{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "/* \n",
       "* @Author: paul\n",
       "* @Date:   2016-02-25 17:35:32\n",
       "* @Last Modified by:   paul\n",
       "* @Last Modified time: 2016-02-25 17:45:54\n",
       "*/\n",
       "<link href='http://fonts.googleapis.com/css?family=Open+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Arvo:400,700,400italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=PT+Mono' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Shadows+Into+Light' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Nixie+One' rel='stylesheet' type='text/css'>\n",
       "<style>\n",
       "\n",
       "@font-face {\n",
       "    font-family: \"Computer Modern\";\n",
       "    src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "}\n",
       "\n",
       "#notebook_panel { /* main background */\n",
       "    background: rgb(245,245,245);\n",
       "}\n",
       "\n",
       "div.cell { /* set cell width */\n",
       "    width: 1000px;\n",
       "}\n",
       "\n",
       "div #notebook { /* centre the content */\n",
       "    background: #fff; /* white background for content */\n",
       "    width: 1200px;\n",
       "    margin: auto;\n",
       "    padding-left: 0em;\n",
       "}\n",
       "\n",
       "#notebook li { /* More space between bullet points */\n",
       "margin-top:0.8em;\n",
       "}\n",
       "\n",
       "/* draw border around running cells */\n",
       "div.cell.border-box-sizing.code_cell.running { \n",
       "    border: 1px solid #111;\n",
       "}\n",
       "\n",
       "/* Put a solid color box around each cell and its output, visually linking them*/\n",
       "div.cell.code_cell {\n",
       "    background-color: rgb(256,256,256); \n",
       "    border-radius: 0px; \n",
       "    padding: 0.5em;\n",
       "    margin-left:1em;\n",
       "    margin-top: 1em;\n",
       "}\n",
       "\n",
       "div.text_cell_render{\n",
       "    font-family: 'Open Sans' sans-serif;\n",
       "    line-height: 140%;\n",
       "    font-size: 125%;\n",
       "    font-weight: 400;\n",
       "    width:900px;\n",
       "    margin-left:auto;\n",
       "    margin-right:auto;\n",
       "}\n",
       "\n",
       "\n",
       "/* Formatting for header cells */\n",
       ".text_cell_render h1 {\n",
       "    font-family: 'Arvo', serif;\n",
       "    font-style:regular;\n",
       "    font-weight: 400;    \n",
       "    font-size: 45pt;\n",
       "    line-height: 100%;\n",
       "    color: rgb(0,51,102);\n",
       "    margin-bottom: 0.5em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}\t\n",
       ".text_cell_render h2 {\n",
       "    font-family: 'Arvo', serif;\n",
       "    font-weight: 400;\n",
       "    font-size: 30pt;\n",
       "    line-height: 100%;\n",
       "    color: rgb(0,51,102);\n",
       "    margin-bottom: 0.1em;\n",
       "    margin-top: 0.3em;\n",
       "    display: block;\n",
       "}\t\n",
       "\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Arvo', serif;\n",
       "    margin-top:16px;\n",
       "\tfont-size: 22pt;\n",
       "    font-weight: 600;\n",
       "    margin-bottom: 3px;\n",
       "    font-style: regular;\n",
       "    color: rgb(102,102,0);\n",
       "}\n",
       "\n",
       ".text_cell_render h4 {    /*Use this for captions*/\n",
       "    font-family: 'Arvo', serif;\n",
       "    font-size: 14pt;\n",
       "    text-align: center;\n",
       "    margin-top: 0em;\n",
       "    margin-bottom: 2em;\n",
       "    font-style: regular;\n",
       "}\n",
       "\n",
       ".text_cell_render h5 {  /*Use this for small titles*/\n",
       "    font-family: 'Arvo', sans-serif;\n",
       "    font-weight: 400;\n",
       "    font-size: 16pt;\n",
       "    color: rgb(163,0,0);\n",
       "    font-style: italic;\n",
       "    margin-bottom: .1em;\n",
       "    margin-top: 0.8em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h6 { /*use this for copyright note*/\n",
       "    font-family: 'PT Mono', sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 9pt;\n",
       "    line-height: 100%;\n",
       "    color: grey;\n",
       "    margin-bottom: 1px;\n",
       "    margin-top: 1px;\n",
       "}\n",
       "\n",
       ".CodeMirror{\n",
       "        font-family: \"PT Mono\";\n",
