643 lines
409 KiB
Text
643 lines
409 KiB
Text
{
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"cells": [
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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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"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, 0]\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"
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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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]
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},
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"execution_count": 24,
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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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"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": 25,
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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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2290.5,1445.43 2292.51,1445.46 \"/>\n",
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"<path clip-path=\"url(#clip630)\" d=\"M2016.5 250.738 L2281.8 250.738 L2281.8 95.2176 L2016.5 95.2176 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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]
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},
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"execution_count": 6,
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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_ohm[:, 3])\n",
|
||
"plot!(saveat, solavg_col[:, 3])"
|
||
]
|
||
},
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{
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||
"cell_type": "code",
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"execution_count": 7,
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"id": "59ac92d9-6a78-402b-91ae-3f5fd22cc6ff",
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"metadata": {},
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||
"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"
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]
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},
|
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{
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "e5b9609e-f467-4bd7-9b51-9a4c1f175738",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"JB_ohm = zeros(N)\n",
|
||
"for i in 1:N\n",
|
||
" JB_ohm[i] = HypothesisTests.JarqueBeraTest(projected_ohm[:, i, 1]).JB\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "51ccaeb8-2b3d-4630-afc3-2640142c4d54",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"JB_col = zeros(N)\n",
|
||
"for i in 1:N\n",
|
||
" JB_col[i] = HypothesisTests.JarqueBeraTest(projected_col[:, i, 1]).JB\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
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"execution_count": 12,
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||
"id": "6c63a170-6eff-4c8b-8b80-542eb705666f",
|
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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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"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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},
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||
"execution_count": 13,
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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": [
|
||
"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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||
},
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{
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"cell_type": "code",
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||
"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: \"-0.010024181624728401 and 2.9355563110404956\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: fail to reject h_0\n",
|
||
" one-sided p-value: 0.3872\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 10000\n",
|
||
" JB statistic: 1.89789\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": {},
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||
"outputs": [],
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||
"source": []
|
||
}
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||
],
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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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||
}
|