activationfunction_and_relu_function_using_6_neurons.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "activationfunction and relu function using 6 neurons.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "YXDe9gHjDbTR"
      },
      "source": [
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "YqU5GKqUDlnp",
        "outputId": "1768eb1c-f710-4440-ca74-5c8c945e00f0"
      },
      "source": [
        "x=np.arange(-10,10,0.5)\n",
        "print(x)\n",
        "def linear_activation(x):\n",
        "  a=[]\n",
        "  for i in x:\n",
        "    a.append(i)\n",
        "  return a\n",
        "y=linear_activation (x)\n",
        "plt.plot(x,y,'--')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-10.   -9.5  -9.   -8.5  -8.   -7.5  -7.   -6.5  -6.   -5.5  -5.   -4.5\n",
            "  -4.   -3.5  -3.   -2.5  -2.   -1.5  -1.   -0.5   0.    0.5   1.    1.5\n",
            "   2.    2.5   3.    3.5   4.    4.5   5.    5.5   6.    6.5   7.    7.5\n",
            "   8.    8.5   9.    9.5]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8aPifnhkDlcp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "be9e4c5f-a5fc-44a3-99ee-97dd63a57d9c"
      },
      "source": [
        "X = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
        "# For OR use this y array\n",
        "# y = np.array([0,1,1,1])\n",
        "# For AND use this y array\n",
        "y = np.array([0,0,0,1])\n",
        " \n",
        "def step_function(x):\n",
        "    return x>=0\n",
        " \n",
        "def perceptron(epochs,aplha,bias):\n",
        "    W = np.random.rand(2)\n",
        "    while(epochs > 0):\n",
        "        for i in range(4):\n",
        "            pred = step_function(W.dot(X[i]) + bias)\n",
        "            W = W - (alpha*(pred-y[i]))*X[i]\n",
        "            bias = bias - (alpha*(pred-y[i]))\n",
        "        epochs = epochs - 1\n",
        "    return (W,bias);\n",
        " \n",
        "def test(x1,x2,weights,bias):\n",
        "    ans1 =(weights[0]*x1 + weights[1]*x2 + bias)\n",
        "    return step_function(ans1)\n",
        " \n",
        " \n",
        "alpha = 0.1\n",
        "epochs = 20\n",
        "bias = 0\n",
        "ans = perceptron(epochs,alpha,bias)\n",
        "weights = ans[0]\n",
        "bias = ans[1]\n",
        " \n",
        "# If you want to test use this\n",
        "x1 = int(input(\"Enter x1: \"))\n",
        "x2 = int(input(\"Enter x2: \"))\n",
        "# Works only if x1 & x2 are binary\n",
        "print(test(x1,x2,weights,bias))\n",
        " \n",
        "X1 = [0,0,1,1]\n",
        "X2 = [0,1,0,1]\n",
        "plt.plot(X1,X2,'ro')\n",
        "pnt1 = (-bias/weights[0])\n",
        "pnt2 = (-bias/weights[1])\n",
        "point1 = [0,pnt1]\n",
        "point2 = [pnt2,0]\n",
        "plt.plot(point1,point2,'b-')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Enter x1: 0\n",
            "Enter x2: 1\n",
            "False\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zfIxzzyVDlY-"
      },
      "source": [
        "def reLu(x):\n",
        "  return np.maximum(0,x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3shluMvnDlV5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3f2c4605-f121-4c28-c1a4-8829b1f31fcc"
      },
      "source": [
        "x = np.arange(-2,2,0.1)\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2.00000000e+00, -1.90000000e+00, -1.80000000e+00, -1.70000000e+00,\n",
              "       -1.60000000e+00, -1.50000000e+00, -1.40000000e+00, -1.30000000e+00,\n",
              "       -1.20000000e+00, -1.10000000e+00, -1.00000000e+00, -9.00000000e-01,\n",
              "       -8.00000000e-01, -7.00000000e-01, -6.00000000e-01, -5.00000000e-01,\n",
              "       -4.00000000e-01, -3.00000000e-01, -2.00000000e-01, -1.00000000e-01,\n",
              "        1.77635684e-15,  1.00000000e-01,  2.00000000e-01,  3.00000000e-01,\n",
              "        4.00000000e-01,  5.00000000e-01,  6.00000000e-01,  7.00000000e-01,\n",
              "        8.00000000e-01,  9.00000000e-01,  1.00000000e+00,  1.10000000e+00,\n",
              "        1.20000000e+00,  1.30000000e+00,  1.40000000e+00,  1.50000000e+00,\n",
              "        1.60000000e+00,  1.70000000e+00,  1.80000000e+00,  1.90000000e+00])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jVpy6mNFDlSv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "a889212f-7a84-4a88-b0e9-8f8c08bc6a26"
      },
      "source": [
        "plt.axhline(0,color='grey')\n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x,reLu(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6e6f64908>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nufq91Q4DlPi"
      },
      "source": [
        "f=x**3+x**2-x-1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RMIWlI8kDlMw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "5d0dcf2c-df9c-472e-e62c-a718844e8be3"
      },
      "source": [
        "plt.plot(x,f)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de6d2b70>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZYzJHW9aDlJm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "4c222469-f662-41a5-b5ce-5655b251ea50"
      },
      "source": [
        "f1=reLu(-5*x-7.7)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de6945f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1UsqFtiDDlGs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "164cd3a3-1b18-4a00-d5c8-ee5285900a7b"
      },
      "source": [
        "f2=reLu(-1.2*x-1.3)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de6ce898>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S-R61ARrDlDo",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "d2708390-48f1-4633-dca3-b6614c2148e9"
      },
      "source": [
        "f3=reLu(1.2*x+1)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de59b6a0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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tw6fA/Nuc8B63JKQWK+5LR7eH7/+9iCk5qdy4aLzb5bjOHy3zpcCngF3GGN9UZnzdWvsPPxxbRPyh/nDvwOWh16GnHeKSYMIyWHSn0/edOcHtKgfkwY2HOFrXxp9uW0h8bP8f949U/ribZSMQncPHIqGqp9MZsDzx2HzNfmf7sAkw9ybfcmlLIT7J3TrPUkVjB7/ecIDVM3O5YEqW2+WEBD0BKhIpGo72PjJf8hp0t0LsEGeF+fxbnQAfPsntKv3iv17aS4/X8o0Pz3S7lJChMBcJVz1dUPqO77H5dVDtW6w4Yxycf4Pz4M6EZZCQ4m6dfrb1SD3PbS/n3y6exLjhyW6XEzIU5iLhpOlY750nJa9BVzPExMP4JTDnRmfwMmtqxC1WfIIz/8oectOGcOfyyW6XE1IU5iKhzNMNpZt7H5uv3O1sTxsD53zM6TqZcCEMGepunUHy4MYS3i1r5OfXn09KlM2K+EF0NURCTXOFb7HitXBwA3Q2Qkycs1jxqu86AZ49PWJb36dTXNnMT9bsZ/XMXK48b5Tb5YQchbmI2zw9UF7Q231S8a6zPXUEzLzSCe+JyyExzc0qXdXj8fKVp3eSkhDLD64+J2rnXzkThbmIG1qqndb3gbXOosUdDWBiYexCuORbToDnzo661vfp/O71EnaWNfKrT8whe+gQt8sJSQpzkWDwepzFiovXOF/HtjvbU3Jg+od7FytOynC3zhBUdLyJ+9bt58PnjuSKc9W9cjoKc5FAaatzWt3Fa5xWeHsdmBgYMx8u/gZMWQkjzhvQYsXRptvj5ctP7SQ9KZ7vXTXb7XJCmsJcxF+8Xji+wzd4uQbKCgALycOdbpMpq5xl05Iz3a40bPzqlQMUHm/itzfOi/qJtD6IwlxkMNrrnTtOTjw231oNGBg9F5Z/zXlwZ9Qctb7Pwu7yRn694QAfPX8Ul80e4XY5IU9hLjIQ1kLFrt6uk9LNzmLFScNg0iW9ixWnaL6Qwejs8fDlp3aSmZLAd65U90p/KMxFPkhHo7NY8YnH5lsqnO0jz4ML7oapl8LoeRATfYsIB8ov1hezr7KZP9ycT3py8JehC0cKc5FTWQtVhb3hXfqOb7HidJi8onex4qG5blcakXaUNvCbVw9yzbwxrJiua9xfCnMRgM5mZ66TE90nTeXO9txzYMkXncHLMQsgVj8ygdTc0c2XntzBiLREvvkRzYg4EPrOlOhkrTPHd/EaZ/DyyFvg7YaEoTBpuW/wciWk6b7mYPF6LV96aidH6tp47DMLSUtU98pAKMwlenS1OqvsnFhxp/Gosz1nJiz6V99ixQtDZrHiaPM/rx5gbWEl37piJgsnDne7nLCjMJfIZa1vseI1zm2DhzeCpwviU5y5Tpbd7fR/Z4x1u9Kot2FfFT9du5+Pnj+KW5bmuV1OWFKYS2TpbndC+8Rj8/WHne1Z02DBHb7FihdDnOb3CBVHalu56/HtTB+Rxg//5VxNonWWFOYS/upKnLtOitfA4Tegp8NZrHjiRbD4806AD8tzu0rpQ1tXD5/9360YY/jdjfNIStDtnWdLYS7hp7sDjrzZ+9h87QFne+YkmHeLE97jl0J8ort1yhlZa/nan3exr7KZP96yQEvADZLCXMJD/ZHe1XYOvQ7dbRCX6CxWPP92J8AjZLHiaPHgxkP8decx/uPSaVw0NdvtcsKewlxCU08XHH2r986Tmn3O9mF5zlqXk1c5QZ6g1lw4evtgLT98cS+XzsrlzuX6EPYHhbmEjsay3vA+9Bp0tUBsgtNlMu9mX+t7shZsCHPHGtr5/GPbyBuezE+uOU8Dnn6iMBf3eLqhdFPvgztVhc729LFw7rW9ixUnpLhbp/hNQ1sXt/5xC509Xn73qXyG6sEgv1GYS3A1He/t+y55FTqbICYexi+GVd/zLVY8Ta3vCNTS2cPND22hpLqVB2/OZ3JOqtslRRSFuQSWpwfKtvS2vit3OduHjoJZVztdJxMuiurFiqNBR7eH2x8uYFd5I//zybksm6IBT39TmIv/NVf2LlZ88BVnClkTC+MWwcr/dAYvc2ep9R0luj1e7nx0G+8cquVn157PpbO00EQgKMxl8LweKN/a2/o+vsPZnpoL0z/irHWpxYqjksdrufvJHbyyt4ofXD2bj84Z7XZJEcsvYW6MuQz4ORALPGCt/ZE/jishrLXGWaz4wFrfYsX1vsWKF8CKbzh937nnaLm0KOb1Wu559l1eePc4X//QdD65cLzbJUW0QYe5MSYW+DWwCigDthhj/mqtLRzssSWEeL1wfHvvrYPlW3EWK86CqZc5fd8TL9ZixQI4T3d+7++FPFVQxhdXTOaOC3UveaD5o2W+ADhgrS0BMMY8AVwFKMzDidcDbbXQXAEtVc7SaC2VTv938zE48ja01eAsVjwPlt/jBPjI89X6lvf52bpiHnrzMLcszePuVVPdLicq+CPMRwOlJ/29DFjoh+O+38v3wrZHAnLocGNxWj9ea/Fa8FoLtnc7ODPA2vf2txicAUdj4MTQozEGgyXB20kMnvefaEg6pObApIudrpNJK7RYsZyWtZafrd3PL145wLX5Y/jmh2fqoaAgCdoAqDHmDuAOgHHjxp3dQcbMB+v1Y1XhodvjpaKpg/rWLhraumlo76axvYuuHvvePnExhoS4GOJjDfGxMb4v53VcbAyxBro9lh6vpdvjpcdr6fF46fZ46fZY6j3xHPemU2UzqLYZVJGBSckhOz2DsZnJTBmWyqwh6cz2DkU3lUlfOns83PPnXTy7vZxr5o3hh/9yLjExCvJg8UeYlwMnz+4/xrftn1hr7wfuB8jPz7envt8vsz7qfEU4ay0Hq1vYsLeaV/dXseVQPV0e50MsK3UIk3NSmDwtlcnZqUzOGcqU3FRyhg4ZVAvI67VUNXdSWt9GWX0bpXXt7/1ZcLiev+w49t6+OUOHMHt0OrNHpTFrdDqzR6czKj1RLbAo1tjWzWf/VMA7JXV8edVUPr9isr4fgswfYb4FmGKMmYAT4tcDn/DDcaNKa2cPbx2s5dV9Vby6r5ryhnYApuSk8ukl47loag6zR6eRkRyYJc1iYgwj0hMZkZ7I/Lz3D2I2dXRTdKyJ3cea2FPeyO5jjby6rwqv72N5RFoiiyZmsnDicBZOyGRCVop+mKNEaV0bNz+0mdK6du677nzdfuiSQYe5tbbHGPN54GWcWxP/YK3dM+jKosT+ymYefuswz20vp63LQ0pCLEsmZ3HnxZO4aGo2Y4aFxqyAaYnxTlCftDZje5eHvRVN7CpvZNOhOjYeqOV5Xws+e+gQFk5wwn3xxEwmZacq3CPQ9qP13P5IAd0eyyO3LWCR1u50jTkxWBZM+fn5tqCgIOjnDRU9Hi/riqp4+K3DvF1SS0JcDFedN4qr54wmPy+ThLjwvDvEWktJTSubSurYdKiWTSV1VDR1ADA6I4kLp2azfFo2SydnkTpEz6uFu5d2H+euJ3aQm5bIQ7fMZ1K25loJNGPMVmttfp/vKcyDp661iye2HOXRd45S3tDO6Iwkblw0nuvmjyUzJfJWhLfWcqS2jbcO1vLa/irePFBLS2cP8bGG/PGZLJ+WzfJpOUzNVas9nFhreXDjIX7wjyLOH5vBAzflMzxVa6oGg8LcZbUtnfxs3X6eKiijq8fLkknD+fSSPC6ZnkNcbHi2ws9GV4+XrUfqeXV/Fa/tq2ZvRTPgtNpXzshh1cwRLJyYSXwUXZNwU9vSyb3P7ealPRVcPnsEP7vufBLjtW5nsCjMXdLV4+WRtw/z8/XFtHd5uCZ/LLcuzWNK7lC3SwsJxxvbeW1fNeuKqth4oJqObi9DE+O4eFoOq2bmsnxatua7DiHrCiv52rO7aGrv5kurp3LHsom69TDIFOYu2LCviu+9UEhJdSsXTs3mW1fMYHKOQvx02rs8vFFczdrCStbvraKutYv4WMPiSVmsnpnL6pm55KRpgWY3NHd08/0XiniyoJQZI9P42XXnMX2Epix2g8I8iA5Wt/D9FwrZsK+aCVkpfPOKGVw8LUd9wgPg8Vq2Ha1nbWEla/ZUcLi2DWNg7rhhXDZrBJfOGqGV3INkU0ktX356J8ca2vnX5ZO465KpYTtAHwkU5kHQ1NHNL9YV88e3DpMUH8sXL5nCp5fk6Rt/kKy1FFe18NLuCl7eU8GeY00AzBiZ5gT77Fym5Q7Vh6WfdXR7+OmafTyw8RDjM5P56bXnM2/8MLfLinoK8wDbWdrA5x/fRll9O9fPH8uXV08jS6P7AVFa18bLe5xgLzhSj7Uwfngyl84aweqZucwZN4xY9eOeNWst64uq+NFLezlQ1cKNi8bx9Q/NIDlBt5KGAoV5gFhr+cObh/nRi0XkDE3kFzfMUesliKqaO3xdMZW8dbCGbo8lKzWBVTNzWT1zBIsnDdedFgPw9sFafvzyXrYdbSBveDLfuWo2F03VTDyhRGEeAA1tXXzl6XdZV1TJyhm5/OSacwP2qL18sOaObjbsq2bNngpe3VdNS2cPKQmxLJ+WwyUzclg+LSci7+X3h52lDfxkzT7eKK5hRFoid62cwsfnjdEtoiFIYe5nW4/U88XHt1PV3ME9l8/glqV56rMNIZ09Ht4+WMuawkrWFlZS3dz53gDqiuk5rJiew/QR6mcvrmzmp2v289KeCjJTErhz+SRuXDRev82EMIW5n3i9lt+/UcKPX97HyIxEfnXDXM4bq3UtQ5nXa9l9rJH1RVVs2FfFu2WNAIxMT3wv2BdOHB410wt4vZa3S2p5YkspL7x7jJSEOG5fNpFbL8jTPf1hQGHuBw1tXdz95A427Kvm8tkj+NHHziU9Sd/84aaqqYNX91Wzfm8lbxTX0NblIS7GcN7YDJZOGs6SyVnMGZfBkLjIap0eqW3lma1lPLutnPKGdoYmxnHDgnF87qJJ6n4KIwrzQaps6uCmBzdzqKaVb1wxg08tGh/1v6JHgs4eDwWH63nzQA1vHqxlV1kDXguJ8THMz8tkyaQsFk8azsyRaWF5i2lLZw//2HWcZwrK2Hy4DmNg2ZRsPj5vDKtn5qo7JQwpzAfhSG0rNz64ibqWLu6/KZ+lk7VkWqRq6uhmU0kdbx6o4a2DNeyvbAEgIS6GWaPSOG9MBnPGZXDemAzGD08OuQ90j9dSdLyJzYfq2Hyojtf2V9Pe7WFiVgofzx/D1XNGMzI9ye0yZRAU5mep6HgTN/1hMz0eL3+8ZYH6x6NMdXMnWw7XsaO0gR2lDewqa6S921kndVhyPOeNzWDWqDQmZqUyITuFSVmppCcHr+utq8fLrvJGX3jXUnC4nubOHgDGZiaxbEo2H5s7hrnjMkLug0fOjsL8LGw9UsctD20hOSGO/71tgSbHEno8XvZXtrCzrIEdR52AP1Ddgsfb+zM0PCWBCVkpTMxOYUJWKiPTE8lIjmdYcgLDkhPISIln6JC4foWrtZba1i7K69spb2invN5Zyq+8oZ2y+nYO17bS0e0sJzg5J5UFEzJZOCGT+XmZjMpQCzwSKcwH6NV9VXzuT1sZmZ7E/962IGRW+5HQ0+3xcrSujUPVrZTUtHCoppWD1a2UVLdS09LZ57+JizFkJMeTnhRPjDHO4tpeLx6Ppdtr8fgW3e7s8dLV888LmKcOiWPMsCRGZySRl5XC/Lxh5Odl6onjKHGmMI+O+7EG4G87j/Glp3YwJWcoD9+6gOyh+iGR04uPjWFSdqpvlZ3cf3qvqaOb6uZOGtq6qG/tpr6ti4Y258/6tm4a27sAiI2JIT7GEBtjiIs1xMXEEBtjGBIXw4j0REZnJDF6WBJjMpJJS+pfq16ij8L8JI9uOsI3nt/N/PGZPHBzPmm671YGIS0xXt9DEjQKc5+ntpRy73O7WTE9h19/Yi5JCbptS0TCh8Ic2LC3inue28WyKVn89sZ5YXlPsYhEt6hPrZ2lDdz56DamjxjKbxTkIhKmojq5jtS2cusftzA8NYGHbpkfNfNziEjkidowr2np5KY/bMZrLQ/fuoCcoVpfUkTCV1Q2Rdu6erjtj1uobOrgsdsX+W4rExEJX1HXMu/xePm3R7exq7yRX94wl7njtDKQiIS/qGqZW2u597ndbNhXzQ+uns2qmbkf/I9ERMJAVAGYQBIAAAgLSURBVLXMf76+mCcLSvnCisl8cuF4t8sREfGbQYW5MebHxpi9xph3jTHPGWNCdlrBtYWV3LeumI/NHcOXVk11uxwREb8abMt8LTDbWnsusB+4Z/Al+V9ZfRtfeXons0al8YOrZ2tuCxGJOIMKc2vtGmttj++v7wBjBl+Sf3V7vHzh8e14vJZff2KuVlcRkYjkzz7zW4EX/Xg8v/jxy/vYfrSBH33sHPKyUtwuR0QkID7wbhZjzDpgRB9v3Wut/Ytvn3uBHuDRMxznDuAOgHHjxp1VsQO1rrCS+18v4VOLxnPFuaOCck4RETd8YJhba1ee6X1jzM3AFcAl9gwrXVhr7wfuB2dxioGVOXDlDe18+emdzByZxr0fnhHo04mIuGpQ95kbYy4DvgpcZK1t809Jg9ft8fKFx7Y5/eSfVD+5iES+wfaZ/woYCqw1xuwwxvzWDzUN2k9e3se2ow388F/OYYL6yUUkCgyqZW6tneyvQvxlfVElv3u9hBsXjeMj56mfXESiQ0Q9AXpyP/k3PjzT7XJERIImYsLc67Xc/cQOunu86icXkagTMWH+2OajbD5cx7evnKV+chGJOhER5hWNHfzoxb0snTyca+aF3EOoIiIBF/Zhbq3lG8/vpsfr5f9efY7mXRGRqBT2Yf7i7grWFVXypVVTGT9c3SsiEp3COswb27r51l/2MHt0GrcuneB2OSIirgnrlYZ+8I9C6tu6ePjW+cTFhvXnkojIoIRtAr55oIanCsq448KJzBqV7nY5IiKuCsswb+/y8PXndpE3PJm7LpnidjkiIq4Ly26W+9bv50htG4/dvlAPB4mIEIYt893ljTzwxiGunz+WJZOy3C5HRCQkhFWY93i8/J8/v0tmSgL3XK45ykVETgirbpYHNx5iz7EmfvPJuaQnx7tdjohIyAirlnlO2hCumTeGy2b3tYqdiEj0CquW+dVzxnD1HM29IiJyqrBqmYuISN8U5iIiEUBhLiISARTmIiIRQGEuIhIBFOYiIhFAYS4iEgEU5iIiEcBYa4N/UmOqgSNn+c+zgBo/luNPqu3sqLazo9rOTjjXNt5am93XG66E+WAYYwqstflu19EX1XZ2VNvZUW1nJ1JrUzeLiEgEUJiLiESAcAzz+90u4AxU29lRbWdHtZ2diKwt7PrMRUTk/cKxZS4iIqcI+TA3xvzYGLPXGPOuMeY5Y0zGafa7zBizzxhzwBjztSDVdo0xZo8xxmuMOe0ItDHmsDFmlzFmhzGmIMRqc+O6ZRpj1hpjin1/DjvNfh7fNdthjPlrgGs643Uwxgwxxjzpe3+TMSYvkPUMsLabjTHVJ12rzwSprj8YY6qMMbtP874xxvzCV/e7xpi5wairn7UtN8Y0nnTNvhXE2sYaYzYYYwp9P6N39bHPwK+dtTakv4DVQJzv9X8B/9XHPrHAQWAikADsBGYGobYZwDTgVSD/DPsdBrKCfN0+sDYXr9v/A77me/21vv6f+t5rCdK1+sDrANwJ/Nb3+nrgyRCq7WbgV8H8/vKd90JgLrD7NO9/CHgRMMAiYFMI1bYceCHY18x37pHAXN/rocD+Pv6fDvjahXzL3Fq7xlrb4/vrO0BfSw0tAA5Ya0ustV3AE8BVQaityFq7L9DnORv9rM2V6+Y7x8O+1w8DHw3COc+kP9fh5JqfAS4xxpgQqc0V1trXgboz7HIV8Ih1vANkGGNGhkhtrrHWHrfWbvO9bgaKgNGn7DbgaxfyYX6KW3E+rU41Gig96e9lvP/iuMkCa4wxW40xd7hdzEncum651trjvtcVQO5p9ks0xhQYY94xxgQy8PtzHd7bx9e4aASGB7CmgdQG8DHfr+PPGGPGBqGu/gj1n8vFxpidxpgXjTGz3CjA1103B9h0ylsDvnYhsQaoMWYd0Ncqzfdaa//i2+deoAd4NNRq64cLrLXlxpgcYK0xZq+v5RAKtQXEmWo7+S/WWmuMOd0tVeN9120i8IoxZpe19qC/a40AfwMet9Z2GmM+i/MbxAqXawp123C+v1qMMR8CngemBLMAY0wq8Gfg3621TYM9XkiEubV25ZneN8bcDFwBXGJ9HUqnKAdObo2M8W0LeG39PEa5788qY8xzOL86DzrM/VCbK9fNGFNpjBlprT3u+9Wx6jTHOHHdSowxr+K0YAIR5v25Dif2KTPGxAHpQG0Aahlwbdbak+t4AGdMIhQE7PtrsE4OT2vtP4wx/2OMybLWBmXOFmNMPE6QP2qtfbaPXQZ87UK+m8UYcxnwVeBKa23baXbbAkwxxkwwxiTgDFAF9O6H/jLGpBhjhp54jTOg2+cIuwvcum5/BT7te/1p4H2/RRhjhhljhvheZwFLgcIA1dOf63ByzR8HXjlNwyLotZ3Sl3olTh9sKPgrcJPvzoxFQONJ3WuuMsaMODHmYYxZgJOFwfhwxnfeB4Eia+1/n2a3gV87N0ZzBzjyewCn72iH7+vEHQWjgH+cMvq7H6fldm+Qarsapy+rE6gEXj61Npy7EHb6vvaEUm0uXrfhwHqgGFgHZPq25wMP+F4vAXb5rtsu4LYA1/S+6wB8F6cRAZAIPO37ftwMTAzGtepnbT/0fW/tBDYA04NU1+PAcaDb9712G/A54HO+9w3wa1/duzjDHV8u1Pb5k67ZO8CSINZ2Ac442rsn5dqHBnvt9ASoiEgECPluFhER+WAKcxGRCKAwFxGJAApzEZEIoDAXEYkACnMRkQigMBcRiQAKcxGRCPD/AdTB9WESVaWRAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6bfwZQI1DlAM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "88a8d1ad-f03b-4846-db61-045a4232bcc6"
      },
      "source": [
        "f4=reLu(1.2*x-2)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de58fbe0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-uh1k2a_Dk9g",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "60c98c27-5a51-4a07-f620-dbef51002c62"
      },
      "source": [
        "f5=reLu(2*x-1.1)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de476dd8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nCfFVieFDk7e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "96f9e997-c201-461d-9c2a-c0258c19aae2"
      },
      "source": [
        "f6=reLu(5*x-5)\n",
        "plt.plot(x,f)\n",
        "plt.plot(x,f6)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de42e908>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "Hk2pAR6T52hO",
        "outputId": "b6955b94-65dd-40bf-a696-0786decde18d"
      },
      "source": [
        "plt.axhline(0,color='grey')\n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x,f)\n",
        "plt.plot(x,-f1-f2-f3+f4+f5+f6)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de378fd0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z8W7PsXk52eH"
      },
      "source": [
        "def reLu(x):\n",
        "  return np.array([xi if xi >= 0 else 0 for xi in x])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "W1XfB9fs52bJ",
        "outputId": "a3dabe2c-a9ab-4fc3-bc79-f0340aa1eef5"
      },
      "source": [
        "x=np.arange(-2,2,0.01)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, reLu(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de7354a8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gA3SMuXp52Yi"
