amd._emd.network_simplex() - Code Metrics - Inspection of "gemmi reader update" - dwiddo/average-minimum-distance - Measure and Improve Code Quality continuously with Scrutinizer

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by Daniel

created 2023-03-21 20:08 UTC

amd._emd.network_simplex() F

↳ Parent: amd._emd

Complexity

Conditions

Size

Total Lines	186
Code Lines	107

Duplication

Lines	0
Ratio	0 %

Importance

Changes

Metric	Value
eloc	107
dl	0
loc	186
rs	0.4199
c	0
b	0
f	0
cc	19
nop	3

How to fix Long Method Complexity

"""An implementation of the Wasserstein metric (Earth Mover's distance)
between two weighted distributions. Aka Earth Mover's distance, the
appropriate metric for comparing two PDDs.

Copyright (C) 2020 Cameron Hargreaves. This code is adapted from the
Element Movers Distance project https://github.com/lrcfmd/ElMD.
"""

from typing import Tuple

import numba
import numpy as np
import numpy.typing as npt


@numba.njit(cache=True)
def network_simplex(
        source_demands: npt.NDArray,
        sink_demands: npt.NDArray,
        network_costs: npt.NDArray
) -> Tuple[float, npt.NDArray[np.float64]]:
    """Calculate the Earth mover's distance (Wasserstien metric) between
    two weighted distributions given by two sets of weights and a cost
    matrix.

    This is a port of the network simplex algorithm implented by Loïc
    Séguin-C for the networkx package to allow acceleration with numba.
    Copyright (C) 2010 Loïc Séguin-C. [email protected]. All rights
    reserved. BSD license.

    Parameters
    ----------
    source_demands : :class:`numpy.ndarray`
        Weights of the first distribution.
    sink_demands : :class:`numpy.ndarray`
        Weights of the second distribution.
    network_costs : :class:`numpy.ndarray`
        Cost matrix of distances between elements of the two
        distributions. Shape (len(source_demands), len(sink_demands)).

    Returns
    -------
    (emd, plan) : Tuple[float, :class:`numpy.ndarray`]
        A tuple of the Earth mover's distance and the optimal matching.

    References
    ----------
    [1] Z. Kiraly, P. Kovacs.
        Efficient implementation of minimum-cost flow algorithms.
        Acta Universitatis Sapientiae, Informatica 4(1), 67--118
        (2012).
    [2] R. Barr, F. Glover, D. Klingman.
        Enhancement of spanning tree labeling procedures for network
        optimization. INFOR 17(1), 16--34 (1979).
    """

    n_sources, n_sinks = source_demands.shape[0], sink_demands.shape[0]
    network_costs = network_costs.ravel()
    n = n_sources + n_sinks
    e = n_sources * n_sinks
    B = np.int64(np.ceil(np.sqrt(e)))
    fp_multiplier = np.int64(1e+6)

    # Add one additional node for a dummy source and sink
    source_d_int = (source_demands * fp_multiplier).astype(np.int64)
    sink_d_int = (sink_demands * fp_multiplier).astype(np.int64)
    sink_source_sum_diff = np.sum(sink_d_int) - np.sum(source_d_int)

    if sink_source_sum_diff > 0:
        source_d_int[np.argmax(source_d_int)] += sink_source_sum_diff
    elif sink_source_sum_diff < 0:
        sink_d_int[np.argmax(sink_d_int)] -= sink_source_sum_diff

    demands = np.empty(n, dtype=np.int64)
    demands[:n_sources] = -source_d_int
    demands[n_sources:] = sink_d_int
    tails = np.empty(e + n, dtype=np.int64)
    heads = np.empty(e + n, dtype=np.int64)

    ind = 0
    for i in range(n_sources):
        for j in range(n_sinks):
            tails[ind] = i
            heads[ind] = n_sources + j
            ind += 1

    for i, demand in enumerate(demands):
        ind = e + i
        if demand > 0:
            tails[ind] = -1
            heads[ind] = -1
        else:
            tails[ind] = i
            heads[ind] = i

