Fix test_singular_covariance_init

Author: William de Vazelhes

metric_learn/lsml.py

@@ -154,7 +154,7 @@ def _total_loss(self, metric, vab, vcd, prior_inv):
     return self._comparison_loss(metric, vab, vcd) + reg_loss
 
   def _gradient(self, metric, vab, vcd, prior_inv):
-    dMetric = prior_inv - np.linalg.inv(metric)
+    dMetric = prior_inv - scipy.linalg.pinvh(metric)
     dabs = np.sum(vab.dot(metric) * vab, axis=1)
     dcds = np.sum(vcd.dot(metric) * vcd, axis=1)
     violations = dabs > dcds

metric_learn/sdml.py

@@ -112,7 +112,11 @@ def _fit(self, pairs, y):
                                                   return_inverse=True)
     diff = pairs[:, 0] - pairs[:, 1]
     loss_matrix = (diff.T * y).dot(diff)
-    emp_cov = prior_inv + self.balance_param * loss_matrix
+    emp_cov = (prior_inv + self.balance_param * loss_matrix +
+               # We add a small value on the diagonal in case the
+               # emp_cov matrix is singular (see
+               # #https://github.com/metric-learn/metric-learn/issues/202)
+               np.eye(diff.shape[1]) * 1e-10)
 
     # our initialization will be the matrix with emp_cov's eigenvalues,
     # with a constant added so that they are all positive (plus an epsilon