Fix #29713 (ldiv! overwrites arguments) (#29715)

* Fix for #29713

* Add tests for #29713

* Fix for #29713

* Copy the argument in the right branch

* Copy the argument in the right branch - take 2

* Update qr.jl

(cherry picked from commit 8d712f6)

stdlib/LinearAlgebra/src/factorization.jl

@@ -100,12 +100,14 @@ function ldiv!(Y::AbstractVecOrMat, A::Factorization, B::AbstractVecOrMat)
     @assert !has_offset_axes(Y, B)
     m, n = size(A, 1), size(A, 2)
     if m > n
-        ldiv!(A, B)
-        return copyto!(Y, view(B, 1:n, :))
+        Bc = copy(B)
+        ldiv!(A, Bc)
+        return copyto!(Y, view(Bc, 1:n, :))
     else
         return ldiv!(A, copyto!(Y, view(B, 1:m, :)))
     end
 end
+
 function ldiv!(Y::AbstractVecOrMat, adjA::Adjoint{<:Any,<:Factorization}, B::AbstractVecOrMat)
     checksquare(adjA)
     return ldiv!(adjA, copyto!(Y, B))

stdlib/LinearAlgebra/test/qr.jl

@@ -220,12 +220,16 @@ end
 end
 
 @testset "Issue Test Factorization fallbacks for rectangular problems" begin
-    A = randn(3,2)
+    A  = randn(3,2)
     Ac = copy(A')
-    b = randn(3)
-    c = randn(2)
+    b  = randn(3)
+    b0 = copy(b)
+    c  = randn(2)
     @test A \b ≈ ldiv!(c, qr(A ), b)
+    @test b == b0
+    c0 = copy(c)
     @test Ac\c ≈ ldiv!(b, qr(Ac, Val(true)), c)
+    @test c0 == c
 end
 
 end # module TestQR