    # Create costs and capacities for the arcs between nodes
    network_costs = network_costs * fp_multiplier
    network_capac = np.empty(shape=(e, ), dtype=np.float64)
    ind = 0
    for i in range(n_sources):
        for j in range(n_sinks):
            network_capac[ind] = min(source_demands[i], sink_demands[j])
            ind += 1
    network_capac *= fp_multiplier

    faux_inf = 3 * max(
        np.sum(network_capac), np.sum(np.abs(network_costs)),
        np.amax(source_d_int), np.amax(sink_d_int)
    )

    costs = np.empty(e + n, dtype=np.int64)
    costs[:e] = network_costs
    costs[e:] = faux_inf

    capac = np.empty(e + n, dtype=np.int64)
    capac[:e] = network_capac
    capac[e:] = fp_multiplier

    flows = np.empty(e + n, dtype=np.int64)
    flows[:e] = 0
    flows[e:e+n_sources] = source_d_int
    flows[e+n_sources:] = sink_d_int

    potentials = np.empty(n, dtype=np.int64)
    demands_neg_mask = demands <= 0
    potentials[demands_neg_mask] = faux_inf
    potentials[~demands_neg_mask] = -faux_inf

    parent = np.full(shape=(n + 1, ), fill_value=-1, dtype=np.int64)
    parent[-1] = -2

    size = np.full(shape=(n + 1, ), fill_value=1, dtype=np.int64)
    size[-1] = n + 1

    next_node = np.arange(1, n + 2, dtype=np.int64)
    next_node[-2] = -1
    next_node[-1] = 0

    last_node = np.arange(n + 1, dtype=np.int64)
    last_node[-1] = n - 1

    prev_node = np.arange(-1, n, dtype=np.int64)
    edge = np.arange(e, e + n, dtype=np.int64)

    # Pivot loop

    f = 0
    while True:
        i, p, q, f = find_entering_edges(
            B, e, f, tails, heads, costs, potentials, flows
        )
        # If no entering edges then the optimal score is found
        if p == -1:
            break

        cycle_nodes, cycle_edges = find_cycle(i, p, q, size, edge, parent)
        j, s, t = find_leaving_edge(
            cycle_nodes, cycle_edges, capac, flows, tails, heads
        )
        res_cap = capac[j] - flows[j] if tails[j] == s else flows[j]

        # Augment flows
        for i_, p_ in zip(cycle_edges, cycle_nodes):
            if tails[i_] == p_:
                flows[i_] += res_cap
            else:
                flows[i_] -= res_cap

        # Do nothing more if the entering edge is the same as the
        # leaving edge.
        if i != j:
            if parent[t] != s:
                # Ensure that s is the parent of t.
                s, t = t, s

            # Ensure that q is in the subtree rooted at t.
            for val in cycle_edges:
                if val == j:
                    p, q = q, p
                    break
                if val == i:
                    break

            remove_edge(
                s, t, size, prev_node, last_node, next_node, parent, edge
            )
            make_root(
                q, parent, size, last_node, prev_node, next_node, edge
            )
            add_edge(
                i, p, q, next_node, prev_node, last_node, size, parent, edge
            )
            update_potentials(
                i, p, q, heads, potentials, costs, last_node, next_node
            )

    final_flows = flows[:e] / fp_multiplier
    edge_costs = costs[:e] / fp_multiplier
    emd = final_flows.dot(edge_costs)

    return emd, final_flows.reshape((n_sources, n_sinks))


@numba.njit(cache=True)
def reduced_cost(i, costs, potentials, tails, heads, flows):
    """Return the reduced cost of an edge i."""
    c = costs[i] - potentials[tails[i]] + potentials[heads[i]]
    if flows[i] == 0:
        return c
    return -c


@numba.njit(cache=True)
def find_entering_edges(B, e, f, tails, heads, costs, potentials, flows):
    """Yield entering edges until none can be found. Entering edges are
    found by combining Dantzig's rule and Bland's rule. The edges are
    cyclically grouped into blocks of size B. Within each block,
    Dantzig's rule is applied to find an entering edge. The blocks to
    search is determined following Bland's rule.
    """

    m = 0

    while m < (e + B - 1) // B:
        # Determine the next block of edges.
        l = f + B
        if l <= e:
            edge_inds = np.arange(f, l)
        else:
            l -= e
            edge_inds = np.empty(e - f + l, dtype=np.int64)
            for i, v in enumerate(range(f, e)):
                edge_inds[i] = v
            for i in range(l):
                edge_inds[e-f+i] = i

