{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Single-Band Period Finding with ``gatspy``\n", "\n", "This shows an example of finding single-band periodograms for RR Lyrae data with [``gatspy``](http://github.com/jakevdp/gatspy/)\n", "\n", "We'll start by doing some preparatory imports:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# use seaborn's default plotting styles for matplotlib\n", "import seaborn; seaborn.set()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Downloading RR Lyrae Data\n", "\n", "``gatspy`` includes loaders for some convenient datasets.\n", "Here we'll take a look at some RR Lyrae light curves from [Sesar 2010](http://iopscience.iop.org/0004-637X/708/1/717/)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from gatspy.datasets import fetch_rrlyrae\n", "rrlyrae = fetch_rrlyrae()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This dataset object has an ``ids`` attribute showing the light curve ids available, and a ``get_lightcurve`` method which returns the light curve:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "483" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(rrlyrae.ids)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lcid = rrlyrae.ids[0]\n", "t, y, dy, filts = rrlyrae.get_lightcurve(lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's quickly visualize this data, to see what we're working with:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dyMkJ3UrgdrsBAEVFRV0RKxERSW5JcQEcbkcggavD78EFZNS5dPWxKDcoIhey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\niCT3/wFfjhszzkiHIgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for filt in 'ugriz':\n", " mask = (filts == filt)\n", " plt.errorbar(t[mask], y[mask], dy[mask], fmt='.', label=filt)\n", "plt.gca().invert_yaxis()\n", "plt.legend(ncol=3, loc='upper left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset has a ``metadata`` attribute, which can tell us things like the period (as determined by Sesar 2010:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.61431831" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "period = rrlyrae.get_metadata(lcid)['P']\n", "period" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's fold the lightcurve on this period and re-plot the points:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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62h5OFdpTQpO7p5+cF0v392Cm/YePH5GU3rqF86RL0ozfLox8buf9/QhRs3X5cMbJNU5D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\nTEkmE5VXsleRxtM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phase = t % period\n", "for filt in 'ugriz':\n", " mask = (filts == filt)\n", " plt.errorbar(phase[mask], y[mask], dy[mask], fmt='.', label=filt)\n", "plt.gca().invert_yaxis()\n", "plt.legend(ncol=3, loc='upper left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the characteristic shape of the RR Lyrae light curve can be seen!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lomb-Scargle Fits to the Data\n", "\n", "\n", "### Lomb-Scargle Period finding\n", "We can now use the Lomb-Scargle periodogram to attempt to fit the period.\n", "We'll use the classic (single-band) version, and examine the best period for each band individually. Because of the large (~10 year) baseline, the fit takes a few seconds per band:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sesar 2010: 0.614318\n", "u: 0.61431570304\n", "g: 0.614316612117\n", "r: 0.614316612117\n", "i: 0.614317748467\n", "z: 0.614316839386\n" ] } ], "source": [ "from gatspy.periodic import LombScargle, LombScargleFast\n", "# LombScargleFast is slightly faster than LombScargle for the simplest case\n", "# Both have the same interface.\n", "\n", "model = LombScargleFast()\n", "model.optimizer.set(quiet=True, period_range=(0.2, 1.2))\n", "\n", "print(\"Sesar 2010:\", period)\n", "for filt in 'ugriz':\n", " mask = (filts == filt)\n", " model.fit(t[mask], y[mask], dy[mask])\n", " print(filt + ': ', model.best_period)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that within each band, the lomb-scargle periodogram lands on the correct peak.\n", "This ``model.best_period`` hides some computation. To find the best period, the model optimizer determines the required resolution for a linear scan search, and computes the periodogram at each of these values.\n", "We can view the periodogram for each model by calling the ``periodogram`` method.