def test2():
v = Vector()
v.p0 = np.ones(3)
assert_true(np.allclose(v, -np.ones(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.zeros(3)))
v = Vector(p=[1., 1., 1.], p0=[1., 1., 1.])
assert_true(np.allclose(v, np.zeros(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v.p0 = np.zeros(3)
assert_true(np.allclose(v, np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v.x = 5.0
assert_equal(v.x, 5.0)
assert_equal(v.x, v.p.x)
v.y = -5.0
assert_equal(v.y, -5.0)
assert_equal(v.y, v.p.y)
v.z = 0.0
assert_equal(v.z, 0.0)
assert_equal(v.z, v.p.z)
v.p0 = np.array([0.5, -10.0, 2.5])
assert_equal(v.p0.x, 0.5)
assert_equal(v.p0.y, -10.0)
assert_equal(v.p0.z, 2.5)
def test1():
v = Vector()
assert_true(np.allclose(v, np.zeros(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.zeros(3)))
v = Vector([1, 1, 1])
assert_true(np.allclose(v, np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v = Vector(p=[1, 1, 1])
assert_true(np.allclose(v, np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v = Vector(p0=[1, 1, 1])
assert_true(np.allclose(v, -np.ones(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.zeros(3)))
v = Vector(p=[1, 1, 1], p0=[1, 1, 1])
assert_true(np.allclose(v, np.zeros(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.ones(3)))
def test13():
u = Vector([5, 6, 7])
assert_true(np.allclose(
u.projection(Vector([1, 0, 0])), Vector([5, 0, 0])))
assert_true(np.allclose(
u.projection(Vector([1, 1, 1])), Vector([6, 6, 6])))
def test29():
u = Vector([5, 0, 0])
v = u.copy()
u *= v
assert_equal(u, 25)
def test27():
v = Vector([5, 0, 0])
v += 5
assert_equal(v, Vector([10, 5, 5]))
v += v
assert_equal(v, Vector([20, 10, 10]))
def __init__(self, o=None, u=None, v=None, w=None):
self._o = Point()
self._u = Vector()
self._v = Vector()
self._w = Vector()
super().__init__()
if o is None:
o = [0, 0, 0]
self.o = o
if u is None:
u = [1, 0, 0]
self.u = u
if v is None:
v = [1, 1, 0]
self.v = v
if w is None:
w = [0, 1, 1]
self.w = w
self.points.append(self.o)
self.vectors.extend([self.u, self.v, self.w])
self.fmtstr = "o={o!r}, u={u!r}, v={v!r}, w={w!r}"
def test29():
u = Vector([5, 0, 0])
v = u.copy()
u *= v
assert_equal(u, 25)
def __init__(self, a=None, b=None, gamma=None,
a1=None, a2=None, cell_matrix=None,
orientation_matrix=None, offset=None):
if cell_matrix is not None:
cell_matrix = np.asarray(cell_matrix)
a1 = np.array(cell_matrix[0, :])
a2 = np.array(cell_matrix[1, :])
if a1 is not None and a2 is not None:
a1 = Vector(a1, nd=3)
a2 = Vector(a2, nd=3)
a = a1.length
b = a2.length
gamma = np.degrees(a1.angle(a2))
cell_matrix = np.matrix(np.vstack((np.asarray(a1),
np.asarray(a2),
np.asarray([0, 0, 1]))))
self._a = a
self._b = b
self._gamma = gamma
if None not in (a, b, gamma):
self._update_ortho_matrix()
super().__init__(nd=2, cell_matrix=cell_matrix,
orientation_matrix=orientation_matrix,
offset=offset)
self.fmtstr = "a={a!r}, b={b!r}, gamma={gamma!r}"
def test32():
u = Vector([5, 0, 0])
v = u.copy()
with assert_raises(TypeError):
v **= v
assert_equal(u, v)
def test18():
u = Vector([1, 2, 3])
v = Vector([1, 2, 3])
w = Vector([1, 1, 1])
assert_equals(u, v)
assert_true(u == v)
assert_not_equals(u, w)
assert_false(u == w)
def test32():
u = Vector([5, 0, 0])
v = u.copy()
with assert_raises(TypeError):
v **= v
assert_equal(u, v)
def test35():
v0 = Vector(np.arange(3) + 2)
I = np.identity(3)
v1 = Vector((v0.row_matrix * I).A.flatten(), p0=v0.p0)
v2 = Vector((I * v0.column_matrix).A.flatten(), p0=v0.p0)
assert_true(np.allclose(v0, v1))
assert_true(np.allclose(v0, v2))
def test20():
a = Vector([1, 1, 1])
b = Vector([1, 0, 0])
assert_equals(vec.scalar_projection(a, b), 1.0)
a = Vector([1, 0, 0])
b = Vector([1, 1, 1])
assert_equals(vec.scalar_projection(a, b), 1.0 / np.sqrt(3))
def generate_bundle_coords(self):
"""Generate coordinates of bundle tubes."""
self.r1 = Vector()
self.r2 = Vector()
self.bundle_coords = []
self.r1.x = self.dt + 2 * self.vdw_radius
if self.bundle_packing in ('cubic', 'ccp'):
self.r2.y = self.r1.x
else:
self.r2.x = self.r1.x * np.cos(2 * np.pi / 3)
self.r2.y = self.r1.x * np.sin(2 * np.pi / 3)
if self.bundle_packing is None:
self._bundle_packing = 'hcp'
if self.bundle_geometry == 'hexagon':
nrows = max(self.nx, self.ny, 3)
if nrows % 2 != 1:
nrows += 1
ntubes_per_end_rows = int((nrows + 1) / 2)
row = 0
ntubes_per_row = nrows
while ntubes_per_row >= ntubes_per_end_rows:
if row == 0:
for n in range(ntubes_per_row):
dr = n * self.r1
self.bundle_coords.append(dr)
else:
for nx in range(ntubes_per_row):
for ny in (-row, row):
dr = Vector()
dr.x = abs(ny * self.r2.x)
dr.y = ny * self.r2.y
dr = nx * self.r1 + dr
self.bundle_coords.append(dr)
row += 1
ntubes_per_row = nrows - row
elif self.bundle_geometry == 'rectangle':
Lx = 10 * self.Lx
for nx in range(self.nx):
for ny in range(self.ny):
dr = nx * self.r1 + ny * self.r2
while dr.x < 0:
dr.x += Lx
self.bundle_coords.append(dr)
elif self.bundle_geometry == 'square':
pass
elif self.bundle_geometry == 'triangle':
pass
else:
for nx in range(self.nx):
for ny in range(self.ny):
dr = nx * self.r1 + ny * self.r2
self.bundle_coords.append(dr)
def test25():
assert_equal(e1 * e1, e1.dot(e1))
assert_equal(e1 * e1, 1.0)
with assert_raises(ValueError):
e1.dot(Vector([1.0, 0.0]))
with assert_raises(ValueError):
Vector([1.0, 0.0]).dot(e1)
def test6():
v1 = Vector([1.0, 0.0, 0.0])
v2 = Vector([1.0, 1.0, 0.0])
c = np.dot(np.asarray(v1), np.asarray(v2))
assert_equal(c, 1.0)
c = vec.dot(v1, v2)
assert_equal(c, 1.0)
def __init__(self,
a=None,
b=None,
c=None,
alpha=None,
beta=None,
gamma=None,
a1=None,
a2=None,
a3=None,
cell_matrix=None,
orientation_matrix=None,
offset=None):
if all([
p is None
for p in (a, b, c, alpha, beta, gamma, a1, a2, a3, cell_matrix)
]):
errmsg = 'Expected lattice parameters ' + \
'`a`, `b`, `c`, `alpha`, `beta`, `gamma`\n' + \
'or lattice vectors `a1`, `a2`, `a3`\n' + \
'or a 3x3 matrix with lattice vectors for columns.'
