{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data release tutorial for Tests of General Relativity with GW170817" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook serves as a tutorial for loading and viewing data released in association with the publication **Tests of General Relativity with GW170817** (https://dcc.ligo.org/LIGO-P1800059/public)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "public_dcc_url ='https://dcc.ligo.org/LIGO-P1800059/public/'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook uses `numpy` (http://www.numpy.org/) to read the data files and `scipy` (https://www.scipy.org) to do some of the analyses. We use `matplotlib` (https://matplotlib.org/) and `seaborn` (https://seaborn.pydata.org/) to produce the figures." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#Used for data analysis\n", "import numpy as np\n", "import scipy as sp\n", "\n", "#Used for plotting\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "import seaborn as sns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Configure plotting options to match published figures" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "sns.set_palette('colorblind')\n", "sns.set_style(\"ticks\")\n", "\n", "matplotlib.rc('text.latex', preamble = '\\usepackage{txfonts}')\n", "matplotlib.rc('text', usetex=True)\n", "matplotlib.rc('font', family='serif')\n", "matplotlib.rc('font', serif='times')\n", "matplotlib.rc('mathtext', default='sf')\n", "matplotlib.rc('axes', labelsize=18)\n", "matplotlib.rc('legend', fontsize=16)\n", "matplotlib.rc('xtick', labelsize=12)\n", "matplotlib.rc('ytick', labelsize=12)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Download and read posterior samples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We download the released eleven-dimensional posterior samples for the parameterized tests of the binary dynamics. The samples can be found in the tarballs `phenompnrt_posteriors.tar.gz` and `seobnrt_posteriors.tar.gz` files for the `PhenomPNRT` and `SEOBNRT` waveforms, respectively. The tarballs contain posterior samples for the tests of each post-Newtonian coefficient. See the paper for details." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " % Total % Received % Xferd Average Speed Time Time Time Current\n", " Dload Upload Total Spent Left Speed\n", "100 161 100 161 0 0 148 0 0:00:01 0:00:01 --:--:-- 148\n", "100 6563k 100 6563k 0 0 1789k 0 0:00:03 0:00:03 --:--:-- 18.6M\n", " % Total % Received % Xferd Average Speed Time Time Time Current\n", " Dload Upload Total Spent Left Speed\n", "100 158 100 158 0 0 276 0 --:--:-- --:--:-- --:--:-- 276\n", "100 11.2M 100 11.2M 0 0 1291k 0 0:00:08 0:00:08 --:--:-- 1876k\n" ] } ], "source": [ "!curl -OL {public_dcc_url}\"phenompnrt_posteriors.tar.gz\"\n", "!curl -OL {public_dcc_url}\"seobnrt_posteriors.tar.gz\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unpack tarballs" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "!tar xzf phenompnrt_posteriors.tar.gz\n", "!tar xzf seobnrt_posteriors.tar.gz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read the posterior samples and store in the notebook. We can access each waveform type's data using `posterior_samples[][][]`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "posterior_samples = {'PhenomPNRT':{}, 'SEOBNRT':{}}\n", "\n", "pn_parameters = {'-1PN':'dchiminus2', '0PN':'dchi0', '0.5PN':'dchi1', '1PN':'dchi2', '1.5PN':'dchi3', \\\n", " '2PN':'dchi4', '2.5PN(l)':'dchi5l', '3PN':'dchi6', '3PN(l)':'dchi6l', '3.5PN':'dchi7'}\n", "\n", "for pn_order in pn_parameters:\n", " posterior_samples['PhenomPNRT'][pn_order] = np.genfromtxt('phenompnrt_%s.dat'%(pn_parameters[pn_order]),names=True)\n", " posterior_samples['SEOBNRT'][pn_order] = np.genfromtxt('seobnrt_%s.dat'%(pn_parameters[pn_order]),names=True)\n", " \n", "pn_labels = {'-1PN':r'$\\delta\\hat{\\varphi}_{-2}$', '0PN':r'$\\delta\\hat{\\varphi}_{0}$',\\\n", " '0.5PN':r'$\\delta\\hat{\\varphi}_{1}$', '1PN':r'$\\delta\\hat{\\varphi}_{2}$',\\\n", " '1.5PN':r'$\\delta\\hat{\\varphi}_{3}$', '2PN':r'$\\delta\\hat{\\varphi}_{4}$',\\\n", " '2.5PN(l)':r'$\\delta\\hat{\\varphi}_{5}^{(\\ell)}$', '3PN':r'$\\delta\\hat{\\varphi}_{6}$',\n", " '3PN(l)':r'$\\delta\\hat{\\varphi}_{6}^{(\\ell)}$', '3.5PN':r'$\\delta\\hat{\\varphi}_{7}$'}" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dtype([('distance', '][dchi{n}]` for future use. Note that there is not a one-to-one correspondence between the points in `posterior_samples['SEOBNRT']` and `posterior_samples['SEOBNRT_reparameterized']`." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "posterior_samples['SEOBNRT_reparameterized'] = {}\n", "\n", "for pn_order in ['-1PN','0PN','0.5PN','1PN','1.5PN','2PN','2.5PN(l)','3PN','3PN(l)','3.5PN']:\n", " posterior_samples['SEOBNRT_reparameterized'][pn_order] = {}\n", " posterior_samples['SEOBNRT_reparameterized'][pn_order][pn_parameters[pn_order]]=convert_SEOBNRT_to_PhenomPNRT_parameterization(posterior_samples['SEOBNRT'][pn_order],\\\n", " pn_parameters[pn_order])\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot the 1D marginalized posterior distribution function on the deviations from GR at each post-Newtonian order. The SEOBNRT posteriors are re-parameterized as in the paper." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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RT9LU1ERlZWVcAxOTV7iznabIDDQozM00ElA7oDGqrG9kkWUpM/0efnKikRSt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\nhiEFo0FPii6FlJQU0GoJRDR9zwtH6A1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1aqO5ZR0fPHkU5911usQhhMg9U5Y8ZlPHfW3j9Wy53e4bev5icrpviOUFFuz9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\nTv4HPk7hXZ+l8I5arO47pEQilgyDlsW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vH5mZmQCUl5ejuar73re+9a2JjU4IMUD3ufc4ZLwDs95PijGgdjgTJichQK/D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\nBHF/8BIafRSpf/xPADS6e7j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hs9nYsmULhYWFoSXG29vbKSkp4fnnnw+dt337dgoLC0NLpx84cCC07PjChQuHJL7g1rHi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\nhS87QjQAAAAASUVORK5CYII=\n", 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Ml8fsq9JT1KgjU5qUAqZi/JepGTWHlP1r0Tmrel1OfLiR+WOjyLtQ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\n2Ry65ODWX+fKOkyDiCSHEUJ1u7j43MO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ZojGdewWgreYxgt1o9rOzOpo9yjTuqXiPqPS5aockxLDQY/Jwu91s29Z56eqK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\nDNykdaCLMOA0T1M7nBEvoIu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7+zQqOj6X1Eh9Qr7W4UyKDPPAJI/vpX2cPzknJY+JMmryqK2t5amnnhpUAlEU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\nzPt0O35H7/HXQQ2QMO86Zv/Zdo53xXG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21QHQ3Nzc55jRaBzSALnRaOzT5WW1Wm8+SDEoW7sFm6UW/1l3uh03WdTE+XXj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\niUQC4+PjAHaH5/b09GB1dfXIc4iIqHac+iTBw1o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XbNo/7rexNA5tSluS3p9sjrqk3yaWSLIRQgyiaRrdZ2o4m7CcH51KJk6n8VGH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\nP0AAHasXpkU7nJjQnHkTFs9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H5betxNp1gvT+i7OuCS2qJ9dJbqAN/4Akm6sx7tpoR44cob6+nvz8fACqq6vR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\n3PnjqpGyl7JJN4b5TF4//96amqRIxWg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for pn_order in ['-1PN','0PN','0.5PN','1PN','1.5PN','2PN','2.5PN(l)','3PN','3PN(l)','3.5PN']:\n", "\n", " sns.distplot(posterior_samples['PhenomPNRT'][pn_order][pn_parameters[pn_order]], hist=True,\\\n", " color=sns.color_palette()[2], label='PhenomPNRT')\n", " sns.distplot(posterior_samples['SEOBNRT_reparameterized'][pn_order][pn_parameters[pn_order]],\\\n", " hist=True, color=sns.color_palette()[0], label='SEOBNRT')\n", " \n", " plt.xlabel(pn_labels[pn_order])\n", " plt.ylabel('PDF')\n", " plt.legend()\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot the violin plot shown in Figure 1 of the paper. The SEOBNRT posteriors are re-parameterized as in the paper." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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i19XVRXd3N319fUWfkMLNnlKQQkdCZOnMmTOZ5cAgde6fuwxiNm3yLRgM8j++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3qWpEgQrRyjxFmGKIo0dsQoHTE8Kx7m2WzixImU5tn47LMGCiZdjFBRw2cH36HMGsdqyJwBXZKs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\nYtGiRT0tQJmqqnoEH+x+FykaJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sections = [['-1PN'], ['0PN', '0.5PN', '1PN', '1.5PN'], ['2PN', '2.5PN(l)', '3PN'], ['3PN(l)', '3.5PN']]\n", "\n", "f, axes = plt.subplots(figsize=(15,4), nrows=1, ncols=len(sections),\\\n", " gridspec_kw={'wspace':0.5,'width_ratios':map(lambda x: len(x),sections)})\n", "\n", "colors = {'PhenomPNRT':sns.color_palette()[2], 'SEOBNRT_reparameterized':sns.color_palette()[0]}\n", "\n", "for (ax, pn_orders) in zip(axes,sections):\n", " for