diff --git a/Acoustic Localization Using Carrier-Phase Measurements b/Acoustic Localization Using Carrier-Phase Measurements
index 2f2f5f8..c9f7a67 100644
--- a/Acoustic Localization Using Carrier-Phase Measurements	
+++ b/Acoustic Localization Using Carrier-Phase Measurements	
@@ -7,15 +7,18 @@ using InteractiveUtils
 # ╔═╡ d3b7f59a-712b-4520-a413-c5f5eb71a12f
 begin
 	using PlutoUI
-	TableOfContents()
-	md"- Pakcages"
+	using Plots
+	using LinearAlgebra
+	# using JuMP, Cbc
+	using Optim, LineSearches
+	using Statistics # for mean...
 end
 
 # ╔═╡ 29893d76-8153-4b84-89ac-289e41327205
 md"""
 # Acoustic Localization Using Carrier-Phase Measurements
 
-## Introduction
+# Introduction
 
 TODO!
 
@@ -44,7 +47,7 @@ TODO!
 
 # ╔═╡ 835ef9c7-727a-4672-bba4-58aa6766b9e6
 md"""
-# Outline of the solution
+## Outline of The Solution
 
 !!! info "This text is copied from the provided document."
 
@@ -54,24 +57,224 @@ md"""
 			      \alpha_i^{-2} (r_i - \|x-b_i\|_2)^2
 			    + \sigma_i^{-2} (\varphi_i - \|x-b_i\|_2 - n_i)^2
 	```
-where n ≜ [n1, n2, · · · , nM]T. Hence, we can obtain a MD position estimate by solving the following mixed integer optimization
-problem:
-ˆx, ˆn =
-arg min
-x∈R3,n∈ZMf(x, n)
+	where ``\mathbf{n} \triangleq [n_1, n_2, · · · , n_M]^T``. Hence, we can obtain a MD position estimate by solving the following mixed integer optimization problem:
+	```math
+	\hat x,\, \hat n =
+	\operatorname*{arg\,min}_{x\in R^3,\, n\in\mathbb{Z}^M}f(x, n)
+	```	
+	We can solve (4) through the following steps:
+	1. Obtain a float solution (FS) of (4) by ignoring the integer constraints.
+	2. Find a decomposition of the objective function around the FS.
+	3. Develop a search algorithm using the FS and the decomposition.
+"""
+
+# ╔═╡ 57546347-5dc6-4f59-9e61-d57bc3bee3e5
+b = [[1  1  10]
+	 [2  6 10]
+	 [7  7 10]
+	 [7 3 10]]'
+
+# ╔═╡ 428c1a49-2825-43a2-920d-46d9a9950455
+begin
+	_, M = size(b)
+	md"""
+	# An Attempt to Solve this Problem...
+	> Note: I try to solve  the problem generally, the examples are for demonstration purposes. 
+	
+	Lets assume that we have `b` beacons as follows, of size ``M=``**$(M)**:
+	
+	"""
+end
+
+# ╔═╡ 4d9c23f1-4544-4b4b-ac59-26d534be10a9
+md"""
+And our mobile device ``x`` is:
+"""
+
+# ╔═╡ b089c934-de4f-483f-a2a7-96aa0d26f29d
+x = [3 5 3]'
+
+# ╔═╡ fdb7ab79-4715-4ed7-92d2-81b4f6ba2734
+md"""
+*Global Variable* such as ``\alpha^2`` and ``\sigma^2`` are defined here for convenience. To help debugging, we force a `seed` to keep things consistant.
+"""
+
+# ╔═╡ 51b790fc-887a-4d05-b9cc-288c6ee22b11
+begin
+	import Random
+	Random.seed!(123)
+	
+end
+
+# ╔═╡ f62bb0be-9891-4670-93c8-bd3207fc49fb
+alpha = 0.1;
+
+# ╔═╡ fbd815c1-994d-4673-a4e6-3501d190edc0
+range_noise = randn(M) * alpha;
+
+# ╔═╡ a5c5c885-a8d2-4b5b-84a6-26d1220bb89e
+sigma = 0.1;
+
+# ╔═╡ 4063cc32-a506-47f9-af52-07fe7594bcd9
+phase_noise = randn(M) * sigma;
+
+# ╔═╡ 11f45a3f-d773-4d20-95fb-c9843b18da62
+phase_n = 0;
+
+# ╔═╡ bdba2216-b866-4b53-9032-50af0b3eec0f
+md"""
+---
+"""
+
+# ╔═╡ 20ba966c-7f63-4e9c-9513-3d217c7b2b77
+md"""
+In the next steps, we try to find ``x`` in the most optimal/efficient method..
