add direction penalties

Direction penalties are estimated by getting the name to address
ratio usage for each partial term in the query and computing the
linear regression of that ratio over the entire phrase. Or to put
it in ither words: we try to determine if the terms at the beginning
or the end of the query are more likely to constitute a name.

Direction penalties are currently used only in classic name queries.

src/nominatim_api/search/query.py

@@ -13,6 +13,10 @@ from collections import defaultdict
 import dataclasses
 
 
+LINFAC = [i * (sum(si * si for si in range(i)) - (i - 1) * i * (i - 1) / 4)
+          for i in range(50)]
+
+
 BreakType = str
 """ Type of break between tokens.
 """
@@ -201,6 +205,15 @@ class QueryNode:
         types of tokens spanning over the gap.
     """
 
+    def name_address_ratio(self) -> float:
+        """ Return the propability that the partial token belonging to
+            this node forms part of a name (as opposed of part of the address).
+        """
+        if self.partial is None:
+            return 0.5
+
+        return self.partial.count / (self.partial.count + self.partial.addr_count)
+
     def adjust_break(self, btype: BreakType, penalty: float) -> None:
         """ Change the break type and penalty for this node.
         """
@@ -242,12 +255,20 @@ class QueryStruct:
         need to be direct neighbours. Thus the query is represented as a
         directed acyclic graph.
 
+        A query also has a direction penalty 'dir_penalty'. This describes
+        the likelyhood if the query should be read from left-to-right or
+        vice versa. A negative 'dir_penalty' should be read as a penalty on
+        right-to-left reading, while a positive value represents a penalty
+        for left-to-right reading. The default value is 0, which is equivalent
+        to having no information about the reading.
+
         When created, a query contains a single node: the start of the
         query. Further nodes can be added by appending to 'nodes'.
     """
 
     def __init__(self, source: List[Phrase]) -> None:
         self.source = source
+        self.dir_penalty = 0.0
         self.nodes: List[QueryNode] = \
             [QueryNode(BREAK_START, source[0].ptype if source else PHRASE_ANY,
                        0.0, '', '')]
@@ -291,6 +312,21 @@ class QueryStruct:
                 else:
                     tlist.append(token)
 
+    def compute_direction_penalty(self) -> None:
+        """ Recompute the direction probability from the partial tokens
+            of each node.
+        """
+        n = len(self.nodes) - 1
+        if n == 1 or n >= 50:
+            self.dir_penalty = 0
+        elif n == 2:
+            self.dir_penalty = (self.nodes[1].name_address_ratio()
+                                - self.nodes[0].name_address_ratio()) / 3
+        else:
+            ratios = [n.name_address_ratio() for n in self.nodes[:-1]]
+            self.dir_penalty = (n * sum(i * r for i, r in enumerate(ratios))
+                                - sum(ratios) * n * (n - 1) / 2) / LINFAC[n]
+
     def get_tokens(self, trange: TokenRange, ttype: TokenType) -> List[Token]:
         """ Get the list of tokens of a given type, spanning the given
             nodes. The nodes must exist. If no tokens exist, an