simonbyrne/Manifest.toml

## Manifest.toml
# This file is machine-generated - editing it directly is not advised

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "0fac443759fa829ed8066db6cf1077d888bb6573"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "2.0.2"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Bzip2_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "5ccb0770e3d1c185a52e6d36e3ffb830639ed3d2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.6+3"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
git-tree-sha1 = "7a15e3690529fd1042f0ab954dff7445b1efc8a5"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.9.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "607c0ea16cb32af49ea2976f90c0c5acbca37d21"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.10.8"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"]
git-tree-sha1 = "5639e44833cfcf78c6a73fbceb4da75611d312cd"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.3"

[[CompilerSupportLibraries_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "7c4f882c41faa72118841185afc58a2eb00ef612"
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "0.3.3+0"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "81685fee51fc5168898e3cbd8b0f01506cd9148e"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.4"

[[DataAPI]]
git-tree-sha1 = "176e23402d80e7743fc26c19c681bfb11246af32"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.3.0"

[[DataStructures]]
deps = ["InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "88d48e133e6d3dd68183309877eac74393daa7eb"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.17.20"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[FFMPEG]]
deps = ["FFMPEG_jll", "x264_jll"]
git-tree-sha1 = "9a73ffdc375be61b0e4516d83d880b265366fe1f"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.0"

[[FFMPEG_jll]]
deps = ["Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "1af4493ff9a069e26a538d6f113816b237d3cc37"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.3.1+1"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[FreeType2_jll]]
deps = ["Bzip2_jll", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "158698cb8b27eccc7a0de16b73ca7912e164d88b"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.1+3"

[[FriBidi_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "94e98e5597e745d9fb3094d89c7b0b754204c9dd"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.5+4"

[[GR]]
deps = ["Base64", "DelimitedFiles", "HTTP", "JSON", "LinearAlgebra", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "e26c513329675092535de20cc4bb9c579c8f85a0"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.51.0"

[[GeometryBasics]]
deps = ["IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "119f32f9c2b497b49cd3f7f513b358b82660294c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.2.15"

[[GeometryTypes]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "34bfa994967e893ab2f17b864eec221b3521ba4d"
uuid = "4d00f742-c7ba-57c2-abde-4428a4b178cb"
version = "0.8.3"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets"]
git-tree-sha1 = "2ac03263ce44be4222342bca1c51c36ce7566161"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.8.17"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "b34d7cef7b337321e97d22242c3c2b91f476748e"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.0"

[[LAME_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "a7999edc634307964d5651265ebf7c2e14b4ef91"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.0+2"

[[LibGit2]]
deps = ["Printf"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibVPX_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "e02378f5707d0f94af22b99e4aba798e20368f6e"
uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
version = "1.9.0+0"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "426a6978b03a97ceb7ead77775a1da066343ec6e"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.2"

[[MbedTLS_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "a0cb0d489819fa7ea5f9fa84c7e7eba19d8073af"
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.16.6+1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "de0a5ce9e5289f27df672ffabef4d1e5861247d5"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "0.4.3"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MsgPack]]
deps = ["Serialization"]
git-tree-sha1 = "a8cbf066b54d793b9a48c5daa5d586cf2b5bd43d"
uuid = "99f44e22-a591-53d1-9472-aa23ef4bd671"
version = "1.1.0"

[[NaNMath]]
git-tree-sha1 = "c84c576296d0e2fbb3fc134d3e09086b3ea617cd"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.4"

[[Ogg_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "4c3275cda1ba99d1244d0b82a9d0ca871c3cf66b"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.4+1"

[[OpenSSL_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "997359379418d233767f926ea0c43f0e731735c0"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.1+5"

[[OpenSpecFun_jll]]
deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.3+3"

[[Opus_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "cc90a125aa70dbb069adbda2b913b02cf2c5f6fe"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.1+2"

[[OrderedCollections]]
git-tree-sha1 = "293b70ac1780f9584c89268a6e2a560d938a7065"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.3.0"