+"""
+
+# ╔═╡ 44ad3946-c1f8-4485-9db2-41d862fb41a2
+md"""
+We can Visualize this configuration in 3D space:
+"""
+
+# ╔═╡ 9a74694b-54f9-4a7e-8777-4d732034f53b
+begin
+	scatter( b[1,:], b[2,:], b[3,:], label="Beacons", markersize = 10)
+	scatter!(x[1,:], x[2,:], x[3,:], label="MD", markersize = 10)
+end
+
+# ╔═╡ 3f34e354-137f-4614-bea9-ea3110715cae
+md"""
+## Using range measurments only
+
+If we ignore the noise and the phase measurments, we notice that our solution can be solved analytically in the form:
+
+```math
+\begin{eqnarray} 
+(x - x_1)^2 + (y - y_1)^2 + (z - z_1)^2 &= r_1^2 \\
+(x - x_2)^2 + (y - y_2)^2 + (z - z_2)^2 &= r_2^2 \\
+(x - x_3)^2 + (y - y_3)^2 + (z - z_3)^2 &= r_3^2 
+
+\end{eqnarray} 
+
+```
+
+Where ``x_i,\, y_i,\, z_i`` are the locations of the beacon ``b_i``, and ``r_i`` is the distance from the beacon to the MD.
+
+*However this method neither scalas well when we increase the number of beacons, nor can it be solved if there is noise withen the data.*
+
+Nevertheless, solving this problem numerically is trivial.
+We know that that distance ``r`` from each beacon is `r_no_phase_or_noise`:
 """
 
+# ╔═╡ 985f2cfb-1965-49de-ad1a-787fe11e9394
+md"""
+we can see that the result of `x_no_phase_or_noise` is very similar to the MD's original position = `x`, as expected.
+"""
+
+# ╔═╡ b239dd0a-5527-4f74-b2fb-d15ff3caa011
+md"""
+## Using Range and Phase
+We now add a noise process of zero mean and variance ``\alpha^2`` to our equation.
+"""
+
+# ╔═╡ a7f1e580-fcb0-4833-b463-d97cf918c4f3
+
+
+# ╔═╡ 786f3a79-424d-4e42-a6af-0624ecc87ff3
+# Acoustic Localization Using Carrier Phase Measurments
+
+# Give  beacons located at  trasmitting signals which are recieved by a mobile device (MD) located at 
+# clear; clc;
+# Starting values...
+# x = [1   2   3]'; % Mobile Device
+# b = [4   3   4;
+#      5   4   6;
+#      7   8   9;
+#      10 11   12]';
+# [~, M] = size(b); % Number of Beacons
+# sigma = 0.1;
+
+# w = rand(1, M) * sigma;   % White Noise
+ 
+# The range measurments for the beacons can be modelled as:
+# (PS: We use a search algorithm because noise would cause us to not have a numerical solution)
+# r = vecnorm(b - x) + w
+# Outline of The Solution
+# To formulate the estimation problem. We have  and , we need to find .
+# f1 = @(point) mean((r - vecnorm(point - b)).^2);
+# fminsearch(f1,x)'
+# Adding Phase
+# The phase data can be described as:
+
+# n = rand(1, M) * 0;
+# v = rand(1, M) * 0.01;
+# phi = vecnorm(b-x) + n + v
+# Soln W/ Phase
+# f2 = @(point) mean((r   - vecnorm(point(1:3) - b)).^2) ...
+#            + mean((phi - vecnorm(point(1:3) - b) - point(4)).^2);
+
+# initial_guess = [x; 5]; % (1:3) => point. (4) => n.
