170010030
/
fr
forked from 170010011/fr
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
fr/fr_env/lib/python3.8/site-packages/scipy/optimize/_qap.py

728 lines
27 KiB
Python
Raw Blame History

import numpy as np
import operator
from . import (linear_sum_assignment, OptimizeResult)
from .optimize import _check_unknown_options
from scipy._lib._util import check_random_state
import itertools
QUADRATIC_ASSIGNMENT_METHODS = ['faq', '2opt']
def quadratic_assignment(A, B, method="faq", options=None):
r"""
Approximates solution to the quadratic assignment problem and
the graph matching problem.
Quadratic assignment solves problems of the following form:
.. math::
\min_P & \ {\ \text{trace}(A^T P B P^T)}\\
\mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\
where :math:`\mathcal{P}` is the set of all permutation matrices,
and :math:`A` and :math:`B` are square matrices.
Graph matching tries to *maximize* the same objective function.
This algorithm can be thought of as finding the alignment of the
nodes of two graphs that minimizes the number of induced edge
disagreements, or, in the case of weighted graphs, the sum of squared
edge weight differences.
Note that the quadratic assignment problem is NP-hard. The results given
here are approximations and are not guaranteed to be optimal.
Parameters
----------
A : 2-D array, square
The square matrix :math:`A` in the objective function above.
B : 2-D array, square
The square matrix :math:`B` in the objective function above.
method : str in {'faq', '2opt'} (default: 'faq')
The algorithm used to solve the problem.
:ref:`'faq' <optimize.qap-faq>` (default) and
:ref:`'2opt' <optimize.qap-2opt>` are available.
options : dict, optional
A dictionary of solver options. All solvers support the following:
maximize : bool (default: False)
Maximizes the objective function if ``True``.
partial_match : 2-D array of integers, optional (default: None)
Fixes part of the matching. Also known as a "seed" [2]_.
Each row of `partial_match` specifies a pair of matched nodes:
node ``partial_match[i, 0]`` of `A` is matched to node
``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``,
where ``m`` is not greater than the number of nodes, :math:`n`.
rng : int, `RandomState`, `Generator` or None, optional (default: None)
Accepts an integer as a seed for the random generator or a
``RandomState`` or ``Generator`` object. If None (default), uses
global `numpy.random` random state.
For method-specific options, see
:func:`show_options('quadratic_assignment') <show_options>`.
Returns
-------
res : OptimizeResult
`OptimizeResult` containing the following fields.
col_ind : 1-D array
Column indices corresponding to the best permutation found of the
nodes of `B`.
fun : float
The objective value of the solution.
nit : int
The number of iterations performed during optimization.
Notes
-----
The default method :ref:`'faq' <optimize.qap-faq>` uses the Fast
Approximate QAP algorithm [1]_; it typically offers the best combination of
speed and accuracy.
Method :ref:`'2opt' <optimize.qap-2opt>` can be computationally expensive,
but may be a useful alternative, or it can be used to refine the solution
returned by another method.
References
----------
.. [1] J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik,
S.G. Kratzer, E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and
C.E. Priebe, "Fast approximate quadratic programming for graph
matching," PLOS one, vol. 10, no. 4, p. e0121002, 2015,
:doi:`10.1371/journal.pone.0121002`
.. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski,
C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019):
203-215, :doi:`10.1016/j.patcog.2018.09.014`
.. [3] "2-opt," Wikipedia.
https://en.wikipedia.org/wiki/2-opt
Examples
--------
>>> import numpy as np
>>> from scipy.optimize import quadratic_assignment
>>> A = np.array([[0, 80, 150, 170], [80, 0, 130, 100],
... [150, 130, 0, 120], [170, 100, 120, 0]])
>>> B = np.array([[0, 5, 2, 7], [0, 0, 3, 8],
... [0, 0, 0, 3], [0, 0, 0, 0]])
>>> res = quadratic_assignment(A, B)
>>> print(res)
col_ind: array([0, 3, 2, 1])
fun: 3260
nit: 9
The see the relationship between the returned ``col_ind`` and ``fun``,
use ``col_ind`` to form the best permutation matrix found, then evaluate
the objective function :math:`f(P) = trace(A^T P B P^T )`.
