import logging
import math
from cctbx import crystal, uctbx, xray
from libtbx import libtbx, phil
from scitbx import fftpack, matrix
from scitbx.array_family import flex
import dials_algorithms_indexing_ext
from dials.algorithms import indexing
from .strategy import Strategy
from .utils import group_vectors, is_approximate_integer_multiple
logger = logging.getLogger(__name__)
fft3d_phil_str = """\
b_iso = Auto
.type = float(value_min=0)
.expert_level = 2
rmsd_cutoff = 15
.type = float(value_min=0)
.expert_level = 1
peak_search = *flood_fill clean
.type = choice
.expert_level = 2
peak_volume_cutoff = 0.15
.type = float
.expert_level = 2
reciprocal_space_grid {
n_points = 256
.type = int(value_min=0)
.expert_level = 1
d_min = Auto
.type = float(value_min=0)
.help = "The high resolution limit in Angstrom for spots to include in "
"the initial indexing."
}
"""
[docs]class FFT3D(Strategy):
"""
Basis vector search using a 3D FFT in reciprocal space.
Reciprocal space is sampled as a 3D Cartesian grid, aligned with the basis of the
laboratory frame. The reciprocal-space positions of the centroids of measured
spots are ascribed a value of 1, with the rest of the grid assigned a value of 0.
A 3D FFT is performed and the three shortest non-collinear reciprocal spatial
wave vectors with appreciable spectral weight correspond to the basis vectors of
the real space lattice.
Because this procedure requires a sampling of all of reciprocal space, up to the
d* value of the measured spot with the highest resolution, it can be more memory
intensive than alternative approaches. To mitigate this, the 3D FFT will
sometimes be curtailed to a region of reciprocal space below a certain
resolution, and higher-resolution spots will be ignored.
See:
Bricogne, G. (1986). Proceedings of the EEC Cooperative Workshop on Position-Sensitive Detector Software (Phase III), p. 28. Paris: LURE.
Campbell, J. W. (1998). J. Appl. Cryst. 31, 407-413.
"""
phil_help = (
"Search for the basis vectors of the direct lattice by performing a 3D FFT in "
"reciprocal space of the density of found spots. Since this can be quite "
"memory-intensive, the data used for indexing may automatically be "
"constrained to just the lower resolution spots."
)
phil_scope = phil.parse(fft3d_phil_str)
[docs] def __init__(self, max_cell, min_cell=3, params=None, *args, **kwargs):
"""Construct an FFT3D object.
Args:
max_cell (float): An estimate of the maximum cell dimension of the primitive
cell.
n_points (int): The size of the fft3d grid.
d_min (float): The high resolution limit in Angstrom for spots to include in
the initial indexing. If `Auto` then calculated as
`d_min = 5 * max_cell/n_points`.
b_iso (float): Apply an isotropic b_factor weight to the points when doing
the FFT. If `Auto` then calculated as
`b_iso = -4 * d_min ** 2 * math.log(0.05)`.
rmsd_cutoff (float): RMSD cutoff applied to the transformed real-space map
prior to performing the peak search.
peak_volume_cutoff (float): Only include peaks that are larger than this
fraction of the volume of the largest peak in the transformed real-space
map.
min_cell (float): A conservative lower bound on the minimum possible
primitive unit cell dimension.
"""
super().__init__(max_cell, params=params, *args, **kwargs)
n_points = self._params.reciprocal_space_grid.n_points
self._gridding = fftpack.adjust_gridding_triple(
(n_points, n_points, n_points), max_prime=5
)
self._n_points = self._gridding[0]
self._min_cell = min_cell
[docs] def find_basis_vectors(self, reciprocal_lattice_vectors):
"""Find a list of likely basis vectors.
Args:
reciprocal_lattice_vectors (scitbx.array_family.flex.vec3_double):
The list of reciprocal lattice vectors to search for periodicity.
Returns:
A tuple containing the list of basis vectors and a flex.bool array
identifying which reflections were used in indexing.
"""
if self._params.reciprocal_space_grid.d_min is libtbx.Auto:
# rough calculation of suitable d_min based on max cell
# see also Campbell, J. (1998). J. Appl. Cryst., 31(3), 407-413.
# fft_cell should be greater than twice max_cell, so say:
# fft_cell = 2.5 * max_cell
# then:
# fft_cell = n_points * d_min/2
# 2.5 * max_cell = n_points * d_min/2
# a little bit of rearrangement:
# d_min = 5 * max_cell/n_points
max_cell = self._max_cell
d_min = 5 * max_cell / self._n_points
d_spacings = 1 / reciprocal_lattice_vectors.norms()
d_min = max(d_min, min(d_spacings))
logger.info("Setting d_min: %.2f", d_min)
else:
d_min = self._params.reciprocal_space_grid.d_min
grid_real, used_in_indexing = self._fft(reciprocal_lattice_vectors, d_min)
self.sites, self.volumes = self._find_peaks(grid_real, d_min)
# hijack the xray.structure class to facilitate calculation of distances
self.crystal_symmetry = crystal.symmetry(
unit_cell=self._fft_cell, space_group_symbol="P1"
)
xs = xray.structure(crystal_symmetry=self.crystal_symmetry)
for i, site in enumerate(self.sites):
xs.add_scatterer(xray.scatterer("C%i" % i, site=site))
xs = xs.sites_mod_short()
sites_cart = xs.sites_cart()
lengths = flex.double([matrix.col(sc).length() for sc in sites_cart])
perm = flex.sort_permutation(lengths)
xs = xs.select(perm)
volumes = self.volumes.select(perm)
vectors = xs.sites_cart()
norms = vectors.norms()
sel = (norms > self._min_cell) & (norms < (2 * self._max_cell))
vectors = vectors.select(sel)
vectors = [matrix.col(v) for v in vectors]
volumes = volumes.select(sel)
vector_groups = group_vectors(vectors, volumes)
vectors = [g.mean for g in vector_groups]
volumes = flex.double(max(g.weights) for g in vector_groups)
# sort by peak size
perm = flex.sort_permutation(volumes, reverse=True)
volumes = volumes.select(perm)
vectors = [vectors[i] for i in perm]
for i, (v, volume) in enumerate(zip(vectors, volumes)):
logger.debug(f"{i} {v.length()} {volume}")
# sort by length
lengths = flex.double(v.length() for v in vectors)
perm = flex.sort_permutation(lengths)
# exclude vectors that are (approximately) integer multiples of a shorter
# vector
unique_vectors = []
unique_volumes = flex.double()
for p in perm:
v = vectors[p]
is_unique = True
for i, v_u in enumerate(unique_vectors):
if (unique_volumes[i] > volumes[p]) and is_approximate_integer_multiple(
v_u, v
):
logger.debug(
"rejecting %s: integer multiple of %s", v.length(), v_u.length()
)
is_unique = False
break
if is_unique:
unique_vectors.append(v)
unique_volumes.append(volumes[p])
# re-sort by peak volume
perm = flex.sort_permutation(unique_volumes, reverse=True)
self.candidate_basis_vectors = [unique_vectors[i] for i in perm]
return self.candidate_basis_vectors, used_in_indexing
def _fft(self, reciprocal_lattice_vectors, d_min):
(
reciprocal_space_grid,
used_in_indexing,
) = self._map_centroids_to_reciprocal_space_grid(
reciprocal_lattice_vectors, d_min
)
logger.info(
"Number of centroids used: %i", (reciprocal_space_grid > 0).count(True)
)
# gb_to_bytes = 1073741824
# bytes_to_gb = 1/gb_to_bytes
# (128**3)*8*2*bytes_to_gb
# 0.03125
# (256**3)*8*2*bytes_to_gb
# 0.25
# (512**3)*8*2*bytes_to_gb
# 2.0
fft = fftpack.complex_to_complex_3d(self._gridding)
grid_complex = flex.complex_double(
reals=reciprocal_space_grid,
imags=flex.double(reciprocal_space_grid.size(), 0),
)
grid_transformed = fft.forward(grid_complex)
grid_real = flex.pow2(flex.real(grid_transformed))
del grid_transformed
return grid_real, used_in_indexing
def _map_centroids_to_reciprocal_space_grid(
self, reciprocal_lattice_vectors, d_min
):
logger.info("FFT gridding: (%i,%i,%i)" % self._gridding)
grid = flex.double(flex.grid(self._gridding), 0)
if self._params.b_iso is libtbx.Auto:
self._params.b_iso = -4 * d_min ** 2 * math.log(0.05)
logger.debug("Setting b_iso = %.1f", self._params.b_iso)
used_in_indexing = flex.bool(reciprocal_lattice_vectors.size(), True)
dials_algorithms_indexing_ext.map_centroids_to_reciprocal_space_grid(
grid,
reciprocal_lattice_vectors,
used_in_indexing, # do we really need this?
d_min,
b_iso=self._params.b_iso,
)
return grid, used_in_indexing
def _find_peaks(self, grid_real, d_min):
grid_real_binary = grid_real.deep_copy()
rmsd = math.sqrt(
flex.mean(
flex.pow2(
grid_real_binary.as_1d() - flex.mean(grid_real_binary.as_1d())
)
)
)
grid_real_binary.set_selected(
grid_real_binary < (self._params.rmsd_cutoff) * rmsd, 0
)
grid_real_binary.as_1d().set_selected(grid_real_binary.as_1d() > 0, 1)
grid_real_binary = grid_real_binary.iround()
from cctbx import masks
# real space FFT grid dimensions
cell_lengths = [self._n_points * d_min / 2 for i in range(3)]
self._fft_cell = uctbx.unit_cell(cell_lengths + [90] * 3)
flood_fill = masks.flood_fill(grid_real_binary, self._fft_cell)
if flood_fill.n_voids() < 4:
# Require at least peak at origin and one peak for each basis vector
raise indexing.DialsIndexError(
"Indexing failed: fft3d peak search failed to find sufficient number of peaks."
)
# the peak at the origin might have a significantly larger volume than the
# rest so exclude any anomalously large peaks from determining minimum volume
from scitbx.math import five_number_summary
outliers = flex.bool(flood_fill.n_voids(), False)
grid_points_per_void = flood_fill.grid_points_per_void()
min_x, q1_x, med_x, q3_x, max_x = five_number_summary(grid_points_per_void)
iqr_multiplier = 5
iqr_x = q3_x - q1_x
cut_x = iqr_multiplier * iqr_x
outliers.set_selected(grid_points_per_void.as_double() > (q3_x + cut_x), True)
# print q3_x + cut_x, outliers.count(True)
isel = (
grid_points_per_void
> int(
self._params.peak_volume_cutoff
* flex.max(grid_points_per_void.select(~outliers))
)
).iselection()
sites = flood_fill.centres_of_mass_frac().select(isel)
volumes = flood_fill.grid_points_per_void().select(isel)
return sites, volumes
