Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.graph_objects as go\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "from sklearn import linear_model\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3]\n"
     ]
    }
   ],
   "source": [
    "Intercept = np.array([3.5])\n",
    "b_1 = np.array([1.4])\n",
    "X = np.array([3])\n",
    "y = np.array([Intercept + (b_1 * X)])\n",
    "\n",
    "theta = np.array([1.4])\n",
    "\n",
    "def cost2(X, y, theta):\n",
    "  return(np.sum((((X.dot(theta) + Intercept) - y)**2))/(2*y.size))\n",
    "print (X)\n",
    "\n",
    "# np.sum((((X.dot(theta) + Intercept) - y)**2))/(2*y.size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "alpha = 0.02 \n",
    "# alpha controls the learning rate (step size) \n",
    "# try 0.2 (and note the spaces and how it jumps side to side \n",
    "# and also 0.005 wich is more typical of relative step \n",
    "\n",
    "num_iters = 100\n",
    "theta = 0\n",
    "#chartPts = NULL need to build array differently\n",
    "\n",
    "epsilon = .001 \n",
    "# epsion controls the threshold - try 2 (note how it's likely to totally miss\n",
    "# or .01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "chartPts = np.empty((0,2))\n",
    "tracerMat = np.empty((0,6))\n",
    "\n",
    "tracerMat2 = np.empty((0,5))\n",
    "\n",
    "# i = 1\n",
    "\n",
    "for i in range(num_iters):\n",
    "    \n",
    " #  error <- ((X %*% theta)+Intercept - y)\n",
    " error =  (X.dot(theta) + Intercept) - y\n",
    " # we keep the sign here bc it detemines the direction of the descent\n",
    " delta = (np.transpose(X).dot(error)) /y.size\n",
    " theta = theta - (alpha * delta)\n",
    " cost = cost2(X, y, theta)\n",
    " chartPts = np.append(chartPts, np.array([[float(theta), cost]]), axis=0)\n",
    " if ((math.sqrt(np.sum(delta**2)))<=epsilon): \n",
    "  break \n",
    " tracerMat = np.append(tracerMat, np.array([[int(i), float(error), float(delta), float(theta), cost, math.sqrt(np.sum(delta**2))]]), axis=0)  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 6)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tracerMat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(49, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chartPts.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    " dfTracer = pd.DataFrame({'ID': tracerMat[:, 0], 'error': tracerMat[:, 1], 'delta': tracerMat[:, 2],'theta': tracerMat[:, 3],'cost': tracerMat[:, 4],'math.sqrt(np.sum(delta**2': tracerMat[:, 5]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# just to check and compare\n",
    "\n",
    "path = 'C:/Users/ellen\\OneDrive/Documents/Spring 2020/DA2/Section 1/Notebooks/tracer.csv'\n",
    "dfTracer.to_csv(path, index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "300"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thetaV = np.arange (0, 3, .01)\n",
    "thetaV.size\n",
    "len(thetaV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "FunchartPts = np.empty((0,2))\n",
    "for i in range(len(thetaV)):\n",
    "  rwt = cost2(X, y, thetaV[i])\n",
    "  FunchartPts = np.append(FunchartPts, np.array([[thetaV[i], rwt]]), axis=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfFunChartPts = pd.DataFrame({'X': FunchartPts[:, 0], 'Cost': FunchartPts[:, 1]})\n",
    "dfFunChartPts = dfFunChartPts.sort_values(by='X', ascending=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfChartPts = pd.DataFrame({'X': chartPts[:, 0], 'Cost': chartPts[:, 1]})\n",
    "dfChartPts = dfChartPts.sort_values(by='X', ascending=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "line": {
          "shape": "spline"
         },
         "mode": "lines",
         "name": "function",
         "type": "scatter",
         "x": [
          0,
          0.01,
          0.02,
          0.03,
          0.04,
          0.05,
          0.06,
          0.07,
          0.08,
          0.09,
          0.1,
          0.11,
          0.12,
          0.13,
          0.14,
          0.15,
          0.16,
          0.17,
          0.18,
          0.19,
          0.2,
