641 lines
396 KiB
Text
641 lines
396 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "e47f1fd3-c09d-43cb-80c8-64f42e8161a4",
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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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"10000"
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]
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},
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"execution_count": 1,
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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 = 1000\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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"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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"s0 = [0, 1, 1]\n",
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"s0 = s0 ./ norm(s0)\n",
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"\n",
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"J0 = 1.\n",
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"JH = Nchain(1, 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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"\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000\u0000"
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]
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}
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],
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"source": [
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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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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"\n",
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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_ohm = zeros(nruns, length(saveat), 3)\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_ohm[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_ohm = mean(sols_ohm, dims=1)[1, :, :];\n",
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"solstd_ohm = std(sols_ohm, dims=1)[1, :, :];"
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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": 3,
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"id": "3422af78-2f32-468c-a8a3-a0732a836fd1",
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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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"source": [
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"α = 0.16\n",
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"ω0 = 1.4\n",
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"Γ = 0.5\n",
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"\n",
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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"\n",
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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_col = zeros(nruns, length(saveat), 3)\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_col[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_col = mean(sols_col, dims=1)[1, :, :];\n",
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"solstd_col = std(sols_col, dims=1)[1, :, :];"
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]
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},
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{
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"cell_type": "code",
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"id": "d16b97dd-b9f5-415c-b388-2b1f3344be45",
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"<polyline clip-path=\"url(#clip570)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2011.46,250.738 2280.54,250.738 2280.54,95.2176 2011.46,95.2176 2011.46,250.738 \"/>\n",
