def exercise_flood_fill():
uc = uctbx.unit_cell('10 10 10 90 90 90')
for uc in (uctbx.unit_cell('10 10 10 90 90 90'),
uctbx.unit_cell('9 10 11 87 91 95')):
gridding = maptbx.crystal_gridding(
unit_cell=uc,
pre_determined_n_real=(5,5,5))
corner_cube = (0,4,20,24,100,104,120,124) # cube across all 8 corners
channel = (12,37,38,39,42,43,62,63,67,68,87,112)
data = flex.int(flex.grid(gridding.n_real()))
for i in (corner_cube + channel): data[i] = 1
flood_fill = masks.flood_fill(data, uc)
assert data.count(0) == 105
for i in corner_cube: assert data[i] == 2
for i in channel: assert data[i] == 3
assert approx_equal(flood_fill.centres_of_mass(),
((-0.5, -0.5, -0.5), (-2.5, 7/3, 2.5)))
assert approx_equal(flood_fill.centres_of_mass_frac(),
((-0.1, -0.1, -0.1), (-0.5, 7/15, 0.5)))
assert approx_equal(flood_fill.centres_of_mass_cart(),
uc.orthogonalize(flood_fill.centres_of_mass_frac()))
assert flood_fill.n_voids() == 2
assert approx_equal(flood_fill.grid_points_per_void(), (8, 12))
if 0:
from crys3d import wx_map_viewer
wx_map_viewer.display(raw_map=data.as_double(), unit_cell=uc, wires=False)
#
gridding = maptbx.crystal_gridding(
unit_cell=uc,
pre_determined_n_real=(10,10,10))
data = flex.int(flex.grid(gridding.n_real()))
# parallelogram
points = [(2,4,5),(3,4,5),(4,4,5),(5,4,5),(6,4,5),
(3,5,5),(4,5,5),(5,5,5),(6,5,5),(7,5,5),
(4,6,5),(5,6,5),(6,6,5),(7,6,5),(8,6,5)]
points_frac = flex.vec3_double()
for p in points:
data[p] = 1
points_frac.append([p[i]/gridding.n_real()[i] for i in range(3)])
points_cart = uc.orthogonalize(points_frac)
flood_fill = masks.flood_fill(data, uc)
assert data.count(2) == 15
assert approx_equal(flood_fill.centres_of_mass_frac(), ((0.5,0.5,0.5),))
pai_cart = math.principal_axes_of_inertia(
points=points_cart, weights=flex.double(points_cart.size(),1.0))
F = matrix.sqr(uc.fractionalization_matrix())
O = matrix.sqr(uc.orthogonalization_matrix())
assert approx_equal(
pai_cart.center_of_mass(), flood_fill.centres_of_mass_cart()[0])
assert approx_equal(
flood_fill.covariance_matrices_cart()[0],
(F.transpose() * matrix.sym(
sym_mat3=flood_fill.covariance_matrices_frac()[0]) * F).as_sym_mat3())
assert approx_equal(
pai_cart.inertia_tensor(), flood_fill.inertia_tensors_cart()[0])
assert approx_equal(pai_cart.eigensystem().vectors(),
flood_fill.eigensystems_cart()[0].vectors())
assert approx_equal(pai_cart.eigensystem().values(),
flood_fill.eigensystems_cart()[0].values())
return
def run():
points = flex.vec3_double([(8.292, 1.817, 6.147), (9.159, 2.144, 7.299),
(10.603, 2.331, 6.885), (11.041, 1.811, 5.855),
(9.061, 1.065, 8.369), (7.665, 0.929, 8.902),
(6.771, 0.021, 8.327), (7.210, 1.756, 9.920),
(5.480, -0.094, 8.796), (5.904, 1.649, 10.416),
(5.047, 0.729, 9.831), (3.766, 0.589, 10.291),
(11.358, 2.999, 7.612)])
pai = principal_axes_of_inertia(points=points)
print pai.center_of_mass()
print pai.inertia_tensor()
es = pai.eigensystem()
print list(es.values())
print list(es.vectors())
def run():
points = flex.vec3_double(
