Identity Fun in normalized Polynomial spaces (#91)

* Fun in normalized polynomial spaces

* bump version to v0.4.17

* Add tests for Ultraspherical

* fix range construction

* actually add identity test

* add approx tolerances

* avoid shadowing variables

Author: jishnub

.github/workflows/ci.yml

@@ -17,7 +17,6 @@ jobs:
         version:
           - '1.5'
           - '1'
-          - '^1.8.0-0'
         os:
           - ubuntu-latest
           - macOS-latest

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.4.16"
+version = "0.4.17"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Spaces/PolynomialSpace.jl

@@ -367,6 +367,15 @@ function Conversion(L::S, M::NormalizedPolynomialSpace{S}) where S<:PolynomialSp
     end
 end
 
+function Fun(::typeof(identity), S::NormalizedPolynomialSpace)
+    C = canonicalspace(S)
+    f = Fun(identity, C)
+    coeffs = coefficients(f)
+    CS = ConcreteConversion(C, S)
+    ApproxFunBase.mul_coefficients!(CS, coeffs)
+    Fun(S, coeffs)
+end
+
 bandwidths(C::ConcreteConversion{NormalizedPolynomialSpace{S,D,R},S}) where {S,D,R} = (0, 0)
 bandwidths(C::ConcreteConversion{S,NormalizedPolynomialSpace{S,D,R}}) where {S,D,R} = (0, 0)
 

test/ChebyshevTest.jl

@@ -220,4 +220,22 @@ import ApproxFunOrthogonalPolynomials: forwardrecurrence
             end
         end
     end
+
+    @testset "Normalized space" begin
+        for f in Any[x -> 3x^3 + 5x^2 + 2, x->x, identity]
+            for dt in Any[(), (0..1,)]
+                S = Chebyshev(dt...)
+                NS = NormalizedPolynomialSpace(S)
+
+                fS = Fun(f, S)
+                fNS = Fun(f, NS)
+                @test space(fNS) == NS
+                d = domain(fS)
+                r = range(leftendpoint(d), rightendpoint(d), length=10)
+                for x in r
+                    @test fS(x) ≈ fNS(x) rtol=1e-7 atol=1e-14
+                end
+            end
+        end
+    end
 end

test/JacobiTest.jl

@@ -297,4 +297,24 @@ import ApproxFunOrthogonalPolynomials: jacobip
         testbandedbelowoperator(C)
         @test norm(C*Fun(exp,Ultraspherical(1))-Fun(exp,Jacobi(0,0))) < 100eps()
     end
+
+    @testset "Normalized space" begin
+        for f in Any[x -> 3x^3 + 5x^2 + 2, x->x, identity]
+            for dt in Any[(), (0..1,)],
+                    S in Any[Jacobi(1,1,dt...),
+                             Jacobi(0.5,1.5,dt...),
+                             Legendre(dt...), ]
+
+                NS = NormalizedPolynomialSpace(S)
+                fS = Fun(f, S)
+                fNS = Fun(f, NS)
+                @test space(fNS) == NS
+                d = domain(fS)
+                r = range(leftendpoint(d), rightendpoint(d), length=10)
+                for x in r
+                    @test fS(x) ≈ fNS(x) rtol=1e-7 atol=1e-14
+                end
+            end
+        end
+    end
 end

test/UltrasphericalTest.jl

@@ -29,4 +29,24 @@ import ApproxFunOrthogonalPolynomials: jacobip
                     ApproxFunBase.ConversionWrapper{TimesOperator{Float64, Tuple{Int64, Int64}}, Float64}};
         @inferred Tallowed Conversion(Ultraspherical(1), Ultraspherical(2));
     end
+
+    @testset "Normalized space" begin
+        for f in Any[x -> 3x^3 + 5x^2 + 2, x->x, identity]
+            for dt in Any[(), (0..1,)],
+                    S in Any[Ultraspherical(1, dt...),
+                             Ultraspherical(0.5,dt...),
+                             Ultraspherical(3, dt...)]
+
+                NS = NormalizedPolynomialSpace(S)
+                fS = Fun(f, S)
+                fNS = Fun(f, NS)
+                @test space(fNS) == NS
+                d = domain(fS)
+                r = range(leftendpoint(d), rightendpoint(d), length=10)
+                for x in r
+                    @test fS(x) ≈ fNS(x) rtol=1e-7 atol=1e-14
+                end
+            end
+        end
+    end
 end