Add explanation and be more conservative

Author: devmotion

src/kernels/transformedkernel.jl

@@ -10,7 +10,14 @@ struct TransformedKernel{Tk<:Kernel,Tr<:Transform} <: Kernel
 end
 
 (k::TransformedKernel)(x, y) = k.kernel(k.transform(x), k.transform(y))
-function (k::TransformedKernel{<:SimpleKernel,<:ScaleTransform})(x, y)
+
+# Optimizations for scale transforms of simple kernels to save allocations:
+# Instead of a multiplying every element of the inputs before evaluating the metric,
+# we perform a scalar multiplcation of the distance of the original inputs, if possible.
+function (k::TransformedKernel{<:SimpleKernel,<:ScaleTransform})(
+    x::AbstractVector{<:Real},
+    y::AbstractVector{<:Real}
+)
     return kappa(k.kernel, _scale(k.transform, metric(k.kernel), x, y))
 end
 
@@ -20,9 +27,7 @@ end
 function _scale(t::ScaleTransform, metric::Union{SqEuclidean,DotProduct}, x, y)
     return first(t.s)^2 * evaluate(metric, x, y)
 end
-function _scale(t::ScaleTransform, metric, x, y)
-    evaluate(metric, t(x), t(y))
-end
+_scale(t::ScaleTransform, metric, x, y) = evaluate(metric, t(x), t(y))
 
 """
 ```julia