        # Find the first edge with the lowest reduced cost.
        f = l
        i = edge_inds[0]
        c = reduced_cost(i, costs, potentials, tails, heads, flows)

        for j in edge_inds[1:]:
            cost = reduced_cost(j, costs, potentials, tails, heads, flows)
            if cost < c:
                c = cost
                i = j

        p = q = -1
        if c >= 0:
            m += 1

        # Entering edge found
        else:
            if flows[i] == 0:
                p = tails[i]
                q = heads[i]
            else:
                p = heads[i]
                q = tails[i]

            return i, p, q, f

    # All edges have nonnegative reduced costs, the flow is optimal
    return -1, -1, -1, -1


@numba.njit(cache=True)
def find_apex(p, q, size, parent):
    """Find the lowest common ancestor of nodes p and q in the spanning
    tree.
    """

    size_p = size[p]
    size_q = size[q]

    while True:
        while size_p < size_q:
            p = parent[p]
            size_p = size[p]
        while size_p > size_q:
            q = parent[q]
            size_q = size[q]
        if size_p == size_q:
            if p != q:
                p = parent[p]
                size_p = size[p]
                q = parent[q]
                size_q = size[q]
            else:
                return p


@numba.njit(cache=True)
def trace_path(p, w, edge, parent):
    """Return the nodes and edges on the path from node p to its
    ancestor w.
    """

    cycle_nodes = [p]
    cycle_edges = []

    while p != w:
        cycle_edges.append(edge[p])
        p = parent[p]
        cycle_nodes.append(p)

    return cycle_nodes, cycle_edges


@numba.njit(cache=True)
def find_cycle(i, p, q, size, edge, parent):
    """Return the nodes and edges on the cycle containing edge
    i == (p, q) when the latter is added to the spanning tree. The cycle
    is oriented in the direction from p to q.
    """

    w = find_apex(p, q, size, parent)
    cycle_nodes, cycle_edges = trace_path(p, w, edge, parent)
    cycle_nodes_rev, cycle_edges_rev = trace_path(q, w, edge, parent)
    len_cycle_nodes = len(cycle_nodes)
    add_to_c_nodes = max(len(cycle_nodes_rev) - 1, 0)
    cycle_nodes_ = np.empty(len_cycle_nodes + add_to_c_nodes, dtype=np.int64)

    for j in range(len_cycle_nodes):
        cycle_nodes_[j] = cycle_nodes[-(j+1)]
    for j in range(add_to_c_nodes):
        cycle_nodes_[len_cycle_nodes+j] = cycle_nodes_rev[j]

    len_cycle_edges = len(cycle_edges)
    len_cycle_edges_ = len_cycle_edges + len(cycle_edges_rev)
    if len_cycle_edges < 1 or cycle_edges[-1] != i:
        cycle_edges_ = np.empty(len_cycle_edges_ + 1, dtype=np.int64)
        cycle_edges_[len_cycle_edges] = i
    else:
        cycle_edges_ = np.empty(len_cycle_edges_, dtype=np.int64)

    for j in range(len_cycle_edges):
        cycle_edges_[j] = cycle_edges[-(j+1)]
    for j in range(1, len(cycle_edges_rev) + 1):
        cycle_edges_[-j] = cycle_edges_rev[-j]

    return cycle_nodes_, cycle_edges_


@numba.njit(cache=True)
def find_leaving_edge(cycle_nodes, cycle_edges, capac, flows, tails, heads):
    """Return the leaving edge in a cycle represented by cycle_nodes and
    cycle_edges.
    """

    j, s = cycle_edges[0], cycle_nodes[0]
    res_caps_min = capac[j] - flows[j] if tails[j] == s else flows[j]

