Computation_with_IPython_notebooks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "",
     "locked": false,
     "solution": false
    }
   },
   "source": [
    "Before you start, make sure that you have the correct kernel. Check if the kernel is \"Python 2\" (there is a legend in the upper right corner, below the \"Logout\" button). If it is not Python 2, select Kernel → Change Kernel → Python 2 in the menu bar.\n",
    "\n",
    "Make sure that you fill any place that says \"YOUR CODE HERE\" or \"YOUR ANSWER HERE\", and that you erase the line \"raise NotImplementedError()\" in the code cells.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "1",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "\n",
    "# Introduction to Computation with IPython notebooks\n",
    "\n",
    "\n",
    "![ipython logo](files/IPy_header.png)\n",
    "![python logo](files/python-logo-generic.svg)\n",
    "\n",
    "### What is it exactly?\n",
    "\n",
    "An IPython Notebook is an interactive environment for writing and running Python code, it is a **complete and self-contained record of a computation** that can be converted to various formats and shared with others.\n",
    "\n",
    "It is particularly popular in the scientific computing community since it is a great tool for interactive data analysis and visualization.\n",
    "\n",
    "You can combine:\n",
    "* Live code\n",
    "* Interactive widgets\n",
    "* Plots\n",
    "* Narrative text\n",
    "* Equations\n",
    "* Images\n",
    "* Video\n",
    "\n",
    " \n",
    "### A bit more...\n",
    "\n",
    "The Ipython project has recently expanded in the latest version 3.0 to include other types of computational kernels such as R, Julia, C++ and Matlab. For more information check the links at the bottom of this Ipython Notebook.\n",
    "\n",
    "### Why should you use Python? (Why not C++, Matlab, etc.)\n",
    "\n",
    "* Python is great for rapid development -- Got an idea? Than making a fast script is super faster.\n",
    "* There is a library for everything!\n",
    "* Learning curve is very small compared to many other languages.\n",
    "\n",
    "more: http://www.quora.com/Why-should-we-go-for-Python-Is-it-more-advanced-than-C++-or-Java\n",
    "\n",
    "### Let's Start!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "2",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "# 1 IPython Basics\n",
    "## Running Code\n",
    "Run a code cell using `Shift-Enter` or pressing the <button class='btn btn-default btn-xs'> <i class=\"icon-play fa fa-play\"></i></button> button in the toolbar above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "3",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "Missing parentheses in call to 'print' (<ipython-input-1-085e5f98785e>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-1-085e5f98785e>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    print \"Hello World\"\u001b[0m\n\u001b[1;37m                      ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m Missing parentheses in call to 'print'\n"
     ]
    }
   ],
   "source": [
    "print \"Hello World\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "4",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2+2 #?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "5",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Iterative computing\n",
    "The kernel maintains the state of a notebook's computations.\n",
    "\n",
    "For example you can save a variable or the result of a computation..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "6",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "saved_var = \"How much is 2 x 4 ?\"\n",
    "saved_result = 2 * 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "7",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "and use later in another cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "8",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "How much is 2 x 4 ?\n",
      "8\n",
      "Magic!\n"
     ]
    }
   ],
   "source": [
    "print(saved_var)\n",
    "print(saved_result)\n",
    "print(\"Magic!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "9",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Stopping code\n",
    "Code is run in a separate process called the IPython Kernel.  The Kernel can be interrupted or restarted.  Try running the following cell and then hit the <button class='btn btn-default btn-xs'><i class='icon-stop fa fa-stop'></i></button> button in the toolbar above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "10",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "import time\n",
    "time.sleep(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "11",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Note: If the kernel is busy (it means it is running code) the dot in the upper right corner will be dark."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "12",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Restarting\n",
    "\n",
    "You can reset this state by restarting the kernel. This is done by clicking on the <button class='btn btn-default btn-xs'><i class='fa fa-repeat icon-repeat'></i></button> in the toolbar above.\n",
    "\n",
    "Note: Every time you re-start a kernel, you need to run again the cells to save the variables, functions or computation results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Do you want to explore more?\n",
    "\n",
    "Take a Tour!!\n",
    "\n",
    "Select Help  → User Interface Tour  in the menu bar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "13",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "# 2 Python: Some Modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "14",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## 2.1 Import modules\n",
    "The modules in python are collections of functions or libraries that we can use by importing them.\n",
