From 693118d19225ea23a14edb68f4d5e9b011327c75 Mon Sep 17 00:00:00 2001 From: Greg Burri Date: Thu, 15 Jul 2021 15:13:25 +0200 Subject: [PATCH] Initial commit --- 3d_plot.jl | 862 +++++++++++++++++++++++++ category.jl | 223 +++++++ drawing.jl | 764 +++++++++++++++++++++++ signal_processing.jl | 49 ++ sine_approximations.jl | 1349 ++++++++++++++++++++++++++++++++++++++++ 5 files changed, 3247 insertions(+) create mode 100644 3d_plot.jl create mode 100644 category.jl create mode 100644 drawing.jl create mode 100644 signal_processing.jl create mode 100644 sine_approximations.jl diff --git a/3d_plot.jl b/3d_plot.jl new file mode 100644 index 0000000..ff89074 --- /dev/null +++ b/3d_plot.jl @@ -0,0 +1,862 @@ +### A Pluto.jl notebook ### +# v0.15.1 + +using Markdown +using InteractiveUtils + +# ╔═╡ 504cc192-eb75-11ea-2b6e-af5d4f828086 +begin + using PlutoUI, Plots, LinearAlgebra + plotly() +end + +# ╔═╡ 5485d760-eb75-11ea-2e25-7b13d58ce554 +let + a = 0 + n = 20 + f(x, y) = let + v = complex(x, y) + c = v + for i ∈ 1:n + v = v^2 + c + a * im + if norm(v) > 2 + return 1-i/n # Normalized. + end + end + 0 + end + x = LinRange(-2, 1, 1000) + y = LinRange(-1.5, 1.5, 1000) + plot(x, y, f, st = :surface, label = false, camera = (45, 80), c = :grays) +end + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" + +[compat] +Plots = "~1.18.2" +PlutoUI = "~0.7.9" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +[[Adapt]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "3.3.1" + +[[ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" + +[[Artifacts]] +uuid = 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["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] +git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb" +uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" +version = "1.3.7+0" + +[[nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" + +[[p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" + +[[x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2020.7.14+2" + +[[x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.0.0+3" + +[[xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "0.9.1+5" +""" + +# ╔═╡ Cell order: +# ╠═504cc192-eb75-11ea-2b6e-af5d4f828086 +# ╠═5485d760-eb75-11ea-2e25-7b13d58ce554 +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 diff --git a/category.jl b/category.jl new file mode 100644 index 0000000..c1adbfe --- /dev/null +++ b/category.jl @@ -0,0 +1,223 @@ +### A Pluto.jl notebook ### +# v0.15.1 + +using Markdown +using InteractiveUtils + +# ╔═╡ ce8225de-f0ee-11ea-392d-8b466e106eba +md""" +# Category theory +From the book \"Category theory for programmers\". + +Some solutions are posted here: + +One of the goals is to understand this video: +""" + +# ╔═╡ 161953b0-f0ef-11ea-10e7-efb9093f3abe +md"## 1.4 Challenge" + +# ╔═╡ 1d939550-f0f0-11ea-0242-6bb6f9d47e07 +md"**1. Implement, as best as you can, the identity function in your favorite language (or the second favorite, if your favorite language happens to be Haskell).**" + +# ╔═╡ 339c9ae0-f0f0-11ea-1782-9741d0cfd212 +id(f) = f # Note: in Julia identity function already exists and is named 'identity'. + +# ╔═╡ 244b06b0-f0f2-11ea-3e9b-bd41d3a7709a +let + f = id(sin) + f(π/4) +end + +# ╔═╡ 5df73200-f0f0-11ea-06d3-7f00df9ff21a +md"**2. Implement the composition function in your favorite language. It takes two functions as arguments and returns a function that is their composition.**" + +# ╔═╡ 2b194650-f0f2-11ea-282b-fb9e41119331 +compose(f, g) = x -> f(g(x)) + +# ╔═╡ 8d5c86d0-f0f0-11ea-1eb7-81b63c1f0391 +let + f = compose(sin, cos) # Composition already exists as 'f ∘ g'. + f(2) +end + +# ╔═╡ 39d69450-f0f1-11ea-380f-657eaa4c2705 +md"**3. Write a program that tries to test that your composition function respects identity.