      },
      "source": [
        "def sigmoid(x, lam=1):\n",
        "  return 1/(1+np.exp(-lam*x))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "vkobVQsI52Ue",
        "outputId": "afe960cd-9cca-4de8-d9fa-ca06d08605cd"
      },
      "source": [
        "x=np.arange(-10,10,0.005)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, sigmoid(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de3c6048>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GFuUHXY7IMVOgS7+3uraZuuY2rpiua7dIdlOgS7+3pGoX+XnG7Km69rlkNwW69HtLq+qZNXkkI0qKgi5F5Lgo0KVf29x4gE0NB7hyuo5ukeynQJd+benaegAuV/+55AAFuvRrS6p2ccb4YYwfPjDoUkSOmwJd+q2G/W28t32fbjUnOUOBLv3W4e6WK09Xd4vkhqQC3czmmNkGM6s2s3uO0u4vzczNrDJ1JYr0jaVr65lSVkLFqMFBlyKSEj0GupnlAw8CVwHTgJvMbFqCdkOAu4G3Ul2kSKrtb+vkzQ92c8W00Zgufi45Ipkt9FlAtbtvdvcOYCEwN0G77wIPAG0prE+kT7yyvoHOsOvsUMkpyQT6eKAm7vWO2LgjzGwmMNHdXzjaG5nZHWa2wsxWNDY29rpYkVRZWlVP+ZBiZkwcHnQpIilz3DtFzSwP+CHwdz21dfeH3b3S3SvLy3VVOwlGa0eYP6xv4PJpo8nLU3eL5I5kAr0WmBj3ekJs3GFDgNOBP5rZVuA8YJF2jEqm+uOGBlo7w1xzxtigSxFJqWQCfTlQYWZTzKwImAcsOjzR3ZvdvczdJ7v7ZGAZcJ27r+iTikWO0+I1uxhZUsS5U0YGXYpISvUY6O4eAu4ClgDrgGfdvcrM7jez6/q6QJFUausM8/K6eq6cPoaCfJ2GIbmlIJlG7r4YWNxl3L3dtL30+MsS6Rt/3NDIoQ51t0hu0iaK9CuLV9cxsqSI805Ud4vkHgW69BsfdreMVneL5CSt1dJv/GljIwc7wlyt7hbJUQp06TcWr65jxKBCzj+xNOhSRPqEAl36hWh3S4OObpGcpjVb+oU/bWzkQHtI3S2S0xTo0i8sWrmT0pIiLjhJ3S2SuxTokvNa2jr5/bp6rj1zrLpbJKdp7Zac97s1u2gPRZg7Y3zPjUWymAJdct5vVu7khNJBulSu5DwFuuS0hv1t/PmD3cw9a5zuTCQ5T4EuOW3R+zuJOOpukX5BgS457Tcrd3LG+GGcVK4bQUvuU6BLzvqg8QCra5uZe/a4oEsRSQsFuuSsX72zgzyDT5+lQJf+QYEuOSkUjvCrd3fwyVNHMXrogKDLEUkLBbrkpNc27aZ+fzs3Vk7subFIjlCgS056dkUNpSVFfGrqqKBLEUkbBbrknKYD7fx+XT2fmTGeogKt4tJ/aG2XnPPrlTvpDDufPUfdLdK/KNAlp7g7zy6v4eyJwzll9JCgyxFJKwW65JT3avaxob6FGysnBF2KSNop0CWn/Oeb2xhcXMDcs3Wqv/Q/CnTJGU0H2nl+VR1/OXM8g4sLgi5HJO0U6JIznllRQ0c4wi3nnRB0KSKBUKBLTghHnCeXbef8E0up0M5Q6acU6JIT/rC+gdp9rXz+fG2dS/+lQJec8PibWxk9tJjLpo0OuhSRwCjQJetV7WzmtU27+fz5kynUTaClH9PaL1nvZ69uZlBRPrecq+4W6d+SCnQzm2NmG8ys2szuSTD962a21sxWmdnLZqZvlqRF7b5WfruqjnnnTGLYoMKgyxEJVI+Bbmb5wIPAVcA04CYzm9al2XtApbufCfwS+OdUFyqSyGOvbwHgixdNDrYQkQyQzBb6LKDa3Te7ewewEJgb38DdX3H3Q7GXywCddy19rrm1k6ff3s6nzxzLhBGDgi5HJHDJBPp4oCbu9Y7YuO7cDryYaIKZ3WFmK8xsRWNjY/JViiTw2BtbONgR5o5LTgq6FJGMkNKdomZ2C1AJfD/RdHd/2N0r3b2yvLw8lbOWfqa5tZNHXt/CFdNGM23c0KDLEckIyVzwohaIv7D0hNi4jzCzy4BvA3/h7u2pKU8ksUde30JLW4ivXXZK0KWIZIxkttCXAxVmNsXMioB5wKL4BmY2A/gpcJ27N6S+TJEPNR/q5LHXtzBn+hhtnYvE6THQ3T0E3AUsAdYBz7p7lZndb2bXxZp9HxgM/MLMVprZom7eTuS4/fz1zbS0h7j7soqgSxHJKEldY9TdFwOLu4y7N274shTXJZJQ/f42fv7aFq45cyynjdXWuUg8nSkqWeUHSzcQjjjfvHJq0KWIZBwFumSNtTv384t3dvCFC05gUqmOOxfpSoEuWcHd+b+L1zFsYCF3fVJ95yKJKNAlK7y4ZhevV+/m7tkVumaLSDcU6JLxWto6+cffVjFt7FBu1e3lRLqlO+lKxvvB0o00tLTz01srKdD1zkW6pW+HZLRVO/bx+JtbueXcEzh74vCgyxHJaAp0yVhtnWH+9pmVlA8p5htzTg26HJGMpy4XyVgP/G49HzQe5InbZzF0gHaEivREW+iSkd6o3s1jb2xl/gWTubhCV+YUSYYCXTJOw/42vvbMSk4qL+Gbc3RGqEiy1OUiGaUzHOHOp97lQFuIJ790LgOL8oMuSSRrKNAlo3zvxfUs37qXf5t3NqeMHhJ0OSJZRV0ukjGeems7j7y+hfkXTGbu2Ue7y6GIJKJAl4zwyvoG/vdv1nDpqeV8+5rTgi5HJCsp0CVwK2v2cedT73La2CE8ePNMCnU2qMgx0TdHArWyZh+3PvIWZYOLeXT+OZQUa7eOyLFSoEtgDof5iEFFPH3HeYwaMiDokkSymgJdAvHKhgZu/tkyhg8q5Ok7zmP88IFBlySS9RToknYL397Ol/5jBZNLS/jlVy5QmIukiDosJW3aQ2H+zwvrePzNbVxySjk/+euZDFafuUjK6NskaVGz5xB3PvUuq3Y08+WLp/D3c6bqaBaRFFOgS5+KRJwn397O9xavIy/P+Omtn+DK6WOCLkskJynQpc9srG/h3t+sYdnmPVx0chn/74YzmDhyUNBlieQsBbqk3O4D7fzLSxt5+u3tlBQX8L0bzuBz50zEzIIuTSSnKdAlZer3t/Hz1zbz1FvbaQtFuPW8E7j7slMYWVIUdGki/YICXY6Lu7Omdj9PvrWN/3q3llAkwrVnjuOrsys4edTgoMsT6VcU6HJMGlraeHH1Lp5ZXsPauv0MKMzjryon8N8uOZETSkuCLk+kX1KgS1LcnQ8aD/LHDQ38bs0u3tm+F3eYPm4o373+dK47axzDBuq+nyJBUqBLQqFwhA8aD/Lu9r28+UETyzY30dDSDsC0sUP52uxTuPL00UwdMzTgSkXkMAV6PxeJOHX729i6+yBbdh9k/a79rKndz7q6/bSHIgCUDynm/BNLOf+kUi46uUyHHopkqKQC3czmAP8G5AM/d/fvdZleDDwOfAJoAj7n7ltTW6r0VnsoTHNrJ7tbOqhvaaNhfxv1+9upjz3X7DnE1qaDR4IbYEhxAdPHD+XW807g9PHDOGPCME4sK9EhhyJZoMdAN7N84EHgcmAHsNzMFrn72rhmtwN73f1kM5sHPAB8ri8KzkbhiBOKRAhHnM6wf+R1KOyEIk44EombFn3dEXLaQmHaOsK0doZp64zEnqOP1o4wbaEwhzrC7G/tpLnLo60zkrCekSVFjBpSzMSRg7jklDIml5UwpbSEyWUljBk6gLw8hbdINkpmC30WUO3umwHMbCEwF4gP9LnAfbHhXwI/NjNzd+/uTZuamliwYEGvC3533wDe2DOQ+Hd2LPYcN875+Lj45yPTE/xs7J9ufxZwt26nxc8/Gql9EZBOoUFhnlNozsD8CAPynYF5zrj8CCcOiQ4PyI9Qkh9hSEGEoYURBudHKMg