def getSymMatricesXmipp(symmetryGroup):
""" Return symmetry matrices related to a point group"""
symmetryGroupLetter = symmetryGroup[0].upper()
if symmetryGroupLetter == 'I':
symmetryGroupNum = int(symmetryGroup[1])
if symmetryGroupNum == 1:
return getSymmetryMatrices(SYM_I222)
if symmetryGroupNum == 2:
return getSymmetryMatrices(SYM_I222r)
if symmetryGroupNum == 3:
return getSymmetryMatrices(SYM_In25)
if symmetryGroupNum == 4:
return getSymmetryMatrices(SYM_In25r)
if symmetryGroupLetter == 'C':
symmetryGroupNum = int(symmetryGroup[1])
return getSymmetryMatrices(SYM_CYCLIC, n=symmetryGroupNum)
if symmetryGroupLetter == 'D':
symmetryGroupNum = int(symmetryGroup[1])
return getSymmetryMatrices(SYM_DIHEDRAL, n=symmetryGroupNum)
if symmetryGroupLetter == 'T':
return getSymmetryMatrices(SYM_TETRAHEDRAL, n=symmetryGroupNum)
if symmetryGroupLetter == 'O':
return getSymmetryMatrices(SYM_TETRAHEDRAL, n=SYM_OCTAHEDRAL)
def testSymmetryCyclic(self):
matrices = getSymmetryMatrices(SYM_CYCLIC, n=3)
m1 = matrices[0]
m2 = matrices[1]
m3 = matrices[2]
#m1 is identity
r = identity_matrix()
self.assertArrayAlmostEqual(r, m1)
#m2 rotated 120 degrees
c = -0.5
s = 0.86602540378
r = [[c, -s, 0, 0], [s, c, 0, 0], [0, 0, 1.0, 0], [0, 0, 0.0, 1.0]]
self.assertArrayAlmostEqual(r, m2)
#m3 rotated -120 degrees
c = -0.5
s = -0.86602540378
r = [[c, -s, 0, 0], [s, c, 0, 0], [0, 0, 1.0, 0], [0, 0, 0.0, 1.0]]
self.assertArrayAlmostEqual(r, m3)
def testSymmetryDihedral(self):
matrices = getSymmetryMatrices(SYM_DIHEDRAL, n=3)
# skip m1, m2 and m3 since there are identical to CYCLIC
m4 = matrices[3]
m5 = matrices[4]
m6 = matrices[5]
#m4 mirrored
r = identity_matrix()
r[1][1] *= -1.
r[2][2] *= -1.
self.assertArrayAlmostEqual(r, m4)
#m5 rotated 120 degrees and mirrored
c = -0.5
s = 0.86602540378
r = [[c, -s, 0, 0], [-s, -c, 0, 0], [0, 0, -1.0, 0], [0, 0, 0.0, 1.0]]
self.assertArrayAlmostEqual(r, m5)
# m6 rotated -120 degrees and mirrored
c = -0.5
s = -0.86602540378
r = [[c, -s, 0, 0], [-s, -c, 0, 0], [0, 0, -1.0, 0], [0, 0, 0.0, 1.0]]
self.assertArrayAlmostEqual(r, m6)
def testSymmetryOctahedral(self):
matrices = getSymmetryMatrices(SYM_OCTAHEDRAL)
refMatrices = [
[
[1., 0., 0., 0.], # 0
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]
],
[
[0., -1., 0., 0.], # 1
[1., 0., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]
],
[
[-1., 0., 0., 0.], # 2
[0., -1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]
],
[
[0., 1., 0., 0.], # 3
[-1., 0., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]
],
[
[1., 0., 0., 0.], # 4
[0., 0., -1., 0.],
[0., 1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., -1., 0., 0.], # 5
[0., 0., -1., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[-1., 0., 0., 0.], # 6
[0., 0., -1., 0.],
[0., -1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 1., 0., 0.], # 7
[0., 0., -1., 0.],
[-1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[1., 0., 0., 0.], # 8
[0., -1., 0., 0.],
[0., 0., -1., 0.],
[0., 0., 0., 1.]
