Source code for networkx.algorithms.isomorphism.matchhelpers

"""Functions which help end users define customize node_match and
edge_match functions to use during isomorphism checks.
"""
from itertools import permutations
import types

__all__ = [
    "categorical_node_match",
    "categorical_edge_match",
    "categorical_multiedge_match",
    "numerical_node_match",
    "numerical_edge_match",
    "numerical_multiedge_match",
    "generic_node_match",
    "generic_edge_match",
    "generic_multiedge_match",
]


def copyfunc(f, name=None):
    """Returns a deepcopy of a function."""
    return types.FunctionType(
        f.__code__, f.__globals__, name or f.__name__, f.__defaults__, f.__closure__
    )


def allclose(x, y, rtol=1.0000000000000001e-05, atol=1e-08):
    """Returns True if x and y are sufficiently close, elementwise.

    Parameters
    ----------
    rtol : float
        The relative error tolerance.
    atol : float
        The absolute error tolerance.

    """
    # assume finite weights, see numpy.allclose() for reference
    for xi, yi in zip(x, y):
        if not (abs(xi - yi) <= atol + rtol * abs(yi)):
            return False
    return True


def close(x, y, rtol=1.0000000000000001e-05, atol=1e-08):
    """Returns True if x and y are sufficiently close.

    Parameters
    ----------
    rtol : float
        The relative error tolerance.
    atol : float
        The absolute error tolerance.

    """
    # assume finite weights, see numpy.allclose() for reference
    return abs(x - y) <= atol + rtol * abs(y)


categorical_doc = """
Returns a comparison function for a categorical node attribute.

The value(s) of the attr(s) must be hashable and comparable via the ==
operator since they are placed into a set([]) object.  If the sets from
G1 and G2 are the same, then the constructed function returns True.

Parameters
----------
attr : string | list
    The categorical node attribute to compare, or a list of categorical
    node attributes to compare.
default : value | list
    The default value for the categorical node attribute, or a list of
    default values for the categorical node attributes.

Returns
-------
match : function
    The customized, categorical `node_match` function.

Examples
--------
>>> import networkx.algorithms.isomorphism as iso
>>> nm = iso.categorical_node_match("size", 1)
>>> nm = iso.categorical_node_match(["color", "size"], ["red", 2])

"""


