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�HH9õtHcɃÀH‰JH�JH9ÍtH˜H‰BM½öº?L‰ùH‰îIƒö?L‰ïD)òHcÒHÒèQüÿÿH�û€ެI��€L‰úL‰ïH‰ÞèïùÿÿH9ÝtNI‹I‰Ø@M‹I‹PøL‰ÆI�@øJ�<ÉH‹H9Ñ~DH‰PH‰ÆH‹PøHƒèH‹ÑH9|èIƒÀL‰I9èu¼HƒÄL‰à[]A\A]A^A_Ãf.„H‰ý»éwþÿÿHÇH‰_HÇGë¿L‰úH‰îL‰ïèJùÿÿë¬L‰ê1ÀéÞþÿÿH�=/è¢ãÿÿf�éËãÿÿHƒìHƒÄÃO|pinvalid cost matrix objectcost matrix is infeasibleOOnumpy._core._multiarray_umathnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API is NULL pointercost_matrixmaximize_lsaplinear_sum_assignmentexpected a matrix (2-D array), got a %d arraymatrix contains invalid numeric entries_ARRAY_API is not PyCapsule objectmodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule was compiled against NumPy C-API version 0x%x (NumPy 1.23) but the running NumPy has C-API version 0x%x. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.FATAL: module compiled as unknown endianFATAL: module compiled as little endian, but detected different endianness at runtimenumpy._core.multiarray failed to importSolves the rectangular linear sum assignment.Solve the linear sum assignment problem.
Parameters
----------
cost_matrix : array
The cost matrix of the bipartite graph.
maximize : bool (default: False)
Calculates a maximum weight matching if true.
Returns
-------
row_ind, col_ind : array
An array of row indices and one of corresponding column indices giving
the optimal assignment. The cost of the assignment can be computed
as ``cost_matrix[row_ind, col_ind].sum()``. The row indices will be
sorted; in the case of a square cost matrix they will be equal to
``numpy.arange(cost_matrix.shape[0])``.
See Also
--------
scipy.sparse.csgraph.min_weight_full_bipartite_matching : for sparse inputs
Notes
-----
The linear sum assignment problem [1]_ is also known as minimum weight
matching in bipartite graphs. A problem instance is described by a matrix
C, where each C[i,j] is the cost of matching vertex i of the first partite
set (a 'worker') and vertex j of the second set (a 'job'). The goal is to
find a complete assignment of workers to jobs of minimal cost.
Formally, let X be a boolean matrix where :math:`X[i,j] = 1` iff row i is
assigned to column j. Then the optimal assignment has cost
.. math::
\min \sum_i \sum_j C_{i,j} X_{i,j}
where, in the case where the matrix X is square, each row is assigned to
exactly one column, and each column to exactly one row.
This function can also solve a generalization of the classic assignment
problem where the cost matrix is rectangular. If it has more rows than
columns, then not every row needs to be assigned to a column, and vice
versa.
This implementation is a modified Jonker-Volgenant algorithm with no
initialization, described in ref. [2]_.
.. versionadded:: 0.17.0
References
----------
.. [1] https://en.wikipedia.org/wiki/Assignment_problem
.. [2] DF Crouse. On implementing 2D rectangular assignment algorithms.
*IEEE Transactions on Aerospace and Electronic Systems*,
52(4):1679-1696, August 2016, :doi:`10.1109/TAES.2016.140952`
Examples
--------
>>> import numpy as np
>>> cost = np.array([[4, 1, 3], [2, 0, 5], [3, 2, 2]])
>>> from scipy.optimize import linear_sum_assignment
>>> row_ind, col_ind = linear_sum_assignment(cost)
>>> col_ind
array([1, 0, 2])
>>> cost[row_ind, col_ind].sum()
5
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