waveform in ['SEOBNRT_reparameterized','PhenomPNRT']:\n", " \n", " # Plot marginalized posterior distribution function for dchi{n}\n", " sns.violinplot(data = [posterior_samples[waveform][pn_order][pn_parameters[pn_order]] \\\n", " for pn_order in pn_orders], scale='width',\\\n", " color=colors[waveform], inner = None, bw='silverman', ax=ax,label=\"b\")\n", " \n", " # Plot error bars corresponding to 90% credible region\n", " for i, pn_order in enumerate(pn_orders):\n", "\n", " med = np.median(posterior_samples[waveform][pn_order][pn_parameters[pn_order]])\n", " perc_05 = np.percentile(posterior_samples[waveform][pn_order][pn_parameters[pn_order]],5)\n", " perc_95 = np.percentile(posterior_samples[waveform][pn_order][pn_parameters[pn_order]],95)\n", " err_low = np.abs(med-perc_05)\n", " err_high= np.abs(perc_95-med)\n", " ax.errorbar(i,med,yerr=[[err_low],[err_high]], ecolor=colors[waveform], marker=None, capthick=2, capsize=28, linewidth=0)\n", "\n", " ax.set_xticklabels(pn_orders)\n", " plt.setp(ax.collections, alpha=.7)\n", "\n", "axes[0].set_ylabel(r'$|\\delta\\hat \\varphi_n|$')\n", "\n", "#Hard-coded plot ranges to match figure in paper\n", "axes[0].set_ylim(-0.000015,0.00004)\n", "axes[1].set_ylim(-0.3,0.9)\n", "axes[2].set_ylim(-1.8,7.0)\n", "axes[3].set_ylim(-17.0,5.0)\n", " \n", "patches = [matplotlib.patches.Patch(color = sns.color_palette()[2],label=\"PhenomPNRT\"),\\\n", " matplotlib.patches.Patch(color = sns.color_palette()[0],label=\"SEOBNRT\")]\n", "axes[1].legend(handles=patches)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we construct the marginalized posterior distributions on $|\\hat{\\varphi}_n|$ and compute the upper bound of the 90% credible region for each waveform model. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "PhenomPNRT_bounds = []\n", "SEOBNRT_bounds = []\n", "\n", "bounds = {'PhenomPNRT':PhenomPNRT_bounds, 'SEOBNRT_reparameterized':SEOBNRT_bounds}\n", "\n", "for pn_order in ['-1PN','0PN','0.5PN','1PN','1.5PN','2PN','2.5PN(l)','3PN','3PN(l)','3.5PN']:\n", " \n", " for waveform in ['PhenomPNRT', 'SEOBNRT_reparameterized']:\n", "\n", " pos_samp = posterior_samples[waveform][pn_order][pn_parameters[pn_order]]\n", "\n", " #Reconstruct posterior distribution function for dchi{n} with kernel density estimation using a Gaussian kernel\n", " pos_kde = sp.stats.gaussian_kde(pos_samp)\n", " centers = np.linspace(0.0, 1.05*max(np.abs(pos_samp)), 1000)\n", "\n", " #Compute the posterior distribution function for |dchi{n}|\n", " counts = pos_kde(centers) + pos_kde(-centers)\n", " counts[0] /= 2\n", "\n", " #Construct cumulative distribution function from the mode for |dchi{n}| \n", " counts_sorted = np.sort(counts.flatten())[::-1]\n", " norm_cumsum_counts_sorted = np.cumsum(counts_sorted) / np.sum(counts)\n", " \n", " #Compute height of PDF for |dchi{n}| at which the 90% credible region ends\n", " index_from_level = sp.interpolate.interp1d(norm_cumsum_counts_sorted, np.arange(len(counts)), bounds_error=False, fill_value=(0.,len(counts)))\n", " height_from_index = sp.interpolate.interp1d(np.arange(len(counts)), counts_sorted, bounds_error=False, fill_value=(counts_sorted[0],0.))\n", " upper_bound_height = height_from_index(index_from_level(0.9))\n", " \n", " #Store value of |dchi{n}| at which the 90% credible region ends\n", " bounds[waveform].append(np.max(centers[np.where(counts>upper_bound_height)]))\n", " " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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HgV/NCKwu8BTf4CUsmPQmXFoGN1PJ93gTaF9dYMxPtsZsNWkV3hOqeKjgoIqH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\n1EQIIaSuro5UV1eTxsZG0tvbSwgh5MWLFyQhIYEEBASQjz/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.semilogy(range(10), PhenomPNRT_bounds, linestyle='', marker='p', color=sns.color_palette()[2], markersize=18, alpha=0.8, label='PhenomPNRT')\n", "plt.semilogy(range(10), SEOBNRT_bounds, linestyle='', marker='v', color=sns.color_palette()[0], markersize=16, alpha=0.8, label='SEOBNRT')\n", "plt.xlim(-0.5, 9.5)\n", "plt.ylabel(r'$|\\delta\\hat \\varphi_n|$', size=20)\n", "plt.xticks(range(10), ['-1PN','0PN','0.5PN','1PN','1.5PN','2PN','2.5PN(l)','3PN','3PN(l)','3.5PN'], rotation=45, size=16)\n", "plt.yticks([1e-5,1e-4,1e-3,1e-2,1e-1,1e0,1e1],size=16)\n", "plt.grid(which='major')\n", "plt.grid(which='minor')\n", "plt.legend(loc='lower right')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }