Method ambiguity multiplying a LowerTriangular and a SymTridiagonal

[DanielVandH]

julia> using ClassicalOrthogonalPolynomials, LinearAlgebra

julia> P = Normalized(Legendre()); X = jacobimatrix(P); L = cholesky(I - X).L;

julia> X * L
ERROR: MethodError: copy(::ArrayLayouts.Mul{ArrayLayouts.SymTridiagonalLayout{LazyArrays.LazyLayout, LazyArrays.LazyLayout}, ArrayLayouts.TriangularLayout{'L', 'N', InfiniteLinearAlgebra.AdaptiveLayout{BandedMatrices.BandedRows{ArrayLayouts.DenseColumnMajor}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}, LowerTriangular{Float64, Adjoint{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Fill{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(-), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}}}}}) is ambiguous.

Candidates:
  copy(M::ArrayLayouts.Mul{<:Union{ArrayLayouts.HermitianLayout{BandedMatrices.BandedColumns{LazyArrays.LazyLayout}}, ArrayLayouts.SymmetricLayout{BandedMatrices.BandedColumns{LazyArrays.LazyLayout}}, BandedMatrices.BandedColumns{LazyArrays.LazyLayout}, BandedMatrices.BandedRows{LazyArrays.LazyLayout}, BlockBandedMatrices.BlockBandedColumns{LazyArrays.LazyLayout}, BlockBandedMatrices.BlockBandedRows{LazyArrays.LazyLayout}, LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout, LazyBandedMatrices.AbstractLazyBandedLayout, LazyBandedMatrices.AbstractLazyBlockBandedLayout, ArrayLayouts.BidiagonalLayout{LazyArrays.LazyLayout}, ArrayLayouts.HermitianLayout{<:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.SymTridiagonalLayout{LazyArrays.LazyLayout}, ArrayLayouts.SymmetricLayout{<:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.TriangularLayout{UPLO, UNIT, BandedMatrices.BandedColumns{LazyArrays.LazyLayout}} where {UPLO, UNIT}, ArrayLayouts.TriangularLayout{UPLO, UNIT, BandedMatrices.BandedRows{LazyArrays.LazyLayout}} where {UPLO, UNIT}, ArrayLayouts.TriangularLayout{'L', 'N', <:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.TriangularLayout{'U', 'N', <:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.TriangularLayout{'L', 'U', <:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.TriangularLayout{'U', 'U', <:LazyBandedMatrices.AbstractLazyBandedBlockBandedLayout}, ArrayLayouts.TridiagonalLayout{LazyArrays.LazyLayout}, BlockArrays.BlockLayout{ArrayLayouts.BidiagonalLayout{LazyArrays.LazyLayout, LazyArrays.LazyLayout}}, BlockArrays.BlockLayout{ArrayLayouts.DiagonalLayout{LazyArrays.LazyLayout}}, BlockArrays.BlockLayout{ArrayLayouts.SymTridiagonalLayout{LazyArrays.LazyLayout, LazyArrays.LazyLayout}}, BlockArrays.BlockLayout{ArrayLayouts.TridiagonalLayout{LazyArrays.LazyLayout, LazyArrays.LazyLayout, LazyArrays.LazyLayout}}, BlockArrays.BlockLayout{LazyArrays.LazyLayout}, BlockArrays.BlockLayout{LazyBandedMatrices.LazyBandedLayout}, BlockBandedMatrices.BandedBlockBandedColumns{<:LazyArrays.AbstractLazyLayout}, BlockBandedMatrices.BandedBlockBandedRows{<:LazyArrays.AbstractLazyLayout}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\LazyBandedMatrices.jl:926
  copy(M::ArrayLayouts.Mul{<:Any, <:Union{LazyArrays.AbstractLazyLayout, ArrayLayouts.HermitianLayout{<:LazyArrays.AbstractLazyLayout}, ArrayLayouts.SymmetricLayout{<:LazyArrays.AbstractLazyLayout}, ArrayLayouts.TriangularLayout{'L', 'N', <:LazyArrays.AbstractLazyLayout}, ArrayLayouts.TriangularLayout{'U', 'N', <:LazyArrays.AbstractLazyLayout}, ArrayLayouts.TriangularLayout{'L', 'U', <:LazyArrays.AbstractLazyLayout}, ArrayLayouts.TriangularLayout{'U', 'U', <:LazyArrays.AbstractLazyLayout}}})
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\linalg\mul.jl:360

Possible fix, define
  copy(::ArrayLayouts.Mul{<:Union{…}, <:Union{…}})

Stacktrace:
 [1] materialize
   @ C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\mul.jl:127 [inlined]
 [2] mul
   @ C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\mul.jl:128 [inlined]
 [3] *(A::LazyBandedMatrices.SymTridiagonal{…}, B::LowerTriangular{…})
   @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\mul.jl:252
 [4] top-level scope
   @ REPL[7]:1
Some type information was truncated. Use `show(err)` to see complete types.

Not exactly sure what the issue with the types are. Just defining a SymTridiagonal and a LowerTriangular directly works fine (if the matrices are finite - if they are infinite, the multiplication works but it just never completes).

[dlfivefifty]

This is fixed:

julia> X * L
(ℵ₀×ℵ₀ LazyBandedMatrices.SymTridiagonal{Float64, Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, BroadcastVector{Float64, typeof(sqrt), Tuple{BroadcastVector{Float64, typeof(*), Tuple{BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}} with indices OneToInf()×OneToInf()) * (ℵ₀×ℵ₀ LowerTriangular{Float64, Adjoint{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, Fill{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, BroadcastVector{Float64, typeof(-), Tuple{BroadcastVector{Float64, typeof(sqrt), Tuple{BroadcastVector{Float64, typeof(*), Tuple{BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}}}} with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf():
 -0.333333   0.471405    ⋅        …  
  0.57735   -0.326599   0.4          
 -0.298142   0.421637  -0.33197      
   ⋅        -0.320713   0.392792     
   ⋅          ⋅        -0.329914     
   ⋅          ⋅          ⋅        …  
   ⋅          ⋅          ⋅           
   ⋅          ⋅          ⋅           
   ⋅          ⋅          ⋅           
   ⋅          ⋅          ⋅           
  ⋮                               ⋱