Introduce cholesky and qr hooks for wrapped sparse matrices (#51220)

This is a follow-up to #51161. It introduces one level in the promotion
pipeline which allows to call out-of-place versions of `cholesky` and
`qr` for arguments whose `similar` copy yields a `SparseMatrixCSC`.

Author: dkarrasch

stdlib/LinearAlgebra/src/cholesky.jl

@@ -399,14 +399,16 @@ true
 ```
 """
 cholesky(A::AbstractMatrix, ::NoPivot=NoPivot(); check::Bool = true) =
-    cholesky!(cholcopy(A); check)
+    _cholesky(cholcopy(A); check)
 @deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false
 
 function cholesky(A::AbstractMatrix{Float16}, ::NoPivot=NoPivot(); check::Bool = true)
-    X = cholesky!(cholcopy(A); check = check)
+    X = _cholesky(cholcopy(A); check = check)
     return Cholesky{Float16}(X)
 end
 @deprecate cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false
+# allow packages like SparseArrays.jl to hook into here and redirect to out-of-place `cholesky`
+_cholesky(A::AbstractMatrix, args...; kwargs...) = cholesky!(A, args...; kwargs...)
 
 ## With pivoting
 """
@@ -465,11 +467,11 @@ true
 ```
 """
 cholesky(A::AbstractMatrix, ::RowMaximum; tol = 0.0, check::Bool = true) =
-    cholesky!(cholcopy(A), RowMaximum(); tol, check)
+    _cholesky(cholcopy(A), RowMaximum(); tol, check)
 @deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{true}; tol = 0.0, check::Bool = true) cholesky(A, RowMaximum(); tol, check) false
 
 function cholesky(A::AbstractMatrix{Float16}, ::RowMaximum; tol = 0.0, check::Bool = true)
-    X = cholesky!(cholcopy(A), RowMaximum(); tol, check)
+    X = _cholesky(cholcopy(A), RowMaximum(); tol, check)
     return CholeskyPivoted{Float16}(X)
 end
 

stdlib/LinearAlgebra/src/qr.jl

@@ -417,12 +417,15 @@ true
 function qr(A::AbstractMatrix{T}, arg...; kwargs...) where T
     require_one_based_indexing(A)
     AA = copy_similar(A, _qreltype(T))
-    return qr!(AA, arg...; kwargs...)
+    return _qr(AA, arg...; kwargs...)
 end
 # TODO: remove in Julia v2.0
 @deprecate qr(A::AbstractMatrix, ::Val{false}; kwargs...) qr(A, NoPivot(); kwargs...)
 @deprecate qr(A::AbstractMatrix, ::Val{true}; kwargs...)  qr(A, ColumnNorm(); kwargs...)
 
+# allow packages like SparseArrays.jl to hook into here and redirect to out-of-place `qr`
+_qr(A::AbstractMatrix, args...; kwargs...) = qr!(A, args...; kwargs...)
+
 qr(x::Number) = qr(fill(x,1,1))
 function qr(v::AbstractVector)
     require_one_based_indexing(v)