HW4_save.ipynb

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  "metadata": {
    "colab": {
      "name": "HW4.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yh08037/Introduction-to-Intelligent-Systems/blob/master/HW4_save.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kxBHturLL6RK",
        "colab_type": "text"
      },
      "source": [
        "# Feedback Neural Network (FBNN)\n",
        "a.k.a. Recurrent Neural Network (RNN)\n",
        "\n",
        "## 1. Generating input data X\n",
        "Generate some input data (X) consisting of 30 sequences of 8 binary numbers, following a uniform distribution, where the probability of generating a “0” is the same as that of generating a “1”. Make the output (y) for each sequence be the sum of its elements."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W4mz_Qa7L1t3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "\n",
        "\n",
        "I = 30  # number of traing data\n",
        "T = 8   # size of binary numbers\n",
        "\n",
        "\n",
        "# Generate training data randomly\n",
        "\n",
        "x = np.hstack((np.zeros((I, 1)), np.random.randint(2, size=(I, T))))  # x0 is not used but for simplicity of code\n",
        "y = x.sum(axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JMrgS4_GNEJn",
        "colab_type": "text"
      },
      "source": [
        "## 2. Implementing sequentail adder using Elman RNN\n",
        "Implement a sequential adder using the Elman recurrent neural network (RNN) with\n",
        "\n",
        "a) backpropagation\n",
        "\n",
        "b) resilient propagation\n",
        "\n",
        "c) gradient clipping."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sEL0ez3Cj0RX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def SSE(yh, y):\n",
        "    if yh.size != y.size :\n",
        "        print(\"Invalid arguments for SEE\")\n",
        "        exit()\n",
        "    result = 0.\n",
        "    for i in range(yh.size):\n",
        "        result += (yh[i] - y[i]) ** 2\n",
        "    return result / 2."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BbqO9GjPptR5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# initialize f0\n",
        "f = np.ones((I, T+1))\n",
        "\n",
        "\n",
        "# define hyperparameters\n",
        "\n",
        "alpha1 = 0.0001\n",
        "alpha2 = 0.0001\n",
        "\n",
        "delta_x = 0.001\n",
        "delta_f = 0.001\n",
        "\n",
        "eta_p = 1.2\n",
        "eta_n = 0.5\n",
        "\n",
        "eta = 1000\n",
        "\n",
        "epsilon = 0.0001\n",
        "\n",
        "\n",
        "# define parameters by random\n",
        "\n",
        "vx_rand = random.uniform(0, 2)\n",
        "vf_rand = random.uniform(0, 1)\n",
        "\n",
        "\n",
        "# initialize list Vx, Vf for plot\n",
        "\n",
        "Vx_bp = []\n",
        "Vf_bp = []\n",
        "\n",
        "Vx_rp = []\n",
        "Vf_rp = []\n",
        "\n",
        "Vx_gc = []\n",
        "Vf_gc = []\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xj-x91UOpvFm",
        "colab_type": "text"
      },
      "source": [
        "### a) Standard Back Propagation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5otOUsX2NUeo",
        "colab_type": "code",
        "outputId": "fcdd123e-4abf-4a0a-a5bd-a98e3c07cc5f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# Main loop for training\n",
        "\n",
        "vx = vx_rand\n",
        "vf = vf_rand\n",
        "\n",
        "cnt = 0\n",
        "E_present = 0.\n",
        "E_previous = 0.\n",
        "\n",
        "while cnt < 1 or abs(E_present - E_previous) > epsilon:\n",
        "\n",
        "    # forward propagation\n",
        "\n",
        "    for t in range(1, T+1):\n",
        "        for i in range(0, I):\n",
        "            f[i, t] = vf * f[i, t-1] + vx * x[i, t]\n",
        "\n",
        "    y_hat = f[:, T]\n",
        "\n",
        "    # back propagation\n",
        "    \n",
        "    for t in range(1, T+1):\n",
        "        for i in range(0, I):\n",
        "            vx -= alpha1 * (y_hat[i] - y[i]) * (vf ** (T-t)) * x[i, t]\n",
        "\n",
        "    sum_T = 0.\n",
        "    for t in range(1, T+1):\n",
        "        sum_I = 0.\n",
        "        for i in range(0, I):\n",
        "            sum_I += (y_hat[i] - y[i]) * f[i, t-1]\n",
        "        sum_T += sum_I * (vf ** (T-t))\n",
        "    vf -= alpha2 * sum_T\n",
        "\n",
        "    E_previous = E_present\n",
        "    E_present = SSE(y_hat, y)\n",
        "    \n",
        "    Vx_bp.append(vx)\n",
        "    Vf_bp.append(vf)\n",
        "    \n",
        "    if cnt % 10 == 0:\n",
        "        print('iteration', cnt)\n",
        "        print('vf :', vf)\n",
        "        print('vx :', vx)\n",
        "        print('error :', E_present)\n",
        "        print()\n",
        "    if cnt == 0:\n",
        "        plt.plot(vx, vf, 'rx')\n",
        "    else:\n",
        "        plt.plot(vx, vf, 'ro')\n",
        "\n",
        "    cnt += 1\n",
        "plt.plot(vx, vf, 'bo')\n",
        "plt.show()"
      ],
      "execution_count": 141,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 0\n",
            "vf : 0.7635686658580072\n",
            "vx : 1.9723522066689048\n",
            "error : 11.34500452670142\n",
            "\n",
            "iteration 10\n",
            "vf : 0.7806700074079947\n",
            "vx : 1.96081257846124\n",
            "error : 9.35976008164315\n",
            "\n",
            "iteration 20\n",
            "vf : 0.7828877315953142\n",
            "vx : 1.946988646569349\n",
            "error : 9.16347148786374\n",
            "\n",
            "iteration 30\n",
            "vf : 0.7850827050981952\n",
            "vx : 1.9332899567298574\n",
            "error : 8.970733045113647\n",
            "\n",
            "iteration 40\n",
            "vf : 0.7872626513800997\n",
            "vx : 1.9197179144395422\n",
            "error : 8.7815162143666\n",
            "\n",
            "iteration 50\n",
            "vf : 0.789427470328659\n",
            "vx : 1.9062726612893057\n",
            "error : 8.595792744008786\n",
            "\n",
            "iteration 60\n",
            "vf : 0.7915770595369166\n",
            "vx : 1.8929543238035529\n",
            "error : 8.41353387439592\n",
            "\n",
            "iteration 70\n",
            "vf : 0.7937113174740094\n",
            "vx : 1.8797630133073286\n",
            "error : 8.234710335565223\n",
            "\n",
            "iteration 80\n",
            "vf : 0.7958301436171494\n",
            "vx : 1.8666988253327075\n",
            "error : 8.059292346461483\n",
            "\n",
            "iteration 90\n",
            "vf : 0.7979334385820335\n",
            "vx : 1.8537618390513197\n",
            "error : 7.887249615657869\n",
            "\n",
            "iteration 100\n",
            "vf : 0.8000211042525592\n",
            "vx : 1.8409521167338108\n",
            "error : 7.718551343543146\n",
            "\n",
            "iteration 110\n",
            "vf : 0.8020930439096534\n",
            "vx : 1.82826970323659\n",
            "error : 7.553166225942132\n",
            "\n",
            "iteration 120\n",
            "vf : 0.8041491623590075\n",
            "vx : 1.8157146255163914\n",
            "error : 7.391062459135684\n",
            "\n",
            "iteration 130\n",
            "vf : 0.8061893660575364\n",
            "vx : 1.8032868921729035\n",
            "error : 7.232207746240838\n",
            "\n",
            "iteration 140\n",
            "vf : 0.80821356323835\n",
            "vx : 1.7909864930198949\n",
            "error : 7.076569304912388\n",
            "\n",
            "iteration 150\n",
            "vf : 0.8102216640340584\n",
            "vx : 1.778813398684972\n",
            "error : 6.924113876321439\n",
            "\n",
            "iteration 160\n",
            "vf : 0.8122135805982063\n",
            "vx : 1.7667675602383148\n",
            "error : 6.77480773536707\n",
            "\n",
            "iteration 170\n",
            "vf : 0.8141892272246559\n",
            "vx : 1.7548489088504324\n",
            "error : 6.628616702072711\n",
            "\n",
            "iteration 180\n",
            "vf : 0.8161485204647327\n",
            "vx : 1.7430573554791\n",
            "error : 6.485506154117932\n",
            "\n",
            "iteration 190\n",
            "vf : 0.8180913792419493\n",
            "vx : 1.7313927905855087\n",
            "error : 6.345441040454261\n",
            "\n",
            "iteration 200\n",
            "vf : 0.8200177249641347\n",
            "vx : 1.7198550838796203\n",
            "error : 6.208385895951632\n",
            "\n",
            "iteration 210\n",
            "vf : 0.8219274816327966\n",
            "vx : 1.7084440840946693\n",
            "error : 6.074304857020668\n",
            "\n",
            "iteration 220\n",
            "vf : 0.8238205759495437\n",
            "vx : 1.6971596187907199\n",
            "error : 5.943161678155076\n",
            "\n",
            "iteration 230\n",
            "vf : 0.8256969374194214\n",