],
[
[0., -1., 0., 0.], # 9
[-1., 0., 0., 0.],
[0., 0., -1., 0.],
[0., 0., 0., 1.]
],
[
[-1., 0., 0., 0.], # 10
[0., 1., 0., 0.],
[0., 0., -1., 0.],
[0., 0., 0., 1.]
],
[
[0., 1., 0., 0.], # 11
[1., 0., 0., 0.],
[0., 0., -1., 0.],
[0., 0., 0., 1.]
],
[
[1., 0., 0., 0.], # 12
[0., 0., 1., 0.],
[0., -1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., -1., 0., 0.], # 13
[0., 0., 1., 0.],
[-1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[-1., 0., 0., 0.], # 14
[0., 0., 1., 0.],
[0., 1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 1., 0., 0.], # 15
[0., 0., 1., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., 1., 0.], # 16
[0., 1., 0., 0.],
[-1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., 1., 0.], # 17
[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., 1., 0.], # 18
[0., -1., 0., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., 1., 0.], # 19
[-1., 0., 0., 0.],
[0., -1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., -1., 0.], # 20
[0., 1., 0., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., -1., 0.], # 21
[1., 0., 0., 0.],
[0., -1., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., -1., 0.], # 22
[0., -1., 0., 0.],
[-1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0., 0., -1., 0.], # 23
[-1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 0., 1.]
],
]
for m1, m2 in zip(matrices[:len(refMatrices)], refMatrices):
self.assertArrayAlmostEqual(m1, m2)
def testSymmetryIcosahedral222(self):
matrices = getSymmetryMatrices(SYM_I222)
refMatrices = [
[
[1., 0., 0., 0.], # 1
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]
],
[
[-0.80901699, -0.5, 0.30901699, 0.], # 2
[-0.5, 0.30901699, -0.80901699, 0.],
[0.30901699, -0.80901699, -0.5, 0.],
[0., 0., 0., 1.]
],
[
[0., 1., 0., 0.], # 3
[0., 0., -1., 0.],
[-1., 0., 0., 0.],
[0., 0., 0., 1.]
],
[
[0.80901699, -0.5, -0.30901699, 0.], # 4
[-0.5, -0.30901699, -0.80901699, 0.],
[0.30901699, 0.80901699, -0.5, 0.],
[0., 0., 0., 1.]
],
[
[0.5, 0.30901699, -0.80901699, 0.], # 5
[-0.30901699, -0.80901699, -0.5, 0.],
[-0.80901699, 0.5, -0.30901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.30901699, -0.80901699, -0.5, 0.], # 6
[-0.80901699, 0.5, -0.30901699, 0.],
[0.5, 0.30901699, -0.80901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.80901699, 0.5, -0.30901699, 0.], # 7
[0.5, 0.30901699, -0.80901699, 0.],
[-0.30901699, -0.80901699, -0.5, 0.],
[0., 0., 0., 1.]
],
[
[-0.80901699, -0.5, -0.30901699, 0.], # 8
[0.5, -0.30901699, -0.80901699, 0.],
[0.30901699, -0.80901699, 0.5, 0.],
[0., 0., 0., 1.]
],
[
[-0.30901699, 0.80901699, -0.5, 0.], # 9
[-0.80901699, -0.5, -0.30901699, 0.],
[-0.5, 0.30901699, 0.80901699, 0.],
[0., 0., 0., 1.]
],
[
[0.5, -0.30901699, -0.80901699, 0.], # 10
[-0.30901699, 0.80901699, -0.5, 0.],
[0.80901699, 0.5, 0.30901699, 0.],
[0., 0., 0., 1.]
],
[
[0., 0., -1., 0.], # 11
[-1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 0., 1.]
],
[
[-0.5, -0.30901699, -0.80901699, 0.], # 12
[0.30901699, 0.80901699, -0.5, 0.],
[0.80901699, -0.5, -0.30901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.5, 0.30901699, -0.80901699, 0.], # 13
[0.30901699, -0.80901699, -0.5, 0.],
[-0.80901699, -0.5, 0.30901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.30901699, -0.80901699, -0.5, 0.], # 14
[0.80901699, -0.5, 0.30901699, 0.],
[-0.5, -0.30901699, 0.80901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.80901699, 0.5, -0.30901699, 0.], # 15
[-0.5, -0.30901699, 0.80901699, 0.],
[0.30901699, 0.80901699, 0.5, 0.],
[0., 0., 0., 1.]
