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#!/usr/bin/env python
import unittest
from math import pi # , isnan
import pickle
from random import random
import gemmi
from common import numpy
def assert_almost_equal_seq(self, a, b, delta=None):
for x,y in zip(a, b):
self.assertAlmostEqual(x, y, delta=delta)
class TestMath(unittest.TestCase):
def test_Vec3(self):
a = gemmi.Vec3(-3, 3, 13)
b = gemmi.Vec3(2, 0, -2)
self.assertEqual((-a).tolist(), [3, -3, -13])
self.assertEqual((a+b).tolist(), [-1, 3, 11])
self.assertEqual((a-b).tolist(), [-5, 3, 15])
a -= b
self.assertEqual(a.tolist(), [-5, 3, 15])
a += b
self.assertEqual(a.tolist(), [-3, 3, 13])
def test_mat33(self):
a = gemmi.Mat33([[3,4,5],[6,7,8],[9,10,11]])
self.assertEqual((a - a).tolist(), [[0]*3]*3)
self.assertEqual((a + a - a).tolist(), a.tolist())
def test_SMat33_transformed_by(self):
tensor = gemmi.SMat33d(random(), random(), random(),
random(), random(), random())
mat = gemmi.Mat33()
mat.fromlist([[random() for _ in range(3)] for _ in range(3)])
t1 = tensor.transformed_by(mat).as_mat33().tolist()
t2 = mat.multiply(tensor.as_mat33()).multiply(mat.transpose()).tolist()
for i in range(3):
for j in range(3):
self.assertAlmostEqual(t1[i][j], t2[i][j])
@unittest.skipIf(numpy is None, 'requires NumPy')
def test_mat33_dunder_array(self):
m = gemmi.Mat33([[1,2,3],[4,5,6],[7,8,9]])
self.assertTrue((numpy.dot(m, m) == m @ m).all())
cn00 = numpy.array(m)
cn32 = numpy.array(m, dtype=numpy.float32)
cn64 = numpy.array(m, dtype=numpy.float64)
ct00 = numpy.array(m, copy=True)
ct32 = numpy.array(m, dtype=numpy.float32, copy=True)
ct64 = numpy.array(m, dtype=numpy.float64, copy=True)
cf00 = numpy.array(m, copy=False)
try:
cf32 = numpy.array(m, dtype=numpy.float32, copy=False)
except ValueError:
cf32 = None
cf64 = numpy.array(m, dtype=numpy.float64, copy=False)
m.fromlist([[50,50,50], [50,50,50], [50,50,50]])
for cx in [cn00, cn32, cn64, ct00, ct32, ct64]:
self.assertEqual(cx[0][0], 1)
for cx in [cf00, cf64]:
self.assertEqual(cx[0][0], 50)
if numpy.__version__ < '2.':
self.assertEqual(cf32[0][0], 1)
else:
self.assertIsNone(cf32)
class TestUnitCell(unittest.TestCase):
def test_dummy_cell(self):
cell = gemmi.UnitCell()
self.assertEqual([cell.a, cell.b, cell.c], [1, 1, 1])
self.assertEqual([cell.alpha, cell.beta, cell.gamma], [90, 90, 90])
self.assertEqual(cell.volume, 1.0)
def test_ortho_cell(self):
cell = gemmi.UnitCell(25.14, 39.50, 45.07, 90, 90, 90)
self.assertTrue(cell.orth.mat.row_copy(1)
.approx(gemmi.Vec3(0, 39.5, 0), 0))
self.assertTrue(cell.orth.mat.column_copy(0)
.approx(gemmi.Vec3(25.14, 0, 0), 0))
pos = gemmi.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 = gemmi.UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
o_f = cell.orth.mat.multiply(cell.frac.mat)
self.assertTrue(o_f.approx(gemmi.Mat33(), 1e-15))
tr_o_f = cell.orth @ cell.frac
self.assertTrue(tr_o_f.approx(gemmi.Transform(), 1e-15))
self.assertTrue(tr_o_f.approx(tr_o_f.inverse(), 1e-15))
mat = cell.orth.mat @ cell.frac.mat
self.assertTrue(mat.approx(gemmi.Mat33(), 1e-15))
pos = gemmi.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)
def test_ortogonalize_box(self):
cell = gemmi.UnitCell(100, 105, 113, 90, 120, 90)
box = gemmi.FractionalBox()
box.minimum = gemmi.Fractional(0, 0, 0)
box.maximum = gemmi.Fractional(1, 1, 1)
obox = cell.orthogonalize_box(box)
self.assertTrue(obox.minimum.x < 0)
self.assertEqual(obox.minimum.y, 0)
self.assertEqual(obox.minimum.z, 0)
self.assertEqual(obox.maximum.x, cell.a)
self.assertEqual(obox.maximum.y, cell.b)
c_spacing = 1. / cell.reciprocal().c
self.assertAlmostEqual(obox.maximum.z, c_spacing, delta=1e-12)
def test_is_similar(self):
cell = gemmi.UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
cell2 = gemmi.UnitCell(36, 42, 46, 67, 67, 75)
self.assertTrue(cell.approx(cell, 1e-6))
self.assertFalse(cell.approx(cell2, 1e-6))
self.assertTrue(cell.approx(cell2, epsilon=0.5))