raise ValueError(errmsg)
if cell_matrix is not None:
cell_matrix = np.asarray(cell_matrix)
a1 = np.array(cell_matrix[0, :])
a2 = np.array(cell_matrix[1, :])
a3 = np.array(cell_matrix[2, :])
if all([v is not None for v in (a1, a2, a3)]):
a1 = Vector(a1)
a2 = Vector(a2)
a3 = Vector(a3)
a = a1.length
b = a2.length
c = a3.length
alpha = np.degrees(a2.angle(a3))
beta = np.degrees(a3.angle(a1))
gamma = np.degrees(a1.angle(a2))
cell_matrix = np.matrix(
np.vstack((np.asarray(a1), np.asarray(a2), np.asarray(a3))))
self._a = a
self._b = b
self._c = c
self._alpha = alpha
self._beta = beta
self._gamma = gamma
if all([p is not None for p in (a, b, c, alpha, beta, gamma)]):
self._update_ortho_matrix()
super().__init__(nd=3,
cell_matrix=cell_matrix,
orientation_matrix=orientation_matrix,
offset=offset)
self.fmtstr = "a={a!r}, b={b!r}, c={c!r}, " + \
"alpha={alpha!r}, beta={beta!r}, gamma={gamma!r}"
def test10():
v = Vector(p0=[1, 1, 1])
assert_true(np.allclose(v, -np.ones(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.array([0, 0, 0])))
v.rotate(np.pi/2, rot_axis='z', rot_point=[1, 1, 1])
assert_is_instance(v.p0, Point)
assert_is_instance(v.p, Point)
assert_true(np.allclose(v, np.array([1, -1, -1])))
assert_true(np.allclose(v.p0, np.array([1, 1, 1])))
assert_true(np.allclose(v.p, np.array([2, 0, 0])))
def test10():
v = Vector(p0=[1, 1, 1])
assert_true(np.allclose(v, -np.ones(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.array([0, 0, 0])))
v.rotate(np.pi / 2, rot_axis='z', rot_point=[1, 1, 1])
assert_is_instance(v.p0, Point)
assert_is_instance(v.p, Point)
assert_true(np.allclose(v, np.array([1, -1, -1])))
assert_true(np.allclose(v.p0, np.array([1, 1, 1])))
assert_true(np.allclose(v.p, np.array([2, 0, 0])))
def test12():
v1 = Vector()
dr = Vector(np.ones(3))
v3 = Vector()
v3 = Vector(v1 + dr)
#v3[:] = v1 + dr
#print('v3: {}'.format(v3))
#print('v3.p: {}'.format(v3.p))
assert_true(np.allclose(v3, np.ones(3)))
assert_true(np.allclose(v3.p0, np.zeros(3)))
assert_true(np.allclose(v3.p, np.ones(3)))
def test13():
u = Vector([5, 6, 7])
assert_true(np.allclose(u.projection(Vector([1, 0, 0])), Vector([5, 0,
0])))
assert_true(np.allclose(u.projection(Vector([1, 1, 1])), Vector([6, 6,
6])))
def test2():
v = Vector()
v.p0 = np.ones(3)
assert_true(np.allclose(v, -np.ones(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.zeros(3)))
v = Vector(p=[1., 1., 1.], p0=[1., 1., 1.])
assert_true(np.allclose(v, np.zeros(3)))
assert_true(np.allclose(v.p0, np.ones(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v.p0 = np.zeros(3)
assert_true(np.allclose(v, np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v.x = 5.0
assert_equal(v.x, 5.0)
assert_equal(v.x, v.p.x)
v.y = -5.0
assert_equal(v.y, -5.0)
assert_equal(v.y, v.p.y)
v.z = 0.0
assert_equal(v.z, 0.0)
assert_equal(v.z, v.p.z)
v.p0 = np.array([0.5, -10.0, 2.5])
assert_equal(v.p0.x, 0.5)
assert_equal(v.p0.y, -10.0)
assert_equal(v.p0.z, 2.5)
def test33():
v1 = Vector([1, 0, 0])
v2 = Vector([0, 1, 0])
v3 = v1.cross(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 = v1.cross(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 = v1.cross(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 = v1.cross(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 compute_centroid(coords):
"""Compute the centroid of coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N}m_i\\mathbf{r}_i}{\\sum_{i=1}^{N}m_i}
Returns
-------
C : `~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(coords, axis=0))
C.rezero()
return C
def test22():
a = Vector([1, 1, 1])
b = Vector([1, 0, 0])
assert_equals(vec.vector_rejection(a, b), Vector([0, 1, 1]))
a = Vector([1, 0, 0])
b = Vector([1, 1, 1])
assert_equals(vec.vector_rejection(a, b), Vector([2 / 3, -1 / 3, -1 / 3]))
a = Vector([5, 6, 7])
b = Vector([1, 1, 1])
assert_equals(vec.vector_rejection(a, b), a - Vector(3 * [6]))
def test21():
a = Vector([1, 1, 1])
b = Vector([1, 0, 0])
assert_equals(vec.vector_projection(a, b), Vector([1, 0, 0]))
a = Vector([1, 0, 0])
b = Vector([1, 1, 1])
assert_equals(vec.vector_projection(a, b), Vector(1 / 3 * np.ones(3)))
a = Vector([5, 6, 7])
b = Vector([1, 1, 1])
assert_equals(vec.vector_projection(a, b), Vector(3 * [6]))
def test1():
print('generating graphene structure')
