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dft working

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This commit is contained in:
Jonas Hahn
2026-02-03 12:22:08 +01:00
parent ec2289e4b8
commit f66f627c2e
4 changed files with 164 additions and 49 deletions
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127
Manifest.toml
View File

@@ -1,8 +1,8 @@
# This file is machine-generated - editing it directly is not advised
julia_version = "1.10.10"
julia_version = "1.12.4"
manifest_format = "2.0"
project_hash = "39d0d5866236472d6bc1a58c4e663ea8a2a2e057"
project_hash = "a13dd6f9886c94a925d8bb34358f1d189196ee72"
[[deps.AliasTables]]
deps = ["PtrArrays", "Random"]
@@ -12,13 +12,15 @@ version = "1.1.3"
[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"
version = "1.1.2"
[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.11.0"
[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
version = "1.11.0"
[[deps.BitFlags]]
git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d"
@@ -54,13 +56,11 @@ deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "67e11ee83a43eb71ddc950302c53bf33f0690dfe"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.12.1"
weakdeps = ["StyledStrings"]
[deps.ColorTypes.extensions]
StyledStringsExt = "StyledStrings"
[deps.ColorTypes.weakdeps]
StyledStrings = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "8b3b6f87ce8f65a2b4f857528fd8d70086cd72b1"
@@ -82,7 +82,7 @@ version = "0.13.1"
[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"
version = "1.3.0+1"
[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
@@ -109,6 +109,7 @@ version = "0.19.3"
[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
version = "1.11.0"
[[deps.Dbus_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"]
@@ -130,7 +131,7 @@ version = "0.9.5"
[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"
version = "1.7.0"
[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -164,6 +165,7 @@ version = "8.0.1+0"
[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
version = "1.11.0"
[[deps.FixedPointNumbers]]
deps = ["Statistics"]
@@ -202,21 +204,21 @@ version = "3.4.1+0"
[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
git-tree-sha1 = "f305bdb91e1f3fcc687944c97f2ede40585b1bd5"
git-tree-sha1 = "ee0585b62671ce88e48d3409733230b401c9775c"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.73.19"
version = "0.73.22"
[deps.GR.extensions]
GRIJuliaExt = "IJulia"
IJuliaExt = "IJulia"
[deps.GR.weakdeps]
IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "de439fbc02b9dc0e639e67d7c5bd5811ff3b6f06"
git-tree-sha1 = "7dd7173f7129a1b6f84e0f03e0890cd1189b0659"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.73.19+1"
version = "0.73.22+0"
[[deps.GettextRuntime_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll"]
@@ -262,6 +264,7 @@ version = "8.5.1+0"
[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
version = "1.11.0"
[[deps.IrrationalConstants]]
git-tree-sha1 = "b2d91fe939cae05960e760110b328288867b5758"
@@ -298,6 +301,11 @@ git-tree-sha1 = "b6893345fd6658c8e475d40155789f4860ac3b21"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "3.1.4+0"
[[deps.JuliaSyntaxHighlighting]]
deps = ["StyledStrings"]
uuid = "ac6e5ff7-fb65-4e79-a425-ec3bc9c03011"
version = "1.12.0"
[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "059aabebaa7c82ccb853dd4a0ee9d17796f7e1bc"
@@ -351,26 +359,28 @@ uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"
[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.4.0+0"
version = "8.15.0+0"
[[deps.LibGit2]]
deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
deps = ["LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
version = "1.11.0"
[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.6.4+0"
version = "1.9.0+0"
[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
deps = ["Artifacts", "Libdl", "OpenSSL_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.0+1"
version = "1.11.3+1"
[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
version = "1.11.0"
[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -411,6 +421,7 @@ version = "2.41.2+0"
[[deps.LinearAlgebra]]
deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
version = "1.12.0"
[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
@@ -430,6 +441,7 @@ version = "0.3.29"
[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
version = "1.11.0"
[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
@@ -443,8 +455,9 @@ uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.16"
[[deps.Markdown]]
deps = ["Base64"]
deps = ["Base64", "JuliaSyntaxHighlighting", "StyledStrings"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
version = "1.11.0"
[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
@@ -453,9 +466,10 @@ uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.9"
[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ff69a2b1330bcb730b9ac1ab7dd680176f5896b8"
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.2+1"
version = "2.28.1010+0"
[[deps.Measures]]
git-tree-sha1 = "b513cedd20d9c914783d8ad83d08120702bf2c77"
@@ -470,10 +484,11 @@ version = "1.2.0"
[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
version = "1.11.0"
[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2023.1.10"
version = "2025.11.4"
[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
@@ -483,7 +498,7 @@ version = "1.1.3"
[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"
version = "1.3.0"
[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -494,12 +509,12 @@ version = "1.3.6+0"
[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.23+4"
version = "0.3.29+0"
[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.5+0"
version = "0.8.7+0"
[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "NetworkOptions", "OpenSSL_jll", "Sockets"]
@@ -508,16 +523,15 @@ uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.6.1"
[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "f19301ae653233bc88b1810ae908194f07f8db9d"
deps = ["Artifacts", "Libdl"]
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "3.5.4+0"
[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "39a11854f0cba27aa41efaedf43c77c5daa6be51"
git-tree-sha1 = "e2bb57a313a74b8104064b7efd01406c0a50d2ff"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.6.0+0"
version = "1.6.1+0"
[[deps.OrderedCollections]]
git-tree-sha1 = "05868e21324cede2207c6f0f466b4bfef6d5e7ee"
@@ -527,7 +541,7 @@ version = "1.8.1"
[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.42.0+1"
version = "10.44.0+1"
[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
@@ -548,9 +562,13 @@ uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.44.2+0"
[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.10.0"
version = "1.12.1"
weakdeps = ["REPL"]
[deps.Pkg.extensions]
REPLExt = "REPL"
[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
@@ -586,9 +604,9 @@ version = "1.41.4"
[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
git-tree-sha1 = "07a921781cab75691315adc645096ed5e370cb77"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"
version = "1.3.3"
[[deps.Preferences]]
deps = ["TOML"]
@@ -599,6 +617,7 @@ version = "1.5.1"
[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
version = "1.11.0"
[[deps.PtrArrays]]
git-tree-sha1 = "1d36ef11a9aaf1e8b74dacc6a731dd1de8fd493d"
@@ -630,12 +649,14 @@ uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3"
version = "6.8.2+2"
[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
deps = ["InteractiveUtils", "JuliaSyntaxHighlighting", "Markdown", "Sockets", "StyledStrings", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
version = "1.11.0"
[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
version = "1.11.0"
[[deps.RecipesBase]]
deps = ["PrecompileTools"]
@@ -678,6 +699,7 @@ version = "1.3.0"
[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
version = "1.11.0"
[[deps.Showoff]]
deps = ["Dates", "Grisu"]
@@ -692,6 +714,7 @@ version = "1.2.0"
[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
version = "1.11.0"
[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
@@ -702,7 +725,7 @@ version = "1.2.2"
[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.10.0"
version = "1.12.0"
[[deps.StableRNGs]]
deps = ["Random"]
@@ -711,9 +734,14 @@ uuid = "860ef19b-820b-49d6-a774-d7a799459cd3"
version = "1.0.4"
[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.10.0"
version = "1.11.1"
weakdeps = ["SparseArrays"]
[deps.Statistics.extensions]
SparseArraysExt = ["SparseArrays"]
[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
@@ -741,10 +769,14 @@ version = "2.6.2"
Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
[[deps.StyledStrings]]
uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
version = "1.11.0"
[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.2.1+1"
version = "7.8.3+2"
[[deps.TOML]]
deps = ["Dates"]
@@ -765,6 +797,7 @@ version = "0.1.1"
[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
version = "1.11.0"
[[deps.TranscodingStreams]]
git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
@@ -779,9 +812,11 @@ version = "1.6.1"
[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
version = "1.11.0"
[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
version = "1.11.0"
[[deps.UnicodeFun]]
deps = ["REPL"]
@@ -953,7 +988,7 @@ version = "1.6.0+0"
[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"
version = "1.3.1+2"
[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -988,7 +1023,7 @@ version = "0.17.4+0"
[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"
version = "5.15.0+0"
[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
@@ -1035,12 +1070,12 @@ version = "1.1.7+0"
[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"
version = "1.64.0+1"
[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"
version = "17.7.0+0"
[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]