    "We need to import them before calling one of their functions.\n",
    "\n",
    "Check out the following examples:\n",
    "\n",
    "(Remember: for importing the module, you will need to execute the cells)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import imageio # This module help us to modify and display images.\n",
    "\n",
    "# This command will allow us to display graphs and images inside of the notebook.\n",
    "%pylab inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random           # This module provides random functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example if we want to print a random number between 0 and 1, we could use a function called random inside of the random module in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-10-98e93cc2c7b2>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-10-98e93cc2c7b2>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    print random.random()   # This module has a function random, that returns a random number between 0 and 1\u001b[0m\n\u001b[1;37m               ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "print random.random()   # This module has a function random, that returns a random number between 0 and 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we call a function, we would like to avoid writing long words, so we can import them and given them a nickname."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np               #  The module numpy (we'll discuss it later) is going to be called np\n",
    "import matplotlib.pyplot as plt  #  This module is for making plots.\n",
    "import matplotlib.image as mpimg #  This module is going to use to create and manipulate images\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's take a closer look to this three modules."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Displaying images:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to \"read\" or \"charge\" an image stored in your computer we can use the module **matplotlib.image** (called **\"mpimg\"**). It will read an image of format (and extension) \".png\".\n",
    "\n",
    "Later, if we want to take a look of what we have store we can use the module **plt**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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Av77LxQEj/c0Xfwn7PucTGQykt8C2KwT4doYADRY1SGjDpM3ght3BZJzGC98yMg4xo1c2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a3c7d470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We'll read the image store in a file in the same directoru called \n",
    "# \"color_wheel.png\"\n",
    "# To do so, let's use the function  \"imread\" \n",
    "img=mpimg.imread('color_wheel.png')\n",
    "\n",
    "\n",
    "# Now, we shown the image store in the variable img, with the function\n",
    "# \"imshow\"\n",
    "plt.imshow(img)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How did we stored the image?** \n",
    "\n",
    "Let's find it out. \n",
    "\n",
    "## Quick exercise: \n",
    "Print the variable **img**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "99",
     "locked": false,
     "points": 2,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]\n",
      "\n",
      " [[ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]\n",
      "\n",
      " [[ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  [ 0.  0.  0.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]\n",
      "\n",
      " ..., \n",
      " [[ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]\n",
      "\n",
      " [[ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]\n",
      "\n",
      " [[ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  ..., \n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]\n",
      "  [ 1.  1.  1.  0.]]]\n"
     ]
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "print (img)\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this images is an array of many numbers (in this format with values between 0 and 1).\n",
    "\n",
    "We need to become experts on changing and manipulating images in Python, that is why we need to learn more about the different properties and ways to transform them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "20",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## 2.3 Arrays\n",
    "When we need to manipulate a list of integers or real numbers, we can use the Numpy module (want to know more? click on the image).\n",
    "\n",
    "[![](files/NumPy_logo.png)](http://www.numpy.org/)\n",
    "\n",
    "Let's check out some capabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### 1 Dimension arrays: Vectors "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "21",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
      " 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\n",
      " 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74\n",
      " 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99]\n"
     ]
    }
   ],
   "source": [
    "numbers = np.arange(0,100,1) # an array of number 0 to 100, in increments of 1, not including 100\n",
    "print(numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "22",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "what about empty arrays? Here we create a 5 x 1 vector of zeros:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "23",
     "locked": true,
     "solution": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.],\n",
       "       [ 0.],\n",
       "       [ 0.],\n",
       "       [ 0.],\n",
       "       [ 0.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_array = np.zeros((5,1))\n",
    "empty_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "24",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "we can change values using \\[ index \\]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "25",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.],\n",
       "       [  0.],\n",
       "       [ 10.],\n",