[
(8.292, 1.817, 6.147),
(9.159, 2.144, 7.299),
(10.603, 2.331, 6.885),
(11.041, 1.811, 5.855),
(9.061, 1.065, 8.369),
(7.665, 0.929, 8.902),
(6.771, 0.021, 8.327),
(7.210, 1.756, 9.920),
(5.480, -0.094, 8.796),
(5.904, 1.649, 10.416),
(5.047, 0.729, 9.831),
(3.766, 0.589, 10.291),
(11.358, 2.999, 7.612),
]
)
pai = principal_axes_of_inertia(points=points)
print pai.center_of_mass()
print pai.inertia_tensor()
es = pai.eigensystem()
print list(es.values())
print list(es.vectors())
def exercise_flood_fill():
uc = uctbx.unit_cell('10 10 10 90 90 90')
for uc in (uctbx.unit_cell('10 10 10 90 90 90'),
uctbx.unit_cell('9 10 11 87 91 95')):
gridding = maptbx.crystal_gridding(unit_cell=uc,
pre_determined_n_real=(5, 5, 5))
corner_cube = (0, 4, 20, 24, 100, 104, 120, 124
) # cube across all 8 corners
channel = (12, 37, 38, 39, 42, 43, 62, 63, 67, 68, 87, 112)
data = flex.int(flex.grid(gridding.n_real()))
for i in (corner_cube + channel):
data[i] = 1
flood_fill = masks.flood_fill(data, uc)
assert data.count(0) == 105
for i in corner_cube:
assert data[i] == 2
for i in channel:
assert data[i] == 3
assert approx_equal(flood_fill.centres_of_mass(),
((-0.5, -0.5, -0.5), (-2.5, 7 / 3, 2.5)))
assert approx_equal(flood_fill.centres_of_mass_frac(),
((-0.1, -0.1, -0.1), (-0.5, 7 / 15, 0.5)))
assert approx_equal(
flood_fill.centres_of_mass_cart(),
uc.orthogonalize(flood_fill.centres_of_mass_frac()))
assert flood_fill.n_voids() == 2
assert approx_equal(flood_fill.grid_points_per_void(), (8, 12))
if 0:
from crys3d import wx_map_viewer
wx_map_viewer.display(raw_map=data.as_double(),
unit_cell=uc,
wires=False)
#
gridding = maptbx.crystal_gridding(unit_cell=uc,
pre_determined_n_real=(10, 10, 10))
data = flex.int(flex.grid(gridding.n_real()))
# parallelogram
points = [(2, 4, 5), (3, 4, 5), (4, 4, 5), (5, 4, 5), (6, 4, 5),
(3, 5, 5), (4, 5, 5), (5, 5, 5), (6, 5, 5), (7, 5, 5),
(4, 6, 5), (5, 6, 5), (6, 6, 5), (7, 6, 5), (8, 6, 5)]
points_frac = flex.vec3_double()
for p in points:
data[p] = 1
points_frac.append([p[i] / gridding.n_real()[i] for i in range(3)])
points_cart = uc.orthogonalize(points_frac)
flood_fill = masks.flood_fill(data, uc)
assert data.count(2) == 15
assert approx_equal(flood_fill.centres_of_mass_frac(),
((0.5, 0.5, 0.5), ))
pai_cart = math.principal_axes_of_inertia(points=points_cart,
weights=flex.double(
points_cart.size(), 1.0))
F = matrix.sqr(uc.fractionalization_matrix())
O = matrix.sqr(uc.orthogonalization_matrix())
assert approx_equal(pai_cart.center_of_mass(),
flood_fill.centres_of_mass_cart()[0])
assert approx_equal(
flood_fill.covariance_matrices_cart()[0],
(F.transpose() *
matrix.sym(sym_mat3=flood_fill.covariance_matrices_frac()[0]) *
F).as_sym_mat3())
assert approx_equal(pai_cart.inertia_tensor(),
flood_fill.inertia_tensors_cart()[0])
assert approx_equal(pai_cart.eigensystem().vectors(),
flood_fill.eigensystems_cart()[0].vectors())
assert approx_equal(pai_cart.eigensystem().values(),
flood_fill.eigensystems_cart()[0].values())
return