          0.21,
          0.22,
          0.23,
          0.24,
          0.25,
          0.26,
          0.27,
          0.28,
          0.29,
          0.3,
          0.31,
          0.32,
          0.33,
          0.34,
          0.35000000000000003,
          0.36,
          0.37,
          0.38,
          0.39,
          0.4,
          0.41000000000000003,
          0.42,
          0.43,
          0.44,
          0.45,
          0.46,
          0.47000000000000003,
          0.48,
          0.49,
          0.5,
          0.51,
          0.52,
          0.53,
          0.54,
          0.55,
          0.56,
          0.5700000000000001,
          0.58,
          0.59,
          0.6,
          0.61,
          0.62,
          0.63,
          0.64,
          0.65,
          0.66,
          0.67,
          0.68,
          0.6900000000000001,
          0.7000000000000001,
          0.71,
          0.72,
          0.73,
          0.74,
          0.75,
          0.76,
          0.77,
          0.78,
          0.79,
          0.8,
          0.81,
          0.8200000000000001,
          0.8300000000000001,
          0.84,
          0.85,
          0.86,
          0.87,
          0.88,
          0.89,
          0.9,
          0.91,
          0.92,
          0.93,
          0.9400000000000001,
          0.9500000000000001,
          0.96,
          0.97,
          0.98,
          0.99,
          1,
          1.01,
          1.02,
          1.03,
          1.04,
          1.05,
          1.06,
          1.07,
          1.08,
          1.09,
          1.1,
          1.11,
          1.12,
          1.1300000000000001,
          1.1400000000000001,
          1.1500000000000001,
          1.16,
          1.17,
          1.18,
          1.19,
          1.2,
          1.21,
          1.22,
          1.23,
          1.24,
          1.25,
          1.26,
          1.27,
          1.28,
          1.29,
          1.3,
          1.31,
          1.32,
          1.33,
          1.34,
          1.35,
          1.36,
          1.37,
          1.3800000000000001,
          1.3900000000000001,
          1.4000000000000001,
          1.41,
          1.42,
          1.43,
          1.44,
          1.45,
          1.46,
          1.47,
          1.48,
          1.49,
          1.5,
          1.51,
          1.52,
          1.53,
          1.54,
          1.55,
          1.56,
          1.57,
          1.58,
          1.59,
          1.6,
          1.61,
          1.62,
          1.6300000000000001,
          1.6400000000000001,
          1.6500000000000001,
          1.6600000000000001,
          1.67,
          1.68,
          1.69,
          1.7,
          1.71,
          1.72,
          1.73,
          1.74,
          1.75,
          1.76,
          1.77,
          1.78,
          1.79,
          1.8,
          1.81,
          1.82,
          1.83,
          1.84,
          1.85,
          1.86,
          1.87,
          1.8800000000000001,
          1.8900000000000001,
          1.9000000000000001,
          1.9100000000000001,
          1.92,
          1.93,
          1.94,
          1.95,
          1.96,
          1.97,
          1.98,
          1.99,
          2,
          2.0100000000000002,
          2.02,
          2.0300000000000002,
          2.04,
          2.05,
          2.06,
          2.07,
          2.08,
          2.09,
          2.1,
          2.11,
          2.12,
          2.13,
          2.14,
          2.15,
          2.16,
          2.17,
          2.18,
          2.19,
          2.2,
          2.21,
          2.22,
          2.23,
          2.24,
          2.25,
          2.2600000000000002,
          2.27,
          2.2800000000000002,
          2.29,
          2.3000000000000003,
          2.31,
          2.32,
          2.33,
          2.34,
          2.35,
          2.36,
          2.37,
          2.38,
          2.39,
          2.4,
          2.41,
          2.42,
          2.43,
          2.44,
          2.45,
          2.46,
          2.47,
          2.48,
          2.49,
          2.5,
          2.5100000000000002,
          2.52,