[[Parsers]]
deps = ["Dates", "Test"]
git-tree-sha1 = "8077624b3c450b15c087944363606a6ba12f925e"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "1.0.10"

[[Pkg]]
deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "c6f5ea535551b3b16835134697f0c65d06c94b91"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.0"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "e18e0e51ff07bf92bb7e06dcb9c082a4e125e20c"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.5"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "GeometryTypes", "JSON", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
git-tree-sha1 = "8c22b5e0b625bda0e784d60805a4cabea8cbf128"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.6.0"

[[Pluto]]
deps = ["Base64", "Distributed", "HTTP", "InteractiveUtils", "Markdown", "MsgPack", "Pkg", "REPL", "Sockets", "UUIDs"]
git-tree-sha1 = "1a45003ca6729c36cda3f5b972abd7fdfc14c2ee"
uuid = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
version = "0.11.6"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RecipesBase]]
git-tree-sha1 = "58de8f7e33b7fda6ee39eff65169cd1e19d0c107"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.0.2"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "84ff6ab4187fb812522e7e3e6447107110171e62"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.1.12"

[[Reexport]]
deps = ["Pkg"]
git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "0.2.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "d37400976e98018ee840e0ca4f9d20baa231dc6b"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.0.1"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[Showoff]]
deps = ["Dates"]
git-tree-sha1 = "e032c9df551fb23c9f98ae1064de074111b7bc39"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "0.3.1"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures", "Random", "Test"]
git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "0.3.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["OpenSpecFun_jll"]
git-tree-sha1 = "d8d8b8a9f4119829410ecd706da4cc8594a1e020"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "0.10.3"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "016d1e1a00fabc556473b07161da3d39726ded35"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "0.12.4"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
git-tree-sha1 = "a6102b1f364befdb05746f386b67c6b7e3262c45"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.0"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "Tables"]
git-tree-sha1 = "8099ed9fb90b6e754d6ba8c6ed8670f010eadca0"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.4.4"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.0"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "b7f762e9820b7fab47544c36f26f54ac59cf8abf"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.0.5"

[[Test]]
deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[Zlib_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "d5bba6485811931e4b8958e2d7ca3738273ac468"
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.11+15"

[[libass_jll]]
deps = ["Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "f02d0db58888592e98c5f4953cef620ce9274eee"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+3"

[[libfdk_aac_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "e17b4513993b4413d31cffd1b36a63625ebbc3d3"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+3"

[[libvorbis_jll]]
deps = ["Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "8014e1c1033009edcfe820ec25877a9f1862ba4c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.6+5"

[[x264_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "e496625b900df1b02ab0e02fad316b77446616ef"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+1"

[[x265_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "ac7d44fa1639a780d0ae79ca1a5a7f4181131825"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+2"

## notebook.jl
### A Pluto.jl notebook ###
# v0.11.6

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 3f996c02-e0a5-11ea-3466-9f2152d94f79
using Plots, SpecialFunctions, LinearAlgebra, Random

# ╔═╡ e2d0b5d6-e0a7-11ea-14a9-57767aa28a1d
function matern(d,ν,ρ=1,σ=1)
	if d == 0
		a = one(d)
	elseif ν == 0
		a = zero(d)
	else
		λ = sqrt(2ν)*d/ρ
		a = 2.0^(1-ν)/gamma(ν) * besselkx(ν,λ) * exp(ν * log(λ) - λ)
	end
	σ^2 * a
end

# ╔═╡ 797fa7ca-e0a9-11ea-2a8c-57a263d29eab
X = 0:0.005:2

# ╔═╡ 3cc76dae-e0ac-11ea-2e10-a1699089f3f4
@bind ν html"<input type=range step=0.1 min=0.1 max=5>"

# ╔═╡ 9a506f62-e0a8-11ea-338e-251d3a12597e
Σ = [matern(abs(x-y),ν,1) for x in X, y in X]

# ╔═╡ 8c4090d8-e0ac-11ea-0d3e-1f5b486148f4
ν

# ╔═╡ e84f6918-e0a8-11ea-00bc-eb8af4ee93f5
let
	Random.seed!(2)
	E = eigen(Σ)
	plot(X, E.vectors * Diagonal(sqrt.(max.(E.values,0))) * randn(length(X),10), color="green", legend=false, alpha=0.3, ylim=(-3,3),
		yticks=(-2:2,["-2α","-α","0","α","2α"]),
		xticks=(0.5:1.5,["0","ρ"] ))
end