            "vx : 1.6860014941870682\n",
            "error : 5.814919749335886\n",
            "\n",
            "iteration 240\n",
            "vf : 0.8275564984509906\n",
            "vx : 1.674969495023335\n",
            "error : 5.689542114240154\n",
            "\n",
            "iteration 250\n",
            "vf : 0.8293991944530145\n",
            "vx : 1.6640633844489379\n",
            "error : 5.566991489194166\n",
            "\n",
            "iteration 260\n",
            "vf : 0.8312249639276015\n",
            "vx : 1.6532829039406884\n",
            "error : 5.447230282812162\n",
            "\n",
            "iteration 270\n",
            "vf : 0.8330337485596827\n",
            "vx : 1.642627773248079\n",
            "error : 5.330220616259407\n",
            "\n",
            "iteration 280\n",
            "vf : 0.8348254933026893\n",
            "vx : 1.6320976903659268\n",
            "error : 5.215924344079942\n",
            "\n",
            "iteration 290\n",
            "vf : 0.8366001464603124\n",
            "vx : 1.6216923315339329\n",
            "error : 5.104303075528416\n",
            "\n",
            "iteration 300\n",
            "vf : 0.8383576597642376\n",
            "vx : 1.6114113512626103\n",
            "error : 4.995318196345577\n",
            "\n",
            "iteration 310\n",
            "vf : 0.8400979884477554\n",
            "vx : 1.601254382385152\n",
            "error : 4.8889308909173455\n",
            "\n",
            "iteration 320\n",
            "vf : 0.8418210913151442\n",
            "vx : 1.5912210361345929\n",
            "error : 4.785102164758546\n",
            "\n",
            "iteration 330\n",
            "vf : 0.8435269308067568\n",
            "vx : 1.5813109022457383\n",
            "error : 4.683792867261732\n",
            "\n",
            "iteration 340\n",
            "vf : 0.8452154730597182\n",
            "vx : 1.5715235490812078\n",
            "error : 4.584963714654109\n",
            "\n",
            "iteration 350\n",
            "vf : 0.8468866879641781\n",
            "vx : 1.5618585237809832\n",
            "error : 4.48857531310518\n",
            "\n",
            "iteration 360\n",
            "vf : 0.8485405492150591\n",
            "vx : 1.5523153524347064\n",
            "error : 4.394588181929257\n",
            "\n",
            "iteration 370\n",
            "vf : 0.8501770343592486\n",
            "vx : 1.5428935402761164\n",
            "error : 4.302962776828862\n",
            "\n",
            "iteration 380\n",
            "vf : 0.8517961248381954\n",
            "vx : 1.5335925718988659\n",
            "error : 4.21365951312579\n",
            "\n",
            "iteration 390\n",
            "vf : 0.8533978060258806\n",
            "vx : 1.5244119114929608\n",
            "error : 4.126638788928467\n",
            "\n",
            "iteration 400\n",
            "vf : 0.8549820672621393\n",
            "vx : 1.5153510031010946\n",
            "error : 4.041861008185746\n",
            "\n",
            "iteration 410\n",
            "vf : 0.8565489018813244\n",
            "vx : 1.5064092708940984\n",
            "error : 3.9592866035792382\n",
            "\n",
            "iteration 420\n",
            "vf : 0.8580983072362965\n",
            "vx : 1.4975861194647309\n",
            "error : 3.87887605920825\n",
            "\n",
            "iteration 430\n",
            "vf : 0.8596302847177631\n",
            "vx : 1.4888809341389873\n",
            "error : 3.800589933022426\n",
            "\n",
            "iteration 440\n",
            "vf : 0.8611448397689551\n",
            "vx : 1.4802930813041946\n",
            "error : 3.724388878960957\n",
            "\n",
            "iteration 450\n",
            "vf : 0.8626419818956813\n",
            "vx : 1.4718219087530262\n",
            "error : 3.6502336687573402\n",
            "\n",
            "iteration 460\n",
            "vf : 0.8641217246717824\n",
            "vx : 1.4634667460426565\n",
            "error : 3.578085213372011\n",
            "\n",
            "iteration 470\n",
            "vf : 0.865584085740018\n",
            "vx : 1.45522690486825\n",
            "error : 3.5079045840170813\n",
            "\n",
            "iteration 480\n",
            "vf : 0.8670290868084374\n",
            "vx : 1.447101679449984\n",
            "error : 3.439653032739302\n",
            "\n",
            "iteration 490\n",
            "vf : 0.8684567536422814\n",
            "vx : 1.4390903469327887\n",
            "error : 3.37329201252996\n",
            "\n",
            "iteration 500\n",
            "vf : 0.8698671160514729\n",
            "vx : 1.4311921677980386\n",
            "error : 3.3087831969324935\n",
            "\n",
            "iteration 510\n",
            "vf : 0.8712602078737749\n",
            "vx : 1.4234063862863189\n",
            "error : 3.246088499120233\n",
            "\n",
            "iteration 520\n",
            "vf : 0.8726360669536664\n",
            "vx : 1.4157322308306146\n",
            "error : 3.1851700904204696\n",
            "\n",
            "iteration 530\n",
            "vf : 0.873994735117039\n",
            "vx : 1.4081689144990253\n",
            "error : 3.125990418261153\n",
            "\n",
            "iteration 540\n",
            "vf : 0.8753362581417823\n",
            "vx : 1.4007156354463126\n",
            "error : 3.0685122235205187\n",
            "\n",
            "iteration 550\n",
            "vf : 0.8766606857243574\n",
            "vx : 1.3933715773734778\n",
            "error : 3.012698557260996\n",
            "\n",
            "iteration 560\n",
            "vf : 0.877968071442459\n",
            "vx : 1.3861359099946675\n",
            "error : 2.958512796831093\n",
            "\n",
            "iteration 570\n",
            "vf : 0.8792584727138566\n",
            "vx : 1.3790077895106339\n",
            "error : 2.9059186613215324\n",
            "\n",
            "iteration 580\n",
            "vf : 0.8805319507515337\n",
            "vx : 1.371986359088076\n",
            "error : 2.854880226363242\n",
            "\n",
            "iteration 590\n",
            "vf : 0.8817885705152292\n",
            "vx : 1.3650707493441336\n",
            "error : 2.805361938257155\n",
            "\n",
            "iteration 600\n",
            "vf : 0.8830284006595035\n",
            "vx : 1.358260078835324\n",
            "error : 2.757328627427688\n",
            "\n",
            "iteration 610\n",
            "vf : 0.8842515134784428\n",
            "vx : 1.3515534545503054\n",
            "error : 2.7107455211935334\n",
            "\n",
            "iteration 620\n",
            "vf : 0.8854579848471332\n",
            "vx : 1.344949972405764\n",
            "error : 2.6655782558512353\n",
            "\n",
            "iteration 630\n",
            "vf : 0.8866478941600242\n",
            "vx : 1.3384487177447943\n",
            "error : 2.621792888068921\n",
            "\n",
            "iteration 640\n",
            "vf : 0.8878213242663184\n",
            "vx : 1.3320487658371536\n",
            "error : 2.5793559055889115\n",
            "\n",
            "iteration 650\n",
            "vf : 0.8889783614025226\n",
            "vx : 1.3257491823807666\n",
            "error : 2.5382342372396454\n",
            "\n",
            "iteration 660\n",
            "vf : 0.8901190951222827\n",
            "vx : 1.3195490240039363\n",
            "error : 2.498395262259515\n",
            "\n",
            "iteration 670\n",
            "vf : 0.8912436182236608\n",
            "vx : 1.3134473387676096\n",
            "error : 2.4598068189353417\n",
            "\n",
            "iteration 680\n",
            "vf : 0.8923520266739781\n",
            "vx : 1.3074431666672035\n",
            "error : 2.4224372125609843\n",
            "\n",
            "iteration 690\n",
            "vf : 0.8934444195323724\n",
            "vx : 1.3015355401334259\n",
            "error : 2.3862552227220784\n",
            "\n",
            "iteration 700\n",
            "vf : 0.8945208988702144\n",
            "vx : 1.2957234845315801\n",
            "error : 2.351230109914367\n",
            "\n",
            "iteration 710\n",
            "vf : 0.8955815696895193\n",
            "vx : 1.2900060186588098\n",
            "error : 2.3173316215043887\n",
            "\n",
            "iteration 720\n",
            "vf : 0.8966265398395077\n",
            "vx : 1.2843821552388597\n",
            "error : 2.2845299970421884\n",
            "\n",
            "iteration 730\n",
            "vf : 0.8976559199314547\n",
            "vx : 1.2788509014138063\n",
            "error : 2.25279597293675\n",
            "\n",
            "iteration 740\n",
            "vf : 0.8986698232519739\n",
            "vx : 1.2734112592323588\n",
            "error : 2.2221007865060303\n",
            "\n",
            "iteration 750\n",
            "vf : 0.8996683656748784\n",
            "vx : 1.2680622261342693\n",
            "error : 2.1924161794142316\n",
            "\n",
            "iteration 760\n",
            "vf : 0.9006516655717689\n",
            "vx : 1.262802795430422\n",
