sum for RectPolynomial (#191)

* sum for RectPolynomial

* Update ci.yml

* Update multivariatelanczos.jl

Author: dlfivefifty

.github/workflows/ci.yml

@@ -10,7 +10,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.10'
+          - 'lts'
+          - '1'
         os:
           - ubuntu-latest
           - windows-latest

Project.toml

@@ -1,6 +1,6 @@
 name = "MultivariateOrthogonalPolynomials"
 uuid = "4f6956fd-4f93-5457-9149-7bfc4b2ce06d"
-version = "0.7.1"
+version = "0.7.2"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

examples/multivariatelanczos.jl

@@ -0,0 +1,30 @@
+using MultivariateOrthogonalPolynomials, ClassicalOrthogonalPolynomials, Test
+
+P = Legendre()
+P² = RectPolynomial(P,P)
+p₀ = expand(P², 𝐱 -> 1)
+𝐱 = axes(P²,1)
+x,y = first.(𝐱),last.(𝐱)
+w = P²/P²\ (x-y).^2
+
+w .* p₀
+
+
+sum(p₀)
+using LazyBandedMatrices
+KronTrav(sum(P;dims=1), sum(P;dims=1))
+
+T = ChebyshevT()
+U = ChebyshevU()
+KronTrav(sum(T;dims=1), sum(Jacobi(1,1);dims=1))
+
+
+
+x = axes(P,1)
+X = zeros(∞,∞); X[1,1] = 1;
+p₀ = P*X*P'
+@test sum(p₀) == 4
+
+sum(x.^2 .* p₀)
+
+P\F/P'

src/rect.jl

@@ -163,3 +163,11 @@ function transform_ldiv(K::KronPolynomial{d,V,<:Fill{<:Legendre}}, f::Union{Abst
     dat = (T \ f).array
     DiagTrav(pad(FastTransforms.th_cheb2leg(paddeddata(dat)), axes(dat)...))
 end
+
+
+## sum
+
+function Base._sum(P::RectPolynomial, dims)
+    @assert dims == 1
+    KronTrav(sum.(P.args; dims=1)...)
+end

test/test_rect.jl

@@ -138,4 +138,12 @@ using ContinuumArrays: plotgridvalues
         @test x == SVector.(ChebyshevGrid{2}(40), ChebyshevGrid{2}(40)')
         @test F == ones(40,40)
     end
+
+    @testset "plot" begin
+        P = RectPolynomial(Legendre(),Legendre())
+        p₀ = expand(P, 𝐱 -> 1)
+        @test sum(p₀) ≈ 4.0
+        f = expand(P, splat((x,y) -> exp(cos(x^2*y))))
+        @test sum(f) ≈ 10.546408460894801 # empirical
+    end
 end