Add a fast method for diag of Cholesky matrices

stdlib/LinearAlgebra/src/cholesky.jl

@@ -835,3 +835,16 @@ then `CC = cholesky(C.U'C.U - v*v')` but the computation of `CC` only uses
 `O(n^2)` operations.
 """
 lowrankdowndate(C::Cholesky, v::AbstractVector) = lowrankdowndate!(copy(C), copy(v))
+
+function diag(C::Cholesky{T}) where {T}
+    N = size(C, 1)
+    z = Vector{T}(undef, N)
+    U = C.U
+    for i=1:N
+        z[i] = zero(T)
+        for j=1:i
+          z[i] += U[j, i]^2
+        end
+    end
+    return z
+end

stdlib/LinearAlgebra/test/cholesky.jl

@@ -548,4 +548,11 @@ end
     @test logabsdet(B)[1] == -Inf
  end
 
+@testset "diag" begin
+    A = randn(100, 100)
+    P = A' * A
+    C = cholesky(P)
+    @test diag(P) ≈ diag(C)
+end
+
 end # module TestCholesky