Define chol for UniformScaling's (#22633)

* Define chol for UniformScaling's

* Move test for chol(lambda*I) to test/linalg/uniformscaling.jl

Author: mschauer

base/linalg/uniformscaling.jl

@@ -313,3 +313,27 @@ function hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScalin
     end
     return hvcat(rows, promote_to_arrays(n,1, promote_to_array_type(A), A...)...)
 end
+
+
+## Cholesky
+function _chol!(J::UniformScaling, uplo)
+    c, info = _chol!(J.λ, uplo)
+    UniformScaling(c), info
+end
+
+chol!(J::UniformScaling, uplo) = ((J, info) = _chol!(J, uplo); @assertposdef J info)
+
+"""
+    chol(J::UniformScaling) -> C
+
+Compute the square root of a non-negative UniformScaling `J`.
+
+# Examples
+```jldoctest
+julia> chol(16I)
+UniformScaling{Float64}
+4.0*I
+```
+"""
+chol(J::UniformScaling, args...) = ((C, info) = _chol!(J, nothing); @assertposdef C info)
+

test/linalg/uniformscaling.jl

@@ -173,3 +173,11 @@ end
             hvcat((2,1,2),B,2eye(3,3),eye(6,6),3eye(3,3),4eye(3,3))
     end
 end
+
+@testset "chol" begin
+    for T in (Float64, Complex64, BigFloat, Int)
+        λ = T(4)
+        @test chol(λ*I) ≈ √λ*I
+        @test_throws LinAlg.PosDefException chol(-λ*I)
+    end
+end