            "error : 2.1637144005095377\n",
            "\n",
            "iteration 770\n",
            "vf : 0.9016198437214908\n",
            "vx : 1.2576319567781944\n",
            "error : 2.135968208076589\n",
            "\n",
            "iteration 780\n",
            "vf : 0.9025730232185941\n",
            "vx : 1.2525486966517352\n",
            "error : 2.1091508715188114\n",
            "\n",
            "iteration 790\n",
            "vf : 0.903511329380954\n",
            "vx : 1.2475519988067414\n",
            "error : 2.0832361724855777\n",
            "\n",
            "iteration 800\n",
            "vf : 0.9044348896566723\n",
            "vx : 1.2426408447394\n",
            "error : 2.0581984054607885\n",
            "\n",
            "iteration 810\n",
            "vf : 0.9053438335304207\n",
            "vx : 1.2378142141391337\n",
            "error : 2.0340123778287342\n",
            "\n",
            "iteration 820\n",
            "vf : 0.9062382924293351\n",
            "vx : 1.2330710853348708\n",
            "error : 2.0106534094349757\n",
            "\n",
            "iteration 830\n",
            "vf : 0.9071183996286236\n",
            "vx : 1.2284104357344543\n",
            "error : 1.9880973316586665\n",
            "\n",
            "iteration 840\n",
            "vf : 0.9079842901569921\n",
            "vx : 1.2238312422569815\n",
            "error : 1.9663204860147612\n",
            "\n",
            "iteration 850\n",
            "vf : 0.9088361007020357\n",
            "vx : 1.2193324817577358\n",
            "error : 1.945299722303391\n",
            "\n",
            "iteration 860\n",
            "vf : 0.909673969515715\n",
            "vx : 1.21491313144545\n",
            "error : 1.9250123963247343\n",
            "\n",
            "iteration 870\n",
            "vf : 0.9104980363200397\n",
            "vx : 1.2105721692916862\n",
            "error : 1.9054363671775583\n",
            "\n",
            "iteration 880\n",
            "vf : 0.9113084422130768\n",
            "vx : 1.2063085744320878\n",
            "error : 1.8865499941598292\n",
            "\n",
            "iteration 890\n",
            "vf : 0.9121053295754045\n",
            "vx : 1.2021213275592695\n",
            "error : 1.8683321332896936\n",
            "\n",
            "iteration 900\n",
            "vf : 0.9128888419771213\n",
            "vx : 1.1980094113071633\n",
            "error : 1.8507621334652042\n",
            "\n",
            "iteration 910\n",
            "vf : 0.9136591240855223\n",
            "vx : 1.1939718106266024\n",
            "error : 1.8338198322811883\n",
            "\n",
            "iteration 920\n",
            "vf : 0.9144163215735425\n",
            "vx : 1.1900075131520251\n",
            "error : 1.8174855515215949\n",
            "\n",
            "iteration 930\n",
            "vf : 0.9151605810290712\n",
            "vx : 1.1861155095590952\n",
            "error : 1.8017400923454427\n",
            "\n",
            "iteration 940\n",
            "vf : 0.9158920498652366\n",
            "vx : 1.1822947939131023\n",
            "error : 1.78656473018431\n",
            "\n",
            "iteration 950\n",
            "vf : 0.916610876231753\n",
            "vx : 1.1785443640080215\n",
            "error : 1.7719412093693334\n",
            "\n",
            "iteration 960\n",
            "vf : 0.9173172089274081\n",
            "vx : 1.1748632216961428\n",
            "error : 1.757851737505372\n",
            "\n",
            "iteration 970\n",
            "vf : 0.9180111973137971\n",
            "vx : 1.171250373208113\n",
            "error : 1.744278979609439\n",
            "\n",
            "iteration 980\n",
            "vf : 0.918692991230363\n",
            "vx : 1.1677048294633445\n",
            "error : 1.7312060520308028\n",
            "\n",
            "iteration 990\n",
            "vf : 0.9193627409108281\n",
            "vx : 1.1642256063707166\n",
            "error : 1.7186165161693865\n",
            "\n",
            "iteration 1000\n",
            "vf : 0.9200205969010877\n",
            "vx : 1.1608117251194932\n",
            "error : 1.7064943720089245\n",
            "\n",
            "iteration 1010\n",
            "vf : 0.9206667099786255\n",
            "vx : 1.1574622124604548\n",
            "error : 1.6948240514811654\n",
            "\n",
            "iteration 1020\n",
            "vf : 0.9213012310735271\n",
            "vx : 1.1541761009771137\n",
            "error : 1.6835904116765148\n",
            "\n",
            "iteration 1030\n",
            "vf : 0.9219243111911324\n",
            "vx : 1.1509524293471325\n",
            "error : 1.6727787279168755\n",
            "\n",
            "iteration 1040\n",
            "vf : 0.9225361013363915\n",
            "vx : 1.147790242593814\n",
            "error : 1.6623746867053313\n",
            "\n",
            "iteration 1050\n",
            "vf : 0.9231367524399722\n",
            "vx : 1.144688592327736\n",
            "error : 1.6523643785673015\n",
            "\n",
            "iteration 1060\n",
            "vf : 0.923726415286156\n",
            "vx : 1.1416465369785347\n",
            "error : 1.642734290797294\n",
            "\n",
            "iteration 1070\n",
            "vf : 0.9243052404425689\n",
            "vx : 1.1386631420168665\n",
            "error : 1.6334713001248702\n",
            "\n",
            "iteration 1080\n",
            "vf : 0.924873378191783\n",
            "vx : 1.1357374801665772\n",
            "error : 1.624562665312921\n",
            "\n",
            "iteration 1090\n",
            "vf : 0.9254309784648147\n",
            "vx : 1.1328686316071486\n",
            "error : 1.6159960197011536\n",
            "\n",
            "iteration 1100\n",
            "vf : 0.9259781907765583\n",
            "vx : 1.1300556841664484\n",
            "error : 1.6077593637067682\n",
            "\n",
            "iteration 1110\n",
            "vf : 0.9265151641631595\n",
            "vx : 1.1272977335039311\n",
            "error : 1.599841057294475\n",
            "\n",
            "iteration 1120\n",
            "vf : 0.9270420471213682\n",
            "vx : 1.1245938832842919\n",
            "error : 1.5922298124267433\n",
            "\n",
            "iteration 1130\n",
            "vf : 0.9275589875498709\n",
            "vx : 1.1219432453417102\n",
            "error : 1.5849146855053813\n",
            "\n",
            "iteration 1140\n",
            "vf : 0.928066132692626\n",
            "vx : 1.1193449398347628\n",
            "error : 1.577885069814613\n",
            "\n",
            "iteration 1150\n",
            "vf : 0.9285636290841977\n",
            "vx : 1.1167980953921568\n",
            "error : 1.5711306879755864\n",
            "\n",
            "iteration 1160\n",
            "vf : 0.9290516224971038\n",
            "vx : 1.1143018492493473\n",
            "error : 1.5646415844216455\n",
            "\n",
            "iteration 1170\n",
            "vf : 0.9295302578911684\n",
            "vx : 1.1118553473762227\n",
            "error : 1.5584081179032647\n",
            "\n",
            "iteration 1180\n",
            "vf : 0.9299996793648897\n",
            "vx : 1.1094577445959277\n",
            "error : 1.552420954030976\n",
            "\n",
            "iteration 1190\n",
            "vf : 0.9304600301088053\n",
            "vx : 1.1071082046950216\n",
            "error : 1.5466710578643639\n",
            "\n",
            "iteration 1200\n",
            "vf : 0.9309114523608486\n",
            "vx : 1.1048059005251178\n",
            "error : 1.5411496865545815\n",
            "\n",
            "iteration 1210\n",
            "vf : 0.9313540873636951\n",
            "vx : 1.1025500140960967\n",
            "error : 1.5358483820472622\n",
            "\n",
            "iteration 1220\n",
            "vf : 0.9317880753240665\n",
            "vx : 1.1003397366611585\n",
            "error : 1.5307589638526822\n",
            "\n",
            "iteration 1230\n",
            "vf : 0.9322135553739933\n",
            "vx : 1.0981742687937592\n",
            "error : 1.5258735218890302\n",
            "\n",
            "iteration 1240\n",
            "vf : 0.932630665534006\n",
            "vx : 1.09605282045671\n",
            "error : 1.5211844094046854\n",
            "\n",
            "iteration 1250\n",
            "vf : 0.9330395426782339\n",
            "vx : 1.093974611063538\n",
            "error : 1.5166842359847232\n",
            "\n",
            "iteration 1260\n",
            "vf : 0.9334403225013946\n",
            "vx : 1.091938869532336\n",
            "error : 1.512365860646521\n",
            "\n",
            "iteration 1270\n",
            "vf : 0.9338331394876351\n",
            "vx : 1.0899448343322629\n",
            "error : 1.5082223850290122\n",
            "\n",
            "iteration 1280\n",
            "vf : 0.934218126881215\n",
            "vx : 1.0879917535228578\n",
            "error : 1.5042471466795593\n",
            "\n",
            "iteration 1290\n",
            "vf : 0.9345954166589794\n",
            "vx : 1.086078884786436\n",
