{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# The Stingray Modeling API Explained\n", "\n", "Some more in-depth explanations of how the Stingray modeling API works.\n", "\n", "Who should be using this API?\n", "Basically, anyone who wants to model power spectral products with parametric functions. The purpose of this API is two-fold:\n", "(1) provide convenient methods and classes in order to model a large range of typical data representations implemented in Stingray\n", "(2) provide a more general framework for users to build their own models\n", "\n", "A note on terminology: in this tutorial, we largely use _model_ to denote both the parametric model describing the underlying process that generated the data, and the statistical model used to account for uncertainties in the measurement process. \n", "\n", "The `modeling` subpackage defines a wider range of classes for typical statistical models than most standard modelling packages in X-ray astronomy, including likelihoods for Gaussian-distributed uncertainties (what astronomers call the $\\chi^2$ likelihood), Poisson-distributed data (e.g. light curves) and $\\chi^2$-distributed data (confusingly, *not* what astronomers call the $\\chi^2$ likelihood, but the likelihood of data with $\\chi^2$-distributed uncertainties appropriate for power spectra). It also defines a superclass `LogLikelihood` that make extending the framework to other types of data uncertainties straightforward. It supports Bayesian modelling via the `Posterior` class and its subclasses (for different types of data, equivalent to the likelihood classes) and provides support for defining priors. \n", "\n", "The class `ParameterEstimation` and its data type-specific subclasses implement a range of operations usually done with power spectra and other products, including optimization (fitting), sampling (via Markov-Chain Monte Carlo), calibrating models comparison metrics (particularly likelihood ratio tests) and outlier statistics (for finding periodic signal candidates).\n", "\n", "Overall, it is designed to be as modular as possible and extensible to new data types and problems in many places, though we do explicitly *not* aim to provide a fully general modelling framework (for example, at the moment, we have given no thought to modeling multi-variate data, though this may change in the future).\n", "\n", "\n", "## Some background\n", "\n", "Modeling power spectra and light curves with parametric models is a fairly standard task. Stingray aims to make solving these problems as easy as possible. \n", "\n", "We aim to integrate our existing code with `astropy.modeling` for for maximum compatibility. Please note, however, that we are only using the models, not the fitting interface, which is too constrained for our purposes. \n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "# ignore warnings to make notebook easier to see online\n", "# COMMENT OUT THESE LINES FOR ACTUAL ANALYSIS\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Install seaborn. It help you make prettier figures!\n" ] } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "try:\n", " import seaborn as sns\n", " sns.set_palette(\"colorblind\")\n", "except ImportError:\n", " print(\"Install seaborn. It help you make prettier figures!\")\n", "\n", "import numpy as np\n", "\n", "from astropy.modeling import models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The models and API of `astropy.modeling.models` is explained in the [astropy documentation](http://docs.astropy.org/en/stable/modeling/) in more detail.\n", "\n", "Here's how you instantiate a simple 1-D Gaussian:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "g = models.Gaussian1D()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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s2VJSBcZm39bV1VXzw7pBr5lItl4PIGwEkgCQAn6Boa27u7sYCA0PD8vY2JjntpZlyejoqAwPD4fe1qRQec1sWXg9gCgQSAJACgQFhiIiY2NjxUDoyJEjSvtV3S6NVF6zcrX8egBRmFvtBgAAgukGhsuXL1faXnW7JLMX1ZQzCQpr4fUA4kSPJACkgG5g2NraKvl8XnK5nOt2uVxOmpubpbW1NbQ2Jo1OUJiF1wOIAoEkACSYXUv72muvDQyMLrzwQrn66qtFRKSurk52794tIjIrmLSv79q1S+rq6iJodTIEBdO2rLweQBQIJAEgJe666y7f/584cUJWrVpVTGPT0dEhfX19smLFipLt8vm89PX1+aYOqgV+wbRTVl4PIAo5S2U5W4jOnDkjjY2NMjk5KQ0NDXE+NACkzvT0tNTX14uIyLFjx2Tp0qW+29sBkzMwso+7IiKDg4PS1taWqZ63QqEgt9xyi2sKoCy+HoAK1XiNHkkAqCFuORGdQdKaNWsyFzR1dHTIoUOHitedicez+HoAYSKQBIAaQ07E2ZzBYktLS8X7s+eu5nI5mZ6ernh/QFoRSAJAjSInIoCoEUgCQI0iJyKAqJGQHABqTC6Xk3w+T05EAJGjRxIAUswtrY1lWbJjxw4WkRhi/iOgjkASAFLCXoXttGzZMtdt29vbo24OABBIAkBarF69etZt//qv/1q87ExrAwBxIJAEgARz9kK6rcK+6aabipfDSGsDADoIJAEgoQqFgrzuda+rdjMAwBOrtgEggQqFgnR2dkpQFVuVKrcLFixQ2g4AdNEjCQAJMzMzI1u2bCH4i4gdWE9NTUl9fT2rs4EKEEgCQMIMDw/L2NhYtZtRU+zg0bIsWbBgQcX7c85dHRoacl1RD2SBViB59913y+WXXy4LFy6UJUuWyHve8x759a9/HVXbACCTdEobuuWRRLQKhYJccsklxevr16+XlStXsmoemaQVSD7++OOyefNmOXDggPzoRz+SP/3pT9LW1saQAACEiNKGyWXPXR0fHy+5fXx8XDo7OwkmkTk5q4JJOMePH5clS5bI448/LmvWrHHd5uzZs3L27Nni9TNnzkhzc7NMTk5KQ0OD6UMDQM2amZmRlStXyvj4uO88yXw+Lz09PXLjjTeKiMixY8dk6dKlIiIyNTUVyhBuLZuenpb6+noRKX29vG633xevaQd2acrDhw9TVQipd+bMGWlsbAyM1yqaIzk5OSkiIosWLfLc5