From 1aba7ec1ec02919135da8e91f75011488a585168 Mon Sep 17 00:00:00 2001 From: lynniknow <135607329+lynniknow@users.noreply.github.com> Date: Sun, 4 Feb 2024 22:48:56 +0800 Subject: [PATCH 1/3] Update tutorial.rst --- docs_using_sphinx/tutorial.rst | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/docs_using_sphinx/tutorial.rst b/docs_using_sphinx/tutorial.rst index 6f153740..cbb5085e 100644 --- a/docs_using_sphinx/tutorial.rst +++ b/docs_using_sphinx/tutorial.rst @@ -291,4 +291,14 @@ The PageRank algorithm **Usage** - For class methods, calling and parameter passing are the same as python. -- For module function, easygraph will select specific codes to execute according to the class of the graph. \ No newline at end of file +- For module function, easygraph will select specific codes to execute according to the class of the graph. + +View the tutorials in Colab. +------------------------- +`tutorial1: Two brief tutorials of how to do graph analysis with EasyGraph. `_ + +`tutorial2: Using C++ code to achieve a better performance. `_ + +`tutorial3: Graph Embedding. `_ + +`tutorial4: Community Detection. `_ From 44b1b0a0aa095a17292a3d4197cd052d7f856fdd Mon Sep 17 00:00:00 2001 From: lynniknow <135607329+lynniknow@users.noreply.github.com> Date: Sun, 4 Feb 2024 22:49:52 +0800 Subject: [PATCH 2/3] Update tutorial.rst --- docs_using_sphinx/tutorial.rst | 10 ---------- 1 file changed, 10 deletions(-) diff --git a/docs_using_sphinx/tutorial.rst b/docs_using_sphinx/tutorial.rst index cbb5085e..09c352d4 100644 --- a/docs_using_sphinx/tutorial.rst +++ b/docs_using_sphinx/tutorial.rst @@ -292,13 +292,3 @@ The PageRank algorithm - For class methods, calling and parameter passing are the same as python. - For module function, easygraph will select specific codes to execute according to the class of the graph. - -View the tutorials in Colab. -------------------------- -`tutorial1: Two brief tutorials of how to do graph analysis with EasyGraph. `_ - -`tutorial2: Using C++ code to achieve a better performance. `_ - -`tutorial3: Graph Embedding. `_ - -`tutorial4: Community Detection. `_ From 149862a1eb082faabad1f74ee9c2adcf22a3f085 Mon Sep 17 00:00:00 2001 From: lynniknow <21307140115@m.fudan.edu.cn> Date: Mon, 5 Feb 2024 12:00:28 +0800 Subject: [PATCH 3/3] first commit --- .vscode/settings.json | 3 + .../_build/doctrees/aboutus.doctree | Bin 9741 -> 9762 bytes .../_build/doctrees/contributorGuide.doctree | Bin 69287 -> 69308 bytes docs_using_sphinx/_build/doctrees/dev.doctree | Bin 3393 -> 3414 bytes .../doctrees/dev/easygraph-doc-source.doctree | Bin 17890 -> 17911 bytes .../doctrees/dev/manual-releasing.doctree | Bin 12058 -> 12079 bytes .../_build/doctrees/dev/releasing.doctree | Bin 8618 -> 8639 bytes .../_build/doctrees/egeps.doctree | Bin 4257 -> 4278 bytes .../_build/doctrees/egeps/egep-0001.doctree | Bin 11066 -> 11087 bytes .../_build/doctrees/egeps/egep-0002.doctree | Bin 8021 -> 8042 bytes 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zcmeyPJW++UfpsdI&_-5&MukBA+`JO~Wc|?M)S_a2Ljz-DGkurT;_Q + + + + + + + easygraph.datapipe.loader - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + +

    + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.datapipe.loader

    +import json
+import pickle as pkl
+import re
+
+from pathlib import Path
+from typing import Callable
+from typing import List
+from typing import Optional
+from typing import Union
+
+
+
    
+[docs]
+def load_from_pickle(
+    file_path: Path, keys: Optional[Union[str, List[str]]] = None, **kwargs
+):
+    r"""Load data from a pickle file.
+
+    Args:
+        ``file_path`` (``Path``): The local path of the file.
+        ``keys`` (``Union[str, List[str]]``, optional): The keys of the data. Defaults to ``None``.
+    """
+    if isinstance(file_path, list):
+        raise ValueError("This function only support loading data from a single file.")
+    with open(file_path, "rb") as f:
+        data = pkl.load(f, **kwargs)
+    if keys is None:
+        return data
+    elif isinstance(keys, str):
+        return data[keys]
+    else:
+        return {key: data[key] for key in keys}
    
+
+
+
+
    
+[docs]
+def load_from_json(file_path: Path, **kwargs):
+    r"""Load data from a json file.
+
+    Args:
+        ``file_path`` (``Path``): The local path of the file.
+    """
+    with open(file_path, "r") as f:
+        data = json.load(f, **kwargs)
+    return data
    
+
+
+
+
    
+[docs]
+def load_from_txt(
+    file_path: Path,
+    dtype: Union[str, Callable],
+    sep: str = ",| |\t",
+    ignore_header: int = 0,
+):
+    r"""Load data from a txt file.
+
+    .. note::
+        The separator is a regular expression of ``re`` module. Multiple separators can be separated by ``|``. More details can refer to `re.split <https://docs.python.org/3/library/re.html#re.split>`_.
+
+    Args:
+        ``file_path`` (``Path``): The local path of the file.
+        ``dtype`` (``Union[str, Callable]``): The data type of the data can be either a string or a callable function.
+        ``sep`` (``str``, optional): The separator of each line in the file. Defaults to ``",| |\t"``.
+        ``ignore_header`` (``int``, optional): The number of lines to ignore in the header of the file. Defaults to ``0``.
+    """
+    cast_fun = ret_cast_fun(dtype)
+    file_path = Path(file_path)
+    assert file_path.exists(), f"{file_path} does not exist."
+    data = []
+    with open(file_path, "r") as f:
+        for _ in range(ignore_header):
+            f.readline()
+        data = [
+            list(map(cast_fun, re.split(sep, line.strip()))) for line in f.readlines()
+        ]
+    return data
    
+
+
+
+
    
+[docs]
+def ret_cast_fun(dtype: Union[str, Callable]):
+    r"""Return the cast function of the data type. The supported data types are: ``int``, ``float``, ``str``.
+
+    Args:
+        ``dtype`` (``Union[str, Callable]``): The data type of the data can be either a string or a callable function.
+    """
+    if isinstance(dtype, str):
+        if dtype == "int":
+            return int
+        elif dtype == "float":
+            return float
+        elif dtype == "str":
+            return str
+        else:
+            raise ValueError("dtype must be one of 'int', 'float', 'str'.")
+    else:
+        return dtype
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/exception.html b/docs_using_sphinx/_build/html/_modules/easygraph/exception.html new file mode 100644 index 00000000..d697d87b --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/exception.html @@ -0,0 +1,532 @@ + + + + + + + + easygraph.exception - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.exception

    +"""
+**********
+Exceptions
+**********
+
+Base exceptions and errors for EasyGraph.
+"""
+
+__all__ = [
+    "HasACycle",
+    "NodeNotFound",
+    "EasyGraphAlgorithmError",
+    "EasyGraphException",
+    "EasyGraphError",
+    "EasyGraphNoCycle",
+    "EasyGraphNoPath",
+    "EasyGraphNotImplemented",
+    "EasyGraphPointlessConcept",
+    "EasyGraphUnbounded",
+    "EasyGraphUnfeasible",
+]
+
+
+
    
+[docs]
+class EasyGraphException(Exception):
+    """Base class for exceptions in EasyGraph."""
    
+
+
+
+
    
+[docs]
+class EasyGraphError(EasyGraphException):
+    """Exception for a serious error in EasyGraph"""
    
+
+
+
+
    
+[docs]
+class EasyGraphPointlessConcept(EasyGraphException):
+    """Raised when a null graph is provided as input to an algorithm
+    that cannot use it.
+
+    The null graph is sometimes considered a pointless concept [1]_,
+    thus the name of the exception.
+
+    References
+    ----------
+    .. [1] Harary, F. and Read, R. "Is the Null Graph a Pointless
+       Concept?"  In Graphs and Combinatorics Conference, George
+       Washington University.  New York: Springer-Verlag, 1973.
+
+    """
    
+
+
+
+
    
+[docs]
+class EasyGraphAlgorithmError(EasyGraphException):
+    """Exception for unexpected termination of algorithms."""
    
+
+
+
+
    
+[docs]
+class EasyGraphUnfeasible(EasyGraphAlgorithmError):
+    """Exception raised by algorithms trying to solve a problem
+    instance that has no feasible solution."""
    
+
+
+
+
    
+[docs]
+class EasyGraphNoPath(EasyGraphUnfeasible):
+    """Exception for algorithms that should return a path when running
+    on graphs where such a path does not exist."""
    
+
+
+
+
    
+[docs]
+class EasyGraphNoCycle(EasyGraphUnfeasible):
+    """Exception for algorithms that should return a cycle when running
+    on graphs where such a cycle does not exist."""
    
+
+
+
+
    
+[docs]
+class HasACycle(EasyGraphException):
+    """Raised if a graph has a cycle when an algorithm expects that it
+    will have no cycles.
+
+    """
    
+
+
+
+
    
+[docs]
+class EasyGraphUnbounded(EasyGraphAlgorithmError):
+    """Exception raised by algorithms trying to solve a maximization
+    or a minimization problem instance that is unbounded."""
    
+
+
+
+
    
+[docs]
+class EasyGraphNotImplemented(EasyGraphException):
+    """Exception raised by algorithms not implemented for a type of graph."""
    
+
+
+
+
    
+[docs]
+class NodeNotFound(EasyGraphException):
+    """Exception raised if requested node is not present in the graph"""
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/basic/predecessor_path_based.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/basic/predecessor_path_based.html new file mode 100644 index 00000000..4d7118a3 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/basic/predecessor_path_based.html @@ -0,0 +1,519 @@ + + + + + + + + easygraph.functions.basic.predecessor_path_based - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
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    + + + + + Back to top + +
    +
    + +
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    +
    +

    Source code for easygraph.functions.basic.predecessor_path_based

    +import easygraph as eg
+
+
+__all__ = [
+    "predecessor",
+]
+
+
+
    
+[docs]
+def predecessor(G, source, target=None, cutoff=None, return_seen=None):
+    """Returns dict of predecessors for the path from source to all nodes in G.
+
+    Parameters
+    ----------
+    G : EasyGraph graph
+
+    source : node label
+       Starting node for path
+
+    target : node label, optional
+       Ending node for path. If provided only predecessors between
+       source and target are returned
+
+    cutoff : integer, optional
+        Depth to stop the search. Only paths of length <= cutoff are returned.
+
+    return_seen : bool, optional (default=None)
+        Whether to return a dictionary, keyed by node, of the level (number of
+        hops) to reach the node (as seen during breadth-first-search).
+
+    Returns
+    -------
+    pred : dictionary
+        Dictionary, keyed by node, of predecessors in the shortest path.
+
+
+    (pred, seen): tuple of dictionaries
+        If `return_seen` argument is set to `True`, then a tuple of dictionaries
+        is returned. The first element is the dictionary, keyed by node, of
+        predecessors in the shortest path. The second element is the dictionary,
+        keyed by node, of the level (number of hops) to reach the node (as seen
+        during breadth-first-search).
+
+    Examples
+    --------
+    >>> G = eg.path_graph(4)
+    >>> list(G)
+    [0, 1, 2, 3]
+    >>> eg.predecessor(G, 0)
+    {0: [], 1: [0], 2: [1], 3: [2]}
+    >>> eg.predecessor(G, 0, return_seen=True)
+    ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3})
+
+
+    """
+
+    if source not in G:
+        raise eg.NodeNotFound(f"Source {source} not in G")
+    level = 0  # the current level
+    nextlevel = [source]  # list of nodes to check at next level
+    seen = {source: level}  # level (number of hops) when seen in BFS
+    pred = {source: []}  # predecessor dictionary
+    while nextlevel:
+        level = level + 1
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in list(G.neighbors(v)):
+                if w not in seen:
+                    pred[w] = [v]
+                    seen[w] = level
+                    nextlevel.append(w)
+                elif seen[w] == level:  # add v to predecessor list if it
+                    pred[w].append(v)  # is at the correct level
+        if cutoff and cutoff <= level:
+            break
+
+    if target is not None:
+        if return_seen:
+            if target not in pred:
+                return ([], -1)  # No predecessor
+            return (pred[target], seen[target])
+        else:
+            if target not in pred:
+                return []  # No predecessor
+            return pred[target]
+    else:
+        if return_seen:
+            return (pred, seen)
+        else:
+            return pred
    
+
+
+
+# def main():
+#     G = eg.path_graph(4)
+#     print(G.edges)
+
+#     print(predecessor(G, 0))
+
+
+# if __name__ == "__main__":
+#     main()
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/assortativity.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/assortativity.html new file mode 100644 index 00000000..51b2fb7c --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/assortativity.html @@ -0,0 +1,606 @@ + + + + + + + + easygraph.functions.hypergraph.assortativity - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
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    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.functions.hypergraph.assortativity

    +"""Algorithms for finding the degree assortativity of a hypergraph."""
+
+import random
+
+from itertools import combinations
+
+import numpy
+import numpy as np
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = ["dynamical_assortativity", "degree_assortativity"]
+
+
+
    
+[docs]
+def dynamical_assortativity(H):
+    """Computes the dynamical assortativity of a uniform hypergraph.
+
+    Parameters
+    ----------
+    H : xgi.Hypergraph
+        Hypergraph of interest
+
+    Returns
+    -------
+    float
+        The dynamical assortativity
+
+    See Also
+    --------
+    degree_assortativity
+
+    Raises
+    ------
+    EasyGraphError
+        If the hypergraph is not uniform, or if there are no nodes
+        or no edges
+
+    References
+    ----------
+    Nicholas Landry and Juan G. Restrepo,
+    Hypergraph assortativity: A dynamical systems perspective,
+    Chaos 2022.
+    DOI: 10.1063/5.0086905
+
+    """
+    if len(H.v) == 0:
+        raise EasyGraphError("Hypergraph must contain nodes")
+    elif len(H.e[0]) == 0:
+        raise EasyGraphError("Hypergraph must contain edges!")
+
+    if not H.is_uniform():
+        raise EasyGraphError("Hypergraph must be uniform!")
+
+    if 1 in H.unique_edge_sizes():
+        raise EasyGraphError("No singleton edges!")
+
+    degs = H.deg_v
+    k1 = sum(degs) / len(degs)
+    k2 = np.mean(numpy.array(degs) ** 2)
+    kk1 = np.mean(
+        [degs[n1] * degs[n2] for e in H.e[0] for n1, n2 in combinations(e, 2)]
+    )
+
+    return kk1 * k1**2 / k2**2 - 1
    
+
+
+
+
    
+[docs]
+def degree_assortativity(H, kind="uniform", exact=False, num_samples=1000):
+    """Computes the degree assortativity of a hypergraph
+
+    Parameters
+    ----------
+    H : Hypergraph
+        The hypergraph of interest
+    kind : str, optional
+        the type of degree assortativity. valid choices are
+        "uniform", "top-2", and "top-bottom". By default, "uniform".
+    exact : bool, optional
+        whether to compute over all edges or sample randomly from the
+        set of edges. By default, False.
+    num_samples : int, optional
+        if not exact, specify the number of samples for the computation.
+        By default, 1000.
+
+    Returns
+    -------
+    float
+        the degree assortativity
+
+    Raises
+    ------
+    EasyGraphError
+        If there are no nodes or no edges
+
+    See Also
+    --------
+    dynamical_assortativity
+
+    References
+    ----------
+    Phil Chodrow,
+    Configuration models of random hypergraphs,
+    Journal of Complex Networks 2020.
+    DOI: 10.1093/comnet/cnaa018
+    """
+
+    if len(H.v) == 0:
+        raise EasyGraphError("Hypergraph must contain nodes")
+    elif len(H.e[0]) == 0:
+        raise EasyGraphError("Hypergraph must contain edges!")
+
+    degs = H.deg_v
+    if exact:
+        k1k2 = [_choose_degrees(e, degs, kind) for e in H.e[0] if len(e) > 1]
+    else:
+        edges = [e for e in H.e[0] if len(e) > 1]
+        k1k2 = [
+            _choose_degrees(random.choice(H.e[0]), degs, kind)
+            for _ in range(num_samples)
+        ]
+
+    rho = np.corrcoef(np.array(k1k2).T)[0, 1]
+    if np.isnan(rho):
+        return 0
+    return rho
    
+
+
+
+def _choose_degrees(e, k, kind="uniform"):
+    """Choose the degrees of two nodes in a hyperedge.
+
+    Parameters
+    ----------
+    e : iterable
+        the members in a hyperedge
+    k : dict
+        the degrees where keys are node IDs and values are degrees
+    kind : str, optional
+        the type of degree assortativity, options are "uniform", "top-2",
+        and "top-bottom". By default, "uniform".
+
+    Returns
+    -------
+    tuple
+        two degrees selected from the edge
+
+    Raises
+    ------
+    EasyGraphError
+        if invalid assortativity function chosen
+
+    See Also
+    --------
+    degree_assortativity
+
+    References
+    ----------
+    Phil Chodrow,
+    Configuration models of random hypergraphs,
+    Journal of Complex Networks 2020.
+    DOI: 10.1093/comnet/cnaa018
+    """
+    e = list(e)
+    if len(e) > 1:
+        if kind == "uniform":
+            i = np.random.randint(len(e))
+            j = i
+            while i == j:
+                j = np.random.randint(len(e))
+            return (k[e[i]], k[e[j]])
+
+        elif kind == "top-2":
+            degs = sorted([k[i] for i in e])[-2:]
+            random.shuffle(degs)
+            return degs
+
+        elif kind == "top-bottom":
+            # this selects the largest and smallest degrees in one line
+            degs = sorted([k[i] for i in e])[:: len(e) - 1]
+            random.shuffle(degs)
+            return degs
+
+        else:
+            raise EasyGraphError("Invalid choice function!")
+    else:
+        raise EasyGraphError("Edge must have more than one member!")
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/cycle_ratio.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/cycle_ratio.html new file mode 100644 index 00000000..f81db5eb --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/cycle_ratio.html @@ -0,0 +1,631 @@ + + + + + + + + easygraph.functions.hypergraph.centrality.cycle_ratio - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
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    +
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    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.functions.hypergraph.centrality.cycle_ratio

