Fix \ for QL (#34)

* Fix \ for QL

* L truncations are banded

* v0.3.5

* Update .travis.yml

Author: dlfivefifty

.travis.yml

@@ -13,8 +13,7 @@ matrix:
     - julia: nightly
 notifications:
   email: false
-after_success:
-- julia -e 'using Pkg; Pkg.add("Coverage"); using Coverage; Codecov.submit(process_folder())'
+codecov: true
 
 # uncomment the following lines to override the default test script
 #script:

Project.toml

@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.3.4"
+version = "0.3.5"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -16,13 +16,13 @@ MatrixFactorizations = "a3b82374-2e81-5b9e-98ce-41277c0e4c87"
 SemiseparableMatrices = "f8ebbe35-cbfb-4060-bf7f-b10e4670cf57"
 
 [compat]
-ArrayLayouts = "0.3.4"
-BandedMatrices = "0.15.11"
-BlockArrays = "0.12.7"
-BlockBandedMatrices = "0.8.5"
-FillArrays = "0.8.10"
-InfiniteArrays = "0.7.2"
-LazyArrays = "0.16.12"
+ArrayLayouts = "0.3.5"
+BandedMatrices = "0.15.13"
+BlockArrays = "0.12.8"
+BlockBandedMatrices = "0.8.7"
+FillArrays = "0.8.11"
+InfiniteArrays = "0.7.3"
+LazyArrays = "0.16.13"
 LazyBandedMatrices = "0.2.11"
 MatrixFactorizations = "0.4.1"
 SemiseparableMatrices = "0.1"

src/banded/infbanded.jl

@@ -309,6 +309,7 @@ end
 
 const BandedToeplitzLayout = BandedColumns{ConstRows}
 const PertToeplitzLayout = BandedColumns{PertConstRows}
+const PertTriangularToeplitzLayout{UPLO,UNIT} = TriangularLayout{UPLO,UNIT,BandedColumns{PertConstRows}}
 
 
 _BandedMatrix(::BandedToeplitzLayout, A::AbstractMatrix) = 

src/banded/infqltoeplitz.jl

@@ -104,11 +104,14 @@ end
 getindex(Q::ProductQ{<:Any,<:Tuple{Vararg{LowerHessenbergQ}}}, i::Integer, j::Integer) = (Q')[j,i]'
 
 
-function (*)(A::ProductQ{T}, x::AbstractVector{S}) where {T,S}
+function _productq_mul(A::ProductQ{T}, x::AbstractVector{S}) where {T,S}
     TS = promote_op(matprod, T, S)
     lmul!(A, Base.copymutable(convert(AbstractVector{TS},x)))
 end
 
+(*)(A::ProductQ, x::AbstractVector) = _productq_mul(A, x)
+(*)(A::ProductQ, x::LazyVector) = _productq_mul(A, x)
+
 
 # LQ where Q is a product of orthogonal operations
 struct QLProduct{T,QQ<:Tuple,LL} <: Factorization{T}

test/test_infql.jl

@@ -164,5 +164,19 @@ import BandedMatrices: _BandedMatrix
     @testset "solve with QL" begin
         A = BandedMatrix(-1 => Fill(2,∞), 0 => Fill(5,∞), 1 => Fill(0.5,∞))
         @test (qr(A)\Vcat(1.0,Zeros(∞)))[1:1000] ≈ (ql(A)\Vcat(1.0,Zeros(∞)))[1:1000]
+
+        J = BandedMatrix(0 => Vcat([1.0], Fill(0.0,∞)), 1 => Vcat(Float64[],Fill(0.5,∞)), -1 => Vcat(Float64[],Fill(0.5,∞)))
+        z = 3.5
+        A = J - z*I
+        F = ql(A)
+        Q,L = F
+        b = [1; zeros(∞)]
+        @test (Q'b)[1] ≈ 0.9892996329463546
+        @test L[1] == L[1,1]
+        
+        @test L[1:5,1:5] isa BandedMatrix
+        @test (L*(L \ b))[1:10] ≈ [1; zeros(9)]
+        u = F \ b
+        @test (A*u)[1:10] ≈ [1; zeros(9)]
     end
 end