Source code for pysal.lib.weights.util

from ..io.fileio import FileIO as psopen
from .weights import W, WSP
from .set_operations import w_subset
import numpy as np
from scipy import sparse
from scipy.spatial import KDTree
import copy
import scipy.spatial
import os
import scipy
from warnings import warn
import numbers
from collections import defaultdict
from ..common import requires

try:
    import geopandas as gpd
except ImportError:
    warn('geopandas not available. Some functionality will be disabled.')

__all__ = ['lat2W', 'block_weights', 'comb', 'order', 'higher_order',
           'shimbel', 'remap_ids', 'full2W', 'full', 'WSP2W',
           'insert_diagonal', 'get_ids', 'get_points_array_from_shapefile',
           'min_threshold_distance', 'lat2SW', 'w_local_cluster',
           'higher_order_sp', 'hexLat2W', 'attach_islands',
           'nonplanar_neighbors', 'fuzzy_contiguity']


KDTREE_TYPES = [scipy.spatial.KDTree, scipy.spatial.cKDTree]

[docs]def hexLat2W(nrows=5, ncols=5): """ Create a W object for a hexagonal lattice. Parameters ---------- nrows : int number of rows ncols : int number of columns 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 pysal.lib.weights import lat2W >>> 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)
[docs]def lat2W(nrows=5, ncols=5, rook=True, id_type='int'): """ 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', ...) 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 pysal.lib.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] neighbors = {} weights = {} for key in w: weights[key] = [1.] * 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. for i in ids] if id_type == 'string' or id_type == 'float': id_dict = dict(list(zip(list(range(n)), ids))) 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[:])
[docs]def block_weights(regimes, ids=None, sparse=False): """ 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 Returns ------- W : spatial weights instance Examples -------- >>> from pysal.lib.weights import lat2W >>> 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 """ 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) 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 Anselin and Smirnov (1996) [Anselin1996b]_ Examples -------- >>> from pysal.lib.weights import lat2W >>> from pysal.lib.weights.contiguity import Rook >>> import pysal.lib >>> w = Rook.from_shapefile(pysal.lib.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): """ Contiguity weights object of order k. Parameters ---------- w : W spatial weights object k : int order of contiguity 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 pysal.lib.weights import lat2W >>> 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)
[docs]def higher_order_sp(w, k=2, shortest_path=True, diagonal=False): """ 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 Returns ------- wk : W WSP, type matches type of w argument Notes ----- Lower order contiguities are removed. Examples -------- >>> from pysal.lib.weights import lat2W >>> import pysal.lib >>> w25 = lat2W(5,5) >>> w25.n 25 >>> w25[0] == {1: 1.0, 5: 1.0} True >>> w25_2 = pysal.lib.weights.util.higher_order_sp(w25, 2) >>> w25_2[0] == {10: 1.0, 2: 1.0, 6: 1.0} True >>> w25_2 = pysal.lib.weights.util.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 = pysal.lib.weights.util.higher_order_sp(w25, 3) >>> w25_3[0] == {15: 1.0, 3: 1.0, 11: 1.0, 7: 1.0} True >>> w25_3 = pysal.lib.weights.util.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 """ 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") wk = w**k rk, ck = wk.nonzero() sk = set(zip(rk, ck)) if shortest_path: for j in range(1, k): wj = w**j rj, cj = wj.nonzero() sj = set(zip(rj, cj)) sk.difference_update(sj) if not diagonal: sk = set([(i,j) for i,j in sk if i!=j]) if id_order: d = dict([(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) 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).sparse)
[docs]def w_local_cluster(w): """ Local clustering coefficients for each unit as a node in a graph. [ws]_ 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`. [Watts1998]_ Examples -------- >>> from pysal.lib.weights import lat2W >>> 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. ]]) True """ 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 pysal.lib.weights import lat2W >>> 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 j 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 pysal.lib.weights import lat2W, W >>> 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): ''' 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 Returns ------- w : W PySAL weights object Examples -------- >>> import pysal.lib >>> 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 = pysal.lib.weights.util.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 = pysal.lib.weights.util.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)
[docs]def WSP2W(wsp, silence_warnings=False): """ Convert a pysal WSP object (thin weights matrix) to a pysal W object. Parameters ---------- wsp : WSP PySAL sparse weights object silence_warnings : boolean Switch to turn off (default on) print statements for every observation with islands Returns ------- w : W PySAL weights object Examples -------- >>> from pysal.lib.weights import lat2W, WSP 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.] """ wsp.sparse indices = wsp.sparse.indices 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 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] start = end ids = copy.copy(wsp.id_order) w = W(neighbors, weights, ids, silence_warnings=silence_warnings) 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.') return fill_diagonal(w, val=val, wsp=wsp) 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 pysal.lib.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=[]): """ 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. Returns ------- implicit : W Spatial weights object with new IDs Examples -------- >>> from pysal.lib.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) else: if w.id_order: id_order = [old2new[i] for i in w.id_order] return W(new_neigh, new_weights, id_order) else: return W(new_neigh, new_weights)