\n", "We'll put this in a function for later use" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ckqmw6OXr3OcXT0bp2IvgtPqTyCqn3ICMjByMn34z3HYdWMaFgpIpKK+6ArOv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_periodogram(model, lcid):\n", " plt.figure()\n", " rrlyrae = fetch_rrlyrae()\n", " t, y, dy, filts = rrlyrae.get_lightcurve(lcid)\n", " period = rrlyrae.get_metadata(lcid)['P']\n", " \n", " periods = np.linspace(0.2, 1.0, 5000)\n", " for i, filt in enumerate('ugriz'):\n", " mask = (filts == filt)\n", " model.fit(t[mask], y[mask], dy[mask])\n", " power = model.periodogram(periods)\n", " plt.plot(periods, i + power, lw=1, label=filt)\n", " plt.xlim(periods[0], periods[-1])\n", " plt.ylim(0, 5)\n", " plt.legend(ncol=3)\n", "\n", "plot_periodogram(LombScargle(), lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The periodogram has very narrow peaks, of width approximately $\\Delta P \\approx P^2 / T$, where $T = (t_{max} - t_{min})$ is the baseline of the measurements. For 10 years of data, the width near the 0.6 day peak turns out to be around $10^{-4}$ days (about 8 seconds), which is why we need such fine sampling of the periodogram to see the peaks." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lomb-Scargle Model Fitting\n", "\n", "The Lomb-Scargle model corresponds to a single-term sinusoid fit to the data.\n", "We can plot these model fits using the ``predict()`` method.\n", "We'll encapsulate this in a function in order to reuse it below:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ccMMNPProo+zZs2fRE5rOXP6Nt7zreUsaU4nFiJx3PuE95+GkJzH7+7FODlI6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\nKIpCX18fDz/88DtmWH/0ox/F6XQC0N3dzde//vXSlLwEFEWhs9lBe6N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_model(model, lcid):\n", " plt.figure()\n", " rrlyrae = fetch_rrlyrae()\n", " t, y, dy, filts = rrlyrae.get_lightcurve(lcid)\n", " period = rrlyrae.get_metadata(lcid)['P']\n", "\n", " phase = t % period\n", " tfit = np.linspace(0, period, 100)\n", " for filt in 'ugriz':\n", " mask = (filts == filt)\n", " pts = plt.errorbar(phase[mask], y[mask], dy[mask], fmt='.', label=filt)\n", " model.fit(t[mask], y[mask], dy[mask])\n", " yfit = model.predict(tfit, period=period)\n", " \n", " plt.plot(tfit, yfit, color=pts[0].get_color(), alpha=0.5)\n", " plt.gca().invert_yaxis()\n", " plt.legend(ncol=3, loc='upper left');\n", " \n", "plot_model(LombScargle(), lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model is clearly fairly biased: that is, it doesn't have enough flexibility to truly fit the data. We can do a bit better by adding more terms to the Fourier series with the ``Nterms`` parameter" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SdiLBD7+3ja62FF1tqVFVhhqX/y2//PUa/vWfmgnGVhKuuZFg5Uq8wVkoehjL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_model(LombScargle(Nterms=4), lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model can also be used within the periodogram, using the same interface as above:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SsqpQOnNl4IjRD585JZFbSwA7TnBhHX1KBsrn3QZA7h3LKlwsUiy0xSTFAiW7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lOLouJNWkWMV0dHR0fHe5Ds4MsNej9tLdMYydKcTc04dxdd8Oro6OjoXJaYHcmccrtTaSE2KNqj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\nufDnuHi4Ooh+piN465l0PDUh1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_periodogram(LombScargle(Nterms=4), lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Supersmoother periodogram and fits\n", "\n", "The package includes the SuperSmoother algorithm using the same API.\n", "Here we'll plot the periodogram and the model fits for the same data using this model.\n", "Because the interface is identical, we can simply swap-in the supersmoother model in the function from above:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Emamy8rxadX7ZClRMWYQlFz2KrAKvEE3PyMTc1b9HUaW/AC2bfhnzHEVFmLX8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\nvn079u7di6ZN6Y3yy5Ytq1dZ+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7CYb9ROrW0r3jMJnt29yV9fpLSTo69KVGZSQbjw9+8tXA6GiVrkwP+wYPkjWy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\naDQ1dL1169YZC/CBdav4wlPb07fHY7eauLC+iAvqPHT0D9LU4afHG+Z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5kv7IEZUFFe5J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\nRK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from gatspy.periodic import SuperSmoother\n", "plot_periodogram(SuperSmoother(), lcid)\n", "plot_model(SuperSmoother(), lcid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nice and easy!" ] } ], "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": "3.3.5" } }, "nbformat": 4, "nbformat_minor": 0 }