graphene = GrapheneGenerator(armchair_edge_length=5, zigzag_edge_length=5)
lattice = graphene.lattice
print('graphene.bounds:\n{}'.format(graphene.bounds))
print('graphene.centroid:\n{}'.format(graphene.centroid))
print('graphene.lattice:\n{}'.format(lattice))
print('graphene.lattice.a1:\n{}'.format(lattice.a1))
print('graphene.lattice.a2:\n{}'.format(lattice.a2))
print('graphene.lattice.a3:\n{}'.format(lattice.a3))
print('graphene.lattice.orientation_matrix:\n{}'.format(
lattice.orientation_matrix))
print('rotating graphene')
graphene.rotate(angle=-np.pi / 2, axis='x')
print('graphene.bounds:\n{}'.format(graphene.bounds))
print('graphene.centroid:\n{}'.format(graphene.centroid))
print('graphene.lattice:\n{}'.format(lattice))
print('graphene.lattice.a1:\n{}'.format(lattice.a1))
print('graphene.lattice.a2:\n{}'.format(lattice.a2))
print('graphene.lattice.a3:\n{}'.format(lattice.a3))
print('graphene.lattice.orientation_matrix:\n{}'.format(
lattice.orientation_matrix))
assert_true(np.allclose(lattice.angles, 3 * [90.0]))
lattice_region = Cuboid(pmax=lattice.lengths)
# lattice_region = Parallelepiped(u=lattice.a * xhat,
# v=lattice.b * yhat,
# w=lattice.c * zhat)
assert_equal(lattice_region.a, lattice.a)
assert_equal(lattice_region.b, lattice.b)
assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
print('\nrotating lattice_region')
lattice_region.rotate(transform_matrix=lattice.orientation_matrix)
# assert_equal(lattice_region.a, lattice.a)
# assert_equal(lattice_region.b, lattice.b)
# assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
print('\ncentering lattice_region on graphene centroid')
tvec = Vector(Point(graphene.centroid) - lattice_region.centroid)
lattice_region.translate(tvec)
# assert_equal(lattice_region.a, lattice.a)
# assert_equal(lattice_region.b, lattice.b)
# assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
bounding_box = generate_bounding_box(from_lattice=lattice,
center=graphene.centroid,
verbose=True)
print('bounding_box:\n{}'.format(bounding_box))
assert_equal(bounding_box, lattice_region)
print('lattice_region.lengths: {}, {}, {}'.format(lattice_region.a,
lattice_region.b,
lattice_region.c))
def __init__(self, *args, vx=None, vy=None, vz=None, **kwargs):
super().__init__(*args, **kwargs)
self._v = Vector([vx, vy, vz])
self.fmtstr = super().fmtstr + \
", vx={vx:.6f}, vy={vy:.6f}, vz={vz:.6f}"
def __init__(self, *args, px=None, py=None, pz=None, **kwargs):
super().__init__(*args, **kwargs)
self._p = Vector([px, py, pz])
self.fmtstr = super().fmtstr + \
", px={px:.6f}, py={py:.6f}, pz={pz:.6f}"
def __init__(self, *args, fx=None, fy=None, fz=None, **kwargs):
super().__init__(*args, **kwargs)
self._f = Vector([fx, fy, fz])
self.fmtstr = super().fmtstr + \
", fx={fx:.6f}, fy={fy:.6f}, fz={fz:.6f}"
def test2():
H = Quaternion(np.arange(4))
assert_equal(H.w, H.real)
assert_equal(H.w, 0.)
assert_is_instance(H.imag, list)
assert_is_instance(H.v, Vector)
assert_true(np.allclose(H.v, Vector(np.arange(3) + 1)))
def vector(self):
"""`Bond` :class:`~sknano.core.math.Vector`.
`Bond` :class:`~sknano.core.math.Vector` points from
:attr:`Bond.atom1` to :attr:`Bond.atom2`.
"""
return Vector(self.atom2.r - self.atom1.r, p0=self.atom1.r.p)
def __init__(self,
nlayers=1,
layer_spacing=3.14,
sulphur_layer_spacing=3.01,
**kwargs):
super().__init__(**kwargs)
self.layer_mass = None
self.Natoms = 0
self.Natoms_per_layer = 0
self.nlayers = nlayers
self.layer_spacing = layer_spacing
self.layer_shift = Vector()
self.cell = Vector()
def centroid(self):
"""Centroid of `Atoms`.
Computes the position vector of the centroid of the `Atoms`
coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N_{\\mathrm{atoms}}}
\\mathbf{r}_i}{N_{\\mathrm{atoms}}}
Returns
-------
C : :class:`~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(self.coords, axis=0))
C.rezero()
return C
def centroid(self):
"""Centroid of `Atoms`.
Computes the position vector of the centroid of the `Atoms`
coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N_{\\mathrm{atoms}}}
\\mathbf{r}_i}{N_{\\mathrm{atoms}}}
Returns
-------
C : :class:`~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(self.coords, axis=0))
C.rezero()
return C
def p(self, value):
"""Set `DipoleAtom` dipole moment :math:`\\mathbf{p}=q\\mathbf{d}`.