            "error : 1.500433712442347\n",
            "\n",
            "iteration 1300\n",
            "vf : 0.9349651395046145\n",
            "vx : 1.084205495453643\n",
            "error : 1.496775871951444\n",
            "\n",
            "iteration 1310\n",
            "vf : 0.9353274247846319\n",
            "vx : 1.0823708625224584\n",
            "error : 1.493267631231749\n",
            "\n",
            "iteration 1320\n",
            "vf : 0.9356824005260603\n",
            "vx : 1.0805742726707959\n",
            "error : 1.4899032064103293\n",
            "\n",
            "iteration 1330\n",
            "vf : 0.9360301933958026\n",
            "vx : 1.0788150222629238\n",
            "error : 1.4866770175405963\n",
            "\n",
            "iteration 1340\n",
            "vf : 0.936370928681627\n",
            "vx : 1.0770924173498408\n",
            "error : 1.4835836825413207\n",
            "\n",
            "iteration 1350\n",
            "vf : 0.9367047302747503\n",
            "vx : 1.0754057736638862\n",
            "error : 1.4806180112521676\n",
            "\n",
            "iteration 1360\n",
            "vf : 0.9370317206539773\n",
            "vx : 1.0737544166077369\n",
            "error : 1.4777749996073302\n",
            "\n",
            "iteration 1370\n",
            "vf : 0.9373520208713519\n",
            "vx : 1.0721376812379788\n",
            "error : 1.475049823928324\n",
            "\n",
            "iteration 1380\n",
            "vf : 0.9376657505392885\n",
            "vx : 1.0705549122434905\n",
            "error : 1.4724378353369167\n",
            "\n",
            "iteration 1390\n",
            "vf : 0.9379730278191357\n",
            "vx : 1.0690054639187847\n",
            "error : 1.4699345542888114\n",
            "\n",
            "iteration 1400\n",
            "vf : 0.9382739694111402\n",
            "vx : 1.0674887001325313\n",
            "error : 1.4675356652285962\n",
            "\n",
            "iteration 1410\n",
            "vf : 0.9385686905457531\n",
            "vx : 1.066003994291458\n",
            "error : 1.4652370113661193\n",
            "\n",
            "iteration 1420\n",
            "vf : 0.9388573049762591\n",
            "vx : 1.064550729299821\n",
            "error : 1.4630345895742984\n",
            "\n",
            "iteration 1430\n",
            "vf : 0.9391399249726708\n",
            "vx : 1.0631282975145824\n",
            "error : 1.4609245454081863\n",
            "\n",
            "iteration 1440\n",
            "vf : 0.93941666131685\n",
            "vx : 1.061736100696585\n",
            "error : 1.4589031682449594\n",
            "\n",
            "iteration 1450\n",
            "vf : 0.9396876232988169\n",
            "vx : 1.0603735499578122\n",
            "error : 1.456966886544174\n",
            "\n",
            "iteration 1460\n",
            "vf : 0.9399529187142063\n",
            "vx : 1.0590400657049581\n",
            "error : 1.4551122632276945\n",
            "\n",
            "iteration 1470\n",
            "vf : 0.940212653862827\n",
            "vx : 1.0577350775794818\n",
            "error : 1.4533359911783335\n",
            "\n",
            "iteration 1480\n",
            "vf : 0.9404669335482825\n",
            "vx : 1.056458024394335\n",
            "error : 1.451634888856283\n",
            "\n",
            "iteration 1490\n",
            "vf : 0.9407158610786144\n",
            "vx : 1.055208354067509\n",
            "error : 1.4500058960321527\n",
            "\n",
            "iteration 1500\n",
            "vf : 0.940959538267927\n",
            "vx : 1.0539855235526083\n",
            "error : 1.4484460696354118\n",
            "\n",
            "iteration 1510\n",
            "vf : 0.941198065438952\n",
            "vx : 1.0527889987665715\n",
            "error : 1.4469525797168046\n",
            "\n",
            "iteration 1520\n",
            "vf : 0.9414315414265223\n",
            "vx : 1.0516182545147388\n",
            "error : 1.4455227055233228\n",
            "\n",
            "iteration 1530\n",
            "vf : 0.941660063581893\n",
            "vx : 1.0504727744134426\n",
            "error : 1.444153831684239\n",
            "\n",
            "iteration 1540\n",
            "vf : 0.941883727777908\n",
            "vx : 1.049352050810199\n",
            "error : 1.4428434445064173\n",
            "\n",
            "iteration 1550\n",
            "vf : 0.9421026284149314\n",
            "vx : 1.0482555847017518\n",
            "error : 1.441589128377381\n",
            "\n",
            "iteration 1560\n",
            "vf : 0.9423168584275458\n",
            "vx : 1.0471828856500582\n",
            "error : 1.4403885622741774\n",
            "\n",
            "iteration 1570\n",
            "vf : 0.9425265092919528\n",
            "vx : 1.0461334716963608\n",
            "error : 1.439239516376366\n",
            "\n",
            "iteration 1580\n",
            "vf : 0.9427316710340585\n",
            "vx : 1.0451068692735004\n",
            "error : 1.4381398487811123\n",
            "\n",
            "iteration 1590\n",
            "vf : 0.942932432238191\n",
            "vx : 1.044102613116654\n",
            "error : 1.4370875023185965\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3Io4AG4Crq/YJ4Kz09dnAwclOKOk84KyIeCoiAngQuKammpt1Ej/C03pAnkCYA+yveH8g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\nDAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DRD0HNaErKcm",
        "colab_type": "text"
      },
      "source": [
        "### b) Resilient Propagation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I1DJkmy5kFcu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "d7c3e34f-30e3-4056-ee1a-578d10028533"
      },
      "source": [
        "# Main loop for training\n",
        "\n",
        "vx = vx_rand\n",
        "vf = vf_rand\n",
        "\n",
        "cnt = 0\n",
        "E_present = 0.\n",
        "E_previous = 0.\n",
        "\n",
        "gradx_present = 0.\n",
        "gradx_previous = 0.\n",
        "\n",
        "gradf_present = 0.\n",
        "gradf_previous = 0.\n",
        "\n",
        "while cnt < 1 or abs(E_present - E_previous) > epsilon:\n",
        "\n",
        "    # forward propagation\n",
        "\n",
        "    for t in range(1, T+1):\n",
        "        for i in range(0, I):\n",
        "            f[i, t] = vf * f[i, t-1] + vx * x[i, t]\n",
        "\n",
        "    y_hat = f[:, T]\n",
        "\n",
        "    \n",
        "    # resilient propagation\n",
        "    \n",
        "    gradx_previous = gradx_present\n",
        "    gradf_previous = gradf_present\n",
        "    \n",
        "    gradx_present = 0.\n",
        "    for t in range(1, T+1):\n",
        "        tmp = 0.\n",
        "        for i in range(0, I):\n",
        "            tmp += (y_hat[i] - y[i]) * x[i, t]\n",
        "        gradx_present += tmp * (vf ** (T-t))\n",
        "    \n",
        "    gradf_present = 0.\n",
        "    for t in range(1, T+1):\n",
        "        tmp = 0.\n",
        "        for i in range(0, I):\n",
        "            tmp += (y_hat[i] - y[i]) * f[i, t-1]\n",
        "        gradf_present += tmp * (vf ** (T-t))\n",
        "    \n",
        "    \n",
        "    if cnt >= 1:\n",
        "        if np.sign(gradx_previous) == np.sign(gradx_present):\n",
        "            delta_x *= eta_p\n",
        "        else:\n",
        "            delta_x *= eta_n\n",
        "    \n",
        "    if cnt >= 1:\n",
        "        if np.sign(gradf_previous) == np.sign(gradf_present):\n",
        "            delta_f *= eta_p\n",
        "        else:\n",
        "            delta_f *= eta_n\n",
        "\n",
        "    vx -= np.sign(gradx_present) * delta_x\n",
        "    vf -= np.sign(gradf_present) * delta_f\n",
        "    \n",
        "    \n",
        "    E_previous = E_present\n",
        "    E_present = SSE(y_hat, y)\n",
        "    \n",
        "    Vx_rp.append(vx)\n",
        "    Vf_rp.append(vf)\n",
        "    \n",
        "    \n",
        "    if cnt % 10 == 0:\n",
        "        print('iteration', cnt)\n",
        "        print('vf :', vf)\n",
        "        print('vx :', vx)\n",
        "        print('error :', E_present)\n",
        "        print()\n",
        "    if cnt == 0: \n",
        "        plt.plot(vx, vf, 'rx')\n",
        "    else: \n",
        "        plt.plot(vx, vf, 'ro')\n",
        "\n",
        "    cnt += 1\n",
        "\n",
        "plt.plot(vx, vf, 'bo')\n",
        "plt.show()"
      ],
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 0\n",
            "vf : 0.7522225741120666\n",
            "vx : 1.9727303823506521\n",
            "error : 11.34500452670142\n",
            "\n",
            "iteration 10\n",
            "vf : 0.7833729926464666\n",
            "vx : 1.9724017612946523\n",
            "error : 9.549340470903104\n",
            "\n",
            "iteration 20\n",
            "vf : 0.7855756657283169\n",
            "vx : 1.8920371025394656\n",
            "error : 8.670950065770567\n",
            "\n",
            "iteration 30\n",
            "vf : 0.8114349554911517\n",
            "vx : 1.7440775214523867\n",