          2.5300000000000002,
          2.54,
          2.5500000000000003,
          2.56,
          2.57,
          2.58,
          2.59,
          2.6,
          2.61,
          2.62,
          2.63,
          2.64,
          2.65,
          2.66,
          2.67,
          2.68,
          2.69,
          2.7,
          2.71,
          2.72,
          2.73,
          2.74,
          2.75,
          2.7600000000000002,
          2.77,
          2.7800000000000002,
          2.79,
          2.8000000000000003,
          2.81,
          2.82,
          2.83,
          2.84,
          2.85,
          2.86,
          2.87,
          2.88,
          2.89,
          2.9,
          2.91,
          2.92,
          2.93,
          2.94,
          2.95,
          2.96,
          2.97,
          2.98,
          2.99
         ],
         "y": [
          8.819999999999997,
          8.69445,
          8.569799999999995,
          8.446049999999998,
          8.323199999999996,
          8.201249999999996,
          8.080199999999998,
          7.960049999999997,
          7.840799999999996,
          7.722449999999997,
          7.604999999999998,
          7.488449999999997,
          7.372799999999998,
          7.258049999999997,
          7.144199999999998,
          7.0312499999999964,
          6.919199999999997,
          6.808049999999998,
          6.697799999999997,
          6.588449999999996,
          6.479999999999999,
          6.372449999999998,
          6.265799999999997,
          6.1600499999999965,
          6.055199999999998,
          5.951249999999997,
          5.848199999999997,
          5.746049999999996,
          5.644799999999998,
          5.544449999999998,
          5.444999999999997,
          5.346449999999999,
          5.2487999999999975,
          5.152049999999997,
          5.056199999999999,
          4.961249999999998,
          4.867199999999998,
          4.77405,
          4.681799999999996,
          4.590449999999998,
          4.499999999999997,
          4.410449999999996,
          4.321799999999999,
          4.234049999999998,
          4.147199999999997,
          4.061249999999999,
          3.976199999999998,
          3.8920499999999976,
          3.8087999999999993,
          3.726449999999999,
          3.6449999999999982,
          3.5644499999999972,
          3.484799999999997,
          3.4060499999999987,
          3.328199999999998,
          3.251249999999997,
          3.175199999999999,
          3.100049999999998,
          3.0257999999999976,
          2.9524499999999994,
          2.8799999999999986,
          2.8084499999999983,
          2.7377999999999996,
          2.668049999999997,
          2.5991999999999984,
          2.5312499999999982,
          2.4641999999999973,
          2.398049999999999,
          2.3327999999999984,
          2.268449999999998,
          2.204999999999999,
          2.142449999999999,
          2.080799999999998,
          2.0200499999999995,
          1.960199999999999,
          1.9012499999999986,
          1.8431999999999982,
          1.7860499999999977,
          1.729799999999999,
          1.6744499999999984,
          1.619999999999998,
          1.5664499999999992,
          1.513799999999999,
          1.4620499999999985,
          1.4111999999999996,
          1.3612499999999992,
          1.3121999999999987,
          1.2640499999999997,
          1.216799999999998,
          1.170449999999999,
          1.1249999999999987,
          1.0804499999999984,
          1.0367999999999993,
          0.994049999999999,
          0.9521999999999986,
          0.9112499999999996,
          0.8711999999999992,
          0.8320499999999988,
          0.7937999999999997,
          0.7564499999999994,
          0.7199999999999992,
          0.6844499999999989,
          0.6497999999999986,
          0.6160499999999993,
          0.5831999999999992,
          0.5512499999999989,
          0.5201999999999996,
          0.4900499999999993,
          0.4607999999999991,
          0.4324499999999989,
          0.4049999999999987,
