Autogenerate parameter types in documentation from python typehints.

For example: if the method is...

```python
def forward(self, x1: Tensor, x2: Optional[Tensor]) -> Union[Tensor, LinearOperator]:
    r"""
    Does the forward thing.

    :param x1: The x1 arg
    :param x2: The x2 arg
    :return: The forward stuff.
    """
    # ...
```

The resulting documentation will include the appropriate types:

```
Parameters:

  - x1 (torch.Tensor) - The x1 arg
  - x2 (torch.Tensor, optional) - The x2 arg

Return type: torch.Tensor or LinearOperator

Returns: The forward stuff.
```

This (hopefully) should prevent a lot of duplicate effort on our end.

This commit also refactors the gpytorch.kernels.Kernel and
gpytorch.distributions.MultivariateNormal docs to utilize
auto-typing.

docs/requirements.txt

@@ -4,6 +4,7 @@ ipython
 ipykernel
 sphinx
 sphinx_rtd_theme
+sphinx_autodoc_typehints
 nbsphinx
 m2r2
 pyro-ppl

docs/source/conf.py

@@ -18,6 +18,8 @@
 import shutil
 import sys
 import sphinx_rtd_theme  # noqa
+import warnings
+from typing import ForwardRef
 
 
 def read(*names, **kwargs):
@@ -80,16 +82,25 @@ def find_version(*file_paths):
 # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
 # ones.
 extensions = [
+    "sphinx.ext.autodoc",
     "sphinx.ext.coverage",
+    "sphinx.ext.githubpages",
+    "sphinx.ext.intersphinx",
     "sphinx.ext.mathjax",
     'sphinx.ext.napoleon',
     "sphinx.ext.viewcode",
-    "sphinx.ext.githubpages",
-    "sphinx.ext.autodoc",
+    "sphinx_autodoc_typehints",
     "nbsphinx",
     "m2r2",
 ]
 
+# Configuration for intersphinx: refer to the Python standard library.
+intersphinx_mapping = {
+    "python": ("https://docs.python.org/3/", None),
+    "torch": ("https://pytorch.org/docs/stable/", None),
+    "linear_operator": ("https://linear-operator.readthedocs.io/en/stable/", None),
+}
+
 # Disable docstring inheritance
 autodoc_inherit_docstrings = False
 
@@ -210,3 +221,97 @@ def find_version(*file_paths):
         "Miscellaneous",
     )
 ]
+
+
+# -- Function to format  typehints ----------------------------------------------
+# Adapted from
+# https://github.com/cornellius-gp/linear_operator/blob/2b33b9f83b45f0cb8cb3490fc5f254cc59393c25/docs/source/conf.py
+def _process(annotation, config):
+    """
+    A function to convert a type/rtype typehint annotation into a :type:/:rtype: string.
+    This function is a bit hacky, and specific to the type annotations we use most frequently.
+    This function is recursive.
+    """
+    # Simple/base case: any string annotation is ready to go
+    if type(annotation) == str:
+        return annotation
+
+    # Convert Ellipsis into "..."
+    elif annotation == Ellipsis:
+        return "..."
+
+    # Convert any class (i.e. torch.Tensor, LinearOperator, gpytorch, etc.) into appropriate strings
+    # For external classes, the format will be e.g. "torch.Tensor"
+    # For any linear_operator class, the format will be e.g. "~linear_operator.operators.TriangularLinearOperator"
+    # For any internal class, the format will be e.g. "~gpytorch.kernels.RBFKernel"
+    elif hasattr(annotation, "__name__"):
+        module = annotation.__module__ + "."
+        if module.split(".")[0] == "linear_operator":
+            if annotation.__name__.endswith("LinearOperator"):
+                module = f"~linear_operator."
+            elif annotation.__name__.endswith("LinearOperator"):
+                module = f"~linear_operator.operators."
+            else:
+                module = "~" + module
+        elif module.split(".")[0] == "gpytorch":
+            module = "~" + module
+        elif module == "builtins.":
+            module = ""
+        res = f"{module}{annotation.__name__}"
+
+    # Convert any Union[*A*, *B*, *C*] into "*A* or *B* or *C*"
+    # Also, convert any Optional[*A*] into "*A*, optional"
+    elif str(annotation).startswith("typing.Union"):
+        is_optional_str = ""
+        args = list(annotation.__args__)
+        # Hack: Optional[*A*] are represented internally as Union[*A*, Nonetype]
+        # This catches this case
+        if args[-1] is type(None):  # noqa E721
+            del args[-1]
+            is_optional_str = ", optional"
+        processed_args = [_process(arg, config) for arg in args]
+        res = " or ".join(processed_args) + is_optional_str
+
+    # Convert any Tuple[*A*, *B*] into "(*A*, *B*)"
+    elif str(annotation).startswith("typing.Tuple"):
+        args = list(annotation.__args__)
+        res = "(" + ", ".join(_process(arg, config) for arg in args) + ")"
+
+    # Convert any List[*A*] into "list(*A*)"
+    elif str(annotation).startswith("typing.List"):
+        arg = annotation.__args__[0]
+        res = "list(" + _process(arg, config) + ")"
+
+    # Convert any Iterable[*A*] into "iterable(*A*)"
+    elif str(annotation).startswith("typing.Iterable"):
+        arg = annotation.__args__[0]
+        res = "iterable(" + _process(arg, config) + ")"
+
+    # Handle "Callable"
+    elif str(annotation).startswith("typing.Callable"):
+        res = "callable"
+
+    # Handle "Any"
+    elif str(annotation).startswith("typing.Any"):
+        res = ""
+
+    # Special cases for forward references.
+    # This is brittle, as it only contains case for a select few forward refs
+    # All others that aren't caught by this are handled by the default case
+    elif isinstance(annotation, ForwardRef):
+        res = str(annotation.__forward_arg__)
+
+    # For everything we didn't catch: use the simplist string representation
+    else:
+        warnings.warn(f"No rule for {annotation}. Using default resolution...", RuntimeWarning)
+        res = str(annotation)
+
+    return res
+
+
+# -- Options for typehints ----------------------------------------------
+always_document_param_types = True
+# typehints_use_rtype = False
+typehints_defaults = None  # or "comma"
+simplify_optional_unions = False
+typehints_formatter = _process

docs/source/distributions.rst

@@ -36,6 +36,7 @@ MultivariateNormal
 
 .. autoclass:: MultivariateNormal
    :members:
+   :special-members: __getitem__
 
 
 MultitaskMultivariateNormal

docs/source/kernels.rst

@@ -17,6 +17,7 @@ Kernel
 
 .. autoclass:: Kernel
    :members:
+   :special-members: __call__, __getitem__
 
 Standard Kernels
 -----------------------------