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

binarybool

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_spbool

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

silentbool

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

__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])

Read a weights file into a W object.

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.ndarray.

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 metadata 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_file(self[, path, format])

Write a weights to a file.

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

classmethod from_array(array, threshold, **kwargs)[source]

Construct a DistanceBand weights from an array. Supports all the same options as libpysal.weights.DistanceBand

classmethod from_dataframe(df, threshold, geom_col='geometry', ids=None, **kwargs)[source]

Make DistanceBand weights from a dataframe.

Parameters
dfpandas.dataframe

a dataframe with a geometry column that can be used to construct a W object

geom_colstr

column name of the geometry stored in df

idsstr or iterable

if string, the column name of the indices from the dataframe if iterable, a list of ids to use for the W if None, df.index is used.

classmethod from_shapefile(filepath, threshold, idVariable=None, **kwargs)[source]

Distance-band based weights from shapefile

Parameters
shapefilestr

shapefile name with shp suffix

idVariablestr

name of column in shapefile’s DBF to use for ids

Returns
Kernel Weights Object