1037 lines
309 KiB
Text
1037 lines
309 KiB
Text
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"10000"
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"using SpiDy\n",
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"using NPZ\n",
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"using DataFrames\n",
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"using CSV\n",
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"using ProgressMeter\n",
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"using Random\n",
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"using Statistics\n",
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"using LinearAlgebra\n",
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"using Plots\n",
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"\n",
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"########################\n",
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"########################\n",
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"\n",
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"Δt = .2\n",
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"N = 600\n",
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"tspan = (0., N*Δt)\n",
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"saveat = (0:1:N)*Δt\n",
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"\n",
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"α = 10. # 0.16\n",
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"ω0 = 7. # 1.4\n",
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"Γ = 5. # 0.5\n",
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"\n",
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"\n",
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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"matrix = AnisoCoupling([-sin(π/4) 0. 0. # coupling to the environment\n",
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" 0. 0. 0.\n",
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" cos(π/4) 0. 0.]);\n",
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"\n",
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"matrix = IsoCoupling(1)\n",
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"\n",
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"T = .01\n",
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"noise = ClassicalNoise(T);\n",
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"\n",
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"nspin = 1 # number of spins\n",
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"\n",
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"s0 = [0, 1, 1] ./ sqrt(2)\n",
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"J0 = 1.\n",
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"JH = Nchain(nspin, J0)\n",
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"\n",
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"nruns = 10000"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "6e3cdf02-c243-4622-a52a-a6d7f987c68d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Starting...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:06:29\u001b[39m3:53\u001b[39m\n"
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]
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}
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],
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"source": [
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"println(\"Starting...\")\n",
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"progress = Progress(nruns);\n",
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"\n",
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"sols = zeros(nruns, length(saveat), 3*nspin)\n",
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"\n",
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"Threads.@threads for i in 1:nruns\n",
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" bfields = [bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise)];\n",
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" sol = diffeqsolver(s0, tspan, J, bfields, matrix; JH=JH, saveat=saveat);\n",
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" sols[i, :, :] = transpose(sol[:, :])\n",
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" next!(progress)\n",
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"end\n",
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"\n",
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"solavg = mean(sols, dims=1)[1, :, :];\n",
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"solstd = std(sols, dims=1)[1, :, :];"
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]
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},
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{
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},
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],
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"source": [
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},
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"id": "a06addc4-47b2-4467-8148-3e68f3eae702",
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"metadata": {},
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"outputs": [
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{
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"plot(saveat, solavg[:, 2], ribbon=solstd[:, 2])"
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]
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},
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{
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"cell_type": "code",
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"id": "bc1686fd-d86d-42b0-9d87-bcb911526d00",
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"metadata": {},
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"outputs": [
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{
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
||
"plot(saveat, solavg[:, 3], ribbon=solstd[:, 3])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "59ac92d9-6a78-402b-91ae-3f5fd22cc6ff",
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"metadata": {},
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"outputs": [],
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"source": [
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||
"projected = zeros(nruns, length(saveat), 2)\n",
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||
"\n",
|
||
"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg)]\n",
|
||
"\n",
|
||
"Threads.@threads for i in 1:length(saveat)\n",
|
||
" n = normalized_avg[i, :][1]\n",
|
||
"\n",
|
||
" u = normalize(cross(n, [0,0,1]))\n",
|
||
" v = cross(u, n)\n",
|
||
"\n",
|
||
" for j in 1:nruns\n",
|
||
" b = sols[j, i, :]\n",
|
||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
|
||
"\n",
|
||
" projected[j, i, 1] = dot(u,b)\n",
|
||
" projected[j, i, 2] = dot(v,b)\n",
|
||
" end\n",
|
||
"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "03467eca-3f0c-4bd4-b3f7-5649b68780bc",
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"metadata": {},
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"outputs": [
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{
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"data": {
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"histogram(projected[:, 500, 2])"
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]
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},
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{
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"execution_count": 9,
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"id": "f6df949c-15b2-447f-a264-8ef48ce1725e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"nth_moment (generic function with 1 method)"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"function nth_moment(data, N)\n",
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" return mean(data .^ N)\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "e4ad51fc-0dc7-4106-99e4-2b29e54b1930",
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"metadata": {},
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"outputs": [],
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"source": [
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"using HypothesisTests"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "e5b9609e-f467-4bd7-9b51-9a4c1f175738",
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"metadata": {},
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"outputs": [],
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"source": [
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"JB = zeros(N)\n",
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"for i in 10:N\n",
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" JB[i] = HypothesisTests.JarqueBeraTest(projected[:, i, 1]).JB\n",
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"end"
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]
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},
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{
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"id": "3ad3f882-caa1-4dfc-b83c-3b57c214ecea",
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"metadata": {},
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"outputs": [
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1854.7,841.386 1858.24,916.561 1861.78,925.339 1865.32,907.513 1868.86,873.117 1872.4,826.396 1875.94,795.084 1879.48,841.093 1883.02,910.932 1886.56,939.335 1890.1,932.316 1893.64,950.635 1897.18,971.389 1900.72,960.536 1904.26,949.658 1907.8,970.994 1911.34,1002.56 1914.88,1034.29 1918.42,1083.69 1921.96,1103.4 1925.5,1112.66 1929.04,1134.87 1932.58,1150.76 1936.12,1170.21 1939.66,1193.83 1943.2,1203.37 1946.74,1234.55 1950.28,1262.13 1953.82,1285.56 1957.36,1280.18 1960.9,1272.6 1964.44,1288.23 1967.98,1302.56 1971.52,1299.55 1975.06,1317.77 1978.6,1344.55 1982.14,1341.97 1985.68,1309.61 1989.22,1293.29 1992.76,1312.06 1996.3,1322.96 1999.84,1304.56 2003.38,1268.51 2006.92,1228.58 2010.46,1187.31 2014,1182.7 2017.54,1232.69 2021.08,1257.59 2024.62,1244.56 2028.16,1243.77 2031.7,1243.1 2035.24,1220.75 2038.77,1226.11 2042.31,1288.09 2045.85,1325.81 2049.39,1298.79 2052.93,1242.13 2056.47,1234.05 2060.01,1282.18 2063.55,1284.62 2067.09,1243.38 2070.63,1238.94 2074.17,1264.2 2077.71,1295.07 2081.25,1311.81 2084.79,1304.21 2088.33,1288.12 2091.87,1286.74 2095.41,1274.85 2098.95,1247.88 2102.49,1198.94 2106.03,1195.18 2109.57,1235.69 2113.11,1265.92 2116.65,1300.28 2120.19,1333.17 2123.73,1331.64 2127.27,1315.52 2130.81,1311.21 2134.35,1311.1 2137.89,1299.72 2141.43,1276.77 2144.97,1251.11 2148.51,1246.64 2152.05,1260.32 2155.59,1260.54 2159.13,1265.15 2162.67,1282.24 2166.21,1283.39 2169.75,1275.83 2173.29,1274.64 2176.83,1280.63 2180.37,1296.57 2183.91,1308.87 2187.45,1309.63 2190.99,1293.18 2194.53,1260.62 2198.07,1242.17 2201.61,1256.2 2205.15,1273.18 2208.69,1285.88 2212.23,1273.34 2215.77,1236.57 2219.31,1241.58 2222.84,1277.74 2226.38,1296 2229.92,1295.23 2233.46,1302.97 2237,1321.28 2240.54,1320.48 2244.08,1294.92 2247.62,1278.28 2251.16,1298.3 2254.7,1334.89 2258.24,1370.53 2261.78,1382.08 2265.32,1367.26 2268.86,1351.67 2272.4,1339.96 2275.94,1300.27 2279.48,1239.19 2283.02,1192.46 2286.56,1189.96 2290.1,1259.36 \"/>\n",
|
||
"<path clip-path=\"url(#clip540)\" d=\"M2005.15 198.898 L2278.96 198.898 L2278.96 95.2176 L2005.15 95.2176 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
|
||
"<polyline clip-path=\"url(#clip540)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2005.15,198.898 2278.96,198.898 2278.96,95.2176 2005.15,95.2176 2005.15,198.898 \"/>\n",
|
||
"<polyline clip-path=\"url(#clip540)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2029.75,147.058 2177.34,147.058 \"/>\n",
|
||
"<path clip-path=\"url(#clip540)\" d=\"M2215.78 166.745 Q2213.97 171.375 2212.26 172.787 Q2210.55 174.199 2207.68 174.199 L2204.27 174.199 L2204.27 170.634 L2206.77 170.634 Q2208.53 170.634 2209.5 169.8 Q2210.48 168.967 2211.66 165.865 L2212.42 163.921 L2201.93 138.412 L2206.45 138.412 L2214.55 158.689 L2222.65 138.412 L2227.17 138.412 L2215.78 166.745 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip540)\" d=\"M2234.46 160.402 L2242.1 160.402 L2242.1 134.037 L2233.79 135.703 L2233.79 131.444 L2242.05 129.778 L2246.73 129.778 L2246.73 160.402 L2254.36 160.402 L2254.36 164.338 L2234.46 164.338 L2234.46 160.402 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
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]
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||
},
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||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot(saveat[10:N], JB[10:N])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "bb3c6b84-5b21-4d79-b5bc-3345a8f2d893",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"Jarque-Bera normality test\n",
|
||
"--------------------------\n",
|
||
"Population details:\n",
|
||
" parameter of interest: skewness and kurtosis\n",
|
||
" value under h_0: \"0 and 3\"\n",
|
||
" point estimate: \"-0.06640955564275836 and 2.878302889621456\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: reject h_0\n",
|
||
" one-sided p-value: 0.0012\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 13.5213\n"
|
||
]
|
||
},
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected[:, 400, 1])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "e331f6c7-fb4b-4f21-84d3-6a3f203a95b6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"Jarque-Bera normality test\n",
|
||
"--------------------------\n",
|
||
"Population details:\n",
|
||
" parameter of interest: skewness and kurtosis\n",
|
||
" value under h_0: \"0 and 3\"\n",
|
||
" point estimate: \"-0.009755563978670194 and 3.0706123545537634\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: fail to reject h_0\n",
|
||
" one-sided p-value: 0.3269\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 2.23616\n"
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected[:, 2, 2])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "240660fb-d008-4dab-8bc1-aaf530885102",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"64"
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"using Base.Threads\n",
|
||
"nthreads()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "8150abab-cacc-4617-9d95-bebdc4c7cac8",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" PID COMMAND VSZ RSS SIZE\n",
|
||
" 54147 julia 20209472 1568276 15911276\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"run(`ps -p $(getpid()) -o pid,comm,vsize,rss,size`);"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "e21d4205-2f8e-4b39-b1ea-ba722ea3fb13",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Julia 1.7.3",
|
||
"language": "julia",
|
||
"name": "julia-1.7"
|
||
},
|
||
"language_info": {
|
||
"file_extension": ".jl",
|
||
"mimetype": "application/julia",
|
||
"name": "julia",
|
||
"version": "1.7.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|