SymTridiagonal support for cholesky (#140)

* make cholesky work better with SymTridiagonal

* begin fixing tests

* work on bug in julia 1.6

Author: TSGut

src/infcholesky.jl

@@ -7,7 +7,9 @@ end
 size(U::AdaptiveCholeskyFactors) = size(U.data.array)
 bandwidths(A::AdaptiveCholeskyFactors) = (0,bandwidth(A.data,2))
 
-function AdaptiveCholeskyFactors(::SymmetricLayout{<:AbstractBandedLayout}, S::AbstractMatrix{T}) where T
+const SymmetricBandedLayouts = Union{SymTridiagonalLayout,SymmetricLayout{<:AbstractBandedLayout},DiagonalLayout}
+
+function AdaptiveCholeskyFactors(::SymmetricBandedLayouts, S::AbstractMatrix{T}) where T
     A = parent(S)
     l,u = bandwidths(A)
     data = BandedMatrix{T}(undef,(0,0),(l,u)) # pad super
@@ -45,6 +47,7 @@ end
 adaptivecholesky(A) = Cholesky(AdaptiveCholeskyFactors(A), :U, 0)
 
 
+ArrayLayouts._cholesky(::SymTridiagonalLayout, ::NTuple{2,OneToInf{Int}}, A, ::CNoPivot) = adaptivecholesky(A)
 ArrayLayouts._cholesky(::SymmetricLayout{<:AbstractBandedLayout}, ::NTuple{2,OneToInf{Int}}, A, ::CNoPivot) = adaptivecholesky(A)
 
 function colsupport(F::AdaptiveCholeskyFactors, j)

test/test_infcholesky.jl

@@ -1,4 +1,5 @@
-using InfiniteLinearAlgebra, LinearAlgebra, BandedMatrices, ArrayLayouts, Test
+using InfiniteLinearAlgebra, LinearAlgebra, BandedMatrices, ArrayLayouts, LazyBandedMatrices, Test
+import InfiniteLinearAlgebra: SymmetricBandedLayouts
 
 @testset "infinite-cholesky" begin
     S = Symmetric(BandedMatrix(0 => 1:∞, 1=> Ones(∞)))
@@ -10,10 +11,16 @@ using InfiniteLinearAlgebra, LinearAlgebra, BandedMatrices, ArrayLayouts, Test
     @test cholesky(S) \ b ≈ qr(S) \ b ≈ S \ b
 
     @testset "singularly perturbed" begin
+        # using Symmetric(BandedMatrix(...))
         ε = 0.0001
         S = Symmetric(BandedMatrix(0 => 2 .+ ε*(1:∞), 1=> -Ones(∞)))
         b = [1; zeros(∞)]
         @test cholesky(S) \ b ≈  S \ b
+        # using SymTridiagonal(...)
+        ε = 0.0001
+        S = LazyBandedMatrices.SymTridiagonal(2 .+ ε*(1:∞), -Ones(∞))
+        @test MemoryLayout(S) isa SymmetricBandedLayouts
+        @test cholesky(S) \ b ≈  S \ b
     end
 
     @testset "long bandwidths" begin