Merge pull request #42 from JuliaDiffEq/issingular

add issingular

Author: ChrisRackauckas

Project.toml

@@ -1,6 +1,6 @@
 name = "ArrayInterface"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "2.5.1"
+version = "2.6.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -15,9 +15,10 @@ julia = "1.2"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
 LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "LabelledArrays", "StaticArrays", "BandedMatrices", "BlockBandedMatrices", "SuiteSparse"]
+test = ["Test", "LabelledArrays", "StaticArrays", "BandedMatrices", "BlockBandedMatrices", "SuiteSparse", "Random"]

README.md

@@ -65,6 +65,10 @@ A `setindex!` which is always allowed.
 Return an instance of the LU factorization object with the correct type
 cheaply.
 
+## issingular(A)
+
+Return an instance of the LU factorization object with the correct type cheaply.
+
 ## List of things to add
 
 - https://github.com/JuliaLang/julia/issues/22216

src/ArrayInterface.jl

@@ -95,7 +95,7 @@ isstructured(::Diagonal) = true
 """
     has_sparsestruct(x::AbstractArray)
 
-determine whether `findstructralnz` accepts the parameter `x`
+Determine whether `findstructralnz` accepts the parameter `x`
 """
 has_sparsestruct(x) = false
 has_sparsestruct(x::AbstractArray) = has_sparsestruct(typeof(x))
@@ -106,6 +106,24 @@ has_sparsestruct(x::Type{<:Bidiagonal}) = true
 has_sparsestruct(x::Type{<:Tridiagonal}) = true
 has_sparsestruct(x::Type{<:SymTridiagonal}) = true
 
+"""
+    issingular(A::AbstractMatrix)
+
+Determine whether a given abstract matrix is singular.
+"""
+issingular(A::AbstractMatrix) = issingular(Matrix(A))
+issingular(A::AbstractSparseMatrix) = !issuccess(lu(A, check=false))
+issingular(A::Matrix) = !issuccess(lu(A, check=false))
+issingular(A::UniformScaling) = A.λ == 0
+issingular(A::Diagonal) = any(iszero,A.diag)
+issingular(B::Bidiagonal) = any(iszero, A.dv)
+issingular(S::SymTridiagonal) = diaganyzero(iszero, ldlt(S).data)
+issingular(T::Tridiagonal) = !issuccess(lu(A, check=false))
+issingular(A::Union{Hermitian,Symmetric}) = diaganyzero(bunchkaufman(A, check=false).LD)
+issingular(A::Union{LowerTriangular,UpperTriangular}) = diaganyzero(A.data)
+issingular(A::Union{UnitLowerTriangular,UnitUpperTriangular}) = false
+diaganyzero(A) = any(iszero, view(A, diagind(A)))
+
 """
     findstructralnz(x::AbstractArray)
 

test/runtests.jl

@@ -141,3 +141,21 @@ using SuiteSparse
   end
   @test lu_instance(1) === 1
 end
+
+using Random
+using ArrayInterface: issingular
+@testset "issingular" begin
+    for T in [Float64, ComplexF64]
+        R = randn(MersenneTwister(2), T, 5, 5)
+        S = Symmetric(R)
+        L = UpperTriangular(R)
+        U = LowerTriangular(R)
+        @test all(!issingular, [R, S, L, U])
+        R[:, 2] .= 0
+        @test all(issingular, [R, L, U])
+        @test !issingular(S)
+        R[2, :] .= 0
+        @test issingular(S)
+        @test all(!issingular, [UnitLowerTriangular(R), UnitUpperTriangular(R)])
+    end
+end