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RFC-00xx-interpolation.md

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+# Interpolation
+
+## Authors
+
+* Allen Goodman (@0x00b1)
+
+## Summary
+
+Interpolation is a technique for adding new data points in a range of a set of known data points. You can use interpolation to fill-in missing data, smooth existing data, make predictions, and more.
+
+Interpolation operators operate on:
+
+* data on a regular grid (i.e., predetermined, not necessarily, uniform, spacing); or 
+* scattered data on an irregular grid.
+
+### `torch.interpolation.interpolate`
+
+```Python
+from typing import Callable, Optional, Tuple
+
+from torch import Tensor
+
+def interpolate(
+        x: Tuple[Tensor],
+        v: Tensor,
+        q: Tuple[Tensor],
+        f: Callable[[Tuple[Tensor]], Tuple[Tensor]],
+        *,
+        out: Optional[Tensor] = None
+):
+    raise NotImplementedError
+```
+
+Interpolate $n$-dimensional data on a regular grid (i.e., predetermined, not necessarily, uniform, spacing).
+
+### `torch.interpolation.unstructured_interpolate`
+
+```Python
+from typing import Callable, Optional, Tuple
+
+from torch import Tensor
+
+def unstructured_interpolate(
+        input: Tensor,
+        points: Tuple[Tensor],
+        x_i: Tuple[Tensor],
+        interpolant: Callable[[Tensor], Tensor],
+        *,
+        out: Optional[Tensor] = None
+):
+    raise NotImplementedError
+```
+
+Interpolate scattered data on an irregular grid.
+
+**Note**—Using this operation in dimensions greater than six is impractical because the memory required by the underlying Delaunay triangulation grows exponentially with its rank.
+
+**Note**—Because this operator uses a Delaunay triangulation, it can be sensitive to scaling issues in `input`. When this occurs, you should standardize `input` to improve the results.
+
+##### Parameters
+
+**input** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – 
+
+**points** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – 
+
+**x_i** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – 
+
+**interpolant** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – 
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.