{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img width=\"800px\" src=\"../fidle/img/00-Fidle-header-01.svg\"></img>\n",
    "\n",
    "# <!-- TITLE --> [ACTF1] - Activation functions\n",
    "<!-- DESC --> Some activation functions, with their derivatives.\n",
    "<!-- AUTHOR : Jean-Luc Parouty (CNRS/SIMaP) -->\n",
    "\n",
    "## Objectives :\n",
    " - View the main activation functions \n",
    "\n",
    "Les fonctions d'activation dans Keras :  \n",
    "https://www.tensorflow.org/api_docs/python/tf/keras/activations\n",
    "\n",
    "## What we're going to do :\n",
    "\n",
    " - Juste visualiser les principales fonctions d'activation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\n",
       "div.warn {    \n",
       "    background-color: #fcf2f2;\n",
       "    border-color: #dFb5b4;\n",
       "    border-left: 5px solid #dfb5b4;\n",
       "    padding: 0.5em;\n",
       "    font-weight: bold;\n",
       "    font-size: 1.1em;;\n",
       "    }\n",
       "\n",
       "\n",
       "\n",
       "div.nota {    \n",
       "    background-color: #DAFFDE;\n",
       "    border-left: 5px solid #92CC99;\n",
       "    padding: 0.5em;\n",
       "    }\n",
       "\n",
       "\n",
       "\n",
       "</style>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "FIDLE 2020 - Practical Work Module\n",
      "Version              : 0.4.2\n",
      "Run time             : Sunday 23 February 2020, 12:48:24\n",
      "TensorFlow version   : 2.0.0\n",
      "Keras version        : 2.2.4-tf\n",
      "Save figs            : True\n",
      "Path figs            : ./figs\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import math\n",
    "from math import erfc, sqrt, exp\n",
    "from math import pi as PI\n",
    "from math import e as E\n",
    "import sys\n",
    "\n",
    "sys.path.append('..')\n",
    "import fidle.pwk as ooo\n",
    "\n",
    "ooo.init()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "SELU_A = -sqrt(2/PI)/(erfc(1/sqrt(2))*exp(1/2)-1)\n",
    "SELU_L = (1-erfc(1/sqrt(2))*sqrt(E))*sqrt(2*PI) / (2*erfc(sqrt(2))*E*E+PI*erfc(1/sqrt(2))**2*E-2*(2+PI)*erfc(1/sqrt(2))*sqrt(E)+PI+2)**0.5\n",
    "\n",
    "\n",
    "def heaviside(z):\n",
    "    return np.where(z<0,0,1)\n",
    "\n",
    "def sign(z):\n",
    "    return np.where(z<0,-1,1)\n",
    "#    return np.sign(z)\n",
    "\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def tanh(z):\n",
    "    return np.tanh(z)\n",
    "\n",
    "def relu(z):\n",
    "    return np.maximum(0, z)\n",
    "\n",
    "def leaky_relu(z,a=0.05):\n",
    "    return np.maximum(a*z, z)\n",
    "\n",
    "def elu(z,a=1):\n",
    "    #y=z.copy()\n",
    "    y=a*(np.exp(z)-1)\n",
    "    y[z>0]=z[z>0]\n",
    "    return y\n",
    "\n",
    "def selu(z):\n",
    "    return SELU_L*elu(z,a=SELU_A)\n",
    "\n",
    "def derivative(f, z, eps=0.000001):\n",
    "    return (f(z + eps) - f(z - eps))/(2 * eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pw=5\n",
    "ph=5\n",
    "\n",
    "z = np.linspace(-5, 5, 200)\n",
    "\n",
    "\n",
    "# ------ Heaviside\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(0, 0, \"rx\", markersize=10)\n",
    "ax.plot(z, sign(z),                linewidth=2, linestyle='-',  color='steelblue', label=\"Heaviside\")\n",
    "ax.plot(z, derivative(np.sign, z),   label=\"dHeaviside/dx\")\n",
    "ax.plot(z, sign(z),                  label=\"Heaviside\")\n",
    "ax.set_title(\"Heaviside\")\n",
    "ooo.save_fig('Heaviside')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# ----- Logit/Sigmoid\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, sigmoid(z),             label=\"Sigmoid\")\n",
    "ax.plot(z, derivative(sigmoid, z), label=\"dSigmoid/dx\")\n",
    "ax.set_title(\"Logit\")\n",
    "ooo.save_fig('Logit')\n",
    "plt.show()\n",
    "\n",
    "# ----- Tanh\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, tanh(z),             label=\"Tanh\")\n",
    "ax.plot(z, derivative(tanh, z), label=\"dTanh/dx\")\n",
    "ax.set_title(\"Tanh\")\n",
    "ooo.save_fig('Tanh')\n",
    "plt.show()\n",
    "\n",
    "# ----- Relu\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, relu(z),             label=\"ReLU\")\n",
    "ax.plot(z, derivative(relu, z), label=\"dReLU/dx\")\n",
    "ax.set_title(\"ReLU\")\n",
    "ooo.save_fig('ReLU')\n",
    "plt.show()\n",
    "\n",
    "# ----- Leaky Relu\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, leaky_relu(z),              label=\"Leaky ReLU\")\n",
    "ax.plot(z, derivative( leaky_relu, z), label=\"dLeakyReLU/dx\")\n",
    "ax.set_title(\"Leaky ReLU (α=0.05)\")\n",
    "ooo.save_fig('LeakyReLU')\n",
    "plt.show()\n",
    "\n",
    "# ----- Elu\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, elu(z),              label=\"ReLU\")\n",
    "ax.plot(z, derivative( elu, z), label=\"dExpReLU/dx\")\n",
    "ax.set_title(\"ELU (α=1)\")\n",
    "ooo.save_fig('ELU')\n",
    "plt.show()\n",
    "\n",
    "# ----- Selu\n",
    "#\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_size_inches(pw,ph)\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.axhline(y=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.axvline(x=0, linewidth=1, linestyle='--', color='lightgray')\n",
    "ax.plot(z, selu(z),              label=\"SeLU\")\n",
    "ax.plot(z, derivative( selu, z), label=\"dSeLU/dx\")\n",
    "ax.set_title(\"ELU (SELU)\")\n",
    "ooo.save_fig('SeLU')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "<img width=\"80px\" src=\"../fidle/img/00-Fidle-logo-01.svg\"></img>"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}