            "error : 6.694671042587048\n",
            "\n",
            "iteration 40\n",
            "vf : 0.8346926866636789\n",
            "vx : 1.6102489757554332\n",
            "error : 5.184941185291581\n",
            "\n",
            "iteration 50\n",
            "vf : 0.8556269326426404\n",
            "vx : 1.4663894131254591\n",
            "error : 3.894215130737687\n",
            "\n",
            "iteration 60\n",
            "vf : 0.8714515001369196\n",
            "vx : 1.4033541534792529\n",
            "error : 3.1740503721960995\n",
            "\n",
            "iteration 70\n",
            "vf : 0.8834764968011479\n",
            "vx : 1.3452979651790529\n",
            "error : 2.723611600885925\n",
            "\n",
            "iteration 80\n",
            "vf : 0.8943727468114724\n",
            "vx : 1.2929931526450547\n",
            "error : 2.3690166478077352\n",
            "\n",
            "iteration 90\n",
            "vf : 0.9042671889774134\n",
            "vx : 1.2458180317393375\n",
            "error : 2.097547751133989\n",
            "\n",
            "iteration 100\n",
            "vf : 0.9091396174667388\n",
            "vx : 1.2099699321479338\n",
            "error : 1.9269384175173048\n",
            "\n",
            "iteration 110\n",
            "vf : 0.9147471874423112\n",
            "vx : 1.1774867750669071\n",
            "error : 1.7964224008350802\n",
            "\n",
            "iteration 120\n",
            "vf : 0.9197992396856822\n",
            "vx : 1.1479901391783343\n",
            "error : 1.6987237725377207\n",
            "\n",
            "iteration 130\n",
            "vf : 0.9252299646653955\n",
            "vx : 1.1298395426876895\n",
            "error : 1.6125145953194264\n",
            "\n",
            "iteration 140\n",
            "vf : 0.9286924849037316\n",
            "vx : 1.1131226376802992\n",
            "error : 1.567344283851722\n",
            "\n",
            "iteration 150\n",
            "vf : 0.9318299898225438\n",
            "vx : 1.098061804233244\n",
            "error : 1.5301501354266356\n",
            "\n",
            "iteration 160\n",
            "vf : 0.935202664038042\n",
            "vx : 1.0844780324083496\n",
            "error : 1.4995184587333106\n",
            "\n",
            "iteration 170\n",
            "vf : 0.9369558060010207\n",
            "vx : 1.0722104833069785\n",
            "error : 1.4773409318077066\n",
            "\n",
            "iteration 180\n",
            "vf : 0.9392605425105051\n",
            "vx : 1.0611145593834286\n",
            "error : 1.4603055653099555\n",
            "\n",
            "iteration 190\n",
            "vf : 0.9407152483724899\n",
            "vx : 1.0510601731293185\n",
            "error : 1.4485384470985307\n",
            "\n",
            "iteration 200\n",
            "vf : 0.9422789906067836\n",
            "vx : 1.0458338259259399\n",
            "error : 1.4396461729139371\n",
            "\n",
            "iteration 210\n",
            "vf : 0.9434638968506968\n",
            "vx : 1.0400852108284613\n",
            "error : 1.4339250761216322\n",
            "\n",
            "iteration 220\n",
            "vf : 0.9445356373777049\n",
            "vx : 1.034910891734467\n",
            "error : 1.4292544582877948\n",
            "\n",
            "iteration 230\n",
            "vf : 0.9456877094013918\n",
            "vx : 1.0302491700795249\n",
            "error : 1.425234819619617\n",
            "\n",
            "iteration 240\n",
            "vf : 0.9465695620087128\n",
            "vx : 1.0260446376082963\n",
            "error : 1.4223987538284821\n",
            "\n",
            "iteration 250\n",
            "vf : 0.9471122052748863\n",
            "vx : 1.0228496378738996\n",
            "error : 1.4205333788649963\n",
            "\n",
            "iteration 260\n",
            "vf : 0.9477090747806957\n",
            "vx : 1.0194151593626113\n",
            "error : 1.4188556824637777\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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txYHjyJHywQAat4rarM04IFh7moyFbQURHk+wruSAYO0p78K2eoOEt8KwLuSAYO2r2sK2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\nmQEOCGZmlnJAMDMzAP4/z1id/aS0Kr0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g0ZgF6JW8ru8",
        "colab_type": "text"
      },
      "source": [
        "### c) Gradient clipping"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FqbGij8b2WXE",
        "colab_type": "code",
        "outputId": "1633374d-1897-43dc-fe68-43d202dc2042",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# Main loop for training\n",
        "\n",
        "vx = vx_rand\n",
        "vf = vf_rand\n",
        "\n",
        "cnt = 0\n",
        "E_present = 0.\n",
        "E_previous = 0.\n",
        "\n",
        "gradx = 0.\n",
        "gradf = 0.\n",
        "\n",
        "while cnt < 1 or abs(E_present - E_previous) > epsilon:\n",
        "\n",
        "    # forward propagation\n",
        "\n",
        "    for t in range(1, T+1):\n",
        "        for i in range(0, I):\n",
        "            f[i, t] = vf * f[i, t-1] + vx * x[i, t]\n",
        "\n",
        "    y_hat = f[:, T]\n",
        "\n",
        "    \n",
        "    # back propagation with gradient clipping\n",
        "    \n",
        "    gradx = 0.\n",
        "    for t in range(1, T+1):\n",
        "        tmp = 0.\n",
        "        for i in range(0, I):\n",
        "            tmp += (y_hat[i] - y[i]) * x[i, t]\n",
        "        gradx += tmp * (vf ** (T-t))\n",
        "    \n",
        "    gradf = 0.\n",
        "    for t in range(1, T+1):\n",
        "        tmp = 0.\n",
        "        for i in range(0, I):\n",
        "            tmp += (y_hat[i] - y[i]) * f[i, t-1]\n",
        "        gradf += tmp * (vf ** (T-t))\n",
        "    \n",
        "    if gradx > eta:\n",
        "        gradx *= eta / abs(gradx)\n",
        "    if gradf > eta:\n",
        "        gradf *= eta / abs(gradf)\n",
        "    \n",
        "    vx -= alpha1 * gradx\n",
        "    vf -= alpha2 * gradf    \n",
        "    \n",
        "    E_previous = E_present\n",
        "    E_present = SSE(y_hat, y)\n",
        "    \n",
        "    Vx_gc.append(vx)\n",
        "    Vf_gc.append(vf)\n",
        "    \n",
        "    \n",
        "    if cnt % 10 == 0:\n",
        "        print('iteration', cnt)\n",
        "        print('vf :', vf)\n",
        "        print('vx :', vx)\n",
        "        print('error :', E_present)\n",
        "        print()\n",
        "    if cnt == 0: \n",
        "        plt.plot(vx, vf, 'rx')\n",
        "    else: \n",
        "        plt.plot(vx, vf, 'ro')\n",
        "\n",
        "    cnt += 1\n",
        "    \n",
        "plt.plot(vx, vf, 'bo')\n",
        "plt.show()"
      ],
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 0\n",
            "vf : 0.7635686658580072\n",
            "vx : 1.972352206668904\n",
            "error : 11.34500452670142\n",
            "\n",
            "iteration 10\n",
            "vf : 0.7806700074079949\n",
            "vx : 1.9608125784612416\n",
            "error : 9.359760081643147\n",
            "\n",
            "iteration 20\n",
            "vf : 0.7828877315953137\n",
            "vx : 1.9469886465693524\n",
            "error : 9.163471487863788\n",
            "\n",
            "iteration 30\n",
            "vf : 0.7850827050981946\n",
            "vx : 1.9332899567298627\n",
            "error : 8.970733045113708\n",
            "\n",
            "iteration 40\n",
            "vf : 0.7872626513800989\n",
            "vx : 1.9197179144395475\n",
            "error : 8.781516214366675\n",
            "\n",
            "iteration 50\n",
            "vf : 0.7894274703286583\n",
            "vx : 1.9062726612893088\n",
            "error : 8.595792744008843\n",
            "\n",
            "iteration 60\n",
            "vf : 0.7915770595369161\n",
            "vx : 1.8929543238035549\n",
            "error : 8.41353387439595\n",
            "\n",
            "iteration 70\n",
            "vf : 0.7937113174740086\n",
            "vx : 1.8797630133073358\n",
            "error : 8.234710335565302\n",
            "\n",
            "iteration 80\n",
            "vf : 0.795830143617148\n",
            "vx : 1.8666988253327166\n",
            "error : 8.059292346461596\n",
            "\n",
            "iteration 90\n",
            "vf : 0.7979334385820316\n",
            "vx : 1.8537618390513328\n",
            "error : 7.887249615658039\n",
            "\n",
            "iteration 100\n",
            "vf : 0.8000211042525575\n",
            "vx : 1.8409521167338225\n",
            "error : 7.718551343543288\n",
            "\n",
            "iteration 110\n",
            "vf : 0.8020930439096513\n",
            "vx : 1.8282697032366035\n",
            "error : 7.553166225942307\n",
            "\n",
            "iteration 120\n",
            "vf : 0.8041491623590054\n",
            "vx : 1.8157146255164038\n",
            "error : 7.391062459135845\n",
            "\n",
            "iteration 130\n",
            "vf : 0.8061893660575339\n",
            "vx : 1.803286892172919\n",
