{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "106e3031-9617-4d5d-8904-56afa48c1aee",
   "metadata": {},
   "source": [
    "<h1>The Sigmoid Activation Function (Logistic Function)</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2a9a57e6-3b0e-4d7d-93d2-a2f57b1eb884",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def sigmoid(z):\n",
    "    sig = 1/(1+np.exp(-z))\n",
    "    return sig\n",
    "\n",
    "\n",
    "def grad_sigmoid(z):\n",
    "    sig = sigmoid(z) * (1 - sigmoid(z))\n",
    "    return sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ca5273d3-3e37-46ae-8e8d-d554d24b1ba3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = [t for t in range(-10, 10)] #input range\n",
    "\n",
    "y = [sigmoid(i) for i in z]\n",
    "y_grad = [grad_sigmoid(i) for i in z]\n",
    "\n",
    "plt.figure('Sigmoid Activation Function')\n",
    "plt.plot(z, y, 'g', label='sigmoid')\n",
    "plt.plot(z, y_grad, 'r', label='gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32ad4fd3-7673-4b5d-bb44-c2b0002b4d6b",
   "metadata": {},
   "source": [
    "<h1>Points to note:</h1>\n",
    "<p> </p>\n",
    "<h3>The sigmoid function is bounded in the range of 0 to 1. (Normalised inputs are better)</h3>\n",
    "<h4>This means that values are always positive potentially creating biased and unstable training. This means training over more epochs.</h4>\n",
    "<h3>The sigmoid (logistic) function is continuous, differentiable and monotonic.</h3>\n",
    "<h3>The gradient curve is smooth, this helps model convergeance.</h3>\n",
    "<h3>Sigmoid is computationally expensive due to exponentials</h3>\n",
    "<h2>BUT...</h2>\n",
    "<h3>the gradient calculation is is cheap and straight forward (See Perceptron slides).</h3>\n",
    "<p> </p>\n",
    "<h2>Watch out for Vanishing Gradients!</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9d28050c-f022-433c-b3c6-693e911aac9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total time taken by scratch implementation is  76.07078552246094  micro-seconds\n",
      "Total time taken by Keras implementation is  47.287940979003906  micro-seconds\n",
      "Total time taken by Tensorflow.Math implementation is  15.999555587768555  micro-seconds\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import time\n",
