More consistent output from link functions (#762)

src/glum/_link.py

@@ -79,7 +79,6 @@ class IdentityLink(Link):
     def __eq__(self, other):  # noqa D
         return isinstance(other, self.__class__)
 
-    # unnecessary type hint for consistency with other methods
     def link(self, mu):
         """Return mu (identity link).
 
@@ -102,7 +101,6 @@ def derivative(self, mu):
         """
         return 1.0 if np.isscalar(mu) else np.ones_like(mu)
 
-    # unnecessary type hint for consistency with other methods
     def inverse(self, lin_pred):
         """Compute the inverse link function ``h(lin_pred)``.
 
@@ -156,7 +154,7 @@ def link(self, mu):
         -------
         numpy.ndarray
         """
-        return np.log(mu)
+        return np.log(_asanyarray(mu))
 
     def derivative(self, mu):
         """Get the derivative of the log link, one over ``mu``.
@@ -169,7 +167,7 @@ def derivative(self, mu):
         -------
         numpy.ndarray
         """
-        return 1 / mu
+        return 1 / _asanyarray(mu)
 
     def inverse(self, lin_pred):
         """Get the inverse of the log link, the exponential function.
@@ -184,7 +182,7 @@ def inverse(self, lin_pred):
         -------
         numpy.ndarray
         """
-        return np.exp(lin_pred)
+        return np.exp(_asanyarray(lin_pred))
 
     def inverse_derivative(self, lin_pred):
         """Compute the derivative of the inverse link function ``h'(lin_pred)``.
@@ -194,17 +192,17 @@ def inverse_derivative(self, lin_pred):
         lin_pred : array-like, shape (n_samples,)
             Usually the (fitted) linear predictor.
         """
-        return np.exp(lin_pred)
+        return np.exp(_asanyarray(lin_pred))
 
     def inverse_derivative2(self, lin_pred):
-        """Compute 2nd derivative of the inverse link function ``h''(lin_pred)``.
+        """Compute second derivative of the inverse link function ``h''(lin_pred)``.
 
         Parameters
         ----------
         lin_pred : array-like, shape (n_samples,)
             Usually the (fitted) linear predictor.
         """
-        return np.exp(lin_pred)
+        return np.exp(_asanyarray(lin_pred))
 
 
 class LogitLink(Link):
@@ -282,7 +280,7 @@ def inverse_derivative(self, lin_pred):
         return ep * (1.0 - ep)
 
     def inverse_derivative2(self, lin_pred):
-        """Compute 2nd derivative of the inverse link function ``h''(lin_pred)``.
+        """Compute second derivative of the inverse link function ``h''(lin_pred)``.
 
         Parameters
         ----------
@@ -324,61 +322,56 @@ def _to_return(*args, **kwargs):
 class TweedieLink(Link):
     """The Tweedie link function ``x^(1-p)`` if ``p≠1`` and ``log(x)`` if ``p=1``."""
 
-    def __new__(cls, p: float):
-        """
-        Create a new ``TweedieLink`` object.
-
-        Parameters
-        ----------
-        p: scalar
-        """
-        if p == 0:
-            return IdentityLink()
-        if p == 1:
-            return LogLink()
-        return super().__new__(cls)
-
     def __init__(self, p):
         self.p = p
 
     def __eq__(self, other):  # noqa D
         return isinstance(other, self.__class__) and (self.p == other.p)
 
     def link(self, mu):
-        """
-        Get the Tweedie canonical link.
+        """Get the Tweedie canonical link.
 
         See superclass documentation.
 
         Parameters
         ----------
         mu: array-like
         """
+        if self.p == 0:
+            return _asanyarray(mu)
+        if self.p == 1:
+            return np.log(_asanyarray(mu))
         return _asanyarray(mu) ** (1 - self.p)
 
     def derivative(self, mu):
-        """
-        Get the derivative of the Tweedie link.
+        """Get the derivative of the Tweedie link.
 
         See superclass documentation.
 
         Parameters
         ----------
         mu: array-like
         """
+        if self.p == 0:
+            return 1.0 if np.isscalar(mu) else np.ones_like(mu)
+        if self.p == 1:
+            return 1 / _asanyarray(mu)
         return (1 - self.p) * _asanyarray(mu) ** (-self.p)
 
     @catch_p
     def inverse(self, lin_pred):
-        """
-        Get the inverse of the Tweedie link.
+        """Get the inverse of the Tweedie link.
 
         See superclass documentation.
 
         Parameters
         ----------
         mu: array-like
         """
+        if self.p == 0:
+            return _asanyarray(lin_pred)
+        if self.p == 1:
+            return np.exp(_asanyarray(lin_pred))
         return _asanyarray(lin_pred) ** (1 / (1 - self.p))
 
     @catch_p
@@ -390,20 +383,30 @@ def inverse_derivative(self, lin_pred):
         lin_pred : array-like, shape (n_samples,)
             Usually the (fitted) linear predictor.
         """
+        if self.p == 0:
+            return 1.0 if np.isscalar(lin_pred) else np.ones_like(lin_pred)
+        if self.p == 1:
+            return np.exp(_asanyarray(lin_pred))
         return (1 / (1 - self.p)) * _asanyarray(lin_pred) ** (self.p / (1 - self.p))
 
     @catch_p
     def inverse_derivative2(self, lin_pred):
-        """Compute secondnd derivative of the inverse Tweedie link function \
+        """Compute second derivative of the inverse Tweedie link function \
             ``h''(lin_pred)``.
 
         Parameters
         ----------
         lin_pred : array, shape (n_samples,)
             Usually the (fitted) linear predictor.
         """
+        if self.p == 0:
+            return 0.0 if np.isscalar(lin_pred) else np.zeros_like(lin_pred)
+        if self.p == 1:
+            return np.exp(_asanyarray(lin_pred))
+
         result = _asanyarray(lin_pred) ** ((2 * self.p - 1) / (1 - self.p))
         result *= self.p / (1 - self.p) ** 2
+
         return result
 
 
@@ -484,7 +487,7 @@ def inverse_derivative(self, lin_pred):
         return np.exp(lin_pred - np.exp(lin_pred))
 
     def inverse_derivative2(self, lin_pred):
-        """Compute 2nd derivative of the inverse link function ``h''(lin_pred)``.
+        """Compute second derivative of the inverse link function ``h''(lin_pred)``.
 
         Parameters
         ----------

tests/glm/test_link.py

@@ -35,7 +35,7 @@ def test_link_properties(link):
 
 def test_equality():
     assert TweedieLink(1.5) == TweedieLink(1.5)
-    assert TweedieLink(1) == LogLink()
+    assert TweedieLink(1) != LogLink()
     assert LogLink() == LogLink()
     assert TweedieLink(1.5) != TweedieLink(2.5)
     assert TweedieLink(1.5) != LogitLink()