            "error : 7.232207746241034\n",
            "\n",
            "iteration 140\n",
            "vf : 0.8082135632383478\n",
            "vx : 1.790986493019907\n",
            "error : 7.076569304912555\n",
            "\n",
            "iteration 150\n",
            "vf : 0.8102216640340565\n",
            "vx : 1.7788133986849837\n",
            "error : 6.924113876321586\n",
            "\n",
            "iteration 160\n",
            "vf : 0.8122135805982046\n",
            "vx : 1.766767560238326\n",
            "error : 6.774807735367203\n",
            "\n",
            "iteration 170\n",
            "vf : 0.8141892272246543\n",
            "vx : 1.7548489088504438\n",
            "error : 6.628616702072838\n",
            "\n",
            "iteration 180\n",
            "vf : 0.8161485204647309\n",
            "vx : 1.7430573554791118\n",
            "error : 6.485506154118069\n",
            "\n",
            "iteration 190\n",
            "vf : 0.8180913792419474\n",
            "vx : 1.7313927905855202\n",
            "error : 6.3454410404544\n",
            "\n",
            "iteration 200\n",
            "vf : 0.8200177249641332\n",
            "vx : 1.7198550838796303\n",
            "error : 6.208385895951739\n",
            "\n",
            "iteration 210\n",
            "vf : 0.8219274816327947\n",
            "vx : 1.7084440840946806\n",
            "error : 6.074304857020793\n",
            "\n",
            "iteration 220\n",
            "vf : 0.823820575949542\n",
            "vx : 1.6971596187907299\n",
            "error : 5.9431616781551915\n",
            "\n",
            "iteration 230\n",
            "vf : 0.82569693741942\n",
            "vx : 1.6860014941870767\n",
            "error : 5.81491974933599\n",
            "\n",
            "iteration 240\n",
            "vf : 0.8275564984509893\n",
            "vx : 1.6749694950233416\n",
            "error : 5.68954211424023\n",
            "\n",
            "iteration 250\n",
            "vf : 0.8293991944530127\n",
            "vx : 1.6640633844489487\n",
            "error : 5.566991489194287\n",
            "\n",
            "iteration 260\n",
            "vf : 0.8312249639275994\n",
            "vx : 1.6532829039407013\n",
            "error : 5.447230282812302\n",
            "\n",
            "iteration 270\n",
            "vf : 0.8330337485596809\n",
            "vx : 1.6426277732480894\n",
            "error : 5.330220616259525\n",
            "\n",
            "iteration 280\n",
            "vf : 0.8348254933026878\n",
            "vx : 1.632097690365936\n",
            "error : 5.215924344080029\n",
            "\n",
            "iteration 290\n",
            "vf : 0.8366001464603111\n",
            "vx : 1.6216923315339382\n",
            "error : 5.104303075528489\n",
            "\n",
            "iteration 300\n",
            "vf : 0.8383576597642367\n",
            "vx : 1.6114113512626165\n",
            "error : 4.995318196345634\n",
            "\n",
            "iteration 310\n",
            "vf : 0.8400979884477541\n",
            "vx : 1.601254382385159\n",
            "error : 4.888930890917427\n",
            "\n",
            "iteration 320\n",
            "vf : 0.8418210913151432\n",
            "vx : 1.5912210361345998\n",
            "error : 4.785102164758607\n",
            "\n",
            "iteration 330\n",
            "vf : 0.8435269308067559\n",
            "vx : 1.5813109022457437\n",
            "error : 4.683792867261782\n",
            "\n",
            "iteration 340\n",
            "vf : 0.845215473059717\n",
            "vx : 1.5715235490812172\n",
            "error : 4.58496371465419\n",
            "\n",
            "iteration 350\n",
            "vf : 0.8468866879641767\n",
            "vx : 1.5618585237809919\n",
            "error : 4.488575313105264\n",
            "\n",
            "iteration 360\n",
            "vf : 0.8485405492150577\n",
            "vx : 1.5523153524347124\n",
            "error : 4.394588181929327\n",
            "\n",
            "iteration 370\n",
            "vf : 0.8501770343592475\n",
            "vx : 1.5428935402761224\n",
            "error : 4.30296277682892\n",
            "\n",
            "iteration 380\n",
            "vf : 0.8517961248381944\n",
            "vx : 1.5335925718988723\n",
            "error : 4.213659513125856\n",
            "\n",
            "iteration 390\n",
            "vf : 0.8533978060258792\n",
            "vx : 1.5244119114929682\n",
            "error : 4.126638788928537\n",
            "\n",
            "iteration 400\n",
            "vf : 0.8549820672621379\n",
            "vx : 1.5153510031011033\n",
            "error : 4.041861008185819\n",
            "\n",
            "iteration 410\n",
            "vf : 0.8565489018813224\n",
            "vx : 1.5064092708941086\n",
            "error : 3.959286603579336\n",
            "\n",
            "iteration 420\n",
            "vf : 0.8580983072362953\n",
            "vx : 1.497586119464737\n",
            "error : 3.8788760592083125\n",
            "\n",
            "iteration 430\n",
            "vf : 0.8596302847177621\n",
            "vx : 1.4888809341389921\n",
            "error : 3.800589933022476\n",
            "\n",
            "iteration 440\n",
            "vf : 0.861144839768954\n",
            "vx : 1.4802930813042008\n",
            "error : 3.724388878961011\n",
            "\n",
            "iteration 450\n",
            "vf : 0.8626419818956802\n",
            "vx : 1.4718219087530335\n",
            "error : 3.6502336687573953\n",
            "\n",
            "iteration 460\n",
            "vf : 0.864121724671781\n",
            "vx : 1.463466746042664\n",
            "error : 3.5780852133720793\n",
            "\n",
            "iteration 470\n",
            "vf : 0.8655840857400164\n",
            "vx : 1.4552269048682587\n",
            "error : 3.507904584017157\n",
            "\n",
            "iteration 480\n",
            "vf : 0.8670290868084356\n",
            "vx : 1.4471016794499947\n",
            "error : 3.4396530327393884\n",
            "\n",
            "iteration 490\n",
            "vf : 0.8684567536422786\n",
            "vx : 1.439090346932806\n",
            "error : 3.3732920125300954\n",
            "\n",
            "iteration 500\n",
            "vf : 0.8698671160514703\n",
            "vx : 1.431192167798054\n",
            "error : 3.3087831969326116\n",
            "\n",
            "iteration 510\n",
            "vf : 0.8712602078737723\n",
            "vx : 1.4234063862863322\n",
            "error : 3.246088499120347\n",
            "\n",
            "iteration 520\n",
            "vf : 0.8726360669536644\n",
            "vx : 1.415732230830625\n",
            "error : 3.1851700904205553\n",
            "\n",
            "iteration 530\n",
            "vf : 0.8739947351170372\n",
            "vx : 1.4081689144990357\n",
            "error : 3.1259904182612304\n",
            "\n",
            "iteration 540\n",
            "vf : 0.8753362581417802\n",
            "vx : 1.4007156354463222\n",
            "error : 3.0685122235206084\n",
            "\n",
            "iteration 550\n",
            "vf : 0.8766606857243556\n",
            "vx : 1.3933715773734883\n",
            "error : 3.012698557261074\n",
            "\n",
            "iteration 560\n",
            "vf : 0.8779680714424573\n",
            "vx : 1.3861359099946766\n",
            "error : 2.9585127968311595\n",
            "\n",
            "iteration 570\n",
            "vf : 0.879258472713855\n",
            "vx : 1.3790077895106427\n",
            "error : 2.905918661321598\n",
            "\n",
            "iteration 580\n",
            "vf : 0.8805319507515319\n",
            "vx : 1.3719863590880879\n",
            "error : 2.854880226363312\n",
            "\n",
            "iteration 590\n",
            "vf : 0.8817885705152272\n",
            "vx : 1.3650707493441452\n",
            "error : 2.8053619382572355\n",
            "\n",
            "iteration 600\n",
            "vf : 0.8830284006595011\n",
            "vx : 1.3582600788353356\n",
            "error : 2.7573286274277793\n",
            "\n",
            "iteration 610\n",
            "vf : 0.8842515134784403\n",
            "vx : 1.3515534545503192\n",
            "error : 2.7107455211936267\n",
            "\n",
            "iteration 620\n",
            "vf : 0.8854579848471302\n",
            "vx : 1.344949972405781\n",
            "error : 2.6655782558513472\n",
            "\n",
            "iteration 630\n",
            "vf : 0.8866478941600207\n",
            "vx : 1.338448717744813\n",
            "error : 2.6217928880690504\n",
            "\n",
            "iteration 640\n",
            "vf : 0.8878213242663155\n",
            "vx : 1.3320487658371698\n",
            "error : 2.579355905589013\n",
            "\n",
            "iteration 650\n",
            "vf : 0.8889783614025195\n",
            "vx : 1.3257491823807839\n",
            "error : 2.538234237239747\n",
            "\n",
            "iteration 660\n",
            "vf : 0.8901190951222797\n",
            "vx : 1.3195490240039531\n",
            "error : 2.498395262259615\n",
            "\n",