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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, solstd_ohm[:, 1])\n",
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"plot!(saveat, solstd_ohm[:, 2])"
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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": 5,
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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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||
"data": {
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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": [
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||
"plot(saveat, solstd_col[:, 1])\n",
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"plot!(saveat, solstd_col[:, 2])"
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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": "bc1686fd-d86d-42b0-9d87-bcb911526d00",
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"metadata": {},
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"outputs": [
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||
{
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||
"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
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1774.36,1445.66 1776.39,1445.66 1778.43,1445.66 1780.46,1445.66 1782.5,1445.66 1784.54,1445.66 1786.57,1445.66 1788.61,1445.67 1790.65,1445.67 1792.68,1445.68 1794.72,1445.69 1796.76,1445.7 1798.79,1445.7 1800.83,1445.69 1802.87,1445.68 1804.9,1445.67 1806.94,1445.66 1808.98,1445.65 1811.01,1445.64 1813.05,1445.64 1815.09,1445.63 1817.12,1445.63 1819.16,1445.63 1821.2,1445.62 1823.23,1445.62 1825.27,1445.61 1827.31,1445.61 1829.34,1445.61 1831.38,1445.6 1833.42,1445.6 1835.45,1445.59 1837.49,1445.59 1839.53,1445.59 1841.56,1445.58 1843.6,1445.58 1845.64,1445.59 1847.67,1445.59 1849.71,1445.6 1851.75,1445.6 1853.78,1445.6 1855.82,1445.6 1857.86,1445.6 1859.89,1445.6 1861.93,1445.59 1863.97,1445.59 1866,1445.59 1868.04,1445.58 1870.08,1445.58 1872.11,1445.58 1874.15,1445.59 1876.19,1445.59 1878.22,1445.59 1880.26,1445.6 1882.3,1445.6 1884.33,1445.6 1886.37,1445.59 1888.41,1445.59 1890.44,1445.58 1892.48,1445.58 1894.52,1445.59 1896.55,1445.59 1898.59,1445.61 1900.63,1445.62 1902.66,1445.64 1904.7,1445.65 1906.74,1445.66 1908.77,1445.66 1910.81,1445.66 1912.85,1445.66 1914.88,1445.65 1916.92,1445.65 1918.96,1445.65 1920.99,1445.65 1923.03,1445.65 1925.07,1445.65 1927.1,1445.66 1929.14,1445.66 1931.18,1445.67 1933.21,1445.67 1935.25,1445.68 1937.28,1445.68 1939.32,1445.68 1941.36,1445.67 1943.39,1445.67 1945.43,1445.65 1947.47,1445.64 1949.5,1445.64 1951.54,1445.63 1953.58,1445.63 1955.61,1445.64 1957.65,1445.64 1959.69,1445.63 1961.72,1445.63 1963.76,1445.63 1965.8,1445.62 1967.83,1445.62 1969.87,1445.61 1971.91,1445.61 1973.94,1445.61 1975.98,1445.6 1978.02,1445.59 1980.05,1445.59 1982.09,1445.59 1984.13,1445.59 1986.16,1445.59 1988.2,1445.59 1990.24,1445.59 1992.27,1445.59 1994.31,1445.58 1996.35,1445.57 1998.38,1445.57 2000.42,1445.56 2002.46,1445.56 2004.49,1445.55 2006.53,1445.55 2008.57,1445.55 2010.6,1445.55 2012.64,1445.55 2014.68,1445.55 2016.71,1445.55 2018.75,1445.56 2020.79,1445.57 2022.82,1445.58 2024.86,1445.59 2026.9,1445.59 2028.93,1445.6 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2287.58,1445.48 2289.62,1445.48 2291.66,1445.48 \"/>\n",
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"<path clip-path=\"url(#clip650)\" d=\"M2012.48 250.738 L2280.8 250.738 L2280.8 95.2176 L2012.48 95.2176 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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"<polyline clip-path=\"url(#clip650)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2012.48,250.738 2280.8,250.738 2280.8,95.2176 2012.48,95.2176 2012.48,250.738 \"/>\n",
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"<polyline clip-path=\"url(#clip650)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2036.47,147.058 2180.39,147.058 \"/>\n",
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"<path clip-path=\"url(#clip650)\" d=\"M2218.22 166.745 Q2216.42 171.375 2214.7 172.787 Q2212.99 174.199 2210.12 174.199 L2206.72 174.199 L2206.72 170.634 L2209.22 170.634 Q2210.98 170.634 2211.95 169.8 Q2212.92 168.967 2214.1 165.865 L2214.86 163.921 L2204.38 138.412 L2208.89 138.412 L2216.99 158.689 L2225.1 138.412 L2229.61 138.412 L2218.22 166.745 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip650)\" d=\"M2236.9 160.402 L2244.54 160.402 L2244.54 134.037 L2236.23 135.703 L2236.23 131.444 L2244.49 129.778 L2249.17 129.778 L2249.17 160.402 L2256.81 160.402 L2256.81 164.338 L2236.9 164.338 L2236.9 160.402 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip650)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2036.47,198.898 2180.39,198.898 \"/>\n",
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"<path clip-path=\"url(#clip650)\" d=\"M2218.22 218.585 Q2216.42 223.215 2214.7 224.627 Q2212.99 226.039 2210.12 226.039 L2206.72 226.039 L2206.72 222.474 L2209.22 222.474 Q2210.98 222.474 2211.95 221.64 Q2212.92 220.807 2214.1 217.705 L2214.86 215.761 L2204.38 190.252 L2208.89 190.252 L2216.99 210.529 L2225.1 190.252 L2229.61 190.252 L2218.22 218.585 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip650)\" d=\"M2240.12 212.242 L2256.44 212.242 L2256.44 216.178 L2234.49 216.178 L2234.49 212.242 Q2237.16 209.488 2241.74 204.858 Q2246.35 200.205 2247.53 198.863 Q2249.77 196.34 2250.65 194.604 Q2251.55 192.844 2251.55 191.155 Q2251.55 188.4 2249.61 186.664 Q2247.69 184.928 2244.59 184.928 Q2242.39 184.928 2239.93 185.692 Q2237.5 186.455 2234.73 188.006 L2234.73 183.284 Q2237.55 182.15 2240 181.571 Q2242.46 180.993 2244.49 180.993 Q2249.86 180.993 2253.06 183.678 Q2256.25 186.363 2256.25 190.854 Q2256.25 192.983 2255.44 194.905 Q2254.66 196.803 2252.55 199.395 Q2251.97 200.067 2248.87 203.284 Q2245.77 206.479 2240.12 212.242 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
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]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot(saveat, solavg_ohm[:, 3])\n",
|
||
"plot!(saveat, solavg_col[:, 3])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "59ac92d9-6a78-402b-91ae-3f5fd22cc6ff",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"projected_ohm = zeros(nruns, length(saveat), 2)\n",
|
||
"\n",
|
||
"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg_ohm)]\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_ohm[j, i, :]\n",
|
||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
|
||
"\n",
|
||
" projected_ohm[j, i, 1] = dot(u,b)\n",
|
||
" projected_ohm[j, i, 2] = dot(v,b)\n",
|
||
" end\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "f1661b24-42b1-4f59-989a-54dc3ed03bf8",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"projected_col = zeros(nruns, length(saveat), 2)\n",
|
||
"\n",
|
||
"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg_col)]\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_col[j, i, :]\n",
|
||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
|
||
"\n",
|
||
" projected_col[j, i, 1] = dot(u,b)\n",
|
||
" projected_col[j, i, 2] = dot(v,b)\n",
|
||
" end\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "e4ad51fc-0dc7-4106-99e4-2b29e54b1930",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"using HypothesisTests\n",
|
||
"using LaTeXStrings"
|
||
]
|
||
},
|
||
{
|
||
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"id": "e5b9609e-f467-4bd7-9b51-9a4c1f175738",
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"source": [
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"JB_ohm = zeros(N)\n",
