import copy
import numbers
import os
from collections import defaultdict
from itertools import tee
from warnings import warn
import numpy as np
# ruff: noqa: N802, N803
import scipy
import scipy.spatial
from packaging.version import Version
from scipy import sparse
from scipy.spatial import KDTree
from ..common import requires
from ..io.fileio import FileIO
from .set_operations import w_subset
from .weights import WSP, W
try:
import geopandas as gpd
GPD_013 = Version(gpd.__version__) >= Version("0.13.0")
except ImportError:
warn("geopandas not available. Some functionality will be disabled.", stacklevel=2)
try:
from shapely.geometry.base import BaseGeometry
HAS_SHAPELY = True
except ImportError:
HAS_SHAPELY = False
__all__ = [
"lat2W",
"block_weights",
"comb",
"order",
"higher_order",
"shimbel",
"remap_ids",
"full2W",
"full",
"WSP2W",
"insert_diagonal",
"fill_diagonal",
"get_ids",
"get_points_array_from_shapefile",
"min_threshold_distance",
"lat2SW",
"w_local_cluster",
"higher_order_sp",
"hexLat2W",
"neighbor_equality",
"attach_islands",
"nonplanar_neighbors",
"fuzzy_contiguity",
]
KDTREE_TYPES = [scipy.spatial.KDTree, scipy.spatial.cKDTree]
[docs]
def hexLat2W(nrows=5, ncols=5, **kwargs):
"""
Create a W object for a hexagonal lattice.
Parameters
----------
nrows : int
number of rows
ncols : int
number of columns
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
w : W
instance of spatial weights class W
Notes
-----
Observations are row ordered: first k observations are in row 0,
next k in row 1, and so on.
Construction is based on shifting every other column of a regular lattice
down 1/2 of a cell.
Examples
--------
>>> from libpysal.weights import lat2W, hexLat2W
>>> w = lat2W()
>>> w.neighbors[1]
[0, 6, 2]
>>> w.neighbors[21]
[16, 20, 22]
>>> wh = hexLat2W()
>>> wh.neighbors[1]
[0, 6, 2, 5, 7]
>>> wh.neighbors[21]
[16, 20, 22]
"""
if nrows == 1 or ncols == 1:
print("Hexagon lattice requires at least 2 rows and columns")
print("Returning a linear contiguity structure")
return lat2W(nrows, ncols)
n = nrows * ncols
rid = [i // ncols for i in range(n)]
cid = [i % ncols for i in range(n)]
r1 = nrows - 1
c1 = ncols - 1
w = lat2W(nrows, ncols).neighbors
for i in range(n):
odd = cid[i] % 2
if odd:
if rid[i] < r1: # odd col index above last row
# new sw neighbor
if cid[i] > 0:
j = i + ncols - 1
w[i] = w.get(i, []) + [j]
# new se neighbor
if cid[i] < c1:
j = i + ncols + 1
w[i] = w.get(i, []) + [j]
else: # even col
# nw
jnw = [i - ncols - 1]
# ne
jne = [i - ncols + 1]
if rid[i] > 0:
w[i]
if cid[i] == 0:
w[i] = w.get(i, []) + jne
elif cid[i] == c1:
w[i] = w.get(i, []) + jnw
else:
w[i] = w.get(i, []) + jne
w[i] = w.get(i, []) + jnw
return W(w, **kwargs)
[docs]
def lat2W(nrows=5, ncols=5, rook=True, id_type="int", **kwargs):
"""
Create a W object for a regular lattice.
Parameters
----------
nrows : int
number of rows
ncols : int
number of columns
rook : boolean
type of contiguity. Default is rook. For queen, rook =False
id_type : string
string defining the type of IDs to use in the final W object;
options are 'int' (0, 1, 2 ...; default), 'float' (0.0,
1.0, 2.0, ...) and 'string' ('id0', 'id1', 'id2', ...)
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
w : W
instance of spatial weights class W
Notes
-----
Observations are row ordered: first k observations are in row 0,
next k in row 1, and so on.
Examples
--------
>>> from libpysal.weights import lat2W
>>> w9 = lat2W(3,3)
>>> "%.3f"%w9.pct_nonzero
'29.630'
>>> w9[0] == {1: 1.0, 3: 1.0}
True
>>> w9[3] == {0: 1.0, 4: 1.0, 6: 1.0}
True
"""
n = nrows * ncols
r1 = nrows - 1
c1 = ncols - 1
rid = [i // ncols for i in range(n)] # must be floor!
cid = [i % ncols for i in range(n)]
w = {}
r = below = 0
for i in range(n - 1):
if rid[i] < r1:
below = rid[i] + 1
r = below * ncols + cid[i]
w[i] = w.get(i, []) + [r]
w[r] = w.get(r, []) + [i]
if cid[i] < c1:
right = cid[i] + 1
c = rid[i] * ncols + right
w[i] = w.get(i, []) + [c]
w[c] = w.get(c, []) + [i]
if not rook:
# southeast bishop
if cid[i] < c1 and rid[i] < r1:
r = (rid[i] + 1) * ncols + 1 + cid[i]
w[i] = w.get(i, []) + [r]
w[r] = w.get(r, []) + [i]
# southwest bishop
if cid[i] > 0 and rid[i] < r1:
r = (rid[i] + 1) * ncols - 1 + cid[i]
w[i] = w.get(i, []) + [r]
w[r] = w.get(r, []) + [i]
weights = {}
for key in w:
weights[key] = [1.0] * len(w[key])
ids = list(range(n))
if id_type == "string":
ids = ["id" + str(i) for i in ids]
elif id_type == "float":
ids = [i * 1.0 for i in ids]
if id_type == "string" or id_type == "float":
id_dict = dict(list(zip(list(range(n)), ids, strict=True)))
alt_w = {}
alt_weights = {}
for i in w:
values = [id_dict[j] for j in w[i]]
key = id_dict[i]
alt_w[key] = values
alt_weights[key] = weights[i]
w = alt_w
weights = alt_weights
return W(w, weights, ids=ids, id_order=ids[:], **kwargs)
[docs]
def block_weights(regimes, ids=None, sparse=False, **kwargs):
"""
Construct spatial weights for regime neighbors.