+# fminsearch(f2, initial_guess)'
+
+
+
+# ╔═╡ f9e80776-0c5e-4ae5-b9ed-e0896bec970d
+
+
 # ╔═╡ 6040b344-d338-11ee-256a-67ae4cb673c6
 md"""
 # Appendex
 """
 
+# ╔═╡ ed6a19ef-fd4f-43b2-aa09-aa7fe38f52ed
+TableOfContents()
+
+# ╔═╡ 1929d137-dcc9-4208-992d-71001f976466
+vecnorm(v) = norm.(eachcol(v))
+
+# ╔═╡ 67c2acf3-52ea-4132-9372-d50d2c837ce8
+r_no_phase_or_noise = vecnorm(b .- x)
+
+# ╔═╡ 6abf7266-8ef4-43e7-a7ec-ced409129ced
+r = vecnorm(b .- x) + range_noise
+
+# ╔═╡ 48843f6a-cda7-4a34-b459-da1b66a48e06
+phi = vecnorm(b .- x) + phase_noise .+ phase_n
+
+# ╔═╡ 3a61a22c-07a4-4cd2-91ad-b573d8b01f30
+function minimize(f, x0) 
+	result = optimize(f,
+		x0,
+		LBFGS(linesearch = LineSearches.HagerZhang()),Optim.Options(extended_trace=true,show_every=0,store_trace = true,show_trace = false))
+end
+
+# ╔═╡ 9d567a1b-4c56-42f9-9762-a9f226bb6a51
+x_no_phase_or_noise = begin
+	f_no_phase_or_noise(point) = # Define the minimization function LSE
+		mean((r_no_phase_or_noise - vecnorm(point .- b)).^2);
+	local x = [0.0, 0.0, 0.0]  # First Guess
+	local res = minimize(f_no_phase_or_noise, x)
+	local vals = map(x-> x.value, res.trace)
+	local iterations = map(x-> x.iteration, res.trace)
+	plot(iterations, vals)
+	local points = map(x-> x.metadata["x"], res.trace)
+end
+
 # ╔═╡ 00000000-0000-0000-0000-000000000001
 PLUTO_PROJECT_TOML_CONTENTS = """
 [deps]
+LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
+LineSearches = "~7.2.0"
+Optim = "~1.9.2"
+Plots = "~1.40.1"
 PlutoUI = "~0.7.58"
 """
 
@@ -81,7 +284,7 @@ PLUTO_MANIFEST_TOML_CONTENTS = """
 
 julia_version = "1.10.1"
 manifest_format = "2.0"
-project_hash = "acf8a7d70217bc877a8d448fd5475fd91c6dd480"
+project_hash = "a67b74f724a1878f5548d5c26434b81fcca4b2c6"
 
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 deps = ["Pkg"]
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+
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+
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+version = "0.4.1"
+
+[[deps.FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.4.4+1"
+
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
+[[deps.FillArrays]]
+deps = ["LinearAlgebra", "Random"]
+git-tree-sha1 = "5b93957f6dcd33fc343044af3d48c215be2562f1"
+uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
+version = "1.9.3"
+
+    [deps.FillArrays.extensions]
+    FillArraysPDMatsExt = "PDMats"
+    FillArraysSparseArraysExt = "SparseArrays"
+    FillArraysStatisticsExt = "Statistics"
+
+    [deps.FillArrays.weakdeps]
+    PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[deps.FiniteDiff]]
+deps = ["ArrayInterface", "LinearAlgebra", "Requires", "Setfield", "SparseArrays"]
+git-tree-sha1 = "73d1214fec245096717847c62d389a5d2ac86504"
+uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
+version = "2.22.0"
+
+    [deps.FiniteDiff.extensions]
+    FiniteDiffBandedMatricesExt = "BandedMatrices"
+    FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
+    FiniteDiffStaticArraysExt = "StaticArrays"
+
+    [deps.FiniteDiff.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
 [[deps.FixedPointNumbers]]
 deps = ["Statistics"]
 git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
 version = "0.8.4"
 
+[[deps.Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.93+0"
+
+[[deps.Formatting]]
+deps = ["Printf"]
+git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
+uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
+version = "0.4.2"
+
+[[deps.ForwardDiff]]
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
+git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
+uuid = "f6369f11-7733-5829-9624-2563aa707210"
+version = "0.10.36"
+
+    [deps.ForwardDiff.extensions]
+    ForwardDiffStaticArraysExt = "StaticArrays"
+
+    [deps.ForwardDiff.weakdeps]
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
+[[deps.FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.13.1+0"
+
+[[deps.FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.10+0"
+
+[[deps.Future]]
+deps = ["Random"]
+uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
+
+[[deps.GLFW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
+git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb"
+uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
+version = "3.3.9+0"
+
+[[deps.GR]]
+deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
+git-tree-sha1 = "3458564589be207fa6a77dbbf8b97674c9836aab"
+uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
+version = "0.73.2"
+
+[[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 = "77f81da2964cc9fa7c0127f941e8bce37f7f1d70"
+uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
+version = "0.73.2+0"
+
+[[deps.Gettext_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
+uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
+version = "0.21.0+0"
+
+[[deps.Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
+git-tree-sha1 = "e94c92c7bf4819685eb80186d51c43e71d4afa17"
+uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
+version = "2.76.5+0"
+
+[[deps.Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.14+0"
+
+[[deps.Grisu]]