       "       [  0.],\n",
       "       [  0.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_array[2] = 10 # manipulate third spot.\n",
    "empty_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "26",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Note: Indexing in python starts with zero! (So the first element of an array is element 0). \n",
    "Now let's generate a list of random integers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "27",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 8, 4, 2, 7, 9, 1, 7, 2, 8, 6, 1, 2, 5, 5, 5, 9, 7, 1, 3, 1, 5, 5,\n",
       "       1, 2, 1, 9, 3, 2, 9, 6, 9, 5, 1, 6, 9, 5, 4, 4, 1, 9, 2, 5, 1, 9, 2,\n",
       "       4, 9, 2, 4, 2, 7, 7, 3, 9, 5, 5, 4, 3, 8, 9, 5, 3, 4, 3, 8, 7, 1, 7,\n",
       "       7, 8, 4, 7, 8, 5, 4, 5, 4, 5, 7, 1, 8, 9, 5, 1, 8, 4, 2, 2, 3, 3, 2,\n",
       "       8, 5, 9, 8, 1, 8, 1, 6])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integers = np.random.randint(low=1,high=10, size=100)\n",
    "integers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "Quick_exercise1_q",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Quick exercise: \n",
    "Now in the next box write code to print the first element of the list of random integers you obtained in the previous box:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "Quick_exercise1",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "\n",
    "### BEGIN SOLUTION\n",
    "print (integers[0])\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "28-7",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "### Array utilities with numpy\n",
    "and we have many useful utilities to operate on arrays... say you want to\n",
    "* **Sort:** the we use **np.sort(array)**\n",
    "* **Find Max, Min:** the we use **np.min(array)**, **np.max(array)**\n",
    "* **Find index of Max or Min:** the we use **np.argmin(array)**, **np.argmax(array)**\n",
    "* **Calculate mean or std :** you guessed it **np.mean(array)**,**np.std(array)**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "29",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sorted : [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4\n",
      " 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 7 7 7 7 7 7 7 7\n",
      " 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9]\n",
      "Max: 9 , Min: 1\n",
      "Max at: 5 , Min at: 0\n",
      "Mean: 4.86 , Std: 2.72036762222\n"
     ]
    }
   ],
   "source": [
    "## For example:\n",
    "\n",
    "print(\"Sorted :\",np.sort(integers))\n",
    "print(\"Max:\",np.max(integers),\", Min:\",np.min(integers))\n",
    "print(\"Max at:\",np.argmax(integers),\", Min at:\",np.argmin(integers))\n",
    "print(\"Mean:\",np.mean(integers),\", Std:\",np.std(integers))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "30",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "### 2 Dimensions: Matrices\n",
    "\n",
    "You can use numpy to create matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "30-2",
     "locked": true,
     "solution": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]\n",
      " [ 1.  1.  1.]\n",
      " [ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "my_matrix = np.ones((5,3))  # A matrix of 5 * 3\n",
    "print(my_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "30-3",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "As before, we can select a certain entry and modify it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "30-4",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.   1.   1.]\n",
      " [  1.   1.  10.]\n",
      " [  1.   1.   1.]\n",
      " [  1.   1.   1.]\n",
      " [  1.   1.   1.]]\n"
     ]
    }
   ],
   "source": [
    "my_matrix[1,2] = 10\n",
    "print(my_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "30-5",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Or we can make numerical operations over it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "30-6",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  2.   2.   2.]\n",
      " [  2.   2.  20.]\n",
      " [  2.   2.   2.]\n",
      " [  2.   2.   2.]\n",
      " [  2.   2.   2.]]\n"
     ]
    }
   ],
   "source": [
    "my_newmatrix = 2*my_matrix\n",
    "print(my_newmatrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make it more interesting, let's modify slices of this matrix (certain row or column):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[   1.    1.    1.]\n",
      " [   2.    2.   20.]\n",
      " [   2.    2.    2.]\n",
      " [   2.    2.    2.]\n",
      " [ 100.  100.  100.]]\n"
     ]
    }
   ],
   "source": [
    "#  The notation [0,:] means \"the row 0 and all the columns\"\n",
    "my_newmatrix[0,:] = np.ones(3)      # we are filling the first row with ones\n",
    "my_newmatrix[4,:] = 100*np.ones(3)  # we are filling the last row with 100.\n",
    "\n",
    "print(my_newmatrix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first row:\n",
      "[ 1.  1.  1.]\n",
      "The first column:\n",
      "[   1.    2.    2.    2.  100.]\n"
     ]
    }
   ],
   "source": [
    "# For printing the first row we'll use:\n",
    "print('The first row:')\n",
    "print(my_newmatrix[0,:]) \n",
    "\n",
    "# For printing the last column we'll use:\n",
    "print('The first column:')\n",
    "print(my_newmatrix[:,0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick exercise: \n",
    "1. Build a 2-dimensional array of shape 5 x 5 of zeros.\n",
    "2. Fill the first column with 35.\n",
    "3. Print it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "444",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "Missing parentheses in call to 'print' (<ipython-input-26-53235fe8c57b>, line 4)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-26-53235fe8c57b>\"\u001b[1;36m, line \u001b[1;32m4\u001b[0m\n\u001b[1;33m    print twodarray\u001b[0m\n\u001b[1;37m                  ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m Missing parentheses in call to 'print'\n"