u6775bGxsbiX3NzcyUPCQA1r66uTnbv3i0i3kPXt912mzz77LNUsImA1/zHoLmrlmXJ6OioDA8PR95GICmMA8nz589LV1eXtLS0yOtf/3rP7bZt2yaTk5PFv9HRUdOHBIDM6OjokL6+PlmxYoXr/7dt2zar14sFIJXzm/+oOndVZ44rkHbGgeTmzZvll7/8pTz44IO+282bN08aGhpK/gAAwTo6OuTQoUPF627z7+zVyP39/XL55ZcXb2cBiL6g+Y+/+c1vlPbDHFdkidEcyZtvvlkGBgZkaGhILrroIq37qo65AwBK5+t5zYH0Sl5uD4v39fVJR0dHjK1OB+drOzk5KZdeeqnv0HVTU5PkcjnPuavMkUQtiWSOpGVZcvPNN8vDDz8s//Ef/6EdRAIAwuWXvNy+rauri2HuACMjI4G5O8fHx2VsbEwsy5o1d9W+vmvXLoJIZIpWILl582bZs2eP9Pb2ysKFC+Xo0aNy9OhR+eMf/xhV+wAAPlgAEo6jR49qbb9s2bKS6/l8np5fZJJWIHnffffJ5OSkXHPNNbJ8+fLi30MPPRRV+wAAPlgAEo7ywDDIwYMHi5cHBwfl8OHDBJHIpLk6G1P3FQCSRXVhBwtAZnMO98/MzEg+n/fN3blixQqZmJgQESkZvl6zZg3D2cgsam0DQJVMT09LLpeTXC5nXCGstbVV8vm8Z77JXC4nzc3N0traWklTa055mp93v/vd8sc//tF1/qPtzjvvjKt5QGoQSAJAivklL2cBiDuvND+nTp0SEZFXvvKVrve77rrrIm8bkDYEkgCQcl7Jy1kAMlvQKvdcLicvf/nLi7eRhxPwpzVHEgBQPXbycTcdHR2ydu1aaWxsFJGXFoC0tbXRE1lGZZW7s6eypaUljmYBqUWPJADUCBaABGP1OhAuAkkAQGaweh0IF4EkACSYPZxtWVaxJCLMBa1yF5GSuabOFEEjIyORtg1IIwJJAEBm+K1ytznT/Kxevbp4mUVLwGwEkgCATPFa5W5zpvnxmlP5+c9/PpK2AWlDIAkAyJyOjg45dOhQ8bozzY9zONvLzp07i5fr6+srSioPpBmBJAAgk5yr2p1pfg4cOKC8D7+5lkAWEEgCQJU4e76GhoaUesIQvWPHjlW7CUBqEEgCQBWU13pev369rFy5kkoqCbB06VLlbb0SxANZQSAJADHzqvU8Pj4unZ2dBJNVdtVVV1W7CUBqEEgCQIyCaj2LiHR1dRkNc5NzMhwNDQ3S39/P/EdAAYEkAMRIpdbz6OioDA8Px9gqlM9XbW9v900RZCPYRNYRSAJAjFRrPVMTOl7OxOP2fFURkf/6r//yvA9BJEAgCQCxUq31TE3oeJUH7vZ81UceeaR4W/l7ks/nZc+ePbG0D0gqAkkAiFFQredcLifNzc3S2toac8uyx28eqj1ftbu7u3jbwYMHi5cHBwfl8OHD0t7eHl0DgRQgkASAGPnVerav79q1qyRZNqIxMjLi+3/LskrmszrfkzVr1vAeAUIgCQCx86r1nM/npa+vTzo6OqrUsmz5wx/+UO0mAKlHIAkAVVBe69keKiWIjE8Y81CpToSsI5AEgCphqLS6VOar5vN5z/tTnQggkAQAZJTKfNWenh7X+w4MDFCdCBACSQBAhgXNV/Valb1161bf6kRbtmyRXC4nuVxOpqenw284kBAEkgCATDOZr1reE+lUvtobqGUEkgCQMNPT0/RmxYz5qoCZudVuAAAASbVgwYLicDVBPTAbPZIAAGhqamoyXu0N1BICSQBIAIazk8/unbQsS770pS+JiP5qb6DWEEgCAKDJdLU3UGsIJAEAMEB1IoBAEgBi4TZ07RwqXbBgQZVbCBOs9kbWEUgCAADACIEkAAAAjBBIAgAQspmZmeLloaGhkutALSGQBABkXpjzVQuFglxyySXF6+vXr5eVK1dKoVCotJlA4hBIAkDC0JuVXoVCQTo7O2fV4h4fH5fOzk6CSdQcAkkASJjVq1cXL9OblR4zMzOyZcuWYklFJ/u2rq4uTgxQUwgkASBhjhw5UnKd3qx0GBkZkbGxMc//W5Ylo6OjMjw8HGOrgGgRSAJAhcIob+jXS0VvVjocPXpUabvyEwUgzQgkASABgnqp6M1KvmXLliltt3z58ohbAsRnbrUbAABZVygU5O///u+VtqU3K1ns1d4iL/Uq5/N5GR8fd50nmcvlJJ/PS2tra9zNBCJDjyQAVJG9yvf06dNK29OblVx1dXWye/duEXkpaHSyr+/atYsyiqgpBJIAEAO3lD5+q3zL5XI5aW5upjcr4To6OqSvr09WrFhRcns+n5e+vj7p6OioUsuAaBBIAkDEvBJU33XXXb6rfMvRm5UOHR0dcujQoeL1wcFBOXz4sGcQGcZiLaBamCMJABGyh67Lex3Hx8fl9ttvV9rH4sWL5etf/zq9WSniDPjXrFnDCQBqFoEkAEREJUG1ioceekje/va3h9k0AAgFQ9sAEJHh4WGtoWs3+XxerrnmmnAaBAAhI5AEgIjopOopX+Vr6+npYVg0JZjriCwikASAiKim6rnjjjtmrfK1tbe3h9kkAAgVgSQAVMgttY+ISGtrq+Tzec/eRjulz2233Vayypea2gDSgkASACrgldqnUChoJah2Dl+3tLTE0HIAqByBJAAYslP7jI+Pl9w+Pj4unZ2dUigUSFANoKYRSAKAAZXUPl1dXTIzM6OdoBoA0oJAEgAMBKX2sSxLRkdHZXh4WERIUA2gNhFIAoAB1dQ+OimAkE1ei7WANCCQBAADqql9VLdDbVmwYIFYliWWZcmCBQs8t/NbrAWkAYEkABhQTe3T2toac8uQFiqLtYCkI5AEAAM6qX3K1dfX+1Y/Ue3NQnrpLNYCkoxAEgACeJW+I7UPnHTmOuou1gKSikASACpAah+I6M91ZLEWagWBJABUKIzUPgxnp5fJXEcWa6FWEEgCAGDIdK4ji7VQKwgkAQAwZDrXsZLFWkCSEEgCQAzsoeupqalqNwUhqmSuI4u1UAsIJAEAMKQ717E8AwCLtZB2BJIAABiqZK6jHVQ2NjYWb6MOO9KGQBIAAEPMdUTWEUgCAFAB5joiy+ZWuwEAAKRdR0eHrF27tjhMPTg4KG1tbfREouZp90gODQ3Ju9/9blmxYoXkcjn57ne/G0GzACDZvMomBtEpo4d0CSMxPZA22oHk9PS0vOlNb5J77703ivYAQOKEFfzpltFDbTA96QDSQHto+53vfKe8853vVN7+7Nmzcvbs2eL1M2fO6D4kAFRNoVCQW265pXh9/fr1ks/npaenp3ibnSMyaD+dnZ2ztrPL6DGXDkAaRb7Y5u6775bGxsbiX3Nzc9QPCQCh8KuhvHHjRuX9mJbRA4CkizyQ3LZtm0xOThb/RkdHo35IAKiYSvCnyrSMHgAkXeSrtufNmyfz5s2L+mEAIFQqwZ+qSsroAUCSkf4HAFyEEdRNT09LfX298vaq5faQXs7pCyMjI8XLU1NTsmDBgmo0CagICckBwEXYQV1TU5NRGT3UltWrVxcvOxdXkQoKaaUdSE5NTclTTz0lTz31lIiIHD58WJ566in5/e9/H3bbAKBqVGoo69i5c6fr/Sijly1ePd2kgkJaaQeSv/jFL+TNb36zvPnNbxYRkVtvvVXe/OY3y/bt20NvHABUi0oNZR3t7e2U0cso1Z5GOxUUwSTSRDuQvOaaa8SyrFl/DzzwQATNA4Dq8auhvGfPHqP9HTp0qHh9cHBQDh8+TBBZ45xzIf2QCgppxBxJAPBRHvyJiIyOjsq1115bvK4zv40yerXLTkxvWVbJwpmjR48q74NUUEgbAkkACOAW7DkXTTC/DX6WLFmifR/VrAGUX0S1EUgCgIHyH3rmt8FNoVCQj3zkI9r3IxUU0oJAEgBCwPw2lLNLbE5MTCjfh1RQSBsCSQAIiT2/be7cuQw1ZpxfiU0vpIJCGhFIAgAQsqASm25IBYU0IpAEgIg4h7ipXJItuiU2404FxSIdhIVAEgD+rNIf11wuJ/l8vnjdbWX3wMBAKG1FsukuliEVFNKKQBIADHhVu+np6Sne5raye+PGjdE3DlUXVGJTRGYlugfSiEASAAwsW7as5Lo9v+1d73qX5310Fl4g3fxKbNruvPPOWbcx5Iy0IZAEAAMHDx4sXnbObwsqh2cHk/v37y+pfoLa41Vi03bdddfF3CIgfASSADJHt9fHLn03OTlZvO3AgQPFy875barl8HQXYyCdyktsmiasp6cSSUUgCQAKCoWCXHLJJcXrXqtry4e8vVC5JDuci2haWlpC3TeZAVBtBJIA4MLZA9Tb2yudnZ0yPj7uuq1zJXZQoEDlEoSl/OSGmu+oBgJJADUtjCHBrVu3+i6U6e7uLvYEOXufvFZ2U7kElbLLL5af3FDzHXEjkASAAF49kbaxsTEZHh4WkdKhxkWLFpVsR+UShMGv/CI13xE3AkkACMGRI0dmDTWePHmyeDnuyiWoXSMjI77lF+2a7/bJDRAlAkkAiRXHStWwHuM3v/mN7zzK06dPM5yNYgYAy7IC0z95fTbJDIAkIZAEgD9zDgU680E2NTX5VihpamqSf/u3f1OeRwmI6AWVTmFkBmC1N8JCIAkAf+asje0cgt65c6eIeFco2bRpk+9Qo0jpPEqgEi0tLb7lF4MyA7DaG2EikASAP/MbCvSrULJq1aqK9w+o8iu/GJQZgNXeCFumA8msVQrI2vMFVKgM6XV3d0t7e7tnhRKSkCMsXtMrynmVX/TLDMBqb0Qh04EkgGxy/lDef//9gdvbw9LOHp62trbi/La2tjbfoUaRl37gSUIOP37Vk9zmNJaXXwzKDDA8PMxqb4SOQBJATVDtcS//sd6+fbvS/v2Gpf2GGm09PT2s2s4olUU1XkPOtksvvbR42Tmn0fmZctZ8d6M6tYIpGMmQllFEAkkAmTEwMOD7Y+1nyZIlvv/3Gmq0tbe3az8mssFvyNl2+vTpkuv2nEZnec4gqlMrmIIBHQSSABIl7LNw55Bg0I+1n02bNgX+aJcPNbJwASqChpzd2D2cn/rUp5Tv09