**" + +# ╔═╡ 3ec58ca0-f0f1-11ea-3122-d999cdd46d59 +let + f = id(sin) + g = sin + f(2) == g(2), + compose(x -> x + 4, id)(5) == 9, + compose(id, x -> x + 4)(5) == 9 +end + +# ╔═╡ a9f8c960-f0f1-11ea-306b-59fd1e640908 +md"**4. Is the world-wide web a category in any sense? Are links morphisms?**" + +# ╔═╡ b27be4f0-f0f1-11ea-3f44-132d777e00c8 +md"Each uri represents a object and each link a morphism to another uri." + +# ╔═╡ 529575a0-f0f2-11ea-2860-439efb6131f8 +md"**5. Is Facebook a category, with people as objects and friendships as morphisms?**" + +# ╔═╡ 5c0cdc40-f0f2-11ea-0b14-e3ea9217d362 +md"No because A → B and B → C do not imply A → C." + +# ╔═╡ 775f27f0-f11a-11ea-0749-a333efba4f47 +md"## 2.7 Challenges" + +# ╔═╡ 295e6200-f115-11ea-0871-bf9192c0ace8 +md""" +**1. Define a higher-order function (or a function object) memoize in your favorite language. This function takes a pure function f as an argument and returns a function that behaves almost exactly like f, except that it only calls the original function once for every argument, stores the result internally, and subsequently returns this stored result every time it’s called with the same argument. You can tell the memoized function from the original by watching its performance. For instance, try to memoize a function that takes a long time to evaluate. You’ll have to wait for the result the first time you call it, but on subsequent calls, with the same argument, you should get the result immediately.** +""" + +# ╔═╡ 88cec670-f1a2-11ea-19b1-93258f66e3c8 +function memoize(f) + dic = Dict() + v -> let + if haskey(dic, v) + dic[v] + else + dic[v] = f(v) + end + end +end + +# ╔═╡ 633b7b60-f1a2-11ea-0826-d727cdf29f3f +let + using Random + function rand_from_seed(seed) + rng = MersenneTwister(seed) + rand(rng) + end + + v1 = rand_from_seed(2) # Always 0.36679641243992434. + memoized_rand = memoize(rand_from_seed) + v2 = memoized_rand(2) # Also always 0.36679641243992434. + md"v1 = $v1, v2 = $v2 (no, it doesn't work)" +end + +# ╔═╡ 8ef36160-f11a-11ea-12ee-474959e79a5a +let + function slow_function(x) + sleep(1) + x + 42 + end + + memoized_slow_function = memoize(slow_function) + + t1 = @elapsed memoized_slow_function(2) + t2 = @elapsed memoized_slow_function(2) + md"First call: $t1 s, second call: $t2 s" +end + +# ╔═╡ 6ca649c0-f1a0-11ea-17ce-85e469a744dc +md"**Try to memoize a function from your standard library that you normally use to produce random numbers. Does it work?**" + +# ╔═╡ 41bca720-f1a2-11ea-3aa6-91c91ce942bd +md"Nope, it will always produce the same output" + +# ╔═╡ 576b30a2-f1a2-11ea-244b-0b664a975ed1 +md"**Most random number generators can be initialized with a seed. Implement a function that takes a seed, calls the random number generator with that seed, and returns the result. Memoize that function. Does it work?**" + +# ╔═╡ 9e4fd750-f1a2-11ea-2e87-bf53e8d90d3d +md""" +**Which of these C++ functions are pure? Try to memoize them and observe what happens when you call them multiple times: memoized and not.** + +```c++ +(a) The factorial function from the example in the text. +(b) std::getchar() +(c) bool f() { + std::cout << "Hello!" << std::endl; + return true; +} +(d) int f(int x) { + static int y = 0; + 25 + y += x; + return y; +} +``` +""" + +# ╔═╡ d39ac400-f1a3-11ea-3828-e9921179e016 +md""" +Only (a) is pure and only this one can be memoized. +""" + +# ╔═╡ 17480d70-f1a4-11ea-1fd5-e3c0cd4de97d +md"**How many different functions are there from Bool to Bool? Can you implement them all?**" + +# ╔═╡ 4028fce0-f1a4-11ea-2e43-af5ca402a53a +let + f1(b) = b # Same. + f2(b) = !b # The inverse. + f3(b) = true # Always true. + f4(b) = false # Always false. + md"There are only four possible functions" +end + +# ╔═╡ 8e9436b0-f1a4-11ea-1a27-95681bae1e4b +md""" +## Notes on Chapter 3 + +A *preorder* is a category with at most one morphism from any object *a* to any object *b*. + +Cycles are forbidden in *partial orders*. + +If any two objects are in relation with each other, one way or another then it's a *total order*. + +A set of morphisms from object *a* to object *b* in a category *C* is called a *hom-set*: *C(a, b)*. + +A *monoid* is a single object with a set of morphisms.""