added ^ method for UniformScaling (#34008)

Co-Authored-By: simeonschaub <[email protected]>

Co-Authored-By: Fredrik Ekre <[email protected]>

NEWS.md

@@ -65,6 +65,8 @@ Standard library changes
 
 * `cond(A, p)` with `p=1` or `p=Inf` now computes the exact condition number instead of an estimate ([#33547]).
 
+* `UniformScaling` objects may now be exponentiated such that `(a*I)^x = a^x * I`.
+
 #### Markdown
 
 * Tables now have the `align` attribute set when `show`n as HTML ([#33849]).

stdlib/LinearAlgebra/src/uniformscaling.jl

@@ -1,7 +1,7 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
 import Base: copy, adjoint, getindex, show, transpose, one, zero, inv,
-             hcat, vcat, hvcat
+             hcat, vcat, hvcat, ^
 
 """
     UniformScaling{T<:Number}
@@ -227,6 +227,14 @@ Broadcast.broadcasted(::typeof(*), J::UniformScaling,x::Number) = UniformScaling
 
 Broadcast.broadcasted(::typeof(/), J::UniformScaling,x::Number) = UniformScaling(J.λ/x)
 
+(^)(J::UniformScaling, x::Number) = UniformScaling((J.λ)^x)
+Base.literal_pow(::typeof(^), J::UniformScaling, x::Val) = UniformScaling(Base.literal_pow(^, J.λ, x))
+
+Broadcast.broadcasted(::typeof(^), J::UniformScaling, x::Number) = UniformScaling(J.λ^x)
+function Broadcast.broadcasted(::typeof(Base.literal_pow), ::typeof(^), J::UniformScaling, x::Val)
+    UniformScaling(Base.literal_pow(^, J.λ, x))
+end
+
 ==(J1::UniformScaling,J2::UniformScaling) = (J1.λ == J2.λ)
 
 ## equality comparison with UniformScaling

stdlib/LinearAlgebra/test/uniformscaling.jl

@@ -66,6 +66,15 @@ end
     @test UniformScaling(α)./α == UniformScaling(1.0)
     @test α * UniformScaling(1.0) == UniformScaling(1.0) * α
     @test UniformScaling(α)/α == UniformScaling(1.0)
+
+    β = rand()
+    @test (α*I)^2    == UniformScaling(α^2)
+    @test (α*I)^(-2) == UniformScaling(α^(-2))
+    @test (α*I)^(.5) == UniformScaling(α^(.5))
+    @test (α*I)^β    == UniformScaling(α^β)
+
+    @test (α * I) .^ 2 == UniformScaling(α^2)
+    @test (α * I) .^ β == UniformScaling(α^β)
 end
 
 @testset "det and logdet" begin