def test_lattice():
chinfo = npc.ChargeInfo([1, 3])
leg = gen_random_legcharge(chinfo, 8)
leg2 = gen_random_legcharge(chinfo, 2)
op1 = npc.Array.from_func(np.random.random, [leg, leg.conj()],
shape_kw='size')
op2 = npc.Array.from_func(np.random.random, [leg2, leg2.conj()],
shape_kw='size')
site1 = lattice.Site(leg, [('up', 0), ('down', -1)], op1=op1)
site2 = lattice.Site(leg2, [('down', 0), ('up', -1)], op2=op2)
for order in ['default', 'Fstyle', 'snake', 'snakeFstyle']:
print("order =", order)
Ls = [5, 2]
basis = [[1., 1.], [0., 1.]]
pos = [[0.1, 0.], [0.2, 0.]]
lat = lattice.Lattice(Ls, [site1, site2],
order=order,
basis=basis,
positions=pos,
bc='periodic',
bc_MPS='infinite')
assert lat.dim == len(Ls)
assert lat.N_sites == np.prod(Ls) * 2
for i in range(lat.N_sites):
assert lat.lat2mps_idx(lat.mps2lat_idx(i)) == i
idx = [4, 1, 0]
assert np.all(lat.mps2lat_idx(lat.lat2mps_idx(idx)) == idx)
# index conversion should also work for arbitrary index arrays and indices outside bc_MPS
# for bc_MPS=infinite
i = np.arange(-3, lat.N_sites * 2 - 3).reshape((-1, 2))
assert np.all(lat.lat2mps_idx(lat.mps2lat_idx(i)) == i)
# test position
npt.assert_equal([4.1, 5.], lat.position(idx))
# test lat.mps2lat_values
A = np.random.random([lat.N_sites, 2, lat.N_sites])
print(A.shape)
Ares = lat.mps2lat_values(A, axes=[-1, 0])
Ares_ma = lat.mps2lat_values_masked(A, [-1, 0], [None] * 2, [None] * 2)
for i in range(lat.N_sites):
idx_i = lat.mps2lat_idx(i)
for j in range(lat.N_sites):
idx_j = lat.mps2lat_idx(j)
for k in range(2):
idx = tuple(idx_i) + (k, ) + tuple(idx_j)
assert Ares[idx] == A[i, k, j]
assert Ares_ma[idx] == A[i, k, j]
# and again for fixed `u` within the unit cell
for u in range(len(lat.unit_cell)):
mps_u = lat.mps_idx_fix_u(u)
A_u = A[np.ix_(mps_u, np.arange(2), mps_u)]
A_u_res = lat.mps2lat_values(A_u, axes=[-1, 0], u=u)
A_u_res_masked = lat.mps2lat_values_masked(A_u,
axes=[-1, 0],
mps_inds=[mps_u] * 2,
include_u=[False] * 2)
A_u_expected = Ares[:, :, u, :, :, :, u]
npt.assert_equal(A_u_res, A_u_expected)
npt.assert_equal(A_u_res_masked, A_u_expected)
def test_npc_Array_reshape():
a = random_Array((20, 15, 10), chinfo, sort=False)
aflat = a.to_ndarray()
for comb_legs, transpose in [([[1]], [0, 1, 2]), ([[1], [2]], [0, 1, 2]),
([[0], [1], [2]], [0, 1, 2]), ([[2, 0]], [1, 2, 0]),
([[2, 0, 1]], [2, 0, 1])]:
print('combine legs', comb_legs)
with warnings.catch_warnings():
warnings.simplefilter("ignore", FutureWarning)
acomb = a.combine_legs(comb_legs) # just sorts second leg
print("=> labels: ", acomb.get_leg_labels())
acomb.test_sanity()
asplit = acomb.split_legs()
asplit.test_sanity()
npt.assert_equal(asplit.to_ndarray(), aflat.transpose(transpose))
print("test squeeze")
b = random_Array((10, 1, 5, 1), chinfo3, sort=True)
bflat = b.to_ndarray()
bs = b.squeeze()
bs.test_sanity()
npt.assert_equal(bs.to_ndarray(), np.squeeze(bflat))
bs.test_sanity()
if b.stored_blocks > 0:
# find a index with non-zero entry
idx = tuple([l.slices[qi] for l, qi in zip(b.legs, b._qdata[0])])
else:
idx = tuple([0] * b.rank)
assert b[idx[0], :, idx[2], :].squeeze() == bflat[idx]
print("test add_trivial_leg")
be = bs.copy(deep=True).add_trivial_leg(1, 'tr1', +1).add_trivial_leg(3, 'tr2', -1)
be.test_sanity()
npt.assert_equal(be.to_ndarray(), bflat)
print("test concatenate")
# create array `c` to concatenate with b along axis 2
legs = b.legs[:]
legs[1] = gen_random_legcharge(b.chinfo, 5)
c1 = npc.Array.from_func(np.random.random, legs, qtotal=b.qtotal, shape_kw='size')
c1flat = c1.to_ndarray()
legs[1] = gen_random_legcharge(b.chinfo, 3)
c2 = npc.Array.from_func(np.random.random, legs, qtotal=b.qtotal, shape_kw='size')
c2flat = c2.to_ndarray()
bc1c2 = npc.concatenate([b, c1, c2], axis=1)
bc1c2.test_sanity()
npt.assert_equal(bc1c2.to_ndarray(), np.concatenate([bflat, c1flat, c2flat], axis=1))
print("trivial charges")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
acomb = a.combine_legs([0, 1])
acomb.test_sanity()
asplit = acomb.split_legs([0])
asplit.test_sanity()
npt.assert_equal(asplit.to_ndarray(), aflat)
def test_npc_grid_concat():
# this is also a heavy test of Array.__getitem__
ci = chinfo3
legs = [gen_random_legcharge(ci, l) for l in [5, 4, 3]]
A = npc.Array.from_func(np.random.random,
legs,
qtotal=[0],
shape_kw='size')
print("orig legs")
for l in legs:
print(l)
print('---')
Aflat = A.to_ndarray()
grid = [A[..., :2, :], A[:, 2:3, ...], A[:, 3:]]
A_full = npc.grid_concat(grid, [1])
npt.assert_equal(Aflat, A_full.to_ndarray())
grid = [[A[:, :1, 2:3], A[:, :1, 0:2]],
[A[:, 2:, 2:3], A[:, 2:, 0:2]]] # yapf: disable
A_part = npc.grid_concat(grid, [1, 2]).to_ndarray()
A_part_exact = Aflat[:, [0, 2, 3], :][:, :, [2, 0, 1]]
npt.assert_equal(A_part, A_part_exact)
grid[1][0] = None
A_part = npc.grid_concat(grid, [1, 2]).to_ndarray()
A_part_exact[:, 1:, 0] = 0.
npt.assert_equal(A_part, A_part_exact)
def test_npc_grid_outer():
ci = chinfo3
p_leg = gen_random_legcharge(ci, 4)
legs_op = [p_leg, p_leg.conj()]
op_0 = 1.j * npc.Array.from_func(np.random.random, legs_op, qtotal=[0], shape_kw='size')
op_pl = npc.Array.from_func(np.random.random, legs_op, qtotal=[1], shape_kw='size')
op_min = npc.Array.from_func(np.random.random, legs_op, qtotal=[-1], shape_kw='size')
op_id = npc.eye_like(op_0)
grid = [[op_id, op_pl, op_min, op_0, None],
[None, None, None, None, op_min],
[None, None, None, None, op_pl],
[None, None, None, None, op_0],
[None, None, None, None, op_id]] # yapf: disable
leg_WL = npc.LegCharge.from_qflat(ci, ci.make_valid([[0], [1], [-1], [0], [0]]))
leg_WR = npc.LegCharge.from_qflat(ci, ci.make_valid([[0], [1], [-1], [0], [0]]), -1)
leg_WR_calc = npc.detect_grid_outer_legcharge(grid, [leg_WL, None], qconj=-1)[1]
leg_WR.test_equal(leg_WR_calc)
W = npc.grid_outer(grid, [leg_WL, leg_WR])
W.test_sanity()
Wflat = np.zeros([5, 5, 4, 4], dtype=W.dtype)
for idx, op in [[(0, 0), op_id], [(0, 1), op_pl], [(0, 2), op_min], [(0, 3), op_0],
[(1, 4), op_min], [(2, 4), op_pl], [(3, 4), op_0], [(4, 4), op_id]]:
Wflat[idx] = op.to_ndarray()
npt.assert_equal(W.to_ndarray(), Wflat)
def test_LegPipe():
shape = (20, 10, 8)
legs = [gen_random_legcharge(ch_1, s) for s in shape]
for sort, bunch in it.product([True, False], repeat=2):
pipe = charges.LegPipe(legs, sort=sort, bunch=bunch)
pipe.test_sanity()
pipe_conj = pipe.conj()
pipe.test_contractible(pipe.conj())
pipe_equal = pipe.flip_charges_qconj()
pipe_equal.test_equal(pipe)
assert (pipe.ind_len == np.prod(shape))
print(pipe.q_map)
# test pipe._map_incoming_qind
qind_inc = pipe.q_map[:, 3:].copy() # all possible qindices
np.random.shuffle(
qind_inc) # different order to make the test non-trivial
qmap_ind = pipe._map_incoming_qind(qind_inc)
for i in range(len(qind_inc)):
npt.assert_equal(pipe.q_map[qmap_ind[i], 3:], qind_inc[i])
size = np.prod([
l.slices[j + 1] - l.slices[j]
for l, j in zip(legs, qind_inc[i])
])
assert size == pipe.q_map[qmap_ind[i], 1] - pipe.q_map[qmap_ind[i],
0]
def test_site():
chinfo = npc.ChargeInfo([1, 3])
leg = gen_random_legcharge(chinfo, 8)
op1 = npc.Array.from_func(np.random.random, [leg, leg.conj()], shape_kw='size')
op2 = npc.Array.from_func(np.random.random, [leg, leg.conj()], shape_kw='size')
labels = ['up'] + [None] * (leg.ind_len - 2) + ['down']
s = site.Site(leg, labels, silly_op=op1)
assert s.state_index('up') == 0
assert s.state_index('down') == leg.ind_len - 1
assert s.opnames == set(['silly_op', 'Id', 'JW'])
assert s.silly_op is op1
s.add_op('op2', op2)
assert s.op2 is op2
assert s.get_op('op2') is op2
assert s.get_op('silly_op') is op1
npt.assert_equal(
s.get_op('silly_op op2').to_ndarray(),
npc.tensordot(op1, op2, [1, 0]).to_ndarray())
leg2 = npc.LegCharge.from_drop_charge(leg, 1)
leg2 = npc.LegCharge.from_change_charge(leg2, 0, 2, 'changed')
s2 = copy.deepcopy(s)
s2.change_charge(leg2)
perm_qind, leg2s = leg2.sort()
perm_flat = leg2.perm_flat_from_perm_qind(perm_qind)
s2s = copy.deepcopy(s2)
s2s.change_charge(leg2s, perm_flat)
for site_check in [s2, s2s]:
print("site_check.leg = ", site_check.leg)
for opn in site_check.opnames:
op1 = s.get_op(opn).to_ndarray()
op2 = site_check.get_op(opn).to_ndarray()
perm = site_check.perm
npt.assert_equal(op1[np.ix_(perm, perm)], op2)
def test_FlatHermitianOperator(n=30, k=5, tol=5.e-15):
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg)
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [leg])
H_sparse = sparse.FlatHermitianOperator.from_NpcArray(H,
charge_sector=qtotal)
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init_flat = H_sparse.npc_to_flat(psi_init)
# check diagonalization
E, psi = scipy.sparse.linalg.eigsh(H_sparse,
k,
v0=psi_init_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
def test_lanczos(n=30, k=5, tol=5.e-15):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg)
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [leg])
H_Op = H # use `matvec` of the array
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
E0, psi0, N = lanczos.lanczos(H_Op, psi_init, {'verbose': 1})
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
psi0_H_psi0 = npc.inner(psi0,
npc.tensordot(H, psi0, axes=[1, 0]),
do_conj=True)
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
print("<psi0_flat|H_flat|psi0_flat> / E0_flat = ", end=' ')
print(np.inner(psi0_flat.conj(), np.dot(H_flat, psi0_flat)) / E0_flat)
ov = np.inner(psi0.to_ndarray().conj(), psi0_flat)
print("|<psi0|psi0_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
# now repeat, but keep orthogonal to original ground state
# -> should give second eigenvector psi1 in the same charge sector
for i in range(1, len(E_flat)):
E1_flat, psi1_flat = E_flat[i], psi_flat[:, i]
qtotal = npc.detect_qtotal(psi1_flat, psi0.legs)
if np.all(qtotal == psi0.qtotal):
break # found psi1 in same charge sector
else:
print(
"warning: test didn't find a second eigenvector in the same charge sector!"
)
return # just ignore the rest....
E1, psi1, N = lanczos.lanczos(H_Op,
psi_init, {'verbose': 1},
orthogonal_to=[psi0])
print("E1 = {E1:.14f} vs exact {E1_flat:.14f}".format(E1=E1,
E1_flat=E1_flat))
print("|E1-E1_flat| / |E1_flat| =", abs((E1 - E1_flat) / E1_flat))
psi1_H_psi1 = npc.inner(psi1,
npc.tensordot(H, psi1, axes=[1, 0]),
do_conj=True)
print("<psi1|H|psi1> / E1 = 1 + ", psi1_H_psi1 / E1 - 1.)
assert (abs(psi1_H_psi1 / E1 - 1.) < tol)
print("<psi1_flat|H_flat|psi1_flat> / E1_flat = ", end=' ')
print(np.inner(psi1_flat.conj(), np.dot(H_flat, psi1_flat)) / E1_flat)
ov = np.inner(psi1.to_ndarray().conj(), psi1_flat)
print("|<psi1|psi1_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
# and finnally check also orthogonality to psi0
ov = npc.inner(psi0, psi1, do_conj=True)
print("|<psi0|psi1>| =", abs(ov))
assert (abs(ov) < tol**0.5)
def test_eig():
size = 10
max_nulp = 10 * size**3
ci = chinfo3
l = gen_random_legcharge(ci, size)
A = npc.Array.from_func(np.random.random, [l, l.conj()],
qtotal=None,
shape_kw='size')
print("hermitian A")
A += A.conj().itranspose()
Aflat = A.to_ndarray()
W, V = npc.eigh(A, sort='m>')
V.test_sanity()
V_W = V.scale_axis(W, axis=-1)
recalc = npc.tensordot(V_W, V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Aflat, recalc.to_ndarray(), max_nulp)
Wflat, Vflat = np.linalg.eigh(Aflat)
npt.assert_array_almost_equal_nulp(np.sort(W), Wflat, max_nulp)
W2 = npc.eigvalsh(A, sort='m>')
npt.assert_array_almost_equal_nulp(W, W2, max_nulp)
print("check complex B")
B = 1.j * npc.Array.from_func(np.random.random, [l, l.conj()],
shape_kw='size')
B += B.conj().itranspose()
B = A + B
Bflat = B.to_ndarray()
W, V = npc.eigh(B, sort='m>')
V.test_sanity()
recalc = npc.tensordot(V.scale_axis(W, axis=-1), V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Bflat, recalc.to_ndarray(), max_nulp)
Wflat, Vflat = np.linalg.eigh(Bflat)
npt.assert_array_almost_equal_nulp(np.sort(W), Wflat, max_nulp)
print("calculate without 'hermitian' knownledge")
W, V = npc.eig(B, sort='m>')
assert (np.max(np.abs(W.imag)) < EPS * max_nulp)
npt.assert_array_almost_equal_nulp(np.sort(W.real), Wflat, max_nulp)
print("sparse speigs")
qi = 1
ch_sect = B.legs[0].get_charge(qi)
k = min(3, B.legs[0].slices[qi + 1] - B.legs[0].slices[qi])
Wsp, Vsp = npc.speigs(B, ch_sect, k=k, which='LM')
for W_i, V_i in zip(Wsp, Vsp):
V_i.test_sanity()
diff = npc.tensordot(B, V_i, axes=1) - V_i * W_i
assert (npc.norm(diff, np.inf) < EPS * max_nulp)
print("for trivial charges")
A = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()],
shape_kw='size')
A = A + A.conj().itranspose()
Aflat = A.to_ndarray()
W, V = npc.eigh(A)
recalc = npc.tensordot(V.scale_axis(W, axis=-1), V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Aflat, recalc.to_ndarray(),
10 * A.shape[0]**3)
def test_expm(size=10):
ci = chinfo3
l = gen_random_legcharge(ci, size)
A = npc.Array.from_func(np.random.random, [l, l.conj()], qtotal=None, shape_kw='size')
A_flat = A.to_ndarray()
exp_A = npc.expm(A)
exp_A.test_sanity()
from scipy.linalg import expm
npt.assert_array_almost_equal_nulp(expm(A_flat), exp_A.to_ndarray(), size * size)
def test_lattice():
chinfo = npc.ChargeInfo([1, 3])
leg = gen_random_legcharge(chinfo, 8)
leg2 = gen_random_legcharge(chinfo, 2)
op1 = npc.Array.from_func(np.random.random, [leg, leg.conj()],
shape_kw='size')
op2 = npc.Array.from_func(np.random.random, [leg2, leg2.conj()],
shape_kw='size')
site1 = lattice.Site(leg, [('up', 0), ('down', -1)], op1=op1)
site2 = lattice.Site(leg2, [('down', 0), ('up', -1)], op2=op2)
for order in ['default', 'Fstyle', 'snake', 'snakeFstyle']:
print("order =", order)
Ls = [5, 2]
basis = [[1., 1.], [0., 1.]]
pos = [[0.1, 0.], [0.2, 0.]]
lat = lattice.Lattice(Ls, [site1, site2],
order=order,
basis=basis,
positions=pos)
nst.eq_(lat.dim, len(Ls))
nst.eq_(lat.N_sites, np.prod(Ls) * 2)
for i in range(lat.N_sites):
nst.eq_(lat.lat2mps_idx(lat.mps2lat_idx(i)), i)
idx = (4, 1, 0)
nst.eq_(lat.mps2lat_idx(lat.lat2mps_idx(idx)), idx)
npt.assert_equal([4.1, 5.], lat.position(idx))
# test lat.mps2lat_values
A = np.random.random([lat.N_sites, 2, lat.N_sites])
print(A.shape)
Ares = lat.mps2lat_values(A, axes=[-1, 0])
for i in range(lat.N_sites):
idx_i = lat.mps2lat_idx(i)
for j in range(lat.N_sites):
idx_j = lat.mps2lat_idx(j)
for k in range(2):
idx = idx_i + (k, ) + idx_j
nst.eq_(Ares[idx], A[i, k, j])
# and again for fixed `u` within the unit cell
for u in range(len(lat.unit_cell)):
A_u = A[np.ix_(lat.mps_idx_fix_u(u), np.arange(2),
lat.mps_idx_fix_u(u))]
A_u_res = lat.mps2lat_values(A_u, axes=[-1, 0], u=u)
npt.assert_equal(A_u_res, Ares[:, :, u, :, :, :, u])
def test_trace():
chinfo = chinfo3
legs = [gen_random_legcharge(chinfo, s) for s in (7, 8, 9)]
legs.append(legs[1].conj())
A = npc.Array.from_func(np.random.random, legs, qtotal=[1], shape_kw='size')
Aflat = A.to_ndarray()
Atr = npc.trace(A, leg1=1, leg2=-1)
Atr.test_sanity()
Aflattr = np.trace(Aflat, axis1=1, axis2=-1)
npt.assert_array_almost_equal_nulp(Atr.to_ndarray(), Aflattr, A.shape[1])
def test_gramschmidt(n=30, k=5, tol=1.e-15):
leg = gen_random_legcharge(ch, n)
vecs_old = [
npc.Array.from_func(np.random.random, [leg], shape_kw='size')
for i in range(k)
]
vecs_new, _ = lanczos.gram_schmidt(vecs_old, rcond=0., verbose=1)
assert all([v == w for v, w in zip(vecs_new, vecs_old)])
vecs_new, _ = lanczos.gram_schmidt(vecs_old, rcond=tol, verbose=1)
vecs = [v.to_ndarray() for v in vecs_new]
ovs = np.zeros((k, k))
for i, v in enumerate(vecs):
for j, w in enumerate(vecs):
ovs[i, j] = np.inner(v.conj(), w)
print(ovs)
assert (np.linalg.norm(ovs - np.eye(k)) < 2 * n * k * k * tol)
def test_arnoldi(n, which):
tol = 5.e-14 if n <= 20 else 1.e-10
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
# if looking for small/large real part, ensure hermitian H
func = rmat.GUE if which[-1] == 'R' else rmat.standard_normal_complex
H = npc.Array.from_func_square(func, leg)
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eig(H_flat)
if which == 'LM':
i = np.argmax(np.abs(E_flat))
elif which == 'LR':
i = np.argmax(np.real(E_flat))
elif which == 'SR':
i = np.argmin(np.real(E_flat))
E0_flat, psi0_flat = E_flat[i], psi_flat[:, i]
qtotal = npc.detect_qtotal(psi0_flat, [leg])
H_Op = H # use `matvec` of the array
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
eng = lanczos.Arnoldi(H_Op, psi_init, {
'which': which,
'num_ev': 1,
'N_max': 20
})
(E0, ), (psi0, ), N = eng.run()
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert abs((E0 - E0_flat) / E0_flat) < tol
psi0_H_psi0 = npc.inner(psi0,
npc.tensordot(H, psi0, axes=[1, 0]),
'range',
do_conj=True)
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
print("<psi0_flat|H_flat|psi0_flat> / E0_flat = ", end=' ')
print(np.inner(psi0_flat.conj(), np.dot(H_flat, psi0_flat)) / E0_flat)
ov = np.inner(psi0.to_ndarray().conj(), psi0_flat)
print("|<psi0|psi0_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
def test_lanczos_evolve(n, N_cache, tol=5.e-15):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {
'verbose': 1,
'N_cache': N_cache
})
for delta in [-0.1j, 0.1j, 1.j]: #, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
psi_final, N = lanc.run(delta)
ov = np.inner(psi_final.to_ndarray().conj(), psi_final_flat)
ov /= np.linalg.norm(psi_final_flat)
print("<psi1|psi1_flat>/norm=", ov)
assert (abs(1. - abs(ov)) < tol)
def test_lanczos_evolve(n, N_cache, tol=5.e-14):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
#psi_init /= npc.norm(psi_init) # not necessary
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {'N_cache': N_cache})
for delta in [-0.1j, 0.1j, 1.j, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
norm = np.linalg.norm(psi_final_flat)
psi_final, N = lanc.run(delta, normalize=False)
diff = np.linalg.norm(psi_final.to_ndarray() - psi_final_flat)
print("norm(|psi_final> - |psi_final_flat>)/norm = ",
diff / norm) # should be 1.
assert diff / norm < tol
psi_final2, N = lanc.run(delta, normalize=True)
assert npc.norm(psi_final / norm - psi_final2) < tol
def test_FlatHermitianOperator(n=30, k=5, tol=1.e-14):
leg = gen_random_legcharge(ch, n // 2)
leg2 = gen_random_legcharge(ch, 2)
pipe = npc.LegPipe([leg, leg2], qconj=+1)
H = npc.Array.from_func_square(rmat.GUE, pipe)
H.iset_leg_labels(["(a.b)", "(a*.b*)"])
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [pipe])
H_sparse = sparse.FlatHermitianOperator.from_NpcArray(H,
charge_sector=qtotal)
psi_init = npc.Array.from_func(np.random.random, [pipe], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init.iset_leg_labels(["(a.b)"])
psi_init_flat = H_sparse.npc_to_flat(psi_init)
# check diagonalization
E, psi = scipy.sparse.linalg.eigsh(H_sparse,
k,
v0=psi_init_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
# split H to check `FlatHermitianOperator.from_guess_with_pipe`.
print("=========")
print("split legs and define separate matvec")
assert psi_init.legs[0] is pipe
psi_init_split = psi_init.split_legs([0])
H_split = H.split_legs()
def H_split_matvec(vec):
vec = npc.tensordot(H_split, vec, [["a*", "b*"], ["a", "b"]])
# TODO as additional challenge, transpose the resulting vector
return vec
H_sparse_split, psi_init_split_flat = sparse.FlatLinearOperator.from_guess_with_pipe(
H_split_matvec, psi_init_split, dtype=H_split.dtype)
# diagonalize
E, psi = scipy.sparse.linalg.eigsh(H_sparse_split,
k,
v0=psi_init_split_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
def test_lanczos_gs(n, N_cache, tol=5.e-14):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg)
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [leg])
H_Op = H # use `matvec` of the array
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
E0, psi0, N = lanczos.lanczos(H_Op, psi_init, {
'verbose': 1,
'N_cache': N_cache
})
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
psi0_H_psi0 = npc.inner(psi0,
npc.tensordot(H, psi0, axes=[1, 0]),
'range',
do_conj=True)
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
print("<psi0_flat|H_flat|psi0_flat> / E0_flat = ", end=' ')
print(np.inner(psi0_flat.conj(), np.dot(H_flat, psi0_flat)) / E0_flat)
ov = np.inner(psi0.to_ndarray().conj(), psi0_flat)
print("|<psi0|psi0_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
print("version with arpack")
E0a, psi0a = lanczos.lanczos_arpack(H_Op, psi_init, {'verbose': 1})
print("E0a = {E0a:.14f} vs exact {E0_flat:.14f}".format(E0a=E0a,
E0_flat=E0_flat))
print("|E0a-E0_flat| / |E0_flat| =", abs((E0a - E0_flat) / E0_flat))
psi0a_H_psi0a = npc.inner(psi0a,
npc.tensordot(H, psi0a, axes=[1, 0]),
'range',
do_conj=True)
print("<psi0a|H|psi0a> / E0a = 1. + ", psi0a_H_psi0a / E0a - 1.)
assert (abs(psi0a_H_psi0a / E0a - 1.) < tol)
ov = np.inner(psi0a.to_ndarray().conj(), psi0_flat)
print("|<psi0a|psi0_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
# now repeat, but keep orthogonal to original ground state
orthogonal_to = [psi0]
# -> should give second eigenvector psi1 in the same charge sector
for i in range(1, len(E_flat)):
E1_flat, psi1_flat = E_flat[i], psi_flat[:, i]
qtotal = npc.detect_qtotal(psi1_flat, psi0.legs, cutoff=1.e-10)
if np.any(qtotal != psi0.qtotal):
continue # not in same charge sector
print("--- excited state #", len(orthogonal_to))
ortho_to = [psi.copy()
for psi in orthogonal_to] # (gets modified inplace)
lanczos_params = {'verbose': 1, 'reortho': True}
if E1_flat > -0.01:
lanczos_params['E_shift'] = -2. * E1_flat - 0.2
E1, psi1, N = lanczos.lanczos(
sparse.OrthogonalNpcLinearOperator(H_Op, ortho_to), psi_init,
lanczos_params)
print("E1 = {E1:.14f} vs exact {E1_flat:.14f}".format(E1=E1,
E1_flat=E1_flat))
print("|E1-E1_flat| / |E1_flat| =", abs((E1 - E1_flat) / E1_flat))
psi1_H_psi1 = npc.inner(psi1,
npc.tensordot(H, psi1, axes=[1, 0]),
'range',
do_conj=True)
print("<psi1|H|psi1> / E1 = 1 + ", psi1_H_psi1 / E1 - 1.)
assert (abs(psi1_H_psi1 / E1 - 1.) < tol)
print("<psi1_flat|H_flat|psi1_flat> / E1_flat = ", end='')
print(np.inner(psi1_flat.conj(), np.dot(H_flat, psi1_flat)) / E1_flat)
ov = np.inner(psi1.to_ndarray().conj(), psi1_flat)
print("|<psi1|psi1_flat>|=", abs(ov))
assert (abs(1. - abs(ov)) < tol)
# and finnally check also orthogonality to previous states
for psi_prev in orthogonal_to:
ov = npc.inner(psi_prev, psi1, 'range', do_conj=True)
assert (abs(ov) < tol)
orthogonal_to.append(psi1)
if len(orthogonal_to) == 1:
print(
"warning: test didn't find a second eigenvector in the same charge sector!"
)