rayhQMhI5AEqmXlu5/xK98GPvEiRPG+xofH5eNGzcGbuccWmxpaTF+PGRHJUPJExMTytsyBQNRIJD8M4IRINnq6+u1vp9Bc850mfZkAkHiHEpmCgbCRiAJILFM05CozDkzobs/08olyBaVIecwMQUDYarpQJJeRiDdnJVmbCqLC0ZGRrTnnAHVojLk7MWrZ1HlMW1MwUAlajqQBJBubnPHNm7cGNiDcvTo0aiaBEQiaMjZy5133hlRiwA1BJIAEkVlODuo+oZqpRldcQ09Ips6Ojrk6aef1rrPddddF1FrADUEkhniVhkBSBq/snAiatU3WlpaQp9zRhCJOBw4cKDaTTDCVLLsynQgqVrTtBaUp0FxVkZww0EB1aI6LF1ppRlddg1jFs8gSkmclsHvQSlej1KZDST9apqGwfSDFsUH1CsNil0ZIWi+GV8axEl1WLo8ZUp5j3t7e7vnnLOtW7dqtSmohjEQFt1pGWQGqF1pGUXMZCAZlF9Op+RU0vmlQbFvC5pvBsQpaAVpLpeT5ubmkuobXj3uIlKS5sTW1dUV2A5nABpUwxgIi8oKatOV2kgP3VHEaspcIKmSX667u7tmAqug0lsq882AODkDNq9h6V27dhW3C+pxf+SRR4weg9WwqIZqfDbT0vOVFV7HtLGxMaVRxLhlLpBUqWk6NjZWM4GVaumtSkp0VRsHwdrifP8WLVo06/979uwpDjGr9Lh3d3f7Pp7XUKLpaliGGhEWr8/mO97xjuLlMI55znytSe75ygKVzq6kjSJmLpDMQmDlpFp6K84SXc45l88991xF8y/T1P2fdHHMhQ16jPL38+TJk7O2cZZwU+lxDzpxPHjwYMnjA0nh9dkMO/Ar/71TnT8fhPn1+tI4ipi5QFI1YFqyZEnELYlHUOktt/lmaVHpIiIki2ptbGcPjOkJnzNLg3Mosa2tjd5EJIZX9RmdwM8rmJs/f77k83nXx2X+fPWksbMrc4Gkak3TTZs21UQg4pcGxb7unG+WFiwiqi06tbGdPTCmPemsvkba+B3LTI55aez5yoIkjiIGqelA0m3unGp+uVrq1fIqvWXnxUvjjyoHwdqiMnfZyf5+Hj9+PLDHffHixb77+v73v6/VVqAaghKV6x7zqtnzxZC3tzSOItZsIOk1d663t1c2bNgglmXJ0qVLPe9vn+Ft2bKlJj7wHR0dJWlQ0p4XL43d//Cm+z7Z389PfvKT8sUvflFE3Hvc7WFqP5/5zGe0HhuIktdirWPHjind/9prr1X6rUpjz1cWqHR2JW0UsSYDSb+5cxs3bixe//KXv+y7H5WJ+mni/OClPS8eB8HaYvI+2T0wF154oWeP+x133CGnTp3y3c/ExIT2YwNx8+v4UOXsCXzLW94Sas8X2TPC4zWKKFKatSIpai6QVJk7Zzt+/HhczYpVGMMGSS8fmcbuf5TS+VHzc+TIkVk97oVCQUZHR+X2228Ps8lA1bz97W8PPObp0On5CgoSvUYAa6m4h1McQXP5Mc3mzFqRFDUXSKrMnbOFcYYXtiSc1fmVj0zKmabpIiLm5iTzNaikNrbdm+m1whWoBSrHPF0qPV9BKdZURwB1JPEYZYsi5ZxXSrwXXnghjCZHz4rZ5OSkJSLW5ORkJPvv7e21RETpb2Jiwvf/uVzOyufzxetTU1Paz1NErEKhoLSP/v5+q6mpqaQN+Xze6u/v13oNpqamXB/P6/byNuRyOd/XxaRNXu07duyY0evrbG/5a9bc3OzZPpXXoNZV8vkI87Hd3nu399Pv+9nc3GydO3fOd9/Lly+P5DsORM3tO+l1zNu7d2/g99rreOv8vXL+3+v3IJfLWblczvrOd75T8v1x287kWJPU43TQ62H6u+j1HjkvV+P1UI3Xai6Q3L9/v3Ig6XyTyj8c9gfD68vpx+/HUDeAU/2Aqhwsgr6c586d8z0oRP2lMf2COA+Cg4ODxcAi6LGTdICKU5IDScsqfT+3bt2q/Bn02vfevXuL24f1HQfi4PWddDvmqQQjKr8N9t/k5GRgkPiqV71K+fc27YFk0O9j+YmtjrQHkjU3tK0yd85NeSkqOzWO7nyEoKTKbnNGkpITUTUFS5xtUlFLi4hQ+n5+8pOfdN3G+vOq1nXr1gXur7293Tf9VRLnHAF+4jjmjYyMBE4TS/s6A50h9KSknEvK9DKnmgskTeeROEtRmabGUUmq3N3dPetDkJQPqE4KlkralPSFPEg2k7lItZb+Coja0aNHQ91fkuc9qggj5VwYr0ESywDXXCAp4p+Ae8+ePa73CeMMT6VHb2xsbFbwlZSciCYpWHTblIaFPGlnerByW+gV9sFf9yTCzqk3NTVVvM10IY3Xd9wrbx9QbWF8Nk1P3MtH6by86lWvUlrsk/ZOg2qknPMqlpC0gik1GUiKzO6BsNOB3HjjjaE+jvOH9vDhw0r3OXLkSMn9LrjgAqX7RZ0TUbV8pJNOm4KG/ZN4pqUjzWfccaTv8DuJABCN1atXFy/rfOdaWlqUUqx95StfKV73k/bvezVSzt12222utydtelnNBpIi8acDUT2DKw++VL+wUedEdE4LCJLL5SSfz8u1116rFDip1lJO0plWmgNDHVGk71B9DFut5psDqs1r1CjoO6eaYq2zs9MzhZCX733ve8XLaRmJMk05Vwm/Eb+4prypqOlAMkjYXe1BAaHIS8Pr5QHhCy+8IGNjY2JZlucHdMeOHTJ37tzIgxp7WkBTU5PnNnabenp6lPeb1oU8lUp6MKqTwD+Kx7C5zR0GoK58akqQoO/c0NBQ4EI1u5fRK3m2l4985CPFy2kaifKbNud8PeKUhDLAmQ4kOzo6JJ/PS39/v+f8E50E4SpJlXt6enzPWMJaPe5Gdb5N+UFh8eLFFbcproU80KOyMtOUHUTPnTvXaO4wADXl00auv/76wPsEfefsAE9ElBaq6fTEnT9/vuR6kkaigvgt3KtGx0ESygBnJpAMmrTq1s1vksHer1KASHB5o7BWj9tMhw2cB4Wnn3664japzgN1SsKZVtKEfaD63e9+F0KrwlHp++08UZo/f37x9rQMnQEmBgYGfKeN+LHv4zXMbf8+PvLII8Xbokg3lLaRqLhSzjU1NVV9ypuKzASSQZNWu7u7S273mzfmdeZk/8hv2LBBnnjiiZJ9lW9TX1/v2p4wPqDOydVhDBs427B69WqjIXaTOapJONOqdUkqE7pkyZJQ9pO1ur/Itq1btxqPHHziE5+Qffv2ydatW13/7/X7GAXnSFQSSgVXi/O5btq0SUTim5NpKjOBZNCkVefQWxgJwp1v7lVXXVW8HEcKhPLnqhL8Rt0Vr/Nhj/JMK64DVH19faLmRTrf5zNnzhRvD3r+pjV8y/mdWds2bdpU8dBWHAuHgCQx6Ym0nThxQm644QbffZT/PkZtYGBAeyQwqt+xuH4fncfhN7zhDcXLd911lyxatEhe+cpXlmxfzTmZbjITSOpQmTemM4fPNP2CDr+AIGnDBn49jVGeaZlMVQiS9MU0bpyfR+dcKp0E/rp27twZuE/7hOfRRx81yp0Xx8IhIAnsaRy9vb0V7SeJ34tdu3ZpjQSmXfnv0smTJ0v+f+rUKTl16lTxehKLKRBIulDN6J+UROIiEhjUJmkBi3MeqNdCHp0vicoiIpOpCrXK6/NYPo/VL4G/Lnv1p99JhOoJj1evskqFKKCW1Nr0H6/Og6g6Q6IcoVLpZAhKiyYis7K5JLEMcGYCyaBesObmZjl37pxYliUXXXSR0j7f9773eX5A4uz5KxQK8v73v19p2yQsYAl7IU+QpNQyryaV5+ZcoGK/F7rZAvwOnh0dHfL1r3/d9/5eJzz2yUJ/f79cfvnlxdvXr19fnLOrWhCgt7eXCjaoCSZFJHTZOYODBM1B/od/+AffxxAJHlkLszMkihEqHaq5lUWSfxKcmUDyrrvucr3dbSg1jC/ngQMHjO9r0zmjOX36tNI+/QLqagzTxrH6LSm1zKtJZW6u8yQjqvfiueeeU9rO7YQn6Oz9f/7nf5T2XWu9OMgunSISKrymtwTlDJ6ZmfFcsGP7whe+4Pm/fD4vXV1dSm0MozOkWiNUzkB59+7dsc49jVJNB5LOIc8bbrjBdRu3oVSVfJBBjh07pryt6QIcnTOaJKUKiJvqgUe1So+XpPRoug3XqE7XUNlXJUyrP6l81h944IFEVIgC4mSnnLvwwguN7m9/L/bt2+eZaDtoZGJ4eDhw0U957kjbbbfdpjX6UemJYLVGqMp7QLdv3x7q/quppgNJJ7cPhd9QalA+SLf9OgNCnbQqpkO5qtVibGEvYIlqfknYPaOmBx7d5+dcxGLzyl8aFa/hGtXeOpV9VXK2HpQGyivYU/msj4+Py0033VTcT/l+RZKTLgMIU0dHh1alMVt5qUOVxONuKukl/Na3viUi4dWyDvr9qMYIVSW5PkXCXfgYhUwEkuU/iLbTp0/7/qiUZ7B3+wH1WpHtTPmj4/Of/7zr7W5BjeqXd/HixZGkCgjKV6kbEEaVMkflAFU+B8gkiHJ7P/7u7/6ueNkZjHq9NjqvWfm2fsM1XlM7nJwnTV4HvkqHfpzfN51gT/WzfvHFFyeuhBkQB5MT5vLvhelUo0p6Ce0KO7q1rE07HKqxSLaSXJ9JDyJFRMSK2eTkpCUi1uTkZCyP19/fb+VyOUtEZv3lcjmrv7/f9/5TU1PF7Y8dO+a6H7e/b37zmyWPo3o/55/z8ZYvX17yv3w+b91xxx1K+/nxj3+s/fxULru9ns7XVHffbrdNTU0Zve/Ox56amip+DsrfC/u2vXv3Fm/bu3ev63tW/vws6/8+z6p/+Xze6u/vn9U+r3arvl+Tk5NWPp/3fW+CPo/Oz2xTU5Pvvpqbm61z5875tmliYqJ4eXBw0Dp37lzJtuWf6ebmZs/v4/79+5Ve3/379896X+zHBmqZyrHI+Z1z+17oHrPtY9S5c+esfD5v/FvX29tbbEN/f/+s44/bsUGlrW7HUJ1jSdDx2O89KBQKRq9F+V9zc3PJ75Ppb6IJ1XitpgNJ+8Ot+oPoxjSQXLFihecPpspfeXDj9n8RsRYvXuz75c3n80bPzyu4cQYHQa9p3IFk0HPxO0A57+sXRJW/poODg9rva/l7qxNIeh2odNrh9XnU+XyL/F/Q5vW6u538OJ+3W6DpReWHyvm+6P4AAGnn/MyrnCzqnKiqHKO8TtZ1/uz9qZwImgaSQccSr9+woOOI2+9LpX9uJ+BJDCRremi7mqt1JyYm5Mc//rFYliXPPPOM0T78VsFZZbmlvLq/e3p6Kp4T5ly09OSTT/pu6/Waes0ljVP5VAWvOUBB81jsoRgR9ZyjNquCkmPlw+3Oduu0w5nHc9++fcXLuu9L0NCPW4UlZ3UZnWE0lQVwYXzWgVrgtajtuuuui+wxVdcVlHPbPspsHrpD6CpU8kHq7MuWxJyRbmo6kKx2wvAbbrhBCoWC0QfBsqzAD6VlWXLy5En553/+Z88vr24eQD+V5KuMo7qPirAOUPbzU12F7GQZlBwLK/WNSGlqqltuuaV4Wfd9cZsXpVJhyVTQD1WYn3UgzZwni3EWW/BbV+B1AnjnnXcq799rXmRQR0X5/byOJeVzRlUWXKpklKirq/Od6+hsR9CCxCSq6UBSdQJwVHnlTp06JZ2dnYGJWit18cUXBy4K8qLaU1hpvkqvYD3uVc1hsZ9fGF/6oEnjYaS+cXIGjF7vy6JFi3z3lc/nXVdPBuVPDSOYNP2sA1nhPEGOOzDxeuwoe0lNOiqCRqhUF1yqZJSYmZmZNYroFBRMq1Rvq6aaDiTDSidQqaBErZVavny555fXL0jxGyp1Ms1XqZIO6DOf+UzgNnFramoyCqKiUmnqGxP2Prz29S//8i/FijLOz5VO/lRT1fyRBGDGtJdUZXW21wlxUCeO1wiV1wjQ2NiYbNiwoaTGueqI5pYtWzxHU6KcchAHo0Dy3nvvlZUrV8r8+fPlyiuvlJ///OdhtysUKvOqos4rpzJE7SaXy0lTU1PgNqaBcNBQqfMLaJqvUmXO3cTEhOzfv1+mpqaU9x+1nTt3ikjwXDyvtFIqVOYR2emQVEv/eaW+MRE0ZcLrwKeaP3X//v2hnFlHWSsXQGWcPWkNDQ3F28M4AVT5rnd3d2sfE1Q6Tpz7VR3R7O3tlR07dhSv19JoinYg+dBDD8mtt94qt99+uzz55JPypje9SdatW6dc+ixufvOq9uzZozUvLK4fKTuAsQMa521OlmXJjh07tANh3S+Kab5K1QUgSaj/7dTe3h44F6/SydU684J0qsGUD9dUwmTKhLMOtpuwRwGCcpkCWZf0YVFTKmWInQsjVal0nDj3q1pS+cSJE/KBD3ygeN2Za7paC1DDoh1IfuELX5CbbrpJPvShD8kll1wiX/3qV+UVr3iFfPOb33Td/uzZs3LmzJmSv7h5/bjqTs437X3SZU/4fde73lW8bdGiRa7bmiwwUP2iPPbYYyKifsZ18uRJWbduXfG6aTm8anCeJNTX18uGDRvkiSeeKN7mDE50hvq96AxltLS0BB6onMPtYfWw+02Z8HLFFVcEbhPmKIDbyvA45iUDMOcV3NrD2PX19YH7UJ1Go9tRobtIV7XeefnvRVIWoIZBK5B88cUX5eDBg7J27dr/28GcObJ27Vr56U9/6nqfu+++WxobG4t/zc3NlbXYkM4Pl9ecjD/84Q/aj6syRO1kT/gVKQ1cT548WbxcaY+L6hfFXnWuesZVzrQcXtzDlV5D1D/84Q+Ll53PZWRkRHvVdSXiTn1TSa9h0GdLdxTAjcrKcJP0SkCahdHzmKbeS9VpNLodFSaLdFXrnTuDyVpagKoVSJ44cUJmZmZmvYFLly71HMbctm2bTE5OFv9GR0fNWxuSqakp5S/K/PnzZ5XPU6U6RO28bc2aNYF1OU0CWifVL4pz1XlQIKPLL19X+XCl26KOsPgNUX/4wx92vY9u7kibc6jca7W8V5AUV+obkzxqOoF+GO0MGgYySa8EQJ9pmcIwqJQhvvDCC+Xqq6/W2q9Kx4nbgkvTeuflkrgANUjkq7bnzZsnDQ0NJX9pUknvkz1E7fzxdBvu/cY3vlG8rDJsWukHTbeHsaurK3DeYLmghSh++bpMV+DpMh2iNskdKVI6L9JrWMN5u81+3uVTNJzJxIN6br3e61e+8pUl101qUqvMVQqi84NkGsgDWRdGj2MSikuoOnHihKxatUrrt6Ourk56enp8fxe8RoDCmKY1MTFR8T5ip1Mu5+zZs1ZdXZ318MMPl9z+gQ98wPqbv/kbpX3EXWvbplNiyLmts6SUzp+zrFNQiUFnSSfdknv2c9Gt3exXg9ztz62GsVstUWdda6993XbbbSUlr/r7+0tKSnr96ZR79Cq/59xG57X2qiGt86dbgtD+86pf7laCsLzco9e2Oq+TW/udl++9917tz2sl30/V983+zAJZE0ZJPbcyhX5lAE1/i4J+U7yOO6qlh8vLNqq0ye34p3IcU6l3rvLnrD1eTZGUSHzZy14mq1evlp/85CfF286fPy8/+clP5G1ve5vOrlJDp/fJ2VvnzEnllQLBTVy9LfZQaXmPlBfnxGKb2xxIlV6+b33rW8XL9tCyyllY0Ao855nyG97whuJl52pe53uhM0XAuW9nD1xQr275Ih1TXV1ds+6vs9DEmcNtcHBQzp07N+vzaFrp55/+6Z+071MJ07m3ANS4JeNeunSpbNiwQSllnOnjOEdCgqagqc719/st0qGyNsF5/KxkGlgSFqBq0Y1QH3zwQWvevHnWAw88YB06dMj6yEc+Yl1wwQXW0aNHQ41ww2baIzk5Oelb4N355+y9VOl5sf+q0SNpe+SRR7R6d5z7c+th0+ktOnfunJXP50M5U/M7U3b+7d27t3if/fv3Kz+u19lv0Fmx8zVyO9vW+du/f3/gGW8ul3N9TZ3tMD0jd/Zemj6XMHoknduWfy/t3ge7BxfIokp6JHVHq+w/e8RI9bco6HHsY7XzfqOjoxUdQys5/qkcQ4N6TO+///7A43dzc7PvyFucVOM17UDSsizrnnvusV796ldbL3vZy6wrrrjCOnDgQOgNC5vpD5XzAx/05fL6oHnt2+1+KoGrcxhY97mUUwlMnB/soEBSdSpAb2+vViBn/7kNV+oc+JzD43Yg63VflX06DwxBwzI6Q8Ber5nuiUbQZ1PnQKo6lOT3F0Yg6Xzfy08empubCSIBQyYn90HHZ5tbB43Ksdp5v0WLFlV8DHJO4VFpq84xNGgKlPP/aTgJjmRo23bzzTfL7373Ozl79qz87Gc/kyuvvNJkN6nht2I27PKHKqledJJZqzyerfzxTFbw6uSO1M3vtWLFCrn22mtLFmToLphxDo8HvdYq+9y+fXvxctCQa6VDwMuXL6/qQpOkJY4PqpULQI9uFbNyqscIlUWs9rHaOaXn1KlTxm2zmRYu0E1LF/SbWf5babLQMSlqutZ2mLySmn/yk5+M5LH8VkjrJLP2+vC7JX4N44Otkzxbdx6IWwBtcuBzHuwqPUnQWWFnehB0zvkzXTFeq7xq5QLQV+nJot8x3WR++sDAgLzuda+rqE1u7PnkOsFkGFW0nK/BM888U7w97SfBBJIa4vyRKg9cvRZt+J0ZuU2Y9vvwly/IMPlg6yTP1k1D5BZAmxz4yg92XicJF110kfa+y4WRTN2yLPn85z8vdXV1ygtNzp07l6j65QCSr5JFHm65FSt9nF27dkWSDscebXJbxOgl7CpatXQSnJlAMqqM/ZXsN2hVmtcKaZUzI69E234f/jA+2ENDQ0q1qu3HCwo6g3oFdQ98Xgc7t+d6/PhxrX3bnwVnABdGjkURkVtvvVUKhYLWVIRq53tze//jqFQEwIxpFTMRvepaKo8zZ45ZeKKaicSyLBkdHS1OddJNrm4Ho1TRylAgmWS6wajXmZEdTPrNGwzzw79gwQLp7+8vKQFpB7Yi4tmj6hQ0jB80dUD3wOc82AUdOLZv3x54YAxK0K5aDzaI2wlA+TC3/Rlat26db1qNuLhNRTAdEgIQPb+Te/v6okWLXO+rU7VKpRPh/Pnzyvtz+tWvfqW1fSXD+RZVtESEQNJV3LWeVfiVaizvpg+aNxjWh9+rlKMd9DzyyCPF2/yGZP2G8b3YQeDcuXOLZalUgkmvg51XfdOg9z5o4dNrXvOawDapsIPET33qU8XbnFMRnK9ZUIlN3aGYpqYmox6KefPmud7PZH4SgHh4ndzn83np7++Xw4cPF2+r5Dsc1ImgY/HixcXLuiNpYeZsTFOt8lCFt1BcTbXS/6hySyniVzFEJ2ej6jZu2+rkZ+zt7TVKi6Cbvsgvb2N5PsOgfaukUHCm1ynfn18eSef9vN6voNQ2dXV1yq+ZaR7SSt4v5+WgfJrOFEgq6X/27t1r1P6gz4dXWimdvHdhVPAAMJtbZRvLUqsgpuPUqVMVHwudaedUK4j5HYNMq5cFpVDTjReqLdL0P7XKZF5hXFTTvhw5ciTSrPj2Gdf+/fs9e7xEZFavp+mZmldN6nJ+vZpBC1REgoc3nD2TOmfhKkM4unp7e31fR7/3RaQ0BZLK+2LPeb3wwgu12hn0+XDOT0riKACQZSpz5sNYyRzGPPKgTCa6qe2czytov14jhVlCIPlnYcwrVPlRNg2odPIzBs0bDOPDH1dOQa/HcRuKDirfGJarrrqqeFllEUvQEI5u4B/GiYJO4GwvoPrv//7vwP3qDlMdOXJEO7sAgGQImq+vwjQ3rk4OZ93Udiq/b/bvqz21SkXNniRH1ifqIalD2yZVViTiLmmdIdLybnqvajz2bXv37p31HHS62nVfL51hfJVhBbfqPirD415DNDp/XsPgQc/ROVTkHG53tm/x4sW+j+01LK06nGP/+VWg8Jre4fzMeH0OVSsb2X933HGH675UqzykYXgISCOv75ZuNbQgUVbrCvoNcAp6XuV/dhUtnepg9rHU735JEmmJxEokNZA0nVcYVyDpV6rR60fXr4Sc24dY54MdVF5QxLyUo24d56BAsjzwc/si+82R9KpfXUnQ4zW/MSgQc9YK99pfU1OT8glHOa9yk+WfO6/XS6cd+Xw+8HUN+kFKw8EYSCOv75bOfH0VOgGc3zx5t3a73c/rOKET0DqDUa+5pEHHUrfOnKQhkNSU9B5J+3F06wurTJg2CSTttvjVIHcGRTqB5H333Wf0Hqj20Ll9kb0COHvbb3/7275t0A16vALJoJ5FlRqv9uIY3VquQXV2nftTWQQV1I477rhD6f1Vrd+b1IMxkEZe3y3VUYfe3l7tx/E6VgQdK1V6AoOOEzqjKX6/x/l83vrOd74TeCx1/j+pxy4W22hSmVdoVwyx/jzH0arCEn/d+sJeE6bDWNwQZilHp6VLlxrdz8nv+Vguc1692mrPpXGml/Dap3PxSJh05wp6JYQPmhekkjbK5jUf1TkH+H3ve59vOy6++GKl5+M3Xymz6TaAKtGZr1/pvvP5vOzZs0drH0GLYr3+r1t+1m9x7g033BBLCr7EiDKadZPUHknLCp5XGDR0GRfTFEJBZ1Gmz89r7p9KOiG3duqmXnDrkTQdHvfqwQ3jLNy0R1LlzNttG6/n4kVneodKz4Db58PZDtVRANUhMgDhiWuOZFA6IZXjpt2+c+fOBaY/85pypfK87Mv2mgWd3xjd34skoEfSgF8iVr+enDQJSnFkslI27NXSfmUA3bidYZpWlPHqwY3yLDwquiUvo2q7VztURwFU6/cCiJ5OmdZK9m1Spnd4eDgw/ZlX7W6V52UbGRkJpUcxSb8XlSCQLKM7dJwmKimOdIrYR8Ueruzv71f6onV3d89qs+7weNDwflCAXO2gJ4ypCiqBXZhUyrGZ/iABiJ5uWp2oVZKWznnMLC8DWT7EbpqyyFbt34uwEUi6qPSsKKmCzqKskOf56cxfc9u2o6NDvv71rwc+ztjYmDz22GMltzlzPXpxvq927kKv+TNhn4V7vTb27VNTU8r76O/vl8svv1z5uXhRCezCloVRAKBWOcu0xt3p4nYMNe3hK89le/LkyeJl+3k5y+vqzKfMwkkygWSG6FTHSYrnnntOabsbbrihJHBqaGiQ/v5+yeVynkFQea/d+Pi4bNy4MfCx4j4L9+tt9JuqoPJcyvkFdl6T3itd8FLLowBAWgWd7FqWJQ0NDcXbk9DpEjSqIjK7aILXMdR2+vTpWc+rpaVFaVrOvn37snGSHMH8TF9JXmxjS3pKkTjqdZu2R2eBjQqd3F6quTS96mbb+whqv+4iFrfXKajmql+OS3thlE66Ht33wu05mr7PKp/XpH/nAMwW9vc26FioctzRSUunsmjGLgJhmtfZ9PciCVhskxH19fWSy+Vkeno6cFvVs6gkzdvQXbxTPsezvLdrx44dSqmB/MQ99cGrDNldd92lnK5Hl9tzJNUOgKTTSUunsmhmbGzMdbqX6rScWp0q50QgmSFpXNyg0xbLY46ncx9LliwJrW26dAIxlWDXfi8BIAtUj6Fu02XsHNDO+1U63YtpOS8hkMyYqBc3hLF62MsFF1ygtJ3fHE/dpLNxcDs4joyM+N7Hsiw5depUHM0DgKoxHQlR6QkMI61bFnocgxBI1jiv1dBRnUWtXr26eNlePWySm9LN/fffr7Sd35deZXg/CVTPlBctWlSV58IwN4C0C/o9EHmpk6W1tZVjng8CyYyK6izKaz5fGMHk1Vdf7ft/lTme1UhxY+Kiiy5S2m7Lli0ikuznAgBJ5Pd7YOvp6clkL6MOAskU0sk1GIf58+dLPp93/Z89ny+MROdh5XI0SXETN9WqL7fddpvvVAXOoAHAW9DiHGf+SLgjkETFhoeHY010LlJ5Lkev4f33ve99iQi+dBZGJX3CN0NCAFTEcaxwm8dffgwNazpWVhBIuuCHT49qAvMwE52HUVEh6ZOkdRZGJf25AEC1lVewcc7jdx4zddPOZd3cajcA6adalsqkfJUd1ItISa7MrAROHR0dsnbtWmlsbBSRl4Lmtra2mn2+ANLDeXxOOruCTXl77Xn8SZnWlEb0SKJiqvP5kpToPE2yEDQzCgAgKjMzM7JlyxbXoNe+rbu7u3gbxyM9BJKoWBoTnVciCweZLDxHANkQVMHGsqzACjemsnAsJZBMsSiTf+uKOtF5JbLwRQYAuFPNywszBJIp5TdpuFqSvnoYAJA9UVY0o6OCQDKV7EnD4+PjJbeHmfzbVBbm8wEAks0Z4LW1tQXO4/fKhYxgBJIpozJpOIzk30nEmR8AQJfKPP6enp7Y21UrCCRTJqzk3wRlAICsCJrHTwUbcwSSKVON5N8AAKQd8/ijQULylIky+XfWpCmZbpBaei4AEBWvefwcQ83RI5kyJP8GAABJQSCZMllL/u0lS3M8s/RcAQDpQiCZQklO/g0AALKDOZIp1dHRIWvXrpXGxkYReWnScFtbW833RAIAgOSgRzLFSP4NAACqiR5JhIqVbwAAZAc9kgAAADBCIAkAAAAjBJIAAAAwwhxJAACQCczjDx89kgAAADBCIAkAAAAjBJIAAAAwQiAJAAAAIwSSAAAAMMKq7RRj9RkAAKgmeiQBAABghEASAAAARggkAQAAYIRAEgAAAEYIJAEAAGCEQBIAAABGCCQBAABghEASAAAARggkAQAAYIRAEgAAAEYIJAEAAGCEQBIAAABGCCQBAABghEASAAAARggkAQAAYGRu3A9oWZaIiJw5cybuhwYAAIACO06z4zYvsQeSzz//vIiINDc3x/3QAAAA0PD8889LY2Oj5/9zVlCoGbLz58/LxMSELFy4UHK5XJwPXZPOnDkjzc3NMjo6Kg0NDdVuDgzwHqYf72G68f6lH+9h+CzLkueff15WrFghc+Z4z4SMvUdyzpw5ks/n437YmtfQ0MCXJ+V4D9OP9zDdeP/Sj/cwXH49kTYW2wAAAMAIgSQAAACMEEim3Lx58+T222+XefPmVbspMMR7mH68h+nG+5d+vIfVE/tiGwAAANQGeiQBAABghEASAAAARggkAQAAYIRAEgAAAEYIJAEAAGCEQLIGnT17Vi677DLJ5XLy1FNPVbs5UPTss8/Khz/8Ybnooovk5S9/uaxatUpuv/12efHFF6vdNPi49957ZeXKlTJ//ny58sor5ec//3m1mwRFd999t1x++eWycOFCWbJkibznPe+RX//619VuFgzt2LFDcrmcdHV1VbspmUIgWYO2bt0qK1asqHYzoOmZZ56R8+fPy9e+9jX51a9+JV/84hflq1/9qvzjP/5jtZsGDw899JDceuutcvvtt8uTTz4pb3rTm2TdunXy3HPPVbtpUPD444/L5s2b5cCBA/KjH/1I/vSnP0lbW5tMT09Xu2nQ9MQTT8jXvvY1eeMb31jtpmQOeSRrzA9+8AO59dZbpb+/Xy699FL5z//8T7nsssuq3SwY+uxnPyv33Xef/O///m+1mwIXV155pVx++eXy5S9/WUREzp8/L83NzfLxj39cPv3pT1e5ddB1/PhxWbJkiTz++OOyZs2aajcHiqampuQtb3mLfOUrX5E777xTLrvsMtm1a1e1m5UZ9EjWkGPHjslNN90k3/72t+UVr3hFtZuDEExOTsqiRYuq3Qy4ePHFF+XgwYOydu3a4m1z5syRtWvXyk9/+tMqtgymJicnRUT4zqXM5s2b5brrriv5LiI+c6vdAITDsizZtGmTfPSjH5W3vvWt8uyzz1a7SajQb3/7W7nnnnvkc5/7XLWbAhcnTpyQmZkZWbp0acntS5culWeeeaZKrYKp8+fPS1dXl7S0tMjrX//6ajcHih588EF58skn5Yknnqh2UzKLHsmE+/SnPy25XM7375lnnpF77rlHnn/+edm2bVu1m4wyqu+h0/j4uLzjHe+Q66+/Xm666aYqtRzIjs2bN8svf/lLefDBB6vdFCgaHR2VLVu2yN69e2X+/PnVbk5mMUcy4Y4fPy4nT5703eYv/uIv5IYbbpDvfe97ksvlirfPzMxIXV2d3HjjjfKtb30r6qbCg+p7+LKXvUxERCYmJuSaa66Rq666Sh544AGZM4fzvSR68cUX5RWveIX09fXJe97znuLtH/zgB+UPf/iDDAwMVK9x0HLzzTfLwMCADA0NyUUXXVTt5kDRd7/7Xfnbv/1bqaurK942MzMjuVxO5syZI2fPni35H6JBIFkjfv/738uZM2eK1ycmJmTdunXS19cnV155peTz+Sq2DqrGx8fl2muvldWrV8uePXs4CCbclVdeKVdccYXcc889IvLS8OirX/1qufnmm1lskwKWZcnHP/5xefjhh+Wxxx6Tiy++uNpNgobnn39efve735Xc9qEPfUj+6q/+Srq7u5miEBPmSNaIV7/61SXX6+vrRURk1apVBJEpMT4+Ltdcc4285jWvkc997nNy/Pjx4v+WLVtWxZbBy6233iof/OAH5a1vfatcccUVsmvXLpmenpYPfehD1W4aFGzevFl6e3tlYGBAFi5cKEePHhURkcbGRnn5y19e5dYhyMKFC2cFiwsWLJDFixcTRMaIQBJIiB/96Efy29/+Vn7729/OCv4ZOEim9773vXL8+HHZvn27HD16VC677DL54Q9/OGsBDpLpvvvuExGRa665puT2f//3f5dNmzbF3yAghRjaBgAAgBFm8QMAAMAIgSQAAACMEEgCAADACIEkAAAAjBBIAgAAwAiBJAAAAIwQSAIAAMAIgSQAAACMEEgCAADACIEkAAAAjBBIAgAAwMj/B0hfjXv6PDGzAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate fake data\n", "np.random.seed(0)\n", "x = np.linspace(-5., 5., 200)\n", "y = 3 * np.exp(-0.5 * (x - 1.3)**2 / 0.8**2)\n", "y += np.random.normal(0., 0.2, x.shape)\n", "yerr = 0.2\n", "\n", "plt.figure(figsize=(8,5))\n", "plt.errorbar(x, y, yerr=yerr, fmt='ko')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Likelihoods and Posteriors\n", "\n", "In general, model fitting will happen either in a frequentist (Maximum Likelihood) or Bayesian framework. Stingray's strategy is to let the user define a posterior in both cases, but ignore the prior in the former case. \n", "\n", "Let's first make some fake data:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# define power law component\n", "pl = models.PowerLaw1D()\n", "\n", "# fix x_0 of power law component\n", "pl.x_0.fixed = True\n", "\n", "# define constant\n", "c = models.Const1D()\n", "\n", "# make compound model\n", "plc = pl + c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to pick some fairly standard parameters for our data:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# parameters for fake data.