78hbQCJ2NsJHoQ2DXrl0Ax7R+igQpmUAfD9TEvd4BnNtdG3cPmVkzUArsjm9kZncAdwCMH39sNwEuyY8wpjj0YUTah3EZH5tHxhkcjtqE7YzupwGYJ37fZOZvkIeTZ5BvTh6QFzfu8HC+JRhvTj7RwC4wjwX3hwGebx/WLiICad4p6u4PAw8DVFZW+vz589M5e5GkHN4y1/opmei2227rdloy1y+tBSbGvZ4QG5ewjZkVAMOI7hwVEZE0SSbQlwMVZjbFzIqAecCiLm0WAV+IDf8V8Iej9Z+LiEjq9djlEusTvwtYQvSwxUfdvcrM7gdWuPsi4BHgCTOrBvYQDX0REUmjpPrQ3X0xsLjLuHvjhtuAG1NbmoiI9IbuASYikiMU6CIiOUKBLiKSIxToIiI5woI6utDMGoFtx/jjZXQ5CzVDqK7eydS6IHNrU129k4t1neDu5YkmBBbox8PMVrh7ZdB1dKW6eidT64LMrU119U5/q0tdLiIiOUKBLiKSI7I10B8OuoBuqK7eydS6IHNrU12906/qyso+dBER+bhs3UIXEZEuFOgiIjkiYwPdzG40syozi5hZZZdp3zKzajPbYGZXdvPzU8zsrVi7Z2KX/k11jc+Y2crYY6uZreym3VYzWx1rtyLVdSSY331mVhtX29XdtJsTW4bVZnZPGur6vpmtN7NVZvacmQ3vpl1alldPv7+ZFcc+4+rYujS5r2qJm+dEM3vFzNbG1v+7E7S51Mya4z7fexO9Vx/UdtTPxaJ+FFteq8xsZhpqOjVuOaw0s/1m9rUubdK2vMzsUTNrMLM1ceNGmtlLZrYp9jyim5/9QqzNJjP7QqI2PXL3jHwApwGnAn8EKuPGTwPeB4qBKcAHQH6Cn38WmBcbfgj4mz6u9wfAvd1M2wqUpXHZ3Qf8zx7a5MeW3YlAUWyZTuvjuq4ACmLDDwAPBLW8kvn9gf8OPBQbngc8k4bPbiwwMzY8hOitXrvWdSnwfLrWp2Q/F+Bq4EWid2A8D3grzfXlA7uInngTyPICLgFmAmvixv0zcE9s+J5E6z0wEtgcex4RGx7R2/ln7Ba6u69z9w0JJs0FFrp7u7tvAaqJ3sj6CDMz4FNEb1gN8B/A9X1Va2x+nwWe7qt59IEjN/929w7g8M2/+4y7L3X3UOzlMqJ3vwpKMr//XKLrDkTXpdmxz7rPuHudu78bG24B1hG9Z282mAs87lHLgOFmNjaN858NfODux3oG+nFz91eJ3hMiXvx61F0WXQm85O573H0v8BIwp7fzz9hAP4pEN63uusKXAvviwiNRm1S6GKh3903dTHdgqZm9E7tRdjrcFftv76Pd/BcvmeXYl75IdGsukXQsr2R+/4/c/Bw4fPPztIh18cwA3kow+Xwze9/MXjSz6WkqqafPJeh1ah7db1QFsbwOG+3udbHhXcDoBG1SsuzSepPorszs98CYBJO+7e6/SXc9iSRZ400cfev8InevNbNRwEtmtj72l7xP6gL+Hfgu0S/gd4l2B33xeOaXiroOLy8z+zYQAp7s5m1SvryyjZkNBn4FfM3d93eZ/C7RboUDsf0jvwYq0lBWxn4usX1k1wHfSjA5qOX1Me7uZtZnx4oHGujuftkx/FgyN61uIvrfvYLYllWiNimp0aI3xb4B+MRR3qM29txgZs8R/e/+cX0Rkl12ZvYz4PkEk5JZjimvy8zmA9cCsz3WeZjgPVK+vBLozc3Pd1gab35uZoVEw/xJd/+vrtPjA97dF5vZT8yszN379CJUSXwufbJOJekq4F13r+86IajlFafezMa6e12sC6ohQZtaon39h00guv+wV7Kxy2URMC92BMIUon9p345vEAuKV4jesBqiN7Duqy3+y4D17r4j0UQzKzGzIYeHie4YXJOobap06bf8TDfzS+bm36muaw7w98B17n6omzbpWl4ZefPzWB/9I8A6d/9hN23GHO7LN7NZRL/HffqHJsnPZRHw+djRLucBzXFdDX2t2/8lB7G8uohfj7rLoiXAFWY2ItZFekVsXO+kY8/vsTyIBtEOoB2oB5bETfs20SMUNgBXxY1fDIyLDZ9INOirgV8AxX1U5wLgK13GjQMWx9XxfuxRRbTroa+X3RPAamBVbGUa27Wu2OuriR5F8UGa6qom2k+4MvZ4qGtd6VxeiX5/4H6if3AABsTWnerYunRiGpbRRUS7ylbFLaerga8cXs+Au2LL5n2iO5cvSENdCT+XLnUZ8GBsea4m7ui0Pq6thGhAD4sbF8jyIvpHpQ7ojOXX7UT3u7wMbAJ+D4yMta0Efh73s1+MrWvVwG3HMn+d+i8ikiOysctFREQSUKCLiOQIBbqISI5QoIuI5AgFuohIjlCgi4jkCAW6iEiO+P/gykB5K8nspAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "BSQcUa8r52Q9",
        "outputId": "62c5567a-c1ad-4eb1-8f4c-b897c104b3b2"
      },
      "source": [
        "# With a different lambda\n",
        "x=np.arange(-10,10,0.005)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, sigmoid(x,10))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6e741ff60>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vdA91hL852Ol"
      },
      "source": [
        "def eLU(x, alpha=1):\n",
        "  return np.array([xi if xi>0 else alpha*(np.exp(xi)-1) for xi in x ])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "FskW_8Wc52MN",
        "outputId": "80862aa7-153f-4c30-cc11-bc7e322f65f5"
      },
      "source": [
        "x=np.arange(-2,2,0.01)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, eLU(x,5))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de2402e8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iYZMQzF92zm0GdB5SPHewvpn7X93C5Ow+3DRpsNdxRMIqbOfIzWy+mRWbWXFVVVW4diudxAOvbaWmoYWfXj9eqxtKp3PSIjezZWa24Rh/Zp7OjpxzC5xzuc653LS0tDNPLHKUNWUHWbiilDvOzWFMRk+v44iE3UlPrTjnpocjiMiZaPM77nt+A2ndk/na5SO8jiPiCU0/lKj2x3c/YP2uGu67dqxupiydVrDTD28ws3LgXOBlM3stNLFETq5sfz2/XrqNS0f359oJGV7HEfFMsLNWngOeC1EWkVPmnOM7z64nPs746fXjNXNKOjWdWpGotHhVOe+U7OPbM0YxsHeK13FEPKUil6hTVdvET1/ezJScPsyelu11HBHPqcgl6vxwyUYaWtq4/8YJmjMugopcoszSjXt5ef0evnLZCIaldfc6jkhEUJFL1DhQ18y9z29gTEZP5n9iqNdxRCJGULNWRMLpey9s4GB9M3+aN5XEeI1BRD6inwaJCkvW7ubldXv46vSRugxf5Cgqcol4FYcaue/5DZyT1ZvP6ZSKyMeoyCWiOef41uJ1NLW28dCss0nQKRWRj9FPhUS0hSvK+Pu2Kr579RiGpHbzOo5IRFKRS8TyVdfx05c3ccHwVObowh+R41KRS0RqbvXz5YXvkxBnPHCTLvwRORFNP5SI9OvXt7K2vIb/mT1Ja6mInIRG5BJx3t5Wxe//vpNbp2Vx1VlanlbkZFTkElH2HW7i64vWMqJ/d+67ZqzXcUSigk6tSMTw+x13L1rLocYW8j87lZSkeK8jiUQFjcglYvzh3Q/4+7Yq7rtmDKPTdfWmyKlSkUtEWOXbz/2vbuGKsQOYk6ephiKnQ0Uuntt3uIn/KHifgb1TePDmibptm8hp0jly8VSb3/GVp9/nQH0zz37xPHqlJHodSSTqqMjFU795fRvvllTzwI0TGDewl9dxRKKSTq2IZ97YXMEjb5bwqdxMZk3J9DqOSNQKqsjN7EEz22Jm68zsOTPrHapgEtvK9tfztWfWMDajJz+aOc7rOCJRLdgR+evAeOfcBGAb8J3gI0msO9zUymefLAbg0TmT6ZKo+eIiwQiqyJ1zS51zrYEPC4HBwUeSWOb3O77+zBq2V9byu9mTyOrX1etIIlEvlOfI5wGvHu9JM5tvZsVmVlxVVRXC3Uo0+c9l21i6qYLvXTOWC0ekeR1HJCacdNaKmS0D0o/x1L3OuRcCr7kXaAUKjrcd59wCYAFAbm6uO6O0EtVeXreHh5eXMCt3MP9+fo7XcURixkmL3Dk3/UTPm9lc4FrgMuecClqOacOuGu7+yxomZ/fhJ9eP10U/IiEU1DxyM5sBfAu4yDlXH5pIEmsqDzUy/0/F9OmaxKNzJpOcoDc3RUIp2HPkjwA9gNfNbI2ZPRqCTBJD6ppamffkSg42tPC/t+eS1iPZ60giMSeoEblzbniogkjsaW3zc9dTq9m8p5bHbs9l/CBduSnSEXRlp3QI5xw/WLKRN7dW8eOZ47hkdH+vI4nELBW5dIgFb++koKiUz100lNnTtCytSEdSkUvIvbh2N794dQvXTsjg21eO9jqOSMxTkUtI/X1bFV9ftIYpOX341c0TiYvTNEORjqYil5BZ5TvA5/+8iuH9e/DYHVO0hopImKjIJSS27q1l3hMr6d8zmSfnTdENIkTCSEUuQSvbX89tjxfRJTGO/M9Mo3+PLl5HEulUdIcgCUrloUZue7yIplY/iz53Lpl9tZqhSLhpRC5nrKq2iVv+t5Cq2ib++O9TGJXew+tIIp2SRuRyRqoPN3Hr/xay+2AjT86byqSsPl5HEum0NCKX03agrpnZjxVRdqCex+fmMnVIX68jiXRqGpHLaampb2HO40Xs3FfHH+6YwnnDUr2OJNLpaUQup2x/XTOzHy9ke8VhFtw2mQtGqMRFIoFG5HJKKmsbmfNYEb7qen5/+2QuHqVFsEQihYpcTmr3wQZmP1ZExaFG/jh3CucN10hcJJKoyOWESqvrufWxQmrqW/jTvKnk5uiNTZFIoyKX4yqprGXOYytobG2j4M5pTBjc2+tIInIMKnI5plW+/cx7opjE+DgW3pnHmIyeXkcSkeNQkcvHvL6pgrueWs3A3in8ad5UXXYvEuFU5PIvFq4o5d7n1nPWoF78Ye4U+nXXzZJFIp2KXID2e2w+/EYJv1m2jYtHpfG7WyfRLVnfHiLRQD+pQkubn++/sIGFK8q4cdJg7r/xLBLjda2YSLQIqsjN7CfATMAPVAJznXO7QxFMwuNgfTNfyF/NP3dW8x+XDOMbV4zCTLdnE4kmwQ67HnTOTXDOnQ28BHw/BJkkTHZWHeaG/36PVb4DPDRrIt+8crRKXCQKBTUid84dOuLDboALLo6Ey7sl+/hC/ioS4+N46s5putBHJIoFfY7czH4G3A7UAJec4HXzgfkAWVlZwe5WgpBf6OMHSzYyLK0bj98xRdMLRaLcSU+tmNkyM9twjD8zAZxz9zrnMoEC4K7jbcc5t8A5l+ucy01LSwvdVyCnrLGljW8vXsf3nt/AJ0ak8tcvnKcSF4kBJx2RO+emn+K2CoBXgB8ElUg6RNn+er5YsJr1u2r40qXD+er0kcTH6Xy4SCwIdtbKCOfc9sCHM4EtwUeSUPv7tiq+8vT7tPkdj92ey/SxA7yOJCIhFOw58vvNbBTt0w99wOeDjySh4vc7fvdmCQ8t28aoAT14dM5kclK7eR1LREIs2FkrN4YqiIRWZW0jdy9ayz+27+P6swfy8387i65Juv5LJBbpJzsGvb2tiq8vWkNtYys/u2E8t07N0vxwkRimIo8hza1+fr10K79/eycjB3TnqTvzGDmgh9exRKSDqchjhK+6ji8vfJ+15TXMnpbFfdeOpUtivNexRCQMVORRzjlHflEpP395M4nxxv/MnsRVZ2V4HUtEwkhFHsV2H2zg239dxz+27+PCEan88sYJDOyd4nUsEQkzFXkUcs7x19W7+NGSjbQ5pzc0RTo5FXmU2VPTwH3Pb2DZ5kqm5vTlVzdPJKufLrMX6cxU5FGize8oKPLxwN+20ur3871rxjDv/CHE6TJ7kU5PRR4Ftu6t5Z5n1/F+6UEuHJHKz64/S6NwEfk/KvII1tjSxiPLS3j07zvomZLIf37qbGaePVDnwkXkX6jII5Bzjtc2VvDTlzdRfqCBGycN5t5rxtC3W5LX0UQkAqnII0xJZS0/XLKJd0r2MTq9BwvvzOPcYf28jiUiEUxFHiEONbbw22XbefK9D+maFM8PrxvLnLxsEnQ3exE5CRW5x1rb/CwqLueh17dSXdfMp6dk8o0rRtGve7LX0UQkSqjIPfLRefAHXtvCzqo6Jmf34Q9zpzBhcG+vo4lIlFGRe6D4w/384tUtrPIdYGhaN35/22SuGDtAs1FE5IyoyMNoe0UtD762laWbKkjrkczPbziLWbmDdR5cRIKiIg+D7RW1/PaN7by8fg/dkhK4+/KRfObCIbpjj4iEhJqkA22vqOXh5SW8tG43KYnxfOGiYXz2wqGaDy4iIaUi7wDbK2r5r+UlvBgo8M9fNIw7VeAi0kFU5CG08sP9PPrWDt7YUknXJBW4iISHijxIfr9j2eYKfv/2Tlb5DtCnayJfnT6C28/NUYGLSFioyM9QQ3Mbz6/ZxWP/2MmOqjoG90nhR58cx6zcTFKSdK9MEQmfkBS5md0N/ApIc87tC8U2I1XZ/nr+XOjjmZVl1DS0MDajJw/fcg5Xj0/XNEIR8UTQRW5mmcAVQGnwcSKTc453Svbx5Hsf8saWSuLMmDEunTvOy2FKTh9dyCMingrFiPw3wLeAF0KwrYhyoK6Z597fRX6Rj51VdfTrlsRdlwzn1mlZZPTSTY5FJDIEVeRmNhPY5Zxbe7JRqZnNB+YDZGVlBbPbDuX3O97bUc3TK0tZurGC5jY/EzN789CsiVwzIYPkBJ3/FpHIctIiN7NlQPoxnroX+C7tp1VOyjm3AFgAkJub604jY1jsPtjA4lXlLCouo/xAA71SErl1WhafmpLJmIyeXscTETmukxa5c276sT5vZmcBQ4CPRuODgdVmNtU5tzekKTtIbWMLf9uwlxfW7Oa9HfvwOzh/eD++NWM0V4wdQJdEjb5FJPKd8akV59x6oP9HH5vZh0BupM9aaWpt462tVbywZhfLNlfS3Oonq29X7rpkODdNztRNjUUk6nSKeeQtbX6Kdu7n5fW7eWX9XmoaWujXLYlbpmQy85xBnJPZWzNPRCRqhazInXM5odpWKDS2tPHO9n38beNelm2u4GB9C12T4rli7ABmnjOIC4ankqh53yISA2JqRF7f3MpbW6t4dcNe3txSyeGmVnp0SWD6mAHMGJ/ORSPTdN5bRGJO1Bd5aXU9y7dUsHxrFYU7q2lu9dOvWxLXTczgynHpnDcslaQEjbxFJHZFXZE3t/op/nA/y7dU8ubWSnZU1QEwNLUbt+VlM33MAKbk9NHl8iLSaURVkT/8xnYWvL2Tw02tJMXHMW1oX2ZPy+bS0f3JSe3mdTwREU9EVZGn9+rCdRMzuGRUf84fnkq35KiKLyLSIaKqCWflZjIrN9PrGCIiEUUnkkVEopyKXEQkyqnIRUSinIpcRCTKqchFRKKcilxEJMqpyEVEopyKXEQkyplz4b/rmplVAb4z/OupQCTevEK5Tl+kZlOu06NcpyeYXNnOubSjP+lJkQfDzIqdc7le5ziacp2+SM2mXKdHuU5PR+TSqRURkSinIhcRiXLRWOQLvA5wHMp1+iI1m3KdHuU6PSHPFXXnyEVE5F9F44hcRESOoCIXEYlyEV/kZvagmW0xs3Vm9pyZ9T7O62aY2VYzKzGze8KQ62Yz22hmfjM77lQiM/vQzNab2RozK46gXGE9XoF99jWz181se+C/fY7zurbA8VpjZks6KMsJv34zSzazZwLPF5lZTkfkOMNsc82s6ohj9NkwZPqDmVWa2YbjPG9m9nAg8zozm9TRmU4x18VmVnPEsfp+mHJlmtmbZrYp8PP4lWO8JnTHzDkX0X+AK4CEwONfAr88xmvigR3AUCAJWAuM7eBcY4BRwFtA7gle9yGQGsbjddJcXhyvwH4fAO4JPL7nWP+WgecOd3COk379wBeBRwOPPw08E6Z/v1PJNhd4JFzfU4F9fgKYBGw4zvNXA68CBuQBRRGS62LgpXAeq8B+M4BJgcc9gG3H+HcM2TGL+BG5c26pc6418GEhMPgYL5sKlDjndjrnmoGngZkdnGuzc25rR+7jTJxirrAfr4CZwJOBx08C14dhn8dyKl//kVkXA5eZmUVItrBzzr0N7D/BS2YCf3LtCoHeZpYRAbk84Zzb45xbHXhcC2wGBh31spAds4gv8qPMo/3/YEcbBJQd8XE5Hz9oXnHAUjNbZWbzvQ4T4NXxGuCc2xN4vBcYcJzXdTGzYjMrNLOOKPtT+fr/7zWBgUQN0K8DspxJNoAbA7+OLzazSLiRbST/DJ5rZmvN7FUzGxfunQdOy50DFB31VMiOWUTcfNnMlgHpx3jqXufcC4HX3Au0AgWRlOsUXOCc22Vm/YHXzWxLYBThda4OcaJsR37gnHNmdry5r9mBYzYUWG5m651zO0KdNYq9CCx0zjWZ2edo/83hUo8zRarVtH8/HTazq4HngRHh2rmZdQf+CnzVOXeoo/YTEUXunJt+oufNbC5wLXCZC5xcOsou4MhRyeDA5zo01yluY1fgv5Vm9hztvzoHVeQhyNUhxwtOnM3MKswswzm3J/ArZOVxtvHRMdtpZm/RPpoJZZGfytf/0WvKzSwB6AVUhzDDGWdzzh2Z4zHa33vwWod9TwXjyPJ0zr1iZv9tZqnOuQ5fTMvMEmkv8QLn3LPHeEnIjlnEn1oxsxnAt4BPOufqj/OylcAIMxtiZkm0vznVIbMdToeZdTOzHh89pv2N22O+ux5mXh2vJcAdgcd3AB/77cHM+phZcuBxKnA+sCnEOU7l6z8y603A8uMMIkLtpNmOOo/6SdrPv3ptCXB7YCZGHlBzxGk0z5hZ+kfvbZjZVNo7r8P/hxzY5+PAZufcQ8d5WeiOWbjfzT2Dd39LaD+PtCbw56OZBAOBV456B3gb7SO3e8OQ6wbaz/DMsBIAAAC+SURBVGk1ARXAa0fnon3mwdrAn42RksuL4xXYZz/gDWA7sAzoG/h8LvBY4PF5wPrAMVsPfKaDsnzs6wd+TPuAAaAL8JfA998KYGg4jtEpZvtF4PtpLfAmMDoMmRYCe4CWwPfXZ4DPA58PPG/A7wKZ13OCmVxhznXXEceqEDgvTLkuoP39sXVHdNfVHXXMdIm+iEiUi/hTKyIicmIqchGRKKciFxGJcipyEZEopyIXEYlyKnIRkSinIhcRiXL/D3J+eg89F6IFAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dgAB8GO052JZ"
      },
      "source": [
        "def logsigmoid(x, lam=1):\n",
        "  return np.log(1/(1+np.exp(-lam*x)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "1WyaFtdh52Gh",
        "outputId": "c0dda99d-569f-4ac7-f686-f8dcb502d059"
      },
      "source": [
        "# With a different lambda\n",
        "x=np.arange(-10,10,0.01)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, logsigmoid(x,5))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de1ad748>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4is6lhHU52Dm"
      },
      "source": [
        "def tanh(x, lam=1):\n",
        "  return (np.exp(lam*x)-np.exp(-lam*x))/(np.exp(lam*x)+np.exp(-lam*x))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "ke1WTL3452BM",
        "outputId": "a70df31a-e421-4e3a-9f20-b1120f0e7879"
      },
      "source": [
        "x=np.arange(-10,10,0.01)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, tanh(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de11b5f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "KYYg8Bz85191",
        "outputId": "59e23507-33eb-40a9-a0b1-535cbcd461e3"
      },
      "source": [
        "x=np.arange(-2,2,0.01)\n",
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x, tanh(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de10f860>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dx20Iqy_8v2k"
      },
      "source": [
        "x = np.arange(-50,50,0.05)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CCnCyfkl8vys"
      },
      "source": [
        "f1 = x**2 + 5*x  + 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "CTuvtMVj8vwq",
        "outputId": "2854f7f6-edce-452a-d302-cc4614483553"
      },
      "source": [
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x,f1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6de085828>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0TPFzOF68vt8"
      },
      "source": [
        "f2 = x**3 + 5*x  + 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "IxJyqiFu9EqQ",
        "outputId": "3f19d492-c92a-4783-9e93-aa96deafeb81"
      },
      "source": [
        "plt.axhline(0,color='grey') \n",
        "plt.axvline(0,color='grey') \n",
        "plt.plot(x,f2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff6ddfe2e80>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bnrehgph9Emb"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NgIFy9WB9EkC"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U_BuRp669Ehl"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1vFIPU59EfN"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WZLPH7Vo9EdE"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}