    for ind in range(1, cycle_edges.shape[0]):
        j_, s_ = cycle_edges[ind], cycle_nodes[ind]
        res_cap = capac[j_] - flows[j_] if tails[j_] == s_ else flows[j_]
        if res_cap < res_caps_min:
            res_caps_min = res_cap
            j, s = j_, s_

    t = heads[j] if tails[j] == s else tails[j]
    return j, s, t


@numba.njit(cache=True)
def remove_edge(s, t, size, prev, last, next_node, parent, edge):
    """Remove an edge (s, t) where parent[t] == s from the spanning
    tree.
    """

    size_t = size[t]
    prev_t = prev[t]
    last_t = last[t]
    next_last_t = next_node[last_t]
    # Remove (s, t)
    parent[t] = -2
    edge[t] = -2
    # Remove the subtree rooted at t from the depth-first thread
    next_node[prev_t] = next_last_t
    prev[next_last_t] = prev_t
    next_node[last_t] = t
    prev[t] = last_t

    # Update the subtree sizes & last descendants of the (old) ancestors of t
    while s != -2:
        size[s] -= size_t
        if last[s] == last_t:
            last[s] = prev_t
        s = parent[s]


@numba.njit(cache=True)
def make_root(q, parent, size, last, prev, next_node, edge):
    """Make a node q the root of its containing subtree."""

    ancestors = []
    # -2 means node is checked
    while q != -2:
        ancestors.insert(0, q)
        q = parent[q]

    for i in range(len(ancestors) - 1):
        p = ancestors[i]
        q = ancestors[i+1]
        size_p = size[p]
        last_p = last[p]
        prev_q = prev[q]
        last_q = last[q]
        next_last_q = next_node[last_q]

        # Make p a child of q
        parent[p] = q
        parent[q] = -2
        edge[p] = edge[q]
        edge[q] = -2
        size[p] = size_p - size[q]
        size[q] = size_p

        # Remove the subtree rooted at q from the depth-first thread
        next_node[prev_q] = next_last_q
        prev[next_last_q] = prev_q
        next_node[last_q] = q
        prev[q] = last_q

        if last_p == last_q:
            last[p] = prev_q
            last_p = prev_q

        # Add the remaining parts of the subtree rooted at p as a subtree of q
        # in the depth-first thread
        prev[p] = last_q
        next_node[last_q] = p
        next_node[last_p] = q
        prev[q] = last_p
        last[q] = last_p


@numba.njit(cache=True)
def add_edge(i, p, q, next_node, prev, last, size, parent, edge):
    """Add an edge (p, q) to the spanning tree where q is the root of a
    subtree.
    """

    last_p = last[p]
    next_last_p = next_node[last_p]
    size_q = size[q]
    last_q = last[q]
    # Make q a child of p
    parent[q] = p
    edge[q] = i
    # Insert the subtree rooted at q into the depth-first thread
    next_node[last_p] = q
    prev[q] = last_p
    prev[next_last_p] = last_q
    next_node[last_q] = next_last_p

    # Update the subtree sizes and last descendants of the (new) ancestors of q
    while p != -2:
        size[p] += size_q
        if last[p] == last_p:
            last[p] = last_q
        p = parent[p]


@numba.njit(cache=True)
def update_potentials(i, p, q, heads, potentials, costs, last_node, next_node):
    """Update the potentials of the nodes in the subtree rooted at a
    node q connected to its parent p by an edge i.
    """

    if q == heads[i]:
        d = potentials[p] - costs[i] - potentials[q]
    else:
        d = potentials[p] + costs[i] - potentials[q]

    potentials[q] += d
    l = last_node[q]
    while q != l:
        q = next_node[q]
        potentials[q] += d


