Support sum with Normalized (#35)

* Support sum with Normalized

* Update test_lanczos.jl

* Update Project.toml

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ClassicalOrthogonalPolynomials"
 uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.3.6"
+version = "0.3.7"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -29,7 +29,7 @@ ArrayLayouts = "0.6.2"
 BandedMatrices = "0.16.5"
 BlockArrays = "0.15"
 BlockBandedMatrices = "0.10"
-ContinuumArrays = "0.7.1"
+ContinuumArrays = "0.7.2"
 DomainSets = "0.4, 0.5"
 FFTW = "1.1"
 FastGaussQuadrature = "0.4.3"

src/ClassicalOrthogonalPolynomials.jl

@@ -30,7 +30,7 @@ import InfiniteArrays: OneToInf, InfAxes, Infinity, AbstractInfUnitRange, Infini
 import ContinuumArrays: Basis, Weight, basis, @simplify, Identity, AbstractAffineQuasiVector, ProjectionFactorization,
     inbounds_getindex, grid, transform, transform_ldiv, TransformFactorization, QInfAxes, broadcastbasis, Expansion,
     AffineQuasiVector, AffineMap, WeightLayout, WeightedBasisLayout, WeightedBasisLayouts, demap, AbstractBasisLayout, BasisLayout,
-    checkpoints, weight, unweightedbasis, MappedBasisLayouts
+    checkpoints, weight, unweightedbasis, MappedBasisLayouts, __sum
 import FastTransforms: Λ, forwardrecurrence, forwardrecurrence!, _forwardrecurrence!, clenshaw, clenshaw!,
                         _forwardrecurrence_next, _clenshaw_next, check_clenshaw_recurrences, ChebyshevGrid, chebyshevpoints
 

src/classical/jacobi.jl

@@ -47,6 +47,7 @@ getproperty(w::LegendreWeight{T}, ::Symbol) where T = zero(T)
 sum(::LegendreWeight{T}) where T = 2one(T)
 
 _weighted(::LegendreWeight, P) = P
+_weighted(::SubQuasiArray{<:Any,1,<:LegendreWeight}, P) = P
 
 broadcasted(::LazyQuasiArrayStyle{1}, ::typeof(*), ::LegendreWeight{T}, ::LegendreWeight{V}) where {T,V} =
     LegendreWeight{promote_type(T,V)}()

src/normalized.jl

@@ -199,3 +199,5 @@ broadcasted(::LazyQuasiArrayStyle{2}, ::typeof(*), x::Inclusion, Q::Weighted) =
     convert(WeightedOrthogonalPolynomial, parent(Ac))' * convert(WeightedOrthogonalPolynomial, wB)
 
 summary(io::IO, Q::Weighted) = print(io, "Weighted($(Q.P))")
+
+__sum(::NormalizedBasisLayout, A, dims) = __sum(ApplyLayout{typeof(*)}(), A, dims)

test/test_lanczos.jl

@@ -1,5 +1,5 @@
 using ClassicalOrthogonalPolynomials, BandedMatrices, ArrayLayouts, Test
-import ClassicalOrthogonalPolynomials: recurrencecoefficients, PaddedLayout, orthogonalityweight
+import ClassicalOrthogonalPolynomials: recurrencecoefficients, PaddedLayout, orthogonalityweight, golubwelsch
 
 @testset "Lanczos" begin
     @testset "Legendre" begin
@@ -220,4 +220,16 @@ import ClassicalOrthogonalPolynomials: recurrencecoefficients, PaddedLayout, ort
         @test X.dv[3:∞][1:5] ≈ X.dv[3:7]
         @test X.dv[3:∞][2:∞][1:5] ≈ X.dv[4:8]
     end
+
+    @testset "golubwelsch" begin
+        x = axes(Legendre(),1)
+        Q = LanczosPolynomial( @.(inv(1+x^2)))
+        x,w = golubwelsch(Q[:,Base.OneTo(10)])
+        @test sum(w) ≈ π/2
+        @test sum(x.^2 .* w) ≈ 2 - π/2
+
+        x̃ = Inclusion(-1..1)
+        Q̃ = LanczosPolynomial( @.(inv(1+x̃^2)))
+        @test all((x,w) .≈ golubwelsch(Q̃[:,Base.OneTo(10)]))
+    end
 end