# ╔═╡ Cell order:
# ╠═3f996c02-e0a5-11ea-3466-9f2152d94f79
# ╠═e2d0b5d6-e0a7-11ea-14a9-57767aa28a1d
# ╠═797fa7ca-e0a9-11ea-2a8c-57a263d29eab
# ╠═9a506f62-e0a8-11ea-338e-251d3a12597e
# ╠═3cc76dae-e0ac-11ea-2e10-a1699089f3f4
# ╠═8c4090d8-e0ac-11ea-0d3e-1f5b486148f4
# ╠═e84f6918-e0a8-11ea-00bc-eb8af4ee93f5

## Project.toml
[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
	# This file is machine-generated - editing it directly is not advised

	[[Adapt]]
	deps = ["LinearAlgebra"]
	git-tree-sha1 = "0fac443759fa829ed8066db6cf1077d888bb6573"
	uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
	version = "2.0.2"

	[[Base64]]
	uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

	[[Bzip2_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "5ccb0770e3d1c185a52e6d36e3ffb830639ed3d2"
	uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
	version = "1.0.6+3"

	[[ColorSchemes]]
	deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
	git-tree-sha1 = "7a15e3690529fd1042f0ab954dff7445b1efc8a5"
	uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
	version = "3.9.0"

	[[ColorTypes]]
	deps = ["FixedPointNumbers", "Random"]
	git-tree-sha1 = "607c0ea16cb32af49ea2976f90c0c5acbca37d21"
	uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
	version = "0.10.8"

	[[Colors]]
	deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"]
	git-tree-sha1 = "5639e44833cfcf78c6a73fbceb4da75611d312cd"
	uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
	version = "0.12.3"

	[[CompilerSupportLibraries_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "7c4f882c41faa72118841185afc58a2eb00ef612"
	uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
	version = "0.3.3+0"

	[[Contour]]
	deps = ["StaticArrays"]
	git-tree-sha1 = "81685fee51fc5168898e3cbd8b0f01506cd9148e"
	uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
	version = "0.5.4"

	[[DataAPI]]
	git-tree-sha1 = "176e23402d80e7743fc26c19c681bfb11246af32"
	uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
	version = "1.3.0"

	[[DataStructures]]
	deps = ["InteractiveUtils", "OrderedCollections"]
	git-tree-sha1 = "88d48e133e6d3dd68183309877eac74393daa7eb"
	uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
	version = "0.17.20"

	[[DataValueInterfaces]]
	git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
	uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
	version = "1.0.0"

	[[Dates]]
	deps = ["Printf"]
	uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

	[[DelimitedFiles]]
	deps = ["Mmap"]
	uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

	[[Distributed]]
	deps = ["Random", "Serialization", "Sockets"]
	uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

	[[FFMPEG]]
	deps = ["FFMPEG_jll", "x264_jll"]
	git-tree-sha1 = "9a73ffdc375be61b0e4516d83d880b265366fe1f"
	uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
	version = "0.4.0"

	[[FFMPEG_jll]]
	deps = ["Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
	git-tree-sha1 = "1af4493ff9a069e26a538d6f113816b237d3cc37"
	uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
	version = "4.3.1+1"

	[[FixedPointNumbers]]
	deps = ["Statistics"]
	git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
	uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
	version = "0.8.4"

	[[FreeType2_jll]]
	deps = ["Bzip2_jll", "Libdl", "Pkg", "Zlib_jll"]
	git-tree-sha1 = "158698cb8b27eccc7a0de16b73ca7912e164d88b"
	uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
	version = "2.10.1+3"

	[[FriBidi_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "94e98e5597e745d9fb3094d89c7b0b754204c9dd"
	uuid = "559328eb-81f9-559d-9380-de523a88c83c"
	version = "1.0.5+4"