1			"""An implementation of the Wasserstein metric (Earth Mover's distance)
2			between two weighted distributions. Aka Earth Mover's distance, the
3			appropriate metric for comparing two PDDs.
4
5			Copyright (C) 2020 Cameron Hargreaves. This code is adapted from the
6			Element Movers Distance project https://github.com/lrcfmd/ElMD.
7			"""
8
9			from typing import Tuple
10
11			import numba
12			import numpy as np
13			import numpy.typing as npt
14
15
16			@numba.njit(cache=True)
17			def network_simplex(
18			source_demands: npt.NDArray,
19			sink_demands: npt.NDArray,
20			network_costs: npt.NDArray
21			) -> Tuple[float, npt.NDArray[np.float64]]:
22			"""Calculate the Earth mover's distance (Wasserstien metric) between
23			two weighted distributions given by two sets of weights and a cost
24			matrix.
25
26			This is a port of the network simplex algorithm implented by Loïc
27			Séguin-C for the networkx package to allow acceleration with numba.
28			Copyright (C) 2010 Loïc Séguin-C. [email protected]. All rights
29			reserved. BSD license.
30
31			Parameters
32			----------
33			source_demands : :class:`numpy.ndarray`
34			Weights of the first distribution.
35			sink_demands : :class:`numpy.ndarray`
36			Weights of the second distribution.
37			network_costs : :class:`numpy.ndarray`
38			Cost matrix of distances between elements of the two
39			distributions. Shape (len(source_demands), len(sink_demands)).
40
41			Returns
42			-------
43			(emd, plan) : Tuple[float, :class:`numpy.ndarray`]
44			A tuple of the Earth mover's distance and the optimal matching.
45
46			References
47			----------
48			[1] Z. Kiraly, P. Kovacs.
49			Efficient implementation of minimum-cost flow algorithms.
50			Acta Universitatis Sapientiae, Informatica 4(1), 67--118
51			(2012).
52			[2] R. Barr, F. Glover, D. Klingman.
53			Enhancement of spanning tree labeling procedures for network
54			optimization. INFOR 17(1), 16--34 (1979).
55			"""
56
57			n_sources, n_sinks = source_demands.shape[0], sink_demands.shape[0]
58			network_costs = network_costs.ravel()
59			n = n_sources + n_sinks
60			e = n_sources * n_sinks
61			B = np.int64(np.ceil(np.sqrt(e)))
62			fp_multiplier = np.int64(1e+6)
63
64			# Add one additional node for a dummy source and sink
65			source_d_int = (source_demands * fp_multiplier).astype(np.int64)
66			sink_d_int = (sink_demands * fp_multiplier).astype(np.int64)
67			sink_source_sum_diff = np.sum(sink_d_int) - np.sum(source_d_int)
68
69			if sink_source_sum_diff > 0:
70			source_d_int[np.argmax(source_d_int)] += sink_source_sum_diff
71			elif sink_source_sum_diff < 0:
72			sink_d_int[np.argmax(sink_d_int)] -= sink_source_sum_diff
73
74			demands = np.empty(n, dtype=np.int64)
75			demands[:n_sources] = -source_d_int
76			demands[n_sources:] = sink_d_int
77			tails = np.empty(e + n, dtype=np.int64)
78			heads = np.empty(e + n, dtype=np.int64)
79
80			ind = 0
81			for i in range(n_sources):
82			for j in range(n_sinks):
83			tails[ind] = i
84			heads[ind] = n_sources + j
85			ind += 1
86
87			for i, demand in enumerate(demands):
88			ind = e + i
89			if demand > 0:
90			tails[ind] = -1
91			heads[ind] = -1
92			else:
93			tails[ind] = i
94			heads[ind] = i
95
96			# Create costs and capacities for the arcs between nodes
97			network_costs = network_costs * fp_multiplier
98			network_capac = np.empty(shape=(e, ), dtype=np.float64)
99			ind = 0
100			for i in range(n_sources):
101			for j in range(n_sinks):
102			network_capac[ind] = min(source_demands[i], sink_demands[j])
103			ind += 1
104			network_capac *= fp_multiplier
105
106			faux_inf = 3 * max(
