + offset))
sl -= offset
assert_allclose(el, sl)
assert_allclose(np.abs(sv.H @ ev), np.eye(el.size), atol=1e-11)
def test_expm_multiply(self, num_workers, bigsparsemat, big_vec):
a = bigsparsemat
k = big_vec
if ((num_workers is not None) and ALREADY_RUNNING_AS_MPI
and num_workers > 1 and num_workers != NUM_MPI_WORKERS):
with pytest.raises(ValueError):
mfn_multiply_slepc_spawn(a, k, num_workers=num_workers)
else:
out = mfn_multiply_slepc_spawn(a, k, num_workers=num_workers)
al, av = eigsys(a.A)
expected = av @ np.diag(np.exp(al)) @ av.conj().T @ k
assert_allclose(out, expected)
def test_sqrt_sparse(self):
import scipy.sparse as sp
a = rand_pos(32, sparse=True, density=0.1)
a = a + 0.001 * sp.eye(32)
k = rand_ket(32)
out = mfn_multiply_slepc(a, k, fntype='sqrt', isherm=True)
al, av = eigsys(a.A)
al[al < 0] = 0.0 # very small neg values spoil sqrt
expected = av @ np.diag(np.sqrt(al)) @ av.conj().T @ k
assert_allclose(out, expected, rtol=1e-6)
def test_quevo_ham_dense_ket_solve(self, ham_rcr_psi, sparse, presolve):
ham, trc, p0, tm, pm = ham_rcr_psi
ham = qu(ham, sparse=sparse)
if presolve:
l, v = eigsys(ham)
sim = QuEvo(p0, (l, v))
assert sim._solved
else:
sim = QuEvo(p0, ham, method='solve')
sim.update_to(tm)
assert_allclose(sim.pt, pm)
assert expec(sim.pt, p0) < 1.0
sim.update_to(trc)
assert_allclose(sim.pt, p0)
assert isinstance(sim.pt, np.matrix)
assert sim.t == trc
def test_explicit_sweeps(self):
# import pdb; pdb.set_trace()
n = 8
chi = 16
ham = MPO_ham_mbl(n, dh=5, run=42)
p0 = MPS_neel_state(n).expand_bond_dimension(chi)
b0 = p0.H
align_TN_1D(p0, ham, b0, inplace=True)
en0 = np.asscalar(p0 & ham & b0 ^ ...)
dmrgx = DMRGX(ham, p0, chi)
dmrgx.sweep_right()
en1 = dmrgx.sweep_left(canonize=False)
assert en0 != en1
dmrgx.sweep_right(canonize=False)
en = dmrgx.sweep_right(canonize=True)
# check normalized
assert_allclose(dmrgx._k.H @ dmrgx._k, 1.0)
k = dmrgx._k.to_dense()
h = ham.to_dense()
el, ev = eigsys(h)
# check variance very low
assert np.abs((k.H @ h @ h @ k) - (k.H @ h @ k)**2) < 1e-12
# check exactly one eigenvalue matched well
assert np.sum(np.abs(el - en) < 1e-12) == 1
# check exactly one eigenvector is matched with high fidelity
ovlps = (ev.H @ k).A**2
big_ovlps = ovlps[ovlps > 1e-12]
assert_allclose(big_ovlps, [1])
# check fully
assert is_eigenvector(k, h)