          0.37844999999999934,
          0.3527999999999991,
          0.32804999999999895,
          0.3041999999999995,
          0.28124999999999933,
          0.2591999999999998,
          0.23804999999999965,
          0.2177999999999995,
          0.19844999999999938,
          0.1799999999999998,
          0.16244999999999965,
          0.14579999999999954,
          0.1300499999999999,
          0.11519999999999977,
          0.10124999999999967,
          0.0881999999999996,
          0.07604999999999953,
          0.0647999999999998,
          0.05444999999999973,
          0.04499999999999968,
          0.036449999999999885,
          0.02879999999999984,
          0.022049999999999806,
          0.016199999999999787,
          0.011249999999999786,
          0.007199999999999906,
          0.004049999999999907,
          0.0017999999999999232,
          0.0004499999999999808,
          3.944304526105059e-31,
          0.00045000000000000747,
          0.0018000000000000299,
          0.0040500000000000674,
          0.0072000000000001195,
          0.011250000000000053,
          0.01620000000000011,
          0.02205000000000018,
          0.02880000000000005,
          0.03645000000000013,
          0.04500000000000021,
          0.05445000000000061,
          0.06480000000000044,
          0.07605000000000023,
          0.08820000000000072,
          0.10125000000000048,
          0.1152000000000002,
          0.1300500000000008,
          0.1458000000000005,
          0.16245000000000015,
          0.18000000000000085,
          0.1984500000000005,
          0.2178000000000001,
          0.23805000000000087,
          0.2592000000000005,
          0.28125,
          0.3042000000000009,
          0.3280500000000004,
          0.3527999999999999,
          0.37845000000000084,
          0.4050000000000003,
          0.4324499999999997,
          0.4608000000000008,
          0.4900500000000002,
          0.5201999999999996,
          0.5512500000000008,
          0.583200000000002,
          0.6160500000000013,
          0.6498000000000006,
          0.684450000000002,
          0.7200000000000013,
          0.7564500000000005,
          0.793800000000002,
          0.8320500000000012,
          0.8712000000000004,
          0.9112500000000019,
          0.952200000000001,
          0.9940500000000002,
          1.036800000000002,
          1.080450000000001,
          1.125,
          1.1704500000000018,
          1.2168000000000008,
          1.2640499999999997,
          1.3122000000000016,
          1.3612500000000005,
          1.4111999999999996,
          1.4620500000000014,
          1.5138000000000005,
          1.5664499999999992,
          1.6200000000000012,
          1.6744500000000033,
          1.7298000000000022,
          1.786050000000001,
          1.8432000000000033,
          1.9012499999999986,
          1.9602000000000008,
          2.0200499999999995,
          2.0808000000000018,
          2.1424500000000006,
          2.205000000000003,
          2.268450000000002,
          2.3328,
          2.3980500000000027,
          2.4642000000000013,
          2.53125,
          2.5992000000000024,
          2.6680500000000014,
          2.737800000000004,
          2.8084500000000023,
          2.8800000000000052,
          2.9524499999999994,
          3.025800000000002,
          3.1000500000000004,
          3.1752000000000034,
          3.251250000000002,
          3.3282000000000047,
          3.406050000000003,
          3.4848000000000017,
          3.5644500000000043,
          3.6450000000000027,
          3.726450000000001,
          3.8087999999999993,
          3.8920500000000025,
          3.976200000000001,
          4.061250000000004,
          4.147200000000002,
          4.234050000000001,
          4.321800000000004,
          4.410450000000002,
          4.5,
          4.590450000000003,
          4.681800000000002,
          4.774050000000005,
          4.867200000000003,
          4.961250000000007,
          5.056199999999999,
          5.152050000000003,
          5.248800000000001,