107			np.sum(network_capac), np.sum(np.abs(network_costs)),
108			np.amax(source_d_int), np.amax(sink_d_int)
109			)
110
111			costs = np.empty(e + n, dtype=np.int64)
112			costs[:e] = network_costs
113			costs[e:] = faux_inf
114
115			capac = np.empty(e + n, dtype=np.int64)
116			capac[:e] = network_capac
117			capac[e:] = fp_multiplier
118
119			flows = np.empty(e + n, dtype=np.int64)
120			flows[:e] = 0
121			flows[e:e+n_sources] = source_d_int
122			flows[e+n_sources:] = sink_d_int
123
124			potentials = np.empty(n, dtype=np.int64)
125			demands_neg_mask = demands <= 0
126			potentials[demands_neg_mask] = faux_inf
127			potentials[~demands_neg_mask] = -faux_inf
128
129			parent = np.full(shape=(n + 1, ), fill_value=-1, dtype=np.int64)
130			parent[-1] = -2
131
132			size = np.full(shape=(n + 1, ), fill_value=1, dtype=np.int64)
133			size[-1] = n + 1
134
135			next_node = np.arange(1, n + 2, dtype=np.int64)
136			next_node[-2] = -1
137			next_node[-1] = 0
138
139			last_node = np.arange(n + 1, dtype=np.int64)
140			last_node[-1] = n - 1
141
142			prev_node = np.arange(-1, n, dtype=np.int64)
143			edge = np.arange(e, e + n, dtype=np.int64)
144
145			# Pivot loop
146
147			f = 0
148			while True:
149			i, p, q, f = find_entering_edges(
150			B, e, f, tails, heads, costs, potentials, flows
151			)
152			# If no entering edges then the optimal score is found
153			if p == -1:
154			break
155
156			cycle_nodes, cycle_edges = find_cycle(i, p, q, size, edge, parent)
157			j, s, t = find_leaving_edge(
158			cycle_nodes, cycle_edges, capac, flows, tails, heads
159			)
160			res_cap = capac[j] - flows[j] if tails[j] == s else flows[j]
161
162			# Augment flows
163			for i_, p_ in zip(cycle_edges, cycle_nodes):
164			if tails[i_] == p_:
165			flows[i_] += res_cap
166			else:
167			flows[i_] -= res_cap
168
169			# Do nothing more if the entering edge is the same as the
170			# leaving edge.
171			if i != j:
172			if parent[t] != s:
173			# Ensure that s is the parent of t.
174			s, t = t, s
175
176			# Ensure that q is in the subtree rooted at t.
177			for val in cycle_edges:
178			if val == j:
179			p, q = q, p
180			break
181			if val == i:
182			break
183
184			remove_edge(
185			s, t, size, prev_node, last_node, next_node, parent, edge
186			)
187			make_root(
188			q, parent, size, last_node, prev_node, next_node, edge
189			)
190			add_edge(
191			i, p, q, next_node, prev_node, last_node, size, parent, edge
192			)
193			update_potentials(
194			i, p, q, heads, potentials, costs, last_node, next_node
195			)
196
197			final_flows = flows[:e] / fp_multiplier
198			edge_costs = costs[:e] / fp_multiplier
199			emd = final_flows.dot(edge_costs)
200
201			return emd, final_flows.reshape((n_sources, n_sinks))
202
203
204			@numba.njit(cache=True)
205			def reduced_cost(i, costs, potentials, tails, heads, flows):
206			"""Return the reduced cost of an edge i."""
207			c = costs[i] - potentials[tails[i]] + potentials[heads[i]]
208			if flows[i] == 0:
209			return c
210			return -c
211
212
213			@numba.njit(cache=True)
214			def find_entering_edges(B, e, f, tails, heads, costs, potentials, flows):
215			"""Yield entering edges until none can be found. Entering edges are
216			found by combining Dantzig's rule and Bland's rule. The edges are
217			cyclically grouped into blocks of size B. Within each block,
218			Dantzig's rule is applied to find an entering edge. The blocks to
219			search is determined following Bland's rule.
220			"""
221
222			m = 0
223
224			while m < (e + B - 1) // B:
225			# Determine the next block of edges.
226			l = f + B
227			if l <= e:
228			edge_inds = np.arange(f, l)