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"for i in 1:N\n",
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" JB_ohm[i] = HypothesisTests.JarqueBeraTest(projected_ohm[:, 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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"source": [
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"JB_col = zeros(N)\n",
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"for i in 1:N\n",
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" JB_col[i] = HypothesisTests.JarqueBeraTest(projected_col[:, 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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"metadata": {},
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575.905,1382.5 577.903,1381.43 579.902,1378.79 581.901,1378.12 583.899,1381.26 585.898,1381.25 587.897,1378.98 589.895,1380.08 591.894,1381.07 593.893,1380.64 595.892,1380.94 597.89,1380.65 599.889,1377.87 601.888,1375.77 603.886,1374.67 605.885,1373.86 607.884,1375.97 609.883,1377.34 611.881,1376.28 613.88,1373.41 615.879,1368.68 617.877,1363.02 619.876,1360.23 621.875,1362.24 623.874,1365.1 625.872,1366.83 627.871,1365.13 629.87,1364.57 631.868,1368.58 633.867,1369.74 635.866,1367.8 637.864,1366.77 639.863,1366.63 641.862,1367.51 643.861,1363.74 645.859,1362.95 647.858,1366.19 649.857,1368.58 651.855,1374.08 653.854,1377.41 655.853,1376.81 657.852,1374.96 659.85,1374.09 661.849,1369.56 663.848,1362.61 665.846,1362.08 667.845,1365.59 669.844,1369.61 671.842,1370.23 673.841,1371.61 675.84,1375.36 677.839,1380.27 679.837,1380.64 681.836,1377.76 683.835,1377.69 685.833,1377.06 687.832,1375.12 689.831,1373.62 691.83,1372.49 693.828,1372.64 695.827,1373.31 697.826,1372.92 699.824,1376.58 701.823,1382.43 703.822,1381.16 705.821,1375.28 707.819,1373.12 709.818,1375.65 711.817,1378.63 713.815,1379.38 715.814,1376.94 717.813,1374.21 719.811,1376.6 721.81,1378.46 723.809,1377.74 725.808,1377.09 727.806,1377.57 729.805,1381.09 731.804,1383.97 733.802,1384.43 735.801,1382.09 737.8,1381.77 739.799,1385.62 741.797,1392.54 743.796,1394.89 745.795,1391.93 747.793,1387.22 749.792,1386.24 751.791,1387.98 753.79,1388.21 755.788,1387.92 757.787,1388.83 759.786,1389.75 761.784,1390.16 763.783,1392.78 765.782,1394.72 767.78,1393.42 769.779,1390.91 771.778,1389.87 773.777,1389.81 775.775,1387.06 777.774,1382.44 779.773,1382.34 781.771,1385.5 783.77,1387.34 785.769,1386.8 787.768,1384.49 789.766,1383.55 791.765,1384.58 793.764,1386.29 795.762,1388.09 797.761,1386.39 799.76,1386.14 801.759,1388.58 803.757,1389.42 805.756,1387 807.755,1382.8 809.753,1378.85 811.752,1373.8 813.751,1372.75 815.749,1374.91 817.748,1378.82 819.747,1380.32 821.746,1379.79 823.744,1383.32 825.743,1389.64 827.742,1392.06 829.74,1391.04 831.739,1386.63 833.738,1384 835.737,1385.8 837.735,1387.28 839.734,1386.99 841.733,1386.66 843.731,1386.31 845.73,1384.59 847.729,1381.83 849.728,1380.17 851.726,1379.43 853.725,1378.45 855.724,1378.62 857.722,1382.61 859.721,1384.83 861.72,1386.94 863.718,1388.61 865.717,1382.81 867.716,1373.43 869.715,1368.5 871.713,1371.05 873.712,1377.01 875.711,1381.49 877.709,1386.13 879.708,1388.18 881.707,1385.66 883.706,1384.66 885.704,1388.48 887.703,1392.93 889.702,1394.43 891.7,1391.77 893.699,1388.58 895.698,1389.59 897.696,1392.46 899.695,1392.93 901.694,1390.72 903.693,1387.94 905.691,1386.93 907.69,1389.08 909.689,1391.49 911.687,1391.85 913.686,1391.45 915.685,1391.37 917.684,1391.01 919.682,1390.08 921.681,1389.14 923.68,1391.32 925.678,1393 927.677,1393.77 929.676,1393.52 931.675,1393.31 933.673,1394.69 935.672,1394.05 937.671,1391.35 939.669,1389.59 941.668,1392.19 943.667,1397.63 945.665,1401.35 947.664,1402.38 949.663,1401.14 951.662,1400.34 953.66,1401.14 955.659,1403.68 957.658,1407.71 959.656,1410.7 961.655,1411.31 963.654,1409.64 965.653,1406.57 967.651,1405.42 