     ]
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "twodarray = np.zeros((5,5))\n",
    "twodarray[:,0] = 35*np.ones(5)\n",
    "print twodarray\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3 Dimensions: Cubes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A 3 dimentional array (M x N x P) can be imaging as a cube of data, or as \"P\" matrices of shapes M x N (M rows y N columns). \n",
    "\n",
    "Some images are stored as arrays of 3 dimensions, each of these matrices are dedicated for a color channel (Red, Green and Blue or RGB)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 3 dimensions\n",
    "empty_3D = np.zeros((2, 4, 3)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imagine this as an array with 3 matrices, of 2 X 4. \n",
    "\n",
    "We can fill each of this matrices in one step **(Note: This will be very usefule when we where using images).**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is the first matrix of our array 3D\n",
      "[[ 1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.]]\n",
      "This is the second matrix of our array 3D\n",
      "[[ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "empty_3D[:,:,0] = np.ones((2,4)) # A single matrix with 1's, two rows and 4 columns\n",
    "\n",
    "print(\"This is the first matrix of our array 3D\")\n",
    "print(empty_3D[:,:,0]) \n",
    "\n",
    "print(\"This is the second matrix of our array 3D\")\n",
    "print(empty_3D[:,:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To figure it out the dimensions of an array, we use **shape**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The dimensions of our array are:\n",
      "(2, 4, 3)\n"
     ]
    }
   ],
   "source": [
    "print(\"The dimensions of our array are:\")\n",
    "print(empty_3D.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick exercise: \n",
    "1. Build a 3-Dimensitonal array with a shape of 4 x 5 x 3, full of zeros. \n",
    "2. Fill the first matrix ([: , : ,0] with 1's and the third matrix with 4´s. \n",
    "3. Print the matrixes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "90",
     "locked": false,
     "points": 3,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.]]\n",
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n",
      "[[ 4.  4.  4.  4.  4.]\n",
      " [ 4.  4.  4.  4.  4.]\n",
      " [ 4.  4.  4.  4.  4.]\n",
      " [ 4.  4.  4.  4.  4.]]\n"
     ]
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "matrix_3D = np.zeros((4,5,3))\n",
    "matrix_3D[:,:,0] = np.ones((4,5))\n",
    "matrix_3D[:,:,2] = 4*np.ones((4,5))\n",
    "\n",
    "print(matrix_3D[:,:,0])\n",
    "print(matrix_3D[:,:,1])\n",
    "print(matrix_3D[:,:,2])\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can always change the shape of our array with the function reshape:\n",
    "    \n",
    "For example, a matrix of 2 x 3 can be reshaped in a 1-Dimentional array of shape 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is a 2 x 3 matrix\n",
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n",
      "This is an array with 6 elements\n",
      "[ 1.  1.  1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "matrix_2D = np.ones((2,3))\n",
    "print('This is a 2 x 3 matrix')\n",
    "print(matrix_2D)\n",
    "\n",
    "array_1D = np.reshape(matrix_2D, 6)\n",
    "print('This is an array with 6 elements')\n",
    "print(array_1D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "31-3",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "*** An small review of Numpy.arrays:***\n",
    "* You can store numbers of a homogeneous type (all the entries must be either all integer numbers or all real numbers).\n",
    "* You can store arrays of multiple dimensions, for example matrices (this will be very useful for linear algebra calculations).\n",
    "* You can use several functions to manipulate them (for example: sort, multiply, linear algebra functions).\n",
    "* Generally they are used for numerical calculations, because numpy functions generally are optimized to have good performance (an efficient way to use time and memory of your computer). \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's return to our image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 Understanding structure of an image "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's read the image again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mys4EcGcI4UwiOh3AQSGEt0RD44cAnIKZ2vAZAMfqSKV5gpde/v1Dsf3Qu0RA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a48c8390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img=mpimg.imread('color_wheel.png')\n",
    "plt.imshow(img)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick exercise: \n",
    "\n",
    "What is the shape of your **img** array?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "990",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(730, 730, 4)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "img.shape\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick question: \n",
    "\n",
    "How many channels does our image have? \n",
    "This as some matrices (2-D) inside of an 3-Dimentional array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "1900",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "4\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Channels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ths digital images generally have 3 channels, Red, Green, and Blue. The first 3 matrices of our variable **img**, are\n",
    "the Red, Green and Blue channels, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "red_channel = img[:,:,0]\n",
    "green_channel = img[:,:,1]\n",
