define lu!(F::LU,A) for general matrices (#1131)

alternative to #1125 . Defines `lu!(F::LU{<:Any,<:AbstractMatrix},A)`
and `lu!(F::LU{<:Any,<:StridedMatrix{<:BlasFloat}},A)`.

closes #1125

Author: ViralBShah

src/lu.jl

@@ -102,6 +102,65 @@ function lu!(A::HermOrSym{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupi
     end
     lu!(A.data, pivot; check, allowsingular)
 end
+
+#lu!(F::LU,A) should be dispatched on the type of matrix stored in the LU factorization.
+"""
+    lu!(F::LU, pivot = RowMaximum(); check = true, allowsingular = false) -> LU
+
+`lu!` is the same as [`lu`](@ref), but saves space by overwriting the
+input `F`, instead of creating a copy.
+
+!!! compat "Julia 1.12"
+    Reusing dense `LU` factorizations in `lu!` require Julia 1.12 or later.
+
+# Examples
+```jldoctest
+julia> A = [4. 3.; 6. 3.]
+2×2 Matrix{Float64}:
+ 4.0  3.0
+ 6.0  3.0
+
+julia> F = lu(A)
+LU{Float64, Matrix{Float64}, Vector{Int64}}
+L factor:
+2×2 Matrix{Float64}:
+ 1.0       0.0
+ 0.666667  1.0
+U factor:
+2×2 Matrix{Float64}:
+ 6.0  3.0
+ 0.0  1.0
+
+julia> B = [8 3; 12 3]
+2×2 Matrix{Int64}:
+  8  3
+ 12  3
+
+julia> F2 = lu!(F,B)
+LU{Float64, Matrix{Float64}, Vector{Int64}}
+L factor:
+2×2 Matrix{Float64}:
+ 1.0       0.0
+ 0.666667  1.0
+U factor:
+2×2 Matrix{Float64}:
+ 12.0  3.0
+  0.0  1.0
+```
+"""
+function lu!(F::LU{<:Any,<:AbstractMatrix}, A; check::Bool = true, allowsingular::Bool = false)
+    copyto!(F.factors, A)
+    return generic_lufact!(F.factors, lupivottype(eltype(A)), F.ipiv; check, allowsingular)
+end
+
+#lu!(F::LU,A) should be dispatched on the type of matrix stored in the LU factorization.
+function lu!(F::LU{<:Any,<:StridedMatrix{<:BlasFloat}}, A; check::Bool = true, allowsingular::Bool = false)
+    copyto!(F.factors, A)
+    lpt = LAPACK.getrf!(F.factors, F.ipiv; check)
+    check && _check_lu_success(lpt[3], allowsingular)
+    return LU{eltype(lpt[1]),typeof(lpt[1]),typeof(lpt[2])}(lpt[1], lpt[2], lpt[3])
+end
+
 # for backward compatibility
 # TODO: remove towards Julia v2
 @deprecate lu!(A::Union{StridedMatrix,HermOrSym,Tridiagonal}, ::Val{true}; check::Bool = true) lu!(A, RowMaximum(); check=check)
@@ -149,7 +208,7 @@ Stacktrace:
 """
 lu!(A::AbstractMatrix, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(eltype(A));
     check::Bool = true, allowsingular::Bool = false) = generic_lufact!(A, pivot; check, allowsingular)
-function generic_lufact!(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(T);
+function generic_lufact!(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(T), ipiv::AbstractVector{BlasInt} = Vector{BlasInt}(undef,min(size(A)...));
                          check::Bool = true, allowsingular::Bool = false) where {T}
     check && LAPACK.chkfinite(A)
     # Extract values
@@ -158,7 +217,6 @@ function generic_lufact!(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot,R
 
     # Initialize variables
     info = 0
-    ipiv = Vector{BlasInt}(undef, minmn)
     @inbounds begin
         for k = 1:minmn
             # find index max

test/lu.jl

@@ -67,6 +67,7 @@ dimg  = randn(n)/2
         @test (l*u)[invperm(p),:] ≈ a
         @test a * inv(lua) ≈ Matrix(I, n, n)
         @test copy(lua) == lua
+        @test lu!(copy(lua),a) == lua
         if eltya <: BlasFloat
             # test conversion of LU factorization's numerical type
             bft = eltya <: Real ? LinearAlgebra.LU{BigFloat} : LinearAlgebra.LU{Complex{BigFloat}}