    +import copy
+import itertools
+
+import easygraph as eg
+
+
+__all__ = [
+    "my_all_shortest_paths",
+    "getandJudgeSimpleCircle",
+    "getSmallestCycles",
+    "StatisticsAndCalculateIndicators",
+    "cycle_ratio_centrality",
+]
+
+
+SmallestCycles = set()
+CycleRatio = {}
+
+
+
    
+[docs]
+def my_all_shortest_paths(G, source, target):
+    pred = eg.predecessor(G, source)
+    if target not in pred:
+        raise eg.EasyGraphNoPath(
+            f"Target {target} cannot be reached from given sources"
+        )
+    sources = {source}
+    seen = {target}
+    stack = [[target, 0]]
+    top = 0
+    while top >= 0:
+        node, i = stack[top]
+        if node in sources:
+            yield [p for p, n in reversed(stack[: top + 1])]
+        if len(pred[node]) > i:
+            stack[top][1] = i + 1
+            next = pred[node][i]
+            if next in seen:
+                continue
+            else:
+                seen.add(next)
+            top += 1
+            if top == len(stack):
+                stack.append([next, 0])
+            else:
+                stack[top][:] = [next, 0]
+        else:
+            seen.discard(node)
+            top -= 1
    
+
+
+
+
    
+[docs]
+def getandJudgeSimpleCircle(objectList):  #
+    numEdge = 0
+    for eleArr in list(itertools.combinations(objectList, 2)):
+        if G.has_edge(eleArr[0], eleArr[1]):
+            numEdge += 1
+    if numEdge != len(objectList):
+        return False
+    else:
+        return True
    
+
+
+
+
    
+[docs]
+def getSmallestCycles(G, NodeGirth, Coreness, DEF_IMPOSSLEN):
+    NodeList = list(G.nodes)
+    # print(NodeList)
+    NodeList.sort()
+    # setp 1
+    curCyc = list()
+    for ix in NodeList[:-2]:  # v1
+        if NodeGirth[ix] == 0:
+            continue
+        curCyc.append(ix)
+        for jx in NodeList[NodeList.index(ix) + 1 : -1]:  # v2
+            if NodeGirth[jx] == 0:
+                continue
+            curCyc.append(jx)
+            if G.has_edge(ix, jx):
+                for kx in NodeList[NodeList.index(jx) + 1 :]:  # v3
+                    if NodeGirth[kx] == 0:
+                        continue
+                    if G.has_edge(kx, ix):
+                        curCyc.append(kx)
+                        if G.has_edge(kx, jx):
+                            SmallestCycles.add(tuple(curCyc))
+                            for i in curCyc:
+                                NodeGirth[i] = 3
+                        curCyc.pop()
+            curCyc.pop()
+        curCyc.pop()
+
+    # setp 2
+    ResiNodeList = []  # Residual Node List
+    for nod in NodeList:
+        if NodeGirth[nod] == DEF_IMPOSSLEN:
+            ResiNodeList.append(nod)
+    if len(ResiNodeList) == 0:
+        return
+    else:
+        visitedNodes = dict.fromkeys(ResiNodeList, set())
+        for nod in ResiNodeList:
+            if Coreness[nod] == 2 and NodeGirth[nod] < DEF_IMPOSSLEN:
+                continue
+            for nei in list(G.neighbors(nod)):
+                if Coreness[nei] == 2 and NodeGirth[nei] < DEF_IMPOSSLEN:
+                    continue
+                if not nei in visitedNodes.keys() or not nod in visitedNodes[nei]:
+                    visitedNodes[nod].add(nei)
+                    if nei not in visitedNodes.keys():
+                        visitedNodes[nei] = set([nod])
+                    else:
+                        visitedNodes[nei].add(nod)
+                    if Coreness[nei] == 2 and NodeGirth[nei] < DEF_IMPOSSLEN:
+                        continue
+                    G.remove_edge(nod, nei)
+                    if eg.single_source_dijkstra(G, nod, nei):
+                        for path in my_all_shortest_paths(G, nod, nei):
+                            lenPath = len(path)
+                            path.sort()
+                            SmallestCycles.add(tuple(path))
+                            for i in path:
+                                if NodeGirth[i] > lenPath:
+                                    NodeGirth[i] = lenPath
+                    G.add_edge(nod, nei)
+
+    return SmallestCycles
    
+
+
+
+
    
+[docs]
+def StatisticsAndCalculateIndicators(SmallestCyclesOfNodes, CycLenDict):  #
+    global NumSmallCycles
+    NumSmallCycles = len(SmallestCycles)
+    for cyc in SmallestCycles:
+        lenCyc = len(cyc)
+        CycLenDict[lenCyc] += 1
+        for nod in cyc:
+            SmallestCyclesOfNodes[nod].add(cyc)
+    for objNode, SmaCycs in SmallestCyclesOfNodes.items():
+        if len(SmaCycs) == 0:
+            continue
+        cycleNeighbors = set()
+        NeiOccurTimes = {}
+        for cyc in SmaCycs:
+            for n in cyc:
+                if n in NeiOccurTimes.keys():
+                    NeiOccurTimes[n] += 1
+                else:
+                    NeiOccurTimes[n] = 1
+            cycleNeighbors = cycleNeighbors.union(cyc)
+        cycleNeighbors.remove(objNode)
+        del NeiOccurTimes[objNode]
+        sum = 0
+        for nei in cycleNeighbors:
+            sum += float(NeiOccurTimes[nei]) / len(SmallestCyclesOfNodes[nei])
+        CycleRatio[objNode] = sum + 1
+    return CycleRatio
    
+
+
+
+
    
+[docs]
+def cycle_ratio_centrality(G):
+    """
+    Parameters
+    ----------
+    G :   eg.Graph
+
+    Returns
+    -------
+    cycle ratio centrality of each node in G : dict
+
+    Example
+    -------
+    >>> G = eg.Graph()
+    >>> G.add_edges([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (1, 5), (2, 5)])
+    >>> cycle_ratio_centrality(G)
+    {1: 4.083333333333333, 2: 4.083333333333333, 3: 2.6666666666666665, 4: 2.6666666666666665, 5: 1.5}
+
+    """
+    CycLenDict = dict()
+    NumNode = G.number_of_nodes()  # update
+    DEF_IMPOSSLEN = NumNode + 1  # Impossible simple cycle length
+    NodeGirth = dict()
+    CycLenDict = dict()
+
+    SmallestCyclesOfNodes = {}  #
+    removeNodes = set()
+    Coreness = dict(zip(list(G.nodes), eg.k_core(G)))
+    for i in list(G.nodes):  #
+        SmallestCyclesOfNodes[i] = set()
+        CycleRatio[i] = 0
+        if G.degree()[i] <= 1 or Coreness[i] <= 1:
+            NodeGirth[i] = 0
+            removeNodes.add(i)
+        else:
+            NodeGirth[i] = DEF_IMPOSSLEN
+    # print('NodeGirth:', NodeGirth)
+
+    G.remove_nodes_from(removeNodes)
+
+    NodeNum = G.number_of_nodes()
+    for i in range(3, NodeNum + 2):
+        CycLenDict[i] = 0
+
+    getSmallestCycles(G, NodeGirth, Coreness, DEF_IMPOSSLEN)
+    cycle_ratio = StatisticsAndCalculateIndicators(SmallestCyclesOfNodes, CycLenDict)
+    return cycle_ratio
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/degree.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/degree.html new file mode 100644 index 00000000..31483faf --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/centrality/degree.html @@ -0,0 +1,445 @@ + + + + + + + + easygraph.functions.hypergraph.centrality.degree - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
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    +
    + +
    + +
    +
    +

    Source code for easygraph.functions.hypergraph.centrality.degree

    +__all__ = ["hyepergraph_degree_centrality"]
+
+
+
    
+[docs]
+def hyepergraph_degree_centrality(G):
+    """
+
+    Parameters
+    ----------
+    G :   eg.Hypergraph
+
+    Returns
+    -------
+    degree centrality of each node in G : dict
+
+    """
+    res = {}
+    node_list = G.v
+    # Get hyperedge list
+    edge_list = G.e[0]
+    for node in node_list:
+        res[node] = 0
+
+    for e in edge_list:
+        for n in e:
+            res[n] += 1
+
+    return res
    
+
+
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    +

    Source code for easygraph.functions.hypergraph.hypergraph_clustering

    +"""Algorithms for computing nodal clustering coefficients."""
+
+import numpy as np
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = [
+    "hypergraph_clustering_coefficient",
+    "hypergraph_local_clustering_coefficient",
+    "hypergraph_two_node_clustering_coefficient",
+]
+
+
+
    
+[docs]
+def hypergraph_clustering_coefficient(H):
+    r"""Return the clustering coefficients for
+    each node in a Hypergraph.
+
+    This clustering coefficient is defined as the
+    clustering coefficient of the unweighted pairwise
+    projection of the hypergraph, i.e.,
+    :math:`c = A^3_{i,i}/\binom{k}{2},`
+    where :math:`A` is the adjacency matrix of the network
+    and :math:`k` is the pairwise degree of :math:`i`.
+
+    Parameters
+    ----------
+    H : Hypergraph
+        Hypergraph
+
+    Returns
+    -------
+    dict
+        nodes are keys, clustering coefficients are values.
+
+    Notes
+    -----
+    The clustering coefficient is undefined when the number of
+    neighbors is 0 or 1, but we set the clustering coefficient
+    to 0 in these cases. For more discussion, see
+    https://arxiv.org/abs/0802.2512
+
+    See Also
+    --------
+    local_clustering_coefficient
+    two_node_clustering_coefficient
+
+    References
+    ----------
+    "Clustering Coefficients in Protein Interaction Hypernetworks"
+    by Suzanne Gallagher and Debra Goldberg.
+    DOI: 10.1145/2506583.2506635
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> H = eg.random_hypergraph(3, [1, 1])
+    >>> cc = eg.clustering_coefficient(H)
+    >>> cc
+    {0: 1.0, 1: 1.0, 2: 1.0}
+    """
+    adj = H.adjacency_matrix()
+    k = np.array(adj.sum(axis=1))
+    l = []
+    for i in k:
+        l.append(i[0])
+    k = np.array(l)
+    denom = k * (k - 1) / 2
+    mat = adj.dot(adj).dot(adj)
+    with np.errstate(divide="ignore", invalid="ignore"):
+        result = np.nan_to_num(0.5 * mat.diagonal() / denom)
+    r = {}
+    for i in range(0, len(H.v)):
+        r[i] = result[i]
+    return r
    
+
+
+
+
    
+[docs]
+def hypergraph_local_clustering_coefficient(H):
+    """Compute the local clustering coefficient.
+
+    This clustering coefficient is based on the
+    overlap of the edges connected to a given node,
+    normalized by the size of the node's neighborhood.
+
+    Parameters
+    ----------
+    H : Hypergraph
+        Hypergraph
+
+    Returns
+    -------
+    dict
+        keys are node IDs and values are the
+        clustering coefficients.
+
+    Notes
+    -----
+    The clustering coefficient is undefined when the number of
+    neighbors is 0 or 1, but we set the clustering coefficient
+    to 0 in these cases. For more discussion, see
+    https://arxiv.org/abs/0802.2512
+
+    See Also
+    --------
+    clustering_coefficient
+    two_node_clustering_coefficient
+
+    References
+    ----------
+    "Properties of metabolic graphs: biological organization or representation
+    artifacts?"  by Wanding Zhou and Luay Nakhleh.
+    https://doi.org/10.1186/1471-2105-12-132
+
+    "Hypergraphs for predicting essential genes using multiprotein complex data"
+    by Florian Klimm, Charlotte M. Deane, and Gesine Reinert.
+    https://doi.org/10.1093/comnet/cnaa028
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> H = eg.random_hypergraph(3, [1, 1])
+    >>> cc = eg.local_clustering_coefficient(H)
+    >>> cc
+    {0: 1.0, 1: 1.0, 2: 1.0}
+
+    """
+    result = {}
+    # 节点属于哪些边
+    memberships = []
+    for n in H.v:
+        tmp = set()
+        for index, e in enumerate(H.e[0]):
+            if n in e:
+                tmp.add(index)
+        memberships.append(tmp)
+
+    # 每条边包含哪些节点
+    members = H.e[0]
+    for n in H.v:
+        ev = memberships[n]
+        dv = len(ev)
+        if dv <= 1:
+            result[n] = 0
+        else:
+            total_eo = 0
+            # go over all pairs of edges pairwise
+            for e1 in range(dv):
+                edge1 = members[e1]
+                for e2 in range(e1):
+                    edge2 = members[e2]
+                    # set differences for the hyperedges
+                    D1 = set(edge1) - set(edge2)
+                    D2 = set(edge2) - set(edge1)
+                    # if edges are the same by definition the extra overlap is zero
+                    if len(D1.union(D2)) == 0:
+                        eo = 0
+                    else:
+                        # otherwise we have to look at their neighbours
+                        # the neighbours of D1 and D2, respectively.
+                        neighD1 = {i for d in D1 for i in H.neighbor_of_node(d)}
+                        neighD2 = {i for d in D2 for i in H.neighbor_of_node(d)}
+                        # compute extra overlap [len() is used for cardinality of edges]
+                        eo = (
+                            len(neighD1.intersection(D2))
+                            + len(neighD2.intersection(D1))
+                        ) / len(
+                            D1.union(D2)
+                        )  # add it up
+                    # add it up
+                    total_eo = total_eo + eo
+
+            # include normalisation by degree k*(k-1)/2
+            result[n] = 2 * total_eo / (dv * (dv - 1))
+    return result
    
+
+
+
+
    
+[docs]
+def hypergraph_two_node_clustering_coefficient(H, kind="union"):
+    """Return the clustering coefficients for
+    each node in a Hypergraph.
+
+    This definition averages over all of the
+    two-node clustering coefficients involving the node.
+
+    Parameters
+    ----------
+    H : Hypergraph
+        Hypergraph
+    kind : string, optional
+        The type of two node clustering coefficient. Options
+        are "union", "max", and "min". By default, "union".
+
+    Returns
+    -------
+    dict
+        nodes are keys, clustering coefficients are values.
+
+    Notes
+    -----
+    The clustering coefficient is undefined when the number of
+    neighbors is 0 or 1, but we set the clustering coefficient
+    to 0 in these cases. For more discussion, see
+    https://arxiv.org/abs/0802.2512
+
+    See Also
+    --------
+    clustering_coefficient
+    local_clustering_coefficient
+
+    References
+    ----------
+    "Clustering Coefficients in Protein Interaction Hypernetworks"
+    by Suzanne Gallagher and Debra Goldberg.
+    DOI: 10.1145/2506583.2506635
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> H = eg.random_hypergraph(3, [1, 1])
+    >>> cc = eg.two_node_clustering_coefficient(H, kind="union")
+    >>> cc
+    {0: 0.5, 1: 0.5, 2: 0.5}
+    """
+    result = {}
+    memberships = {}
+    for n in H.v:
+        tmp = set()
+        for index, e in enumerate(H.e[0]):
+            if n in e:
+                tmp.add(index)
+        memberships[n] = tmp
+
+    for n in H.v:
+        neighbors = H.neighbor_of_node(n)
+        result[n] = 0.0
+        for v in neighbors:
+            result[n] += _uv_cc(n, v, memberships, kind=kind) / len(neighbors)
+    return result
    
+
+
+
+def _uv_cc(u, v, memberships, kind="union"):
+    """Helper function to compute the two-node
+    clustering coefficient.
+
+    Parameters
+    ----------
+    u : hashable
+        First node
+    v : hashable
+        Second node
+    memberships : dict
+        node IDs are keys, edge IDs to which they belong
+        are values.
+    kind : str, optional
+        Type of clustering coefficient to compute, by default "union".
+        Options:
+
+        - "union"
+        - "max"
+        - "min"
+
+    Returns
+    -------
+    float
+        The clustering coefficient
+
+    Raises
+    ------
+    EasyGraphError
+        If an invalid clustering coefficient kind
+        is specified.
+
+    References
+    ----------
+    "Clustering Coefficients in Protein Interaction Hypernetworks"
+    by Suzanne Gallagher and Debra Goldberg.
+    DOI: 10.1145/2506583.2506635
+    """
+    m_u = memberships[u]
+    m_v = memberships[v]
+
+    num = len(m_u.intersection(m_v))
+
+    if kind == "union":
+        denom = len(m_u.union(m_v))
+    elif kind == "min":
+        denom = min(len(m_u), len(m_v))
+    elif kind == "max":
+        denom = max(len(m_u), len(m_v))
+    else:
+        raise EasyGraphError("Invalid kind of clustering.")
+
+    if denom == 0:
+        return np.nan
+
+    return num / denom
+
    +
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    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/hypergraph_classic.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/hypergraph_classic.html new file mode 100644 index 00000000..f8dcb342 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/hypergraph_classic.html @@ -0,0 +1,460 @@ + + + + + + + + easygraph.functions.hypergraph.hypergraph_generator.hypergraph_classic - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for easygraph.functions.hypergraph.hypergraph_generator.hypergraph_classic

    +import itertools
+
+import easygraph as eg
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = ["empty_hypergraph", "complete_hypergraph"]
+
+
+
    
+[docs]
+def empty_hypergraph(N=1):
+    """
+
+    Parameters
+    ----------
+    N number of node in Hypergraph, default 1
+
+    Returns
+    -------
+    A eg.Hypergraph with n_num node, without any hyperedge.
+
+    """
+    return eg.Hypergraph(N)
    
+
+
+
+
    
+[docs]
+def complete_hypergraph(n, include_singleton=False):
+    if n == 0:
+        raise EasyGraphError("The number of nodes in a Hypergraph can not be zero")
+    # init
+    # print("easygraph:",eg)
+    hypergraph = eg.Hypergraph(n)
+    total_hyperedegs = []
+    if n > 1:
+        start = 1 if include_singleton else 2
+        for size in range(start, n + 1):
+            hyperedges = itertools.combinations(list(range(n)), size)
+            total_hyperedegs.extend(list(hyperedges))
+        hypergraph.add_hyperedges(total_hyperedegs)
+    return hypergraph
    
+
+
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    + Copyright © 2020-2023, DataNET Group, Fudan University +
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    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/lattice.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/lattice.html new file mode 100644 index 00000000..0e38f7b4 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/lattice.html @@ -0,0 +1,487 @@ + + + + + + + + easygraph.functions.hypergraph.hypergraph_generator.lattice - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for easygraph.functions.hypergraph.hypergraph_generator.lattice

    +"""Generators for some lattice hypergraphs.
+
+All the functions in this module return a Hypergraph class (i.e. a simple, undirected
+hypergraph).
+
+"""
+
+from warnings import warn
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = [
+    "ring_lattice",
+]
+
+
+
    
+[docs]
+def ring_lattice(n, d, k, l):
+    """A ring lattice hypergraph.
+
+    A d-uniform hypergraph on n nodes where each node is part of k edges and the
+    overlap between consecutive edges is d-l.
+
+    Parameters
+    ----------
+    n : int
+        Number of nodes
+    d : int
+        Edge size
+    k : int
+        Number of edges of which a node is a part. Should be a multiple of 2.
+    l : int
+        Overlap between edges
+
+    Returns
+    -------
+    Hypergraph
+        The generated hypergraph
+
+    Raises
+    ------
+    EasyGraphError
+        If k is negative.
+
+    Notes
+    -----
+    ring_lattice(n, 2, k, 0) is a ring lattice graph where each node has k//2 edges on
+    either side.
+
+    """
+    from easygraph.classes.hypergraph import Hypergraph
+
+    if k < 0:
+        raise EasyGraphError("Invalid k value!")
+
+    if k < 2:
+        warn("This creates a completely disconnected hypergraph!")
+
+    if k % 2 != 0:
+        warn("k is not divisible by 2")
+
+    edges = [
+        [node] + [(start + l + i) % n for i in range(d - 1)]
+        for node in range(n)
+        for start in range(node + 1, node + k // 2 + 1)
+    ]
+    H = Hypergraph(num_v=n)
+    H.add_hyperedges(edges)
+    return H
    
+
+
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    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/random.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/random.html new file mode 100644 index 00000000..8acb4761 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/random.html @@ -0,0 +1,797 @@ + + + + + + + + easygraph.functions.hypergraph.hypergraph_generator.random - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for easygraph.functions.hypergraph.hypergraph_generator.random

    +import math
+import random
+import warnings
+
+from collections import defaultdict
+from itertools import combinations
+
+import easygraph as eg
+import numpy as np
+
+# from easygraph.classes.hypergraph import Hypergraph
+from easygraph.utils.exception import EasyGraphError
+from scipy.special import comb
+
+from .lattice import *
+
+
+__all__ = [
+    "random_hypergraph",
+    "chung_lu_hypergraph",
+    "dcsbm_hypergraph",
+    "watts_strogatz_hypergraph",
+]
+
+
+
    
+[docs]
+def dcsbm_hypergraph(k1, k2, g1, g2, omega, seed=None):
+    """A function to generate a Degree-Corrected Stochastic Block Model
+    (DCSBM) hypergraph.
+
+    Parameters
+    ----------
+    k1 : dict
+        This is a dictionary where the keys are node ids
+        and the values are node degrees.
+    k2 : dict
+        This is a dictionary where the keys are edge ids
+        and the values are edge sizes.
+    g1 : dict
+        This a dictionary where the keys are node ids
+        and the values are the group ids to which the node belongs.
+        The keys must match the keys of k1.
+    g2 : dict
+        This a dictionary where the keys are edge ids
+        and the values are the group ids to which the edge belongs.
+        The keys must match the keys of k2.
+    omega : 2D numpy array
+        This is a matrix with entries which specify the number of edges
+        between a given node community and edge community.
+        The number of rows must match the number of node communities
+        and the number of columns must match the number of edge
+        communities.
+    seed : int or None (default)
+        Seed for the random number generator.
+
+    Returns
+    -------
+    Hypergraph
+
+    Warns
+    -----
+    warnings.warn
+        If the sums of the edge sizes and node degrees are not equal, the
+        algorithm still runs, but raises a warning.
+        Also if the sum of the omega matrix does not match the sum of degrees,
+        a warning is raised.
+
+    Notes
+    -----
+    The sums of k1 and k2 should be the same. If they are not the same, this function
+    returns a warning but still runs. The sum of k1 (and k2) and omega should be the
+    same. If they are not the same, this function returns a warning but still runs and
+    the number of entries in the incidence matrix is determined by the omega matrix.
+
+    References
+    ----------
+    Implemented by Mirah Shi in HyperNetX and described for bipartite networks by
+    Larremore et al. in https://doi.org/10.1103/PhysRevE.90.012805
+
+    Examples
+    --------
+    >>> import easygraph as eg; import random; import numpy as np
+    >>> n = 50
+    >>> k1 = {i : random.randint(1, n) for i in range(n)}
+    >>> k2 = {i : sorted(k1.values())[i] for i in range(n)}
+    >>> g1 = {i : random.choice([0, 1]) for i in range(n)}
+    >>> g2 = {i : random.choice([0, 1]) for i in range(n)}
+    >>> omega = np.array([[n//2, 10], [10, n//2]])
+    >>> H = eg.dcsbm_hypergraph(k1, k2, g1, g2, omega)
+
+    """
+    if seed is not None:
+        random.seed(seed)
+
+    # sort dictionary by degree in decreasing order
+    node_labels = [n for n, _ in sorted(k1.items(), key=lambda d: d[1], reverse=True)]
+    edge_labels = [m for m, _ in sorted(k2.items(), key=lambda d: d[1], reverse=True)]
+
+    # Verify that the sum of node and edge degrees and the sum of node degrees and the
+    # sum of community connection matrix differ by less than a single edge.
+    if abs(sum(k1.values()) - sum(k2.values())) > 1:
+        warnings.warn(
+            "The sum of the degree sequence does not match the sum of the size sequence"
+        )
+
+    if abs(sum(k1.values()) - np.sum(omega)) > 1:
+        warnings.warn(
+            "The sum of the degree sequence does not "
+            "match the entries in the omega matrix"
+        )
+
+    # get indices for each community
+    community1_nodes = defaultdict(list)
+    for label in node_labels:
+        group = g1[label]
+        community1_nodes[group].append(label)
+
+    community2_nodes = defaultdict(list)
+    for label in edge_labels:
+        group = g2[label]
+        community2_nodes[group].append(label)
+
+    H = eg.Hypergraph(num_v=len(node_labels))
+
+    kappa1 = defaultdict(lambda: 0)
+    kappa2 = defaultdict(lambda: 0)
+    for id, g in g1.items():
+        kappa1[g] += k1[id]
+    for id, g in g2.items():
+        kappa2[g] += k2[id]
+
+    tmp_hyperedges = []
+    for group1 in community1_nodes.keys():
+        for group2 in community2_nodes.keys():
+            # for each constant probability patch
+            try:
+                group_constant = omega[group1, group2] / (
+                    kappa1[group1] * kappa2[group2]
+                )
+            except ZeroDivisionError:
+                group_constant = 0
+
+            for u in community1_nodes[group1]:
+                j = 0
+                v = community2_nodes[group2][j]  # start from beginning every time
+                # max probability
+                p = min(k1[u] * k2[v] * group_constant, 1)
+                while j < len(community2_nodes[group2]):
+                    if p != 1:
+                        r = random.random()
+                        try:
+                            j = j + math.floor(math.log(r) / math.log(1 - p))
+                        except ZeroDivisionError:
+                            j = np.inf
+                    if j < len(community2_nodes[group2]):
+                        v = community2_nodes[group2][j]
+                        q = min((k1[u] * k2[v]) * group_constant, 1)
+                        r = random.random()
+                        if r < q / p:
+                            # no duplicates
+                            if v < len(tmp_hyperedges):
+                                tmp_hyperedges[v].append(u)
+                            else:
+                                tmp_hyperedges.append([u])
+
+                        p = q
+                        j = j + 1
+
+    H.add_hyperedges(tmp_hyperedges)
+    return H
    
+
+
+
+
    
+[docs]
+def watts_strogatz_hypergraph(n, d, k, l, p, seed=None):
+    """
+
+    Parameters
+    ----------
+    n : int
+    The number of nodes
+    d : int
+        Edge size
+    k: int
+        Number of edges of which a node is a part. Should be a multiple of 2.
+    l: int
+        Overlap between edges
+    p  : float
+        The probability of rewiring each edge
+    seed
+
+    Returns
+    -------
+
+    """
+    if seed is not None:
+        np.random.seed(seed)
+    H = ring_lattice(n, d, k, l)
+    to_remove = []
+    to_add = []
+    H_edges = H.e[0]
+    for e in H_edges:
+        if np.random.random() < p:
+            to_remove.append(e)
+            node = min(e)
+            neighbors = np.random.choice(H.v, size=d - 1)
+            to_add.append(np.append(neighbors, node))
+    H.remove_hyperedges(to_remove)
+    H.add_hyperedges(to_add)
+    return H
    
+
+
+
+
    
+[docs]
+def chung_lu_hypergraph(k1, k2, seed=None):
+    """A function to generate a Chung-Lu hypergraph
+
+    Parameters
+    ----------
+    k1 : dict
+        Dict where the keys are node ids
+        and the values are node degrees.
+    k2 : dict
+        dict where the keys are edge ids
+        and the values are edge sizes.
+    seed : integer or None (default)
+            The seed for the random number generator.
+
+    Returns
+    -------
+    Hypergraph object
+        The generated hypergraph
+
+    Warns
+    -----
+    warnings.warn
+        If the sums of the edge sizes and node degrees are not equal, the
+        algorithm still runs, but raises a warning.
+
+    Notes
+    -----
+    The sums of k1 and k2 should be the same. If they are not the same,
+    this function returns a warning but still runs.
+
+    References
+    ----------
+    Implemented by Mirah Shi in HyperNetX and described for
+    bipartite networks by Aksoy et al. in https://doi.org/10.1093/comnet/cnx001
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> import random
+    >>> n = 100
+    >>> k1 = {i : random.randint(1, 100) for i in range(n)}
+    >>> k2 = {i : sorted(k1.values())[i] for i in range(n)}
+    >>> H = eg.chung_lu_hypergraph(k1, k2)
+
+    """
+    if seed is not None:
+        random.seed(seed)
+
+    # sort dictionary by degree in decreasing order
+    node_labels = [n for n, _ in sorted(k1.items(), key=lambda d: d[1], reverse=True)]
+    edge_labels = [m for m, _ in sorted(k2.items(), key=lambda d: d[1], reverse=True)]
+
+    m = len(k2)
+
+    if sum(k1.values()) != sum(k2.values()):
+        warnings.warn(
+            "The sum of the degree sequence does not match the sum of the size sequence"
+        )
+
+    S = sum(k1.values())
+
+    H = eg.Hypergraph(len(node_labels))
+
+    tmp_hyperedges = []
+    for u in node_labels:
+        j = 0
+        v = edge_labels[j]  # start from beginning every time
+        p = min((k1[u] * k2[v]) / S, 1)
+
+        while j < m:
+            if p != 1:
+                r = random.random()
+                try:
+                    j = j + math.floor(math.log(r) / math.log(1 - p))
+                except ZeroDivisionError:
+                    j = np.inf
+
+            if j < m:
+                v = edge_labels[j]
+                q = min((k1[u] * k2[v]) / S, 1)
+                r = random.random()
+                if r < q / p:
+                    # no duplicates
+                    if v < len(tmp_hyperedges):
+                        tmp_hyperedges[v].append(u)
+                    else:
+                        tmp_hyperedges.append([u])
+                p = q
+                j = j + 1
+
+    H.add_hyperedges(tmp_hyperedges)
+    return H
    
+
+
+
+
    
+[docs]
+def random_hypergraph(N, ps, order=None, seed=None):
+    """Generates a random hypergraph
+
+    Generate N nodes, and connect any d+1 nodes
+    by a hyperedge with probability ps[d-1].
+
+    Parameters
+    ----------
+    N : int
+        Number of nodes
+    ps : list of float
+        List of probabilities (between 0 and 1) to create a
+        hyperedge at each order d between any d+1 nodes. For example,
+        ps[0] is the wiring probability of any edge (2 nodes), ps[1]
+        of any triangles (3 nodes).
+    order: int of None (default)
+        If None, ignore. If int, generates a uniform hypergraph with edges
+        of order `order` (ps must have only one element).
+    seed : integer or None (default)
+            Seed for the random number generator.
+
+    Returns
+    -------
+    Hypergraph object
+        The generated hypergraph
+
+    References
+    ----------
+    Described as 'random hypergraph' by M. Dewar et al. in https://arxiv.org/abs/1703.07686
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> H = eg.random_hypergraph(50, [0.1, 0.01])
+
+    """
+    if seed is not None:
+        np.random.seed(seed)
+
+    if order is not None:
+        if len(ps) != 1:
+            raise EasyGraphError("ps must contain a single element if order is an int")
+
+    if (np.any(np.array(ps) < 0)) or (np.any(np.array(ps) > 1)):
+        raise EasyGraphError("All elements of ps must be between 0 and 1 included.")
+
+    nodes = range(N)
+    hyperedges = []
+
+    for i, p in enumerate(ps):
+        if order is not None:
+            d = order
+        else:
+            d = i + 1  # order, ps[0] is prob of edges (d=1)
+
+        potential_edges = combinations(nodes, d + 1)
+        n_comb = comb(N, d + 1, exact=True)
+        mask = np.random.random(size=n_comb) <= p  # True if edge to keep
+
+        edges_to_add = [e for e, val in zip(potential_edges, mask) if val]
+
+        hyperedges += edges_to_add
+
+    H = eg.Hypergraph(num_v=N)
+    H.add_hyperedges(hyperedges)
+
+    return H
    
+
+
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    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/simple.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/simple.html new file mode 100644 index 00000000..84d3333b --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/simple.html @@ -0,0 +1,495 @@ + + + + + + + + easygraph.functions.hypergraph.hypergraph_generator.simple - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for easygraph.functions.hypergraph.hypergraph_generator.simple

    +from itertools import combinations
+
+import easygraph as eg
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = [
+    "star_clique",
+]
+
+
+
    
+[docs]
+def star_clique(n_star, n_clique, d_max):
+    """Generate a star-clique structure
+
+    That is a star network and a clique network,
+    connected by one pairwise edge connecting the centre of the star to the clique.
+    network, the each clique is promoted to a hyperedge
+    up to order d_max.
+
+    Parameters
+    ----------
+    n_star : int
+        Number of legs of the star
+    n_clique : int
+        Number of nodes in the clique
+    d_max : int
+        Maximum order up to which to promote
+        cliques to hyperedges
+
+    Returns
+    -------
+    H : Hypergraph
+
+    Examples
+    --------
+    >>> import easygraph as eg
+    >>> H = eg.star_clique(6, 7, 2)
+
+    Notes
+    -----
+    The total number of nodes is n_star + n_clique.
+
+    """
+
+    if n_star <= 0:
+        raise ValueError("n_star must be an integer > 0.")
+    if n_clique <= 0:
+        raise ValueError("n_clique must be an integer > 0.")
+    if d_max < 0:
+        raise ValueError("d_max must be an integer >= 0.")
+    elif d_max > n_clique - 1:
+        raise ValueError("d_max must be <= n_clique - 1.")
+
+    nodes_star = range(n_star)
+    nodes_clique = range(n_star, n_star + n_clique)
+    nodes = list(nodes_star) + list(nodes_clique)
+
+    H = eg.Hypergraph(num_v=len(nodes))
+
+    # add star edges (center of the star is 0-th node)
+    H.add_hyperedges([[nodes_star[0], nodes_star[i]] for i in range(1, n_star)])
+
+    # connect clique and star by adding last star leg
+    H.add_hyperedges([nodes_star[0], nodes_clique[0]])
+
+    # add clique hyperedges up to order d_max
+
+    H.add_hyperedges(
+        [
+            e
+            for d in range(1, d_max + 1)
+            for e in list(combinations(nodes_clique, d + 1))
+        ]
+    )
+
+    return H
    
+
+
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    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/uniform.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/uniform.html new file mode 100644 index 00000000..1c245186 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/hypergraph/hypergraph_generator/uniform.html @@ -0,0 +1,802 @@ + + + + + + + + easygraph.functions.hypergraph.hypergraph_generator.uniform - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +
    +