    "blue_channel = img[:,:,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the 4th channel? This channel is called alpha and it controls the transparency. We'll ignore it for the moment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha_channel = img[:,:,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's say we want to see only the red channel. We need to set all the other channels (green and blue) to zero and fill the red and alpha channels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0ETk7mEsIuPKonbIUPgNb3CYUyJLOFRAugVAqoSA09yqu0HIJgbhCwSUoGgJS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\nhEJAQEAR/j8uRvU1qpfMTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a4fde4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We define an empty array with the same dimensions of the image.\n",
    "img_red = np.zeros((730, 730, 4))\n",
    "\n",
    "# Let's fill the the red channel of img_red with the red channel of img\n",
    "img_red[:,:,0] = red_channel\n",
    "\n",
    "# Also, we are going to fix the alpha channel with same value of img \n",
    "img_red[:,:,3] = alpha_channel\n",
    "\n",
    "plt.imshow(img_red)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick exercise: \n",
    "Now it is your turn. Print just the blue and green channels, as we did for the red one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "876",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HPFd2M4qFdE4grT/LOYUkyKLMLIkgpCxD5XemCQk3sHnnZtxwe35/IG9a86FHrjb4kJXp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\ngFjB1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a58ce668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Write the code for your green image here\n",
    "### BEGIN SOLUTION\n",
    "img_green = np.zeros((730, 730, 4))\n",
    "img_green[:,:,1] = green_channel\n",
    "img_green[:,:,3] = alpha_channel\n",
    "plt.imshow(img_green)\n",
    "plt.show()\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "kl",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ox7DF1+Vs2kZRYihLGjYhdmmBPrKIJYfQ+1/2Oenwle9Dmbrd2LVrlzM96O2D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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a59394e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Write the code for your green image here\n",
    "### BEGIN SOLUTION\n",
    "img_blue= np.zeros((730, 730, 4))\n",
    "img_blue[:,:,2] = blue_channel\n",
    "img_blue[:,:,3] = alpha_channel\n",
    "plt.imshow(img_blue)\n",
    "plt.show()\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's return to review some Python Basics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "31-4",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "# Python Basics.\n",
    "\n",
    "## For loops\n",
    "A for loop goes over each element of a list, **note the spacing/indentation** after starting the for loop!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "32",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "taco\n",
      "pastor\n",
      "carnitas\n",
      "alambre\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "a_list = [\"taco\",\"pastor\",\"carnitas\",\"alambre\"]\n",
    "\n",
    "for i in a_list:\n",
    "    print(i)\n",
    "\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "33",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "You can write a nested loop, for example a double loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "34",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "taco taco\n",
      "taco pastor\n",
      "taco carnitas\n",
      "taco alambre\n",
      "pastor taco\n",
      "pastor pastor\n",
      "pastor carnitas\n",
      "pastor alambre\n",
      "carnitas taco\n",
      "carnitas pastor\n",
      "carnitas carnitas\n",
      "carnitas alambre\n",
      "alambre taco\n",
      "alambre pastor\n",
      "alambre carnitas\n",
      "alambre alambre\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "for i in a_list:\n",
    "    for j in a_list:\n",
    "        print(i,j)\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "35",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "or a for loop running along with the index:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "36",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 taco\n",
      "1 pastor\n",
      "2 carnitas\n",
      "3 alambre\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "for index,item in enumerate(a_list):\n",
    "    print(index,item)\n",
    "\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "37",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "**What if you want to sample randomly from this list?**\n",
    "\n",
    "Module *random* that we imported a few cells above comes to rescue! Re-run the cell many times to check if they are random.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "38",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'rnd' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-43-d3e7e7b8067b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mrnd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msample\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumbers\u001b[0m\u001b[1;33m,\u001b[0m  \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# select 1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'rnd' is not defined"
     ]
    }
   ],
   "source": [
    "rnd.sample(numbers,  1) # select 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'rnd' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-44-61459e7ebf74>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mrnd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msample\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumbers\u001b[0m\u001b[1;33m,\u001b[0m  \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'rnd' is not defined"
     ]
    }
   ],
   "source": [
    "rnd.sample(numbers,  3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39_1",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "### What if you want to do a for loop over a series of numbers?\n",
