{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting with Matplotlib\n", "\n", "Matplotlib is the \"standard\" Python plotting package (although there are a few other good contenders).\n", "\n", "Let's get on to that all important step of visualizing data. We will be using the matplotlib Python package for that. Let's start by plotting the function $f(x) = x^2$.\n", "\n", "First, let's generate the numbers using Numpy:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = np.arange(0,10,0.4)\n", "f = x ** 2\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's create a noisy version of $f$ by adding some random Gaussian noise:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 3.46691539, 4.64636688, 0.59870757, -0.72098424,\n", " 3.03366575, -0.64962963, 3.470377 , -0.16024531,\n", " 10.31670909, 17.26267781, 12.06994539, 11.29261335,\n", " 22.07280293, 28.90578863, 31.00590777, 34.54253274,\n", " 39.84082801, 48.96084072, 51.45467624, 48.04451804,\n", " 61.52306571, 69.52322718, 78.19145804, 83.18332532, 94.00811677])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu, sigma = 0, 5 # mean and standard deviation\n", "f_noisy = f + np.random.normal(mu, sigma, len(f))\n", "f_noisy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot the data, first import the **pyplot** module of matplotlib:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, f, '-k', label=\"f(x)\") # plot the function using a black line\n", "plt.plot(x, f_noisy, 'ob', label=\"noisy f\") # plot the noisy version using blue circles\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can add additional features to the plot such as a legend and axis labels, and note the use of semi-colons to suppress the output of the commands:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, f, '-k', label=\"f(x)\"); # plot the function using a black line\n", "plt.plot(x, f_noisy, 'ob', label=\"noisy f\"); # plot the noisy version using blue circles\n", "plt.xlabel(\"x\", size=\"xx-large\");\n", "plt.ylabel(\"f(x)\", size=\"xx-large\");\n", "plt.ylim(-5, 100);\n", "plt.legend(loc=\"upper left\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: histograms\n", "\n", "Let's generate two datasets from a normal distribution and plot their histograms:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mu = 100 # mean of distribution\n", "sigma = 15 # standard deviation of distribution\n", "x1 = mu + sigma * np.random.randn(10000)\n", "x2 = mu + 10 + sigma * np.random.randn(10000)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we'll generate a histogram of the two datasets, showing some features of Matplotlib's hist function. The 'normed' flag normalizes the bin heights such that it represents a probability distribution. 'alpha' is the opacity." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JhjxnlLs/BxyT0PZAwvbEFMcmnQwQlvU5O1MxiohI5kQpmTMT+KGZJXu2IyIi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\nE/dxBJUe6gj+ciorsvhvJyh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_bins = 50\n", "# the histogram of the data\n", "plt.hist(x1, num_bins, normed=True, facecolor='green', alpha=0.4, label='first');\n", "plt.hist(x2, num_bins, normed=True, facecolor='blue', alpha=0.4, label='second');\n", "plt.xlabel('x',size=\"xx-large\");\n", "plt.ylabel('normalized counts', size=\"xx-large\");\n", "plt.legend(loc='upper right');\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }