def act(self, element, a, b=None):
shifted = lambda site, delta: site.family(*ta.add(site.tag, delta))
delta = (self.period * element[0], ) + (len(a.tag) - 1) * (0, )
if b is None:
return shifted(a, delta)
else:
return shifted(a, delta), shifted(b, delta)
def act(self, element, a, b=None):
shifted = lambda site, delta: site.family(*ta.add(site.tag, delta))
delta = (self.period * element[0],) + (len(a.tag) - 1) * (0,)
if b is None:
return shifted(a, delta)
else:
return shifted(a, delta), shifted(b, delta)
def test_translational_symmetry():
ts = lattice.TranslationalSymmetry
f2 = lattice.general(np.identity(2), norbs=1)
f3 = lattice.general(np.identity(3), norbs=1)
shifted = lambda site, delta: site.family(*ta.add(site.tag, delta))
raises(ValueError, ts, (0, 0, 4), (0, 5, 0), (0, 0, 2))
sym = ts((3.3, 0))
raises(ValueError, sym.add_site_family, f2)
# Test lattices with dimension smaller than dimension of space.
f2in3 = lattice.general([[4, 4, 0], [4, -4, 0]], norbs=1)
sym = ts((8, 0, 0))
sym.add_site_family(f2in3)
sym = ts((8, 0, 1))
raises(ValueError, sym.add_site_family, f2in3)
# Test automatic fill-in of transverse vectors.
sym = ts((1, 2))
sym.add_site_family(f2)
assert sym.site_family_data[f2][2] != 0
sym = ts((1, 0, 2), (3, 0, 2))
sym.add_site_family(f3)
assert sym.site_family_data[f3][2] != 0
transl_vecs = np.array([[10, 0], [7, 7]], dtype=int)
sym = ts(*transl_vecs)
assert sym.num_directions == 2
sym2 = ts(*transl_vecs[:1, :])
sym2.add_site_family(f2, transl_vecs[1:, :])
for site in [f2(0, 0), f2(4, 0), f2(2, 1), f2(5, 5), f2(15, 6)]:
assert sym.in_fd(site)
assert sym2.in_fd(site)
assert sym.which(site) == (0, 0)
assert sym2.which(site) == (0, )
for v in [(1, 0), (0, 1), (-1, 0), (0, -1), (5, 10), (-111, 573)]:
site2 = shifted(site, np.dot(v, transl_vecs))
assert not sym.in_fd(site2)
assert (v[0] != 0) != sym2.in_fd(site2)
assert sym.to_fd(site2) == site
assert (v[1] == 0) == (sym2.to_fd(site2) == site)
assert sym.which(site2) == v
assert sym2.which(site2) == v[:1]
for hop in [(0, 0), (100, 0), (0, 5), (-2134, 3213)]:
assert (sym.to_fd(site2,
shifted(site2,
hop)) == (site, shifted(site, hop)))
# Test act for hoppings belonging to different lattices.
f2p = lattice.general(2 * np.identity(2), norbs=1)
sym = ts(*(2 * np.identity(2)))
assert sym.act((1, 1), f2(0, 0), f2p(0, 0)) == (f2(2, 2), f2p(1, 1))
assert sym.act((1, 1), f2p(0, 0), f2(0, 0)) == (f2p(1, 1), f2(2, 2))
# Test add_site_family on random lattices and symmetries by ensuring that
# it's possible to add site groups that are compatible with a randomly
# generated symmetry with proper vectors.
rng = ensure_rng(30)
vec = rng.randn(3, 5)
lat = lattice.general(vec, norbs=1)
total = 0
for k in range(1, 4):
for i in range(10):
sym_vec = rng.randint(-10, 10, size=(k, 3))
if np.linalg.matrix_rank(sym_vec) < k:
continue
total += 1
sym_vec = np.dot(sym_vec, vec)
sym = ts(*sym_vec)
sym.add_site_family(lat)
assert total > 20
def test_translational_symmetry():
ts = lattice.TranslationalSymmetry
f2 = lattice.general(np.identity(2))
f3 = lattice.general(np.identity(3))
shifted = lambda site, delta: site.family(*ta.add(site.tag, delta))
assert_raises(ValueError, ts, (0, 0, 4), (0, 5, 0), (0, 0, 2))
sym = ts((3.3, 0))
assert_raises(ValueError, sym.add_site_family, f2)
# Test lattices with dimension smaller than dimension of space.
f2in3 = lattice.general([[4, 4, 0], [4, -4, 0]])
sym = ts((8, 0, 0))
sym.add_site_family(f2in3)
sym = ts((8, 0, 1))
assert_raises(ValueError, sym.add_site_family, f2in3)
# Test automatic fill-in of transverse vectors.
sym = ts((1, 2))
sym.add_site_family(f2)
assert_not_equal(sym.site_family_data[f2][2], 0)
sym = ts((1, 0, 2), (3, 0, 2))
sym.add_site_family(f3)
assert_not_equal(sym.site_family_data[f3][2], 0)
transl_vecs = np.array([[10, 0], [7, 7]], dtype=int)
sym = ts(*transl_vecs)
assert_equal(sym.num_directions, 2)
sym2 = ts(*transl_vecs[:1, :])
sym2.add_site_family(f2, transl_vecs[1:, :])
for site in [f2(0, 0), f2(4, 0), f2(2, 1), f2(5, 5), f2(15, 6)]:
assert sym.in_fd(site)
assert sym2.in_fd(site)
assert_equal(sym.which(site), (0, 0))
assert_equal(sym2.which(site), (0,))
for v in [(1, 0), (0, 1), (-1, 0), (0, -1), (5, 10), (-111, 573)]:
site2 = shifted(site, np.dot(v, transl_vecs))
assert not sym.in_fd(site2)
assert (v[0] != 0) != sym2.in_fd(site2)
assert_equal(sym.to_fd(site2), site)
assert (v[1] == 0) == (sym2.to_fd(site2) == site)
assert_equal(sym.which(site2), v)
assert_equal(sym2.which(site2), v[:1])
for hop in [(0, 0), (100, 0), (0, 5), (-2134, 3213)]:
assert_equal(sym.to_fd(site2, shifted(site2, hop)), (site, shifted(site, hop)))
# Test act for hoppings belonging to different lattices.
f2p = lattice.general(2 * np.identity(2))
sym = ts(*(2 * np.identity(2)))
assert sym.act((1, 1), f2(0, 0), f2p(0, 0)) == (f2(2, 2), f2p(1, 1))
assert sym.act((1, 1), f2p(0, 0), f2(0, 0)) == (f2p(1, 1), f2(2, 2))
# Test add_site_family on random lattices and symmetries by ensuring that
# it's possible to add site groups that are compatible with a randomly
# generated symmetry with proper vectors.
np.random.seed(30)
vec = np.random.randn(3, 5)
lat = lattice.general(vec)
total = 0
for k in range(1, 4):
for i in range(10):
sym_vec = np.random.randint(-10, 10, size=(k, 3))
if np.linalg.matrix_rank(sym_vec) < k:
continue
total += 1
sym_vec = np.dot(sym_vec, vec)
sym = ts(*sym_vec)
sym.add_site_family(lat)
assert total > 20