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1621 lines
54 KiB
1621 lines
54 KiB
### A Pluto.jl notebook ###
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# v0.19.39
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using Markdown
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using InteractiveUtils
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# ╔═╡ d3b7f59a-712b-4520-a413-c5f5eb71a12f
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begin
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using PlutoUI
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using Plots
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using LinearAlgebra
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# using JuMP, Cbc
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using Optim, LineSearches
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using Statistics # for mean...
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end
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# ╔═╡ 29893d76-8153-4b84-89ac-289e41327205
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md"""
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# Acoustic Localization Using Carrier-Phase Measurements
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# Introduction
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TODO!
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## Problem Statment
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!!! info "This text is copied from the provided document."
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We assume an acoustic localization system with $M$ beacons transmitting signals of a certain carrier frequency. The signals are received by a mobile device (MD) located at ``x = [x, y, z]^T``, while the beacons are located at ``b_i = v = [x_i, y_i, z_i]^T``, ``i = 1, 2, \ldots, M``. The beacons and the MD are all synchronized.
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By processing the received signal from each beacon, the MD estimates its range from each beacon. In addition, the MD can also obtain the phase of the carrier signal received from each beacon. The range measurements for beacon ``i`` can be modelled as
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```math
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r_i =\|x − b_i\|_2 + w_i,
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```
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where wi is additive noise and ``\|\cdot\|_2`` is the Euclidean norm. On the other hand, the phase data can be described as
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```math
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\varphi_i = \|x − b_i\|_2 + n_i + v_i,
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```
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where ``v_i`` is additive noise and ``n_i \in \mathbb{Z}`` is an integer phase ambiguity. In (1) and (2), we assume that the range and phase are
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measured in units of cycles or wavelengths. Hence, ``\varphi_i \in [−0.5, 0.5)``.
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The objective of this work is to use both sets of measurements in (1) and (2) to estimate the MD position ``x``. To motivate the
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use of the carrier phase data, we assume generally that ``\|v_i\|_2 \ll \|w_i\|_2,\, \forall i \in {1, 2, · · · , M}``. However, this is not a necessary condition for the carrier-phase use to be beneficial. To proceed further, we assume that ``w_i`` and ``v_i`` are independent for all ``i``
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values, and that these noise processes are of zero mean and variances ``\alpha_i^2`` and ``\sigma_i^2``, respectively.
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"""
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# ╔═╡ 835ef9c7-727a-4672-bba4-58aa6766b9e6
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md"""
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## Outline of The Solution
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!!! info "This text is copied from the provided document."
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To formulate the estimation problem, we can define the objective function:
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```math
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f(\mathbf{x}, \mathbf{n}) = \sum_{i=1}^M
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\alpha_i^{-2} (r_i - \|x-b_i\|_2)^2
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+ \sigma_i^{-2} (\varphi_i - \|x-b_i\|_2 - n_i)^2
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```
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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:
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```math
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\hat x,\, \hat n =
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\operatorname*{arg\,min}_{x\in R^3,\, n\in\mathbb{Z}^M}f(x, n)
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```
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We can solve (4) through the following steps:
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1. Obtain a float solution (FS) of (4) by ignoring the integer constraints.
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2. Find a decomposition of the objective function around the FS.
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3. Develop a search algorithm using the FS and the decomposition.
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"""
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# ╔═╡ 57546347-5dc6-4f59-9e61-d57bc3bee3e5
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b = [[1 1 10]
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[2 6 10]
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[7 7 10]
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[7 3 10]]'
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# ╔═╡ 428c1a49-2825-43a2-920d-46d9a9950455
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begin
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_, M = size(b)
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md"""
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# An Attempt to Solve this Problem...
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> Note: I try to solve the problem generally, the examples are for demonstration purposes.
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Lets assume that we have `b` beacons as follows, of size ``M=``**$(M)**:
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"""
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end
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# ╔═╡ 4d9c23f1-4544-4b4b-ac59-26d534be10a9
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md"""
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And our mobile device ``x`` is:
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"""
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# ╔═╡ b089c934-de4f-483f-a2a7-96aa0d26f29d
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x = [3 5 3]'
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# ╔═╡ fdb7ab79-4715-4ed7-92d2-81b4f6ba2734
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md"""
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*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.