+git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
+uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
+version = "1.0.2"
+
+[[deps.HTTP]]
+deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
+git-tree-sha1 = "ac7b73d562b8f4287c3b67b4c66a5395a19c1ae8"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "1.10.2"
+
+[[deps.HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.8.1+1"
+
 [[deps.Hyperscript]]
 deps = ["Test"]
 git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
@@ -150,12 +679,78 @@ version = "0.2.4"
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
+[[deps.IrrationalConstants]]
+git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.2.2"
+
+[[deps.JLFzf]]
+deps = ["Pipe", "REPL", "Random", "fzf_jll"]
+git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af"
+uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
+version = "0.1.7"
+
+[[deps.JLLWrappers]]
+deps = ["Artifacts", "Preferences"]
+git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
+uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
+version = "1.5.0"
+
 [[deps.JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
 git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.4"
 
+[[deps.JpegTurbo_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "3336abae9a713d2210bb57ab484b1e065edd7d23"
+uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
+version = "3.0.2+0"
+
+[[deps.LAME_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
+uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
+version = "3.100.1+0"
+
+[[deps.LERC_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
+uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
+version = "3.0.0+1"
+
+[[deps.LLVMOpenMP_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713"
+uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
+version = "15.0.7+0"
+
+[[deps.LZO_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
+uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
+version = "2.10.1+0"
+
+[[deps.LaTeXStrings]]
+git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
+uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+version = "1.3.1"
+
+[[deps.Latexify]]
+deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
+git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.16.1"
+
+    [deps.Latexify.extensions]
+    DataFramesExt = "DataFrames"
+    SymEngineExt = "SymEngine"
+
+    [deps.Latexify.weakdeps]
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
+
 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
@@ -183,27 +778,132 @@ version = "1.11.0+1"
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[deps.Libffi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
+uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
+version = "3.2.2+1"
+
+[[deps.Libgcrypt_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
+git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
+uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
+version = "1.8.7+0"
+
+[[deps.Libglvnd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
+git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
+uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
+version = "1.6.0+0"
+
+[[deps.Libgpg_error_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
+uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
+version = "1.42.0+0"
+
+[[deps.Libiconv_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
+uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
+version = "1.17.0+0"
+
+[[deps.Libmount_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
+uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
+version = "2.35.0+0"
+
+[[deps.Libtiff_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a"
+uuid = "89763e89-9b03-5906-acba-b20f662cd828"
+version = "4.5.1+1"
+
+[[deps.Libuuid_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
+uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
+version = "2.36.0+0"
+
+[[deps.LineSearches]]
+deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
+git-tree-sha1 = "7bbea35cec17305fc70a0e5b4641477dc0789d9d"
+uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
+version = "7.2.0"
+
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[deps.LogExpFunctions]]
+deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.3.27"
+
+    [deps.LogExpFunctions.extensions]
+    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
+    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
+    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"
+
+    [deps.LogExpFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[deps.LoggingExtras]]
+deps = ["Dates", "Logging"]
+git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075"
+uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
+version = "1.0.3"
+
 [[deps.MIMEs]]
 git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
 uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
 version = "0.1.4"
 
+[[deps.MacroTools]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
+uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+version = "0.5.13"
+