    Source code for easygraph.functions.hypergraph.hypergraph_generator.uniform

    +"""Generate random uniform hypergraphs."""
+import itertools
+import operator
+import random
+import warnings
+
+from functools import reduce
+
+import easygraph as eg
+import numpy as np
+
+from easygraph.utils.exception import EasyGraphError
+
+
+__all__ = [
+    "uniform_hypergraph_configuration_model",
+    "uniform_HSBM",
+    "uniform_HPPM",
+    "uniform_erdos_renyi_hypergraph",
+]
+
+
+
    
+[docs]
+def uniform_hypergraph_configuration_model(k, m, seed=None):
+    """
+    A function to generate an m-uniform configuration model
+
+    Parameters
+    ----------
+    k : dictionary
+        This is a dictionary where the keys are node ids
+        and the values are node degrees.
+    m : int
+        specifies the hyperedge size
+    seed : integer or None (default)
+        The seed for the random number generator
+
+    Returns
+    -------
+    Hypergraph object
+        The generated hypergraph
+
+    Warns
+    -----
+    warnings.warn
+        If the sums of the degrees are not divisible by m, the
+        algorithm still runs, but raises a warning and adds an
+        additional connection to random nodes to satisfy this
+        condition.
+
+    Notes
+    -----
+    This algorithm normally creates multi-edges and loopy hyperedges.
+    We remove the loopy hyperedges.
+
+    References
+    ----------
+    "The effect of heterogeneity on hypergraph contagion models"
+    by Nicholas W. Landry and Juan G. Restrepo
+    https://doi.org/10.1063/5.0020034
+
+
+    Example
+    -------
+    >>> import easygraph as eg
+    >>> import random
+    >>> n = 1000
+    >>> m = 3
+    >>> k = {1: 1, 2: 2, 3: 3, 4: 3}
+    >>> H = eg.uniform_hypergraph_configuration_model(k, m)
+
+    """
+    if seed is not None:
+        random.seed(seed)
+
+    # Making sure we have the right number of stubs
+    remainder = sum(k.values()) % m
+    if remainder != 0:
+        warnings.warn(
+            "This degree sequence is not realizable. "
+            "Increasing the degree of random nodes so that it is."
+        )
+        random_ids = random.sample(list(k.keys()), int(round(m - remainder)))
+        for id in random_ids:
+            k[id] = k[id] + 1
+
+    stubs = []
+    # Creating the list to index through
+    for id in k:
+        stubs.extend([id] * int(k[id]))
+
+    H = eg.Hypergraph(num_v=len(k))
+
+    while len(stubs) != 0:
+        u = random.sample(range(len(stubs)), m)
+        edge = set()
+        for index in u:
+            edge.add(stubs[index])
+        if len(edge) == m:
+            H.add_hyperedges(list(edge))
+
+        for index in sorted(u, reverse=True):
+            del stubs[index]
+
+    return H
    
+
+
+
+
    
+[docs]
+def uniform_HSBM(n, m, p, sizes, seed=None):
+    """Create a uniform hypergraph stochastic block model (HSBM).
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes
+    m : int
+        The hyperedge size
+    p : m-dimensional numpy array
+        tensor of probabilities between communities
+    sizes : list or 1D numpy array
+        The sizes of the community blocks in order
+    seed : integer or None (default)
+        The seed for the random number generator
+
+    Returns
+    -------
+    Hypergraph
+        The constructed SBM hypergraph
+
+    Raises
+    ------
+    EasyGraphError
+        - If the length of sizes and p do not match.
+        - If p is not a tensor with every dimension equal
+        - If p is not m-dimensional
+        - If the entries of p are not in the range [0, 1]
+        - If the sum of the vector of sizes does not equal the number of nodes.
+    Exception
+        If there is an integer overflow error
+
+    See Also
+    --------
+    uniform_HPPM
+
+    References
+    ----------
+    Nicholas W. Landry and Juan G. Restrepo.
+    "Polarization in hypergraphs with community structure."
+    Preprint, 2023. https://doi.org/10.48550/arXiv.2302.13967
+    """
+    # Check if dimensions match
+    if len(sizes) != np.size(p, axis=0):
+        raise EasyGraphError("'sizes' and 'p' do not match.")
+    if len(np.shape(p)) != m:
+        raise EasyGraphError("The dimension of p does not match m")
+    # Check that p has the same length over every dimension.
+    if len(set(np.shape(p))) != 1:
+        raise EasyGraphError("'p' must be a square tensor.")
+    if np.max(p) > 1 or np.min(p) < 0:
+        raise EasyGraphError("Entries of 'p' not in [0,1].")
+    if np.sum(sizes) != n:
+        raise EasyGraphError("Sum of sizes does not match n")
+
+    if seed is not None:
+        np.random.seed(seed)
+
+    node_labels = range(n)
+    H = eg.Hypergraph(num_v=n)
+
+    block_range = range(len(sizes))
+    # Split node labels in a partition (list of sets).
+    size_cumsum = [sum(sizes[0:x]) for x in range(0, len(sizes) + 1)]
+    partition = [
+        list(node_labels[size_cumsum[x] : size_cumsum[x + 1]])
+        for x in range(0, len(size_cumsum) - 1)
+    ]
+
+    for block in itertools.product(block_range, repeat=m):
+        if p[block] == 1:  # Test edges cases p_ij = 0 or 1
+            edges = itertools.product((partition[i] for i in block_range))
+            for e in edges:
+                H.add_hyperedges(list(e))
+        elif p[block] > 0:
+            partition_sizes = [len(partition[i]) for i in block]
+            max_index = reduce(operator.mul, partition_sizes, 1)
+            if max_index < 0:
+                raise Exception("Index overflow error!")
+            index = np.random.geometric(p[block]) - 1
+
+            while index < max_index:
+                indices = _index_to_edge_partition(index, partition_sizes, m)
+                e = {partition[block[i]][indices[i]] for i in range(m)}
+                if len(e) == m:
+                    H.add_hyperedges(list(e))
+                index += np.random.geometric(p[block])
+    return H
    
+
+
+
+
    
+[docs]
+def uniform_HPPM(n, m, rho, k, epsilon, seed=None):
+    """Construct the m-uniform hypergraph planted partition model (m-HPPM)
+
+    Parameters
+    ----------
+    n : int > 0
+        Number of nodes
+    m : int > 0
+        Hyperedge size
+    rho : float between 0 and 1
+        The fraction of nodes in community 1
+    k : float > 0
+        Mean degree
+    epsilon : float > 0
+        Imbalance parameter
+    seed : integer or None (default)
+        The seed for the random number generator
+
+    Returns
+    -------
+    Hypergraph
+        The constructed m-HPPM hypergraph.
+
+    Raises
+    ------
+    EasyGraphError
+        - If rho is not between 0 and 1
+        - If the mean degree is negative.
+        - If epsilon is not between 0 and 1
+
+    See Also
+    --------
+    uniform_HSBM
+
+    References
+    ----------
+    Nicholas W. Landry and Juan G. Restrepo.
+    "Polarization in hypergraphs with community structure."
+    Preprint, 2023. https://doi.org/10.48550/arXiv.2302.13967
+    """
+
+    if rho < 0 or rho > 1:
+        raise EasyGraphError("The value of rho must be between 0 and 1")
+    if k < 0:
+        raise EasyGraphError("The mean degree must be non-negative")
+    if epsilon < 0 or epsilon > 1:
+        raise EasyGraphError("epsilon must be between 0 and 1")
+
+    sizes = [int(rho * n), n - int(rho * n)]
+
+    p = k / (m * n ** (m - 1))
+    # ratio of inter- to intra-community edges
+    q = rho**m + (1 - rho) ** m
+    r = 1 / q - 1
+    p_in = (1 + r * epsilon) * p
+    p_out = (1 - epsilon) * p
+
+    p = p_out * np.ones([2] * m)
+    p[tuple([0] * m)] = p_in
+    p[tuple([1] * m)] = p_in
+
+    return uniform_HSBM(n, m, p, sizes, seed=seed)
    
+
+
+
+
    
+[docs]
+def uniform_erdos_renyi_hypergraph(n, m, p, p_type="degree", seed=None):
+    """Generate an m-uniform Erdős–Rényi hypergraph
+
+    This creates a hypergraph with `n` nodes where
+    hyperedges of size `m` are created at random to
+    obtain a mean degree of `k`.
+
+    Parameters
+    ----------
+    n : int > 0
+        Number of nodes
+    m : int > 0
+        Hyperedge size
+    p : float or int > 0
+        Mean expected degree if p_type="degree" and
+        probability of an m-hyperedge if p_type="prob"
+    p_type : str
+        "degree" or "prob", by default "degree"
+    seed : integer or None (default)
+        The seed for the random number generator
+
+    Returns
+    -------
+    Hypergraph
+        The Erdos Renyi hypergraph
+
+
+    See Also
+    --------
+    random_hypergraph
+    """
+    if seed is not None:
+        np.random.seed(seed)
+
+    node_labels = range(n)
+    H = eg.Hypergraph(num_v=n)
+
+    if p_type == "degree":
+        q = p / (m * n ** (m - 1))  # wiring probability
+    elif p_type == "prob":
+        q = p
+    else:
+        raise EasyGraphError("Invalid p_type!")
+
+    if q > 1 or q < 0:
+        raise EasyGraphError("Probability not in [0,1].")
+
+    index = np.random.geometric(q) - 1  # -1 b/c zero indexing
+    max_index = n**m
+    while index < max_index:
+        e = set(_index_to_edge(index, n, m))
+        if len(e) == m:
+            H.add_hyperedges(list(e))
+        index += np.random.geometric(q)
+    return H
    
+
+
+
+def _index_to_edge(index, n, m):
+    """Generate a hyperedge given an index in the list of possible edges.
+
+    Parameters
+    ----------
+    index : int > 0
+        The index of the hyperedge in the list of all possible hyperedges.
+    n : int > 0
+        The number of nodes
+    m : int > 0
+        The hyperedge size.
+
+    Returns
+    -------
+    list
+        The reconstructed hyperedge
+
+    See Also
+    --------
+    _index_to_edge_partition
+
+    References
+    ----------
+    https://stackoverflow.com/questions/53834707/element-at-index-in-itertools-product
+    """
+    return [(index // (n**r) % n) for r in range(m - 1, -1, -1)]
+
+
+def _index_to_edge_partition(index, partition_sizes, m):
+    """Generate a hyperedge given an index in the list of possible edges
+    and a partition of community labels.
+
+    Parameters
+    ----------
+    index : int > 0
+        The index of the hyperedge in the list of all possible hyperedges.
+    n : int > 0
+        The number of nodes
+    m : int > 0
+        The hyperedge size.
+
+    Returns
+    -------
+    list
+        The reconstructed hyperedge
+
+    See Also
+    --------
+    _index_to_edge
+
+    """
+    try:
+        return [
+            int(index // np.prod(partition_sizes[r + 1 :]) % partition_sizes[r])
+            for r in range(m)
+        ]
+    except KeyError:
+        raise Exception("Invalid parameters")
+
    +
    +
    +
    + +
    + + +
    +
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    + Copyright © 2020-2023, DataNET Group, Fudan University +
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    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/functions/path/diameter.html b/docs_using_sphinx/_build/html/_modules/easygraph/functions/path/diameter.html new file mode 100644 index 00000000..50329874 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/functions/path/diameter.html @@ -0,0 +1,526 @@ + + + + + + + + easygraph.functions.path.diameter - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.functions.path.diameter

    +import easygraph as eg
+import easygraph.functions.path
+
+
+
    
+[docs]
+def eccentricity(G, v=None, sp=None):
+    """Returns the eccentricity of nodes in G.
+
+    The eccentricity of a node v is the maximum distance from v to
+    all other nodes in G.
+
+    Parameters
+    ----------
+    G : EasyGraph graph
+       A graph
+
+    v : node, optional
+       Return value of specified node
+
+    sp : dict of dicts, optional
+       All pairs shortest path lengths as a dictionary of dictionaries
+
+    Returns
+    -------
+    ecc : dictionary
+       A dictionary of eccentricity values keyed by node.
+
+    Examples
+    --------
+    >>> G = eg.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
+    >>> dict(eg.eccentricity(G))
+    {1: 2, 2: 3, 3: 2, 4: 2, 5: 3}
+
+    >>> dict(eg.eccentricity(G, v=[1, 5]))  # This returns the eccentrity of node 1 & 5
+    {1: 2, 5: 3}
+
+    """
+    #    if v is None:                # none, use entire graph
+    #        nodes=G.nodes()
+    #    elif v in G:               # is v a single node
+    #        nodes=[v]
+    #    else:                      # assume v is a container of nodes
+    #        nodes=v
+    order = G.order()
+
+    e = {}
+    for n in G.nbunch_iter(v):
+        if sp is None:
+            length = eg.single_source_dijkstra(G, n)
+            L = len(length)
+        else:
+            try:
+                length = sp[n]
+                L = len(length)
+            except TypeError as err:
+                raise eg.EasyGraphError('Format of "sp" is invalid.') from err
+        if L != order:
+            if G.is_directed():
+                msg = (
+                    "Found infinite path length because the digraph is not"
+                    " strongly connected"
+                )
+            else:
+                msg = "Found infinite path length because the graph is not connected"
+            raise eg.EasyGraphError(msg)
+
+        e[n] = max(length.values())
+
+    if v in G:
+        return e[v]  # return single value
+    else:
+        return e
    
+
+
+
+
    
+[docs]
+def diameter(G, e=None):
+    """Returns the diameter of the graph G.
+
+    The diameter is the maximum eccentricity.
+
+    Parameters
+    ----------
+    G : EasyGraph graph
+       A graph
+
+    e : eccentricity dictionary, optional
+      A precomputed dictionary of eccentricities.
+
+    Returns
+    -------
+    d : integer
+       Diameter of graph
+
+    Examples
+    --------
+    >>> G = eg.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
+    >>> eg.diameter(G)
+    3
+
+    See Also
+    --------
+    eccentricity
+    """
+
+    if e is None:
+        e = eccentricity(G)
+    return max(e.values())
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/ml_metrics.html b/docs_using_sphinx/_build/html/_modules/easygraph/ml_metrics.html new file mode 100644 index 00000000..e552247f --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/ml_metrics.html @@ -0,0 +1,463 @@ + + + + + + + + easygraph.ml_metrics - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
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    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.ml_metrics

    +try:
+    from typing import Dict
+    from typing import List
+    from typing import Union
+
+    from easygraph._global import AUTHOR_EMAIL
+
+    from .base import BaseEvaluator
+    from .classification import VertexClassificationEvaluator
+    from .classification import available_classification_metrics
+    from .hypergraphs import HypergraphVertexClassificationEvaluator
+except:
+    print(
+        "Warning raise in module:ml_metrics. Please install Pytorch before you use"
+        " functions related to nueral network"
+    )
+
+
+
    
+[docs]
+def build_evaluator(
+    task: str,
+    metric_configs: List[Union[str, Dict[str, dict]]],
+    validate_index: int = 0,
+):
+    r"""Return the metric evaluator for the given task.
+
+    Args:
+        ``task`` (``str``): The type of the task. The supported types include: ``graph_vertex_classification``, ``hypergraph_vertex_classification``, and ``user_item_recommender``.
+        ``metric_configs`` (``List[Union[str, Dict[str, dict]]]``): The list of metric names.
+        ``validate_index`` (``int``): The specified metric index used for validation. Defaults to ``0``.
+    """
+    if task == "hypergraph_vertex_classification":
+        return HypergraphVertexClassificationEvaluator(metric_configs, validate_index)
+    else:
+        raise ValueError(
+            f"{task} is not supported yet. Please email '{AUTHOR_EMAIL}' to add it."
+        )
    
+
+
+
+# __all__ = [
+#     "BaseEvaluator",
+#     "build_evaluator",
+#     "available_classification_metrics",
+#     "VertexClassificationEvaluator",
+#     "HypergraphVertexClassificationEvaluator",
+# ]
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/utils/download.html b/docs_using_sphinx/_build/html/_modules/easygraph/utils/download.html new file mode 100644 index 00000000..ba4e13a1 --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/utils/download.html @@ -0,0 +1,519 @@ + + + + + + + + easygraph.utils.download - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.utils.download

    +import hashlib
+import warnings
+
+from functools import wraps
+from pathlib import Path
+
+import requests
+
+
+__all__ = [
+    "check_file",
+    "download_file",
+    "download_and_check",
+]
+
+
+
    
+[docs]
+def download_file(url: str, file_path: Path):
+    r"""Download a file from a url.
+
+    Args:
+        ``url`` (``str``): the url of the file
+        ``file_path`` (``str``): the path to the file
+    """
+    file_path.parent.mkdir(parents=True, exist_ok=True)
+    r = requests.get(url, stream=True, verify=True)
+    if r.status_code != 200:
+        raise requests.HTTPError(f"{url} is not accessible.")
+    with open(file_path, "wb") as f:
+        for chunk in r.iter_content(chunk_size=1024):
+            if chunk:
+                f.write(chunk)
    
+
+
+
+
    
+[docs]
+def check_file(file_path: Path, md5: str):
+    r"""Check if a file is valid.
+
+    Args:
+        ``file_path`` (``Path``): The local path of the file.
+        ``md5`` (``str``): The md5 of the file.
+
+    Raises:
+        FileNotFoundError: Not found the file.
+    """
+    if not file_path.exists():
+        raise FileNotFoundError(f"{file_path} does not exist.")
+    else:
+        with open(file_path, "rb") as f:
+            data = f.read()
+        cur_md5 = hashlib.md5(data).hexdigest()
+        return cur_md5 == md5
    