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"""
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# ╔═╡ 51b790fc-887a-4d05-b9cc-288c6ee22b11
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begin
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import Random
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Random.seed!(123)
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end
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# ╔═╡ f62bb0be-9891-4670-93c8-bd3207fc49fb
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alpha = 0.1;
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# ╔═╡ fbd815c1-994d-4673-a4e6-3501d190edc0
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range_noise = randn(M) * alpha;
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# ╔═╡ a5c5c885-a8d2-4b5b-84a6-26d1220bb89e
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sigma = 0.1;
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# ╔═╡ 4063cc32-a506-47f9-af52-07fe7594bcd9
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phase_noise = randn(M) * sigma;
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# ╔═╡ 11f45a3f-d773-4d20-95fb-c9843b18da62
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phase_n = 0;
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# ╔═╡ bdba2216-b866-4b53-9032-50af0b3eec0f
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md"""
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---
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"""
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# ╔═╡ 20ba966c-7f63-4e9c-9513-3d217c7b2b77
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md"""
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In the next steps, we try to find ``x`` in the most optimal/efficient method..
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"""
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# ╔═╡ 44ad3946-c1f8-4485-9db2-41d862fb41a2
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md"""
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We can Visualize this configuration in 3D space:
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"""
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# ╔═╡ 9a74694b-54f9-4a7e-8777-4d732034f53b
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begin
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scatter( b[1,:], b[2,:], b[3,:], label="Beacons", markersize = 10)
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scatter!(x[1,:], x[2,:], x[3,:], label="MD", markersize = 10)
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end
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# ╔═╡ 3f34e354-137f-4614-bea9-ea3110715cae
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md"""
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## Using range measurments only
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If we ignore the noise and the phase measurments, we notice that our solution can be solved analytically in the form:
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```math
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\begin{eqnarray}
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(x - x_1)^2 + (y - y_1)^2 + (z - z_1)^2 &= r_1^2 \\
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(x - x_2)^2 + (y - y_2)^2 + (z - z_2)^2 &= r_2^2 \\
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(x - x_3)^2 + (y - y_3)^2 + (z - z_3)^2 &= r_3^2
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\end{eqnarray}
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```
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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.
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*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.*
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Nevertheless, solving this problem numerically is trivial.
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We know that that distance ``r`` from each beacon is `r_no_phase_or_noise`:
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"""
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# ╔═╡ 985f2cfb-1965-49de-ad1a-787fe11e9394
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md"""
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we can see that the result of `x_no_phase_or_noise` is very similar to the MD's original position = `x`, as expected.
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"""
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# ╔═╡ b239dd0a-5527-4f74-b2fb-d15ff3caa011
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md"""
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## Using Range and Phase
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We now add a noise process of zero mean and variance ``\alpha^2`` to our equation.
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"""
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# ╔═╡ a7f1e580-fcb0-4833-b463-d97cf918c4f3
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# ╔═╡ 786f3a79-424d-4e42-a6af-0624ecc87ff3
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# Acoustic Localization Using Carrier Phase Measurments
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# Give beacons located at trasmitting signals which are recieved by a mobile device (MD) located at
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# clear; clc;
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# Starting values...
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# x = [1 2 3]'; % Mobile Device
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# b = [4 3 4;
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# 5 4 6;
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# 7 8 9;
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# 10 11 12]';
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# [~, M] = size(b); % Number of Beacons
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# sigma = 0.1;
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# w = rand(1, M) * sigma; % White Noise
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# The range measurments for the beacons can be modelled as:
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# (PS: We use a search algorithm because noise would cause us to not have a numerical solution)
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# r = vecnorm(b - x) + w
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# Outline of The Solution
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# To formulate the estimation problem. We have and , we need to find .
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# f1 = @(point) mean((r - vecnorm(point - b)).^2);
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# fminsearch(f1,x)'
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# Adding Phase
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# The phase data can be described as:
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# n = rand(1, M) * 0;
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# v = rand(1, M) * 0.01;
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# phi = vecnorm(b-x) + n + v
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# Soln W/ Phase
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# f2 = @(point) mean((r - vecnorm(point(1:3) - b)).^2) ...
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# + mean((phi - vecnorm(point(1:3) - b) - point(4)).^2);
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# initial_guess = [x; 5]; % (1:3) => point. (4) => n.
