libpysal.weights.DistanceBand

class libpysal.weights.DistanceBand(data, threshold, p=2, alpha=-1.0, binary=True, ids=None, build_sp=True, silence_warnings=False, distance_metric='euclidean', radius=None)[source]

Spatial weights based on distance band.

Parameters
dataarray

(n,k) or KDTree where KDtree.data is array (n,k) n observations on k characteristics used to measure distances between the n objects

thresholdfloat

distance band

pfloat

Minkowski p-norm distance metric parameter: 1<=p<=infinity 2: Euclidean distance 1: Manhattan distance

binaryboolean

If true w_{ij}=1 if d_{i,j}<=threshold, otherwise w_{i,j}=0 If false wij=dij^{alpha}

alphafloat

distance decay parameter for weight (default -1.0) if alpha is positive the weights will not decline with distance. If binary is True, alpha is ignored

idslist

values to use for keys of the neighbors and weights dicts

build_spboolean

True to build sparse distance matrix and false to build dense distance matrix; significant speed gains may be obtained dending on the sparsity of the of distance_matrix and threshold that is applied

silentboolean

By default libpysal will print a warning if the dataset contains any disconnected observations or islands. To silence this warning set this parameter to True.

Notes

This was initially implemented running scipy 0.8.0dev (in epd 6.1). earlier versions of scipy (0.7.0) have a logic bug in scipy/sparse/dok.py so serge changed line 221 of that file on sal-dev to fix the logic bug.

Examples

>>> import libpysal
>>> points=[(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)]
>>> wcheck = libpysal.weights.W({0: [1, 3], 1: [0, 3], 2: [], 3: [0, 1], 4: [5], 5: [4]})

WARNING: there is one disconnected observation (no neighbors) Island id: [2] >>> w=libpysal.weights.DistanceBand(points,threshold=11.2)

WARNING: there is one disconnected observation (no neighbors) Island id: [2] >>> libpysal.weights.util.neighbor_equality(w, wcheck) True >>> w=libpysal.weights.DistanceBand(points,threshold=14.2) >>> wcheck = libpysal.weights.W({0: [1, 3], 1: [0, 3, 4], 2: [4], 3: [1, 0], 4: [5, 2, 1], 5: [4]}) >>> libpysal.weights.util.neighbor_equality(w, wcheck) True

inverse distance weights

>>> w=libpysal.weights.DistanceBand(points,threshold=11.2,binary=False)

WARNING: there is one disconnected observation (no neighbors) Island id: [2] >>> w.weights[0] [0.1, 0.08944271909999159] >>> w.neighbors[0].tolist() [1, 3]

gravity weights

>>> w=libpysal.weights.DistanceBand(points,threshold=11.2,binary=False,alpha=-2.)

WARNING: there is one disconnected observation (no neighbors) Island id: [2] >>> w.weights[0] [0.01, 0.007999999999999998]

Attributes
weightsdict

of neighbor weights keyed by observation id

neighborsdict

of neighbors keyed by observation id

Methods

asymmetry(self[, intrinsic])

Asymmetry check.

from_adjlist(adjlist[, focal_col, …])

Return an adjacency list representation of a weights object.

from_array(array, threshold, \*\*kwargs)

Construct a DistanceBand weights from an array.

from_dataframe(df, threshold[, geom_col, ids])

Make DistanceBand weights from a dataframe.

from_networkx(graph[, weight_col])

Convert a networkx graph to a PySAL W object.

from_shapefile(filepath, threshold[, idVariable])

Distance-band based weights from shapefile

full(self)

Generate a full numpy array.

get_transform(self)

Getter for transform property.

plot(self, gdf[, indexed_on, ax, color, …])

Plot spatial weights objects.

remap_ids(self, new_ids)

In place modification throughout W of id values from w.id_order to new_ids in all

set_shapefile(self, shapefile[, idVariable, …])

Adding meta data for writing headers of gal and gwt files.

set_transform(self[, value])

Transformations of weights.

symmetrize(self[, inplace])

Construct a symmetric KNN weight.

to_WSP(self)

Generate a WSP object.

to_adjlist(self[, remove_symmetric, …])

Compute an adjacency list representation of a weights object.

to_networkx(self)

Convert a weights object to a networkx graph

from_WSP

from_file

__init__(self, data, threshold, p=2, alpha=-1.0, binary=True, ids=None, build_sp=True, silence_warnings=False, distance_metric='euclidean', radius=None)[source]

Casting to floats is a work around for a bug in scipy.spatial. See detail in pysal issue #126.

Methods

__init__(self, data, threshold[, p, alpha, …])

Casting to floats is a work around for a bug in scipy.spatial.

asymmetry(self[, intrinsic])

Asymmetry check.

from_WSP(WSP[, silence_warnings])

from_adjlist(adjlist[, focal_col, …])

Return an adjacency list representation of a weights object.

from_array(array, threshold, \*\*kwargs)

Construct a DistanceBand weights from an array.

from_dataframe(df, threshold[, geom_col, ids])

Make DistanceBand weights from a dataframe.

from_file([path, format])

from_networkx(graph[, weight_col])

Convert a networkx graph to a PySAL W object.

from_shapefile(filepath, threshold[, idVariable])

Distance-band based weights from shapefile

full(self)

Generate a full numpy array.

get_transform(self)

Getter for transform property.

plot(self, gdf[, indexed_on, ax, color, …])

Plot spatial weights objects.

remap_ids(self, new_ids)

In place modification throughout W of id values from w.id_order to new_ids in all

set_shapefile(self, shapefile[, idVariable, …])

Adding meta data for writing headers of gal and gwt files.

set_transform(self[, value])

Transformations of weights.

symmetrize(self[, inplace])

Construct a symmetric KNN weight.

to_WSP(self)

Generate a WSP object.

to_adjlist(self[, remove_symmetric, …])

Compute an adjacency list representation of a weights object.

to_networkx(self)

Convert a weights object to a networkx graph

Attributes

asymmetries

List of id pairs with asymmetric weights.

cardinalities

Number of neighbors for each observation.

component_labels

Store the graph component in which each observation falls.

diagW2

Diagonal of \(WW\).

diagWtW

Diagonal of \(W^{'}W\).

diagWtW_WW

Diagonal of \(W^{'}W + WW\).

histogram

Cardinality histogram as a dictionary where key is the id and value is the number of neighbors for that unit.

id2i

Dictionary where the key is an ID and the value is that ID’s index in W.id_order.

id_order

Returns the ids for the observations in the order in which they would be encountered if iterating over the weights.

id_order_set

Returns True if user has set id_order, False if not.

islands

List of ids without any neighbors.

max_neighbors

Largest number of neighbors.

mean_neighbors

Average number of neighbors.

min_neighbors

Minimum number of neighbors.

n

Number of units.

n_components

Store whether the adjacency matrix is fully connected.

neighbor_offsets

Given the current id_order, neighbor_offsets[id] is the offsets of the id’s neighbors in id_order.

nonzero

Number of nonzero weights.

pct_nonzero

Percentage of nonzero weights.

s0

s0 is defined as

s1

s1 is defined as

s2

s2 is defined as

s2array

Individual elements comprising s2.

sd

Standard deviation of number of neighbors.

sparse

Sparse matrix object.

transform

Getter for transform property.

trcW2

Trace of \(WW\).

trcWtW

Trace of \(W^{'}W\).

trcWtW_WW

Trace of \(W^{'}W + WW\).