def test7():
v1 = Vector([1, 0, 0])
v2 = Vector([0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_true(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 0, 0], p0=[1, 1, 1])
v2 = Vector([0, 1, 0], p0=[1, 1, 1])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_true(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 0, 0], p0=[1, 0, 0])
v2 = Vector([0, 1, 0], p0=[0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_false(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 2, 3], p0=[1, 0, 0])
v2 = Vector([4, 5, 6], p0=[0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_false(np.allclose(v3.p0, v2.p0))
def test7():
v1 = Vector([1, 0, 0])
v2 = Vector([0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_true(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 0, 0], p0=[1, 1, 1])
v2 = Vector([0, 1, 0], p0=[1, 1, 1])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_true(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 0, 0], p0=[1, 0, 0])
v2 = Vector([0, 1, 0], p0=[0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_false(np.allclose(v3.p0, v2.p0))
v1 = Vector([1, 2, 3], p0=[1, 0, 0])
v2 = Vector([4, 5, 6], p0=[0, 1, 0])
v3 = vec.cross(v1, v2)
assert_is_instance(v3, Vector)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
assert_true(np.allclose(v3.p0, v1.p0))
assert_false(np.allclose(v3.p0, v2.p0))
def test5():
v1 = Vector([1.0, 0.0])
v2 = Vector([1.0, 1.0])
v3 = vec.cross(v1, v2)
assert_equal(v3, np.cross(np.asarray(v1), np.asarray(v2)))
v1 = Vector([1, 0], p0=[1, 1])
v2 = Vector([0, 1], p0=[1, 1])
v3 = vec.cross(v1, v2)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
v1 = Vector([1, 0], p0=[1, 0])
v2 = Vector([0, 1], p0=[0, 1])
v3 = vec.cross(v1, v2)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
def test5():
v1 = Vector([1.0, 0.0])
v2 = Vector([1.0, 1.0])
v3 = vec.cross(v1, v2)
assert_equal(v3, np.cross(np.asarray(v1), np.asarray(v2)))
v1 = Vector([1, 0], p0=[1, 1])
v2 = Vector([0, 1], p0=[1, 1])
v3 = vec.cross(v1, v2)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
v1 = Vector([1, 0], p0=[1, 0])
v2 = Vector([0, 1], p0=[0, 1])
v3 = vec.cross(v1, v2)
assert_true(np.allclose(v3, np.cross(np.asarray(v1), np.asarray(v2))))
def reciprocal_v3(self):
"""Reciprocal :class:`~sknano.core.math.Vector` \
:math:`\\mathbf{v}_3^{*}`.
Defined as:
.. math::
\\mathbf{v}_3^{*} =
\\frac{\\mathbf{v}_1\\times\\mathbf{v}_2}
{|\\mathbf{v}_1\\cdot(\\mathbf{v}_2\\times\\mathbf{v}_3)|}
"""
with warnings.catch_warnings():
warnings.filterwarnings('error')
try:
return vec.cross(self.v1, self.v2) / self.Vv1v2v3
except Warning:
return vec.cross(self.v1, self.v2)
def reciprocal_v3(self):
"""Reciprocal :class:`~sknano.core.math.Vector` \
:math:`\\mathbf{v}_3^{*}`.
Defined as:
.. math::
\\mathbf{v}_3^{*} =
\\frac{\\mathbf{v}_1\\times\\mathbf{v}_2}
{|\\mathbf{v}_1\\cdot(\\mathbf{v}_2\\times\\mathbf{v}_3)|}
"""
with warnings.catch_warnings():
warnings.filterwarnings('error')
try:
return vec.cross(self.v1, self.v2) / self.Vv1v2v3
except Warning:
return vec.cross(self.v1, self.v2)
def compute_POAVs(self):
"""Compute `POAV1`, `POAV2`, `POAVR`."""
