GaussianAreaPlot.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian threshold visualizations\n",
    "\n",
    "For Kevin Weinfurt. Updated for Altair 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import altair as alt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate static gaussian in DataFrame\n",
    "\n",
    "We use this increment throughout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "inc = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = 1.0\n",
    "x0 = 1.0\n",
    "sig = 1.0\n",
    "\n",
    "df_gauss = pd.DataFrame({'x':np.arange(-5,10+inc,inc)})\n",
    "df_gauss['y1'] = df_gauss['x'].apply(lambda x: A*np.exp(-(pow((x-x0),2)/pow(sig,2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize static gaussian with line + area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-3e8c6b811c544d85a1324257eb9137ba.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-3e8c6b811c544d85a1324257eb9137ba.vega-embed details,\n",
       "  #altair-viz-3e8c6b811c544d85a1324257eb9137ba.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-3e8c6b811c544d85a1324257eb9137ba\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-3e8c6b811c544d85a1324257eb9137ba\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-3e8c6b811c544d85a1324257eb9137ba\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"layer\": [{\"mark\": {\"type\": \"line\", \"color\": \"black\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"y1\", \"type\": \"quantitative\"}}}, {\"mark\": {\"type\": \"area\", \"color\": \"lightblue\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"y1\", \"type\": \"quantitative\"}}}], \"data\": {\"name\": \"data-3da6bb8cb3cbb8a025cce6f316f5d476\"}, \"height\": 150, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-3da6bb8cb3cbb8a025cce6f316f5d476\": [{\"x\": -5.0, \"y1\": 2.3195228302435696e-16}, {\"x\": -4.9, \"y1\": 7.624459905389723e-16}, {\"x\": -4.800000000000001, \"y1\": 2.4565953687921255e-15}, {\"x\": -4.700000000000001, \"y1\": 7.758402075696e-15}, {\"x\": -4.600000000000001, \"y1\": 2.4017347816209182e-14}, {\"x\": -4.500000000000002, \"y1\": 7.287724095819537e-14}, {\"x\": -4.400000000000002, \"y1\": 2.1675688826189155e-13}, {\"x\": -4.3000000000000025, \"y1\": 6.31928588517521e-13}, {\"x\": -4.200000000000003, \"y1\": 1.8058314375131594e-12}, {\"x\": -4.100000000000003, \"y1\": 5.058252742843624e-12}, {\"x\": -4.0000000000000036, \"y1\": 1.3887943864963527e-11}, {\"x\": -3.900000000000004, \"y1\": 3.7375713279441235e-11}, {\"x\": -3.8000000000000043, \"y1\": 9.859505575991096e-11}, {\"x\": -3.7000000000000046, \"y1\": 2.5493818803918604e-10}, {\"x\": -3.600000000000005, \"y1\": 6.46143177310581e-10}, {\"x\": -3.5000000000000053, \"y1\": 1.6052280551855318e-09}, {\"x\": -3.4000000000000057, \"y1\": 3.90893843426467e-09}, {\"x\": -3.300000000000006, \"y1\": 9.330287574504509e-09}, {\"x\": -3.2000000000000064, \"y1\": 2.1829577951253617e-08}, {\"x\": -3.1000000000000068, \"y1\": 5.006218020766764e-08}, {\"x\": -3.000000000000007, \"y1\": 1.1253517471925272e-07}, {\"x\": -2.9000000000000075, \"y1\": 2.4795960180448864e-07}, {\"x\": -2.800000000000008, \"y1\": 5.355347802792786e-07}, {\"x\": -2.700000000000008, \"y1\": 1.1337271387478977e-06}, {\"x\": -2.6000000000000085, \"y1\": 2.352575200009629e-06}, {\"x\": -2.500000000000009, \"y1\": 4.7851173921287114e-06}, {\"x\": -2.4000000000000092, \"y1\": 9.540162873078638e-06}, {\"x\": -2.3000000000000096, \"y1\": 1.8643742331515662e-05}, {\"x\": -2.20000000000001, \"y1\": 3.571284964163293e-05}, {\"x\": -2.1000000000000103, \"y1\": 6.705482430280684e-05}, {\"x\": -2.0000000000000107, \"y1\": 0.00012340980408667165}, {\"x\": -1.900000000000011, \"y1\": 0.00022262985691887474}, {\"x\": -1.8000000000000114, \"y1\": 0.0003936690406550531}, {\"x\": -1.7000000000000117, \"y1\": 0.0006823280527563335}, {\"x\": -1.600000000000012, \"y1\": 0.0011592291739045183}, {\"x\": -1.5000000000000124, \"y1\": 0.0019304541362275892}, {\"x\": -1.4000000000000128, \"y1\": 0.003151111598444248}, {\"x\": -1.3000000000000131, \"y1\": 0.0050417602596906745}, {\"x\": -1.2000000000000135, \"y1\": 0.007907054051592971}, {\"x\": -1.1000000000000139, \"y1\": 0.012155178329914234}, {\"x\": -1.0000000000000142, \"y1\": 0.018315638888733138}, {\"x\": -0.9000000000000146, \"y1\": 0.027051846866348914}, {\"x\": -0.8000000000000149, \"y1\": 0.03916389509898498}, {\"x\": -0.7000000000000153, \"y1\": 0.05557621261148017}, {\"x\": -0.6000000000000156, \"y1\": 0.07730474044329587}, {\"x\": -0.500000000000016, \"y1\": 0.10539922456185928}, {\"x\": -0.40000000000001634, \"y1\": 0.14085842092103856}, {\"x\": -0.3000000000000167, \"y1\": 0.18451952399298124}, {\"x\": -0.20000000000001705, \"y1\": 0.23692775868211205}, {\"x\": -0.10000000000001741, \"y1\": 0.29819727942987595}, {\"x\": -1.7763568394002505e-14, \"y1\": 0.36787944117142923}, {\"x\": 0.09999999999998188, \"y1\": 0.4448580662229266}, {\"x\": 0.19999999999998153, \"y1\": 0.527292424043033}, {\"x\": 0.29999999999998117, \"y1\": 0.6126263941843999}, {\"x\": 0.3999999999999808, \"y1\": 0.697676326071015}, {\"x\": 0.49999999999998046, \"y1\": 0.7788007830713897}, {\"x\": 0.5999999999999801, \"y1\": 0.8521437889661978}, {\"x\": 0.6999999999999797, \"y1\": 0.9139311852712171}, {\"x\": 0.7999999999999794, \"y1\": 0.9607894391523153}, {\"x\": 0.899999999999979, \"y1\": 0.9900498337491639}, {\"x\": 0.9999999999999787, \"y1\": 1.0}, {\"x\": 1.0999999999999783, \"y1\": 0.9900498337491723}, {\"x\": 1.199999999999978, \"y1\": 0.9607894391523317}, {\"x\": 1.2999999999999776, \"y1\": 0.9139311852712405}, {\"x\": 1.3999999999999773, \"y1\": 0.8521437889662268}, {\"x\": 1.499999999999977, \"y1\": 0.7788007830714229}, {\"x\": 1.5999999999999766, \"y1\": 0.6976763260710507}, {\"x\": 1.6999999999999762, \"y1\": 0.6126263941844364}, {\"x\": 1.7999999999999758, \"y1\": 0.527292424043069}, {\"x\": 1.8999999999999755, \"y1\": 0.44485806622296076}, {\"x\": 1.9999999999999751, \"y1\": 0.3678794411714606}, {\"x\": 2.0999999999999748, \"y1\": 0.2981972794299039}, {\"x\": 2.1999999999999744, \"y1\": 0.23692775868213628}, {\"x\": 2.299999999999974, \"y1\": 0.1845195239930017}, {\"x\": 2.3999999999999737, \"y1\": 0.14085842092105536}, {\"x\": 2.4999999999999734, \"y1\": 0.10539922456187276}, {\"x\": 2.599999999999973, \"y1\": 0.07730474044330643}, {\"x\": 2.6999999999999726, \"y1\": 0.05557621261148824}, {\"x\": 2.7999999999999723, \"y1\": 0.03916389509899098}, {\"x\": 2.899999999999972, \"y1\": 0.0270518468663533}, {\"x\": 2.9999999999999716, \"y1\": 0.018315638888736264}, {\"x\": 3.0999999999999712, \"y1\": 0.012155178329916404}, {\"x\": 3.199999999999971, \"y1\": 0.007907054051594453}, {\"x\": 3.2999999999999705, \"y1\": 0.005041760259691664}, {\"x\": 3.39999999999997, \"y1\": 0.003151111598444892}, {\"x\": 3.49999999999997, \"y1\": 0.0019304541362280007}, {\"x\": 3.5999999999999694, \"y1\": 0.0011592291739047757}, {\"x\": 3.699999999999969, \"y1\": 0.0006823280527564905}, {\"x\": 3.7999999999999687, \"y1\": 0.00039366904065514714}, {\"x\": 3.8999999999999684, \"y1\": 0.0002226298569189297}, {\"x\": 3.999999999999968, \"y1\": 0.00012340980408670322}, {\"x\": 4.099999999999968, \"y1\": 6.705482430282459e-05}, {\"x\": 4.199999999999967, \"y1\": 3.571284964164269e-05}, {\"x\": 4.299999999999967, \"y1\": 1.8643742331520893e-05}, {\"x\": 4.399999999999967, \"y1\": 9.540162873081399e-06}, {\"x\": 4.499999999999966, \"y1\": 4.7851173921301395e-06}, {\"x\": 4.599999999999966, \"y1\": 2.352575200010352e-06}, {\"x\": 4.6999999999999655, \"y1\": 1.133727138748254e-06}, {\"x\": 4.799999999999965, \"y1\": 5.355347802794526e-07}, {\"x\": 4.899999999999965, \"y1\": 2.47959601804571e-07}, {\"x\": 4.9999999999999645, \"y1\": 1.125351747192911e-07}, {\"x\": 5.099999999999964, \"y1\": 5.0062180207685073e-08}, {\"x\": 5.199999999999964, \"y1\": 2.1829577951261448e-08}, {\"x\": 5.299999999999963, \"y1\": 9.330287574507922e-09}, {\"x\": 5.399999999999963, \"y1\": 3.908938434266128e-09}, {\"x\": 5.499999999999963, \"y1\": 1.6052280551861534e-09}, {\"x\": 5.599999999999962, \"y1\": 6.461431773108357e-10}, {\"x\": 5.699999999999962, \"y1\": 2.549381880392884e-10}, {\"x\": 5.799999999999962, \"y1\": 9.859505575995125e-11}, {\"x\": 5.899999999999961, \"y1\": 3.737571327945677e-11}, {\"x\": 5.999999999999961, \"y1\": 1.3887943864969448e-11}, {\"x\": 6.099999999999961, \"y1\": 5.058252742845834e-12}, {\"x\": 6.19999999999996, \"y1\": 1.8058314375139613e-12}, {\"x\": 6.29999999999996, \"y1\": 6.319285885178062e-13}, {\"x\": 6.3999999999999595, \"y1\": 2.1675688826199089e-13}, {\"x\": 6.499999999999959, \"y1\": 7.28772409582298e-14}, {\"x\": 6.599999999999959, \"y1\": 2.40173478162207e-14}, {\"x\": 6.699999999999958, \"y1\": 7.75840207569975e-15}, {\"x\": 6.799999999999958, \"y1\": 2.4565953687933475e-15}, {\"x\": 6.899999999999958, \"y1\": 7.624459905393568e-16}, {\"x\": 6.999999999999957, \"y1\": 2.319522830244756e-16}, {\"x\": 7.099999999999957, \"y1\": 6.91675397554508e-17}, {\"x\": 7.199999999999957, \"y1\": 2.021715848696424e-17}, {\"x\": 7.299999999999956, \"y1\": 5.79231288539804e-18}, {\"x\": 7.399999999999956, \"y1\": 1.626664621454156e-18}, {\"x\": 7.499999999999956, \"y1\": 4.477732441720878e-19}, {\"x\": 7.599999999999955, \"y1\": 1.2081820199006834e-19}, {\"x\": 7.699999999999955, \"y1\": 3.195366717750272e-20}, {\"x\": 7.7999999999999545, \"y1\": 8.283677007687981e-21}, {\"x\": 7.899999999999954, \"y1\": 2.104939978341067e-21}, {\"x\": 7.999999999999954, \"y1\": 5.242885663366854e-22}, {\"x\": 8.099999999999953, \"y1\": 1.2800153190524921e-22}, {\"x\": 8.199999999999953, \"y1\": 3.0631908645795196e-23}, {\"x\": 8.299999999999953, \"y1\": 7.185335635907151e-24}, {\"x\": 8.399999999999952, \"y1\": 1.652091782315434e-24}, {\"x\": 8.499999999999952, \"y1\": 3.7233631217531826e-25}, {\"x\": 8.599999999999952, \"y1\": 8.225280651612705e-26}, {\"x\": 8.699999999999951, \"y1\": 1.7810666347584217e-26}, {\"x\": 8.799999999999951, \"y1\": 3.780277844778973e-27}, {\"x\": 8.89999999999995, \"y1\": 7.864685935772566e-28}, {\"x\": 8.99999999999995, \"y1\": 1.6038108905499141e-28}, {\"x\": 9.09999999999995, \"y1\": 3.205819323397598e-29}, {\"x\": 9.19999999999995, \"y1\": 6.2811481476111985e-30}, {\"x\": 9.29999999999995, \"y1\": 1.2062939277821599e-30}, {\"x\": 9.399999999999949, \"y1\": 2.27081292202836e-31}, {\"x\": 9.499999999999948, \"y1\": 4.190093194498089e-32}, {\"x\": 9.599999999999948, \"y1\": 7.578445267625107e-33}, {\"x\": 9.699999999999948, \"y1\": 1.3435401977599626e-33}, {\"x\": 9.799999999999947, \"y1\": 2.3347227834894295e-34}, {\"x\": 9.899999999999947, \"y1\": 3.97680309790541e-35}, {\"x\": 9.999999999999947, \"y1\": 6.639677199587151e-36}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base = alt.Chart(df_gauss).encode(\n",
    "    x = 'x',\n",
    "    y = 'y1'\n",
    ")\n",
    "\n",
    "line = base.mark_line(color='black')\n",
    "\n",
    "area = base.mark_area(color='lightblue')\n",
    "\n",
    "(line + area).properties(\n",
    "    height = 150\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Area above cutoff in static gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-a281dc5e94134cb5a1dba43fee810146.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-a281dc5e94134cb5a1dba43fee810146.vega-embed details,\n",
       "  #altair-viz-a281dc5e94134cb5a1dba43fee810146.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-a281dc5e94134cb5a1dba43fee810146\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-a281dc5e94134cb5a1dba43fee810146\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-a281dc5e94134cb5a1dba43fee810146\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"hconcat\": [{\"layer\": [{\"mark\": {\"type\": \"area\", \"color\": \"lightblue\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"y1\", \"type\": \"quantitative\"}}, \"transform\": [{\"filter\": \"(datum.x >= param_46)\"}]}, {\"mark\": {\"type\": \"line\", \"color\": \"black\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"y1\", \"type\": \"quantitative\"}}}], \"height\": 150}, {\"mark\": {\"type\": \"bar\"}, \"encoding\": {\"y\": {\"aggregate\": \"sum\", \"axis\": {\"title\": \"Area of blue region\"}, \"field\": \"y1\", \"scale\": {\"domain\": [0, 20]}, \"type\": \"quantitative\"}}, \"height\": 150, \"transform\": [{\"filter\": \"(datum.x >= param_46)\"}], \"width\": 100}], \"data\": {\"name\": \"data-3da6bb8cb3cbb8a025cce6f316f5d476\"}, \"params\": [{\"name\": \"param_46\", \"bind\": {\"input\": \"range\", \"max\": 10, \"min\": -5, \"name\": \"cutoff:\", \"step\": 0.1}, \"value\": 0}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-3da6bb8cb3cbb8a025cce6f316f5d476\": [{\"x\": -5.0, \"y1\": 2.3195228302435696e-16}, {\"x\": -4.9, \"y1\": 7.624459905389723e-16}, {\"x\": -4.800000000000001, \"y1\": 2.4565953687921255e-15}, {\"x\": -4.700000000000001, \"y1\": 7.758402075696e-15}, {\"x\": -4.600000000000001, \"y1\": 2.4017347816209182e-14}, {\"x\": -4.500000000000002, \"y1\": 7.287724095819537e-14}, {\"x\": -4.400000000000002, \"y1\": 2.1675688826189155e-13}, {\"x\": -4.3000000000000025, \"y1\": 6.31928588517521e-13}, {\"x\": -4.200000000000003, \"y1\": 1.8058314375131594e-12}, {\"x\": -4.100000000000003, \"y1\": 5.058252742843624e-12}, {\"x\": -4.0000000000000036, \"y1\": 1.3887943864963527e-11}, {\"x\": -3.900000000000004, \"y1\": 3.7375713279441235e-11}, {\"x\": -3.8000000000000043, \"y1\": 9.859505575991096e-11}, {\"x\": -3.7000000000000046, \"y1\": 2.5493818803918604e-10}, {\"x\": -3.600000000000005, \"y1\": 6.46143177310581e-10}, {\"x\": -3.5000000000000053, \"y1\": 1.6052280551855318e-09}, {\"x\": -3.4000000000000057, \"y1\": 3.90893843426467e-09}, {\"x\": -3.300000000000006, \"y1\": 9.330287574504509e-09}, {\"x\": -3.2000000000000064, \"y1\": 2.1829577951253617e-08}, {\"x\": -3.1000000000000068, \"y1\": 5.006218020766764e-08}, {\"x\": -3.000000000000007, \"y1\": 1.1253517471925272e-07}, {\"x\": -2.9000000000000075, \"y1\": 2.4795960180448864e-07}, {\"x\": -2.800000000000008, \"y1\": 5.355347802792786e-07}, {\"x\": -2.700000000000008, \"y1\": 1.1337271387478977e-06}, {\"x\": -2.6000000000000085, \"y1\": 2.352575200009629e-06}, {\"x\": -2.500000000000009, \"y1\": 4.7851173921287114e-06}, {\"x\": -2.4000000000000092, \"y1\": 9.540162873078638e-06}, {\"x\": -2.3000000000000096, \"y1\": 1.8643742331515662e-05}, {\"x\": -2.20000000000001, \"y1\": 3.571284964163293e-05}, {\"x\": -2.1000000000000103, \"y1\": 6.705482430280684e-05}, {\"x\": -2.0000000000000107, \"y1\": 0.00012340980408667165}, {\"x\": -1.900000000000011, \"y1\": 0.00022262985691887474}, {\"x\": -1.8000000000000114, \"y1\": 0.0003936690406550531}, {\"x\": -1.7000000000000117, \"y1\": 0.0006823280527563335}, {\"x\": -1.600000000000012, \"y1\": 0.0011592291739045183}, {\"x\": -1.5000000000000124, \"y1\": 0.0019304541362275892}, {\"x\": -1.4000000000000128, \"y1\": 0.003151111598444248}, {\"x\": -1.3000000000000131, \"y1\": 0.0050417602596906745}, {\"x\": -1.2000000000000135, \"y1\": 0.007907054051592971}, {\"x\": -1.1000000000000139, \"y1\": 0.012155178329914234}, {\"x\": -1.0000000000000142, \"y1\": 0.018315638888733138}, {\"x\": -0.9000000000000146, \"y1\": 0.027051846866348914}, {\"x\": -0.8000000000000149, \"y1\": 0.03916389509898498}, {\"x\": -0.7000000000000153, \"y1\": 0.05557621261148017}, {\"x\": -0.6000000000000156, \"y1\": 0.07730474044329587}, {\"x\": -0.500000000000016, \"y1\": 0.10539922456185928}, {\"x\": -0.40000000000001634, \"y1\": 0.14085842092103856}, {\"x\": -0.3000000000000167, \"y1\": 0.18451952399298124}, {\"x\": -0.20000000000001705, \"y1\": 0.23692775868211205}, {\"x\": -0.10000000000001741, \"y1\": 0.29819727942987595}, {\"x\": -1.7763568394002505e-14, \"y1\": 0.36787944117142923}, {\"x\": 0.09999999999998188, \"y1\": 0.4448580662229266}, {\"x\": 0.19999999999998153, \"y1\": 0.527292424043033}, {\"x\": 0.29999999999998117, \"y1\": 0.6126263941843999}, {\"x\": 0.3999999999999808, \"y1\": 0.697676326071015}, {\"x\": 0.49999999999998046, \"y1\": 0.7788007830713897}, {\"x\": 0.5999999999999801, \"y1\": 0.8521437889661978}, {\"x\": 0.6999999999999797, \"y1\": 0.9139311852712171}, {\"x\": 0.7999999999999794, \"y1\": 0.9607894391523153}, {\"x\": 0.899999999999979, \"y1\": 0.9900498337491639}, {\"x\": 0.9999999999999787, \"y1\": 1.0}, {\"x\": 1.0999999999999783, \"y1\": 0.9900498337491723}, {\"x\": 1.199999999999978, \"y1\": 0.9607894391523317}, {\"x\": 1.2999999999999776, \"y1\": 0.9139311852712405}, {\"x\": 1.3999999999999773, \"y1\": 0.8521437889662268}, {\"x\": 1.499999999999977, \"y1\": 0.7788007830714229}, {\"x\": 1.5999999999999766, \"y1\": 0.6976763260710507}, {\"x\": 1.6999999999999762, \"y1\": 0.6126263941844364}, {\"x\": 1.7999999999999758, \"y1\": 0.527292424043069}, {\"x\": 1.8999999999999755, \"y1\": 0.44485806622296076}, {\"x\": 1.9999999999999751, \"y1\": 0.3678794411714606}, {\"x\": 2.0999999999999748, \"y1\": 0.2981972794299039}, {\"x\": 2.1999999999999744, \"y1\": 0.23692775868213628}, {\"x\": 2.299999999999974, \"y1\": 0.1845195239930017}, {\"x\": 2.3999999999999737, \"y1\": 0.14085842092105536}, {\"x\": 2.4999999999999734, \"y1\": 0.10539922456187276}, {\"x\": 2.599999999999973, \"y1\": 0.07730474044330643}, {\"x\": 2.6999999999999726, \"y1\": 0.05557621261148824}, {\"x\": 2.7999999999999723, \"y1\": 0.03916389509899098}, {\"x\": 2.899999999999972, \"y1\": 0.0270518468663533}, {\"x\": 2.9999999999999716, \"y1\": 0.018315638888736264}, {\"x\": 3.0999999999999712, \"y1\": 0.012155178329916404}, {\"x\": 3.199999999999971, \"y1\": 0.007907054051594453}, {\"x\": 3.2999999999999705, \"y1\": 0.005041760259691664}, {\"x\": 3.39999999999997, \"y1\": 0.003151111598444892}, {\"x\": 3.49999999999997, \"y1\": 0.0019304541362280007}, {\"x\": 3.5999999999999694, \"y1\": 0.0011592291739047757}, {\"x\": 3.699999999999969, \"y1\": 0.0006823280527564905}, {\"x\": 3.7999999999999687, \"y1\": 0.00039366904065514714}, {\"x\": 3.8999999999999684, \"y1\": 0.0002226298569189297}, {\"x\": 3.999999999999968, \"y1\": 0.00012340980408670322}, {\"x\": 4.099999999999968, \"y1\": 6.705482430282459e-05}, {\"x\": 4.199999999999967, \"y1\": 3.571284964164269e-05}, {\"x\": 4.299999999999967, \"y1\": 1.8643742331520893e-05}, {\"x\": 4.399999999999967, \"y1\": 9.540162873081399e-06}, {\"x\": 4.499999999999966, \"y1\": 4.7851173921301395e-06}, {\"x\": 4.599999999999966, \"y1\": 2.352575200010352e-06}, {\"x\": 4.6999999999999655, \"y1\": 1.133727138748254e-06}, {\"x\": 4.799999999999965, \"y1\": 5.355347802794526e-07}, {\"x\": 4.899999999999965, \"y1\": 2.47959601804571e-07}, {\"x\": 4.9999999999999645, \"y1\": 1.125351747192911e-07}, {\"x\": 5.099999999999964, \"y1\": 5.0062180207685073e-08}, {\"x\": 5.199999999999964, \"y1\": 2.1829577951261448e-08}, {\"x\": 5.299999999999963, \"y1\": 9.330287574507922e-09}, {\"x\": 5.399999999999963, \"y1\": 3.908938434266128e-09}, {\"x\": 5.499999999999963, \"y1\": 1.6052280551861534e-09}, {\"x\": 5.599999999999962, \"y1\": 6.461431773108357e-10}, {\"x\": 5.699999999999962, \"y1\": 2.549381880392884e-10}, {\"x\": 5.799999999999962, \"y1\": 9.859505575995125e-11}, {\"x\": 5.899999999999961, \"y1\": 3.737571327945677e-11}, {\"x\": 5.999999999999961, \"y1\": 1.3887943864969448e-11}, {\"x\": 6.099999999999961, \"y1\": 5.058252742845834e-12}, {\"x\": 6.19999999999996, \"y1\": 1.8058314375139613e-12}, {\"x\": 6.29999999999996, \"y1\": 6.319285885178062e-13}, {\"x\": 6.3999999999999595, \"y1\": 2.1675688826199089e-13}, {\"x\": 6.499999999999959, \"y1\": 7.28772409582298e-14}, {\"x\": 6.599999999999959, \"y1\": 2.40173478162207e-14}, {\"x\": 6.699999999999958, \"y1\": 7.75840207569975e-15}, {\"x\": 6.799999999999958, \"y1\": 2.4565953687933475e-15}, {\"x\": 6.899999999999958, \"y1\": 7.624459905393568e-16}, {\"x\": 6.999999999999957, \"y1\": 2.319522830244756e-16}, {\"x\": 7.099999999999957, \"y1\": 6.91675397554508e-17}, {\"x\": 7.199999999999957, \"y1\": 2.021715848696424e-17}, {\"x\": 7.299999999999956, \"y1\": 5.79231288539804e-18}, {\"x\": 7.399999999999956, \"y1\": 1.626664621454156e-18}, {\"x\": 7.499999999999956, \"y1\": 4.477732441720878e-19}, {\"x\": 7.599999999999955, \"y1\": 1.2081820199006834e-19}, {\"x\": 7.699999999999955, \"y1\": 3.195366717750272e-20}, {\"x\": 7.7999999999999545, \"y1\": 8.283677007687981e-21}, {\"x\": 7.899999999999954, \"y1\": 2.104939978341067e-21}, {\"x\": 7.999999999999954, \"y1\": 5.242885663366854e-22}, {\"x\": 8.099999999999953, \"y1\": 1.2800153190524921e-22}, {\"x\": 8.199999999999953, \"y1\": 3.0631908645795196e-23}, {\"x\": 8.299999999999953, \"y1\": 7.185335635907151e-24}, {\"x\": 8.399999999999952, \"y1\": 1.652091782315434e-24}, {\"x\": 8.499999999999952, \"y1\": 3.7233631217531826e-25}, {\"x\": 8.599999999999952, \"y1\": 8.225280651612705e-26}, {\"x\": 8.699999999999951, \"y1\": 1.7810666347584217e-26}, {\"x\": 8.799999999999951, \"y1\": 3.780277844778973e-27}, {\"x\": 8.89999999999995, \"y1\": 7.864685935772566e-28}, {\"x\": 8.99999999999995, \"y1\": 1.6038108905499141e-28}, {\"x\": 9.09999999999995, \"y1\": 3.205819323397598e-29}, {\"x\": 9.19999999999995, \"y1\": 6.2811481476111985e-30}, {\"x\": 9.29999999999995, \"y1\": 1.2062939277821599e-30}, {\"x\": 9.399999999999949, \"y1\": 2.27081292202836e-31}, {\"x\": 9.499999999999948, \"y1\": 4.190093194498089e-32}, {\"x\": 9.599999999999948, \"y1\": 7.578445267625107e-33}, {\"x\": 9.699999999999948, \"y1\": 1.3435401977599626e-33}, {\"x\": 9.799999999999947, \"y1\": 2.3347227834894295e-34}, {\"x\": 9.899999999999947, \"y1\": 3.97680309790541e-35}, {\"x\": 9.999999999999947, \"y1\": 6.639677199587151e-36}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.HConcatChart(...)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slider = alt.binding_range(min=-5, max=10, step=inc, name='cutoff:')\n",