969.65,1405.02 971.649,1405.98 973.647,1407.68 975.646,1407.26 977.645,1406.13 979.644,1405.59 981.642,1405.92 983.641,1407.49 985.64,1408.9 987.638,1406.51 989.637,1401.65 991.636,1401.27 993.634,1403.18 995.633,1402.53 997.632,1400.53 999.631,1399.59 1001.63,1400.32 1003.63,1400.88 1005.63,1399.57 1007.63,1397.91 1009.62,1397.94 1011.62,1397.73 1013.62,1396.05 1015.62,1395.8 1017.62,1395.18 1019.62,1393.38 1021.62,1396.37 1023.62,1399.76 1025.61,1400.87 1027.61,1398.55 1029.61,1393.35 1031.61,1393.41 1033.61,1397.43 1035.61,1398.2 1037.61,1394.2 1039.6,1392.32 1041.6,1395.8 1043.6,1397.58 1045.6,1397.84 1047.6,1399.48 1049.6,1400.29 1051.6,1399.75 1053.6,1399.84 1055.59,1400 1057.59,1400.17 1059.59,1403.16 1061.59,1406.37 1063.59,1408.85 1065.59,1409.83 1067.59,1407.34 1069.59,1402.15 1071.58,1397.81 1073.58,1397.37 1075.58,1399.94 1077.58,1400.59 1079.58,1399.84 1081.58,1399.62 1083.58,1399.34 1085.58,1397.39 1087.57,1394.13 1089.57,1392.91 1091.57,1390.73 1093.57,1388.31 1095.57,1390.7 1097.57,1392.66 1099.57,1388.7 1101.56,1384.68 1103.56,1387.7 1105.56,1392.03 1107.56,1393.49 1109.56,1392.54 1111.56,1389.96 1113.56,1386.02 1115.56,1383.23 1117.55,1381.46 1119.55,1382.62 1121.55,1381.98 1123.55,1380.68 1125.55,1377.65 1127.55,1377.47 1129.55,1378.51 1131.55,1378.06 1133.54,1372.17 1135.54,1367.39 1137.54,1364.98 1139.54,1358.43 1141.54,1351.74 1143.54,1353.41 1145.54,1358.43 1147.53,1358.54 1149.53,1354.2 1151.53,1351.88 1153.53,1351.42 1155.53,1350.72 1157.53,1346.02 1159.53,1340.47 1161.53,1339.41 1163.52,1339.42 1165.52,1339.4 1167.52,1336.97 1169.52,1333.68 1171.52,1334.12 1173.52,1334.61 1175.52,1328.66 1177.52,1323.33 1179.51,1322.59 1181.51,1320.33 1183.51,1320 1185.51,1325.69 1187.51,1324.89 1189.51,1316.53 1191.51,1309.65 1193.51,1310.03 1195.5,1311.89 1197.5,1313.62 1199.5,1317.66 1201.5,1317.09 1203.5,1315.62 1205.5,1323.18 1207.5,1329.8 1209.49,1326.12 1211.49,1320.96 1213.49,1323.03 1215.49,1324.83 1217.49,1323.89 1219.49,1326.25 1221.49,1324.74 1223.49,1323.69 1225.48,1324.6 1227.48,1322.71 1229.48,1315.83 1231.48,1311.6 1233.48,1312.8 1235.48,1316.4 1237.48,1315.58 1239.48,1306.95 1241.47,1300.63 1243.47,1309.09 1245.47,1317.49 1247.47,1323.51 1249.47,1323.61 1251.47,1323.8 1253.47,1328.45 1255.47,1332.3 1257.46,1329.33 1259.46,1324.74 1261.46,1325.27 1263.46,1327.61 1265.46,1326.38 1267.46,1326.43 1269.46,1329.43 1271.45,1329.91 1273.45,1325.84 1275.45,1324.71 1277.45,1323.73 1279.45,1327.43 1281.45,1335.03 1283.45,1340.84 1285.45,1340.88 1287.44,1339.86 1289.44,1334.44 1291.44,1325.66 1293.44,1313.94 1295.44,1310.69 1297.44,1309.63 1299.44,1306.45 1301.44,1307.31 1303.43,1311.67 1305.43,1313.46 1307.43,1313.07 1309.43,1312.9 1311.43,1312.02 1313.43,1309.82 1315.43,1306.82 1317.43,1312.26 1319.42,1319.36 1321.42,1319.29 1323.42,1314.21 1325.42,1310.93 1327.42,1318.86 1329.42,1329.9 1331.42,1336.61 1333.41,1337.22 1335.41,1331.11 1337.41,1327.85 1339.41,1328.52 1341.41,1331.67 1343.41,1333.12 1345.41,1336.11 1347.41,1340.26 1349.4,1336.08 1351.4,1324.74 1353.4,1322.22 1355.4,1330.15 1357.4,1333.46 1359.4,1331.23 1361.4,1331.13 1363.4,1330.77 1365.39,1327.61 1367.39,1326.12 1369.39,1332.26 1371.39,1336.81 1373.39,1341.09 1375.39,1343.22 1377.39,1344.92 1379.39,1343.02 1381.38,1337.43 1383.38,1338.18 1385.38,1343.59 1387.38,1339.97 1389.38,1333.64 1391.38,1333.49 1393.38,1334.7 1395.37,1337.09 1397.37,1338.81 1399.37,1337.26 1401.37,1338.28 1403.37,1340.59 1405.37,1340.19 1407.37,1336.86 1409.37,1337.73 1411.36,1343.73 1413.36,1347.84 1415.36,1346.67 1417.36,1345.76 1419.36,1342.45 1421.36,1339.26 1423.36,1342.15 1425.36,1345.81 1427.35,1348.97 1429.35,1349.89 1431.35,1348.68 1433.35,1348.95 1435.35,1350.98 1437.35,1353.67 1439.35,1353.55 1441.35,1352.66 1443.34,1354.28 1445.34,1354.11 1447.34,1355.64 1449.34,1353.7 1451.34,1353.04 1453.34,1352.9 