Add BandedPlusSemiseparable and QR

.github/workflows/ci.yml

@@ -10,7 +10,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.10'
+          - 'lts'
+          - '1'
         os:
           - ubuntu-latest
           - macOS-latest

Project.toml

@@ -1,7 +1,7 @@
 name = "SemiseparableMatrices"
 uuid = "f8ebbe35-cbfb-4060-bf7f-b10e4670cf57"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.4.0"
+version = "0.5.0"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/SemiseparableMatrices.jl

@@ -2,7 +2,7 @@ module SemiseparableMatrices
 using LinearAlgebra: BlasFloat
 using ArrayLayouts, BandedMatrices, LazyArrays, LinearAlgebra, MatrixFactorizations, Base
 
-import Base: size, getindex, setindex!, convert, copyto!
+import Base: size, getindex, setindex!, convert, copyto!, copy, axes
 import MatrixFactorizations: QR, QRPackedQ, getQ, getR, QRPackedQLayout, AdjQRPackedQLayout
 import LinearAlgebra: qr, qr!, lmul!, ldiv!, rmul!, triu!, factorize, rank
 import BandedMatrices: _banded_qr!, bandeddata, resize
@@ -11,7 +11,7 @@ import ArrayLayouts: MemoryLayout, sublayout, sub_materialize, MatLdivVec, mater
                         triangulardata, zero!, _copyto!, colsupport, rowsupport,
                         _qr, _qr!, _factorize
 
-export SemiseparableMatrix, AlmostBandedMatrix, LowRankMatrix, ApplyMatrix, ApplyArray, almostbandwidths, almostbandedrank
+export SemiseparableMatrix, AlmostBandedMatrix, LowRankMatrix, ApplyMatrix, ApplyArray, almostbandwidths, almostbandedrank, BandedPlusSemiseparableMatrix
 
 LazyArraysBandedMatricesExt = Base.get_extension(LazyArrays, :LazyArraysBandedMatricesExt)
 BandedLayouts = LazyArraysBandedMatricesExt.BandedLayouts
@@ -30,5 +30,6 @@ separablerank(A) = size(arguments(ApplyLayout{typeof(*)}(),A)[1],2)
 include("SemiseparableMatrix.jl")
 include("AlmostBandedMatrix.jl")
 include("invbanded.jl")
+include("BandedPlusSemiseparableMatrices.jl")
 
 end # module

test/runtests.jl

@@ -2,4 +2,6 @@ using SemiseparableMatrices, BandedMatrices, LinearAlgebra, Test
 
 include("test_semiseparable.jl")
 include("test_almostbanded.jl")
-include("test_invbanded.jl")
+include("test_invbanded.jl")
+include("test_bandedplussemiseparable.jl")
+include("test_qr.jl")

test/test_bandedplussemiseparable.jl

@@ -0,0 +1,10 @@
+using SemiseparableMatrices, Test
+
+@testset "BandedPlusSemiseparable" begin
+    n = 20
+    l, m, r, p = 4, 5, 2, 3
+    B = brandn(n,n,l,m)
+    U,V = randn(n,r), randn(n,r)
+    W,S = randn(n,p), randn(n,p)
+    @test BandedPlusSemiseparableMatrix(B, (U,V), (W,S)) ≈ B + tril(U*V',-1) + triu(W*S',1)
+end

test/test_getindex.jl

@@ -0,0 +1,39 @@
+using BandedMatrices
+using Test, LinearAlgebra
+using Random
+import .BandedPlusSemiseparableMatrices: BandedPlusSemiseparableMatrix, BandedPlusSemiseparableQRPerturbedFactors
+
+# test get index for BandedPlusSemiseparableQRPerturbedFactors
+
+n = 10
+l = 2
+m = 3
+r = 4
+p = 5
+B = brandn(n,n,l,m)
+U = randn(n,r)
+V = randn(n,r)
+W = randn(n,p)
+S = randn(n,p)
+Q = randn(r,p)
+K = randn(r,r)
+Eₛ = randn(r,min(l+m,n))
+Xₛ = randn(min(l,n),p)
+Yₛ = randn(min(l,n),r)
+Zₛ = randn(min(l,n),min(l+m,n))
+A = BandedPlusSemiseparableQRPerturbedFactors(U,V,W,S,B)
+A.Q[:,:] = Q
+A.K[:,:] = K
+A.Eₛ[:,:] = Eₛ
+A.Xₛ[:,:] = Xₛ
+A.Yₛ[:,:] = Yₛ
+A.Zₛ[:,:] = Zₛ
+
+E = [Eₛ zeros(r,max(n-(l+m),0))]
+X = [Xₛ; zeros(max(n - l, 0),p)]
+Y = [Yₛ; zeros(max(n - l, 0),r)]
+Z = [Zₛ zeros(min(l,n),max(n-(l+m),0)); zeros(max(n-l,0),min(l+m,n)) zeros(max(n-l,0), max(n-(l+m),0))]
+
+A₀ = tril(U*V',-1) + Matrix(B) + triu(W*S',1)
+AA = A₀ + U*Q*S' + U*K*U'*A₀ + U*E + X*S' + Y*U'*A₀ + Z
+@test Matrix(A) ≈ AA

test/test_qr.jl

@@ -0,0 +1,31 @@
+using BandedMatrices, LinearAlgebra, Random, SemiseparableMatrices, Test
+using SemiseparableMatrices: BandedPlusSemiseparableQRPerturbedFactors
+#Random.seed!(1234)
+
+@testset "QR" begin
+    n = 20
+    l, m, r, p = 4, 5, 2, 3
+    B = brandn(n,n,l,m)
+
+    @testset "BandedPlusSemiseparableQRPerturbedFactors" begin
+        U,V = randn(n,r), randn(n,r)
+        W,S = randn(n,p), randn(n,p)
+        A = BandedPlusSemiseparableQRPerturbedFactors(B, (U,V), (W,S))
+        fact_true = LinearAlgebra.qrfactUnblocked!(Matrix(A))
+        fact = qr!(A)
+        @test A ≈ fact_true.factors ≈ fact.factors
+        @test fact_true.τ ≈ fact.τ
+    end
+
+    @testset "BandedPlusSemiseparableMatrix" begin
+        U,V = randn(n,r), randn(n,r)
+        W,S = randn(n,p), randn(n,p)
+        A = BandedPlusSemiseparableMatrix(B,(U,V),(W,S))
+        A_true = Matrix(A)
+        fact_true = LinearAlgebra.qrfactUnblocked!(Matrix(A))
+        fact = qr(A)
+        @test A ≈ A_true
+        @test fact_true.factors ≈ fact.factors
+        @test fact_true.τ ≈ fact.τ
+    end
+end