1622 lines
54 KiB
Plaintext
1622 lines
54 KiB
Plaintext
### 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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"""
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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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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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[[deps.CommonSubexpressions]]
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deps = ["MacroTools", "Test"]
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[[deps.Compat]]
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deps = ["TOML", "UUIDs"]
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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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deps = ["LinearAlgebra"]
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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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[[deps.Contour]]
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[[deps.DataAPI]]
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[[deps.DelimitedFiles]]
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[[deps.DiffRules]]
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[[deps.DocStringExtensions]]
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[[deps.Downloads]]
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[[deps.EpollShim_jll]]
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[[deps.ExceptionUnwrapping]]
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[[deps.FFMPEG]]
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[[deps.FFMPEG_jll]]
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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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||
[deps.FiniteDiff.extensions]
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||
FiniteDiffBandedMatricesExt = "BandedMatrices"
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||
FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
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||
FiniteDiffStaticArraysExt = "StaticArrays"
|
||
|
||
[deps.FiniteDiff.weakdeps]
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[deps.ForwardDiff.weakdeps]
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
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||
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||
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||
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||
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||
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||
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|
||
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
|