          5.346450000000004,
          5.445000000000002,
          5.5444500000000065,
          5.6448000000000045,
          5.746050000000002,
          5.848200000000006,
          5.9512500000000035,
          6.055200000000002,
          6.160049999999999,
          6.265800000000003,
          6.372450000000001,
          6.480000000000005,
          6.588450000000003,
          6.697800000000001,
          6.808050000000005,
          6.919200000000003,
          7.03125,
          7.144200000000004,
          7.258050000000002,
          7.372800000000006,
          7.488450000000004,
          7.605000000000008,
          7.7224499999999985,
          7.840800000000003,
          7.960050000000001,
          8.080200000000005,
          8.201250000000003,
          8.323200000000007,
          8.446050000000005,
          8.569800000000003,
          8.694450000000007,
          8.820000000000004,
          8.946450000000002,
          9.073799999999999,
          9.202050000000003,
          9.3312,
          9.461250000000007,
          9.592200000000004,
          9.72405,
          9.856800000000005,
          9.990450000000003,
          10.125,
          10.260450000000006,
          10.396800000000002,
          10.534050000000008,
          10.672200000000005,
          10.81125000000001,
          10.951199999999998,
          11.092050000000004,
          11.2338,
          11.376450000000007
         ]
        },
        {
         "mode": "markers",
         "name": "GD",
         "type": "scatter",
         "x": [
          0.25199999999999995,
          0.4586399999999999,
          0.6280847999999999,
          0.7670295359999999,
          0.8809642195199999,
          0.9743906600064,
          1.051000341205248,
          1.1138202797883032,
          1.1653326294264086,
          1.207572756129655,
          1.242209660026317,
          1.2706119212215798,
          1.2939017754016955,
          1.3129994558293903,
          1.3286595537801,
          1.341500834099682,
          1.352030683961739,
          1.360665160848626,
          1.3677454318958733,
          1.373551254154616,
          1.3783120284067851,
          1.3822158632935637,
          1.3854170079007222,
          1.3880419464785922,
          1.3901943961124457,
          1.3919594048122055,
          1.3934067119460085,
          1.3945935037957269,
          1.395566673112496,
          1.3963646719522467,
          1.3970190310008423,
          1.3975556054206906,
          1.3979955964449662,
          1.3983563890848723,
          1.3986522390495952,
          1.398894836020668,
          1.3990937655369478,
          1.399256887740297,
          1.3993906479470435,
          1.3995003313165757,
          1.399590271679592,
          1.3996640227772654,
          1.3997244986773576,
          1.3997740889154333,
          1.3998147529106553,
          1.3998480973867373,
          1.3998754398571245,
          1.399897860682842,
          1.3999162457599303
         ],
         "y": [
          5.9305679999999965,
          3.9877139231999985,
          2.681338841959679,
          1.802932237333688,
          1.2122916363831724,
          0.8151448963040442,
          0.5481034282748395,
          0.3685447451720021,
          0.24780948665365457,
          0.16662709882591703,
          0.11204006125054668,
          0.07533573718486761,
          0.05065574968310505,
          0.03406092608691967,
          0.022902566700844826,
          0.015399685849648063,
          0.010354748765303366,
          0.006962533069790012,
          0.00468160723612678,
          0.0031479127055717105,
          0.0021166565032264112,
          0.0014232398327694029,
          0.0009569864635541636,
          0.000643477698093826,
          0.0004326744041982593,
          0.00029093026938290184,
          0.00019562151313306673,
          0.00013153590543068386,
          8.844474281158521e-05,
          5.947024506651377e-05,
          3.9987792782717026e-05,
          2.688779186709945e-05,
          1.807935125144066e-05,