[docs]def categorical_node_match(attr, default): if isinstance(attr, str): def match(data1, data2): return data1.get(attr, default) == data2.get(attr, default) else: attrs = list(zip(attr, default)) # Python 3 def match(data1, data2): return all(data1.get(attr, d) == data2.get(attr, d) for attr, d in attrs) return match
categorical_edge_match = copyfunc(categorical_node_match, "categorical_edge_match")
[docs]def categorical_multiedge_match(attr, default): if isinstance(attr, str): def match(datasets1, datasets2): values1 = {data.get(attr, default) for data in datasets1.values()} values2 = {data.get(attr, default) for data in datasets2.values()} return values1 == values2 else: attrs = list(zip(attr, default)) # Python 3 def match(datasets1, datasets2): values1 = set() for data1 in datasets1.values(): x = tuple(data1.get(attr, d) for attr, d in attrs) values1.add(x) values2 = set() for data2 in datasets2.values(): x = tuple(data2.get(attr, d) for attr, d in attrs) values2.add(x) return values1 == values2 return match
# Docstrings for categorical functions. categorical_node_match.__doc__ = categorical_doc categorical_edge_match.__doc__ = categorical_doc.replace("node", "edge") tmpdoc = categorical_doc.replace("node", "edge") tmpdoc = tmpdoc.replace("categorical_edge_match", "categorical_multiedge_match") categorical_multiedge_match.__doc__ = tmpdoc numerical_doc = """ Returns a comparison function for a numerical node attribute. The value(s) of the attr(s) must be numerical and sortable. If the sorted list of values from G1 and G2 are the same within some tolerance, then the constructed function returns True. Parameters ---------- attr : string | list The numerical node attribute to compare, or a list of numerical node attributes to compare. default : value | list The default value for the numerical node attribute, or a list of default values for the numerical node attributes. rtol : float The relative error tolerance. atol : float The absolute error tolerance. Returns ------- match : function The customized, numerical `node_match` function. Examples -------- >>> import networkx.algorithms.isomorphism as iso >>> nm = iso.numerical_node_match("weight", 1.0) >>> nm = iso.numerical_node_match(["weight", "linewidth"], [0.25, 0.5]) """
[docs]def numerical_node_match(attr, default, rtol=1.0000000000000001e-05, atol=1e-08): if isinstance(attr, str): def match(data1, data2): return close( data1.get(attr, default), data2.get(attr, default), rtol=rtol, atol=atol ) else: attrs = list(zip(attr, default)) # Python 3 def match(data1, data2): values1 = [data1.get(attr, d) for attr, d in attrs] values2 = [data2.get(attr, d) for attr, d in attrs] return allclose(values1, values2, rtol=rtol, atol=atol) return match
numerical_edge_match = copyfunc(numerical_node_match, "numerical_edge_match")
[docs]def numerical_multiedge_match(attr, default, rtol=1.0000000000000001e-05, atol=1e-08): if isinstance(attr, str): def match(datasets1, datasets2): values1 = sorted([data.get(attr, default) for data in datasets1.values()]) values2 = sorted([data.get(attr, default) for data in datasets2.values()]) return allclose(values1, values2, rtol=rtol, atol=atol) else: attrs = list(zip(attr, default)) # Python 3 def match(datasets1, datasets2): values1 = [] for data1 in datasets1.values(): x = tuple(data1.get(attr, d) for attr, d in attrs) values1.append(x) values2 = [] for data2 in datasets2.values(): x = tuple(data2.get(attr, d) for attr, d in attrs) values2.append(x) values1.sort() values2.sort() for xi, yi in zip(values1, values2): if not allclose(xi, yi, rtol=rtol, atol=atol): return False else: return True return match
# Docstrings for numerical functions. numerical_node_match.__doc__ = numerical_doc numerical_edge_match.__doc__ = numerical_doc.replace("node", "edge") tmpdoc = numerical_doc.replace("node", "edge") tmpdoc = tmpdoc.replace("numerical_edge_match", "numerical_multiedge_match") numerical_multiedge_match.__doc__ = tmpdoc generic_doc = """ Returns a comparison function for a generic attribute. The value(s) of the attr(s) are compared using the specified operators. If all the attributes are equal, then the constructed function returns True. Parameters ---------- attr : string | list The node attribute to compare, or a list of node attributes to compare. default : value | list The default value for the node attribute, or a list of default values for the node attributes. op : callable | list The operator to use when comparing attribute values, or a list of operators to use when comparing values for each attribute. Returns ------- match : function The customized, generic `node_match` function. Examples -------- >>> from operator import eq >>> from networkx.algorithms.isomorphism.matchhelpers import close >>> from networkx.algorithms.isomorphism import generic_node_match >>> nm = generic_node_match("weight", 1.0, close) >>> nm = generic_node_match("color", "red", eq) >>> nm = generic_node_match(["weight", "color"], [1.0, "red"], [close, eq]) """
[docs]def generic_node_match(attr, default, op): if isinstance(attr, str): def match(data1, data2): return op(data1.get(attr, default), data2.get(attr, default)) else: attrs = list(zip(attr, default, op)) # Python 3 def match(data1, data2): for attr, d, operator in attrs: if not operator(data1.get(attr, d), data2.get(attr, d)): return False else: return True return match
generic_edge_match = copyfunc(generic_node_match, "generic_edge_match")
[docs]def generic_multiedge_match(attr, default, op): """Returns a comparison function for a generic attribute. The value(s) of the attr(s) are compared using the specified operators. If all the attributes are equal, then the constructed function returns True. Potentially, the constructed edge_match function can be slow since it must verify that no isomorphism exists between the multiedges before it returns False. Parameters ---------- attr : string | list The edge attribute to compare, or a list of node attributes to compare. default : value | list The default value for the edge attribute, or a list of default values for the dgeattributes. op : callable | list The operator to use when comparing attribute values, or a list of operators to use when comparing values for each attribute. Returns ------- match : function The customized, generic `edge_match` function. Examples -------- >>> from operator import eq >>> from networkx.algorithms.isomorphism.matchhelpers import close >>> from networkx.algorithms.isomorphism import generic_node_match >>> nm = generic_node_match("weight", 1.0, close) >>> nm = generic_node_match("color", "red", eq) >>> nm = generic_node_match(["weight", "color"], [1.0, "red"], [close, eq]) ... """ # This is slow, but generic. # We must test every possible isomorphism between the edges. if isinstance(attr, str): attr = [attr] default = [default] op = [op] attrs = list(zip(attr, default)) # Python 3 def match(datasets1, datasets2): values1 = [] for data1 in datasets1.values(): x = tuple(data1.get(attr, d) for attr, d in attrs) values1.append(x) values2 = [] for data2 in datasets2.values(): x = tuple(data2.get(attr, d) for attr, d in attrs) values2.append(x) for vals2 in permutations(values2): for xi, yi in zip(values1, vals2): if not all(map(lambda x, y, z: z(x, y), xi, yi, op)): # This is not an isomorphism, go to next permutation. break else: # Then we found an isomorphism. return True else: # Then there are no isomorphisms between the multiedges. return False return match
# Docstrings for numerical functions. generic_node_match.__doc__ = generic_doc generic_edge_match.__doc__ = generic_doc.replace("node", "edge")