self.assertTrue(cell.is_similar(cell2, rel=0.01, deg=0.5))
self.assertFalse(cell.is_similar(cell2, rel=0.01, deg=0.3))
self.assertFalse(cell.is_similar(cell2, rel=0.009, deg=0.5))
def test_change_of_basis(self):
uc = gemmi.UnitCell(20, 30, 39, 73, 93, 99)
op = gemmi.Op('y-x/2,-2/3*z+2/3*y,3*x')
uc2 = uc.changed_basis_backward(op, set_images=False)
# compare with result from cctbx:
# from cctbx import sgtbx, uctbx
# u = uctbx.unit_cell((20,30,39, 73,93,99))
# op = sgtbx.change_of_basis_op('y-x/2,-2/3*z+2/3*y,3*x').inverse()
# print(u.change_basis(cb_op=op).parameters())
expected = (117.9468784563987, 25.977921933207348, 20.0,
130.5, 107.65517573180257, 82.63132106791868)
assert_almost_equal_seq(self, uc2.parameters, expected)
uc3 = uc2.changed_basis_forward(op, set_images=True)
assert_almost_equal_seq(self, uc3.parameters, uc.parameters)
def test_atom_to_site(self):
cell = gemmi.UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
atom = gemmi.Atom()
atom.aniso = gemmi.SMat33f(13.1, 20.1, 11.1, -3.5, 5.5, -0.4)
site = gemmi.SmallStructure.Site(atom, cell)
# tested against values from cctbx:
# from cctbx import uctbx, adptbx
# uc = uctbx.unit_cell((35.996, 41.601, 45.756, 67.40, 66.90, 74.85))
# aniso = (13.1, 20.1, 11.1, -3.5, 5.5, -0.4)
# ucif = adptbx.u_cart_as_u_cif(uc, aniso)
ucif = [11.537759976524049, 19.43436271641311, 11.1,
-8.078683096677723, 1.4787260755519491, -3.9018967241279157]
assert_almost_equal_seq(self, site.aniso.elements_pdb(), ucif,
delta=1e-6)
def test_pickling(self):
cell = gemmi.UnitCell(35.996, 41.601, 45.756, 67.40, 66.90, 74.85)
pkl_string = pickle.dumps(cell, protocol=pickle.HIGHEST_PROTOCOL)
result = pickle.loads(pkl_string)
self.assertTrue(isinstance(result, gemmi.UnitCell))
self.assertEqual(cell.parameters, result.parameters)
class TestAngles(unittest.TestCase):
def test_dihedral_special_cases(self):
a = gemmi.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 = gemmi.Position(0, 0, 0)
p100 = gemmi.Position(1, 0, 0)
p010 = gemmi.Position(0, 1, 0)
def xy_dihedral(last_point):
return gemmi.calculate_dihedral(p100, p000, p010, last_point)
self.assertEqual(xy_dihedral(gemmi.Position(1, 1, 0)), 0.0)
self.assertEqual(xy_dihedral(gemmi.Position(-1, 1, 0)), pi)
p01_ = gemmi.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 = gemmi.Position(24.969, 13.428, 30.692) # N
p1 = gemmi.Position(24.044, 12.661, 29.808) # CA
p2 = gemmi.Position(22.785, 13.482, 29.543) # C
p3 = gemmi.Position(21.951, 13.670, 30.431) # O
p4 = gemmi.Position(23.672, 11.328, 30.466) # CB
p5 = gemmi.Position(22.881, 10.326, 29.620) # CG
p6 = gemmi.Position(23.691, 9.935, 28.389) # CD1
p7 = gemmi.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)
class TestGruber(unittest.TestCase):
def test_reduction(self):
cell = gemmi.UnitCell(687.9, 687.9, 1933.3, 90.0, 90.0, 90.0)
sg = gemmi.SpaceGroup('I 4 2 2')
gv = gemmi.GruberVector(cell, sg)
gv.niggli_reduce()
self.assertTrue(gv.is_niggli())
self.assertTrue(gv.is_buerger())
self.assertTrue(gv.is_normalized())
p = cell.a
q = 1082.134662368783
t = 108.5325886
par = (p*p, p*p, q*q, -p*p, -p*p, 0)
assert_almost_equal_seq(self, gv.parameters, par)
assert_almost_equal_seq(self, gv.cell_parameters(), (p, p, q, t, t, 90))
def test_near_degenerate(self):
cell = gemmi.UnitCell(15.53, 91.94, 4.35, 110.326, 7.337, 103.014)
gv = gemmi.GruberVector(cell, None)
self.assertFalse(gv.is_normalized())
gv.normalize()
self.assertTrue(gv.is_normalized())
self.assertFalse(gv.is_buerger())
self.assertFalse(gv.is_niggli())
n = gv.niggli_reduce(iteration_limit=100)
self.assertEqual(n, 100)
self.assertFalse(gv.is_niggli())
n = gv.niggli_reduce(iteration_limit=100)
self.assertTrue(n < 100)
self.assertTrue(gv.is_niggli())
expected = (2.814597242, 3.077205425, 7.408935896,
100.42421409, 94.02885284, 95.07179187)
assert_almost_equal_seq(self, gv.cell_parameters(), expected)
if __name__ == '__main__':
unittest.main()
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