Merge pull request #35 from simon-hirsch/links_derivatives

Links derivatives

src/rolch/abc.py

@@ -13,7 +13,6 @@
     update_inverted_gram,
     update_y_gram,
 )
-from rolch.utils import handle_param_dict
 
 if HAS_PANDAS:
     import pandas as pd
@@ -37,9 +36,15 @@ def link_derivative(self, x: np.ndarray) -> np.ndarray:
         """Calculate the first derivative of the link function"""
         raise NotImplementedError("Currently not implemented. Will be needed for GLMs")
 
+    @abstractmethod
+    def link_second_derivative(self, x: np.ndarray) -> np.ndarray:
+        """Calculate the second derivative for the link function"""
+        raise NotImplementedError("Currently not implemented.")
+
     @abstractmethod
     def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         """Calculate the first derivative for the inverse link function"""
+        raise NotImplementedError("Currently not implemented.")
 
 
 class Distribution(ABC):

src/rolch/link.py

@@ -32,6 +32,9 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
         return 1 / x
 
+    def link_second_derivative(self, x: np.ndarray) -> np.ndarray:
+        return -1 / x**2
+
 
 class IdentityLink(LinkFunction):
     """
@@ -55,6 +58,9 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.ones_like(x)
 
+    def link_second_derivative(self, x: np.ndarray) -> np.ndarray:
+        return np.zeros_like(x)
+
 
 class LogShiftValueLink(LinkFunction):
     """
@@ -81,7 +87,10 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.fmax(np.exp(np.fmin(x, EXP_UPPER_BOUND)), LOG_LOWER_BOUND)
 
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
-        return super().link_derivative(x)
+        return 1 / (x - self.value)
+
+    def link_second_derivative(self, x: np.ndarray) -> np.ndarray:
+        return -1 / (x - self.value) ** 2
 
 
 class LogShiftTwoLink(LogShiftValueLink):
@@ -120,6 +129,9 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
         return 1 / (2 * np.sqrt(x))
 
+    def link_second_derivative(self, x) -> np.ndarray:
+        return -1 / (4 * x ** (3 / 2))
+
 
 class SqrtShiftValueLink(LinkFunction):
     """
@@ -144,7 +156,10 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return 2 * x
 
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
-        return super().link_derivative(x)
+        return 1 / (2 * np.sqrt(x - self.value))
+
+    def link_second_derivative(self, x) -> np.ndarray:
+        return -1 / (4 * (x - self.value) ** (3 / 2))
 
 
 class SqrtShiftTwoLink(SqrtShiftValueLink):
@@ -185,6 +200,9 @@ def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
     def link_derivative(self, x: np.ndarray) -> np.ndarray:
         return super().link_derivative(x)
 
+    def link_second_derivative(self, x) -> np.ndarray:
+        return super().link_second_derivative(x)
+
 
 __all__ = [
     "LogLink",