diff --git a/notebooks/circular.jl b/notebooks/circular.jl index 15c5a7b..9a85919 100644 --- a/notebooks/circular.jl +++ b/notebooks/circular.jl @@ -67,6 +67,12 @@ function circular2(n) U = qr(A).Q .* cis.(2π*rand(n)) end +# ╔═╡ 148317c1-e48f-4d39-833c-b51d2c43e5fd +function circular1(n) + A = randn(n,n) .+ im * randn(n,n) + U = qr(A).Q * transpose( Matrix(qr(A).Q )) +end + # ╔═╡ e14122da-9861-401c-bb56-3693b25e6e15 circular2(5) @@ -83,8 +89,20 @@ let end -# ╔═╡ 77bd8022-bb83-4e7d-adb6-f49c6bb74134 -sqrt(.36) +# ╔═╡ 63bf73bf-b312-49cc-a909-c043bfc80fd1 +circular1(5) + +# ╔═╡ 82ce98e9-37a9-4023-ac62-5c092a8fa932 +let + n = 5 + t = 50_000 + m = [ smallabs(circular1(n)) for i=1:t] + display((mean(m),var(m))) + stephist(m,normalize=true,label="dense") + mh = [ smallabs(circular(n,1)) for i=1:t] + display((mean(mh),var(mh))) + stephist!(mh,normalize=true,label="Hessenberg") +end # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ @@ -1236,8 +1254,10 @@ version = "1.4.1+1" # ╠═63cd9672-d3d2-4b2a-8076-f98b60dc11e6 # ╠═02db4122-8e3c-477c-b1ef-d9c236787910 # ╠═14b4a088-ff74-43f3-b301-4057593c0447 +# ╠═148317c1-e48f-4d39-833c-b51d2c43e5fd # ╠═e14122da-9861-401c-bb56-3693b25e6e15 # ╠═5cd13d1b-9bb4-4a19-9e6a-07e214572639 -# ╠═77bd8022-bb83-4e7d-adb6-f49c6bb74134 +# ╠═63bf73bf-b312-49cc-a909-c043bfc80fd1 +# ╠═82ce98e9-37a9-4023-ac62-5c092a8fa932 # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002