+
+
+
+def _retry(n: int, exception_type=requests.HTTPError):
+    r"""A decorator for retrying a function for n times.
+
+    Args:
+        ``n`` (``int``): The number of times to retry.
+    """
+
+    def decorator(fetcher):
+        @wraps(fetcher)
+        def wrapper(*args, **kwargs):
+            for i in range(n - 1):
+                try:
+                    return fetcher(*args, **kwargs)
+                except exception_type as e:
+                    warnings.warn(f"Retry downloading({i + 1}/{n}): {str(e)}")
+                except Exception as e:
+                    raise e
+            return fetcher(*args, **kwargs)
+            # raise FileNotFoundError
+
+        return wrapper
+
+    return decorator
+
+
+
    
+[docs]
+@_retry(3)
+def download_and_check(url: str, file_path: Path, md5: str):
+    r"""Download a file from a url and check its integrity.
+
+    Args:
+        ``url`` (``str``): The url of the file.
+        ``file_path`` (``Path``): The path to the file.
+        ``md5`` (``str``): The md5 of the file.
+    """
+    if not file_path.exists():
+        download_file(url, file_path)
+    if not check_file(file_path, md5):
+        file_path.unlink()
+        raise ValueError(
+            f"{file_path} is corrupted. We will delete it, and try to download it"
+            " again."
+        )
+    return True
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/easygraph/utils/logging.html b/docs_using_sphinx/_build/html/_modules/easygraph/utils/logging.html new file mode 100644 index 00000000..2e78537c --- /dev/null +++ b/docs_using_sphinx/_build/html/_modules/easygraph/utils/logging.html @@ -0,0 +1,465 @@ + + + + + + + + easygraph.utils.logging - EasyGraph 1.0 + + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    EasyGraph 1.0
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    +
    + +
    + +
    +
    +

    Source code for easygraph.utils.logging

    +import logging
+import sys
+
+from pathlib import Path
+from typing import Union
+
+
+__all__ = ["default_log_formatter", "simple_stdout2file"]
+
+
+
    
+[docs]
+def default_log_formatter() -> logging.Formatter:
+    r"""Create a default formatter of log messages for logging."""
+
+    return logging.Formatter("[%(levelname)s %(asctime)s]-> %(message)s")
    
+
+
+
+
    
+[docs]
+def simple_stdout2file(file_path: Union[str, Path]) -> None:
+    r"""This function simply wraps the ``sys.stdout`` stream, and outputs messages to the ``sys.stdout`` and a specified file, simultaneously.
+
+    Parameters:
+        ``file_path`` (``file_path: Union[str, Path]``): The path of the file to output the messages.
+    """
+
+    class SimpleLogger:
+        def __init__(self, file_path: Path):
+            file_path = Path(file_path).absolute()
+            assert (
+                file_path.parent.exists()
+            ), f"The parent directory of {file_path} does not exist."
+            self.file_path = file_path
+            self.terminal = sys.stdout
+            self.file = open(file_path, "a")
+
+        def write(self, message):
+            self.terminal.write(message)
+            self.file.write(message)
+            self.flush()
+
+        def flush(self):
+            self.terminal.flush()
+            self.file.flush()
+
+    file_path = Path(file_path)
+    sys.stdout = SimpleLogger(file_path)
    