],
[
[0.5, 0.30901699, -0.80901699, 0.], # 16
[0.30901699, 0.80901699, 0.5, 0.],
[0.80901699, -0.5, 0.30901699, 0.],
[0., 0., 0., 1.]
],
[
[-0.5, 0.30901699, -0.80901699, 0.], # 17
[-0.30901699, 0.80901699, 0.5, 0.],
[0.80901699, 0.5, -0.30901699, 0.],
[0., 0., 0., 1.]
],
[[0., 0., -1., 0.], [1., 0., 0., 0.], [0., -1., 0., 0.],
[0., 0., 0., 1.]],
[[-0.5, -0.30901699, -0.80901699, 0.],
[-0.30901699, -0.80901699, 0.5, 0.],
[-0.80901699, 0.5, 0.30901699, 0.], [0., 0., 0., 1.]],
[[0., -1., 0., 0.], [0., 0., 1., 0.], [-1., 0., 0., 0.],
[0., 0., 0., 1.]],
[[-0.80901699, 0.5, 0.30901699, 0.],
[0.5, 0.30901699, 0.80901699, 0.],
[0.30901699, 0.80901699, -0.5, 0.], [0., 0., 0., 1.]],
[[0.80901699, 0.5, -0.30901699, 0.],
[0.5, -0.30901699, 0.80901699, 0.],
[0.30901699, -0.80901699, -0.5, 0.], [0., 0., 0., 1.]],
[[-0.30901699, 0.80901699, -0.5, 0.],
[0.80901699, 0.5, 0.30901699, 0.],
[0.5, -0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[0.5, -0.30901699, -0.80901699, 0.],
[0.30901699, -0.80901699, 0.5, 0.],
[-0.80901699, -0.5, -0.30901699, 0.], [0., 0., 0., 1.]],
[[-0.80901699, -0.5, -0.30901699, 0.],
[-0.5, 0.30901699, 0.80901699, 0.],
[-0.30901699, 0.80901699, -0.5, 0.], [0., 0., 0., 1.]],
[[-0.30901699, -0.80901699, 0.5, 0.],
[-0.80901699, 0.5, 0.30901699, 0.],
[-0.5, -0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[-0.30901699, 0.80901699, 0.5, 0.],
[0.80901699, 0.5, -0.30901699, 0.],
[-0.5, 0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[1., 0., 0., 0.], [0., -1., 0., 0.], [0., 0., -1., 0.],
[0., 0., 0., 1.]],
[[0.30901699, 0.80901699, -0.5, 0.],
[0.80901699, -0.5, -0.30901699, 0.],
[-0.5, -0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[0.30901699, -0.80901699, -0.5, 0.],
[-0.80901699, -0.5, 0.30901699, 0.],
[-0.5, 0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[-1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., -1., 0.],
[0., 0., 0., 1.]],
[[0.80901699, 0.5, -0.30901699, 0.],
[-0.5, 0.30901699, -0.80901699, 0.],
[-0.30901699, 0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[0., -1., 0., 0.], [0., 0., -1., 0.], [1., 0., 0., 0.],
[0., 0., 0., 1.]],
[[-0.80901699, 0.5, 0.30901699, 0.],
[-0.5, -0.30901699, -0.80901699, 0.],
[-0.30901699, -0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[-0.5, -0.30901699, 0.80901699, 0.],
[-0.30901699, -0.80901699, -0.5, 0.],
[0.80901699, -0.5, 0.30901699, 0.], [0., 0., 0., 1.]],
[[0.30901699, 0.80901699, 0.5, 0.],
[-0.80901699, 0.5, -0.30901699, 0.],
[-0.5, -0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]],
[[0.80901699, -0.5, 0.30901699, 0.],
[0.5, 0.30901699, -0.80901699, 0.],
[0.30901699, 0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[0.80901699, 0.5, 0.30901699, 0.],
[0.5, -0.30901699, -0.80901699, 0.],