229			else:
230			l -= e
231			edge_inds = np.empty(e - f + l, dtype=np.int64)
232			for i, v in enumerate(range(f, e)):
233			edge_inds[i] = v
234			for i in range(l):
235			edge_inds[e-f+i] = i
236
237			# Find the first edge with the lowest reduced cost.
238			f = l
239			i = edge_inds[0]
240			c = reduced_cost(i, costs, potentials, tails, heads, flows)
241
242			for j in edge_inds[1:]:
243			cost = reduced_cost(j, costs, potentials, tails, heads, flows)
244			if cost < c:
245			c = cost
246			i = j
247
248			p = q = -1
249			if c >= 0:
250			m += 1
251
252			# Entering edge found
253			else:
254			if flows[i] == 0:
255			p = tails[i]
256			q = heads[i]
257			else:
258			p = heads[i]
259			q = tails[i]
260
261			return i, p, q, f
262
263			# All edges have nonnegative reduced costs, the flow is optimal
264			return -1, -1, -1, -1
265
266
267			@numba.njit(cache=True)
268			def find_apex(p, q, size, parent):
269			"""Find the lowest common ancestor of nodes p and q in the spanning
270			tree.
271			"""
272
273			size_p = size[p]
274			size_q = size[q]
275
276			while True:
277			while size_p < size_q:
278			p = parent[p]
279			size_p = size[p]
280			while size_p > size_q:
281			q = parent[q]
282			size_q = size[q]
283			if size_p == size_q:
284			if p != q:
285			p = parent[p]
286			size_p = size[p]
287			q = parent[q]
288			size_q = size[q]
289			else:
290			return p
291
292
293			@numba.njit(cache=True)
294			def trace_path(p, w, edge, parent):
295			"""Return the nodes and edges on the path from node p to its
296			ancestor w.
297			"""
298
299			cycle_nodes = [p]
300			cycle_edges = []
301
302			while p != w:
303			cycle_edges.append(edge[p])
304			p = parent[p]
305			cycle_nodes.append(p)
306
307			return cycle_nodes, cycle_edges
308
309
310			@numba.njit(cache=True)
311			def find_cycle(i, p, q, size, edge, parent):
312			"""Return the nodes and edges on the cycle containing edge
313			i == (p, q) when the latter is added to the spanning tree. The cycle
314			is oriented in the direction from p to q.
315			"""
316
317			w = find_apex(p, q, size, parent)
318			cycle_nodes, cycle_edges = trace_path(p, w, edge, parent)
319			cycle_nodes_rev, cycle_edges_rev = trace_path(q, w, edge, parent)
320			len_cycle_nodes = len(cycle_nodes)
321			add_to_c_nodes = max(len(cycle_nodes_rev) - 1, 0)
322			cycle_nodes_ = np.empty(len_cycle_nodes + add_to_c_nodes, dtype=np.int64)
323
324			for j in range(len_cycle_nodes):
325			cycle_nodes_[j] = cycle_nodes[-(j+1)]
326			for j in range(add_to_c_nodes):
327			cycle_nodes_[len_cycle_nodes+j] = cycle_nodes_rev[j]
328
329			len_cycle_edges = len(cycle_edges)
330			len_cycle_edges_ = len_cycle_edges + len(cycle_edges_rev)
331			if len_cycle_edges < 1 or cycle_edges[-1] != i:
332			cycle_edges_ = np.empty(len_cycle_edges_ + 1, dtype=np.int64)
333			cycle_edges_[len_cycle_edges] = i
334			else:
335			cycle_edges_ = np.empty(len_cycle_edges_, dtype=np.int64)
336
337			for j in range(len_cycle_edges):
338			cycle_edges_[j] = cycle_edges[-(j+1)]
339			for j in range(1, len(cycle_edges_rev) + 1):
340			cycle_edges_[-j] = cycle_edges_rev[-j]
341
342			return cycle_nodes_, cycle_edges_
343
344
345			@numba.njit(cache=True)
346			def find_leaving_edge(cycle_nodes, cycle_edges, capac, flows, tails, heads):
347			"""Return the leaving edge in a cycle represented by cycle_nodes and
348			cycle_edges.
349			"""
350
351			j, s = cycle_edges[0], cycle_nodes[0]
352			res_caps_min = capac[j] - flows[j] if tails[j] == s else flows[j]
353
354			for ind in range(1, cycle_edges.shape[0]):
355			j_, s_ = cycle_edges[ind], cycle_nodes[ind]
