Make style updates conditional

If there are no style pages in the first place, don't bother including
style terms in the climber base updates, and don't update the style
ratings on each iteration.

This optimization halves the number of calls to get_bt_derivatives.
This corresponds to a time saving of approximately 35%.

climbing_ratings/whole_history_rating.py

@@ -212,6 +212,7 @@ class WholeHistoryRating:
     __slots__ = (
         "_bases",
         "_styles",
+        "_has_styles",
         "_route_ratings",
         "_route_var",
         "_route_ascents",
@@ -257,6 +258,7 @@ def __init__(
             hparams.style_prior_variance,
             hparams.style_wiener_variance,
         )
+        self._has_styles = len(style_pages) > 0
         self._route_ratings: _Array = np.array(routes_rating)
         self._route_var = np.empty_like(self._route_ratings)
         self._route_ascents = _make_route_ascents(
@@ -277,6 +279,7 @@ def __copy__(self) -> "WholeHistoryRating":
         whr: WholeHistoryRating = self.__class__.__new__(self.__class__)
         whr._bases = copy.copy(self._bases)
         whr._styles = copy.copy(self._styles)
+        whr._has_styles = self._has_styles
         whr._route_ratings = self._route_ratings.copy()
         whr._route_var = self._route_var.copy()
         whr._route_ascents = self._route_ascents
@@ -316,20 +319,21 @@ def route_var(self) -> _Array:
         return self._route_var
 
     def __get_page_bt_derivatives(
-        self, pages: "_PageModel", aux_pages: "_PageModel"
+        self, pages: "_PageModel", aux_pages: Optional["_PageModel"]
     ) -> Tuple[_Array, _Array]:
         """Gets the Bradley-Terry terms for page/style-page ratings.
 
         Gets the first and second derivative of the Bradley-Terry model with
-        respect to the player's natural rating.  Auxilliary ratings allow the
+        respect to the player's natural rating.  Auxiliary ratings allow the
         player to be modeled with either base-ratings or style-ratings.
 
         Parameters
         ----------
         pages
             A slicing of ascents for the player's ratings.
         aux_pages
-            A slicing of ascents for the auxilliary ratings.
+            An optional slicing of ascents for the auxiliary ratings.  None is
+            equivalent to auxiliary ratings of 0 for all pages.
 
         Returns
         -------
@@ -342,9 +346,11 @@ def __get_page_bt_derivatives(
         num_ascents = len(ascents.adversary)
 
         page_ratings = expand_to_slices(ratings, ascents.slices, num_ascents)
-        page_ratings += expand_to_slices_sparse(
-            aux_pages.ratings, aux_pages.ascents.slices, num_ascents
-        )
+
+        if aux_pages is not None:
+            page_ratings += expand_to_slices_sparse(
+                aux_pages.ratings, aux_pages.ascents.slices, num_ascents
+            )
 
         route_ratings = self.route_ratings[ascents.adversary]
 
@@ -356,7 +362,10 @@ def __get_page_bt_derivatives(
         )
 
     def __update_page_ratings(
-        self, pages: "_PageModel", aux_pages: "_PageModel", only_variance: bool
+        self,
+        pages: "_PageModel",
+        aux_pages: Optional["_PageModel"],
+        only_variance: bool,
     ) -> None:
         """Update the ratings of all pages.
 
@@ -365,7 +374,8 @@ def __update_page_ratings(
         pages
             Pages of the player to update.
         aux_pages
-            Auxilliary pages for the player.
+            Optional auxiliary pages for the player.  None is equivalent to an
+            auxiliary rating of 0 for all pages.
         only_variance
             If true, only updates the page variance and covariance.
             The ratings estimates are left unchanged.
@@ -402,7 +412,8 @@ def update_base_ratings(self, only_variance: bool = False) -> None:
             If true, only updates the base variance and covariance.
             The ratings estimates are left unchanged.
         """
-        self.__update_page_ratings(self._bases, self._styles, only_variance)
+        styles = self._styles if self._has_styles else None
+        self.__update_page_ratings(self._bases, styles, only_variance)
 
     def update_style_ratings(self, only_variance: bool = False) -> None:
         """Update the ratings of all style pages.
@@ -462,7 +473,8 @@ def update_ratings(self) -> None:
         # the routes.
         self.update_base_ratings()
         self.update_route_ratings()
-        self.update_style_ratings()
+        if self._has_styles:
+            self.update_style_ratings()
 
     def update_covariance(self) -> None:
         """Update covariance estimates for all routes and pages."""