    "We can use the for loops to go over a series of consecutive numbers with the use of range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39_2",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "for i in range(2,5):  # Consecutive numbers from 2 to 5 (not including 5)\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39_3",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Or we can use the indexes to do calculations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39_4",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "res = 1\n",
    "for i in range(1,9):\n",
    "    res = res*i\n",
    "print(res)             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39-5",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "The indexes are also important to fill a vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "39-6",
     "locked": true,
     "solution": false
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "my_vector = np.zeros((3,1))\n",
    "for i in range(3):\n",
    "    my_vector[i] = i\n",
    "print(my_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "Quick_exercise2_q",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Quick exercise: \n",
    "Starting from an empty matrix of size 3x3, use a double loop to get the following matrix and print it:\n",
    "```\n",
    "[[ 0.  1.  2.]\n",
    " [ 3.  4.  5.]\n",
    " [ 6.  7.  8.]]\n",
    " ```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "Quick_exercise2",
     "locked": false,
     "points": 2,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "my_array = np.zeros((3,3))\n",
    "### BEGIN SOLUTION\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        my_array[i,j] = i*3 + j\n",
    "### END SOLUTION\n",
    "print(my_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "40",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Help!\n",
    "\n",
    "*** What if you don't know how to use a function or all the available functions of a module? ***\n",
    "\n",
    "The help function is the solution :)\n",
    "\n",
    "Let's say we need to print, from the largest to the smallest, odd numbers between 11 to 2, and we know that the range function returns series. Let's see all of its capabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "40-2",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "help(range)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "40-3",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Hence we can write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "40-4",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "for i in range(11,2,-2):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, that we know how to use these two control structures (for loops and conditionals).\n",
    "Let's use this for manipulating our image.\n",
    "\n",
    "Let's change to black the pixels with a red value bigger than 0.99."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First let's make a copy of the red channel.\n",
    "red_channel_copy = np.copy(img[:,:,0])\n",
    "\n",
    "# and we made a copy of the image that we'll manipulate\n",
    "img_copy = np.copy(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's use what we've learned, let's use a nested for loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dim1 = img.shape[0]\n",
    "dim2 = img.shape[1]\n",
    "for ind1 in range(dim1): # We iterate over all the rows\n",
    "    for ind2 in range(dim2): # and inside each row, we iterate the columns\n",
    "        if red_channel_copy[ind1, ind2] > 0.99: # if the pixes satifies the condition, \n",
    "            img_copy[ind1, ind2, 0] = 0 # We change it to black (R=G=B=0)\n",
    "            img_copy[ind1, ind2, 1] = 0\n",
    "            img_copy[ind1, ind2, 2] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check out the identation after the conditional if."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The original matrix\n",
    "plt.imshow(img)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now, we display the modified image.\n",
    "# Check that part of the yellow/orange fraction also satisfies the condition.\n",
    "plt.imshow(img_copy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick exercise: \n",
    "Now it is your turn, find the pixels where the blue channel has a value bigger than 0.8.\n",
    "And change those pixels to white.\n",
    "\n",
    "**Note: Remember to make a copy of the original image**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "00990",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'img' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-9-433451a7c149>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m### BEGIN SOLUTION\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;31m# First let's make a copy of the red channel.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mblue_channel_copy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mimg\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# and we made a copy of the image that we'll manipulate\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'img' is not defined"
     ]
    }
   ],
   "source": [
    "### BEGIN SOLUTION\n",
    "# First let's make a copy of the red channel.\n",
    "blue_channel_copy = np.copy(img[:,:,2])\n",
    "\n",
    "# and we made a copy of the image that we'll manipulate\n",
    "img_copy = np.copy(img)\n",
    "\n",
    "dim1 = img.shape[0]\n",
    "dim2 = img.shape[1]\n",
    "for ind1 in range(dim1): # We iterate over all the rows\n",
    "    for ind2 in range(dim2): # and inside each row, we iterate the columns\n",
    "        if blue_channel_copy[ind1, ind2] > 0.99: # if the pixes satifies the condition, \n",
    "            img_copy[ind1, ind2, 0] = 1 # We change it to white (R=G=B=0)\n",
    "            img_copy[ind1, ind2, 1] = 1\n",
    "            img_copy[ind1, ind2, 2] = 1\n",
    "\n",
    "plt.imshow(img_copy)\n",
    "plt.show()\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "41",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Functions\n",
