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using Plots
using Distributions
num_velocities = 100000
num_dimensions = 3
println("Starting Random Speed Simualtions...\n")
function make_random_velocity()
# pull 3 nums randomly from normal distribution
N = Normal(0, 1)
if num_dimensions == 1
return (rand(N), 0, 0)
end
if num_dimensions == 2
return (rand(N), rand(N), 0)
end
return (rand(N), rand(N), rand(N))
end
function plot_frequencies(x)
# make a map each positions to it's Frequency
freqs = Dict()
for xi in x
if haskey(freqs, xi)
freqs[xi] += 1
else
freqs[xi] = 1
end
end
num_points = length(x)
plt = scatter(
collect(keys(freqs)), collect(values(freqs)),
label="Frequency", xlabel="Position", ylabel="Frequency",
title="Freq of Positions ($num_points points)",
msw=0, color=:green, legend=false)
return plt
end
# make velocities
velocities = [make_random_velocity() for _ in 1:num_velocities]
# plot these velocities on 1d plots
px = histogram([v[1] for v in velocities], bins=30, title="X Velocity")
py = histogram([v[2] for v in velocities], bins=30, title="Y Velocity")
pz = histogram([v[3] for v in velocities], bins=30, title="Z Velocity")
# print the mean and standard deviation of each velocity distribution
println("X->\tμ:$(mean([v[1] for v in velocities])), σ:$(std([v[1] for v in velocities])), n:$(length([v[1] for v in velocities]))")
println("Y->\tμ:$(mean([v[2] for v in velocities])), σ:$(std([v[2] for v in velocities])), n:$(length([v[2] for v in velocities]))")
println("Z->\tμ:$(mean([v[3] for v in velocities])), σ:$(std([v[3] for v in velocities])), n:$(length([v[3] for v in velocities]))")
p = plot(px, py, pz, layout=(3, 1), size=(800, 800))
savefig(p, "figs/rs-1dvels.png")
# plot these velocities in 3d space
p = Plots.scatter(
[v[1] for v in velocities],
[v[2] for v in velocities],
[v[3] for v in velocities],
title="Velocities")
savefig(p, "figs/rs-3dvels.png")
speeds = [sqrt(v[1]^2 + v[2]^2 + v[3]^2) for v in velocities]
p = histogram(
speeds, title="Randomly Generated Speeds (n=$num_velocities, d=$num_dimensions)",
legend=false, xlabel="Speed = \$ √(v_x^2 + v_y^2 + v_z^2) \$", ylabel="Frequency")
savefig(p, "figs/rs-speeds.png")
# plot their energy
energies = [.5 * (v[1]^2 + v[2]^2 + v[3]^2) for v in velocities]
p = histogram(
energies, title="Randomly Generate`d Energies (n=$num_velocities, d=$num_dimensions)",
legend=false, xlabel="Energy = \$ .5m(v_x^2 + v_y^2 + v_z^2) \$", ylabel="Frequency")
savefig(p, "figs/rs-energies.png")
# print the mean and standard deviation of the speed distribution
println("\tEnergies->\tμ:$(mean(energies)), σ:$(std(energies)), n:$(length(energies))")
println("\nRandom Speed Simualtions Complete!")
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