Add a function normalizedspace that dispatches to the appropriate type (#459)

* Add normalize for spaces

* remove doctest example

* rename normalize to normalizedspace

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.8.20"
+version = "0.8.21"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/ApproxFunBase.jl

@@ -104,6 +104,8 @@ export pad!, pad, chop!, sample,
 export .., Interval, ChebyshevInterval, leftendpoint, rightendpoint
 export endpoints, cache
 
+export normalizedspace
+
 import Base: oneto
 
 # assert that the conversion succeeds. This helps with inference as well as sanity

src/Spaces/Spaces.jl

@@ -199,3 +199,12 @@ end
 
 include("HeavisideSpace.jl")
 include("DiracSpace.jl")
+
+"""
+    normalizedspace(S::Space)
+
+Return a normalized space (or a direct sum of such spaces) over `domain(S)`.
+For polynomial spaces, this corresponds to normalized polynomials over the same domain.
+For a `DirectSumSpace`, this returns a direct sum over normalized spaces.
+"""
+normalizedspace

src/Spaces/SumSpace.jl

@@ -499,3 +499,8 @@ component(sp::TensorSpace{Tuple{S1,S2}},k::Integer) where {S1,S2<:DirectSumSpace
 
 component(sp::TensorSpace{Tuple{S1,S2}},k::Integer,j::Integer) where {S1<:DirectSumSpace,S2<:DirectSumSpace} =
     component(factor(sp,1),k) ⊗ component(factor(sp,2),j)
+
+# Normalized space
+normalizedspace(S::DirectSumSpace) = mapreduce(normalizedspace, ⊕, components(S))
+normalizedspace(S::SumSpace) = SumSpace(map(normalizedspace, components(S)))
+normalizedspace(S::PiecewiseSpace) = _PiecewiseSpace(map(normalizedspace, components(S)))