Define Base.isstored for Diagonals and Triangular matrices (#50391)

X-ref #50377

stdlib/LinearAlgebra/src/bidiag.jl

@@ -143,6 +143,19 @@ end
     end
 end
 
+@inline function Base.isstored(A::Bidiagonal, i::Int, j::Int)
+    @boundscheck checkbounds(A, i, j)
+    if i == j
+        return @inbounds Base.isstored(A.dv, i)
+    elseif A.uplo == 'U' && (i == j - 1)
+        return @inbounds Base.isstored(A.ev, i)
+    elseif A.uplo == 'L' && (i == j + 1)
+        return @inbounds Base.isstored(A.ev, j)
+    else
+        return false
+    end
+end
+
 @inline function getindex(A::Bidiagonal{T}, i::Integer, j::Integer) where T
     @boundscheck checkbounds(A, i, j)
     if i == j

stdlib/LinearAlgebra/src/diagonal.jl

@@ -150,6 +150,16 @@ end
     r
 end
 
+@inline function Base.isstored(D::Diagonal, i::Int, j::Int)
+    @boundscheck checkbounds(D, i, j)
+    if i == j
+        @inbounds r = Base.isstored(D.diag, i)
+    else
+        r = false
+    end
+    r
+end
+
 @inline function getindex(D::Diagonal, i::Int, j::Int)
     @boundscheck checkbounds(D, i, j)
     if i == j

stdlib/LinearAlgebra/src/triangular.jl

@@ -231,6 +231,15 @@ Base.isassigned(A::UnitUpperTriangular, i::Int, j::Int) =
 Base.isassigned(A::UpperTriangular, i::Int, j::Int) =
     i <= j ? isassigned(A.data, i, j) : true
 
+Base.isstored(A::UnitLowerTriangular, i::Int, j::Int) =
+    i > j ? Base.isstored(A.data, i, j) : false
+Base.isstored(A::LowerTriangular, i::Int, j::Int) =
+    i >= j ? Base.isstored(A.data, i, j) : false
+Base.isstored(A::UnitUpperTriangular, i::Int, j::Int) =
+    i < j ? Base.isstored(A.data, i, j) : false
+Base.isstored(A::UpperTriangular, i::Int, j::Int) =
+    i <= j ? Base.isstored(A.data, i, j) : false
+
 getindex(A::UnitLowerTriangular{T}, i::Integer, j::Integer) where {T} =
     i > j ? A.data[i,j] : ifelse(i == j, oneunit(T), zero(T))
 getindex(A::LowerTriangular, i::Integer, j::Integer) =

stdlib/LinearAlgebra/src/tridiag.jl

@@ -427,6 +427,19 @@ logabsdet(A::SymTridiagonal; shift::Number=false) = logabsdet(ldlt(A; shift=shif
     end
 end
 
+@inline function Base.isstored(A::SymTridiagonal, i::Int, j::Int)
+    @boundscheck checkbounds(A, i, j)
+    if i == j
+        return @inbounds Base.isstored(A.dv, i)
+    elseif i == j + 1
+        return @inbounds Base.isstored(A.ev, j)
+    elseif i + 1 == j
+        return @inbounds Base.isstored(A.ev, i)
+    else
+        return false
+    end
+end
+
 @inline function getindex(A::SymTridiagonal{T}, i::Integer, j::Integer) where T
     @boundscheck checkbounds(A, i, j)
     if i == j
@@ -632,6 +645,19 @@ end
     end
 end
 
+@inline function Base.isstored(A::Tridiagonal, i::Int, j::Int)
+    @boundscheck checkbounds(A, i, j)
+    if i == j
+        return @inbounds Base.isstored(A.d, i)
+    elseif i == j + 1
+        return @inbounds Base.isstored(A.dl, j)
+    elseif i + 1 == j
+        return @inbounds Base.isstored(A.du, i)
+    else
+        return false
+    end
+end
+
 @inline function getindex(A::Tridiagonal{T}, i::Integer, j::Integer) where T
     @boundscheck checkbounds(A, i, j)
     if i == j

stdlib/LinearAlgebra/test/bidiag.jl

@@ -120,6 +120,21 @@ Random.seed!(1)
         @test_throws ArgumentError Bl[4, 5] = 1
     end
 
+    @testset "isstored" begin
+        ubd = Bidiagonal(dv, ev, :U)
+        lbd = Bidiagonal(dv, ev, :L)
+        # bidiagonal isstored / upper & lower
+        @test_throws BoundsError Base.isstored(ubd, n + 1, 1)
+        @test_throws BoundsError Base.isstored(ubd, 1, n + 1)
+        @test Base.isstored(ubd, 2, 2)
+        # bidiagonal isstored / upper
+        @test Base.isstored(ubd, 2, 3)
+        @test !Base.isstored(ubd, 3, 2)
+        # bidiagonal isstored / lower
+        @test Base.isstored(lbd, 3, 2)
+        @test !Base.isstored(lbd, 2, 3)
+    end
+
     @testset "show" begin
         BD = Bidiagonal(dv, ev, :U)
         dstring = sprint(Base.print_matrix,BD.dv')

stdlib/LinearAlgebra/test/diagonal.jl

@@ -78,6 +78,9 @@ Random.seed!(1)
         @test !istril(D, -1)
         @test istril(D, 1)
         @test istril(Diagonal(zero(diag(D))), -1)
+        @test Base.isstored(D,1,1)
+        @test !Base.isstored(D,1,2)
+        @test_throws BoundsError Base.isstored(D, n + 1, 1)
         if elty <: Real
             @test ishermitian(D)
         end