          1.2156555781469402e-05,
          8.17406810745981e-06,
          5.496243395454798e-06,
          3.6956740591054485e-06,
          2.484971237340761e-06,
          1.6708946599899411e-06,
          1.123509569376331e-06,
          7.554478344491253e-07,
          5.079631238836993e-07,
          3.415544044994875e-07,
          2.2966118158480531e-07,
          1.5442417849797847e-07,
          1.0383481762181406e-07,
          6.981853136908037e-08,
          4.694598049235736e-08,
          3.156647728333781e-08
         ]
        }
       ],
       "layout": {
        "autosize": false,
        "height": 400,
        "plot_bgcolor": "#FFFFFF",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "width": 500
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"1053f88f-3847-45da-a37e-c1d1eb0a9589\" class=\"plotly-graph-div\" style=\"height:400px; width:500px;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"1053f88f-3847-45da-a37e-c1d1eb0a9589\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        '1053f88f-3847-45da-a37e-c1d1eb0a9589',\n",
       "                        [{\"line\": {\"shape\": \"spline\"}, \"mode\": \"lines\", \"name\": \"function\", \"type\": \"scatter\", \"x\": [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35000000000000003, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41000000000000003, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47000000000000003, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.5700000000000001, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.6900000000000001, 0.7000000000000001, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8, 0.81, 0.8200000000000001, 0.8300000000000001, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.9400000000000001, 0.9500000000000001, 0.96, 0.97, 0.98, 0.99, 1.0, 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09, 1.1, 1.11, 1.12, 1.1300000000000001, 1.1400000000000001, 1.1500000000000001, 1.16, 1.17, 1.18, 1.19, 1.2, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.3, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.3800000000000001, 1.3900000000000001, 1.4000000000000001, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.5, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.6, 1.61, 1.62, 1.6300000000000001, 1.6400000000000001, 1.6500000000000001, 1.6600000000000001, 1.67, 1.68, 1.69, 1.7, 1.71, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, 1.79, 1.8, 1.81, 1.82, 1.83, 1.84, 1.85, 1.86, 1.87, 1.8800000000000001, 1.8900000000000001, 1.9000000000000001, 1.9100000000000001, 1.92, 1.93, 1.94, 1.95, 1.96, 1.97, 1.98, 1.99, 2.0, 2.0100000000000002, 2.02, 2.0300000000000002, 2.04, 2.05, 2.06, 2.07, 2.08, 2.09, 2.1, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19, 2.2, 2.21, 2.22, 2.23, 2.24, 2.25, 2.2600000000000002, 2.27, 2.2800000000000002, 2.29, 2.3000000000000003, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, 2.39, 2.4, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, 2.5, 2.5100000000000002, 2.52, 2.5300000000000002, 2.54, 2.5500000000000003, 2.56, 2.57, 2.58, 2.59, 2.6, 2.61, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, 2.69, 2.7, 2.71, 2.72, 2.73, 2.74, 2.75, 2.7600000000000002, 2.77, 2.7800000000000002, 2.79, 2.8000000000000003, 2.81, 2.82, 2.83, 2.84, 2.85, 2.86, 2.87, 2.88, 2.89, 2.9, 2.91, 2.92, 2.93, 2.94, 2.95, 2.96, 2.97, 2.98, 2.99], \"y\": [8.819999999999997, 8.69445, 8.569799999999995, 8.446049999999998, 8.323199999999996, 8.201249999999996, 8.080199999999998, 7.960049999999997, 7.840799999999996, 7.722449999999997, 7.604999999999998, 7.488449999999997, 7.372799999999998, 7.258049999999997, 7.144199999999998, 7.0312499999999964, 6.919199999999997, 6.808049999999998, 6.697799999999997, 6.588449999999996, 6.479999999999999, 6.372449999999998, 6.265799999999997, 6.1600499999999965, 6.055199999999998, 5.951249999999997, 5.848199999999997, 5.746049999999996, 5.644799999999998, 5.544449999999998, 5.444999999999997, 5.346449999999999, 5.2487999999999975, 5.152049999999997, 5.056199999999999, 4.961249999999998, 4.867199999999998, 4.77405, 