    "selector = alt.param(value=0, bind=slider)\n",
    "\n",
    "base = alt.Chart(df_gauss).encode(\n",
    "    x = 'x',\n",
    "    y = 'y1'\n",
    ")\n",
    "\n",
    "line = base.mark_line(color='black')\n",
    "\n",
    "area = base.mark_area(\n",
    "    color='lightblue'\n",
    ").add_params(\n",
    "    selector\n",
    ").transform_filter(\n",
    "    alt.datum.x >= selector\n",
    ")\n",
    "\n",
    "bar = alt.Chart(df_gauss).mark_bar().encode(\n",
    "    y = alt.Y('sum(y1)', \n",
    "              scale = alt.Scale(domain=(0, 20)),\n",
    "              axis = alt.Axis(title='Area of blue region')\n",
    "             )\n",
    ").transform_filter(\n",
    "    alt.datum.x >= selector\n",
    ")\n",
    "\n",
    "(area + line).properties(height = 150) | bar.properties(height = 150, width=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Change width, center & cutoff of normalized gaussian\n",
    "\n",
    "- Creating a new dataframe with an extended X range so areas off the edge of the plot will be calculated properly\n",
    "- Requires `clip=True` for all `mark_line()`, `mark_area()` specifications to keep data in axis domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'x':np.arange(-10,20+inc,inc)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-bebfcc56eae447e3b385bde99debf309.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-bebfcc56eae447e3b385bde99debf309.vega-embed details,\n",
       "  #altair-viz-bebfcc56eae447e3b385bde99debf309.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-bebfcc56eae447e3b385bde99debf309\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-bebfcc56eae447e3b385bde99debf309\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-bebfcc56eae447e3b385bde99debf309\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"hconcat\": [{\"layer\": [{\"mark\": {\"type\": \"area\", \"clip\": true, \"color\": \"#C84E0099\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-5, 10]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"ycalc\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * param_48)) * exp((-0.5 * (pow((datum.x - param_47),2) / pow(param_48,2)))))\", \"as\": \"ycalc\"}, {\"filter\": \"(datum.x >= param_49)\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#262626\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-5, 10]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"ycalc\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * param_48)) * exp((-0.5 * (pow((datum.x - param_47),2) / pow(param_48,2)))))\", \"as\": \"ycalc\"}]}], \"height\": 150}, {\"mark\": {\"type\": \"bar\", \"color\": \"#C84E00CC\", \"size\": 50}, \"encoding\": {\"y\": {\"aggregate\": \"sum\", \"axis\": {\"title\": \"Area of orange region\"}, \"field\": \"ycalc\", \"scale\": {\"domain\": [0, 10]}, \"type\": \"quantitative\"}}, \"height\": 150, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * param_48)) * exp((-0.5 * (pow((datum.x - param_47),2) / pow(param_48,2)))))\", \"as\": \"ycalc\"}, {\"filter\": \"(datum.x >= param_49)\"}], \"width\": 100}], \"data\": {\"name\": \"data-51ae1ed5cb2212e7b4639c38a9c226e2\"}, \"params\": [{\"name\": \"param_49\", \"bind\": {\"input\": \"range\", \"max\": 10, \"min\": -5, \"name\": \"cutoff:\", \"step\": 0.1}, \"value\": 0}, {\"name\": \"param_48\", \"bind\": {\"input\": \"range\", \"max\": 10, \"min\": 0.1, \"name\": \"width:\", \"step\": 0.1}, \"value\": 1}, {\"name\": \"param_47\", \"bind\": {\"input\": \"range\", \"max\": 10, \"min\": -5, \"name\": \"center:\", \"step\": 0.1}, \"value\": 0}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-51ae1ed5cb2212e7b4639c38a9c226e2\": [{\"x\": -10.0}, {\"x\": -9.9}, {\"x\": -9.8}, {\"x\": -9.700000000000001}, {\"x\": -9.600000000000001}, {\"x\": -9.500000000000002}, {\"x\": -9.400000000000002}, {\"x\": -9.300000000000002}, {\"x\": -9.200000000000003}, {\"x\": -9.100000000000003}, {\"x\": -9.000000000000004}, {\"x\": -8.900000000000004}, {\"x\": -8.800000000000004}, {\"x\": -8.700000000000005}, {\"x\": -8.600000000000005}, {\"x\": -8.500000000000005}, {\"x\": -8.400000000000006}, {\"x\": -8.300000000000006}, {\"x\": -8.200000000000006}, {\"x\": -8.100000000000007}, {\"x\": -8.000000000000007}, {\"x\": -7.9000000000000075}, {\"x\": -7.800000000000008}, {\"x\": -7.700000000000008}, {\"x\": -7.6000000000000085}, {\"x\": -7.500000000000009}, {\"x\": -7.400000000000009}, {\"x\": -7.30000000000001}, {\"x\": -7.20000000000001}, {\"x\": -7.10000000000001}, {\"x\": -7.000000000000011}, {\"x\": -6.900000000000011}, {\"x\": -6.800000000000011}, {\"x\": -6.700000000000012}, {\"x\": -6.600000000000012}, {\"x\": -6.500000000000012}, {\"x\": -6.400000000000013}, {\"x\": -6.300000000000013}, {\"x\": -6.2000000000000135}, {\"x\": -6.100000000000014}, {\"x\": -6.000000000000014}, {\"x\": -5.900000000000015}, {\"x\": -5.800000000000015}, {\"x\": -5.700000000000015}, {\"x\": -5.600000000000016}, {\"x\": -5.500000000000016}, {\"x\": -5.400000000000016}, {\"x\": -5.300000000000017}, {\"x\": -5.200000000000017}, {\"x\": -5.100000000000017}, {\"x\": -5.000000000000018}, {\"x\": -4.900000000000018}, {\"x\": -4.8000000000000185}, {\"x\": -4.700000000000019}, {\"x\": -4.600000000000019}, {\"x\": -4.5000000000000195}, {\"x\": -4.40000000000002}, {\"x\": -4.30000000000002}, {\"x\": -4.200000000000021}, {\"x\": -4.100000000000021}, {\"x\": -4.000000000000021}, {\"x\": -3.9000000000000217}, {\"x\": -3.800000000000022}, {\"x\": -3.7000000000000224}, {\"x\": -3.6000000000000227}, {\"x\": -3.500000000000023}, {\"x\": -3.4000000000000234}, {\"x\": -3.300000000000024}, {\"x\": -3.200000000000024}, {\"x\": -3.1000000000000245}, {\"x\": -3.000000000000025}, {\"x\": -2.9000000000000252}, {\"x\": -2.8000000000000256}, {\"x\": -2.700000000000026}, {\"x\": -2.6000000000000263}, {\"x\": -2.5000000000000266}, {\"x\": -2.400000000000027}, {\"x\": -2.3000000000000274}, {\"x\": -2.2000000000000277}, {\"x\": -2.100000000000028}, {\"x\": -2.0000000000000284}, {\"x\": -1.9000000000000288}, {\"x\": -1.8000000000000291}, {\"x\": -1.7000000000000295}, {\"x\": -1.6000000000000298}, {\"x\": -1.5000000000000302}, {\"x\": -1.4000000000000306}, {\"x\": -1.300000000000031}, {\"x\": -1.2000000000000313}, {\"x\": -1.1000000000000316}, {\"x\": -1.000000000000032}, {\"x\": -0.9000000000000323}, {\"x\": -0.8000000000000327}, {\"x\": -0.700000000000033}, {\"x\": -0.6000000000000334}, {\"x\": -0.5000000000000338}, {\"x\": -0.4000000000000341}, {\"x\": -0.30000000000003446}, {\"x\": -0.20000000000003482}, {\"x\": -0.10000000000003517}, {\"x\": -3.552713678800501e-14}, {\"x\": 0.09999999999996412}, {\"x\": 0.19999999999996376}, {\"x\": 0.2999999999999634}, {\"x\": 0.39999999999996305}, {\"x\": 0.4999999999999627}, {\"x\": 0.5999999999999623}, {\"x\": 0.699999999999962}, {\"x\": 0.7999999999999616}, {\"x\": 0.8999999999999613}, {\"x\": 0.9999999999999609}, {\"x\": 1.0999999999999606}, {\"x\": 1.1999999999999602}, {\"x\": 1.2999999999999599}, {\"x\": 1.3999999999999595}, {\"x\": 1.4999999999999591}, {\"x\": 1.5999999999999588}, {\"x\": 1.6999999999999584}, {\"x\": 1.799999999999958}, {\"x\": 1.8999999999999577}, {\"x\": 1.9999999999999574}, {\"x\": 2.099999999999957}, {\"x\": 2.1999999999999567}, {\"x\": 2.2999999999999563}, {\"x\": 2.399999999999956}, {\"x\": 2.4999999999999556}, {\"x\": 2.5999999999999552}, {\"x\": 2.699999999999955}, {\"x\": 2.7999999999999545}, {\"x\": 2.899999999999954}, {\"x\": 2.999999999999954}, {\"x\": 3.0999999999999535}, {\"x\": 3.199999999999953}, {\"x\": 3.2999999999999527}, {\"x\": 3.3999999999999524}, {\"x\": 3.499999999999952}, {\"x\": 3.5999999999999517}, {\"x\": 3.6999999999999513}, {\"x\": 3.799999999999951}, {\"x\": 3.8999999999999506}, {\"x\": 3.9999999999999503}, {\"x\": 4.09999999999995}, {\"x\": 4.1999999999999496}, {\"x\": 4.299999999999949}, {\"x\": 4.399999999999949}, {\"x\": 4.4999999999999485}, {\"x\": 4.599999999999948}, {\"x\": 4.699999999999948}, {\"x\": 4.799999999999947}, {\"x\": 4.899999999999947}, {\"x\": 4.999999999999947}, {\"x\": 5.099999999999946}, {\"x\": 5.199999999999946}, {\"x\": 5.299999999999946}, {\"x\": 5.399999999999945}, {\"x\": 5.499999999999945}, {\"x\": 5.599999999999945}, {\"x\": 5.699999999999944}, {\"x\": 5.799999999999944}, {\"x\": 5.8999999999999435}, {\"x\": 5.999999999999943}, {\"x\": 6.099999999999945}, {\"x\": 6.1999999999999424}, {\"x\": 6.29999999999994}, {\"x\": 6.399999999999942}, {\"x\": 6.499999999999943}, {\"x\": 6.599999999999941}, {\"x\": 6.699999999999939}, {\"x\": 6.79999999999994}, {\"x\": 6.899999999999942}, {\"x\": 6.99999999999994}, {\"x\": 7.0999999999999375}, {\"x\": 7.199999999999939}, {\"x\": 7.29999999999994}, {\"x\": 7.399999999999938}, {\"x\": 7.499999999999936}, {\"x\": 7.5999999999999375}, {\"x\": 7.699999999999939}, {\"x\": 7.799999999999937}, {\"x\": 7.899999999999935}, {\"x\": 7.999999999999936}, {\"x\": 8.099999999999937}, {\"x\": 8.199999999999935}, {\"x\": 8.299999999999933}, {\"x\": 8.399999999999935}, {\"x\": 8.499999999999936}, {\"x\": 8.599999999999934}, {\"x\": 8.699999999999932}, {\"x\": 8.799999999999933}, {\"x\": 8.899999999999935}, {\"x\": 8.999999999999932}, {\"x\": 9.09999999999993}, {\"x\": 9.199999999999932}, {\"x\": 9.299999999999933}, {\"x\": 9.399999999999931}, {\"x\": 9.499999999999929}, {\"x\": 9.59999999999993}, {\"x\": 9.699999999999932}, {\"x\": 9.79999999999993}, {\"x\": 9.899999999999928}, {\"x\": 9.999999999999929}, {\"x\": 10.09999999999993}, {\"x\": 10.199999999999928}, {\"x\": 10.299999999999926}, {\"x\": 10.399999999999928}, {\"x\": 10.499999999999929}, {\"x\": 10.599999999999927}, {\"x\": 10.699999999999925}, {\"x\": 10.799999999999926}, {\"x\": 10.899999999999928}, {\"x\": 10.999999999999925}, {\"x\": 11.099999999999923}, {\"x\": 11.199999999999925}, {\"x\": 11.299999999999926}, {\"x\": 11.399999999999924}, {\"x\": 11.499999999999922}, {\"x\": 11.599999999999923}, {\"x\": 11.699999999999925}, {\"x\": 11.799999999999923}, {\"x\": 11.89999999999992}, {\"x\": 11.999999999999922}, {\"x\": 12.099999999999923}, {\"x\": 12.199999999999921}, {\"x\": 12.299999999999919}, {\"x\": 12.39999999999992}, {\"x\": 12.499999999999922}, {\"x\": 12.59999999999992}, {\"x\": 12.699999999999918}, {\"x\": 12.799999999999919}, {\"x\": 12.89999999999992}, {\"x\": 12.999999999999918}, {\"x\": 13.099999999999916}, {\"x\": 13.199999999999918}, {\"x\": 13.299999999999919}, {\"x\": 13.399999999999917}, {\"x\": 13.499999999999915}, {\"x\": 13.599999999999916}, {\"x\": 13.699999999999918}, {\"x\": 13.799999999999915}, {\"x\": 13.899999999999913}, {\"x\": 13.999999999999915}, {\"x\": 14.099999999999916}, {\"x\": 14.199999999999914}, {\"x\": 14.299999999999912}, {\"x\": 14.399999999999913}, {\"x\": 14.499999999999915}, {\"x\": 14.599999999999913}, {\"x\": 14.69999999999991}, {\"x\": 14.799999999999912}, {\"x\": 14.899999999999913}, {\"x\": 14.999999999999911}, {\"x\": 15.099999999999909}, {\"x\": 15.19999999999991}, {\"x\": 15.299999999999912}, {\"x\": 15.39999999999991}, {\"x\": 15.499999999999908}, {\"x\": 15.599999999999909}, {\"x\": 15.69999999999991}, {\"x\": 15.799999999999908}, {\"x\": 15.899999999999906}, {\"x\": 15.999999999999908}, {\"x\": 16.09999999999991}, {\"x\": 16.199999999999907}, {\"x\": 16.299999999999905}, {\"x\": 16.399999999999906}, {\"x\": 16.499999999999908}, {\"x\": 16.599999999999905}, {\"x\": 16.699999999999903}, {\"x\": 16.799999999999905}, {\"x\": 16.899999999999906}, {\"x\": 16.999999999999904}, {\"x\": 17.099999999999902}, {\"x\": 17.199999999999903}, {\"x\": 17.299999999999905}, {\"x\": 17.399999999999903}, {\"x\": 17.4999999999999}, {\"x\": 17.599999999999902}, {\"x\": 17.699999999999903}, {\"x\": 17.7999999999999}, {\"x\": 17.8999999999999}, {\"x\": 17.9999999999999}, {\"x\": 18.099999999999902}, {\"x\": 18.1999999999999}, {\"x\": 18.299999999999898}, {\"x\": 18.3999999999999}, {\"x\": 18.4999999999999}, {\"x\": 18.5999999999999}, {\"x\": 18.699999999999896}, {\"x\": 18.799999999999898}, {\"x\": 18.8999999999999}, {\"x\": 18.999999999999897}, {\"x\": 19.099999999999895}, {\"x\": 19.199999999999896}, {\"x\": 19.299999999999898}, {\"x\": 19.399999999999896}, {\"x\": 19.499999999999893}, {\"x\": 19.599999999999895}, {\"x\": 19.699999999999896}, {\"x\": 19.799999999999894}, {\"x\": 19.899999999999892}, {\"x\": 19.999999999999893}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.HConcatChart(...)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center_slider = alt.binding_range(min=-5, max=10, step=inc, name='center:')\n",
    "center_selector = alt.param(bind=center_slider, value=0)\n",
    "\n",
    "width_slider = alt.binding_range(min=inc, max=10, step=inc, name='width:')\n",
    "width_selector = alt.param(bind=width_slider, value=1)\n",
    "\n",
    "cutoff_slider = alt.binding_range(min=-5, max=10, step=inc, name='cutoff:')\n",
    "cutoff_selector = alt.param(bind=cutoff_slider, value=0)\n",
    "\n",
    "base = alt.Chart(df).transform_calculate(\n",
    "    ycalc = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*width_selector))*alt.expr.exp(-0.5*(pow((alt.datum.x - center_selector),2)/pow(width_selector,2)))\n",
    ")\n",
    "\n",
    "gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[-5,10]), title=''),\n",
    "    y = alt.Y('ycalc:Q', title='')\n",
    ")\n",
    "\n",
    "line = gauss_base.mark_line(\n",
    "    color='#262626',\n",
    "    clip=True\n",
    ").add_params(\n",
    "    cutoff_selector, \n",
    "    width_selector,\n",
    "    center_selector\n",
    ")\n",
    "\n",
    "area = gauss_base.mark_area(\n",
    "    color='#C84E0099',\n",
    "    clip=True\n",
    ").transform_filter(\n",
    "    alt.datum.x >= cutoff_selector\n",
    ")\n",
    "\n",
    "bar = base.mark_bar(size=50, color='#C84E00CC').encode(\n",
    "    y = alt.Y('sum(ycalc):Q', \n",
    "              scale=alt.Scale(domain=(0, 10)),\n",
    "              axis = alt.Axis(title='Area of orange region')\n",
    "             )\n",
    ").transform_filter(\n",
    "    alt.datum.x >= cutoff_selector\n",
    ")\n",
    "\n",
    "combo = (area + line).properties(height = 150) | bar.properties(height = 150, width=100)\n",
    "combo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "combo.save('gaussian_cutoff.html')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Treatment vs static Control group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-71f829286f4b4fdeb885ca96b92764c6.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-71f829286f4b4fdeb885ca96b92764c6.vega-embed details,\n",
       "  #altair-viz-71f829286f4b4fdeb885ca96b92764c6.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-71f829286f4b4fdeb885ca96b92764c6\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-71f829286f4b4fdeb885ca96b92764c6\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-71f829286f4b4fdeb885ca96b92764c6\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"hconcat\": [{\"layer\": [{\"mark\": {\"type\": \"area\", \"clip\": true, \"color\": \"#C84E0099\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"c_y\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"filter\": \"(datum.x >= param_51)\"}]}, {\"mark\": {\"type\": \"area\", \"clip\": true, \"color\": \"#33989899\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"filter\": \"(datum.x >= param_51)\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#666666\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"c_y\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#262626\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}]}], \"height\": 200, \"width\": 350}, {\"mark\": {\"type\": \"bar\", \"color\": \"#C84E00AA\", \"size\": 30}, \"encoding\": {\"y\": {\"aggregate\": \"sum\", \"field\": \"c_yn\", \"scale\": {\"domain\": [0, 1]}, \"title\": \"Control area\", \"type\": \"quantitative\"}}, \"height\": 200, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"filter\": \"(datum.x >= param_51)\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#339898BB\", \"size\": 30}, \"encoding\": {\"y\": {\"aggregate\": \"sum\", \"field\": \"t_yn\", \"scale\": {\"domain\": [0, 1]}, \"title\": \"Treatment area\", \"type\": \"quantitative\"}}, \"height\": 200, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"filter\": \"(datum.x >= param_51)\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#993399BB\", \"size\": 30}, \"encoding\": {\"y\": {\"aggregate\": \"sum\", \"field\": \"tc_diff\", \"scale\": {\"domain\": [0, 1]}, \"title\": \"Area difference\", \"type\": \"quantitative\"}}, \"height\": 200, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_50) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"filter\": \"(datum.x >= param_51)\"}, {\"calculate\": \"(datum.t_yn - datum.c_yn)\", \"as\": \"tc_diff\"}], \"width\": 50}], \"data\": {\"name\": \"data-51ae1ed5cb2212e7b4639c38a9c226e2\"}, \"params\": [{\"name\": \"param_51\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": -3, \"name\": \"Responder threshold:\", \"step\": 0.1}, \"value\": 0.5}, {\"name\": \"param_50\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": -3, \"name\": \"Treatment center:\", \"step\": 0.1}, \"value\": 2}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-51ae1ed5cb2212e7b4639c38a9c226e2\": [{\"x\": -10.0}, {\"x\": -9.9}, {\"x\": -9.8}, {\"x\": -9.700000000000001}, {\"x\": -9.600000000000001}, {\"x\": -9.500000000000002}, {\"x\": -9.400000000000002}, {\"x\": -9.300000000000002}, {\"x\": -9.200000000000003}, {\"x\": -9.100000000000003}, {\"x\": -9.000000000000004}, {\"x\": -8.900000000000004}, {\"x\": -8.800000000000004}, {\"x\": -8.700000000000005}, {\"x\": -8.600000000000005}, {\"x\": -8.500000000000005}, {\"x\": -8.400000000000006}, {\"x\": -8.300000000000006}, {\"x\": -8.200000000000006}, {\"x\": -8.100000000000007}, {\"x\": -8.000000000000007}, {\"x\": -7.9000000000000075}, {\"x\": -7.800000000000008}, {\"x\": -7.700000000000008}, {\"x\": -7.6000000000000085}, {\"x\": -7.500000000000009}, {\"x\": -7.400000000000009}, {\"x\": -7.30000000000001}, {\"x\": -7.20000000000001}, {\"x\": -7.10000000000001}, {\"x\": -7.000000000000011}, {\"x\": -6.900000000000011}, {\"x\": -6.800000000000011}, {\"x\": -6.700000000000012}, {\"x\": -6.600000000000012}, {\"x\": -6.500000000000012}, {\"x\": -6.400000000000013}, {\"x\": -6.300000000000013}, {\"x\": -6.2000000000000135}, {\"x\": -6.100000000000014}, {\"x\": -6.000000000000014}, {\"x\": -5.900000000000015}, {\"x\": -5.800000000000015}, {\"x\": -5.700000000000015}, {\"x\": -5.600000000000016}, {\"x\": -5.500000000000016}, {\"x\": -5.400000000000016}, {\"x\": -5.300000000000017}, {\"x\": -5.200000000000017}, {\"x\": -5.100000000000017}, {\"x\": -5.000000000000018}, {\"x\": -4.900000000000018}, {\"x\": -4.8000000000000185}, {\"x\": -4.700000000000019}, {\"x\": -4.600000000000019}, {\"x\": -4.5000000000000195}, {\"x\": -4.40000000000002}, {\"x\": -4.30000000000002}, {\"x\": -4.200000000000021}, {\"x\": -4.100000000000021}, {\"x\": -4.000000000000021}, {\"x\": -3.9000000000000217}, {\"x\": -3.800000000000022}, {\"x\": -3.7000000000000224}, {\"x\": -3.6000000000000227}, {\"x\": -3.500000000000023}, {\"x\": -3.4000000000000234}, {\"x\": -3.300000000000024}, {\"x\": -3.200000000000024}, {\"x\": -3.1000000000000245}, {\"x\": -3.000000000000025}, {\"x\": -2.9000000000000252}, {\"x\": -2.8000000000000256}, {\"x\": -2.700000000000026}, {\"x\": -2.6000000000000263}, {\"x\": -2.5000000000000266}, {\"x\": -2.400000000000027}, {\"x\": -2.3000000000000274}, {\"x\": -2.2000000000000277}, {\"x\": -2.100000000000028}, {\"x\": -2.0000000000000284}, {\"x\": -1.9000000000000288}, {\"x\": -1.8000000000000291}, {\"x\": -1.7000000000000295}, {\"x\": -1.6000000000000298}, {\"x\": -1.5000000000000302}, {\"x\": -1.4000000000000306}, {\"x\": -1.300000000000031}, {\"x\": -1.2000000000000313}, {\"x\": -1.1000000000000316}, {\"x\": -1.000000000000032}, {\"x\": -0.9000000000000323}, {\"x\": -0.8000000000000327}, {\"x\": -0.700000000000033}, {\"x\": -0.6000000000000334}, {\"x\": -0.5000000000000338}, {\"x\": -0.4000000000000341}, {\"x\": -0.30000000000003446}, {\"x\": -0.20000000000003482}, {\"x\": -0.10000000000003517}, {\"x\": -3.552713678800501e-14}, {\"x\": 