improve inference in space tensor product (#203)

* improve inference in space tensor product

* Fix ones for ArraySpace

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.7.4"
+version = "0.7.5"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Multivariate/TensorSpace.jl

@@ -254,7 +254,11 @@ setdomain(sp::TensorSpace, d::ProductDomain) = TensorSpace(setdomain.(factors(sp
 *(A::Space, B::Space) = A⊗B
 function ^(A::Space, p::Integer)
     p >= 1 || throw(ArgumentError("exponent must be >= 1, received $p"))
-    p == 1 ? A : foldl(*, ntuple(_ -> A, p))
+    # Enumerate common cases to help with constant propagation
+    p == 1 ? A :
+    p == 2 ? A * A :
+    p == 3 ? A * A * A :
+    foldl(*, ntuple(_ -> A, p))
 end
 
 

src/Spaces/ArraySpace.jl

@@ -234,8 +234,8 @@ Fun(M::UniformScaling,sp::MatrixSpace) = Fun(M.λ*Matrix(I,size(sp)...),sp)
 
 
 
-ones(::Type{T},A::ArraySpace) where {T<:Number} = Fun(ones.(T,spaces(A)))
-ones(A::ArraySpace) = Fun(ones.(spaces(A)))
+ones(::Type{T},A::ArraySpace) where {T<:Number} = Fun(ones.(T,A.spaces))
+ones(A::ArraySpace) = ones(Float64, A)
 
 
 ## EuclideanSpace

test/SpacesTest.jl

@@ -62,11 +62,19 @@ using LinearAlgebra
             end
         end
         @testset "intpow" begin
+            sp = PointSpace(1:3)
+            f = Fun(sp, Float64[1:3;])
             @test ApproxFunBase.intpow(f, 0) == f^0 == Fun(space(f), ones(ncoefficients(f)))
             for n in 1:3
                 @test ApproxFunBase.intpow(f, n) == f^n == reduce(*, fill(f, n))
             end
             @test ApproxFunBase.intpow(f,-2) == f^-2 == 1/(f*f)
+
+            @test sp^1 == sp
+            @test sp^2 == sp * sp
+            @test sp^3 == sp * sp * sp
+            @test sp^4 == sp * sp * sp * sp
+            @test sp^5 == sp * sp * sp * sp * sp
         end
 
         @testset "Fun accepts callables" begin