Use absolute values to calculate normalizing factor for relative norm…

…s in adaptivity (#125)

* When taking relative norm differences in similarity calculation, use absolute values to get the normalizing factor

* Fix comments with respect to earlier changes

* Add CHANGELOG entry

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## latest
 
+- Use absolute values to calculate normalizing factor for relative norms in adaptivity https://github.com/precice/micro-manager/pull/125
 - Add option to use only one micro simulation object in the snapshot computation https://github.com/precice/micro-manager/pull/123
 - Explicitly check if time window has converged using the API function `is_time_window_complete()` https://github.com/precice/micro-manager/pull/118
 - Add `MicroManagerSnapshot` enabling snapshot computation and storage of microdata in HDF5 format https://github.com/precice/micro-manager/pull/101

micro_manager/adaptivity/adaptivity.py

@@ -61,7 +61,7 @@ def _get_similarity_dists(
         for name in data.keys():
             data_vals = data[name]
             if data_vals.ndim == 1:
-                # If the adaptivity-data is a scalar for each simulation,
+                # If the adaptivity data is a scalar for each simulation,
                 # expand the dimension to make it a 2D array to unify the calculation.
                 # The axis is later reduced with a norm.
                 data_vals = np.expand_dims(data_vals, axis=1)
@@ -274,7 +274,7 @@ def _l2(self, data: np.ndarray) -> np.ndarray:
     def _l1rel(self, data: np.ndarray) -> np.ndarray:
         """
         Calculate L1 norm of relative difference of data.
-        The relative difference is calculated by dividing the difference of two data points by the maximum of the two data points.
+        The relative difference is calculated by dividing the difference of two data points by the maximum of the absolute value of the two data points.
 
         Parameters
         ----------
@@ -288,16 +288,21 @@ def _l1rel(self, data: np.ndarray) -> np.ndarray:
         """
         pointwise_diff = data[np.newaxis, :] - data[:, np.newaxis]
         # divide by data to get relative difference
-        # divide i,j by max(data[i],data[j]) to get relative difference
+        # divide i,j by max(abs(data[i]),abs(data[j])) to get relative difference
         relative = np.nan_to_num(
-            (pointwise_diff / np.maximum(data[np.newaxis, :], data[:, np.newaxis]))
+            (
+                pointwise_diff
+                / np.maximum(
+                    np.absolute(data[np.newaxis, :]), np.absolute(data[:, np.newaxis])
+                )
+            )
         )
         return np.linalg.norm(relative, ord=1, axis=-1)
 
     def _l2rel(self, data: np.ndarray) -> np.ndarray:
         """
         Calculate L2 norm of relative difference of data.
-        The relative difference is calculated by dividing the difference of two data points by the maximum of the two data points.
+        The relative difference is calculated by dividing the difference of two data points by the maximum of the absolute value of the two data points.
 
         Parameters
         ----------
@@ -311,8 +316,13 @@ def _l2rel(self, data: np.ndarray) -> np.ndarray:
         """
         pointwise_diff = data[np.newaxis, :] - data[:, np.newaxis]
         # divide by data to get relative difference
-        # divide i,j by max(data[i],data[j]) to get relative difference
+        # divide i,j by max(abs(data[i]),abs(data[j])) to get relative difference
         relative = np.nan_to_num(
-            (pointwise_diff / np.maximum(data[np.newaxis, :], data[:, np.newaxis]))
+            (
+                pointwise_diff
+                / np.maximum(
+                    np.absolute(data[np.newaxis, :]), np.absolute(data[:, np.newaxis])
+                )
+            )
         )
         return np.linalg.norm(relative, ord=2, axis=-1)