{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# freud.density.RDF: Choosing Bin Widths\n", "The `freud.density` module is intended to compute a variety of quantities that relate spatial distributions of particles with other particles.\n", "This example demonstrates the calculation of the [radial distribution function](https://en.wikipedia.org/wiki/Radial_distribution_function) $g(r)$ using different bin sizes." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import freud\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Define some helper plotting functions.\n", "\n", "\n", "def plot_rdf(box, points, prop, r_max=3.5, bins_array=[20, 75, 3000]):\n", " \"\"\"Helper function for plotting RDFs.\"\"\"\n", " fig, axes = plt.subplots(1, len(bins_array), figsize=(16, 3))\n", " for i, bins in enumerate(bins_array):\n", " rdf = freud.density.RDF(bins, r_max)\n", " rdf.compute(system=(box, points))\n", " axes[i].plot(rdf.bin_centers, getattr(rdf, prop))\n", " axes[i].set_title(f\"Bin width: {r_max/bins:.3f}\", fontsize=16)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To start, we construct and visualize a set of points sitting on a simple square lattice." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "box, points = freud.data.UnitCell.square().generate_system(5, scale=2)\n", "aq = freud.AABBQuery(box, points)\n", "aq.plot(ax=plt.gca())\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we try to compute the RDF directly from this, we will get something rather uninteresting since we have a perfect crystal.\n", "Indeed, we will observe that as we bin more and more finely, we approach the true behavior of the RDF for perfect crystals, which is a simple delta function." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_rdf(box, points, \"rdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In these RDFs, we see two sharply defined peaks, with the first corresponding to the nearest neighbors on the lattice (which are all at a distance 2 from each other), and the second, smaller peak caused by the particles on the diagonal (which sit at distance $\\sqrt{2^2+2^2} \\approx 2.83$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, in more realistic systems, we expect that the lattice will not be perfectly formed.\n", "In this case, the RDF will exhibit more features.\n", "To demonstrate this fact, we reconstruct the square lattice of points from above, but we now introduce some noise into the system." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "box, clean_points = freud.data.UnitCell.square().generate_system(\n", " 10, scale=2, sigma_noise=0\n", ")\n", "box, noisy_points = freud.data.UnitCell.square().generate_system(\n", " 10, scale=2, sigma_noise=0.1\n", ")\n", "aq_clean = freud.AABBQuery(box, clean_points)\n", "aq_clean.plot(ax=plt.gca(), c=\"k\", s=3)\n", "aq_noisy = freud.AABBQuery(box, noisy_points)\n", "deviations = np.linalg.norm(box.wrap(noisy_points - clean_points), axis=-1)\n", "_, sc = aq_noisy.plot(ax=plt.gca(), c=deviations)\n", "cbar = plt.colorbar(sc)\n", "cbar.set_label(\"Distance from lattice site\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_rdf(box, noisy_points, \"rdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this RDF, we see the same rough features as we saw with the perfect lattice.\n", "However, the signal is much noisier, and in fact we see that increasing the number of bins essentially leads to overfitting of the data.\n", "As a result, we have to be careful with how we choose to bin our data when constructing the RDF object." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An alternative route for avoiding this problem can be using the cumulative RDF instead.\n", "The relationship between the cumulative RDF and the RDF is akin to that between a cumulative density and a probability density function, providing a measure of the total density of particles experienced up to some distance rather than the value at that distance.\n", "Just as a CDF can help avoid certain mistakes common to plotting a PDF, plotting the cumulative RDF may be helpful in some cases.\n", "Here, we see that decreasing the bin size slightly alters the features of the plot, but only in very minor way (*i.e.* decreasing the smoothness of the line due to small jitters)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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