super().update_attrs()
POAV_classes = {'POAV1': POAV1, 'POAV2': POAV2, 'POAVR': POAVR}
for atom in self:
# the central atom must have 3 bonds for POAV analysis.
if atom.bonds.Nbonds == 3:
for POAV_name, POAV_class in list(POAV_classes.items()):
setattr(atom, POAV_name, POAV_class(atom.bonds))
for atom in self:
# the central atom must have 3 bonds for POAV analysis.
if atom.bonds.Nbonds == 3:
for POAV_name in ('POAV1', 'POAV2', 'POAVR'):
POAV = getattr(atom, POAV_name)
sigma_pi_angles = []
pyramidalization_angles = []
misalignment_angles = []
for bond, NN in zip(atom.bonds, atom.NN):
# first compute the pyramidalization angle
sigma_pi_angle = vec.angle(POAV.Vpi, bond.vector)
if sigma_pi_angle < np.pi / 2:
sigma_pi_angle = np.pi - sigma_pi_angle
sigma_pi_angles.append(sigma_pi_angle)
pyramidalization_angles.append(sigma_pi_angle -
np.pi / 2)
# the bonded atom must have a POAV to compute the
# misalignment angles
if getattr(NN, POAV_name) is not None:
NN_POAV = getattr(NN, POAV_name)
# compute vector that is orthogonal to the plane
# defined by the bond vector and the POAV of the
# center atom.
nvec = vec.cross(bond.vector, POAV.Vpi)
# the misalignment angle is the angle between the
# nearest neighbor's POAV and the plane defined by
# the bond vector and the POAV of the center atom,
# which is pi/2 minus the angle between
# the NN POAV and the normal vector to the plane
# computed above.
misalignment_angles.append(
np.abs(np.pi / 2 -
vec.angle(NN_POAV.Vpi, nvec)))
else:
misalignment_angles.append(np.nan)
POAV.pyramidalization_angles = pyramidalization_angles
POAV.misalignment_angles = misalignment_angles
POAV.sigma_pi_angles = sigma_pi_angles
def compute_POAVs(self):
"""Compute `POAV1`, `POAV2`, `POAVR`."""
super().update_attrs()
POAV_classes = {'POAV1': POAV1, 'POAV2': POAV2, 'POAVR': POAVR}
for atom in self:
# the central atom must have 3 bonds for POAV analysis.
if atom.bonds.Nbonds == 3:
for POAV_name, POAV_class in list(POAV_classes.items()):
setattr(atom, POAV_name, POAV_class(atom.bonds))
for atom in self:
# the central atom must have 3 bonds for POAV analysis.
if atom.bonds.Nbonds == 3:
for POAV_name in ('POAV1', 'POAV2', 'POAVR'):
POAV = getattr(atom, POAV_name)
sigma_pi_angles = []
pyramidalization_angles = []
misalignment_angles = []
for bond, NN in zip(atom.bonds, atom.NN):
# first compute the pyramidalization angle
sigma_pi_angle = vec.angle(POAV.Vpi, bond.vector)
if sigma_pi_angle < np.pi / 2:
sigma_pi_angle = np.pi - sigma_pi_angle
sigma_pi_angles.append(sigma_pi_angle)
pyramidalization_angles.append(
sigma_pi_angle - np.pi / 2)
# the bonded atom must have a POAV to compute the
# misalignment angles
if getattr(NN, POAV_name) is not None:
NN_POAV = getattr(NN, POAV_name)
# compute vector that is orthogonal to the plane
# defined by the bond vector and the POAV of the
# center atom.
nvec = vec.cross(bond.vector, POAV.Vpi)
# the misalignment angle is the angle between the
# nearest neighbor's POAV and the plane defined by
# the bond vector and the POAV of the center atom,
# which is pi/2 minus the angle between
# the NN POAV and the normal vector to the plane
# computed above.
misalignment_angles.append(np.abs(
np.pi / 2 - vec.angle(NN_POAV.Vpi, nvec)))
else:
misalignment_angles.append(np.nan)
POAV.pyramidalization_angles = pyramidalization_angles
POAV.misalignment_angles = misalignment_angles
POAV.sigma_pi_angles = sigma_pi_angles
def test8():
assert_true(np.allclose(vec.cross(e1, e2), e3))
assert_equal(vec.cross(e1, e2), e3)
assert_true(np.allclose(vec.cross(e1, e3), -e2))
assert_equal(vec.cross(e1, e3), -e2)
assert_true(np.allclose(vec.cross(e2, e3), e1))
assert_equal(vec.cross(e2, e3), e1)
def test8():
assert_true(np.allclose(vec.cross(e1, e2), e3))
assert_equal(vec.cross(e1, e2), e3)
assert_true(np.allclose(vec.cross(e1, e3), -e2))
assert_equal(vec.cross(e1, e3), -e2)
assert_true(np.allclose(vec.cross(e2, e3), e1))
assert_equal(vec.cross(e2, e3), e1)