[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 pysal.lib.weights.util import get_ids >>> import pysal.lib >>> polyids = get_ids(pysal.lib.examples.get_path("columbus.shp"), "POLYID") >>> polyids[:5] [1, 2, 3, 4, 5] >>> from pysal.lib.weights.util import get_ids >>> import pysal.lib >>> import geopandas as gpd >>> gdf = gpd.read_file(pysal.lib.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 type(in_shps) == str: dbname = os.path.splitext(in_shps)[0] + '.dbf' db = psopen(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 IOError: msg = 'The shapefile "%s" appears to be missing its DBF file. '\ + ' The DBF file "%s" could not be found.' % (in_shps, dbname) raise IOError(msg) except (AttributeError, KeyError): msg = 'The variable "%s" not found in the DBF/GDF. The the following '\ + 'variables are present: %s.' % (idVariable, ','.join(cols)) raise KeyError(msg)
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 """ try: data = np.vstack([np.array(shape.centroid) for shape in iterable]) except AttributeError: data = np.vstack([shape for shape in iterable]) 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 pysal.lib >>> from pysal.lib.weights.util import get_points_array_from_shapefile >>> xy = get_points_array_from_shapefile(pysal.lib.examples.get_path('juvenile.shp')) >>> xy[:3] array([[94., 93.], [80., 95.], [79., 90.]]) Polygon shapefile >>> xy = get_points_array_from_shapefile(pysal.lib.examples.get_path('columbus.shp')) >>> xy[:3] array([[ 8.82721847, 14.36907602], [ 8.33265837, 14.03162401], [ 9.01226541, 13.81971908]]) """ f = psopen(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 pysal.lib.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 pysal.lib.weights import lat2W >>> w9 = lat2SW(3,3) >>> w9[0,1] 1 >>> w9[3,6] 1 >>> 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. / m.sum(1).T, 0, *m.shape) * m return m
def write_gal(file, k=10): f = open(file, 'w') n = k * k f.write("0 %d" % n) for i in range(n): row = i / k col = i % k 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() 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 ------- Boolean Notes ----- Only set membership is evaluated, no check of the weight values is carried out. Examples -------- >>> from pysal.lib.weights.util import neighbor_equality >>> from pysal.lib.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 for i in ids_1: if set(w1.neighbors[i]) != set(w2.neighbors[i]): return False return True 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])
[docs]def attach_islands(w, w_knn1): """ Attach nearest neighbor to islands in spatial weight w. Parameters ---------- w : pysal.lib.weights.W pysal spatial weight object (unstandardized). w_knn1 : pysal.lib.weights.W Nearest neighbor pysal spatial weight object (k=1). Returns ------- : pysal.lib.weights.W pysal spatial weight object w without islands. Examples -------- >>> from pysal.lib.weights import lat2W >>> import pysal.lib >>> w = pysal.lib.weights.contiguity.Rook.from_shapefile(pysal.lib.examples.get_path('10740.shp')) >>> w.islands [163] >>> w_knn1 = pysal.lib.weights.distance.KNN.from_shapefile(pysal.lib.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 type(island) is 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)
[docs]def nonplanar_neighbors(w, geodataframe, tolerance=0.001): """ 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. 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 pysal.lib >>> df = gpd.read_file(pysal.lib.examples.get_path('map_RS_BR.shp')) >>> w = pysal.lib.weights.contiguity.Queen.from_dataframe(df) >>> import pysal.lib >>> 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 = pysal.lib.weights.util.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 """ 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) w.non_planar_joins = fixes return w
[docs]@requires('geopandas') def fuzzy_contiguity(gdf, tolerance=0.005, buffering=False, drop=True): """ 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. Returns ------- w: PySAL W Spatial weights based on fuzzy contiguity. Weights are binary. Examples -------- >>> import pysal.lib as lps >>> import geopandas as gpd >>> rs = lps.examples.get_path('map_RS_BR.shp') >>> rs_df = gpd.read_file(rs) >>> wq = lps.weights.contiguity.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 >>> import pysal.lib as lps >>> import geopandas as gpd >>> 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} 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: # 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 = gpd.GeoSeries([feature.buffer(buffer) for feature in gdf.geometry]) gdf['_buffer'] = new_geometry old_geometry_name = gdf.geometry.name gdf.set_geometry('_buffer', inplace=True) assert gdf.sindex, 'GeoDataFrame must have a spatial index. Please make sure you have `libspatialindex` installed' tree = gdf.sindex neighbors = {} n,k = gdf.shape for i in range(n): geom = gdf.geometry.iloc[i] hits = list(tree.intersection(geom.bounds)) possible = gdf.iloc[hits] ids = possible.intersects(geom).index.tolist() ids.remove(i) neighbors[i] = ids if buffering: gdf.set_geometry(old_geometry_name, inplace=True) if drop: gdf.drop(columns=['_buffer'], inplace=True) return W(neighbors)
if __name__ == "__main__": from pysal import lat2W 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()