0.09999999999996412}, {\"x\": 0.19999999999996376}, {\"x\": 0.2999999999999634}, {\"x\": 0.39999999999996305}, {\"x\": 0.4999999999999627}, {\"x\": 0.5999999999999623}, {\"x\": 0.699999999999962}, {\"x\": 0.7999999999999616}, {\"x\": 0.8999999999999613}, {\"x\": 0.9999999999999609}, {\"x\": 1.0999999999999606}, {\"x\": 1.1999999999999602}, {\"x\": 1.2999999999999599}, {\"x\": 1.3999999999999595}, {\"x\": 1.4999999999999591}, {\"x\": 1.5999999999999588}, {\"x\": 1.6999999999999584}, {\"x\": 1.799999999999958}, {\"x\": 1.8999999999999577}, {\"x\": 1.9999999999999574}, {\"x\": 2.099999999999957}, {\"x\": 2.1999999999999567}, {\"x\": 2.2999999999999563}, {\"x\": 2.399999999999956}, {\"x\": 2.4999999999999556}, {\"x\": 2.5999999999999552}, {\"x\": 2.699999999999955}, {\"x\": 2.7999999999999545}, {\"x\": 2.899999999999954}, {\"x\": 2.999999999999954}, {\"x\": 3.0999999999999535}, {\"x\": 3.199999999999953}, {\"x\": 3.2999999999999527}, {\"x\": 3.3999999999999524}, {\"x\": 3.499999999999952}, {\"x\": 3.5999999999999517}, {\"x\": 3.6999999999999513}, {\"x\": 3.799999999999951}, {\"x\": 3.8999999999999506}, {\"x\": 3.9999999999999503}, {\"x\": 4.09999999999995}, {\"x\": 4.1999999999999496}, {\"x\": 4.299999999999949}, {\"x\": 4.399999999999949}, {\"x\": 4.4999999999999485}, {\"x\": 4.599999999999948}, {\"x\": 4.699999999999948}, {\"x\": 4.799999999999947}, {\"x\": 4.899999999999947}, {\"x\": 4.999999999999947}, {\"x\": 5.099999999999946}, {\"x\": 5.199999999999946}, {\"x\": 5.299999999999946}, {\"x\": 5.399999999999945}, {\"x\": 5.499999999999945}, {\"x\": 5.599999999999945}, {\"x\": 5.699999999999944}, {\"x\": 5.799999999999944}, {\"x\": 5.8999999999999435}, {\"x\": 5.999999999999943}, {\"x\": 6.099999999999945}, {\"x\": 6.1999999999999424}, {\"x\": 6.29999999999994}, {\"x\": 6.399999999999942}, {\"x\": 6.499999999999943}, {\"x\": 6.599999999999941}, {\"x\": 6.699999999999939}, {\"x\": 6.79999999999994}, {\"x\": 6.899999999999942}, {\"x\": 6.99999999999994}, {\"x\": 7.0999999999999375}, {\"x\": 7.199999999999939}, {\"x\": 7.29999999999994}, {\"x\": 7.399999999999938}, {\"x\": 7.499999999999936}, {\"x\": 7.5999999999999375}, {\"x\": 7.699999999999939}, {\"x\": 7.799999999999937}, {\"x\": 7.899999999999935}, {\"x\": 7.999999999999936}, {\"x\": 8.099999999999937}, {\"x\": 8.199999999999935}, {\"x\": 8.299999999999933}, {\"x\": 8.399999999999935}, {\"x\": 8.499999999999936}, {\"x\": 8.599999999999934}, {\"x\": 8.699999999999932}, {\"x\": 8.799999999999933}, {\"x\": 8.899999999999935}, {\"x\": 8.999999999999932}, {\"x\": 9.09999999999993}, {\"x\": 9.199999999999932}, {\"x\": 9.299999999999933}, {\"x\": 9.399999999999931}, {\"x\": 9.499999999999929}, {\"x\": 9.59999999999993}, {\"x\": 9.699999999999932}, {\"x\": 9.79999999999993}, {\"x\": 9.899999999999928}, {\"x\": 9.999999999999929}, {\"x\": 10.09999999999993}, {\"x\": 10.199999999999928}, {\"x\": 10.299999999999926}, {\"x\": 10.399999999999928}, {\"x\": 10.499999999999929}, {\"x\": 10.599999999999927}, {\"x\": 10.699999999999925}, {\"x\": 10.799999999999926}, {\"x\": 10.899999999999928}, {\"x\": 10.999999999999925}, {\"x\": 11.099999999999923}, {\"x\": 11.199999999999925}, {\"x\": 11.299999999999926}, {\"x\": 11.399999999999924}, {\"x\": 11.499999999999922}, {\"x\": 11.599999999999923}, {\"x\": 11.699999999999925}, {\"x\": 11.799999999999923}, {\"x\": 11.89999999999992}, {\"x\": 11.999999999999922}, {\"x\": 12.099999999999923}, {\"x\": 12.199999999999921}, {\"x\": 12.299999999999919}, {\"x\": 12.39999999999992}, {\"x\": 12.499999999999922}, {\"x\": 12.59999999999992}, {\"x\": 12.699999999999918}, {\"x\": 12.799999999999919}, {\"x\": 12.89999999999992}, {\"x\": 12.999999999999918}, {\"x\": 13.099999999999916}, {\"x\": 13.199999999999918}, {\"x\": 13.299999999999919}, {\"x\": 13.399999999999917}, {\"x\": 13.499999999999915}, {\"x\": 13.599999999999916}, {\"x\": 13.699999999999918}, {\"x\": 13.799999999999915}, {\"x\": 13.899999999999913}, {\"x\": 13.999999999999915}, {\"x\": 14.099999999999916}, {\"x\": 14.199999999999914}, {\"x\": 14.299999999999912}, {\"x\": 14.399999999999913}, {\"x\": 14.499999999999915}, {\"x\": 14.599999999999913}, {\"x\": 14.69999999999991}, {\"x\": 14.799999999999912}, {\"x\": 14.899999999999913}, {\"x\": 14.999999999999911}, {\"x\": 15.099999999999909}, {\"x\": 15.19999999999991}, {\"x\": 15.299999999999912}, {\"x\": 15.39999999999991}, {\"x\": 15.499999999999908}, {\"x\": 15.599999999999909}, {\"x\": 15.69999999999991}, {\"x\": 15.799999999999908}, {\"x\": 15.899999999999906}, {\"x\": 15.999999999999908}, {\"x\": 16.09999999999991}, {\"x\": 16.199999999999907}, {\"x\": 16.299999999999905}, {\"x\": 16.399999999999906}, {\"x\": 16.499999999999908}, {\"x\": 16.599999999999905}, {\"x\": 16.699999999999903}, {\"x\": 16.799999999999905}, {\"x\": 16.899999999999906}, {\"x\": 16.999999999999904}, {\"x\": 17.099999999999902}, {\"x\": 17.199999999999903}, {\"x\": 17.299999999999905}, {\"x\": 17.399999999999903}, {\"x\": 17.4999999999999}, {\"x\": 17.599999999999902}, {\"x\": 17.699999999999903}, {\"x\": 17.7999999999999}, {\"x\": 17.8999999999999}, {\"x\": 17.9999999999999}, {\"x\": 18.099999999999902}, {\"x\": 18.1999999999999}, {\"x\": 18.299999999999898}, {\"x\": 18.3999999999999}, {\"x\": 18.4999999999999}, {\"x\": 18.5999999999999}, {\"x\": 18.699999999999896}, {\"x\": 18.799999999999898}, {\"x\": 18.8999999999999}, {\"x\": 18.999999999999897}, {\"x\": 19.099999999999895}, {\"x\": 19.199999999999896}, {\"x\": 19.299999999999898}, {\"x\": 19.399999999999896}, {\"x\": 19.499999999999893}, {\"x\": 19.599999999999895}, {\"x\": 19.699999999999896}, {\"x\": 19.799999999999894}, {\"x\": 19.899999999999892}, {\"x\": 19.999999999999893}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.HConcatChart(...)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmin = -3\n",
    "xmax = 5\n",
    "\n",
    "c_width = 1.0\n",
    "t_width = 1.0\n",
    "\n",
    "t_center_slider = alt.binding_range(min=xmin, max=xmax, step=inc, name='Treatment center:')\n",
    "t_center_selector = alt.param(bind=t_center_slider, value=2)\n",
    "\n",
    "thresh_slider = alt.binding_range(min=xmin, max=xmax, step=inc, name='Responder threshold:')\n",
    "thresh_selector = alt.param(bind=thresh_slider, value=0.5)\n",
    "\n",
    "base = alt.Chart(df).transform_calculate(\n",
    "    c_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*c_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - 0.0)/c_width,2))),\n",
    "    t_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*t_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - t_center_selector)/t_width,2))),\n",
    "    c_yn = inc*alt.datum.c_y,\n",
    "    t_yn = inc*alt.datum.t_y\n",
    ")\n",
    "\n",
    "c_gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[xmin,xmax]), title=''),\n",
    "    y = alt.Y('c_y:Q', title='')\n",
    ")\n",
    "c_line = c_gauss_base.mark_line(color='#666666',clip=True).add_params(\n",
    "    thresh_selector, \n",
    "    t_center_selector\n",
    ")\n",
    "c_area = c_gauss_base.mark_area(color='#C84E0099',clip=True).transform_filter( alt.datum.x >= thresh_selector )\n",
    "\n",
    "t_gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[xmin,xmax]), title=''),\n",
    "    y = alt.Y('t_y:Q', scale=alt.Scale(domain=[0,0.45]), title='')\n",
    ")\n",
    "t_line = t_gauss_base.mark_line(color='#262626',clip=True)\n",
    "t_area = t_gauss_base.mark_area(color='#33989899',clip=True).transform_filter( alt.datum.x >= thresh_selector )\n",
    "\n",
    "c_bar = base.mark_bar(size=30, color='#C84E00AA').encode(\n",
    "    y = alt.Y('sum(c_yn):Q', scale=alt.Scale(domain=(0, 1)), title='Control area')\n",
    ").transform_filter( alt.datum.x >= thresh_selector )\n",
    "t_bar = base.mark_bar(size=30, color='#339898BB').encode(\n",
    "    y = alt.Y('sum(t_yn):Q', scale=alt.Scale(domain=(0, 1)), title='Treatment area')\n",
    ").transform_filter( alt.datum.x >= thresh_selector )\n",
    "diff_bar = base.mark_bar(size=30, color='#993399BB').encode(\n",
    "    y = alt.Y('sum(tc_diff):Q', scale=alt.Scale(domain=(0, 1)), title='Area difference')\n",
    ").transform_filter( alt.datum.x >= thresh_selector ).transform_calculate(\n",
    "    tc_diff = alt.datum.t_yn - alt.datum.c_yn\n",
    ")\n",
    "\n",
    "diff_combo = (c_area + t_area + c_line + t_line).properties(height = 200, width=350) | \\\n",
    "        c_bar.properties(height = 200, width=50) | \\\n",
    "        t_bar.properties(height = 200, width=50) | \\\n",
    "        diff_bar.properties(height = 200, width=50)\n",
    "\n",
    "diff_combo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_combo.save('responder_threshold.html')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fancier version with people who got worse\n",
    "\n",
    "<img src=\"images/FancierVersion.png\" width=500 />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### If conditional to set values to zero in threshold range\n",
    "\n",
    "**NOTE: Realize now that need to incorporate `inc` in normalization of integration**\n",
    "\n",
    "Evidently not all Vega expressions can be created with alt.expr(), so sometimes you need to use a Vega expression string:\n",
    "https://github.com/altair-viz/altair/issues/2194\n",
    "\n",
    "\"Yep, alt.expr is a convenience wrapper for creating simple expressions, but cannot represent all possible vega expression strings. In the cases that it doesn't cover, the recommended approach is to write the vega expression string directlyl\" -JVDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-06bc9e953e8444cda061a3467206479f.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-06bc9e953e8444cda061a3467206479f.vega-embed details,\n",
       "  #altair-viz-06bc9e953e8444cda061a3467206479f.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-06bc9e953e8444cda061a3467206479f\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-06bc9e953e8444cda061a3467206479f\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-06bc9e953e8444cda061a3467206479f\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"layer\": [{\"mark\": {\"type\": \"area\", \"clip\": true, \"color\": \"#33989899\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y2\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_69) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"inrange(datum.x,[-thresh_sel,thresh_sel]) ? 0 :datum.t_y\", \"as\": \"t_y2\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#262626\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_69) / 1.0),2))))\", \"as\": \"t_y\"}]}], \"data\": {\"name\": \"data-054233818168e3a8a734619df8700ec9\"}, \"height\": 200, \"params\": [{\"name\": \"thresh_sel\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": 0, \"name\": \"Responder threshold:\", \"step\": 0.01}, \"value\": 0.5}, {\"name\": \"param_69\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": -3, \"name\": \"Treatment center:\", \"step\": 0.01}, \"value\": 1.5}], \"width\": 350, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-054233818168e3a8a734619df8700ec9\": [{\"x\": -10.0}, {\"x\": -9.99}, {\"x\": -9.98}, {\"x\": -9.97}, {\"x\": -9.96}, {\"x\": -9.950000000000001}, {\"x\": -9.940000000000001}, {\"x\": -9.930000000000001}, {\"x\": -9.920000000000002}, {\"x\": -9.910000000000002}, {\"x\": -9.900000000000002}, {\"x\": -9.890000000000002}, {\"x\": -9.880000000000003}, {\"x\": -9.870000000000003}, {\"x\": -9.860000000000003}, {\"x\": -9.850000000000003}, {\"x\": -9.840000000000003}, {\"x\": -9.830000000000004}, {\"x\": -9.820000000000004}, {\"x\": -9.810000000000004}, {\"x\": -9.800000000000004}, {\"x\": -9.790000000000004}, {\"x\": -9.780000000000005}, {\"x\": -9.770000000000005}, {\"x\": -9.760000000000005}, {\"x\": -9.750000000000005}, {\"x\": -9.740000000000006}, {\"x\": -9.730000000000006}, {\"x\": -9.720000000000006}, {\"x\": -9.710000000000006}, {\"x\": -9.700000000000006}, {\"x\": -9.690000000000007}, {\"x\": -9.680000000000007}, {\"x\": -9.670000000000007}, {\"x\": -9.660000000000007}, {\"x\": -9.650000000000007}, {\"x\": -9.640000000000008}, {\"x\": -9.630000000000008}, {\"x\": -9.620000000000008}, {\"x\": -9.610000000000008}, {\"x\": -9.600000000000009}, {\"x\": -9.590000000000009}, {\"x\": -9.580000000000009}, {\"x\": -9.57000000000001}, {\"x\": -9.56000000000001}, {\"x\": -9.55000000000001}, {\"x\": -9.54000000000001}, {\"x\": -9.53000000000001}, {\"x\": -9.52000000000001}, {\"x\": -9.51000000000001}, {\"x\": -9.50000000000001}, {\"x\": -9.49000000000001}, {\"x\": -9.480000000000011}, {\"x\": -9.470000000000011}, {\"x\": -9.460000000000012}, {\"x\": -9.450000000000012}, {\"x\": -9.440000000000012}, {\"x\": -9.430000000000012}, {\"x\": -9.420000000000012}, {\"x\": -9.410000000000013}, {\"x\": -9.400000000000013}, {\"x\": -9.390000000000013}, {\"x\": -9.380000000000013}, {\"x\": -9.370000000000013}, {\"x\": -9.360000000000014}, {\"x\": -9.350000000000014}, {\"x\": -9.340000000000014}, {\"x\": -9.330000000000014}, {\"x\": -9.320000000000014}, {\"x\": -9.310000000000015}, {\"x\": -9.300000000000015}, {\"x\": -9.290000000000015}, {\"x\": -9.280000000000015}, {\"x\": -9.270000000000016}, {\"x\": -9.260000000000016}, {\"x\": -9.250000000000016}, {\"x\": -9.240000000000016}, {\"x\": -9.230000000000016}, {\"x\": -9.220000000000017}, {\"x\": -9.210000000000017}, {\"x\": -9.200000000000017}, {\"x\": -9.190000000000017}, {\"x\": -9.180000000000017}, {\"x\": -9.170000000000018}, {\"x\": -9.160000000000018}, {\"x\": -9.150000000000018}, {\"x\": -9.140000000000018}, {\"x\": -9.130000000000019}, {\"x\": -9.120000000000019}, {\"x\": -9.110000000000019}, {\"x\": -9.10000000000002}, {\"x\": -9.09000000000002}, {\"x\": -9.08000000000002}, {\"x\": -9.07000000000002}, {\"x\": -9.06000000000002}, {\"x\": -9.05000000000002}, {\"x\": -9.04000000000002}, {\"x\": -9.03000000000002}, {\"x\": -9.020000000000021}, {\"x\": -9.010000000000021}, {\"x\": -9.000000000000021}, {\"x\": -8.990000000000022}, {\"x\": -8.980000000000022}, {\"x\": -8.970000000000022}, {\"x\": -8.960000000000022}, {\"x\": -8.950000000000022}, {\"x\": -8.940000000000023}, {\"x\": -8.930000000000023}, {\"x\": -8.920000000000023}, {\"x\": -8.910000000000023}, {\"x\": -8.900000000000023}, {\"x\": -8.890000000000024}, {\"x\": -8.880000000000024}, {\"x\": -8.870000000000024}, {\"x\": -8.860000000000024}, {\"x\": -8.850000000000025}, {\"x\": -8.840000000000025}, {\"x\": -8.830000000000025}, {\"x\": -8.820000000000025}, {\"x\": -8.810000000000025}, {\"x\": -8.800000000000026}, {\"x\": -8.790000000000026}, {\"x\": -8.780000000000026}, {\"x\": -8.770000000000026}, {\"x\": -8.760000000000026}, {\"x\": -8.750000000000027}, {\"x\": -8.740000000000027}, {\"x\": -8.730000000000027}, {\"x\": -8.720000000000027}, {\"x\": -8.710000000000027}, {\"x\": -8.700000000000028}, {\"x\": -8.690000000000028}, {\"x\": -8.680000000000028}, {\"x\": -8.670000000000028}, {\"x\": -8.660000000000029}, {\"x\": -8.650000000000029}, {\"x\": -8.640000000000029}, {\"x\": -8.63000000000003}, {\"x\": -8.62000000000003}, {\"x\": -8.61000000000003}, {\"x\": -8.60000000000003}, {\"x\": -8.59000000000003}, {\"x\": -8.58000000000003}, {\"x\": -8.57000000000003}, {\"x\": -8.56000000000003}, {\"x\": -8.550000000000031}, {\"x\": -8.540000000000031}, {\"x\": -8.530000000000031}, {\"x\": -8.520000000000032}, {\"x\": -8.510000000000032}, {\"x\": -8.500000000000032}, {\"x\": -8.490000000000032}, {\"x\": -8.480000000000032}, {\"x\": -8.470000000000033}, {\"x\": -8.460000000000033}, {\"x\": -8.450000000000033}, {\"x\": -8.440000000000033}, {\"x\": -8.430000000000033}, {\"x\": -8.420000000000034}, {\"x\": -8.410000000000034}, {\"x\": -8.400000000000034}, {\"x\": -8.390000000000034}, {\"x\": -8.380000000000035}, {\"x\": -8.370000000000035}, {\"x\": -8.360000000000035}, {\"x\": -8.350000000000035}, {\"x\": -8.340000000000035}, {\"x\": -8.330000000000036}, {\"x\": -8.320000000000036}, {\"x\": -8.310000000000036}, {\"x\": -8.300000000000036}, {\"x\": -8.290000000000036}, {\"x\": -8.280000000000037}, {\"x\": -8.270000000000037}, {\"x\": -8.260000000000037}, {\"x\": -8.250000000000037}, {\"x\": -8.240000000000038}, {\"x\": -8.230000000000038}, {\"x\": -8.220000000000038}, {\"x\": -8.210000000000038}, {\"x\": -8.200000000000038}, {\"x\": -8.190000000000039}, {\"x\": -8.180000000000039}, {\"x\": -8.170000000000039}, {\"x\": -8.16000000000004}, {\"x\": -8.15000000000004}, {\"x\": -8.14000000000004}, {\"x\": -8.13000000000004}, {\"x\": -8.12000000000004}, {\"x\": -8.11000000000004}, {\"x\": -8.10000000000004}, {\"x\": -8.09000000000004}, {\"x\": -8.080000000000041}, {\"x\": -8.070000000000041}, {\"x\": -8.060000000000041}, {\"x\": -8.050000000000042}, {\"x\": -8.040000000000042}, {\"x\": -8.030000000000042}, {\"x\": -8.020000000000042}, {\"x\": -8.010000000000042}, {\"x\": -8.000000000000043}, {\"x\": -7.990000000000043}, {\"x\": -7.980000000000043}, {\"x\": -7.970000000000043}, {\"x\": -7.9600000000000435}, {\"x\": -7.950000000000044}, {\"x\": -7.940000000000044}, {\"x\": -7.930000000000044}, {\"x\": -7.920000000000044}, {\"x\": -7.9100000000000446}, {\"x\": -7.900000000000045}, {\"x\": -7.890000000000045}, {\"x\": -7.880000000000045}, {\"x\": -7.870000000000045}, {\"x\": -7.860000000000046}, {\"x\": -7.850000000000046}, {\"x\": -7.840000000000046}, {\"x\": -7.830000000000046}, {\"x\": -7.8200000000000465}, {\"x\": -7.810000000000047}, {\"x\": -7.800000000000047}, {\"x\": -7.790000000000047}, {\"x\": -7.780000000000047}, {\"x\": -7.7700000000000475}, {\"x\": -7.760000000000048}, {\"x\": -7.750000000000048}, {\"x\": -7.740000000000048}, {\"x\": -7.730000000000048}, {\"x\": -7.720000000000049}, {\"x\": -7.710000000000049}, {\"x\": -7.700000000000049}, {\"x\": -7.690000000000049}, {\"x\": -7.6800000000000495}, {\"x\": -7.67000000000005}, {\"x\": -7.66000000000005}, {\"x\": -7.65000000000005}, {\"x\": -7.64000000000005}, {\"x\": -7.6300000000000505}, {\"x\": -7.620000000000051}, {\"x\": -7.610000000000051}, {\"x\": -7.600000000000051}, {\"x\": -7.590000000000051}, {\"x\": -7.580000000000052}, {\"x\": -7.570000000000052}, {\"x\": -7.560000000000052}, {\"x\": -7.550000000000052}, {\"x\": -7.540000000000052}, {\"x\": -7.530000000000053}, {\"x\": -7.520000000000053}, {\"x\": -7.510000000000053}, {\"x\": -7.500000000000053}, {\"x\": -7.4900000000000535}, {\"x\": -7.480000000000054}, {\"x\": -7.470000000000054}, {\"x\": -7.460000000000054}, {\"x\": -7.450000000000054}, {\"x\": -7.440000000000055}, {\"x\": -7.430000000000055}, {\"x\": -7.420000000000055}, {\"x\": -7.410000000000055}, {\"x\": -7.400000000000055}, {\"x\": -7.390000000000056}, {\"x\": -7.380000000000056}, {\"x\": -7.370000000000056}, {\"x\": -7.360000000000056}, {\"x\": -7.3500000000000565}, {\"x\": -7.340000000000057}, {\"x\": -7.330000000000057}, {\"x\": -7.320000000000057}, {\"x\": -7.310000000000057}, {\"x\": -7.3000000000000576}, {\"x\": -7.290000000000058}, {\"x\": -7.280000000000058}, {\"x\": -7.270000000000058}, {\"x\": -7.260000000000058}, {\"x\": -7.250000000000059}, {\"x\": -7.240000000000059}, {\"x\": -7.230000000000059}, {\"x\": -7.220000000000059}, {\"x\": -7.2100000000000595}, {\"x\": -7.20000000000006}, {\"x\": -7.19000000000006}, {\"x\": -7.18000000000006}, {\"x\": -7.17000000000006}, {\"x\": -7.1600000000000605}, {\"x\": -7.150000000000061}, {\"x\": -7.140000000000061}, {\"x\": -7.130000000000061}, {\"x\": -7.120000000000061}, {\"x\": -7.110000000000062}, {\"x\": -7.100000000000062}, {\"x\": -7.090000000000062}, {\"x\": -7.080000000000062}, {\"x\": -7.0700000000000625}, {\"x\": -7.060000000000063}, {\"x\": -7.050000000000063}, {\"x\": -7.040000000000063}, {\"x\": -7.030000000000063}, {\"x\": -7.0200000000000635}, {\"x\": -7.010000000000064}, {\"x\": -7.000000000000064}, {\"x\": -6.990000000000064}, {\"x\": -6.980000000000064}, {\"x\": -6.970000000000065}, {\"x\": -6.960000000000065}, {\"x\": -6.950000000000065}, {\"x\": -6.940000000000065}, {\"x\": -6.930000000000065}, {\"x\": -6.920000000000066}, {\"x\": -6.910000000000066}, {\"x\": -6.900000000000066}, {\"x\": -6.890000000000066}, {\"x\": -6.8800000000000665}, {\"x\": -6.870000000000067}, {\"x\": -6.860000000000067}, {\"x\": -6.850000000000067}, {\"x\": -6.840000000000067}, {\"x\": -6.830000000000068}, {\"x\": -6.820000000000068}, {\"x\": -6.810000000000068}, {\"x\": -6.800000000000068}, {\"x\": -6.790000000000068}, {\"x\": -6.780000000000069}, {\"x\": -6.770000000000069}, {\"x\": -6.760000000000069}, {\"x\": -6.750000000000069}, {\"x\": -6.7400000000000695}, {\"x\": -6.73000000000007}, {\"x\": -6.72000000000007}, {\"x\": -6.71000000000007}, {\"x\": -6.70000000000007}, {\"x\": -6.690000000000071}, {\"x\": -6.680000000000071}, {\"x\": -6.670000000000071}, {\"x\": -6.660000000000071}, {\"x\": -6.650000000000071}, {\"x\": -6.640000000000072}, {\"x\": -6.630000000000072}, {\"x\": -6.620000000000072}, {\"x\": -6.610000000000072}, {\"x\": -6.6000000000000725}, {\"x\": -6.590000000000073}, {\"x\": -6.580000000000073}, {\"x\": -6.570000000000073}, {\"x\": -6.560000000000073}, {\"x\": -6.5500000000000735}, {\"x\": -6.540000000000074}, {\"x\": -6.530000000000074}, {\"x\": -6.520000000000074}, {\"x\": -6.510000000000074}, {\"x\": -6.500000000000075}, {\"x\": -6.490000000000075}, {\"x\": -6.480000000000075}, {\"x\": -6.470000000000075}, {\"x\": -6.4600000000000755}, {\"x\": -6.450000000000076}, {\"x\": -6.440000000000076}, {\"x\": -6.430000000000076}, {\"x\": -6.420000000000076}, {\"x\": -6.4100000000000765}, {\"x\": -6.400000000000077}, {\"x\": -6.390000000000077}, {\"x\": -6.380000000000077}, {\"x\": -6.370000000000077}, {\"x\": -6.360000000000078}, {\"x\": -6.350000000000078}, {\"x\": -6.340000000000078}, {\"x\": -6.330000000000078}, {\"x\": -6.320000000000078}, {\"x\": -6.310000000000079}, {\"x\": -6.300000000000079}, {\"x\": -6.290000000000079}, {\"x\": -6.280000000000079}, {\"x\": -6.2700000000000795}, {\"x\": -6.26000000000008}, {\"x\": -6.25000000000008}, {\"x\": -6.24000000000008}, {\"x\": -6.23000000000008}, {\"x\": -6.220000000000081}, {\"x\": -6.210000000000081}, {\"x\": -6.200000000000081}, {\"x\": -6.190000000000081}, {\"x\": -6.180000000000081}, {\"x\": -6.170000000000082}, {\"x\": -6.160000000000082}, {\"x\": -6.150000000000082}, {\"x\": -6.140000000000082}, {\"x\": -6.1300000000000825}, {\"x\": -6.120000000000083}, {\"x\": -6.110000000000083}, {\"x\": -6.100000000000083}, {\"x\": -6.090000000000083}, {\"x\": -6.080000000000084}, {\"x\": -6.070000000000084}, {\"x\": -6.060000000000084}, {\"x\": -6.050000000000084}, {\"x\": -6.040000000000084}, {\"x\": -6.030000000000085}, {\"x\": -6.020000000000085}, {\"x\": -6.010000000000085}, {\"x\": -6.000000000000085}, {\"x\": -5.9900000000000855}, {\"x\": -5.980000000000086}, {\"x\": -5.970000000000086}, {\"x\": -5.960000000000086}, {\"x\": -5.950000000000086}, {\"x\": -5.9400000000000865}, {\"x\": -5.930000000000087}, {\"x\": -5.920000000000087}, {\"x\": -5.910000000000087}, {\"x\": -5.900000000000087}, {\"x\": -5.890000000000088}, {\"x\": -5.880000000000088}, {\"x\": -5.870000000000088}, {\"x\": -5.860000000000088}, {\"x\": -5.8500000000000885}, {\"x\": -5.840000000000089}, {\"x\": -5.830000000000089}, {\"x\": -5.820000000000089}, {\"x\": -5.810000000000089}, {\"x\": -5.8000000000000895}, {\"x\": -5.79000000000009}, {\"x\": -5.78000000000009}, {\"x\": -5.77000000000009}, {\"x\": -5.76000000000009}, {\"x\": -5.750000000000091}, {\"x\": -5.740000000000091}, {\"x\": -5.730000000000091}, {\"x\": -5.720000000000091}, {\"x\": -5.7100000000000914}, {\"x\": -5.700000000000092}, {\"x\": -5.690000000000092}, {\"x\": -5.680000000000092}, {\"x\": -5.670000000000092}, {\"x\": -5.6600000000000925}, {\"x\": -5.650000000000093}, {\"x\": -5.640000000000093}, {\"x\": -5.630000000000093}, {\"x\": -5.620000000000093}, {\"x\": -5.610000000000094}, {\"x\": -5.600000000000094}, {\"x\": -5.590000000000094}, {\"x\": -5.580000000000094}, {\"x\": -5.570000000000094}, {\"x\": -5.560000000000095}, {\"x\": -5.550000000000095}, {\"x\": -5.540000000000095}, {\"x\": -5.530000000000095}, {\"x\": -5.5200000000000955}, {\"x\": -5.510000000000096}, {\"x\": -5.500000000000096}, {\"x\": -5.490000000000096}, {\"x\": -5.480000000000096}, {\"x\": -5.470000000000097}, {\"x\": -5.460000000000097}, {\"x\": -5.450000000000097}, {\"x\": -5.440000000000097}, {\"x\": -5.430000000000097}, {\"x\": -5.420000000000098}, {\"x\": -5.410000000000098}, {\"x\": -5.400000000000098}, {\"x\": -5.390000000000098}, {\"x\": -5.3800000000000985}, {\"x\": -5.370000000000099}, {\"x\": -5.360000000000099}, {\"x\": -5.350000000000099}, {\"x\": -5.340000000000099}, {\"x\": -5.3300000000000995}, {\"x\": -5.3200000000001}, {\"x\": -5.3100000000001}, {\"x\": -5.3000000000001}, {\"x\": -5.2900000000001}, {\"x\": -5.280000000000101}, {\"x\": -5.270000000000101}, {\"x\": -5.260000000000101}, {\"x\": -5.250000000000101}, {\"x\": -5.2400000000001015}, {\"x\": -5.230000000000102}, {\"x\": -5.220000000000102}, {\"x\": -5.210000000000102}, {\"x\": -5.200000000000102}, {\"x\": -5.1900000000001025}, {\"x\": -5.180000000000103}, {\"x\": -5.170000000000103}, {\"x\": -5.160000000000103}, {\"x\": -5.150000000000103}, {\"x\": -5.140000000000104}, {\"x\": -5.130000000000104}, {\"x\": -5.120000000000104}, {\"x\": -5.110000000000104}, {\"x\": -5.1000000000001044}, {\"x\": -5.090000000000105}, {\"x\": -5.080000000000105}, {\"x\": -5.070000000000105}, {\"x\": -5.060000000000105}, {\"x\": -5.0500000000001055}, {\"x\": -5.040000000000106}, {\"x\": -5.030000000000106}, {\"x\": -5.020000000000106}, {\"x\": -5.010000000000106}, {\"x\": -5.000000000000107}, {\"x\": -4.990000000000107}, {\"x\": -4.980000000000107}, {\"x\": -4.970000000000107}, {\"x\": -4.960000000000107}, {\"x\": -4.950000000000108}, {\"x\": -4.940000000000108}, {\"x\": -4.930000000000108}, {\"x\": -4.920000000000108}, {\"x\": -4.9100000000001085}, {\"x\": -4.900000000000109}, {\"x\": -4.890000000000109}, {\"x\": -4.880000000000109}, {\"x\": -4.870000000000109}, {\"x\": -4.86000000000011}, {\"x\": -4.85000000000011}, {\"x\": -4.84000000000011}, {\"x\": -4.83000000000011}, {\"x\": -4.82000000000011}, {\"x\": -4.810000000000111}, {\"x\": -4.800000000000111}, {\"x\": -4.790000000000111}, {\"x\": -4.780000000000111}, {\"x\": -4.7700000000001115}, {\"x\": -4.760000000000112}, {\"x\": -4.750000000000112}, {\"x\": -4.740000000000112}, {\"x\": -4.730000000000112}, {\"x\": -4.7200000000001125}, {\"x\": -4.710000000000113}, {\"x\": -4.700000000000113}, {\"x\": -4.690000000000113}, {\"x\": -4.680000000000113}, {\"x\": -4.670000000000114}, {\"x\": -4.660000000000114}, {\"x\": -4.650000000000114}, {\"x\": -4.640000000000114}, {\"x\": -4.6300000000001145}, {\"x\": -4.620000000000115}, {\"x\": -4.610000000000115}, {\"x\": -4.600000000000115}, {\"x\": -4.590000000000115}, {\"x\": -4.5800000000001155}, {\"x\": -4.570000000000116}, {\"x\": -4.560000000000116}, {\"x\": -4.550000000000116}, {\"x\": -4.540000000000116}, {\"x\": -4.530000000000117}, {\"x\": -4.520000000000117}, {\"x\": -4.510000000000117}, {\"x\": -4.500000000000117}, {\"x\": -4.4900000000001175}, {\"x\": -4.480000000000118}, {\"x\": -4.470000000000118}, {\"x\": -4.460000000000118}, {\"x\": -4.450000000000118}, {\"x\": -4.4400000000001185}, {\"x\": -4.430000000000119}, {\"x\": -4.420000000000119}, {\"x\": -4.410000000000119}, {\"x\": -4.400000000000119}, {\"x\": -4.39000000000012}, {\"x\": -4.38000000000012}, {\"x\": -4.37000000000012}, {\"x\": -4.36000000000012}, {\"x\": -4.35000000000012}, {\"x\": -4.340000000000121}, {\"x\": -4.330000000000121}, {\"x\": -4.320000000000121}, {\"x\": -4.310000000000121}, {\"x\": -4.3000000000001215}, {\"x\": -4.290000000000122}, {\"x\": -4.280000000000122}, {\"x\": -4.270000000000122}, {\"x\": -4.260000000000122}, {\"x\": -4.250000000000123}, {\"x\": -4.240000000000123}, {\"x\": -4.230000000000123}, {\"x\": -4.220000000000123}, {\"x\": -4.210000000000123}, {\"x\": -4.200000000000124}, {\"x\": -4.190000000000124}, {\"x\": -4.180000000000124}, {\"x\": -4.170000000000124}, {\"x\": -4.1600000000001245}, {\"x\": -4.150000000000125}, {\"x\": -4.140000000000125}, {\"x\": -4.130000000000125}, {\"x\": -4.120000000000125}, {\"x\": -4.1100000000001256}, {\"x\": -4.100000000000126}, {\"x\": -4.090000000000126}, {\"x\": -4.080000000000126}, {\"x\": -4.070000000000126}, {\"x\": -4.060000000000127}, {\"x\": -4.050000000000127}, {\"x\": -4.040000000000127}, {\"x\": -4.030000000000127}, {\"x\": -4.0200000000001275}, {\"x\": -4.010000000000128}, {\"x\": -4.000000000000128}, {\"x\": -3.990000000000128}, {\"x\": -3.9800000000001283}, {\"x\": -3.9700000000001285}, {\"x\": -3.9600000000001288}, {\"x\": -3.950000000000129}, {\"x\": -3.940000000000129}, {\"x\": -3.9300000000001294}, {\"x\": -3.9200000000001296}, {\"x\": -3.91000000000013}, {\"x\": -3.90000000000013}, {\"x\": -3.8900000000001302}, {\"x\": -3.8800000000001305}, {\"x\": -3.8700000000001307}, {\"x\": -3.860000000000131}, {\"x\": -3.850000000000131}, {\"x\": -3.8400000000001313}, {\"x\": -3.8300000000001315}, {\"x\": -3.8200000000001317}, {\"x\": -3.810000000000132}, {\"x\": -3.800000000000132}, {\"x\": -3.7900000000001324}, {\"x\": -3.7800000000001326}, {\"x\": -3.770000000000133}, {\"x\": -3.760000000000133}, {\"x\": -3.7500000000001332}, {\"x\": -3.7400000000001334}, {\"x\": -3.7300000000001337}, {\"x\": -3.720000000000134}, {\"x\": -3.710000000000134}, {\"x\": -3.7000000000001343}, {\"x\": -3.6900000000001345}, {\"x\": -3.6800000000001347}, {\"x\": -3.670000000000135}, {\"x\": -3.660000000000135}, {\"x\": -3.6500000000001354}, {\"x\": -3.6400000000001356}, {\"x\": -3.630000000000136}, {\"x\": -3.620000000000136}, {\"x\": -3.610000000000136}, {\"x\": -3.6000000000001364}, {\"x\": -3.5900000000001366}, {\"x\": -3.580000000000137}, {\"x\": -3.570000000000137}, {\"x\": -3.5600000000001373}, {\"x\": -3.5500000000001375}, {\"x\": -3.5400000000001377}, {\"x\": -3.530000000000138}, {\"x\": -3.520000000000138}, {\"x\": -3.5100000000001383}, {\"x\": -3.5000000000001386}, {\"x\": -3.4900000000001388}, {\"x\": -3.480000000000139}, {\"x\": -3.470000000000139}, {\"x\": -3.4600000000001394}, {\"x\": -3.4500000000001396}, {\"x\": -3.44000000000014}, {\"x\": -3.43000000000014}, {\"x\": -3.4200000000001403}, {\"x\": -3.4100000000001405}, {\"x\": -3.4000000000001407}, {\"x\": -3.390000000000141}, {\"x\": -3.380000000000141}, {\"x\": -3.3700000000001413}, {\"x\": -3.3600000000001415}, {\"x\": -3.3500000000001418}, {\"x\": -3.340000000000142}, {\"x\": -3.330000000000142}, {\"x\": -3.3200000000001424}, {\"x\": -3.3100000000001426}, {\"x\": -3.300000000000143}, {\"x\": -3.290000000000143}, {\"x\": -3.2800000000001432}, {\"x\": -3.2700000000001435}, {\"x\": -3.2600000000001437}, {\"x\": -3.250000000000144}, {\"x\": -3.240000000000144}, {\"x\": -3.2300000000001443}, {\"x\": -3.2200000000001445}, {\"x\": -3.2100000000001447}, {\"x\": -3.200000000000145}, {\"x\": -3.190000000000145}, {\"x\": -3.1800000000001454}, {\"x\": -3.1700000000001456}, {\"x\": -3.160000000000146}, {\"x\": -3.150000000000146}, {\"x\": -3.1400000000001462}, {\"x\": -3.1300000000001464}, {\"x\": -3.1200000000001467}, {\"x\": -3.110000000000147}, {\"x\": -3.100000000000147}, {\"x\": -3.0900000000001473}, {\"x\": -3.0800000000001475}, {\"x\": -3.0700000000001477}, {\"x\": -3.060000000000148}, {\"x\": -3.050000000000148}, {\"x\": -3.0400000000001484}, {\"x\": -3.0300000000001486}, {\"x\": -3.020000000000149}, {\"x\": -3.010000000000149}, {\"x\": -3.000000000000149}, {\"x\": -2.9900000000001494}, {\"x\": -2.9800000000001496}, {\"x\": -2.97000000000015}, {\"x\": -2.96000000000015}, {\"x\": -2.9500000000001503}, {\"x\": -2.9400000000001505}, {\"x\": -2.9300000000001507}, {\"x\": -2.920000000000151}, {\"x\": -2.910000000000151}, {\"x\": -2.9000000000001513}, {\"x\": -2.8900000000001516}, {\"x\": -2.8800000000001518}, {\"x\": -2.870000000000152}, {\"x\": -2.860000000000152}, {\"x\": -2.8500000000001524}, {\"x\": -2.8400000000001526}, {\"x\": -2.830000000000153}, {\"x\": -2.820000000000153}, {\"x\": -2.8100000000001533}, {\"x\": -2.8000000000001535}, {\"x\": -2.7900000000001537}, {\"x\": -2.780000000000154}, {\"x\": -2.770000000000154}, {\"x\": -2.7600000000001543}, {\"x\": -2.7500000000001545}, {\"x\": -2.7400000000001548}, {\"x\": -2.730000000000155}, {\"x\": -2.720000000000155}, {\"x\": -2.7100000000001554}, {\"x\": -2.7000000000001556}, {\"x\": -2.690000000000156}, {\"x\": -2.680000000000156}, {\"x\": -2.6700000000001562}, {\"x\": -2.6600000000001565}, {\"x\": -2.6500000000001567}, {\"x\": -2.640000000000157}, {\"x\": -2.630000000000157}, {\"x\": -2.6200000000001573}, {\"x\": -2.6100000000001575}, {\"x\": -2.6000000000001577}, {\"x\": -2.590000000000158}, {\"x\": -2.580000000000158}, {\"x\": -2.5700000000001584}, {\"x\": -2.5600000000001586}, {\"x\": -2.550000000000159}, {\"x\": -2.540000000000159}, {\"x\": -2.5300000000001592}, {\"x\": -2.5200000000001594}, {\"x\": -2.5100000000001597}, {\"x\": -2.50000000000016}, {\"x\": -2.49000000000016}, {\"x\": -2.4800000000001603}, {\"x\": -2.4700000000001605}, {\"x\": -2.4600000000001607}, {\"x\": -2.450000000000161}, {\"x\": -2.440000000000161}, {\"x\": -2.4300000000001614}, {\"x\": -2.4200000000001616}, {\"x\": -2.410000000000162}, {\"x\": -2.400000000000162}, {\"x\": -2.390000000000162}, {\"x\": -2.3800000000001624}, {\"x\": -2.3700000000001626}, {\"x\": -2.360000000000163}, {\"x\": -2.350000000000163}, {\"x\": -2.3400000000001633}, {\"x\": -2.3300000000001635}, {\"x\": -2.3200000000001637}, {\"x\": -2.310000000000164}, {\"x\": -2.300000000000164}, {\"x\": -2.2900000000001643}, {\"x\": -2.2800000000001646}, {\"x\": -2.2700000000001648}, {\"x\": -2.260000000000165}, {\"x\": -2.250000000000165}, {\"x\": -2.2400000000001654}, {\"x\": -2.2300000000001656}, {\"x\": -2.220000000000166}, {\"x\": -2.210000000000166}, {\"x\": -2.2000000000001663}, {\"x\": -2.1900000000001665}, {\"x\": -2.1800000000001667}, {\"x\": -2.170000000000167}, {\"x\": -2.160000000000167}, {\"x\": -2.1500000000001673}, {\"x\": -2.1400000000001675}, {\"x\": -2.1300000000001678}, {\"x\": -2.120000000000168}, {\"x\": -2.110000000000168}, {\"x\": -2.1000000000001684}, {\"x\": -2.0900000000001686}, {\"x\": -2.080000000000169}, {\"x\": -2.070000000000169}, {\"x\": -2.0600000000001693}, {\"x\": -2.0500000000001695}, {\"x\": -2.0400000000001697}, {\"x\": -2.03000000000017}, {\"x\": -2.02000000000017}, {\"x\": -2.0100000000001703}, {\"x\": -2.0000000000001705}, {\"x\": -1.9900000000001707}, {\"x\": -1.980000000000171}, {\"x\": -1.9700000000001712}, {\"x\": -1.9600000000001714}, {\"x\": -1.9500000000001716}, {\"x\": -1.9400000000001718}, {\"x\": -1.930000000000172}, {\"x\": -1.9200000000001722}, {\"x\": -1.9100000000001724}, {\"x\": -1.9000000000001727}, {\"x\": -1.8900000000001729}, {\"x\": -1.880000000000173}, {\"x\": -1.8700000000001733}, {\"x\": -1.8600000000001735}, {\"x\": -1.8500000000001737}, {\"x\": -1.840000000000174}, {\"x\": -1.8300000000001742}, {\"x\": -1.8200000000001744}, {\"x\": -1.8100000000001746}, {\"x\": -1.8000000000001748}, {\"x\": -1.790000000000175}, {\"x\": -1.7800000000001752}, {\"x\": -1.7700000000001754}, {\"x\": -1.7600000000001756}, {\"x\": -1.7500000000001759}, {\"x\": -1.740000000000176}, {\"x\": -1.7300000000001763}, {\"x\": -1.7200000000001765}, {\"x\": -1.7100000000001767}, {\"x\": -1.700000000000177}, {\"x\": -1.6900000000001771}, {\"x\": -1.6800000000001774}, {\"x\": -1.6700000000001776}, {\"x\": -1.6600000000001778}, {\"x\": -1.650000000000178}, {\"x\": -1.6400000000001782}, {\"x\": -1.6300000000001784}, {\"x\": -1.6200000000001786}, {\"x\": -1.6100000000001788}, {\"x\": -1.600000000000179}, {\"x\": -1.5900000000001793}, {\"x\": -1.5800000000001795}, {\"x\": -1.5700000000001797}, {\"x\": -1.56000000000018}, {\"x\": -1.5500000000001801}, {\"x\": -1.5400000000001803}, {\"x\": -1.5300000000001805}, {\"x\": -1.5200000000001808}, {\"x\": -1.510000000000181}, {\"x\": -1.5000000000001812}, {\"x\": -1.4900000000001814}, {\"x\": -1.4800000000001816}, {\"x\": -1.4700000000001818}, {\"x\": -1.460000000000182}, {\"x\": -1.4500000000001823}, {\"x\": -1.4400000000001825}, {\"x\": -1.4300000000001827}, {\"x\": -1.420000000000183}, {\"x\": -1.410000000000183}, {\"x\": -1.4000000000001833}, {\"x\": -1.3900000000001835}, {\"x\": -1.3800000000001837}, {\"x\": -1.370000000000184}, {\"x\": -1.3600000000001842}, {\"x\": -1.3500000000001844}, {\"x\": -1.3400000000001846}, {\"x\": -1.3300000000001848}, {\"x\": -1.320000000000185}, {\"x\": -1.3100000000001852}, {\"x\": -1.3000000000001855}, {\"x\": -1.2900000000001857}, {\"x\": -1.2800000000001859}, {\"x\": -1.270000000000186}, {\"x\": -1.2600000000001863}, {\"x\": -1.2500000000001865}, {\"x\": -1.2400000000001867}, {\"x\": -1.230000000000187}, {\"x\": -1.2200000000001872}, {\"x\": -1.2100000000001874}, {\"x\": -1.2000000000001876}, {\"x\": -1.1900000000001878}, {\"x\": -1.180000000000188}, {\"x\": -1.1700000000001882}, {\"x\": -1.1600000000001884}, {\"x\": -1.1500000000001886}, {\"x\": -1.1400000000001889}, {\"x\": -1.130000000000189}, {\"x\": -1.1200000000001893}, {\"x\": -1.1100000000001895}, {\"x\": -1.1000000000001897}, {\"x\": -1.09000000000019}, {\"x\": -1.0800000000001901}, {\"x\": -1.0700000000001904}, {\"x\": -1.0600000000001906}, {\"x\": -1.0500000000001908}, {\"x\": -1.040000000000191}, {\"x\": -1.0300000000001912}, {\"x\": -1.0200000000001914}, {\"x\": -1.0100000000001916}, {\"x\": -1.0000000000001918}, {\"x\": -0.9900000000001921}, {\"x\": -0.9800000000001923}, {\"x\": -0.9700000000001925}, {\"x\": -0.9600000000001927}, {\"x\": -0.9500000000001929}, {\"x\": -0.9400000000001931}, {\"x\": -0.9300000000001933}, {\"x\": -0.9200000000001936}, {\"x\": -0.9100000000001938}, {\"x\": -0.900000000000194}, {\"x\": -0.8900000000001942}, {\"x\": -0.8800000000001944}, {\"x\": -0.8700000000001946}, {\"x\": -0.8600000000001948}, {\"x\": -0.850000000000195}, {\"x\": -0.8400000000001953}, {\"x\": -0.8300000000001955}, {\"x\": -0.8200000000001957}, {\"x\": -0.8100000000001959}, {\"x\": -0.8000000000001961}, {\"x\": -0.7900000000001963}, {\"x\": -0.7800000000001965}, {\"x\": -0.7700000000001967}, {\"x\": -0.760000000000197}, {\"x\": -0.7500000000001972}, {\"x\": -0.7400000000001974}, {\"x\": -0.7300000000001976}, {\"x\": -0.7200000000001978}, {\"x\": -0.710000000000198}, {\"x\": -0.7000000000001982}, {\"x\": -0.6900000000001985}, {\"x\": -0.6800000000001987}, {\"x\": -0.6700000000001989}, {\"x\": -0.6600000000001991}, {\"x\": -0.6500000000001993}, {\"x\": -0.6400000000001995}, {\"x\": -0.6300000000001997}, {\"x\": -0.6200000000002}, {\"x\": -0.6100000000002002}, {\"x\": -0.6000000000002004}, {\"x\": -0.5900000000002006}, {\"x\": -0.5800000000002008}, {\"x\": -0.570000000000201}, {\"x\": -0.5600000000002012}, {\"x\": -0.5500000000002014}, {\"x\": -0.5400000000002017}, {\"x\": -0.5300000000002019}, {\"x\": -0.5200000000002021}, {\"x\": -0.5100000000002023}, {\"x\": -0.5000000000002025}, {\"x\": -0.4900000000002027}, {\"x\": -0.48000000000020293}, {\"x\": -0.47000000000020314}, {\"x\": -0.46000000000020336}, {\"x\": -0.45000000000020357}, {\"x\": -0.4400000000002038}, {\"x\": -0.430000000000204}, {\"x\": -0.4200000000002042}, {\"x\": -0.4100000000002044}, {\"x\": -0.40000000000020464}, {\"x\": -0.39000000000020485}, {\"x\": -0.38000000000020506}, {\"x\": -0.3700000000002053}, {\"x\": -0.3600000000002055}, {\"x\": -0.3500000000002057}, {\"x\": -0.3400000000002059}, {\"x\": -0.33000000000020613}, {\"x\": -0.32000000000020634}, {\"x\": -0.31000000000020655}, {\"x\": -0.30000000000020677}, {\"x\": -0.290000000000207}, {\"x\": -0.2800000000002072}, {\"x\": -0.2700000000002074}, {\"x\": -0.2600000000002076}, {\"x\": -0.25000000000020783}, {\"x\": -0.24000000000020805}, {\"x\": -0.23000000000020826}, {\"x\": -0.22000000000020847}, {\"x\": -0.2100000000002087}, {\"x\": -0.2000000000002089}, {\"x\": -0.1900000000002091}, {\"x\": -0.18000000000020933}, {\"x\": -0.17000000000020954}, {\"x\": -0.16000000000020975}, {\"x\": -0.15000000000020997}, {\"x\": -0.14000000000021018}, {\"x\": -0.1300000000002104}, {\"x\": -0.1200000000002106}, {\"x\": -0.11000000000021082}, {\"x\": -0.10000000000021103}, {\"x\": -0.09000000000021124}, {\"x\": -0.08000000000021146}, {\"x\": -0.07000000000021167}, {\"x\": -0.060000000000211884}, {\"x\": -0.0500000000002121}, {\"x\": -0.04000000000021231}, {\"x\": -0.030000000000212523}, {\"x\": -0.020000000000212736}, {\"x\": -0.01000000000021295}, {\"x\": -2.1316282072803006e-13}, {\"x\": 0.009999999999786624}, {\"x\": 0.01999999999978641}, {\"x\": 0.029999999999786198}, {\"x\": 0.039999999999785985}, {\"x\": 0.04999999999978577}, {\"x\": 0.05999999999978556}, {\"x\": 0.06999999999978535}, {\"x\": 0.07999999999978513}, {\"x\": 0.08999999999978492}, {\"x\": 0.0999999999997847}, {\"x\": 0.10999999999978449}, {\"x\": 0.11999999999978428}, {\"x\": 0.12999999999978407}, {\"x\": 0.13999999999978385}, {\"x\": 0.14999999999978364}, {\"x\": 0.15999999999978343}, {\"x\": 0.1699999999997832}, {\"x\": 0.179999999999783}, {\"x\": 0.1899999999997828}, {\"x\": 0.19999999999978257}, {\"x\": 0.20999999999978236}, {\"x\": 0.21999999999978215}, {\"x\": 0.22999999999978193}, {\"x\": 0.23999999999978172}, {\"x\": 0.2499999999997815}, {\"x\": 0.2599999999997813}, {\"x\": 0.2699999999997811}, {\"x\": 0.27999999999978087}, {\"x\": 0.28999999999978066}, {\"x\": 0.29999999999978044}, {\"x\": 0.30999999999978023}, {\"x\": 0.31999999999978}, {\"x\": 0.3299999999997798}, {\"x\": 0.3399999999997796}, {\"x\": 0.3499999999997794}, {\"x\": 0.35999999999977916}, {\"x\": 0.36999999999977895}, {\"x\": 0.37999999999977874}, {\"x\": 0.3899999999997785}, {\"x\": 0.3999999999997783}, {\"x\": 0.4099999999997781}, {\"x\": 0.4199999999997779}, {\"x\": 0.42999999999977767}, {\"x\": 0.43999999999977746}, {\"x\": 0.44999999999977724}, {\"x\": 0.45999999999977703}, {\"x\": 0.4699999999997768}, {\"x\": 0.4799999999997766}, {\"x\": 0.4899999999997764}, {\"x\": 0.4999999999997762}, {\"x\": 0.509999999999776}, {\"x\": 0.5199999999997758}, {\"x\": 0.5299999999997755}, {\"x\": 0.5399999999997753}, {\"x\": 0.5499999999997751}, {\"x\": 0.5599999999997749}, {\"x\": 0.5699999999997747}, {\"x\": 0.5799999999997745}, {\"x\": 0.5899999999997743}, {\"x\": 0.599999999999774}, {\"x\": 0.6099999999997738}, {\"x\": 0.6199999999997736}, {\"x\": 0.6299999999997734}, {\"x\": 0.6399999999997732}, {\"x\": 0.649999999999773}, {\"x\": 0.6599999999997728}, {\"x\": 0.6699999999997726}, {\"x\": 0.6799999999997723}, {\"x\": 0.6899999999997721}, {\"x\": 0.6999999999997719}, {\"x\": 0.7099999999997717}, {\"x\": 0.7199999999997715}, {\"x\": 0.7299999999997713}, {\"x\": 0.7399999999997711}, {\"x\": 0.7499999999997708}, {\"x\": 0.7599999999997706}, {\"x\": 0.7699999999997704}, {\"x\": 0.7799999999997702}, {\"x\": 0.78999999999977}, {\"x\": 0.7999999999997698}, {\"x\": 0.8099999999997696}, {\"x\": 0.8199999999997694}, {\"x\": 0.8299999999997691}, {\"x\": 0.8399999999997689}, {\"x\": 0.8499999999997687}, {\"x\": 0.8599999999997685}, {\"x\": 0.8699999999997683}, {\"x\": 0.8799999999997681}, {\"x\": 0.8899999999997679}, {\"x\": 0.8999999999997677}, {\"x\": 0.9099999999997674}, {\"x\": 0.9199999999997672}, {\"x\": 0.929999999999767}, {\"x\": 0.9399999999997668}, {\"x\": 0.9499999999997666}, {\"x\": 0.9599999999997664}, {\"x\": 0.9699999999997662}, {\"x\": 0.979999999999766}, {\"x\": 0.9899999999997657}, {\"x\": 0.9999999999997655}, {\"x\": 1.0099999999997653}, {\"x\": 1.019999999999765}, {\"x\": 1.0299999999997649}, {\"x\": 1.0399999999997647}, {\"x\": 1.0499999999997645}, {\"x\": 1.0599999999997642}, {\"x\": 1.069999999999764}, {\"x\": 1.0799999999997638}, {\"x\": 1.0899999999997636}, {\"x\": 1.0999999999997634}, {\"x\": 1.1099999999997632}, {\"x\": 1.119999999999763}, {\"x\": 1.1299999999997627}, {\"x\": 1.1399999999997625}, {\"x\": 1.1499999999997623}, {\"x\": 1.159999999999762}, {\"x\": 1.169999999999762}, {\"x\": 1.1799999999997617}, {\"x\": 1.1899999999997615}, {\"x\": 1.1999999999997613}, {\"x\": 1.209999999999761}, {\"x\": 1.2199999999997608}, {\"x\": 1.2299999999997606}, {\"x\": 1.2399999999997604}, {\"x\": 1.2499999999997602}, {\"x\": 1.25999999999976}, {\"x\": 1.2699999999997598}, {\"x\": 1.2799999999997596}, {\"x\": 1.2899999999997593}, {\"x\": 1.2999999999997591}, {\"x\": 1.309999999999759}, {\"x\": 1.3199999999997587}, {\"x\": 1.3299999999997585}, {\"x\": 1.3399999999997583}, {\"x\": 1.349999999999758}, {\"x\": 1.3599999999997578}, {\"x\": 1.3699999999997576}, {\"x\": 1.3799999999997574}, {\"x\": 1.3899999999997572}, {\"x\": 1.399999999999757}, {\"x\": 1.4099999999997568}, {\"x\": 1.4199999999997566}, {\"x\": 1.4299999999997564}, {\"x\": 1.4399999999997561}, {\"x\": 1.449999999999756}, {\"x\": 1.4599999999997557}, {\"x\": 1.4699999999997555}, {\"x\": 1.4799999999997553}, {\"x\": 1.489999999999755}, {\"x\": 1.4999999999997549}, {\"x\": 1.5099999999997546}, {\"x\": 1.5199999999997544}, {\"x\": 1.5299999999997542}, {\"x\": 1.539999999999754}, {\"x\": 1.5499999999997538}, {\"x\": 1.5599999999997536}, {\"x\": 1.5699999999997534}, {\"x\": 1.5799999999997532}, {\"x\": 1.589999999999753}, {\"x\": 1.5999999999997527}, {\"x\": 1.6099999999997525}, {\"x\": 1.6199999999997523}, {\"x\": 1.629999999999752}, {\"x\": 1.6399999999997519}, {\"x\": 1.6499999999997517}, {\"x\": 1.6599999999997515}, {\"x\": 1.6699999999997512}, {\"x\": 1.679999999999751}, {\"x\": 1.6899999999997508}, {\"x\": 1.6999999999997506}, {\"x\": 1.7099999999997504}, {\"x\": 1.7199999999997502}, {\"x\": 1.72999999999975}, {\"x\": 1.7399999999997497}, {\"x\": 1.7499999999997495}, {\"x\": 1.7599999999997493}, {\"x\": 1.769999999999749}, {\"x\": 1.779999999999749}, {\"x\": 1.7899999999997487}, {\"x\": 1.7999999999997485}, {\"x\": 1.8099999999997483}, {\"x\": 1.819999999999748}, {\"x\": 1.8299999999997478}, {\"x\": 1.8399999999997476}, {\"x\": 1.8499999999997474}, {\"x\": 1.8599999999997472}, {\"x\": 1.869999999999747}, {\"x\": 1.8799999999997468}, {\"x\": 1.8899999999997465}, {\"x\": 1.8999999999997463}, {\"x\": 1.9099999999997461}, {\"x\": 1.919999999999746}, {\"x\": 1.9299999999997457}, {\"x\": 1.9399999999997455}, {\"x\": 1.9499999999997453}, {\"x\": 1.959999999999745}, {\"x\": 1.9699999999997448}, {\"x\": 1.9799999999997446}, {\"x\": 1.9899999999997444}, {\"x\": 1.9999999999997442}, {\"x\": 2.009999999999744}, {\"x\": 2.019999999999744}, {\"x\": 2.0299999999997436}, {\"x\": 2.0399999999997434}, {\"x\": 2.049999999999743}, {\"x\": 2.059999999999743}, {\"x\": 2.0699999999997427}, {\"x\": 2.0799999999997425}, {\"x\": 2.0899999999997423}, {\"x\": 2.099999999999742}, {\"x\": 2.109999999999742}, {\"x\": 2.1199999999997416}, {\"x\": 2.1299999999997414}, {\"x\": 2.139999999999741}, {\"x\": 2.149999999999741}, {\"x\": 2.159999999999741}, {\"x\": 2.1699999999997406}, {\"x\": 2.1799999999997404}, {\"x\": 2.18999999999974}, {\"x\": 2.19999999999974}, {\"x\": 2.2099999999997397}, {\"x\": 2.2199999999997395}, {\"x\": 2.2299999999997393}, {\"x\": 2.239999999999739}, {\"x\": 2.249999999999739}, {\"x\": 2.2599999999997387}, {\"x\": 2.2699999999997384}, {\"x\": 2.2799999999997382}, {\"x\": 2.289999999999738}, {\"x\": 2.299999999999738}, {\"x\": 2.3099999999997376}, {\"x\": 2.3199999999997374}, {\"x\": 2.329999999999737}, {\"x\": 2.339999999999737}, {\"x\": 2.3499999999997367}, {\"x\": 2.3599999999997365}, {\"x\": 2.3699999999997363}, {\"x\": 2.379999999999736}, {\"x\": 2.389999999999736}, {\"x\": 2.3999999999997357}, {\"x\": 2.4099999999997355}, {\"x\": 2.4199999999997353}, {\"x\": 2.429999999999735}, {\"x\": 2.439999999999735}, {\"x\": 2.4499999999997346}, {\"x\": 2.4599999999997344}, {\"x\": 2.469999999999734}, {\"x\": 2.479999999999734}, {\"x\": 2.4899999999997338}, {\"x\": 2.4999999999997335}, {\"x\": 2.5099999999997333}, {\"x\": 2.519999999999733}, {\"x\": 2.529999999999733}, {\"x\": 2.5399999999997327}, {\"x\": 2.5499999999997325}, {\"x\": 2.5599999999997323}, {\"x\": 2.569999999999732}, {\"x\": 2.579999999999732}, {\"x\": 2.5899999999997316}, {\"x\": 2.5999999999997314}, {\"x\": 2.609999999999731}, {\"x\": 2.619999999999731}, {\"x\": 2.6299999999997308}, {\"x\": 2.6399999999997306}, {\"x\": 2.6499999999997303}, {\"x\": 2.65999999999973}, {\"x\": 2.66999999999973}, {\"x\": 2.6799999999997297}, {\"x\": 2.6899999999997295}, {\"x\": 2.6999999999997293}, {\"x\": 2.709999999999729}, {\"x\": 2.719999999999729}, {\"x\": 2.7299999999997286}, {\"x\": 2.7399999999997284}, {\"x\": 2.749999999999728}, {\"x\": 2.759999999999728}, {\"x\": 2.769999999999728}, {\"x\": 2.7799999999997276}, {\"x\": 2.7899999999997274}, {\"x\": 2.799999999999727}, {\"x\": 2.809999999999727}, {\"x\": 2.8199999999997267}, {\"x\": 2.8299999999997265}, {\"x\": 2.8399999999997263}, {\"x\": 2.849999999999726}, {\"x\": 2.859999999999726}, {\"x\": 2.8699999999997257}, {\"x\": 2.8799999999997254}, {\"x\": 2.8899999999997252}, {\"x\": 2.899999999999725}, {\"x\": 2.909999999999725}, {\"x\": 2.9199999999997246}, {\"x\": 2.9299999999997244}, {\"x\": 2.939999999999724}, {\"x\": 2.949999999999724}, {\"x\": 2.9599999999997237}, {\"x\": 2.9699999999997235}, {\"x\": 2.9799999999997233}, {\"x\": 2.989999999999723}, {\"x\": 2.999999999999723}, {\"x\": 3.0099999999997227}, {\"x\": 3.0199999999997225}, {\"x\": 3.0299999999997222}, {\"x\": 3.039999999999722}, {\"x\": 3.049999999999722}, {\"x\": 3.0599999999997216}, {\"x\": 3.0699999999997214}, {\"x\": 3.079999999999721}, {\"x\": 3.089999999999721}, {\"x\": 3.0999999999997208}, {\"x\": 3.1099999999997205}, {\"x\": 3.1199999999997203}, {\"x\": 3.12999999999972}, {\"x\": 3.13999999999972}, {\"x\": 3.1499999999997197}, {\"x\": 3.1599999999997195}, {\"x\": 3.1699999999997193}, {\"x\": 3.179999999999719}, {\"x\": 3.189999999999719}, {\"x\": 3.1999999999997186}, {\"x\": 3.2099999999997184}, {\"x\": 3.219999999999718}, {\"x\": 3.229999999999718}, {\"x\": 3.2399999999997178}, {\"x\": 3.2499999999997176}, {\"x\": 3.2599999999997173}, {\"x\": 3.269999999999717}, {\"x\": 3.279999999999717}, {\"x\": 3.2899999999997167}, {\"x\": 3.2999999999997165}, {\"x\": 3.3099999999997163}, {\"x\": 3.319999999999716}, {\"x\": 3.329999999999716}, {\"x\": 3.3399999999997156}, {\"x\": 3.3499999999997154}, {\"x\": 3.359999999999715}, {\"x\": 3.369999999999715}, {\"x\": 3.379999999999715}, {\"x\": 3.3899999999997146}, {\"x\": 3.3999999999997144}, {\"x\": 3.409999999999714}, {\"x\": 3.419999999999714}, {\"x\": 3.4299999999997137}, {\"x\": 3.4399999999997135}, {\"x\": 3.4499999999997133}, {\"x\": 3.459999999999713}, {\"x\": 3.469999999999713}, {\"x\": 3.4799999999997127}, {\"x\": 3.4899999999997124}, {\"x\": 3.4999999999997122}, {\"x\": 3.509999999999712}, {\"x\": 3.519999999999712}, {\"x\": 3.5299999999997116}, {\"x\": 3.5399999999997114}, {\"x\": 3.549999999999711}, {\"x\": 3.559999999999711}, {\"x\": 3.5699999999997107}, {\"x\": 3.5799999999997105}, {\"x\": 3.5899999999997103}, {\"x\": 3.59999999999971}, {\"x\": 3.60999999999971}, {\"x\": 3.6199999999997097}, {\"x\": 3.6299999999997095}, {\"x\": 3.6399999999997092}, {\"x\": 3.649999999999709}, {\"x\": 3.659999999999709}, {\"x\": 3.6699999999997086}, {\"x\": 3.6799999999997084}, {\"x\": 3.689999999999708}, {\"x\": 3.699999999999708}, {\"x\": 3.7099999999997078}, {\"x\": 3.7199999999997075}, {\"x\": 3.7299999999997073}, {\"x\": 3.739999999999707}, {\"x\": 3.749999999999707}, {\"x\": 3.7599999999997067}, {\"x\": 3.7699999999997065}, {\"x\": 3.7799999999997063}, {\"x\": 3.789999999999706}, {\"x\": 3.799999999999706}, {\"x\": 3.8099999999997056}, {\"x\": 3.8199999999997054}, {\"x\": 3.829999999999705}, {\"x\": 3.839999999999705}, {\"x\": 3.8499999999997048}, {\"x\": 3.8599999999997046}, {\"x\": 3.8699999999997043}, {\"x\": 3.879999999999704}, {\"x\": 3.889999999999704}, {\"x\": 3.8999999999997037}, {\"x\": 3.9099999999997035}, {\"x\": 3.9199999999997033}, {\"x\": 3.929999999999703}, {\"x\": 3.939999999999703}, {\"x\": 3.9499999999997026}, {\"x\": 3.9599999999997024}, {\"x\": 3.969999999999702}, {\"x\": 3.979999999999702}, {\"x\": 3.989999999999702}, {\"x\": 3.9999999999997016}, {\"x\": 4.009999999999701}, {\"x\": 4.019999999999701}, {\"x\": 4.029999999999701}, {\"x\": 4.039999999999701}, {\"x\": 4.0499999999997005}, {\"x\": 4.0599999999997}, {\"x\": 4.0699999999997}, {\"x\": 4.0799999999997}, {\"x\": 4.0899999999997}, {\"x\": 4.099999999999699}, {\"x\": 4.109999999999699}, {\"x\": 4.119999999999699}, {\"x\": 4.129999999999699}, {\"x\": 4.139999999999699}, {\"x\": 4.149999999999698}, {\"x\": 4.159999999999698}, {\"x\": 4.169999999999698}, {\"x\": 4.179999999999698}, {\"x\": 4.1899999999996975}, {\"x\": 4.199999999999697}, {\"x\": 4.209999999999697}, {\"x\": 4.219999999999697}, {\"x\": 4.229999999999697}, {\"x\": 4.2399999999996965}, {\"x\": 4.249999999999696}, {\"x\": 4.259999999999696}, {\"x\": 4.269999999999696}, {\"x\": 4.279999999999696}, {\"x\": 4.289999999999695}, {\"x\": 4.299999999999695}, {\"x\": 4.309999999999695}, {\"x\": 4.319999999999695}, {\"x\": 4.3299999999996945}, {\"x\": 4.339999999999694}, {\"x\": 4.349999999999694}, {\"x\": 4.359999999999694}, {\"x\": 4.369999999999694}, {\"x\": 4.3799999999996935}, {\"x\": 4.389999999999693}, {\"x\": 4.399999999999693}, {\"x\": 4.409999999999693}, {\"x\": 4.419999999999693}, {\"x\": 4.429999999999692}, {\"x\": 4.439999999999692}, {\"x\": 4.449999999999692}, {\"x\": 4.459999999999692}, {\"x\": 4.4699999999996916}, {\"x\": 4.479999999999691}, {\"x\": 4.489999999999691}, {\"x\": 4.499999999999691}, {\"x\": 4.509999999999691}, {\"x\": 4.5199999999996905}, {\"x\": 4.52999999999969}, {\"x\": 4.53999999999969}, {\"x\": 4.54999999999969}, {\"x\": 4.55999999999969}, {\"x\": 4.569999999999689}, {\"x\": 4.579999999999689}, {\"x\": 4.589999999999689}, {\"x\": 4.599999999999689}, {\"x\": 4.609999999999689}, {\"x\": 4.619999999999688}, {\"x\": 4.629999999999688}, {\"x\": 4.639999999999688}, {\"x\": 4.649999999999688}, {\"x\": 4.6599999999996875}, {\"x\": 4.669999999999687}, {\"x\": 4.679999999999687}, {\"x\": 4.689999999999687}, {\"x\": 4.699999999999687}, {\"x\": 4.709999999999686}, {\"x\": 4.719999999999686}, {\"x\": 4.729999999999686}, {\"x\": 4.739999999999686}, {\"x\": 4.749999999999686}, {\"x\": 4.759999999999685}, {\"x\": 4.769999999999685}, {\"x\": 4.779999999999685}, {\"x\": 4.789999999999685}, {\"x\": 4.7999999999996845}, {\"x\": 4.809999999999684}, {\"x\": 4.819999999999684}, {\"x\": 4.829999999999684}, {\"x\": 4.839999999999684}, {\"x\": 4.8499999999996835}, {\"x\": 4.859999999999683}, {\"x\": 4.869999999999683}, {\"x\": 4.879999999999683}, {\"x\": 4.889999999999683}, {\"x\": 4.899999999999682}, {\"x\": 4.909999999999682}, {\"x\": 4.919999999999682}, {\"x\": 4.929999999999682}, {\"x\": 4.9399999999996815}, {\"x\": 4.949999999999681}, {\"x\": 4.959999999999681}, {\"x\": 4.969999999999681}, {\"x\": 4.979999999999681}, {\"x\": 4.9899999999996805}, {\"x\": 4.99999999999968}, {\"x\": 5.00999999999968}, {\"x\": 5.01999999999968}, {\"x\": 5.02999999999968}, {\"x\": 5.039999999999679}, {\"x\": 5.049999999999679}, {\"x\": 5.059999999999679}, {\"x\": 5.069999999999679}, {\"x\": 5.0799999999996786}, {\"x\": 5.089999999999678}, {\"x\": 5.099999999999678}, {\"x\": 5.109999999999678}, {\"x\": 5.119999999999678}, {\"x\": 5.1299999999996775}, {\"x\": 5.139999999999677}, {\"x\": 5.149999999999677}, {\"x\": 5.159999999999677}, {\"x\": 5.169999999999677}, {\"x\": 5.179999999999676}, {\"x\": 5.189999999999676}, {\"x\": 5.199999999999676}, {\"x\": 5.209999999999676}, {\"x\": 5.219999999999676}, {\"x\": 5.229999999999675}, {\"x\": 5.239999999999675}, {\"x\": 5.249999999999675}, {\"x\": 5.259999999999675}, {\"x\": 5.2699999999996745}, {\"x\": 5.279999999999674}, {\"x\": 5.289999999999674}, {\"x\": 5.299999999999674}, {\"x\": 5.309999999999674}, {\"x\": 5.319999999999673}, {\"x\": 5.329999999999673}, {\"x\": 5.339999999999673}, {\"x\": 5.349999999999673}, {\"x\": 5.359999999999673}, {\"x\": 5.369999999999672}, {\"x\": 5.379999999999672}, {\"x\": 5.389999999999672}, {\"x\": 5.399999999999672}, {\"x\": 5.4099999999996715}, {\"x\": 5.419999999999671}, {\"x\": 5.429999999999671}, {\"x\": 5.439999999999671}, {\"x\": 5.449999999999671}, {\"x\": 5.4599999999996705}, {\"x\": 5.46999999999967}, {\"x\": 5.47999999999967}, {\"x\": 5.48999999999967}, {\"x\": 5.49999999999967}, {\"x\": 5.509999999999669}, {\"x\": 5.519999999999669}, {\"x\": 5.529999999999669}, {\"x\": 5.539999999999669}, {\"x\": 5.5499999999996685}, {\"x\": 5.559999999999668}, {\"x\": 5.569999999999668}, {\"x\": 5.579999999999668}, {\"x\": 5.589999999999668}, {\"x\": 5.5999999999996675}, {\"x\": 5.609999999999667}, {\"x\": 5.619999999999667}, {\"x\": 5.629999999999667}, {\"x\": 5.639999999999667}, {\"x\": 5.649999999999666}, {\"x\": 5.659999999999666}, {\"x\": 5.669999999999666}, {\"x\": 5.679999999999666}, {\"x\": 5.6899999999996655}, {\"x\": 5.699999999999665}, {\"x\": 5.709999999999665}, {\"x\": 5.719999999999665}, {\"x\": 5.729999999999665}, {\"x\": 5.7399999999996645}, {\"x\": 5.749999999999664}, {\"x\": 5.759999999999664}, {\"x\": 5.769999999999664}, {\"x\": 5.779999999999664}, {\"x\": 5.789999999999663}, {\"x\": 5.799999999999663}, {\"x\": 5.809999999999663}, {\"x\": 5.819999999999663}, {\"x\": 5.829999999999663}, {\"x\": 5.839999999999662}, {\"x\": 5.849999999999662}, {\"x\": 5.859999999999662}, {\"x\": 5.869999999999662}, {\"x\": 5.8799999999996615}, {\"x\": 5.889999999999661}, {\"x\": 5.899999999999661}, {\"x\": 5.909999999999661}, {\"x\": 5.919999999999661}, {\"x\": 5.92999999999966}, {\"x\": 5.93999999999966}, {\"x\": 5.94999999999966}, {\"x\": 5.95999999999966}, {\"x\": 5.96999999999966}, {\"x\": 5.979999999999659}, {\"x\": 5.989999999999659}, {\"x\": 5.999999999999659}, {\"x\": 6.009999999999657}, {\"x\": 6.0199999999996585}, {\"x\": 6.02999999999966}, {\"x\": 6.039999999999658}, {\"x\": 6.049999999999656}, {\"x\": 6.059999999999658}, {\"x\": 6.069999999999659}, {\"x\": 6.079999999999657}, {\"x\": 6.089999999999655}, {\"x\": 6.099999999999657}, {\"x\": 6.109999999999658}, {\"x\": 6.119999999999656}, {\"x\": 6.129999999999654}, {\"x\": 6.139999999999656}, {\"x\": 6.1499999999996575}, {\"x\": 6.1599999999996555}, {\"x\": 6.1699999999996535}, {\"x\": 6.179999999999655}, {\"x\": 6.189999999999657}, {\"x\": 6.199999999999655}, {\"x\": 6.209999999999653}, {\"x\": 6.219999999999654}, {\"x\": 6.229999999999656}, {\"x\": 6.239999999999654}, {\"x\": 6.249999999999652}, {\"x\": 6.259999999999653}, {\"x\": 6.269999999999655}, {\"x\": 6.279999999999653}, {\"x\": 6.289999999999651}, {\"x\": 6.2999999999996525}, {\"x\": 6.309999999999654}, {\"x\": 6.319999999999652}, {\"x\": 6.32999999999965}, {\"x\": 6.339999999999652}, {\"x\": 6.349999999999653}, {\"x\": 6.359999999999651}, {\"x\": 6.369999999999649}, {\"x\": 6.379999999999651}, {\"x\": 6.389999999999652}, {\"x\": 6.39999999999965}, {\"x\": 6.409999999999648}, {\"x\": 6.41999999999965}, {\"x\": 6.4299999999996515}, {\"x\": 6.43999999999965}, {\"x\": 6.449999999999648}, {\"x\": 6.459999999999649}, {\"x\": 6.469999999999651}, {\"x\": 6.479999999999649}, {\"x\": 6.489999999999647}, {\"x\": 6.499999999999648}, {\"x\": 6.50999999999965}, {\"x\": 6.519999999999648}, {\"x\": 6.529999999999646}, {\"x\": 6.539999999999647}, {\"x\": 6.549999999999649}, {\"x\": 6.559999999999647}, {\"x\": 6.569999999999645}, {\"x\": 6.579999999999647}, {\"x\": 6.589999999999648}, {\"x\": 6.599999999999646}, {\"x\": 6.609999999999644}, {\"x\": 6.619999999999646}, {\"x\": 6.629999999999647}, {\"x\": 6.639999999999645}, {\"x\": 6.649999999999643}, {\"x\": 6.659999999999645}, {\"x\": 6.669999999999646}, {\"x\": 6.6799999999996444}, {\"x\": 6.6899999999996425}, {\"x\": 6.699999999999644}, {\"x\": 6.709999999999646}, {\"x\": 6.719999999999644}, {\"x\": 6.729999999999642}, {\"x\": 6.739999999999643}, {\"x\": 6.749999999999645}, {\"x\": 6.759999999999643}, {\"x\": 6.769999999999641}, {\"x\": 6.779999999999642}, {\"x\": 6.789999999999644}, {\"x\": 6.799999999999642}, {\"x\": 6.80999999999964}, {\"x\": 6.8199999999996415}, {\"x\": 6.829999999999643}, {\"x\": 6.839999999999641}, {\"x\": 6.849999999999639}, {\"x\": 6.859999999999641}, {\"x\": 6.869999999999642}, {\"x\": 6.87999999999964}, {\"x\": 6.889999999999638}, {\"x\": 6.89999999999964}, {\"x\": 6.909999999999641}, {\"x\": 6.919999999999639}, {\"x\": 6.929999999999637}, {\"x\": 6.939999999999639}, {\"x\": 6.9499999999996405}, {\"x\": 6.9599999999996385}, {\"x\": 6.9699999999996365}, {\"x\": 6.979999999999638}, {\"x\": 6.98999999999964}, {\"x\": 6.999999999999638}, {\"x\": 7.009999999999636}, {\"x\": 7.019999999999637}, {\"x\": 7.029999999999639}, {\"x\": 7.039999999999637}, {\"x\": 7.049999999999635}, {\"x\": 7.059999999999636}, {\"x\": 7.069999999999638}, {\"x\": 7.079999999999636}, {\"x\": 7.089999999999634}, {\"x\": 7.0999999999996355}, {\"x\": 7.109999999999637}, {\"x\": 7.119999999999635}, {\"x\": 7.129999999999633}, {\"x\": 7.139999999999635}, {\"x\": 7.149999999999636}, {\"x\": 7.159999999999634}, {\"x\": 7.169999999999632}, {\"x\": 7.179999999999634}, {\"x\": 7.189999999999635}, {\"x\": 7.199999999999633}, {\"x\": 7.209999999999631}, {\"x\": 7.219999999999633}, {\"x\": 7.2299999999996345}, {\"x\": 7.2399999999996325}, {\"x\": 7.2499999999996305}, {\"x\": 7.259999999999632}, {\"x\": 7.269999999999634}, {\"x\": 7.279999999999632}, {\"x\": 7.28999999999963}, {\"x\": 7.299999999999631}, {\"x\": 7.309999999999633}, {\"x\": 7.319999999999631}, {\"x\": 7.329999999999629}, {\"x\": 7.33999999999963}, {\"x\": 7.349999999999632}, {\"x\": 7.35999999999963}, {\"x\": 7.369999999999628}, {\"x\": 7.3799999999996295}, {\"x\": 7.389999999999631}, {\"x\": 7.399999999999629}, {\"x\": 7.409999999999627}, {\"x\": 7.419999999999629}, {\"x\": 7.42999999999963}, {\"x\": 7.439999999999628}, {\"x\": 7.449999999999626}, {\"x\": 7.459999999999628}, {\"x\": 7.469999999999629}, {\"x\": 7.479999999999627}, {\"x\": 7.489999999999625}, {\"x\": 7.499999999999627}, {\"x\": 7.5099999999996285}, {\"x\": 7.5199999999996265}, {\"x\": 7.5299999999996245}, {\"x\": 7.539999999999626}, {\"x\": 7.549999999999628}, {\"x\": 7.559999999999626}, {\"x\": 7.569999999999624}, {\"x\": 7.579999999999625}, {\"x\": 7.589999999999627}, {\"x\": 7.599999999999625}, {\"x\": 7.609999999999623}, {\"x\": 7.619999999999624}, {\"x\": 7.629999999999626}, {\"x\": 7.639999999999624}, {\"x\": 7.649999999999622}, {\"x\": 7.6599999999996236}, {\"x\": 7.669999999999625}, {\"x\": 7.679999999999623}, {\"x\": 7.689999999999621}, {\"x\": 7.699999999999623}, {\"x\": 7.709999999999624}, {\"x\": 7.719999999999622}, {\"x\": 7.72999999999962}, {\"x\": 7.739999999999622}, {\"x\": 7.749999999999623}, {\"x\": 7.759999999999621}, {\"x\": 7.769999999999619}, {\"x\": 7.779999999999621}, {\"x\": 7.789999999999623}, {\"x\": 7.799999999999621}, {\"x\": 7.809999999999619}, {\"x\": 7.81999999999962}, {\"x\": 7.829999999999622}, {\"x\": 7.83999999999962}, {\"x\": 7.849999999999618}, {\"x\": 7.859999999999619}, {\"x\": 7.869999999999621}, {\"x\": 7.879999999999619}, {\"x\": 7.889999999999617}, {\"x\": 7.899999999999618}, {\"x\": 7.90999999999962}, {\"x\": 7.919999999999618}, {\"x\": 7.929999999999616}, {\"x\": 7.939999999999618}, {\"x\": 7.949999999999619}, {\"x\": 7.959999999999617}, {\"x\": 7.969999999999615}, {\"x\": 7.979999999999617}, {\"x\": 7.989999999999618}, {\"x\": 7.999999999999616}, {\"x\": 8.009999999999614}, {\"x\": 8.019999999999616}, {\"x\": 8.029999999999617}, {\"x\": 8.039999999999615}, {\"x\": 8.049999999999613}, {\"x\": 8.059999999999615}, {\"x\": 8.069999999999617}, {\"x\": 8.079999999999615}, {\"x\": 8.089999999999613}, {\"x\": 8.099999999999614}, {\"x\": 8.109999999999616}, {\"x\": 8.119999999999614}, {\"x\": 8.129999999999612}, {\"x\": 8.139999999999613}, {\"x\": 8.149999999999615}, {\"x\": 8.159999999999613}, {\"x\": 8.169999999999611}, {\"x\": 8.179999999999612}, {\"x\": 8.189999999999614}, {\"x\": 8.199999999999612}, {\"x\": 8.20999999999961}, {\"x\": 8.219999999999612}, {\"x\": 8.229999999999613}, {\"x\": 8.239999999999611}, {\"x\": 8.24999999999961}, {\"x\": 8.25999999999961}, {\"x\": 8.269999999999612}, {\"x\": 8.27999999999961}, {\"x\": 8.289999999999608}, {\"x\": 8.29999999999961}, {\"x\": 8.309999999999611}, {\"x\": 8.31999999999961}, {\"x\": 8.329999999999607}, {\"x\": 8.339999999999609}, {\"x\": 8.34999999999961}, {\"x\": 8.359999999999609}, {\"x\": 8.369999999999607}, {\"x\": 8.379999999999608}, {\"x\": 8.38999999999961}, {\"x\": 8.399999999999608}, {\"x\": 8.409999999999606}, {\"x\": 8.419999999999607}, {\"x\": 8.429999999999609}, {\"x\": 8.439999999999607}, {\"x\": 8.449999999999605}, {\"x\": 8.459999999999607}, {\"x\": 8.469999999999608}, {\"x\": 8.479999999999606}, {\"x\": 8.489999999999604}, {\"x\": 8.499999999999606}, {\"x\": 8.509999999999607}, {\"x\": 8.519999999999605}, {\"x\": 8.529999999999603}, {\"x\": 8.539999999999605}, {\"x\": 8.549999999999606}, {\"x\": 8.559999999999604}, {\"x\": 8.569999999999602}, {\"x\": 8.579999999999604}, {\"x\": 8.589999999999606}, {\"x\": 8.599999999999604}, {\"x\": 8.609999999999602}, {\"x\": 8.619999999999603}, {\"x\": 8.629999999999605}, {\"x\": 8.639999999999603}, {\"x\": 8.6499999999996}, {\"x\": 8.659999999999602}, {\"x\": 8.669999999999604}, {\"x\": 8.679999999999602}, {\"x\": 8.6899999999996}, {\"x\": 8.699999999999601}, {\"x\": 8.709999999999603}, {\"x\": 8.719999999999601}, {\"x\": 8.729999999999599}, {\"x\": 8.7399999999996}, {\"x\": 8.749999999999602}, {\"x\": 8.7599999999996}, {\"x\": 8.769999999999598}, {\"x\": 8.7799999999996}, {\"x\": 8.789999999999601}, {\"x\": 8.7999999999996}, {\"x\": 8.809999999999597}, {\"x\": 8.819999999999599}, {\"x\": 8.8299999999996}, {\"x\": 8.839999999999598}, {\"x\": 8.849999999999596}, {\"x\": 8.859999999999598}, {\"x\": 8.8699999999996}, {\"x\": 8.879999999999598}, {\"x\": 8.889999999999596}, {\"x\": 8.899999999999597}, {\"x\": 8.909999999999599}, {\"x\": 8.919999999999597}, {\"x\": 8.929999999999595}, {\"x\": 8.939999999999596}, {\"x\": 8.949999999999598}, {\"x\": 8.959999999999596}, {\"x\": 8.969999999999594}, {\"x\": 8.979999999999595}, {\"x\": 8.989999999999597}, {\"x\": 8.999999999999595}, {\"x\": 9.009999999999593}, {\"x\": 9.019999999999595}, {\"x\": 9.029999999999596}, {\"x\": 9.039999999999594}, {\"x\": 9.049999999999592}, {\"x\": 9.059999999999594}, {\"x\": 9.069999999999595}, {\"x\": 9.079999999999593}, {\"x\": 9.089999999999591}, {\"x\": 9.099999999999593}, {\"x\": 9.109999999999594}, {\"x\": 9.119999999999592}, {\"x\": 9.12999999999959}, {\"x\": 9.139999999999592}, {\"x\": 9.149999999999594}, {\"x\": 9.159999999999592}, {\"x\": 9.16999999999959}, {\"x\": 9.179999999999591}, {\"x\": 9.189999999999593}, {\"x\": 9.19999999999959}, {\"x\": 9.209999999999589}, {\"x\": 9.21999999999959}, {\"x\": 9.229999999999592}, {\"x\": 9.23999999999959}, {\"x\": 9.249999999999588}, {\"x\": 9.25999999999959}, {\"x\": 9.269999999999591}, {\"x\": 9.279999999999589}, {\"x\": 9.289999999999587}, {\"x\": 9.299999999999589}, {\"x\": 9.30999999999959}, {\"x\": 9.319999999999588}, {\"x\": 9.329999999999586}, {\"x\": 9.339999999999588}, {\"x\": 9.34999999999959}, {\"x\": 9.359999999999587}, {\"x\": 9.369999999999585}, {\"x\": 9.379999999999587}, {\"x\": 9.389999999999588}, {\"x\": 9.399999999999586}, {\"x\": 9.409999999999584}, {\"x\": 9.419999999999586}, {\"x\": 9.429999999999588}, {\"x\": 9.439999999999586}, {\"x\": 9.449999999999584}, {\"x\": 9.459999999999585}, {\"x\": 9.469999999999587}, {\"x\": 9.479999999999585}, {\"x\": 9.489999999999583}, {\"x\": 9.499999999999584}, {\"x\": 9.509999999999586}, {\"x\": 9.519999999999584}, {\"x\": 9.529999999999582}, {\"x\": 9.539999999999583}, {\"x\": 9.549999999999585}, {\"x\": 9.559999999999583}, {\"x\": 9.569999999999581}, {\"x\": 9.579999999999583}, {\"x\": 9.589999999999584}, {\"x\": 9.599999999999582}, {\"x\": 9.60999999999958}, {\"x\": 9.619999999999582}, {\"x\": 9.629999999999583}, {\"x\": 9.639999999999581}, {\"x\": 9.64999999999958}, {\"x\": 9.659999999999581}, {\"x\": 9.669999999999582}, {\"x\": 9.67999999999958}, {\"x\": 9.689999999999579}, {\"x\": 9.69999999999958}, {\"x\": 9.709999999999582}, {\"x\": 9.71999999999958}, {\"x\": 9.729999999999578}, {\"x\": 9.73999999999958}, {\"x\": 9.74999999999958}, {\"x\": 9.759999999999579}, {\"x\": 9.769999999999577}, {\"x\": 9.779999999999578}, {\"x\": 9.78999999999958}, {\"x\": 9.799999999999578}, {\"x\": 9.809999999999576}, {\"x\": 9.819999999999578}, {\"x\": 9.829999999999579}, {\"x\": 9.839999999999577}, {\"x\": 9.849999999999575}, {\"x\": 9.859999999999577}, {\"x\": 9.869999999999578}, {\"x\": 9.879999999999576}, {\"x\": 9.889999999999574}, {\"x\": 9.899999999999576}, {\"x\": 9.909999999999577}, {\"x\": 9.919999999999575}, {\"x\": 9.929999999999573}, {\"x\": 9.939999999999575}, {\"x\": 9.949999999999577}, {\"x\": 9.959999999999575}, {\"x\": 9.969999999999573}, {\"x\": 9.979999999999574}, {\"x\": 9.989999999999576}, {\"x\": 9.999999999999574}, {\"x\": 10.009999999999572}, {\"x\": 10.019999999999573}, {\"x\": 10.029999999999575}, {\"x\": 10.039999999999573}, {\"x\": 10.04999999999957}, {\"x\": 10.059999999999572}, {\"x\": 10.069999999999574}, {\"x\": 10.079999999999572}, {\"x\": 10.08999999999957}, {\"x\": 10.099999999999572}, {\"x\": 10.109999999999573}, {\"x\": 10.119999999999571}, {\"x\": 10.12999999999957}, {\"x\": 10.13999999999957}, {\"x\": 10.149999999999572}, {\"x\": 10.15999999999957}, {\"x\": 10.169999999999568}, {\"x\": 10.17999999999957}, {\"x\": 10.189999999999571}, {\"x\": 10.19999999999957}, {\"x\": 10.209999999999567}, {\"x\": 10.219999999999569}, {\"x\": 10.22999999999957}, {\"x\": 10.239999999999569}, {\"x\": 10.249999999999567}, {\"x\": 10.259999999999568}, {\"x\": 10.26999999999957}, {\"x\": 10.279999999999568}, {\"x\": 10.289999999999566}, {\"x\": 10.299999999999567}, {\"x\": 10.309999999999569}, {\"x\": 10.319999999999567}, {\"x\": 10.329999999999565}, {\"x\": 10.339999999999566}, {\"x\": 10.349999999999568}, {\"x\": 10.359999999999566}, {\"x\": 10.369999999999564}, {\"x\": 10.379999999999566}, {\"x\": 10.389999999999567}, {\"x\": 10.399999999999565}, {\"x\": 10.409999999999563}, {\"x\": 10.419999999999565}, {\"x\": 10.429999999999566}, {\"x\": 10.439999999999564}, {\"x\": 10.449999999999562}, {\"x\": 10.459999999999564}, {\"x\": 10.469999999999565}, {\"x\": 10.479999999999563}, {\"x\": 10.489999999999561}, {\"x\": 10.499999999999563}, {\"x\": 10.509999999999565}, {\"x\": 10.519999999999563}, {\"x\": 10.52999999999956}, {\"x\": 10.539999999999562}, {\"x\": 10.549999999999564}, {\"x\": 10.559999999999562}, {\"x\": 10.56999999999956}, {\"x\": 10.579999999999561}, {\"x\": 10.589999999999563}, {\"x\": 10.59999999999956}, {\"x\": 10.609999999999559}, {\"x\": 10.61999999999956}, {\"x\": 10.629999999999562}, {\"x\": 10.63999999999956}, {\"x\": 10.649999999999558}, {\"x\": 10.65999999999956}, {\"x\": 10.669999999999561}, {\"x\": 10.67999999999956}, {\"x\": 10.689999999999557}, {\"x\": 10.699999999999559}, {\"x\": 10.70999999999956}, {\"x\": 10.719999999999558}, {\"x\": 10.729999999999556}, {\"x\": 10.739999999999558}, {\"x\": 10.74999999999956}, {\"x\": 10.759999999999557}, {\"x\": 10.769999999999555}, {\"x\": 10.779999999999557}, {\"x\": 10.789999999999559}, {\"x\": 10.799999999999557}, {\"x\": 10.809999999999555}, {\"x\": 10.819999999999556}, {\"x\": 10.829999999999558}, {\"x\": 10.839999999999556}, {\"x\": 10.849999999999554}, {\"x\": 10.859999999999555}, {\"x\": 10.869999999999557}, {\"x\": 10.879999999999555}, {\"x\": 10.889999999999553}, {\"x\": 10.899999999999554}, {\"x\": 10.909999999999556}, {\"x\": 10.919999999999554}, {\"x\": 10.929999999999552}, {\"x\": 10.939999999999554}, {\"x\": 10.949999999999555}, {\"x\": 10.959999999999553}, {\"x\": 10.969999999999551}, {\"x\": 10.979999999999553}, {\"x\": 10.989999999999554}, {\"x\": 10.999999999999552}, {\"x\": 11.00999999999955}, {\"x\": 11.019999999999552}, {\"x\": 11.029999999999553}, {\"x\": 11.039999999999552}, {\"x\": 11.04999999999955}, {\"x\": 11.059999999999551}, {\"x\": 11.069999999999553}, {\"x\": 11.07999999999955}, {\"x\": 11.089999999999549}, {\"x\": 11.09999999999955}, {\"x\": 11.109999999999552}, {\"x\": 11.11999999999955}, {\"x\": 11.129999999999548}, {\"x\": 11.13999999999955}, {\"x\": 11.149999999999551}, {\"x\": 11.159999999999549}, {\"x\": 11.169999999999547}, {\"x\": 11.179999999999549}, {\"x\": 11.18999999999955}, {\"x\": 11.199999999999548}, {\"x\": 11.209999999999546}, {\"x\": 11.219999999999548}, {\"x\": 11.22999999999955}, {\"x\": 11.239999999999547}, {\"x\": 11.249999999999545}, {\"x\": 11.259999999999547}, {\"x\": 11.269999999999548}, {\"x\": 11.279999999999546}, {\"x\": 11.289999999999544}, {\"x\": 11.299999999999546}, {\"x\": 11.309999999999548}, {\"x\": 11.319999999999546}, {\"x\": 11.329999999999544}, {\"x\": 11.339999999999545}, {\"x\": 11.349999999999547}, {\"x\": 11.359999999999545}, {\"x\": 11.369999999999543}, {\"x\": 11.379999999999544}, {\"x\": 11.389999999999546}, {\"x\": 11.399999999999544}, {\"x\": 11.409999999999542}, {\"x\": 11.419999999999543}, {\"x\": 11.429999999999545}, {\"x\": 11.439999999999543}, {\"x\": 11.449999999999541}, {\"x\": 11.459999999999543}, {\"x\": 11.469999999999544}, {\"x\": 11.479999999999542}, {\"x\": 11.48999999999954}, {\"x\": 11.499999999999542}, {\"x\": 11.509999999999543}, {\"x\": 11.519999999999541}, {\"x\": 11.52999999999954}, {\"x\": 11.53999999999954}, {\"x\": 11.549999999999542}, {\"x\": 11.55999999999954}, {\"x\": 11.569999999999538}, {\"x\": 11.57999999999954}, {\"x\": 11.589999999999542}, {\"x\": 11.59999999999954}, {\"x\": 11.609999999999538}, {\"x\": 11.61999999999954}, {\"x\": 11.62999999999954}, {\"x\": 11.639999999999539}, {\"x\": 11.649999999999537}, {\"x\": 11.659999999999538}, {\"x\": 11.66999999999954}, {\"x\": 11.679999999999538}, {\"x\": 11.689999999999536}, {\"x\": 11.699999999999537}, {\"x\": 11.709999999999539}, {\"x\": 11.719999999999537}, {\"x\": 11.729999999999535}, {\"x\": 11.739999999999537}, {\"x\": 11.749999999999538}, {\"x\": 11.759999999999536}, {\"x\": 11.769999999999534}, {\"x\": 11.779999999999536}, {\"x\": 11.789999999999537}, {\"x\": 11.799999999999535}, {\"x\": 11.809999999999533}, {\"x\": 11.819999999999535}, {\"x\": 11.829999999999536}, {\"x\": 11.839999999999534}, {\"x\": 11.849999999999532}, {\"x\": 11.859999999999534}, {\"x\": 11.869999999999536}, {\"x\": 11.879999999999534}, {\"x\": 11.889999999999532}, {\"x\": 11.899999999999533}, {\"x\": 11.909999999999535}, {\"x\": 11.919999999999533}, {\"x\": 11.92999999999953}, {\"x\": 11.939999999999532}, {\"x\": 11.949999999999534}, {\"x\": 11.959999999999532}, {\"x\": 11.96999999999953}, {\"x\": 11.979999999999531}, {\"x\": 11.989999999999533}, {\"x\": 11.999999999999531}, {\"x\": 12.009999999999529}, {\"x\": 12.01999999999953}, {\"x\": 12.029999999999532}, {\"x\": 12.03999999999953}, {\"x\": 12.049999999999528}, {\"x\": 12.05999999999953}, {\"x\": 12.069999999999531}, {\"x\": 12.07999999999953}, {\"x\": 12.089999999999527}, {\"x\": 12.099999999999529}, {\"x\": 12.10999999999953}, {\"x\": 12.119999999999528}, {\"x\": 12.129999999999526}, {\"x\": 12.139999999999528}, {\"x\": 12.14999999999953}, {\"x\": 12.159999999999528}, {\"x\": 12.169999999999526}, {\"x\": 12.179999999999527}, {\"x\": 12.189999999999529}, {\"x\": 12.199999999999527}, {\"x\": 12.209999999999525}, {\"x\": 12.219999999999526}, {\"x\": 12.229999999999528}, {\"x\": 12.239999999999526}, {\"x\": 12.249999999999524}, {\"x\": 12.259999999999525}, {\"x\": 12.269999999999527}, {\"x\": 12.279999999999525}, {\"x\": 12.289999999999523}, {\"x\": 12.299999999999525}, {\"x\": 12.309999999999526}, {\"x\": 12.319999999999524}, {\"x\": 12.329999999999522}, {\"x\": 12.339999999999524}, {\"x\": 12.349999999999525}, {\"x\": 12.359999999999523}, {\"x\": 12.369999999999521}, {\"x\": 12.379999999999523}, {\"x\": 12.389999999999525}, {\"x\": 12.399999999999523}, {\"x\": 12.40999999999952}, {\"x\": 12.419999999999522}, {\"x\": 12.429999999999524}, {\"x\": 12.439999999999522}, {\"x\": 12.44999999999952}, {\"x\": 12.459999999999521}, {\"x\": 12.469999999999523}, {\"x\": 12.47999999999952}, {\"x\": 12.489999999999519}, {\"x\": 12.49999999999952}, {\"x\": 12.509999999999522}, {\"x\": 12.51999999999952}, {\"x\": 12.529999999999518}, {\"x\": 12.53999999999952}, {\"x\": 12.549999999999521}, {\"x\": 12.559999999999519}, {\"x\": 12.569999999999517}, {\"x\": 12.579999999999519}, {\"x\": 12.58999999999952}, {\"x\": 12.599999999999518}, {\"x\": 12.609999999999516}, {\"x\": 12.619999999999518}, {\"x\": 12.62999999999952}, {\"x\": 12.639999999999517}, {\"x\": 12.649999999999515}, {\"x\": 12.659999999999517}, {\"x\": 12.669999999999519}, {\"x\": 12.679999999999517}, {\"x\": 12.689999999999515}, {\"x\": 12.699999999999516}, {\"x\": 12.709999999999518}, {\"x\": 12.719999999999516}, {\"x\": 12.729999999999514}, {\"x\": 12.739999999999515}, {\"x\": 12.749999999999517}, {\"x\": 12.759999999999515}, {\"x\": 12.769999999999513}, {\"x\": 12.779999999999514}, {\"x\": 12.789999999999516}, {\"x\": 12.799999999999514}, {\"x\": 12.809999999999512}, {\"x\": 12.819999999999514}, {\"x\": 12.829999999999515}, {\"x\": 12.839999999999513}, {\"x\": 12.849999999999511}, {\"x\": 12.859999999999513}, {\"x\": 12.869999999999514}, {\"x\": 12.879999999999512}, {\"x\": 12.88999999999951}, {\"x\": 12.899999999999512}, {\"x\": 12.909999999999513}, {\"x\": 12.919999999999511}, {\"x\": 12.92999999999951}, {\"x\": 12.939999999999511}, {\"x\": 12.949999999999513}, {\"x\": 12.95999999999951}, {\"x\": 12.969999999999509}, {\"x\": 12.97999999999951}, {\"x\": 12.989999999999512}, {\"x\": 12.99999999999951}, {\"x\": 13.009999999999508}, {\"x\": 13.01999999999951}, {\"x\": 13.02999999999951}, {\"x\": 13.039999999999509}, {\"x\": 13.049999999999507}, {\"x\": 13.059999999999508}, {\"x\": 13.06999999999951}, {\"x\": 13.079999999999508}, {\"x\": 13.089999999999506}, {\"x\": 13.099999999999508}, {\"x\": 13.10999999999951}, {\"x\": 13.119999999999507}, {\"x\": 13.129999999999505}, {\"x\": 13.139999999999507}, {\"x\": 13.149999999999508}, {\"x\": 13.159999999999506}, {\"x\": 13.169999999999504}, {\"x\": 13.179999999999506}, {\"x\": 13.189999999999507}, {\"x\": 13.199999999999505}, {\"x\": 13.209999999999503}, {\"x\": 13.219999999999505}, {\"x\": 13.229999999999507}, {\"x\": 13.239999999999505}, {\"x\": 13.249999999999503}, {\"x\": 13.259999999999504}, {\"x\": 13.269999999999506}, {\"x\": 13.279999999999504}, {\"x\": 13.289999999999502}, {\"x\": 13.299999999999503}, {\"x\": 13.309999999999505}, {\"x\": 13.319999999999503}, {\"x\": 13.329999999999501}, {\"x\": 13.339999999999502}, {\"x\": 13.349999999999504}, {\"x\": 13.359999999999502}, {\"x\": 13.3699999999995}, {\"x\": 13.379999999999502}, {\"x\": 13.389999999999503}, {\"x\": 13.399999999999501}, {\"x\": 13.4099999999995}, {\"x\": 13.4199999999995}, {\"x\": 13.429999999999502}, {\"x\": 13.4399999999995}, {\"x\": 13.449999999999498}, {\"x\": 13.4599999999995}, {\"x\": 13.469999999999501}, {\"x\": 13.4799999999995}, {\"x\": 13.489999999999498}, {\"x\": 13.499999999999499}, {\"x\": 13.5099999999995}, {\"x\": 13.519999999999499}, {\"x\": 13.529999999999497}, {\"x\": 13.539999999999498}, {\"x\": 13.5499999999995}, {\"x\": 13.559999999999498}, {\"x\": 13.569999999999496}, {\"x\": 13.579999999999497}, {\"x\": 13.589999999999499}, {\"x\": 13.599999999999497}, {\"x\": 13.609999999999495}, {\"x\": 13.619999999999497}, {\"x\": 13.629999999999498}, {\"x\": 13.639999999999496}, {\"x\": 13.649999999999494}, {\"x\": 13.659999999999496}, {\"x\": 13.669999999999497}, {\"x\": 13.679999999999495}, {\"x\": 13.689999999999493}, {\"x\": 13.699999999999495}, {\"x\": 13.709999999999496}, {\"x\": 13.719999999999494}, {\"x\": 13.729999999999492}, {\"x\": 13.739999999999494}, {\"x\": 13.749999999999496}, {\"x\": 13.759999999999494}, {\"x\": 13.769999999999492}, {\"x\": 13.779999999999493}, {\"x\": 13.789999999999495}, {\"x\": 13.799999999999493}, {\"x\": 13.80999999999949}, {\"x\": 13.819999999999492}, {\"x\": 