Block contiguity structures are relevant when defining neighbor relations
based on membership in a regime. For example, all counties belonging to
the same state could be defined as neighbors, in an analysis of all
counties in the US.
Parameters
----------
regimes : list, array
ids of which regime an observation belongs to
ids : list, array
Ordered sequence of IDs for the observations
sparse : boolean
If True return WSP instance
If False return W instance
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
W : spatial weights instance
Examples
--------
>>> from libpysal.weights import block_weights
>>> import numpy as np
>>> regimes = np.ones(25)
>>> regimes[range(10,20)] = 2
>>> regimes[range(21,25)] = 3
>>> regimes
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 2., 2., 2., 2., 2., 2.,
2., 2., 2., 1., 3., 3., 3., 3.])
>>> w = block_weights(regimes)
>>> w.weights[0]
[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
>>> w.neighbors[0]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 20]
>>> regimes = ['n','n','s','s','e','e','w','w','e']
>>> n = len(regimes)
>>> w = block_weights(regimes)
>>> w.neighbors == {0: [1], 1: [0], 2: [3], 3: [2], 4: [5, 8], 5: [4, 8], 6: [7], 7: [6], 8: [4, 5]}
True
""" # noqa: E501
rids = np.unique(regimes)
neighbors = {}
npnz = np.nonzero
regimes = np.array(regimes)
for rid in rids:
members = npnz(regimes == rid)[0]
for member in members:
neighbors[member] = members[npnz(members != member)[0]].tolist()
w = W(neighbors, **kwargs)
if ids is not None:
w.remap_ids(ids)
if sparse:
w = WSP(w.sparse, id_order=ids)
return w
[docs]
def comb(items, n=None):
"""
Combinations of size n taken from items
Parameters
----------
items : list
items to be drawn from
n : integer
size of combinations to take from items
Returns
-------
implicit : generator
combinations of size n taken from items
Examples
--------
>>> x = range(4)
>>> for c in comb(x, 2):
... print(c)
...
[0, 1]
[0, 2]
[0, 3]
[1, 2]
[1, 3]
[2, 3]
"""
items = list(items)
if n is None:
n = len(items)
for i in list(range(len(items))):
v = items[i : i + 1]
if n == 1:
yield v
else:
rest = items[i + 1 :]
for c in comb(rest, n - 1):
yield v + c
[docs]
def order(w, kmax=3):
"""
Determine the non-redundant order of contiguity up to a specific
order.
Parameters
----------
w : W
spatial weights object
kmax : int
maximum order of contiguity
Returns
-------
info : dictionary
observation id is the key, value is a list of contiguity
orders with a negative 1 in the ith position
Notes
-----
Implements the algorithm in :cite:`Anselin1996b`.
Examples
--------
>>> from libpysal.weights import order, Rook
>>> import libpysal
>>> w = Rook.from_shapefile(libpysal.examples.get_path('10740.shp'))
WARNING: there is one disconnected observation (no neighbors)
Island id: [163]
>>> w3 = order(w, kmax = 3)
>>> w3[1][0:5]
[1, -1, 1, 2, 1]
"""
ids = w.id_order
info = {}
for id_ in ids:
s = [0] * w.n
s[ids.index(id_)] = -1
for j in w.neighbors[id_]:
s[ids.index(j)] = 1
k = 1
while k < kmax:
knext = k + 1
if s.count(k):
# get neighbors of order k
js = [ids[j] for j, val in enumerate(s) if val == k]
# get first order neighbors for order k neighbors
for j in js:
next_neighbors = w.neighbors[j]
for neighbor in next_neighbors:
nid = ids.index(neighbor)
if s[nid] == 0:
s[nid] = knext
k = knext
info[id_] = s
return info
[docs]
def higher_order(w, k=2, **kwargs):
"""
Contiguity weights object of order k.
Parameters
----------
w : W
spatial weights object
k : int
order of contiguity
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
implicit : W
spatial weights object
Notes
-----
Proper higher order neighbors are returned such that i and j are k-order
neighbors iff the shortest path from i-j is of length k.
Examples
--------
>>> from libpysal.weights import lat2W, higher_order
>>> w10 = lat2W(10, 10)
>>> w10_2 = higher_order(w10, 2)
>>> w10_2[0] == {2: 1.0, 11: 1.0, 20: 1.0}
True
>>> w5 = lat2W()
>>> w5[0] == {1: 1.0, 5: 1.0}
True
>>> w5[1] == {0: 1.0, 2: 1.0, 6: 1.0}
True
>>> w5_2 = higher_order(w5,2)
>>> w5_2[0] == {10: 1.0, 2: 1.0, 6: 1.0}
True
"""
return higher_order_sp(w, k, **kwargs)
[docs]
def higher_order_sp(
w, k=2, shortest_path=True, diagonal=False, lower_order=False, **kwargs
):
"""
Contiguity weights for either a sparse W or W for order k.
