{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# freud.density.GaussianDensity\n", "The `freud.density` module is intended to compute a variety of quantities that relate spatial distributions of particles with other particles.\n", "In this notebook, we demonstrate `freud`'s Gaussian density calculation, which provides a way to interpolate particle configurations onto a regular grid in a meaningful way that can then be processed by other algorithms that require regularity, such as a [Fast Fourier Transform](https://en.wikipedia.org/wiki/Fft)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import freud\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy import stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate the basic concept, consider a toy example: a simple set of point particles with unit mass on a line.\n", "For analytical purposes, the standard way to accomplish this would be using [Dirac delta functions](https://en.wikipedia.org/wiki/Dirac_delta_function)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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FxP6I+OGga6xbhWv7goj4dkTc1+zzWK/aGhE7IuJoRDx4jv3151dmjuQ/Gkv1/h/wJmAZcB+woa3N1cB3aXxi0hXAfw677gH0+feBi5pfb1oMfW5p9wMaq35+aNh1D+D3fCFwAFjT3H79sOseQJ//Bvhc8+sJ4Glg2bBrP48+/yHwDuDBc+yvPb9GeYR+OTCdmYcy8ySwE9jc1mYz8JVsuBe4MCIuHnShNera58y8JzOfaW7eS+PTocZZld8zwCeBbwBHB1lcn1Tp84eBOzLzMYDMHPd+V+lzAq+JiACW0wj0ucGWWZ/MvJtGH86l9vwa5UA/1wdPL7TNOFlofz5G4//w46xrnyNiJfBBYBtlqPJ7vgS4KCLuioi9EXHdwKrrjyp9vhV4G42Pr3wA+FRmnh5MeUNRe35V+oCLIantw6nHSOX+RMR7aQT6H/S1ov6r0ucvADdl5qnG4G3sVenzUuAy4H3AbwD/ERH3ZubD/S6uT6r0+SpgH/BHwJuB70fEjzLzuX4XNyS159coB/pi/HDqSv2JiLcDtwGbMvOpAdXWL1X6PAnsbIb5CuDqiJjLzG8OpsTaVb22j2XmCeBERNwNXAqMa6BX6fP1wGezMcE8HRGPAG8F/mswJQ5c7fk1ylMui/HDqbv2OSLWAHcAHx3j0Vqrrn3OzHWZuTYz1wJfB/5yjMMcql3b3wLeHRFLI+JVwLuAhwZcZ52q9PkxGn+REBFvAN4CHBpolYNVe36N7Ag9F+GHU1fs86eB1wFfao5Y53KMV6qr2OeiVOlzZj4UEd8D7gdOA7dlZsfb38ZBxd/zLcDtEfEAjemImzJzbJfVjYivAlcCKyJiBvgM8AroX3756L8kFWKUp1wkSQtgoEtSIQx0SSqEgS5JhTDQJakQBrokFcJAl6RC/D+Y2K62sVeBzAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_p = 10000\n", "np.random.seed(129)\n", "x = np.linspace(0, 1, n_p)\n", "y = np.zeros(n_p)\n", "points = np.random.rand(10)\n", "y[(points * n_p).astype(\"int\")] = 1\n", "plt.plot(x, y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, delta functions can be cumbersome to work with, so we might instead want to smooth out these particles.\n", "One option is to instead represent particles as Gaussians centered at the location of the points.\n", "In that case, the total particle density at any point in the interval $[0, 1]$ represented above would be based on the sum of the densities of those Gaussians at those points." ] }, { "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": [ "# Note that we use a Gaussian with a small standard deviation\n", "# to emphasize the differences on this small scale\n", "dists = [stats.norm(loc=i, scale=0.1) for i in points]\n", "y_gaussian = 0\n", "for dist in dists:\n", " y_gaussian += dist.pdf(x)\n", "plt.plot(x, y_gaussian)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of the GaussianDensity class is to perform the same interpolation for points on a 2D or 3D grid, accounting for Box periodicity." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 1000 # Number of points\n", "L = 10 # Box length\n", "\n", "box, points = freud.data.make_random_system(L, N, is2D=True, seed=0)\n", "aq = freud.AABBQuery(box, points)\n", "gd = freud.density.GaussianDensity(L * L, L / 3, 1)\n", "gd.compute(aq)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 6))\n", "aq.plot(ax=axes[0])\n", "gd.plot(ax=axes[1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effects are much more striking if we explicitly construct our points to be centered at certain regions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 1000 # Number of points\n", "L = 10 # Box length\n", "box = freud.box.Box.square(L)\n", "centers = np.array(\n", " [[L / 4, L / 4, 0], [-L / 4, L / 4, 0], [L / 4, -L / 4, 0], [-L / 4, -L / 4, 0]]\n", ")\n", "\n", "points = []\n", "for center in centers:\n", " points.append(\n", " np.random.multivariate_normal(\n", " center, cov=np.diag([1, 1, 0]), size=(int(N / 4),)\n", " )\n", " )\n", "points = box.wrap(np.concatenate(points))\n", "aq = freud.AABBQuery(box, points)\n", "\n", "gd = freud.density.GaussianDensity(L * L, L / 3, 1)\n", "gd.compute(aq)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 6))\n", "aq.plot(ax=axes[0])\n", "gd.plot(ax=axes[1])\n", "plt.show()" ] } ], "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": "3.7.3" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }