def test():
import random
import textwrap
from cctbx.uctbx import unit_cell
from libtbx.test_utils import approx_equal
def random_direction_close_to(vector):
return vector.rotate_around_origin(
matrix.col((random.random(), random.random(),
random.random())).normalize(),
random.gauss(0, 1.0),
deg=True,
)
# make a random P1 crystal and parameterise it
a = random.uniform(10, 50) * random_direction_close_to(
matrix.col((1, 0, 0)))
b = random.uniform(10, 50) * random_direction_close_to(
matrix.col((0, 1, 0)))
c = random.uniform(10, 50) * random_direction_close_to(
matrix.col((0, 0, 1)))
xl = Crystal(a, b, c, space_group_symbol="P 1")
xl_op = CrystalOrientationParameterisation(xl)
xl_ucp = CrystalUnitCellParameterisation(xl)
null_mat = matrix.sqr((0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0))
# compare analytical and finite difference derivatives
an_ds_dp = xl_op.get_ds_dp()
fd_ds_dp = get_fd_gradients(xl_op, [1.0e-6 * pi / 180] * 3)
for e, f in zip(an_ds_dp, fd_ds_dp):
assert approx_equal((e - f), null_mat, eps=1.0e-6)
an_ds_dp = xl_ucp.get_ds_dp()
fd_ds_dp = get_fd_gradients(xl_ucp, [1.0e-7] * xl_ucp.num_free())
for e, f in zip(an_ds_dp, fd_ds_dp):
assert approx_equal((e - f), null_mat, eps=1.0e-6)
# random initial orientations with a random parameter shift at each
attempts = 100
for i in range(attempts):
# make a random P1 crystal and parameterise it
a = random.uniform(10, 50) * random_direction_close_to(
matrix.col((1, 0, 0)))
b = random.uniform(10, 50) * random_direction_close_to(
matrix.col((0, 1, 0)))
c = random.uniform(10, 50) * random_direction_close_to(
matrix.col((0, 0, 1)))
xl = Crystal(a, b, c, space_group_symbol="P 1")
xl_op = CrystalOrientationParameterisation(xl)
xl_uc = CrystalUnitCellParameterisation(xl)
# apply a random parameter shift to the orientation
p_vals = xl_op.get_param_vals()
p_vals = random_param_shift(
p_vals, [1000 * pi / 9, 1000 * pi / 9, 1000 * pi / 9])
xl_op.set_param_vals(p_vals)
# compare analytical and finite difference derivatives
xl_op_an_ds_dp = xl_op.get_ds_dp()
xl_op_fd_ds_dp = get_fd_gradients(xl_op, [1.0e-5 * pi / 180] * 3)
# apply a random parameter shift to the unit cell. We have to
# do this in a way that is respectful to metrical constraints,
# so don't modify the parameters directly; modify the cell
# constants and extract the new parameters
cell_params = xl.get_unit_cell().parameters()
cell_params = random_param_shift(cell_params, [1.0] * 6)
new_uc = unit_cell(cell_params)
newB = matrix.sqr(new_uc.fractionalization_matrix()).transpose()
S = symmetrize_reduce_enlarge(xl.get_space_group())
S.set_orientation(orientation=newB)
X = S.forward_independent_parameters()
xl_uc.set_param_vals(X)
xl_uc_an_ds_dp = xl_ucp.get_ds_dp()
# now doing finite differences about each parameter in turn
xl_uc_fd_ds_dp = get_fd_gradients(xl_ucp, [1.0e-7] * xl_ucp.num_free())
for j in range(3):
assert approx_equal((xl_op_fd_ds_dp[j] - xl_op_an_ds_dp[j]),
null_mat,
eps=1.0e-6), textwrap.dedent("""\
Failure in try {i}
failure for parameter number {j}
of the orientation parameterisation
with fd_ds_dp =
{fd}
and an_ds_dp =
{an}
so that difference fd_ds_dp - an_ds_dp =
{diff}
""").format(
i=i,
j=j,
fd=xl_op_fd_ds_dp[j],
an=xl_op_an_ds_dp[j],
diff=xl_op_fd_ds_dp[j] - xl_op_an_ds_dp[j],
)
for j in range(xl_ucp.num_free()):
assert approx_equal((xl_uc_fd_ds_dp[j] - xl_uc_an_ds_dp[j]),
null_mat,
eps=1.0e-6), textwrap.dedent("""\
Failure in try {i}
failure for parameter number {j}
of the unit cell parameterisation
with fd_ds_dp =
{fd}
and an_ds_dp =
{an}
so that difference fd_ds_dp - an_ds_dp =
{diff}
""").format(
i=i,
j=j,
fd=xl_uc_fd_ds_dp[j],
an=xl_uc_an_ds_dp[j],
diff=xl_uc_fd_ds_dp[j] - xl_uc_an_ds_dp[j],
)