Parameters
----------
w : W
sparse_matrix, spatial weights object or
scipy.sparse.csr.csr_instance
k : int
Order of contiguity
shortest_path : boolean
True: i,j and k-order neighbors if the
shortest path for i,j is k.
False: i,j are k-order neighbors if there
is a path from i,j of length k.
diagonal : boolean
True: keep k-order (i,j) joins when i==j
False: remove k-order (i,j) joins when i==j
lower_order : boolean
True: include lower order contiguities
False: return only weights of order k
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
wk : W
WSP, type matches type of w argument
Examples
--------
>>> from libpysal.weights import lat2W, higher_order_sp
>>> w25 = lat2W(5,5)
>>> w25.n
25
>>> w25[0] == {1: 1.0, 5: 1.0}
True
>>> w25_2 = higher_order_sp(w25, 2)
>>> w25_2[0] == {10: 1.0, 2: 1.0, 6: 1.0}
True
>>> w25_2 = higher_order_sp(w25, 2, diagonal=True)
>>> w25_2[0] == {0: 1.0, 10: 1.0, 2: 1.0, 6: 1.0}
True
>>> w25_3 = higher_order_sp(w25, 3)
>>> w25_3[0] == {15: 1.0, 3: 1.0, 11: 1.0, 7: 1.0}
True
>>> w25_3 = higher_order_sp(w25, 3, shortest_path=False)
>>> w25_3[0] == {1: 1.0, 3: 1.0, 5: 1.0, 7: 1.0, 11: 1.0, 15: 1.0}
True
>>> w25_3 = higher_order_sp(w25, 3, lower_order=True)
>>> w25_3[0] == {
... 5: 1.0, 7: 1.0, 11: 1.0, 2: 1.0, 15: 1.0, 6: 1.0, 10: 1.0, 1: 1.0, 3: 1.0
... }
True
"""
id_order = None
if issubclass(type(w), W) or isinstance(w, W):
if np.unique(np.hstack(list(w.weights.values()))) == np.array([1.0]):
id_order = w.id_order
w = w.sparse
else:
raise ValueError("Weights are not binary (0,1)")
elif scipy.sparse.isspmatrix_csr(w):
if not np.unique(w.data) == np.array([1.0]):
raise ValueError(
"Sparse weights matrix is not binary (0,1) weights matrix."
)
else:
raise TypeError(
"Weights provided are neither a binary W object nor "
"a scipy.sparse.csr_matrix"
)
if lower_order:
wk = sum(w**x for x in range(1, k + 1))
shortest_path = False
else:
wk = w**k
rk, ck = wk.nonzero()
sk = set(zip(rk, ck, strict=True))
if shortest_path:
for j in range(1, k):
wj = w**j
rj, cj = wj.nonzero()
sj = set(zip(rj, cj, strict=True))
sk.difference_update(sj)
if not diagonal:
sk = {(i, j) for i, j in sk if i != j}
if id_order:
d = {i: [] for i in id_order}
for pair in sk:
k, v = pair
k = id_order[k]
v = id_order[v]
d[k].append(v)
return W(neighbors=d, **kwargs)
else:
d = {}
for pair in sk:
k, v = pair
if k in d:
d[k].append(v)
else:
d[k] = [v]
return WSP(W(neighbors=d, **kwargs).sparse)
[docs]
def w_local_cluster(w):
r"""
Local clustering coefficients for each unit as a node in a graph.
Parameters
----------
w : W
spatial weights object
Returns
-------
c : array
(w.n,1)
local clustering coefficients
Notes
-----
The local clustering coefficient :math:`c_i` quantifies how close the
neighbors of observation :math:`i` are to being a clique:
.. math::
c_i = | \{w_{j,k}\} |/ (k_i(k_i - 1)): j,k \in N_i
where :math:`N_i` is the set of neighbors to :math:`i`, :math:`k_i =
|N_i|` and :math:`\{w_{j,k}\}` is the set of non-zero elements of the
weights between pairs in :math:`N_i` :cite:`Watts1998`.
Examples
--------
>>> from libpysal.weights import lat2W, w_local_cluster
>>> w = lat2W(3,3, rook=False)
>>> w_local_cluster(w)
array([[1. ],
[0.6 ],
[1. ],
[0.6 ],
[0.42857143],
[0.6 ],
[1. ],
[0.6 ],
[1. ]])
"""
c = np.zeros((w.n, 1), float)
w.transformation = "b"
for i, id_ in enumerate(w.id_order):
ki = max(w.cardinalities[id_], 1) # deal with islands
ni = w.neighbors[id_]
wi = w_subset(w, ni).full()[0]
c[i] = wi.sum() / (ki * (ki - 1))
return c
[docs]
def shimbel(w):
"""
Find the Shimbel matrix for first order contiguity matrix.
Parameters
----------
w : W
spatial weights object
Returns
-------
info : list
list of lists; one list for each observation which stores
the shortest order between it and each of the the other observations.
