02. Activation Functions/16. Bent Identity/16. Bent Identity - MXNet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ArcTan - MXNet.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "from mxnet import nd\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "dRW8XFq59RaM"
      },
      "source": [
        "## __Defining Bent Identity function__"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "def bent_identity(x):\n",
        "    return ((nd.sqrt(nd.square(x) + 1.0) - 1.0)/2.0) + x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "xs = nd.arange(-10, 10, 0.1)\n",
        "ys = bent_identity(xs)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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      ],
      "source": [
        "# matplotlib doesn't support mxnet's ndarray but it supports numpy's ndarray, so we need to convert xs and ys to numpy ndarray by calling .asnumpy() method\n",
        "plt.plot(xs.asnumpy(), ys.asnumpy())\n",
        "plt.xlabel('Values of x')\n",
        "plt.ylabel('Values of Bent Identity of x')\n",
        "plt.title('Bent Identity Function')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4cIIBfRD_HB3"
      },
      "source": [
        "## __Now defining derivative of bent identity funciton__"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "def bent_identity_derivative(x):\n",
        "    return (x/(2 * nd.sqrt(nd.square(x) + 1))) + 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "dxs = nd.arange(-10, 10, 0.1)\n",
        "dys = bent_identity_derivative(dxs)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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2YKyROVcgzIw7X36XWWMHceC4wdkOxxWgdJeGvh6+n5aJQJwrVPNWb2XJxu389JOzsh2KK1Ad3jVkZuvDyS+b2erUF/DlzITnXO9396trKC8r5vSDxmQ7FFegotw++tF2lp3S04E4V4h2NbXw+JsbOOWAUfQvi/J8p3M9L10bwZcIvvlPlrQgpWgA8ELcgTlXCJ5dUsX2hmbmHOy1AZc96b6C3Ak8BvyE9z5Utt3MOhtwxjkXwUNvrKOivJSjJg/LdiiugKVrI6gxs1Vhn0GVQBNgQLkk7xLRub1U19DM04ur+Pis0RT7eAMui6L0PvoV4EqCnkeT4WID/PZR5/bCc0uqaWhOcuqs0dkOxRW4KK1TlwLTzWxz3ME4V0ieXryRwf1KOGzCkGyH4gpclProGqAm7kCcKyQtSeOZJVWcMH2EXxZyWRelRrACeFbS/wENrQvN7NrYonKul3vt3a1s3dHEiTNGZDsU5yIlgnfDV2n4cs7tpacWb6Q4IY7d18fgdtnXaSIwsx8ASOpvZvXxh+Rc7/f8O5uYPXEIA/uUZDsU5zpvI5B0lKRFwOJw/iBJN8YemXO91Jb6Rhavr+WDUyqyHYpzQLTG4p8DHwM2w+7uqY+NMyjnerN/LA9uwDt6qicClxsi3a5gZmvaLGqJIRbnCsILyzdRXlbMQeMGZTsU54BojcVrJB0NmKRS4GuEl4mcc1334rJNfGDSUL9t1OWMKH+JFwOXAGMJupo4OJx3znXR2m07WbV5h18Wcjklyl1Dm4DzMhCLc73e3FVBf41HTh6a5Uic2yNdN9TXE/Qp1C4z+1osETnXi81dtZX+pUXsN2pgtkNxbrd0l4bmAvOAPsChwNLwdTDeWOxct8xdvZVD9hlCUULZDsW53TqsEZjZbQCSLgBOMLOmcP4m4ImMROdcL7J9VxNLNtTy1Q9Py3Yozr1HlMbiMQSjkrUqD5c557pg/pptJA3vbdTlnCi3j/4UeF3SM+H8cQTjEzjnumDuqq1IcMg+g7MdinPvEeWuod9Legz4QLjocjPbEG9YzvU+r727lekjBzDA+xdyOSbdXUOHtlnU+nTxGEljzOy1+MJyrncxMxZU1nDKAaOyHYpz75OuRnBNmjIDPpxuw5JuAU4DqszsgHbKzwMuC2frgC+F/Rg51+us2bKTmp1NzPJuJVwOSnfX0Al7ue1bgRuAP3RQvhI4zsy2SjoFuJk9l5+c61UWrN0GwEHjvH3A5Z4ojcXdYmbPS5qYpvzFlNmXgHFxxeJcti2srKG0KMG+Iwd0vrJzGZYrvV79C/BYR4WSLpI0V9Lc6urqDIblXM9YUFnDjNEDKC3OlX855/bI+l+lpBMIEsFlHa1jZjeb2Wwzmz18uA/t5/JLMmm8ubbG2wdczooyQtnTUZZ1h6QDgd8CZ5jZ5p7YpnO5ZtXmerY3NHPgWG8fcLkp3e2jfYB+QIWkIUBr5ygD6YEniyXtA9wPfM7M3tnb7TmXq95cVwvA/mO9ozmXm9I1Fv8rcCnBSX8eexJBLfDLzjYs6S7geIJEUgl8HygBMLObgCuAYcCNkgCazWx2t34K53LY2+trKU6IqSPKsx2Kc+1Kd/vodcB1kr5qZtd3dcNmdk4n5V8AvtDV7TqXbxavr2XqiHLKiouyHYpz7YrSxcT14VCVE1PXN7OOng9wzqVYvH47R00Zlu0wnOtQp4lA0u3AFGA+e8YhMDp+UMw5F9pa38iG2l3MGO3PD7jcFeWBstnATDPrcLQy51z7Fq8PGopnjPaGYpe7ojxH8CbgPWU51w2LPBG4PBClRlABLJL0CtDQutDM5sQWlXO9xOL12xk+oIyK8rJsh+Jch6IkgivjDsK53urtDbXsN8rbB1xu6/TSkJk9B6wCSsLpVwEfi8C5TrQkjWVVdUz3juZcjovSxcQXgfuAX4eLxgIPxBmUc73Bu1t20NCcZF+vEbgcF6Wx+BLggwRPFGNmS4ERcQblXG/wzsbtAN71tMt5URJBg5k1ts5IKiZ4jsA5l8bSMBFM864lXI6Lkgiek/QdoK+kjwL3Ag/HG5Zz+e+djXWMHdyX/mWxjf/kXI+IkgguB6qBhQQd0T0K/GecQTnXG7yzcTv7jvTagMt9UfoaSgK/CV/OuQiaW5KsqK7nuH19ICWX+zqsEUiaJulWSddKGifpMUl1kt6QdHgmg3Qu36zavIPGlqQ3FLu8kO7S0O+BF4F1wMvALQRPGX8LuCH+0JzLX7sbiv3SkMsD6RJBeThW8M+AnWZ2r5ntMrMnAX9e3rk0llfXATBluCcCl/vSJYJkynRtmjLnXBvLq+sZM6iP3zHk8kK6v9L9JC0gGKJySjhNOD859sicy2PLq+uY4s8PuDyRLhHMyFgUzvUiZsbyqjrOmj0+26E4F0m6MYtXZzIQ53qLjbUN1De2MGV4/2yH4lwkUR4oc851gTcUu3zjicC5HrY7EXgbgcsT6R4oezp8vzpz4TiX/5ZX1VFeVsyIAX6XtcsP6RqLR0s6Dpgj6W6Cu4V2MzMfnMa5diyvrmfK8P5I6nxl53JAukRwBUGHc+OAa9uUGfDhuIJyLp8tr67jqMnDsh2Gc5Glu2voPuA+Sd8zs6syGJNzeauuoZn1Nbu8fcDllSi9j14laQ5wbLjoWTN7JN6wnMtPK6vrAfzWUZdXooxZ/BPg68Ci8PX1cJlzrg2/ddTloygdoXwcODgclwBJtwGvA9+OMzDn8tHy6jqKEmKfYf2yHYpzkUV9jmBwyvSgOAJxrjdYXl3HPkP7UVZclO1QnIssSo3gJ8Drkp4huIX0WLw24Fy7llfVe/uAyzud1gjM7C7gSOD+8HWUmd3d2eck3SKpStKbHZRL0i8kLZO0QNKhXQ3euVzSkjRWbqr39gGXdyJdGjKz9Wb2kJk9aGYbIm77VuDkNOWnANPC10XAryJu17mcVLk1GJ7SE4HLN7H1NWRmzwNb0qxyBvAHC7wEDJY0Oq54nIvbnj6G/NKQyy/Z7HRuLLAmZb4yXPY+ki6SNFfS3Orq6owE51xXLa8KniGYXOE1ApdfojxHMEVSWTh9vKSvSRrc2eciaK8jFmtvxXDs5NlmNnv48OE9sGvnet7y6jqG9S9lSP/SbIfiXJdEqRH8GWiRNBX4HTAJuLMH9l0JpA7hNA5Y1wPbdS4rllfXefuAy0tREkHSzJqBM4Gfm9k3gJ64lv8Q8Pnw7qEjgRozW98D23UuK5ZX13v7gMtLUZ4jaJJ0DnA+cHq4rKSzD0m6CzgeqJBUCXy/9XNmdhPwKHAqsAzYAVzY1eCdyxVb6hvZUt/oNQKXl6IkgguBi4Efm9lKSZOAP3b2ITM7p5NyAy6JFKVzOW6F9zHk8liU3kcXSboM2CecXwn8NO7AnMsn3tmcy2dR7ho6HZgP/DWcP1jSQ3EH5lw+WV5dT2lxgrFD+mY7FOe6LEpj8ZXAEcA2ADObT3DnkHMutLyqjskV/SlK+PCULv9ESQTNZlbTZlm79/s7V6j81lGXz6IkgjclnQsUSZom6XrgxZjjci5v7Gpq4d0tO7zXUZe3oiSCrwL7Aw0ED5LVAJfGGZRz+WTlpnqSBtNGDsh2KM51S5TbR6eb2XeB78YdjHP5aGlVcMfQtJF+acjlpyg1gmslvS3pKkn7xx6Rc3lm2cbtJASTKvzSkMtPUQamOYHgCeFq4GZJCyX9Z9yBOZcvllbVMXFYfx+e0uWtqAPTbDCzXxA8YTwfuCLWqJzLI0ur6pg6wi8LufwV5YGyGZKuDIecvIHgjqFxsUfmXB5obE6yalO9tw+4vBalsfj3wF3ASWbm3UQ7l2L15nqak8a0EX7HkMtfUfoaOjITgTiXj1rvGPJLQy6fdZgIJN1jZp+RtJD3Pkksgs5DD4w9Oudy3NKNdUje2ZzLb+lqBF8P30/LRCDO5aNl1XWMH9KPvqV+x5DLXx02FqeMFvZlM1ud+gK+nJnwnMttSzduZ5pfFnJ5Lsrtox9tZ9kpPR2Ic/mmuSXJik313j7g8l66NoIvEXzznyxpQUrRAOCFuANzLtet2bqTxuakJwKX99K1EdwJPAb8BLg8Zfl2M9sSa1TO5YGlG7cD3tmcy38dJoJwDIIa4BwASSOAPkC5pHIzezczITqXm/zWUddbRBqqUtJSYCXwHLCKoKbgXEFbVlXHmEF9KC+L8lymc7krSmPxj4AjgXfMbBJwIt5G4BxLq7Yz1S8LuV4gSiJoMrPNQEJSwsyeAQ6OOS7nclpL0lhWVcdUf5DM9QJR6rTbJJUDzwN3SKoCmuMNy7nctnpzPbuakuw32msELv9FqRGcAewAvgH8FVgOnB5nUM7lusXrgzuGZo4emOVInNt7UWoEFwH3mlklcFvM8TiXFxavr6UoIb9jyPUKUWoEA4HHJf1N0iWSRsYdlHO5bvH6WqYM70+fEu9jyOW/KENV/sDM9gcuAcYAz0l6KvbInMthi9fXMsMvC7leItJQlaEqYAOwGRgRTzjO5b5tOxpZV7PLE4HrNaI8UPYlSc8CTwMVwBd9LAJXyFobij0RuN4iSmPxBOBSM5sfdzDO5YPF62sBmOG3jrpeosMagaTWrzv/DbwraWjqK8rGJZ0saYmkZZIub6d8kKSHJb0h6S1JF3bvx3Auc95cV0NFeRnDy8uyHYpzPaKz3kdPA+YRDFWplDIDJqfbsKQi4JcE4xlUAq9KesjMFqWsdgmwyMxOlzQcWCLpDjNr7PqP4lxmLKys4aBxg5DU+crO5YF0vY+epuAv/bhu9jR6BLDMzFYASLqb4OG01ERgwIBwP+XAFvypZZfD6huaWVZdx8cPHJ3tUJzrMWkbi83MgL90c9tjgTUp85XhslQ3ADOAdcBC4Otmlmy7IUkXSZoraW51dXU3w3Fu7721rhYzOHDcoGyH4lyPiXL76EuSDu/GtturN1ub+Y8B8wmeTzgYuCGlbWLPh8xuNrPZZjZ7+PDh3QjFuZ6xoHIbAAeM9UTgeo8oieAEgmSwXNI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            "text/plain": "<Figure size 432x288 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# matplotlib doesn't support mxnet's ndarray but it supports numpy's ndarray, so we need to convert xs and ys to numpy ndarray by calling .asnumpy() method\n",
        "plt.plot(dxs.asnumpy(), dys.asnumpy())\n",
        "plt.xlabel('Values of x')\n",
        "plt.ylabel('Values of derivatives of Bent Identity of x')\n",
        "plt.title('Bent Identity Derivative')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "oHyKa2Uh_vqg"
      },
      "source": [
        "## __Plotting Bent Identity function and it's derivative together__"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": "<Figure size 720x360 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
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          "output_type": "display_data"
        }
      ],
      "source": [
        "# matplotlib doesn't support mxnet's ndarray but it supports numpy's ndarray, so we need to convert xs and ys to numpy ndarray by calling .asnumpy() method\n",
        "plt.figure(figsize = (10, 5))\n",
        "plt.plot(xs.asnumpy(), ys.asnumpy(), label = 'Bent Identity function')\n",
        "plt.plot(dxs.asnumpy(), dys.asnumpy(), label = 'Bent Identity function derivative')\n",
        "plt.xlabel('Values of x')\n",
        "plt.ylabel('Values of Bent Identity of x and its derivatives')\n",
        "plt.title(\"Bent Identity Function and it's derivative\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": "1.4974686"
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dys.max().asscalar() "
      ]
    }
  ]
}