pysal.lib.weights.DistanceBand

class pysal.lib.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:
data : array

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

threshold : float

distance band

p : float

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

binary : boolean

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

alpha : float

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

ids : list

values to use for keys of the neighbors and weights dicts

build_sp : boolean

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

silent : boolean

By default pysal.lib 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 pysal.lib
>>> points=[(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)]
>>> wcheck = pysal.lib.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=pysal.lib.weights.distance.DistanceBand(points,threshold=11.2)

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

inverse distance weights

>>> w=pysal.lib.weights.distance.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=pysal.lib.weights.distance.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:
weights : dict

of neighbor weights keyed by observation id

neighbors : dict

of neighbors keyed by observation id

Methods

asymmetry([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() Generate a full numpy array.
get_transform() Getter for transform property.
plot(gdf[, indexed_on, ax, color, node_kws, …]) Plot spatial weights objects.
remap_ids(new_ids) In place modification throughout W of id values from w.id_order to new_ids in all
set_shapefile(shapefile[, idVariable, full]) Adding meta data for writing headers of gal and gwt files.
set_transform([value]) Transformations of weights.
symmetrize([inplace]) Construct a symmetric KNN weight.
to_WSP() Generate a WSP object.
to_adjlist([remove_symmetric, focal_col, …]) Compute an adjacency list representation of a weights object.
to_networkx() Convert a weights object to a networkx graph
from_WSP  
from_file  
__init__(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__(data, threshold[, p, alpha, …]) Casting to floats is a work around for a bug in scipy.spatial.
asymmetry([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() Generate a full numpy array.
get_transform() Getter for transform property.
plot(gdf[, indexed_on, ax, color, node_kws, …]) Plot spatial weights objects.
remap_ids(new_ids) In place modification throughout W of id values from w.id_order to new_ids in all
set_shapefile(shapefile[, idVariable, full]) Adding meta data for writing headers of gal and gwt files.
set_transform([value]) Transformations of weights.
symmetrize([inplace]) Construct a symmetric KNN weight.
to_WSP() Generate a WSP object.
to_adjlist([remove_symmetric, focal_col, …]) Compute an adjacency list representation of a weights object.
to_networkx() 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 \(W^{'}W + WW\).