	[[GR]]
	deps = ["Base64", "DelimitedFiles", "HTTP", "JSON", "LinearAlgebra", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
	git-tree-sha1 = "e26c513329675092535de20cc4bb9c579c8f85a0"
	uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
	version = "0.51.0"

	[[GeometryBasics]]
	deps = ["IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
	git-tree-sha1 = "119f32f9c2b497b49cd3f7f513b358b82660294c"
	uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
	version = "0.2.15"

	[[GeometryTypes]]
	deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "StaticArrays"]
	git-tree-sha1 = "34bfa994967e893ab2f17b864eec221b3521ba4d"
	uuid = "4d00f742-c7ba-57c2-abde-4428a4b178cb"
	version = "0.8.3"

	[[HTTP]]
	deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets"]
	git-tree-sha1 = "2ac03263ce44be4222342bca1c51c36ce7566161"
	uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
	version = "0.8.17"

	[[IniFile]]
	deps = ["Test"]
	git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
	uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
	version = "0.5.0"

	[[InteractiveUtils]]
	deps = ["Markdown"]
	uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

	[[IterTools]]
	git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
	uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
	version = "1.3.0"

	[[IteratorInterfaceExtensions]]
	git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
	uuid = "82899510-4779-5014-852e-03e436cf321d"
	version = "1.0.0"

	[[JSON]]
	deps = ["Dates", "Mmap", "Parsers", "Unicode"]
	git-tree-sha1 = "b34d7cef7b337321e97d22242c3c2b91f476748e"
	uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
	version = "0.21.0"

	[[LAME_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "a7999edc634307964d5651265ebf7c2e14b4ef91"
	uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
	version = "3.100.0+2"

	[[LibGit2]]
	deps = ["Printf"]
	uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

	[[LibVPX_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "e02378f5707d0f94af22b99e4aba798e20368f6e"
	uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
	version = "1.9.0+0"

	[[Libdl]]
	uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

	[[LinearAlgebra]]
	deps = ["Libdl"]
	uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

	[[Logging]]
	uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

	[[Markdown]]
	deps = ["Base64"]
	uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

	[[MbedTLS]]
	deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
	git-tree-sha1 = "426a6978b03a97ceb7ead77775a1da066343ec6e"
	uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
	version = "1.0.2"

	[[MbedTLS_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "a0cb0d489819fa7ea5f9fa84c7e7eba19d8073af"
	uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
	version = "2.16.6+1"

	[[Measures]]
	git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
	uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
	version = "0.3.1"

	[[Missings]]
	deps = ["DataAPI"]
	git-tree-sha1 = "de0a5ce9e5289f27df672ffabef4d1e5861247d5"
	uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
	version = "0.4.3"

	[[Mmap]]
	uuid = "a63ad114-7e13-5084-954f-fe012c677804"

	[[MsgPack]]
	deps = ["Serialization"]
	git-tree-sha1 = "a8cbf066b54d793b9a48c5daa5d586cf2b5bd43d"
	uuid = "99f44e22-a591-53d1-9472-aa23ef4bd671"
	version = "1.1.0"

	[[NaNMath]]
	git-tree-sha1 = "c84c576296d0e2fbb3fc134d3e09086b3ea617cd"
	uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
	version = "0.3.4"

	[[Ogg_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "4c3275cda1ba99d1244d0b82a9d0ca871c3cf66b"
	uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
	version = "1.3.4+1"

	[[OpenSSL_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "997359379418d233767f926ea0c43f0e731735c0"
	uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
	version = "1.1.1+5"

	[[OpenSpecFun_jll]]
	deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
	git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
	uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
	version = "0.5.3+3"

	[[Opus_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "cc90a125aa70dbb069adbda2b913b02cf2c5f6fe"
	uuid = "91d4177d-7536-5919-b921-800302f37372"
	version = "1.3.1+2"

	[[OrderedCollections]]
	git-tree-sha1 = "293b70ac1780f9584c89268a6e2a560d938a7065"
	uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
	version = "1.3.0"

