def test_extended_huckel_hamiltonian_if_s_orthogonal():
S = np.eye(2)
m = Molecule([Atom(C, 0, 0, 0), Atom(N, 0, 0, 0)])
h = ExtendedHuckelHamiltonian(S=S, molecule=m).matrix()
assert is_diagonal(h)
assert h[0, 0] == -C.voie
assert h[1, 1] == -N.voie
def test_eigenbasis_transformation_non_orthogonal():
basis = [HarmonicOscillator(n=i, center=0.25) for i in range(2)] + [
HarmonicOscillator(n=i, center=-0.25) for i in range(2)
]
S = pairwise_array_from_func(basis, Overlap())
H = pairwise_array_from_func(basis, Hamiltonian(Harmonic(center=0.0)))
eigb = EigenBasis.from_basis(basis, H, S)
xform_H = eigb.transformed(H)
assert is_diagonal(xform_H)
assert np.allclose(np.diag(xform_H), eigb.energies, atol=conf.small_number)
def test_eigenbasis_transformation_orthogonal():
basis = [lambda _: 2 for _ in range(2)]
d = 0.1
e = 1.0
H = np.array([[e, d], [d, e]])
S = np.eye(2)
eigb = EigenBasis.from_basis(basis, H, S)
xform_H = eigb.transformed(H)
assert is_diagonal(xform_H)
assert np.allclose(np.diag(xform_H), eigb.energies, atol=conf.small_number)
def group_objects(self, laparams, objs):
obj0 = None
line = None
for obj1 in objs:
if obj0 is not None:
# halign: obj0 and obj1 is horizontally aligned.
#
# +------+ - - -
# | obj0 | - - +------+ -
# | | | obj1 | | (line_overlap)
# +------+ - - | | -
# - - - +------+
#
# |<--->|
# (char_margin)
halign = (obj0.neighbor_compatible_reason(obj1)
and is_diagonal(obj0.matrix)
and is_diagonal(obj1.matrix)
and obj0.is_voverlap(obj1)
and (min(obj0.height, obj1.height) *
laparams.line_overlap < obj0.voverlap(obj1)) and
(obj0.hdistance(obj1) <
max(obj0.width, obj1.width) * laparams.char_margin))
# valign: obj0 and obj1 is vertically aligned.
#
# +------+
# | obj0 |
# | |
# +------+ - - -
# | | | (char_margin)
# +------+ - -
# | obj1 |
# | |
# +------+
#
# |<-->|
# (line_overlap)
valign = (
laparams.detect_vertical
and obj0.neighbor_compatible_reason(obj1)
and not is_diagonal(obj0.matrix)
and not is_diagonal(obj1.matrix) and obj0.is_hoverlap(obj1)
and (min(obj0.width, obj1.width) * laparams.line_overlap <
obj0.hoverlap(obj1))
and (obj0.vdistance(obj1) <
max(obj0.height, obj1.height) * laparams.char_margin))
if ((halign and isinstance(line, LTTextLineHorizontal))
or (valign and isinstance(line, LTTextLineVertical))):
line.add(obj1)
elif line is not None:
yield line
line = None
else:
if valign and not halign:
line = LTTextLineVertical(laparams.word_margin)
line.add(obj0)
line.add(obj1)
elif halign and not valign:
line = LTTextLineHorizontal(laparams.word_margin)
line.add(obj0)
line.add(obj1)
else:
line = LTTextLineHorizontal(laparams.word_margin)
line.add(obj0)
yield line
line = None
obj0 = obj1
if line is None:
line = LTTextLineHorizontal(laparams.word_margin)
line.add(obj0)
yield line
return
def test_ho_eigen_basis_hamiltonian(ho_eigen_basis):
H = op.Hamiltonian(ho_eigen_basis[0].potential).matrix(ho_eigen_basis)
energies = np.asarray([b.energy for b in ho_eigen_basis])
assert np.allclose(np.diag(H), energies)
assert is_diagonal(H)
def test_ho_eigen_basis_overlap_is_diagonal(ho_eigen_basis):
S = op.Overlap().matrix(ho_eigen_basis)
assert is_diagonal(S)
assert is_identity(S)