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# fminsearch(f2, initial_guess)'
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# ╔═╡ f9e80776-0c5e-4ae5-b9ed-e0896bec970d
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# ╔═╡ 6040b344-d338-11ee-256a-67ae4cb673c6
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md"""
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# Appendex
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"""
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# ╔═╡ ed6a19ef-fd4f-43b2-aa09-aa7fe38f52ed
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TableOfContents()
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# ╔═╡ 1929d137-dcc9-4208-992d-71001f976466
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vecnorm(v) = norm.(eachcol(v))
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# ╔═╡ 67c2acf3-52ea-4132-9372-d50d2c837ce8
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r_no_phase_or_noise = vecnorm(b .- x)
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# ╔═╡ 6abf7266-8ef4-43e7-a7ec-ced409129ced
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r = vecnorm(b .- x) + range_noise
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# ╔═╡ 48843f6a-cda7-4a34-b459-da1b66a48e06
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phi = vecnorm(b .- x) + phase_noise .+ phase_n
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# ╔═╡ 3a61a22c-07a4-4cd2-91ad-b573d8b01f30
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function minimize(f, x0)
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result = optimize(f,
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x0,
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LBFGS(linesearch = LineSearches.HagerZhang()),Optim.Options(extended_trace=true,show_every=0,store_trace = true,show_trace = false))
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end
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# ╔═╡ 9d567a1b-4c56-42f9-9762-a9f226bb6a51
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x_no_phase_or_noise = begin
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f_no_phase_or_noise(point) = # Define the minimization function LSE
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mean((r_no_phase_or_noise - vecnorm(point .- b)).^2);
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local x = [0.0, 0.0, 0.0] # First Guess
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local res = minimize(f_no_phase_or_noise, x)
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local vals = map(x-> x.value, res.trace)
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local iterations = map(x-> x.iteration, res.trace)
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plot(iterations, vals)
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local points = map(x-> x.metadata["x"], res.trace)
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end
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# ╔═╡ 00000000-0000-0000-0000-000000000001
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PLUTO_PROJECT_TOML_CONTENTS = """
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[deps]
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LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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Optim = "429524aa-4258-5aef-a3af-852621145aeb"
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Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
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Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
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[compat]
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LineSearches = "~7.2.0"
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Optim = "~1.9.2"
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Plots = "~1.40.1"
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PlutoUI = "~0.7.58"
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"""
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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PLUTO_MANIFEST_TOML_CONTENTS = """
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# This file is machine-generated - editing it directly is not advised
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julia_version = "1.10.1"
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manifest_format = "2.0"
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project_hash = "a67b74f724a1878f5548d5c26434b81fcca4b2c6"
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[deps.Adapt.extensions]
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AdaptStaticArraysExt = "StaticArrays"
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[deps.Adapt.weakdeps]
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StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
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[[deps.ArgTools]]
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ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
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ArrayInterfaceCUDAExt = "CUDA"
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ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
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ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
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ArrayInterfaceTrackerExt = "Tracker"
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[deps.ArrayInterface.weakdeps]
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version = "0.10.0"
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weakdeps = ["SpecialFunctions"]
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[deps.ColorVectorSpace.extensions]
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|
SpecialFunctionsExt = "SpecialFunctions"
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|
[[deps.Colors]]
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|
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
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git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
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uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
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version = "0.12.10"
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[[deps.CommonSubexpressions]]
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deps = ["MacroTools", "Test"]
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git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
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uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
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version = "0.3.0"
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[[deps.Compat]]
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deps = ["TOML", "UUIDs"]
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git-tree-sha1 = "c955881e3c981181362ae4088b35995446298b80"
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uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
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version = "4.14.0"
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weakdeps = ["Dates", "LinearAlgebra"]
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[deps.Compat.extensions]
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|
CompatLinearAlgebraExt = "LinearAlgebra"
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|
[[deps.CompilerSupportLibraries_jll]]
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deps = ["Artifacts", "Libdl"]
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uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
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version = "1.1.0+0"
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[[deps.ConcurrentUtilities]]
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deps = ["Serialization", "Sockets"]
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git-tree-sha1 = "9c4708e3ed2b799e6124b5673a712dda0b596a9b"
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uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
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version = "2.3.1"
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[[deps.ConstructionBase]]
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deps = ["LinearAlgebra"]
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git-tree-sha1 = "c53fc348ca4d40d7b371e71fd52251839080cbc9"
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uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
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version = "1.5.4"
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[deps.ConstructionBase.extensions]
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ConstructionBaseIntervalSetsExt = "IntervalSets"
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ConstructionBaseStaticArraysExt = "StaticArrays"
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[deps.ConstructionBase.weakdeps]
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IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
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StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
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[[deps.Contour]]
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git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
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uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
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[[deps.DataAPI]]
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git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
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[[deps.DataStructures]]
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deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
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git-tree-sha1 = "1fb174f0d48fe7d142e1109a10636bc1d14f5ac2"
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[[deps.Dates]]
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deps = ["Printf"]
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uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
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[[deps.DelimitedFiles]]
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deps = ["Mmap"]
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git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
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uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
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[[deps.DiffResults]]
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deps = ["StaticArraysCore"]
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git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
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uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
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[[deps.DiffRules]]
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deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
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git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272"
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uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
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[[deps.Distributed]]
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deps = ["Random", "Serialization", "Sockets"]
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uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
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[[deps.DocStringExtensions]]
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deps = ["LibGit2"]
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git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
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uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
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version = "0.8.6"
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[[deps.Downloads]]
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deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
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uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
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version = "1.6.0"
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[[deps.EpollShim_jll]]