       "        font-size: 90%;\n",
       "}\n",
       "\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"],\n",
       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Notebook Styling\n",
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    sheet = '../css/custom.css'\n",
    "    styles = open(sheet, \"r\").read() \n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Structuring Data Exercise: Numpy dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before looking at Python Classes and Objects, we motivate the need for structured data using some simple image data. In this exercise you will be prompted to fill in sections using what you now know about structuring data with dtypes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "# The image pixel size - constant for all images in this exercise\n",
    "Nx = Ny = 72"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Portable Greymap ( `.pgm`) Format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You have been provided with some image files i.e. `img1, .. img4` in the `data` directory in *portable greymap* (.pgm) format. Although admittedly a primitive image format, `.pgm` files are simple to manipulate as they contain only one pixel grey value per $x, y$ pixel in the image: the scale runs from 0 (black) to 255 (white). This represents a common task in scientific computing where you must read in some field data on a grid of points. **You are provided with the code to read and reshape this data from a file!**\n",
    "\n",
    "Here's a demonstration of a greymap image that might be stored in `.pgm` format using a simple gradient of white to black - it is displayed here using a contour plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 255.          253.20422535  251.4084507  ...,  131.0915493   129.29577465\n",
      "   127.5       ]\n",
      " [ 253.20422535  251.4084507   249.61267606 ...,  129.29577465  127.5\n",
      "   125.70422535]\n",
      " [ 251.4084507   249.61267606  247.81690141 ...,  127.5         125.70422535\n",
      "   123.9084507 ]\n",
      " ..., \n",
      " [ 131.0915493   129.29577465  127.5        ...,    7.18309859\n",
      "     5.38732394    3.5915493 ]\n",
      " [ 129.29577465  127.5         125.70422535 ...,    5.38732394    3.5915493\n",
      "     1.79577465]\n",
      " [ 127.5         125.70422535  123.9084507  ...,    3.5915493     1.79577465\n",
      "     0.        ]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f0054993b00>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rVMUiAYKihC1BUcbWsIpGAgRFCVuCooytpSoeCRAUJWwJijK2FqsTSICgKGFLUJSxNVhn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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f001834d390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nx = 72\n",
    "Ny = 72\n",
    "img_x = np.linspace(1, 0, Nx)\n",
    "img_y = np.linspace(1, 0, Ny)\n",
    "X, Y = np.meshgrid(img_x, img_y)\n",
    "\n",
    "# Generate the gradient image - this could be stored in .pgm format!\n",
    "img_z = (X+Y) * 255*0.5\n",
    "print(img_z)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.contourf(img_x, img_y, img_z, 20, cmap=cm.Greys_r)\n",
    "ax.set_xlabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task Breakdown\n",
    "\n",
    "Create a structured array of images in the next cell: for this we will need to define the `dtype` for the array. This should involve passing a list of length 3 as an argument to `np.dtype` defining the 3 data types required by elements (images) in the array:\n",
    "\n",
    "1. An $x$ component - The array of regularly spaced pixels x values from 1 to 0 (image colour values in pgm files start from top right pixel). Array of type float64, length $Nx$.\n",
    "\n",
    "2. A $y$ component - similar to $x$, but with length $Ny$\n",
    "\n",
    "3. A $z$ component - the array of grey levels for each pixel in the image. Array of float64, shape ($Nx, Ny$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create the dtype\n",
    "dt = np.dtype([('x', np.float64, (Nx)), ('y', np.float64, (Ny)), \n",
    "               ('z', np.float64, (Nx,Ny))])\n",
    "\n",
    "# create a new zero'ed array of length 4 using your dtype\n",
    "imgs = np.zeros(4, dtype=dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create the normalised x and y values between 1 and 0 - these are the same for each image.\n",