Examples
--------
>>> from libpysal.weights import lat2W, shimbel
>>> w5 = lat2W()
>>> w5_shimbel = shimbel(w5)
>>> w5_shimbel[0][24]
8
>>> w5_shimbel[0][0:4]
[-1, 1, 2, 3]
"""
info = {}
ids = w.id_order
for i in ids:
s = [0] * w.n
s[ids.index(i)] = -1
for j in w.neighbors[i]:
s[ids.index(j)] = 1
k = 1
flag = s.count(0)
while flag:
p = -1
knext = k + 1
for _ in range(s.count(k)):
neighbor = s.index(k, p + 1)
p = neighbor
next_neighbors = w.neighbors[ids[p]]
for neighbor in next_neighbors:
nid = ids.index(neighbor)
if s[nid] == 0:
s[nid] = knext
k = knext
flag = s.count(0)
info[i] = s
return info
[docs]
def full(w):
"""
Generate a full numpy array.
Parameters
----------
w : W
spatial weights object
Returns
-------
(fullw, keys) : tuple
first element being the full numpy array and second element
keys being the ids associated with each row in the array.
Examples
--------
>>> from libpysal.weights import W, full
>>> neighbors = {'first':['second'],'second':['first','third'],'third':['second']}
>>> weights = {'first':[1],'second':[1,1],'third':[1]}
>>> w = W(neighbors, weights)
>>> wf, ids = full(w)
>>> wf
array([[0., 1., 0.],
[1., 0., 1.],
[0., 1., 0.]])
>>> ids
['first', 'second', 'third']
"""
return w.full()
[docs]
def full2W(m, ids=None, **kwargs):
"""
Create a PySAL W object from a full array.
Parameters
----------
m : array
nxn array with the full weights matrix
ids : list
User ids assumed to be aligned with m
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
w : W
PySAL weights object
Examples
--------
>>> from libpysal.weights import full2W
>>> import numpy as np
Create an array of zeros
>>> a = np.zeros((4, 4))
For loop to fill it with random numbers
>>> for i in range(len(a)):
... for j in range(len(a[i])):
... if i!=j:
... a[i, j] = np.random.random(1)
Create W object
>>> w = full2W(a)
>>> w.full()[0] == a
array([[ True, True, True, True],
[ True, True, True, True],
[ True, True, True, True],
[ True, True, True, True]])
Create list of user ids
>>> ids = ['myID0', 'myID1', 'myID2', 'myID3']
>>> w = full2W(a, ids=ids)
>>> w.full()[0] == a
array([[ True, True, True, True],
[ True, True, True, True],
[ True, True, True, True],
[ True, True, True, True]])
"""
if m.shape[0] != m.shape[1]:
raise ValueError("Your array is not square")
neighbors, weights = {}, {}
for i in range(m.shape[0]):
# for i, row in enumerate(m):
row = m[i]
if ids:
i = ids[i]
ngh = list(row.nonzero()[0])
weights[i] = list(row[ngh])
ngh = list(ngh)
if ids:
ngh = [ids[j] for j in ngh]
neighbors[i] = ngh
return W(neighbors, weights, id_order=ids, **kwargs)
[docs]
def WSP2W(wsp, **kwargs):
"""
Convert a pysal WSP object (thin weights matrix) to a pysal W object.
Parameters
----------
wsp : WSP
PySAL sparse weights object
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
w : W
PySAL weights object
Examples
--------
>>> from libpysal.weights import lat2W, WSP, WSP2W
Build a 10x10 scipy.sparse matrix for a rectangular 2x5 region of cells
(rook contiguity), then construct a PySAL sparse weights object (wsp).
>>> sp = lat2SW(2, 5)
>>> wsp = WSP(sp)
>>> wsp.n
10
>>> wsp.sparse[0].todense()
matrix([[0, 1, 0, 0, 0, 1, 0, 0, 0, 0]], dtype=int8)
Convert this sparse weights object to a standard PySAL weights object.
>>> w = WSP2W(wsp)
>>> w.n
10
>>> print(w.full()[0][0])
[0. 1. 0. 0. 0. 1. 0. 0. 0. 0.]
"""
data = wsp.sparse.data
indptr = wsp.sparse.indptr
id_order = wsp.id_order
if id_order:
# replace indices with user IDs
indices = [id_order[i] for i in wsp.sparse.indices]
else:
id_order = list(range(wsp.n))
neighbors, weights = {}, {}
start = indptr[0]
for i in range(wsp.n):
oid = id_order[i]
end = indptr[i + 1]
neighbors[oid] = indices[start:end]
weights[oid] = data[start:end].tolist()
start = end
ids = copy.copy(wsp.id_order)
w = W(neighbors, weights, ids, **kwargs)
w._sparse = copy.deepcopy(wsp.sparse)
w._cache["sparse"] = w._sparse
return w
def insert_diagonal(w, val=1.0, wsp=False):
warn("This function is deprecated. Use fill_diagonal instead.", stacklevel=2)
return fill_diagonal(w, val=val, wsp=wsp)
[docs]
def fill_diagonal(w, val=1.0, wsp=False):
"""
Returns a new weights object with values inserted along the main diagonal.
Parameters
----------
w : W
Spatial weights object
diagonal : float, int or array
Defines the value(s) to which the weights matrix diagonal should
be set. If a constant is passed then each element along the
diagonal will get this value (default is 1.0). An array of length
w.n can be passed to set explicit values to each element along
the diagonal (assumed to be in the same order as w.id_order).
wsp : boolean
If True return a thin weights object of the type WSP, if False
return the standard W object.
Returns
-------
w : W
Spatial weights object
Examples
--------
>>> from libpysal.weights import lat2W
>>> import numpy as np
Build a basic rook weights matrix, which has zeros on the diagonal, then
insert ones along the diagonal.