+
+
    +
    +
    +
    + +
    + + +
    +
    +
    +
    + Copyright © 2020-2023, DataNET Group, Fudan University +
    + Made with Sphinx and @pradyunsg's + + Furo + +
    +
    + +
    +
    + +
    +
    + +
    +
    + + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_modules/index.html b/docs_using_sphinx/_build/html/_modules/index.html index cbad9425..437696c3 100644 --- a/docs_using_sphinx/_build/html/_modules/index.html +++ b/docs_using_sphinx/_build/html/_modules/index.html @@ -1,15 +1,15 @@ - + - + Overview: module code - EasyGraph 1.0 - - - - + + + + @@ -143,7 +143,7 @@ - - - - - - - + + + + + \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.dynamic.rst.txt b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.dynamic.rst.txt new file mode 100644 index 00000000..e4f172c3 --- /dev/null +++ b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.dynamic.rst.txt @@ -0,0 +1,45 @@ +easygraph.datasets.dynamic package +================================== + +Submodules +---------- + +easygraph.datasets.dynamic.email\_enron module +---------------------------------------------- + +.. automodule:: easygraph.datasets.dynamic.email_enron + :members: + :undoc-members: + :show-inheritance: + +easygraph.datasets.dynamic.email\_eu module +------------------------------------------- + +.. automodule:: easygraph.datasets.dynamic.email_eu + :members: + :undoc-members: + :show-inheritance: + +easygraph.datasets.dynamic.hospital\_lyon module +------------------------------------------------ + +.. automodule:: easygraph.datasets.dynamic.hospital_lyon + :members: + :undoc-members: + :show-inheritance: + +easygraph.datasets.dynamic.load\_dataset module +----------------------------------------------- + +.. automodule:: easygraph.datasets.dynamic.load_dataset + :members: + :undoc-members: + :show-inheritance: + +Module contents +--------------- + +.. automodule:: easygraph.datasets.dynamic + :members: + :undoc-members: + :show-inheritance: diff --git a/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.hypergraph.rst.txt b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.hypergraph.rst.txt index f167acca..68b35407 100644 --- a/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.hypergraph.rst.txt +++ b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.hypergraph.rst.txt @@ -12,10 +12,10 @@ easygraph.datasets.hypergraph.House\_Committees module :undoc-members: :show-inheritance: -easygraph.datasets.hypergraph.base module +easygraph.datasets.hypergraph.Yelp module ----------------------------------------- -.. automodule:: easygraph.datasets.hypergraph.base +.. automodule:: easygraph.datasets.hypergraph.Yelp :members: :undoc-members: :show-inheritance: @@ -28,6 +28,14 @@ easygraph.datasets.hypergraph.cat\_edge\_Cooking module :undoc-members: :show-inheritance: +easygraph.datasets.hypergraph.coauthorship module +------------------------------------------------- + +.. automodule:: easygraph.datasets.hypergraph.coauthorship + :members: + :undoc-members: + :show-inheritance: + easygraph.datasets.hypergraph.cocitation module ----------------------------------------------- @@ -44,10 +52,18 @@ easygraph.datasets.hypergraph.contact\_primary\_school module :undoc-members: :show-inheritance: -easygraph.datasets.hypergraph.load\_dataset module --------------------------------------------------- +easygraph.datasets.hypergraph.cooking\_200 module +------------------------------------------------- + +.. automodule:: easygraph.datasets.hypergraph.cooking_200 + :members: + :undoc-members: + :show-inheritance: + +easygraph.datasets.hypergraph.hypergraph\_dataset\_base module +-------------------------------------------------------------- -.. automodule:: easygraph.datasets.hypergraph.load_dataset +.. automodule:: easygraph.datasets.hypergraph.hypergraph_dataset_base :members: :undoc-members: :show-inheritance: diff --git a/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.rst.txt b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.rst.txt index 715af066..2d6682e0 100644 --- a/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.rst.txt +++ b/docs_using_sphinx/_build/html/_sources/reference/easygraph.datasets.rst.txt @@ -7,19 +7,12 @@ Subpackages .. toctree:: :maxdepth: 4 + easygraph.datasets.dynamic easygraph.datasets.hypergraph Submodules ---------- -easygraph.datasets.base module ------------------------------- - -.. automodule:: easygraph.datasets.base - :members: - :undoc-members: - :show-inheritance: - easygraph.datasets.citation\_graph module ----------------------------------------- @@ -28,38 +21,6 @@ easygraph.datasets.citation\_graph module :undoc-members: :show-inheritance: -easygraph.datasets.cooking\_200 module --------------------------------------- - -.. automodule:: easygraph.datasets.cooking_200 - :members: - :undoc-members: - :show-inheritance: - -easygraph.datasets.eg\_dataset module -------------------------------------- - -.. automodule:: easygraph.datasets.eg_dataset - :members: - :undoc-members: - :show-inheritance: - -easygraph.datasets.email\_enron module --------------------------------------- - -.. automodule:: easygraph.datasets.email_enron - :members: - :undoc-members: - :show-inheritance: - -easygraph.datasets.email\_eu module ------------------------------------ - -.. automodule:: easygraph.datasets.email_eu - :members: - :undoc-members: - :show-inheritance: - easygraph.datasets.get\_sample\_graph module -------------------------------------------- @@ -76,10 +37,10 @@ easygraph.datasets.gnn\_benchmark module :undoc-members: :show-inheritance: -easygraph.datasets.hospital\_lyon module ----------------------------------------- +easygraph.datasets.graph\_dataset\_base module +---------------------------------------------- -.. automodule:: easygraph.datasets.hospital_lyon +.. automodule:: easygraph.datasets.graph_dataset_base :members: :undoc-members: :show-inheritance: diff --git a/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.centrality.rst.txt b/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.centrality.rst.txt index 87d19355..82dedfcb 100644 --- a/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.centrality.rst.txt +++ b/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.centrality.rst.txt @@ -20,6 +20,30 @@ easygraph.functions.hypergraph.centrality.degree module :undoc-members: :show-inheritance: +easygraph.functions.hypergraph.centrality.hypercoreness module +-------------------------------------------------------------- + +.. automodule:: easygraph.functions.hypergraph.centrality.hypercoreness + :members: + :undoc-members: + :show-inheritance: + +easygraph.functions.hypergraph.centrality.s\_centrality module +-------------------------------------------------------------- + +.. automodule:: easygraph.functions.hypergraph.centrality.s_centrality + :members: + :undoc-members: + :show-inheritance: + +easygraph.functions.hypergraph.centrality.vector\_centrality module +------------------------------------------------------------------- + +.. automodule:: easygraph.functions.hypergraph.centrality.vector_centrality + :members: + :undoc-members: + :show-inheritance: + Module contents --------------- diff --git a/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.rst.txt b/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.rst.txt index f070dc4c..166c0057 100644 --- a/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.rst.txt +++ b/docs_using_sphinx/_build/html/_sources/reference/easygraph.functions.hypergraph.rst.txt @@ -29,6 +29,14 @@ easygraph.functions.hypergraph.hypergraph\_clustering module :undoc-members: :show-inheritance: +easygraph.functions.hypergraph.hypergraph\_operation module +----------------------------------------------------------- + +.. automodule:: easygraph.functions.hypergraph.hypergraph_operation + :members: + :undoc-members: + :show-inheritance: + Module contents --------------- diff --git a/docs_using_sphinx/_build/html/_sources/tutorial.rst.txt b/docs_using_sphinx/_build/html/_sources/tutorial.rst.txt index 6f153740..368e09c9 100644 --- a/docs_using_sphinx/_build/html/_sources/tutorial.rst.txt +++ b/docs_using_sphinx/_build/html/_sources/tutorial.rst.txt @@ -291,4 +291,14 @@ The PageRank algorithm **Usage** - For class methods, calling and parameter passing are the same as python. -- For module function, easygraph will select specific codes to execute according to the class of the graph. \ No newline at end of file +- For module function, easygraph will select specific codes to execute according to the class of the graph. + +View the tutorials in Colab. +------------------------- +`tutorial1: Two brief tutorials of how to do graph analysis with EasyGraph. `_ + +`tutorial2: Using C++ code to achieve a better performance. `_ + +`tutorial3: Graph Embedding. `_ + +`tutorial4: Community Detection. `_ \ No newline at end of file diff --git a/docs_using_sphinx/_build/html/_static/pygments.css b/docs_using_sphinx/_build/html/_static/pygments.css index ed1f4cf6..17e498a6 100644 --- a/docs_using_sphinx/_build/html/_static/pygments.css +++ b/docs_using_sphinx/_build/html/_static/pygments.css @@ -17,7 +17,6 @@ .highlight .cs { color: #408090; background-color: #fff0f0 } /* Comment.Special */ .highlight .gd { color: #A00000 } /* Generic.Deleted */ .highlight .ge { font-style: italic } /* Generic.Emph */ -.highlight .ges { font-weight: bold; font-style: italic } /* Generic.EmphStrong */ .highlight .gr { color: #FF0000 } /* Generic.Error */ .highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */ .highlight .gi { color: #00A000 } /* Generic.Inserted */ @@ -99,7 +98,6 @@ body[data-theme="dark"] .highlight .c1 { color: #ababab; font-style: italic } /* body[data-theme="dark"] .highlight .cs { color: #e50808; font-weight: bold; background-color: #520000 } /* Comment.Special */ body[data-theme="dark"] .highlight .gd { color: #d22323 } /* Generic.Deleted */ body[data-theme="dark"] .highlight .ge { color: #d0d0d0; font-style: italic } /* Generic.Emph */ -body[data-theme="dark"] .highlight .ges { color: #d0d0d0; font-weight: bold; font-style: italic } /* Generic.EmphStrong */ body[data-theme="dark"] .highlight .gr { color: #d22323 } /* Generic.Error */ body[data-theme="dark"] .highlight .gh { color: #ffffff; font-weight: bold } /* Generic.Heading */ body[data-theme="dark"] .highlight .gi { color: #589819 } /* Generic.Inserted */ @@ -185,7 +183,6 @@ body:not([data-theme="light"]) .highlight .c1 { color: #ababab; font-style: ital body:not([data-theme="light"]) .highlight .cs { color: #e50808; font-weight: bold; background-color: #520000 } /* Comment.Special */ body:not([data-theme="light"]) .highlight .gd { 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detail,\n });\n\n // Dispatch the event\n elem.dispatchEvent(event);\n };\n\n /**\n * Get an element's distance from the top of the Document.\n * @param {Node} elem The element\n * @return {Number} Distance from the top in pixels\n */\n var getOffsetTop = function (elem) {\n var location = 0;\n if (elem.offsetParent) {\n while (elem) {\n location += elem.offsetTop;\n elem = elem.offsetParent;\n }\n }\n return location >= 0 ? location : 0;\n };\n\n /**\n * Sort content from first to last in the DOM\n * @param {Array} contents The content areas\n */\n var sortContents = function (contents) {\n if (contents) {\n contents.sort(function (item1, item2) {\n var offset1 = getOffsetTop(item1.content);\n var offset2 = getOffsetTop(item2.content);\n if (offset1 < offset2) return -1;\n return 1;\n });\n }\n };\n\n /**\n * Get the offset to use for calculating position\n * @param {Object} settings The settings for this instantiation\n * @return {Float} The number of pixels to offset the 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var bounds = elem.getBoundingClientRect();\n var offset = getOffset(settings);\n if (bottom) {\n return (\n parseInt(bounds.bottom, 10) <\n (window.innerHeight || document.documentElement.clientHeight)\n );\n }\n return parseInt(bounds.top, 10) <= offset;\n };\n\n /**\n * Check if at the bottom of the viewport\n * @return {Boolean} If true, page is at the bottom of the viewport\n */\n var isAtBottom = function () {\n if (\n Math.ceil(window.innerHeight + window.pageYOffset) >=\n getDocumentHeight()\n )\n return true;\n return false;\n };\n\n /**\n * Check if the last item should be used (even if not at the top of the page)\n * @param {Object} item The last item\n * @param {Object} settings The settings for this instantiation\n * @return {Boolean} If true, use the last item\n */\n var useLastItem = function (item, settings) {\n if (isAtBottom() && isInView(item.content, settings, true)) return true;\n return false;\n };\n\n /**\n * Get the active content\n * @param {Array} contents The content areas\n * @param {Object} settings The settings for this instantiation\n * @return {Object} The content area and matching navigation link\n */\n var getActive = function (contents, settings) {\n var last = contents[contents.length - 1];\n if (useLastItem(last, settings)) return last;\n for (var i = contents.length - 1; i >= 0; i--) {\n if (isInView(contents[i].content, settings)) return contents[i];\n }\n };\n\n /**\n * Deactivate parent navs in a nested navigation\n * @param {Node} nav The starting navigation element\n * @param {Object} settings The settings for this instantiation\n */\n var deactivateNested = function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested || !nav.parentNode) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Remove the active class\n li.classList.remove(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n deactivateNested(li, 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false,\n nestedClass: \"active\",\n\n // Offset & reflow\n offset: 0,\n reflow: false,\n\n // Event support\n events: true,\n };\n\n //\n // Methods\n //\n\n /**\n * Merge two or more objects together.\n * @param {Object} objects The objects to merge together\n * @returns {Object} Merged values of defaults and options\n */\n var extend = function () {\n var merged = {};\n Array.prototype.forEach.call(arguments, function (obj) {\n for (var key in obj) {\n if (!obj.hasOwnProperty(key)) return;\n merged[key] = obj[key];\n }\n });\n return merged;\n };\n\n /**\n * Emit a custom event\n * @param {String} type The event type\n * @param {Node} elem The element to attach the event to\n * @param {Object} detail Any details to pass along with the event\n */\n var emitEvent = function (type, elem, detail) {\n // Make sure events are enabled\n if (!detail.settings.events) return;\n\n // Create a new event\n var event = new CustomEvent(type, {\n bubbles: true,\n cancelable: true,\n detail: detail,\n });\n\n // Dispatch the event\n elem.dispatchEvent(event);\n };\n\n /**\n * Get an element's distance from the top of the Document.\n * @param {Node} elem The element\n * @return {Number} Distance from the top in pixels\n */\n var getOffsetTop = function (elem) {\n var location = 0;\n if (elem.offsetParent) {\n while (elem) {\n location += elem.offsetTop;\n elem = elem.offsetParent;\n }\n }\n return location >= 0 ? location : 0;\n };\n\n /**\n * Sort content from first to last in the DOM\n * @param {Array} contents The content areas\n */\n var sortContents = function (contents) {\n if (contents) {\n contents.sort(function (item1, item2) {\n var offset1 = getOffsetTop(item1.content);\n var offset2 = getOffsetTop(item2.content);\n if (offset1 < offset2) return -1;\n return 1;\n });\n }\n };\n\n /**\n * Get the offset to use for calculating position\n * @param {Object} settings The settings for this instantiation\n * @return {Float} The number of pixels to offset the 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function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Add the active class\n li.classList.add(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n activateNested(li, settings);\n };\n\n /**\n * Activate a nav and content area\n * @param {Object} items The nav item and content to activate\n * @param {Object} settings The settings for this instantiation\n */\n var activate = function (items, settings) {\n // Make sure there are items to activate\n if (!items) return;\n\n // Get the parent list item\n var li = items.nav.closest(\"li\");\n if (!li) return;\n\n // Add the active class to the nav and content\n li.classList.add(settings.navClass);\n items.content.classList.add(settings.contentClass);\n\n // Activate any parent navs in a nested navigation\n activateNested(li, settings);\n\n // Emit a custom event\n emitEvent(\"gumshoeActivate\", li, {\n link: items.nav,\n content: items.content,\n settings: settings,\n });\n };\n\n /**\n * Create the Constructor object\n * @param {String} selector The selector to use for navigation items\n * @param {Object} options User options and settings\n */\n var Constructor = function (selector, options) {\n //\n // Variables\n //\n\n var publicAPIs = {};\n var navItems, contents, current, timeout, settings;\n\n //\n // Methods\n //\n\n /**\n * Set variables from DOM elements\n */\n publicAPIs.setup = function () {\n // Get all nav items\n navItems = document.querySelectorAll(selector);\n\n // Create contents array\n contents = [];\n\n // Loop through each item, get it's matching content, and push to the array\n Array.prototype.forEach.call(navItems, function (item) {\n // Get the content for the nav item\n var content = document.getElementById(\n decodeURIComponent(item.hash.substr(1)),\n );\n if (!content) return;\n\n // Push to the contents array\n 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window.cancelAnimationFrame(timeout);\n }\n\n // Setup debounce callback\n timeout = window.requestAnimationFrame(publicAPIs.detect);\n };\n\n /**\n * Update content sorting on resize\n * Debounced for performance\n */\n var resizeHandler = function (event) {\n // If there's a timer, cancel it\n if (timeout) {\n window.cancelAnimationFrame(timeout);\n }\n\n // Setup debounce callback\n timeout = window.requestAnimationFrame(function () {\n sortContents(contents);\n publicAPIs.detect();\n });\n };\n\n /**\n * Destroy the current instantiation\n */\n publicAPIs.destroy = function () {\n // Undo DOM changes\n if (current) {\n deactivate(current, settings);\n }\n\n // Remove event listeners\n window.removeEventListener(\"scroll\", scrollHandler, false);\n if (settings.reflow) {\n window.removeEventListener(\"resize\", resizeHandler, false);\n }\n\n // Reset variables\n contents = null;\n navItems = null;\n current = null;\n timeout = null;\n settings = null;\n };\n\n /**\n * Initialize the 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Correct the color inheritance from `fieldset` elements in IE.\n * 3. Remove the padding so developers are not caught out when they zero out\n * `fieldset` elements in all browsers.\n */\n\nlegend {\n box-sizing: border-box; /* 1 */\n color: inherit; /* 2 */\n display: table; /* 1 */\n max-width: 100%; /* 1 */\n padding: 0; /* 3 */\n white-space: normal; /* 1 */\n}\n\n/**\n * Add the correct vertical alignment in Chrome, Firefox, and Opera.\n */\n\nprogress {\n vertical-align: baseline;\n}\n\n/**\n * Remove the default vertical scrollbar in IE 10+.\n */\n\ntextarea {\n overflow: auto;\n}\n\n/**\n * 1. Add the correct box sizing in IE 10.\n * 2. Remove the padding in IE 10.\n */\n\n[type=\"checkbox\"],\n[type=\"radio\"] {\n box-sizing: border-box; /* 1 */\n padding: 0; /* 2 */\n}\n\n/**\n * Correct the cursor style of increment and decrement buttons in Chrome.\n */\n\n[type=\"number\"]::-webkit-inner-spin-button,\n[type=\"number\"]::-webkit-outer-spin-button {\n height: auto;\n}\n\n/**\n * 1. Correct the odd appearance in Chrome and Safari.\n * 2. Correct the outline style in Safari.\n */\n\n[type=\"search\"] {\n -webkit-appearance: textfield; /* 1 */\n outline-offset: -2px; /* 2 */\n}\n\n/**\n * Remove the inner padding in Chrome and Safari on macOS.\n */\n\n[type=\"search\"]::-webkit-search-decoration {\n -webkit-appearance: none;\n}\n\n/**\n * 1. Correct the inability to style clickable types in iOS and Safari.\n * 2. Change font properties to `inherit` in Safari.\n */\n\n::-webkit-file-upload-button {\n -webkit-appearance: button; /* 1 */\n font: inherit; /* 2 */\n}\n\n/* Interactive\n ========================================================================== */\n\n/*\n * Add the correct display in Edge, IE 10+, and Firefox.\n */\n\ndetails {\n display: block;\n}\n\n/*\n * Add the correct display in all browsers.\n */\n\nsummary {\n display: list-item;\n}\n\n/* Misc\n ========================================================================== */\n\n/**\n * Add the correct display in IE 10+.\n */\n\ntemplate {\n display: none;\n}\n\n/**\n * Add the correct display in IE 10.\n */\n\n[hidden] {\n display: none;\n}\n","// This file contains styles for managing print media.\n\n////////////////////////////////////////////////////////////////////////////////\n// Hide elements not relevant to print media.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Hide icon container.\n .content-icon-container\n display: none !important\n\n // Hide showing header links if hovering over when printing.\n .headerlink\n display: none !important\n\n // Hide mobile header.\n .mobile-header\n display: none !important\n\n // Hide navigation links.\n .related-pages\n display: none !important\n\n////////////////////////////////////////////////////////////////////////////////\n// Tweaks related to decolorization.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Apply a border around code which no longer have a color background.\n .highlight\n border: 0.1pt solid var(--color-foreground-border)\n\n////////////////////////////////////////////////////////////////////////////////\n// Avoid page break in some relevant cases.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n ul, ol, dl, a, table, pre, blockquote\n page-break-inside: avoid\n\n h1, h2, h3, h4, h5, h6, img, figure, caption\n page-break-inside: avoid\n page-break-after: avoid\n\n ul, ol, dl\n page-break-before: avoid\n",".visually-hidden\n position: absolute !important\n width: 1px !important\n height: 1px !important\n padding: 0 !important\n margin: -1px !important\n overflow: hidden !important\n clip: rect(0,0,0,0) !important\n white-space: nowrap !important\n border: 0 !important\n\n:-moz-focusring\n outline: auto\n","// This file serves as the \"skeleton\" of the theming logic.