 [[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[deps.MathOptInterface]]
+deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "DataStructures", "ForwardDiff", "JSON", "LinearAlgebra", "MutableArithmetics", "NaNMath", "OrderedCollections", "PrecompileTools", "Printf", "SparseArrays", "SpecialFunctions", "Test", "Unicode"]
+git-tree-sha1 = "e8b98c868029d007102dc5f98986c81f33b0ec37"
+uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+version = "1.26.0"
+
+[[deps.MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
+git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.1.9"
+
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 version = "2.28.2+1"
 
+[[deps.Measures]]
+git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
+version = "0.3.2"
+
+[[deps.Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "1.1.0"
+
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
@@ -211,32 +911,156 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.1.10"
 
+[[deps.MutableArithmetics]]
+deps = ["LinearAlgebra", "SparseArrays", "Test"]
+git-tree-sha1 = "302fd161eb1c439e4115b51ae456da4e9984f130"
+uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
+version = "1.4.1"
+
+[[deps.NLSolversBase]]
+deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
+git-tree-sha1 = "a0b464d183da839699f4c79e7606d9d186ec172c"
+uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
+version = "7.8.3"
+
+[[deps.NaNMath]]
+deps = ["OpenLibm_jll"]
+git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+version = "1.0.2"
+
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
 
+[[deps.Ogg_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
+uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
+version = "1.3.5+1"
+
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 version = "0.3.23+4"
 
+[[deps.OpenLibm_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
+version = "0.8.1+2"
+
+[[deps.OpenSSL]]
+deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
+git-tree-sha1 = "51901a49222b09e3743c65b8847687ae5fc78eb2"
+uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
+version = "1.4.1"
+
+[[deps.OpenSSL_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "60e3045590bd104a16fefb12836c00c0ef8c7f8c"
+uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
+version = "3.0.13+0"
+
+[[deps.OpenSpecFun_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.5+0"
+
+[[deps.Optim]]
+deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "MathOptInterface", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "d024bfb56144d947d4fafcd9cb5cafbe3410b133"
+uuid = "429524aa-4258-5aef-a3af-852621145aeb"
+version = "1.9.2"
+
+[[deps.Opus_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
+uuid = "91d4177d-7536-5919-b921-800302f37372"
+version = "1.3.2+0"
+
+[[deps.OrderedCollections]]
+git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.6.3"
+
+[[deps.PCRE2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
+version = "10.42.0+1"
+
+[[deps.Parameters]]
+deps = ["OrderedCollections", "UnPack"]
+git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
+uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
+version = "0.12.3"
+
 [[deps.Parsers]]
 deps = ["Dates", "PrecompileTools", "UUIDs"]
 git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.8.1"
 
+[[deps.Pipe]]
+git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
+uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
+version = "1.3.0"
+
+[[deps.Pixman_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
+git-tree-sha1 = "64779bc4c9784fee475689a1752ef4d5747c5e87"
+uuid = "30392449-352a-5448-841d-b1acce4e97dc"
+version = "0.42.2+0"
+
 [[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.10.0"
 
+[[deps.PlotThemes]]
+deps = ["PlotUtils", "Statistics"]
+git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
+uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
+version = "3.1.0"
+
+[[deps.PlotUtils]]
+deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
+git-tree-sha1 = "862942baf5663da528f66d24996eb6da85218e76"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "1.4.0"
+
+[[deps.Plots]]
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
+git-tree-sha1 = "c4fa93d7d66acad8f6f4ff439576da9d2e890ee0"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+version = "1.40.1"
+
+    [deps.Plots.extensions]
+    FileIOExt = "FileIO"
+    GeometryBasicsExt = "GeometryBasics"
+    IJuliaExt = "IJulia"
+    ImageInTerminalExt = "ImageInTerminal"
+    UnitfulExt = "Unitful"
+
+    [deps.Plots.weakdeps]
+    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
+    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
 [[deps.PlutoUI]]
 deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
 git-tree-sha1 = "71a22244e352aa8c5f0f2adde4150f62368a3f2e"
 uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
 version = "0.7.58"
 
+[[deps.PositiveFactorizations]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
+uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
+version = "0.2.4"
+
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "03b4c25b43cb84cee5c90aa9b5ea0a78fd848d2f"
@@ -253,6 +1077,16 @@ version = "1.4.1"
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[deps.Profile]]
+deps = ["Printf"]
+uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
+
+[[deps.Qt6Base_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
+git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b"
+uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
+version = "6.5.3+1"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -261,31 +1095,117 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[deps.RecipesBase]]
+deps = ["PrecompileTools"]
+git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
+uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+version = "1.3.4"
+
+[[deps.RecipesPipeline]]
+deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
+git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
+uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
+version = "0.6.12"
+
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
+[[deps.RelocatableFolders]]
+deps = ["SHA", "Scratch"]
+git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
+uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
+version = "1.0.1"
+
+[[deps.Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "1.3.0"
+
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.Scratch]]
+deps = ["Dates"]
+git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
+uuid = "6c6a2e73-6563-6170-7368-637461726353"
+version = "1.2.1"
+
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
+[[deps.Setfield]]
+deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
+git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
+uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+version = "1.1.1"
+
+[[deps.Showoff]]
+deps = ["Dates", "Grisu"]
+git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "1.0.3"
+
+[[deps.SimpleBufferStream]]
+git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
+uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
+version = "1.1.0"
+
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
+[[deps.SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.2.1"
+
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 version = "1.10.0"
 
+[[deps.SpecialFunctions]]
+deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "e2cfc4012a19088254b3950b85c3c1d8882d864d"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.3.1"
+
+    [deps.SpecialFunctions.extensions]
+    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"
+
+    [deps.SpecialFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[[deps.StaticArraysCore]]
+git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d"
+uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+version = "1.4.2"
+
 [[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 version = "1.10.0"
 
+[[deps.StatsAPI]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.7.0"
+
+[[deps.StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "1d77abd07f617c4868c33d4f5b9e1dbb2643c9cf"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.34.2"
+
+[[deps.SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
 [[deps.SuiteSparse_jll]]
 deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
@@ -301,10 +1221,25 @@ deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 version = "1.10.0"
 
+[[deps.TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
 [[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[deps.TranscodingStreams]]
+git-tree-sha1 = "54194d92959d8ebaa8e26227dbe3cdefcdcd594f"
+uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
+version = "0.10.3"
+weakdeps = ["Random", "Test"]
+
+    [deps.TranscodingStreams.extensions]
+    TestExt = ["Test", "Random"]
+
 [[deps.Tricks]]
 git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f"
 uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
@@ -319,19 +1254,307 @@ version = "1.5.1"
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
+[[deps.UnPack]]
+git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
+uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+version = "1.0.2"
+
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
+[[deps.Unitful]]
+deps = ["Dates", "LinearAlgebra", "Random"]
+git-tree-sha1 = "3c793be6df9dd77a0cf49d80984ef9ff996948fa"
+uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "1.19.0"
+
+    [deps.Unitful.extensions]
+    ConstructionBaseUnitfulExt = "ConstructionBase"
+    InverseFunctionsUnitfulExt = "InverseFunctions"
+
+    [deps.Unitful.weakdeps]
+    ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
+[[deps.UnitfulLatexify]]
+deps = ["LaTeXStrings", "Latexify", "Unitful"]
+git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
+uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
+version = "1.6.3"
+
+[[deps.Unzip]]
+git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.2.0"
+
+[[deps.Vulkan_Loader_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
+git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
+uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
+version = "1.3.243+0"
+
+[[deps.Wayland_jll]]
+deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
+uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
+version = "1.21.0+1"
+
+[[deps.Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
+uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
+version = "1.31.0+0"
+
+[[deps.XML2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
+git-tree-sha1 = "801cbe47eae69adc50f36c3caec4758d2650741b"
+uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
+version = "2.12.2+0"
+
+[[deps.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"
+
+[[deps.XZ_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632"
+uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
+version = "5.4.6+0"
+
+[[deps.Xorg_libICE_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "e5becd4411063bdcac16be8b66fc2f9f6f1e8fe5"
+uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
+version = "1.0.10+1"
+
+[[deps.Xorg_libSM_jll]]
+deps = ["Libdl", "Pkg", "Xorg_libICE_jll"]
+git-tree-sha1 = "4a9d9e4c180e1e8119b5ffc224a7b59d3a7f7e18"
+uuid = "c834827a-8449-5923-a945-d239c165b7dd"
+version = "1.2.3+0"
+
+[[deps.Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
+uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
+version = "1.8.6+0"
+
+[[deps.Xorg_libXau_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
+uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
+version = "1.0.11+0"
+
+[[deps.Xorg_libXcursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
+version = "1.2.0+4"
+
+[[deps.Xorg_libXdmcp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
+uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
+version = "1.1.4+0"
+
+[[deps.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"
+
+[[deps.Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[deps.Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[deps.Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
+version = "1.1.4+4"
+
+[[deps.Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
+version = "1.5.2+4"
+
+[[deps.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"
+
+[[deps.Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
+version = "0.1.1+0"
+
+[[deps.Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.15.0+0"
+
+[[deps.Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.2+0"
+
+[[deps.Xorg_xcb_util_cursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
+git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
+uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
+version = "0.1.4+0"
+
+[[deps.Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[deps.Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[deps.Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.6+0"
+
+[[deps.Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.39.0+0"
+
+[[deps.Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.5.0+0"
+
 [[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.13+1"
 
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.5+0"
+
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.43.0+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
+
+[[deps.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"
+
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
 version = "5.8.0+1"
 
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[deps.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "873b4f805771d3e4bafe63af759a26ea8ca84d14"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.42+0"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
@@ -341,12 +1564,58 @@ version = "1.52.0+1"
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 version = "17.4.0+2"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+1"
 """
 
 # ╔═╡ Cell order:
 # ╟─29893d76-8153-4b84-89ac-289e41327205
-# ╠═835ef9c7-727a-4672-bba4-58aa6766b9e6
+# ╟─835ef9c7-727a-4672-bba4-58aa6766b9e6
+# ╟─428c1a49-2825-43a2-920d-46d9a9950455
+# ╟─57546347-5dc6-4f59-9e61-d57bc3bee3e5
+# ╟─4d9c23f1-4544-4b4b-ac59-26d534be10a9
+# ╟─b089c934-de4f-483f-a2a7-96aa0d26f29d
+# ╟─fdb7ab79-4715-4ed7-92d2-81b4f6ba2734
+# ╟─51b790fc-887a-4d05-b9cc-288c6ee22b11
+# ╠═f62bb0be-9891-4670-93c8-bd3207fc49fb
+# ╠═fbd815c1-994d-4673-a4e6-3501d190edc0
+# ╠═a5c5c885-a8d2-4b5b-84a6-26d1220bb89e
+# ╠═4063cc32-a506-47f9-af52-07fe7594bcd9
+# ╠═11f45a3f-d773-4d20-95fb-c9843b18da62
+# ╟─bdba2216-b866-4b53-9032-50af0b3eec0f
+# ╟─20ba966c-7f63-4e9c-9513-3d217c7b2b77
+# ╟─44ad3946-c1f8-4485-9db2-41d862fb41a2
+# ╟─9a74694b-54f9-4a7e-8777-4d732034f53b
+# ╟─3f34e354-137f-4614-bea9-ea3110715cae
+# ╠═67c2acf3-52ea-4132-9372-d50d2c837ce8
+# ╠═9d567a1b-4c56-42f9-9762-a9f226bb6a51
+# ╟─985f2cfb-1965-49de-ad1a-787fe11e9394
+# ╟─b239dd0a-5527-4f74-b2fb-d15ff3caa011
+# ╠═6abf7266-8ef4-43e7-a7ec-ced409129ced
+# ╠═48843f6a-cda7-4a34-b459-da1b66a48e06
+# ╠═a7f1e580-fcb0-4833-b463-d97cf918c4f3
+# ╠═786f3a79-424d-4e42-a6af-0624ecc87ff3
+# ╠═f9e80776-0c5e-4ae5-b9ed-e0896bec970d
 # ╟─6040b344-d338-11ee-256a-67ae4cb673c6
-# ╟─d3b7f59a-712b-4520-a413-c5f5eb71a12f
+# ╠═d3b7f59a-712b-4520-a413-c5f5eb71a12f
+# ╠═ed6a19ef-fd4f-43b2-aa09-aa7fe38f52ed
+# ╠═1929d137-dcc9-4208-992d-71001f976466
+# ╠═3a61a22c-07a4-4cd2-91ad-b573d8b01f30
 # ╟─00000000-0000-0000-0000-000000000001
 # ╟─00000000-0000-0000-0000-000000000002