main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximate Bayesian Computation As An Informed Fuzzy Inference System\n",
    "\n",
    "Author: Chris Vaisnor\n",
    "\n",
    "This notebook is a companion to the paper \"Approximate Bayesian Computation As An Informed Fuzzy Inference System\" by Chris Vaisnor as part of the M.S. in Articial Intelligence program at The Johns Hopkins University."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7fad6899e450>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import tqdm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.graph_objects as go\n",
    "import plotly.figure_factory as ff\n",
    "import random\n",
    "\n",
    "# GLOBALS\n",
    "torch.manual_seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Black Box Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fuzz_test(particles):\n",
    "    '''\n",
    "    This function will test if a batch of particles satisfies the following criteria:\n",
    "\n",
    "    Criteria:\n",
    "    For each particle:\n",
    "    - if the first dimension is within the range of -0.5 and 0.5, then the particle passes the test\n",
    "\n",
    "    The count represents the number of particles that pass the fuzz test\n",
    "    '''\n",
    "    count = 0\n",
    "    for particle in particles:\n",
    "        # if particle[0] is within the range of -0.5 and 0.5, add 1 to the counter\n",
    "        if particle[0] >= -0.5 and particle[0] <= 0.5:\n",
    "            count += 1\n",
    "    \n",
    "    # return the percentage of particles that pass the fuzz test\n",
    "    return count / len(particles) * 100 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prior Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prior(N, D, mu=0, sigma=1.0, shuffle=True, modify=False, dimension_to_modify=None, percentage_to_modify=None) -> torch.Tensor:\n",
    "    '''\n",
    "    Each dimension will have a mean of mu and a standard deviation of sigma.\n",
    "    The prior is assumed to be a Gaussian distribution.\n",
    "    '''\n",
    "    particles = torch.normal(mean=mu, std=sigma, size=(N, D))\n",
    "\n",
    "    if shuffle:\n",
    "        indices = torch.randperm(N)\n",
    "        particles = particles[indices]\n",
    "\n",
    "    if modify:\n",
    "        particles = prior_modification(particles, dimension_to_modify, percentage_to_modify)\n",
    "    \n",
    "    return particles\n",
    "\n",
    "\n",
    "def prior_modification(particles, dimension_to_modify, percentage_to_modify):\n",
    "    '''\n",
    "    Manual modification of the prior\n",
    "    '''\n",
    "    particles_modified = particles.clone()\n",
    "\n",
    "    # base cases\n",
    "    if percentage_to_modify is None:\n",
    "        percentage_to_modify = 0.3 # modify 30% of the particles\n",
    "\n",
    "    if dimension_to_modify is None:\n",
    "        dimension_to_modify = 0 # select dimension 0\n",
    "\n",
    "    modified_dimension_value = 0 # set the new dimension value to 0\n",
    "\n",
    "    if particles_modified.shape[0] == 1:\n",
    "        particles_modified[0, dimension_to_modify] = modified_dimension_value\n",
    "        print(f\"Modifying 1 particle out of 1 particle\")\n",
    "        return particles_modified\n",
    "\n",
    "    # modify the particles\n",
    "    num_particles_to_modify = int(particles.shape[0] * percentage_to_modify)\n",
    "    print(f\"Modifying {num_particles_to_modify} particles out of {particles.shape[0]} particles\")\n",
    "    particles_modified[:num_particles_to_modify, dimension_to_modify] = modified_dimension_value\n",
    "\n",
    "    return particles_modified"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing prior functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Modifying 3 particles out of 10 particles\n",
      "Prior samples:\n",
      "tensor([[-1.2633,  0.3500,  0.3081],\n",
      "        [-0.1023,  0.7924, -0.2897],\n",
      "        [-0.4339,  0.8487,  0.6920]])\n",
      "Shape: torch.Size([10, 3])\n",
      "\n",
      "Prior samples (modified):\n",
      "tensor([[ 0.0000,  1.1687,  0.3945],\n",
      "        [ 0.0000,  0.5073, -0.5515],\n",
      "        [ 0.0000,  0.3582, -0.0033]])\n",
      "Shape: torch.Size([10, 3])\n",
      "\n",
      "Fuzz test (prior samples):\n",
      "80.0\n",
      "\n",
      "Fuzz test (prior samples modified):\n",
      "50.0\n"
     ]
    }
   ],
   "source": [
    "# generate N prior samples\n",
    "prior_samples = prior(N=10, D=3, modify=False)\n",
    "prior_samples_modified = prior(N=10, D=3, modify=True)\n",
    "\n",
    "print(\"Prior samples:\")\n",
    "print(prior_samples[:3])\n",
    "print('Shape:', prior_samples.shape)\n",
    "print()\n",
    "print(\"Prior samples (modified):\")\n",
    "print(prior_samples_modified[:3])\n",
    "print('Shape:', prior_samples_modified.shape)\n",
    "print()\n",
    "\n",
    "# fuzz test the prior samples\n",
    "print(\"Fuzz test (prior samples):\")\n",
    "print(fuzz_test(prior_samples))\n",
    "print()\n",
    "print(\"Fuzz test (prior samples modified):\")\n",
    "print(fuzz_test(prior_samples_modified))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)"
         },
         "name": "Dimension 0",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          -1.2633347511291504,
          -0.10230965167284012,
          -0.4338788092136383,
          -0.31601276993751526,
          -1.1258398294448853,
          0.05250748619437218,
          0.11241118609905243,
          0.11984150856733322,
          -0.1116093322634697,
          -0.4926769733428955
         ],
         "xaxis": "x",
         "xbins": {
          "end": 0.11984150856733322,
          "size": 0.2,
          "start": -1.2633347511291504
         },
         "yaxis": "y"
        },
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)"
         },
         "name": "Dimension 1",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          0.34998318552970886,
          0.7924439907073975,
          0.8487103581428528,
          -2.1152193546295166,
          -1.152360200881958,
          0.5228604674339294,
          -0.8410648107528687,
          1.237657904624939,
          -0.6135830879211426,
          0.2484147548675537
         ],
         "xaxis": "x",
         "xbins": {
          "end": 1.237657904624939,
          "size": 0.2,
          "start": -2.1152193546295166
         },
         "yaxis": "y"
        },
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)"
         },
         "name": "Dimension 2",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          0.30813392996788025,
          -0.28966769576072693,
          0.6920091509819031,
          0.32227492332458496,
          -0.2505785822868347,
          2.3022053241729736,
          -2.316041946411133,
          -0.14347384870052338,
          0.03159274160861969,
          0.4396958351135254
         ],
         "xaxis": "x",
         "xbins": {
          "end": 2.3022053241729736,
          "size": 0.2,
          "start": -2.316041946411133
         },
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)"
         },
         "mode": "lines",
         "name": "Dimension 0",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -1.2633347511291504,
          -1.2605683986097573,
          -1.2578020460903645,
          -1.2550356935709714,
          -1.2522693410515786,
          -1.2495029885321856,
          -1.2467366360127925,
          -1.2439702834933997,
          -1.2412039309740066,
          -1.2384375784546138,
          -1.2356712259352207,
          -1.2329048734158277,
          -1.2301385208964348,
          -1.2273721683770418,
          -1.224605815857649,
          -1.2218394633382559,
          -1.2190731108188628,
          -1.21630675829947,
          -1.213540405780077,
          -1.210774053260684,
          -1.208007700741291,
          -1.205241348221898,
          -1.2024749957025052,
          -1.199708643183112,
          -1.1969422906637193,
          -1.1941759381443262,
          -1.1914095856249332,
          -1.1886432331055403,
          -1.1858768805861473,
          -1.1831105280667544,
          -1.1803441755473614,
          -1.1775778230279683,
          -1.1748114705085755,
          -1.1720451179891824,
          -1.1692787654697896,
          -1.1665124129503965,
          -1.1637460604310035,
          -1.1609797079116106,
          -1.1582133553922176,
          -1.1554470028728248,
          -1.1526806503534317,
          -1.1499142978340386,
          -1.1471479453146458,
          -1.1443815927952528,
          -1.14161524027586,
          -1.1388488877564669,
          -1.1360825352370738,
          -1.133316182717681,
          -1.130549830198288,
          -1.127783477678895,
          -1.125017125159502,
          -1.122250772640109,
          -1.1194844201207161,
          -1.116718067601323,
          -1.1139517150819302,
          -1.1111853625625372,
          -1.1084190100431441,
          -1.1056526575237513,
          -1.1028863050043582,
          -1.1001199524849654,
          -1.0973535999655724,
          -1.0945872474461793,
          -1.0918208949267865,
          -1.0890545424073934,
          -1.0862881898880006,
          -1.0835218373686075,
          -1.0807554848492145,
          -1.0779891323298216,
          -1.0752227798104286,
          -1.0724564272910357,
          -1.0696900747716427,
          -1.0669237222522496,
          -1.0641573697328568,
          -1.0613910172134637,
          -1.058624664694071,
          -1.0558583121746778,
          -1.0530919596552848,
          -1.050325607135892,
          -1.047559254616499,
          -1.044792902097106,
          -1.042026549577713,
          -1.03926019705832,
          -1.0364938445389271,
          -1.033727492019534,
          -1.0309611395001412,
          -1.0281947869807482,
          -1.0254284344613551,
          -1.0226620819419623,
          -1.0198957294225692,
          -1.0171293769031764,
          -1.0143630243837833,
          -1.0115966718643903,
          -1.0088303193449975,
          -1.0060639668256044,
          -1.0032976143062116,
          -1.0005312617868185,
          -0.9977649092674256,
          -0.9949985567480326,
          -0.9922322042286396,
          -0.9894658517092466,
          -0.9866994991898537,
          -0.9839331466704607,
          -0.9811667941510678,
          -0.9784004416316747,
          -0.9756340891122818,
          -0.9728677365928888,
          -0.9701013840734959,
          -0.9673350315541029,
          -0.9645686790347099,
          -0.9618023265153169,
          -0.959035973995924,
          -0.956269621476531,
          -0.9535032689571381,
          -0.950736916437745,
          -0.9479705639183521,
          -0.9452042113989592,
          -0.9424378588795662,
          -0.9396715063601733,
          -0.9369051538407802,
          -0.9341388013213873,
          -0.9313724488019943,
          -0.9286060962826014,
          -0.9258397437632084,
          -0.9230733912438154,
          -0.9203070387244224,
          -0.9175406862050295,
          -0.9147743336856365,
          -0.9120079811662436,
          -0.9092416286468505,
          -0.9064752761274576,
          -0.9037089236080647,
          -0.9009425710886717,
          -0.8981762185692788,
          -0.8954098660498857,
          -0.8926435135304928,
          -0.8898771610110998,
          -0.8871108084917069,
          -0.8843444559723139,
          -0.8815781034529209,
          -0.8788117509335279,
          -0.876045398414135,
          -0.873279045894742,
          -0.8705126933753491,
          -0.867746340855956,
          -0.8649799883365631,
          -0.8622136358171701,
          -0.8594472832977772,
          -0.8566809307783843,
          -0.8539145782589912,
          -0.8511482257395983,
          -0.8483818732202053,
          -0.8456155207008124,
          -0.8428491681814194,
          -0.8400828156620264,
          -0.8373164631426334,
          -0.8345501106232405,
          -0.8317837581038475,
          -0.8290174055844546,
          -0.8262510530650615,
          -0.8234847005456686,
          -0.8207183480262756,
          -0.8179519955068827,
          -0.8151856429874897,
          -0.8124192904680967,
          -0.8096529379487037,
          -0.8068865854293108,
          -0.8041202329099179,
          -0.8013538803905249,
          -0.7985875278711319,
          -0.7958211753517389,
          -0.793054822832346,
          -0.790288470312953,
          -0.7875221177935601,
          -0.784755765274167,
          -0.7819894127547741,
          -0.7792230602353811,
          -0.7764567077159882,
          -0.7736903551965952,
          -0.7709240026772022,
          -0.7681576501578092,
          -0.7653912976384163,
          -0.7626249451190233,
          -0.7598585925996304,
          -0.7570922400802373,
          -0.7543258875608444,
          -0.7515595350414515,
          -0.7487931825220585,
          -0.7460268300026656,
          -0.7432604774832725,
          -0.7404941249638796,
          -0.7377277724444866,
          -0.7349614199250937,
          -0.7321950674057007,
          -0.7294287148863077,
          -0.7266623623669147,
          -0.7238960098475218,
          -0.7211296573281288,
          -0.7183633048087359,
          -0.7155969522893428,
          -0.7128305997699499,
          -0.710064247250557,
          -0.707297894731164,
          -0.7045315422117711,
          -0.701765189692378,
          -0.698998837172985,
          -0.6962324846535921,
          -0.6934661321341992,
          -0.6906997796148062,
          -0.6879334270954132,
          -0.6851670745760202,
          -0.6824007220566273,
          -0.6796343695372343,
          -0.6768680170178414,
          -0.6741016644984483,
          -0.6713353119790554,
          -0.6685689594596624,
          -0.6658026069402695,
          -0.6630362544208765,
          -0.6602699019014835,
          -0.6575035493820905,
          -0.6547371968626976,
          -0.6519708443433047,
          -0.6492044918239117,
          -0.6464381393045187,
          -0.6436717867851257,
          -0.6409054342657328,
          -0.6381390817463398,
          -0.6353727292269469,
          -0.6326063767075538,
          -0.6298400241881609,
          -0.6270736716687679,
          -0.624307319149375,
          -0.621540966629982,
          -0.618774614110589,
          -0.616008261591196,
          -0.6132419090718031,
          -0.6104755565524101,
          -0.6077092040330172,
          -0.6049428515136241,
          -0.6021764989942312,
          -0.5994101464748383,
          -0.5966437939554453,
          -0.5938774414360524,
          -0.5911110889166593,
          -0.5883447363972664,
          -0.5855783838778734,
          -0.5828120313584805,
          -0.5800456788390875,
          -0.5772793263196945,
          -0.5745129738003015,
          -0.5717466212809086,
          -0.5689802687615156,
          -0.5662139162421227,
          -0.5634475637227296,
          -0.5606812112033367,
          -0.5579148586839437,
          -0.5551485061645508,
          -0.5523821536451579,
          -0.5496158011257648,
          -0.5468494486063719,
          -0.5440830960869789,
          -0.541316743567586,
          -0.538550391048193,
          -0.5357840385288,
          -0.533017686009407,
          -0.5302513334900141,
          -0.5274849809706211,
          -0.5247186284512282,
          -0.5219522759318351,
          -0.5191859234124422,
          -0.5164195708930492,
          -0.5136532183736563,
          -0.5108868658542634,
          -0.5081205133348703,
          -0.5053541608154773,
          -0.5025878082960844,
          -0.49982145577669146,
          -0.4970551032572985,
          -0.49428875073790546,
          -0.4915223982185125,
          -0.48875604569911957,
          -0.4859896931797266,
          -0.4832233406603337,
          -0.4804569881409406,
          -0.4776906356215477,
          -0.47492428310215473,
          -0.4721579305827618,
          -0.46939157806336884,
          -0.4666252255439758,
          -0.46385887302458284,
          -0.4610925205051899,
          -0.45832616798579695,
          -0.455559815466404,
          -0.45279346294701095,
          -0.450027110427618,
          -0.44726075790822506,
          -0.4444944053888321,
          -0.44172805286943917,
          -0.4389617003500461,
          -0.43619534783065317,
          -0.4334289953112602,
          -0.4306626427918673,
          -0.42789629027247433,
          -0.4251299377530813,
          -0.42236358523368833,
          -0.4195972327142954,
          -0.41683088019490244,
          -0.4140645276755095,
          -0.41129817515611644,
          -0.4085318226367235,
          -0.40576547011733055,
          -0.4029991175979376,
          -0.40023276507854466,
          -0.3974664125591516,
          -0.39470006003975866,
          -0.3919337075203657,
          -0.38916735500097277,
          -0.3864010024815798,
          -0.38363464996218677,
          -0.3808682974427938,
          -0.3781019449234009,
          -0.37533559240400793,
          -0.372569239884615,
          -0.36980288736522193,
          -0.367036534845829,
          -0.36427018232643604,
          -0.3615038298070431,
          -0.35873747728765015,
          -0.3559711247682571,
          -0.35320477224886415,
          -0.3504384197294712,
          -0.34767206721007826,
          -0.3449057146906853,
          -0.34213936217129226,
          -0.3393730096518993,
          -0.33660665713250637,
          -0.3338403046131134,
          -0.3310739520937205,
          -0.3283075995743274,
          -0.3255412470549345,
          -0.32277489453554153,
          -0.3200085420161486,
          -0.31724218949675564,
          -0.3144758369773626,
          -0.31170948445796964,
          -0.3089431319385767,
          -0.30617677941918375,
          -0.3034104268997908,
          -0.30064407438039775,
          -0.2978777218610048,
          -0.29511136934161186,
          -0.2923450168222189,
          -0.28957866430282597,
          -0.2868123117834329,
          -0.28404595926403997,
          -0.281279606744647,
          -0.2785132542252541,
          -0.27574690170586114,
          -0.2729805491864681,
          -0.27021419666707513,
          -0.2674478441476822,
          -0.26468149162828924,
          -0.2619151391088963,
          -0.25914878658950324,
          -0.2563824340701104,
          -0.25361608155071735,
          -0.2508497290313243,
          -0.24808337651193146,
          -0.2453170239925384,
          -0.24255067147314557,
          -0.23978431895375252,
          -0.23701796643435946,
          -0.23425161391496663,
          -0.23148526139557357,
          -0.22871890887618074,
          -0.22595255635678768,
          -0.22318620383739463,
          -0.2204198513180018,
          -0.21765349879860874,
          -0.2148871462792159,
          -0.21212079375982285,
          -0.2093544412404298,
          -0.20658808872103696,
          -0.2038217362016439,
          -0.20105538368225107,
          -0.198289031162858,
          -0.19552267864346495,
          -0.19275632612407212,
          -0.18998997360467906,
          -0.18722362108528623,
          -0.18445726856589317,
          -0.18169091604650012,
          -0.17892456352710728,
          -0.17615821100771423,
          -0.1733918584883214,
          -0.17062550596892834,
          -0.16785915344953528,
          -0.16509280093014245,
          -0.1623264484107494,
          -0.15956009589135656,
          -0.1567937433719635,
          -0.15402739085257044,
          -0.1512610383331776,
          -0.14849468581378455,
          -0.14572833329439172,
          -0.14296198077499866,
          -0.1401956282556056,
          -0.13742927573621277,
          -0.13466292321681972,
          -0.13189657069742688,
          -0.12913021817803383,
          -0.12636386565864077,
          -0.12359751313924794,
          -0.12083116061985488,
          -0.11806480810046205,
          -0.11529845558106899,
          -0.11253210306167594,
          -0.1097657505422831,
          -0.10699939802289005,
          -0.10423304550349721,
          -0.10146669298410416,
          -0.0987003404647111,
          -0.09593398794531827,
          -0.09316763542592521,
          -0.09040128290653238,
          -0.08763493038713932,
          -0.08486857786774626,
          -0.08210222534835343,
          -0.07933587282896037,
          -0.07656952030956754,
          -0.07380316779017448,
          -0.07103681527078143,
          -0.0682704627513886,
          -0.06550411023199554,
          -0.0627377577126027,
          -0.05997140519320965,
          -0.05720505267381659,
          -0.05443870015442376,
          -0.0516723476350307,
          -0.04890599511563787,
          -0.04613964259624481,
          -0.043373290076851756,
          -0.04060693755745892,
          -0.037840585038065866,
          -0.03507423251867303,
          -0.032307879999279976,
          -0.02954152747988692,
          -0.026775174960494086,
          -0.02400882244110103,
          -0.021242469921708196,
          -0.01847611740231514,
          -0.015709764882922084,
          -0.01294341236352925,
          -0.010177059844136194,
          -0.00741070732474336,
          -0.004644354805350304,
          -0.0018780022859572476,
          0.0008883502334355864,
          0.0036547027528286424,
          0.006421055272221476,
          0.009187407791614532,
          0.011953760311007589,
          0.014720112830400423,
          0.01748646534979348,
          0.020252817869186313,
          0.02301917038857937,
          0.025785522907972425,
          0.02855187542736526,
          0.031318227946758315,
          0.03408458046615115,
          0.036850932985544205,
          0.03961728550493726,
          0.042383638024330095,
          0.04514999054372315,
          0.047916343063115985,
          0.05068269558250904,
          0.0534490481019021,
          0.05621540062129493,
          0.05898175314068799,
          0.06174810566008082,
          0.06451445817947388,
          0.06728081069886693,
          0.07004716321825977,
          0.07281351573765282,
          0.07557986825704566,
          0.07834622077643871,
          0.08111257329583177,
          0.0838789258152246,
          0.08664527833461766,
          0.0894116308540105,
          0.09217798337340355,
          0.0949443358927966,
          0.09771068841218944,
          0.1004770409315825,
          0.10324339345097533,
          0.10600974597036839,
          0.10877609848976144,
          0.11154245100915428,
          0.11430880352854733,
          0.11707515604794017
         ],
         "xaxis": "x",
         "y": [
          0.25601810962083,
          0.2567310361348822,
          0.2574315989471685,
          0.2581197891066056,
          0.2587956024093776,
          0.25945903942906584,
          0.2601101055449863,
          0.2607488109687137,
          0.26137517076876954,
          0.2619892048934525,
          0.2625909381917921,
          0.2631804004326045,
          0.2637576263216341,
          0.26432265551676154,
          0.26487553264126124,
          0.26541630729509474,
          0.26594503406422143,
          0.266461772527917,
          0.26696658726408296,
          0.2674595478525355,
          0.26794072887626613,
          0.2684102099206589,
          0.2688680755706586,
          0.2693144154058813,
          0.2697493239936578,
          0.2701729008800078,
          0.270585250578535,
          0.27098648255724367,
          0.27137671122327045,
          0.2717560559055306,
          0.2721246408352776,
          0.27248259512457573,
          0.2728300527426882,
          0.2731671524903811,
          0.27349403797214794,
          0.27381085756635803,
          0.2741177643933346,
          0.27441491628136927,
          0.2747024757306807,
          0.27498060987532325,
          0.27524949044306046,
          0.27550929371320787,
          0.2757602004724624,
          0.2760023959687267,
          0.27623606986294563,
          0.27646141617896725,
          0.2766786332514457,
          0.2768879236718019,
          0.277089494232261,
          0.2772835558679842,
          0.2774703235973166,
          0.27765001646017007,
          0.2778228574545647,
          0.2779890734713504,
          0.27814889522713426,
          0.2783025571954361,
          0.27845029753610057,
          0.2785923580229898,
          0.27872898396998774,
          0.2788604241553398,
          0.2789869307443633,
          0.27910875921055267,
          0.2792261682551165,
          0.27933941972497334,
          0.2794487785292429,
          0.2795545125542643,
          0.2796568925771762,
          0.2797561921780947,
          0.2798526876509241,
          0.27994665791283774,
          0.280038384412467,
          0.2801281510368347,
          0.2802162440170751,
          0.28030295183297543,
          0.2803885651163842,
          0.28047337655352317,
          0.2805576807862461,
          0.2806417743122863,
          0.2807259553845353,
          0.2808105239093947,
          0.280895781344247,
          0.2809820305940876,
          0.2810695759073631,
          0.28115872277106174,
          0.28124977780509847,
          0.28134304865604554,
          0.2814388438902492,
          0.28153747288638337,
          0.28163924572748417,
          0.28174447309251416,
          0.2818534661475029,
          0.2819665364363117,
          0.2820839957710704,
          0.28220615612233385,
          0.2823333295090069,
          0.28246582788808555,
          0.28260396304426283,
          0.28274804647944884,
          0.28289838930225153,
          0.283055302117469,
          0.28321909491564035,
          0.28339007696270413,
          0.28356855668981346,
          0.28375484158335484,
          0.28394923807522054,
          0.28415205143338157,
          0.28436358565281006,
          0.28458414334679816,
          0.2848140256387217,
          0.28505353205429534,
          0.2853029604143673,
          0.285562606728299,
          0.28583276508797795,
          0.28611372756250825,
          0.2864057840936253,
          0.28670922239188085,
          0.28702432783364173,
          0.287351383358948,
          0.2876906693702739,
          0.2880424636322356,
          0.2884070411722892,
          0.2887846741824592,
          0.28917563192214246,
          0.2895801806220273,
          0.2899985833891675,
          0.2904311001132544,
          0.2908779873741224,
          0.29133949835052997,
          0.2918158827302527,
          0.29230738662152594,
          0.292814252465873,
          0.2933367189523563,
          0.29387502093328455,
          0.29442938934141155,
          0.2950000511086592,
          0.2955872290863981,
          0.2961911419673166,
          0.2968120042089091,
          0.2974500259586143,
          0.2981054129806325,
          0.2987783665844482,
          0.2994690835550876,
          0.3001777560851358,
          0.30090457170853907,
          0.3016497132362167,
          0.3024133586935055,
          0.30319568125946017,
          0.30399684920802833,
          0.3048170258511237,
          0.3056563694836137,
          0.30651503333024244,
          0.3073931654945023,
          0.30829090890947497,
          0.3092084012906524,
          0.3101457750907548,
          0.31110315745655676,
          0.312080670187733,
          0.31307842969773625,
          0.3140965469767147,
          0.3151351275564779,
          0.3161942714775198,
          0.31727407325810264,
          0.31837462186541016,
          0.3194960006887698,
          0.3206382875149509,
          0.321801554505538,
          0.3229858681763812,
          0.32419128937912184,
          0.3254178732847941,
          0.32666566936949715,
          0.32793472140213625,
          0.32922506743422714,
          0.3305367397917577,
          0.3318697650691,
          0.3332241641249645,
          0.3345999520803878,
          0.3359971383187435,
          0.33741572648776447,
          0.33885571450356405,
          0.34031709455664483,
          0.3417998531198781,
          0.3433039709584407,
          0.34482942314169107,
          0.3463761790569692,
          0.3479442024253009,
          0.3495334513189876,
          0.3511438781810611,
          0.3527754298465834,
          0.35442804756576846,
          0.3561016670289027,
          0.3577962183930427,
          0.3595116263104631,
          0.3612478099588305,
          0.3630046830730772,
          0.3647821539789465,
          0.3665801256281844,
          0.3683984956353467,
          0.3702371563161919,
          0.3720959947276336,
          0.3739748927092167,
          0.37587372692608967,
          0.37779236891344076,
          0.379730685122362,
          0.38168853696711336,
          0.3836657808737475,
          0.3856622683300648,
          0.38767784593686394,
          0.38971235546044874,
          0.39176563388635927,
          0.39383751347428936,
          0.39592782181415553,
          0.3980363818832764,
          0.40016301210462946,
          0.4023075264061448,
          0.4044697342809984,
          0.4066494408488672,
          0.40884644691810534,
          0.411060549048806,
          0.4132915396167053,
          0.4155392068778936,
          0.41780333503429185,
          0.42008370429985376,
          0.4223800909674554,
          0.42469226747643096,
          0.4270200024807164,
          0.4293630609175603,
          0.4317212040767633,
          0.43409418967040336,
          0.43648177190301257,
          0.43888370154216044,
          0.44129972598940886,
          0.44372958935159607,
          0.4461730325124126,
          0.4486297932042307,
          0.45109960608014615,
          0.45358220278619843,
          0.4560773120337262,
          0.45858465967182505,
          0.4611039687598673,
          0.46363495964004764,
          0.4661773500099191,
          0.4687308549948819,
          0.47129518722058983,
          0.47387005688524025,
          0.47645517183171016,
          0.4790502376195084,
          0.4816549575965063,
          0.48426903297041624,
          0.48689216287998477,
          0.48952404446586806,
          0.492164372941161,
          0.4948128416615447,
          0.4974691421950275,
          0.5001329643912482,
          0.5028039964503104,
          0.5054819249911268,
          0.5081664351192398,
          0.510857210494096,
          0.5135539333957483,
          0.5162562847909604,
          0.5189639443986915,
          0.5216765907549363,
          0.5243939012768997,
          0.5271155523264839,
          0.5298412192730687,
          0.532570576555565,
          0.5353032977437213,
          0.5380390555986697,
          0.5407775221326889,
          0.5435183686681739,
          0.5462612658957946,
          0.5490058839318281,
          0.5517518923746553,
          0.5544989603604078,
          0.5572467566177515,
          0.5599949495218031,
          0.5627432071471631,
          0.5654911973200619,
          0.5682385876696109,
          0.5709850456781497,
          0.5737302387306882,
          0.576473834163436,
          0.5792154993114169,
          0.581954901555166,
          0.5846917083665081,
          0.5874255873534165,
          0.5901562063039538,
          0.592883233229293,
          0.5956063364058258,
          0.5983251844163563,
          0.6010394461903898,
          0.6037487910435159,
          0.6064528887158966,
          0.609151409409864,
          0.6118440238266343,
          0.6145304032021517,
          0.6172102193420637,
          0.6198831446558453,
          0.6225488521900806,
          0.6252070156609109,
          0.6278573094856679,
          0.6304994088136999,
          0.6331329895564083,
          0.6357577284165092,
          0.6383733029165343,
          0.6409793914265887,
          0.6435756731913836,
          0.6461618283565587,
          0.6487375379943152,
          0.6513024841283787,
          0.6538563497583084,
          0.6563988188831773,
          0.65892957652464,
          0.661448308749412,
          0.6639547026911798,
          0.6664484465719688,
          0.6689292297229841,
          0.6713967426049549,
          0.6738506768280006,
          0.6762907251710459,
          0.6787165816008057,
          0.6811279412903682,
          0.683524500637398,
          0.6859059572819843,
          0.688272010124163,
          0.6906223593411321,
          0.6929567064041925,
          0.6952747540954345,
          0.6975762065242009,
          0.6998607691433475,
          0.702128148765331,
          0.70437805357815,
          0.7066101931611617,
          0.7088242785008055,
          0.711020022006255,
          0.7131971375250263,
          0.7153553403585693,
          0.7174943472778659,
          0.7196138765390597,
          0.7217136478991463,
          0.7237933826317456,
          0.7258528035429812,
          0.727891634987494,
          0.72990960288461,
          0.7319064347346907,
          0.7338818596356858,
          0.7358356082999121,
          0.7377674130710835,
          0.7396770079416106,
          0.7415641285701937,
          0.7434285122997313,
          0.7452698981755603,
          0.747088026964056,
          0.7488826411716001,
          0.7506534850639469,
          0.7524003046859985,
          0.7541228478820097,
          0.7558208643162381,
          0.757494105494058,
          0.7591423247835482,
          0.7607652774375775,
          0.7623627206163921,
          0.7639344134107247,
          0.7654801168654355,
          0.7669995940036971,
          0.7684926098517338,
          0.7699589314641263,
          0.771398327949688,
          0.7728105704979272,
          0.7741954324060948,
          0.7755526891068317,
          0.7768821181964147,
          0.7781834994636104,
          0.7794566149191399,
          0.7807012488257543,
          0.7819171877289275,
          0.7831042204881627,
          0.784262138308917,
          0.785390734775138,
          0.786489805882416,
          0.7875591500717459,
          0.7885985682638929,
          0.7896078638943622,
          0.7905868429489643,
          0.7915353139999662,
          0.7924530882428276,
          0.793339979533506,
          0.7941958044263263,
          0.7950203822124027,
          0.7958135349585983,
          0.7965750875470169,
          0.7973048677150043,
          0.7980027060956539,
          0.7986684362587927,
          0.7993018947524391,
