{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mvMOFZM5R5XA"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Sample data\n",
        "X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]])\n",
        "y = np.array([[0,0,1,1]]).T\n",
        "lr = 0.5\n",
        "it = 10"
      ],
      "metadata": {
        "id": "BUBP_HqSg62i"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# initialize weights\n",
        "np.random.seed([69])\n",
        "W = 2*np.random.random((len(X[0]),1))-1"
      ],
      "metadata": {
        "id": "fxhaGX9Xhzx5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def sig(x):\n",
        "  return 1 /(1+np.exp(-x))"
      ],
      "metadata": {
        "id": "9ha5tlkEhdh6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def lineral (X, y, lr, it, W):\n",
        "  er = np.zeros(it)\n",
        "  for i in range(it):\n",
        "    for n in range(len(X)):\n",
        "      \n",
        "      x_ = np.reshape(X[n], (len(X[0]),1))\n",
        "      y_ = y[n]\n",
        "\n",
        "      out = np.dot(W.T,x_)\n",
        "\n",
        "      er[i] = (y_-out)**2\n",
        "\n",
        "      W_delta = lr*(y_ - out)*x_\n",
        "      W += W_delta\n",
        "\n",
        "    er[i] /= len(X)\n",
        "  return (er, W)"
      ],
      "metadata": {
        "id": "6f6upObGhjfb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "MSE_lin, W_lin = lineral(X, y, lr, it, W)\n",
        "output_lin = np.dot(X,W_lin)"
      ],
      "metadata": {
        "id": "w-Xf_o7bpMfj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"output after training (\",it,\"iterations):\\n\",output_lin)\n",
        "print(\"target output:\\n\",y)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(range(it),MSE_lin,color=\"blue\",label=\"MSE\")\n",
        "plt.title(\"MSE with LINEAR activation\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "MxP0GUdcrq3x",
        "outputId": "c48162b7-0b0f-43cf-cfc1-ecf0e912176f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "output after training ( 10 iterations):\n",
            " [[-1.08941748e-05]\n",
            " [-5.96048113e-06]\n",
            " [ 9.99990133e-01]\n",
            " [ 9.99995066e-01]]\n",
            "target output:\n",
            " [[0]\n",
            " [0]\n",
            " [1]\n",
