Types_Activation_function_ANN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#example plot for the relu activation function\n",
    "from matplotlib import pyplot\n",
    "\n",
    "#rectified linear function\n",
    "def rectified(x):\n",
    "    return max(0.0, x)\n",
    "\n",
    "#define input data\n",
    "inputs = [x for x in range(-20, 20)]\n",
    "\n",
    "#calculate outputs\n",
    "outputs = [rectified(x) for x in inputs]\n",
    "\n",
    "#plot input vs outputs\n",
    "pyplot.plot(inputs, outputs)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#example plot for the sigmoid activation function\n",
    "from math import exp\n",
    "from matplotlib import pyplot\n",
    "\n",
    "\n",
    "#sigmoid activation function\n",
    "def sigmoid(x):\n",
    "    return 1.0 / (1.0 + exp(-x))\n",
    "\n",
    "#define input data\n",
    "inputs = [x for x in range(-10, 10)]\n",
    "\n",
    "#calculate outputs\n",
    "outputs = [sigmoid(x) for x in inputs]\n",
    "\n",
    "#plot input vs outputs\n",
    "pyplot.plot(inputs, outputs)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#example plot for the tanh activation function\n",
    "from matplotlib import pyplot\n",
    "from math import exp\n",
    "\n",
    "#tanh activation function\n",
    "def tanh(x):\n",
    "    return (exp(x) - exp(-x)) / (exp(x) + exp(-x))\n",
    "\n",
    "#define input data\n",
    "inputs = [x for x in range(-10, 10)]\n",
    "\n",
    "#calculate outputs\n",
    "outputs = [tanh(x) for x in inputs]\n",
    "\n",
    "#plot input vs outputs\n",
    "pyplot.plot(inputs, outputs)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#example plot for the linear activation function\n",
    "from matplotlib import pyplot\n",
    "\n",
    "#linear activation function\n",
    "def linear(x):\n",
    "    return x\n",
    "\n",
    "#define input data\n",
    "inputs = [x for x in range(-10, 10)]\n",
    "\n",
    "#calculate outputs\n",
    "outputs = [linear(x) for x in inputs]\n",
    "\n",
    "#plot input vs outputs\n",
    "pyplot.plot(inputs, outputs)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.09003057 0.66524096 0.24472847]\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "from numpy import exp\n",
    "\n",
    "#softmax activation function\n",
    "def softmax(x):\n",
    "    return exp(x) / exp(x).sum()\n",
    "\n",
    "#define input data\n",
    "inputs = [1.0, 3.0, 2.0]\n",
    "\n",
    "#calculate outputs\n",
    "outputs = softmax(inputs)\n",
    "\n",
    "#report the probabilities\n",
    "print(outputs)\n",
    "\n",
    "#report the sum of probabilities\n",
    "print(outputs.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "data = [1, 3, 2]\n",
    "result = max(data)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "from numpy import argmax\n",
    "data = [1, 3, 2]\n",
    "result = argmax(data)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09003057317038046 0.6652409557748219 0.24472847105479767\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "from math import exp\n",
    "p1 = exp(1) / (exp(1) + exp(3) + exp(2))\n",
    "p2 = exp(3) / (exp(1) + exp(3) + exp(2))\n",
    "p3 = exp(2) / (exp(1) + exp(3) + exp(2))\n",
    "print(p1, p2, p3)\n",
    "print(p1 + p2 + p3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}