ul inv fixes (#44)

* ul inv fixes

* qr approx lu

* Update Project.toml

* Use latest banded matrices

Author: dlfivefifty

Project.toml

@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.4.0"
+version = "0.4.1"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -16,19 +16,18 @@ MatrixFactorizations = "a3b82374-2e81-5b9e-98ce-41277c0e4c87"
 SemiseparableMatrices = "f8ebbe35-cbfb-4060-bf7f-b10e4670cf57"
 
 [compat]
-ArrayLayouts = "0.4.3"
-BandedMatrices = "0.15.17"
+ArrayLayouts = "0.4.4"
+BandedMatrices = "0.15.19"
 BlockArrays = "0.12.12"
 BlockBandedMatrices = "0.9"
-FillArrays = "0.9.4"
+FillArrays = "0.9.5"
 InfiniteArrays = "0.8"
-LazyArrays = "0.17.3"
-LazyBandedMatrices = "0.3.1"
-MatrixFactorizations = "0.5.2"
-SemiseparableMatrices = "0.1.2"
+LazyArrays = "0.17.5"
+LazyBandedMatrices = "0.3.2"
+MatrixFactorizations = "0.6"
+SemiseparableMatrices = "0.1.3"
 julia = "1.5"
 
-
 [extras]
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

src/infqr.jl

@@ -312,4 +312,5 @@ ldiv!(F::QR{<:Any,<:AdaptiveQRFactors}, b::LayoutVector) = ldiv!(F.R, lmul!(F.Q'
 \(F::QR{<:Any,<:AdaptiveQRFactors}, B::LayoutVector) = ldiv!(F.R, F.Q'B)
 
 
-factorize(A::BandedMatrix{<:Any,<:Any,<:OneToInf}) = qr(A)
+factorize(A::BandedMatrix{<:Any,<:Any,<:OneToInf}) = qr(A)
+qr(A::SymTridiagonal{T,<:AbstractFill{T,1,Tuple{OneToInf{Int}}}}) where T = adaptiveqr(A)

test/runtests.jl

@@ -110,6 +110,8 @@ end
             @test A*B isa MulMatrix
             @test B'A isa MulMatrix
 
+            @test all(diag(A[1:6,1:6]) .=== zeros(6))
+
             @test (A*B)[1:7,1:5] ≈ A[1:7,1:6] * B[1:6,1:5]
             @test (B'A)[1:5,1:7] ≈ (B')[1:5,1:6] * A[1:6,1:7]
         end

test/test_infqr.jl

@@ -259,4 +259,12 @@ import SemiseparableMatrices: AlmostBandedLayout, VcatAlmostBandedLayout
         θ,φ = acos(x),acos(y)
         @test (sin.((1:100) .* φ)/sin(φ))' * InvDiagTrav(u[Block.(1:100)]) * sin.((1:100) .* θ)/sin(θ) ≈ 1/(2x+y-8)
     end
+
+    @testset "SymTridiagonal Toeplitz" begin
+        Δ = SymTridiagonal(Fill(-2,∞), Fill(1,∞))
+        h = 0.01
+        A = I - h*Δ
+        b = [1; 2; 3; zeros(∞)]
+        @test (qr(A) \ b) ≈ (ul(A) \ b)
+    end
 end