1 - Theano Basics/Exercises.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import theano\n",
    "import theano.tensor as T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercises\n",
    "====="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Logistic function\n",
    "----------\n",
    "Create an expression for the logistic function $s(x) = \\frac{1}{1+exp(-x)}$. Plot the function and its derivative, and verify that $\\frac{ds}{dx} = s(x)(1-s(x))$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Uncomment and run this cell for one solution\n",
    "#%load spoilers/logistic.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Fibonacci sequence\n",
    "--------\n",
    "Calculate the 3rd to 10th terms of the sequence, defined by the recurrance relation $F_n = F_{n-2} + F_{n-1}$, with $F_1=1$ and $F_2=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Uncomment and run this cell for one solution\n",
    "#%load spoilers/fib.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Game of Life\n",
    "-------\n",
    "Implement [Conway's Game of Life](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) with periodic boundary conditions (wrapping borders)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "board = theano.shared(np.zeros((100, 100), dtype='uint8'))\n",
    "\n",
    "initial = np.random.binomial(1, 0.1, size=(100, 100)).astype('uint8')\n",
    "board.set_value(initial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a function f that updates board with new values and return the current state\n",
    "# Uncomment the line below and run for a solution\n",
    "#%load spoilers/life.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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hpNQrADAmehgAgC6BAQDoEhgAgC6BAQDoUvQIcEzmDcg2S8EzY6WHAQDoEhgAgC6BAQDo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\nAAB0CQwAQNf/B4i5Ftl789kaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5ac9923dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# After creating your f function, run this cell to animate the output\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from IPython import display\n",
    "import time\n",
    "\n",
    "for i in range(50):\n",
    "    plt.gca().cla()\n",
    "    current = f()\n",
    "    plt.imshow(current, interpolation='nearest', cmap='gray')\n",
    "    display.clear_output(wait=True)\n",
    "    display.display(plt.gcf()) \n",
    "    time.sleep(0.1) "
   ]
  }
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