libpysal.weights.W¶

class libpysal.weights.W(neighbors, weights=None, id_order=None, silence_warnings=False, ids=None)[source]¶

Spatial weights class.

Parameters:

Parameters:	neighbors : dictionary Key is region ID, value is a list of neighbor IDS. Example: {‘a’:[‘b’],’b’:[‘a’,’c’],’c’:[‘b’]} weights : dictionary Key is region ID, value is a list of edge weights. If not supplied all edge weights are assumed to have a weight of 1. Example: {‘a’:[0.5],’b’:[0.5,1.5],’c’:[1.5]} id_order : list An ordered list of ids, defines the order of observations when iterating over W if not set, lexicographical ordering is used to iterate and the id_order_set property will return False. This can be set after creation by setting the ‘id_order’ property. silent_island_warning: boolean 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. silent_connected_components : boolean By default PySAL will print a warning if the dataset contains any disconnected components in the adjacency matrix. These are disconnected groups of islands. To silence this warning set this parameter to True. ids : list Values to use for keys of the neighbors and weights dicts. Attributes (NOTE: these are described by their docstrings. to view, use the `help` function) ———- asymmetries cardinalities component_labels diagW2 diagWtW diagWtW_WW histogram id2i id_order id_order_set islands max_neighbors mean_neighbors min_neighbors n n_components neighbor_offsets nonzero pct_nonzero s0 s1 s2 s2array sd sparse trcW2 trcWtW trcWtW_WW transform

neighbors : dictionary

Key is region ID, value is a list of neighbor IDS. Example: {‘a’:[‘b’],’b’:[‘a’,’c’],’c’:[‘b’]}

weights : dictionary

Key is region ID, value is a list of edge weights. If not supplied all edge weights are assumed to have a weight of 1. Example: {‘a’:[0.5],’b’:[0.5,1.5],’c’:[1.5]}

id_order : list

An ordered list of ids, defines the order of observations when iterating over W if not set, lexicographical ordering is used to iterate and the id_order_set property will return False. This can be set after creation by setting the ‘id_order’ property.

silent_island_warning: boolean

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.

silent_connected_components : boolean

By default PySAL will print a warning if the dataset contains any disconnected components in the adjacency matrix. These are disconnected groups of islands. To silence this warning set this parameter to True.

ids : list

Values to use for keys of the neighbors and weights dicts.

Attributes (NOTE: these are described by their docstrings. to view, use the `help` function)

———-

asymmetries

cardinalities

component_labels

diagW2

diagWtW

diagWtW_WW

histogram

id2i

id_order

id_order_set

islands

max_neighbors

mean_neighbors

min_neighbors

n_components

neighbor_offsets

nonzero

pct_nonzero

s2array

sparse

trcW2

trcWtW

trcWtW_WW

transform

Examples

>>> from libpysal.weights.weights import W
>>> neighbors = {0: [3, 1], 1: [0, 4, 2], 2: [1, 5], 3: [0, 6, 4], 4: [1, 3, 7, 5], 5: [2, 4, 8], 6: [3, 7], 7: [4, 6, 8], 8: [5, 7]}
>>> weights = {0: [1, 1], 1: [1, 1, 1], 2: [1, 1], 3: [1, 1, 1], 4: [1, 1, 1, 1], 5: [1, 1, 1], 6: [1, 1], 7: [1, 1, 1], 8: [1, 1]}
>>> w = W(neighbors, weights)
>>> "%.3f"%w.pct_nonzero
'29.630'

Read from external gal file

>>> import libpysal
>>> w = libpysal.io.open(libpysal.examples.get_path("stl.gal")).read()
>>> w.n
78
>>> "%.3f"%w.pct_nonzero
'6.542'

Set weights implicitly

>>> neighbors = {0: [3, 1], 1: [0, 4, 2], 2: [1, 5], 3: [0, 6, 4], 4: [1, 3, 7, 5], 5: [2, 4, 8], 6: [3, 7], 7: [4, 6, 8], 8: [5, 7]}
>>> w = W(neighbors)
>>> round(w.pct_nonzero,3)
29.63
>>> from libpysal.weights import lat2W
>>> w = lat2W(100, 100)
>>> w.trcW2
39600.0
>>> w.trcWtW
39600.0
>>> w.transform='r'
>>> round(w.trcW2, 3)
2530.722
>>> round(w.trcWtW, 3)
2533.667

Cardinality Histogram >>> w.histogram [(2, 4), (3, 392), (4, 9604)]

Disconnected observations (islands)

>>> from libpysal.weights import W
>>> w = W({1:[0],0:[1],2:[], 3:[]})

WARNING: there are 2 disconnected observations Island ids: [2, 3]

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

Methods

`asymmetry`([intrinsic])	Asymmetry check.
`from_WSP`(WSP[, silence_warnings])
`from_adjlist`(adjlist[, focal_col, …])	Return an adjacency list representation of a weights object.
`from_file`([path, format])
`from_networkx`(graph[, weight_col])	Convert a networkx graph to a PySAL W object.
`from_shapefile`(args, *kwargs)
`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

__init__(neighbors, weights=None, id_order=None, silence_warnings=False, ids=None)[source]¶: Initialize self. See help(type(self)) for accurate signature.

Methods

`__init__`(neighbors[, weights, id_order, …])	Initialize self.
`asymmetry`([intrinsic])	Asymmetry check.
`from_WSP`(WSP[, silence_warnings])
`from_adjlist`(adjlist[, focal_col, …])	Return an adjacency list representation of a weights object.
`from_file`([path, format])
`from_networkx`(graph[, weight_col])	Convert a networkx graph to a PySAL W object.
`from_shapefile`(args, *kwargs)
`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 \(W^{'}W + WW\).