          0.7999029211447094,
          0.8004713580661584,
          0.801007051252533,
          0.801509849587921,
          0.8019796051482719,
          0.8024161732452713,
          0.802819412470543,
          0.8031891847401581,
          0.8035253553394269,
          0.8038277929679468,
          0.8040963697848839,
          0.8043309614544597,
          0.8045314471916145,
          0.8046977098078256,
          0.8048296357570451,
          0.8049271151817329,
          0.8049900419589527,
          0.8050183137465033,
          0.8050118320290508,
          0.8049705021642349,
          0.804894233428712,
          0.8047829390641088,
          0.8046365363228475,
          0.8044549465138132,
          0.8042380950478298,
          0.8039859114829058,
          0.8036983295692227,
          0.8033752872938245,
          0.8030167269249759,
          0.8026225950561553,
          0.8021928426496442,
          0.8017274250796772,
          0.8012263021751205,
          0.8006894382616357,
          0.8001168022033004,
          0.799508367443642,
          0.7988641120460537,
          0.7981840187335538,
          0.7974680749278491,
          0.7967162727876729,
          0.7959286092463536,
          0.7951050860485833,
          0.7942457097863459,
          0.7933504919339712,
          0.79241944888228,
          0.7914526019717814,
          0.7904499775248895,
          0.7894116068771244,
          0.7883375264072601,
          0.7872277775663897,
          0.7860824069058685,
          0.7849014661041068,
          0.783685011992174,
          0.7824331065781854,
          0.7811458170704391,
          0.7798232158992677,
          0.7784653807375795,
          0.7770723945200549,
          0.7756443454609673,
          0.7741813270706048,
          0.7726834381702578,
          0.7711507829057489,
          0.7695834707594768,
          0.7679816165609469,
          0.7663453404957672,
          0.764674768113077,
          0.7629700303313944,
          0.7612312634428512,
          0.7594586091157983,
          0.7576522143957579,
          0.7558122317047031,
          0.7539388188386464,
          0.7520321389635157,
          0.7500923606093044,
          0.7481196576624765,
          0.746114209356612,
          0.7440762002612791,
          0.7420058202691187,
          0.7399032645811275,
          0.7377687336901363,
          0.735602433362459,
          0.7334045746177202,
          0.7311753737068405,
          0.7289150520881776,
          0.7266238364018207,
          0.724301958442027,
          0.7219496551278031,
          0.7195671684716254,
          0.7171547455462995,
          0.7147126384499609,
          0.7122411042692128,
          0.7097404050404121,
          0.7072108077090973,
          0.7046525840875721,
          0.7020660108106451,
          0.6994513692895341,
          0.696808945663945,
          0.6941390307523336,
          0.6914419200003604,
          0.688717913427552,
          0.6859673155721793,
          0.6831904354343716,
          0.6803875864174769,
          0.6775590862676856,
          0.6747052570119403
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)"
         },
         "mode": "lines",
         "name": "Dimension 1",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -2.1152193546295166,
          -2.108513600111008,
          -2.1018078455924987,
          -2.09510209107399,
          -2.0883963365554807,
          -2.081690582036972,
          -2.0749848275184632,
          -2.068279072999954,
          -2.0615733184814453,
          -2.0548675639629366,
          -2.0481618094444274,
          -2.0414560549259186,
          -2.03475030040741,
          -2.0280445458889007,
          -2.021338791370392,
          -2.0146330368518828,
          -2.007927282333374,
          -2.0012215278148653,
          -1.994515773296356,
          -1.9878100187778474,
          -1.9811042642593384,
          -1.9743985097408294,
          -1.9676927552223207,
          -1.9609870007038117,
          -1.9542812461853027,
          -1.9475754916667938,
          -1.9408697371482848,
          -1.934163982629776,
          -1.927458228111267,
          -1.9207524735927581,
          -1.9140467190742494,
          -1.9073409645557404,
          -1.9006352100372315,
          -1.8939294555187225,
          -1.8872237010002135,
          -1.8805179464817048,
          -1.8738121919631958,
          -1.8671064374446869,
          -1.860400682926178,
          -1.8536949284076691,
          -1.8469891738891602,
          -1.8402834193706512,
          -1.8335776648521422,
          -1.8268719103336335,
          -1.8201661558151245,
          -1.8134604012966156,
          -1.8067546467781068,
          -1.8000488922595979,
          -1.7933431377410889,
          -1.78663738322258,
          -1.779931628704071,
          -1.7732258741855622,
          -1.7665201196670532,
          -1.7598143651485443,
          -1.7531086106300355,
          -1.7464028561115266,
          -1.7396971015930176,
          -1.7329913470745086,
          -1.7262855925559997,
          -1.719579838037491,
          -1.712874083518982,
          -1.706168329000473,
          -1.6994625744819642,
          -1.692756819963455,
          -1.6860510654449463,
          -1.6793453109264374,
          -1.6726395564079284,
          -1.6659338018894196,
          -1.6592280473709107,
          -1.6525222928524017,
          -1.6458165383338927,
          -1.6391107838153838,
          -1.632405029296875,
          -1.625699274778366,
          -1.618993520259857,
          -1.6122877657413484,
          -1.6055820112228394,
          -1.5988762567043304,
          -1.5921705021858217,
          -1.5854647476673125,
          -1.5787589931488037,
          -1.5720532386302948,
          -1.5653474841117858,
          -1.558641729593277,
          -1.551935975074768,
          -1.5452302205562591,
          -1.5385244660377504,
          -1.5318187115192412,
          -1.5251129570007325,
          -1.5184072024822235,
          -1.5117014479637145,
          -1.5049956934452058,
          -1.4982899389266968,
          -1.4915841844081879,
          -1.484878429889679,
          -1.47817267537117,
          -1.4714669208526612,
          -1.4647611663341522,
          -1.4580554118156432,
          -1.4513496572971345,
          -1.4446439027786255,
          -1.4379381482601166,
          -1.4312323937416078,
          -1.4245266392230986,
          -1.41782088470459,
          -1.411115130186081,
          -1.404409375667572,
          -1.3977036211490632,
          -1.3909978666305542,
          -1.3842921121120453,
          -1.3775863575935365,
          -1.3708806030750273,
          -1.3641748485565186,
          -1.3574690940380096,
          -1.3507633395195007,
          -1.344057585000992,
          -1.337351830482483,
          -1.330646075963974,
          -1.3239403214454653,
          -1.317234566926956,
          -1.3105288124084473,
          -1.3038230578899384,
          -1.2971173033714294,
          -1.2904115488529206,
          -1.2837057943344117,
          -1.2770000398159027,
          -1.2702942852973937,
          -1.2635885307788848,
          -1.256882776260376,
          -1.250177021741867,
          -1.243471267223358,
          -1.2367655127048494,
          -1.2300597581863402,
          -1.2233540036678314,
          -1.2166482491493225,
          -1.2099424946308135,
          -1.2032367401123047,
          -1.1965309855937958,
          -1.1898252310752868,
          -1.183119476556778,
          -1.1764137220382689,
          -1.1697079675197601,
          -1.1630022130012512,
          -1.1562964584827422,
          -1.1495907039642335,
          -1.1428849494457245,
          -1.1361791949272155,
          -1.1294734404087068,
          -1.1227676858901976,
          -1.1160619313716889,
          -1.1093561768531799,
          -1.102650422334671,
          -1.0959446678161622,
          -1.0892389132976532,
          -1.0825331587791442,
          -1.0758274042606353,
          -1.0691216497421265,
          -1.0624158952236176,
          -1.0557101407051086,
          -1.0490043861865996,
          -1.042298631668091,
          -1.035592877149582,
          -1.028887122631073,
          -1.022181368112564,
          -1.0154756135940552,
          -1.0087698590755463,
          -1.0020641045570373,
          -0.9953583500385284,
          -0.9886525955200196,
          -0.9819468410015106,
          -0.9752410864830017,
          -0.9685353319644927,
          -0.961829577445984,
          -0.955123822927475,
          -0.948418068408966,
          -0.9417123138904571,
          -0.9350065593719483,
          -0.9283008048534394,
          -0.9215950503349304,
          -0.9148892958164214,
          -0.9081835412979127,
          -0.9014777867794037,
          -0.8947720322608947,
          -0.8880662777423858,
          -0.881360523223877,
          -0.8746547687053681,
          -0.8679490141868591,
          -0.8612432596683501,
          -0.8545375051498414,
          -0.8478317506313324,
          -0.8411259961128235,
          -0.8344202415943145,
          -0.8277144870758057,
          -0.8210087325572968,
          -0.8143029780387878,
          -0.8075972235202789,
          -0.8008914690017701,
          -0.7941857144832611,
          -0.7874799599647522,
          -0.7807742054462432,
          -0.7740684509277345,
          -0.7673626964092255,
          -0.7606569418907165,
          -0.7539511873722076,
          -0.7472454328536988,
          -0.7405396783351899,
          -0.7338339238166809,
          -0.7271281692981719,
          -0.7204224147796632,
          -0.7137166602611542,
          -0.7070109057426452,
          -0.7003051512241363,
          -0.6935993967056275,
          -0.6868936421871186,
          -0.6801878876686096,
          -0.6734821331501006,
          -0.6667763786315919,
          -0.6600706241130829,
          -0.653364869594574,
          -0.646659115076065,
          -0.6399533605575563,
          -0.6332476060390473,
          -0.6265418515205383,
          -0.6198360970020294,
          -0.6131303424835206,
          -0.6064245879650116,
          -0.5997188334465027,
          -0.5930130789279937,
          -0.586307324409485,
          -0.579601569890976,
          -0.572895815372467,
          -0.5661900608539581,
          -0.5594843063354493,
          -0.5527785518169404,
          -0.5460727972984314,
          -0.5393670427799224,
          -0.5326612882614137,
          -0.5259555337429047,
          -0.5192497792243957,
          -0.5125440247058868,
          -0.505838270187378,
          -0.49913251566886907,
          -0.4924267611503601,
          -0.48572100663185114,
          -0.4790152521133424,
          -0.4723094975948334,
          -0.46560374307632446,
          -0.4588979885578155,
          -0.45219223403930675,
          -0.4454864795207978,
          -0.4387807250022888,
          -0.43207497048377985,
          -0.4253692159652709,
          -0.41866346144676214,
          -0.4119577069282532,
          -0.4052519524097442,
          -0.39854619789123524,
          -0.3918404433727265,
          -0.38513468885421753,
          -0.37842893433570857,
          -0.3717231798171996,
          -0.36501742529869086,
          -0.3583116707801819,
          -0.3516059162616729,
          -0.34490016174316396,
          -0.3381944072246552,
          -0.33148865270614625,
          -0.3247828981876373,
          -0.3180771436691283,
          -0.31137138915061957,
          -0.3046656346321106,
          -0.29795988011360164,
          -0.29125412559509267,
          -0.28454837107658393,
          -0.27784261655807496,
          -0.271136862039566,
          -0.26443110752105703,
          -0.2577253530025483,
          -0.2510195984840393,
          -0.24431384396553035,
          -0.2376080894470214,
          -0.23090233492851264,
          -0.22419658041000368,
          -0.2174908258914947,
          -0.21078507137298574,
          -0.204079316854477,
          -0.19737356233596803,
          -0.19066780781745907,
          -0.1839620532989501,
          -0.17725629878044136,
          -0.1705505442619324,
          -0.16384478974342342,
          -0.15713903522491446,
          -0.15043328070640571,
          -0.14372752618789675,
          -0.13702177166938778,
          -0.13031601715087882,
          -0.12361026263237007,
          -0.1169045081138611,
          -0.11019875359535236,
          -0.10349299907684317,
          -0.09678724455833443,
          -0.09008149003982524,
          -0.0833757355213165,
          -0.07666998100280775,
          -0.06996422648429856,
          -0.06325847196578982,
          -0.056552717447281076,
          -0.04984696292877189,
          -0.04314120841026314,
          -0.036435453891753955,
          -0.02972969937324521,
          -0.023023944854736467,
          -0.01631819033622728,
          -0.009612435817718534,
          -0.00290668129920979,
          0.003799073219299398,
          0.010504827737808142,
          0.01721058225631733,
          0.023916336774826075,
          0.03062209129333482,
          0.03732784581184401,
          0.04403360033035275,
          0.050739354848861495,
          0.057445109367370684,
          0.06415086388587943,
          0.07085661840438862,
          0.07756237292289736,
          0.0842681274414061,
          0.09097388195991529,
          0.09767963647842404,
          0.10438539099693278,
          0.11109114551544197,
          0.11779690003395071,
          0.1245026545524599,
          0.13120840907096865,
          0.1379141635894774,
          0.14461991810798658,
          0.15132567262649532,
          0.15803142714500407,
          0.16473718166351325,
          0.171442936182022,
          0.1781486907005312,
          0.18485444521903993,
          0.19156019973754868,
          0.19826595425605786,
          0.2049717087745666,
          0.21167746329307535,
          0.21838321781158454,
          0.22508897233009328,
          0.23179472684860247,
          0.23850048136711122,
          0.24520623588561996,
          0.25191199040412915,
          0.2586177449226379,
          0.26532349944114664,
          0.2720292539596558,
          0.27873500847816457,
          0.28544076299667376,
          0.2921465175151825,
          0.29885227203369125,
          0.30555802655220043,
          0.3122637810707092,
          0.3189695355892179,
          0.3256752901077271,
          0.33238104462623586,
          0.33908679914474504,
          0.3457925536632538,
          0.35249830818176253,
          0.3592040627002717,
          0.36590981721878046,
          0.3726155717372892,
          0.3793213262557984,
          0.38602708077430714,
          0.39273283529281633,
          0.3994385898113251,
          0.4061443443298338,
          0.412850098848343,
          0.41955585336685175,
          0.42626160788536094,
          0.4329673624038697,
          0.4396731169223784,
          0.4463788714408876,
          0.45308462595939636,
          0.4597903804779051,
          0.4664961349964143,
          0.47320188951492304,
          0.4799076440334322,
          0.48661339855194097,
          0.4933191530704497,
          0.5000249075889589,
          0.5067306621074676,
          0.5134364166259764,
          0.5201421711444856,
          0.5268479256629943,
          0.5335536801815035,
          0.5402594347000123,
          0.546965189218521,
          0.5536709437370302,
          0.5603766982555389,
          0.5670824527740477,
          0.5737882072925569,
          0.5804939618110656,
          0.5871997163295748,
          0.5939054708480835,
          0.6006112253665923,
          0.6073169798851015,
          0.6140227344036102,
          0.620728488922119,
          0.6274342434406281,
          0.6341399979591369,
          0.6408457524776461,
          0.6475515069961548,
          0.6542572615146636,
          0.6609630160331728,
          0.6676687705516815,
          0.6743745250701902,
          0.6810802795886994,
          0.6877860341072082,
          0.6944917886257174,
          0.7011975431442261,
          0.7079032976627349,
          0.714609052181244,
          0.7213148066997528,
          0.7280205612182615,
          0.7347263157367707,
          0.7414320702552795,
          0.7481378247737887,
          0.7548435792922974,
          0.7615493338108061,
          0.7682550883293153,
          0.7749608428478241,
          0.7816665973663328,
          0.788372351884842,
          0.7950781064033507,
          0.8017838609218599,
          0.8084896154403687,
          0.8151953699588774,
          0.8219011244773866,
          0.8286068789958954,
          0.8353126335144041,
          0.8420183880329133,
          0.848724142551422,
          0.8554298970699312,
          0.86213565158844,
          0.8688414061069487,
          0.8755471606254579,
          0.8822529151439666,
          0.8889586696624754,
          0.8956644241809846,
          0.9023701786994933,
          0.9090759332180025,
          0.9157816877365113,
          0.92248744225502,
          0.9291931967735292,
          0.9358989512920379,
          0.9426047058105467,
          0.9493104603290559,
          0.9560162148475646,
          0.9627219693660738,
          0.9694277238845825,
          0.9761334784030913,
          0.9828392329216005,
          0.9895449874401092,
          0.996250741958618,
          1.0029564964771271,
          1.009662250995636,
          1.016368005514145,
          1.0230737600326538,
          1.0297795145511626,
          1.0364852690696718,
          1.0431910235881805,
          1.0498967781066892,
          1.0566025326251984,
          1.0633082871437072,
          1.0700140416622164,
          1.076719796180725,
          1.0834255506992339,
          1.090131305217743,
          1.0968370597362518,
          1.1035428142547605,
          1.1102485687732697,
          1.1169543232917785,
          1.1236600778102876,
          1.1303658323287964,
          1.1370715868473051,
          1.1437773413658143,
          1.150483095884323,
          1.1571888504028318,
          1.163894604921341,
          1.1706003594398497,
          1.177306113958359,
          1.1840118684768677,
          1.1907176229953764,
          1.1974233775138856,
          1.2041291320323944,
          1.210834886550903,
          1.2175406410694123,
          1.224246395587921,
          1.2309521501064302
         ],
         "xaxis": "x",
         "y": [
          0.09557073717844553,
          0.09617861739064038,
          0.09678759145123472,
          0.09739767282998617,
          0.09800887523028169,
          0.09862121256315284,
          0.09923469892082441,
          0.09984934854981942,
          0.10046517582364362,
          0.10108219521507408,
          0.10170042126807637,
          0.10231986856937568,
          0.10294055171970819,
          0.10356248530477886,
          0.10418568386595288,
          0.10481016187070877,
          0.10543593368288029,
          0.10606301353271738,
          0.10669141548679335,
          0.10732115341778903,
          0.10795224097418384,
          0.10858469154988311,
          0.10921851825381332,
          0.10985373387951558,
          0.11049035087476873,
          0.11112838131127391,
          0.11176783685443185,
          0.11240872873324509,
          0.11305106771037766,
          0.11369486405240335,
          0.11434012750027642,
          0.11498686724005636,
          0.11563509187391903,
          0.11628480939148748,
          0.11693602714151463,
          0.11758875180394991,
          0.11824298936242289,
          0.11889874507717589,
          0.11955602345847738,
          0.12021482824054898,
          0.12087516235603706,
          0.12153702791106022,
          0.12220042616086522,
          0.12286535748612042,
          0.12353182136987867,
          0.12419981637523904,
          0.12486934012373756,
          0.1255403892744961,
          0.12621295950415776,
          0.12688704548763793,
          0.12756264087971803,
          0.1282397382975092,
          0.12891832930381267,
          0.12959840439140266,
          0.13027995296825662,
          0.13096296334375782,
          0.1316474227158939,
          0.13233331715947383,
          0.13302063161538635,
          0.13370934988092037,
          0.13439945460116856,
          0.13509092726153296,
          0.13578374818135194,
          0.13647789650866612,
          0.13717335021613958,
          0.13787008609815285,
          0.1385680797690817,
          0.13926730566277637,
          0.13996773703325302,
          0.14066934595660954,
          0.14137210333417632,
          0.14207597889691043,
          0.14278094121104332,
          0.1434869576849867,
          0.14419399457750476,
          0.14490201700715594,
          0.14561098896300867,
          0.14632087331663246,
          0.14703163183536697,
          0.14774322519686703,
          0.14845561300492338,
          0.14916875380655667,
          0.14988260511037943,
          0.1505971234062229,
          0.15131226418601978,
          0.1520279819659373,
          0.15274423030975062,
          0.15346096185344593,
          0.154178128331042,
          0.15489568060161843,
          0.15561356867753356,
          0.1563317417538199,
          0.1570501482387382,
          0.1577687357854726,
          0.1584874513249482,
          0.1592062410997505,
          0.15992505069912347,
          0.1606438250950261,
          0.16136250867922045,
          0.16208104530136735,
          0.16279937830810334,
          0.1635174505830702,
          0.16423520458786836,
          0.16495258240390548,
          0.16566952577510674,
          0.16638597615145723,
          0.1671018747333411,
          0.1678171625166438,
          0.16853178033858282,
          0.16924566892422957,
          0.16995876893368506,
          0.1706710210098724,
          0.1713823658269053,
          0.17209274413899373,
          0.1728020968298455,
          0.17351036496252156,
          0.17421748982970375,
          0.1749234130043302,
          0.17562807639055583,
          0.17633142227499274,
          0.17703339337818508,
          0.17773393290627282,
          0.17843298460279794,
          0.1791304928006066,
          0.17982640247379877,
          0.18052065928967823,
          0.18121320966065507,
          0.18190400079605126,
          0.1825929807537607,
          0.18328009849171498,
          0.18396530391910448,
          0.1846485479473065,
          0.1853297825404696,
          0.18600896076570478,
          0.1866860368428341,
          0.1873609661936458,
          0.1880337054906071,
          0.18870421270498475,
          0.1893724471543232,
          0.1900383695492318,
          0.19070194203943167,
          0.19136312825901247,
          0.1920218933708523,
          0.1926782041101506,
          0.19333202882702796,
          0.19398333752814467,
          0.19463210191729102,
          0.19527829543490424,
          0.1959218932964655,
          0.19656287252973184,
          0.19720121201076035,
          0.197836892498679,
          0.198469896669163,
          0.19910020914657398,
          0.19972781653472105,
          0.20035270744620426,
          0.2009748725303002,
          0.20159430449935284,
          0.20221099815363114,
          0.20282495040461887,
          0.20343616029670034,
          0.20404462902720916,
          0.20465035996480743,
          0.20525335866616318,
          0.20585363289089714,
          0.20645119261476927,
          0.20704605004107765,
          0.2076382196102441,
          0.2082277180075614,
          0.20881456416907918,
          0.20939877928560618,
          0.20998038680480907,
          0.21055941243138862,
          0.21113588412531648,
          0.21170983209811603,
          0.21228128880717356,
          0.2128502889480678,
          0.21341686944490562,
          0.21398106943865577,
          0.21454293027347224,
          0.21510249548100183,
          0.21565981076267118,
          0.21621492396995096,
          0.21676788508259656,
          0.21731874618486524,
          0.21786756143971348,
          0.21841438706097788,
          0.21895928128354644,
          0.21950230433152715,
          0.2200435183844242,
          0.2205829875413325,
          0.22112077778316402,
          0.22165695693292048,
          0.22219159461402838,
          0.2227247622067557,
          0.22325653280272922,
          0.2237869811575745,
          0.22431618364170192,
          0.22484421818926395,
          0.22537116424530945,
          0.22589710271116506,
          0.22642211588807232,
          0.22694628741911219,
          0.2274697022294514,
          0.2279924464649441,
          0.2285146074291263,
          0.2290362735186401,
          0.22955753415712774,
          0.2300784797276365,
          0.2305992015035764,
          0.23111979157827447,
          0.23164034279317144,
          0.23216094866470682,
          0.23268170330994017,
          0.23320270137095828,
          0.23372403793811836,
          0.23424580847217866,
          0.2347681087253697,
          0.2352910346614603,
          0.2358146823748724,
          0.23633914800890166,
          0.23686452767310173,
          0.2373909173598875,
          0.2379184128604198,
          0.23844710967982874,
          0.23897710295183763,
          0.23950848735284885,
          0.2400413570155535,
          0.240575805442128,
          0.2411119254170811,
          0.24164980891981497,
          0.24218954703696632,
          0.24273122987459028,
          0.24327494647025524,
          0.2438207847051123,
          0.24436883121600683,
          0.24491917130769814,
          0.24547188886525428,
          0.2460270662666874,
          0.24658478429589908,
          0.24714512205600003,
          0.2477081568830727,
          0.24827396426044304,
          0.24884261773352817,
          0.24941418882532682,
          0.24998874695261847,
          0.2505663593429374,
          0.25114709095238796,
          0.25173100438436474,
          0.2523181598092442,
          0.25290861488511146,
          0.2535024246795856,
          0.2540996415928073,
          0.2547003152816508,
          0.25530449258522253,
          0.25591221745170667,
          0.2565235308666184,
          0.2571384707825242,
          0.25775707205028714,
          0.25837936635189485,
          0.2590053821349264,
          0.2596351445487142,
          0.26026867538225407,
          0.26090599300391654,
          0.261547112303013,
          0.26219204463326456,
          0.26284079775822616,
          0.2634933757987104,
          0.26414977918226085,
          0.26481000459471793,
          0.26547404493392335,
          0.266141889265602,
          0.26681352278146575,
          0.26748892675957625,
          0.2681680785270048,
          0.2688509514248254,
          0.26953751477547505,
          0.27022773385251536,
          0.2709215698528242,
          0.2716189798712483,
          0.2723199168777444,
          0.27302432969703333,
          0.2737321629907925,
          0.274443357242408,
          0.2751578487443066,
          0.27587556958788706,
          0.27659644765606584,
          0.277320406618453,
          0.278047365929171,
          0.2787772408273268,
          0.2795099423401464,
          0.28024537728877935,
          0.280983448296778,
          0.2817240538012543,
          0.2824670880667167,
          0.28321244120158456,
          0.2839599991773798,
          0.2847096438505895,
          0.28546125298719366,
          0.2862147002898499,
          0.2869698554277247,
          0.2877265840689587,
          0.2884847479157534,
          0.28924420474206103,
          0.29000480843386167,
          0.2907664090320079,
          0.2915288527776138,
          0.2922919821599673,
          0.2930556359669396,
          0.2938196493378642,
          0.2945838538188586,
          0.29534807742055685,
          0.2961121446782217,
          0.29687587671420246,
          0.297639091302703,
          0.29840160293682316,
          0.29916322289783553,
          0.29992375932665516,
          0.30068301729746477,
          0.30144079889344766,
          0.3021969032845873,
          0.30295112680748526,
          0.30370326304715145,
          0.30445310292071753,
          0.3052004347630236,
          0.3059450444140256,
          0.30668671530797376,
          0.3074252285643049,
          0.3081603630801964,
          0.3088918956247247,
          0.30961960093457147,
          0.31034325181121963,
          0.3110626192195802,
          0.31177747238799,
          0.3124875789095195,
          0.31319270484452977,
          0.313892614824415,
          0.3145870721564689,
          0.3152758389298102,
          0.31595867612230355,
          0.316635343708411,
          0.31730560076790726,
          0.3179692055953951,
          0.31862591581055194,
          0.31927548846904347,
          0.319917680174035,
          0.3205522471882344,
          0.32117894554639914,
          0.321797531168239,
          0.32240775997164695,
          0.3230093879861906,
          0.32360217146679526,
          0.3241858670075517,
          0.32476023165558016,
          0.3253250230248832,
          0.3258799994101189,
          0.3264249199002288,
          0.3269595444918509,
          0.32748363420245397,
          0.32799695118312366,
          0.3284992588309372,
          0.3289903219008584,
          0.32946990661709014,
          0.3299377807838188,
          0.330393713895286,
          0.3308374772451258,
          0.3312688440349035,
          0.3316875894817941,
          0.33209349092534085,
          0.3324863279332307,
          0.332865882406029,
          0.33323193868081513,
          0.3335842836336588,
          0.3339227067808832,
          0.3342470003790565,
          0.3345569595236585,
          0.3348523822463677,
          0.3351330696109165,
          0.3353988258074622,
          0.3356494582454246,
          0.3358847776447382,
          0.3361045981254754,
          0.3363087372957876,
          0.33649701633812446,
          0.3366692600936829,
          0.33682529714504467,
          0.3369649598969592,
          0.33708808465523304,
          0.3371945117036857,
          0.3372840853791334,
          0.33735665414436655,
          0.33741207065908335,
          0.3374501918487485,
          0.33747087897134337,
          0.33747399768197717,
          0.3374594180953307,
          0.3374270148459043,
          0.3373766671460443,
          0.3373082588417224,
          0.33722167846604634,
          0.3371168192904783,
          0.33699357937374236,
          0.3368518616084017,
          0.33669157376508774,
          0.33651262853436714,
          0.33631494356623176,
          0.33609844150719703,
          0.33586305003500233,
          0.335608701890898,
          0.3353353349095165,
          0.3350428920463159,
          0.3347313214025952,
          0.3344005762480745,
          0.33405061504103983,
          0.33368140144605113,
          0.33329290434921427,
          0.33288509787101983,
          0.3324579613767513,
          0.33201147948446946,
          0.3315456420705766,
          0.3310604442729723,
          0.33055588649180656,
          0.3300319743878425,
          0.32948871887844106,
          0.32892613613117894,
          0.32834424755511693,
          0.32774307978973266,
          0.3271226646915351,
          0.32648303931837985,
          0.32582424591150455,
          0.325146331875304,
          0.32444934975486944,
          0.323733357211312,
          0.32299841699489684,
          0.32224459691601226,
          0.32147196981400017,
          0.3206806135238756,
          0.31987061084096335,
          0.31904204948348125,
          0.318195022053101,
          0.3173296259935165,
          0.31644596354705384,
          0.31554414170935363,
          0.31462427218216205,
          0.313686471324264,
          0.31273086010059375,
          0.3117575640295599,
          0.31076671312862225,
          0.309758441858157,
          0.30873288906364893,
          0.3076901979162524,
          0.3066305158517553,
          0.30555399450799214,
          0.3044607896607426,
          0.30335106115815985,
          0.3022249728537689,
          0.3010826925380776,
          0.2999243918688429,
          0.2987502463000362,
          0.2975604350095498,
          0.29635514082569114,
          0.29513455015250384,
          0.29389885289396656,
          0.29264824237710896,
          0.2913829152740916,
          0.2901030715232961,
          0.2888089142494685,
          0.2875006496829623,
          0.28617848707812743,
          0.2848426386308894,
          0.2834933193955642,
          0.28213074720095693,
          0.28075514256578493,
          0.27936672861347706,
          0.2779657309863907,
          0.27655237775949104,
          0.2751268993535425,
          0.273689528447853,
          0.2722404998926178,
          0.27078005062090926,
          0.269308419560354,
          0.26782584754454375,
          0.26633257722422543,
          0.2648288529783099,
          0.2633149208247481,
          0.26179102833131396,
          0.26025742452633865,
          0.25871435980943874,
          0.2571620858622789,
          0.25560085555941303,
          0.25403092287924356,
          0.2524525428151392,
          0.25086597128675414,
          0.24927146505158498,
          0.24766928161680732,
          0.24605967915143068,
          0.24444291639880775,
          0.24281925258953924,
          0.24118894735480828,
          0.23955226064018265
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)"
         },
         "mode": "lines",
         "name": "Dimension 2",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -2.316041946411133,
          -2.3068054518699648,
          -2.2975689573287963,
          -2.2883324627876283,
          -2.2790959682464598,
          -2.2698594737052917,
          -2.2606229791641237,
          -2.251386484622955,
          -2.242149990081787,
          -2.2329134955406187,
          -2.2236770009994506,
          -2.2144405064582826,
          -2.205204011917114,
          -2.195967517375946,
          -2.1867310228347776,
          -2.1774945282936096,
          -2.1682580337524415,
          -2.159021539211273,
          -2.149785044670105,
          -2.140548550128937,
          -2.1313120555877685,
          -2.1220755610466004,
          -2.112839066505432,
