Layout issue for conversion with b=-1
#123
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Actually this for some reason I'm also not sure about for a temporary workaround when julia> P = SemiclassicalJacobi(2.0, -1 / 2, 1.0, -1 / 2)
SemiclassicalJacobi with weight x^-0.5 * (1-x)^1.0 * (2.0-x)^-0.5 on 0..1
julia> Q = SemiclassicalJacobi(2.0, 1 / 2, 1.0, 1 / 2)
SemiclassicalJacobi with weight x^0.5 * (1-x)^1.0 * (2.0-x)^0.5 on 0..1
julia> R = Q \ P
(ℵ₀×ℵ₀ UpperTriangular{Float64, BroadcastMatrix{Float64, typeof(/), Tuple{InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, SubArray{Float64, 1, ClassicalOrthogonalPolynomials.CholeskyJacobiData{Float64}, Tuple{Base.Slice{InfiniteArrays.OneToInf{Int64}}, Int64}, false}, SubArray{Float64, 1, ClassicalOrthogonalPolynomials.CholeskyJacobiData{Float64}, Tuple{Base.Slice{InfiniteArrays.OneToInf{Int64}}, Int64}, false}}}, Float64}}} with indices OneToInf()×OneToInf()) * (ℵ₀×ℵ₀ UpperTriangular{Float64, BroadcastMatrix{Float64, typeof(/), Tuple{InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, BroadcastVector{Float64, typeof(-), Tuple{Float64, ClassicalOrthogonalPolynomials.LanczosJacobiBand{Float64}}}, BroadcastVector{Float64, typeof(-), Tuple{ClassicalOrthogonalPolynomials.LanczosJacobiBand{Float64}}}}}, Float64}}} with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf():
1.0 0.879719 -0.16154 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ …
⋅ 1.03167 0.867507 -0.172406 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ 1.0391 0.866366 -0.175603 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ 1.04182 0.866144 -0.176996 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ 1.0431 0.866077 -0.177733 ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ 1.0438 0.866052 -0.178171 ⋅ ⋅ ⋅ ⋅ …
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04422 0.86604 -0.178453 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04449 0.866034 -0.178645 ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04468 0.866031 -0.178782 ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04481 0.866029 -0.178883
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04491 0.866028 …
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04499
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋮ ⋮ ⋮ ⋱
julia> R.
args
f |
|
Try R[band(0)]
R[band(1)]
R[band(2)] |
|
Oh of course, that'll work for that second case thanks. |
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SemiclassicalOrthogonalPolynomials.jl/src/SemiclassicalOrthogonalPolynomials.jl
Lines 453 to 463 in ed25acf
I'm trying to find a better way to do the above conversion since it's giving me some layout headaches. Basically, how can I better compute this conversion matrix of the form$\textrm{diag}(1, \boldsymbol R)$ with better layouts (e.g. $\boldsymbol R$ could be a dense upper triangular matrix.
colsupportshould give the expected results and it should be a banded matrix ifRis) than this awkwardVcat/Hcatmess? I could maybe rewrap it as a banded matrix but it might not necessarily be banded e.g.To see the issues that I'm running into, consider
julia> R vcat(hcat(Float64, 1×ℵ₀ Zeros{Float64, 2, Tuple{Base.OneTo{Int64}, InfiniteArrays.OneToInf{Int64}}} with indices Base.OneTo(1)×OneToInf()) with indices Base.OneTo(1)×OneToInf(), hcat(ℵ₀-element Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}} with indices OneToInf(), (ℵ₀×ℵ₀ UpperTriangular{Float64, BroadcastMatrix{Float64, typeof(/), Tuple{InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, SubArray{Float64, 1, ClassicalOrthogonalPolynomials.CholeskyJacobiData{Float64}, Tuple{Base.Slice{InfiniteArrays.OneToInf{Int64}}, Int64}, false}, SubArray{Float64, 1, ClassicalOrthogonalPolynomials.CholeskyJacobiData{Float64}, Tuple{Base.Slice{InfiniteArrays.OneToInf{Int64}}, Int64}, false}}}, Float64}}} with indices OneToInf()×OneToInf()) * (ℵ₀×ℵ₀ UpperTriangular{Float64, BroadcastMatrix{Float64, typeof(/), Tuple{InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, LazyBandedMatrices.SymTridiagonal{Float64, BroadcastVector{Float64, typeof(-), Tuple{Float64, SubArray{Float64, 1, ClassicalOrthogonalPolynomials.LanczosJacobiBand{Float64}, Tuple{InfiniteArrays.InfUnitRange{Int64}}, false}}}, BroadcastVector{Float64, typeof(-), Tuple{SubArray{Float64, 1, ClassicalOrthogonalPolynomials.LanczosJacobiBand{Float64}, Tuple{InfiniteArrays.InfUnitRange{Int64}}, false}}}}}, Float64}}} with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf(): 1.0 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ … ⋅ 1.0 0.879719 -0.16154 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.03167 0.867507 -0.172406 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.0391 0.866366 -0.175603 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04182 0.866144 -0.176996 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.0431 0.866077 -0.177733 ⋅ ⋅ ⋅ ⋅ … ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.0438 0.866052 -0.178171 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04422 0.86604 -0.178453 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04449 0.866034 -0.178645 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04468 0.866031 -0.178782 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04481 0.866029 … ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.04491 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋮ ⋮ ⋮ ⋱Then
This seems to lead to issues when multiplying
Rby other banded matrices. For example,and e.g.
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