Merge pull request #11631 from pmla/lsap-constant-cost

Revert to old behaviour for constant cost matrices in `linear_sum_assignment`
scipy · Mar 7, 2020 · e3bf555 · e3bf555
2 parents c5b9f5e + c050fd9
commit e3bf555
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diff --git a/scipy/optimize/rectangular_lsap/rectangular_lsap.cpp b/scipy/optimize/rectangular_lsap/rectangular_lsap.cpp
@@ -59,7 +59,9 @@ augmenting_path(int nc, std::vector<double>& cost, std::vector<double>& u,
     int num_remaining = nc;
     std::vector<int> remaining(nc);
     for (int it = 0; it < nc; it++) {
-        remaining[it] = it;
+        // Filling this up in reverse order ensures that the solution of a
+        // constant cost matrix is the identity matrix (c.f. #11602).
+        remaining[it] = nc - it - 1;
     }
 
     std::fill(SR.begin(), SR.end(), false);

diff --git a/scipy/optimize/tests/test_linear_assignment.py b/scipy/optimize/tests/test_linear_assignment.py
@@ -91,3 +91,12 @@ def test_linear_sum_assignment_input_validation():
     I = np.identity(3)
     I[:, 0] = np.inf
     assert_raises(ValueError, linear_sum_assignment, I)
+
+
+def test_constant_cost_matrix():
+    # Fixes #11602
+    n = 8
+    C = np.ones((n, n))
+    row_ind, col_ind = linear_sum_assignment(C)
+    assert_array_equal(row_ind, np.arange(n))
+    assert_array_equal(col_ind, np.arange(n))