1455.34,1350.5 1457.33,1356.8 1459.33,1367.93 1461.33,1372.49 1463.33,1372.08 1465.33,1366.62 1467.33,1362.77 1469.33,1362.15 1471.33,1363.11 1473.32,1367.24 1475.32,1366.1 1477.32,1357.81 1479.32,1348.12 1481.32,1340.42 1483.32,1338.34 1485.32,1344.49 1487.32,1351.71 1489.31,1352.81 1491.31,1353.41 1493.31,1356.77 1495.31,1359.54 1497.31,1360.09 1499.31,1363.19 1501.31,1362.92 1503.31,1358.35 1505.3,1359.45 1507.3,1362.18 1509.3,1367.18 1511.3,1373.9 1513.3,1377.47 1515.3,1373.58 1517.3,1368.76 1519.29,1363.38 1521.29,1361.04 1523.29,1367.45 1525.29,1374.87 1527.29,1375.75 1529.29,1371.3 1531.29,1367.98 1533.29,1372.96 1535.28,1378.31 1537.28,1376.23 1539.28,1369.89 1541.28,1364.87 1543.28,1364.1 1545.28,1369.06 1547.28,1372.73 1549.28,1374.2 1551.27,1375.92 1553.27,1372.73 1555.27,1368.56 1557.27,1365.4 1559.27,1361.38 1561.27,1361.57 1563.27,1362.25 1565.26,1362.5 1567.26,1365.35 1569.26,1369.36 1571.26,1369 1573.26,1371.32 1575.26,1377.17 1577.26,1381.29 1579.26,1382 1581.25,1378.99 1583.25,1378.93 1585.25,1379.76 1587.25,1378.34 1589.25,1376.17 1591.25,1373.79 1593.25,1374.57 1595.25,1375.46 1597.24,1368.37 1599.24,1361.35 1601.24,1367.54 1603.24,1376 1605.24,1381.04 1607.24,1380.82 1609.24,1377.16 1611.24,1379.21 1613.23,1385.45 1615.23,1386.33 1617.23,1378.28 1619.23,1371.15 1621.23,1377.22 1623.23,1385.55 1625.23,1390.95 1627.22,1388.61 1629.22,1380.27 1631.22,1376.77 1633.22,1377.9 1635.22,1380.44 1637.22,1379.46 1639.22,1379.63 1641.22,1383.16 1643.21,1384.34 1645.21,1384.78 1647.21,1384.42 1649.21,1383.53 1651.21,1386.57 1653.21,1388.08 1655.21,1386.23 1657.21,1380.92 1659.2,1374.07 1661.2,1372.58 1663.2,1371.22 1665.2,1369.54 1667.2,1367.22 1669.2,1370.99 1671.2,1373.65 1673.2,1377.1 1675.19,1379.45 1677.19,1380.08 1679.19,1379.96 1681.19,1381.2 1683.19,1375.17 1685.19,1371.81 1687.19,1372.87 1689.18,1375.1 1691.18,1379.37 1693.18,1379.07 1695.18,1372.32 1697.18,1365.58 1699.18,1360.28 1701.18,1355.31 1703.18,1358.4 1705.17,1363.39 1707.17,1367.59 1709.17,1369.11 1711.17,1366.93 1713.17,1361.25 1715.17,1359.82 1717.17,1362.76 1719.17,1365.46 1721.16,1367.92 1723.16,1371.43 1725.16,1372.06 1727.16,1368.35 1729.16,1361.22 1731.16,1354.89 1733.16,1357.23 1735.16,1361.73 1737.15,1367.35 1739.15,1368.74 1741.15,1369.2 1743.15,1370.71 1745.15,1369.22 1747.15,1366.41 1749.15,1367.2 1751.14,1372.7 1753.14,1377.53 1755.14,1377.43 1757.14,1376.15 1759.14,1373.32 1761.14,1370.37 1763.14,1370.74 1765.14,1381.86 1767.13,1384.16 1769.13,1378.06 1771.13,1377.12 1773.13,1382.82 1775.13,1387.74 1777.13,1387.12 1779.13,1384.47 1781.13,1384.64 1783.12,1384.52 1785.12,1383.33 1787.12,1380.95 1789.12,1383.22 1791.12,1389.09 1793.12,1386.55 1795.12,1376.46 1797.12,1372.15 1799.11,1376.3 1801.11,1378.98 1803.11,1380.05 1805.11,1385.19 1807.11,1390.76 1809.11,1390.48 1811.11,1389.18 1813.1,1385.85 1815.1,1385.18 1817.1,1388.06 1819.1,1390.59 1821.1,1391.9 1823.1,1393.7 1825.1,1396.76 1827.1,1398.76 1829.09,1398.37 1831.09,1395.94 1833.09,1393.59 1835.09,1390.01 1837.09,1390.2 1839.09,1394.24 1841.09,1397.83 1843.09,1399.96 1845.08,1403.35 1847.08,1404.22 1849.08,1402.46 1851.08,1398.17 1853.08,1395.78 1855.08,1392.93 1857.08,1391.6 1859.08,1391.23 1861.07,1392.73 1863.07,1396.07 1865.07,1400.33 1867.07,1403.88 1869.07,1405.78 1871.07,1405.24 1873.07,1404 1875.06,1404.98 1877.06,1405.96 1879.06,1401.88 1881.06,1398.43 1883.06,1400.51 1885.06,1403.52 1887.06,1402.07 1889.06,1396.51 1891.05,1395.74 1893.05,1399.34 1895.05,1400.63 1897.05,1403.09 1899.05,1412.2 1901.05,1418.56 1903.05,1419.66 1905.05,1419.59 1907.04,1418.67 1909.04,1416.2 1911.04,1414.55 1913.04,1416.44 1915.04,1417.7 1917.04,1417.88 1919.04,1418.45 1921.03,1417.46 1923.03,1414.94 1925.03,1411.13 1927.03,1407.57 1929.03,1404.78 1931.03,1404.51 1933.03,1405.92 1935.03,1407.48 1937.02,1409.15 1939.02,1409.76 1941.02,1408.79 