ELF                      @                @ 8  @                                 8      8                                                                                                                       $       $              Ptd   4      4      4      t       t              Qtd                                                  Rtd                   p      p                      GNU b<{zHMϒ                                                                	                                                                              u                                                                                      e                                            }                                            F   "                   %                                                                _                     w                      U                      2                     ]                                                                B                                                                                                                                                        ,                       R    D%      H       __gmon_start__ _ITM_deregisterTMCloneTable _ITM_registerTMCloneTable __cxa_finalize _ZdlPvm memmove __stack_chk_guard _Znwm memset memcpy _ZSt20__throw_length_errorPKc __stack_chk_fail _Unwind_Resume __gcc_personality_v0 PyArg_ParseTupleAndKeywords Py_BuildValue _Py_Dealloc PyExc_ValueError PyErr_Format PyErr_SetString PyExc_TypeError PyInit__lsap PyImport_ImportModule PyObject_GetAttrString PyCapsule_Type PyCapsule_GetPointer PyModule_Create2 PyExc_RuntimeError PyErr_Print PyExc_ImportError libstdc++.so.6 libgcc_s.so.1 libc.so.6 ld-linux-aarch64.so.1 CXXABI_1.3.9 GLIBCXX_3.4 GLIBC_2.17 GCC_3.0 GCC_3.3.1                                             0   yѯ   /     t)   <                    H             0   P&y   S     a_&	   [                    H                                                                      x4                  4                  @4                 H4                 @     @           @+      H           !      X           X+                                                 	                                                                                                                                                                                                                                                 
           (                   0                   8                   @                   H                   P                   X                   `                   h                   p                   x                                                                                                                   { a  {_        {  G?     @   @"   
@B   @b   @   @   @   @   "@  &@"  *@B  .@b  2@  6@  :@  >@  B@  F@"  J@B  N@b  R@    G@  _        ! ?    T  !Ga   _     ! !  "A!A    BGb   _ {   `"F9@ 7   G     X@  R`"9@{¨_     O ?#{P @O A? J T @ & |Ө  hf
xhmyfnyjЊЈx)ЌT  FA m T @K  x%? 
 Txf h@BBIydBA?KT  {#_P B BBTB xb    {#_ ?#{ c      TS[
 @"  D @z`(_bzgezdfzh  T_  T  T %_dzdfzc  T     @fzc T`ze  * T@   _fze T  T   _@@dzdfzc T `ze  KT    T  M T8  T_   T #@ z %_@CA
 !A  ! zaCA" @@ BC 8" _" TSA[BcC{Ĩ#_  ?#{    @  {#A@!  {#_  ?#{    @  {#A@!  ˶{#_  ?#{     @  a@!  ˧ 
 
   @{¨#_ ?  ` T?#{ S  [ c?   T @t@@xtxc J Tb_   T`  s" TSA[BcC{Ĩ#_d_c" ѡxd * T d d_'@xd KT Tc _?#{   c $@k Rs3 C  G  @   ! T   GA @B  A\ TC*cCkDsE3@{Ǩ#_ |t  q A/ T@/   T   g  B _   Tzb  aG  `!  R  *49 @  @!  AAAAAAAA/@  ?  hU T/@  !G }O 8   R     ? HT T  !G4} ; 6  R   # ?|  !  # a   `= T   T;@"   R2@ ;@  R  O@  R    R  ; s { /@w @  F}W AFD@ !}?    3 S  R  j   F}[  |!F%@ !}C    7 _ c    R L;@e;@  c #@k A     T;@' "   R:'@k@Rc@ /@" K! KC $$"!g   g   A a{    	T@' T?@ R 3@CD  @G@  @     @?`$ TC@ R 7@CD  @K@  @       T  T /	1  ՟    @!@ FAD* a    "  @""!    &}{d   g `{a {`az``xb(` 8e 8c a T0 b T  b  Tz` Ba! ? T@ h` T`{e} @z`_ D   !  @!FD *!` !    ""  @f{p  fk%   _  TD@`   ( T  !Gw}       T  RB     c@  - T@   T@} }ӵ    T @     ? Tc    aT@/  7Z@c  T@ @/   @ @a   TI"@`@`z `z  ;@`[@]W@ZW@  @!  R;@NKHO@E* {w  @0  (b {7F"zb? @  Tx` {`azaA8a (a {    AT  0  F""{b?   Taz`{`A8a 8a{    	T Հzrz2x`x  AT T@  ? l TB/@`x x`x    kT R7@ @K@    3@`@G@   o  ?2@}˹C  T   G    ? ` T ?  T"  R @   T      Cx!?  ! T R%C B K B|a@?@ T  @@@  T"_
_gxbexji
 m T  _'@exb KT!  
