{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CrossCorrelation\n", "\n", "This Tutorial is intended to give a demostration of How to make a CrossCorrelation Object in Stingray Library." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from stingray import Lightcurve\n", "from stingray.crosscorrelation import CrossCorrelation\n", "\n", "import matplotlib.pyplot as plt\n", "import matplotlib.font_manager as font_manager\n", "%matplotlib inline\n", "font_prop = font_manager.FontProperties(size=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# CrossCorrelation Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# 1. Create two light curves\n", "\n", "There are two ways to create a Lightcurve.
\n", "1) Using an array of time stamps and an array of counts.
\n", "2) From the Photon Arrival times.\n", "\n", "In this example, Lightcurve is created using arrays of time stamps and counts.\n", "\n", "Generate an array of relative timestamps that's 10 seconds long, with dt = 0.03125 s, and make two signals in units of counts. The signal is a sine wave with amplitude = 300 cts/s, frequency = 2 Hz, phase offset of pi/2 radians, and mean = 1000 cts/s. We then add Poisson noise to the light curve." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dt = 0.03125 # seconds\n", "exposure = 10. # seconds\n", "freq = 1 # Hz\n", "times = np.arange(0, exposure, dt) # seconds\n", "\n", "signal_1 = 300 * np.sin(2.*np.pi*freq*times) + 1000 # counts/s\n", "signal_2 = 300 * np.sin(2.*np.pi*freq*times + np.pi/2) + 1000 # counts/s\n", "noisy_1 = np.random.poisson(signal_1*dt) # counts\n", "noisy_2 = np.random.poisson(signal_2*dt) # counts" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's turn noisy_1 and noisy_2 into Lightcurve objects. This way we have two Lightcurves to calculate CrossCorrelation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "320" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lc1 = Lightcurve(times, noisy_1)\n", "lc2 = Lightcurve(times, noisy_2)\n", "\n", "len(lc1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xdT6TOnVAt1K3dq0vucBUfHhoSF25DBxyCHDEEWqCYYq/c8HFs9SUOkvqLGIh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\nMjGBGVNfaQGukpW6JrZfIVMaiG/aSoQ66HmKmfdf3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(10,6))\n", "ax.plot(lc1.time, lc1.counts, lw=2, color='blue')\n", "ax.plot(lc1.time, lc2.counts, lw=2, color='red')\n", "ax.set_xlabel(\"Time (s)\", fontproperties=font_prop)\n", "ax.set_ylabel(\"Counts (cts)\", fontproperties=font_prop)\n", "ax.tick_params(axis='x', labelsize=16)\n", "ax.tick_params(axis='y', labelsize=16)\n", "ax.tick_params(which='major', width=1.5, length=7)\n", "ax.tick_params(which='minor', width=1.5, length=4)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Create a CrossCorrelation Object from two Light curves created above\n", "\n", "To create a CrossCorrelation Object from LightCurves, simply pass both Lightvurves created above into the CrossCorrelation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cr = CrossCorrelation(lc1, lc2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, Cross Correlation values are stored in attribute corr, which is called below. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 201.553125 , 1412.10121094, 2828.54304688, 3948.95050781,\n", " 5370.02359375, 5750.04355469, 6222.50101563, 6664.92722656,\n", " 5969.0503125 , 6770.80464844])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr.corr[:10]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.03125" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Time Resolution for Cross Correlation is same as that of each of the Lightcurves\n", "cr.dt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Plot Cross Correlation for Different lags\n", "\n", "To visulaize correlation for different values of time lags, simply call plot function on cs." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dfvfXRkuGZlDX3iSzH4vvYY7tI6PcNorphJBpqaKw24POdrwZwOet7z8P4Kcd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\nlIS/++ArBxbYReHwVBZ/9ngPPVVHOhHH05frODSVFd5AV8o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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cr.plot(labels = ['Time Lags (seconds)','Correlation'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given the Phase offset of pi/2 between two lightcurves created above, and freq=1 Hz, `time_shift` should be close to 0.25 sec. Small error is due to time resolution." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.26645768025078276" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr.time_shift #seconds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modes of Correlation\n", "\n", "You can also specify an optional argument on modes of cross-correlation.
\n", "There are three modes : 1) same 2) valid 3) full \n", "\n", "Visit following ink on more details on mode : https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.signal.correlate.html\n", "\n", "Default mode is 'same' and it gives output equal to the size of larger lightcurve and is most common in astronomy. You can see mode of your CrossCorrelation by calling mode attribute on the object." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'same'" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr.mode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The number of data points in corr and largest lightcurve are same in this mode." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "320" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr.n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating CrossCorrelation with full mode now using same data as above." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cr1 = CrossCorrelation(lc1, lc2, mode = 'full') " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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e4bNYyp+5EQ9y6o0ewvyUHnnsHK31XCtpRi1Za5PxwRIICZtTdXBqoQNKgQ+9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\nlvH2a3bGG69uzgJIk0eYt1jU9JcCEM/tiMkjR+SRuNumksd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cr1.plot()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'full'" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr1.mode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Full mode does a full cross-correlation." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "639" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cr1.n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Another Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also create CrossCorrelation Object by using Cross Correlation data. This can be useful in some cases when you have correlation data and want to calculate time shift for max. correlation. You need to specify time resolution for correlation(default value of 1.0 seconds is used otherwise)." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cs = CrossCorrelation()\n", "cs.corr = np.array([ 660, 1790, 3026, 4019, 5164, 6647, 8105, 7023, 6012, 5162])\n", "time_shift, time_lags, n = cs.cal_timeshift(dt=0.5)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.83333333333333348" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "time_shift" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NavHh/ZdzSa1KDE9I5j+LN5ObWzrvg/i75/EysEhVLwXaARuBJ4AlqhoNLHFeIyItgf5A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\nClQEPnUeJohs23e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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cs.plot( ['Time Lags (seconds)','Correlation'])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Yet another Example with longer Lightcurve\n", "\n", "I will be using same lightcurves as in the example above but with much longer duration and shorter lags.
\n", "Both Lightcurves are chosen to be more or less same with a certain phase shift to demonstrate Correlation in a better way.\n", "\n", "Again Generating two signals this time without poission noise so that time lag can be demonstrated. For noisy lightcurves, accurate calculation requires interpolation." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dt = 0.0001 # seconds\n", "exposure = 50. # seconds\n", "freq = 1 # Hz\n", "times = np.arange(0, exposure, dt) # seconds\n", "\n", "signal_1 = 300 * np.sin(2.*np.pi*freq*times) + 1000 * dt # counts/s\n", "signal_2 = 200 * np.sin(2.*np.pi*freq*times + np.pi/2) + 900 * dt # counts/s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Converting noisy signals into Lightcurves." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "500000" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lc1 = Lightcurve(times, signal_1)\n", "lc2 = Lightcurve(times, signal_2)\n", "\n", "len(lc1)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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P4MAPH49/xIvdel/5CobHvQGn4ZluvcsuA170IvzTtqdhBat2bEYj4GlPwysv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\nmNAYQhRtUaH5tqc0gfa3scnB0bf6rXvNZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(10,6))\n", "ax.plot(lc1.time, lc1.counts, lw=2, color='blue')\n", "ax.plot(lc1.time, lc2.counts, lw=2, color='red')\n", "ax.set_xlabel(\"Time (s)\", fontproperties=font_prop)\n", "ax.set_ylabel(\"Counts (cts)\", fontproperties=font_prop)\n", "ax.tick_params(axis='x', labelsize=16)\n", "ax.tick_params(axis='y', labelsize=16)\n", "ax.tick_params(which='major', width=1.5, length=7)\n", "ax.tick_params(which='minor', width=1.5, length=4)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, creating CrossCorrelation Object by passing lc1 and lc2 into the constructor." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done\n" ] } ], "source": [ "cs = CrossCorrelation(lc1, lc2)\n", "print('Done')" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 2.86241768e-05, 4.71238867e+06, 9.42481318e+06,\n", " 1.41372717e+07, 1.88497623e+07, 2.35622831e+07,\n", " 2.82748324e+07, 3.29874082e+07, 3.77000087e+07,\n", " 4.24126319e+07, 4.71252762e+07, 5.18379395e+07,\n", " 5.65506201e+07, 6.12633160e+07, 6.59760255e+07,\n", " 7.06887466e+07, 7.54014775e+07, 8.01142163e+07,\n", " 8.48269612e+07, 8.95397103e+07, 9.42524618e+07,\n", " 9.89652137e+07, 1.03677964e+08, 1.08390712e+08,\n", " 1.13103454e+08, 1.17816189e+08, 1.22528916e+08,\n", " 1.27241631e+08, 1.31954335e+08, 1.36667023e+08,\n", " 1.41379696e+08, 1.46092350e+08, 1.50804985e+08,\n", " 1.55517598e+08, 1.60230186e+08, 1.64942750e+08,\n", " 1.69655286e+08, 1.74367792e+08, 1.79080268e+08,\n", " 1.83792710e+08, 1.88505118e+08, 1.93217489e+08,\n", " 1.97929821e+08, 2.02642113e+08, 2.07354363e+08,\n", " 2.12066568e+08, 2.16778727e+08, 2.21490839e+08,\n", " 2.26202900e+08, 2.30914910e+08])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cs.corr[:50]" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "9.9999999999766942e-05" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Time Resolution for Cross Correlation is same as that of each of the Lightcurves\n", "cs.dt" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hQ1jevTi37v1Q1ap379E5rsYf6nwvNOWiqUEVdNLzl/W1j1HYZ81HjlP43qnG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cs.plot( ['Time Lags (seconds)','Correlation'])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.2495504991004161" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cs.time_shift #seconds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`time_shift` is very close to 0.25 sec, in this case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## AutoCorrelation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stingray has also separate class for AutoCorrelation. AutoCorrealtion is similar to crosscorrelation but involves only One Lightcurve.i.e. Correlation of Lightcurve with itself." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "AutoCorrelation is part of `stingray.crosscorrelation` module. Following line imports AutoCorrelation." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from stingray.crosscorrelation import AutoCorrelation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create `AutoCorrelation` object, simply pass lightcurve into AutoCorrelation Constructor.
