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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compatibility with Python 3\n",
      "from __future__ import print_function  # print('me') instead of print 'me'\n",
      "from __future__ import division  # 1/2 = 0.5, not 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Show figures inside the notebook\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we will work with a 3D brain image.\n",
      "\n",
      "Like the camera image in [the camera notebook](camera.ipynb), the pixel data for the 3D image is in a text file called `anatomical.txt`.  I happen to know this image has is length 32 on the third dimension, but I don't know what the size of the first two dimensions are.\n",
      "\n",
      "So, I know the image is of shape (`I`, `J`, 32), but I don't know what `I` and `J` are.\n",
      "\n",
      "Here are the first four lines of `anatomical.txt`. \n",
      "\n",
      "```\n",
      "0.0000\n",
      "0.0000\n",
      "0.0000\n",
      "0.0000\n",
      "```\n",
      "\n",
      "So the data is in the same floating point text format as the camera picture pixel data.\n",
      "\n",
      "Real all the lines of the file into a list of float values, as before."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How many pixel values does this file contain?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When I have my image array correctly shaped, then, if I take a slice over the third dimension:\n",
      "\n",
      "```\n",
      "slice_on_third = image_array[:, :, 0]\n",
      "```\n",
      "\n",
      "`slice_on_third` will be shape `(I, J)` (the size of the first two dimensions).\n",
      "\n",
      "\n",
      "So, how many pixel values does a slice in the third dimension contain - given that we know the third dimension is length 32?  Put another way, what is the value for `I * J`?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Find the size of a slice over the third dimension\n",
      "# P = ?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Call `P` the number of values per slice on the third dimension (so `P == I * J` where we don't yet know `I` or `J`).\n",
      "\n",
      "Is this slice over the third dimension square (does `I == J`)?\n",
      "\n",
      "We need to find the values for `I` and `J`.\n",
      "\n",
      "Find candidates for `I` by using the modulus operator (`%`) to find a few numbers between 120 and 200 that divide exactly into the slice size `P`.  Hint: the first value will be 120."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These numbers are candidates for `I` - the first number in the pair `(I, J)`.  We now need to find the corresponding `J` for each candidate for `I`.\n",
      "\n",
      "Use the integer division operator (`//`) to get a list of pairs of numbers `I` and `J` such that `I * J == P`.  Hint: the first pair of `I, J` is (120, 221)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The full image shape will be three values, with one of these `(I, J)` pairs followed by 32.  For example, the correct shape might be (120, 221 , 32) (it isn't!).  Try reshaping the pixel data with a few of the `(I, J, 32)` candidates to see which one is likely to be right.  You might want to plot a slice over the third dimension to see how it looks."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
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