1943.02,1406.57 1945.02,1405.33 1947.02,1402.92 1949.02,1397.09 1951.02,1391.8 1953.01,1391.27 1955.01,1388.3 1957.01,1383.88 1959.01,1387.93 1961.01,1396.51 1963.01,1398.96 1965.01,1397.19 1967.01,1393.85 1969,1394.96 1971,1397.12 1973,1397.22 1975,1398.06 1977,1400.51 1979,1402.22 1981,1404.88 1982.99,1406.84 1984.99,1406.68 1986.99,1409.15 1988.99,1409.9 1990.99,1408.97 1992.99,1410.63 1994.99,1413.18 1996.99,1414.22 1998.98,1414.4 2000.98,1416.1 2002.98,1418.9 2004.98,1420.82 2006.98,1420.76 2008.98,1419.57 2010.98,1418.65 2012.98,1418.12 2014.97,1418.82 2016.97,1419.47 2018.97,1421.08 2020.97,1422.66 2022.97,1422.73 2024.97,1421.2 2026.97,1419.54 2028.97,1421.27 2030.96,1422.62 2032.96,1422.79 2034.96,1422.4 2036.96,1421.37 2038.96,1420.09 2040.96,1420.34 2042.96,1419.42 2044.95,1418.98 2046.95,1420.15 2048.95,1420.74 2050.95,1420.42 2052.95,1418.9 2054.95,1418.66 2056.95,1419.12 2058.95,1419.69 2060.94,1419.71 2062.94,1418.53 2064.94,1418.67 2066.94,1421.15 2068.94,1422.58 2070.94,1423.06 2072.94,1423.05 2074.94,1423.05 2076.93,1423.1 2078.93,1423.16 2080.93,1423.02 2082.93,1422.58 2084.93,1422.13 2086.93,1422.65 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]
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},
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"execution_count": 12,
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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, JB_ohm, title=\"JB Test for Ohmic and Non-Ohmic Coupling\", label=\"Ohmic\", linewidth=2, xlabel=\"Time\", ylabel=\"JB Test\", legend=:topleft, ylimits=(0, 200))\n",
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"plot!(saveat, JB_col, label=\"Non-Ohmic\", linewidth=2)"
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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": 13,
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"id": "ad2674ba-9711-4feb-96ab-a39d88b27ce5",
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"metadata": {},
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"outputs": [
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{
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653.673,1376.58 655.473,1382.43 657.274,1381.16 659.075,1375.28 660.875,1373.12 662.676,1375.65 664.477,1378.63 666.277,1379.38 668.078,1376.94 669.879,1374.21 671.679,1376.6 673.48,1378.46 675.28,1377.74 677.081,1377.09 678.882,1377.57 680.682,1381.09 682.483,1383.97 684.284,1384.43 686.084,1382.09 687.885,1381.77 689.685,1385.62 691.486,1392.54 693.287,1394.89 695.087,1391.93 696.888,1387.22 698.689,1386.24 700.489,1387.98 702.29,1388.21 704.091,1387.92 705.891,1388.83 707.692,1389.75 709.492,1390.16 711.293,1392.78 713.094,1394.72 714.894,1393.42 716.695,1390.91 718.496,1389.87 720.296,1389.81 722.097,1387.06 723.898,1382.44 725.698,1382.34 727.499,1385.5 729.299,1387.34 731.1,1386.8 732.901,1384.49 734.701,1383.55 736.502,1384.58 738.303,1386.29 740.103,1388.09 741.904,1386.39 743.704,1386.14 745.505,1388.58 747.306,1389.42 749.106,1387 750.907,1382.8 752.708,1378.85 754.508,1373.8 756.309,1372.75 758.11,1374.91 759.91,1378.82 761.711,1380.32 763.511,1379.79 765.312,1383.32 767.113,1389.64 768.913,1392.06 770.714,1391.04 772.515,1386.63 774.315,1384 776.116,1385.8 777.916,1387.28 779.717,1386.99 781.518,1386.66 783.318,1386.31 785.119,1384.59 786.92,1381.83 788.72,1380.17 790.521,1379.43 792.322,1378.45 794.122,1378.62 795.923,1382.61 797.723,1384.83 799.524,1386.94 801.325,1388.61 803.125,1382.81 804.926,1373.43 806.727,1368.5 808.527,1371.05 810.328,1377.01 812.129,1381.49 813.929,1386.13 815.73,1388.18 817.53,1385.66 819.331,1384.66 821.132,1388.48 822.932,1392.93 824.733,1394.43 826.534,1391.77 828.334,1388.58 830.135,1389.59 831.935,1392.46 833.736,1392.93 835.537,1390.72 837.337,1387.94 839.138,1386.93 840.939,1389.08 842.739,1391.49 844.54,1391.85 846.341,1391.45 848.141,1391.37 849.942,1391.01 851.742,1390.08 853.543,1389.14 855.344,1391.32 857.144,1393 858.945,1393.77 860.746,1393.52 862.546,1393.31 864.347,1394.69 866.147,1394.05 867.948,1391.35 869.749,1389.59 871.549,1392.19 873.35,1397.63 875.151,1401.35 876.951,1402.38 878.752,1401.14 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1906.91,1422.58 1908.71,1422.44 1910.51,1423.1 1912.32,1422.18 1914.12,1420.89 1915.92,1421.18 1917.72,1421.79 1919.52,1422.63 1921.32,1422.7 1923.12,1422.76 1924.92,1422.8 1926.72,1422.7 1928.52,1421.94 1930.32,1420.93 1932.12,1420.68 1933.92,1418.82 1935.72,1416.83 1937.52,1417.53 1939.32,1419.68 1941.13,1420.59 1942.93,1420.51 1944.73,1420.43 1946.53,1420.53 1948.33,1421.63 1950.13,1422.1 1951.93,1422.23 1953.73,1422.78 1955.53,1423.08 1957.33,1421.99 1959.13,1420.94 1960.93,1419.99 1962.73,1417.67 1964.53,1413.8 1966.33,1409.85 1968.13,1408.55 1969.94,1410.28 1971.74,1410.37 1973.54,1407.98 1975.34,1405.69 1977.14,1402.33 1978.94,1403.87 1980.74,1408.89 1982.54,1411.79 1984.34,1412 1986.14,1407.95 1987.94,1404.36 1989.74,1403.23 1991.54,1402.55 1993.34,1403.32 1995.14,1404.57 1996.94,1405.43 1998.75,1404.63 2000.55,1401.36 2002.35,1398.8 2004.15,1397.76 2005.95,1399.2 2007.75,1401.62 2009.55,1402.83 2011.35,1402.56 2013.15,1403.83 2014.95,1405.95 2016.75,1404.95 2018.55,1403.71 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]
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},
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||
"execution_count": 13,
|
||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
|
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],
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||
"source": [
|
||
"right_axis = twinx()\n",
|
||
"\n",
|
||
"plot!(right_axis, saveat, solavg_ohm[:, 3], label=\"Ohmic\", ls=:dash, ylabel=L\"S_z\", ylimits=(-1.5, 1.5))\n",
|
||
"plot!(right_axis, saveat, solavg_col[:, 3], label=\"Non-Ohmic\", ls=:dash)"
|
||
]
|
||
},
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||
{
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||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "a1c77edf-652b-42ea-8bc0-445749a22a2c",
|
||
"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: \"-0.3052333801108836 and 3.1710040046492263\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: reject h_0\n",
|
||
" one-sided p-value: <1e-36\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 167.463\n"
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected_col[:, 125, 1])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "48b2963f-d070-46c9-a077-fe4aad09155a",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
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||
"metadata": {
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||
"kernelspec": {
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||
"display_name": "Julia 1.7.3",
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||
"language": "julia",
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||
"name": "julia-1.7"
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||
},
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"language_info": {
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"file_extension": ".jl",
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||
"mimetype": "application/julia",
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||
"name": "julia",
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||
"version": "1.7.3"
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||
}
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||
},
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"nbformat": 4,
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"nbformat_minor": 5
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||
}
|