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)