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +[[Random]] +deps = ["Serialization"] +uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" + +[[Serialization]] +uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" +""" + +# ╔═╡ Cell order: +# ╟─ce8225de-f0ee-11ea-392d-8b466e106eba +# ╟─161953b0-f0ef-11ea-10e7-efb9093f3abe +# ╟─1d939550-f0f0-11ea-0242-6bb6f9d47e07 +# ╠═339c9ae0-f0f0-11ea-1782-9741d0cfd212 +# ╠═244b06b0-f0f2-11ea-3e9b-bd41d3a7709a +# ╟─5df73200-f0f0-11ea-06d3-7f00df9ff21a +# ╠═2b194650-f0f2-11ea-282b-fb9e41119331 +# ╠═8d5c86d0-f0f0-11ea-1eb7-81b63c1f0391 +# ╟─39d69450-f0f1-11ea-380f-657eaa4c2705 +# ╠═3ec58ca0-f0f1-11ea-3122-d999cdd46d59 +# ╟─a9f8c960-f0f1-11ea-306b-59fd1e640908 +# ╟─b27be4f0-f0f1-11ea-3f44-132d777e00c8 +# ╟─529575a0-f0f2-11ea-2860-439efb6131f8 +# ╟─5c0cdc40-f0f2-11ea-0b14-e3ea9217d362 +# ╟─775f27f0-f11a-11ea-0749-a333efba4f47 +# ╟─295e6200-f115-11ea-0871-bf9192c0ace8 +# ╠═88cec670-f1a2-11ea-19b1-93258f66e3c8 +# ╠═8ef36160-f11a-11ea-12ee-474959e79a5a +# ╟─6ca649c0-f1a0-11ea-17ce-85e469a744dc +# ╟─41bca720-f1a2-11ea-3aa6-91c91ce942bd +# ╟─576b30a2-f1a2-11ea-244b-0b664a975ed1 +# ╠═633b7b60-f1a2-11ea-0826-d727cdf29f3f +# ╟─9e4fd750-f1a2-11ea-2e87-bf53e8d90d3d +# ╟─d39ac400-f1a3-11ea-3828-e9921179e016 +# ╟─17480d70-f1a4-11ea-1fd5-e3c0cd4de97d +# ╠═4028fce0-f1a4-11ea-2e43-af5ca402a53a +# ╠═8e9436b0-f1a4-11ea-1a27-95681bae1e4b +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 diff --git a/drawing.jl b/drawing.jl new file mode 100644 index 0000000..fb3cc4f --- /dev/null +++ b/drawing.jl @@ -0,0 +1,764 @@ +### A Pluto.jl notebook ### +# v0.15.1 + +using Markdown +using InteractiveUtils + +# ╔═╡ 56760c70-eb66-11ea-2335-c9c8cbcb56f3 +begin + using Luxor, PlutoUI, Colors +end + +# ╔═╡ 9f433e5e-3606-11eb-2a5c-d70bb3978644 +html"""""" + +# ╔═╡ ebf8a9e0-fe37-11ea-39ae-8b0f814fed81 +#= +* https://en.wikipedia.org/wiki/Tessellation +* https://en.wikipedia.org/wiki/Penrose_tiling +=# + +# ╔═╡ 1d2fa270-3493-11eb-33a8-092f981b3b0d +begin + function drawstars(colors) + sethue(colors[1]) + circle(O, 200, :fill) + sethue("white") + radii = [180, 200, 150] + rotations = [π/28, 0, 0] + for (n, r) in enumerate(radii) + sethue(colors[n + 1]) + star(O, r, 28, 0.7, rotations[n], :fill) + end + sethue("black") + star(O, 120, 28, 0.7, 0, :fill) + end + + blues = [ + RGB(0.455,0.753,0.89), # main + RGB(0.322,0.557,0.639), + RGB(0.243,0.396,0.463), + RGB(0.133,0.298,0.357)] + + browns = [ + RGB(0.549,0.384,0.224), # main + RGB(0.459,0.298,0.141), + RGB(0.376,0.22,0.075), + RGB(0.259,0.129,0.043)] +end + +# ╔═╡ 68fd3a00-356f-11eb-288b-d95699f8f8ab +@draw begin + background("black") + + sector(O, 100, 200, π, 3π/2) + clip() + drawstars(browns) + clipreset() + + sector(O, 100, 200, 3π/2, π) + clip() + drawstars(blues) + clipreset() +end + +# ╔═╡ d6ae6110-3609-11eb-27ed-61a7f8ddd3ae +let + d = Dict{String, String}() + d["abc"] = "123" + typeof(d) +end + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" +Luxor = "ae8d54c2-7ccd-5906-9d76-62fc9837b5bc" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" + +[compat] +Colors = "~0.12.8" +Luxor = "~2.13.0" +PlutoUI = "~0.7.9" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +[[AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.0.1" + +[[Adapt]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "3.3.1" + +[[ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" + +[[Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" + +[[Base64]] +uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" + +[[Bzip2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" +uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" +version = "1.0.8+0" + +[[Cairo]] +deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"] +git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b" +uuid = "159f3aea-2a34-519c-b102-8c37f9878175" +version = "1.0.5" + +[[Cairo_jll]] +deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] +git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99" +uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" +version = "1.16.1+0" + +[[ChainRulesCore]] +deps = ["Compat", "LinearAlgebra", "SparseArrays"] +git-tree-sha1 = "dcc25ff085cf548bc8befad5ce048391a7c07d40" +uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" +version = "0.10.11" + +[[ColorTypes]] +deps = ["FixedPointNumbers", 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+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" + +[[SharedArrays]] +deps = ["Distributed", "Mmap", "Random", "Serialization"] +uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383" + +[[Sockets]] +uuid = "6462fe0b-24de-5631-8697-dd941f90decc" + +[[SparseArrays]] +deps = ["LinearAlgebra", "Random"] +uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" + +[[SpecialFunctions]] +deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"] +git-tree-sha1 = "a50550fa3164a8c46747e62063b4d774ac1bcf49" +uuid = "276daf66-3868-5448-9aa4-cd146d93841b" +version = "1.5.1" + +[[StackViews]] +deps = ["OffsetArrays"] +git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c" +uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15" +version = "0.1.1" + +[[Statistics]] +deps = ["LinearAlgebra", "SparseArrays"] +uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[[Suppressor]] +git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787" +uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb" +version = "0.2.0" + +[[TOML]] +deps = ["Dates"] +uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" + +[[Tar]] +deps = ["ArgTools", "SHA"] +uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" + +[[TensorCore]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6" +uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50" +version = "0.1.1" + +[[Test]] +deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] +uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[[UUIDs]] +deps = ["Random", "SHA"] +uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" + +[[Unicode]] +uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" + +[[XML2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"] +git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a" +uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" +version = "2.9.12+0" + +[[XSLT_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"] +git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a" +uuid = "aed1982a-8fda-507f-9586-7b0439959a61" +version = "1.1.34+0" + +[[Xorg_libX11_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"] +git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527" +uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc" +version = "1.6.9+4" + +[[Xorg_libXau_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e" +uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" +version = "1.0.9+4" + +[[Xorg_libXdmcp_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4" +uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" +version = "1.1.3+4" + +[[Xorg_libXext_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] +git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3" +uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3" +version = "1.3.4+4" + +[[Xorg_libXrender_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] +git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96" +uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" +version = "0.9.10+4" + +[[Xorg_libpthread_stubs_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb" +uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" +version = "0.1.0+3" + +[[Xorg_libxcb_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] +git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6" +uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" +version = "1.13.0+3" + +[[Xorg_xtrans_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" +uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" +version = "1.4.0+3" + +[[Zlib_jll]] +deps = ["Libdl"] +uuid = "83775a58-1f1d-513f-b197-d71354ab007a" + +[[Zstd_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6" +uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" +version = "1.5.0+0" + +[[gdk_pixbuf_jll]] +deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"] +git-tree-sha1 = "031f60d4362fba8f8778b31047491823f5a73000" +uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0" +version = "2.38.2+9" + +[[libass_jll]] +deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] +git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" +uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" +version = "0.15.1+0" + +[[libfdk_aac_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" +uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" +version = "2.0.2+0" + +[[libpng_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] +git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" +uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" +version = "1.6.38+0" + +[[libvorbis_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] +git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb" +uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" +version = "1.3.7+0" + +[[nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" + +[[p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" + +[[x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2021.5.5+0" + +[[x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" +""" + +# ╔═╡ Cell order: +# ╟─9f433e5e-3606-11eb-2a5c-d70bb3978644 +# ╠═56760c70-eb66-11ea-2335-c9c8cbcb56f3 +# ╠═ebf8a9e0-fe37-11ea-39ae-8b0f814fed81 +# ╠═1d2fa270-3493-11eb-33a8-092f981b3b0d +# ╠═68fd3a00-356f-11eb-288b-d95699f8f8ab +# ╠═d6ae6110-3609-11eb-27ed-61a7f8ddd3ae +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 diff --git a/signal_processing.jl b/signal_processing.jl new file mode 100644 index 0000000..0583c4c --- /dev/null +++ b/signal_processing.jl @@ -0,0 +1,49 @@ +### A Pluto.jl notebook ### +# v0.11.12 + +using Markdown +using InteractiveUtils + +# ╔═╡ bd48bd00-ed0d-11ea-2663-f731a2d178a0 +using PlutoUI, Plots, LinearAlgebra + +# ╔═╡ 1e0d6c70-ed0f-11ea-1ebb-673f3c8820c5 +md"## Week 4 - Discrete Fourier series" + +# ╔═╡ 2f414340-ed0f-11ea-15bf-39c2f92785d5 +begin + synthesis(X, n, N) = 1 / N * sum(X(k) * exp(im * 2π / N * n * k) for k ∈ 0:N-1) + analysis(x, k, N) = sum(x(n) * exp(-im * 2π / N * n * k) for n ∈ 0:N-1) + + # Input signal 'f'. + f(n) = sin(n * 2π / 100) + 0.2 * sin(10 * n * 2π / 100 + π / 4) + + # Analysis of 'f'. + N = 100 + points_in_freq_domain = [analysis(f, k, N) for k ∈ 0:N-1] + F(n) = points_in_freq_domain[n % length(points_in_freq_domain) + 1] + + # Synthesis of 'F'. + points_in_time_domain = [synthesis(F, n, N) for n ∈ 0:N-1] .|> real +end + +# ╔═╡ 8fb32ce0-ed12-11ea-0d7c-b3d725a40f62 +scatter(0:N-1, f, label = false, title = "Input: f(n)") + +# ╔═╡ 47488270-ed12-11ea-0350-876a454b79c8 +scatter(0:N-1, points_in_freq_domain |> imag, label = false, title = "Frequency domain: F(n): Imaginary") + +# ╔═╡ 5e0c5710-ed13-11ea-149e-91be4a55745d +scatter(0:N-1, points_in_freq_domain |> real, label = false, title = "Frequency domain: F(n): Real") + +# ╔═╡ f0d0a020-ed12-11ea-1c5b-8959ad6e2ec1 +scatter(0:N-1, points_in_time_domain |> real, label = false, title = "Back to time domain") + +# ╔═╡ Cell order: +# ╠═bd48bd00-ed0d-11ea-2663-f731a2d178a0 +# ╟─1e0d6c70-ed0f-11ea-1ebb-673f3c8820c5 +# ╠═2f414340-ed0f-11ea-15bf-39c2f92785d5 +# ╠═8fb32ce0-ed12-11ea-0d7c-b3d725a40f62 +# ╠═47488270-ed12-11ea-0350-876a454b79c8 +# ╠═5e0c5710-ed13-11ea-149e-91be4a55745d +# ╠═f0d0a020-ed12-11ea-1c5b-8959ad6e2ec1 diff --git a/sine_approximations.jl b/sine_approximations.jl new file mode 100644 index 0000000..28b78e6 --- /dev/null +++ b/sine_approximations.jl @@ -0,0 +1,1349 @@ +### A Pluto.jl notebook ### +# v0.15.1 + +using Markdown +using InteractiveUtils + +# ╔═╡ 0b68706f-ec74-4184-9a4b-d1d455356310 +using LinearAlgebra, Statistics, Plots, PlutoUI, Images, FileIO, DataFrames, Printf + +# ╔═╡ dff4f0db-bbca-4796-adca-708c3eb428da +html""" +""" + +# ╔═╡ 56760c70-eb66-11ea-2335-c9c8cbcb56f3 +begin + default(label = false, minorgrid = true) # Default values for plots. + plotly() +end + +# ╔═╡ 9f9e6944-a21c-40b1-a57c-02226f537d64 +let + # From http://jeanmariechauvet.com/papers/curttrig.html . + sin_poly(x) = 1.5706268 * x - 0.6432292 * x^3 + 0.0727102 * x^5 # Number of multiplications: 7, Number of additions: 2. + + sin_ref(x) = sin(pi/2 * x) + + function sin_bhaskara(x) + x₂ = abs(pi/2 * x) + # Number of multiplications: 4, Number of division: 1 Number of additions: 3. + y = 16 * x₂ * (π - x₂) / (5 * π^2 - 4 * x₂ * (π - x₂)) + y * sign(x) + end + + delta_poly(x) = abs(sin_poly(x) - sin_ref(x)) + delta_bhaskara(x) = abs(sin_bhaskara(x) - sin_ref(x)) * 200 + + #plot(LinRange(-2, 2, 1000), delta) + #plot!(LinRange(-2, 2, 1000), sin_poly) + plot(LinRange(-2, 2, 1000), sin_ref) + plot!(LinRange(-2, 2, 1000), sin_bhaskara) + plot!(LinRange(-2, 2, 1000), delta_bhaskara) +end + +# ╔═╡ 33678d31-93b2-4f6c-a2a4-a88cfdfea323 +md"---" + +# ╔═╡ 476f7d9e-3b3c-455d-90ce-8b70f8984eda +function throughput(array_size, speed) + sample_per_sec_for_unit_speed = 200 # For 1 m/s. + one_sample_size = 112 + header_size = 6 + array_sizes_size = 14 * 4 + speed * sample_per_sec_for_unit_speed / array_size * (array_size * one_sample_size + array_sizes_size + header_size) +end + +# ╔═╡ 54d970a1-2bb7-4ec2-9dc2-6249497447d7 +function format_bytes(bytes) + if bytes / 1024^2 > 1 + @sprintf("%.2f MB", bytes / 1024^2) + else + @sprintf("%.0f kB", bytes / 1024) + end +end + +# ╔═╡ 268abf9c-d869-4e7e-b02e-079d1be2d9cf +let + df = DataFrame(speed = Float64[], array_size = Float64[], throughput = Float64[], formatted_throughput = String[]) + + for array_size ∈ [1 10 100] + for speed ∈ [10 50 100 150] + tp = throughput(array_size, speed) + push!( + df, + [ + speed + array_size + tp + format_bytes(tp) * "/s" + ] + ) + end + end + df +end + +# ╔═╡ 31c1ddf4-c7a5-45b3-93b2-acf5ebef8d5e +14 * 4 + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" +Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" +Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[compat] +DataFrames = "~1.2.0" +FileIO = "~1.10.1" +Images = "~0.24.1" +Plots = "~1.18.2" +PlutoUI = "~0.7.9" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +[[AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.0.1" + +[[Adapt]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "3.3.1" + +[[ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" + +[[ArrayInterface]] +deps = ["IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"] +git-tree-sha1 = "045ff5e1bc8c6fb1ecb28694abba0a0d55b5f4f5" +uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9" +version = "3.1.17" + 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"JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2020.7.14+2" + +[[x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.0.0+3" + +[[xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "0.9.1+5" +""" + +# ╔═╡ Cell order: +# ╠═dff4f0db-bbca-4796-adca-708c3eb428da +# ╠═0b68706f-ec74-4184-9a4b-d1d455356310 +# ╠═56760c70-eb66-11ea-2335-c9c8cbcb56f3 +# ╠═9f9e6944-a21c-40b1-a57c-02226f537d64 +# ╟─33678d31-93b2-4f6c-a2a4-a88cfdfea323 +# ╠═476f7d9e-3b3c-455d-90ce-8b70f8984eda +# ╠═54d970a1-2bb7-4ec2-9dc2-6249497447d7 +# ╠═268abf9c-d869-4e7e-b02e-079d1be2d9cf +# ╠═31c1ddf4-c7a5-45b3-93b2-acf5ebef8d5e +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 -- 2.45.2