{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prior functions illustration" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "%config InlineBackend.figure_format = \"retina\"" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from lightspot.priors import *" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "plt.rc('lines', linewidth=1.0, linestyle='-', color='black')\n", "plt.rc('font', family='sans-serif', weight='normal', size=12.0)\n", "plt.rc('text', color='black', usetex=True)\n", "plt.rc('text.latex', preamble='\\\\usepackage{cmbright}')\n", "plt.rc('axes', edgecolor='black', facecolor='white', linewidth=1.0, grid=False,\n", " titlesize='x-large', labelsize='x-large', labelweight='normal', labelcolor='black')\n", "plt.rc('axes.formatter', limits=(-4, 4))\n", "plt.rc(('xtick', 'ytick'), labelsize='x-large', direction='in')\n", "plt.rc('xtick', top=True)\n", "plt.rc('ytick', right=True)\n", "plt.rc(('xtick.major', 'ytick.major'), size=7, pad=6, width=1.0)\n", "plt.rc(('xtick.minor', 'ytick.minor'), size=4, pad=6, width=1.0, visible=True)\n", "plt.rc('legend', numpoints=1, fontsize='x-large', shadow=False, frameon=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Univariate distributions" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": { "image/png": { "width": 606, "height": 659 }, "needs_background": "light" } } ], "source": [ "uni_priors = {\n", " \"Uniform\" : Uniform(xmin=2, xmax=4),\n", " \"Sine Uniform\" : SineUniform(sinxmin=0, sinxmax=1),\n", " \"Log Uniform\" : LogUniform(logxmin=-1, logxmax=2),\n", " \"Normal\" : Normal(mu=0, sd=1),\n", " \"Truncated Normal\" : TruncNormal(mu=0.3, sd=0.3, xmin=0, xmax=1),\n", " \"Log Normal\" : LogNormal(logmu=2, logsd=0.5)\n", "}\n", "\n", "fig, axs = plt.subplots(3, 2, figsize=(9.6, 10.8))\n", "fig.subplots_adjust(hspace=0.4, wspace=0.4)\n", "\n", "for i, (prior_name, prior) in enumerate(uni_priors.items()):\n", " samples = prior(np.random.rand(30_000, 1))\n", " ax = axs[i // 2][i % 2]\n", " _ = ax.hist(samples, density=True, histtype='step', bins=50)\n", " ax.set(title=prior_name, xlabel='$x$', ylabel='pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bivariate distributions" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": { "image/png": { "width": 404, "height": 277 }, "needs_background": "light" } } ], "source": [ "tri = np.array([[0, 0], [0.4, 0.9], [1.1, 0.2]])\n", "prior = Triangular(tri)\n", "samples = prior(np.random.rand(100_000, 2))\n", "\n", "cmap = plt.cm.get_cmap('rainbow')\n", "cmap.set_under('w')\n", "_ = plt.plot(tri[:, 0], tri[:, 1], 'o', ms=10, color='k')\n", "_ = plt.hist2d(x=samples[:,0], y=samples[:,1], bins=50, density=True, cmap=cmap, vmin=1e-3)\n", "_ = plt.colorbar(label=\"pdf\")\n", "_ = plt.gca().set(xlim=(-0.1, 1.2), ylim=(-0.1, 1.0), xlabel=\"$x_1$\", ylabel=\"$x_2$\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": { "image/png": { "width": 426, "height": 271 }, "needs_background": "light" } } ], "source": [ "poly = np.array([[0, 0], [0.4, 0.5], [1.1, 0.2], [0.9, -0.1], [0.5, -0.3], [-0.1, -0.6]])\n", "prior = Polygon(poly)\n", "samples = prior(np.random.rand(100_000, 2))\n", "\n", "cmap = plt.cm.get_cmap('rainbow')\n", "cmap.set_under('w')\n", "_ = plt.plot(poly[:, 0], poly[:, 1], 'o', ms=10, color='k')\n", "_ = plt.hist2d(x=samples[:,0], y=samples[:,1], bins=50, density=True, cmap=cmap, vmin=1e-3)\n", "_ = plt.colorbar(label=\"pdf\")\n", "_ = plt.gca().set(xlim=(-0.2, 1.2), ylim=(-0.7, 0.6), xlabel=\"$x_1$\", ylabel=\"$x_2$\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.11 64-bit ('lightspot': pipenv)", "language": "python", "name": "python381164bitlightspotpipenv52c66f8fb923460ebd05a58a78e18b51" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.11-final" } }, "nbformat": 4, "nbformat_minor": 4 }