  T  h`@bxah @Ah     T R" @@   G  AA @   ҁ T     K   G  AA @    T    ?6   G  AA @   T     .   G  AA @   aT     "$ @AA @   ҁTL$  !G  q$  !G  YWe$  !G  $ S@j   G eC$ ^   G $  !G  $ $ _@-S@K$  !G  ?#  cG{ S [c b @      c B    4c  ЀR@S@"@3A@ ?  $R R R`?  @_ q	 T@  @ @X@ R @ ;  R(tAҕ    R! R ? 
 @ R R   	@  R! RuA ? 
 @
@  q$@< 1  T 1 T    `" b@7B b b  z"@ 7B "    @ 7! с  SDcF;@     G  !    @a`@ 7  ` @ SDcF    G@ @B  	 T{C[E#_N`@7  `   ;@EBSDcF;@b@ Ң6 @@7      4SDcF;@SDcF;@   G  !!  @:b@b6  @7    `   G  !   @)`@ 6   G  !@!  @ b@7 ҊSc; ?#{     " 	 S   ! #@  7! с a  a@   G?   T   a@  7! a      @3R r  ? k T@ LC  ?0 q T@ HC  ? 
 4 q TSA  {¨#   ` ~R@   G  !@#  @`@ 7  `  SA   G  !`,  @{¨#  _SA@   G! @ @  ? **  !`$SA@   G!LC @  ? *  !%RSA   G  ! +  @SA   G  !@*  @SA   G  !#  @SA { {_vector::_M_default_append       cannot create std::vector larger than max_size()        O|p     expected a matrix (2-D array), got a %d array   invalid cost matrix object      cost matrix is infeasible       matrix contains invalid numeric entries OO      numpy.core._multiarray_umath    _ARRAY_API      _ARRAY_API is not PyCapsule object      _ARRAY_API is NULL pointer      module compiled against ABI version 0x%x but this version of numpy is 0x%x      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 . FATAL: module compiled as unknown endian        FATAL: module compiled as little endian, but detected different endianness at runtime   numpy.core.multiarray failed to import  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
     _lsap   Solves the rectangular linear sum assignment.   cost_matrix     maximize    ;p               \   l     T    <    8  0  X         zR x       0          ,   (<           @   TH    A BN       d              (   |   x<   B-Au
 A-AS A- 8         A-A@BECqAB A-   (      `8    A-AE
 A-CA A- (     t8    A-AE
 A-CA A- $   <  L    A-A BM A-   D   d      C-A@BBB^
 A-AR -          zPLR x  x       @  w  A-ApFDHQ
pFH A-ACBB
B	]
AAAAA
AAAAAAA
A	   D  t   A-AD
	NCD[@AAALAL A-A
	-ICC
AAAK
AAAA
AAAQIJAAA`     PH   A-A Fm
B A-DSH A-B -C
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AG
AG
AG     T           H                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          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                                h                                                       c                         p                             n                         |                             t             '      '                                    z      2       '      '                                               4      4      t                                           5      5      L                                          T8      T8      X                                                                                                                                                                                                                   X                                                                                                                                                                                                                         N                                                         4                                                                                      