\n", "alpha = 2.0\n", "amplitude = 5.0\n", "white_noise = 2.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now a frequency array:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "freq = np.linspace(0.01, 10.0, int(10.0/0.01))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can set the parameters in the model:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from astropy.modeling.fitting import fitter_to_model_params\n", "\n", "fitter_to_model_params(plc, [amplitude, alpha, white_noise])\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "psd_shape = plc(freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a last step, we need to add noise by picking from a chi-square distribution with 2 degrees of freedom:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "powers = psd_shape*np.random.chisquare(2, size=psd_shape.shape[0])/2.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the result:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,7))\n", "plt.loglog(freq, powers, ds=\"steps-mid\", label=\"periodogram realization\")\n", "plt.loglog(freq, psd_shape, label=\"power spectrum\")\n", "\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Maximum Likelihood Fitting\n", "\n", "Let's assume we've observed this periodogram from our source. We would now like to estimate the parameters. \n", "This requires the definition of *likelihood*, which describes the probability of observing the data plotted above given some underlying model with a specific set of parameters. To say it differently, the likelihood encodes what we know about the underlying model (here a power law and a constant) and the statistical properties of the data (power spectra generally follow a chi-square distribution) and then allows us to compare data and model for various parameters under the assumption of the statistical uncertainties.\n", "\n", "In order to find the best parameter set, one generally maximizes the likelihood function using an optimization algorithm. Because optimization algorithms generally *minimize* functions, they effectively minimize the log-likelihood, which comes out to be the same as maximizing the likelihood itself.\n", "\n", "Below is an implementation of the $\\chi^2$ likelihood as appropriate for power spectral analysis, with comments for easier understanding. The same is also implemented in `posterior.py` in Stingray:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [], "source": [ "logmin = -1e16\n", "class PSDLogLikelihood(object):\n", "\n", " def __init__(self, freq, power, model, m=1):\n", " \"\"\"\n", " A Chi-square likelihood as appropriate for power spectral analysis.\n", "\n", " Parameters\n", " ----------\n", " freq : iterable\n", " x-coordinate of the data\n", "\n", " power : iterable\n", " y-coordinte of the data\n", "\n", " model: an Astropy Model instance\n", " The model to use in the likelihood.\n", "\n", " m : int\n", " 1/2 of the degrees of freedom, i.e. the number of powers\n", " that were averaged to obtain the power spectrum input into\n", " this routine.\n", "\n", " \"\"\"\n", "\n", " self.x = ps.freq # the x-coordinate of the data (frequency array)\n", " self.y = ps.power # the y-coordinate of the data (powers)\n", " self.model = model # an astropy.models instance\n", " self.m = m\n", "\n", " self.params = [k for k,l in self.model.fixed.items() if not l]\n", " self.npar = len(self.params) # number of free parameters\n", "\n", " def evaluate(self, pars, neg=False):\n", " \"\"\"\n", " Evaluate the log-likelihood.\n", "\n", " Parameters\n", " ----------\n", " pars : iterable\n", " The list of parameters for which to evaluate the model.\n", "\n", " neg : bool, default False\n", " If True, compute the *negative* log-likelihood, otherwise\n", " compute the *positive* log-likelihood.\n", "\n", " Returns\n", " -------\n", " loglike : float\n", " The log-likelihood of the model\n", "\n", " \"\"\"\n", " # raise an error if the length of the parameter array input into\n", " # this method doesn't match the number of free parameters in the model\n", " if np.size(pars) != self.npar:\n", " raise Exception(\"Input parameters must\" +\n", " \" match model parameters!