>>> w = lat2W(5, 5, id_type='string')
>>> w_const = insert_diagonal(w)
>>> w['id0'] == {'id5': 1.0, 'id1': 1.0}
True
>>> w_const['id0'] == {'id5': 1.0, 'id0': 1.0, 'id1': 1.0}
True
Insert different values along the main diagonal.
>>> diag = np.arange(100, 125)
>>> w_var = insert_diagonal(w, diag)
>>> w_var['id0'] == {'id5': 1.0, 'id0': 100.0, 'id1': 1.0}
True
"""
w_new = copy.deepcopy(w.sparse)
w_new = w_new.tolil()
if issubclass(type(val), np.ndarray):
if w.n != val.shape[0]:
raise Exception("shape of w and diagonal do not match")
w_new.setdiag(val)
elif isinstance(val, numbers.Number):
w_new.setdiag([val] * w.n)
else:
raise Exception("Invalid value passed to diagonal")
w_out = WSP(w_new, copy.copy(w.id_order))
if wsp:
return w_out
else:
return WSP2W(w_out)
[docs]
def remap_ids(w, old2new, id_order=[], **kwargs): # noqa: B006
"""
Remaps the IDs in a spatial weights object.
Parameters
----------
w : W
Spatial weights object
old2new : dictionary
Dictionary where the keys are the IDs in w (i.e. "old IDs") and
the values are the IDs to replace them (i.e. "new IDs")
id_order : list
An ordered list of new IDs, which defines the order of observations when
iterating over W. If not set then the id_order in w will be
used.
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
implicit : W
Spatial weights object with new IDs
Examples
--------
>>> from libpysal.weights import lat2W
>>> w = lat2W(3,2)
>>> w.id_order
[0, 1, 2, 3, 4, 5]
>>> w.neighbors[0]
[2, 1]
>>> old_to_new = {0:'a', 1:'b', 2:'c', 3:'d', 4:'e', 5:'f'}
>>> w_new = remap_ids(w, old_to_new)
>>> w_new.id_order
['a', 'b', 'c', 'd', 'e', 'f']
>>> w_new.neighbors['a']
['c', 'b']
"""
if not isinstance(w, W):
raise Exception("w must be a spatial weights object")
new_neigh = {}
new_weights = {}
for key, value in list(w.neighbors.items()):
new_values = [old2new[i] for i in value]
new_key = old2new[key]
new_neigh[new_key] = new_values
new_weights[new_key] = copy.copy(w.weights[key])
if id_order:
return W(new_neigh, new_weights, id_order, **kwargs)
else:
if w.id_order:
id_order = [old2new[i] for i in w.id_order]
return W(new_neigh, new_weights, id_order, **kwargs)
else:
return W(new_neigh, new_weights, **kwargs)
[docs]
def get_ids(in_shps, idVariable):
"""
Gets the IDs from the DBF file that moves with a given shape file or
a geopandas.GeoDataFrame.
Parameters
----------
in_shps : str or geopandas.GeoDataFrame
The input geographic data. Either
(1) a path to a shapefile including suffix (str); or
(2) a geopandas.GeoDataFrame.
idVariable : str
name of a column in the shapefile's DBF or the
geopandas.GeoDataFrame to use for ids.
Returns
-------
ids : list
a list of IDs
Examples
--------
>>> from libpysal.weights.util import get_ids
>>> import libpysal
>>> polyids = get_ids(libpysal.examples.get_path("columbus.shp"), "POLYID")
>>> polyids[:5]
[1, 2, 3, 4, 5]
>>> from libpysal.weights.util import get_ids
>>> import libpysal
>>> import geopandas as gpd
>>> gdf = gpd.read_file(libpysal.examples.get_path("columbus.shp"))
>>> polyids = gdf["POLYID"]
>>> polyids[:5]
0 1
1 2
2 3
3 4
4 5
Name: POLYID, dtype: int64
"""
try:
if isinstance(in_shps, str):
dbname = os.path.splitext(in_shps)[0] + ".dbf"
db = FileIO(dbname)
cols = db.header
var = db.by_col[idVariable]
db.close()
else:
cols = list(in_shps.columns)
var = list(in_shps[idVariable])
return var
except OSError:
msg = (
f'The shapefile "{in_shps}" appears to be missing its DBF file. '
f' The DBF file "{dbname}" could not be found.'
)
raise OSError(msg) from None
except (AttributeError, KeyError):
msg = (
f'The variable "{idVariable}" not found in the DBF/GDF. '
f"The the following variables are present: {','.join(cols)}."
)
raise KeyError(msg) from None
def get_points_array(iterable):
"""
Gets a data array of x and y coordinates from a given iterable
Parameters
----------
iterable : iterable
arbitrary collection of shapes that supports iteration
Returns
-------
points : array
(n, 2)
a data array of x and y coordinates
Notes
-----
If the given shape file includes polygons,
this function returns x and y coordinates of the polygons' centroids
"""
first_choice, backup = tee(iterable)
try:
if HAS_SHAPELY:
data = np.vstack(
[
np.array(shape.centroid.coords)[0]
if isinstance(shape, BaseGeometry)
else np.array(shape.centroid)
for shape in first_choice
]
)
else:
data = np.vstack([np.array(shape.centroid) for shape in first_choice])
except AttributeError:
data = np.vstack(list(backup))
return data
[docs]
def get_points_array_from_shapefile(shapefile):
"""
Gets a data array of x and y coordinates from a given shapefile.
