Minor improvements

pde/fields/tensorial.py

@@ -25,7 +25,14 @@
 
 
 class Tensor2Field(DataFieldBase):
-    """Tensor field of rank 2 discretized on a grid"""
+    """Tensor field of rank 2 discretized on a grid
+
+    Warning:
+        Components of the tensor field are given in the local basis. While the local
+        basis is identical to the global basis in Cartesian coordinates, the local basis
+        depends on position in curvilinear coordinate systems. Moreover, the field
+        always contains all components, even if the underlying grid assumes symmetries.
+    """
 
     rank = 2
 

pde/fields/vectorial.py

@@ -27,7 +27,14 @@
 
 
 class VectorField(DataFieldBase):
-    """Vector field discretized on a grid"""
+    """Vector field discretized on a grid
+
+    Warning:
+        Components of the vector field are given in the local basis. While the local
+        basis is identical to the global basis in Cartesian coordinates, the local basis
+        depends on position in curvilinear coordinate systems. Moreover, the field
+        always contains all components, even if the underlying grid assumes symmetries.
+    """
 
     rank = 1
 

pde/grids/base.py

@@ -601,9 +601,9 @@ def _boundary_coordinates(self, axis: int, upper: bool) -> np.ndarray:
         return np.stack(points, -1).reshape(shape)  # type: ignore
 
     @property
-    @abstractmethod
     def volume(self) -> float:
         """float: total volume of the grid"""
+        raise NotImplementedError
 
     @abstractmethod
     def point_to_cartesian(
@@ -913,7 +913,6 @@ def get_boundary_conditions(
 
         return bcs
 
-    @abstractmethod
     def get_line_data(self, data: np.ndarray, extract: str = "auto") -> dict[str, Any]:
         """return a line cut through the grid
 
@@ -928,8 +927,8 @@ def get_line_data(self, data: np.ndarray, extract: str = "auto") -> dict[str, An
             dict: A dictionary with information about the line cut, which is convenient
             for plotting.
         """
+        raise NotImplementedError
 
-    @abstractmethod
     def get_image_data(self, data: np.ndarray) -> dict[str, Any]:
         """return a 2d-image of the data
 
@@ -940,6 +939,7 @@ def get_image_data(self, data: np.ndarray) -> dict[str, Any]:
         Returns:
             dict: A dictionary with information about the data convenient for plotting.
         """
+        raise NotImplementedError
 
     def get_vector_data(self, data: np.ndarray) -> dict[str, Any]:
         """return data to visualize vector field
@@ -953,7 +953,6 @@ def get_vector_data(self, data: np.ndarray) -> dict[str, Any]:
         """
         raise NotImplementedError
 
-    @abstractmethod
     def get_random_point(
         self,
         *,
@@ -976,6 +975,7 @@ def get_random_point(
         Returns:
             :class:`~numpy.ndarray`: The coordinates of the random point
         """
+        raise NotImplementedError
 
     @classmethod
     def register_operator(