\")\n", "\n", " # set parameters in self.model to the parameter set to be used for\n", " # evaluation\n", " fitter_to_model_params(self.model, pars)\n", "\n", " # compute the values of the model at the positions self.x\n", " mean_model = self.model(self.x)\n", "\n", " # if the power spectrum isn't averaged, compute simple exponential\n", " # likelihood (chi-square likelihood for 2 degrees of freedom)\n", " if self.m == 1:\n", " loglike = -np.sum(np.log(mean_model)) - \\\n", " np.sum(self.y/mean_model)\n", " # otherwise use chi-square distribution to compute likelihood\n", " else:\n", " loglike = -2.0*self.m*(np.sum(np.log(mean_model)) +\n", " np.sum(self.y/mean_model) +\n", " np.sum((2.0 / (2. * self.m) - 1.0) *\n", " np.log(self.y)))\n", "\n", " if not np.isfinite(loglike):\n", " loglike = logmin\n", "\n", " if neg:\n", " return -loglike\n", " else:\n", " return loglike\n", "\n", " def __call__(self, parameters, neg=False):\n", " return self.evaluate(parameters, neg)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make an object and see what it calculates if we put in different parameter sets. First, we have to make our sample PSD into an actual `Powerspectrum` object:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "from stingray import Powerspectrum\n", "\n", "ps = Powerspectrum()\n", "ps.freq = freq\n", "ps.power = powers\n", "ps.df = ps.freq[1] - ps.freq[0]\n", "ps.m = 1" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-4835.88214847462" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_pars = [1, 5, 100]\n", "loglike(test_pars)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2869.5582486265116" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_pars = [4.0, 10, 2.5]\n", "loglike(test_pars)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2375.704120812954" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_pars = [2.0, 5.0, 2.0]\n", "loglike(test_pars)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Something close to the parameters we put in should yield the largest log-likelihood. Feel free to play around with the test parameters to verify that this is true.\n", "\n", "You can similarly import the `PSDLogLikelihood` class from `stingray.modeling` and do the same:\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2375.704120812954" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from stingray.modeling import PSDLogLikelihood\n", "\n", "loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m)\n", "loglike(test_pars)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To estimate the parameters, we can use an optimization routine, such as those implemented in `scipy.optimize.minimize`.\n", "We have wrapped some code around that, to make your lives easier. We will not reproduce the full code here, just demonstrate its functionality.\n", "\n", "Now we can instantiate the `PSDParEst` (for PSD Parameter Estimation) object. This can do more than simply optimize a single model, but we'll get to that later.\n", "\n", "The `PSDParEst` object allows one to specify the fit method to use (however, this must be one of the optimizers in `scipy.optimize`). The parameter `max_post` allows for doing maximum-a-posteriori fits on the Bayesian posterior rather than maximum likelihood fits (see below for more details). We'll set it to `False` for now, since we haven't defined any priors:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import PSDParEst\n", "\n", "parest = PSDParEst(ps, fitmethod=\"L-BFGS-B\", max_post=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to fit a model, make an instance of the appropriate `LogLikelihood` or `Posterior` subclass, andsimply call the `fit` method with that instance and starting parameters you would like to fit." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2., 1., 5., 2.])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "loglike.model.parameters" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "loglike.npar" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "starting_pars = [3.0, 1.0, 2.4]\n", "res = parest.fit(loglike, starting_pars)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an `OptimizationResults` object, which computes various summaries and useful quantities.\n", "\n", "For example, here's the value of the likelihood function at the maximum the optimizer found:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2183.7896770356615" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: Optimizers routinely get stuck in *local* minima (corresponding to local maxima of the likelihood function). It is usually useful to run an optimizer several times with different starting parameters in order to get close to the global maximum.\n", "\n", "Most useful are the estimates of the parameters at the maximum likelihood and their uncertainties:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4.72915772 2.09193133 2.10372299]\n", "[3.8037075 0.73336812 0.55239425]\n" ] } ], "source": [ "print(res.p_opt)\n", "print(res.err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: uncertainties are estimated here via the covariance matrix between parameters, i.e. the inverse of the Hessian at the maximum. This only represents the true uncertainties for specific assumptions about the likelihood function (Gaussianity), so use with care!