            "iteration 670\n",
            "vf : 0.891243618223658\n",
            "vx : 1.313447338767624\n",
            "error : 2.459806818935432\n",
            "\n",
            "iteration 680\n",
            "vf : 0.8923520266739756\n",
            "vx : 1.307443166667215\n",
            "error : 2.422437212561063\n",
            "\n",
            "iteration 690\n",
            "vf : 0.8934444195323706\n",
            "vx : 1.3015355401334374\n",
            "error : 2.386255222722142\n",
            "\n",
            "iteration 700\n",
            "vf : 0.8945208988702126\n",
            "vx : 1.2957234845315897\n",
            "error : 2.3512301099144213\n",
            "\n",
            "iteration 710\n",
            "vf : 0.8955815696895174\n",
            "vx : 1.2900060186588203\n",
            "error : 2.317331621504448\n",
            "\n",
            "iteration 720\n",
            "vf : 0.8966265398395059\n",
            "vx : 1.2843821552388697\n",
            "error : 2.284529997042243\n",
            "\n",
            "iteration 730\n",
            "vf : 0.8976559199314531\n",
            "vx : 1.278850901413816\n",
            "error : 2.252795972936796\n",
            "\n",
            "iteration 740\n",
            "vf : 0.8986698232519719\n",
            "vx : 1.2734112592323705\n",
            "error : 2.2221007865060907\n",
            "\n",
            "iteration 750\n",
            "vf : 0.899668365674876\n",
            "vx : 1.2680622261342824\n",
            "error : 2.1924161794143027\n",
            "\n",
            "iteration 760\n",
            "vf : 0.9006516655717671\n",
            "vx : 1.2628027954304317\n",
            "error : 2.1637144005095887\n",
            "\n",
            "iteration 770\n",
            "vf : 0.9016198437214891\n",
            "vx : 1.257631956778202\n",
            "error : 2.135968208076637\n",
            "\n",
            "iteration 780\n",
            "vf : 0.9025730232185929\n",
            "vx : 1.2525486966517425\n",
            "error : 2.109150871518843\n",
            "\n",
            "iteration 790\n",
            "vf : 0.9035113293809525\n",
            "vx : 1.2475519988067494\n",
            "error : 2.0832361724856225\n",
            "\n",
            "iteration 800\n",
            "vf : 0.9044348896566712\n",
            "vx : 1.2426408447394064\n",
            "error : 2.058198405460817\n",
            "\n",
            "iteration 810\n",
            "vf : 0.9053438335304191\n",
            "vx : 1.2378142141391408\n",
            "error : 2.0340123778287724\n",
            "\n",
            "iteration 820\n",
            "vf : 0.9062382924293341\n",
            "vx : 1.2330710853348756\n",
            "error : 2.010653409435\n",
            "\n",
            "iteration 830\n",
            "vf : 0.9071183996286225\n",
            "vx : 1.2284104357344596\n",
            "error : 1.9880973316586972\n",
            "\n",
            "iteration 840\n",
            "vf : 0.9079842901569906\n",
            "vx : 1.2238312422569906\n",
            "error : 1.9663204860148011\n",
            "\n",
            "iteration 850\n",
            "vf : 0.9088361007020339\n",
            "vx : 1.219332481757745\n",
            "error : 1.9452997223034318\n",
            "\n",
            "iteration 860\n",
            "vf : 0.9096739695157138\n",
            "vx : 1.2149131314454564\n",
            "error : 1.925012396324765\n",
            "\n",
            "iteration 870\n",
            "vf : 0.9104980363200388\n",
            "vx : 1.2105721692916913\n",
            "error : 1.9054363671775758\n",
            "\n",
            "iteration 880\n",
            "vf : 0.9113084422130759\n",
            "vx : 1.2063085744320932\n",
            "error : 1.8865499941598514\n",
            "\n",
            "iteration 890\n",
            "vf : 0.9121053295754031\n",
            "vx : 1.2021213275592775\n",
            "error : 1.8683321332897234\n",
            "\n",
            "iteration 900\n",
            "vf : 0.9128888419771202\n",
            "vx : 1.1980094113071684\n",
            "error : 1.8507621334652289\n",
            "\n",
            "iteration 910\n",
            "vf : 0.9136591240855214\n",
            "vx : 1.1939718106266053\n",
            "error : 1.833819832281205\n",
            "\n",
            "iteration 920\n",
            "vf : 0.9144163215735417\n",
            "vx : 1.1900075131520278\n",
            "error : 1.8174855515216133\n",
            "\n",
            "iteration 930\n",
            "vf : 0.9151605810290707\n",
            "vx : 1.1861155095590965\n",
            "error : 1.8017400923454496\n",
            "\n",
            "iteration 940\n",
            "vf : 0.9158920498652372\n",
            "vx : 1.1822947939131006\n",
            "error : 1.7865647301843006\n",
            "\n",
            "iteration 950\n",
            "vf : 0.916610876231753\n",
            "vx : 1.1785443640080218\n",
            "error : 1.7719412093693356\n",
            "\n",
            "iteration 960\n",
            "vf : 0.9173172089274076\n",
            "vx : 1.1748632216961465\n",
            "error : 1.7578517375053828\n",
            "\n",
            "iteration 970\n",
            "vf : 0.9180111973137964\n",
            "vx : 1.1712503732081172\n",
            "error : 1.744278979609449\n",
            "\n",
            "iteration 980\n",
            "vf : 0.9186929912303624\n",
            "vx : 1.1677048294633472\n",
            "error : 1.7312060520308163\n",
            "\n",
            "iteration 990\n",
            "vf : 0.9193627409108281\n",
            "vx : 1.1642256063707155\n",
            "error : 1.7186165161693843\n",
            "\n",
            "iteration 1000\n",
            "vf : 0.9200205969010876\n",
            "vx : 1.1608117251194943\n",
            "error : 1.7064943720089254\n",
            "\n",
            "iteration 1010\n",
            "vf : 0.9206667099786259\n",
            "vx : 1.1574622124604528\n",
            "error : 1.6948240514811586\n",
            "\n",
            "iteration 1020\n",
            "vf : 0.9213012310735276\n",
            "vx : 1.154176100977112\n",
            "error : 1.683590411676506\n",
            "\n",
            "iteration 1030\n",
            "vf : 0.9219243111911328\n",
            "vx : 1.1509524293471303\n",
            "error : 1.672778727916866\n",
            "\n",
            "iteration 1040\n",
            "vf : 0.9225361013363926\n",
            "vx : 1.1477902425938082\n",
            "error : 1.6623746867053115\n",
            "\n",
            "iteration 1050\n",
            "vf : 0.923136752439974\n",
            "vx : 1.1446885923277264\n",
            "error : 1.6523643785672713\n",
            "\n",
            "iteration 1060\n",
            "vf : 0.9237264152861578\n",
            "vx : 1.141646536978524\n",
            "error : 1.6427342907972646\n",
            "\n",
            "iteration 1070\n",
            "vf : 0.9243052404425707\n",
            "vx : 1.1386631420168574\n",
            "error : 1.6334713001248407\n",
            "\n",
            "iteration 1080\n",
            "vf : 0.9248733781917842\n",
            "vx : 1.1357374801665714\n",
            "error : 1.6245626653129028\n",
            "\n",
            "iteration 1090\n",
            "vf : 0.9254309784648164\n",
            "vx : 1.1328686316071401\n",
            "error : 1.6159960197011256\n",
            "\n",
            "iteration 1100\n",
            "vf : 0.9259781907765597\n",
            "vx : 1.1300556841664406\n",
            "error : 1.6077593637067478\n",
            "\n",
            "iteration 1110\n",
            "vf : 0.9265151641631607\n",
            "vx : 1.1272977335039256\n",
            "error : 1.5998410572944581\n",
            "\n",
            "iteration 1120\n",
            "vf : 0.9270420471213691\n",
            "vx : 1.1245938832842877\n",
            "error : 1.5922298124267307\n",
            "\n",
            "iteration 1130\n",
            "vf : 0.9275589875498722\n",
            "vx : 1.1219432453417029\n",
            "error : 1.5849146855053649\n",
            "\n",
            "iteration 1140\n",
            "vf : 0.9280661326926277\n",
            "vx : 1.1193449398347535\n",
            "error : 1.5778850698145883\n",
            "\n",
            "iteration 1150\n",
            "vf : 0.9285636290841996\n",
            "vx : 1.1167980953921464\n",
            "error : 1.5711306879755609\n",
            "\n",
            "iteration 1160\n",
            "vf : 0.929051622497105\n",
            "vx : 1.114301849249341\n",
            "error : 1.5646415844216324\n",
            "\n",
            "iteration 1170\n",
            "vf : 0.9295302578911694\n",
            "vx : 1.1118553473762178\n",
            "error : 1.5584081179032492\n",
            "\n",
            "iteration 1180\n",
            "vf : 0.9299996793648909\n",
            "vx : 1.1094577445959215\n",
            "error : 1.5524209540309577\n",
            "\n",
            "iteration 1190\n",
            "vf : 0.9304600301088063\n",
            "vx : 1.1071082046950165\n",
            "error : 1.546671057864351\n",
            "\n",