\n//\n// This contains the bulk of the logic for handling dark mode, color scheme\n// toggling and the handling of color-scheme-specific hiding of elements.\n\nbody\n @include fonts\n @include spacing\n @include icons\n @include admonitions\n @include default-admonition(#651fff, \"abstract\")\n @include default-topic(#14B8A6, \"pencil\")\n\n @include colors\n\n.only-light\n display: block !important\nhtml body .only-dark\n display: none !important\n\n// Ignore dark-mode hints if print media.\n@media not print\n // Enable dark-mode, if requested.\n body[data-theme=\"dark\"]\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n // Enable dark mode, unless explicitly told to avoid.\n @media (prefers-color-scheme: dark)\n body:not([data-theme=\"light\"])\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n//\n// Theme toggle presentation\n//\nbody[data-theme=\"auto\"]\n .theme-toggle svg.theme-icon-when-auto\n display: block\n\nbody[data-theme=\"dark\"]\n .theme-toggle svg.theme-icon-when-dark\n display: block\n\nbody[data-theme=\"light\"]\n .theme-toggle svg.theme-icon-when-light\n display: block\n","// Fonts used by this theme.\n//\n// There are basically two things here -- using the system font stack and\n// defining sizes for various elements in %ages. We could have also used `em`\n// but %age is easier to reason about for me.\n\n@mixin fonts {\n // These are adapted from https://systemfontstack.com/\n --font-stack: -apple-system, BlinkMacSystemFont, Segoe UI, Helvetica, Arial,\n sans-serif, Apple Color Emoji, Segoe UI Emoji;\n --font-stack--monospace: \"SFMono-Regular\", Menlo, Consolas, Monaco,\n Liberation Mono, Lucida Console, monospace;\n\n --font-size--normal: 100%;\n --font-size--small: 87.5%;\n --font-size--small--2: 81.25%;\n --font-size--small--3: 75%;\n --font-size--small--4: 62.5%;\n\n // Sidebar\n --sidebar-caption-font-size: var(--font-size--small--2);\n --sidebar-item-font-size: var(--font-size--small);\n --sidebar-search-input-font-size: var(--font-size--small);\n\n // Table of Contents\n --toc-font-size: var(--font-size--small--3);\n --toc-font-size--mobile: var(--font-size--normal);\n --toc-title-font-size: var(--font-size--small--4);\n\n // Admonitions\n //\n // These aren't defined in terms of %ages, since nesting these is permitted.\n --admonition-font-size: 0.8125rem;\n --admonition-title-font-size: 0.8125rem;\n\n // Code\n --code-font-size: var(--font-size--small--2);\n\n // API\n --api-font-size: var(--font-size--small);\n}\n","// Spacing for various elements on the page\n//\n// If the user wants to tweak things in a certain way, they are permitted to.\n// They also have to deal with the consequences though!\n\n@mixin spacing {\n // Header!\n --header-height: calc(\n var(--sidebar-item-line-height) + 4 * #{var(--sidebar-item-spacing-vertical)}\n );\n --header-padding: 0.5rem;\n\n // Sidebar\n --sidebar-tree-space-above: 1.5rem;\n --sidebar-caption-space-above: 1rem;\n\n --sidebar-item-line-height: 1rem;\n --sidebar-item-spacing-vertical: 0.5rem;\n --sidebar-item-spacing-horizontal: 1rem;\n --sidebar-item-height: calc(\n var(--sidebar-item-line-height) + 2 *#{var(--sidebar-item-spacing-vertical)}\n );\n\n --sidebar-expander-width: var(--sidebar-item-height); // be square\n\n --sidebar-search-space-above: 0.5rem;\n --sidebar-search-input-spacing-vertical: 0.5rem;\n --sidebar-search-input-spacing-horizontal: 0.5rem;\n --sidebar-search-input-height: 1rem;\n --sidebar-search-icon-size: var(--sidebar-search-input-height);\n\n // Table of Contents\n --toc-title-padding: 0.25rem 0;\n --toc-spacing-vertical: 1.5rem;\n --toc-spacing-horizontal: 1.5rem;\n --toc-item-spacing-vertical: 0.4rem;\n --toc-item-spacing-horizontal: 1rem;\n}\n","// Expose theme icons as CSS variables.\n\n$icons: (\n // Adapted from tabler-icons\n // url: https://tablericons.com/\n \"search\":\n url('data:image/svg+xml;charset=utf-8,'),\n // Factored out from mkdocs-material on 24-Aug-2020.\n // url: https://squidfunk.github.io/mkdocs-material/reference/admonitions/\n \"pencil\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"abstract\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"info\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"flame\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"question\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"warning\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"failure\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"spark\":\n url('data:image/svg+xml;charset=utf-8,')\n);\n\n@mixin icons {\n @each $name, $glyph in $icons {\n --icon-#{$name}: #{$glyph};\n }\n}\n","// Admonitions\n\n// Structure of these is:\n// admonition-class: color \"icon-name\";\n//\n// The colors are translated into CSS variables below. The icons are\n// used directly in the main declarations to set the `mask-image` in\n// the title.\n\n// prettier-ignore\n$admonitions: (\n // Each of these has an reST directives for it.\n \"caution\": #ff9100 \"spark\",\n \"warning\": #ff9100 \"warning\",\n \"danger\": #ff5252 \"spark\",\n \"attention\": #ff5252 \"warning\",\n \"error\": #ff5252 \"failure\",\n \"hint\": #00c852 \"question\",\n \"tip\": #00c852 \"info\",\n \"important\": #00bfa5 \"flame\",\n \"note\": #00b0ff \"pencil\",\n \"seealso\": #448aff \"info\",\n \"admonition-todo\": #808080 \"pencil\"\n);\n\n@mixin default-admonition($color, $icon-name) {\n --color-admonition-title: #{$color};\n --color-admonition-title-background: #{rgba($color, 0.2)};\n\n --icon-admonition-default: var(--icon-#{$icon-name});\n}\n\n@mixin default-topic($color, $icon-name) {\n --color-topic-title: #{$color};\n --color-topic-title-background: #{rgba($color, 0.2)};\n\n --icon-topic-default: var(--icon-#{$icon-name});\n}\n\n@mixin admonitions {\n @each $name, $values in $admonitions {\n --color-admonition-title--#{$name}: #{nth($values, 1)};\n --color-admonition-title-background--#{$name}: #{rgba(\n nth($values, 1),\n 0.2\n )};\n }\n}\n","// Colors used throughout this theme.\n//\n// The aim is to give the user more control. Thus, instead of hard-coding colors\n// in various parts of the stylesheet, the approach taken is to define all\n// colors as CSS variables and reusing them in all the places.\n//\n// `colors-dark` depends on `colors` being included at a lower specificity.\n\n@mixin colors {\n --color-problematic: #b30000;\n\n // Base Colors\n --color-foreground-primary: black; // for main text and headings\n --color-foreground-secondary: #5a5c63; // for secondary text\n --color-foreground-muted: #646776; // for muted text\n --color-foreground-border: #878787; // for content borders\n\n --color-background-primary: white; // for content\n --color-background-secondary: #f8f9fb; // for navigation + ToC\n --color-background-hover: #efeff4ff; // for navigation-item hover\n --color-background-hover--transparent: #efeff400;\n --color-background-border: #eeebee; // for UI borders\n --color-background-item: #ccc; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #2962ff;\n --color-brand-content: #2a5adf;\n\n // API documentation\n --color-api-background: var(--color-background-hover--transparent);\n --color-api-background-hover: var(--color-background-hover);\n --color-api-overall: var(--color-foreground-secondary);\n --color-api-name: var(--color-problematic);\n --color-api-pre-name: var(--color-problematic);\n --color-api-paren: var(--color-foreground-secondary);\n --color-api-keyword: var(--color-foreground-primary);\n --color-highlight-on-target: #ffffcc;\n\n // Inline code background\n --color-inline-code-background: var(--color-background-secondary);\n\n // Highlighted text (search)\n --color-highlighted-background: #ddeeff;\n --color-highlighted-text: var(--color-foreground-primary);\n\n // GUI Labels\n --color-guilabel-background: #ddeeff80;\n --color-guilabel-border: #bedaf580;\n --color-guilabel-text: var(--color-foreground-primary);\n\n // Admonitions!\n --color-admonition-background: transparent;\n\n //////////////////////////////////////////////////////////////////////////////\n // Everything below this should be one of:\n // - var(...)\n // - *-gradient(...)\n // - special literal values (eg: transparent, none)\n //////////////////////////////////////////////////////////////////////////////\n\n // Tables\n --color-table-header-background: var(--color-background-secondary);\n --color-table-border: var(--color-background-border);\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: transparent;\n --color-card-marginals-background: var(--color-background-secondary);\n\n // Header\n --color-header-background: var(--color-background-primary);\n --color-header-border: var(--color-background-border);\n --color-header-text: var(--color-foreground-primary);\n\n // Sidebar (left)\n --color-sidebar-background: var(--color-background-secondary);\n --color-sidebar-background-border: var(--color-background-border);\n\n --color-sidebar-brand-text: var(--color-foreground-primary);\n --color-sidebar-caption-text: var(--color-foreground-muted);\n --color-sidebar-link-text: var(--color-foreground-secondary);\n --color-sidebar-link-text--top-level: var(--color-brand-primary);\n\n --color-sidebar-item-background: var(--color-sidebar-background);\n --color-sidebar-item-background--current: var(\n --color-sidebar-item-background\n );\n --color-sidebar-item-background--hover: linear-gradient(\n 90deg,\n var(--color-background-hover--transparent) 0%,\n var(--color-background-hover) var(--sidebar-item-spacing-horizontal),\n var(--color-background-hover) 100%\n );\n\n --color-sidebar-item-expander-background: transparent;\n --color-sidebar-item-expander-background--hover: var(\n --color-background-hover\n );\n\n --color-sidebar-search-text: var(--color-foreground-primary);\n --color-sidebar-search-background: var(--color-background-secondary);\n --color-sidebar-search-background--focus: var(--color-background-primary);\n --color-sidebar-search-border: var(--color-background-border);\n --color-sidebar-search-icon: var(--color-foreground-muted);\n\n // Table of Contents (right)\n --color-toc-background: var(--color-background-primary);\n --color-toc-title-text: var(--color-foreground-muted);\n --color-toc-item-text: var(--color-foreground-secondary);\n --color-toc-item-text--hover: var(--color-foreground-primary);\n --color-toc-item-text--active: var(--color-brand-primary);\n\n // Actual page contents\n --color-content-foreground: var(--color-foreground-primary);\n --color-content-background: transparent;\n\n // Links\n --color-link: var(--color-brand-content);\n --color-link--hover: var(--color-brand-content);\n --color-link-underline: var(--color-background-border);\n --color-link-underline--hover: var(--color-foreground-border);\n}\n\n@mixin colors-dark {\n --color-problematic: #ee5151;\n\n // Base Colors\n --color-foreground-primary: #ffffffcc; // for main text and headings\n --color-foreground-secondary: #9ca0a5; // for secondary text\n --color-foreground-muted: #81868d; // for muted text\n --color-foreground-border: #666666; // for content borders\n\n --color-background-primary: #131416; // for content\n --color-background-secondary: #1a1c1e; // for navigation + ToC\n --color-background-hover: #1e2124ff; // for navigation-item hover\n --color-background-hover--transparent: #1e212400;\n --color-background-border: #303335; // for UI borders\n --color-background-item: #444; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #2b8cee;\n --color-brand-content: #368ce2;\n\n // Highlighted text (search)\n --color-highlighted-background: #083563;\n\n // GUI Labels\n --color-guilabel-background: #08356380;\n --color-guilabel-border: #13395f80;\n\n // API documentation\n --color-api-keyword: var(--color-foreground-secondary);\n --color-highlight-on-target: #333300;\n\n // Admonitions\n --color-admonition-background: #18181a;\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: #18181a;\n --color-card-marginals-background: var(--color-background-hover);\n}\n","// This file contains the styling for making the content throughout the page,\n// including fonts, paragraphs, headings and spacing among these elements.\n\nbody\n font-family: var(--font-stack)\npre,\ncode,\nkbd,\nsamp\n font-family: var(--font-stack--monospace)\n\n// Make fonts look slightly nicer.\nbody\n -webkit-font-smoothing: antialiased\n -moz-osx-font-smoothing: grayscale\n\n// Line height from Bootstrap 4.1\narticle\n line-height: 1.5\n\n//\n// Headings\n//\nh1,\nh2,\nh3,\nh4,\nh5,\nh6\n line-height: 1.25\n font-weight: bold\n\n border-radius: 0.5rem\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n margin-left: -0.5rem\n margin-right: -0.5rem\n padding-left: 0.5rem\n padding-right: 0.5rem\n\n + p\n margin-top: 0\n\nh1\n font-size: 2.5em\n margin-top: 1.75rem\n margin-bottom: 1rem\nh2\n font-size: 2em\n margin-top: 1.75rem\nh3\n font-size: 1.5em\nh4\n font-size: 1.25em\nh5\n font-size: 1.125em\nh6\n font-size: 1em\n\nsmall\n opacity: 75%\n font-size: 80%\n\n// Paragraph\np\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n\n// Horizontal rules\nhr.docutils\n height: 1px\n padding: 0\n margin: 2rem 0\n background-color: var(--color-background-border)\n border: 0\n\n.centered\n text-align: center\n\n// Links\na\n text-decoration: underline\n\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n &:hover\n color: var(--color-link--hover)\n text-decoration-color: var(--color-link-underline--hover)\n &.muted-link\n color: inherit\n &:hover\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline--hover)\n","// This file contains the styles for the overall layouting of the documentation\n// skeleton, including the responsive changes as well as sidebar toggles.\n//\n// This is implemented as a mobile-last design, which isn't ideal, but it is\n// reasonably good-enough and I got pretty tired by the time I'd finished this\n// to move the rules around to fix this. Shouldn't take more than 3-4 hours,\n// if you know what you're doing tho.\n\n// HACK: Not all browsers account for the scrollbar width in media queries.\n// This results in horizontal scrollbars in the breakpoint where we go\n// from displaying everything to hiding the ToC. We accomodate for this by\n// adding a bit of padding to the TOC drawer, disabling the horizontal\n// scrollbar and allowing the scrollbars to cover the padding.\n// https://www.456bereastreet.com/archive/201301/media_query_width_and_vertical_scrollbars/\n\n// HACK: Always having the scrollbar visible, prevents certain browsers from\n// causing the content to stutter horizontally between taller-than-viewport and\n// not-taller-than-viewport pages.\n\nhtml\n overflow-x: hidden\n overflow-y: scroll\n scroll-behavior: smooth\n\n.sidebar-scroll, .toc-scroll, article[role=main] *\n // Override Firefox scrollbar style\n scrollbar-width: thin\n scrollbar-color: var(--color-foreground-border) transparent\n\n // Override Chrome scrollbar styles\n &::-webkit-scrollbar\n width: 0.25rem\n height: 0.25rem\n &::-webkit-scrollbar-thumb\n background-color: var(--color-foreground-border)\n border-radius: 0.125rem\n\n//\n// Overalls\n//\nhtml,\nbody\n height: 100%\n color: var(--color-foreground-primary)\n background: var(--color-background-primary)\n\narticle\n color: var(--color-content-foreground)\n background: var(--color-content-background)\n overflow-wrap: break-word\n\n.page\n display: flex\n // fill the viewport for pages with little content.\n min-height: 100%\n\n.mobile-header\n width: 100%\n height: var(--header-height)\n background-color: var(--color-header-background)\n color: var(--color-header-text)\n border-bottom: 1px solid var(--color-header-border)\n\n // Looks like sub-script/super-script have this, and we need this to\n // be \"on top\" of those.\n z-index: 10\n\n // We don't show the header on large screens.\n display: none\n\n // Add shadow when scrolled\n &.scrolled\n border-bottom: none\n box-shadow: 0 0 0.2rem rgba(0, 0, 0, 0.1), 0 0.2rem 0.4rem rgba(0, 0, 0, 0.2)\n\n .header-center\n a\n color: var(--color-header-text)\n text-decoration: none\n\n.main\n display: flex\n flex: 1\n\n// Sidebar (left) also covers the entire left portion of screen.\n.sidebar-drawer\n box-sizing: border-box\n\n border-right: 1px solid var(--color-sidebar-background-border)\n background: var(--color-sidebar-background)\n\n display: flex\n justify-content: flex-end\n // These next two lines took me two days to figure out.\n width: calc((100% - #{$full-width}) / 2 + #{$sidebar-width})\n min-width: $sidebar-width\n\n// Scroll-along sidebars\n.sidebar-container,\n.toc-drawer\n box-sizing: border-box\n width: $sidebar-width\n\n.toc-drawer\n background: var(--color-toc-background)\n // See HACK described on top of this document\n padding-right: 1rem\n\n.sidebar-sticky,\n.toc-sticky\n position: sticky\n top: 0\n height: min(100%, 100vh)\n height: 100vh\n\n display: flex\n flex-direction: column\n\n.sidebar-scroll,\n.toc-scroll\n flex-grow: 1\n flex-shrink: 1\n\n overflow: auto\n scroll-behavior: smooth\n\n// Central items.\n.content\n padding: 0 $content-padding\n width: $content-width\n\n display: flex\n flex-direction: column\n justify-content: space-between\n\n.icon\n display: inline-block\n height: 1rem\n width: 1rem\n svg\n width: 100%\n height: 100%\n\n//\n// Accommodate announcement banner\n//\n.announcement\n background-color: var(--color-announcement-background)\n color: var(--color-announcement-text)\n\n height: var(--header-height)\n display: flex\n align-items: center\n overflow-x: auto\n & + .page\n min-height: calc(100% - var(--header-height))\n\n.announcement-content\n box-sizing: border-box\n padding: 0.5rem\n min-width: 100%\n white-space: nowrap\n text-align: center\n\n a\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-announcement-text)\n\n &:hover\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-link--hover)\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for theme\n////////////////////////////////////////////////////////////////////////////////\n.no-js .theme-toggle-container // don't show theme toggle if there's no JS\n display: none\n\n.theme-toggle-container\n vertical-align: middle\n\n.theme-toggle\n cursor: pointer\n border: none\n padding: 0\n background: transparent\n\n.theme-toggle svg\n vertical-align: middle\n height: 1rem\n width: 1rem\n color: var(--color-foreground-primary)\n display: none\n\n.theme-toggle-header\n float: left\n padding: 1rem 0.5rem\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for elements\n////////////////////////////////////////////////////////////////////////////////\n.toc-overlay-icon, .nav-overlay-icon\n display: none\n cursor: pointer\n\n .icon\n color: var(--color-foreground-secondary)\n height: 1rem\n width: 1rem\n\n.toc-header-icon, .nav-overlay-icon\n // for when we set display: flex\n justify-content: center\n align-items: center\n\n.toc-content-icon\n height: 1.5rem\n width: 1.5rem\n\n.content-icon-container\n float: right\n display: flex\n margin-top: 1.5rem\n margin-left: 1rem\n margin-bottom: 1rem\n gap: 0.5rem\n\n .edit-this-page svg\n color: inherit\n height: 1rem\n width: 1rem\n\n.sidebar-toggle\n position: absolute\n display: none\n// \n.sidebar-toggle[name=\"__toc\"]\n left: 20px\n.sidebar-toggle:checked\n left: 40px\n// \n\n.overlay\n position: fixed\n top: 0\n width: 0\n height: 0\n\n transition: width 0ms, height 0ms, opacity 250ms ease-out\n\n opacity: 0\n background-color: rgba(0, 0, 0, 0.54)\n.sidebar-overlay\n z-index: 20\n.toc-overlay\n z-index: 40\n\n// Keep things on top and smooth.\n.sidebar-drawer\n z-index: 30\n transition: left 250ms ease-in-out\n.toc-drawer\n z-index: 50\n transition: right 250ms ease-in-out\n\n// Show the Sidebar\n#__navigation:checked\n & ~ .sidebar-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .sidebar-drawer\n top: 0\n left: 0\n // Show the toc sidebar\n#__toc:checked\n & ~ .toc-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .toc-drawer\n top: 0\n right: 0\n\n////////////////////////////////////////////////////////////////////////////////\n// Back to top\n////////////////////////////////////////////////////////////////////////////////\n.back-to-top\n text-decoration: none\n\n display: none\n position: fixed\n left: 0\n top: 1rem\n padding: 0.5rem\n padding-right: 0.75rem\n border-radius: 1rem\n font-size: 0.8125rem\n\n background: var(--color-background-primary)\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), #6b728080 0px 0px 1px 0px\n\n z-index: 10\n\n margin-left: 50%\n transform: translateX(-50%)\n svg\n height: 1rem\n width: 1rem\n fill: currentColor\n display: inline-block\n\n span\n margin-left: 0.25rem\n\n .show-back-to-top &\n display: flex\n align-items: center\n\n////////////////////////////////////////////////////////////////////////////////\n// Responsive layouting\n////////////////////////////////////////////////////////////////////////////////\n// Make things a bit bigger on bigger screens.\n@media (min-width: $full-width + $sidebar-width)\n html\n font-size: 110%\n\n@media (max-width: $full-width)\n // Collapse \"toc\" into the icon.\n .toc-content-icon\n display: flex\n .toc-drawer\n position: fixed\n height: 100vh\n top: 0\n right: -$sidebar-width\n border-left: 1px solid var(--color-background-muted)\n .toc-tree\n border-left: none\n font-size: var(--toc-font-size--mobile)\n\n // Accomodate for a changed content width.\n .sidebar-drawer\n width: calc((100% - #{$full-width - $sidebar-width}) / 2 + #{$sidebar-width})\n\n@media (max-width: $full-width - $sidebar-width)\n // Collapse \"navigation\".\n .nav-overlay-icon\n display: flex\n .sidebar-drawer\n position: fixed\n height: 100vh\n width: $sidebar-width\n\n top: 0\n left: -$sidebar-width\n\n // Swap which icon is visible.\n .toc-header-icon\n display: flex\n .toc-content-icon, .theme-toggle-content\n display: none\n .theme-toggle-header\n display: block\n\n // Show the header.\n .mobile-header\n position: sticky\n top: 0\n display: flex\n justify-content: space-between\n align-items: center\n\n .header-left,\n .header-right\n display: flex\n height: var(--header-height)\n padding: 0 var(--header-padding)\n label\n height: 100%\n width: 100%\n user-select: none\n\n .nav-overlay-icon .icon,\n .theme-toggle svg\n height: 1.25rem\n width: 1.25rem\n\n // Add a scroll margin for the content\n :target\n scroll-margin-top: var(--header-height)\n\n // Show back-to-top below the header\n .back-to-top\n top: calc(var(--header-height) + 0.5rem)\n\n // Center the page, and accommodate for the header.