Using same Lighrcurve created above to demonstrate `AutoCorrelation`." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lc = lc1" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "500000" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac = AutoCorrelation(lc)\n", "ac.n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.12500000e+10, 1.12499978e+10, 1.12499911e+10,\n", " 1.12499800e+10, 1.12499645e+10, 1.12499445e+10,\n", " 1.12499201e+10, 1.12498912e+10, 1.12498579e+10,\n", " 1.12498201e+10])" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.corr[:10]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([-25. , -24.9999, -24.9998, ..., 24.9998, 24.9999, 25. ])" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.time_lags" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`time_Shift` for `AutoCorrelation` is always zero. Since signals are maximally correlated at zero lag." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5.0000099997734535e-05" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.time_shift" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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STkRPOnf1X1x3Uoz954jo+Se0r7A9+cJ4QRDYeeyYCz+9iNkEPUPGvru/L0P8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\npQZk8ASZvPT0Eunl3qgfB4GeCmbai6uTdTzpRi8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2eK5lYJNoArlAS40CgGEw1JFoVNEo\nlGgQFAN/u3qBhaOlW8mF1LVzpZsoeFqEpAcTCp6b9wYtjL3guXkau9sPE4R5Xrb+88Julkhaaftn\n8sOTYuCimq4Nlwjo6/41Y8c6TuO5gd1RxBs2vZ3M+E1pMseEiF0xjeHX6o4rWPnnpP7eiOMC7Dtb\nywzTwYpVzlSGNkPWUgMr/wLzjbx8ZGdyIhKzv3442WqJAxI1+VrjBdjLeKyNCcmZfGQddhnIHtp9\n/mMr3XjB1mKYPP+dgb2D1QjvS8oYqt8BZLlEV1a+wQJEZeypDeCc0K/e9uVZ+TAwKDNS1VuG5H48\n5p9TyPyJhLMHgqelBJmngXNoi9cOMkmlBMRuqWYJpXafnXPjVYo3yemJPddjVc+LuG/eCo//P5zi\nU/i8tGcegbq4DJw19ponIS3ERQO4jB9JAOdVyqa3Y01JKEIGwgxW7tfmDD3+mSDWSSsgjk0p2Kr9\nnEY7k8DOUowpArZioIYLXLX0rdreLKGEVk/UHlr0n9floRPZlyxCB08tgPe99vryd8iJIBmbGg4w\n0NjFAONKl/IYUcZAgOW69Vhu1zBwyVJFP2aG5jpQ28CW706VLFjaIOuxQhYm98vkGyWtuJILBFsj\nxg7BU/S3G2cHrF74M76V09oga0KTEzwtAuT4u+VqJyV9bn5gsK381IpNTYpi/86KINTYOwb2gLFP\nTNjGlfRqRI0psdptTqBixkiNpSFZ6lJ9x4HR3icZMyc9+bkSTc7gEGrkikjgy0rjhQ2ejv/X4Oni\nY9/d1izFgOQSLX1WcIFrpipPBMENaUFVDeCs43v12FVGam5Mvi8FrFmNXaJO2Bfr0cWIv2XsvnSD\nQTW5UsDtiQRjdxi1XEKj+8VnozbwzBY8BEtm4Cs4Z1UiAMAprLsOJQXY1rhPlsCXXHsMn6gBctS/\nwmtUJRcrM4SOkkGzVMmo1XOxwyFUhjgj2Ssp4BEErsfv7YdIMHaQH3dp7F5QdTwHLXsQ2eeu3R82\nKggAzw3APbK0EbIqUTNhoERTbY3GHsl4MRLEgwBf8H2uGMM7jXYmgR3foIRaOi99DgDwcQllmTww\nfMPkgXXUh7AxdimtjCVXW/qzlWJ0zRkiwbTQo5tB65TWrEADVf5joSsOA7XVDlgwD+EaSQD3QAgT\nUXSSjZUxcD9yIpBJPEQkSgS0LEz+TFQiQEsuvB/aLbkAM8cMVlf3H+xkVoHXSDR+ILlKNM7qZQyq\n1kvRGLv4Xv7uSIqTMRbUzK1bCkoTiOeid54j/tyVDTJ2raUjwzc5HWrs2DyJcVJBBp784Gm1KQKw\nTyv8HgCfk/6sRIPve9DnfAkI3wEwdpRurmwWjX1WW3cjOB1u+1qnmagtjfDCr4CBr1f+THsQbO8l\nX+g3KwnGXlBa4bex6IezpS0X8xBiXXf+bvUC7z0MvL2Aw/rYiYTkYhgYa+wa8Dnxxwy8QQ8wzBi1\nAzXQoZnhCdCq6e8DyA/JZ+AS/PDcJJOXstGu4ClKNBnO2Z2cis3O5X7GoMZqtR9eMXbnWqBDRJ/b\nvBgLWzltcF7HJ1bQj55u/r8+L8C0x6J7dvsaDOX9S4YfAL6NT+XJ7ogAztcImXlLOEJJx5NoapZ3\nvRZ+kDRy3a2A4TeNfQH2nU0CMi7FuF9uZ5ZEsFRqTN7vtyUIBiW5dPVhtgNvnSfXgvNwNk+vZh11\nuQoTAT/88jvNEjooHYAAiwOSBx67HJCN8kCNEosw+YalFfR6j+8w9aUe6d3mv42slhzAL/UtRxjo\nM4CMwVMp0RTymfzQXqKNwc0yfcYLqkomj7bGWtOmTn569YKVMb1rYVY1yKhrxuhul4sXVC+DJQJ8\nLkfbICaz1Ss8/hzqzSvxHCmNnfuBzHSKLOkCWl1ONUFJj5EsSFeC/vHlGDKtf3wRxqCSB7m/L04M\nD/DlAADcBFUN4LdjutrtTAK7XPrIi8XBU54hz3Xd2I9+9ZW+8IbJZ32jUDM/2hYqg50IWHKRDxsv\nibG6G2fD9UUX4OcIvpR6xv6Tc8UQ2QEZ2R3b9pGtDROUGtNyg61FW/80+PlxhRHMarcKJBKRzobc\nydj9YCtq8hXMON6QqG5P5NTHUZ57Z/ILfO+RWwatn/Ja4IoQg6E5iX6XgQc2yNyeR7k9jy+MvUQE\noXm3/e0ZMP3nwst41tINEbtZxv3g5FcrryrC197fIAGcM9j7Xk8ENSMdJyfU0tEtc+QTwcuLxj6v\nyZkQl1ZERI8eagBf1Zl2q35HzQxtjVcgGLKqE4qt45ISV4PUr8BivW4Eag/wLZjVCQIeWqlPV1mC\nXTQOIOultQ7cHRnGPg1UGJC5DmAIkgEIyZdaENliT03G0MHTem6DTuIhanZEvHb8hiO05lWQg1VN\nzVQ1JQUQ8En9jz5mnWGqGT6fs/T0qwqYbvKVlqWUX1344fkYOJDsMfbILeMFhr2SAru0eiIbe0EX\nlYzhEFniIF9SowFcSC5OpjK/k9SQpX4wTF5KK672jv25BU9RPiWS8QME6m3Q708Ejy4+9nlNArtm\nuyyh6OApLonOrfz+SHtvtiafyY/fnUw1SCIB1KVUZsnb88DTTL5ZrbyH2Va0g6V1ECSVtjYiy8Cb\nfU2nRctVityPfaGGHqhjso7dDwZPiZp+XIqVH5rUU7una1qEhNL6scyv3I8bbBUMHz36fO1Crz8G\nSQPtHX3vfLzmzUq5+dXl+2X5OziQrBi7dMvAROBr5kFMhic/x0VF5DFzDeA44dsVHsuYXAp7IhpG\nY9cEBIOwRDK4WYKxFks0aINk2zSumolGxq5ieBiTQ7wAs8UBAv5id9zdGvBu1Q1h++Kjh/4NsUEP\n7tfBDeuK0aCFMzb/zCzVMnanEl1u/R6YWRbRNHa5H1Otj8HMBEkx6KUBfB+Tb/362vGxImNn2cAu\nxckAezcxc5nQNO6rATtOBCp4CnVTjL890Js5eGqBffyeDQJ4MMmF8QbJzIPJD7X0EKj5/osaNfzd\nKG+N3+EncaHLZZ90h5KLcVGFBMEPwmOmKmrsMsO0HpMjS/GqVo81KcVo8sP96IrZOAxfMvA1jHGi\nBuCVOAIuGKmXieZKsJOr3M4ksPMFffSoN8EQogb4vCytEg1kgKHvHZeNVjMDxi6/Wzwk9iEsJlI/\nArWuA8/b80Oo99M0dgy2eq/9agNyAnDwjZsldAoGKrofEqm/V3aJoNVH1SCLkVxGsCFfZnDAbwVy\ngpJcipRcNDM370jtfL2Z/84BQ2TsbRWU1d9LoKUzOHmTH65SqrTiWD8ZwG225Qj4qL2HZRQCYJf2\nSJTuIiLAz0U2z5cfVLVB++ka9XpSlMe0LVozr/XSzWQ2OcqMFMMlAixjr/72rMcm0Vj1FccaEdGl\nQ40ja0Eoifb720+jnUlgb1r6VgG71NjPdfZGRZILA3VbWmnGjiyCSxAoViCSHdDWuJmWhyjdeEAt\n33xkSg1A7RoiwbQgLdr4jA3g2/rdYz8O4PF7joCBoX3NVn2EKpFKV9YDkl0uUp+W51ZwwIuknJRI\n2SDlm5XMS64dxu752w2AwzmgvIXMPHqhRuRv93zpGDyv/QOp7auEIrJ5eXvpBEJm7sVetHTnr1LQ\n5XIIsmRkg0RC4b50xlh/k6uZV/mxR8mlyZXeGMTV9KpLtNnyuxXk/htjl98rCaVUBDCGhxmp0HJW\nPgAAIABJREFUqL2fRjujwM4z5LZebKK21Ll0tFVsumnpkDEG9iWb6KRnYKLxZmLRMO6/Ag8t0fiQ\ntNIBenWBJQh4P9WLi6zWtU2yrVGXKkWgxoCO0dI7PYDbwEbGrsHpCNirYuaiGmTTj4uRExicpKTD\n3+HJUjn7Xu+IjVbvtueW8Vwxhpm3/YzXCLV6ms4Z3+c69QfauyczdfJazJBc5CrFMHax/1aaIuuS\nAsi0A6kkYtoRgF8JGDv38/MiC+IVZyXHBgN3VVtsEp/n9eeM1I3xt2dT6I9IEz4vqHr5qKcDoQhI\nwJe/V5xafOzzGl+gR4CxM0A+etQbnZvIArgtQZBge52RSjSyBW8GXuckGD4CdRCphxIE4zm0ZAoj\nuRSr1Y/MjOjIcdEQWW20DsgN9u9mWkcwQXRmItDfW5k5Mm2oLUPUwEkm8fAxVMYOS24ES7k9+tub\nrREAOY0stb59CALDPGmhj92wWhk8dVwxXpC0bh9JMaY/K6BW19SdILK7IsiJCYIu9hbd/9qPrpga\nw9Eyg9HkgURdAbcMfwa1d/6sN7HXVa2RN30AX3XTGNl6GrvjQJMAvrKA/+iRJpQrQTSJHNPGoTZt\nnEY708B+CS58u5A6qFp96Ue9ejkw1kuWbyVKKXC/dNkkLnH/lSP70NaHx9HSfc281VHHpIw6gJ1J\n63DbA/PfsyTe+kvicCIAxm6Z3KQ3y0QkB7QwqMr7bPKDvkbF0dijoCqz3VaVUe8/KhFQ7ZGGsUf9\nvnd7ZxKXk2HKjiJXS8egao4nAs/r3aVWpsEjCCYLd7pWhyA/1v49KzmzItzo2E5X+/V++Biq773z\nz806xIqRN7nUANogpSyJLjr2w6+BvBFZ192BAGpPEXj0cEurnEzm8SMM+Auw727yrSvn1AWebshG\nAz7//CgCvnDXjJ+XNze7dZTXXaLLVXLRkwdq9URaA3dZB+qBAvyMdDNp9Qh+RONDiy6asR+XxG0i\nkJ/ft7TGAdwCjP7S3WWXOVUPuGWp4/2U8SUlJyjmb+u18DEVR3KpwdOZkktl5mjxzPqcMasWJwJV\nqrh4Wbh29aIm8DmMPbfAMG4fOkoGwdjhubCJSADg+1wxzMwhtlPBdWvJUpeTCfLzZ/pSJlJkyZIv\nb1obpIyZKc1clAjAYCvRiAseMx/NGfp4xn6NOyklWnepXiO5r6vdziawS9Du7Mw5DLq/MvZNr7dn\njf3QPmzrLlUGjrM8lv/ln7E0wdgvkiBc94ujjU4RfHQ/tIfWspHDTW988mN/EPQKmblmbAhmVqKx\nOnRKFIBNwNgzlwgAZi6YdiRX6IAhvJhDHKu0QaLkgn51/r/2wyolysKMfO9Y9VH27wqe4mTGhdV8\noLYM3712Im7Bv8tzw7LN0X