14
justfile
View File

@@ -3,7 +3,7 @@ default: test_langs
test_langs:
# Test all languages and tools in this project
uv run python ./main.py
julia ./src/main.jl
julia --project=. ./src/main.jl
bun run ./index.ts
go run ./src/main.go
bash ./src/bscript.sh
@@ -13,7 +13,17 @@ test_langs:
nix flake metadata
neville:
julia -i ./src/neville-algo-ml.jl
julia --project=. -i ./src/neville-algo-ml.jl
doc:
typst compile ./src/ocs.typ
j:
@echo $(pwd)
julia --project=. -i ./src/dft.jl
# Setup python environment with uv
setup:
uv sync
# Instantiate julia
julia --project=. -e 'using Pkg; Pkg.instantiate()'

70
src/dft.jl Normal file
View File

@@ -0,0 +1,70 @@
using Plots
# https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition
function dft(x)
N = length(x)
[sum(x[n] * exp(-2im*pi*(k-1)*(n-1)/N) for n in 1:N) for k in 1:N]
end
# https://en.wikipedia.org/wiki/DFT_matrix
dft_matrix(N) = [exp(-2im*pi*(k-1)*(n-1)/N) for k=1:N, n=1:N]
function dft_matrix_transform(x)
N = length(x)
dft_matrix(N) * x
end
function evaluate_coefficients(x, coeffs)
res = 0
for (i, coeff) in enumerate(coeffs)
res += coeff * exp(2pi * im * (i - 1) * x)
end
return 1/length(coeffs) * res
end
function f(n)
xs = (0:n-1) ./ n
[x < 1/2 ? (x, x) : (x, 1 - x) for x in xs]
end
function main()
ns = [3, 6, 10, 15, 20, 25]
plt = plot(layout = (length(ns), 2), size = (1000, 1000))
for (row, n) in enumerate(ns)
points = f(n)
xs = getindex.(points, 1)
ys = getindex.(points, 2)
coeffs = dft_matrix_transform(ys)
xfine = range(0, 1, length=1000)
poly = [evaluate_coefficients(x, coeffs) for x in xfine]
plot!(
plt[row, 1],
xfine,
real.(poly),
title = "n = $n (real part)",
legend = false
)
scatter!(
plt[row, 1],
xs,
ys
)
plot!(
plt[row, 2],
xfine,
imag.(poly),
title = "n = $n (imag part)",
legend = false
)
end
gui(plt)
end
main()

2
src/neville-algo-ml.jl
View File

@@ -314,4 +314,4 @@ Erkenntnisse:
# Start the interactive part
# inter()
println("Use f() to start ml and inter() to start interactive mode.")
# println("Use f() to start ml and inter() to start interactive mode.")