4.681799999999996, 4.590449999999998, 4.499999999999997, 4.410449999999996, 4.321799999999999, 4.234049999999998, 4.147199999999997, 4.061249999999999, 3.976199999999998, 3.8920499999999976, 3.8087999999999993, 3.726449999999999, 3.6449999999999982, 3.5644499999999972, 3.484799999999997, 3.4060499999999987, 3.328199999999998, 3.251249999999997, 3.175199999999999, 3.100049999999998, 3.0257999999999976, 2.9524499999999994, 2.8799999999999986, 2.8084499999999983, 2.7377999999999996, 2.668049999999997, 2.5991999999999984, 2.5312499999999982, 2.4641999999999973, 2.398049999999999, 2.3327999999999984, 2.268449999999998, 2.204999999999999, 2.142449999999999, 2.080799999999998, 2.0200499999999995, 1.960199999999999, 1.9012499999999986, 1.8431999999999982, 1.7860499999999977, 1.729799999999999, 1.6744499999999984, 1.619999999999998, 1.5664499999999992, 1.513799999999999, 1.4620499999999985, 1.4111999999999996, 1.3612499999999992, 1.3121999999999987, 1.2640499999999997, 1.216799999999998, 1.170449999999999, 1.1249999999999987, 1.0804499999999984, 1.0367999999999993, 0.994049999999999, 0.9521999999999986, 0.9112499999999996, 0.8711999999999992, 0.8320499999999988, 0.7937999999999997, 0.7564499999999994, 0.7199999999999992, 0.6844499999999989, 0.6497999999999986, 0.6160499999999993, 0.5831999999999992, 0.5512499999999989, 0.5201999999999996, 0.4900499999999993, 0.4607999999999991, 0.4324499999999989, 0.4049999999999987, 0.37844999999999934, 0.3527999999999991, 0.32804999999999895, 0.3041999999999995, 0.28124999999999933, 0.2591999999999998, 0.23804999999999965, 0.2177999999999995, 0.19844999999999938, 0.1799999999999998, 0.16244999999999965, 0.14579999999999954, 0.1300499999999999, 0.11519999999999977, 0.10124999999999967, 0.0881999999999996, 0.07604999999999953, 0.0647999999999998, 0.05444999999999973, 0.04499999999999968, 0.036449999999999885, 0.02879999999999984, 0.022049999999999806, 0.016199999999999787, 0.011249999999999786, 0.007199999999999906, 0.004049999999999907, 0.0017999999999999232, 0.0004499999999999808, 3.944304526105059e-31, 0.00045000000000000747, 0.0018000000000000299, 0.0040500000000000674, 0.0072000000000001195, 0.011250000000000053, 0.01620000000000011, 0.02205000000000018, 0.02880000000000005, 0.03645000000000013, 0.04500000000000021, 0.05445000000000061, 0.06480000000000044, 0.07605000000000023, 0.08820000000000072, 0.10125000000000048, 0.1152000000000002, 0.1300500000000008, 0.1458000000000005, 0.16245000000000015, 0.18000000000000085, 0.1984500000000005, 0.2178000000000001, 0.23805000000000087, 0.2592000000000005, 0.28125, 0.3042000000000009, 0.3280500000000004, 0.3527999999999999, 0.37845000000000084, 0.4050000000000003, 0.4324499999999997, 0.4608000000000008, 0.4900500000000002, 0.5201999999999996, 0.5512500000000008, 0.583200000000002, 0.6160500000000013, 0.6498000000000006, 0.684450000000002, 0.7200000000000013, 0.7564500000000005, 0.793800000000002, 0.8320500000000012, 0.8712000000000004, 0.9112500000000019, 0.952200000000001, 0.9940500000000002, 1.036800000000002, 1.080450000000001, 1.125, 1.1704500000000018, 1.2168000000000008, 1.2640499999999997, 1.3122000000000016, 1.3612500000000005, 1.4111999999999996, 1.4620500000000014, 1.5138000000000005, 1.5664499999999992, 1.6200000000000012, 1.6744500000000033, 1.7298000000000022, 1.786050000000001, 1.8432000000000033, 1.9012499999999986, 1.9602000000000008, 2.0200499999999995, 2.0808000000000018, 2.1424500000000006, 2.205000000000003, 2.268450000000002, 2.3328, 2.3980500000000027, 2.4642000000000013, 2.53125, 2.5992000000000024, 2.6680500000000014, 2.737800000000004, 2.8084500000000023, 2.8800000000000052, 2.9524499999999994, 3.025800000000002, 3.1000500000000004, 3.1752000000000034, 3.251250000000002, 3.3282000000000047, 3.406050000000003, 3.4848000000000017, 3.5644500000000043, 3.6450000000000027, 3.726450000000001, 3.8087999999999993, 3.8920500000000025, 3.976200000000001, 4.061250000000004, 4.147200000000002, 4.234050000000001, 4.321800000000004, 4.410450000000002, 4.5, 4.590450000000003, 4.681800000000002, 4.774050000000005, 4.867200000000003, 4.961250000000007, 