    "\n",
    "Functions are named sections of a program that perform specific tasks. In a computational sense a function could either receive an input and *return* an output (in this sense it would be like a function in a more mathematical sense), but it can also be a routine, that just performs certain tasks without producing any output. \n",
    "\n",
    "This is an example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This function let us visualize an image in a \"nicer\" way.\n",
    "def visualize_image(image):                   # use def to define the function\n",
    "    '''This function displays an image store in the variable image\n",
    "    INPUT:\n",
    "        image -> a 3dimentional array\n",
    "    OUTPUT:\n",
    "        nothing\n",
    "    '''\n",
    "    fig = plt.figure(figsize=(7,7))            # take note of the indentation!!!\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.imshow(image, interpolation=\"gaussian\")\n",
    "    ax.set_axis_bgcolor('k')\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    plt.show()\n",
    "    return\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Now that we have that function, we can use it.\n",
    "visualize_image(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dictionaries \n",
    "\n",
    "Just like a list or an array, a dictionary is a collection of many values. But unlike indexes for lists o arrays, indexes of dictionaries, we can use many different data types, not just integers. Indexes of dictionaries are called keys, and a key with its associated value is called a key-value pair. Unlike lists, items in dictionaries are unordered. The first item in a list named \"colors\" would be \"colors[0]\". There is no \"first\" item in a dictionary. \n",
    "\n",
    "Even though dictionaries are not ordered, the fact that you can have arbitrary values for the keys allows you to organize your data in powerful ways. Say you wanted your program to store data about your friend's telephone numbers. You can use a dictionary with the names as keys and the numbers as values. \n",
    "\n",
    "The following is an example of a dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Say you want to create a new image from scratch, you want to define the channels and their entries. Yuo can use a\n",
    "dictionary to store the informtarion regarding this new image. You can then call every channel by their key value\n",
    "(name) and display its values (numeric entries).\n",
    "\"\"\"\n",
    "\n",
    "img2_channels = {\"red\": np.zeros((1,3)), \"blue\": np.ones((1,3)), \"green\": np.zeros((1,3))}\n",
    "\n",
    "#In the next for loop, we call the \"items()\" method dictionaries to print the keys and the values of the dictionary.\n",
    "\n",
    "for i in img2_channels.items():\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's analyze a more challenging example. We are going to create a dictionary that is going to store the \"RGB\" vector's numeric information. We will use this dictionary to convert a list of colors in text format, into a image! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First we create the dictionary with the rgb vectors\n",
    "rgb_vectors = {\"red\": np.array([1,0,0]), \"green\": np.array([0,1,0]), \"blue\": np.array([0,0,1])}\n",
    "\n",
    "# In the next line we create nested list that resembles a matrix whose entries a the colors in string format\n",
    "your_image_keys = [[\"blue\", \"blue\", \"red\"], [\"green\", \"red\", \"red\"], [\"green\", \"blue\", \"green\"]]\n",
    "\n",
    "# Here we initialize the matrix that is going to be converted into your image (with all the entries as zeroes)\n",
    "matrix_your_image = np.zeros((3,3,3))\n",
    "\n",
    "#Let's take a look at all the elements that we just created\n",
    "\n",
    "print(rgb_vectors)\n",
    "print(\"\\n\")\n",
    "print(your_image_keys)\n",
    "print(\"\\n\")\n",
    "print(matrix_your_image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Now we make use of a nested for loop in order replace the entries of your numeric matrix by the corresponding rgb \n",
    "vectors. In order to do thos, we first iterate over the elements of your nested list of colors. Then we map that\n",
    "information into our dictionary and replace every element of the null matrix by every rgb vector of the dictionary. \n",
    "\"\"\"\n",
    "\n",
    "for i,row in enumerate(your_image_keys): # Iterate over every row of the nested list\n",
    "    for j,element in enumerate(row): # Second iteration to scan every element of every row\n",
    "        color = str(element) # We take the string oof every element of the list \n",
    "        matrix_your_image[i,j,:] = rgb_vectors[color] # The dictionary take every string and pass that info as a vector\n",
    "        \n",
    "print(matrix_your_image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finally, we create our image making use of our past function to map matrices into images!\n",
    "visualize_image(matrix_your_image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "42",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## <i class=\"fa fa-line-chart\"></i> Basic Plotting\n",
    "[![](files/matplotlib_logo.png)](http://matplotlib.org/)\n",
    "\n",
    "First we load the module and inline plotting (want to know more? click on the image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "43",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt # import module\n",
    "             \n",
    "# make plots appear on your ipython notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "44",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Now we can make simple plots via the following syntax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "45",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gzIJvZrOB+rt/CnDALc65v2UqmGRHtWowaJB/W7ECnnrKt2cKC/2eN7Vr+7eq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\nvohIjlDBFxHJEf8PJfVoa7XRzOUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a595b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-np.pi, np.pi, 0.1) # array between -pi and pi, in steps of 0.1\n",