13.829999999999494}, {\"x\": 13.839999999999492}, {\"x\": 13.84999999999949}, {\"x\": 13.859999999999491}, {\"x\": 13.869999999999493}, {\"x\": 13.879999999999491}, {\"x\": 13.889999999999489}, {\"x\": 13.89999999999949}, {\"x\": 13.909999999999492}, {\"x\": 13.91999999999949}, {\"x\": 13.929999999999488}, {\"x\": 13.93999999999949}, {\"x\": 13.949999999999491}, {\"x\": 13.95999999999949}, {\"x\": 13.969999999999487}, {\"x\": 13.979999999999489}, {\"x\": 13.98999999999949}, {\"x\": 13.999999999999488}, {\"x\": 14.009999999999486}, {\"x\": 14.019999999999488}, {\"x\": 14.02999999999949}, {\"x\": 14.039999999999488}, {\"x\": 14.049999999999486}, {\"x\": 14.059999999999487}, {\"x\": 14.069999999999489}, {\"x\": 14.079999999999487}, {\"x\": 14.089999999999485}, {\"x\": 14.099999999999486}, {\"x\": 14.109999999999488}, {\"x\": 14.119999999999486}, {\"x\": 14.129999999999484}, {\"x\": 14.139999999999485}, {\"x\": 14.149999999999487}, {\"x\": 14.159999999999485}, {\"x\": 14.169999999999483}, {\"x\": 14.179999999999485}, {\"x\": 14.189999999999486}, {\"x\": 14.199999999999484}, {\"x\": 14.209999999999482}, {\"x\": 14.219999999999484}, {\"x\": 14.229999999999485}, {\"x\": 14.239999999999483}, {\"x\": 14.249999999999481}, {\"x\": 14.259999999999483}, {\"x\": 14.269999999999484}, {\"x\": 14.279999999999482}, {\"x\": 14.28999999999948}, {\"x\": 14.299999999999482}, {\"x\": 14.309999999999484}, {\"x\": 14.319999999999482}, {\"x\": 14.32999999999948}, {\"x\": 14.339999999999481}, {\"x\": 14.349999999999483}, {\"x\": 14.35999999999948}, {\"x\": 14.369999999999479}, {\"x\": 14.37999999999948}, {\"x\": 14.389999999999482}, {\"x\": 14.39999999999948}, {\"x\": 14.409999999999478}, {\"x\": 14.41999999999948}, {\"x\": 14.429999999999481}, {\"x\": 14.439999999999479}, {\"x\": 14.449999999999477}, {\"x\": 14.459999999999479}, {\"x\": 14.46999999999948}, {\"x\": 14.479999999999478}, {\"x\": 14.489999999999476}, {\"x\": 14.499999999999478}, {\"x\": 14.50999999999948}, {\"x\": 14.519999999999477}, {\"x\": 14.529999999999475}, {\"x\": 14.539999999999477}, {\"x\": 14.549999999999478}, {\"x\": 14.559999999999476}, {\"x\": 14.569999999999474}, {\"x\": 14.579999999999476}, {\"x\": 14.589999999999478}, {\"x\": 14.599999999999476}, {\"x\": 14.609999999999474}, {\"x\": 14.619999999999475}, {\"x\": 14.629999999999477}, {\"x\": 14.639999999999475}, {\"x\": 14.649999999999473}, {\"x\": 14.659999999999474}, {\"x\": 14.669999999999476}, {\"x\": 14.679999999999474}, {\"x\": 14.689999999999472}, {\"x\": 14.699999999999473}, {\"x\": 14.709999999999475}, {\"x\": 14.719999999999473}, {\"x\": 14.729999999999471}, {\"x\": 14.739999999999473}, {\"x\": 14.749999999999474}, {\"x\": 14.759999999999472}, {\"x\": 14.76999999999947}, {\"x\": 14.779999999999472}, {\"x\": 14.789999999999473}, {\"x\": 14.799999999999471}, {\"x\": 14.80999999999947}, {\"x\": 14.819999999999471}, {\"x\": 14.829999999999472}, {\"x\": 14.83999999999947}, {\"x\": 14.849999999999469}, {\"x\": 14.85999999999947}, {\"x\": 14.869999999999472}, {\"x\": 14.87999999999947}, {\"x\": 14.889999999999468}, {\"x\": 14.89999999999947}, {\"x\": 14.90999999999947}, {\"x\": 14.919999999999469}, {\"x\": 14.929999999999467}, {\"x\": 14.939999999999468}, {\"x\": 14.94999999999947}, {\"x\": 14.959999999999468}, {\"x\": 14.969999999999466}, {\"x\": 14.979999999999468}, {\"x\": 14.989999999999469}, {\"x\": 14.999999999999467}, {\"x\": 15.009999999999465}, {\"x\": 15.019999999999467}, {\"x\": 15.029999999999468}, {\"x\": 15.039999999999466}, {\"x\": 15.049999999999464}, {\"x\": 15.059999999999466}, {\"x\": 15.069999999999467}, {\"x\": 15.079999999999465}, {\"x\": 15.089999999999463}, {\"x\": 15.099999999999465}, {\"x\": 15.109999999999467}, {\"x\": 15.119999999999465}, {\"x\": 15.129999999999463}, {\"x\": 15.139999999999464}, {\"x\": 15.149999999999466}, {\"x\": 15.159999999999464}, {\"x\": 15.169999999999462}, {\"x\": 15.179999999999463}, {\"x\": 15.189999999999465}, {\"x\": 15.199999999999463}, {\"x\": 15.20999999999946}, {\"x\": 15.219999999999462}, {\"x\": 15.229999999999464}, {\"x\": 15.239999999999462}, {\"x\": 15.24999999999946}, {\"x\": 15.259999999999462}, {\"x\": 15.269999999999463}, {\"x\": 15.279999999999461}, {\"x\": 15.28999999999946}, {\"x\": 15.29999999999946}, {\"x\": 15.309999999999462}, {\"x\": 15.31999999999946}, {\"x\": 15.329999999999458}, {\"x\": 15.33999999999946}, {\"x\": 15.349999999999461}, {\"x\": 15.35999999999946}, {\"x\": 15.369999999999457}, {\"x\": 15.379999999999459}, {\"x\": 15.38999999999946}, {\"x\": 15.399999999999459}, {\"x\": 15.409999999999457}, {\"x\": 15.419999999999458}, {\"x\": 15.42999999999946}, {\"x\": 15.439999999999458}, {\"x\": 15.449999999999456}, {\"x\": 15.459999999999457}, {\"x\": 15.469999999999459}, {\"x\": 15.479999999999457}, {\"x\": 15.489999999999455}, {\"x\": 15.499999999999456}, {\"x\": 15.509999999999458}, {\"x\": 15.519999999999456}, {\"x\": 15.529999999999454}, {\"x\": 15.539999999999456}, {\"x\": 15.549999999999457}, {\"x\": 15.559999999999455}, {\"x\": 15.569999999999453}, {\"x\": 15.579999999999455}, {\"x\": 15.589999999999456}, {\"x\": 15.599999999999454}, {\"x\": 15.609999999999452}, {\"x\": 15.619999999999454}, {\"x\": 15.629999999999455}, {\"x\": 15.639999999999453}, {\"x\": 15.649999999999451}, {\"x\": 15.659999999999453}, {\"x\": 15.669999999999455}, {\"x\": 15.679999999999453}, {\"x\": 15.68999999999945}, {\"x\": 15.699999999999452}, {\"x\": 15.709999999999454}, {\"x\": 15.719999999999452}, {\"x\": 15.72999999999945}, {\"x\": 15.739999999999451}, {\"x\": 15.749999999999453}, {\"x\": 15.759999999999451}, {\"x\": 15.769999999999449}, {\"x\": 15.77999999999945}, {\"x\": 15.789999999999452}, {\"x\": 15.79999999999945}, {\"x\": 15.809999999999448}, {\"x\": 15.81999999999945}, {\"x\": 15.829999999999451}, {\"x\": 15.83999999999945}, {\"x\": 15.849999999999447}, {\"x\": 15.859999999999449}, {\"x\": 15.86999999999945}, {\"x\": 15.879999999999448}, {\"x\": 15.889999999999446}, {\"x\": 15.899999999999448}, {\"x\": 15.90999999999945}, {\"x\": 15.919999999999447}, {\"x\": 15.929999999999445}, {\"x\": 15.939999999999447}, {\"x\": 15.949999999999449}, {\"x\": 15.959999999999447}, {\"x\": 15.969999999999445}, {\"x\": 15.979999999999446}, {\"x\": 15.989999999999448}, {\"x\": 15.999999999999446}, {\"x\": 16.009999999999444}, {\"x\": 16.019999999999445}, {\"x\": 16.029999999999447}, {\"x\": 16.039999999999445}, {\"x\": 16.049999999999443}, {\"x\": 16.059999999999444}, {\"x\": 16.069999999999446}, {\"x\": 16.079999999999444}, {\"x\": 16.089999999999442}, {\"x\": 16.099999999999444}, {\"x\": 16.109999999999445}, {\"x\": 16.119999999999443}, {\"x\": 16.12999999999944}, {\"x\": 16.139999999999443}, {\"x\": 16.149999999999444}, {\"x\": 16.159999999999442}, {\"x\": 16.16999999999944}, {\"x\": 16.179999999999442}, {\"x\": 16.189999999999444}, {\"x\": 16.19999999999944}, {\"x\": 16.20999999999944}, {\"x\": 16.21999999999944}, {\"x\": 16.229999999999443}, {\"x\": 16.23999999999944}, {\"x\": 16.24999999999944}, {\"x\": 16.25999999999944}, {\"x\": 16.269999999999442}, {\"x\": 16.27999999999944}, {\"x\": 16.289999999999438}, {\"x\": 16.29999999999944}, {\"x\": 16.30999999999944}, {\"x\": 16.31999999999944}, {\"x\": 16.329999999999437}, {\"x\": 16.33999999999944}, {\"x\": 16.34999999999944}, {\"x\": 16.359999999999438}, {\"x\": 16.369999999999436}, {\"x\": 16.379999999999438}, {\"x\": 16.38999999999944}, {\"x\": 16.399999999999437}, {\"x\": 16.409999999999435}, {\"x\": 16.419999999999437}, {\"x\": 16.42999999999944}, {\"x\": 16.439999999999436}, {\"x\": 16.449999999999434}, {\"x\": 16.459999999999436}, {\"x\": 16.469999999999438}, {\"x\": 16.479999999999436}, {\"x\": 16.489999999999434}, {\"x\": 16.499999999999435}, {\"x\": 16.509999999999437}, {\"x\": 16.519999999999435}, {\"x\": 16.529999999999433}, {\"x\": 16.539999999999434}, {\"x\": 16.549999999999436}, {\"x\": 16.559999999999434}, {\"x\": 16.569999999999432}, {\"x\": 16.579999999999433}, {\"x\": 16.589999999999435}, {\"x\": 16.599999999999433}, {\"x\": 16.60999999999943}, {\"x\": 16.619999999999433}, {\"x\": 16.629999999999434}, {\"x\": 16.639999999999432}, {\"x\": 16.64999999999943}, {\"x\": 16.65999999999943}, {\"x\": 16.669999999999433}, {\"x\": 16.67999999999943}, {\"x\": 16.68999999999943}, {\"x\": 16.69999999999943}, {\"x\": 16.709999999999432}, {\"x\": 16.71999999999943}, {\"x\": 16.72999999999943}, {\"x\": 16.73999999999943}, {\"x\": 16.74999999999943}, {\"x\": 16.75999999999943}, {\"x\": 16.769999999999428}, {\"x\": 16.77999999999943}, {\"x\": 16.78999999999943}, {\"x\": 16.79999999999943}, {\"x\": 16.809999999999427}, {\"x\": 16.81999999999943}, {\"x\": 16.82999999999943}, {\"x\": 16.839999999999428}, {\"x\": 16.849999999999426}, {\"x\": 16.859999999999427}, {\"x\": 16.86999999999943}, {\"x\": 16.879999999999427}, {\"x\": 16.889999999999425}, {\"x\": 16.899999999999427}, {\"x\": 16.909999999999428}, {\"x\": 16.919999999999426}, {\"x\": 16.929999999999424}, {\"x\": 16.939999999999426}, {\"x\": 16.949999999999427}, {\"x\": 16.959999999999425}, {\"x\": 16.969999999999423}, {\"x\": 16.979999999999425}, {\"x\": 16.989999999999426}, {\"x\": 16.999999999999424}, {\"x\": 17.009999999999422}, {\"x\": 17.019999999999424}, {\"x\": 17.029999999999426}, {\"x\": 17.039999999999424}, {\"x\": 17.04999999999942}, {\"x\": 17.059999999999423}, {\"x\": 17.069999999999425}, {\"x\": 17.079999999999423}, {\"x\": 17.08999999999942}, {\"x\": 17.099999999999422}, {\"x\": 17.109999999999424}, {\"x\": 17.119999999999422}, {\"x\": 17.12999999999942}, {\"x\": 17.13999999999942}, {\"x\": 17.149999999999423}, {\"x\": 17.15999999999942}, {\"x\": 17.16999999999942}, {\"x\": 17.17999999999942}, {\"x\": 17.189999999999422}, {\"x\": 17.19999999999942}, {\"x\": 17.209999999999418}, {\"x\": 17.21999999999942}, {\"x\": 17.22999999999942}, {\"x\": 17.23999999999942}, {\"x\": 17.249999999999417}, {\"x\": 17.25999999999942}, {\"x\": 17.26999999999942}, {\"x\": 17.27999999999942}, {\"x\": 17.289999999999417}, {\"x\": 17.299999999999418}, {\"x\": 17.30999999999942}, {\"x\": 17.319999999999418}, {\"x\": 17.329999999999416}, {\"x\": 17.339999999999417}, {\"x\": 17.34999999999942}, {\"x\": 17.359999999999417}, {\"x\": 17.369999999999415}, {\"x\": 17.379999999999416}, {\"x\": 17.389999999999418}, {\"x\": 17.399999999999416}, {\"x\": 17.409999999999414}, {\"x\": 17.419999999999416}, {\"x\": 17.429999999999417}, {\"x\": 17.439999999999415}, {\"x\": 17.449999999999413}, {\"x\": 17.459999999999415}, {\"x\": 17.469999999999416}, {\"x\": 17.479999999999414}, {\"x\": 17.489999999999412}, {\"x\": 17.499999999999414}, {\"x\": 17.509999999999415}, {\"x\": 17.519999999999413}, {\"x\": 17.52999999999941}, {\"x\": 17.539999999999413}, {\"x\": 17.549999999999415}, {\"x\": 17.559999999999413}, {\"x\": 17.56999999999941}, {\"x\": 17.579999999999412}, {\"x\": 17.589999999999414}, {\"x\": 17.59999999999941}, {\"x\": 17.60999999999941}, {\"x\": 17.61999999999941}, {\"x\": 17.629999999999413}, {\"x\": 17.63999999999941}, {\"x\": 17.64999999999941}, {\"x\": 17.65999999999941}, {\"x\": 17.669999999999412}, {\"x\": 17.67999999999941}, {\"x\": 17.689999999999408}, {\"x\": 17.69999999999941}, {\"x\": 17.70999999999941}, {\"x\": 17.71999999999941}, {\"x\": 17.729999999999407}, {\"x\": 17.73999999999941}, {\"x\": 17.74999999999941}, {\"x\": 17.75999999999941}, {\"x\": 17.769999999999406}, {\"x\": 17.779999999999408}, {\"x\": 17.78999999999941}, {\"x\": 17.799999999999407}, {\"x\": 17.809999999999405}, {\"x\": 17.819999999999407}, {\"x\": 17.82999999999941}, {\"x\": 17.839999999999407}, {\"x\": 17.849999999999405}, {\"x\": 17.859999999999406}, {\"x\": 17.869999999999408}, {\"x\": 17.879999999999406}, {\"x\": 17.889999999999404}, {\"x\": 17.899999999999405}, {\"x\": 17.909999999999407}, {\"x\": 17.919999999999405}, {\"x\": 17.929999999999403}, {\"x\": 17.939999999999404}, {\"x\": 17.949999999999406}, {\"x\": 17.959999999999404}, {\"x\": 17.969999999999402}, {\"x\": 17.979999999999404}, {\"x\": 17.989999999999405}, {\"x\": 17.999999999999403}, {\"x\": 18.0099999999994}, {\"x\": 18.019999999999403}, {\"x\": 18.029999999999404}, {\"x\": 18.039999999999402}, {\"x\": 18.0499999999994}, {\"x\": 18.059999999999402}, {\"x\": 18.069999999999403}, {\"x\": 18.0799999999994}, {\"x\": 18.0899999999994}, {\"x\": 18.0999999999994}, {\"x\": 18.109999999999403}, {\"x\": 18.1199999999994}, {\"x\": 18.1299999999994}, {\"x\": 18.1399999999994}, {\"x\": 18.1499999999994}, {\"x\": 18.1599999999994}, {\"x\": 18.169999999999398}, {\"x\": 18.1799999999994}, {\"x\": 18.1899999999994}, {\"x\": 18.1999999999994}, {\"x\": 18.209999999999397}, {\"x\": 18.2199999999994}, {\"x\": 18.2299999999994}, {\"x\": 18.239999999999398}, {\"x\": 18.249999999999396}, {\"x\": 18.259999999999398}, {\"x\": 18.2699999999994}, {\"x\": 18.279999999999397}, {\"x\": 18.289999999999395}, {\"x\": 18.299999999999397}, {\"x\": 18.3099999999994}, {\"x\": 18.319999999999396}, {\"x\": 18.329999999999394}, {\"x\": 18.339999999999396}, {\"x\": 18.349999999999397}, {\"x\": 18.359999999999395}, {\"x\": 18.369999999999393}, {\"x\": 18.379999999999395}, {\"x\": 18.389999999999397}, {\"x\": 18.399999999999395}, {\"x\": 18.409999999999393}, {\"x\": 18.419999999999394}, {\"x\": 18.429999999999396}, {\"x\": 18.439999999999394}, {\"x\": 18.44999999999939}, {\"x\": 18.459999999999393}, {\"x\": 18.469999999999395}, {\"x\": 18.479999999999393}, {\"x\": 18.48999999999939}, {\"x\": 18.499999999999392}, {\"x\": 18.509999999999394}, {\"x\": 18.519999999999392}, {\"x\": 18.52999999999939}, {\"x\": 18.53999999999939}, {\"x\": 18.549999999999393}, {\"x\": 18.55999999999939}, {\"x\": 18.56999999999939}, {\"x\": 18.57999999999939}, {\"x\": 18.589999999999392}, {\"x\": 18.59999999999939}, {\"x\": 18.60999999999939}, {\"x\": 18.61999999999939}, {\"x\": 18.62999999999939}, {\"x\": 18.63999999999939}, {\"x\": 18.649999999999388}, {\"x\": 18.65999999999939}, {\"x\": 18.66999999999939}, {\"x\": 18.67999999999939}, {\"x\": 18.689999999999387}, {\"x\": 18.699999999999388}, {\"x\": 18.70999999999939}, {\"x\": 18.719999999999388}, {\"x\": 18.729999999999386}, {\"x\": 18.739999999999387}, {\"x\": 18.74999999999939}, {\"x\": 18.759999999999387}, {\"x\": 18.769999999999385}, {\"x\": 18.779999999999387}, {\"x\": 18.789999999999388}, {\"x\": 18.799999999999386}, {\"x\": 18.809999999999384}, {\"x\": 18.819999999999386}, {\"x\": 18.829999999999387}, {\"x\": 18.839999999999385}, {\"x\": 18.849999999999383}, {\"x\": 18.859999999999385}, {\"x\": 18.869999999999386}, {\"x\": 18.879999999999384}, {\"x\": 18.889999999999382}, {\"x\": 18.899999999999384}, {\"x\": 18.909999999999386}, {\"x\": 18.919999999999384}, {\"x\": 18.92999999999938}, {\"x\": 18.939999999999383}, {\"x\": 18.949999999999385}, {\"x\": 18.959999999999383}, {\"x\": 18.96999999999938}, {\"x\": 18.979999999999382}, {\"x\": 18.989999999999384}, {\"x\": 18.999999999999382}, {\"x\": 19.00999999999938}, {\"x\": 19.01999999999938}, {\"x\": 19.029999999999383}, {\"x\": 19.03999999999938}, {\"x\": 19.04999999999938}, {\"x\": 19.05999999999938}, {\"x\": 19.069999999999382}, {\"x\": 19.07999999999938}, {\"x\": 19.089999999999378}, {\"x\": 19.09999999999938}, {\"x\": 19.10999999999938}, {\"x\": 19.11999999999938}, {\"x\": 19.129999999999377}, {\"x\": 19.13999999999938}, {\"x\": 19.14999999999938}, {\"x\": 19.15999999999938}, {\"x\": 19.169999999999376}, {\"x\": 19.179999999999378}, {\"x\": 19.18999999999938}, {\"x\": 19.199999999999378}, {\"x\": 19.209999999999376}, {\"x\": 19.219999999999377}, {\"x\": 19.22999999999938}, {\"x\": 19.239999999999377}, {\"x\": 19.249999999999375}, {\"x\": 19.259999999999376}, {\"x\": 19.269999999999378}, {\"x\": 19.279999999999376}, {\"x\": 19.289999999999374}, {\"x\": 19.299999999999375}, {\"x\": 19.309999999999377}, {\"x\": 19.319999999999375}, {\"x\": 19.329999999999373}, {\"x\": 19.339999999999375}, {\"x\": 19.349999999999376}, {\"x\": 19.359999999999374}, {\"x\": 19.369999999999372}, {\"x\": 19.379999999999374}, {\"x\": 19.389999999999375}, {\"x\": 19.399999999999373}, {\"x\": 19.40999999999937}, {\"x\": 19.419999999999373}, {\"x\": 19.429999999999374}, {\"x\": 19.439999999999372}, {\"x\": 19.44999999999937}, {\"x\": 19.459999999999372}, {\"x\": 19.469999999999374}, {\"x\": 19.47999999999937}, {\"x\": 19.48999999999937}, {\"x\": 19.49999999999937}, {\"x\": 19.509999999999373}, {\"x\": 19.51999999999937}, {\"x\": 19.52999999999937}, {\"x\": 19.53999999999937}, {\"x\": 19.549999999999372}, {\"x\": 19.55999999999937}, {\"x\": 19.569999999999368}, {\"x\": 19.57999999999937}, {\"x\": 19.58999999999937}, {\"x\": 19.59999999999937}, {\"x\": 19.609999999999367}, {\"x\": 19.61999999999937}, {\"x\": 19.62999999999937}, {\"x\": 19.639999999999368}, {\"x\": 19.649999999999366}, {\"x\": 19.659999999999368}, {\"x\": 19.66999999999937}, {\"x\": 19.679999999999367}, {\"x\": 19.689999999999365}, {\"x\": 19.699999999999367}, {\"x\": 19.70999999999937}, {\"x\": 19.719999999999366}, {\"x\": 19.729999999999364}, {\"x\": 19.739999999999366}, {\"x\": 19.749999999999368}, {\"x\": 19.759999999999366}, {\"x\": 19.769999999999364}, {\"x\": 19.779999999999365}, {\"x\": 19.789999999999367}, {\"x\": 19.799999999999365}, {\"x\": 19.809999999999363}, {\"x\": 19.819999999999364}, {\"x\": 19.829999999999366}, {\"x\": 19.839999999999364}, {\"x\": 19.849999999999362}, {\"x\": 19.859999999999363}, {\"x\": 19.869999999999365}, {\"x\": 19.879999999999363}, {\"x\": 19.88999999999936}, {\"x\": 19.899999999999363}, {\"x\": 19.909999999999364}, {\"x\": 19.919999999999362}, {\"x\": 19.92999999999936}, {\"x\": 19.939999999999362}, {\"x\": 19.949999999999363}, {\"x\": 19.95999999999936}, {\"x\": 19.96999999999936}, {\"x\": 19.97999999999936}, {\"x\": 19.989999999999363}, {\"x\": 19.99999999999936}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fine_inc = 0.01\n",
    "df_fine = pd.DataFrame({'x':np.arange(-10,20+fine_inc,fine_inc)})\n",
    "\n",
    "xmin = -3\n",
    "xmax = 5\n",
    "\n",
    "c_width = 1.0\n",
    "t_width = 1.0\n",
    "\n",
    "t_center_slider = alt.binding_range(min=xmin, max=xmax, step=fine_inc, name='Treatment center:')\n",
    "t_center_selector = alt.param(bind=t_center_slider, value=1.5)\n",
    "\n",
    "thresh_slider = alt.binding_range(min=0, max=xmax, step=fine_inc, name='Responder threshold:')\n",
    "# Seem to need to give this param and internal name to refer to it in a Vega expression string for calculation\n",
    "thresh_selector = alt.param(bind=thresh_slider, value=0.5, name='thresh_sel')\n",
    "\n",
    "base = alt.Chart(df_fine).transform_calculate(\n",
    "    c_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*c_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - 0.0)/c_width,2))),\n",
    "    t_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*t_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - t_center_selector)/t_width,2)))\n",
    ")\n",
    "\n",
    "t_gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[xmin,xmax]), title='')\n",
    ")\n",
    "t_line = t_gauss_base.mark_line(color='#262626',clip=True).encode(\n",
    "    y = alt.Y('t_y:Q', scale=alt.Scale(domain=[0,0.45]), title='')\n",
    ").add_params(\n",
    "    thresh_selector, \n",
    "    t_center_selector\n",
    ")\n",
    "t_area = t_gauss_base.mark_area(\n",
    "    color='#33989899',\n",
    "    clip=True\n",
    ").encode(\n",
    "    y = alt.Y('t_y2:Q', scale=alt.Scale(domain=[0,0.45]), title='')\n",
    ").transform_calculate( \n",
    "    # t_temp = alt.expr.inrange(alt.datum.x,(-thresh_selector,thresh_selector)),\n",
    "    # t_y2 = alt.expr.if_(alt.datum.t_temp,0,alt.datum.t_y)\n",
    "    # Had too much trouble getting the alt.expr statements to work, so needed a Vega expression string\n",
    "    t_y2 = 'inrange(datum.x,[-thresh_sel,thresh_sel]) ? 0 :datum.t_y'\n",
    ")\n",
    "\n",
    "fancy_combo = (t_area + t_line).properties(height = 200, width=350)\n",
    "\n",
    "fancy_combo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Separate filtered versions added together\n",
    "\n",
    "Vega-lite bug where tooltips don't show up in a compound chart (seems to be closed now...)\n",
