Jacobi matrices for RectPolynomial

[MikaelSlevinsky]

I just added these in commit b2f95fe, but they cannot be instantiated like T² \ (x .* T²), like those on the Dunkl-Xu disk or the JacobiTriangle for reasons I don't understand. The code is so simple that the error must be somewhere else. I suspect it's because the Jacobi matrices for the basis are lazy tridiagonals instead of banded-block-banded matrices for the nontrivial Koornwinder classes, which means the error is not really in this code.

julia> using MultivariateOrthogonalPolynomials, ClassicalOrthogonalPolynomials

julia> J = JacobiTriangle(0, 0, 0)
JacobiTriangle(0, 0, 0)

julia> jacobimatrix(Val{1}(), J); # works

julia> x,y = first.(axes(J,1)), last.(axes(J,1))
(first.(Inclusion(UnitSimplex(Val(2)))), last.(Inclusion(UnitSimplex(Val(2)))))

julia> jacobimatrix(Val{1}(), J)^C

julia> J \ (x .* J); # also works

julia> T² = RectPolynomial(ChebyshevT(), ChebyshevT())
ChebyshevT() ⊗ ChebyshevT()

julia> jacobimatrix(Val{1}(), T²); # works. This is what I just added

julia> x,y = first.(axes(T²,1)), last.(axes(T²,1))
(first.(Inclusion((-1.0 .. 1.0 (Chebyshev)) × (-1.0 .. 1.0 (Chebyshev)))), last.(Inclusion((-1.0 .. 1.0 (Chebyshev)) × (-1.0 .. 1.0 (Chebyshev)))))

julia> T² \ (x .* T²) # errs
ERROR: DimensionMismatch: Second axis of A, 1:1:ℵ₀, and first axis of B, Inclusion((-1.0 .. 1.0 (Chebyshev)) × (-1.0 .. 1.0 (Chebyshev))) must match
Stacktrace:
 [1] _check_mul_axes(A::RectPolynomial{Float64, Tuple{…}}, B::QuasiArrays.ApplyQuasiMatrix{Float64, typeof(*), Tuple{…}})
   @ ArrayLayouts ~/.julia/packages/ArrayLayouts/i3v9G/src/mul.jl:95
 [2] check_mul_axes(::RectPolynomial{Float64, Tuple{…}}, ::QuasiArrays.ApplyQuasiMatrix{Float64, typeof(*), Tuple{…}})
   @ ArrayLayouts ~/.julia/packages/ArrayLayouts/i3v9G/src/mul.jl:111
 [3] instantiate
   @ ~/.julia/packages/ArrayLayouts/i3v9G/src/mul.jl:123 [inlined]
 [4] materialize
   @ ~/.julia/packages/ArrayLayouts/i3v9G/src/mul.jl:127 [inlined]
 [5] mul
   @ ~/.julia/packages/ArrayLayouts/i3v9G/src/mul.jl:128 [inlined]
 [6] *(A::RectPolynomial{Float64, Tuple{…}}, B::QuasiArrays.ApplyQuasiMatrix{Float64, typeof(*), Tuple{…}})
   @ QuasiArrays ~/.julia/packages/QuasiArrays/ZCn0F/src/matmul.jl:23
 [7] broadcasted(::QuasiArrays.LazyQuasiArrayStyle{…}, ::typeof(*), x::QuasiArrays.BroadcastQuasiVector{…}, P::RectPolynomial{…})
   @ HarmonicOrthogonalPolynomials ~/.julia/packages/HarmonicOrthogonalPolynomials/ViYwn/src/multivariateops.jl:45
 [8] broadcasted(::typeof(*), ::QuasiArrays.BroadcastQuasiVector{…}, ::RectPolynomial{…})
   @ Base.Broadcast ./broadcast.jl:1347
 [9] top-level scope
   @ REPL[119]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> 

[MikaelSlevinsky]

Closed by @dlfivefifty in 089ad3c.