    "\n",
    "*(Hint: Numpy linspace works backwards too ....)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xs = np.linspace(1., 0, Nx)\n",
    "ys = np.linspace(1., 0., Ny)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in the exercise in the next section to input $xs$ and $ys$ data. Also look at the format of the code: hopefully this is more readable and neater than creating separate unstructured arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['data/img1.pgm', 'data/img2.pgm', 'data/img3.pgm', 'data/img4.pgm']\n"
     ]
    },
    {
     "data": {
      "image/png": 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qfh/A1SLSi0kFXWsMXbMXoM1tJ0YkDgJ4wXp+fvFa1jEXPMcQQjoIE5eEkExy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\n9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0018358278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0018358128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9QC2JxElxy7+QMtvDDPVHdIdaEgkRsidICpRNebqGGRob0R0qEolRddhRZNb3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00162513c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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exGUde28HngLuWmdSqonNSflPs/7EZZ3rfCfwxXnZHwG+Bkx6bO8fAx+Z/32W\nIzf+1T2oHz8FfK3kvcZtr3VPwgc2+aqOvcCHgVcDfzLvmV909/M9t/nER1ZuZGpAvXpx3cy+ADwJ\nvARcdfdpX+0FdoE/j4YbP+ju31uHvQEz+2vgbcBrzOzfgY9wJHILtz1NphJCZNEqUCFEFomEECKL\nREIIkUUiIYTIIpEQQmSRSAghskgkhBBZJBJCiCz/D59LSOaL1PsPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f001618a710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The image file names\n",
    "names = ['img1.pgm', 'img2.pgm', 'img3.pgm', 'img4.pgm']\n",
    "files = [os.path.join('data', name) for name in names]\n",
    "\n",
    "print(files)\n",
    "\n",
    "for i, file in enumerate(files):\n",
    "    # This reads in the color data (top 4 rows are headings)\n",
    "    imgs['z'][i] = np.loadtxt(file, skiprows=4).reshape(Nx, Ny)\n",
    "    \n",
    "    # Input data in to the structured format\n",
    "    (imgs['x'][i], imgs['y'][i]) = (xs, ys)\n",
    "\n",
    "# A typical program would do something clever with the data here\n",
    "\n",
    "# Visualisation: Notice we can iterate over imgs directly\n",
    "for img in imgs:\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, aspect='equal')\n",
    "    ax.contourf(img['x'], img['y'], img['z'], cmap=cm.Greys_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For your entertainment, we'll sum the pixel value of those images and plot the (normalised) result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x7f00161448d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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s1GxyXuNlubcR0UUieu+Y9rXY4lMvbiOix4joJ0T08Ng2ara46sWriejUsg4/\nSUTvn8BM3aYHiGiXiJ6wlAlre8wc9Q97wvMMgDUArwTwOICDWpk7APzP8v+/AvBIbDsi23sIwLXL\n/w9Paa+vzUq5/wXw3wDem7rNAK4F8BSAA8vXr03c3n8C8KnGVgC/AnD1xNf57QBuAfBEy+fBbW8I\nTyK3wVdOe5n5EWb+3fLlI9gbAzIlPtcYAD4E4BsAfjmmcS342HwXgG8y83kAYOYXR7ZRxcdeBnDN\n8v9rAPyKmf84oo1XwMzfB/AbS5HgtjeESJgGX+mNqm3w1RT42KvyAQDfGdQiN06bieh1AN7DzF8E\nkEKvks91fiOA64joYSJ6lIjeN5p1V+Jj73EAMyJ6HsBpAB8eybY+BLc9GUwVABG9A3s9N2+f2hYP\nPgtAjaNTEAoXVwN4C4B3AvgzAD8goh8w8zPTmtXK7QAeY+Z3EtGNAB4iopuZ+fdTGxaTIUTiPIAb\nlNfXL9/Ty7zeUWYsfOwFEd0M4ASAw8xsc+fGwMfmtwI4SUSEvXj5DiK6yMynRrJRx8fmcwBeZOaX\nALxERAsAG9jLDYyNj713A/gUADDzs0T0cwAHAfx4FAu7Ed72BkicvAIvJ3xehb2Ez7pW5t14OXly\nCNMmLn3svQHAWQCHpkxKhdislf8Kpk9c+lzngwAeWpb9UwBPApglbO/nAXx8+f8q9tz46xKoH38B\n4MmWz4LbXnRPgjMbfOVjL4CPAbgOwBeWT+aLzKxPckvN5n1fGd1I3QC/enGGiL4H4AkAlwCcYOat\nVO0FsAng35Xuxo8w86+nsLeBiL4G4DYAryGiXwD4OPZErnPbk8FUgiBYkYVwBUGwIiIhCIIVEQlB\nEKyISAiCYEVEQhAEKyISgiBYEZEQBMGKiIQgCFb+HzlwOnaii29oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f001630d908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "combined = np.zeros(1, dtype=dt)\n",
    "combined['x'][0] = xs\n",
    "combined['y'][0] =  ys\n",
    "\n",
    "for img in imgs:\n",
    "    combined['z'][0] += img['z']\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.contourf(combined['x'][0], combined['y'][0], combined['z'][0], cmap=cm.Greys_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## [Solutions](../soln/03-dtypes.ipynb)"
   ]
  }
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