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 near-neighbor 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 as freud.locality.LinkCell, freud.locality.NearestNeighbors, or freud.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 – Boolean-like array of bonds to keep (True means the bond stays)

Note

This method modifies this object in-place.

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 in-place.

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 (Array-like of unsigned ints, length num_bonds) – Array of integers corresponding to indices in the set of reference points
index_j (Array-like of unsigned ints, length num_bonds) – Array of integers corresponding to indices in the set of target points
weights (Array-like of floats, length num_bonds) – Array of per-bond weights (if None is given, use a value of 1 for each weight)

index_i¶: The reference point indices from the last set of points this object was evaluated with. This array is read-only 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 read-only 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 per-bond 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

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

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

nlist¶: The neighbor list stored by this object, generated by compute().

num_cells¶: The number of cells in this 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 of UINT_MAX assigned.
strict_cut == False (default): rmax will be expanded to find the requested number of neighbors. If rmax 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 if strict_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

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.

nlist¶: Returns the neighbor list stored by this object, generated by compute().

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 of UINT_MAX assigned.
strict_cut == False: rmax will be expanded to find the requested number of neighbors. If rmax 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.