Preallocate GPU interpolant

The interpolants we in `Interpolations.jl` are described by two arrays:
the knots and the coeffs. When `Adapt` is called on these interpolants,
CuArrays are allocated on the GPU. For large data, this is inefficient.

In this commit, I add a system to avoid these allocations. This is
accomplished by add a dictionary to `InterpolationsRegridder`. This
dictionary has keys that identify the size of the knots and coefficients
and values the adapted splines. When `regrid` is called, we check if we
have already allocated some suitable space in this dictionary, if not,
we create a new spline, if we do, we write in place.

This removes GPU allocations in the hot path (ie, the regridder is used
in a time evolution with always the same data and dimensions), while
also keeping the flexibility of reusing the same regridder with any
input data.

ext/InterpolationsRegridderExt.jl

@@ -12,6 +12,7 @@ struct InterpolationsRegridder{
     SPACE <: ClimaCore.Spaces.AbstractSpace,
     FIELD <: ClimaCore.Fields.Field,
     BC,
+    GITP,
 } <: Regridders.AbstractRegridder
 
     """ClimaCore.Space where the output Field will be defined"""
@@ -22,6 +23,14 @@ struct InterpolationsRegridder{
 
     """Tuple of extrapolation conditions as accepted by Interpolations.jl"""
     extrapolation_bc::BC
+
+    # This is needed because Adapt moves from CPU to GPU and allocates new memory.
+    """Dictionary of preallocated areas of memory where to store the GPU interpolant (if
+    needed). Every time new data/dimensions are used in regrid, a new entry in the
+    dictionary is created. The keys of the dictionary a tuple of tuple
+    `(size(dimensions), size(data))`, with `dimensions` and `data` defined in `regrid`.
+    """
+    _gpuitps::GITP
 end
 
 # Note, we swap Lat and Long! This is because according to the CF conventions longitude
@@ -75,13 +84,38 @@ function Regridders.InterpolationsRegridder(
         "Number of boundary conditions does not match the number of dimensions",
     )
 
+    # Let's figure out the type of _gpuitps by creating a simple spline
+    FT = ClimaCore.Spaces.undertype(target_space)
+    dimensions = ntuple(_ -> [zero(FT), one(FT)], num_dimensions)
+    data = zeros(FT, ntuple(_ -> 2, num_dimensions))
+    itp = _create_linear_spline(FT, data, dimensions, extrapolation_bc)
+    fake_gpuitp = Adapt.adapt(ClimaComms.array_type(target_space), itp)
+    gpuitps = Dict((size.(dimensions), size(data)) => fake_gpuitp)
+
     return InterpolationsRegridder(
         target_space,
         coordinates,
-        extrapolation_bc
+        extrapolation_bc,
+        gpuitps,
+    )
+end
+
+"""
+    _create_linear_spline(regridder::InterpolationsRegridder, data, dimensions)
+
+Create a linear spline for the given data on the given dimension (on the CPU).
+"""
+function _create_linear_spline(FT, data, dimensions, extrapolation_bc)
+    dimensions_FT = map(d -> FT.(d), dimensions)
+
+    # Make a linear spline
+    return Intp.extrapolate(
+        Intp.interpolate(dimensions_FT, FT.(data), Intp.Gridded(Intp.Linear())),
+        extrapolation_bc,
     )
 end
 
+
 """
     regrid(regridder::InterpolationsRegridder, data, dimensions)::Field
 
@@ -91,16 +125,31 @@ This function is allocating.
 """
 function Regridders.regrid(regridder::InterpolationsRegridder, data, dimensions)
     FT = ClimaCore.Spaces.undertype(regridder.target_space)
-    dimensions_FT = map(d -> FT.(d), dimensions)
-
-    # Make a linear spline
-    itp = Intp.extrapolate(
-        Intp.interpolate(dimensions_FT, FT.(data), Intp.Gridded(Intp.Linear())),
-        regridder.extrapolation_bc,
-    )
+    itp =
+        _create_linear_spline(FT, data, dimensions, regridder.extrapolation_bc)
+
+    key = (size.(dimensions), size(data))
+
+    if haskey(regridder._gpuitps, key)
+        for (k, k_new) in zip(
+            regridder._gpuitps[key].itp.knots,
+            Adapt.adapt(
+                ClimaComms.array_type(regridder.target_space),
+                itp.itp.knots,
+            ),
+        )
+            k .= k_new
+        end
+        regridder._gpuitps[key].itp.coefs .= Adapt.adapt(
+            ClimaComms.array_type(regridder.target_space),
+            itp.itp.coefs,
+        )
+    else
+        regridder._gpuitps[key] =
+            Adapt.adapt(ClimaComms.array_type(regridder.target_space), itp)
+    end
 
-    # Move it to GPU (if needed)
-    gpuitp = Adapt.adapt(ClimaComms.array_type(regridder.target_space), itp)
+    gpuitp = regridder._gpuitps[key]
 
     return map(regridder.coordinates) do coord
         gpuitp(totuple(coord)...)