GPU-friendly SVD + correct gaugefix

Author: lkdvos

src/implementations/svd.jl

@@ -248,17 +248,18 @@ function svd_full!(A::AbstractMatrix, USVᴴ, alg::DiagonalAlgorithm)
     check_input(svd_full!, A, USVᴴ, alg)
     Ad = diagview(A)
     U, S, Vᴴ = USVᴴ
-    Sd = diagview(S)
-    Sd .= abs.(Ad)
-    p = sortperm(Sd; rev=true)
-    permute!(Sd, p)
-    T = eltype(Vᴴ)
+    p = sortperm(Ad; by=abs, rev=true)
     zero!(U)
     zero!(Vᴴ)
-    @inbounds for (i, pi) in enumerate(p)
-        s = Ad[pi]
-        U[pi, i] = sign_safe(s)
-        Vᴴ[i, pi] = one(T)
+    T = eltype(U)
+    U[CartesianIndex.(reverse.(enumerate(p)))] .= Ref(one(T))
+    Vᴴ[CartesianIndex.(enumerate(p))] .= sign_safe.(view(Ad, p))
+    Sd = diagview(S)
+    if Ad === Sd
+        @. Sd = abs(Ad)
+        permute!(Sd, p)
+    else
+        Sd .= abs.(view(Ad, p))
     end
     return U, S, Vᴴ
 end