          -2.103602571964264,
          -2.094366077423096,
          -2.0851295828819274,
          -2.0758930883407594,
          -2.066656593799591,
          -2.057420099258423,
          -2.048183604717255,
          -2.0389471101760863,
          -2.0297106156349183,
          -2.0204741210937502,
          -2.0112376265525818,
          -2.0020011320114137,
          -1.9927646374702452,
          -1.9835281429290772,
          -1.974291648387909,
          -1.9650551538467407,
          -1.9558186593055726,
          -1.9465821647644044,
          -1.9373456702232361,
          -1.9281091756820679,
          -1.9188726811408996,
          -1.9096361865997316,
          -1.9003996920585633,
          -1.891163197517395,
          -1.8819267029762268,
          -1.8726902084350585,
          -1.8634537138938905,
          -1.8542172193527222,
          -1.844980724811554,
          -1.8357442302703857,
          -1.8265077357292174,
          -1.8172712411880494,
          -1.8080347466468811,
          -1.7987982521057129,
          -1.7895617575645448,
          -1.7803252630233763,
          -1.7710887684822083,
          -1.76185227394104,
          -1.7526157793998718,
          -1.7433792848587037,
          -1.7341427903175353,
          -1.7249062957763672,
          -1.715669801235199,
          -1.7064333066940307,
          -1.6971968121528627,
          -1.6879603176116942,
          -1.6787238230705261,
          -1.6694873285293579,
          -1.6602508339881896,
          -1.6510143394470216,
          -1.6417778449058533,
          -1.632541350364685,
          -1.6233048558235168,
          -1.6140683612823485,
          -1.6048318667411805,
          -1.5955953722000122,
          -1.586358877658844,
          -1.577122383117676,
          -1.5678858885765075,
          -1.5586493940353394,
          -1.5494128994941712,
          -1.540176404953003,
          -1.5309399104118349,
          -1.5217034158706664,
          -1.5124669213294983,
          -1.50323042678833,
          -1.4939939322471618,
          -1.4847574377059938,
          -1.4755209431648253,
          -1.4662844486236573,
          -1.457047954082489,
          -1.4478114595413207,
          -1.4385749650001527,
          -1.4293384704589842,
          -1.4201019759178162,
          -1.410865481376648,
          -1.4016289868354797,
          -1.3923924922943116,
          -1.3831559977531434,
          -1.373919503211975,
          -1.3646830086708068,
          -1.3554465141296386,
          -1.3462100195884705,
          -1.3369735250473023,
          -1.327737030506134,
          -1.318500535964966,
          -1.3092640414237977,
          -1.3000275468826294,
          -1.2907910523414612,
          -1.281554557800293,
          -1.2723180632591247,
          -1.2630815687179566,
          -1.2538450741767884,
          -1.24460857963562,
          -1.2353720850944518,
          -1.2261355905532836,
          -1.2168990960121155,
          -1.2076626014709473,
          -1.198426106929779,
          -1.1891896123886108,
          -1.1799531178474427,
          -1.1707166233062745,
          -1.1614801287651062,
          -1.152243634223938,
          -1.1430071396827697,
          -1.1337706451416016,
          -1.1245341506004334,
          -1.1152976560592651,
          -1.1060611615180969,
          -1.0968246669769288,
          -1.0875881724357606,
          -1.0783516778945923,
          -1.069115183353424,
          -1.0598786888122558,
          -1.0506421942710877,
          -1.0414056997299195,
          -1.0321692051887512,
          -1.022932710647583,
          -1.0136962161064147,
          -1.0044597215652467,
          -0.9952232270240784,
          -0.9859867324829101,
          -0.9767502379417419,
          -0.9675137434005738,
          -0.9582772488594056,
          -0.9490407543182373,
          -0.939804259777069,
          -0.9305677652359008,
          -0.9213312706947328,
          -0.9120947761535645,
          -0.9028582816123962,
          -0.893621787071228,
          -0.8843852925300597,
          -0.8751487979888917,
          -0.8659123034477234,
          -0.8566758089065551,
          -0.8474393143653869,
          -0.8382028198242188,
          -0.8289663252830506,
          -0.8197298307418823,
          -0.8104933362007141,
          -0.8012568416595458,
          -0.7920203471183778,
          -0.7827838525772095,
          -0.7735473580360412,
          -0.764310863494873,
          -0.7550743689537049,
          -0.7458378744125367,
          -0.7366013798713684,
          -0.7273648853302002,
          -0.7181283907890319,
          -0.7088918962478639,
          -0.6996554017066956,
          -0.6904189071655273,
          -0.6811824126243591,
          -0.6719459180831908,
          -0.6627094235420228,
          -0.6534729290008545,
          -0.6442364344596863,
          -0.634999939918518,
          -0.62576344537735,
          -0.6165269508361817,
          -0.6072904562950134,
          -0.5980539617538452,
          -0.5888174672126769,
          -0.5795809726715089,
          -0.5703444781303406,
          -0.5611079835891724,
          -0.5518714890480041,
          -0.5426349945068358,
          -0.5333984999656678,
          -0.5241620054244995,
          -0.5149255108833313,
          -0.505689016342163,
          -0.496452521800995,
          -0.4872160272598267,
          -0.47797953271865845,
          -0.4687430381774902,
          -0.45950654363632193,
          -0.4502700490951539,
          -0.44103355455398563,
          -0.43179706001281737,
          -0.4225605654716491,
          -0.41332407093048085,
          -0.4040875763893128,
          -0.39485108184814455,
          -0.3856145873069763,
          -0.376378092765808,
          -0.36714159822464,
          -0.3579051036834717,
          -0.34866860914230347,
          -0.3394321146011352,
          -0.33019562005996694,
          -0.3209591255187989,
          -0.31172263097763064,
          -0.3024861364364626,
          -0.2932496418952941,
          -0.2840131473541261,
          -0.2747766528129576,
          -0.26554015827178956,
          -0.2563036637306215,
          -0.24706716918945304,
          -0.237830674648285,
          -0.22859418010711652,
          -0.21935768556594848,
          -0.21012119102478044,
          -0.20088469648361196,
          -0.19164820194244392,
          -0.18241170740127544,
          -0.1731752128601074,
          -0.16393871831893936,
          -0.15470222377777088,
          -0.14546572923660284,
          -0.13622923469543435,
          -0.12699274015426631,
          -0.11775624561309828,
          -0.1085197510719298,
          -0.09928325653076175,
          -0.09004676198959372,
          -0.08081026744842523,
          -0.0715737729072572,
          -0.06233727836608871,
          -0.05310078382492067,
          -0.04386428928375263,
          -0.03462779474258415,
          -0.02539130020141611,
          -0.01615480566024763,
          -0.00691831111907959,
          0.002318183422088449,
          0.011554677963256932,
          0.02079117250442497,
          0.030027667045593454,
          0.03926416158676149,
          0.04850065612792953,
          0.057737150669098014,
          0.06697364521026605,
          0.07621013975143454,
          0.08544663429260257,
          0.09468312883377061,
          0.1039196233749391,
          0.11315611791610714,
          0.12239261245727517,
          0.13162910699844366,
          0.1408656015396117,
          0.15010209608078018,
          0.15933859062194822,
          0.16857508516311626,
          0.17781157970428474,
          0.18704807424545278,
          0.19628456878662126,
          0.2055210633277893,
          0.21475755786895734,
          0.22399405241012582,
          0.23323054695129386,
          0.24246704149246234,
          0.2517035360336304,
          0.2609400305747984,
          0.2701765251159669,
          0.27941301965713494,
          0.2886495141983034,
          0.29788600873947146,
          0.3071225032806395,
          0.316358997821808,
          0.325595492362976,
          0.3348319869041445,
          0.34406848144531255,
          0.3533049759864806,
          0.36254147052764907,
          0.3717779650688171,
          0.38101445960998515,
          0.39025095415115363,
          0.39948744869232167,
          0.40872394323349015,
          0.4179604377746582,
          0.4271969323158262,
          0.4364334268569947,
          0.44566992139816275,
          0.45490641593933123,
          0.46414291048049927,
          0.4733794050216673,
          0.4826158995628358,
          0.49185239410400383,
          0.5010888886451723,
          0.5103253831863404,
          0.5195618777275084,
          0.5287983722686769,
          0.5380348668098449,
          0.5472713613510134,
          0.5565078558921814,
          0.5657443504333495,
          0.574980844974518,
          0.584217339515686,
          0.593453834056854,
          0.6026903285980225,
          0.6119268231391906,
          0.621163317680359,
          0.6303998122215271,
          0.6396363067626951,
          0.6488728013038636,
          0.6581092958450316,
          0.6673457903862001,
          0.6765822849273682,
          0.6858187794685362,
          0.6950552740097047,
          0.7042917685508727,
          0.7135282630920412,
          0.7227647576332092,
          0.7320012521743773,
          0.7412377467155458,
          0.7504742412567138,
          0.7597107357978823,
          0.7689472303390503,
          0.7781837248802184,
          0.7874202194213868,
          0.7966567139625549,
          0.8058932085037229,
          0.8151297030448914,
          0.8243661975860594,
          0.8336026921272279,
          0.842839186668396,
          0.852075681209564,
          0.8613121757507325,
          0.8705486702919005,
          0.879785164833069,
          0.889021659374237,
          0.8982581539154051,
          0.9074946484565736,
          0.9167311429977416,
          0.9259676375389101,
          0.9352041320800781,
          0.9444406266212462,
          0.9536771211624147,
          0.9629136157035827,
          0.9721501102447512,
          0.9813866047859192,
          0.9906230993270873,
          0.9998595938682557,
          1.0090960884094238,
          1.0183325829505923,
          1.0275690774917603,
          1.0368055720329283,
          1.0460420665740968,
          1.0552785611152649,
          1.064515055656433,
          1.0737515501976014,
          1.0829880447387694,
          1.092224539279938,
          1.101461033821106,
          1.110697528362274,
          1.1199340229034425,
          1.1291705174446105,
          1.138407011985779,
          1.147643506526947,
          1.156880001068115,
          1.1661164956092835,
          1.1753529901504516,
          1.18458948469162,
          1.193825979232788,
          1.2030624737739561,
          1.2122989683151246,
          1.2215354628562927,
          1.2307719573974611,
          1.2400084519386292,
          1.2492449464797972,
          1.2584814410209657,
          1.2677179355621337,
          1.2769544301033018,
          1.2861909246444703,
          1.2954274191856383,
          1.3046639137268068,
          1.3139004082679748,
          1.3231369028091429,
          1.3323733973503114,
          1.3416098918914794,
          1.3508463864326479,
          1.360082880973816,
          1.369319375514984,
          1.3785558700561524,
          1.3877923645973205,
          1.397028859138489,
          1.406265353679657,
          1.415501848220825,
          1.4247383427619935,
          1.4339748373031616,
          1.44321133184433,
          1.452447826385498,
          1.4616843209266661,
          1.4709208154678346,
          1.4801573100090026,
          1.4893938045501711,
          1.4986302990913392,
          1.5078667936325072,
          1.5171032881736757,
          1.5263397827148437,
          1.5355762772560118,
          1.5448127717971802,
          1.5540492663383483,
          1.5632857608795168,
          1.5725222554206848,
          1.5817587499618528,
          1.5909952445030213,
          1.6002317390441894,
          1.6094682335853578,
          1.6187047281265259,
          1.627941222667694,
          1.6371777172088624,
          1.6464142117500304,
          1.655650706291199,
          1.664887200832367,
          1.674123695373535,
          1.6833601899147035,
          1.6925966844558715,
          1.70183317899704,
          1.7110696735382076,
          1.720306168079376,
          1.7295426626205446,
          1.738779157161713,
          1.7480156517028806,
          1.7572521462440491,
          1.7664886407852176,
          1.7757251353263852,
          1.7849616298675537,
          1.7941981244087222,
          1.8034346189498898,
          1.8126711134910583,
          1.8219076080322267,
          1.8311441025733952,
          1.8403805971145628,
          1.8496170916557313,
          1.8588535861968998,
          1.8680900807380674,
          1.8773265752792359,
          1.8865630698204043,
          1.895799564361572,
          1.9050360589027404,
          1.914272553443909,
          1.9235090479850765,
          1.932745542526245,
          1.9419820370674135,
          1.951218531608582,
          1.9604550261497495,
          1.969691520690918,
          1.9789280152320865,
          1.988164509773254,
          1.9974010043144226,
          2.006637498855591,
          2.0158739933967587,
          2.025110487937927,
          2.0343469824790956,
          2.043583477020264,
          2.0528199715614317,
          2.0620564661026,
          2.0712929606437687,
          2.0805294551849363,
          2.0897659497261047,
          2.0990024442672732,
          2.108238938808441,
          2.1174754333496093,
          2.126711927890778,
          2.1359484224319454,
          2.145184916973114,
          2.1544214115142823,
          2.163657906055451,
          2.1728944005966184,
          2.182130895137787,
          2.1913673896789554,
          2.200603884220123,
          2.2098403787612915,
          2.21907687330246,
          2.2283133678436275,
          2.237549862384796,
          2.2467863569259645,
          2.256022851467133,
          2.2652593460083006,
          2.274495840549469,
          2.2837323350906376,
          2.292968829631805
         ],
         "xaxis": "x",
         "y": [
          0.05859990283167367,
          0.05870746345159699,
          0.05880965130588627,
          0.05890658846183361,
          0.0589984041813752,
          0.05908523493743852,
          0.059167224425476055,
          0.059244523570143134,
          0.05931729052708118,
          0.059385690679770634,
          0.059449896631421854,
          0.059510088191875234,
          0.059566452359485364,
          0.05961918329796784,
          0.059668482308190114,
          0.05971455779489183,
          0.0597576252283229,
          0.059797907100791435,
          0.0598356328781165,
          0.059871038945984646,
          0.059904368551211354,
          0.0599358717379131,
          0.05996580527859789,
          0.05999443260018566,
          0.06002202370497341,
          0.0600488550865621,
          0.06007520964076661,
          0.06010137657153196,
          0.06012765129188229,
          0.06015433531993266,
          0.06018173616999517,
          0.060210167238815275,
          0.06023994768697564,
          0.06027140231550828,
          0.0603048614377582,
          0.06034066074654432,
          0.060379141176665964,
          0.060420648762805736,
          0.06046553449288219,
          0.06051415415690762,
          0.06056686819140946,
          0.060624041519475105,
          0.06068604338648286,
          0.06075324719158397,
          0.06082603031500229,
          0.0609047739412207,
          0.060989862878125564,
          0.061081685372181865,
          0.061180632919714734,
          0.061287100074373844,
          0.06140148425085996,
          0.06152418552499447,
          0.061655606430214505,
          0.061796151750578336,
          0.06194622831036727,
          0.0621062447603722,
          0.06227661136095472,
          0.06245773976197438,
          0.06265004277967529,
          0.06285393417062737,
          0.06306982840281859,
          0.06329814042399672,
          0.06353928542736068,
          0.06379367861470307,
          0.06406173495710697,
          0.06434386895330256,
          0.06464049438578921,
          0.06495202407483208,
          0.06527886963044273,
          0.06562144120245468,
          0.0659801472288081,
          0.06635539418215707,
          0.06674758631491663,
          0.06715712540286728,
          0.06758441048743619,
          0.06802983761677703,
          0.06849379958577047,
          0.06897668567507073,
          0.06947888138932361,
          0.070000768194684,
          0.07054272325576288,
          0.07110511917213416,
          0.07168832371453447,
          0.0722926995608907,
          0.07291860403231083,
          0.07356638882917607,
          0.07423639976747387,
          0.07492897651551245,
          0.07564445233116002,
          0.0763831537997526,
          0.07714540057281645,
          0.07793150510775285,
          0.07874177240863368,
          0.0795764997682594,
          0.08043597651163029,
          0.08132048374098569,
          0.08223029408256578,
          0.08316567143525208,
          0.08412687072124549,
          0.08511413763893948,
          0.086127708418151,
          0.0871678095778685,
          0.08823465768668162,
          0.08932845912605557,
          0.0904494098566156,
          0.09159769518760695,
          0.0927734895496979,
          0.09397695627129252,
          0.09520824735852206,
          0.09646750327908385,
          0.09775485275009678,
          0.09907041253014305,
          0.1004142872156673,
          0.10178656904190198,
          0.10318733768849059,
          0.10461666008997804,
          0.10607459025133933,
          0.10756116906871505,
          0.1090764241555246,
          0.11062036967412427,
          0.11219300617317937,
          0.113794320430917,
          0.11542428530442521,
          0.1170828595851643,
          0.11876998786085266,
          0.12048560038388932,
          0.12222961294647434,
          0.12400192676258329,
          0.12580242835695443,
          0.1276309894612406,
          0.1294874669174782,
          0.13137170258902203,
          0.13328352327909226,
          0.13522274065707587,
          0.13718915119272354,
          0.13918253609837727,
          0.14120266127936282,
          0.14324927729267523,
          0.1453221193140832,
          0.14742090711377243,
          0.14954534504064623,
          0.15169512201539367,
          0.15386991153243393,
          0.15606937167083873,
          0.15829314511433015,
          0.16054085918044614,
          0.1628121258589602,
          0.16510654185963594,
          0.16742368866939078,
          0.16976313261893988,
          0.17212442495898064,
          0.1745071019459753,
          0.1769106849375823,
          0.17933468049777712,
          0.181778580511702,
          0.18424186231027162,
          0.18672398880455762,
          0.1892244086299674,
          0.19174255630022397,
          0.19427785237114714,
          0.1968297036142289,
          0.19939750319998706,
          0.20198063089107357,
          0.20457845324510818,
          0.2071903238271955,
          0.20981558343208134,
          0.21245356031589008,
          0.21510357043738124,
          0.21776491770865294,
          0.22043689425521096,
          0.22311878068531768,
          0.2258098463685192,
          0.2285093497232511,
          0.23121653851340393,
          0.23393065015372977,
          0.23665091202395858,
          0.23937654179148393,
          0.24210674774247395,
          0.24484072912124968,
          0.24757767647776907,
          0.250316772023044,
          0.25305718999231097,
          0.25579809701576806,
          0.25853865249668256,
          0.2612780089966664,
          0.2640153126279079,
          0.266749703452142,
          0.2694803158861337,
          0.2722062791134404,
          0.274926717502216,
          0.27764075102880537,
          0.28034749570688117,
          0.2830460640218584,
          0.2857355653703229,
          0.2884151065042001,
          0.29108379197938594,
          0.293740724608556,
          0.29638500591786265,
          0.2990157366072263,
          0.3016320170139195,
          0.3042329475791406,
          0.3068176293172672,
          0.3093851642874763,
          0.31193465606741383,
          0.3144652102285913,
          0.3169759348131885,
          0.31946594081193064,
          0.3219343426427124,
          0.32438025862963554,
          0.32680281148212265,
          0.32920112877377417,
          0.331574343420626,
          0.33392159415847034,
          0.33624202601889586,
          0.3385347908037101,
          0.34079904755739615,
          0.3430339630372664,
          0.3452387121809682,
          0.3474124785710021,
          0.34955445489591064,
          0.3516638434077989,
          0.3537398563758499,
          0.3557817165354975,
          0.3577886575329237,
          0.3597599243645498,
          0.36169477381119053,
          0.363592474866549,
          0.36545230915972765,
          0.36727357137143796,
          0.36905556964359487,
          0.37079762598198496,
          0.37249907665170445,
          0.3741592725650641,
          0.37577757966166825,
          0.3773533792803762,
          0.37888606852286216,
          0.38037506060849585,
          0.3818197852202712,
          0.38321968884151814,
          0.38457423508313837,
          0.38588290500111316,
          0.38714519740403913,
          0.3883606291504543,
          0.3895287354357252,
          0.3906490700682743,
          0.39172120573493174,
          0.3927447342552095,
          0.3937192668242991,
          0.39464443424460394,
          0.3955198871456309,
          0.3963452961920654,
          0.3971203522798733,
          0.39784476672027563,
          0.39851827141145335,
          0.39914061899785047,
          0.39971158301695114,
          0.40023095803341735,
          0.4006985597604837,
          0.40111422516851514,
          0.4014778125806441,
          0.4017892017554128,
          0.40204829395635805,
          0.4022550120084838,
          0.4024093003415793,
          0.4025111250203493,
          0.4025604737613339,
          0.40255735593660513,
          0.40250180256423873,
          0.4023938662855684,
          0.40223362132924156,
          0.4020211634621047,
          0.4017566099269566,
          0.4014400993672196,
          0.4010717917385859,
          0.4006518682077096,
          0.4001805310380206,
          0.3996580034627526,
          0.3990845295452803,
          0.3984603740268752,
          0.3977858221619968,
          0.39706117954124737,
          0.3962867719021244,
          0.39546294492771794,
          0.394590064033506,
          0.39366851414241066,
          0.392698699448289,
          0.3916810431680359,
          0.3906159872824897,
          0.3895039922663376,
          0.3883455368072232,
          0.3871411175142727,
          0.3858912486162556,
          0.38459646164961087,
          0.38325730513657186,
          0.381874344253632,
          0.3804481604905989,
          0.3789793513004938,
          0.37746852974055495,
          0.37591632410461495,
          0.37432337754712275,
          0.3726903476990908,
          0.3710179062762502,
          0.3693067386797027,
          0.367557543589365,
          0.3657710325505022,
          0.3639479295536528,
          0.36208897060825396,
          0.36019490331027504,
          0.35826648640417547,
          0.35630448933950254,
          0.35430969182245,
          0.3522828833627012,
          0.3502248628158793,
          0.3481364379219349,
          0.3460184248397993,
          0.34387164767863276,
          0.3416969380260025,
          0.33949513447332125,
          0.33726708213888207,
          0.3350136321888233,
          0.33273564135635725,
          0.3304339714595991,
          0.32810948891833014,
          0.32576306427002666,
          0.32339557168549143,
          0.3210078884844157,
          0.3186008946512048,
          0.31617547235139587,
          0.31373250544899245,
          0.31127287902504497,
          0.3087974788977945,
          0.3063071911447046,
          0.3038029016266949,
          0.3012854955148912,
          0.2987558568202042,
          0.29621486792604135,
          0.2936634091244571,
          0.29110235815604046,
          0.28853258975383433,
          0.28595497519157675,
          0.2833703818365537,
          0.28077967270733845,
          0.27818370603670023,
          0.2755833348399481,
          0.2729794064889791,
          0.2703727622922893,
          0.267764237081201,
          0.2651546588025575,
          0.2625448481181244,
          0.25993561801093673,
          0.25732777339881924,
          0.2547221107553043,
          0.25211941773816493,
          0.24952047282577072,
          0.24692604496147125,
          0.24433689320620416,
          0.24175376639951296,
          0.23917740282916136,
          0.2366085299095138,
          0.23404786386885335,
          0.23149610944579355,
          0.22895395959493753,
          0.22642209520192969,
          0.22390118480803434,
          0.2213918843443724,
          0.21889483687593783,
          0.21641067235550382,
          0.2139400073875287,
          0.21148344500215693,
          0.20904157443940385,
          0.20661497094360953,
          0.20420419556823163,
          0.20180979499104654,
          0.19943230133981527,
          0.19707223202846355,
          0.1947300896038206,
          0.19240636160294827,
          0.19010152042108908,
          0.18781602319025065,
          0.18555031166843747,
          0.18330481213953362,
          0.18107993532383082,
          0.17887607629919058,
          0.17669361443282028,
          0.1745329133236343,
          0.17239432075516892,
          0.17027816865900391,
          0.16818477308864554,
          0.16611443420381228,
          0.16406743626505876,
          0.162044047638669,
          0.1600445208117395,
          0.15806909241736755,
          0.1561179832698551,
          0.15419139840982746,
          0.15228952715916494,
          0.15041254318563527,
          0.1485606045771093,
          0.14673385392523805,
          0.1449324184184605,
          0.14315640994420792,
          0.14140592520016404,
          0.1396810458144329,
          0.13798183847446566,
          0.13630835506458522,
          0.13466063281195023,
          0.1330386944407883,
          0.1314425483347272,
          0.12987218870704792,
          0.12832759577867636,
          0.12680873596372952,
          0.12531556206242556,
          0.12384801346116278,
          0.12240601633957132,
          0.1209894838843336,
          0.11959831650957038,
          0.1182324020835826,
          0.11689161616173657,
          0.11557582222527948,
          0.11428487192586538,
          0.11301860533557213,
          0.11177685120218643,
          0.1105594272095311,
          0.10936614024260716,
          0.1081967866573217,
          0.10705115255456893,
          0.10592901405843334,
          0.10483013759827858,
          0.10375428019448754,
          0.10270118974761706,
          0.10167060533072803,
          0.10066225748465432,
          0.09967586851597017,
          0.09871115279741727,
          0.09776781707055192,
          0.09684556075037216,
          0.09594407623168649,
          0.09506304919698341,
          0.09420215892556534,
          0.09336107860370679,
          0.09253947563560129,
          0.09173701195486017,
          0.09095334433632933,
          0.09018812470798944,
          0.08944100046270793,
          0.08871161476961396,
          0.08799960688486592,
          0.08730461246158672,
          0.08662626385874278,
          0.08596419044874401,
          0.08531801892354723,
          0.08468737359904496,
          0.0840718767175276,
          0.08347114874800725,
          0.08288480868419598,
          0.08231247433993547,
          0.08175376264187557,
          0.08120828991920613,
          0.0806756721902486,
          0.08015552544571695,
          0.07964746592846353,
          0.07915111040952812,
          0.07866607646031296,
          0.07819198272071116,
          0.07772844916302027,
          0.07727509735147786,
          0.07683155069725933,
          0.07639743470878489,
          0.0759723772371864,
          0.07555600871678968,
          0.07514796240047376,
          0.07474787458977393,
          0.07435538485959918,
          0.07397013627744244,
          0.07359177561696498,
          0.07321995356584461,
          0.07285432492778009,
          0.07249454881855202,
          0.07214028885604576,
          0.0717912133441467,
          0.07144699545042538,
          0.07110731337753527,
          0.07077185052825205,
          0.07044029566408873,
          0.07011234305742835,
          0.06978769263712001,
          0.0694660501274921,
          0.06914712718074076,
          0.06883064150265948,
          0.0685163169716802,
          0.06820388375120319,
          0.06789307839519937,
          0.06758364394707365,
          0.06727533003178456,
          0.06696789294122205,
          0.06666109571284957,
          0.0663547082016243,
          0.0660485071452139,
          0.0657422762225349,
          0.06543580610564267
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 0",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -1.2633347511291504,
          -0.10230965167284012,
          -0.4338788092136383,
          -0.31601276993751526,
          -1.1258398294448853,
          0.05250748619437218,
          0.11241118609905243,
          0.11984150856733322,
          -0.1116093322634697,
          -0.4926769733428955
         ],
         "xaxis": "x",
         "y": [
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0"
         ],
         "yaxis": "y2"
        },
        {
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 1",
         "showlegend": false,
         "type": "scatter",
         "x": [
          0.34998318552970886,
          0.7924439907073975,
          0.8487103581428528,
          -2.1152193546295166,
          -1.152360200881958,
          0.5228604674339294,
          -0.8410648107528687,
          1.237657904624939,
          -0.6135830879211426,
          0.2484147548675537
         ],
         "xaxis": "x",
         "y": [
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1"
         ],
         "yaxis": "y2"
        },
        {
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 2",
         "showlegend": false,
         "type": "scatter",
         "x": [
          0.30813392996788025,
          -0.28966769576072693,
          0.6920091509819031,
          0.32227492332458496,
          -0.2505785822868347,
          2.3022053241729736,
          -2.316041946411133,
          -0.14347384870052338,
          0.03159274160861969,
          0.4396958351135254
         ],
         "xaxis": "x",
         "y": [
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2"
         ],
         "yaxis": "y2"
        }
       ],
       "layout": {
        "barmode": "overlay",
        "hovermode": "closest",
        "legend": {
         "traceorder": "reversed"
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Prior Distribution"
        },
        "xaxis": {
         "anchor": "y2",
         "domain": [
          0,
          1
         ],
         "zeroline": false
        },
        "yaxis": {
         "anchor": "free",
         "domain": [
          0.35,
          1
         ],
         "position": 0
        },
        "yaxis2": {
         "anchor": "x",
         "domain": [
          0,
          0.25
         ],
         "dtick": 1,
         "showticklabels": false
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution of non-modified (normal-gaussian) prior\n",
    "\n",
    "# for loop to get the data from each dimension if more than 1 dimension\n",
    "data = []\n",
    "group_labels = []\n",
    "for i in range(prior_samples.shape[1]):\n",
    "    data.append(prior_samples[:, i].numpy())\n",
    "    group_labels.append(f'Dimension {i}')\n",
    "\n",
    "fig = ff.create_distplot(data, group_labels, bin_size=0.2)\n",
    "fig.update_layout(title='Prior Distribution')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "type": "surface",
         "z": [
          [
           -1.2633347511291504,
           0.34998318552970886,
           0.30813392996788025
          ],
          [
           -0.10230965167284012,
           0.7924439907073975,
           -0.28966769576072693
          ],
          [
           -0.4338788092136383,
           0.8487103581428528,
           0.6920091509819031
          ],
          [
           -0.31601276993751526,
           -2.1152193546295166,
           0.32227492332458496
          ],
          [
           -1.1258398294448853,
           -1.152360200881958,
           -0.2505785822868347
          ],
          [
           0.05250748619437218,
           0.5228604674339294,
           2.3022053241729736
          ],
          [
           0.11241118609905243,
           -0.8410648107528687,
           -2.316041946411133
          ],
          [
           0.11984150856733322,
           1.237657904624939,
           -0.14347384870052338
          ],
          [
           -0.1116093322634697,
           -0.6135830879211426,
           0.03159274160861969
          ],
          [
           -0.4926769733428955,
           0.2484147548675537,
           0.4396958351135254
          ]
         ]
        }
       ],
       "layout": {
        "scene": {
         "zaxis": {
          "range": [
           -5,
           5
          ]
         }
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Prior Distribution (Surface Plot)"
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotly surface plot for the prior\n",
    "fig = go.Figure(data=[go.Surface(z=prior_samples.numpy())])\n",
    "# set z axis range\n",
    "fig.update_layout(scene = dict(zaxis = dict(range=[-5,5])))\n",
    "fig.update_layout(title='Prior Distribution (Surface Plot)')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)"
         },
         "name": "Dimension 0",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          0,
          0,
          0,
          -0.5730770826339722,
          -0.4949253499507904,
          0.7100865840911865,
          0.966303288936615,
          -0.3951575458049774,
          -1.3253259658813477,
          1.9414620399475098
         ],
         "xaxis": "x",
         "xbins": {
          "end": 1.9414620399475098,
          "size": 0.2,
          "start": -1.3253259658813477
         },
         "yaxis": "y"
        },
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)"
         },
         "name": "Dimension 1",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          1.1686878204345703,
          0.5073344111442566,
          0.3581531047821045,
          -0.5553584098815918,
          -1.4959149360656738,
          -1.5352871417999268,
          1.6247831583023071,
          0.20552566647529602,
          0.1885535717010498,
          -0.9565008282661438
         ],
         "xaxis": "x",
         "xbins": {
          "end": 1.6247831583023071,
          "size": 0.2,
          "start": -1.5352871417999268
         },
         "yaxis": "y"
        },
        {
         "autobinx": false,
         "histnorm": "probability density",
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)"
         },
         "name": "Dimension 2",
         "opacity": 0.7,
         "type": "histogram",
         "x": [
          0.39450275897979736,
          -0.5515286922454834,
          -0.003303872887045145,
          0.5943230390548706,
          -0.4000341594219208,
          -0.41267913579940796,
          -0.3656187951564789,
          -0.4503297507762909,
          -0.06907268613576889,
          0.03353185951709747
         ],
         "xaxis": "x",
         "xbins": {
          "end": 0.5943230390548706,
          "size": 0.2,
          "start": -0.5515286922454834
         },
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)"
         },
         "mode": "lines",
         "name": "Dimension 0",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -1.3253259658813477,
          -1.31879238986969,
          -1.3122588138580322,
          -1.3057252378463746,
          -1.2991916618347168,
          -1.2926580858230592,
          -1.2861245098114014,
          -1.2795909337997438,
          -1.273057357788086,
          -1.2665237817764283,
          -1.2599902057647705,
          -1.253456629753113,
          -1.246923053741455,
          -1.2403894777297975,
          -1.2338559017181396,
          -1.227322325706482,
          -1.2207887496948242,
          -1.2142551736831666,
          -1.2077215976715088,
          -1.2011880216598512,
          -1.1946544456481933,
          -1.1881208696365357,
          -1.181587293624878,
          -1.1750537176132203,
          -1.1685201416015625,
          -1.1619865655899049,
          -1.155452989578247,
          -1.1489194135665894,
          -1.1423858375549316,
          -1.135852261543274,
          -1.1293186855316162,
          -1.1227851095199586,
          -1.1162515335083008,
          -1.1097179574966431,
          -1.1031843814849853,
          -1.0966508054733277,
          -1.09011722946167,
          -1.0835836534500123,
          -1.0770500774383545,
          -1.0705165014266969,
          -1.063982925415039,
          -1.0574493494033814,
          -1.0509157733917236,
          -1.044382197380066,
          -1.0378486213684082,
          -1.0313150453567506,
          -1.0247814693450927,
          -1.0182478933334351,
          -1.0117143173217773,
          -1.0051807413101197,
          -0.9986471652984619,
          -0.9921135892868043,
          -0.9855800132751464,
          -0.9790464372634888,
          -0.972512861251831,
          -0.9659792852401734,
          -0.9594457092285156,
          -0.952912133216858,
          -0.9463785572052001,
          -0.9398449811935425,
          -0.9333114051818847,
          -0.9267778291702271,
          -0.9202442531585693,
          -0.9137106771469117,
          -0.9071771011352538,
          -0.9006435251235962,
          -0.8941099491119384,
          -0.8875763731002808,
          -0.881042797088623,
          -0.8745092210769654,
          -0.8679756450653076,
          -0.86144206905365,
          -0.8549084930419921,
          -0.8483749170303345,
          -0.8418413410186767,
          -0.8353077650070191,
          -0.8287741889953613,
          -0.8222406129837037,
          -0.8157070369720459,
          -0.8091734609603882,
          -0.8026398849487305,
          -0.7961063089370728,
          -0.7895727329254151,
          -0.7830391569137574,
          -0.7765055809020996,
          -0.7699720048904419,
          -0.7634384288787842,
          -0.7569048528671265,
          -0.7503712768554688,
          -0.7438377008438111,
          -0.7373041248321534,
          -0.7307705488204956,
          -0.7242369728088379,
          -0.7177033967971802,
          -0.7111698207855225,
          -0.7046362447738648,
          -0.6981026687622071,
          -0.6915690927505493,
          -0.6850355167388916,
          -0.6785019407272339,
          -0.6719683647155762,
          -0.6654347887039185,
          -0.6589012126922608,
          -0.652367636680603,
          -0.6458340606689453,
          -0.6393004846572876,
          -0.6327669086456299,
          -0.6262333326339722,
          -0.6196997566223145,
          -0.6131661806106568,
          -0.606632604598999,
          -0.6000990285873413,
          -0.5935654525756836,
          -0.5870318765640259,
          -0.5804983005523682,
          -0.5739647245407105,
          -0.5674311485290527,
          -0.560897572517395,
          -0.5543639965057373,
          -0.5478304204940796,
          -0.5412968444824219,
          -0.5347632684707642,
          -0.5282296924591064,
          -0.5216961164474487,
          -0.515162540435791,
          -0.5086289644241333,
          -0.5020953884124756,
          -0.49556181240081787,
          -0.48902823638916015,
          -0.48249466037750244,
          -0.4759610843658447,
          -0.469427508354187,
          -0.4628939323425293,
          -0.4563603563308716,
          -0.44982678031921386,
          -0.44329320430755614,
          -0.4367596282958984,
          -0.4302260522842407,
          -0.423692476272583,
          -0.4171589002609253,
          -0.41062532424926756,
          -0.40409174823760985,
          -0.39755817222595213,
          -0.3910245962142944,
          -0.3844910202026367,
          -0.377957444190979,
          -0.37142386817932127,
          -0.36489029216766355,
          -0.35835671615600584,
          -0.3518231401443481,
          -0.3452895641326904,
          -0.3387559881210327,
          -0.332222412109375,
          -0.32568883609771726,
          -0.31915526008605966,
          -0.31262168407440183,
          -0.3060881080627442,
          -0.2995545320510864,
          -0.2930209560394288,
          -0.28648738002777097,
          -0.27995380401611336,
          -0.27342022800445553,
          -0.26688665199279793,
          -0.2603530759811401,
          -0.2538194999694825,
          -0.24728592395782467,
          -0.24075234794616707,
          -0.23421877193450924,
          -0.22768519592285164,
          -0.2211516199111938,
          -0.2146180438995362,
          -0.20808446788787838,
          -0.20155089187622077,
          -0.19501731586456295,
          -0.18848373985290534,
          -0.18195016384124751,
          -0.1754165878295899,
          -0.16888301181793208,
          -0.16234943580627448,
          -0.15581585979461665,
          -0.14928228378295905,
          -0.14274870777130122,
          -0.13621513175964362,
          -0.1296815557479858,
          -0.12314797973632818,
          -0.11661440372467036,
          -0.11008082771301275,
          -0.10354725170135493,
          -0.09701367568969732,
          -0.0904800996780395,
          -0.08394652366638189,
          -0.07741294765472406,
          -0.07087937164306646,
          -0.06434579563140863,
          -0.057812219619751026,
          -0.0512786436080932,
          -0.044745067596435595,
          -0.03821149158477777,
          -0.03167791557312016,
          -0.025144339561462337,
          -0.018610763549804732,
          -0.012077187538146905,
          -0.0055436115264893004,
          0.0009899644851685263,
          0.007523540496826131,
          0.014057116508483958,
          0.020590692520141562,
          0.02712426853179939,
          0.033657844543456994,
          0.04019142055511482,
          0.046724996566772425,
          0.05325857257843025,
          0.05979214859008786,
          0.06632572460174568,
          0.07285930061340329,
          0.07939287662506112,
          0.08592645263671872,
          0.09246002864837655,
          0.09899360466003415,
          0.10552718067169198,
          0.11206075668334958,
          0.11859433269500741,
          0.12512790870666501,
          0.13166148471832284,
          0.13819506072998045,
          0.14472863674163827,
          0.15126221275329588,
          0.1577957887649537,
          0.1643293647766113,
          0.17086294078826914,
          0.17739651679992674,
          0.18393009281158457,
          0.19046366882324217,
          0.1969972448349,
          0.2035308208465576,
          0.21006439685821543,
          0.21659797286987303,
          0.22313154888153086,
          0.22966512489318847,
          0.2361987009048463,
          0.2427322769165039,
          0.24926585292816172,
          0.25579942893981933,
          0.26233300495147716,
          0.26886658096313476,
          0.2754001569747926,
          0.2819337329864502,
          0.288467308998108,
          0.2950008850097656,
          0.30153446102142345,
          0.30806803703308105,
          0.31460161304473866,
          0.3211351890563965,
          0.3276687650680541,
          0.3342023410797119,
          0.3407359170913695,
          0.34726949310302735,
          0.35380306911468495,
          0.3603366451263428,
          0.3668702211380004,
          0.3734037971496582,
          0.3799373731613158,
          0.38647094917297364,
          0.39300452518463125,
          0.3995381011962891,
          0.4060716772079467,
          0.4126052532196045,
          0.4191388292312621,
          0.42567240524291994,
          0.43220598125457754,
          0.43873955726623537,
          0.445273133277893,
          0.4518067092895508,
          0.4583402853012084,
          0.46487386131286623,
          0.47140743732452384,
          0.47794101333618166,
          0.48447458934783927,
          0.4910081653594971,
          0.4975417413711547,
          0.5040753173828125,
          0.5106088933944701,
          0.517142469406128,
          0.5236760454177856,
          0.5302096214294434,
          0.536743197441101,
          0.5432767734527588,
          0.5498103494644164,
          0.5563439254760743,
          0.5628775014877319,
          0.5694110774993897,
          0.5759446535110473,
          0.5824782295227051,
          0.5890118055343627,
          0.5955453815460205,
          0.6020789575576782,
          0.608612533569336,
          0.6151461095809936,
          0.6216796855926514,
          0.628213261604309,
          0.6347468376159668,
          0.6412804136276244,
          0.6478139896392823,
          0.6543475656509399,
          0.6608811416625977,
          0.6674147176742553,
          0.6739482936859131,
          0.6804818696975707,
          0.6870154457092283,
          0.6935490217208864,
          0.700082597732544,
          0.7066161737442016,
          0.7131497497558592,
          0.7196833257675173,
          0.7262169017791749,
          0.7327504777908325,
          0.7392840538024901,
          0.7458176298141481,
          0.7523512058258057,
          0.7588847818374633,
          0.7654183578491209,
          0.771951933860779,
          0.7784855098724366,
          0.7850190858840942,
          0.7915526618957518,
          0.7980862379074098,
          0.8046198139190675,
          0.811153389930725,
          0.8176869659423827,
          0.8242205419540407,
          0.8307541179656983,
          0.8372876939773559,
          0.8438212699890135,
          0.8503548460006716,
          0.8568884220123292,
          0.8634219980239868,
          0.8699555740356444,
          0.8764891500473024,
          0.88302272605896,
          0.8895563020706176,
          0.8960898780822752,
          0.9026234540939333,
          0.9091570301055909,
          0.9156906061172485,
          0.9222241821289061,
          0.9287577581405642,
          0.9352913341522218,
          0.9418249101638794,
          0.948358486175537,
          0.954892062187195,
          0.9614256381988526,
          0.9679592142105102,
          0.9744927902221678,
          0.9810263662338259,
          0.9875599422454835,
          0.9940935182571411,
          1.0006270942687987,
          1.0071606702804567,
          1.0136942462921144,
          1.020227822303772,
          1.0267613983154296,
          1.0332949743270876,
          1.0398285503387452,
          1.0463621263504028,
          1.0528957023620604,
          1.0594292783737185,
          1.065962854385376,
          1.0724964303970337,
          1.0790300064086913,
          1.0855635824203493,
          1.092097158432007,
          1.0986307344436645,
          1.1051643104553222,
          1.1116978864669802,
          1.1182314624786378,
          1.1247650384902954,
          1.131298614501953,
          1.1378321905136106,
          1.1443657665252687,
          1.1508993425369263,
          1.1574329185485839,
          1.1639664945602415,
          1.1705000705718995,
          1.1770336465835571,
          1.1835672225952147,
          1.1901007986068723,
          1.1966343746185304,
          1.203167950630188,
          1.2097015266418456,
          1.2162351026535032,
          1.2227686786651613,
          1.2293022546768189,
          1.2358358306884765,
          1.242369406700134,
          1.2489029827117921,
          1.2554365587234497,
          1.2619701347351073,
          1.268503710746765,
          1.275037286758423,
          1.2815708627700806,
          1.2881044387817382,
          1.2946380147933958,
          1.3011715908050538,
          1.3077051668167115,
          1.314238742828369,
          1.3207723188400267,
          1.3273058948516847,
          1.3338394708633423,
          1.340373046875,
          1.3469066228866575,
          1.3534401988983156,
          1.3599737749099732,
          1.3665073509216308,
          1.3730409269332884,
          1.3795745029449464,
          1.386108078956604,
          1.3926416549682616,
          1.3991752309799192,
          1.4057088069915773,
          1.412242383003235,
          1.4187759590148925,
          1.4253095350265501,
          1.4318431110382082,
          1.4383766870498658,
          1.4449102630615234,
          1.451443839073181,
          1.457977415084839,
          1.4645109910964966,
          1.4710445671081542,
          1.4775781431198118,
          1.4841117191314699,
          1.4906452951431275,
          1.497178871154785,
          1.5037124471664427,
          1.5102460231781007,
          1.5167795991897584,
          1.523313175201416,
          1.5298467512130736,
          1.5363803272247316,
          1.5429139032363892,
          1.5494474792480468,
          1.5559810552597044,
          1.5625146312713625,
          1.56904820728302,
          1.5755817832946777,
          1.5821153593063353,
          1.5886489353179933,
          1.595182511329651,
          1.6017160873413085,
          1.6082496633529662,
          1.6147832393646242,
          1.6213168153762818,
          1.6278503913879394,
          1.634383967399597,
          1.640917543411255,
          1.6474511194229127,
          1.6539846954345703,
          1.6605182714462279,
          1.667051847457886,
          1.6735854234695435,
          1.6801189994812011,
          1.6866525754928587,
          1.6931861515045168,
          1.6997197275161744,
          1.706253303527832,
          1.7127868795394896,
          1.7193204555511477,
          1.7258540315628053,
          1.7323876075744629,
          1.7389211835861205,
          1.7454547595977785,
          1.7519883356094361,
          1.7585219116210937,
          1.7650554876327513,
          1.7715890636444094,
          1.778122639656067,
          1.7846562156677246,
          1.7911897916793822,
          1.7977233676910402,
          1.8042569437026978,
          1.8107905197143555,
          1.817324095726013,
          1.823857671737671,
          1.8303912477493287,
          1.8369248237609863,
          1.843458399772644,
          1.849991975784302,
          1.8565255517959596,
          1.8630591278076172,
          1.8695927038192748,
          1.8761262798309328,
          1.8826598558425904,
          1.889193431854248,
          1.8957270078659056,
          1.9022605838775637,
          1.9087941598892213,
          1.915327735900879,
          1.9218613119125365,
          1.9283948879241946,
          1.9349284639358522
         ],
         "xaxis": "x",
         "y": [
          0.1575671428295789,
          0.15914374213220925,
          0.16072959646121862,
          0.16232468083011065,
          0.16392896756955183,
          0.16554242624756457,
          0.1671650235897815,
          0.16879672339984245,
          0.17043748648002163,
          0.17208727055216871,
          0.173746030179054,
          0.1754137166862033,
          0.17709027808431488,
          0.17877565899234465,
          0.18046980056135514,
          0.18217264039921469,
          0.18388411249624403,
          0.18560414715189671,
          0.18733267090257266,
          0.18906960645065124,
          0.19081487259484264,
          0.19256838416194583,
          0.19433005194010994,
          0.19609978261368857,
          0.19787747869978242,
          0.19966303848655917,
          0.20145635597344563,
          0.20325732081327913,
          0.20506581825651243,
          0.20688172909755728,
          0.2087049296233588,
          0.21053529156428474,
          0.21237268204741805,
          0.21421696355233596,
          0.21606799386946016,
          0.217925626061059,
          0.21978970842498288,
          0.22166008446121058,
          0.22353659284128438,
          0.2254190673807071,
          0.22730733701437664,
          0.2292012257751252,
          0.23110055277543554,
          0.2330051321923968,
          0.23491477325596696,
          0.2368292802406002,
          0.23874845246030116,
          0.24067208426715828,
          0.24259996505341372,
          0.24453187925711606,
          0.2464676063714073,
          0.24840692095748498,
          0.2503495926612841,
          0.252295386233914,
          0.2542440615558889,
          0.25619537366517925,
          0.2581490727891176,
          0.26010490438017897,
          0.26206260915566126,
          0.2640219231412813,
          0.2659825777187022,
          0.26794429967700195,
          0.2699068112680922,
          0.27186983026608863,
          0.2738330700306345,
          0.27579623957417226,
          0.27775904363315723,
          0.27972118274319874,
          0.28168235331811803,
          0.28364224773289914,
          0.2856005544105133,
          0.2875569579125885,
          0.2895111390338939,
          0.2914627749006047,
          0.29341153907230877,
          0.2953571016477154,
          0.2972991293740156,
          0.2992372857598494,
          0.30117123119182354,
          0.3031006230545229,
          0.3050251158539572,
          0.3069443613443743,
          0.3088580086583767,
          0.31076570444026563,
          0.31266709298254036,
          0.31456181636547326,
          0.3164495145996772,
          0.31832982577158253,
          0.3202023861917332,
          0.3220668305458099,
          0.32392279204828744,
          0.3257699025986251,
          0.32760779293989195,
          0.3294360928197212,
          0.3312544311534878,
          0.33306243618959913,
          0.3348597356767874,
          0.3366459570332886,
          0.3384207275177906,
          0.34018367440203245,
          0.3419344251449309,
          0.3436726075681126,
          0.3453978500327247,
          0.347109781617397,
          0.34880803229722507,
          0.3504922331236455,
          0.35216201640506734,
          0.35381701588812803,
          0.355456866939438,
          0.35708120672767646,
          0.358689674405902,
          0.36028191129393683,
          0.3618575610606901,
          0.3634162699062748,
          0.36495768674378093,
          0.36648146338056387,
          0.36798725469890553,
          0.36947471883590727,
          0.37094351736247433,
          0.3723933154612486,
          0.3738237821033507,
          0.37523459022379035,
          0.3766254168954034,
          0.3779959435011795,
          0.3793458559048386,
          0.38067484461952117,
          0.3819826049744545,
          0.38326883727946065,
          0.3845332469871711,
          0.3857755448528174,
          0.3869954470914656,
          0.38819267553256664,
          0.38936695777169483,
          0.39051802731934904,
          0.3916456237466959,
          0.39274949282813104,
          0.39382938668054224,
          0.39488506389915856,
          0.3959162896898708,
          0.39692283599791506,
          0.3979044816328091,
          0.3988610123894397,
          0.39979222116519586,
          0.4006979080730532,
          0.40157788055051197,
          0.40243195346429594,
          0.40325994921072694,
          0.40406169781168727,
          0.4048370370060899,
          0.40558581233677865,
          0.40630787723278516,
          0.4070030930868719,
          0.40767132932829625,
          0.4083124634907331,
          0.4089263812752982,
          0.40951297660861896,
          0.4100721516959031,
          0.41060381706896043,
          0.4111078916291355,
          0.41158430268511653,
          0.4120329859855867,
          0.41245388574669234,
          0.41284695467430194,
          0.41321215398104055,
          0.4135494533980824,
          0.4138588311816941,
          0.4141402741145234,
          0.41439377750163175,
          0.41461934516127513,
          0.4148169894104438,
          0.41498673104517086,
          0.41512859931563045,
          0.41524263189604693,
          0.41532887484944025,
          0.4153873825872433,
          0.41541821782382204,
          0.41542145152594295,
          0.41539716285722994,
          0.4153454391176619,
          0.41526637567816366,
          0.41516007591034665,
          0.4150266511114653,
          0.4148662204246516,
          0.4146789107544996,
          0.41446485667807575,
          0.4142242003514312,
          0.4139570914116994,
          0.41366368687486704,
          0.4133441510293039,
          0.4129986553251505,
          0.41262737825965606,
          0.4122305052585704,
          0.41180822855369364,
          0.41136074705668835,
          0.41088826622926805,
          0.4103909979498729,
          0.40986916037695215,
          0.4093229778089673,
          0.40875268054124503,
          0.40815850471979775,
          0.4075406921922442,
          0.4068994903559554,
          0.40623515200356025,
          0.4055479351659435,
          0.4048381029528713,
          0.40410592339138235,
          0.40335166926208343,
          0.40257561793349045,
          0.40177805119455545,
          0.40095925508552527,
          0.40011951972727344,
          0.39925913914925226,
          0.3983784111162116,
          0.3974776369538282,
          0.39655712137339644,
          0.3956171722957251,
          0.3946581006743893,
          0.3936802203184848,
          0.39268384771503284,
          0.39166930185118204,
          0.3906369040363546,
          0.38958697772448436,
          0.38851984833648984,
          0.3874358430831297,
          0.38633529078838313,
          0.3852185217134969,
          0.38408586738184297,
          0.38293766040472327,
          0.3817742343082637,
          0.3805959233615292,
          0.37940306240599897,
          0.3781959866865318,
          0.37697503168395335,
          0.3757405329493915,
          0.3744928259404896,
          0.37323224585961545,
          0.371959127494191,
          0.37067380505925973,
          0.36937661204240346,
          0.36806788105112437,
          0.36674794366280006,
          0.36541713027731415,
          0.3640757699724695,
          0.3627241903622778,
          0.36136271745822496,
          0.35999167553359945,
          0.358611386990977,
          0.3572221722329386,
          0.3558243495361095,
          0.35441823492858826,
          0.35300414207084396,
          0.35158238214014514,
          0.3501532637185866,
          0.3487170926847743,
          0.3472741721092207,
          0.34582480215350636,
          0.3443692799732493,
          0.34290789962492874,
          0.3414409519765996,
          0.33996872462253086,
          0.3384915018017969,
          0.33700956432084883,
          0.3355231894800822,
          0.3340326510044198,
          0.33253821897791985,
          0.33104015978241574,
          0.32953873604019074,
          0.3280342065606853,
          0.3265268262912298,
          0.32501684627179284,
          0.3235045135937294,
          0.3219900713625091,
          0.3204737586644018,
          0.31895581053709277,
          0.3174364579441917,
          0.31591592775360644,
          0.31439444271973405,
          0.31287222146943,
          0.3113494784917049,
          0.30982642413109823,
          0.3083032645846735,
          0.30678020190257493,
          0.3052574339920843,
          0.3037351546251113,
          0.3022135534490465,
          0.3006928160009082,
          0.29917312372470334,
          0.2976546539919265,
          0.2961375801251138,
          0.2946220714243691,
          0.29310829319677323,
          0.29159640678858917,
          0.29008656962016993,
          0.288578935223475,
          0.28707365328209944,
          0.2855708696737188,
          0.2840707265148456,
          0.2825733622078021,
          0.2810789114897995,
          0.27958750548402306,
          0.27809927175261584,
          0.2766143343514539,
          0.2751328138866044,
          0.2736548275723589,
          0.27218048929073124,
          0.2707099096523097,
          0.2692431960583538,
          0.26778045276402435,
          0.26632178094263603,
          0.2648672787508213,
          0.2634170413944956,
          0.2619711611955137,
          0.26052972765890636,
          0.25909282754058927,
          0.2576605449154359,
          0.2562329612456058,
          0.2548101554490233,
          0.2533922039679004,
          0.251979180837201,
          0.25057115775294264,
          0.24916820414023727,
          0.2477703872209695,
          0.24637777208101708,
          0.24499042173691704,
          0.24360839720188526,
          0.24223175755109813,
          0.24086055998614816,
          0.23949485989858543,
          0.23813471093246458,
          0.23678016504581287,
          0.23543127257094323,
          0.23408808227353506,
          0.2327506414104114,
          0.2314189957859425,
          0.2300931898070088,
          0.228773266536459,
          0.2274592677450048,
          0.22615123396149392,
          0.22484920452150756,
          0.22355321761423202,
          0.222263310327558,
          0.22097951869136306,
          0.21970187771893876,
          0.2184304214465227,
          0.21716518297090692,
          0.21590619448508908,
          0.2146534873119437,
          0.2134070919358887,
          0.2121670380325302,
          0.21093335449627035,
          0.20970606946586634,
          0.2084852103479322,
          0.20727080383838087,
          0.20606287594180384,
          0.20486145198879305,
          0.20366655665120925,
          0.20247821395540874,
          0.20129644729344037,
          0.20012127943223046,
          0.19895273252077364,
          0.1977908280953556,
          0.1966355870828318,
          0.19548702980199387,
          0.19434517596305373,
          0.19321004466528424,
          0.19208165439285294,
          0.190960023008891,
          0.18984516774784244,
          0.1887371052061391,
          0.18763585133125316,
          0.18654142140917757,
          0.1854538300503894,
          0.18437309117435427,
          0.18329921799262894,
          0.18223222299062514,
          0.18117211790809679,
          0.18011891371841635,
          0.1790726206067066,
          0.17803324794689723,
          0.17700080427777592,
          0.17597529727810501,
          0.17495673374087783,
          0.17394511954678757,
          0.17294045963698476,
          0.17194275798519823,
          0.17095201756929804,
          0.16996824034237631,
          0.1689914272034257,
          0.16802157796769204,
          0.1670586913367827,
          0.166102764868607,
          0.16515379494723065,
          0.16421177675271964,
          0.16327670423105695,
          0.16234857006420678,
          0.1614273656404069,
          0.16051308102476536,
          0.15960570493023946,
          0.15870522468907233,
          0.1578116262247637,
          0.1569248940246467,
          0.15604501111314695,
          0.15517195902579278,
          0.15430571778405014,
          0.1534462658710476,
          0.15259358020826314,
          0.1517476361332351,
          0.15090840737836406,
          0.1500758660508654,
          0.1492499826139356,
          0.1484307258691886,
          0.14761806294041968,
          0.14681195925874985,
          0.14601237854920382,
          0.14521928281877022,
          0.14443263234599152,
          0.1436523856721278,
          0.1428784995939372,
          0.14211092915811213,
          0.14134962765740863,
          0.14059454662850213,
          0.1398456358516022,
          0.13910284335185472,
          0.13836611540255708,
          0.13763539653020987,
          0.13691062952142521,
          0.1361917554317094,
          0.13547871359613395,
          0.1347714416419069,
          0.1340698755028529,
          0.13337394943580794,
          0.13268359603893196,
          0.13199874627193806,
          0.13131932947823663,
          0.13064527340898785,
          0.12997650424905388,
          0.12931294664483892,
          0.128654523734003,
          0.12800115717703198,
          0.1273527671906438,
          0.1267092725830081,
          0.1260705907907534,
          0.12543663791773468,
          0.12480732877552943,
          0.12418257692562915,
          0.12356229472329122,
          0.12294639336301189,
          0.1223347829255804,
          0.12172737242667077,
          0.12112406986692659,
          0.12052478228349102,
          0.11992941580293273,
          0.1193378756955161,
          0.11875006643076211,
          0.11816589173424547,
          0.11758525464556938,
          0.11700805757746033,
          0.11643420237592206,
          0.11586359038138686,
          0.11529612249080062,
          0.11473169922057716,
          0.11417022077035573,
          0.11361158708749475,
          0.1130556979322336,
          0.11250245294345312,
          0.11195175170496507,
          0.11140349381226004,
          0.11085757893964214,
          0.1103139069076784,
          0.10977237775089105,
          0.10923289178561953,
          0.10869534967797934,
          0.10815965251184465,
          0.10762570185678122,
          0.1070933998358571,
          0.10656264919325734,
          0.10603335336163046,
          0.10550541652909391,
          0.10497874370582705,
          0.10445324079017956,
          0.10392881463422474,
          0.10340537310868755,
          0.10288282516717834,
          0.10236108090966331,
          0.10184005164510435,
          0.10131964995320242,
          0.10079978974517871,
          0.10028038632352967,
          0.09976135644069326,
          0.09924261835656514,
          0.098724091894805,
          0.09820569849787467,
          0.09768736128075106,
          0.09716900508325922,
          0.09665055652097211,
          0.09613194403462554,
          0.09561309793799824,
          0.09509395046421008,
          0.09457443581039174,
          0.09405449018068279
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)"
         },
         "mode": "lines",
         "name": "Dimension 1",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -1.5352871417999268,
          -1.5289670011997223,
          -1.5226468605995178,
          -1.5163267199993133,
          -1.5100065793991089,
          -1.5036864387989044,
          -1.4973662981987,
          -1.4910461575984955,
          -1.484726016998291,
          -1.4784058763980865,
          -1.472085735797882,
          -1.4657655951976776,
          -1.459445454597473,
          -1.4531253139972686,
          -1.4468051733970642,
          -1.4404850327968597,
          -1.4341648921966552,
          -1.4278447515964507,
          -1.4215246109962463,
          -1.4152044703960418,
          -1.4088843297958373,
          -1.4025641891956329,
          -1.3962440485954284,
          -1.389923907995224,
          -1.3836037673950194,
          -1.377283626794815,
          -1.3709634861946105,
          -1.364643345594406,
          -1.3583232049942016,
          -1.352003064393997,
          -1.3456829237937926,
          -1.3393627831935881,
          -1.3330426425933837,
          -1.3267225019931792,
          -1.3204023613929747,
          -1.3140822207927703,
          -1.307762080192566,
          -1.3014419395923615,
          -1.295121798992157,
          -1.2888016583919526,
          -1.2824815177917481,
          -1.2761613771915437,
          -1.2698412365913392,
          -1.2635210959911347,
          -1.2572009553909302,
          -1.2508808147907258,
          -1.2445606741905213,
          -1.2382405335903168,
          -1.2319203929901124,
          -1.2256002523899079,
          -1.2192801117897034,
          -1.212959971189499,
          -1.2066398305892945,
          -1.20031968998909,
          -1.1939995493888855,
          -1.187679408788681,
          -1.1813592681884766,
          -1.1750391275882721,
          -1.1687189869880676,
          -1.1623988463878632,
          -1.1560787057876587,
          -1.1497585651874542,
          -1.1434384245872498,
          -1.1371182839870453,
          -1.1307981433868408,
          -1.1244780027866363,
          -1.1181578621864319,
          -1.1118377215862274,
          -1.105517580986023,
          -1.0991974403858185,
          -1.092877299785614,
          -1.0865571591854095,
          -1.080237018585205,
          -1.0739168779850006,
          -1.067596737384796,
          -1.0612765967845916,
          -1.0549564561843872,
          -1.0486363155841827,
          -1.0423161749839782,
          -1.0359960343837737,
          -1.0296758937835695,
          -1.023355753183365,
          -1.0170356125831606,
          -1.010715471982956,
          -1.0043953313827516,
          -0.998075190782547,
          -0.9917550501823426,
          -0.9854349095821381,
          -0.9791147689819336,
          -0.9727946283817291,
          -0.9664744877815247,
          -0.9601543471813202,
          -0.9538342065811157,
          -0.9475140659809113,
          -0.9411939253807068,
          -0.9348737847805023,
          -0.9285536441802978,
          -0.9222335035800934,
          -0.9159133629798889,
          -0.9095932223796844,
          -0.90327308177948,
          -0.8969529411792755,
          -0.890632800579071,
          -0.8843126599788665,
          -0.8779925193786621,
          -0.8716723787784576,
          -0.8653522381782531,
          -0.8590320975780487,
          -0.8527119569778442,
          -0.8463918163776397,
          -0.8400716757774354,
          -0.8337515351772309,
          -0.8274313945770264,
          -0.8211112539768219,
          -0.8147911133766175,
          -0.808470972776413,
          -0.8021508321762085,
          -0.7958306915760041,
          -0.7895105509757996,
          -0.7831904103755951,
          -0.7768702697753906,
          -0.7705501291751862,
          -0.7642299885749817,
          -0.7579098479747772,
          -0.7515897073745728,
          -0.7452695667743683,
          -0.7389494261741638,
          -0.7326292855739593,
          -0.7263091449737549,
          -0.7199890043735504,
          -0.7136688637733459,
          -0.7073487231731415,
          -0.701028582572937,
          -0.6947084419727325,
          -0.688388301372528,
          -0.6820681607723236,
          -0.6757480201721191,
          -0.6694278795719146,
          -0.6631077389717102,
          -0.6567875983715057,
          -0.6504674577713012,
          -0.6441473171710969,
          -0.6378271765708924,
          -0.6315070359706879,
          -0.6251868953704834,
          -0.618866754770279,
          -0.6125466141700745,
          -0.60622647356987,
          -0.5999063329696656,
          -0.5935861923694611,
          -0.5872660517692566,
          -0.5809459111690521,
          -0.5746257705688477,
          -0.5683056299686432,
          -0.5619854893684387,
          -0.5556653487682343,
          -0.5493452081680298,
          -0.5430250675678253,
          -0.5367049269676208,
          -0.5303847863674165,
          -0.524064645767212,
          -0.5177445051670075,
          -0.5114243645668031,
          -0.5051042239665986,
          -0.4987840833663941,
          -0.49246394276618966,
          -0.4861438021659852,
          -0.4798236615657807,
          -0.47350352096557624,
          -0.46718338036537177,
          -0.4608632397651673,
          -0.4545430991649628,
          -0.44822295856475836,
          -0.4419028179645539,
          -0.4355826773643494,
          -0.42926253676414494,
          -0.42294239616394047,
          -0.416622255563736,
          -0.41030211496353153,
          -0.40398197436332706,
          -0.3976618337631226,
          -0.3913416931629181,
          -0.38502155256271364,
          -0.37870141196250917,
          -0.3723812713623047,
          -0.36606113076210023,
          -0.35974099016189576,
          -0.3534208495616913,
          -0.3471007089614868,
          -0.34078056836128234,
          -0.33446042776107787,
          -0.3281402871608734,
          -0.32182014656066893,
          -0.31550000596046446,
          -0.30917986536026,
          -0.3028597247600555,
          -0.29653958415985104,
          -0.2902194435596466,
          -0.2838993029594421,
          -0.27757916235923763,
          -0.27125902175903316,
          -0.2649388811588287,
          -0.2586187405586242,
          -0.25229859995841974,
          -0.24597845935821527,
          -0.2396583187580108,
          -0.23333817815780633,
          -0.22701803755760186,
          -0.2206978969573974,
          -0.21437775635719292,
          -0.20805761575698845,
          -0.20173747515678397,
          -0.1954173345565795,
          -0.18909719395637503,
          -0.18277705335617056,
          -0.1764569127559661,
          -0.17013677215576162,
          -0.16381663155555715,
          -0.15749649095535267,
          -0.15117635035514843,
          -0.14485620975494395,
          -0.13853606915473948,
          -0.132215928554535,
          -0.12589578795433054,
          -0.11957564735412607,
          -0.1132555067539216,
          -0.10693536615371713,
          -0.10061522555351265,
          -0.09429508495330818,
          -0.08797494435310371,
          -0.08165480375289924,
          -0.07533466315269477,
          -0.0690145225524903,
          -0.06269438195228583,
          -0.056374241352081356,
          -0.050054100751876884,
          -0.04373396015167241,
          -0.03741381955146794,
          -0.03109367895126347,
          -0.024773538351059,
          -0.018453397750854528,
          -0.012133257150650056,
          -0.005813116550445585,
          0.0005070240497588863,
          0.006827164649963358,
          0.013147305250167829,
          0.0194674458503723,
          0.02578758645057677,
          0.03210772705078124,
          0.038427867650985714,
          0.044748008251190186,
          0.05106814885139466,
          0.05738828945159913,
          0.0637084300518036,
          0.07002857065200807,
          0.07634871125221254,
          0.08266885185241701,
          0.08898899245262148,
          0.09530913305282596,
          0.10162927365303043,
          0.1079494142532349,
          0.11426955485343937,
          0.12058969545364384,
          0.1269098360538483,
          0.13322997665405278,
          0.13955011725425726,
          0.14587025785446173,
          0.1521903984546662,
          0.15851053905487067,
          0.16483067965507514,
          0.1711508202552796,
          0.17747096085548408,
          0.18379110145568855,
          0.19011124205589303,
          0.1964313826560975,
          0.20275152325630197,
          0.20907166385650644,
          0.2153918044567109,
          0.22171194505691538,
          0.22803208565711985,
          0.23435222625732433,
          0.2406723668575288,
          0.24699250745773305,
          0.2533126480579375,
          0.259632788658142,
          0.26595292925834646,
          0.27227306985855093,
          0.2785932104587554,
          0.2849133510589599,
          0.29123349165916435,
          0.2975536322593688,
          0.3038737728595733,
          0.31019391345977776,
          0.31651405405998223,
          0.3228341946601867,
          0.3291543352603912,
          0.33547447586059564,
          0.3417946164608001,
          0.3481147570610046,
          0.35443489766120906,
          0.36075503826141353,
          0.367075178861618,
          0.3733953194618225,
          0.37971546006202694,
          0.3860356006622314,
          0.3923557412624359,
          0.39867588186264036,
          0.40499602246284483,
          0.4113161630630493,
          0.41763630366325377,
          0.42395644426345824,
          0.4302765848636627,
          0.4365967254638672,
          0.44291686606407166,
          0.44923700666427613,
          0.4555571472644806,
          0.46187728786468507,
          0.4681974284648893,
          0.4745175690650938,
          0.48083770966529826,
          0.48715785026550273,
          0.4934779908657072,
          0.4997981314659117,
          0.5061182720661161,
          0.5124384126663206,
          0.5187585532665251,
          0.5250786938667296,
          0.531398834466934,
          0.5377189750671385,
          0.544039115667343,
          0.5503592562675474,
          0.5566793968677519,
          0.5629995374679564,
          0.5693196780681609,
          0.5756398186683653,
          0.5819599592685698,
          0.5882800998687743,
          0.5946002404689787,
          0.6009203810691832,
          0.6072405216693877,
          0.6135606622695922,
          0.6198808028697966,
          0.6262009434700011,
          0.6325210840702056,
          0.63884122467041,
          0.6451613652706145,
          0.651481505870819,
          0.6578016464710235,
          0.6641217870712279,
          0.6704419276714324,
          0.6767620682716369,
          0.6830822088718413,
          0.6894023494720458,
          0.6957224900722503,
          0.7020426306724548,
          0.7083627712726592,
          0.7146829118728637,
          0.7210030524730682,
          0.7273231930732726,
          0.7336433336734771,
          0.7399634742736816,
          0.7462836148738861,
          0.7526037554740905,
          0.758923896074295,
          0.7652440366744995,
          0.7715641772747039,
          0.7778843178749084,
          0.7842044584751129,
          0.7905245990753174,
          0.7968447396755218,
          0.8031648802757263,
          0.8094850208759308,
          0.8158051614761352,
          0.8221253020763397,
          0.8284454426765442,
          0.8347655832767487,
          0.8410857238769531,
          0.8474058644771576,
          0.8537260050773621,
          0.8600461456775665,
          0.866366286277771,
          0.8726864268779755,
          0.87900656747818,
          0.8853267080783844,
          0.8916468486785889,
          0.8979669892787934,
          0.9042871298789978,
          0.9106072704792023,
          0.9169274110794068,
          0.9232475516796113,
          0.9295676922798157,
          0.9358878328800202,
          0.9422079734802247,
          0.9485281140804291,
          0.9548482546806336,
          0.9611683952808381,
          0.9674885358810426,
          0.973808676481247,
          0.9801288170814515,
          0.986448957681656,
          0.9927690982818604,
          0.9990892388820649,
          1.0054093794822694,
          1.0117295200824739,
          1.0180496606826783,
          1.0243698012828828,
          1.0306899418830873,
          1.0370100824832917,
          1.0433302230834962,
          1.0496503636837007,
          1.0559705042839052,
          1.0622906448841096,
          1.068610785484314,
          1.0749309260845186,
          1.081251066684723,
          1.0875712072849275,
          1.093891347885132,
          1.1002114884853365,
          1.106531629085541,
          1.1128517696857454,
          1.1191719102859499,
          1.1254920508861543,
          1.1318121914863588,
          1.1381323320865633,
          1.1444524726867678,
          1.1507726132869722,
          1.1570927538871767,
          1.1634128944873812,
          1.1697330350875856,
          1.17605317568779,
          1.1823733162879946,
          1.188693456888199,
          1.1950135974884035,
          1.201333738088608,
          1.2076538786888125,
          1.213974019289017,
          1.2202941598892214,
          1.2266143004894259,
          1.23293444108963,
          1.2392545816898344,
          1.2455747222900388,
          1.2518948628902433,
          1.2582150034904478,
          1.2645351440906523,
          1.2708552846908567,
          1.2771754252910612,
          1.2834955658912657,
          1.2898157064914701,
          1.2961358470916746,
          1.302455987691879,
          1.3087761282920836,
          1.315096268892288,
          1.3214164094924925,
          1.327736550092697,
          1.3340566906929014,
          1.340376831293106,
          1.3466969718933104,
          1.3530171124935149,
          1.3593372530937193,
          1.3656573936939238,
          1.3719775342941283,
          1.3782976748943327,
          1.3846178154945372,
          1.3909379560947417,
          1.3972580966949462,
          1.4035782372951506,
          1.409898377895355,
          1.4162185184955596,
          1.422538659095764,
          1.4288587996959685,
          1.435178940296173,
          1.4414990808963775,
          1.447819221496582,
          1.4541393620967864,
          1.4604595026969909,
          1.4667796432971953,
          1.4730997838973998,
          1.4794199244976043,
          1.4857400650978088,
          1.4920602056980132,
          1.4983803462982177,
          1.5047004868984222,
          1.5110206274986266,
          1.5173407680988311,
          1.5236609086990356,
          1.52998104929924,
          1.5363011898994445,
          1.542621330499649,
          1.5489414710998535,
          1.555261611700058,
          1.5615817523002624,
          1.5679018929004669,
          1.5742220335006714,
          1.5805421741008758,
          1.5868623147010803,
          1.5931824553012848,
          1.5995025959014892,
          1.6058227365016937,
          1.6121428771018982,
          1.6184630177021027
         ],
         "xaxis": "x",
         "y": [
          0.1859275667495029,
          0.1867200261939332,
          0.1875064243253394,
          0.18828672482929207,
          0.18906089362181525,
          0.1898288988632735,
          0.19059071097128247,
          0.19134630263263236,
          0.1920956488142178,
          0.19283872677296388,
          0.19357551606474122,
          0.19430599855226294,
          0.1950301584119562,
          0.19574798213980227,
          0.1964594585561385,
          0.197164578809418,
          0.1978633363789206,
          0.19855572707641184,
          0.19924174904674563,
          0.1999214027674066,
          0.20059469104699013,
          0.20126161902261694,
          0.20192219415628057,
          0.2025764262301262,
          0.20322432734065962,
          0.203865911891887,
          0.20450119658738358,
          0.20513020042129432,
          0.20575294466826505,
          0.2063694528723079,
          0.20697975083460166,
          0.20758386660023045,
          0.20818183044386354,
          0.2087736748543796,
          0.20935943451844005,
          0.20993914630301647,
          0.21051284923687538,
          0.21108058449102846,
          0.21164239535815213,
          0.2121983272309847,
          0.21274842757970722,
          0.2132927459283158,
          0.21383133382999345,
          0.2143642448414905,
          0.21489153449652165,
          0.21541326027818977,
          0.21592948159044628,
          0.21644025972859854,
          0.21694565784887485,
          0.21744574093705882,
          0.21794057577620485,
          0.21843023091344618,
          0.21891477662590952,
          0.21939428488574816,
          0.21986882932430793,
          0.22033848519543958,
          0.2208033293379718,
          0.22126344013736074,
          0.22171889748652976,
          0.22216978274591623,
          0.2226161787027411,
          0.2230581695295176,
          0.22349584074181555,
          0.22392927915529998,
          0.22435857284205915,
          0.2247838110862429,
          0.2252050843390271,
          0.22562248417292471,
          0.22603610323546144,
          0.22644603520223602,
          0.22685237472938455,
          0.2272552174054691,
          0.22765465970281118,
          0.22805079892829014,
          0.2284437331736284,
          0.22883356126518445,
          0.2292203827132752,
          0.22960429766104945,
          0.22998540683293564,
          0.23036381148268475,
          0.230739613341033,
          0.23111291456300548,
          0.2314838176748855,
          0.2318524255208726,
          0.23221884120945196,
          0.2325831680595017,
          0.23294550954615895,
          0.23330596924647193,
          0.23366465078486104,
          0.23402165777841388,
          0.23437709378203997,
          0.234731062233509,
          0.2350836663983991,
          0.23543500931497965,
          0.23578519373905485,
          0.23613432208879293,
          0.23648249638956803,
          0.23682981821883925,
          0.2371763886510938,
          0.23752230820288034,
          0.23786767677795817,
          0.23821259361258879,
          0.23855715722099663,
          0.2389014653410243,
          0.23924561488000945,
          0.23958970186090967,
          0.2399338213687014,
          0.24027806749707975,
          0.2406225332954855,
          0.2409673107164851,
          0.2413124905635312,
          0.24165816243912897,
          0.24200441469343484,
          0.24235133437331416,
          0.24269900717188303,
          0.2430475173785614,
          0.24339694782966256,
          0.24374737985954473,
          0.24409889325235118,
          0.24445156619436342,
          0.24480547522699359,
          0.24516069520044081,
          0.2455172992280361,
          0.24587535864130194,
          0.24623494294574907,
          0.2465961197774371,
          0.2469589548603211,
          0.24732351196440924,
          0.2476898528647546,
          0.24805803730130443,
          0.24842812293962993,
          0.24880016533255972,
          0.24917421788273802,
          0.24955033180613187,
          0.24992855609650638,
          0.2503089374908916,
          0.250691520436061,
          0.2510763470560417,
          0.25146345712067764,
          0.2518528880152652,
          0.25224467471127915,
          0.2526388497382108,
          0.2530354431565333,
          0.25343448253181444,
          0.2538359929099938,
          0.254239996793841,
          0.2546465141206113,
          0.2550555622409149,
          0.2554671558988155,
          0.25588130721317226,
          0.2562980256602399,
          0.25671731805754083,
          0.2571391885490215,
          0.25756363859150705,
          0.2579906669424644,
          0.2584202696490862,
          0.2588524400387059,
          0.259287168710554,
          0.25972444352886476,
          0.26016424961734186,
          0.26060656935499116,
          0.26105138237332837,
          0.2614986655549668,
          0.2619483930335926,
          0.26240053619533144,
          0.2628550636815124,
          0.26331194139283076,
          0.263771132494915,
          0.2642325974252982,
          0.26469629390179616,
          0.26516217693229355,
          0.26563019882593586,
          0.266100309205729,
          0.2665724550225427,
          0.2670465805705161,
          0.267522627503862,
          0.268000534855067,
          0.2684802390544792,
          0.2689616739512829,
          0.26944477083584856,
          0.26992945846345456,
          0.27041566307937054,
          0.27090330844529437,
          0.2713923158671322,
          0.2718826042241118,
          0.27237408999921736,
          0.2728666873109337,
          0.27336030794628596,
          0.27385486139516313,
          0.2743502548859077,
          0.2748463934221592,
          0.275343179820933,
          0.27584051475191707,
          0.2763382967779722,
          0.27683642239681283,
          0.2773347860838513,
          0.2778332803361856,
          0.27833179571770805,
          0.27883022090531495,
          0.27932844273619367,
          0.2798263462561639,
          0.2803238147690501,
          0.2808207298870591,
          0.281316971582139,
          0.28181241823829173,
          0.2823069467048145,
          0.2828004323504402,
          0.2832927491183513,
          0.2837837695820366,
          0.28427336500196276,
          0.2847614053830296,
          0.2852477595327798,
          0.2857322951203313,
          0.28621487873600027,
          0.2866953759515833,
          0.28717365138126616,
          0.28764956874312486,
          0.28812299092118643,
          0.2885937800280146,
          0.28906179746778626,
          0.28952690399982356,
          0.28998895980254547,
          0.29044782453780427,
          0.29090335741557055,
          0.2913554172589289,
          0.2918038625693496,
          0.29224855159219787,
          0.2926893423824436,
          0.2931260928705343,
          0.29355866092839367,
          0.2939869044355071,
          0.2944106813450571,
          0.29482984975006904,
          0.2952442679495307,
          0.2956537945144458,
          0.29605828835378317,
          0.2964576087802841,
          0.2968516155760885,
          0.2972401690581413,
          0.2976231301433424,
          0.2980003604133988,
          0.2983717221793443,
          0.29873707854568593,
          0.2990962934741407,
          0.29944923184692473,
          0.2997957595295573,
          0.30013574343314225,
          0.30046905157609055,
          0.300795553145247,
          0.3011151185563845,
          0.3014276195140314,
          0.30173292907059407,
          0.3020309216847418,
          0.3023214732790187,
          0.30260446129664753,
          0.3028797647574931,
          0.3031472643131513,
          0.3034068423011316,
          0.30365838279810026,
          0.3039017716721541,
          0.30413689663409227,
          0.304363647287658,
          0.30458191517871847,
          0.30479159384335613,
          0.304992578854842,
          0.3051847678694643,
          0.30536806067118544,
          0.30554235921510187,
          0.30570756766968166,
          0.3058635924577554,
          0.306010342296238,
          0.30614772823455716,
          0.3062756636917693,
          0.30639406449233964,
          0.30650284890056934,
          0.30660193765364785,
          0.30669125399331626,
          0.3067707236961203,
          0.3068402751022411,
          0.3068998391428863,
          0.30694934936622775,
          0.3069887419618739,
          0.3070179557838639,
          0.3070369323721725,
          0.3070456159727169,
          0.3070439535558547,
          0.3070318948333676,
          0.3070093922739222,
          0.3069764011170026,
          0.30693287938531105,
          0.30687878789563255,
          0.3068140902681598,
          0.3067387529342797,
          0.3066527451428185,
          0.3065560389647477,
          0.3064486092963524,
          0.3063304338608652,
          0.30620149320856827,
          0.30606177071537094,
          0.3059112525798673,
          0.30574992781888055,
          0.30557778826150445,
          0.30539482854164934,
          0.30520104608910303,
          0.3049964411191193,
          0.3047810166205453,
          0.3045547783425006,
          0.3043177347796247,
          0.3040698971559049,
          0.3038112794071042,
          0.303541898161804,
          0.30326177272108135,
          0.302970925036839,
          0.3026693796888086,
          0.3023571638602486,
          0.30203430731235714,
          0.3017008423574242,
          0.30135680383074614,
          0.3010022290613251,
          0.300637157841382,
          0.3002616323947055,
          0.29987569734386543,
          0.2994793996763173,
          0.2990727887094273,
          0.29865591605444364,
          0.2982288355794478,
          0.2977916033713109,
          0.2973442776966905,
          0.29688691896209535,
          0.2964195896730522,
          0.29594235439240596,
          0.29545527969778546,
          0.29495843413827005,
          0.2944518881902881,
          0.29393571421278386,
          0.29340998640168575,
          0.2928747807437111,
          0.2923301749695434,
          0.29177624850641637,
          0.2912130824301414,
          0.29064075941661394,
          0.2900593636928354,
          0.28946898098748636,
          0.2888696984810879,
          0.2882616047557883,
          0.28764478974481084,
          0.2870193446815994,
          0.2863853620486999,
          0.28574293552641383,
          0.28509215994125936,
          0.2844331312142785,
          0.2837659463092266,
          0.2830907031806795,
          0.28240750072209614,
          0.2817164387138716,
          0.2810176177714177,
          0.2803111392933058,
          0.27959710540950783,
          0.2788756189297702,
          0.27814678329215686,
          0.2774107025117934,
          0.2766674811298495,
          0.2759172241627903,
          0.2751600370519321,
          0.2743960256133351,
          0.273625295988064,
          0.2728479545928501,
          0.272064108071185,
          0.27127386324487734,
          0.2704773270661029,
          0.26967460656997666,
          0.26886580882767713,
          0.2680510409001508,
          0.26723040979242363,
          0.2664040224085484,
          0.2655719855072124,
          0.2647344056580323,
          0.26389138919856064,
          0.2630430421920284,
          0.2621894703858466,
          0.2613307791708899,
          0.2604670735415845,
          0.2595984580568194,
          0.258725036801705,
          0.2578469133501941,
          0.2569641907285866,
          0.2560769713799358,
          0.2551853571293701,
          0.2542894491503515,
          0.2533893479318792,
          0.2524851532466589,
          0.2515769641202466,
          0.2506648788011828,
          0.24974899473212495,
          0.24882940852199217,
          0.24790621591913053,
          0.24697951178550737,
          0.2460493900719432,
          0.24511594379438856,
          0.24417926501125053,
          0.24323944480177614,
          0.24229657324549472,
          0.24135073940272514,
          0.24040203129614776,
          0.23945053589344506,
          0.23849633909100992,
          0.23753952569872291,
          0.23658017942579598,
          0.23561838286768239,
          0.23465421749404836,
          0.23368776363780452,
          0.23271910048519112,
          0.23174830606691338,
          0.23077545725031948,
          0.22980062973261495,
          0.22882389803510575,
          0.22784533549846178,
          0.22686501427899075,
          0.22588300534591335,
          0.22489937847962874,
          0.2239142022709582,
          0.2229275441213561,
          0.2219394702440739,
          0.2209500456662648,
          0.21995933423201414,
          0.21896739860628106,
          0.2179743002797359,
          0.21698009957447703,
          0.21598485565061085,
          0.21498862651367778,
          0.21399146902290597,
          0.21299343890027503,
          0.21199459074037064,
          0.21099497802101103,
          0.20999465311462548,
          0.20899366730036453,
          0.2079920707769218,
          0.20698991267604583,
          0.20598724107672095,
          0.20498410301999548,
          0.20398054452443523,
          0.20297661060217956,
          0.2019723452755782,
          0.20096779159438477,
          0.1999629916534849,
          0.1989579866111352,
          0.19795281670768952,
          0.19694752128478862,
          0.19594213880498973,
          0.19493670687181155,
          0.19393126225017107,
          0.19292584088718776,
          0.1919204779333308,
          0.1909152077638851,
          0.1899100640007119,
          0.18890507953427965,
          0.18790028654594076,
          0.18689571653043008,
          0.18589140031856072,
          0.18488736810009357,
          0.18388364944675606,
          0.18288027333538698,
          0.18187726817118247,
          0.18087466181102152,
          0.17987248158684516,
          0.17887075432906924,
          0.17786950639000468,
          0.17686876366726537,
          0.17586855162713938,
          0.1748688953279024,
          0.17386981944305085,
          0.17287134828443423,
          0.17187350582526417,
          0.17087631572298045,
          0.16987980134195318,
          0.16888398577600047,
          0.16788889187070297,
          0.16689454224549502,
          0.165900959315514,
          0.16490816531318925,
          0.16391618230955263,
          0.16292503223525295,
          0.16193473690125748,
          0.16094531801922374,
          0.15995679722152498,
          0.1589691960809147,
          0.15798253612981428,
          0.15699683887920868,
          0.15601212583713756,
          0.15502841852676655,
          0.1540457385040267,
          0.15306410737480936,
          0.15208354681170358,
          0.15110407857026648,
          0.15012572450481368,
          0.14914850658372053,
          0.14817244690422468,
          0.1471975677067195,
          0.1462238913885312,
          0.14525144051717034
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)"
         },
         "mode": "lines",
         "name": "Dimension 2",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -0.5515286922454834,
          -0.5492369887828827,
          -0.546945285320282,
          -0.5446535818576813,
          -0.5423618783950805,
          -0.5400701749324799,
          -0.5377784714698791,
          -0.5354867680072785,
          -0.5331950645446777,
          -0.530903361082077,
          -0.5286116576194764,
          -0.5263199541568756,
          -0.5240282506942749,
          -0.5217365472316742,
          -0.5194448437690735,
          -0.5171531403064727,
          -0.5148614368438721,
          -0.5125697333812713,
          -0.5102780299186707,
          -0.50798632645607,
          -0.5056946229934692,
          -0.5034029195308686,
          -0.5011112160682678,
          -0.4988195126056671,
          -0.4965278091430664,
          -0.4942361056804657,
          -0.491944402217865,
          -0.4896526987552643,
          -0.4873609952926636,
          -0.48506929183006287,
          -0.48277758836746215,
          -0.48048588490486144,
          -0.4781941814422607,
          -0.47590247797966,
          -0.47361077451705935,
          -0.47131907105445864,
          -0.4690273675918579,
          -0.4667356641292572,
          -0.4644439606666565,
          -0.4621522572040558,
          -0.45986055374145507,
          -0.45756885027885436,
          -0.45527714681625364,
          -0.452985443353653,
          -0.4506937398910522,
          -0.44840203642845156,
          -0.44611033296585084,
          -0.44381862950325013,
          -0.4415269260406494,
          -0.4392352225780487,
          -0.436943519115448,
          -0.4346518156528473,
          -0.4323601121902466,
          -0.43006840872764585,
          -0.4277767052650452,
          -0.4254850018024444,
          -0.42319329833984376,
          -0.42090159487724305,
          -0.41860989141464233,
          -0.4163181879520416,
          -0.4140264844894409,
          -0.41173478102684025,
          -0.4094430775642395,
          -0.4071513741016388,
          -0.40485967063903805,
          -0.4025679671764374,
          -0.4002762637138367,
          -0.39798456025123596,
          -0.39569285678863525,
          -0.39340115332603454,
          -0.3911094498634339,
          -0.3888177464008331,
          -0.38652604293823245,
          -0.3842343394756317,
          -0.381942636013031,
          -0.3796509325504303,
          -0.3773592290878296,
          -0.3750675256252289,
          -0.37277582216262817,
          -0.37048411870002745,
          -0.36819241523742674,
          -0.3659007117748261,
          -0.3636090083122253,
          -0.36131730484962465,
          -0.3590256013870239,
          -0.3567338979244232,
          -0.3544421944618225,
          -0.3521504909992218,
          -0.3498587875366211,
          -0.34756708407402037,
          -0.3452753806114197,
          -0.34298367714881894,
          -0.3406919736862183,
          -0.3384002702236175,
          -0.33610856676101686,
          -0.33381686329841614,
          -0.33152515983581543,
          -0.3292334563732147,
          -0.326941752910614,
          -0.32465004944801334,
          -0.3223583459854126,
          -0.3200666425228119,
          -0.31777493906021115,
          -0.3154832355976105,
          -0.3131915321350098,
          -0.31089982867240906,
          -0.30860812520980835,
          -0.30631642174720763,
          -0.3040247182846069,
          -0.3017330148220062,
          -0.2994413113594055,
          -0.29714960789680483,
          -0.2948579044342041,
          -0.2925662009716034,
          -0.2902744975090027,
          -0.287982794046402,
          -0.28569109058380127,
          -0.28339938712120055,
          -0.28110768365859984,
          -0.2788159801959991,
          -0.2765242767333984,
          -0.27423257327079775,
          -0.27194086980819704,
          -0.2696491663455963,
          -0.2673574628829956,
          -0.2650657594203949,
          -0.2627740559577942,
          -0.26048235249519347,
          -0.25819064903259276,
          -0.25589894556999204,
          -0.2536072421073914,
          -0.25131553864479067,
          -0.24902383518218996,
          -0.24673213171958924,
          -0.24444042825698853,
          -0.24214872479438782,
          -0.2398570213317871,
          -0.2375653178691864,
          -0.23527361440658567,
          -0.23298191094398496,
          -0.2306902074813843,
          -0.2283985040187836,
          -0.22610680055618287,
          -0.22381509709358216,
          -0.22152339363098145,
          -0.21923169016838073,
          -0.21693998670578002,
          -0.2146482832431793,
          -0.2123565797805786,
          -0.21006487631797788,
          -0.20777317285537722,
          -0.2054814693927765,
          -0.2031897659301758,
          -0.20089806246757508,
          -0.19860635900497436,
          -0.19631465554237365,
          -0.19402295207977294,
          -0.19173124861717222,
          -0.1894395451545715,
          -0.18714784169197085,
          -0.18485613822937014,
          -0.18256443476676942,
          -0.1802727313041687,
          -0.177981027841568,
          -0.17568932437896728,
          -0.17339762091636657,
          -0.17110591745376585,
          -0.16881421399116514,
          -0.16652251052856443,
          -0.16423080706596377,
          -0.16193910360336305,
          -0.15964740014076234,
          -0.15735569667816163,
          -0.1550639932155609,
          -0.1527722897529602,
          -0.15048058629035949,
          -0.14818888282775877,
          -0.14589717936515806,
          -0.1436054759025574,
          -0.1413137724399567,
          -0.13902206897735597,
          -0.13673036551475526,
          -0.13443866205215455,
          -0.13214695858955383,
          -0.12985525512695312,
          -0.1275635516643524,
          -0.1252718482017517,
          -0.12298014473915098,
          -0.12068844127655032,
          -0.1183967378139496,
          -0.11610503435134889,
          -0.11381333088874818,
          -0.11152162742614746,
          -0.10922992396354675,
          -0.10693822050094604,
          -0.10464651703834532,
          -0.10235481357574461,
          -0.1000631101131439,
          -0.09777140665054324,
          -0.09547970318794252,
          -0.09318799972534181,
          -0.0908962962627411,
          -0.08860459280014038,
          -0.08631288933753967,
          -0.08402118587493895,
          -0.08172948241233824,
          -0.07943777894973753,
          -0.07714607548713687,
          -0.07485437202453615,
          -0.07256266856193544,
          -0.07027096509933473,
          -0.06797926163673401,
          -0.0656875581741333,
          -0.06339585471153258,
          -0.06110415124893187,
          -0.05881244778633116,
          -0.05652074432373044,
          -0.054229040861129785,
          -0.05193733739852907,
          -0.04964563393592836,
          -0.04735393047332759,
          -0.04506222701072693,
          -0.04277052354812627,
          -0.0404788200855255,
          -0.038187116622924844,
          -0.035895413160324074,
          -0.033603709697723416,
          -0.03131200623512265,
          -0.02902030277252199,
          -0.02672859930992122,
          -0.02443689584732056,
          -0.022145192384719903,
          -0.019853488922119134,
          -0.017561785459518475,
          -0.015270081996917706,
          -0.012978378534317048,
          -0.010686675071716278,
          -0.00839497160911562,
          -0.006103268146514851,
          -0.0038115646839141926,
          -0.0015198612213134233,
          0.000771842241287235,
          0.0030635457038878933,
          0.0053552491664886626,
          0.007646952629089321,
          0.00993865609169009,
          0.012230359554290748,
          0.014522063016891518,
          0.016813766479492176,
          0.019105469942092945,
          0.021397173404693604,
          0.023688876867294262,
          0.02598058032989503,
          0.02827228379249569,
          0.03056398725509646,
          0.03285569071769712,
          0.035147394180297886,
          0.037439097642898544,
          0.039730801105499314,
          0.04202250456809997,
          0.04431420803070063,
          0.0466059114933014,
          0.04889761495590206,
          0.05118931841850283,
          0.053481021881103485,
          0.055772725343704255,
          0.05806442880630491,
          0.06035613226890568,
          0.06264783573150634,
          0.06493953919410711,
          0.06723124265670777,
          0.06952294611930843,
          0.0718146495819092,
          0.07410635304450985,
          0.07639805650711062,
          0.07868975996971128,
          0.08098146343231205,
          0.08327316689491271,
          0.08556487035751348,
          0.08785657382011414,
          0.0901482772827148,
          0.09243998074531556,
          0.09473168420791622,
          0.09702338767051699,
          0.09931509113311765,
          0.10160679459571842,
          0.10389849805831908,
          0.10619020152091985,
          0.1084819049835205,
          0.11077360844612116,
          0.11306531190872193,
          0.11535701537132259,
          0.11764871883392336,
          0.11994042229652402,
          0.12223212575912479,
          0.12452382922172545,
          0.12681553268432622,
          0.12910723614692687,
          0.13139893960952764,
          0.1336906430721283,
          0.13598234653472896,
          0.13827404999732973,
          0.1405657534599304,
          0.14285745692253116,
          0.14514916038513181,
          0.14744086384773258,
          0.14973256731033324,
          0.152024270772934,
          0.15431597423553467,
          0.15660767769813533,
          0.1588993811607361,
          0.16119108462333676,
          0.16348278808593752,
          0.16577449154853818,
          0.16806619501113895,
          0.1703578984737396,
          0.17264960193634038,
          0.17494130539894104,
          0.1772330088615417,
          0.17952471232414247,
          0.18181641578674312,
          0.1841081192493439,
          0.18639982271194455,
          0.18869152617454532,
          0.19098322963714598,
          0.19327493309974675,
          0.1955666365623474,
          0.19785834002494807,
          0.20015004348754883,
          0.2024417469501495,
          0.20473345041275026,
          0.20702515387535092,
          0.2093168573379517,
          0.21160856080055235,
          0.21390026426315312,
          0.21619196772575378,
          0.21848367118835454,
          0.2207753746509552,
          0.22306707811355586,
          0.22535878157615663,
          0.2276504850387573,
          0.22994218850135806,
          0.23223389196395872,
          0.23452559542655949,
          0.23681729888916014,
          0.2391090023517609,
          0.24140070581436157,
          0.24369240927696223,
          0.245984112739563,
          0.24827581620216366,
          0.2505675196647644,
          0.2528592231273651,
          0.25515092658996585,
          0.2574426300525665,
          0.2597343335151673,
          0.26202603697776794,
          0.2643177404403686,
          0.26660944390296937,
          0.26890114736557,
          0.2711928508281708,
          0.27348455429077145,
          0.2757762577533722,
          0.2780679612159729,
          0.28035966467857365,
          0.2826513681411743,
          0.2849430716037751,
          0.28723477506637574,
          0.2895264785289764,
          0.29181818199157716,
          0.2941098854541778,
          0.2964015889167786,
          0.29869329237937925,
          0.30098499584198,
          0.3032766993045807,
          0.30556840276718145,
          0.3078601062297821,
          0.31015180969238276,
          0.31244351315498353,
          0.3147352166175842,
          0.31702692008018496,
          0.3193186235427856,
          0.3216103270053864,
          0.32390203046798705,
          0.3261937339305878,
          0.3284854373931885,
          0.33077714085578913,
          0.3330688443183899,
          0.33536054778099056,
          0.33765225124359133,
          0.339943954706192,
          0.34223565816879276,
          0.3445273616313934,
          0.3468190650939942,
          0.34911076855659484,
          0.3514024720191956,
          0.35369417548179627,
          0.3559858789443969,
          0.3582775824069977,
          0.36056928586959835,
          0.3628609893321991,
          0.3651526927947998,
          0.36744439625740055,
          0.3697360997200012,
          0.372027803182602,
          0.37431950664520264,
          0.3766112101078033,
          0.37890291357040407,
          0.3811946170330047,
          0.3834863204956055,
          0.38577802395820615,
          0.3880697274208069,
          0.3903614308834076,
          0.39265313434600835,
          0.394944837808609,
          0.39723654127120966,
          0.39952824473381043,
          0.4018199481964111,
          0.40411165165901186,
          0.4064033551216125,
          0.4086950585842133,
          0.41098676204681395,
          0.4132784655094147,
          0.4155701689720154,
          0.41786187243461614,
          0.4201535758972168,
          0.42244527935981746,
          0.42473698282241823,
          0.4270286862850189,
          0.42932038974761966,
          0.4316120932102203,
          0.4339037966728211,
          0.43619550013542174,
          0.4384872035980225,
          0.44077890706062317,
          0.44307061052322383,
          0.4453623139858246,
          0.44765401744842526,
          0.449945720911026,
          0.4522374243736267,
          0.45452912783622734,
          0.4568208312988282,
          0.4591125347614289,
          0.46140423822402954,
          0.4636959416866302,
          0.46598764514923086,
          0.46827934861183174,
          0.4705710520744324,
          0.47286275553703305,
          0.4751544589996337,
          0.4774461624622346,
          0.47973786592483525,
          0.4820295693874359,
          0.48432127285003657,
          0.4866129763126372,
          0.4889046797752381,
          0.49119638323783876,
          0.4934880867004394,
          0.4957797901630401,
          0.49807149362564096,
          0.5003631970882416,
          0.5026549005508423,
          0.5049466040134429,
          0.5072383074760436,
          0.5095300109386445,
          0.5118217144012451,
          0.5141134178638458,
          0.5164051213264464,
          0.5186968247890473,
          0.520988528251648,
          0.5232802317142486,
          0.5255719351768493,
          0.5278636386394502,
          0.5301553421020508,
          0.5324470455646515,
          0.5347387490272522,
          0.5370304524898528,
          0.5393221559524537,
          0.5416138594150544,
          0.543905562877655,
          0.5461972663402557,
          0.5484889698028566,
          0.5507806732654572,
          0.5530723767280579,
          0.5553640801906585,
          0.5576557836532592,
          0.5599474871158601,
          0.5622391905784607,
          0.5645308940410614,
          0.566822597503662,
          0.5691143009662629,
          0.5714060044288636,
          0.5736977078914642,
          0.5759894113540649,
          0.5782811148166656,
          0.5805728182792664,
          0.5828645217418671,
          0.5851562252044678,
          0.5874479286670684,
          0.5897396321296693,
          0.59203133559227
         ],
         "xaxis": "x",
         "y": [
          0.7568129760894658,
          0.7607309864223989,
          0.7646171759586137,
          0.7684709952848378,
          0.7722919027817299,
          0.7760793648214198,
          0.7798328559616363,
          0.7835518591362876,
          0.7872358658423796,
          0.7908843763231503,
          0.7944968997473074,
          0.798072954384248,
          0.801612067775154,
          0.8051137768998516,
          0.8085776283393228,
          0.8120031784337728,
          0.8153899934361387,
          0.8187376496609512,
          0.8220457336284452,
          0.8253138422038258,
          0.8285415827316012,
          0.8317285731648916,
          0.83487444218963,
          0.8379788293435736,
          0.8410413851300449,
          0.8440617711263314,
          0.8470396600866661,
          0.849974736039726,
          0.8528666943805819,
          0.8557152419570357,
          0.8585200971502932,
          0.8612809899499125,
          0.8639976620229824,
          0.8666698667774849,
          0.8692973694197956,
          0.8718799470062887,
          0.8744173884890087,
          0.8769094947553816,
          0.8793560786619361,
          0.8817569650620186,
          0.8841119908274757,
          0.8864210048643002,
          0.8886838681222228,
          0.8909004535982511,
          0.8930706463341492,
          0.8951943434078665,
          0.8972714539189176,
          0.899301898967733,
          0.9012856116289857,
          0.9032225369189271,
          0.9051126317567447,
          0.90695586491998,
          0.9087522169940325,
          0.9105016803157943,
          0.9122042589114487,
          0.9138599684284878,
          0.91546883606199,
          0.9170309004752192,
          0.9185462117145992,
          0.9200148311191264,
          0.9214368312242893,
          0.9228122956605617,
          0.9241413190465473,
          0.9254240068768511,
          0.9266604754047603,
          0.927850851519821,
          0.9289952726203997,
          0.9300938864813223,
          0.9311468511166878,
          0.9321543346379553,
          0.9331165151074098,
          0.934033580387114,
          0.9349057279834506,
          0.9357331648873782,
          0.9365161074105064,
          0.937254781017118,
          0.9379494201522564,
          0.9386002680660022,
          0.9392075766340705,
          0.939771606174857,
          0.9402926252630638,
          0.9407709105400457,
          0.941206746521008,
          0.9416004253992,
          0.9419522468472445,
          0.9422625178157465,
          0.9425315523293283,
          0.9427596712802341,
          0.9429472022196601,
          0.9430944791469521,
          0.9432018422968289,
          0.9432696379247804,
          0.9432982180907953,
          0.9432879404415755,
          0.9432391679913881,
          0.9431522689017162,
          0.9430276162598644,
          0.9428655878566722,
          0.9426665659635011,
          0.942430937108645,
          0.9421590918533271,
          0.9418514245674405,
          0.941508333205188,
          0.9411302190807812,
          0.9407174866443531,
          0.940270543258244,
          0.9397897989738111,
          0.9392756663089221,
          0.9387285600262832,
          0.9381488969127532,
          0.9375370955597981,
          0.9368935761452339,
          0.936218760216406,
          0.9355130704749535,
          0.9347769305633006,
          0.9340107648530228,
          0.9332149982352231,
          0.9323900559130633,
          0.9315363631965812,
          0.9306543452999341,
          0.929744427141196,
          0.9288070331448411,
          0.9278425870470365,
          0.9268515117038734,
          0.9258342289026534,
          0.9247911591763505,
          0.9237227216213629,
          0.9226293337186668,
          0.9215114111584812,
          0.9203693676685487,
          0.9192036148461334,
          0.9180145619938376,
          0.9168026159593261,
          0.9155681809790572,
          0.9143116585261002,
          0.9130334471621272,
          0.911733942393661,
          0.9104135365326476,
          0.9090726185614335,
          0.9077115740022119,
          0.9063307847909996,
          0.904930629156208,
          0.9035114815018633,
          0.9020737122955226,
          0.9006176879609413,
          0.8991437707755258,
          0.8976523187726169,
          0.8961436856486337,
          0.89461822067511,
          0.8930762686156497,
          0.8915181696478183,
          0.8899442592899933,
          0.8883548683331804,
          0.886750322777808,
          0.8851309437754995,
          0.8834970475758293,
          0.8818489454780483,
          0.8801869437877804,
          0.8785113437786677,
          0.8768224416589517,
          0.8751205285429677,
          0.8734058904275241,
          0.8716788081731406,
          0.8699395574901061,
          0.868188408929322,
          0.8664256278778857,
          0.8646514745593701,
          0.8628662040387468,
          0.8610700662319005,
          0.8592633059196761,
          0.8574461627663978,
          0.8556188713427916,
          0.8537816611532486,
          0.8519347566673504,
          0.8500783773555866,
          0.8482127377291793,
          0.8463380473839391,
          0.8444545110480624,
          0.8425623286337824,
          0.8406616952927863,
          0.8387528014752976,
          0.836835832992733,
          0.8349109710838306,
          0.832978392484149,
          0.8310382694988305,
          0.829090770078525,
          0.8271360578983612,
          0.8251742924398564,
          0.8232056290756514,
          0.8212302191569552,
          0.8192482101035803,
          0.8172597454964537,
          0.8152649651724805,
          0.8132640053216388,
          0.8112569985861855,
          0.8092440741618441,
          0.8072253579008553,
          0.8052009724167583,
          0.8031710371907806,
          0.8011356686797064,
          0.7990949804250952,
          0.7970490831637232,
          0.7949980849391182,
          0.7929420912140586,
          0.7908812049839062,
          0.7888155268906469,
          0.7867451553375071,
          0.7846701866040178,
          0.7825907149613998,
          0.7805068327881398,
          0.7784186306856344,
          0.7763261975937684,
          0.7742296209063111,
          0.7721289865859985,
          0.7700243792791834,
          0.7679158824299273,
          0.7658035783934171,
          0.7636875485485839,
          0.7615678734098092,
          0.7594446327376001,
          0.7573179056481201,
          0.7551877707214647,
          0.7530543061085666,
          0.7509175896366289,
          0.7487776989129747,
          0.746634711427209,
          0.7444887046515968,
          0.7423397561395509,
          0.7401879436221382,
          0.7380333451025068,
          0.7358760389481447,
          0.7337161039808784,
          0.7315536195645307,
          0.7293886656901476,
          0.7272213230587194,
          0.7250516731613169,
          0.7228797983565675,
          0.7207057819454036,
          0.7185297082430099,
          0.7163516626479113,
          0.7141717317081342,
          0.7119900031843882,
          0.7098065661102075,
          0.7076215108490074,
          0.705434929148003,
          0.7032469141889456,
          0.7010575606356405,
          0.6988669646782006,
          0.6966752240740107,
          0.6944824381853636,
          0.6922887080137472,
          0.6900941362307547,
          0.6878988272056002,
          0.6857028870292237,
          0.6835064235349677,
          0.6813095463158249,
          0.6791123667382397,
          0.6769149979524729,
          0.6747175548995197,
          0.6725201543145938,
          0.6703229147271803,
          0.668125956457672,
          0.6659294016106024,
          0.6637333740644916,
          0.6615379994583314,
          0.6593434051747286,
          0.6571497203197397,
          0.6549570756994225,
          0.652765603793145,
          0.6505754387236834,
          0.6483867162241528,
          0.6461995736018132,
          0.6440141496987971,
          0.6418305848498074,
          0.6396490208368375,
          0.6374696008409703,
          0.6352924693913093,
          0.6331177723111079,
          0.6309456566611515,
          0.6287762706804663,
          0.6266097637244129,
          0.6244462862002433,
          0.6222859895001869,
          0.62012902593214,
          0.6179755486480396,
          0.6158257115699936,
          0.6136796693142526,
          0.6115375771130991,
          0.6093995907347451,
          0.6072658664013157,
          0.6051365607050105,
          0.6030118305225293,
          0.6008918329278499,
          0.5987767251034524,
          0.5966666642500773,
          0.5945618074951154,
          0.592462311799718,
          0.5903683338647274,
          0.5882800300355202,
          0.58619755620586,
          0.5841210677208573,
          0.5820507192791349,
          0.5799866648342938,
          0.5779290574957809,
          0.5758780494292546,
          0.5738337917565485,
          0.5717964344553317,
          0.5697661262585622,
          0.5677430145538351,
          0.5657272452827209,
          0.5637189628401942,
          0.5617183099742479,
          0.5597254276857916,
          0.5577404551289303,
          0.5557635295117187,
          0.5537947859974867,
          0.5518343576068279,
          0.54988237512035,
          0.5479389669822714,
          0.546004259204962,
          0.5440783752745153,
          0.5421614360574387,
          0.5402535597085548,
          0.5383548615801925,
          0.5364654541327605,
          0.534585446846779,
          0.5327149461364566,
          0.5308540552648888,
          0.5290028742609577,
          0.5271614998380098,
          0.5253300253143846,
          0.5235085405358695,
          0.5216971318001481,
          0.5198958817833137,
          0.5181048694685131,
          0.5163241700767869,
          0.5145538550001653,
          0.5127939917370842,
          0.5110446438301763,
          0.5093058708064941,
          0.5075777281202184,
          0.505860267097904,
          0.5041535348863098,
          0.5024575744028611,
          0.5007724242887879,
          0.49909811886498023,
          0.4974346880905998,
          0.49578215752448507,
          0.4941405482893832,
          0.4925098770390412,
          0.4908901559281837,
          0.4892813925854072,
          0.48768359008900997,
          0.4860967469457845,
          0.4845208570727868,
          0.4829559097821012,
          0.48140188976861464,
          0.47985877710081,
          0.4783265472145894,
          0.4768051709101315,
          0.4752946143517885,
          0.47379483907102116,
          0.4723058019723747,
          0.47082745534248777,
          0.4693597468621297,
          0.4679026196212585,
          0.46645601213708643,
          0.46501985837514115,
          0.4635940877733063,
          0.4621786252688214,
          0.4607733913282253,
          0.45937830198021395,
          0.45799326885139346,
          0.4566181992048969,
          0.45525299598183816,
          0.4538975578455706,
          0.45255177922871526,
          0.4512155503829267,
          0.44988875743135426,
          0.44857128242376343,
          0.44726300339427266,
          0.4459637944216638,
          0.4446735256922211,
          0.44339206356505145,
          0.4421192706398357,
          0.4408550058269642,
          0.4395991244200017,
          0.4383514781704288,
          0.43711191536460536,
          0.4358802809029002,
          0.4346564163809261,
          0.4334401601728255,
          0.43223134751654213,
          0.4310298106010206,
          0.42983537865526644,
          0.4286478780392094,
          0.42746713233629624,
          0.4262929624477562,
          0.42512518668846444,
          0.4239636208843407,
          0.422808078471212,
          0.4216583705950704,
          0.42051430621365715,
          0.4193756921992999,
          0.41824233344293443,
          0.41711403295923655,
          0.41599059199279376,
          0.41487181012524343,
          0.41375748538330337,
          0.41264741434762425,
          0.4115413922623856,
          0.41043921314556847,
          0.40934066989982326,
          0.4082455544238653,
          0.4071536577243208,
          0.4060647700279499,
          0.4049786808941749,
          0.40389517932783703,
          0.40281405389211206,
          0.40173509282150854,
          0.4006580841348788,
          0.3995828157483674,
          0.3985090755882297,
          0.3974366517034421,
          0.396365332378043,
          0.3952949062431229,
          0.39422516238840444,
          0.3931558904733361,
          0.39208688083763515,
          0.3910179246112114,
          0.3899488138234043,
          0.3888793415114697,
          0.38780930182824846,
          0.38673849014895634,
          0.3856667031770284,
          0.38459373904896016,
          0.3835193974380809,
          0.38244347965720105,
          0.38136578876007576,
          0.3802861296416241,
          0.3792043091368515,
          0.3781201361184167,
          0.37703342159279174,
          0.37594397879496005,
          0.37485162328160504,
          0.37375617302273423,
          0.3726574484916939,
          0.37155527275352607,
          0.3704494715516205,
          0.36933987339261953,
          0.36822630962953173,
          0.36710861454301,
          0.3659866254207598,
          0.36486018263503345,
          0.3637291297181757,
          0.3625933134361855,
          0.3614525838602573,
          0.3603067944362735,
          0.3591558020522113,
          0.3579994671034406,
          0.35683765355588,
          0.35567022900698747,
          0.35449706474456005,
          0.3533180358033185,
          0.35213302101925736,
          0.350941903081738,
          0.3497445685833066,
          0.3485409080672229,
          0.3473308160726808,
          0.346114191177708,
          0.3448909360397335,
          0.34366095743381275,
          0.3424241662884987,
          0.34118047771935384,
          0.33992981106009557,
          0.33867208989137254,
          0.33740724206716577,
          0.33613519973881595,
          0.33485589937667565,
          0.3335692817893884,
          0.33227529214079704,
          0.3309738799644873,
          0.3296649991759696,
          0.3283486080825099,
          0.3270246693906151,
          0.3256931502111863,
          0.32435402206234815,
          0.3230072608699687,
          0.3216528469658849,
          0.320290765083846,
          0.31892100435319626,
          0.31754355829030945,
          0.31615842478779893,
          0.3147656061015218,
          0.3133651088353976,
          0.3119569439240674,
          0.3105411266134136,
          0.30911767643896887,
          0.3076866172022367,
          0.3062479769449556
         ],
         "yaxis": "y"
        },
        {
         "legendgroup": "Dimension 0",
         "marker": {
          "color": "rgb(31, 119, 180)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 0",
         "showlegend": false,
         "type": "scatter",
         "x": [
          0,
          0,
          0,
          -0.5730770826339722,
          -0.4949253499507904,
          0.7100865840911865,
          0.966303288936615,
          -0.3951575458049774,
          -1.3253259658813477,
          1.9414620399475098
         ],
         "xaxis": "x",
         "y": [
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0",
          "Dimension 0"
         ],
         "yaxis": "y2"
        },
        {
         "legendgroup": "Dimension 1",
         "marker": {
          "color": "rgb(255, 127, 14)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 1",
         "showlegend": false,
         "type": "scatter",
         "x": [
          1.1686878204345703,
          0.5073344111442566,
          0.3581531047821045,
          -0.5553584098815918,
          -1.4959149360656738,
          -1.5352871417999268,
          1.6247831583023071,
          0.20552566647529602,
          0.1885535717010498,
          -0.9565008282661438
         ],
         "xaxis": "x",
         "y": [
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1",
          "Dimension 1"
         ],
         "yaxis": "y2"
        },
        {
         "legendgroup": "Dimension 2",
         "marker": {
          "color": "rgb(44, 160, 44)",
          "symbol": "line-ns-open"
         },
         "mode": "markers",
         "name": "Dimension 2",
         "showlegend": false,
         "type": "scatter",
         "x": [
          0.39450275897979736,
          -0.5515286922454834,
          -0.003303872887045145,
          0.5943230390548706,
          -0.4000341594219208,
          -0.41267913579940796,
          -0.3656187951564789,
          -0.4503297507762909,
          -0.06907268613576889,
          0.03353185951709747
         ],
         "xaxis": "x",
         "y": [
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2",
          "Dimension 2"
         ],
         "yaxis": "y2"
        }
       ],
       "layout": {
        "barmode": "overlay",
        "hovermode": "closest",
        "legend": {
         "traceorder": "reversed"
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Prior Distribution (Modified)"
        },
        "xaxis": {
         "anchor": "y2",
         "domain": [
          0,
          1
         ],
         "zeroline": false
        },
        "yaxis": {
         "anchor": "free",
         "domain": [
          0.35,
          1
         ],
         "position": 0
        },
        "yaxis2": {
         "anchor": "x",
         "domain": [
          0,
          0.25
         ],
         "dtick": 1,
         "showticklabels": false
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution of modified prior\n",
    "\n",
    "# for loop to get the data from each dimension if more than 1 dimension\n",
    "data = []\n",
    "group_labels = []\n",
    "\n",
    "for i in range(prior_samples_modified.shape[1]):\n",
    "    data.append(prior_samples_modified[:, i].numpy())\n",
    "    group_labels.append(f'Dimension {i}')\n",
    "\n",
    "fig = ff.create_distplot(data, group_labels, bin_size=0.2)\n",
    "fig.update_layout(title='Prior Distribution (Modified)')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "type": "surface",
         "z": [
          [
           0,
           1.1686878204345703,
           0.39450275897979736
          ],
          [
           0,
           0.5073344111442566,
           -0.5515286922454834
          ],
          [
           0,
           0.3581531047821045,
           -0.003303872887045145
          ],
          [
           -0.5730770826339722,
           -0.5553584098815918,
           0.5943230390548706
          ],
          [
           -0.4949253499507904,
           -1.4959149360656738,
           -0.4000341594219208
          ],
          [
           0.7100865840911865,
           -1.5352871417999268,
           -0.41267913579940796
          ],
          [
           0.966303288936615,
           1.6247831583023071,
           -0.3656187951564789
          ],
          [
           -0.3951575458049774,
           0.20552566647529602,
           -0.4503297507762909
          ],
          [
           -1.3253259658813477,
           0.1885535717010498,
           -0.06907268613576889
          ],
          [
           1.9414620399475098,
           -0.9565008282661438,
           0.03353185951709747
          ]
         ]
        }
       ],
       "layout": {
        "scene": {
         "zaxis": {
          "range": [
           -5,
           5
          ]
         }
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Prior Distribution (Modified, Surface Plot)"
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotly surface plot for the prior (modified)\n",
    "fig = go.Figure(data=[go.Surface(z=prior_samples_modified.numpy())])\n",
    "# set z axis range\n",
    "fig.update_layout(scene = dict(zaxis = dict(range=[-5,5])))\n",
    "fig.update_layout(title='Prior Distribution (Modified, Surface Plot)')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sequential Monte Carlo Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transition(states):\n",
    "    \"\"\"\n",
    "    The transition model.\n",
    "    We will just add a small noise to each dimension of each state.\n",
    "    \"\"\"\n",
    "    noise = torch.normal(mean=0, std=0.1, size=states.shape)\n",
    "    return states + noise\n",
    "\n",
    "\n",
    "def likelihood(state_seq, dimensions):\n",
    "    \"\"\"\n",
    "    Returns a weighted likelihood considering zero in the first dimension and the Euclidean distance to a specific target point for a sequence of states.\n",
    "    Returns a Torch tensor.\n",
    "    \"\"\"\n",
    "    target = torch.tensor([0.0] * dimensions) # target point at the center\n",
    "    square_diff = (state_seq - target) ** 2\n",
    "    euclidean_distance = torch.sqrt(square_diff.sum(dim=-1))\n",
    "    \n",
    "    # Penalty for not being within -0.5 and 0.5 in the first dimension\n",
    "    first_dimension_penalty = torch.where(state_seq[:, 0] >= -0.5, torch.where(state_seq[:, 0] <= 0.5, torch.zeros_like(state_seq[:, 0]), torch.abs(state_seq[:, 0] - 0.5)), torch.abs(state_seq[:, 0] + 0.5))\n",
    "\n",
    "    # The alpha parameter controls how much more we care about the first dimension being zero than the Euclidean distance.\n",
    "    alpha = 0.7\n",
    "    return alpha*first_dimension_penalty + (1 - alpha)*euclidean_distance\n",
    "\n",
    "\n",
    "def plot_convergence_smc(weight_history):\n",
    "    \"\"\"\n",
    "    Plots the total weight over time to check for convergence of SMC\n",
    "    \"\"\"\n",
    "    fig = go.Figure()\n",
    "    \n",
    "    # Line plot of weight history\n",
    "    fig.add_trace(go.Scatter(x=list(range(len(weight_history))), y=weight_history,\n",
    "                            mode='lines',\n",
    "                            name='Total Weight'))\n",
    "\n",
    "    # Layout\n",
    "    fig.update_layout(title='Convergence of Sequential Monte Carlo',\n",
    "                      xaxis_title='Iteration',\n",
    "                      yaxis_title='Sum of Weights')\n",
    "\n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sequential Monte Carlo Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def smc(prior, timesteps, num_samples, record_weights=False):\n",
    "    \"\"\"\n",
    "    The SMC loop\n",
    "    \"\"\"\n",
    "\n",
    "    dimensions = prior.shape[-1]\n",
    "    weight_history = []\n",
    "\n",
    "    for t in tqdm.tqdm(range(timesteps)):\n",
    "        proposed_states = transition(states=prior)\n",
    "        # we will apply the negative exponential to convert distances into weights,\n",
    "        # which results in a higher weight to closer states because the close distance results in a large exponential value\n",
    "        weights = torch.exp(-likelihood(proposed_states, dimensions))\n",
    "        weights /= weights.sum() # normalize weights\n",
    "        if record_weights:\n",
    "            weight_history.append(weights.sum().item())\n",
    "        indices = torch.multinomial(weights, num_samples=num_samples, replacement=True) \n",
    "        states = proposed_states[indices]\n",
    "\n",
    "    return states, weight_history if record_weights else states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Chain Monte Carlo Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def proposal(state, std=0.1):\n",
    "    \"\"\"\n",
    "    Adds Gaussian noise to the current state to make it more likely to generate adjacent states\n",
    "    \"\"\"\n",
    "    return torch.normal(mean=state, std=std)\n",
    "\n",
    "\n",
    "def acceptance(curr, prop, dimensions):\n",
    "    \"\"\"\n",
    "    Determines whether to accept or reject the proposed state\n",
    "    \"\"\"\n",
    "    likelihood_curr = torch.exp(-likelihood(curr, dimensions))\n",
    "    likelihood_prop = torch.exp(-likelihood(prop, dimensions))\n",
    "    return min(1, (likelihood_prop / likelihood_curr).item())\n",
    "\n",
    "\n",
    "def plot_convergence_mcmc(mcmc_samples, dimension=0):\n",
    "    \"\"\"\n",
    "    Plots the trace and histogram of the MCMC sampler, which can help to\n",
    "    diagnose whether the Markov chain has converged.\n",
    "    \"\"\"\n",
    "    values = mcmc_samples[:, 0, dimension].numpy()\n",
    "\n",
    "    fig = go.Figure()\n",
    "    \n",
    "    # Trace plot\n",
    "    fig.add_trace(go.Scatter(x=list(range(len(values))), y=values,\n",
    "                               mode='lines',\n",
    "                               name='Trace'))\n",
    "\n",
    "    # Layout\n",
    "    fig.update_layout(title=f'MCMC: Convergence for Dimension {dimension}',\n",
    "                      xaxis_title='Iteration',\n",
    "                      yaxis_title='Value',\n",
    "                      bargap=0.2,\n",
    "                      bargroupgap=0.1)\n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Chain Monte Carlo Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mcmc(init_state, iterations, dimensions, burn_in=0, lag=1):\n",
