def __init__(self, metric=None):
"""
Parameters
----------
metric : function or str or None, default: None
Refer to the `metric` argument
in :func:`region.util.get_metric_function`.
"""
self.metric = get_metric_function(metric)
def __init__(self, metric=None):
"""
Parameters
----------
metric : function or str or None, default: None
Refer to the `metric` argument
in :func:`region.util.get_metric_function`.
"""
self.metric = get_metric_function(metric)
def fit_from_scipy_sparse_matrix(self,
adj,
attr,
n_regions,
method="flow",
solver="cbc",
metric="euclidean"):
"""
Solve the p-regions problem as MIP as described in [DCM2011]_.
The resulting region labels are assigned to the instance's
:attr:`labels_` attribute.
Parameters
----------
adj : class:`scipy.sparse.csr_matrix`
Adjacency matrix representing the areas' contiguity relation.
attr : :class:`numpy.ndarray`
Array (number of areas x number of attributes) of areas' attributes
relevant to clustering.
n_regions : `int`
Number of desired regions.
method : {"flow", "order", "tree"}, default: "flow"
The method to translate the clustering problem into an exact
optimization model.
* "flow" - Flow model on p. 112-113 in [DCM2011]_
* "order" - Order model on p. 110-112 in [DCM2011]_
* "tree" - Tree model on p. 108-110 in [DCM2011]_
solver : {"cbc", "cplex", "glpk", "gurobi"}, default: "cbc"
The solver to use. Unless the default solver is used, the user has
to make sure that the specified solver is installed.
* "cbc" - the Cbc (Coin-or branch and cut) solver
* "cplex" - the CPLEX solver
* "glpk" - the GLPK (GNU Linear Programming Kit) solver
* "gurobi" - the Gurobi Optimizer
metric : str or function, default: "euclidean"
See the `metric` argument in
:func:`region.util.get_metric_function`.
"""
if not isinstance(n_regions, numbers.Integral) or n_regions <= 0:
raise ValueError("The n_regions argument must be a positive "
"integer.")
if adj.shape[0] < n_regions:
raise ValueError("The number of regions must be less than the "
"number of areas.")
if attr.ndim == 1:
attr = attr.reshape(adj.shape[0], -1)
self._check_method(method)
check_solver(solver)
metric = get_metric_function(metric)
opt_func = {
"flow": _flow,
"order": _order,
"tree": _tree
}[method.lower()]
result_dict = opt_func(adj, attr, n_regions, solver, metric)
self.labels_ = result_dict
self.n_regions = n_regions
self.method = method
self.metric = metric
self.solver = solver
def fit_from_scipy_sparse_matrix(self,
adj,
attr,
spatially_extensive_attr,
threshold,
solver="cbc",
metric="euclidean"):
"""
Solve the max-p-regions problem as MIP as described in [DAR2012]_.
The resulting region labels are assigned to the instance's
:attr:`labels_` attribute.
Parameters
----------
adj : class:`scipy.sparse.csr_matrix`
Adjacency matrix representing the areas' contiguity relation.
attr : :class:`numpy.ndarray`
Array (number of areas x number of attributes) of areas' attributes
relevant to clustering.
spatially_extensive_attr : :class:`numpy.ndarray`
Array (number of areas x number of attributes) of areas' attributes
relevant to ensuring the threshold condition.
threshold : numbers.Real or :class:`numpy.ndarray`
The lower bound for a region's sum of spatially extensive
attributes. The argument's type is numbers.Real if there is only
one spatially extensive attribute per area, otherwise it is a
one-dimensional array with as many entries as there are spatially
extensive attributes per area.
solver : {"cbc", "cplex", "glpk", "gurobi"}, default: "cbc"
The solver to use. Unless the default solver is used, the user has
to make sure that the specified solver is installed.
* "cbc" - the Cbc (Coin-or branch and cut) solver
* "cplex" - the CPLEX solver
* "glpk" - the GLPK (GNU Linear Programming Kit) solver
* "gurobi" - the Gurobi Optimizer
metric : str or function, default: "euclidean"
See the `metric` argument in
:func:`region.util.get_metric_function`.
"""
self.metric = get_metric_function(metric)
check_solver(solver)
prob = LpProblem("Max-p-Regions", LpMinimize)
# Parameters of the optimization problem
n_areas = adj.shape[0]
I = list(range(n_areas)) # index for areas
II = [(i, j) for i in I for j in I]
II_upper_triangle = [(i, j) for i, j in II if i < j]
# index of potential regions, called k in [DAR2012]_:
K = range(n_areas)
# index of contiguity order, called c in [DAR2012]_:
O = range(n_areas)
d = {(i, j): self.metric(attr[i].reshape(1, -1),
attr[j].reshape(1, -1))
for i, j in II_upper_triangle}
h = 1 + floor(log10(sum(d[(i, j)] for i, j in II_upper_triangle)))
# Decision variables
t = LpVariable.dicts("t", ((i, j) for i, j in II_upper_triangle),
lowBound=0,
upBound=1,
cat=LpInteger)
x = LpVariable.dicts("x", ((i, k, o) for i in I for k in K for o in O),
lowBound=0,
upBound=1,
cat=LpInteger)
# Objective function
# (1) in Duque et al. (2012): "The Max-p-Regions Problem"
prob += -10**h * lpSum(x[i, k, 0] for k in K for i in I) \
+ lpSum(d[i, j] * t[i, j] for i, j in II_upper_triangle)
# Constraints
# (2) in Duque et al. (2012): "The Max-p-Regions Problem"
for k in K:
prob += lpSum(x[i, k, 0] for i in I) <= 1
# (3) in Duque et al. (2012): "The Max-p-Regions Problem"
for i in I:
prob += lpSum(x[i, k, o] for k in K for o in O) == 1
# (4) in Duque et al. (2012): "The Max-p-Regions Problem"
for i in I:
for k in K:
for o in range(1, len(O)):
prob += x[i, k, o] <= lpSum(x[j, k, o - 1]
for j in neighbors(adj, i))
# (5) in Duque et al. (2012): "The Max-p-Regions Problem"
if isinstance(spatially_extensive_attr[I[0]], numbers.Real):
for k in K:
lhs = lpSum(x[i, k, o] * spatially_extensive_attr[i] for i in I
for o in O)
prob += lhs >= threshold * lpSum(x[i, k, 0] for i in I)
elif isinstance(spatially_extensive_attr[I[0]], collections.Iterable):
for el in range(len(spatially_extensive_attr[I[0]])):
for k in K:
lhs = lpSum(x[i, k, o] * spatially_extensive_attr[i][el]
for i in I for o in O)
if isinstance(threshold, numbers.Real):
rhs = threshold * lpSum(x[i, k, 0] for i in I)
prob += lhs >= rhs
elif isinstance(threshold, np.ndarray):
rhs = threshold[el] * lpSum(x[i, k, 0] for i in I)
prob += lhs >= rhs
# (6) in Duque et al. (2012): "The Max-p-Regions Problem"
for i, j in II_upper_triangle:
for k in K:
prob += t[i, j] >= \
lpSum(x[i, k, o] + x[j, k, o] for o in O) - 1
# (7) in Duque et al. (2012): "The Max-p-Regions Problem"
# already in LpVariable-definition
# (8) in Duque et al. (2012): "The Max-p-Regions Problem"
# already in LpVariable-definition
# additional constraint for speedup (p. 405 in [DAR2012]_)
for o in O:
prob += x[I[0], K[0], o] == (1 if o == 0 else 0)
# Solve the optimization problem
solver = get_solver_instance(solver)
print("start solving with", solver)
prob.solve(solver)
print("solved")
result = np.zeros(n_areas)
for i in I:
for k in K:
for o in O:
if x[i, k, o].varValue == 1:
result[i] = k
self.labels_ = result
self.solver = solver
