92 lines
30 KiB
Plaintext
92 lines
30 KiB
Plaintext
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“& HÑêHÁâH‰ØfÉHÚf HƒÀfWÁ@ðH9ÐuëL‰àHƒàþAöÄ„ÿÿÿH‹\$HH�Ãò fWG& ò éãþÿÿH�¼$ H�´$à è9 H‹¼$ H‹”$ H9útmL‹„$à L‹L$xH)ú1ÀL‹”$€ H‹ I‹4ÈI‰4I‰ HƒÀH9ÐuçH‹´$ H)þèñèÿÿéýÿÿIƒü… ÿÿÿé´þÿÿL‹D$M‰Ó@„í„QþÿÿéÿÿÿH…ÿ„Ôüÿÿë»HÇ„$� L‹D$M‰Ó@„í„$þÿÿéqþÿÿf. „ òAL‹\$M‰ÐHÇ„$� òAéDþÿÿI‰Çéíéÿÿé•êÿÿH‰ÃéðéÿÿH‰ÃéèéÿÿH‰ÃéíéÿÿH‰ÃéÿéÿÿH‰ÃéêÿÿH‰ÃéêÿÿH‰Ãéêÿÿépêÿÿ ¶ÉéHñÿÿ „ SH‰ûH‹?H…ÿt1H‹s H)þèøçÿÿHÇ ÇC HÇC ÇC HÇC [Ã�H9þ„¿ AWAVI‰öAUATI‰üUSH�_HƒìH9Þt~I‰×½ ë*H‰ÚL)âHƒú~|H‰ïL‰æH)×HßèóçÿÿHƒÃM‰,$I9ÞtJL‹+I‹I‹$J�4éH‹>H;<Á|¿H‹SøH�CøH;<Ñ}A�H‰PH‰ÇH‹PøHƒèL‹ÑL9|èL‰/HƒÃI9Þu¶HƒÄ[]A\A]A^A_à D u“H‰ëŽ�H‰ßL‰/ëÓÃf. „ f. „ f. „ f. „ f. „ D H�BÿAWI‰ÉAVAUI‰ÕATI‰ÄAƒåUIÁì?H‰ÕSIÄIÑüL‰l$øL9æ�: M‹I‰òëf�N‰<×H‰ÊI9ÌŽ I‰
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H�JI9Ì…Õ L‰ãL)ëH‰ØHÁø„ H½ÀH˜H� L‰ñL‰æL‰ïè`üÿÿH�û€ Žñ I��€ L‰òL‰ïH‰ÞèžùÿÿI9Üt]I‹f D L‹H‹SøH�CøJ�4ÁH‹<ÑH9>�Ì ff. „ f „ H‰PH‰ÇH‹PøHƒèL‹ ÑL9|èHƒÃL‰I9Üu¬HƒÄH‰è[]A\A]A^A_Ãf. „ HÇG ëÚ�HHcÉH‰JH�JI9Ì„ÿÿÿƒÀH˜H‰BL‰ãHÇÂþÿÿÿL)ëH‰ØHÁø…ÿÿÿé ÿÿÿL‰ñHÇÂþÿÿÿL‰æL‰ïèbûÿÿL‰òL‰æL‰ïè´øÿÿésÿÿÿ € H‰ßHƒÃL‰I9Ü…ÿÿÿéTÿÿÿL‰ê1ÀéˆþÿÿH�=× è*àÿÿ ó úHƒìHƒÄÃ
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Parameters
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----------
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cost_matrix : array
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The cost matrix of the bipartite graph.
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maximize : bool (default: False)
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Calculates a maximum weight matching if true.
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Returns
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-------
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row_ind, col_ind : array
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An array of row indices and one of corresponding column indices giving
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the optimal assignment. The cost of the assignment can be computed
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as ``cost_matrix[row_ind, col_ind].sum()``. The row indices will be
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sorted; in the case of a square cost matrix they will be equal to
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``numpy.arange(cost_matrix.shape[0])``.
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See Also
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--------
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scipy.sparse.csgraph.min_weight_full_bipartite_matching : for sparse inputs
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Notes
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-----
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The linear sum assignment problem [1]_ is also known as minimum weight
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matching in bipartite graphs. A problem instance is described by a matrix
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C, where each C[i,j] is the cost of matching vertex i of the first partite
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set (a 'worker') and vertex j of the second set (a 'job'). The goal is to
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find a complete assignment of workers to jobs of minimal cost.
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Formally, let X be a boolean matrix where :math:`X[i,j] = 1` iff row i is
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assigned to column j. Then the optimal assignment has cost
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.. math::
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\min \sum_i \sum_j C_{i,j} X_{i,j}
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where, in the case where the matrix X is square, each row is assigned to
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exactly one column, and each column to exactly one row.
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This function can also solve a generalization of the classic assignment
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problem where the cost matrix is rectangular. If it has more rows than
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columns, then not every row needs to be assigned to a column, and vice
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versa.
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This implementation is a modified Jonker-Volgenant algorithm with no
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initialization, described in ref. [2]_.
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.. versionadded:: 0.17.0
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Assignment_problem
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.. [2] DF Crouse. On implementing 2D rectangular assignment algorithms.
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*IEEE Transactions on Aerospace and Electronic Systems*,
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52(4):1679-1696, August 2016, :doi:`10.1109/TAES.2016.140952`
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Examples
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--------
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>>> import numpy as np
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>>> cost = np.array([[4, 1, 3], [2, 0, 5], [3, 2, 2]])
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>>> from scipy.optimize import linear_sum_assignment
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>>> row_ind, col_ind = linear_sum_assignment(cost)
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>>> col_ind
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array([1, 0, 2])
|
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|
>>> cost[row_ind, col_ind].sum()
|
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|
5
|
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|
|
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