Locality Module¶
The locality module contains data structures to efficiently locate points based on their proximity to other points.
NeighborList¶

class
freud.locality.
NeighborList
¶ Class representing a certain number of “bonds” between particles. Computation methods will iterate over these bonds when searching for neighboring particles.
NeighborList objects are constructed for two sets of position arrays A (alternatively reference points; of length \(n_A\)) and B (alternatively target points; of length \(n_B\)) and hold a set of \(\left(i, j\right): i < n_A, j < n_B\) index pairs corresponding to nearneighbor points in A and B, respectively.
For efficiency, all bonds for a particular reference particle \(i\) are contiguous and bonds are stored in order based on reference particle index \(i\). The first bond index corresponding to a given particle can be found in \(\log(n_{bonds})\) time using
find_first_index()
.Module author: Matthew Spellings <mspells@umich.edu>
New in version 0.6.4.
Note
Typically, there is no need to instantiate this class directly. In most cases, users should manipulate
freud.locality.NeighborList
objects received from a neighbor search algorithm, such asfreud.locality.LinkCell
,freud.locality.NearestNeighbors
, orfreud.voronoi.Voronoi
.Example:
# Assume we have position as Nx3 array lc = LinkCell(box, 1.5).compute(box, positions) nlist = lc.nlist # Get all vectors from central particles to their neighbors rijs = positions[nlist.index_j]  positions[nlist.index_i] box.wrap(rijs)

copy
(self, other=None)¶ Create a copy. If other is given, copy its contents into this object. Otherwise, return a copy of this object.

filter
(self, filt)¶ Removes bonds that satisfy a boolean criterion.
Parameters: filt – Booleanlike array of bonds to keep (True means the bond stays) Note
This method modifies this object inplace.
Example:
# Keep only the bonds between particles of type A and type B nlist.filter(types[nlist.index_i] != types[nlist.index_j])

filter_r
(self, box, ref_points, points, float rmax, float rmin=0)¶ Removes bonds that are outside of a given radius range.
Parameters:  ref_points (
numpy.ndarray
, shape= \(\left(N_{points}, 3\right)\), dtype=numpy.float32
) – reference points to use for filtering  points (
numpy.ndarray
, shape= \(\left(N_{points}, 3\right)\), dtype=numpy.float32
) – target points to use for filtering  rmax (float) – maximum bond distance in the resulting neighbor list
 rmin (float) – minimum bond distance in the resulting neighbor list
Note
This method modifies this object inplace.
 ref_points (

find_first_index
(self, unsigned int i)¶ Returns the lowest bond index corresponding to a reference particle with an index \(\geq i\).

from_arrays
(type cls, Nref, Ntarget, index_i, index_j, weights=None)¶ Create a NeighborList from a set of bond information arrays.
Parameters:  Nref (unsigned int) – Number of reference points (corresponding to
index_i
)  Ntarget (unsigned int) – Number of target points (corresponding to
index_j
)  index_i (Arraylike of unsigned ints, length
num_bonds
) – Array of integers corresponding to indices in the set of reference points  index_j (Arraylike of unsigned ints, length
num_bonds
) – Array of integers corresponding to indices in the set of target points  weights (Arraylike of floats, length
num_bonds
) – Array of perbond weights (ifNone
is given, use a value of 1 for each weight)
 Nref (unsigned int) – Number of reference points (corresponding to

index_i
¶ The reference point indices from the last set of points this object was evaluated with. This array is readonly to prevent breakage of
find_first_index()
.

index_j
¶ The target point indices from the last set of points this object was evaluated with. This array is readonly to prevent breakage of
find_first_index()
.

neighbor_counts
¶ A neighbor count array, which is an array of length \(N_{ref}\) indicating the number of neighbors for each reference particle from the last set of points this object was evaluated with.

segments
¶ A segment array, which is an array of length \(N_{ref}\) indicating the first bond index for each reference particle from the last set of points this object was evaluated with.

weights
¶ The perbond weights from the last set of points this object was evaluated with.

