def facepole_goniometricangles(facepole, unitcell):
"""
Return the goniometric angles (:math:`\\phi` and :math:`\\rho`)
for a face pole of a given unit cell.
:type facepole: :class:`vectors.Vector3D`
:type unitcell: :class:`unitcell.UnitCell`
:return: (:math:`\\phi`, :math:`\\rho`)
:rtype: :class:`tuple`
**References**
Example 2.20 from Mathematical Crystallography
"""
b = matrices.inverse(matrices.transpose(unitcell.cartesianmatrix))
# Change basis of face pole (reciprocal basis) into the cartesian basis
s_c = b * facepole
# Normalize r_c to have a unit length
s_c.normalize()
# Find phi and rho
rho = acos(s_c[2])
phi = atan2(s_c[0], s_c[1])
return phi, rho
def testcartesianmatrix(self):
alpha = 93.11 / 180.0 * pi
beta = 115.91 / 180.0 * pi
gamma = 91.26 / 180.0 * pi
L = unitcell.create_triclinic_unitcell(8.173, 12.869, 14.165, alpha,
beta, gamma)
cartesianmatrix = L.cartesianmatrix
expected_cartesianmatrix = matrices.Matrix3D(
[7.3513, -0.65437, 0.0], [0.0, 12.8333, 0.0],
[-3.5716, -0.69886, 14.165])
self.assertTrue(
matrices.almostequal(cartesianmatrix, expected_cartesianmatrix, 2))
# Identity G = A^T A
g = matrices.transpose(cartesianmatrix) * cartesianmatrix
self.assertTrue(matrices.almostequal(g, L.metricalmatrix, 4))
def testcartesianmatrix(self):
alpha = 93.11 / 180.0 * pi
beta = 115.91 / 180.0 * pi
gamma = 91.26 / 180.0 * pi
L = unitcell.create_triclinic_unitcell(8.173, 12.869, 14.165,
alpha, beta, gamma)
cartesianmatrix = L.cartesianmatrix
expected_cartesianmatrix = matrices.Matrix3D([7.3513, -0.65437, 0.0],
[0.0, 12.8333, 0.0],
[-3.5716, -0.69886, 14.165])
self.assertTrue(matrices.almostequal(cartesianmatrix,
expected_cartesianmatrix, 2))
# Identity G = A^T A
g = matrices.transpose(cartesianmatrix) * cartesianmatrix
self.assertTrue(matrices.almostequal(g, L.metricalmatrix, 4))
def interplanarangle(plane1, plane2, unitcell):
"""
Return the interplanar angle between *plane1* and *plane2* of a unit cell.
:type plane1: :class:`plane.Plane`
:type plane2: :class:`plane.Plane`
:arg unitcell: unit cell of *plane1* and *plane2*
:type unitcell: :class:`unitcell.UnitCell`
:return: angle between *plane1* and *plane2* in radians
:rtype: :class:`float`
"""
b = matrices.inverse(matrices.transpose(unitcell.cartesianmatrix))
plane1_c = b * plane1
plane2_c = b * plane2
return vectors.angle(plane1_c, plane2_c)
def testtranspose(self):
expected_m1_transpose = matrices.Matrix3D(1, 0, 5, 2, 1, 6, 3, 4, 0)
m1_transpose = matrices.transpose(self.m1)
self.assertEqual(expected_m1_transpose, m1_transpose)
def testtranspose(self):
m1 = copy.deepcopy(self.m1)
m1.transpose()
self.assertEqual(m1, matrices.transpose(self.m1))
def testtranspose(self):
expected_m1_transpose = matrices.Matrix3D(1, 0, 5, 2, 1, 6, 3, 4, 0)
m1_transpose = matrices.transpose(self.m1)
self.assertEqual(expected_m1_transpose, m1_transpose)
def testtranspose(self):
m1 = copy.deepcopy(self.m1)
m1.transpose()
self.assertEqual(m1, matrices.transpose(self.m1))