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_XXZChain():
pars = dict(L=4, Jxx=1., Jz=1., hz=0., bc_MPS='finite')
chain = XXZChain(pars)
chain.test_sanity()
for Hb in chain.H_bond[1:]: # check bond eigenvalues
Hb2 = Hb.combine_legs([['p0', 'p1'], ['p0*', 'p1*']], qconj=[+1, -1])
print(Hb2.to_ndarray())
W = npc.eigvalsh(Hb2)
npt.assert_array_almost_equal_nulp(np.sort(W),
np.sort([-0.75, 0.25, 0.25, 0.25]),
16**3)
# now check with non-trivial onsite terms
pars['hz'] = 0.2
print("hz =", pars['hz'])
chain = XXZChain(pars)
chain.test_sanity()
Hb = chain.H_bond[
2] # the only central bonds: boundaries have different hz.
Hb2 = Hb.combine_legs([['p0', 'p1'], ['p0*', 'p1*']], qconj=[+1, -1])
print(Hb2.to_ndarray())
W = npc.eigvalsh(Hb2)
print(W)
npt.assert_array_almost_equal_nulp(
np.sort(W),
np.sort([
-0.75, 0.25 - 2 * 0.5 * 0.5 * pars['hz'], 0.25,
0.25 + 2. * 0.5 * 0.5 * pars['hz']
]), 16**3)
pars['bc_MPS'] = 'infinite'
for L in [2, 3, 4, 5, 6]:
print("L =", L)
pars['L'] = L
chain = XXZChain(pars)
pprint.pprint(chain.coupling_terms)
assert len(chain.H_bond) == L
Hb0 = chain.H_bond[0]
for Hb in chain.H_bond[1:]:
assert (npc.norm(Hb - Hb0, np.inf) == 0.) # exactly equal
pars['Jxx'] = 0.
chain = XXZChain(pars)
chain.test_sanity()