[-0.30901699, 0.80901699, -0.5, 0.], [0., 0., 0., 1.]],
[[0.30901699, -0.80901699, 0.5, 0.],
[-0.80901699, -0.5, -0.30901699, 0.],
[0.5, -0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[-0.5, 0.30901699, 0.80901699, 0.],
[-0.30901699, 0.80901699, -0.5, 0.],
[-0.80901699, -0.5, -0.30901699, 0.], [0., 0., 0., 1.]],
[[0., 0., 1., 0.], [-1., 0., 0., 0.], [0., -1., 0., 0.],
[0., 0., 0., 1.]],
[[0.5, 0.30901699, 0.80901699, 0.],
[0.30901699, 0.80901699, -0.5, 0.],
[-0.80901699, 0.5, 0.30901699, 0.], [0., 0., 0., 1.]],
[[0.5, -0.30901699, 0.80901699, 0.],
[0.30901699, -0.80901699, -0.5, 0.],
[0.80901699, 0.5, -0.30901699, 0.], [0., 0., 0., 1.]],
[[0.30901699, 0.80901699, 0.5, 0.],
[0.80901699, -0.5, 0.30901699, 0.],
[0.5, 0.30901699, -0.80901699, 0.], [0., 0., 0., 1.]],
[[0.80901699, -0.5, 0.30901699, 0.],
[-0.5, -0.30901699, 0.80901699, 0.],
[-0.30901699, -0.80901699, -0.5, 0.], [0., 0., 0., 1.]],
[[-0.5, -0.30901699, 0.80901699, 0.],
[0.30901699, 0.80901699, 0.5, 0.],
[-0.80901699, 0.5, -0.30901699, 0.], [0., 0., 0., 1.]],
[[0.5, -0.30901699, 0.80901699, 0.],
[-0.30901699, 0.80901699, 0.5, 0.],
[-0.80901699, -0.5, 0.30901699, 0.], [0., 0., 0., 1.]],
[[0., 0., 1., 0.], [1., 0., 0., 0.], [0., 1., 0., 0.],
[0., 0., 0., 1.]],
[[0.5, 0.30901699, 0.80901699, 0.],
[-0.30901699, -0.80901699, 0.5, 0.],
[0.80901699, -0.5, -0.30901699, 0.], [0., 0., 0., 1.]],
[[0., 1., 0., 0.], [0., 0., 1., 0.], [1., 0., 0., 0.],
[0., 0., 0., 1.]],
[[0.80901699, -0.5, -0.30901699, 0.],
[0.5, 0.30901699, 0.80901699, 0.],
[-0.30901699, -0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[-0.80901699, -0.5, 0.30901699, 0.],
[0.5, -0.30901699, 0.80901699, 0.],
[-0.30901699, 0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[0.30901699, -0.80901699, 0.5, 0.],
[0.80901699, 0.5, 0.30901699, 0.],
[-0.5, 0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]],
[[-0.5, 0.30901699, 0.80901699, 0.],
[0.30901699, -0.80901699, 0.5, 0.],
[0.80901699, 0.5, 0.30901699, 0.], [0., 0., 0., 1.]],
[[0.80901699, 0.5, 0.30901699, 0.],
[-0.5, 0.30901699, 0.80901699, 0.],
[0.30901699, -0.80901699, 0.5, 0.], [0., 0., 0., 1.]],
[[0.30901699, 0.80901699, -0.5, 0.],
[-0.80901699, 0.5, 0.30901699, 0.],
[0.5, 0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]],
[[0.30901699, -0.80901699, -0.5, 0.],
[0.80901699, 0.5, -0.30901699, 0.],
[0.5, -0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]],
[[-1., 0., 0., 0.], [0., -1., 0., 0.], [0., 0., 1., 0.],
[0., 0., 0., 1.]],
[[-0.30901699, -0.80901699, 0.5, 0.],
[0.80901699, -0.5, -0.30901699, 0.],
[0.5, 0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]],
[[-0.30901699, 0.80901699, 0.5, 0.],
[-0.80901699, -0.5, 0.30901699, 0.],
[0.5, -0.30901699, 0.80901699, 0.], [0., 0., 0., 1.]]
