Use LinearAlgebra traited matrix operations

.gitignore

@@ -0,0 +1,9 @@
+# ignore org
+*.org
+.vscode
+
+# ignore newly added matrices 
+Manifest.toml
+
+*.mem
+*.cov

src/SparseArrays.jl

@@ -64,6 +64,11 @@ TransposeFact = isdefined(LinearAlgebra, :TransposeFactorization) ?
     LinearAlgebra.TransposeFactorization :
     Transpose
 
+struct SparseStorage{T} <: LinearAlgebra.AbstractStorageTrait{T}
+    data::T
+    SparseStorage(x::T) where T = new{T}(x)
+end
+
 include("readonly.jl")
 include("abstractsparse.jl")
 include("sparsematrix.jl")
@@ -73,6 +78,7 @@ include("higherorderfns.jl")
 include("linalg.jl")
 include("deprecated.jl")
 
+LinearAlgebra.storage_trait(::Type{<:AbstractSparseArray}) = SparseStorage
 
 
 # Convert from 0-based to 1-based indices

src/sparseconvert.jl

@@ -1,6 +1,64 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
-import LinearAlgebra: AbstractTriangular
+import LinearAlgebra: AbstractTriangular, DenseStorage
+
+# direct to appropriate sparse versions
+function (*)(ta::SparseStorage, tb::DenseStorage)
+    A = unwrap1a(ta.data)
+    B = tb.data
+    TS = promote_op(matprod, eltype(A), eltype(B))
+    mul!(similar(B, TS, (size(A, 1), size(B, 2))), A, B, true, false)
+end
+function (*)(ta::DenseStorage, tb::SparseStorage)
+    A = ta.data
+    B = unwrap1a(tb.data)
+    TS = promote_op(matprod, eltype(A), eltype(B))
+    mul!(similar(A, TS, (size(A, 1), size(B, 2))), A, B, true, false)
+end
+function (*)(ta::SparseStorage, tb::SparseStorage)
+    A = unwrap1(ta.data)
+    B = unwrap1(tb.data)
+    if A === ta.data && B === tb.data
+        DenseStorage(A) * DenseStorage(B)
+    else
+        A * B
+    end
+end
+
+function (\)(ta::SparseStorage, B::AbstractVecOrMat)
+    A = unwrap1a(ta.data)
+    if A === ta.data
+        DenseStorage(A) \ B
+    else
+        A \ B
+    end
+end
+
+unwrap1(A::AbstractArray) = _sparsewrap(A)
+unwrap1a(A::Union{Transpose,Adjoint}) = _sparsewrap(A)
+unwrap1a(A::AbstractArray) = unwrap(A)
+unwrap2a(A::AbstractTriangular{<:Any,<:Union{Transpose,Adjoint}}) = _sparsewrap(A, 2)
+unwrap2a(A::AbstractArray) = _sparsewrap(A)
+
+# as long as these are not defined in "linalg.jl" fall back to generic algo
+import LinearAlgebra: _lmul!, _ldiv!, _rmul!, _rdiv!
+
+function lmul!(ta::SparseStorage, B::AbstractVecOrMat)
+    A = unwrap2a(ta.data)
+    _lmul!(A, B)
+end
+function ldiv!(ta::SparseStorage, B::AbstractVecOrMat)
+A = unwrap1(ta.data)
+_ldiv!(A, B)
+end
+function rmul!(A::AbstractMatrix, tb::SparseStorage)
+    B = unwrap2a(tb.data)
+    _rmul!(A, B)
+end
+function rdiv!(A::AbstractMatrix, tb::SparseStorage)
+B = unwrap2a(tb.data)
+_rdiv!(A, B)
+end
 
 """
     SparseMatrixCSCSymmHerm
@@ -53,19 +111,26 @@ for wr in (Symmetric, Hermitian,
 end
 
 # convert parent and re-wrap in same wrapper
-_sparsewrap(A::Symmetric) = Symmetric(_sparsem(parent(A)), A.uplo == 'U' ? :U : :L)
-_sparsewrap(A::Hermitian) = Hermitian(_sparsem(parent(A)), A.uplo == 'U' ? :U : :L)
-_sparsewrap(A::SubArray) = SubArray(_sparsem(parent(A)), A.indices)
+_sparsewrap(A) = _sparsewrap(A, 1)
+_sparsewrap(A, i::Int) = i <= 0 ? _sparsem(A) : _sparsewr(A, i)
+_sparsewr(A::AbstractArray, _::Int) = _sparsem(A)
+for ty in ( Symmetric, Hermitian)
+    @eval function _sparsewr(A::$ty, i::Int)
+        $ty(_sparsewrap(parent(A), i - 1), sym_uplo(A.uplo))
+    end
+end
+_sparsewr(A::SubArray, i::Int) = SubArray(_sparsewrap(parent(A), i - 1), A.indices)
 for ty in ( LowerTriangular, UnitLowerTriangular,
             UpperTriangular, UnitUpperTriangular,
             Transpose, Adjoint)
 
-    @eval _sparsewrap(A::$ty) = $ty(_sparsem(parent(A)))
+    @eval _sparsewr(A::$ty, i::Int) = $ty(_sparsewrap(parent(A), i - 1))
 end
-function _sparsewrap(A::Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal})
+function _sparsewr(A::Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}, _::Int)
     dropzeros!(sparse(A))
 end
 
+
 """
     unwrap(A::AbstractMatrix)
 
@@ -283,4 +348,3 @@ function _sparse_gen(m, n, newcolptr, newrowval, newnzval)
     newcolptr[1] = 1
     SparseMatrixCSC(m, n, newcolptr, newrowval, newnzval)
 end
-