{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka 06/21/2015 \n",
      "\n",
      "CPython 3.4.3\n",
      "IPython 3.1.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -v -d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Activation Functions Cheatsheet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear:  $$g(z) = z$$ \n",
    "\n",
    "Unit step: $$g(z) = \\begin{cases} 0 & z < 0, \\\\ 1 & z \\ge 0 \\end{cases}$$\n",
    "\n",
    "logistic (sigmoid): $$g(z) = \\frac{1}{1 + e^{-z}}$$\n",
    "\n",
    "hyperbolic tangent (sigmoid): $$g(z) = tanh(z) = \\frac{e^{z}-e^{-z}}{e^{z}+e^{-z}}$$\n",
    "\n",
    "\n",
    "Piecewise linear: $$g(z) = \\begin{cases}\n",
    " 1 & \\mbox{for } z \\geq \\frac{1}{2} \\\\\n",
    " z + \\frac{1}{2} & \\mbox{for } -\\frac{1}{2} < z < \\frac{1}{2} \\\\\n",
    " 0 & \\mbox{for } z \\leq -\\frac{1}{2}\n",
    " \\end{cases}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def activation(z, kind):\n",
    "    \n",
    "    implemented = ('linear', 'unit step', 'logistic', 'piecewise linear', 'tanh')\n",
    "    if kind not in implemented:\n",
    "        raise AttributeError('%s not in %s' % (kind, implemented))\n",
    "    \n",
    "    if kind == 'unit step':\n",
    "        return np.where(z >= 0.0, 1, 0)\n",
    "    \n",
    "    elif kind == 'logistic':\n",
    "        return 1.0 / (1.0 + np.exp(-z))\n",
    "    \n",
    "    elif kind == 'tanh':\n",
    "        e_p = np.exp(z) \n",
    "        e_m = np.exp(-z)\n",
    "        return (e_p - e_m) / (e_p + e_m)  \n",
    "    \n",
    "    elif kind == 'piecewise linear':\n",
    "        if z >= 0.5:\n",
    "            return 1\n",
    "        elif z <= -0.5:\n",
    "            return 0\n",
    "        else:\n",
    "            return z + 0.5\n",
    "        \n",
    "    else:\n",
    "        return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106729908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1067cb080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069f6b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106abd208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zicw2FYdjVojvdWPWhMRRwC4RHFh1LGaD8b1uzEZuBnBh1UGYtYMLfUlS7hOmlpvEu4G3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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b71e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5, 5, 0.005)\n",
    "for a in ('linear', 'unit step', 'logistic', 'piecewise linear', 'tanh'):\n",
    "    y = [activation(z, kind=a) for z in x]\n",
    "    plt.plot(x, y)\n",
    "    plt.title(a)\n",
    "    plt.ylim([-1.5, 1.5])\n",
    "    plt.xlabel('z')\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}