Preserve bandwidth in multiplication (#132)

* preserve bandwidth in multiplication

* Add test for NormalizedJacobi

* Fix for Fun in normalized space

* tests for banded operator

* version bump to v0.5.11

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.5.10"
+version = "0.5.11"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Spaces/PolynomialSpace.jl

@@ -421,8 +421,11 @@ hasconversion(a::NormalizedPolynomialSpace,b::NormalizedPolynomialSpace) = hasco
 
 
 function Multiplication(f::Fun{U},sp::NormalizedPolynomialSpace) where U <: PolynomialSpace
-    csp = space(f)
-    MultiplicationWrapper(f,Conversion(csp,sp)*Multiplication(f,csp)*Conversion(sp,csp))
+    fsp = space(f)
+    unnorm_sp = sp.space
+    O = Conversion(unnorm_sp,sp) *
+            Multiplication(f,unnorm_sp) * Conversion(sp, unnorm_sp)
+    MultiplicationWrapper(f, O)
 end
 
 function Multiplication(f::Fun{U},sp::PolynomialSpace) where U <: NormalizedPolynomialSpace
@@ -432,5 +435,5 @@ end
 function Multiplication(f::Fun{U},sp::NormalizedPolynomialSpace) where U <: NormalizedPolynomialSpace
     csp = canonicalspace(f)
     fc = Conversion(space(f), csp)*f
-    MultiplicationWrapper(f,Conversion(csp,sp)*Multiplication(fc,csp)*Conversion(sp,csp))
+    Multiplication(fc, sp)
 end

test/JacobiTest.jl

@@ -377,6 +377,18 @@ import ApproxFunOrthogonalPolynomials: jacobip
                 end
             end
         end
+
+        @testset "Multiplication" begin
+            xJ = Fun(NormalizedJacobi(1,1))
+            xC = Fun()
+            xNC = Fun(NormalizedChebyshev())
+            @test (Multiplication(xC) * xJ)(0.4) ≈ (0.4)^2
+            @test (Multiplication(xNC) * xJ)(0.4) ≈ (0.4)^2
+            @test ApproxFunBase.isbanded(Multiplication(xC, NormalizedLegendre()))
+            @test ApproxFunBase.isbanded(Multiplication(xNC, NormalizedLegendre()))
+            @test ApproxFunBase.isbanded(Multiplication(xC, NormalizedJacobi(1,1)))
+            @test ApproxFunBase.isbanded(Multiplication(xNC, NormalizedJacobi(1,1)))
+        end
     end
 
     @testset "casting bug ApproxFun.jl#770" begin