def test_triclinic_cell(self):
cell = UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
pos = Position(-15, -17, 190)
frac = cell.fractionalize(pos)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
# tested against values from uctbx:
# from cctbx import uctbx
# uc = uctbx.unit_cell((35.996, 41.601, 45.756, 67.40, 66.90, 74.85))
# uc.d_star_sq((-3, -2, 1))
# uc.d((3, 4, 5))
self.assertAlmostEqual(cell.calculate_1_d2([-3, -2, 1]),
0.0128229081865688, delta=1e-17)
self.assertAlmostEqual(cell.calculate_d([3, 4, 5]),
7.7319559244298, delta=1e-13)
# uc.metrical_matrix()
cctbx_mm = [1295.712016, 1730.643201, 2093.611536,
391.3591013825865, 646.1921687548228, 731.5043620154578]
mt = cell.metric_tensor()
for a, b in zip(mt.elements(), cctbx_mm):
self.assertAlmostEqual(a, b, delta=1e-12)
# uc.reciprocal_metrical_matrix()
cctbx_rmm = [0.00092792089082916, 0.000689632633981, 0.0006277651322979,
-0.000104162588996, -0.000250008091601, -0.000208806754807]
rmt = cell.reciprocal_metric_tensor()
for a, b in zip(rmt.elements(), cctbx_rmm):
self.assertAlmostEqual(a, b, delta=1e-15)
def test_triclinic_cell(self):
cell = UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
pos = Position(-15, -17, 190)
frac = cell.fractionalize(pos)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
def test_dihedral_special_cases(self):
a = Position(random(), random(), random())
# not sure what it should be in such undefined cases
#self.assertTrue(isnan(gemmi.calculate_dihedral(a, a, a, a)))
self.assertEqual(gemmi.calculate_dihedral(a, a, a, a), 0.0)
# Special cases from scitbx tst_math.py
# atan2 is guaranteed to give exact values (I think)
p000 = Position(0, 0, 0)
p100 = Position(1, 0, 0)
p010 = Position(0, 1, 0)
def xy_dihedral(last_point):
return gemmi.calculate_dihedral(p100, p000, p010, last_point)
self.assertEqual(xy_dihedral(Position(1, 1, 0)), 0.0)
self.assertEqual(xy_dihedral(Position(-1, 1, 0)), pi)
p01_ = Position(0, 1, -1)
self.assertEqual(xy_dihedral(p01_), pi/2)
p01_.z = 1
self.assertEqual(xy_dihedral(p01_), -pi/2)
def test_dihedral(self):
# based on from https://stackoverflow.com/questions/20305272/
p0 = Position(24.969, 13.428, 30.692) # N
p1 = Position(24.044, 12.661, 29.808) # CA
p2 = Position(22.785, 13.482, 29.543) # C
p3 = Position(21.951, 13.670, 30.431) # O
p4 = Position(23.672, 11.328, 30.466) # CB
p5 = Position(22.881, 10.326, 29.620) # CG
p6 = Position(23.691, 9.935, 28.389) # CD1
p7 = Position(22.557, 9.096, 30.459) # CD2
def check_dihedral(a, b, c, d, angle):
deg = gemmi.calculate_dihedral(a, b, c, d) * 180 / pi
self.assertAlmostEqual(deg, angle, places=4)
check_dihedral(p0, p1, p2, p3, -71.21515)
check_dihedral(p0, p1, p4, p5, -171.94319)
check_dihedral(p1, p4, p5, p6, 60.82226)
check_dihedral(p1, p4, p5, p7, -177.63641)
def test_ortho_cell(self):
cell = UnitCell(25.14, 39.50, 45.07, 90, 90, 90)
pos = Position(5, -6, 7)
frac = cell.fractionalize(pos)
self.assertAlmostEqual(frac.x, 0.198886, delta=1e-6)
self.assertAlmostEqual(frac.y, -0.151899, delta=1e-6)