    "\n",
    "z = [t for t in np.arange(-500.0, 500.0, 0.01)]\n",
    "\n",
    "t3 = time.time()\n",
    "out3 = [sigmoid(i) for i in z]\n",
    "total_time_3 = (time.time() - t3)*1000\n",
    "print(\"Total time taken by scratch implementation is \", total_time_3, \" micro-seconds\")\n",
    "\n",
    "t2 = time.time()\n",
    "out2 = tf.keras.activations.sigmoid(z)\n",
    "total_time_2 = (time.time() - t2)*1000\n",
    "print(\"Total time taken by Keras implementation is \", total_time_2, \" micro-seconds\")\n",
    "\n",
    "t1 = time.time()\n",
    "out = tf.math.sigmoid(z)\n",
    "total_time = (time.time() - t1)*1000\n",
    "print(\"Total time taken by Tensorflow.Math implementation is \", total_time, \" micro-seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "66ea2cff-cc33-450d-999a-c93946068e2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result of scratch:  [7.124576406741285e-218, 7.196179590032893e-218, 7.268502397280336e-218, 7.341552060824613e-218, 7.415335885692952e-218, 7.489861250329325e-218, 7.565135607332301e-218, 7.641166484200311e-218, 7.717961484084399e-218, 7.795528286548549e-218, 7.873874648337649e-218, 7.953008404153165e-218, 8.032937467436625e-218, 8.113669831160963e-218, 8.195213568629829e-218, 8.277576834284924e-218, 8.360767864521451e-218, 8.444794978511757e-218, 8.529666579037267e-218, 8.615391153328758e-218, 8.701977273915094e-218, 8.789433599480497e-218, 8.877768875730394e-218, 8.966991936266031e-218, 9.057111703467809e-218, 9.14813718938755e-218, 9.240077496649702e-218, 9.33294181936161e-218, 9.426739444032928e-218, 9.52147975050429e-218, 9.617172212885293e-218, 9.71382640050192e-218, 9.811451978853477e-218, 9.910058710579156e-218, 1.00096564564343e-217, 1.0110255176276496e-217, 1.0211864930061555e-217, 1.0314495878849536e-217, 1.0418158285820844e-217, 1.0522862517302556e-217, 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      "\n",
      "result of Keras:  tf.Tensor(\n",
      "[7.12457641e-218 7.19617959e-218 7.26850240e-218 ... 1.00000000e+000\n",
      " 1.00000000e+000 1.00000000e+000], shape=(100000,), dtype=float64)\n",
      "\n",
      "result of Tensorflow.Math:  tf.Tensor(\n",