	[[Parsers]]
	deps = ["Dates", "Test"]
	git-tree-sha1 = "8077624b3c450b15c087944363606a6ba12f925e"
	uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
	version = "1.0.10"

	[[Pkg]]
	deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
	uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

	[[PlotThemes]]
	deps = ["PlotUtils", "Requires", "Statistics"]
	git-tree-sha1 = "c6f5ea535551b3b16835134697f0c65d06c94b91"
	uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
	version = "2.0.0"

	[[PlotUtils]]
	deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
	git-tree-sha1 = "e18e0e51ff07bf92bb7e06dcb9c082a4e125e20c"
	uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
	version = "1.0.5"

	[[Plots]]
	deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "GeometryTypes", "JSON", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
	git-tree-sha1 = "8c22b5e0b625bda0e784d60805a4cabea8cbf128"
	uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
	version = "1.6.0"

	[[Pluto]]
	deps = ["Base64", "Distributed", "HTTP", "InteractiveUtils", "Markdown", "MsgPack", "Pkg", "REPL", "Sockets", "UUIDs"]
	git-tree-sha1 = "1a45003ca6729c36cda3f5b972abd7fdfc14c2ee"
	uuid = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
	version = "0.11.6"

	[[Printf]]
	deps = ["Unicode"]
	uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

	[[REPL]]
	deps = ["InteractiveUtils", "Markdown", "Sockets"]
	uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

	[[Random]]
	deps = ["Serialization"]
	uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

	[[RecipesBase]]
	git-tree-sha1 = "58de8f7e33b7fda6ee39eff65169cd1e19d0c107"
	uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
	version = "1.0.2"

	[[RecipesPipeline]]
	deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
	git-tree-sha1 = "84ff6ab4187fb812522e7e3e6447107110171e62"
	uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
	version = "0.1.12"

	[[Reexport]]
	deps = ["Pkg"]
	git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
	uuid = "189a3867-3050-52da-a836-e630ba90ab69"
	version = "0.2.0"

	[[Requires]]
	deps = ["UUIDs"]
	git-tree-sha1 = "d37400976e98018ee840e0ca4f9d20baa231dc6b"
	uuid = "ae029012-a4dd-5104-9daa-d747884805df"
	version = "1.0.1"

	[[SHA]]
	uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

	[[Serialization]]
	uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

	[[Showoff]]
	deps = ["Dates"]
	git-tree-sha1 = "e032c9df551fb23c9f98ae1064de074111b7bc39"
	uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
	version = "0.3.1"

	[[Sockets]]
	uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

	[[SortingAlgorithms]]
	deps = ["DataStructures", "Random", "Test"]
	git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
	uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
	version = "0.3.1"

	[[SparseArrays]]
	deps = ["LinearAlgebra", "Random"]
	uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

	[[SpecialFunctions]]
	deps = ["OpenSpecFun_jll"]
	git-tree-sha1 = "d8d8b8a9f4119829410ecd706da4cc8594a1e020"
	uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
	version = "0.10.3"

	[[StaticArrays]]
	deps = ["LinearAlgebra", "Random", "Statistics"]
	git-tree-sha1 = "016d1e1a00fabc556473b07161da3d39726ded35"
	uuid = "90137ffa-7385-5640-81b9-e52037218182"
	version = "0.12.4"

	[[Statistics]]
	deps = ["LinearAlgebra", "SparseArrays"]
	uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

	[[StatsBase]]
	deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
	git-tree-sha1 = "a6102b1f364befdb05746f386b67c6b7e3262c45"
	uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
	version = "0.33.0"

	[[StructArrays]]
	deps = ["Adapt", "DataAPI", "Tables"]
	git-tree-sha1 = "8099ed9fb90b6e754d6ba8c6ed8670f010eadca0"
	uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
	version = "0.4.4"

	[[TableTraits]]
	deps = ["IteratorInterfaceExtensions"]
	git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e"
	uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
	version = "1.0.0"

	[[Tables]]
	deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
	git-tree-sha1 = "b7f762e9820b7fab47544c36f26f54ac59cf8abf"
	uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
	version = "1.0.5"

	[[Test]]
	deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
	uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

	[[UUIDs]]
	deps = ["Random", "SHA"]
	uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

	[[Unicode]]
	uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

	[[Zlib_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "d5bba6485811931e4b8958e2d7ca3738273ac468"
	uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
	version = "1.2.11+15"

	[[libass_jll]]
	deps = ["Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "Libdl", "Pkg", "Zlib_jll"]
	git-tree-sha1 = "f02d0db58888592e98c5f4953cef620ce9274eee"
	uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
	version = "0.14.0+3"

	[[libfdk_aac_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "e17b4513993b4413d31cffd1b36a63625ebbc3d3"
	uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
	version = "0.1.6+3"

	[[libvorbis_jll]]
	deps = ["Libdl", "Ogg_jll", "Pkg"]
	git-tree-sha1 = "8014e1c1033009edcfe820ec25877a9f1862ba4c"
	uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
	version = "1.3.6+5"

	[[x264_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "e496625b900df1b02ab0e02fad316b77446616ef"
	uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
	version = "2020.7.14+1"

	[[x265_jll]]
	deps = ["Libdl", "Pkg"]
	git-tree-sha1 = "ac7d44fa1639a780d0ae79ca1a5a7f4181131825"
	uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
	version = "3.0.0+2"
	### A Pluto.jl notebook ###
	# v0.11.6

	using Markdown
	using InteractiveUtils

	# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
	macro bind(def, element)
	quote
	local el = $(esc(element))
	global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
	el
	end
	end

	# ╔═╡ 3f996c02-e0a5-11ea-3466-9f2152d94f79
	using Plots, SpecialFunctions, LinearAlgebra, Random

	# ╔═╡ e2d0b5d6-e0a7-11ea-14a9-57767aa28a1d
	function matern(d,ν,ρ=1,σ=1)
	if d == 0
	a = one(d)
	elseif ν == 0
	a = zero(d)
	else
	λ = sqrt(2ν)*d/ρ
	a = 2.0^(1-ν)/gamma(ν) * besselkx(ν,λ) * exp(ν * log(λ) - λ)
	end
	σ^2 * a
	end

	# ╔═╡ 797fa7ca-e0a9-11ea-2a8c-57a263d29eab
	X = 0:0.005:2

	# ╔═╡ 3cc76dae-e0ac-11ea-2e10-a1699089f3f4
	@bind ν html"<input type=range step=0.1 min=0.1 max=5>"

	# ╔═╡ 9a506f62-e0a8-11ea-338e-251d3a12597e
	Σ = [matern(abs(x-y),ν,1) for x in X, y in X]

	# ╔═╡ 8c4090d8-e0ac-11ea-0d3e-1f5b486148f4
	ν

	# ╔═╡ e84f6918-e0a8-11ea-00bc-eb8af4ee93f5
	let
	Random.seed!(2)
	E = eigen(Σ)
	plot(X, E.vectors * Diagonal(sqrt.(max.(E.values,0))) * randn(length(X),10), color="green", legend=false, alpha=0.3, ylim=(-3,3),
	yticks=(-2:2,["-2α","-α","0","α","2α"]),
	xticks=(0.5:1.5,["0","ρ"] ))
	end

	# ╔═╡ Cell order:
	# ╠═3f996c02-e0a5-11ea-3466-9f2152d94f79
	# ╠═e2d0b5d6-e0a7-11ea-14a9-57767aa28a1d
	# ╠═797fa7ca-e0a9-11ea-2a8c-57a263d29eab
	# ╠═9a506f62-e0a8-11ea-338e-251d3a12597e
	# ╠═3cc76dae-e0ac-11ea-2e10-a1699089f3f4
	# ╠═8c4090d8-e0ac-11ea-0d3e-1f5b486148f4
	# ╠═e84f6918-e0a8-11ea-00bc-eb8af4ee93f5
	[deps]
	LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
	Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
	Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
	Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
	SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"