Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/optimize/_lsap.py

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+# Wrapper for the shortest augmenting path algorithm for solving the
+# rectangular linear sum assignment problem.  The original code was an
+# implementation of the Hungarian algorithm (Kuhn-Munkres) taken from
+# scikit-learn, based on original code by Brian Clapper and adapted to NumPy
+# by Gael Varoquaux. Further improvements by Ben Root, Vlad Niculae, Lars
+# Buitinck, and Peter Larsen.
+#
+# Copyright (c) 2008 Brian M. Clapper <bmc@clapper.org>, Gael Varoquaux
+# Author: Brian M. Clapper, Gael Varoquaux
+# License: 3-clause BSD
+
+import numpy as np
+from . import _lsap_module
+
+
+def linear_sum_assignment(cost_matrix, maximize=False):
+    """Solve the linear sum assignment problem.
+
+    The linear sum assignment problem 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.
+
+    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])``.
+
+    Notes
+    -----
+    .. 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, https://doi.org/10.1109/TAES.2016.140952
+
+    Examples
+    --------
+    >>> 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
+    """
+    cost_matrix = np.asarray(cost_matrix)
+    if len(cost_matrix.shape) != 2:
+        raise ValueError("expected a matrix (2-D array), got a %r array"
+                         % (cost_matrix.shape,))
+
+    if not (np.issubdtype(cost_matrix.dtype, np.number) or
+            cost_matrix.dtype == np.dtype(np.bool_)):
+        raise ValueError("expected a matrix containing numerical entries, got %s"
+                         % (cost_matrix.dtype,))
+
+    if maximize:
+        cost_matrix = -cost_matrix
+
+    if np.any(np.isneginf(cost_matrix) | np.isnan(cost_matrix)):
+        raise ValueError("matrix contains invalid numeric entries")
+
+    cost_matrix = cost_matrix.astype(np.double)
+    a = np.arange(np.min(cost_matrix.shape))
+
+    # The algorithm expects more columns than rows in the cost matrix.
+    if cost_matrix.shape[1] < cost_matrix.shape[0]:
+        b = _lsap_module.calculate_assignment(cost_matrix.T)
+        indices = np.argsort(b)
+        return (b[indices], a[indices])
+    else:
+        b = _lsap_module.calculate_assignment(cost_matrix)
+        return (a, b)