04-Visualisation-with-matplotlib.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualisation with matplotlib\n",
    "\n",
    "It is possible to create visualisations with [matplotlib](https://matplotlib.org):\n",
    "\n",
    "> Matplotlib is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.\n",
    "\n",
    "In this section we will see how to:\n",
    "\n",
    "- Create scatter plots;\n",
    "- Create histograms and line plots.\n",
    "\n",
    "\n",
    "## Creating scatter plots\n",
    "\n",
    "Let us create some simple data to use for our plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = range(1, 25)\n",
    "ys = [1 / x for x in xs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before plotting in Jupyter we need to run a command to tell it to display the plots directly in the notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us use matplotlib to plot our scatter plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(xs, ys);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might want to combine this plot with another set of points. Let us create another set of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "zs = [1 / (25 - x) for x in xs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(xs, ys)\n",
    "plt.scatter(xs, zs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add a legend to our plot (which can include LaTeX) as well as axes labels and a title:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(xs, ys, label=\"$y=\\\\frac{1}{x}$\")\n",
    "plt.scatter(xs, zs, label=\"$y=\\\\frac{1}{25 - x}$\")\n",
    "\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"Value\")\n",
    "plt.title(\"My scatter plot\")\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Exercise**\n",
    "\n",
    "Plot a scatter plot with the following $x$, $y$ data:\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = range(200)\n",
    "ys = [(100 - x) ** 2 for x in xs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating histograms\n",
    "\n",
    "Let us create some random data sampled from the exponential distribution to use for a histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random  # Allows us to create random data\n",
    "number_of_data_points = 50000\n",
    "data = [random.expovariate(lambd=.5) for _ in range(number_of_data_points)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us know plot the histogram for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can change the number of bins and also specify that we would like the plot to be normalised (so as to show probabilities and not frequencies):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data, bins=35, density=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is known that the exponential distribution with rate $\\lambda$ has probability distribution function (pdf):\n",
    "\n",
    "$$\n",
    "f(x) = \\lambda e ^{-\\lambda x}\n",
    "$$\n",
    "\n",
    "Let us include a line plot of that on our plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "lambd = 0.5\n",
    "values = range(16)\n",
    "fs = [lambd * math.exp(- lambd * x ) for x in values]\n",
    "\n",
    "plt.hist(data, bins=35, density=True)\n",
    "plt.plot(values, fs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we might want to save this figure and output it to a file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data, bins=35, density=True)\n",
    "plt.plot(values, fs)\n",
    "plt.savefig(\"the-exponential-distribution.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By changing the file format name (`.pdf`, `.png`, `.svg` etc) we can change the format of the saved file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**EXERCISE** Using the same code as for the scatter plots: add a title, axes labels and legend to the histogram.\n",
    "\n",
    "---\n",
    "\n",
    "---\n",
    "\n",
    "**EXERCISE** Draw a histogram for randomly sampled data from the normal distribution (using `random.normalvariate`).\n",
    "\n",
    "---\n",
    "\n",
    "## Summary\n",
    "\n",
    "In this section we have seen how to matplotib:\n",
    "\n",
    "- To draw scatter plots;\n",
    "- To draw histograms;\n",
    "- To add labels and titles to plots;\n",
    "- To save plots to a file.\n",
    "\n",
    "This just touches on the capabilities of matplotlib."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python [conda env:mwp]",
   "language": "python",
   "name": "conda-env-mwp-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}