LinkCell¶

class
freud.locality.
LinkCell
(box, cell_width)¶ Supports efficiently finding all points in a set within a certain distance from a given point.
Module author: Joshua Anderson <joaander@umich.edu>
Parameters:  box (
freud.box.Box
) – simulation box  cell_width (float) – Maximum distance to find particles within
Note
2D:
freud.locality.LinkCell
properly handles 2D boxes. The points must be passed in as[x, y, 0]
. Failing to set z=0 will lead to undefined behavior.Example:
# Assume positions are an Nx3 array lc = LinkCell(box, 1.5) lc.computeCellList(box, positions) for i in range(positions.shape[0]): # Cell containing particle i cell = lc.getCell(positions[0]) # List of cell's neighboring cells cellNeighbors = lc.getCellNeighbors(cell) # Iterate over neighboring cells (including our own) for neighborCell in cellNeighbors: # Iterate over particles in each neighboring cell for neighbor in lc.itercell(neighborCell): pass # Do something with neighbor index # Using NeighborList API dens = density.LocalDensity(1.5, 1, 1) dens.compute(box, positions, nlist=lc.nlist)

box
¶ freud Box.

compute
(self, box, ref_points, points=None, exclude_ii=None)¶ Update the data structure for the given set of points and compute a NeighborList
Parameters:  box (
freud.box.Box
) – simulation box  ref_points (
numpy.ndarray
, shape= \(\left(N_{refpoints}, 3\right)\), dtype=numpy.float32
) – reference point coordinates  points (
numpy.ndarray
, shape= \(\left(N_{points}, 3\right)\), dtype=numpy.float32
) – point coordinates  exclude_ii – True if pairs of points with identical indices should be excluded; if None, is set to True if points is None or the same object as ref_points
 box (

computeCellList
(self, box, ref_points, points=None, exclude_ii=None)¶ Update the data structure for the given set of points and compute a NeighborList
Parameters:  box (
freud.box.Box
) – simulation box  ref_points (
numpy.ndarray
, shape= \(\left(N_{refpoints}, 3\right)\), dtype=numpy.float32
) – reference point coordinates  points (
numpy.ndarray
, shape= \(\left(N_{points}, 3\right)\), dtype=numpy.float32
) – point coordinates  exclude_ii – True if pairs of points with identical indices should be excluded; if None, is set to True if points is None or the same object as ref_points
 box (

getBox
(self)¶ Get the freud Box.
Returns: freud Box Return type: freud.box.Box

getCell
(self, point)¶ Returns the index of the cell containing the given point.
Parameters: point ( numpy.ndarray
, shape= \(\left(3\right)\), dtype=numpy.float32
) – point coordinates \(\left(x,y,z\right)\)Returns: cell index Return type: unsigned int

getCellNeighbors
(self, cell)¶ Returns the neighboring cell indices of the given cell.
Parameters: cell (unsigned int) – Cell index Returns: array of cell neighbors Return type: numpy.ndarray
, shape= \(\left(N_{neighbors}\right)\), dtype=numpy.uint32

getNumCells
(self)¶ Get the number of cells in this box.
Returns: the number of cells in this box Return type: unsigned int

itercell
(self, unsigned int cell)¶ Return an iterator over all particles in the given cell.
Parameters: cell (unsigned int) – Cell index Returns: iterator to particle indices in specified cell Return type: iter

num_cells
¶ The number of cells in this box.
 box (
NearestNeighbors¶

class
freud.locality.
NearestNeighbors
(rmax, n_neigh, scale=1.1, strict_cut=False)¶ Supports efficiently finding the \(N\) nearest neighbors of each point in a set for some fixed integer \(N\).
strict_cut == True
:rmax
will be strictly obeyed, and any particle which has fewer than \(N\) neighbors will have values ofUINT_MAX
assigned.strict_cut == False
(default):rmax
will be expanded to find the requested number of neighbors. Ifrmax
increases to the point that a cell list cannot be constructed, a warning will be raised and the neighbors already found will be returned.
Module author: Eric Harper <harperic@umich.edu>
Parameters:  rmax (float) – Initial guess of a distance to search within to find N neighbors
 n_neigh (unsigned int) – Number of neighbors to find for each point
 scale (float) – Multiplier by which to automatically increase
rmax
value if the requested number of neighbors is not found. Only utilized ifstrict_cut
is False. Scale must be greater than 1.  strict_cut (bool) – Whether to use a strict
rmax
or allow for automatic expansion, default is False
Example:
nn = NearestNeighbors(2, 6) nn.compute(box, positions, positions) hexatic = order.HexOrderParameter(2) hexatic.compute(box, positions, nlist=nn.nlist)