Parameters
----------
value : array_like
electric dipole moment vector
"""
self._p[:] = Vector(value, nd=3)
def axis(self):
""":class:`Cone` axis :class:`Vector` from \
:math:`\\boldsymbol{\\ell}=p_2 - p_1`
Returns
-------
:class:`Vector`
"""
return Vector(p0=self.p1, p=self.p2)
def test11():
v = Vector()
v += np.ones(3)
assert_true(np.allclose(v, np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, np.ones(3)))
v.p += np.ones(3)
assert_true(np.allclose(v, 2 * np.ones(3)))
assert_true(np.allclose(v.p0, np.zeros(3)))
assert_true(np.allclose(v.p, 2 * np.ones(3)))
v1 = Vector()
dr = Vector(np.ones(3))
v2 = v1 + dr
#print('v2: {}'.format(v2))
#print('v2.p: {}'.format(v2.p))
assert_true(np.allclose(v2, np.ones(3)))
assert_true(np.allclose(v2.p0, np.zeros(3)))
assert_true(np.allclose(v2.p, np.ones(3)))
def center_of_mass(self):
"""Center-of-Mass coordinates of `Atoms`.
Computes the position vector of the center-of-mass coordinates:
.. math::
\\mathbf{R}_{COM} = \\frac{1}{M}\\sum_{i=1}^{N_{\\mathrm{atoms}}}
m_i\\mathbf{r}_i
Returns
-------
com : :class:`~sknano.core.math.Vector`
The position vector of the center of mass coordinates.
"""
masses = np.asarray([self.masses])
coords = self.coords
MxR = masses.T * coords
com = Vector(np.sum(MxR, axis=0) / np.sum(masses))
com.rezero()
return com
def __init__(self, a=None, b=None, c=None,
alpha=None, beta=None, gamma=None,
a1=None, a2=None, a3=None, cell_matrix=None,
orientation_matrix=None, offset=None):
if all([p is None for p in (a, b, c, alpha, beta, gamma,
a1, a2, a3, cell_matrix)]):
errmsg = 'Expected lattice parameters ' + \
'`a`, `b`, `c`, `alpha`, `beta`, `gamma`\n' + \
'or lattice vectors `a1`, `a2`, `a3`\n' + \
'or a 3x3 matrix with lattice vectors for columns.'
raise ValueError(errmsg)
if cell_matrix is not None:
cell_matrix = np.asarray(cell_matrix)
a1 = np.array(cell_matrix[0, :])
a2 = np.array(cell_matrix[1, :])
a3 = np.array(cell_matrix[2, :])
if all([v is not None for v in (a1, a2, a3)]):
a1 = Vector(a1)
a2 = Vector(a2)
a3 = Vector(a3)
a = a1.length
b = a2.length
c = a3.length
alpha = np.degrees(a2.angle(a3))
beta = np.degrees(a3.angle(a1))
gamma = np.degrees(a1.angle(a2))
cell_matrix = np.matrix(np.vstack((np.asarray(a1),
np.asarray(a2),
np.asarray(a3))))
self._a = a
self._b = b
self._c = c
self._alpha = alpha
self._beta = beta
self._gamma = gamma
if all([p is not None for p in (a, b, c, alpha, beta, gamma)]):
self._update_ortho_matrix()
super().__init__(nd=3, cell_matrix=cell_matrix,
orientation_matrix=orientation_matrix,
offset=offset)
self.fmtstr = "a={a!r}, b={b!r}, c={c!r}, " + \
"alpha={alpha!r}, beta={beta!r}, gamma={gamma!r}"
def a1(self):
"""2D lattice vector :math:`\\mathbf{a}_1=\\mathbf{a}`."""
b2 = Vector()
b2[:2] = self.b2
return b2.cross(zhat) / self.cell_area
def test_translation_matrix():
for l in ([1, 1], [1, 1, 1]):
v = Vector(l)
assert_equal(v, Vector(translation_matrix(v.tolist())[:v.nd, v.nd]))
assert_equal(v, translation_from_matrix(translation_matrix(v)))
def test36():
v0 = Vector(np.arange(10))
assert_equal(v0.argmax(), len(v0)-1)
def test19():
u = Vector([10, 10, 17])
v = Vector([10, 10, 17])
assert_true(u == v)
v.normalize()
assert_true(np.allclose(u.unit_vector, v))
def b1(self):
"""2D reciprocal lattice vector :math:`\\mathbf{b}_1=\\mathbf{a}^{*}`.
"""
a2 = Vector()
a2[:2] = self.a2
return a2.cross(zhat)[:2] / self.cell_area