    "y = np.sin(x)                     # sin evaluated on x\n",
    "\n",
    "plt.plot(x,y,label='Sin')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "45-5",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "we can even add more context to this plot with more functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "46",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+8x/Yf//QxbTzzrGjEcl+ShCRnXwy7LAD3HBD7EjymzscfXQYlO7VK3Y0IrlB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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a1b7a2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y,label='Sin')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.title('Sine plot')\n",
    "plt.autoscale(tight=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "47",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "### <i class=\"fa fa-line-chart\"></i> Histograms\n",
    "It's as simple as writing \"histogram\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "48",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EgS5JjTDQJakRBrokNcJAl6RGGOiS1Ij/B/KQccdCPnNQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a5851128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integers = np.random.randint(low=0,high=10, size=100)\n",
    "plt.hist(integers)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check out the distribution of values of the red channel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(730, 730)\n"
     ]
    }
   ],
   "source": [
    "reds = img[:,:,0]    ## As before we are grabing just one chanel\n",
    "print (reds.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Converting matrix to array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(532900,)\n"
     ]
    }
   ],
   "source": [
    "reds_array = np.reshape(reds, (1, 730*730)) \n",
    "reds_array = reds_array[0,:]\n",
    "print (reds_array.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e0a5835208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(reds_array, 10)  ## Plotting the histrogram of intesities, with 10 bins\n",
    "plt.title('Frequency of intensities of red channel in 10 intervals')\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Intensity')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "49",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "### When plotting, don't forget to...\n",
    "\n",
    "* Label your axis.\n",
    "* Title your graph.\n",
    "* If plotting many items, use a legend.\n",
    "* Plot your data in an appropriate range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "51",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "# <i class=\"fa fa-bug\"></i> Debugging\n",
    "\n",
    "\n",
    "People make mistakes when they write computer programs. An error in a program that causes it to produce an incorrect or unexpected result is commonly called a *bug*, and the process of preventing and correcting bugs is called *debugging*. Programming bugs can be classified in different ways, but here we will just make a difference between *source code* bugs and *design* bugs. We will use the term \"source code bugs\" for those errors which are caused by either bad syntax or misinterpretation of the structures in the program, e.g., bad indentation in a for loop or trying to take the square root of a character type. Source code errors frequently produce error messages which help us to track them. By \"design errors,\" we will make reference to logic mistakes in the program. Specifically to those occasions in which your code runs and does not produce error messages but it does not do what it is supposed to do. In those cases you will have to look at the program and try to find what you are missing or doing wrong. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "bugs",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## Before you venture into this brave new world of code\n",
    "### Check the following flow chart that might help\n",
    " **credits to: http://pythonforbiologists.com/ **\n",
    " \n",
    " ![](files/error_flowchart.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "87",
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "## <i class=\"fa fa-book\"></i> Further reading:\n",
    "\n",
    "### Installing Ipython on your computer:\n",
    "* http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/PythonInstallation.ipynb\n",
    " \n",
    "### Squeezing all the juice from Ipython\n",
    "* https://github.com/odewahn/ipynb-examples\n",
    "* Ipython minibook: https://github.com/rossant/ipython-minibook http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/00_Lesson00_QuickPythonIntro.ipynb\n",
    " \n",
    "### Scientific computing con Python:\n",
    "* http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/PythonForScientificComputing.ipynb\n",
    "* http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-1-Introduction-to-Python-Programming.ipynb\n",
    "\n",
    "### A gallery of interesting IPython Notebooks\n",
    "* https://github.com/ipython/ipython/wiki/A-gallery-of-interesting-IPython-Notebooks#introductory-tutorials\n",
    "\n",
    "### Kernels\n",
    "* Python(https://github.com/ipython/ipython)\n",
    "* Julia (https://github.com/JuliaLang/IJulia.jl)\n",
    "* R (https://github.com/takluyver/IRkernel)\n",
    "* Ruby (https://github.com/minrk/iruby)\n",
    "* Haskell (https://github.com/gibiansky/IHaskell)\n",
    "* Scala (https://github.com/Bridgewater/scala-notebook)\n",
    "* node.js (https://gist.github.com/Carreau/4279371)\n",
    "* Go (https://github.com/takluyver/igo)"
   ]
  },
  {
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