UINTMAX
¶ Value of C++ UINTMAX used to pad the arrays.

box
¶ freud Box.

compute
(self, box, ref_points, points, exclude_ii=None)¶ Update the data structure for the given set of points.
Parameters:  box (
freud.box.Box
) – simulation box  ref_points (
numpy.ndarray
, shape=(\(N_{particles}\), 3), dtype=numpy.float32
) – coordinates of reference points  points (
numpy.ndarray
, shape=(\(N_{particles}\), 3), dtype=numpy.float32
) – coordinates of points  exclude_ii – True if pairs of points with identical indices should be excluded; if None, is set to True if points is None or the same object as ref_points
 box (

getBox
(self)¶ Get the freud Box.
Returns: freud Box Return type: freud.box.Box

getNRef
(self)¶ Get the number of particles this object found neighbors of.
Returns: the number of particles this object found neighbors of Return type: unsigned int

getNeighborList
(self)¶ Return the entire neighbor list.
Returns: Neighbor List Return type: numpy.ndarray
, shape= \(\left(N_{particles}, N_{neighbors}\right)\), dtype=numpy.uint32

getNeighbors
(self, unsigned int i)¶ Return the \(N\) nearest neighbors of the reference point with index \(i\).
Parameters: i (unsigned int) – index of the reference point whose neighbors will be returned

getNumNeighbors
(self)¶ The number of neighbors this object will find.
Returns: the number of neighbors this object will find Return type: unsigned int

getRMax
(self)¶ Return the current neighbor search distance guess.
Returns: nearest neighbors search radius Return type: float

getRsq
(self, unsigned int i)¶ Return the squared distances to the \(N\) nearest neighbors of the reference point with index \(i\).
Parameters: i (unsigned int) – index of the reference point of which to fetch the neighboring point distances Returns: squared distances to the \(N\) nearest neighbors Return type: numpy.ndarray
, shape= \(\left(N_{particles}\right)\), dtype=numpy.float32

getRsqList
(self)¶ Return the entire Rsq values list.
Returns: Rsq list Return type: numpy.ndarray
, shape= \(\left(N_{particles}, N_{neighbors}\right)\), dtype=numpy.float32

getUINTMAX
(self)¶ Returns: value of C++ UINTMAX used to pad the arrays Return type: unsigned int

getWrappedVectors
(self)¶ Return the wrapped vectors for computed neighbors. Array padded with 1 for empty neighbors.
Returns: wrapped vectors Return type: numpy.ndarray
, shape= \(\left(N_{particles}\right)\), dtype=numpy.float32

n_ref
¶ The number of particles this object found neighbors of.

num_neighbors
¶ The number of neighbors this object will find.

r_max
¶ Return the current neighbor search distance guess.
Returns: nearest neighbors search radius Return type: float

r_sq_list
¶ Return the entire Rsq values list.
Returns: Rsq list Return type: numpy.ndarray
, shape= \(\left(N_{particles}, N_{neighbors}\right)\), dtype=numpy.float32

setCutMode
(self, strict_cut)¶ Set mode to handle
rmax
by Nearest Neighbors.strict_cut == True
:rmax
will be strictly obeyed, and any particle which has fewer than \(N\) neighbors will have values ofUINT_MAX
assigned.strict_cut == False
:rmax
will be expanded to find the requested number of neighbors. Ifrmax
increases to the point that a cell list cannot be constructed, a warning will be raised and the neighbors already found will be returned.
Parameters: strict_cut (bool) – whether to use a strict rmax
or allow for automatic expansion

setRMax
(self, float rmax)¶ Update the neighbor search distance guess.
Parameters: rmax (float) – nearest neighbors search radius

wrapped_vectors
¶ Return the wrapped vectors for computed neighbors. Array padded with 1 for empty neighbors.