Conversion methods sparse matrix -> special linalg type (JuliaLang#40988)

Author: carstenbauer

stdlib/SparseArrays/src/SparseArrays.jl

@@ -12,7 +12,7 @@ using LinearAlgebra
 
 import Base: +, -, *, \, /, &, |, xor, ==, zero
 import LinearAlgebra: mul!, ldiv!, rdiv!, cholesky, adjoint!, diag, eigen, dot,
-    issymmetric, istril, istriu, lu, tr, transpose!, tril!, triu!,
+    issymmetric, istril, istriu, lu, tr, transpose!, tril!, triu!, isbanded,
     cond, diagm, factorize, ishermitian, norm, opnorm, lmul!, rmul!, tril, triu, matprod
 
 import Base: acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,

stdlib/SparseArrays/src/sparsematrix.jl

@@ -683,6 +683,17 @@ Array(S::AbstractSparseMatrixCSC) = Matrix(S)
 
 convert(T::Type{<:AbstractSparseMatrixCSC}, m::AbstractMatrix) = m isa T ? m : T(m)
 
+convert(T::Type{<:Diagonal},       m::AbstractSparseMatrixCSC) = m isa T ? m :
+    isdiag(m) ? T(m) : throw(ArgumentError("matrix cannot be represented as Diagonal"))
+convert(T::Type{<:SymTridiagonal}, m::AbstractSparseMatrixCSC) = m isa T ? m :
+    issymmetric(m) && isbanded(m, -1, 1) ? T(m) : throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
+convert(T::Type{<:Tridiagonal},    m::AbstractSparseMatrixCSC) = m isa T ? m :
+    isbanded(m, -1, 1) ? T(m) : throw(ArgumentError("matrix cannot be represented as Tridiagonal"))
+convert(T::Type{<:LowerTriangular}, m::AbstractSparseMatrixCSC) = m isa T ? m :
+    istril(m) ? T(m) : throw(ArgumentError("matrix cannot be represented as LowerTriangular"))
+convert(T::Type{<:UpperTriangular}, m::AbstractSparseMatrixCSC) = m isa T ? m :
+    istriu(m) ? T(m) : throw(ArgumentError("matrix cannot be represented as UpperTriangular"))
+
 float(S::SparseMatrixCSC) = SparseMatrixCSC(size(S, 1), size(S, 2), copy(getcolptr(S)), copy(rowvals(S)), float.(nonzeros(S)))
 complex(S::SparseMatrixCSC) = SparseMatrixCSC(size(S, 1), size(S, 2), copy(getcolptr(S)), copy(rowvals(S)), complex(copy(nonzeros(S))))
 

stdlib/SparseArrays/test/sparse.jl

@@ -78,6 +78,24 @@ end
     @test Array(SparseMatrixCSC{eltype(a), Int8}(a)) == Array(a)
 end
 
+@testset "conversion to special LinearAlgebra types" begin
+    # issue 40924
+    @test convert(Diagonal, sparse(Diagonal(1:2))) isa Diagonal
+    @test convert(Diagonal, sparse(Diagonal(1:2))) == Diagonal(1:2)
+    @test convert(Tridiagonal, sparse(Tridiagonal(1:3, 4:7, 8:10))) isa Tridiagonal
+    @test convert(Tridiagonal, sparse(Tridiagonal(1:3, 4:7, 8:10))) == Tridiagonal(1:3, 4:7, 8:10)
+    @test convert(SymTridiagonal, sparse(SymTridiagonal(1:4, 5:7))) isa SymTridiagonal
+    @test convert(SymTridiagonal, sparse(SymTridiagonal(1:4, 5:7))) == SymTridiagonal(1:4, 5:7)
+
+    lt = LowerTriangular([1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0])
+    @test convert(LowerTriangular, sparse(lt)) isa LowerTriangular
+    @test convert(LowerTriangular, sparse(lt)) == lt
+
+    ut = UpperTriangular([1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0])
+    @test convert(UpperTriangular, sparse(ut)) isa UpperTriangular
+    @test convert(UpperTriangular, sparse(ut)) == ut
+end
+
 @testset "sparse matrix construction" begin
     @test (A = fill(1.0+im,5,5); isequal(Array(sparse(A)), A))
     @test_throws ArgumentError sparse([1,2,3], [1,2], [1,2,3], 3, 3)