>>> perm = res['col_ind']
>>> P = np.eye(len(A), dtype=int)[perm]
>>> fun = np.trace(A.T @ P @ B @ P.T)
>>> print(fun)
3260
Alternatively, to avoid constructing the permutation matrix explicitly,
directly permute the rows and columns of the distance matrix.
>>> fun = np.trace(A.T @ B[perm][:, perm])
>>> print(fun)
3260
Although not guaranteed in general, ``quadratic_assignment`` happens to
have found the globally optimal solution.
>>> from itertools import permutations
>>> perm_opt, fun_opt = None, np.inf
>>> for perm in permutations([0, 1, 2, 3]):
... perm = np.array(perm)
... fun = np.trace(A.T @ B[perm][:, perm])
... if fun < fun_opt:
... fun_opt, perm_opt = fun, perm
>>> print(np.array_equal(perm_opt, res['col_ind']))
True
Here is an example for which the default method,
:ref:`'faq' <optimize.qap-faq>`, does not find the global optimum.
>>> A = np.array([[0, 5, 8, 6], [5, 0, 5, 1],
... [8, 5, 0, 2], [6, 1, 2, 0]])
>>> B = np.array([[0, 1, 8, 4], [1, 0, 5, 2],
... [8, 5, 0, 5], [4, 2, 5, 0]])
>>> res = quadratic_assignment(A, B)
>>> print(res)
col_ind: array([1, 0, 3, 2])
fun: 178
nit: 13
If accuracy is important, consider using :ref:`'2opt' <optimize.qap-2opt>`
to refine the solution.
>>> guess = np.array([np.arange(len(A)), res.col_ind]).T
>>> res = quadratic_assignment(A, B, method="2opt",
... options = {'partial_guess': guess})
>>> print(res)
col_ind: array([1, 2, 3, 0])
fun: 176
nit: 17
"""
if options is None:
options = {}
method = method.lower()
methods = {"faq": _quadratic_assignment_faq,
"2opt": _quadratic_assignment_2opt}
if method not in methods:
raise ValueError(f"method {method} must be in {methods}.")
res = methods[method](A, B, **options)
return res
def _calc_score(A, B, perm):
# equivalent to objective function but avoids matmul
return np.sum(A * B[perm][:, perm])
def _common_input_validation(A, B, partial_match):
A = np.atleast_2d(A)
B = np.atleast_2d(B)
if partial_match is None:
partial_match = np.array([[], []]).T
partial_match = np.atleast_2d(partial_match).astype(int)
msg = None
if A.shape[0] != A.shape[1]:
msg = "`A` must be square"
elif B.shape[0] != B.shape[1]:
msg = "`B` must be square"
elif A.ndim != 2 or B.ndim != 2:
msg = "`A` and `B` must have exactly two dimensions"
elif A.shape != B.shape:
msg = "`A` and `B` matrices must be of equal size"
elif partial_match.shape[0] > A.shape[0]:
msg = "`partial_match` can have only as many seeds as there are nodes"
elif partial_match.shape[1] != 2:
msg = "`partial_match` must have two columns"
elif partial_match.ndim != 2:
msg = "`partial_match` must have exactly two dimensions"
elif (partial_match < 0).any():
msg = "`partial_match` must contain only positive indices"
elif (partial_match >= len(A)).any():
msg = "`partial_match` entries must be less than number of nodes"
elif (not len(set(partial_match[:, 0])) == len(partial_match[:, 0]) or
not len(set(partial_match[:, 1])) == len(partial_match[:, 1])):
msg = "`partial_match` column entries must be unique"
if msg is not None:
raise ValueError(msg)
return A, B, partial_match
def _quadratic_assignment_faq(A, B,
maximize=False, partial_match=None, rng=None,
P0="barycenter", shuffle_input=False, maxiter=30,
tol=0.03, **unknown_options
):
r"""
Solve the quadratic assignment problem (approximately).
This function solves the Quadratic Assignment Problem (QAP) and the
Graph Matching Problem (GMP) using the Fast Approximate QAP Algorithm
(FAQ) [1]_.
Quadratic assignment solves problems of the following form:
.. math::
\min_P & \ {\ \text{trace}(A^T P B P^T)}\\
\mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\
where :math:`\mathcal{P}` is the set of all permutation matrices,
and :math:`A` and :math:`B` are square matrices.
Graph matching tries to *maximize* the same objective function.
This algorithm can be thought of as finding the alignment of the
nodes of two graphs that minimizes the number of induced edge
disagreements, or, in the case of weighted graphs, the sum of squared
edge weight differences.
Note that the quadratic assignment problem is NP-hard. The results given
here are approximations and are not guaranteed to be optimal.
Parameters
----------
A : 2-D array, square
The square matrix :math:`A` in the objective function above.
B : 2-D array, square
The square matrix :math:`B` in the objective function above.
method : str in {'faq', '2opt'} (default: 'faq')
The algorithm used to solve the problem. This is the method-specific
documentation for 'faq'.
:ref:`'2opt' <optimize.qap-2opt>` is also available.
Options
-------
maximize : bool (default: False)
Maximizes the objective function if ``True``.
partial_match : 2-D array of integers, optional (default: None)
Fixes part of the matching. Also known as a "seed" [2]_.
Each row of `partial_match` specifies a pair of matched nodes:
node ``partial_match[i, 0]`` of `A` is matched to node
``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``, where
``m`` is not greater than the number of nodes, :math:`n`.
rng : int, `RandomState`, `Generator` or None, optional (default: None)
Accepts an integer as a seed for the random generator or a
``RandomState`` or ``Generator`` object. If None (default), uses
global `numpy.random` random state.
P0 : 2-D array, "barycenter", or "randomized" (default: "barycenter")
Initial position. Must be a doubly-stochastic matrix [3]_.
If the initial position is an array, it must be a doubly stochastic
matrix of size :math:`m' \times m'` where :math:`m' = n - m`.
If ``"barycenter"`` (default), the initial position is the barycenter
of the Birkhoff polytope (the space of doubly stochastic matrices).
This is a :math:`m' \times m'` matrix with all entries equal to
:math:`1 / m'`.
If ``"randomized"`` the initial search position is
:math:`P_0 = (J + K) / 2`, where :math:`J` is the barycenter and
:math:`K` is a random doubly stochastic matrix.
shuffle_input : bool (default: False)
Set to `True` to resolve degenerate gradients randomly. For
non-degenerate gradients this option has no effect.
maxiter : int, positive (default: 30)
Integer specifying the max number of Frank-Wolfe iterations performed.
tol : float (default: 0.03)
Tolerance for termination. Frank-Wolfe iteration terminates when
:math:`\frac{||P_{i}-P_{i+1}||_F}{\sqrt{m')}} \leq tol`,
where :math:`i` is the iteration number.
Returns
-------
res : OptimizeResult
`OptimizeResult` containing the following fields.
col_ind : 1-D array
Column indices corresponding to the best permutation found of the
nodes of `B`.
fun : float
The objective value of the solution.
nit : int
The number of Frank-Wolfe iterations performed.
Notes
-----
The algorithm may be sensitive to the initial permutation matrix (or
search "position") due to the possibility of several local minima
within the feasible region. A barycenter initialization is more likely to
result in a better solution than a single random initialization. However,
calling ``quadratic_assignment`` several times with different random
initializations may result in a better optimum at the cost of longer
total execution time.
Examples
--------
As mentioned above, a barycenter initialization often results in a better
solution than a single random initialization.
>>> np.random.seed(0)
>>> n = 15
>>> A = np.random.rand(n, n)
>>> B = np.random.rand(n, n)
>>> res = quadratic_assignment(A, B) # FAQ is default method
>>> print(res.fun)
46.871483385480545
>>> options = {"P0": "randomized"} # use randomized initialization
>>> res = quadratic_assignment(A, B, options=options)
>>> print(res.fun)
47.224831071310625 # may vary
However, consider running from several randomized initializations and
keeping the best result.
>>> res = min([quadratic_assignment(A, B, options=options)
... for i in range(30)], key=lambda x: x.fun)
>>> print(res.fun)
46.671852533681516 # may vary
The '2-opt' method can be used to further refine the results.
>>> options = {"partial_guess": np.array([np.arange(n), res.col_ind]).T}
>>> res = quadratic_assignment(A, B, method="2opt", options=options)
>>> print(res.fun)
46.47160735721583 # may vary
References
----------
.. [1] J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik,
S.G. Kratzer, E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and
C.E. Priebe, "Fast approximate quadratic programming for graph
matching," PLOS one, vol. 10, no. 4, p. e0121002, 2015,
:doi:`10.1371/journal.pone.0121002`
.. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski,
C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019):
203-215, :doi:`10.1016/j.patcog.2018.09.014`
.. [3] "Doubly stochastic Matrix," Wikipedia.
https://en.wikipedia.org/wiki/Doubly_stochastic_matrix
"""
_check_unknown_options(unknown_options)
maxiter = operator.index(maxiter)
# ValueError check
A, B, partial_match = _common_input_validation(A, B, partial_match)
msg = None
if isinstance(P0, str) and P0 not in {'barycenter', 'randomized'}:
msg = "Invalid 'P0' parameter string"
elif maxiter <= 0:
msg = "'maxiter' must be a positive integer"
elif tol <= 0:
msg = "'tol' must be a positive float"
if msg is not None:
raise ValueError(msg)
rng = check_random_state(rng)
n = len(A) # number of vertices in graphs
n_seeds = len(partial_match) # number of seeds
n_unseed = n - n_seeds
# [1] Algorithm 1 Line 1 - choose initialization
if not isinstance(P0, str):
P0 = np.atleast_2d(P0)
if P0.shape != (n_unseed, n_unseed):
msg = "`P0` matrix must have shape m' x m', where m'=n-m"
elif ((P0 < 0).any() or not np.allclose(np.sum(P0, axis=0), 1)
or not np.allclose(np.sum(P0, axis=1), 1)):
msg = "`P0` matrix must be doubly stochastic"
if msg is not None:
raise ValueError(msg)
elif P0 == 'barycenter':
P0 = np.ones((n_unseed, n_unseed)) / n_unseed
elif P0 == 'randomized':
J = np.ones((n_unseed, n_unseed)) / n_unseed
# generate a nxn matrix where each entry is a random number [0, 1]
# would use rand, but Generators don't have it
# would use random, but old mtrand.RandomStates don't have it
K = _doubly_stochastic(rng.uniform(size=(n_unseed, n_unseed)))
P0 = (J + K) / 2
# check trivial cases
if n == 0 or n_seeds == n:
score = _calc_score(A, B, partial_match[:, 1])
res = {"col_ind": partial_match[:, 1], "fun": score, "nit": 0}
return OptimizeResult(res)
obj_func_scalar = 1
if maximize:
obj_func_scalar = -1
nonseed_B = np.setdiff1d(range(n), partial_match[:, 1])
if shuffle_input:
nonseed_B = rng.permutation(nonseed_B)
nonseed_A = np.setdiff1d(range(n), partial_match[:, 0])
perm_A = np.concatenate([partial_match[:, 0], nonseed_A])
perm_B = np.concatenate([partial_match[:, 1], nonseed_B])
# definitions according to Seeded Graph Matching [2].
A11, A12, A21, A22 = _split_matrix(A[perm_A][:, perm_A], n_seeds)
B11, B12, B21, B22 = _split_matrix(B[perm_B][:, perm_B], n_seeds)
const_sum = A21 @ B21.T + A12.T @ B12
P = P0
# [1] Algorithm 1 Line 2 - loop while stopping criteria not met
for n_iter in range(1, maxiter+1):
# [1] Algorithm 1 Line 3 - compute the gradient of f(P) = -tr(APB^tP^t)
grad_fp = (const_sum + A22 @ P @ B22.T + A22.T @ P @ B22)
# [1] Algorithm 1 Line 4 - get direction Q by solving Eq. 8
_, cols = linear_sum_assignment(grad_fp, maximize=maximize)
Q = np.eye(n_unseed)[cols]
# [1] Algorithm 1 Line 5 - compute the step size
# Noting that e.g. trace(Ax) = trace(A)*x, expand and re-collect
# terms as ax**2 + bx + c. c does not affect location of minimum
# and can be ignored. Also, note that trace(A@B) = (A.T*B).sum();
# apply where possible for efficiency.
R = P - Q
b21 = ((R.T @ A21) * B21).sum()
b12 = ((R.T @ A12.T) * B12.T).sum()
AR22 = A22.T @ R
BR22 = B22 @ R.T
b22a = (AR22 * B22.T[cols]).sum()
b22b = (A22 * BR22[cols]).sum()
a = (AR22.T * BR22).sum()
b = b21 + b12 + b22a + b22b
# critical point of ax^2 + bx + c is at x = -d/(2*e)
# if a * obj_func_scalar > 0, it is a minimum
# if minimum is not in [0, 1], only endpoints need to be considered
if a*obj_func_scalar > 0 and 0 <= -b/(2*a) <= 1:
alpha = -b/(2*a)
else:
alpha = np.argmin([0, (b + a)*obj_func_scalar])
# [1] Algorithm 1 Line 6 - Update P
P_i1 = alpha * P + (1 - alpha) * Q
if np.linalg.norm(P - P_i1) / np.sqrt(n_unseed) < tol:
P = P_i1
break
P = P_i1
# [1] Algorithm 1 Line 7 - end main loop
# [1] Algorithm 1 Line 8 - project onto the set of permutation matrices
_, col = linear_sum_assignment(P, maximize=True)
perm = np.concatenate((np.arange(n_seeds), col + n_seeds))
unshuffled_perm = np.zeros(n, dtype=int)
unshuffled_perm[perm_A] = perm_B[perm]
score = _calc_score(A, B, unshuffled_perm)
res = {"col_ind": unshuffled_perm, "fun": score, "nit": n_iter}
return OptimizeResult(res)
def _split_matrix(X, n):
# definitions according to Seeded Graph Matching [2].
upper, lower = X[:n], X[n:]
return upper[:, :n], upper[:, n:], lower[:, :n], lower[:, n:]
def _doubly_stochastic(P, tol=1e-3):
# Adapted from @btaba implementation
# https://github.com/btaba/sinkhorn_knopp
# of Sinkhorn-Knopp algorithm
# https://projecteuclid.org/euclid.pjm/1102992505
max_iter = 1000
c = 1 / P.sum(axis=0)
r = 1 / (P @ c)
P_eps = P
for it in range(max_iter):
if ((np.abs(P_eps.sum(axis=1) - 1) < tol).all() and
(np.abs(P_eps.sum(axis=0) - 1) < tol).all()):
# All column/row sums ~= 1 within threshold
break
c = 1 / (r @ P)
r = 1 / (P @ c)
P_eps = r[:, None] * P * c
return P_eps
def _quadratic_assignment_2opt(A, B, maximize=False, rng=None,
partial_match=None,
partial_guess=None,
**unknown_options):
r"""
Solve the quadratic assignment problem (approximately).
This function solves the Quadratic Assignment Problem (QAP) and the
Graph Matching Problem (GMP) using the 2-opt algorithm [1]_.
Quadratic assignment solves problems of the following form:
.. math::
\min_P & \ {\ \text{trace}(A^T P B P^T)}\\
\mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\
where :math:`\mathcal{P}` is the set of all permutation matrices,
and :math:`A` and :math:`B` are square matrices.
Graph matching tries to *maximize* the same objective function.
This algorithm can be thought of as finding the alignment of the
nodes of two graphs that minimizes the number of induced edge
disagreements, or, in the case of weighted graphs, the sum of squared
edge weight differences.
Note that the quadratic assignment problem is NP-hard. The results given
here are approximations and are not guaranteed to be optimal.
Parameters
----------
A : 2-D array, square
The square matrix :math:`A` in the objective function above.
B : 2-D array, square
The square matrix :math:`B` in the objective function above.
method : str in {'faq', '2opt'} (default: 'faq')
The algorithm used to solve the problem. This is the method-specific
documentation for '2opt'.
:ref:`'faq' <optimize.qap-faq>` is also available.
Options
-------
maximize : bool (default: False)
Maximizes the objective function if ``True``.
rng : int, `RandomState`, `Generator` or None, optional (default: None)
Accepts an integer as a seed for the random generator or a
``RandomState`` or ``Generator`` object. If None (default), uses
global `numpy.random` random state.
partial_match : 2-D array of integers, optional (default: None)
Fixes part of the matching. Also known as a "seed" [2]_.