Parameters
----------
shapefile : string
name of a shape file including suffix
Returns
-------
points : array
(n, 2)
a data array of x and y coordinates
Notes
-----
If the given shape file includes polygons,
this function returns x and y coordinates of the polygons' centroids
Examples
--------
Point shapefile
>>> import libpysal
>>> from libpysal.weights.util import get_points_array_from_shapefile
>>> xy = get_points_array_from_shapefile(
... libpysal.examples.get_path('juvenile.shp')
... )
>>> xy[:3]
array([[94., 93.],
[80., 95.],
[79., 90.]])
Polygon shapefile
>>> xy = get_points_array_from_shapefile(
... libpysal.examples.get_path('columbus.shp')
... )
>>> xy[:3]
array([[ 8.82721847, 14.36907602],
[ 8.33265837, 14.03162401],
[ 9.01226541, 13.81971908]])
"""
f = FileIO(shapefile)
data = get_points_array(f)
return data
[docs]
def min_threshold_distance(data, p=2):
"""
Get the maximum nearest neighbor distance.
Parameters
----------
data : array
(n,k) or KDTree where KDtree.data is array (n,k)
n observations on k attributes
p : float
Minkowski p-norm distance metric parameter:
1<=p<=infinity
2: Euclidean distance
1: Manhattan distance
Returns
-------
nnd : float
maximum nearest neighbor distance between the n observations
Examples
--------
>>> from libpysal.weights.util import min_threshold_distance
>>> import numpy as np
>>> x, y = np.indices((5, 5))
>>> x.shape = (25, 1)
>>> y.shape = (25, 1)
>>> data = np.hstack([x, y])
>>> min_threshold_distance(data)
1.0
"""
if issubclass(type(data), scipy.spatial.KDTree):
kd = data
data = kd.data
else:
kd = KDTree(data)
nn = kd.query(data, k=2, p=p)
nnd = nn[0].max(axis=0)[1]
return nnd
[docs]
def lat2SW(nrows=3, ncols=5, criterion="rook", row_st=False):
"""
Create a sparse W matrix for a regular lattice.
Parameters
----------
nrows : int
number of rows
ncols : int
number of columns
rook : {"rook", "queen", "bishop"}
type of contiguity. Default is rook.
row_st : boolean
If True, the created sparse W object is row-standardized so
every row sums up to one. Defaults to False.
Returns
-------
w : scipy.sparse.dia_matrix
instance of a scipy sparse matrix
Notes
-----
Observations are row ordered: first k observations are in row 0,
next k in row 1, and so on. This method directly creates the W
matrix using the strucuture of the contiguity type.
Examples
--------
>>> from libpysal.weights import lat2SW
>>> w9 = lat2SW(3,3)
>>> w9[0,1] == 1
True
>>> w9[3,6] == 1
True
>>> w9r = lat2SW(3,3, row_st=True)
>>> w9r[3,6] == 1./3
True
"""
n = nrows * ncols
diagonals = []
offsets = []
if criterion == "rook" or criterion == "queen":
d = np.ones((1, n))
for i in range(ncols - 1, n, ncols):
d[0, i] = 0
diagonals.append(d)
offsets.append(-1)
d = np.ones((1, n))
diagonals.append(d)
offsets.append(-ncols)
if criterion == "queen" or criterion == "bishop":
d = np.ones((1, n))
for i in range(0, n, ncols):
d[0, i] = 0
diagonals.append(d)
offsets.append(-(ncols - 1))
d = np.ones((1, n))
for i in range(ncols - 1, n, ncols):
d[0, i] = 0
diagonals.append(d)
offsets.append(-(ncols + 1))
data = np.concatenate(diagonals)
offsets = np.array(offsets)
m = sparse.dia_matrix((data, offsets), shape=(n, n), dtype=np.int8)
m = m + m.T
if row_st:
m = sparse.spdiags(1.0 / m.sum(1).T, 0, *m.shape) * m
m = m.tocsc()
m.eliminate_zeros()
return m
def write_gal(file, k=10):
with open(file, "w") as f:
n = k * k
f.write("0 %d" % n)
for i in range(n):
neighs = [i - i, i + 1, i - k, i + k]
neighs = [j for j in neighs if j >= 0 and j < n]
f.write("\n%d %d\n" % (i, len(neighs)))
f.write(" ".join(map(str, neighs)))
f.close()
[docs]
def neighbor_equality(w1, w2):
"""
Test if the neighbor sets are equal between two weights objects
Parameters
----------
w1 : W
instance of spatial weights class W
w2 : W
instance of spatial weights class W
Returns
-------
bool
Notes
-----
Only set membership is evaluated, no check of the weight values is carried out.
Examples
--------
>>> from libpysal.weights.util import neighbor_equality
>>> from libpysal.weights import lat2W, W
>>> w1 = lat2W(3,3)
>>> w2 = lat2W(3,3)
>>> neighbor_equality(w1, w2)
True
>>> w3 = lat2W(5,5)
>>> neighbor_equality(w1, w3)
False
>>> n4 = w1.neighbors.copy()
>>> n4[0] = [1]
>>> n4[1] = [4, 2]
>>> w4 = W(n4)
>>> neighbor_equality(w1, w4)
False
>>> n5 = w1.neighbors.copy()
>>> n5[0]
[3, 1]
>>> n5[0] = [1, 3]
>>> w5 = W(n5)
>>> neighbor_equality(w1, w5)
True
"""
n1 = w1.neighbors
n2 = w2.neighbors
ids_1 = set(n1.keys())
ids_2 = set(n2.keys())
if ids_1 != ids_2:
return False
return all(set(w1.neighbors[i]) == set(w2.neighbors[i]) for i in ids_1)
def isKDTree(obj):
"""
This is a utility function to determine whether or not an object is a
KDTree, since KDTree and cKDTree have no common parent type
"""
return any([issubclass(type(obj), KDTYPE) for KDTYPE in KDTREE_TYPES]) # noqa: C419
[docs]
def attach_islands(w, w_knn1, **kwargs):
"""
Attach nearest neighbor to islands in spatial weight w.
Parameters
----------
w : libpysal.weights.W
pysal spatial weight object (unstandardized).
w_knn1 : libpysal.weights.W
Nearest neighbor pysal spatial weight object (k=1).
**kwargs : keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
: libpysal.weights.W
pysal spatial weight object w without islands.
Examples
--------
>>> from libpysal.weights import lat2W, Rook, KNN, attach_islands
>>> import libpysal
>>> w = Rook.from_shapefile(libpysal.examples.get_path('10740.shp'))
>>> w.islands
[163]
>>> w_knn1 = KNN.from_shapefile(libpysal.examples.get_path('10740.shp'),k=1)
>>> w_attach = attach_islands(w, w_knn1)
>>> w_attach.islands
[]
>>> w_attach[w.islands[0]]
{166: 1.0}
"""
neighbors, weights = copy.deepcopy(w.neighbors), copy.deepcopy(w.weights)
if not len(w.islands):
print("There are no disconnected observations (no islands)!")
return w
else:
for island in w.islands:
nb = w_knn1.neighbors[island][0]
if isinstance(island, float):
nb = float(nb)
neighbors[island] = [nb]
weights[island] = [1.0]
neighbors[nb] = neighbors[nb] + [island]
weights[nb] = weights[nb] + [1.0]
return W(neighbors, weights, id_order=w.id_order, **kwargs)
[docs]
def nonplanar_neighbors(w, geodataframe, tolerance=0.001, **kwargs):
"""
Detect neighbors for non-planar polygon collections
Parameters
----------
w: pysal W
A spatial weights object with reported islands
geodataframe: GeoDataframe
The polygon dataframe from which w was constructed.
tolerance: float
The percentage of the minimum horizontal or vertical extent (minextent)
of the dataframe to use in defining a buffering distance to allow for
fuzzy contiguity detection. The buffering distance is equal to
tolerance*minextent.
**kwargs: keyword arguments
optional arguments for :class:`pysal.weights.W`
Attributes
----------
non_planar_joins : dictionary
Stores the new joins detected. Key is the id of the focal unit,
value is a list of neighbor ids.
Returns
-------
w: pysal W
Spatial weights object that encodes fuzzy neighbors.
This will have an attribute `non_planar_joins` to indicate
what new joins were detected.
Notes
-----
This relaxes the notion of contiguity neighbors for the case of shapefiles
that violate the condition of planar enforcement. It handles three types
of conditions present in such files that would result in islands when using
the regular PySAL contiguity methods. The first are edges for nearby
polygons that should be shared, but are digitized separately for the
individual polygons and the resulting edges do not coincide, but instead
the edges intersect. The second case is similar to the first, only the
resultant edges do not intersect but are "close". The final case arises
when one polygon is "inside" a second polygon but is not encoded to
represent a hole in the containing polygon.
The buffering check assumes the geometry coordinates are projected.
Examples
--------
>>> import geopandas as gpd
>>> import libpysal
>>> df = gpd.read_file(libpysal.examples.get_path('map_RS_BR.shp'))
>>> w = libpysal.weights.Queen.from_dataframe(df)
>>> w.islands
[0, 4, 23, 27, 80, 94, 101, 107, 109, 119, 122, 139, 169, 175, 223, 239, 247, 253, 254, 255, 256, 261, 276, 291, 294, 303, 321, 357, 374]
>>> wnp = libpysal.weights.nonplanar_neighbors(w, df)
>>> wnp.islands
[]
>>> w.neighbors[0]
[]
>>> wnp.neighbors[0]
[23, 59, 152, 239]
>>> wnp.neighbors[23]
[0, 45, 59, 107, 152, 185, 246]
Also see `nonplanarweights.ipynb`
References
----------
Planar Enforcement:
http://ibis.geog.ubc.ca/courses/klink/gis.notes/ncgia/u12.html#SEC12.6
""" # noqa: E501
gdf = geodataframe
assert gdf.sindex, (
"GeoDataFrame must have a spatial index. "
"Please make sure you have `libspatialindex` installed"
)
islands = w.islands
joins = copy.deepcopy(w.neighbors)
candidates = gdf.geometry
fixes = defaultdict(list)
# first check for intersecting polygons
for island in islands:
focal = gdf.iloc[island].geometry
neighbors = [
j
for j, candidate in enumerate(candidates)
if focal.intersects(candidate) and j != island
]
if len(neighbors) > 0:
for neighbor in neighbors:
if neighbor not in joins[island]:
fixes[island].append(neighbor)
joins[island].append(neighbor)
if island not in joins[neighbor]:
fixes[neighbor].append(island)
joins[neighbor].append(island)
# if any islands remain, dilate them and check for intersection
if islands:
x0, y0, x1, y1 = gdf.total_bounds
distance = tolerance * min(x1 - x0, y1 - y0)
for island in islands:
dilated = gdf.iloc[island].geometry.buffer(distance)
neighbors = [
j
for j, candidate in enumerate(candidates)
if dilated.intersects(candidate) and j != island
]
if len(neighbors) > 0:
for neighbor in neighbors:
if neighbor not in joins[island]:
fixes[island].append(neighbor)
joins[island].append(neighbor)
if island not in joins[neighbor]:
fixes[neighbor].append(island)
joins[neighbor].append(island)
w = W(joins, **kwargs)
w.non_planar_joins = fixes
return w
[docs]
@requires("geopandas")
def fuzzy_contiguity(
gdf,
tolerance=0.005,
buffering=False,
drop=True,
buffer=None,
predicate="intersects",
**kwargs,
):
"""
Fuzzy contiguity spatial weights
Parameters
----------
gdf: GeoDataFrame
tolerance: float
The percentage of the length of the minimum side of the bounding
rectangle for the GeoDataFrame to use in determining the buffering
distance.