356			res_cap = capac[j_] - flows[j_] if tails[j_] == s_ else flows[j_]
357			if res_cap < res_caps_min:
358			res_caps_min = res_cap
359			j, s = j_, s_
360
361			t = heads[j] if tails[j] == s else tails[j]
362			return j, s, t
363
364
365			@numba.njit(cache=True)
366			def remove_edge(s, t, size, prev, last, next_node, parent, edge):
367			"""Remove an edge (s, t) where parent[t] == s from the spanning
368			tree.
369			"""
370
371			size_t = size[t]
372			prev_t = prev[t]
373			last_t = last[t]
374			next_last_t = next_node[last_t]
375			# Remove (s, t)
376			parent[t] = -2
377			edge[t] = -2
378			# Remove the subtree rooted at t from the depth-first thread
379			next_node[prev_t] = next_last_t
380			prev[next_last_t] = prev_t
381			next_node[last_t] = t
382			prev[t] = last_t
383
384			# Update the subtree sizes & last descendants of the (old) ancestors of t
385			while s != -2:
386			size[s] -= size_t
387			if last[s] == last_t:
388			last[s] = prev_t
389			s = parent[s]
390
391
392			@numba.njit(cache=True)
393			def make_root(q, parent, size, last, prev, next_node, edge):
394			"""Make a node q the root of its containing subtree."""
395
396			ancestors = []
397			# -2 means node is checked
398			while q != -2:
399			ancestors.insert(0, q)
400			q = parent[q]
401
402			for i in range(len(ancestors) - 1):
403			p = ancestors[i]
404			q = ancestors[i+1]
405			size_p = size[p]
406			last_p = last[p]
407			prev_q = prev[q]
408			last_q = last[q]
409			next_last_q = next_node[last_q]
410
411			# Make p a child of q
412			parent[p] = q
413			parent[q] = -2
414			edge[p] = edge[q]
415			edge[q] = -2
416			size[p] = size_p - size[q]
417			size[q] = size_p
418
419			# Remove the subtree rooted at q from the depth-first thread
420			next_node[prev_q] = next_last_q
421			prev[next_last_q] = prev_q
422			next_node[last_q] = q
423			prev[q] = last_q
424
425			if last_p == last_q:
426			last[p] = prev_q
427			last_p = prev_q
428
429			# Add the remaining parts of the subtree rooted at p as a subtree of q
430			# in the depth-first thread
431			prev[p] = last_q
432			next_node[last_q] = p
433			next_node[last_p] = q
434			prev[q] = last_p
435			last[q] = last_p
436
437
438			@numba.njit(cache=True)
439			def add_edge(i, p, q, next_node, prev, last, size, parent, edge):
440			"""Add an edge (p, q) to the spanning tree where q is the root of a
441			subtree.
442			"""
443
444			last_p = last[p]
445			next_last_p = next_node[last_p]
446			size_q = size[q]
447			last_q = last[q]
448			# Make q a child of p
449			parent[q] = p
450			edge[q] = i
451			# Insert the subtree rooted at q into the depth-first thread
452			next_node[last_p] = q
453			prev[q] = last_p
454			prev[next_last_p] = last_q
455			next_node[last_q] = next_last_p
456
457			# Update the subtree sizes and last descendants of the (new) ancestors of q
458			while p != -2:
459			size[p] += size_q
460			if last[p] == last_p:
461			last[p] = last_q
462			p = parent[p]
463
464
465			@numba.njit(cache=True)
466			def update_potentials(i, p, q, heads, potentials, costs, last_node, next_node):
467			"""Update the potentials of the nodes in the subtree rooted at a
468			node q connected to its parent p by an edge i.
469			"""
470
471			if q == heads[i]:
472			d = potentials[p] - costs[i] - potentials[q]
473			else:
474			d = potentials[p] + costs[i] - potentials[q]
475
476			potentials[q] += d
477			l = last_node[q]
478			while q != l:
479			q = next_node[q]
480			potentials[q] += d
481

dwiddo / average-minimum-distance

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amd._emd.network_simplex() F

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