\n .page\n flex-direction: column\n justify-content: center\n .content\n margin-left: auto\n margin-right: auto\n\n@media (max-width: $content-width + 2* $content-padding)\n // Content should respect window limits.\n .content\n width: 100%\n overflow-x: auto\n\n@media (max-width: $content-width)\n .content\n padding: 0 $content-padding--small\n // Don't float sidebars to the right.\n article aside.sidebar\n float: none\n width: 100%\n margin: 1rem 0\n","//\n// The design here is strongly inspired by mkdocs-material.\n.admonition, .topic\n margin: 1rem auto\n padding: 0 0.5rem 0.5rem 0.5rem\n\n background: var(--color-admonition-background)\n\n border-radius: 0.2rem\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n font-size: var(--admonition-font-size)\n\n overflow: hidden\n page-break-inside: avoid\n\n // First element should have no margin, since the title has it.\n > :nth-child(2)\n margin-top: 0\n\n // Last item should have no margin, since we'll control that w/ padding\n > :last-child\n margin-bottom: 0\n\n.admonition p.admonition-title,\np.topic-title\n position: relative\n margin: 0 -0.5rem 0.5rem\n padding-left: 2rem\n padding-right: .5rem\n padding-top: .4rem\n padding-bottom: .4rem\n\n font-weight: 500\n font-size: var(--admonition-title-font-size)\n line-height: 1.3\n\n // Our fancy icon\n &::before\n content: \"\"\n position: absolute\n left: 0.5rem\n width: 1rem\n height: 1rem\n\n// Default styles\np.admonition-title\n background-color: var(--color-admonition-title-background)\n &::before\n background-color: var(--color-admonition-title)\n mask-image: var(--icon-admonition-default)\n mask-repeat: no-repeat\n\np.topic-title\n background-color: var(--color-topic-title-background)\n &::before\n background-color: var(--color-topic-title)\n mask-image: var(--icon-topic-default)\n mask-repeat: no-repeat\n\n//\n// Variants\n//\n.admonition\n border-left: 0.2rem solid var(--color-admonition-title)\n\n @each $type, $value in $admonitions\n &.#{$type}\n border-left-color: var(--color-admonition-title--#{$type})\n > .admonition-title\n background-color: var(--color-admonition-title-background--#{$type})\n &::before\n background-color: var(--color-admonition-title--#{$type})\n mask-image: var(--icon-#{nth($value, 2)})\n\n.admonition-todo > .admonition-title\n text-transform: uppercase\n","// This file stylizes the API documentation (stuff generated by autodoc). It's\n// deeply nested due to how autodoc structures the HTML without enough classes\n// to select the relevant items.\n\n// API docs!\ndl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)\n // Tweak the spacing of all the things!\n dd\n margin-left: 2rem\n > :first-child\n margin-top: 0.125rem\n > :last-child\n margin-bottom: 0.75rem\n\n // This is used for the arguments\n .field-list\n margin-bottom: 0.75rem\n\n // \"Headings\" (like \"Parameters\" and \"Return\")\n > dt\n text-transform: uppercase\n font-size: var(--font-size--small)\n\n dd:empty\n margin-bottom: 0.5rem\n dd > ul\n margin-left: -1.2rem\n > li\n > p:nth-child(2)\n margin-top: 0\n // When the last-empty-paragraph follows a paragraph, it doesn't need\n // to augument the existing spacing.\n > p + p:last-child:empty\n margin-top: 0\n margin-bottom: 0\n\n // Colorize the elements\n > dt\n color: var(--color-api-overall)\n\n.sig:not(.sig-inline)\n font-weight: bold\n\n font-size: var(--api-font-size)\n font-family: var(--font-stack--monospace)\n\n margin-left: -0.25rem\n margin-right: -0.25rem\n padding-top: 0.25rem\n padding-bottom: 0.25rem\n padding-right: 0.5rem\n\n // These are intentionally em, to properly match the font size.\n padding-left: 3em\n text-indent: -2.5em\n\n border-radius: 0.25rem\n\n background: var(--color-api-background)\n transition: background 100ms ease-out\n\n &:hover\n background: var(--color-api-background-hover)\n\n // adjust the size of the [source] link on the right.\n a.reference\n .viewcode-link\n font-weight: normal\n width: 3.5rem\n\nem.property\n font-style: normal\n &:first-child\n color: var(--color-api-keyword)\n.sig-name\n color: var(--color-api-name)\n.sig-prename\n font-weight: normal\n color: var(--color-api-pre-name)\n.sig-paren\n color: var(--color-api-paren)\n.sig-param\n font-style: normal\n\n.versionmodified\n font-style: italic\ndiv.versionadded, div.versionchanged, div.deprecated\n p\n margin-top: 0.125rem\n margin-bottom: 0.125rem\n\n// Align the [docs] and [source] to the right.\n.viewcode-link, .viewcode-back\n float: right\n text-align: right\n",".line-block\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n .line-block\n margin-top: 0rem\n margin-bottom: 0rem\n padding-left: 1rem\n","// Captions\narticle p.caption,\ntable > caption,\n.code-block-caption\n font-size: var(--font-size--small)\n text-align: center\n\n// Caption above a TOCTree\n.toctree-wrapper.compound\n .caption, :not(.caption) > .caption-text\n font-size: var(--font-size--small)\n text-transform: uppercase\n\n text-align: initial\n margin-bottom: 0\n\n > ul\n margin-top: 0\n margin-bottom: 0\n","// Inline code\ncode.literal, .sig-inline\n background: var(--color-inline-code-background)\n border-radius: 0.2em\n // Make the font smaller, and use padding to recover.\n font-size: var(--font-size--small--2)\n padding: 0.1em 0.2em\n\n pre.literal-block &\n font-size: inherit\n padding: 0\n\n p &\n border: 1px solid var(--color-background-border)\n\n.sig-inline\n font-family: var(--font-stack--monospace)\n\n// Code and Literal Blocks\n$code-spacing-vertical: 0.625rem\n$code-spacing-horizontal: 0.875rem\n\n// Wraps every literal block + line numbers.\ndiv[class*=\" highlight-\"],\ndiv[class^=\"highlight-\"]\n margin: 1em 0\n display: flex\n\n .table-wrapper\n margin: 0\n padding: 0\n\npre\n margin: 0\n padding: 0\n overflow: auto\n\n // Needed to have more specificity than pygments' \"pre\" selector. :(\n article[role=\"main\"] .highlight &\n line-height: 1.5\n\n &.literal-block,\n .highlight &\n font-size: var(--code-font-size)\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n // Make it look like all the other blocks.\n &.literal-block\n margin-top: 1rem\n margin-bottom: 1rem\n\n border-radius: 0.2rem\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n\n// All code is always contained in this.\n.highlight\n width: 100%\n border-radius: 0.2rem\n\n // Make line numbers and prompts un-selectable.\n .gp, span.linenos\n user-select: none\n pointer-events: none\n\n // Expand the line-highlighting.\n .hll\n display: block\n margin-left: -$code-spacing-horizontal\n margin-right: -$code-spacing-horizontal\n padding-left: $code-spacing-horizontal\n padding-right: $code-spacing-horizontal\n\n/* Make code block captions be nicely integrated */\n.code-block-caption\n display: flex\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n border-radius: 0.25rem\n border-bottom-left-radius: 0\n border-bottom-right-radius: 0\n font-weight: 300\n border-bottom: 1px solid\n\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n border-color: var(--color-background-border)\n\n + div[class]\n margin-top: 0\n pre\n border-top-left-radius: 0\n border-top-right-radius: 0\n\n// When `html_codeblock_linenos_style` is table.\n.highlighttable\n width: 100%\n display: block\n tbody\n display: block\n\n tr\n display: flex\n\n // Line numbers\n td.linenos\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n padding: $code-spacing-vertical $code-spacing-horizontal\n padding-right: 0\n border-top-left-radius: 0.2rem\n border-bottom-left-radius: 0.2rem\n\n .linenodiv\n padding-right: $code-spacing-horizontal\n font-size: var(--code-font-size)\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n\n // Actual code\n td.code\n padding: 0\n display: block\n flex: 1\n overflow: hidden\n\n .highlight\n border-top-left-radius: 0\n border-bottom-left-radius: 0\n\n// When `html_codeblock_linenos_style` is inline.\n.highlight\n span.linenos\n display: inline-block\n padding-left: 0\n padding-right: $code-spacing-horizontal\n margin-right: $code-spacing-horizontal\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n","// Inline Footnote Reference\n.footnote-reference\n font-size: var(--font-size--small--4)\n vertical-align: super\n\n// Definition list, listing the content of each note.\n// docutils <= 0.17\ndl.footnote.brackets\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\n display: grid\n grid-template-columns: max-content auto\n dt\n margin: 0\n > .fn-backref\n margin-left: 0.25rem\n\n &:after\n content: \":\"\n\n .brackets\n &:before\n content: \"[\"\n &:after\n content: \"]\"\n\n dd\n margin: 0\n padding: 0 1rem\n\n// docutils >= 0.18\naside.footnote\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\naside.footnote > span,\ndiv.citation > span\n float: left\n font-weight: 500\n padding-right: 0.25rem\n\naside.footnote > p,\ndiv.citation > p\n margin-left: 2rem\n","//\n// Figures\n//\nimg\n box-sizing: border-box\n max-width: 100%\n height: auto\n\narticle\n figure, .figure\n border-radius: 0.2rem\n\n margin: 0\n :last-child\n margin-bottom: 0\n\n .align-left\n float: left\n clear: left\n margin: 0 1rem 1rem\n\n .align-right\n float: right\n clear: right\n margin: 0 1rem 1rem\n\n .align-default,\n .align-center\n display: block\n text-align: center\n margin-left: auto\n margin-right: auto\n\n // WELL, table needs to be stylised like a table.\n table.align-default\n display: table\n text-align: initial\n",".genindex-jumpbox, .domainindex-jumpbox\n border-top: 1px solid var(--color-background-border)\n border-bottom: 1px solid var(--color-background-border)\n padding: 0.25rem\n\n.genindex-section, .domainindex-section\n h2\n margin-top: 0.75rem\n margin-bottom: 0.5rem\n ul\n margin-top: 0\n margin-bottom: 0\n","ul,\nol\n padding-left: 1.2rem\n\n // Space lists out like paragraphs\n margin-top: 1rem\n margin-bottom: 1rem\n // reduce margins within li.\n li\n > p:first-child\n margin-top: 0.25rem\n margin-bottom: 0.25rem\n\n > p:last-child\n margin-top: 0.25rem\n\n > ul,\n > ol\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n\nol\n &.arabic\n list-style: decimal\n &.loweralpha\n list-style: lower-alpha\n &.upperalpha\n list-style: upper-alpha\n &.lowerroman\n list-style: lower-roman\n &.upperroman\n list-style: upper-roman\n\n// Don't space lists out when they're \"simple\" or in a `.. toctree::`\n.simple,\n.toctree-wrapper\n li\n > ul,\n > ol\n margin-top: 0\n margin-bottom: 0\n\n// Definition Lists\n.field-list,\n.option-list,\ndl:not([class]),\ndl.simple,\ndl.footnote,\ndl.glossary\n dt\n font-weight: 500\n margin-top: 0.25rem\n + dt\n margin-top: 0\n\n .classifier::before\n content: \":\"\n margin-left: 0.2rem\n margin-right: 0.2rem\n\n dd\n > p:first-child,\n ul\n margin-top: 0.125rem\n\n ul\n margin-bottom: 0.125rem\n",".math-wrapper\n width: 100%\n overflow-x: auto\n\ndiv.math\n position: relative\n text-align: center\n\n .headerlink,\n &:focus .headerlink\n display: none\n\n &:hover .headerlink\n display: inline-block\n\n span.eqno\n position: absolute\n right: 0.5rem\n top: 50%\n transform: translate(0, -50%)\n z-index: 1\n","// Abbreviations\nabbr[title]\n cursor: help\n\n// \"Problematic\" content, as identified by Sphinx\n.problematic\n color: var(--color-problematic)\n\n// Keyboard / Mouse \"instructions\"\nkbd:not(.compound)\n margin: 0 0.2rem\n padding: 0 0.2rem\n border-radius: 0.2rem\n border: 1px solid var(--color-foreground-border)\n color: var(--color-foreground-primary)\n vertical-align: text-bottom\n\n font-size: var(--font-size--small--3)\n display: inline-block\n\n box-shadow: 0 0.0625rem 0 rgba(0, 0, 0, 0.2), inset 0 0 0 0.125rem var(--color-background-primary)\n\n background-color: var(--color-background-secondary)\n\n// Blockquote\nblockquote\n border-left: 4px solid var(--color-background-border)\n background: var(--color-background-secondary)\n\n margin-left: 0\n margin-right: 0\n padding: 0.5rem 1rem\n\n .attribution\n font-weight: 600\n text-align: right\n\n &.pull-quote,\n &.highlights\n font-size: 1.25em\n\n &.epigraph,\n &.pull-quote\n border-left-width: 0\n border-radius: 0.5rem\n\n &.highlights\n border-left-width: 0\n background: transparent\n\n// Center align embedded-in-text images\np .reference img\n vertical-align: middle\n","p.rubric\n line-height: 1.25\n font-weight: bold\n font-size: 1.125em\n\n // For Numpy-style documentation that's got rubrics within it.\n // https://github.com/pradyunsg/furo/discussions/505\n dd &\n line-height: inherit\n font-weight: inherit\n\n font-size: var(--font-size--small)\n text-transform: uppercase\n","article .sidebar\n float: right\n clear: right\n width: 30%\n\n margin-left: 1rem\n margin-right: 0\n\n border-radius: 0.2rem\n background-color: var(--color-background-secondary)\n border: var(--color-background-border) 1px solid\n\n > *\n padding-left: 1rem\n padding-right: 1rem\n\n > ul, > ol // lists need additional padding, because bullets.\n padding-left: 2.2rem\n\n .sidebar-title\n margin: 0\n padding: 0.5rem 1rem\n border-bottom: var(--color-background-border) 1px solid\n\n font-weight: 500\n\n// TODO: subtitle\n// TODO: dedicated variables?\n",".table-wrapper\n width: 100%\n overflow-x: auto\n margin-top: 1rem\n margin-bottom: 0.5rem\n padding: 0.2rem 0.2rem 0.75rem\n\ntable.docutils\n border-radius: 0.2rem\n border-spacing: 0\n border-collapse: collapse\n\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n th\n background: var(--color-table-header-background)\n\n td,\n th\n // Space things out properly\n padding: 0 0.25rem\n\n // Get the borders looking just-right.\n border-left: 1px solid var(--color-table-border)\n border-right: 1px solid var(--color-table-border)\n border-bottom: 1px solid var(--color-table-border)\n\n p\n margin: 0.25rem\n\n &:first-child\n border-left: none\n &:last-child\n border-right: none\n\n // MyST-parser tables set these classes for control of column alignment\n &.text-left\n text-align: left\n &.text-right\n text-align: right\n &.text-center\n text-align: center\n",":target\n scroll-margin-top: 0.5rem\n\n@media (max-width: $full-width - $sidebar-width)\n :target\n scroll-margin-top: calc(0.5rem + var(--header-height))\n\n // When a heading is selected\n section > span:target\n scroll-margin-top: calc(0.8rem + var(--header-height))\n\n// Permalinks\n.headerlink\n font-weight: 100\n user-select: none\n\nh1,\nh2,\nh3,\nh4,\nh5,\nh6,\ndl dt,\np.caption,\nfigcaption p,\ntable > caption,\n.code-block-caption\n > .headerlink\n margin-left: 0.5rem\n visibility: hidden\n &:hover > .headerlink\n visibility: visible\n\n // Don't change to link-like, if someone adds the contents directive.\n > .toc-backref\n color: inherit\n text-decoration-line: none\n\n// Figure and table captions are special.\nfigure:hover > figcaption > p > .headerlink,\ntable:hover > caption > .headerlink\n visibility: visible\n\n:target >, // Regular section[id] style anchors\nspan:target ~ // Non-regular span[id] style \"extra\" anchors\n h1,\n h2,\n h3,\n h4,\n h5,\n h6\n &:nth-of-type(1)\n background-color: var(--color-highlight-on-target)\n // .headerlink\n // visibility: visible\n code.literal\n background-color: transparent\n\ntable:target > caption,\nfigure:target\n background-color: var(--color-highlight-on-target)\n\n// Inline page contents\n.this-will-duplicate-information-and-it-is-still-useful-here li :target\n background-color: var(--color-highlight-on-target)\n\n// Code block permalinks\n.literal-block-wrapper:target .code-block-caption\n background-color: var(--color-highlight-on-target)\n\n// When a definition list item is selected\n//\n// There isn't really an alternative to !important here, due to the\n// high-specificity of API documentation's selector.\ndt:target\n background-color: var(--color-highlight-on-target) !important\n\n// When a footnote reference is selected\n.footnote > dt:target + dd,\n.footnote-reference:target\n background-color: var(--color-highlight-on-target)\n",".guilabel\n background-color: var(--color-guilabel-background)\n border: 1px solid var(--color-guilabel-border)\n color: var(--color-guilabel-text)\n\n padding: 0 0.3em\n border-radius: 0.5em\n font-size: 0.9em\n","// This file contains the styles used for stylizing the footer that's shown\n// below the content.\n\nfooter\n font-size: var(--font-size--small)\n display: flex\n flex-direction: column\n\n margin-top: 2rem\n\n// Bottom of page information\n.bottom-of-page\n display: flex\n align-items: center\n justify-content: space-between\n\n margin-top: 1rem\n padding-top: 1rem\n padding-bottom: 1rem\n\n color: var(--color-foreground-secondary)\n border-top: 1px solid var(--color-background-border)\n\n line-height: 1.5\n\n @media (max-width: $content-width)\n text-align: center\n flex-direction: column-reverse\n gap: 0.25rem\n\n .left-details\n font-size: var(--font-size--small)\n\n .right-details\n display: flex\n flex-direction: column\n gap: 0.25rem\n text-align: right\n\n .icons\n display: flex\n justify-content: flex-end\n gap: 0.25rem\n font-size: 1rem\n\n a\n text-decoration: none\n\n svg,\n img\n font-size: 1.125rem\n height: 1em\n width: 1em\n\n// Next/Prev page information\n.related-pages\n a\n display: flex\n align-items: center\n\n text-decoration: none\n &:hover .page-info .title\n text-decoration: underline\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n svg.furo-related-icon,\n svg.furo-related-icon > use\n flex-shrink: 0\n\n color: var(--color-foreground-border)\n\n width: 0.75rem\n height: 0.75rem\n margin: 0 0.5rem\n\n &.next-page\n max-width: 50%\n\n float: right\n clear: right\n text-align: right\n\n &.prev-page\n max-width: 50%\n\n float: left\n clear: left\n\n svg\n transform: rotate(180deg)\n\n.page-info\n display: flex\n flex-direction: column\n overflow-wrap: anywhere\n\n .next-page &\n align-items: flex-end\n\n .context\n display: flex\n align-items: center\n\n padding-bottom: 0.1rem\n\n color: var(--color-foreground-muted)\n font-size: var(--font-size--small)\n text-decoration: none\n","// This file contains the styles for the contents of the left sidebar, which\n// contains the navigation tree, logo, search etc.\n\n////////////////////////////////////////////////////////////////////////////////\n// Brand on top of the scrollable tree.\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-brand\n display: flex\n flex-direction: column\n flex-shrink: 0\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n text-decoration: none\n\n.sidebar-brand-text\n color: var(--color-sidebar-brand-text)\n overflow-wrap: break-word\n margin: var(--sidebar-item-spacing-vertical) 0\n font-size: 1.5rem\n\n.sidebar-logo-container\n margin: var(--sidebar-item-spacing-vertical) 0\n\n.sidebar-logo\n margin: 0 auto\n display: block\n max-width: 100%\n\n////////////////////////////////////////////////////////////////////////////////\n// Search\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-search-container\n display: flex\n align-items: center\n margin-top: var(--sidebar-search-space-above)\n\n position: relative\n\n background: var(--color-sidebar-search-background)\n &:hover,\n &:focus-within\n background: var(--color-sidebar-search-background--focus)\n\n &::before\n content: \"\"\n position: absolute\n left: var(--sidebar-item-spacing-horizontal)\n width: var(--sidebar-search-icon-size)\n height: var(--sidebar-search-icon-size)\n\n background-color: var(--color-sidebar-search-icon)\n mask-image: var(--icon-search)\n\n.sidebar-search\n box-sizing: border-box\n\n border: none\n border-top: 1px solid var(--color-sidebar-search-border)\n border-bottom: 1px solid var(--color-sidebar-search-border)\n\n padding-top: var(--sidebar-search-input-spacing-vertical)\n padding-bottom: var(--sidebar-search-input-spacing-vertical)\n padding-right: var(--sidebar-search-input-spacing-horizontal)\n padding-left: calc(var(--sidebar-item-spacing-horizontal) + var(--sidebar-search-input-spacing-horizontal) + var(--sidebar-search-icon-size))\n\n width: 100%\n\n color: var(--color-sidebar-search-foreground)\n background: transparent\n z-index: 10\n\n &:focus\n outline: none\n\n &::placeholder\n font-size: var(--sidebar-search-input-font-size)\n\n//\n// Hide Search Matches link\n//\n#searchbox .highlight-link\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal) 0\n margin: 0\n text-align: center\n\n a\n color: var(--color-sidebar-search-icon)\n font-size: var(--font-size--small--2)\n\n////////////////////////////////////////////////////////////////////////////////\n// Structure/Skeleton of the navigation tree (left)\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-tree\n font-size: var(--sidebar-item-font-size)\n margin-top: var(--sidebar-tree-space-above)\n margin-bottom: var(--sidebar-item-spacing-vertical)\n\n ul\n padding: 0\n margin-top: 0\n margin-bottom: 0\n\n display: flex\n flex-direction: column\n\n list-style: none\n\n li\n position: relative\n margin: 0\n\n > ul\n margin-left: var(--sidebar-item-spacing-horizontal)\n\n .icon\n color: var(--color-sidebar-link-text)\n\n .reference\n box-sizing: border-box\n color: var(--color-sidebar-link-text)\n\n // Fill the parent.\n display: inline-block\n line-height: var(--sidebar-item-line-height)\n text-decoration: none\n\n // Don't allow long words to cause wrapping.\n overflow-wrap: anywhere\n\n height: 100%\n width: 100%\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n &:hover\n background: var(--color-sidebar-item-background--hover)\n\n // Add a nice little \"external-link\" arrow here.\n &.external::after\n content: url('data:image/svg+xml,')\n margin: 0 0.25rem\n vertical-align: middle\n color: var(--color-sidebar-link-text)\n\n // Make the current page reference bold.\n .current-page > .reference\n font-weight: bold\n\n label\n position: absolute\n top: 0\n right: 0\n height: var(--sidebar-item-height)\n width: var(--sidebar-expander-width)\n\n cursor: pointer\n user-select: none\n\n display: flex\n justify-content: center\n align-items: center\n\n .caption, :not(.caption) > .caption-text\n font-size: var(--sidebar-caption-font-size)\n color: var(--color-sidebar-caption-text)\n\n font-weight: bold\n text-transform: uppercase\n\n margin: var(--sidebar-caption-space-above) 0 0 0\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n // If it has children, add a bit more padding to wrap the content to avoid\n // overlapping with the

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