3G5wX7EcBNMD/rcYuEgn8+2nLNGXuNUN7k5wvHjlyxuyv5DdgaA6CW\nNmh01xCNZAZZuYzbLW9Q2tPkTVBSjLM8Imoz8KYf1DY5Ty6XQFq55EoxgpkD4CNL4c9eqW8vd9gI\nRvYF+HlM3itZQDQCNU4QY3+ggcLS1/QjgENma11ab228oSXT+GV4pQ2yXovJl45BVS49a1iq5wEX\n2jsfB5GXecrnTNO5oeTC/X7macTMjUQjVi+qDopg8lENehsk58S14k4Etmhc3jGJ2ozULJ4j/j55\nLlEJCgRqDJ5iUB1Xfvw3rwKilGhwbG4qk9er6VoHPlssuLLxY2/I2KUrxpNiNv3gau94nPJ6nKYM\nQ3RWgV0Y/RWwZ7//AG6+bAyY499AcnGlmNzeuJQTbK+DJ0Tjg33oBFX5JdSeBctbQtcEJccSRmQ1\ndvSf80dWewZq9Gq8QxyoIMUYB8fgxA8kYzeJSMVMBDmn+uo93yGCTM5n7GxrNIBvJBcfwCMbpHUg\n6WunXpwxDApEeVWDgUEJvBIwcrZvaOLv8iQdnhS9yZVovM+eDl3vZ9b9sSvGr4B6CGSG3S9XvFWt\nAHCURLxg6zr78mZ7J6k1KhCxy8WRbo961xXzKEgunvVxPB4fa4gaDp1m4JTorAK7M4tif3RDcEbl\n33NCFplFgFEz5MvgV639G8tepVvG9bGD3VHWr9A6ZEtQ8vTAw61lZkRTobSsa4iM/cFANYwdNVa9\nPU4E/PNmO5gldKuyCEEy5ezIqr++gKPT+6nWvzn+9gwZphFQR9o7MvngWpj9CC3dSiuywJl/LfTq\npZWa8OQqzx7pvXRC3mfveTncajKT9z0XUI8da5Djd2BhLexfG8D3nGZMiuxq1ysRsBYSiocFPEZa\nP0/INIuZ88qfyAI4X6dzq45Os51NYA+kmOjCy5uGM2qL5vv95mcJ1KClezUhxonAsg62NW6AOTX9\nEANDbYCtYf9EttKlZFrI/Md+/6UjKN3wV+1LOFFgkxMd9b6tzatBL4On8ja0VYqVaNh/jt/r1nWf\nbI1eFibRjuBpKMWAJh8x/9yAHQPGVR7y5CqwTbbtHcbeCcbe4X7IuKiiFV6ceRww805v367RuL/G\nwPUzjAlK3B8DvpMb0smJQE9+fEwesRsGO2aJHL+6I+OM37V75Y/bEzV1YZFiZrRQigmYPEencXv5\nGQR8LzjCP0/4YLV09yHMLuuovnTDwP0AkGRUHoCjK0YOvDWwHe6Xx4RLaMvYoxRxOyBXOZnaMvyZ\nOPmmhK+D8yQaL1mnAr4TbCWS2bMakKvGntv+5fbI5E0RsDpBRCsCLQ3xZ0vItHUJgnpunlyVpMau\nr3UtuOUQgcNtccnLvkQkm9msiUBKSQM1MvatI8V0OZwI9jN/S+yOttbfjtsQtXGKwVC5zbkZMTwi\n+bpNH0fOlBSTUvqmlNLtKaWSUnreSR3UvqYLfwXAHiyJzIxaZ1p/Bsa/xauCXAc8PiQe4LN9Eb3b\nq9zADJelRCOAR0toj+Ff2fQG/Mbtd2cYGskFBnxK42v/sDQBb9MAglQ/OkSINBuNAom+19uy4LGE\nsQ/s+4t66fgBAjJaPPncbP323cy/nlsht1YMa/LeqsYGSUWwVTzC47V2Cq5JYHcnv/F5kZmqREJa\nCbR0JCFef8TMVwLwMfkOJxSiKc7lyJs64zv4OXLRBTgSrvwRXyLiyFLM+gwBOxHdRkTfSES/fwLH\nMrvJiy21qy6nuhS0M2cA4GxHMlLM8ZZjnoecj6np0Jo54TsSx37hZnAYu2EXwjd8nAEc+tiBIUXB\nM/7upjfrc4sYe3WIwLXjgmgemO2qIeOxYM/fTjSjcmUI+NO16DRQY0mBqOoj7qedQzGSi7pGZjIL\nkr64ZjlIK1xbCL3hfEzehL/rOSKyjB1XcvxzqyGjV4ue3TFm4DmUaOqqWR1rxNL9MatxxAfwCOSj\nFT7iS5ViTtHqSPQYgX0YhvcMw3DHSR3M3CYv0g0HOijBF/hi0B9p6fZG7QftaPkWTQSRVo8lC4im\nLDnnAcNAjwRqXBHw9i5j3/hghkwrCqoSjYCGlkD+bi9FnIOhXiCxd2yQDGYeS+XXuBnr32Qh9HRl\nllwwuNk0cz4vn2lHTJ6v9VEQhEUmL48VVyPVu4/n3ElZSgN4lJFaBjLuKmlrRNlr7O8Na+bt1bXY\nNeF3uVp8O/UM72Dse7X3YBzNMExE23vJSuN+/JW/JI6RCeMAgqQX1yuzn9Nop/ZtKaUXpJRuSSnd\nct999z2mfcnZ9eK5lfobX+Dza32B+SZiPxbsqdvnxvBT2v9gRAzfS//n7QePdXQM7NqCFWmjfNxx\nkDRi7EW9wHdvIoqz6ljlbFwRRCNARgkn+KYc7i+FfKD2QC6L2uQAisNAtMHgKZxb5GZBAEdAjpK1\n+JJsYFLkQ/MYO78FCie56t13ANzLSJUBZi8mc9QXA6JEU0Kb87xETD4Ktkf2xUPHYBBJK132c0lU\n8FROEOGqOVhZq58FmAcMfKcvPdTSx89cBHy58fyITzccaJy62m0vsKeUXpdSus359w3H+aJhGF48\nDMPzhmF43k033fTZHzHpwWwZ+/i3C2ufsV9Y443yAR+LF9X9BA+G5y3H7aNtvJ9NULUyeawJ4/fL\nAawDUuPPtrYMDmCtN0dyAgN+BwMs2n5bBvX2+tavq0FyfxnILWTFVkHv2h1toYTt9GOUYWoBnNQ5\n8++2omUwEYhAYk7+qmb03NuKhuzdj5xAptJlAPhyAtf9bXXhyRiHW1sWmmhcQUoisE9jr4x9jsbe\n+Ss8qb17xzRuExGtGYxd7Edq4Fpy0YSPxzPiC+8XlYIbJuJ5w7nTBfa93zYMw9eexoF8tu0izITM\nrmNghxtSgxv+BIEzMy45cT/yu3CbSLqJ9hMx7ZXDUmZr7F1ytzcv1BDgl1OQYSqYmQZeq+Hz+aAO\nzd8xBk8tYx8BP5v9VEeJIzNsDGi1fpR6iJxVShD03KfJY3CW/+ZNcrvkqvZqRH1ufT+oOuD8WQ/w\n5SSnYzjj/8bHnhpBiBi7B4pRUS+2lkbB0JDYgCbvrWpDySXYT6Sr69IkbfxHduq2354uAICfnyYG\n7L9xAnRm7qfVTlf4uQrthnP6QvItxAtcmXzQfz5w0ZwHhh9Fyec9bAGrDz8bLA8dph191kg0cqA6\ngO8PvOwOYB0Yhu2d/eTsB1WllQ/lisjZ4ZX/lQCbPSmmx4mD6vby81ibnr8j0t4xHR/PwZViZHzC\nsbvGjN2px+7U6d/H2A/h7UBye09jRzstZ896wVMv6D9u4xMe1OG9nzWhCIiQE6vCbeR4Pm4+jPwd\nV/hPOrcmIsvYnzQB+o2nzNgfE7CnlP7rlNI9RPSVRPTvU0qvPZnDmt+efH6tfucbhBc+uiFx/3hz\nMWMsSiue0x89hJ4kIo9h7Pd1+2iy8Aat/BmZf01QcXzDUjNHphVJLn5QNblAoPRmh/lFZXuNJi8Y\nuHduqB9HpQNMIhIEW2OG7/jVo2uU/BrkWTh7fO++c408Tb4y9kCiC3zsR1vfjXUIQXveF7tTjgvg\nsRS5X3IJ7cdq7PhjUI5nmQ9zLgB2BGreLa78mZFfAAXhXIBHV7s9pmlkGIZXEtErT+hYjtU4gPaM\nJ51T/TwIkcmzxhVpY8jMI8bO/QddNi9/aPv0AXmO0yZcTmb/AfbYGO7HW2V4OjdRzNiPHGklJ9+v\nPEo0Ntgqt8fkmwjMdr1copSmf+M5eMFTI8UIJs/7lf0I1EaKMf3BSyScVU0WsgQy88rYnUlucPYT\nlfOt18KZzMZ+//5LPTjq579tev2GJjzPeY6y/WMEs7Pd7cV+JJBGtkaJBVFtKQRqfp4vHPjBU8SX\nBP+fVjuzUswLv/FL6Es/7yn0OU8+r/q5HshTLx6ofp55jfY+PSRzXTSVyRvA9x9atSQMZZz5Gjvu\nJ3II7GPsuP9mCQyCpI5ffdU1jR0TlNp+SG3vgVzT0m0Z3p1WPvRuCwDHhKaxfyDR3QA/KAK2175o\nGL5m/ryNm6AUMXaxPTL5BuD6GSnFvi9UTkLefT7cgK1R2B2j2Itl7Gww0P2RPBjLhv6zPc+XHgRD\nA1+6HLdSlsU66nWbYPxjP7+s5ek3aAXhv/rzz6JnPfUC/Y0v+Vw6zXa6ws8Jtr/zvGfT33nes00/\nA/jTAdj5wUV7ZJVuQHLhWRv797lo8G9dINF0wQN5XH0+BO1oP8FSlzVTLtyFDKwxbVKf95KvtESj\nGbuvNzf3Cx6rW0BLMGoveIpgJkHODZ7uqa+OkktYaiAIhoa1xqvGntX2frB1BPCByMhMbratYub+\nKmVWsD0gAvJvBvCDeFDE5OdJNP7PcqwpySVwuUgpRhovopR/lGL4GUPTBpsvbjyngf05N91Ib/zH\nX+Pu+2q2M8vYo/a//LUvoufcdAN9wTNvVP1ci/tpF/WFZ43eSC4hMx9/t1XcxMOmSgmLh2rtP+To\n3W3HELGXzx7wI/CXn+9goIaSU46BOspIjECLXyuHssFOjzaCkGLmEbD7DF9+PgLq6lfnySzwq2Pg\n1gX8qL+L4xackeoHhufVFopiLLJQVsSyu5nPS7N77nh25qxegwQiuT2+E8HtD/YjWXdUfRHNFvyy\nlqcBM/+Or/58+rM33UDPu/lp7n5Ou51Zxh6153/x59Lzv9guexiInwTB1idfWE3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ac.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Another Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another example is demonstrated using a `Lightcurve` with Poisson Noise." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from stingray.crosscorrelation import AutoCorrelation\n", "dt = 0.001 # seconds\n", "exposure = 20. # seconds\n", "freq = 1 # Hz\n", "times = np.arange(0, exposure, dt) # seconds\n", "\n", "signal_1 = 300 * np.sin(2.*np.pi*freq*times) + 1000 # counts/s\n", "noisy_1 = np.random.poisson(signal_1*dt) # counts\n", "lc = Lightcurve(times, noisy_1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`AutoCorrelation` also supports `{full,same,valid}` modes similar to `CrossCorrelation`" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ac = AutoCorrelation(lc, mode = 'full')" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([-0.00487599, -0.00485198, -0.99992797, ..., -0.99992797,\n", " -0.00485198, -0.00487599])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.corr" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([-19.999, -19.998, -19.997, ..., 19.997, 19.998, 19.999])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.time_lags" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ac.time_shift" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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