    "    \"\"\"\n",
    "    The MCMC loop\n",
    "    \"\"\"\n",
    "    state = init_state.clone()\n",
    "    samples = []\n",
    "    \n",
    "    for _ in tqdm.tqdm(range(iterations)):\n",
    "        proposed_state = proposal(state)\n",
    "        if random.random() < acceptance(state, proposed_state, dimensions):\n",
    "            state = proposed_state\n",
    "        samples.append(state)\n",
    "\n",
    "    return torch.stack(samples[burn_in::lag])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SMC Model Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Modifying 3 particles out of 10 particles\n",
      "Prior size (SMC): torch.Size([10, 100])\n"
     ]
    }
   ],
   "source": [
    "# Params\n",
    "DIMENSIONS = 100 # State dimension\n",
    "N_prior = 10 # initial number of particles\n",
    "MU = 0.0 # Mean of the prior\n",
    "SIGMA = 10.0 # Variance of the prior\n",
    "\n",
    "TIMESTEPS = 1000 # Number of timesteps\n",
    "N_smc = 1000 # Number of particles for SMC to generate\n",
    "\n",
    "dimension_to_modify=0\n",
    "percentage_to_modify=0.3\n",
    "\n",
    "# Generate prior\n",
    "particles_prior_smc = prior(mu=MU, sigma=SIGMA, N=N_prior, D=DIMENSIONS, shuffle=True, modify=True, dimension_to_modify=dimension_to_modify, percentage_to_modify=percentage_to_modify)\n",
    "print('Prior size (SMC):', particles_prior_smc.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 10284.52it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior size: (SMC) torch.Size([1000, 100])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Run SMC and record weights\n",
    "particles_posterior_smc, weight_history = smc(prior=particles_prior_smc, timesteps=TIMESTEPS, num_samples=N_smc, record_weights=True)\n",
    "\n",
    "# check size of posterior\n",
    "print('Posterior size: (SMC)', particles_posterior_smc.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fuzz test (prior):\n",
      "30.0\n",
      "\n",
      "Fuzz test (posterior):\n",
      "89.7\n"
     ]
    }
   ],
   "source": [
    "# fuzz test the prior and posterior\n",
    "print(\"Fuzz test (prior):\")\n",
    "print(fuzz_test(particles_prior_smc))\n",
    "print()\n",
    "print(\"Fuzz test (posterior):\")\n",
    "print(fuzz_test(particles_posterior_smc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "lines",
         "name": "Total Weight",
         "type": "scatter",
         "x": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79,
          80,
          81,
          82,
          83,
          84,
          85,
          86,
          87,
          88,
          89,
          90,
          91,
          92,
          93,
          94,
          95,
          96,
          97,
          98,
          99,
          100,
          101,
          102,
          103,
          104,
          105,
          106,
          107,
          108,
          109,
          110,
          111,
          112,
          113,
          114,
          115,
          116,
          117,
          118,
          119,
          120,
          121,
          122,
          123,
          124,
          125,
          126,
          127,
          128,
          129,
          130,
          131,
          132,
          133,
          134,
          135,
          136,
          137,
          138,
          139,
          140,
          141,
          142,
          143,
          144,
          145,
          146,
          147,
          148,
          149,
          150,
          151,
          152,
          153,
          154,
          155,
          156,
          157,
          158,
          159,
          160,
          161,
          162,
          163,
          164,
          165,
          166,
          167,
          168,
          169,
          170,
          171,
          172,
          173,
          174,
          175,
          176,
          177,
          178,
          179,
          180,
          181,
          182,
          183,
          184,
          185,
          186,
          187,
          188,
          189,
          190,
          191,
          192,
          193,
          194,
          195,
          196,
          197,
          198,
          199,
          200,
          201,
          202,
          203,
          204,
          205,
          206,
          207,
          208,
          209,
          210,
          211,
          212,
          213,
          214,
          215,
          216,
          217,
          218,
          219,
          220,
          221,
          222,
          223,
          224,
          225,
          226,
          227,
          228,
          229,
          230,
          231,
          232,
          233,
          234,
          235,
          236,
          237,
          238,
          239,
          240,
          241,
          242,
          243,
          244,
          245,
          246,
          247,
          248,
          249,
          250,
          251,
          252,
          253,
          254,
          255,
          256,
          257,
          258,
          259,
          260,
          261,
          262,
          263,
          264,
          265,
          266,
          267,
          268,
          269,
          270,
          271,
          272,
          273,
          274,
          275,
          276,
          277,
          278,
          279,
          280,
          281,
          282,
          283,
          284,
          285,
          286,
          287,
          288,
          289,
          290,
          291,
          292,
          293,
          294,
          295,
          296,
          297,
          298,
          299,
          300,
          301,
          302,
          303,
          304,
          305,
          306,
          307,
          308,
          309,
          310,
          311,
          312,
          313,
          314,
          315,
          316,
          317,
          318,
          319,
          320,
          321,
          322,
          323,
          324,
          325,
          326,
          327,
          328,
          329,
          330,
          331,
          332,
          333,
          334,
          335,
          336,
          337,
          338,
          339,
          340,
          341,
          342,
          343,
          344,
          345,
          346,
          347,
          348,
          349,
          350,
          351,
          352,
          353,
          354,
          355,
          356,
          357,
          358,
          359,
          360,
          361,
          362,
          363,
          364,
          365,
          366,
          367,
          368,
          369,
          370,
          371,
          372,
          373,
          374,
          375,
          376,
          377,
          378,
          379,
          380,
          381,
          382,
          383,
          384,
          385,
          386,
          387,
          388,
          389,
          390,
          391,
          392,
          393,
          394,
          395,
          396,
          397,
          398,
          399,
          400,
          401,
          402,
          403,
          404,
          405,
          406,
          407,
          408,
          409,
          410,
          411,
          412,
          413,
          414,
          415,
          416,
          417,
          418,
          419,
          420,
          421,
          422,
          423,
          424,
          425,
          426,
          427,
          428,
          429,
          430,
          431,
          432,
          433,
          434,
          435,
          436,
          437,
          438,
          439,
          440,
          441,
          442,
          443,
          444,
          445,
          446,
          447,
          448,
          449,
          450,
          451,
          452,
          453,
          454,
          455,
          456,
          457,
          458,
          459,
          460,
          461,
          462,
          463,
          464,
          465,
          466,
          467,
          468,
          469,
          470,
          471,
          472,
          473,
          474,
          475,
          476,
          477,
          478,
          479,
          480,
          481,
          482,
          483,
          484,
          485,
          486,
          487,
          488,
          489,
          490,
          491,
          492,
          493,
          494,
          495,
          496,
          497,
          498,
          499,
          500,
          501,
          502,
          503,
          504,
          505,
          506,
          507,
          508,
          509,
          510,
          511,
          512,
          513,
          514,
          515,
          516,
          517,
          518,
          519,
          520,
          521,
          522,
          523,
          524,
          525,
          526,
          527,
          528,
          529,
          530,
          531,
          532,
          533,
          534,
          535,
          536,
          537,
          538,
          539,
          540,
          541,
          542,
          543,
          544,
          545,
          546,
          547,
          548,
          549,
          550,
          551,
          552,
          553,
          554,
          555,
          556,
          557,
          558,
          559,
          560,
          561,
          562,
          563,
          564,
          565,
          566,
          567,
          568,
          569,
          570,
          571,
          572,
          573,
          574,
          575,
          576,
          577,
          578,
          579,
          580,
          581,
          582,
          583,
          584,
          585,
          586,
          587,
          588,
          589,
          590,
          591,
          592,
          593,
          594,
          595,
          596,
          597,
          598,
          599,
          600,
          601,
          602,
          603,
          604,
          605,
          606,
          607,
          608,
          609,
          610,
          611,
          612,
          613,
          614,
          615,
          616,
          617,
          618,
          619,
          620,
          621,
          622,
          623,
          624,
          625,
          626,
          627,
          628,
          629,
          630,
          631,
          632,
          633,
          634,
          635,
          636,
          637,
          638,
          639,
          640,
          641,
          642,
          643,
          644,
          645,
          646,
          647,
          648,
          649,
          650,
          651,
          652,
          653,
          654,
          655,
          656,
          657,
          658,
          659,
          660,
          661,
          662,
          663,
          664,
          665,
          666,
          667,
          668,
          669,
          670,
          671,
          672,
          673,
          674,
          675,
          676,
          677,
          678,
          679,
          680,
          681,
          682,
          683,
          684,
          685,
          686,
          687,
          688,
          689,
          690,
          691,
          692,
          693,
          694,
          695,
          696,
          697,
          698,
          699,
          700,
          701,
          702,
          703,
          704,
          705,
          706,
          707,
          708,
          709,
          710,
          711,
          712,
          713,
          714,
          715,
          716,
          717,
          718,
          719,
          720,
          721,
          722,
          723,
          724,
          725,
          726,
          727,
          728,
          729,
          730,
          731,
          732,
          733,
          734,
          735,
          736,
          737,
          738,
          739,
          740,
          741,
          742,
          743,
          744,
          745,
          746,
          747,
          748,
          749,
          750,
          751,
          752,
          753,
          754,
          755,
          756,
          757,
          758,
          759,
          760,
          761,
          762,
          763,
          764,
          765,
          766,
          767,
          768,
          769,
          770,
          771,
          772,
          773,
          774,
          775,
          776,
          777,
          778,
          779,
          780,
          781,
          782,
          783,
          784,
          785,
          786,
          787,
          788,
          789,
          790,
          791,
          792,
          793,
          794,
          795,
          796,
          797,
          798,
          799,
          800,
          801,
          802,
          803,
          804,
          805,
          806,
          807,
          808,
          809,
          810,
          811,
          812,
          813,
          814,
          815,
          816,
          817,
          818,
          819,
          820,
          821,
          822,
          823,
          824,
          825,
          826,
          827,
          828,
          829,
          830,
          831,
          832,
          833,
          834,
          835,
          836,
          837,
          838,
          839,
          840,
          841,
          842,
          843,
          844,
          845,
          846,
          847,
          848,
          849,
          850,
          851,
          852,
          853,
          854,
          855,
          856,
          857,
          858,
          859,
          860,
          861,
          862,
          863,
          864,
          865,
          866,
          867,
          868,
          869,
          870,
          871,
          872,
          873,
          874,
          875,
          876,
          877,
          878,
          879,
          880,
          881,
          882,
          883,
          884,
          885,
          886,
          887,
          888,
          889,
          890,
          891,
          892,
          893,
          894,
          895,
          896,
          897,
          898,
          899,
          900,
          901,
          902,
          903,
          904,
          905,
          906,
          907,
          908,
          909,
          910,
          911,
          912,
          913,
          914,
          915,
          916,
          917,
          918,
          919,
          920,
          921,
          922,
          923,
          924,
          925,
          926,
          927,
          928,
          929,
          930,
          931,
          932,
          933,
          934,
          935,
          936,
          937,
          938,
          939,
          940,
          941,
          942,
          943,
          944,
          945,
          946,
          947,
          948,
          949,
          950,
          951,
          952,
          953,
          954,
          955,
          956,
          957,
          958,
          959,
          960,
          961,
          962,
          963,
          964,
          965,
          966,
          967,
          968,
          969,
          970,
          971,
          972,
          973,
          974,
          975,
          976,
          977,
          978,
          979,
          980,
          981,
          982,
          983,
          984,
          985,
          986,
          987,
          988,
          989,
          990,
          991,
          992,
          993,
          994,
          995,
          996,
          997,
          998,
          999
         ],
         "y": [
          0.9999998211860657,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          0.9999999403953552,
          0.9999998211860657,
          1,
          1.000000238418579,
          1,
          0.9999999403953552,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1.000000238418579,
          1.000000238418579,
          1,
          0.9999999403953552,
          1,
          0.9999998211860657,
          1,
          1.0000001192092896,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          1,
          0.9999999403953552,
          1.000000238418579,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999998211860657,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          0.9999998807907104,
          0.9999998807907104,
          0.9999999403953552,
          1,
          0.9999998211860657,
          1,
          0.9999997615814209,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          0.9999998807907104,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          0.9999999403953552,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998211860657,
          1,
          1,
          1.0000001192092896,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          0.9999998807907104,
          1,
          0.9999998211860657,
          1,
          0.9999998211860657,
          1,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          1.000000238418579,
          0.9999998807907104,
          0.9999998807907104,
          0.9999998807907104,
          0.9999999403953552,
          0.9999998807907104,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          0.9999998211860657,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          1,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1.000000238418579,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          0.9999998211860657,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          0.9999998211860657,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998211860657,
          1,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.000000238418579,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          0.9999999403953552,
          0.9999998211860657,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999999403953552,
          0.9999998807907104,
          0.9999998807907104,
          1,
          0.9999998211860657,
          0.9999998807907104,
          0.9999998807907104,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          0.9999998807907104,
          0.9999998807907104,
          1,
          0.9999998211860657,
          0.9999999403953552,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999998807907104,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998807907104,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1,
          0.9999998807907104,
          0.9999998211860657,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1.000000238418579,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1,
          1,
          1.000000238418579,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1,
          0.9999998211860657,
          1.0000001192092896,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1.0000001192092896,
          0.9999998807907104,
          1,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          1,
          1.000000238418579,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          1.000000238418579,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1.000000238418579,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999999403953552,
          0.9999998807907104,
          0.9999998807907104,
          1.0000001192092896,
          0.9999998807907104,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999998211860657,
          0.9999998807907104,
          0.9999998807907104,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1.000000238418579,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999998211860657,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999999403953552,
          0.9999998211860657,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          1.000000238418579,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          1,
          1.000000238418579,
          1,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.000000238418579,
          1,
          1,
          0.9999998211860657,
          0.9999998807907104,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1,
          1.000000238418579,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999998807907104,
          0.9999998807907104,
          0.9999998807907104,
          1,
          0.9999999403953552,
          0.9999997615814209,
          1.0000001192092896,
          0.9999999403953552,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          0.9999999403953552,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1.0000001192092896,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999998211860657,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999998807907104,
          1,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1,
          0.9999998807907104,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999998807907104,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999997615814209,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999998807907104,
          0.9999998807907104,
          0.9999998211860657,
          1,
          0.9999997615814209,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998807907104,
          0.9999998807907104,
          1,
          0.9999998807907104,
          1,
          1.0000001192092896,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1.0000001192092896,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999998211860657,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          1,
          0.9999998807907104,
          1,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          0.9999998807907104,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          0.9999999403953552,
          0.9999998807907104,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          0.9999998807907104,
          0.9999999403953552,
          1,
          1,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          0.9999998807907104,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          0.9999998807907104,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999998807907104,
          1.000000238418579,
          1,
          1,
          0.9999998807907104,
          1,
          1,
          1,
          1,
          1,
          1,
          0.9999999403953552,
          0.9999999403953552,
          0.9999998807907104,
          1.0000001192092896,
          1.0000001192092896,
          0.9999997615814209,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999998211860657,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          1,
          0.9999998807907104,
          1,
          0.9999998211860657,
          0.9999999403953552,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          1,
          1,
          1,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998807907104,
          1.0000001192092896,
          1,
          0.9999999403953552,
          0.9999999403953552,
          0.9999998807907104,
          1,
          0.9999998807907104,
          0.9999998807907104,
          1,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          1.0000001192092896,
          1,
          1,
          1,
          1.0000001192092896,
          1,
          0.9999999403953552,
          1.0000001192092896,
          0.9999998211860657,
          0.9999998807907104,
          1,
          1,
          1,
          1.000000238418579,
          1.0000001192092896,
          1.0000001192092896,
          1,
          1,
          1,
          0.9999998807907104,
          0.9999997615814209
         ]
        }
       ],
       "layout": {
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Convergence of Sequential Monte Carlo"
        },
        "xaxis": {
         "title": {
          "text": "Iteration"
         }
        },
        "yaxis": {
         "title": {
          "text": "Sum of Weights"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot convergence SMC\n",
    "plot_convergence_smc(weight_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior particle:\n",
      "tensor([ 1.2779e+00,  1.3795e+01,  2.3919e+00,  2.8090e+00, -7.5565e-01,\n",
      "         1.6204e+01, -1.2334e+00, -1.3949e+01,  1.9015e+01,  1.8478e+01,\n",
      "         7.2020e+00,  3.1246e-01, -8.5704e+00,  5.3704e+00, -5.1797e+00,\n",
      "        -1.3240e+01, -3.5537e+00,  1.3409e+01, -2.0553e+01,  5.1985e+00,\n",
      "         5.8123e+00, -4.1630e+00,  4.5400e+00, -4.0123e+00,  4.4671e+00,\n",
      "        -1.4327e+01, -8.9286e-01,  4.8381e+00,  7.0724e+00,  5.1205e-01,\n",
      "        -4.2980e+00, -6.8372e+00, -3.4354e+00,  1.7759e+01, -1.0544e+01,\n",
      "        -2.2939e+00, -1.2781e+01,  5.5652e+00,  1.6189e+00,  1.0277e+01,\n",
      "        -1.2254e+00,  6.7192e+00, -1.8032e+01,  6.8495e+00,  1.1792e+01,\n",
      "         1.3239e+01, -3.3268e+00,  1.1828e+01,  4.3132e+00,  9.8188e+00,\n",
      "        -9.3791e+00, -2.1573e+01,  3.9526e+00, -4.1467e+00, -7.5831e+00,\n",
      "         1.6588e+01,  3.5947e+00,  9.9527e+00,  4.9854e+00,  2.6107e+00,\n",
      "         1.4936e+01,  3.3727e+00,  1.6338e+01,  6.1012e+00, -9.1671e+00,\n",
      "         2.1064e+01, -3.1539e-02,  8.8827e+00, -8.0690e-03,  3.7662e-01,\n",
      "         5.7691e+00, -1.5962e+01, -1.2691e+01, -6.5294e+00,  6.9696e+00,\n",
      "        -5.6426e+00, -3.9065e+00, -3.8688e-01,  5.1290e+00,  7.6425e+00,\n",
      "         1.9691e-01, -1.0510e+01, -1.1675e+00, -6.0909e+00,  8.6782e+00,\n",
      "         1.5148e+00,  1.1174e+01,  1.1042e+01,  1.0321e+01,  2.4595e+00,\n",
      "        -1.3590e+01, -7.6307e+00, -2.1302e+00, -2.5191e+00, -7.7170e+00,\n",
      "         1.4116e+01, -1.1293e-01,  9.9106e+00, -8.4526e+00, -3.0597e+00])\n"
     ]
    }
   ],
   "source": [
    "# print one of the posterior particles\n",
    "print(\"Posterior particle:\")\n",
    "print(particles_posterior_smc[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MCMC Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Modifying 1 particle out of 1 particle\n",
      "Prior size (MCMC): torch.Size([1, 100])\n"
     ]
    }
   ],
   "source": [
    "# Generate single particle for MCMC\n",
    "\n",
    "init_state = prior(mu=MU, sigma=SIGMA, N=1, D=DIMENSIONS, shuffle=True, modify=True, dimension_to_modify=dimension_to_modify, percentage_to_modify=percentage_to_modify)\n",
    "print('Prior size (MCMC):', init_state.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:00<00:00, 10257.17it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior size (MCMC): torch.Size([900, 1, 100])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "burn_in = 500\n",
    "lag = 5\n",
    "TIMESTEPS_MCMC = 5000\n",
    "\n",
    "# Run MCMC\n",
    "particles_posterior_mcmc = mcmc(init_state=init_state, iterations=TIMESTEPS_MCMC, dimensions=DIMENSIONS, burn_in=burn_in, lag=lag)\n",
    "\n",
    "# check size of posterior\n",
    "print('Posterior size (MCMC):', particles_posterior_mcmc.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# modification of fuzz_test to work with MCMC tensor sample shape (TIMESTEPS, 1, DIMENSIONS)\n",
    "\n",
    "def fuzz_test_mcmc(particles):\n",
    "    '''\n",
    "    This function will test if a batch of particles satisfies the following criteria:\n",
    "\n",
    "    Criteria:\n",
    "    For each particle:\n",
    "    - if the first dimension is 0, add 1 to the counter\n",
    "\n",
    "    The count represents the number of particles that pass the fuzz test\n",
    "    '''\n",
    "    count = 0\n",
    "    for particle in particles:\n",
    "        # if particle[0] is within the range of -0.5 and 0.5, add 1 to the counter\n",
    "        if particle[0][0] >= -0.5 and particle[0][0] <= 0.5:\n",
    "            count += 1\n",
    "    \n",
    "    # return the percentage of particles that pass the fuzz test\n",
    "    return count / len(particles) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fuzz test (prior):\n",
      "100.0\n",
      "\n",
      "Fuzz test (posterior):\n",
      "31.11111111111111\n"
     ]
    }
   ],
   "source": [
    "# fuzz test the prior and posterior\n",
    "print(\"Fuzz test (prior):\")\n",
    "print(fuzz_test(init_state))\n",
    "print()\n",
    "print(\"Fuzz test (posterior):\")\n",
    "print(fuzz_test_mcmc(particles_posterior_mcmc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "lines",
         "name": "Trace",
         "type": "scatter",
         "x": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79,
          80,
          81,
          82,
          83,
          84,
          85,
          86,
          87,
          88,
          89,
          90,
          91,
          92,
          93,
          94,
          95,
          96,
          97,
          98,
          99,
          100,
          101,
          102,
          103,
          104,
          105,
          106,
          107,
          108,
          109,
          110,
          111,
          112,
          113,
          114,
          115,
          116,
          117,
          118,
          119,
          120,
          121,
          122,
          123,
          124,
          125,
          126,
          127,
          128,
          129,
          130,
          131,
          132,
          133,
          134,
          135,
          136,
          137,
          138,
          139,
          140,
          141,
          142,
          143,
          144,
          145,
          146,
          147,
          148,
          149,
          150,
          151,
          152,
          153,
          154,
          155,
          156,
          157,
          158,
          159,
          160,
          161,
          162,
          163,
          164,
          165,
          166,
          167,
          168,
          169,
          170,
          171,
          172,
          173,
          174,
          175,
          176,
          177,
          178,
          179,
          180,
          181,
          182,
          183,
          184,
          185,
          186,
          187,
          188,
          189,
          190,
          191,
          192,
          193,
          194,
          195,
          196,
          197,
          198,
          199,
          200,
          201,
          202,
          203,
          204,
          205,
          206,
          207,
          208,
          209,
          210,
          211,
          212,
          213,
          214,
          215,
          216,
          217,
          218,
          219,
          220,
          221,
          222,
          223,
          224,
          225,
          226,
          227,
          228,
          229,
          230,
          231,
          232,
          233,
          234,
          235,
          236,
          237,
          238,
          239,
          240,
          241,
          242,
          243,
          244,
          245,
          246,
          247,
          248,
          249,
          250,
          251,
          252,
          253,
          254,
          255,
          256,
          257,
          258,
          259,
          260,
          261,
          262,
          263,
          264,
          265,
          266,
          267,
          268,
          269,
          270,
          271,
          272,
          273,
          274,
          275,
          276,
          277,
          278,
          279,
          280,
          281,
          282,
          283,
          284,
          285,
          286,
          287,
          288,
          289,
          290,
          291,
          292,
          293,
          294,
          295,
          296,
          297,
          298,
          299,
          300,
          301,
          302,
          303,
          304,
          305,
          306,
          307,
          308,
          309,
          310,
          311,
          312,
          313,
          314,
          315,
          316,
          317,
          318,
          319,
          320,
          321,
          322,
          323,
          324,
          325,
          326,
          327,
          328,
          329,
          330,
          331,
          332,
          333,
          334,
          335,
          336,
          337,
          338,
          339,
          340,
          341,
          342,
          343,
          344,
          345,
          346,
          347,
          348,
          349,
          350,
          351,
          352,
          353,
          354,
          355,
          356,
          357,
          358,
          359,
          360,
          361,
          362,
          363,
          364,
          365,
          366,
          367,
          368,
          369,
          370,
          371,
          372,
          373,
          374,
          375,
          376,
          377,
          378,
          379,
          380,
          381,
          382,
          383,
          384,
          385,
          386,
          387,
          388,
          389,
          390,
          391,
          392,
          393,
          394,
          395,
          396,
          397,
          398,
          399,
          400,
          401,
          402,
          403,
          404,
          405,
          406,
          407,
          408,
          409,
          410,
          411,
          412,
          413,
          414,
          415,
          416,
          417,
          418,
          419,
          420,
          421,
          422,
          423,
          424,
          425,
          426,
          427,
          428,
          429,
          430,
          431,
          432,
          433,
          434,
          435,
          436,
          437,
          438,
          439,
          440,
          441,
          442,
          443,
          444,
          445,
          446,
          447,
          448,
          449,
          450,
          451,
          452,
          453,