            "iteration 1200\n",
            "vf : 0.93091145236085\n",
            "vx : 1.10480590052511\n",
            "error : 1.5411496865545622\n",
            "\n",
            "iteration 1210\n",
            "vf : 0.9313540873636964\n",
            "vx : 1.1025500140960909\n",
            "error : 1.5358483820472473\n",
            "\n",
            "iteration 1220\n",
            "vf : 0.9317880753240676\n",
            "vx : 1.1003397366611523\n",
            "error : 1.53075896385267\n",
            "\n",
            "iteration 1230\n",
            "vf : 0.9322135553739945\n",
            "vx : 1.0981742687937532\n",
            "error : 1.5258735218890167\n",
            "\n",
            "iteration 1240\n",
            "vf : 0.9326306655340071\n",
            "vx : 1.0960528204567028\n",
            "error : 1.5211844094046727\n",
            "\n",
            "iteration 1250\n",
            "vf : 0.9330395426782354\n",
            "vx : 1.0939746110635309\n",
            "error : 1.5166842359847075\n",
            "\n",
            "iteration 1260\n",
            "vf : 0.9334403225013957\n",
            "vx : 1.0919388695323304\n",
            "error : 1.51236586064651\n",
            "\n",
            "iteration 1270\n",
            "vf : 0.9338331394876366\n",
            "vx : 1.0899448343322553\n",
            "error : 1.5082223850289989\n",
            "\n",
            "iteration 1280\n",
            "vf : 0.9342181268812157\n",
            "vx : 1.087991753522854\n",
            "error : 1.50424714667955\n",
            "\n",
            "iteration 1290\n",
            "vf : 0.9345954166589802\n",
            "vx : 1.0860788847864329\n",
            "error : 1.5004337124423375\n",
            "\n",
            "iteration 1300\n",
            "vf : 0.9349651395046154\n",
            "vx : 1.0842054954536389\n",
            "error : 1.496775871951438\n",
            "\n",
            "iteration 1310\n",
            "vf : 0.9353274247846325\n",
            "vx : 1.0823708625224542\n",
            "error : 1.4932676312317432\n",
            "\n",
            "iteration 1320\n",
            "vf : 0.9356824005260602\n",
            "vx : 1.0805742726707974\n",
            "error : 1.4899032064103288\n",
            "\n",
            "iteration 1330\n",
            "vf : 0.9360301933958018\n",
            "vx : 1.078815022262927\n",
            "error : 1.4866770175406074\n",
            "\n",
            "iteration 1340\n",
            "vf : 0.9363709286816262\n",
            "vx : 1.0770924173498428\n",
            "error : 1.4835836825413273\n",
            "\n",
            "iteration 1350\n",
            "vf : 0.9367047302747501\n",
            "vx : 1.0754057736638876\n",
            "error : 1.4806180112521692\n",
            "\n",
            "iteration 1360\n",
            "vf : 0.9370317206539772\n",
            "vx : 1.0737544166077366\n",
            "error : 1.4777749996073282\n",
            "\n",
            "iteration 1370\n",
            "vf : 0.9373520208713517\n",
            "vx : 1.0721376812379801\n",
            "error : 1.4750498239283272\n",
            "\n",
            "iteration 1380\n",
            "vf : 0.9376657505392879\n",
            "vx : 1.0705549122434934\n",
            "error : 1.4724378353369192\n",
            "\n",
            "iteration 1390\n",
            "vf : 0.9379730278191356\n",
            "vx : 1.0690054639187867\n",
            "error : 1.4699345542888163\n",
            "\n",
            "iteration 1400\n",
            "vf : 0.9382739694111396\n",
            "vx : 1.0674887001325322\n",
            "error : 1.4675356652286022\n",
            "\n",
            "iteration 1410\n",
            "vf : 0.9385686905457525\n",
            "vx : 1.0660039942914608\n",
            "error : 1.465237011366123\n",
            "\n",
            "iteration 1420\n",
            "vf : 0.9388573049762593\n",
            "vx : 1.0645507292998189\n",
            "error : 1.463034589574295\n",
            "\n",
            "iteration 1430\n",
            "vf : 0.9391399249726714\n",
            "vx : 1.0631282975145795\n",
            "error : 1.460924545408183\n",
            "\n",
            "iteration 1440\n",
            "vf : 0.9394166613168502\n",
            "vx : 1.0617361006965842\n",
            "error : 1.4589031682449536\n",
            "\n",
            "iteration 1450\n",
            "vf : 0.9396876232988166\n",
            "vx : 1.0603735499578133\n",
            "error : 1.4569668865441752\n",
            "\n",
            "iteration 1460\n",
            "vf : 0.939952918714206\n",
            "vx : 1.0590400657049588\n",
            "error : 1.4551122632276983\n",
            "\n",
            "iteration 1470\n",
            "vf : 0.9402126538628269\n",
            "vx : 1.057735077579482\n",
            "error : 1.4533359911783352\n",
            "\n",
            "iteration 1480\n",
            "vf : 0.9404669335482826\n",
            "vx : 1.0564580243943338\n",
            "error : 1.4516348888562802\n",
            "\n",
            "iteration 1490\n",
            "vf : 0.9407158610786145\n",
            "vx : 1.055208354067509\n",
            "error : 1.450005896032154\n",
            "\n",
            "iteration 1500\n",
            "vf : 0.9409595382679269\n",
            "vx : 1.0539855235526072\n",
            "error : 1.4484460696354153\n",
            "\n",
            "iteration 1510\n",
            "vf : 0.9411980654389529\n",
            "vx : 1.0527889987665673\n",
            "error : 1.446952579716799\n",
            "\n",
            "iteration 1520\n",
            "vf : 0.9414315414265226\n",
            "vx : 1.0516182545147366\n",
            "error : 1.4455227055233215\n",
            "\n",
            "iteration 1530\n",
            "vf : 0.941660063581894\n",
            "vx : 1.0504727744134392\n",
            "error : 1.4441538316842335\n",
            "\n",
            "iteration 1540\n",
            "vf : 0.9418837277779083\n",
            "vx : 1.0493520508101963\n",
            "error : 1.4428434445064175\n",
            "\n",
            "iteration 1550\n",
            "vf : 0.9421026284149312\n",
            "vx : 1.0482555847017534\n",
            "error : 1.4415891283773832\n",
            "\n",
            "iteration 1560\n",
            "vf : 0.9423168584275453\n",
            "vx : 1.047182885650061\n",
            "error : 1.4403885622741832\n",
            "\n",
            "iteration 1570\n",
            "vf : 0.9425265092919528\n",
            "vx : 1.0461334716963597\n",
            "error : 1.4392395163763643\n",
            "\n",
            "iteration 1580\n",
            "vf : 0.9427316710340582\n",
            "vx : 1.045106869273502\n",
            "error : 1.4381398487811135\n",
            "\n",
            "iteration 1590\n",
            "vf : 0.9429324322381909\n",
            "vx : 1.0441026131166553\n",
            "error : 1.437087502318598\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3Io4AG4Crq/YJ4Kz09dnAwclOKOk84KyIeCoiAngQuKammpt1Ej/C03pAnkCYA+yveH8g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\nDAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l1bkCgFkfjBx",
        "colab_type": "text"
      },
      "source": [
        "## 3. Show the results of model (Plot Vx, Vf)\n",
        "Show the results by comparing the outputs of your model to the actual output values for all three methods (backpropagation, resilient propagation and gradient clipping)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rt6l-QmNiSsx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 389
        },
        "outputId": "51e4e1cc-67be-4ad7-c271-41d443db8553"
      },
      "source": [
        "plt.plot(Vx_bp, Vf_bp, 'bs', label='Back Propagation')\n",
        "plt.plot(Vx_rp, Vf_rp, 'ro', label='Resilient Propagation')\n",
        "plt.plot(Vx_gc, Vf_gc, 'y^', label='Gradient Clipping')\n",
        "\n",
        "plt.title('Convergence of vx, vf for each model')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print()\n",
        "print('models\\t\\t\\t| vx*\\t\\t| vf*\\t\\t| iteration')\n",
        "print('-----------------------------------------------------------------------')\n",
        "print('Back Propagation\\t| %.6f\\t| %.6f\\t| %d' %(Vx_bp[-1], Vf_bp[-1], len(Vx_bp)))\n",
        "print('Resilient Propagation\\t| %.6f\\t| %.6f\\t| %d'%(Vx_rp[-1], Vf_rp[-1], len(Vx_rp)))\n",
        "print('Gradient Clipping\\t| %.6f\\t| %.6f\\t| %d' %(Vx_gc[-1], Vf_gc[-1], len(Vx_gc)))"
      ],
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j9OzZk169epVI5/Dhw9x+++28+uqrtG7dmvnz5zNp0iSee+45wCmBrFy5ksWL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\nGGMACwjGGGNcFhCMMcYAFhCMMca4/j94Jxp5APoihgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "models\t\t\t| vx*\t\t| vf*\t\t| iteration\n",
            "-----------------------------------------------------------------------\n",
            "Back Propagation\t| 1.043315\t| 0.943090\t| 1599\n",
            "Resilient Propagation\t| 1.018989\t| 0.947859\t| 264\n",
            "Gradient Clipping\t| 1.043315\t| 0.943090\t| 1599\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WaVWNiJvnzTz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}