    "https://github.com/altair-viz/altair/issues/2009"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-6c900016fcf74714bbb36c0e40d4506b.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-6c900016fcf74714bbb36c0e40d4506b.vega-embed details,\n",
       "  #altair-viz-6c900016fcf74714bbb36c0e40d4506b.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-6c900016fcf74714bbb36c0e40d4506b\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-6c900016fcf74714bbb36c0e40d4506b\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-6c900016fcf74714bbb36c0e40d4506b\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.8.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.8.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"hconcat\": [{\"layer\": [{\"mark\": {\"type\": \"area\", \"blend\": \"multiply\", \"clip\": true, \"color\": \"#C84E0099\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"c_y\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"filter\": \"(datum.x >= param_55)\"}]}, {\"mark\": {\"type\": \"area\", \"blend\": \"multiply\", \"clip\": true, \"color\": \"#C84E0099\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"c_y\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"filter\": \"(datum.x <= (-param_55))\"}]}, {\"mark\": {\"type\": \"area\", \"blend\": \"multiply\", \"clip\": true, \"color\": \"#33989899\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"filter\": \"(datum.x >= param_55)\"}]}, {\"mark\": {\"type\": \"area\", \"blend\": \"multiply\", \"clip\": true, \"color\": \"#33989899\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"filter\": \"(datum.x <= (-param_55))\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#666666\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"c_y\", \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}]}, {\"mark\": {\"type\": \"line\", \"clip\": true, \"color\": \"#262626\"}, \"encoding\": {\"x\": {\"field\": \"x\", \"scale\": {\"domain\": [-3, 5]}, \"title\": \"\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"t_y\", \"scale\": {\"domain\": [0, 0.45]}, \"title\": \"\", \"type\": \"quantitative\"}}, \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}]}], \"height\": 200, \"width\": 350}, {\"mark\": {\"type\": \"bar\", \"color\": \"#C84E00AA\", \"size\": 30}, \"encoding\": {\"tooltip\": {\"aggregate\": \"sum\", \"field\": \"c_ynPos\", \"format\": \"0.4f\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"sum\", \"field\": \"c_ynPos\", \"scale\": {\"domain\": [-1, 1]}, \"title\": \"Control pos area \\u00b7 p(CI)\", \"type\": \"quantitative\"}}, \"height\": 200, \"name\": \"view_11\", \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#C84E00AA\", \"size\": 30}, \"encoding\": {\"tooltip\": {\"aggregate\": \"sum\", \"field\": \"Minusc_ynNeg\", \"format\": \"0.4f\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"sum\", \"field\": \"Minusc_ynNeg\", \"scale\": {\"domain\": [-1, 1]}, \"title\": \"Control neg area \\u00b7 p(CW)\", \"type\": \"quantitative\"}}, \"height\": 200, \"name\": \"view_12\", \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"calculate\": \"(-1 * datum.c_ynNeg)\", \"as\": \"Minusc_ynNeg\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#339898BB\", \"size\": 30}, \"encoding\": {\"tooltip\": {\"aggregate\": \"sum\", \"field\": \"t_ynPos\", \"format\": \"0.4f\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"sum\", \"field\": \"t_ynPos\", \"scale\": {\"domain\": [-1, 1]}, \"title\": \"Treatment pos area \\u00b7 p(TI)\", \"type\": \"quantitative\"}}, \"height\": 200, \"name\": \"view_13\", \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#339898BB\", \"size\": 30}, \"encoding\": {\"tooltip\": {\"aggregate\": \"sum\", \"field\": \"Minust_ynNeg\", \"format\": \"0.4f\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"sum\", \"field\": \"Minust_ynNeg\", \"scale\": {\"domain\": [-1, 1]}, \"title\": \"Treatment neg area \\u00b7 p(TW)\", \"type\": \"quantitative\"}}, \"height\": 200, \"name\": \"view_14\", \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"calculate\": \"(-1 * datum.t_ynNeg)\", \"as\": \"Minust_ynNeg\"}], \"width\": 50}, {\"mark\": {\"type\": \"bar\", \"color\": \"#993399BB\", \"size\": 30}, \"encoding\": {\"tooltip\": {\"field\": \"pB\", \"format\": \"0.4f\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"pB\", \"scale\": {\"domain\": [-1, 1]}, \"title\": \"Net benefit \\u00b7 p(B)\", \"type\": \"quantitative\"}}, \"height\": 200, \"name\": \"view_15\", \"transform\": [{\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - 0.0) / 1.0),2))))\", \"as\": \"c_y\"}, {\"calculate\": \"((1.0 / (sqrt((2 * PI)) * 1.0)) * exp((-0.5 * pow(((datum.x - param_54) / 1.0),2))))\", \"as\": \"t_y\"}, {\"calculate\": \"(0.1 * datum.c_y)\", \"as\": \"c_yn\"}, {\"calculate\": \"(0.1 * datum.t_y)\", \"as\": \"t_yn\"}, {\"calculate\": \"if((datum.x >= param_55),datum.c_yn,0)\", \"as\": \"c_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.c_yn,0)\", \"as\": \"c_ynNeg\"}, {\"calculate\": \"if((datum.x >= param_55),datum.t_yn,0)\", \"as\": \"t_ynPos\"}, {\"calculate\": \"if((datum.x <= (-param_55)),datum.t_yn,0)\", \"as\": \"t_ynNeg\"}, {\"aggregate\": [{\"op\": \"sum\", \"field\": \"t_ynPos\", \"as\": \"pTI\"}, {\"op\": \"sum\", \"field\": \"t_ynNeg\", \"as\": \"pTW\"}, {\"op\": \"sum\", \"field\": \"c_ynPos\", \"as\": \"pCI\"}, {\"op\": \"sum\", \"field\": \"c_ynNeg\", \"as\": \"pCW\"}]}, {\"calculate\": \"(datum.pTI-datum.pTW) - (datum.pCI-datum.pCW) + datum.pTW*datum.pCI - datum.pTI*datum.pCW\", \"as\": \"pB\"}], \"width\": 50}], \"data\": {\"name\": \"data-51ae1ed5cb2212e7b4639c38a9c226e2\"}, \"params\": [{\"name\": \"param_55\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": 0, \"name\": \"Responder threshold:\", \"step\": 0.1}, \"value\": 0.5}, {\"name\": \"param_54\", \"bind\": {\"input\": \"range\", \"max\": 5, \"min\": -3, \"name\": \"Treatment center:\", \"step\": 0.1}, \"value\": 2.0}, {\"name\": \"param_56\", \"select\": {\"type\": \"point\"}, \"views\": [\"view_11\"]}, {\"name\": \"param_57\", \"select\": {\"type\": \"point\"}, \"views\": [\"view_12\"]}, {\"name\": \"param_58\", \"select\": {\"type\": \"point\"}, \"views\": [\"view_13\"]}, {\"name\": \"param_59\", \"select\": {\"type\": \"point\"}, \"views\": [\"view_14\"]}, {\"name\": \"param_60\", \"select\": {\"type\": \"point\"}, \"views\": [\"view_15\"]}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.8.0.json\", \"datasets\": {\"data-51ae1ed5cb2212e7b4639c38a9c226e2\": [{\"x\": -10.0}, {\"x\": -9.9}, {\"x\": -9.8}, {\"x\": -9.700000000000001}, {\"x\": -9.600000000000001}, {\"x\": -9.500000000000002}, {\"x\": -9.400000000000002}, {\"x\": -9.300000000000002}, {\"x\": -9.200000000000003}, {\"x\": -9.100000000000003}, {\"x\": -9.000000000000004}, {\"x\": -8.900000000000004}, {\"x\": -8.800000000000004}, {\"x\": -8.700000000000005}, {\"x\": -8.600000000000005}, {\"x\": -8.500000000000005}, {\"x\": -8.400000000000006}, {\"x\": -8.300000000000006}, {\"x\": -8.200000000000006}, {\"x\": -8.100000000000007}, {\"x\": -8.000000000000007}, {\"x\": -7.9000000000000075}, {\"x\": -7.800000000000008}, {\"x\": -7.700000000000008}, {\"x\": -7.6000000000000085}, {\"x\": -7.500000000000009}, {\"x\": -7.400000000000009}, {\"x\": -7.30000000000001}, {\"x\": -7.20000000000001}, {\"x\": -7.10000000000001}, {\"x\": -7.000000000000011}, {\"x\": -6.900000000000011}, {\"x\": -6.800000000000011}, {\"x\": -6.700000000000012}, {\"x\": -6.600000000000012}, {\"x\": -6.500000000000012}, {\"x\": -6.400000000000013}, {\"x\": -6.300000000000013}, {\"x\": -6.2000000000000135}, {\"x\": -6.100000000000014}, {\"x\": -6.000000000000014}, {\"x\": -5.900000000000015}, {\"x\": -5.800000000000015}, {\"x\": -5.700000000000015}, {\"x\": -5.600000000000016}, {\"x\": -5.500000000000016}, {\"x\": -5.400000000000016}, {\"x\": -5.300000000000017}, {\"x\": -5.200000000000017}, {\"x\": -5.100000000000017}, {\"x\": -5.000000000000018}, {\"x\": -4.900000000000018}, {\"x\": -4.8000000000000185}, {\"x\": -4.700000000000019}, {\"x\": -4.600000000000019}, {\"x\": -4.5000000000000195}, {\"x\": -4.40000000000002}, {\"x\": -4.30000000000002}, {\"x\": -4.200000000000021}, {\"x\": -4.100000000000021}, {\"x\": -4.000000000000021}, {\"x\": -3.9000000000000217}, {\"x\": -3.800000000000022}, {\"x\": -3.7000000000000224}, {\"x\": -3.6000000000000227}, {\"x\": -3.500000000000023}, {\"x\": -3.4000000000000234}, {\"x\": -3.300000000000024}, {\"x\": -3.200000000000024}, {\"x\": -3.1000000000000245}, {\"x\": -3.000000000000025}, {\"x\": -2.9000000000000252}, {\"x\": -2.8000000000000256}, {\"x\": -2.700000000000026}, {\"x\": -2.6000000000000263}, {\"x\": -2.5000000000000266}, {\"x\": -2.400000000000027}, {\"x\": -2.3000000000000274}, {\"x\": -2.2000000000000277}, {\"x\": -2.100000000000028}, {\"x\": -2.0000000000000284}, {\"x\": -1.9000000000000288}, {\"x\": -1.8000000000000291}, {\"x\": -1.7000000000000295}, {\"x\": -1.6000000000000298}, {\"x\": -1.5000000000000302}, {\"x\": -1.4000000000000306}, {\"x\": -1.300000000000031}, {\"x\": -1.2000000000000313}, {\"x\": -1.1000000000000316}, {\"x\": -1.000000000000032}, {\"x\": -0.9000000000000323}, {\"x\": -0.8000000000000327}, {\"x\": -0.700000000000033}, {\"x\": -0.6000000000000334}, {\"x\": -0.5000000000000338}, {\"x\": -0.4000000000000341}, {\"x\": -0.30000000000003446}, {\"x\": -0.20000000000003482}, {\"x\": -0.10000000000003517}, {\"x\": -3.552713678800501e-14}, {\"x\": 0.09999999999996412}, {\"x\": 0.19999999999996376}, {\"x\": 0.2999999999999634}, {\"x\": 0.39999999999996305}, {\"x\": 0.4999999999999627}, {\"x\": 0.5999999999999623}, {\"x\": 0.699999999999962}, {\"x\": 0.7999999999999616}, {\"x\": 0.8999999999999613}, {\"x\": 0.9999999999999609}, {\"x\": 1.0999999999999606}, {\"x\": 1.1999999999999602}, {\"x\": 1.2999999999999599}, {\"x\": 1.3999999999999595}, {\"x\": 1.4999999999999591}, {\"x\": 1.5999999999999588}, {\"x\": 1.6999999999999584}, {\"x\": 1.799999999999958}, {\"x\": 1.8999999999999577}, {\"x\": 1.9999999999999574}, {\"x\": 2.099999999999957}, {\"x\": 2.1999999999999567}, {\"x\": 2.2999999999999563}, {\"x\": 2.399999999999956}, {\"x\": 2.4999999999999556}, {\"x\": 2.5999999999999552}, {\"x\": 2.699999999999955}, {\"x\": 2.7999999999999545}, {\"x\": 2.899999999999954}, {\"x\": 2.999999999999954}, {\"x\": 3.0999999999999535}, {\"x\": 3.199999999999953}, {\"x\": 3.2999999999999527}, {\"x\": 3.3999999999999524}, {\"x\": 3.499999999999952}, {\"x\": 3.5999999999999517}, {\"x\": 3.6999999999999513}, {\"x\": 3.799999999999951}, {\"x\": 3.8999999999999506}, {\"x\": 3.9999999999999503}, {\"x\": 4.09999999999995}, {\"x\": 4.1999999999999496}, {\"x\": 4.299999999999949}, {\"x\": 4.399999999999949}, {\"x\": 4.4999999999999485}, {\"x\": 4.599999999999948}, {\"x\": 4.699999999999948}, {\"x\": 4.799999999999947}, {\"x\": 4.899999999999947}, {\"x\": 4.999999999999947}, {\"x\": 5.099999999999946}, {\"x\": 5.199999999999946}, {\"x\": 5.299999999999946}, {\"x\": 5.399999999999945}, {\"x\": 5.499999999999945}, {\"x\": 5.599999999999945}, {\"x\": 5.699999999999944}, {\"x\": 5.799999999999944}, {\"x\": 5.8999999999999435}, {\"x\": 5.999999999999943}, {\"x\": 6.099999999999945}, {\"x\": 6.1999999999999424}, {\"x\": 6.29999999999994}, {\"x\": 6.399999999999942}, {\"x\": 6.499999999999943}, {\"x\": 6.599999999999941}, {\"x\": 6.699999999999939}, {\"x\": 6.79999999999994}, {\"x\": 6.899999999999942}, {\"x\": 6.99999999999994}, {\"x\": 7.0999999999999375}, {\"x\": 7.199999999999939}, {\"x\": 7.29999999999994}, {\"x\": 7.399999999999938}, {\"x\": 7.499999999999936}, {\"x\": 7.5999999999999375}, {\"x\": 7.699999999999939}, {\"x\": 7.799999999999937}, {\"x\": 7.899999999999935}, {\"x\": 7.999999999999936}, {\"x\": 8.099999999999937}, {\"x\": 8.199999999999935}, {\"x\": 8.299999999999933}, {\"x\": 8.399999999999935}, {\"x\": 8.499999999999936}, {\"x\": 8.599999999999934}, {\"x\": 8.699999999999932}, {\"x\": 8.799999999999933}, {\"x\": 8.899999999999935}, {\"x\": 8.999999999999932}, {\"x\": 9.09999999999993}, {\"x\": 9.199999999999932}, {\"x\": 9.299999999999933}, {\"x\": 9.399999999999931}, {\"x\": 9.499999999999929}, {\"x\": 9.59999999999993}, {\"x\": 9.699999999999932}, {\"x\": 9.79999999999993}, {\"x\": 9.899999999999928}, {\"x\": 9.999999999999929}, {\"x\": 10.09999999999993}, {\"x\": 10.199999999999928}, {\"x\": 10.299999999999926}, {\"x\": 10.399999999999928}, {\"x\": 10.499999999999929}, {\"x\": 10.599999999999927}, {\"x\": 10.699999999999925}, {\"x\": 10.799999999999926}, {\"x\": 10.899999999999928}, {\"x\": 10.999999999999925}, {\"x\": 11.099999999999923}, {\"x\": 11.199999999999925}, {\"x\": 11.299999999999926}, {\"x\": 11.399999999999924}, {\"x\": 11.499999999999922}, {\"x\": 11.599999999999923}, {\"x\": 11.699999999999925}, {\"x\": 11.799999999999923}, {\"x\": 11.89999999999992}, {\"x\": 11.999999999999922}, {\"x\": 12.099999999999923}, {\"x\": 12.199999999999921}, {\"x\": 12.299999999999919}, {\"x\": 12.39999999999992}, {\"x\": 12.499999999999922}, {\"x\": 12.59999999999992}, {\"x\": 12.699999999999918}, {\"x\": 12.799999999999919}, {\"x\": 12.89999999999992}, {\"x\": 12.999999999999918}, {\"x\": 13.099999999999916}, {\"x\": 13.199999999999918}, {\"x\": 13.299999999999919}, {\"x\": 13.399999999999917}, {\"x\": 13.499999999999915}, {\"x\": 13.599999999999916}, {\"x\": 13.699999999999918}, {\"x\": 13.799999999999915}, {\"x\": 13.899999999999913}, {\"x\": 13.999999999999915}, {\"x\": 14.099999999999916}, {\"x\": 14.199999999999914}, {\"x\": 14.299999999999912}, {\"x\": 14.399999999999913}, {\"x\": 14.499999999999915}, {\"x\": 14.599999999999913}, {\"x\": 14.69999999999991}, {\"x\": 14.799999999999912}, {\"x\": 14.899999999999913}, {\"x\": 14.999999999999911}, {\"x\": 15.099999999999909}, {\"x\": 15.19999999999991}, {\"x\": 15.299999999999912}, {\"x\": 15.39999999999991}, {\"x\": 15.499999999999908}, {\"x\": 15.599999999999909}, {\"x\": 15.69999999999991}, {\"x\": 15.799999999999908}, {\"x\": 15.899999999999906}, {\"x\": 15.999999999999908}, {\"x\": 16.09999999999991}, {\"x\": 16.199999999999907}, {\"x\": 16.299999999999905}, {\"x\": 16.399999999999906}, {\"x\": 16.499999999999908}, {\"x\": 16.599999999999905}, {\"x\": 16.699999999999903}, {\"x\": 16.799999999999905}, {\"x\": 16.899999999999906}, {\"x\": 16.999999999999904}, {\"x\": 17.099999999999902}, {\"x\": 17.199999999999903}, {\"x\": 17.299999999999905}, {\"x\": 17.399999999999903}, {\"x\": 17.4999999999999}, {\"x\": 17.599999999999902}, {\"x\": 17.699999999999903}, {\"x\": 17.7999999999999}, {\"x\": 17.8999999999999}, {\"x\": 17.9999999999999}, {\"x\": 18.099999999999902}, {\"x\": 18.1999999999999}, {\"x\": 18.299999999999898}, {\"x\": 18.3999999999999}, {\"x\": 18.4999999999999}, {\"x\": 18.5999999999999}, {\"x\": 18.699999999999896}, {\"x\": 18.799999999999898}, {\"x\": 18.8999999999999}, {\"x\": 18.999999999999897}, {\"x\": 19.099999999999895}, {\"x\": 19.199999999999896}, {\"x\": 19.299999999999898}, {\"x\": 19.399999999999896}, {\"x\": 19.499999999999893}, {\"x\": 19.599999999999895}, {\"x\": 19.699999999999896}, {\"x\": 19.799999999999894}, {\"x\": 19.899999999999892}, {\"x\": 19.999999999999893}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.HConcatChart(...)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmin = -3\n",
    "xmax = 5\n",
    "\n",
    "c_width = 1.0\n",
    "t_width = 1.0\n",
    "\n",
    "# Selectors (sliders)\n",
    "t_center_slider = alt.binding_range(min=xmin, max=xmax, step=inc, name='Treatment center:')\n",
    "t_center_selector = alt.param(bind=t_center_slider, value=2.0)\n",
    "\n",
    "thresh_slider = alt.binding_range(min=0, max=xmax, step=inc, name='Responder threshold:')\n",
    "thresh_selector = alt.param(bind=thresh_slider, value=0.5)\n",
    "\n",
    "# Base calculations used in later charts\n",
    "# Proper integration (approximation) requires not just sum(y) but sum(y*dx)\n",
    "base = alt.Chart(df).transform_calculate(\n",
    "    c_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*c_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - 0.0)/c_width,2))),\n",
    "    t_y = (1.0/(alt.expr.sqrt(2*alt.expr.PI)*t_width))*alt.expr.exp(-0.5*(pow((alt.datum.x - t_center_selector)/t_width,2))),\n",
    "    c_yn = inc*alt.datum.c_y,\n",
    "    t_yn = inc*alt.datum.t_y,\n",
    "    c_ynPos = alt.expr.if_(alt.datum.x >= thresh_selector, alt.datum.c_yn, 0),\n",
    "    c_ynNeg = alt.expr.if_(alt.datum.x <= -thresh_selector, alt.datum.c_yn, 0),\n",
    "    t_ynPos = alt.expr.if_(alt.datum.x >= thresh_selector, alt.datum.t_yn, 0),\n",
    "    t_ynNeg = alt.expr.if_(alt.datum.x <= -thresh_selector, alt.datum.t_yn, 0)\n",
    ")\n",
    "\n",
    "# Control Gaussians\n",
    "c_gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[xmin,xmax]), title=''),\n",
    "    y = alt.Y('c_y:Q', title='')\n",
    ")\n",
    "c_line = c_gauss_base.mark_line(color='#666666',clip=True).add_params(\n",
    "    thresh_selector, \n",
    "    t_center_selector\n",
    ")\n",
    "c_area_base = c_gauss_base.mark_area(color='#C84E0099',blend='multiply',clip=True)\n",
    "c_areaPos = c_area_base.transform_filter( alt.datum.x >= thresh_selector )\n",
    "c_areaNeg = c_area_base.transform_filter( alt.datum.x <= -thresh_selector )\n",
    "\n",
    "# Treatment Gaussians\n",
    "t_gauss_base = base.encode(\n",
    "    x = alt.X('x:Q', scale=alt.Scale(domain=[xmin,xmax]), title=''),\n",
    "    y = alt.Y('t_y:Q', scale=alt.Scale(domain=[0,0.45]), title='')\n",
    ")\n",
    "t_line = t_gauss_base.mark_line(color='#262626',clip=True)\n",
    "t_area_base = t_gauss_base.mark_area(color='#33989899',blend='multiply',clip=True)\n",
    "t_areaPos = t_area_base.transform_filter( alt.datum.x >= thresh_selector )\n",
    "t_areaNeg = t_area_base.transform_filter( alt.datum.x <= -thresh_selector )\n",
    "\n",
    "# Bars\n",
    "cPos_bar = base.mark_bar(size=30, color='#C84E00AA').encode(\n",
    "    y = alt.Y('sum(c_ynPos):Q', scale=alt.Scale(domain=(-1, 1)), title='Control pos area · p(CI)'),\n",
    "    tooltip = alt.Tooltip('sum(c_ynPos):Q', format='0.4f')\n",
    ").add_params(alt.selection_point())\n",
    "cNeg_bar = base.mark_bar(size=30, color='#C84E00AA').encode(\n",
    "    y = alt.Y('sum(Minusc_ynNeg):Q', scale=alt.Scale(domain=(-1,1)), title='Control neg area · p(CW)'),\n",
    "    tooltip = alt.Tooltip('sum(Minusc_ynNeg):Q', format='0.4f')\n",
    ").add_params(alt.selection_point()).transform_calculate(Minusc_ynNeg = -1*alt.datum.c_ynNeg)\n",
    "tPos_bar = base.mark_bar(size=30, color='#339898BB').encode(\n",
    "    y = alt.Y('sum(t_ynPos):Q', scale=alt.Scale(domain=(-1, 1)), title='Treatment pos area · p(TI)'),\n",
    "    tooltip = alt.Tooltip('sum(t_ynPos):Q', format='0.4f')\n",
    ").add_params(alt.selection_point())\n",
    "tNeg_bar = base.mark_bar(size=30, color='#339898BB').encode(\n",
    "    y = alt.Y('sum(Minust_ynNeg):Q', scale=alt.Scale(domain=(-1,1)), title='Treatment neg area · p(TW)'),\n",
    "    tooltip = alt.Tooltip('sum(Minust_ynNeg):Q', format='0.4f')\n",
    ").add_params(alt.selection_point()).transform_calculate(Minust_ynNeg = -1*alt.datum.t_ynNeg)\n",
    "\n",
    "calc_bar = base.mark_bar(size=30, color='#993399BB').encode(\n",
    "    y = alt.Y('pB:Q', scale=alt.Scale(domain=(-1, 1)), title='Net benefit · p(B)'),\n",
    "    tooltip = alt.Tooltip('pB:Q', format='0.4f')\n",
    ").transform_aggregate(\n",
    "    pTI = 'sum(t_ynPos)',\n",
    "    pTW = 'sum(t_ynNeg)',\n",
    "    pCI = 'sum(c_ynPos)',\n",
    "    pCW = 'sum(c_ynNeg)'\n",
    ").transform_calculate(\n",
    "    pB = '(datum.pTI-datum.pTW) - (datum.pCI-datum.pCW) + datum.pTW*datum.pCI - datum.pTI*datum.pCW'\n",
    ").add_params(alt.selection_point())\n",
    "\n",
    "fancy_combo = (c_areaPos + c_areaNeg + t_areaPos + t_areaNeg + c_line + t_line).properties(height = 200, width=350) | \\\n",
    "        cPos_bar.properties(height = 200, width=50) | \\\n",
    "        cNeg_bar.properties(height = 200, width=50) | \\\n",
    "        tPos_bar.properties(height = 200, width=50) | \\\n",
    "        tNeg_bar.properties(height = 200, width=50) | \\\n",
    "        calc_bar.properties(height = 200, width=50)\n",
    "\n",
    "fancy_combo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "fancy_combo.save('net_benefit.html')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}