          454,
          455,
          456,
          457,
          458,
          459,
          460,
          461,
          462,
          463,
          464,
          465,
          466,
          467,
          468,
          469,
          470,
          471,
          472,
          473,
          474,
          475,
          476,
          477,
          478,
          479,
          480,
          481,
          482,
          483,
          484,
          485,
          486,
          487,
          488,
          489,
          490,
          491,
          492,
          493,
          494,
          495,
          496,
          497,
          498,
          499,
          500,
          501,
          502,
          503,
          504,
          505,
          506,
          507,
          508,
          509,
          510,
          511,
          512,
          513,
          514,
          515,
          516,
          517,
          518,
          519,
          520,
          521,
          522,
          523,
          524,
          525,
          526,
          527,
          528,
          529,
          530,
          531,
          532,
          533,
          534,
          535,
          536,
          537,
          538,
          539,
          540,
          541,
          542,
          543,
          544,
          545,
          546,
          547,
          548,
          549,
          550,
          551,
          552,
          553,
          554,
          555,
          556,
          557,
          558,
          559,
          560,
          561,
          562,
          563,
          564,
          565,
          566,
          567,
          568,
          569,
          570,
          571,
          572,
          573,
          574,
          575,
          576,
          577,
          578,
          579,
          580,
          581,
          582,
          583,
          584,
          585,
          586,
          587,
          588,
          589,
          590,
          591,
          592,
          593,
          594,
          595,
          596,
          597,
          598,
          599,
          600,
          601,
          602,
          603,
          604,
          605,
          606,
          607,
          608,
          609,
          610,
          611,
          612,
          613,
          614,
          615,
          616,
          617,
          618,
          619,
          620,
          621,
          622,
          623,
          624,
          625,
          626,
          627,
          628,
          629,
          630,
          631,
          632,
          633,
          634,
          635,
          636,
          637,
          638,
          639,
          640,
          641,
          642,
          643,
          644,
          645,
          646,
          647,
          648,
          649,
          650,
          651,
          652,
          653,
          654,
          655,
          656,
          657,
          658,
          659,
          660,
          661,
          662,
          663,
          664,
          665,
          666,
          667,
          668,
          669,
          670,
          671,
          672,
          673,
          674,
          675,
          676,
          677,
          678,
          679,
          680,
          681,
          682,
          683,
          684,
          685,
          686,
          687,
          688,
          689,
          690,
          691,
          692,
          693,
          694,
          695,
          696,
          697,
          698,
          699,
          700,
          701,
          702,
          703,
          704,
          705,
          706,
          707,
          708,
          709,
          710,
          711,
          712,
          713,
          714,
          715,
          716,
          717,
          718,
          719,
          720,
          721,
          722,
          723,
          724,
          725,
          726,
          727,
          728,
          729,
          730,
          731,
          732,
          733,
          734,
          735,
          736,
          737,
          738,
          739,
          740,
          741,
          742,
          743,
          744,
          745,
          746,
          747,
          748,
          749,
          750,
          751,
          752,
          753,
          754,
          755,
          756,
          757,
          758,
          759,
          760,
          761,
          762,
          763,
          764,
          765,
          766,
          767,
          768,
          769,
          770,
          771,
          772,
          773,
          774,
          775,
          776,
          777,
          778,
          779,
          780,
          781,
          782,
          783,
          784,
          785,
          786,
          787,
          788,
          789,
          790,
          791,
          792,
          793,
          794,
          795,
          796,
          797,
          798,
          799,
          800,
          801,
          802,
          803,
          804,
          805,
          806,
          807,
          808,
          809,
          810,
          811,
          812,
          813,
          814,
          815,
          816,
          817,
          818,
          819,
          820,
          821,
          822,
          823,
          824,
          825,
          826,
          827,
          828,
          829,
          830,
          831,
          832,
          833,
          834,
          835,
          836,
          837,
          838,
          839,
          840,
          841,
          842,
          843,
          844,
          845,
          846,
          847,
          848,
          849,
          850,
          851,
          852,
          853,
          854,
          855,
          856,
          857,
          858,
          859,
          860,
          861,
          862,
          863,
          864,
          865,
          866,
          867,
          868,
          869,
          870,
          871,
          872,
          873,
          874,
          875,
          876,
          877,
          878,
          879,
          880,
          881,
          882,
          883,
          884,
          885,
          886,
          887,
          888,
          889,
          890,
          891,
          892,
          893,
          894,
          895,
          896,
          897,
          898,
          899
         ],
         "y": [
          -1.3873594999313354,
          -1.5193367004394531,
          -1.5554684400558472,
          -1.6131362915039062,
          -1.660426378250122,
          -1.6141895055770874,
          -1.6437638998031616,
          -1.5992317199707031,
          -1.5275636911392212,
          -1.3384532928466797,
          -1.2848397493362427,
          -1.0184022188186646,
          -0.5903580188751221,
          -0.8050041794776917,
          -0.47873398661613464,
          -0.5647258162498474,
          -0.3801022171974182,
          -0.4910253882408142,
          -0.7234930396080017,
          -0.7744021415710449,
          -1.0708019733428955,
          -1.0321015119552612,
          -1.0628573894500732,
          -0.7979520559310913,
          -0.6604520082473755,
          -0.683381974697113,
          -0.41295671463012695,
          -0.43338900804519653,
          -0.30592286586761475,
          -0.4493159055709839,
          -0.9208183884620667,
          -0.8732568025588989,
          -0.6472013592720032,
          -0.6774123907089233,
          -0.3790217339992523,
          -0.08913447707891464,
          -0.2785454988479614,
          0.03599918261170387,
          -0.26298752427101135,
          -0.18596094846725464,
          -0.39760565757751465,
          -0.41563063859939575,
          -0.11958460509777069,
          -0.04802381992340088,
          0.2935154438018799,
          0.5158253908157349,
          0.0974692702293396,
          -0.23179781436920166,
          -0.6598535776138306,
          -1.0597143173217773,
          -1.0659153461456299,
          -1.3120203018188477,
          -1.365336537361145,
          -1.5302479267120361,
          -1.4615497589111328,
          -1.2925174236297607,
          -1.3386276960372925,
          -1.2160917520523071,
          -1.1467645168304443,
          -1.398310661315918,
          -1.4952465295791626,
          -1.1071834564208984,
          -0.6924853920936584,
          -0.8067869544029236,
          -0.9581946730613708,
          -0.7897133827209473,
          -0.7491140961647034,
          -0.7986049652099609,
          -0.8725064396858215,
          -1.0110870599746704,
          -1.2896219491958618,
          -1.3929461240768433,
          -1.1783510446548462,
          -1.2377220392227173,
          -1.0527746677398682,
          -1.0349905490875244,
          -0.7479186058044434,
          -0.6884458661079407,
          -0.6902588605880737,
          -0.8761391043663025,
          -0.8723995685577393,
          -0.8140290975570679,
          -0.7810189127922058,
          -0.8782624006271362,
          -0.6957622170448303,
          -0.6947458982467651,
          -0.7337507605552673,
          -1.1331992149353027,
          -0.9861815571784973,
          -0.9426885843276978,
          -1.0857157707214355,
          -0.9817178845405579,
          -0.7977756261825562,
          -0.7460750341415405,
          -0.5828989744186401,
          -0.6649683713912964,
          -0.4956951141357422,
          -0.6384482979774475,
          -0.5277310609817505,
          -0.45063674449920654,
          -0.5140492916107178,
          -0.605976402759552,
          -0.2385709285736084,
          -0.32112768292427063,
          -0.10663852095603943,
          -0.2085769921541214,
          0.11618530005216599,
          0.16632826626300812,
          0.14867247641086578,
          0.2932918667793274,
          0.3017263412475586,
          0.26095980405807495,
          0.41702142357826233,
          0.36997586488723755,
          0.016409818083047867,
          0.09812768548727036,
          0.2676442265510559,
          0.055235739797353745,
          0.1813884675502777,
          0.2170923501253128,
          0.3123306632041931,
          0.3594047427177429,
          0.5400494337081909,
          0.7589505910873413,
          1.0052776336669922,
          1.0510486364364624,
          1.1298635005950928,
          1.2083836793899536,
          0.9795764088630676,
          0.9924806356430054,
          1.0426009893417358,
          0.9621427059173584,
          0.711065411567688,
          0.32844045758247375,
          0.4952285885810852,
          0.5525887608528137,
          0.6334991455078125,
          0.9171033501625061,
          0.2800036072731018,
          0.31564953923225403,
          0.3556782007217407,
          0.14869429171085358,
          -0.06739401072263718,
          0.031605254858732224,
          0.008219771087169647,
          0.27203795313835144,
          -0.005285859107971191,
          0.06442911922931671,
          -0.19889162480831146,
          0.15429335832595825,
          -0.01836605928838253,
          0.22525957226753235,
          0.1682925522327423,
          0.07691055536270142,
          0.06381324678659439,
          0.13990098237991333,
          -0.11729487031698227,
          0.07707087695598602,
          0.12950322031974792,
          0.2105836719274521,
          0.7875205278396606,
          0.9274821281433105,
          1.037822961807251,
          1.2750351428985596,
          1.1974210739135742,
          1.4604601860046387,
          1.5042855739593506,
          1.5686001777648926,
          1.5736809968948364,
          1.4872288703918457,
          1.4220906496047974,
          1.7822320461273193,
          1.6888903379440308,
          2.008071184158325,
          1.8969343900680542,
          1.6547460556030273,
          1.866056203842163,
          2.116748809814453,
          2.0178616046905518,
          1.6880887746810913,
          1.638919711112976,
          1.422876000404358,
          1.6686699390411377,
          1.619608998298645,
          1.307472825050354,
          1.13192617893219,
          1.0825974941253662,
          1.479013204574585,
          1.4959676265716553,
          1.47126042842865,
          1.4376076459884644,
          1.1521204710006714,
          1.1605554819107056,
          1.0832087993621826,
          1.2000700235366821,
          1.2000935077667236,
          1.0687103271484375,
          0.8080635070800781,
          0.7801825404167175,
          0.8197952508926392,
          0.7261270880699158,
          0.8720174431800842,
          0.8140650987625122,
          0.9341716766357422,
          0.45741933584213257,
          0.33535927534103394,
          0.11907798051834106,
          -0.03294861316680908,
          -0.0428825318813324,
          0.028890371322631836,
          -0.16626089811325073,
          -0.35316529870033264,
          -0.25761449337005615,
          -0.3915417194366455,
          -0.34071773290634155,
          -0.39549872279167175,
          -0.4772825241088867,
          -0.12111813575029373,
          -0.002987608313560486,
          -0.409618616104126,
          -0.49872922897338867,
          -0.759376049041748,
          -0.6550633311271667,
          -0.8235905766487122,
          -0.6632885336875916,
          -0.5561506748199463,
          0.10752581059932709,
          -0.06920992583036423,
          -0.07517189532518387,
          0.12227996438741684,
          -0.04386462643742561,
          -0.4116472005844116,
          -0.375567764043808,
          0.15311336517333984,
          0.015077564865350723,
          0.013023126870393753,
          0.2542516589164734,
          0.5126000642776489,
          0.3884791135787964,
          0.3535606861114502,
          0.1575835645198822,
          0.13516846299171448,
          0.5060518980026245,
          0.3480461835861206,
          -0.252130925655365,
          -0.33384203910827637,
          -0.4776298403739929,
          -0.1746680587530136,
          -0.19196927547454834,
          -0.09996949136257172,
          -0.06557416915893555,
          -0.28839075565338135,
          -0.0006940290331840515,
          0.046862006187438965,
          -0.1320846527814865,
          0.07275744527578354,
          0.17737361788749695,
          -0.23905852437019348,
          -0.0803927332162857,
          -0.008760951459407806,
          0.07404400408267975,
          0.0896415263414383,
          -0.3747296631336212,
          -0.30205047130584717,
          -0.3020203113555908,
          -0.15305766463279724,
          -0.000788399949669838,
          -0.08020424842834473,
          -0.25123900175094604,
          -0.4914286732673645,
          -0.521623432636261,
          -0.5937753915786743,
          -0.9231047630310059,
          -0.6658946871757507,
          -0.5146214962005615,
          -0.09637629240751266,
          -0.5027176141738892,
          -0.7999567985534668,
          -0.31513112783432007,
          -0.3383142054080963,
          -0.3711007833480835,
          -0.49358540773391724,
          -0.2647004723548889,
          -0.36763644218444824,
          -0.3957216143608093,
          -0.2403680980205536,
          0.17933034896850586,
          0.4039531946182251,
          0.003657604567706585,
          0.021680638194084167,
          0.2328379899263382,
          0.3826533854007721,
          0.520479679107666,
          0.47488918900489807,
          0.3662780225276947,
          0.18483757972717285,
          0.0970466360449791,
          0.008018657565116882,
          -0.1513213813304901,
          -0.07159948348999023,
          0.19816166162490845,
          0.09042608737945557,
          0.3418872356414795,
          0.3051850497722626,
          0.1335928738117218,
          0.11460939049720764,
          0.34069445729255676,
          0.41937097907066345,
          0.6678176522254944,
          0.4665411710739136,
          0.7827016711235046,
          0.6205792427062988,
          0.5918172001838684,
          0.8047978281974792,
          0.8152509331703186,
          0.9056631326675415,
          0.8936758637428284,
          0.6779941320419312,
          0.6411076188087463,
          0.5424392819404602,
          0.29674261808395386,
          0.4053008556365967,
          0.2828414738178253,
          0.23136621713638306,
          0.23894591629505157,
          0.23911863565444946,
          0.188026562333107,
          0.641137957572937,
          0.3930942118167877,
          0.5251740217208862,
          0.9087573289871216,
          1.1317590475082397,
          1.268364429473877,
          1.6445156335830688,
          1.5357484817504883,
          1.3703535795211792,
          1.2548161745071411,
          1.1912084817886353,
          1.2233963012695312,
          1.079953670501709,
          1.2848637104034424,
          1.6175670623779297,
          1.674283504486084,
          1.826447606086731,
          1.3031158447265625,
          1.3932170867919922,
          1.4768346548080444,
          1.5251773595809937,
          1.0784462690353394,
          1.0084487199783325,
          1.1841167211532593,
          1.2514387369155884,
          1.40379798412323,
          1.5328376293182373,
          1.5022553205490112,
          1.3619301319122314,
          1.6155222654342651,
          1.798919677734375,
          1.8520587682724,
          2.269073009490967,
          2.5319769382476807,
          2.5443708896636963,
          2.449920892715454,
          2.4348936080932617,
          2.4362094402313232,
          2.416724681854248,
          2.387985944747925,
          2.392373561859131,
          2.4534599781036377,
          2.6633729934692383,
          2.7075910568237305,
          2.7768115997314453,
          2.9116909503936768,
          2.5191490650177,
          2.293820381164551,
          2.172229766845703,
          1.9466315507888794,
          1.9560211896896362,
          1.9067307710647583,
          1.8274481296539307,
          1.8524720668792725,
          2.0147864818573,
          1.9243332147598267,
          1.4335216283798218,
          1.0546720027923584,
          1.25894296169281,
          1.2750391960144043,
          1.159013032913208,
          1.1313111782073975,
          0.9357244372367859,
          0.8377184271812439,
          1.145720362663269,
          1.1206873655319214,
          1.122177004814148,
          1.1604520082473755,
          1.0318279266357422,
          0.924934983253479,
          1.0563609600067139,
          0.7667649984359741,
          0.9100497961044312,
          0.8279476165771484,
          0.8713006377220154,
          0.8846667408943176,
          1.2788599729537964,
          1.5465182065963745,
          1.6019303798675537,
          2.220350742340088,
          2.265559196472168,
          2.2188720703125,
          2.211456775665283,
          2.1061859130859375,
          2.459083080291748,
          2.270860433578491,
          2.2170157432556152,
          2.514545440673828,
          2.776989459991455,
          2.99375319480896,
          3.2678723335266113,
          3.5000574588775635,
          3.1566355228424072,
          2.851672887802124,
          2.530291795730591,
          2.496391773223877,
          2.5447757244110107,
          2.515427827835083,
          2.4944262504577637,
          2.574374198913574,
          2.5103440284729004,
          2.7548232078552246,
          2.5108354091644287,
          2.500525712966919,
          2.128178119659424,
          2.0159292221069336,
          1.9579555988311768,
          1.582261323928833,
          1.56387460231781,
          1.4066542387008667,
          1.057936191558838,
          1.1031843423843384,
          0.977983295917511,
          0.3142019212245941,
          -0.0981551930308342,
          0.023814041167497635,
          -0.27592670917510986,
          0.06519954651594162,
          -0.010111123323440552,
          -0.1047607809305191,
          -0.4803471863269806,
          -0.39976975321769714,
          -0.3957527279853821,
          -0.2322922646999359,
          -0.5223483443260193,
          -0.3495457172393799,
          -0.2869727909564972,
          -0.3619095981121063,
          -0.2854548394680023,
          0.02127993106842041,
          -0.5722042918205261,
          -0.620021402835846,
          -0.6277442574501038,
          -0.44989991188049316,
          -0.6732954978942871,
          -0.4438652992248535,
          -0.7664100527763367,
          -0.6456494927406311,
          -0.7181521058082581,
          -1.038925290107727,
          -0.6981241106987,
          -0.4080057740211487,
          -0.12301018834114075,
          -0.3159114122390747,
          -0.3454304039478302,
          -0.5002576112747192,
          -0.428392231464386,
          -0.8217562437057495,
          -0.5843899846076965,
          -0.4306947886943817,
          -0.47595325112342834,
          -0.3927842378616333,
          0.014373138546943665,
          -0.0572371706366539,
          -0.2819457948207855,
          -0.3364829123020172,
          -0.40237095952033997,
          -0.3731127977371216,
          -0.04352976381778717,
          -0.017024865373969078,
          0.07966892421245575,
          -0.03766189515590668,
          0.05697616562247276,
          -0.3765665888786316,
          -0.5481511950492859,
          -0.7928664088249207,
          -0.9657629132270813,
          -1.2299795150756836,
          -1.2642693519592285,
          -1.682297706604004,
          -1.152280330657959,
          -0.9939944744110107,
          -1.1160151958465576,
          -1.0444852113723755,
          -1.1838767528533936,
          -0.9746836423873901,
          -1.2005915641784668,
          -1.0089479684829712,
          -1.0351250171661377,
          -1.242545485496521,
          -1.4229552745819092,
          -1.3451894521713257,
          -1.1827601194381714,
          -1.1566437482833862,
          -0.7490375638008118,
          -0.9528391361236572,
          -0.7649596929550171,
          -0.7749817967414856,
          -0.5117063522338867,
          -0.3846019506454468,
          -0.12416692078113556,
          -0.012198120355606079,
          -0.132745623588562,
          -0.38396310806274414,
          -0.6103173494338989,
          -0.6013544797897339,
          -0.7388656735420227,
          -0.9118589758872986,
          -0.911871612071991,
          -0.7496441006660461,
          -0.5901368260383606,
          -0.8366478681564331,
          -0.7218002676963806,
          -0.7830540537834167,
          -0.801540732383728,
          -0.6971411108970642,
          -0.26827287673950195,
          -0.44026392698287964,
          -0.29383355379104614,
          -0.5822146534919739,
          -0.31361228227615356,
          -0.5403933525085449,
          -0.6609624624252319,
          -0.9336844086647034,
          -0.737516462802887,
          -0.7022123336791992,
          -0.6560521125793457,
          -0.5837773084640503,
          -0.8830468058586121,
          -0.9368228912353516,
          -1.1408190727233887,
          -0.8447744846343994,
          -0.837669849395752,
          -0.8519452810287476,
          -0.6368033289909363,
          -0.14087915420532227,
          -0.07232693582773209,
          -0.26919686794281006,
          -0.25138741731643677,
          -0.07852042466402054,
          -0.10006354004144669,
          -0.1260363608598709,
          -0.258476585149765,
          -0.190784752368927,
          -0.4011489748954773,
          -0.29443445801734924,
          -0.54573655128479,
          -0.4139557480812073,
          -1.2541016340255737,
          -0.8464854955673218,
          -0.595916748046875,
          -0.3841215968132019,
          -0.506003201007843,
          -0.22254495322704315,
          -0.38455918431282043,
          -0.4471035599708557,
          -0.7630842924118042,
          -0.749026894569397,
          -0.8208491802215576,
          -1.2723894119262695,
          -1.4600719213485718,
          -1.5685639381408691,
          -1.2828558683395386,
          -1.1238617897033691,
          -1.3462682962417603,
          -1.2228597402572632,
          -1.2983653545379639,
          -1.3134033679962158,
          -1.212263822555542,
          -1.1329028606414795,
          -1.1422438621520996,
          -0.9385702013969421,
          -1.2483172416687012,
          -1.1905102729797363,
          -1.2736436128616333,
          -1.0451548099517822,
          -0.808727502822876,
          -1.1759998798370361,
          -1.2136263847351074,
          -1.2585511207580566,
          -1.4710556268692017,
          -1.3741133213043213,
          -1.298599123954773,
          -1.5915467739105225,
          -1.8642065525054932,
          -1.8049978017807007,
          -1.5534688234329224,
          -1.5163493156433105,
          -2.114872932434082,
          -2.2025415897369385,
          -1.7892869710922241,
          -1.7755495309829712,
          -1.8056776523590088,
          -1.7530075311660767,
          -1.5409187078475952,
          -1.7514820098876953,
          -1.6432298421859741,
          -1.2679800987243652,
          -1.2082387208938599,
          -1.041421890258789,
          -1.1110302209854126,
          -1.2833898067474365,
          -1.469530701637268,
          -1.217313528060913,
          -1.0818978548049927,
          -0.982322633266449,
          -1.0056828260421753,
          -1.2068288326263428,
          -1.4960747957229614,
          -1.408362865447998,
          -1.5071327686309814,
          -1.5496575832366943,
          -1.791029691696167,
          -1.9723466634750366,
          -2.102602481842041,
          -1.71342134475708,
          -1.4097963571548462,
          -1.4377497434616089,
          -1.002835988998413,
          -0.9303518533706665,
          -0.9716675281524658,
          -0.9563794732093811,
          -0.9464197754859924,
          -1.017337441444397,
          -1.095403790473938,
          -1.0574097633361816,
          -1.1704481840133667,
          -1.063066840171814,
          -0.9980902671813965,
          -0.931167721748352,
          -1.1630662679672241,
          -1.2064200639724731,
          -1.0917404890060425,
          -1.0727624893188477,
          -1.1252182722091675,
          -0.9950685501098633,
          -0.6949673295021057,
          -0.8243044018745422,
          -0.8308613300323486,
          -0.7629302144050598,
          -0.6699737906455994,
          -0.8869591355323792,
          -0.4433140456676483,
          -0.2679827809333801,
          0.08058623969554901,
          -0.015750041231513023,
          -0.5300657749176025,
          -0.12379100918769836,
          -0.3815031349658966,
          -0.27076447010040283,
          -0.19776049256324768,
          -0.5979092121124268,
          -0.3382408618927002,
          -0.6404862403869629,
          -0.6486462950706482,
          -1.2538539171218872,
          -1.4939262866973877,
          -1.4461497068405151,
          -1.6016780138015747,
          -1.8231315612792969,
          -2.099550247192383,
          -2.057048797607422,
          -1.4408844709396362,
          -1.393369436264038,
          -0.9557927846908569,
          -0.6926125288009644,
          -0.7983129024505615,
          -1.0410550832748413,
          -1.1158723831176758,
          -1.4540077447891235,
          -1.388103723526001,
          -1.3543659448623657,
          -1.820660948753357,
          -1.9929957389831543,
          -1.9505141973495483,
          -1.593305230140686,
          -1.2042797803878784,
          -0.795607328414917,
          -0.7716462016105652,
          -0.5595754981040955,
          -0.38297325372695923,
          -0.1636812686920166,
          0.2618664503097534,
          -0.31421950459480286,
          -0.2685427665710449,
          -0.16861072182655334,
          -0.3818970024585724,
          -0.04647307097911835,
          0.0361117459833622,
          0.4333032965660095,
          0.30667629837989807,
          0.1937696933746338,
          0.3999677300453186,
          0.08387262374162674,
          -0.31566348671913147,
          -0.4378971755504608,
          -0.7556549906730652,
          -0.7760828137397766,
          -0.935738742351532,
          -0.9695759415626526,
          -0.6719304919242859,
          -0.3898792266845703,
          -0.3876856863498688,
          -0.4168519675731659,
          -0.41922372579574585,
          -0.7052099108695984,
          -0.9016109704971313,
          -1.244179606437683,
          -1.3371399641036987,
          -1.101096749305725,
          -0.9202731847763062,
          -0.7709790468215942,
          -1.0514905452728271,
          -0.7978185415267944,
          -0.603480339050293,
          -0.3868168592453003,
          -0.5532780885696411,
          -0.44325852394104004,
          -0.5284443497657776,
          -0.5030621290206909,
          0.02194829285144806,
          -0.18966339528560638,
          0.05748714134097099,
          0.10207699239253998,
          0.266801655292511,
          0.39065253734588623,
          0.5153982639312744,
          0.5325201153755188,
          0.783057451248169,
          0.9521983861923218,
          0.9263831377029419,
          1.1371865272521973,
          0.9039795398712158,
          0.5899144411087036,
          0.6281328797340393,
          0.2795732021331787,
          0.21737425029277802,
          0.3984898626804352,
          0.439561128616333,
          0.2980302572250366,
          0.11441777646541595,
          0.2172495424747467,
          0.049477048218250275,
          -0.05178934708237648,
          -0.020363405346870422,
          -0.4505980610847473,
          -0.333149790763855,
          -0.35249632596969604,
          -0.37939903140068054,
          -0.4423474669456482,
          -0.3933621346950531,
          -0.6218687891960144,
          -0.6912689208984375,
          -1.1494319438934326,
          -1.5051991939544678,
          -1.6248176097869873,
          -1.7909040451049805,
          -1.9006690979003906,
          -2.025418996810913,
          -2.11861515045166,
          -1.9986220598220825,
          -1.9904849529266357,
          -2.3031554222106934,
          -2.5100455284118652,
          -2.6741368770599365,
          -2.6917176246643066,
          -2.648348569869995,
          -2.6377556324005127,
          -2.863615036010742,
          -2.925706148147583,
          -2.953009605407715,
          -2.7529914379119873,
          -2.513068914413452,
          -2.4598567485809326,
          -2.7170820236206055,
          -2.8446054458618164,
          -2.590719699859619,
          -2.643723726272583,
          -2.217647075653076,
          -2.018164873123169,
          -2.253420829772949,
          -2.4416849613189697,
          -2.249833822250366,
          -2.4230360984802246,
          -2.8098154067993164,
          -2.720644235610962,
          -2.7299883365631104,
          -2.9148969650268555,
          -3.0333123207092285,
          -3.318777322769165,
          -3.6280689239501953,
          -3.9892678260803223,
          -4.0939459800720215,
          -3.781879186630249,
          -3.691225051879883,
          -3.665499687194824,
          -3.567978620529175,
          -3.8305418491363525,
          -4.064037322998047,
          -4.161384582519531,
          -3.994649887084961,
          -3.8672268390655518,
          -3.7756619453430176,
          -3.592813730239868,
          -3.390453577041626,
          -3.116975784301758,
          -3.0075583457946777,
          -3.207512378692627,
          -3.276108503341675,
          -3.2242488861083984,
          -3.0710294246673584,
          -2.84767746925354,
          -3.1854248046875,
          -3.07973051071167,
          -2.6146554946899414,
          -2.897338628768921,
          -2.9525222778320312,
          -2.9793195724487305,
          -3.0501255989074707,
          -2.742486000061035,
          -2.5150630474090576,
          -2.639888286590576,
          -2.654958963394165,
          -2.8446388244628906,
          -2.8103833198547363,
          -2.9563639163970947,
          -2.917786121368408,
          -2.5965070724487305,
          -2.450312614440918,
          -2.499819278717041,
          -2.626840829849243,
          -2.600335121154785,
          -2.489778757095337,
          -2.4347479343414307,
          -2.215284585952759,
          -2.5700764656066895,
          -2.9017419815063477,
          -2.803933620452881,
          -2.6486053466796875,
          -2.7339320182800293,
          -2.9235010147094727,
          -2.7388107776641846,
          -2.768399238586426,
          -2.645230531692505,
          -2.6536412239074707,
          -2.600769519805908,
          -2.6792051792144775,
          -2.0832505226135254,
          -2.1939330101013184,
          -1.8532261848449707,
          -2.041815757751465,
          -1.9794700145721436,
          -1.91790771484375,
          -2.0519347190856934,
          -2.1778147220611572,
          -2.076963186264038,
          -1.9243654012680054,
          -1.9508602619171143,
          -1.9123064279556274,
          -1.9562333822250366,
          -1.9104336500167847,
          -1.7960336208343506,
          -1.859390377998352,
          -1.8097052574157715,
          -2.453357696533203,
          -2.5491185188293457,
          -2.2603821754455566,
          -2.4997963905334473,
          -2.3692471981048584,
          -2.6805503368377686,
          -2.549750566482544,
          -2.5101423263549805,
          -2.363363265991211,
          -2.7168619632720947,
          -2.861022472381592,
          -2.5691885948181152,
          -2.7137351036071777,
          -2.10752534866333,
          -1.8482799530029297,
          -1.9586502313613892,
          -2.118370294570923,
          -1.8722524642944336,
          -1.8635308742523193
         ]
        }
       ],
       "layout": {
        "bargap": 0.2,
        "bargroupgap": 0.1,
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "MCMC: Convergence for Dimension 0"
        },
        "xaxis": {
         "title": {
          "text": "Iteration"
         }
        },
        "yaxis": {
         "title": {
          "text": "Value"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Convergence MCMC\n",
    "plot_convergence_mcmc(particles_posterior_mcmc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}