      "[7.12457641e-218 7.19617959e-218 7.26850240e-218 ... 1.00000000e+000\n",
      " 1.00000000e+000 1.00000000e+000], shape=(100000,), dtype=float64)\n"
     ]
    }
   ],
   "source": [
    "print(\"result of scratch: \", out3)\n",
    "print()\n",
    "print(\"result of Keras: \", out2)\n",
    "print()\n",
    "print(\"result of Tensorflow.Math: \", out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "40d7a396-b2cb-4389-9c84-edfe7c4bbabb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vvPBCm8+Tl5enmpoa362srCyQbgIIIqymAdChs//cv2CMMW3+VbNv3z7l5ORowYIFKioq0rZt23To0CFlZ2e3+fgul0vR0dF+NwDdE9M0AMIDaRwbGyun09liFKSqqqrFaIlXfn6+brrpJv3sZz+TJH33u99Vr169lJ6eriVLlighIaGDXQfQHXgLWFlNA4SugP4UiYiIUGpqqgoLC/22FxYWKi0trdV9Tp48qbAw/6dxOp2SvnkTAhC6GBkBEPDZn5ubqzVr1mjdunXav3+/HnnkEZWWlvqmXfLy8jR16lRf+0mTJmnr1q1avXq1Dh48qA8++EA5OTm68cYblZiYeOleCYCgRAErgICmaSQpKytLx44d0+LFi1VRUaGUlBQVFBRoyJAhkqSKigq/a45MmzZNtbW1WrFihR599FHFxMTo5ptv1tNPP33pXgWAoEUBKwCHCYK5Eo/HI7fbrZqaGopZgW4m580cvfDRC5qfPl9Lbl5iuzsALqH2fn7zpwgAq7gcPADCCACruBw8AM5+AFaxmgYAZz8Aq7wFrKymAUIXYQSAVYyMAODsB2AVBawACCMArKKAFQBnPwCrmsU0DRDqOPsBWOX7ojwKWIGQRRgBYBUFrAA4+wFYRRgBwNkPwCrfdUZYTQOELMIIAKsYGQHA2Q/AKt91RihgBUIWYQSAVVxnBABnPwCrmKYBwNkPwCoKWAEQRgBYxcgIAM5+AFYRRgBw9gOwisvBAyCMALCKkREAnP0ArPJdZ4QCViBkEUYAWOVdTcPICBC6OPsBWMU0DQDOfgBWUcAKgDACwCpGRgBw9gOwijACgLMfgFVcDh4AYQSAVYyMAODsB2CV7zojFLACIYswAsAq72oaRkaA0MXZD8AqpmkAcPYDsIoCVgCEEQBWMTICgLMfgFWEEQCc/QCs4nLwAAgjAKxiZAQAZz8AqwgjADj7AVjFahoAhBEAVjEyAoCzH4BVFLACIIwAsIqREQCc/QCsIowA4OwHYBUFrAAIIwCsYmQEAGc/AKsIIwA4+wFYxWoaAIQRAFYxMgKAsx+AVRSwAiCMALCKkREAnP0ArCKMAODsB2AVBawACCMArGJkBABnPwCrvAWshBEgdHH2A7DKOzLCahogdBFGAFjFNA2ADp39q1atUnJysiIjI5WamqodO3act31dXZ3mz5+vIUOGyOVy6eqrr9a6des61GEA3QsFrADCA91h8+bNmjt3rlatWqWbbrpJL730kjIzM7Vv3z4NHjy41X3uuOMOffnll1q7dq2GDh2qqqoqNTY2XnTnAQQ/RkYAOIz3z5J2GjVqlEaMGKHVq1f7tg0bNkyTJ09Wfn5+i/bbtm3TlClTdPDgQfXt27ddz1FXV6e6ujrfzx6PR0lJSaqpqVF0dHQg3QXQxUXnR6u2vlZ/eegvGtp3qO3uALiEPB6P3G73BT+/A/pTpL6+XkVFRcrIyPDbnpGRoZ07d7a6zxtvvKGRI0fqmWee0cCBA/Xtb39bjz32mE6dOtXm8+Tn58vtdvtuSUlJgXQTQBDhcvAAApqmqa6uVlNTk+Li4vy2x8XFqbKystV9Dh48qD/96U+KjIzU73//e1VXV+vBBx/U//3f/7VZN5KXl6fc3Fzfz96REQDdD9M0AAKuGZFaFpoZY9osPmtubpbD4dCGDRvkdrslSc8//7x+/OMfa+XKlYqKimqxj8vlksvl6kjXAAQZ70wxYQQIXQGd/bGxsXI6nS1GQaqqqlqMlnglJCRo4MCBviAinakxMcboyJEjHegygO7Ed50RVtMAISugMBIREaHU1FQVFhb6bS8sLFRaWlqr+9x0000qLy/XV1995dv2+eefKywsTIMGDepAlwF0J0zTAAj47M/NzdWaNWu0bt067d+/X4888ohKS0uVnZ0t6Uy9x9SpU33t77rrLvXr10/Tp0/Xvn37tH37dv3sZz/T/fff3+oUDYDQQgErgIBrRrKysnTs2DEtXrxYFRUVSklJUUFBgYYMGSJJqqioUGlpqa/9FVdcocLCQj300EMaOXKk+vXrpzvuuENLliy5dK8CQNBiZARAwNcZsaG965QBBB/H42dGRCofrVTcFa3XngEITp1ynREAuJTO/luIAlYgdBFGAFjjrReRmKYBQhlnPwBrzh4ZIYwAoYuzH4A13uJVidU0QCgjjACw5uwwwsgIELo4+wFYQ80IAIkwAsAiv2kaVtMAIYswAsAapmkASIQRABb5XWeEAlYgZBFGAFjDyAgAiTACwCIKWAFIhBEAFlHACkAijACwiGkaABJhBIBFFLACkAgjACximgaARBgBYJE3jDBFA4Q23gEAWONdTcMUDRDaCCMArGFkBIBEGAFgkbeAlTAChDbeAQBY4x0ZoXgVCG2EEQDWME0DQCKMALDIW8BKGAFCG+8AAKzxTdOwmgYIaYQRANZQwApAIowAsIgCVgASYQSARRSwApAIIwAsooAVgEQYAWARBawAJMIIAIuYpgEgEUYAWMRqGgASYQSARaymASARRgBYRAErAIkwAsAiClgBSIQRABZRwApAIowAsIgCVgASYQSARRSwApAIIwAsYpoGgEQYAWARq2kASIQRABaxmgaARBgBYBEFrAAkwggAi6gZASARRgBYxGoaABJhBIBFFLACkAgjACyigBWARBgBYBE1IwAkwggAi1hNA0AijACwiAJWABJhBIBFFLACkAgjACyiZgSARBgBYBGraQBIhBEAFlHACkAijACwiAJWABJhBIBF1IwAkAgjACxiNQ0AiTACwCIKWAFIhBEAFlHACkDqYBhZtWqVkpOTFRkZqdTUVO3YsaNd+33wwQcKDw/X8OHDO/K0ALoZakYASB0II5s3b9bcuXM1f/58FRcXKz09XZmZmSotLT3vfjU1NZo6darGjx/f4c4C6F5YTQNA6kAYef755zVjxgzNnDlTw4YN07Jly5SUlKTVq1efd78HHnhAd911l0aPHt3hzgLoXihgBSAFGEbq6+tVVFSkjIwMv+0ZGRnauXNnm/utX79eBw4c0MKFC9v1PHV1dfJ4PH43AN0PBawApADDSHV1tZqamhQXF+e3PS4uTpWVla3u85e//EXz5s3Thg0bFB4e3q7nyc/Pl9vt9t2SkpIC6SaAIEEBKwCpgwWs587vGmNanfNtamrSXXfdpccff1zf/va32/34eXl5qqmp8d3Kyso60k0AXRwFrAAkqX1DFX8TGxsrp9PZYhSkqqqqxWiJJNXW1mr37t0qLi7WnDlzJEnNzc0yxig8PFxvv/22br755hb7uVwuuVyuQLoGIAhRwApACnBkJCIiQqmpqSosLPTbXlhYqLS0tBbto6OjVVJSor179/pu2dnZuuaaa7R3716NGjXq4noPIKh5C1ipGQFCW0AjI5KUm5ure++9VyNHjtTo0aP18ssvq7S0VNnZ2ZLOTLEcPXpUr7/+usLCwpSSkuK3/4ABAxQZGdliO4DQ4x0ZcYY5LfcEgE0Bh5GsrCwdO3ZMixcvVkVFhVJSUlRQUKAhQ4ZIkioqKi54zREAkFhNA+AMh/GWs3dhHo9HbrdbNTU1io6Ott0dAJfIyo9Was6bc/STv/uJ/v0n/267OwAusfZ+flPCDsAaVtMAkAgjACxiNQ0AiTACwCJGRgBIhBEAFvHdNAAkwggAixgZASARRgBYxNJeABJhBIBFfFEeAIkwAsAipmkASIQRABYxTQNAIowAsIiREQASYQSARSztBSARRgBYxBVYAUiEEQAWMU0DQCKMALCIpb0AJMIIAItYTQNAIowAsIhpGgASYQSARYQRABJhBIBFLO0FIBFGAFjE0l4AEmEEgEVM0wCQCCMALGJpLwCJMALAIpb2ApAIIwAsYpoGgEQYAWARq2kASIQRABaxmgaARBgBYBHTNAAkwggAiwgjACTCCACLvEt7WU0DhDbCCABrGBkBIBFGAFjULMIIAMIIAIu4AisAiTACwCKW9gKQCCMALKJmBIBEGAFgEWEEgEQYAWCR93LwLO0FQhthBIA1jIwAkAgjACwijACQCCMALPJdgZXVNEBII4wAsIaREQASYQSARYQRABJhBIBFrKYBIBFGAFjEyAgAiTACwCLCCACJMALAIsIIAIkwAsAilvYCkAgjACxiZASARBgBYBFhBIBEGAFgEUt7AUiEEQAWMTICQCKMALCIMAJAIowAsMgbRlhNA4Q2wggAa7xLexkZAUIb7wAArGGaBoBEGAFgkW+ahtU0QEgjjACwxru0l5ERILTxDgDAGqZpAEgdDCOrVq1ScnKyIiMjlZqaqh07drTZduvWrbr11lvVv39/RUdHa/To0Xrrrbc63GEA3QdhBIDUgTCyefNmzZ07V/Pnz1dxcbHS09OVmZmp0tLSVttv375dt956qwoKClRUVKRx48Zp0qRJKi4uvujOAwhuLO0FIEkO411b106jRo3SiBEjtHr1at+2YcOGafLkycrPz2/XY1x33XXKysrSggUL2tXe4/HI7XarpqZG0dHRgXQXQBc2/MXh+vjLj/XWPW8p4+oM290BcIm19/M7oJGR+vp6FRUVKSPD/00jIyNDO3fubNdjNDc3q7a2Vn379m2zTV1dnTwej98NQPfDahoAUoBhpLq6Wk1NTYqLi/PbHhcXp8rKynY9xnPPPaevv/5ad9xxR5tt8vPz5Xa7fbekpKRAugkgSHjDiDPMabknAGzqUNXYufO7xph2zflu3LhRixYt0ubNmzVgwIA22+Xl5ammpsZ3Kysr60g3AXRxTaZJEgWsQKgLD6RxbGysnE5ni1GQqqqqFqMl59q8ebNmzJih3/72t7rlllvO29blcsnlcgXSNQBBqKn5TBhxOhgZAUJZQH+OREREKDU1VYWFhX7bCwsLlZaW1uZ+Gzdu1LRp0/Rv//ZvmjhxYsd6CqDb8Y6MME0DhLaARkYkKTc3V/fee69Gjhyp0aNH6+WXX1Zpaamys7MlnZliOXr0qF5//XVJZ4LI1KlT9atf/Urf+973fKMqUVFRcrvdl/ClAAg2vpoRRkaAkBZwGMnKytKxY8e0ePFiVVRUKCUlRQUFBRoyZIgkqaKiwu+aIy+99JIaGxs1e/ZszZ4927f9vvvu06uvvnrxrwBA0PJO01AzAoS2gK8zYgPXGQG6p4HPD1R5bbmK/l+RRiSMsN0dAJdYp1xnBAAuJaZpAEiEEQAW+VbTUMAKhDTCCABruM4IAIkwAsAirjMCQCKMALCIy8EDkAgjACzyXfSMkREgpBFGAFjDdUYASIQRABZxOXgAEmEEgEVcZwSARBgBYIkxhgJWAJIIIwAs8QYRiZoRINTxDgDAirPDCNM0QGgjjACwwlu8KjFNA4Q6wggAK7zLeiVGRoBQRxgBYMXZIyPUjAChjXcAAFb41YwwTQOENMIIACuYpgHgRRgBYAXTNAC8eAcAYIV3msYhhxwOh+XeALCJMALACu80DfUiAAgjAKzwfUke9SJAyCOMALCCkREAXoQRAFZ4a0YoXgXAuwAAK5imAeBFGAFgBdM0ALwIIwCsaGhukCT1COthuScAbCOMALCisblRkhQeFm65JwBsI4wAsKKh6W8jI05GRoBQRxgBYAXTNAC8CCMArPCOjDBNA4AwAsAK38gI0zRAyCOMALDCW8DKNA0AwggAKyhgBeBFGAFghXeahpoRAIQRAFb4RkaYpgFCHmEEgBUUsALwIowAsIICVgBehBEAVnCdEQBehBEAVjBNA8CLMALACgpYAXgRRgBYwcgIAC/CCAAr6pvqJUkRYRGWewLANsIIACtONZySJEX1iLLcEwC2EUYAWHG68bQkKTI80nJPANhGGAFgxanGv42MhDMyAoQ6wggAK3xhhGkaIOQRRgBYwTQNAC/CCAArfAWsTNMAIY8wAsAK78gI0zQACCMArPDWjDBNA4AwAsCK2rpaSVLviN6WewLANsIIACtOnD4hSYqJjLHaDwD2EUYAWEEYAeBFGAFw2RljVFNXI0lyR7ot9waAbYQRAJedp86jZtMsiZERAIQRABYc8RyRdCaI9OzR03JvANjWoTCyatUqJScnKzIyUqmpqdqxY8d527///vtKTU1VZGSkrrrqKr344osd6iyA7qHMUyZJGuwebLknALqCgMPI5s2bNXfuXM2fP1/FxcVKT09XZmamSktLW21/6NAh/fCHP1R6erqKi4v1i1/8Qjk5OdqyZctFdx5AcCr5skSSNLTvUMs9AdAVOIwxJpAdRo0apREjRmj16tW+bcOGDdPkyZOVn5/fov3Pf/5zvfHGG9q/f79vW3Z2tj7++GPt2rWrXc/p8XjkdrtVU1Oj6OjoQLp7XtUnq/V1/ddt3m/U9qG50GE7374X2v9i9r3Q/vS7az13KPa72TRr7ltztadij5699Vk9lvbYeR8LQPBq7+d3eCAPWl9fr6KiIs2bN89ve0ZGhnbu3NnqPrt27VJGRobftgkTJmjt2rVqaGhQjx49WuxTV1enuro6vxfTGXLezNHGTzd2ymMDOL/I8EhNSZliuxsAuoCAwkh1dbWampoUFxfntz0uLk6VlZWt7lNZWdlq+8bGRlVXVyshIaHFPvn5+Xr88ccD6VqHRDgjLvglXQ6Ho+371PZ9F9r3QvtfzL4X2p9+d63nDsV+9+vZT4vHLtag6EHnfQwAoSGgMOJ17puQMeb8b4ittG9tu1deXp5yc3N9P3s8HiUlJXWkq+f16uRX9erkVy/54wIAgPYLKIzExsbK6XS2GAWpqqpqMfrhFR8f32r78PBw9evXr9V9XC6XXC5XIF0DAABBKqDVNBEREUpNTVVhYaHf9sLCQqWlpbW6z+jRo1u0f/vttzVy5MhW60UAAEBoCXhpb25urtasWaN169Zp//79euSRR1RaWqrs7GxJZ6ZYpk6d6mufnZ2tL774Qrm5udq/f7/WrVuntWvX6rHHqKAHAAAdqBnJysrSsWPHtHjxYlVUVCglJUUFBQUaMmSIJKmiosLvmiPJyckqKCjQI488opUrVyoxMVHLly/X7bfffuleBQAACFoBX2fEhs66zggAAOg87f385rtpAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFUBXw7eBu9FYj0ej+WeAACA9vJ+bl/oYu9BEUZqa2slSUlJSZZ7AgAAAlVbWyu3293m/UHx3TTNzc0qLy9X79695XA4bHfHKo/Ho6SkJJWVlfE9PZ2MY315cJwvD47z5cFx9meMUW1trRITExUW1nZlSFCMjISFhWnQoEG2u9GlREdH84t+mXCsLw+O8+XBcb48OM7fON+IiBcFrAAAwCrCCAAAsIowEmRcLpcWLlwol8tluyvdHsf68uA4Xx4c58uD49wxQVHACgAAui9GRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGgkBdXZ2GDx8uh8OhvXv3+t1XWlqqSZMmqVevXoqNjVVOTo7q6+v92pSUlGjMmDGKiorSwIEDtXjx4gt+T0CoOHz4sGbMmKHk5GRFRUXp6quv1sKFC1scQ45z51i1apWSk5MVGRmp1NRU7dixw3aXgkp+fr7+/u//Xr1799aAAQM0efJk/c///I9fG2OMFi1apMTEREVFRWns2LH67LPP/NrU1dXpoYceUmxsrHr16qV//Md/1JEjRy7nSwkq+fn5cjgcmjt3rm8bx/kiGXR5OTk5JjMz00gyxcXFvu2NjY0mJSXFjBs3zuzZs8cUFhaaxMREM2fOHF+bmpoaExcXZ6ZMmWJKSkrMli1bTO/evc3SpUstvJKu58033zTTpk0zb731ljlw4ID5wx/+YAYMGGAeffRRXxuOc+fYtGmT6dGjh3nllVfMvn37zMMPP2x69eplvvjiC9tdCxoTJkww69evN59++qnZu3evmThxohk8eLD56quvfG2eeuop07t3b7NlyxZTUlJisrKyTEJCgvF4PL422dnZZuDAgaawsNDs2bPHjBs3zlx//fWmsbHRxsvq0j766CNz5ZVXmu9+97vm4Ycf9m3nOF8cwkgXV1BQYK699lrz2WeftQgjBQUFJiwszBw9etS3bePGjcblcpmamhpjjDGrVq0ybrfbnD592tcmPz/fJCYmmubm5sv2OoLJM888Y5KTk30/c5w7x4033miys7P9tl177bVm3rx5lnoU/Kqqqowk8/777xtjjGlubjbx8fHmqaee8rU5ffq0cbvd5sUXXzTGGHPixAnTo0cPs2nTJl+bo0ePmrCwMLNt27bL+wK6uNraWvOtb33LFBYWmjFjxvjCCMf54jFN04V9+eWXmjVrln7961+rZ8+eLe7ftWuXUlJSlJiY6Ns2YcIE1dXVqaioyNdmzJgxfhfgmTBhgsrLy3X48OFOfw3BqKamRn379vX9zHG+9Orr61VUVKSMjAy/7RkZGdq5c6elXgW/mpoaSfL9/h46dEiVlZV+x9nlcmnMmDG+41xUVKSGhga/NomJiUpJSeH/4hyzZ8/WxIkTdcstt/ht5zhfPMJIF2WM0bRp05Sdna2RI0e22qayslJxcXF+2/r06aOIiAhVVla22cb7s7cNvnHgwAG98MILys7O9m3jOF961dXVampqavWYcbw6xhij3Nxcff/731dKSoqkb373znecKysrFRERoT59+rTZBtKmTZu0Z88e5efnt7iP43zxCCOX2aJFi+RwOM572717t1544QV5PB7l5eWd9/EcDkeLbcYYv+3ntjF/K6psbd/uor3H+Wzl5eW67bbb9JOf/EQzZ870u4/j3DlaO2Ycr46ZM2eOPvnkE23cuLHFfR05zvxffKOsrEwPP/ywfvOb3ygyMrLNdhznjgu33YFQM2fOHE2ZMuW8ba688kotWbJEH374YYvvNxg5cqTuvvtuvfbaa4qPj9d///d/+91//PhxNTQ0+BJ6fHx8i9RdVVUlqWWK707ae5y9ysvLNW7cOI0ePVovv/yyXzuO86UXGxsrp9PZ6jHjeAXuoYce0htvvKHt27dr0KBBvu3x8fGSzvxVnpCQ4Nt+9nGOj49XfX29jh8/7vdXe1VVldLS0i7TK+jaioqKVFVVpdTUVN+2pqYmbd++XStWrPCtYOI4XwRLtSq4gC+++MKUlJT4bm+99ZaRZH73u9+ZsrIyY8w3hZXl5eW+/TZt2tSisDImJsbU1dX52jz11FMUVp7lyJEj5lvf+paZMmVKq1XtHOfOceONN5qf/vSnftuGDRtGAWsAmpubzezZs01iYqL5/PPPW70/Pj7ePP30075tdXV1rRZWbt682demvLycwsqzeDwev/fjkpISM3LkSHPPPfeYkpISjvMlQBgJEocOHWpzae/48ePNnj17zDvvvGMGDRrkt+T0xIkTJi4uztx5552mpKTEbN261URHR7Pk9G+OHj1qhg4dam6++WZz5MgRU1FR4bt5cZw7h3dp79q1a82+ffvM3LlzTa9evczhw4dtdy1o/PSnPzVut9u89957fr+7J0+e9LV56qmnjNvtNlu3bjUlJSXmzjvvbHXJ6aBBg8w777xj9uzZY26++WaWnF7A2atpjOE4XyzCSJBoLYwYc2YEZeLEiSYqKsr07dvXzJkzx295qTHGfPLJJyY9Pd24XC4THx9vFi1axF/rf7N+/XojqdXb2TjOnWPlypVmyJAhJiIiwowYMcK3JBXt09bv7vr1631tmpubzcKFC018fLxxuVzmBz/4gSkpKfF7nFOnTpk5c+aYvn37mqioKPMP//APprS09DK/muBybhjhOF8chzFcIhIAANjDahoAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAWHH48GE5HI4Wt7Fjx9ruGoDLLNx2BwCEpqSkJFVUVPh+rqys1C233KIf/OAHFnsFwAa+tReAdadPn9bYsWPVv39//eEPf1BYGIO2QChhZASAdTNmzFBtba0KCwsJIkAIIowAsGrJkiXatm2bPvroI/Xu3dt2dwBYwDQNAGu2bNmiO++8U2+++abGjx9vuzsALCGMALDi008/1ahRo5Sbm6vZs2f7tkdERKhv374WewbgciOMALDi1Vdf1fTp01tsHzNmjN57773L3yEA1hBGAACAVZStAwAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsOr/A3eUPCRz1QQyAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, out3, 'g', label='ReLU Scratch')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.plot(z, out2, 'g', label='ReLU Keras')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.plot(z, out, 'g', label='ReLU TF.Math')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c872f017-08d8-40a7-a834-c0df4f2e86fa",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}