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Server: Apache/2.4.46 (Win64) OpenSSL/1.1.1j PHP/8.4.25
System: Windows NT DESKTOP-4TAV2RJ 10.0 build 19045 (Windows 10) AMD64
User: fred (0)
PHP: 8.4.25
Disabled: NONE
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File: C:/Users/fred/anaconda3/Lib/site-packages/scipy/optimize/_lsap.cp312-win_amd64.pyd
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 a��<�=�А8a aHa`a�a�aА����@8a�����@�a�a�a�a0�����@�a�a�a b��<�=���a b`b��<�=�0��a`b�c��D����`��8h���������� �����������������������d�c0d@d������@dexpected a matrix (2-D array), got a %d arraycost_matrixmodule compiled against ABI version 0x%x but this version of numpy is 0x%xnumpy.core.multiarray failed to importlinear_sum_assignmentinvalid cost matrix object_ARRAY_API is not PyCapsule objectmatrix contains invalid numeric entries_ARRAY_API is NULL pointerO|p_lsapUnknown exceptionFATAL: module compiled as unknown endianbad array new lengthnumpy.core._multiarray_umathvector too longmaximizeFATAL: module compiled as little endian, but detected different endianness at runtimecost matrix is infeasibleOO_ARRAY_APISolves the rectangular linear sum assignment.module compiled against API version 0x%x but this version of numpy is 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 .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()
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