5.056199999999999, 5.152050000000003, 5.248800000000001, 5.346450000000004, 5.445000000000002, 5.5444500000000065, 5.6448000000000045, 5.746050000000002, 5.848200000000006, 5.9512500000000035, 6.055200000000002, 6.160049999999999, 6.265800000000003, 6.372450000000001, 6.480000000000005, 6.588450000000003, 6.697800000000001, 6.808050000000005, 6.919200000000003, 7.03125, 7.144200000000004, 7.258050000000002, 7.372800000000006, 7.488450000000004, 7.605000000000008, 7.7224499999999985, 7.840800000000003, 7.960050000000001, 8.080200000000005, 8.201250000000003, 8.323200000000007, 8.446050000000005, 8.569800000000003, 8.694450000000007, 8.820000000000004, 8.946450000000002, 9.073799999999999, 9.202050000000003, 9.3312, 9.461250000000007, 9.592200000000004, 9.72405, 9.856800000000005, 9.990450000000003, 10.125, 10.260450000000006, 10.396800000000002, 10.534050000000008, 10.672200000000005, 10.81125000000001, 10.951199999999998, 11.092050000000004, 11.2338, 11.376450000000007]}, {\"mode\": \"markers\", \"name\": \"GD\", \"type\": \"scatter\", \"x\": [0.25199999999999995, 0.4586399999999999, 0.6280847999999999, 0.7670295359999999, 0.8809642195199999, 0.9743906600064, 1.051000341205248, 1.1138202797883032, 1.1653326294264086, 1.207572756129655, 1.242209660026317, 1.2706119212215798, 1.2939017754016955, 1.3129994558293903, 1.3286595537801, 1.341500834099682, 1.352030683961739, 1.360665160848626, 1.3677454318958733, 1.373551254154616, 1.3783120284067851, 1.3822158632935637, 1.3854170079007222, 1.3880419464785922, 1.3901943961124457, 1.3919594048122055, 1.3934067119460085, 1.3945935037957269, 1.395566673112496, 1.3963646719522467, 1.3970190310008423, 1.3975556054206906, 1.3979955964449662, 1.3983563890848723, 1.3986522390495952, 1.398894836020668, 1.3990937655369478, 1.399256887740297, 1.3993906479470435, 1.3995003313165757, 1.399590271679592, 1.3996640227772654, 1.3997244986773576, 1.3997740889154333, 1.3998147529106553, 1.3998480973867373, 1.3998754398571245, 1.399897860682842, 1.3999162457599303], \"y\": [5.9305679999999965, 3.9877139231999985, 2.681338841959679, 1.802932237333688, 1.2122916363831724, 0.8151448963040442, 0.5481034282748395, 0.3685447451720021, 0.24780948665365457, 0.16662709882591703, 0.11204006125054668, 0.07533573718486761, 0.05065574968310505, 0.03406092608691967, 0.022902566700844826, 0.015399685849648063, 0.010354748765303366, 0.006962533069790012, 0.00468160723612678, 0.0031479127055717105, 0.0021166565032264112, 0.0014232398327694029, 0.0009569864635541636, 0.000643477698093826, 0.0004326744041982593, 0.00029093026938290184, 0.00019562151313306673, 0.00013153590543068386, 8.844474281158521e-05, 5.947024506651377e-05, 3.9987792782717026e-05, 2.688779186709945e-05, 1.807935125144066e-05, 1.2156555781469402e-05, 8.17406810745981e-06, 5.496243395454798e-06, 3.6956740591054485e-06, 2.484971237340761e-06, 1.6708946599899411e-06, 1.123509569376331e-06, 7.554478344491253e-07, 5.079631238836993e-07, 3.415544044994875e-07, 2.2966118158480531e-07, 1.5442417849797847e-07, 1.0383481762181406e-07, 6.981853136908037e-08, 4.694598049235736e-08, 3.156647728333781e-08]}],\n",
       "                        {\"autosize\": false, \"height\": 400, \"plot_bgcolor\": \"#FFFFFF\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 500},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('1053f88f-3847-45da-a37e-c1d1eb0a9589');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = go.Figure()\n",
    "p1.add_trace(go.Scatter(x=dfFunChartPts.X, y=dfFunChartPts.Cost,\n",
    "                    mode='lines',\n",
    "                    line_shape='spline',\n",
    "                    name = 'function'                            \n",
    "                    ))\n",
    "p1.add_trace(go.Scatter(x=dfChartPts.X, y=dfChartPts.Cost,\n",
    "                    mode='markers',\n",
    "                    name = \"GD\"    \n",
    "                    ))\n",
    "p1.update_layout(autosize = False, width = 500, height = 400, \n",
    "                 plot_bgcolor = '#FFFFFF')\n",
    "p1.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}