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|
deps = ["Artifacts", "JLLWrappers", "Libdl"]
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git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
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uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
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version = "0.0.20230411+0"
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[[deps.ExceptionUnwrapping]]
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deps = ["Test"]
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git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
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uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
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version = "0.1.10"
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[[deps.Expat_jll]]
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|
deps = ["Artifacts", "JLLWrappers", "Libdl"]
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git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c"
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uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
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version = "2.5.0+0"
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[[deps.FFMPEG]]
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deps = ["FFMPEG_jll"]
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git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
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uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
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version = "0.4.1"
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[[deps.FFMPEG_jll]]
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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"]
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git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
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uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
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[[deps.FileWatching]]
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uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
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[[deps.FillArrays]]
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deps = ["LinearAlgebra", "Random"]
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git-tree-sha1 = "5b93957f6dcd33fc343044af3d48c215be2562f1"
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uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
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version = "1.9.3"
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[deps.FillArrays.extensions]
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|
FillArraysPDMatsExt = "PDMats"
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|
FillArraysSparseArraysExt = "SparseArrays"
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|
FillArraysStatisticsExt = "Statistics"
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|
|
|
[deps.FillArrays.weakdeps]
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|
PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
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[[deps.FiniteDiff]]
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deps = ["ArrayInterface", "LinearAlgebra", "Requires", "Setfield", "SparseArrays"]
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git-tree-sha1 = "73d1214fec245096717847c62d389a5d2ac86504"
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uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
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version = "2.22.0"
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[deps.FiniteDiff.extensions]
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|
FiniteDiffBandedMatricesExt = "BandedMatrices"
|
|
FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
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|
FiniteDiffStaticArraysExt = "StaticArrays"
|
|
|
|
[deps.FiniteDiff.weakdeps]
|
|
BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
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BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
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StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
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[[deps.FixedPointNumbers]]
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deps = ["Statistics"]
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git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
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version = "0.8.4"
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[[deps.Fontconfig_jll]]
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|
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
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git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
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[[deps.Formatting]]
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deps = ["Printf"]
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git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
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[[deps.ForwardDiff]]
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deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
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git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
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version = "0.10.36"
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[deps.ForwardDiff.extensions]
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|
ForwardDiffStaticArraysExt = "StaticArrays"
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[deps.ForwardDiff.weakdeps]
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|
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
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[[deps.FreeType2_jll]]
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|
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
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git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
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[[deps.FriBidi_jll]]
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|
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
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[[deps.Future]]
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uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
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[[deps.GLFW_jll]]
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|
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
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git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb"
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[[deps.GR]]
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deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
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git-tree-sha1 = "3458564589be207fa6a77dbbf8b97674c9836aab"
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[[deps.GR_jll]]
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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"]
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[[deps.Gettext_jll]]
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git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
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[[deps.Glib_jll]]
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git-tree-sha1 = "e94c92c7bf4819685eb80186d51c43e71d4afa17"
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[[deps.Graphite2_jll]]
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git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
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[[deps.HTTP]]
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deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
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git-tree-sha1 = "ac7b73d562b8f4287c3b67b4c66a5395a19c1ae8"
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[[deps.HarfBuzz_jll]]
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deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
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git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
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[[deps.Hyperscript]]
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[[deps.HypertextLiteral]]
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git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
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[[deps.IOCapture]]
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git-tree-sha1 = "8b72179abc660bfab5e28472e019392b97d0985c"
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[[deps.InteractiveUtils]]
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deps = ["Markdown"]
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[[deps.IrrationalConstants]]
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git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
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[[deps.JLFzf]]
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git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af"
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[[deps.JLLWrappers]]
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git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
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[[deps.JSON]]
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git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
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[[deps.JpegTurbo_jll]]
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git-tree-sha1 = "3336abae9a713d2210bb57ab484b1e065edd7d23"
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version = "3.0.2+0"
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[[deps.LAME_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
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[[deps.LERC_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
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[[deps.LLVMOpenMP_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl"]
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git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713"
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[[deps.LZO_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
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[deps.Latexify.extensions]
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DataFramesExt = "DataFrames"
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SymEngineExt = "SymEngine"
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[deps.Latexify.weakdeps]
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DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
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deps = ["LibCURL_jll", "MozillaCACerts_jll"]
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[[deps.Libffi_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
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[deps.LogExpFunctions.extensions]
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LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
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LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
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LogExpFunctionsInverseFunctionsExt = "InverseFunctions"
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[deps.LogExpFunctions.weakdeps]
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ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
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ImageInTerminalExt = "ImageInTerminal"
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UnitfulExt = "Unitful"
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[deps.Plots.weakdeps]
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|
|
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"
|
|
version = "1.52.0+1"
|
|
|
|
[[deps.p7zip_jll]]
|
|
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
|
|
# ╟─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
|
|
# ╠═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
|
|
|