buffering: boolean
If False (default) joins will only be detected for features that
intersect (touch, contain, within). If True then features will be
buffered and intersections will be based on buffered features.
drop: boolean
If True (default), the buffered features are removed from the GeoDataFrame.
If False, buffered features are added to the GeoDataFrame.
buffer : float
Specify exact buffering distance. Ignores `tolerance`.
predicate : {'intersects', 'within', 'contains', 'overlaps', 'crosses', 'touches'}
The predicate to use for determination of neighbors. Default is
'intersects'. If None is passed, neighbours are determined based on
the intersection of bounding boxes.
**kwargs: keyword arguments
optional arguments for :class:`pysal.weights.W`
Returns
-------
w: PySAL W
Spatial weights based on fuzzy contiguity. Weights are binary.
Examples
--------
>>> import libpysal
>>> from libpysal.weights import fuzzy_contiguity
>>> import geopandas as gpd
>>> rs = libpysal.examples.get_path('map_RS_BR.shp')
>>> rs_df = gpd.read_file(rs)
>>> wq = libpysal.weights.Queen.from_dataframe(rs_df)
>>> len(wq.islands)
29
>>> wq[0]
{}
>>> wf = fuzzy_contiguity(rs_df)
>>> wf.islands
[]
>>> wf[0] == dict({239: 1.0, 59: 1.0, 152: 1.0, 23: 1.0, 107: 1.0})
True
Example needing to use buffering
>>> from shapely.geometry import Polygon
>>> p0 = Polygon([(0,0), (10,0), (10,10)])
>>> p1 = Polygon([(10,1), (10,2), (15,2)])
>>> p2 = Polygon([(12,2.001), (14, 2.001), (13,10)])
>>> gs = gpd.GeoSeries([p0,p1,p2])
>>> gdf = gpd.GeoDataFrame(geometry=gs)
>>> wf = fuzzy_contiguity(gdf)
>>> wf.islands
[2]
>>> wfb = fuzzy_contiguity(gdf, buffering=True)
>>> wfb.islands
[]
>>> wfb[2]
{1: 1.0}
Example with a custom index
>>> rs_df_ix = rs_df.set_index("NM_MUNICIP")
>>> wf_ix = fuzzy_contiguity(rs_df)
>>> wf_ix.neighbors["TAVARES"]
['SÃO JOSÉ DO NORTE', 'MOSTARDAS']
Notes
-----
This relaxes the notion of contiguity neighbors for the case of feature
collections that violate the condition of planar enforcement. It handles
three types of conditions present in such collections that would result in
islands when using the regular PySAL contiguity methods. The first are
edges for nearby polygons that should be shared, but are digitized
separately for the individual polygons and the resulting edges do not
coincide, but instead the edges intersect. The second case is similar to
the first, only the resultant edges do not intersect but are "close". The
final case arises when one polygon is "inside" a second polygon but is not
encoded to represent a hole in the containing polygon.
Detection of the second case will require setting buffering=True
and exploring different values for tolerance.
The buffering check assumes the geometry coordinates are projected.
References
----------
Planar Enforcement:
http://ibis.geog.ubc.ca/courses/klink/gis.notes/ncgia/u12.html#SEC12.6
"""
if buffering:
if not buffer:
# buffer each shape
minx, miny, maxx, maxy = gdf.total_bounds
buffer = tolerance * 0.5 * abs(min(maxx - minx, maxy - miny))
# create new geometry column
new_geometry = gdf.geometry.buffer(buffer)
gdf["_buffer"] = new_geometry
old_geometry_name = gdf.geometry.name
gdf.set_geometry("_buffer", inplace=True)
neighbors = {}
if GPD_013:
# query tree based on set predicate
inp, res = gdf.sindex.query(gdf.geometry, predicate=predicate)
else:
inp, res = gdf.sindex.query_bulk(gdf.geometry, predicate=predicate)
# remove self hits
itself = inp == res
inp = inp[~itself]
res = res[~itself]
# extract index values of neighbors
for i, ix in enumerate(gdf.index):
ids = gdf.index[res[inp == i]].tolist()
neighbors[ix] = ids
if buffering:
gdf.set_geometry(old_geometry_name, inplace=True)
if drop:
gdf.drop(columns=["_buffer"], inplace=True)
return W(neighbors, **kwargs)
if __name__ == "__main__":
assert (lat2W(5, 5).sparse.todense() == lat2SW(5, 5).todense()).all()
assert (lat2W(5, 3).sparse.todense() == lat2SW(5, 3).todense()).all()
assert (
lat2W(5, 3, rook=False).sparse.todense() == lat2SW(5, 3, "queen").todense()
).all()
assert (
lat2W(50, 50, rook=False).sparse.todense() == lat2SW(50, 50, "queen").todense()
).all()