            " [1]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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E/Cl7/kugv6ThwFpgVNGsddm4ttYzJyLqI6J+xIgR3S2rVYUCvPwyLF3aI6s3M6tI3Q56SftLUvZ8UrbOjcBi4BBJB0saAMwAbu3u+3VHQ0N6dPONmdWSUk6vnAs8ABwqqUnSuZLOl3R+NstHgcckPQJcBcyIZDtwIXAnsBK4MSKW98zHKM3IkTB2rA/Imllt6dfRDBExs4PpVwNXtzHtl8Avu1ZazygU4JZb4I030l0tzcyqXc1FXUMDbNoEy3PdtzAz231qLugLhfTo5hszqxU1F/RjxsDo0Q56M6sdNRf0kJpvFiyAiLwrMTPreTUZ9IUCrF8Pjz+edyVmZj2vZoMe3HxjZrWhJoP+bW+D/fd30JtZbajJoJfSVr3b6c2sFtRk0EMK+rVrYfXqvCsxM+tZNRv0zfe9cfONmVW7mg36ceNg+HDf4MzMql/NBr2Utuq9RW9m1a5mgx5S0K9ZA08/nXclZmY9p6aDvvl8ejffmFk1q+mgP/JI2HtvN9+YWXWr6aDv2xemTnXQm1l1q+mgh9RO/4c/wLp1eVdiZtYzaj7o3U5vZtWu5oN+4kQYMsTNN2ZWvUrpHPxaSeslPdbG9I9JWibpUUn3SzqqaNqabPxSSY3lLLxc+vWDKVO8RW9m1auULfrrgJPbmf4kUIiII4HLgDktpr87IiZERH3XSux5hULqQ/b55/OuxMys/DoM+ohYAGxqZ/r9EfFC9nIRUFem2nYbt9ObWTUrdxv9ucDtRa8DuEvSEkmz21tQ0mxJjZIaN2zYUOay2ldfD4MGuZ3ezKpTv3KtSNK7SUF/QtHoEyJiraS/AOZL+l22h7CLiJhD1uxTX1+/W+8SP2AATJ7sLXozq05l2aKXNB64Bjg1IjY2j4+ItdnjeuCnwKRyvF9PKBTgkUfghRc6ntfMrDfpdtBLGg3cDJwREb8vGj9Y0l7Nz4GTgFbP3KkEDQ2pt6n77su7EjOz8uqw6UbSXOBdwHBJTcDFQH+AiPgu8EVgGPBtSQDbszNs9gN+mo3rB/wwIu7ogc9QFscdl5pwFiyAU07Juxozs/LpMOgjYmYH088Dzmtl/GrgqF2XqEyDBqWw9wFZM6s2NX9lbLGGBnjoIXjllbwrMTMrHwd9kUIBduyA++/PuxIzs/Jx0Bd55zvTLRHcfGNm1cRBX2TwYDjmGAe9mVUXB30LhQIsXgyvvZZ3JWZm5eGgb6FQgG3bYNGivCsxMysPB30LU6ZAnz5uvjGz6uGgb2HoUJgwwfe9MbPq4aBvRaGQmm62bs27EjOz7nPQt6JQgC1b4MEH867EzKz7HPStOCG70bKbb8ysGjjoWzFsGBx5pA/Imll1cNC3oVBIt0LYti3vSszMusdB34aGBnj1VViyJO9KzMy6x0HfhoaG9Oh2ejPr7Rz0bdhvPzjsMLfTm1nv56BvR0ND6lpwx468KzEz6zoHfTsKBXj55dRpuJlZb1VS0Eu6VtJ6Sa127q3kKkmrJC2TdHTRtDMl/SEbzixX4btDczu9m2/MrDcrdYv+OuDkdqZ/ADgkG2YD3wGQtC+pM/HjgEnAxZL26Wqxu1tdHbz1rQ56M+vdSgr6iFgAbGpnllOB6yNZBOwt6QDg/cD8iNgUES8A82n/B6PiFAqwcCG88UbelZiZdU252uhHAs8UvW7KxrU1fheSZktqlNS4YcOGMpXVfYUCbNoEy5fnXYmZWddUzMHYiJgTEfURUT9ixIi8y3mT2+nNrLcrV9CvBUYVva7LxrU1vtcYMwZGjfKFU2bWe5Ur6G8F/jY7++Z44KWIWAfcCZwkaZ/sIOxJ2bheQ0rNN/feCxF5V2Nm1nmlnl45F3gAOFRSk6RzJZ0v6fxsll8Cq4FVwPeAvweIiE3AZcDibLg0G9erFAqwfj08/njelZiZdV6/UmaKiJkdTA/ggjamXQtc2/nSKkfxfW8OOyzfWszMOqtiDsZWskMOgf339wFZM+udHPQlcDu9mfVmDvoSNTTA2rXw5JN5V2Jm1jkO+hIVCunRzTdm1ts46Es0bhwMH+6gN7Pex0FfIgmmTnXQm1nv46DvhEIB1qyBp5/OuxIzs9I56DuhuZ3et0Mws97EQd8JRx4JQ4e6+cbMehcHfSf07Zva6b1Fb2a9iYO+kwoF+P3vYd26vCsxMyuNg76Tiu97Y2bWGzjoO+noo2HIEAe9mfUeDvpO6tcPpkzxAVkz6z0c9F3Q0JD6kH3++bwrMTPrmIO+C5rPp1+4MN86zMxK4aDvgmOPhYED3XxjZr2Dg74LBgyAyZMd9GbWOzjou6hQgEcegRdfzLsSM7P2ldo5+MmSHpe0StJnW5n+dUlLs+H3kl4smrajaNqt5Sw+T4VC6m3qvvvyrsTMrH0ddg4uqS/wLeB9QBOwWNKtEbGieZ6I+GTR/P8ATCxaxeaImFC+kivDccelJpx774Vp0/KuxsysbaVs0U8CVkXE6oh4HZgHnNrO/DOBueUorpINGgSTJvnCKTOrfKUE/UjgmaLXTdm4XUg6CDgYuLto9EBJjZIWSfpQW28iaXY2X+OGDRtKKCt/hQIsWQKvvJJ3JWZmbSv3wdgZwE0RsaNo3EERUQ/MAq6UNLa1BSNiTkTUR0T9iBEjylxWzygUYMcOuP/+vCsxM2tbKUG/FhhV9LouG9eaGbRotomItdnjauAedm6/79UmT063LvZplmZWyUoJ+sXAIZIOljSAFOa7nD0j6TBgH+CBonH7SNojez4cmAKsaLlsbzVkCNTXu53ezCpbh0EfEduBC4E7gZXAjRGxXNKlkqYXzToDmBcRUTTucKBR0iPAr4GvFJ+tUw0KBXjwQXjttbwrMTNrnXbO5cpQX18fjY2NeZdRkttuS6dX/upX8J735F2NmdUqSUuy46G78JWx3XTCCdCnj5tvzKxyOei7aehQmDDBB2TNrHI56MugoQEWLYKtW/OuxMxsVw76MigUYMsWWLw470rMzHbloC+DqVPTo5tvzKwSOejLYNgwOOIIB72ZVSYHfZkUCulWCNu25V2JmdnOHPRlUijAq6/CQw/lXYmZ2c4c9GXidnozq1QO+jLZf3849FBfOGVmlcdBX0aFAixcmG5dbGZWKRz0ZVQowMsvp07DzcwqhYO+jBoa0qObb8yskjjoy6iuDt76Vh+QNbPK4qAvs0IhbdG/8UbelZiZJQ76MmtogE2bYPnyvCsxM0sc9GX23vemfmS/8AVv1ZtZZXDQl9moUfCf/wk/+xlcdlne1ZiZlRj0kk6W9LikVZI+28r0syRtkLQ0G84rmnampD9kw5nlLL5SXXQRnHkmXHIJ3HJL3tWYWa3r19EMkvoC3wLeBzQBiyXd2kon3z+KiAtbLLsvcDFQDwSwJFv2hbJUX6Ek+O53YcUKOOOM1CnJO96Rd1VmVqtK2aKfBKyKiNUR8TowDzi1xPW/H5gfEZuycJ8PnNy1UnuXgQPh5pth8GD40Ifghar+aTOzSlZK0I8Enil63ZSNa+kjkpZJuknSqE4ui6TZkholNW7YsKGEsipfXR385Cfw1FMwa5ZvjWBm+SjXwdifA2MiYjxpq/1/O7uCiJgTEfURUT9ixIgylZW/KVPg6qvhjjvg85/Puxozq0WlBP1aYFTR67ps3JsiYmNENHeNfQ1wTKnL1oLZs+H88+Hyy2HevLyrMbNaU0rQLwYOkXSwpAHADODW4hkkHVD0cjqwMnt+J3CSpH0k7QOclI2rOd/4BpxwApxzDjz8cN7VmFkt6TDoI2I7cCEpoFcCN0bEckmXSpqezXaRpOWSHgEuAs7Klt0EXEb6sVgMXJqNqzkDBsBNN6X+ZT/0IaiSwxBm1gsoIvKuYRf19fXR2NiYdxk9orExbdlPngx33QX9++ddkZlVA0lLIqK+tWm+MnY3q6+H730P7rkHPvWpvKsxs1rQ4QVTVn5nnJHa6b/+dZg4Ec4+O++KzKyaeYs+J5dfnm6Adv758Nvf5l2NmVUzB31O+vWDH/0IRo6ED38Y1q3LuyIzq1YO+hwNG5Zuevbii/CRj8DWrR0vY2bWWQ76nI0fD//7v/DAA3DhhVCBJ0GZWS/noK8AH/1ouj3CNdeku16amZWTg75CXHYZ/OVfpnvZL1iQdzVmVk0c9BWiTx+44QYYOzZt4T/9dN4VmVm1cNBXkKFD08HZrVvhr/4KNm/OuyIzqwYO+gpz2GFpy/7hh+Hv/s4HZ82s+xz0FWjatNRmf8MN6epZM7PucNBXqM9/Pp1b/5nPwPz5eVdjZr2Zg75CSXDddTBuHJx2GjzxRN4VmVlv5aCvYEOGpIOzkO5h/6c/5VuPmfVODvoKN3Ys3HgjrFgBZ53lg7Nm1nkO+l7gxBPhiivgJz+BL38572rMrLdx0PcSn/wknH46fOEL8Itf5F2NmfUmJQW9pJMlPS5plaTPtjL9HyWtkLRM0q8kHVQ0bYekpdlwa8tlrTQSzJkDRx8Ns2bB736Xd0Vm1lt0GPSS+gLfAj4AjANmShrXYraHgfqIGA/cBFxeNG1zREzIhulYlw0aBD/9KQwcCKeeCi+9lHdFZtYblLJFPwlYFRGrI+J1YB5wavEMEfHriHgte7kIqCtvmdZs1KjUVr96NXzsY7BjR94VmVmlKyXoRwLPFL1uysa15Vzg9qLXAyU1Slok6UNdqNFamDoVrroKbrsNLr4472rMrNKVtXNwSacD9UChaPRBEbFW0luBuyU9GhG7XP4jaTYwG2D06NHlLKsqnX9+uh/Ov/0bTJiQ7nhpZtaaUrbo1wKjil7XZeN2IulE4J+B6RHxZqd4EbE2e1wN3ANMbO1NImJORNRHRP2IESNK/gC1SoJvfhMmT4Yzz4Rly/KuyMwqVSlBvxg4RNLBkgYAM4Cdzp6RNBH4L1LIry8av4+kPbLnw4EpwIpyFV/r9tgjtdfvvXe6cnbjxrwrMrNK1GHQR8R24ELgTmAlcGNELJd0qaTms2iuAIYAP25xGuXhQKOkR4BfA1+JCAd9GR1wQDoTZ+3adE+c7dvzrsjMKo2iAq+pr6+vj8bGxrzL6FWuuw7OPjtdWPW1r+VdjZntbpKWRER9a9PKejDW8nPWWeng7Ne/DhMnwhln5F2RmVUK3wKhinz1q/Dud6eeqbxDZGbNHPRVpH//dKfL/fdPfc4+91zeFZlZJXDQV5nhw9M97DduTD1UPf543hWZWd4c9FVowoR0cHbRotTZ+PHHw3e+A5s25V2ZmeXBQV+l/uZv4Jln0n3sX30V/v7v06mYH/0o/PznsG1b3hWa2e7ioK9iBxwAn/50umr2oYdS2C9YANOnw8iR8IlPpPEVeIatmZWRg74GSOmUy69/PV1YdeutUCik5pxjjoHx49MZO+vW5V2pmfUEB32N6d8fTjkFfvzjFOzf+U7qhPwzn4G6OvjAB2DuXNi8Oe9KzaxcHPQ1bN99010wH3ggnZ3zuc+lTshnzUqnaJ53Hixc6KYds97OQW8AvP3t8KUvwZNPwt13p/Pw582DhgYYOxYuuSR1dmJmvY+D3nbSp0+6uva669IFV9dfn4L+0kvT49SpcM017sbQrDdx0FubBg9O98yZPx+eegq+/GXYsCHdYmH//WHmTLjjDt8x06zSOeitJKNGpTb8lSvht7+Fc8+Fu+5KB29HjUoHcx99NO8qzaw1DnrrFAkmTYKrr4Y//hFuvhmOOw6uvDKdpnn00en5+vUdr8vMdg8HvXXZHnukg7a33JJC/6qrUhv/Jz+ZLsiaPh1uugm2bu14XWbWc9zxiJXd8uXpIO4PfpB+AAYMgAMPTOfpFw8jR/75+f77Qz/3jmDWZe11POKgtx6zYwf86lfpdM2mpnRVblNTGrZs2XnePn3SLRta/gAU/yiMHJn2IsxsV+5hynLRty+cdFIaikWkO2k2h37xD0BTUzrg+3//By+/vOs6R4xofY+geNyQIbvn85n1FiUFvaSTgW8AfYFrIuIrLabvAVwPHANsBE6LiDXZtM8B5wI7gIsi4s6yVW+9kgTDhqXhqKPanu/ll3f+ESh+/vTTcP/96b77LQ0d2noT0fDhMGgQDBzY/rDHHqlGs2rRYdBL6gt8C3gf0AQslnRrRKwomu1c4IWIeJukGcB/AKdJGgfMAKic3SoAAASiSURBVN4BHAj8n6S3R8SOcn8Qqz5veUsaDj+87Xk2b07HAYr3CIp/EJYtg2ef7fxtHPbYo7QfheKh1Pn7909NVX36pL2e1p63N60ry/iHq7aVskU/CVgVEasBJM0DTgWKg/5U4JLs+U3A1ZKUjZ8XEVuBJyWtytb3QHnKt1o3aFC6Ynfs2Lbn2bYthf3GjenYQCnD5s3tT9+0qe15K/Fe/9KuPwDN4S+1/7zU+br7vLWaSxnX2fGdXUdndHcdw4enW4mXWylBPxJ4puh1E3BcW/NExHZJLwHDsvGLWiw7srU3kTQbmA0wevToUmo3K0n//umirlGjds/77diRTilt6wdk+3Z444003xtvtP+81Pk6u8yObJ864s97O609b29aOZ+31Nr4zsxbrnV0RjnWMXRo99fRmoo5GBsRc4A5kM66ybkcsy7r2xf23DMNZpWglAum1gLF20J12bhW55HUDxhKOihbyrJmZtaDSgn6xcAhkg6WNIB0cPXWFvPcCpyZPf8ocHekE/RvBWZI2kPSwcAhwIPlKd3MzErRYdNN1uZ+IXAn6fTKayNiuaRLgcaIuBX4b+D72cHWTaQfA7L5biQduN0OXOAzbszMdi9fGWtmVgXauzLWNzUzM6tyDnozsyrnoDczq3IOejOzKleRB2MlbQCe6uLiw4Hny1hOb+bvYmf+Pnbm7+PPquG7OCgiRrQ2oSKDvjskNbZ15LnW+LvYmb+Pnfn7+LNq/y7cdGNmVuUc9GZmVa4ag35O3gVUEH8XO/P3sTN/H39W1d9F1bXRm5nZzqpxi97MzIo46M3MqlzVBL2kkyU9LmmVpM/mXU+eJI2S9GtJKyQtl/TxvGvKm6S+kh6W9Iu8a8mbpL0l3STpd5JWSpqcd015kvTJ7O/kMUlzJQ3Mu6Zyq4qgL+rA/APAOGBm1jF5rdoOfCoixgHHAxfU+PcB8HFgZd5FVIhvAHdExGHAUdTw9yJpJHARUB8RR5BuxT4j36rKryqCnqIOzCPidaC5A/OaFBHrIuKh7PkrpD/kVvvqrQWS6oC/BK7Ju5a8SRoKNJD6kCAiXo+IF/OtKnf9gEFZ73h7An/MuZ6yq5agb60D85oNtmKSxgATgd/mW0murgT+CXgj70IqwMHABuB/sqasayQNzruovETEWuCrwNPAOuCliLgr36rKr1qC3lohaQjwE+ATEfFy3vXkQdI0YH1ELMm7lgrRDzga+E5ETAReBWr2mJakfUh7/wcDBwKDJZ2eb1XlVy1B707IW5DUnxTyN0TEzXnXk6MpwHRJa0hNeu+R9IN8S8pVE9AUEc17eDeRgr9WnQg8GREbImIbcDPwzpxrKrtqCfpSOjCvGZJEaoNdGRFfy7uePEXE5yKiLiLGkP5f3B0RVbfFVqqIeBZ4RtKh2aj3kvp0rlVPA8dL2jP7u3kvVXhwusPOwXuDtjowz7msPE0BzgAelbQ0G/f5iPhljjVZ5fgH4IZso2g1cHbO9eQmIn4r6SbgIdLZag9ThbdD8C0QzMyqXLU03ZiZWRsc9GZmVc5Bb2ZW5Rz0ZmZVzkFvZlblHPRmZlXOQW9mVuX+P+7VDeor6C7wAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def sigm (X, y, lr, it, W):\n",
        "  er = np.zeros(it)\n",
        "  for it in range(it):\n",
        "    for n in range(len(X)):\n",
        "      x_ = np.reshape(X[n], (len(X[0]),1))\n",
        "      y_ = y[n]\n",
        "      \n",
        "      out = sig(np.dot(W.T,x_))\n",
        "      \n",
        "      er[it] += (y_-out)**2\n",
        "      \n",
        "      W_delta = lr * (y_ - out) * out * (1-out) * x_\n",
        "      W += W_delta\n",
        "\n",
        "    er[it] /= len(X)\n",
        "  return (er, W)"
      ],
      "metadata": {
        "id": "KA8xGYeWr44m"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "MSE_sig, W_sig = sigm(X, y, lr, it, W)\n",
        "output_sig = np.dot(X,W_sig)"
      ],
      "metadata": {
        "id": "M3a25yk1sfB9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"output after training (\",it,\"iterations):\\n\",output_sig)\n",
        "print(\"target output:\\n\",y)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(range(it),MSE_sig,color=\"red\",label=\"MSE\")\n",
        "plt.title(\"MSE with SIGMOID activation\")\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "TOUPqiaJsksl",
        "outputId": "5c1121ae-f0ce-44a9-c42d-f5c648899858"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "output after training ( 10 iterations):\n",
            " [[-0.44099307]\n",
            " [-0.6178648 ]\n",
            " [ 1.15406727]\n",
            " [ 0.97719555]]\n",
            "target output:\n",
            " [[0]\n",
            " [0]\n",
            " [1]\n",
            " [1]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}