Add autodiff

Draft for minimal integration of automatic differentiation. Tensorflow and Torch backend were removed (apart from AutoDiffOp.create_tensorlfow())

Only tests without LBM or tf/torch dependencies have been added. This implies that also numeric gradient checking is missing (depends on either tf or torch). Should we really move the backends into separate modules?

Apart from adding auto-differentiation functionality I added two more changes. Would be happy to AutoDiffOp.create_tensorflow() after feedback.

pystencils/simp/assignment_collection.py

@@ -3,6 +3,7 @@ from copy import copy
 from typing import List, Optional, Dict, Any, Set, Sequence, Iterator, Iterable, Union
 from pystencils.assignment import Assignment
 from pystencils.sympyextensions import fast_subs, count_operations, sort_assignments_topologically
+import pystencils
 
 
 class AssignmentCollection:
@@ -360,6 +361,25 @@ class AssignmentCollection:
         self.sub_expressions = [Assignment(k, v)
                                 for k, v in sub_expressions_dict.items()]
 
+    def has_exclusive_writes(self):
+        """
+        Simple check for exclusive (non-overlapping) writes.
+        I.e. AssignmentCollection can be executed safely in parallel without caring about race conditions.
+        """
+
+        assignments = self.main_assignments
+        write_field_accesses = [a.lhs for a in assignments if isinstance(a.lhs, pystencils.Field.Access)]
+
+        exclusive_writes = set()
+        for a in write_field_accesses:
+
+            if (a.field, a.index) in exclusive_writes:
+                return False
+            else:
+                exclusive_writes.add((a.field, a.index))
+
+        return True
+
 
 class SymbolGen:
     """Default symbol generator producing number symbols ζ_0, ζ_1, ..."""