Each row of `partial_match` specifies a pair of matched nodes: node
``partial_match[i, 0]`` of `A` is matched to node
``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``,
where ``m`` is not greater than the number of nodes, :math:`n`.
partial_guess : 2-D array of integers, optional (default: None)
A guess for the matching between the two matrices. Unlike
`partial_match`, `partial_guess` does not fix the indices; they are
still free to be optimized.
Each row of `partial_guess` specifies a pair of matched nodes: node
``partial_guess[i, 0]`` of `A` is matched to node
``partial_guess[i, 1]`` of `B`. The array has shape ``(m, 2)``,
where ``m`` is not greater than the number of nodes, :math:`n`.
Returns
-------
res : OptimizeResult
`OptimizeResult` containing the following fields.
col_ind : 1-D array
Column indices corresponding to the best permutation found of the
nodes of `B`.
fun : float
The objective value of the solution.
nit : int
The number of iterations performed during optimization.
Notes
-----
This is a greedy algorithm that works similarly to bubble sort: beginning
with an initial permutation, it iteratively swaps pairs of indices to
improve the objective function until no such improvements are possible.
References
----------
.. [1] "2-opt," Wikipedia.
https://en.wikipedia.org/wiki/2-opt
.. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski,
C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019):
203-215, https://doi.org/10.1016/j.patcog.2018.09.014
"""
_check_unknown_options(unknown_options)
rng = check_random_state(rng)
A, B, partial_match = _common_input_validation(A, B, partial_match)
N = len(A)
# check trivial cases
if N == 0 or partial_match.shape[0] == N:
score = _calc_score(A, B, partial_match[:, 1])
res = {"col_ind": partial_match[:, 1], "fun": score, "nit": 0}
return OptimizeResult(res)
if partial_guess is None:
partial_guess = np.array([[], []]).T
partial_guess = np.atleast_2d(partial_guess).astype(int)
msg = None
if partial_guess.shape[0] > A.shape[0]:
msg = ("`partial_guess` can have only as "
"many entries as there are nodes")
elif partial_guess.shape[1] != 2:
msg = "`partial_guess` must have two columns"
elif partial_guess.ndim != 2:
msg = "`partial_guess` must have exactly two dimensions"
elif (partial_guess < 0).any():
msg = "`partial_guess` must contain only positive indices"
elif (partial_guess >= len(A)).any():
msg = "`partial_guess` entries must be less than number of nodes"
elif (not len(set(partial_guess[:, 0])) == len(partial_guess[:, 0]) or
not len(set(partial_guess[:, 1])) == len(partial_guess[:, 1])):
msg = "`partial_guess` column entries must be unique"
if msg is not None:
raise ValueError(msg)
fixed_rows = None
if partial_match.size or partial_guess.size:
# use partial_match and partial_guess for initial permutation,
# but randomly permute the rest.
guess_rows = np.zeros(N, dtype=bool)
guess_cols = np.zeros(N, dtype=bool)
fixed_rows = np.zeros(N, dtype=bool)
fixed_cols = np.zeros(N, dtype=bool)
perm = np.zeros(N, dtype=int)
rg, cg = partial_guess.T
guess_rows[rg] = True
guess_cols[cg] = True
perm[guess_rows] = cg
# match overrides guess
rf, cf = partial_match.T
fixed_rows[rf] = True
fixed_cols[cf] = True
perm[fixed_rows] = cf
random_rows = ~fixed_rows & ~guess_rows
random_cols = ~fixed_cols & ~guess_cols
perm[random_rows] = rng.permutation(np.arange(N)[random_cols])
else:
perm = rng.permutation(np.arange(N))
best_score = _calc_score(A, B, perm)
i_free = np.arange(N)
if fixed_rows is not None:
i_free = i_free[~fixed_rows]
better = operator.gt if maximize else operator.lt
n_iter = 0
done = False
while not done:
# equivalent to nested for loops i in range(N), j in range(i, N)
for i, j in itertools.combinations_with_replacement(i_free, 2):
n_iter += 1
perm[i], perm[j] = perm[j], perm[i]
score = _calc_score(A, B, perm)
if better(score, best_score):
best_score = score
break
# faster to swap back than to create a new list every time
perm[i], perm[j] = perm[j], perm[i]
else: # no swaps made
done = True
res = {"col_ind": perm, "fun": best_score, "nit": n_iter}
return OptimizeResult(res)
Reference in New Issue View Git Blame Copy Permalink