self.assertAlmostEqual(frac.z, 0.155314, delta=1e-6)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
corner = cell.orthogonalize(Fractional(1, 1, 1))
self.assertAlmostEqual(corner.x, cell.a, delta=1e-12)
self.assertAlmostEqual(corner.y, cell.b, delta=1e-12)
self.assertAlmostEqual(corner.z, cell.c, delta=1e-12)
def test_ortho_cell(self):
cell = UnitCell(25.14, 39.50, 45.07, 90, 90, 90)
pos = Position(5, -6, 7)
frac = cell.fractionalize(pos)
self.assertAlmostEqual(frac.x, 0.198886, delta=1e-6)
self.assertAlmostEqual(frac.y, -0.151899, delta=1e-6)
self.assertAlmostEqual(frac.z, 0.155314, delta=1e-6)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
corner = cell.orthogonalize(gemmi.Fractional(1, 1, 1))
self.assertAlmostEqual(corner.x, cell.a, delta=1e-12)
self.assertAlmostEqual(corner.y, cell.b, delta=1e-12)
self.assertAlmostEqual(corner.z, cell.c, delta=1e-12)
rec = cell.reciprocal()
self.assertEqual([rec.alpha, rec.beta, rec.gamma], [90, 90, 90])
self.assertAlmostEqual(rec.a, 1 / cell.a, delta=1e-17)
def test_triclinic_cell(self):
cell = UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
pos = Position(-15, -17, 190)
frac = cell.fractionalize(pos)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
# tested against values from uctbx:
# from cctbx import uctbx
# uc = uctbx.unit_cell((35.996, 41.601, 45.756, 67.40, 66.90, 74.85))
# uc.d_star_sq((-3, -2, 1))
# uc.d((3, 4, 5))
self.assertAlmostEqual(cell.calculate_1_d2(-3, -2, 1),
0.0128229081865688,
delta=1e-17)
self.assertAlmostEqual(cell.calculate_d(3, 4, 5),
7.7319559244298,
delta=1e-13)
def test_triclinic_cell(self):
cell = UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
# this would give syntax error with Python < 3.5
#o_f = cell.orthogonalization_matrix @ cell.fractionalization_matrix
o_f = cell.orthogonalization_matrix.multiply(
cell.fractionalization_matrix)
self.assertTrue(o_f.approx(gemmi.Mat33(), 1e-15))
pos = Position(-15, -17, 190)
frac = cell.fractionalize(pos)
pos2 = cell.orthogonalize(frac)
self.assertAlmostEqual(pos.x, pos2.x, delta=1e-12)
self.assertAlmostEqual(pos.y, pos2.y, delta=1e-12)
self.assertAlmostEqual(pos.z, pos2.z, delta=1e-12)
# tested against values from uctbx:
# from cctbx import uctbx
# uc = uctbx.unit_cell((35.996, 41.601, 45.756, 67.40, 66.90, 74.85))
# uc.d_star_sq((-3, -2, 1))
# uc.d((3, 4, 5))
self.assertAlmostEqual(cell.calculate_1_d2([-3, -2, 1]),
0.0128229081865688,
delta=1e-17)
self.assertAlmostEqual(cell.calculate_d([3, 4, 5]),
7.7319559244298,
delta=1e-13)
# uc.metrical_matrix()
cctbx_mm = [
1295.712016, 1730.643201, 2093.611536, 391.3591013825865,
646.1921687548228, 731.5043620154578
]
mt = cell.metric_tensor()
assert_almost_equal_seq(self, mt.elements_pdb(), cctbx_mm, delta=1e-12)
# uc.reciprocal_metrical_matrix()
cctbx_rmm = [
0.00092792089082916, 0.000689632633981, 0.0006277651322979,
-0.000104162588996, -0.000250008091601, -0.000208806754807
]
rmt = cell.reciprocal_metric_tensor()
assert_almost_equal_seq(self,
rmt.elements_pdb(),
cctbx_rmm,
delta=1e-15)