]
for m1, m2 in zip(matrices[:len(refMatrices)], refMatrices):
self.assertArrayAlmostEqual(m1, m2)
def testSymmetryTetrahedral(self):
matrices = getSymmetryMatrices(SYM_TETRAHEDRAL)
refMatrices = [
[[1.00000000e+00, 6.40987562e-17, -4.53246652e-17, 0.00000000e+00],
[5.55111512e-17, 1.00000000e+00, -5.55111512e-17, 0.00000000e+00],
[0.00000000e+00, -5.55111512e-17, 1.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[2.22044605e-16, 5.77350269e-01, 8.16496581e-01, 0.00000000e+00],
[5.77350269e-01, -6.66666667e-01, 4.71404521e-01, 0.00000000e+00],
[8.16496581e-01, 4.71404521e-01, -3.33333333e-01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[
-2.22044605e-16, -5.77350269e-01, -8.16496581e-01,
0.00000000e+00
],
[
-5.77350269e-01, -6.66666667e-01, 4.71404521e-01,
0.00000000e+00
],
[
-8.16496581e-01, 4.71404521e-01, -3.33333333e-01,
0.00000000e+00
],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[
-1.00000000e+00, 8.58760498e-18, -1.56346968e-16,
0.00000000e+00
],
[5.55111512e-17, 3.33333333e-01, -9.42809042e-01, 0.00000000e+00],
[
1.66533454e-16, -9.42809042e-01, -3.33333333e-01,
0.00000000e+00
],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[
-5.00000000e-01, -8.66025404e-01, 1.21208789e-16,
0.00000000e+00
],
[
8.66025404e-01, -5.00000000e-01, -5.55111512e-17,
0.00000000e+00
],
[0.00000000e+00, 1.38777878e-16, 1.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[-5.00000000e-01, 8.66025404e-01, 1.01864860e-17, 0.00000000e+00],
[
-8.66025404e-01, -5.00000000e-01, 5.55111512e-17,
0.00000000e+00
],
[1.66533454e-16, 0.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[-0.5, 0.28867513, -0.81649658, 0.],
[-0.28867513, 0.83333333, 0.47140452, 0.],
[0.81649658, 0.47140452, -0.33333333, 0.], [0., 0., 0., 1.]],
[[-0.5, -0.28867513, 0.81649658, 0.],
[0.28867513, 0.83333333, 0.47140452, 0.],
[-0.81649658, 0.47140452, -0.33333333, 0.], [0., 0., 0., 1.]],
[[5.00000000e-01, -2.88675135e-01, 8.16496581e-01, 0.00000000e+00],
[
-8.66025404e-01, -1.66666667e-01, 4.71404521e-01,
0.00000000e+00
],
[
-5.55111512e-17, -9.42809042e-01, -3.33333333e-01,
0.00000000e+00
],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[5.00000000e-01, -8.66025404e-01, 2.32231091e-16, 0.00000000e+00],
[
-2.88675135e-01, -1.66666667e-01, -9.42809042e-01,
0.00000000e+00
],
[8.16496581e-01, 4.71404521e-01, -3.33333333e-01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[5.00000000e-01, 8.66025404e-01, -1.56346968e-16, 0.00000000e+00],
[
2.88675135e-01, -1.66666667e-01, -9.42809042e-01,
0.00000000e+00
],
[
-8.16496581e-01, 4.71404521e-01, -3.33333333e-01,
0.00000000e+00
],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]],
[[5.00000000e-01, 2.88675135e-01, -8.16496581e-01, 0.00000000e+00],
[8.66025404e-01, -1.66666667e-01, 4.71404521e-01, 0.00000000e+00],
[
-5.55111512e-16, -9.42809042e-01, -3.33333333e-01,
0.00000000e+00
],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]]
]
for m1, m2 in zip(matrices, refMatrices):
self.assertArrayAlmostEqual(m1, m2)