\n", "\n", "It also computes Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) for model comparison purposes:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AIC: 2189.7896770356615\n", "BIC: 2204.5129428726077\n" ] } ], "source": [ "print(\"AIC: \" + str(res.aic))\n", "print(\"BIC: \" + str(res.bic))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, it also produces the values of the mean function for the parameters at the maximum. Let's plot that and compare with the power spectrum we put in:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,8))\n", "plt.loglog(ps.freq, psd_shape, label=\"true power spectrum\",lw=3)\n", "plt.loglog(ps.freq, ps.power, label=\"simulated data\")\n", "plt.loglog(ps.freq, res.mfit, label=\"best fit\", lw=3)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That looks pretty good!\n", "\n", "You can print a summary of the fitting results by calling `print_summary`:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "The best-fit model parameters plus errors are:\n", " 0) Parameter amplitude_0 : \n", "4.72916 +/- 3.80371 \n", "[ None None]\n", " 1) Parameter x_0_0 : \n", "1.00000 (Fixed) \n", " 2) Parameter alpha_0 : \n", "2.09193 +/- 0.73337 \n", "[ None None]\n", " 3) Parameter amplitude_1 : \n", "2.10372 +/- 0.55239 \n", "[ None None]\n", "\n", "\n", "Fitting statistics: \n", " -- number of data points: 1000\n", " -- Deviance [-2 log L] D = 4367.579354.3\n", " -- The Akaike Information Criterion of the model is: 2189.7896770356615.\n", " -- The Bayesian Information Criterion of the model is: 2204.5129428726077.\n", " -- The figure-of-merit function for this model is: 1079.683266.5f and the fit for 997 dof is 1.082932.3f\n", " -- Summed Residuals S = 69266.959968.5f\n", " -- Expected S ~ 6000.000000.5 +/- 109.544512.5\n" ] } ], "source": [ "res.print_summary(loglike)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Likelihood Ratios\n", "\n", "The parameter estimation code has more functionality than act as a simple wrapper around `scipy.optimize`. For example, it allows for easy computation of likelihood ratios. Likelihood ratios are a standard way to perform comparisons between two models (though they are not always statistically meaningful, and should be used with caution!).\n", "\n", "To demonstrate that, let's make a broken power law model" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# broken power law model\n", "bpl = models.BrokenPowerLaw1D()\n", "\n", "# add constant\n", "bplc = bpl + c" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('amplitude_0', 'x_break_0', 'alpha_1_0', 'alpha_2_0', 'amplitude_1')" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bplc.param_names" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# define starting parameters\n", "bplc_start_pars = [2.0, 1.0, 3.0, 1.0, 2.5]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "loglike_bplc = PSDLogLikelihood(ps.freq, ps.power, bplc, m=ps.m)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "pval, plc_opt, bplc_opt = parest.compute_lrt(loglike, starting_pars, loglike_bplc, bplc_start_pars)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Likelihood Ratio: 0.36080561093513097\n" ] } ], "source": [ "print(\"Likelihood Ratio: \" + str(pval))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Bayesian Parameter Estimation\n", "\n", "For Bayesian parameter estimation, we require a prior along with the likelihood defined above. Together, they form the *posterior*, the probability of the parameters given the data, which is what we generally want to compute in science.\n", "\n", "Since there are no universally accepted priors for a model (they depend on the problem at hand and your physical knowledge about the system), they cannot be easily hard-coded in stingray. Consequently, setting priors is slightly more complex. \n", "\n", "Analogously to the `LogLikelihood` above, we can also define a `Posterior` object. Each posterior object has three methods: `logprior`, `loglikelihood` and `logposterior`. \n", "\n", "We have pre-defined some `Posterior` objects in `posterior.py` for common problems, including power spectral analysis. We start by making a `PSDPosterior` object:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import PSDPosterior" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "lpost = PSDPosterior(ps.freq, ps.power, plc, m=ps.m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The priors are set as a dictionary of functions:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "import scipy.stats\n", "\n", "# flat prior for the power law index\n", "p_alpha = lambda alpha: ((-1. <= alpha) & (alpha <= 5.))\n", "\n", "# flat prior for the power law amplitude\n", "p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0))\n", "\n", "# normal prior for the white noise parameter\n", "p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise)\n", "\n", "priors = {}\n", "priors[\"alpha_0\"] = p_alpha\n", "priors[\"amplitude_0\"] = p_amplitude\n", "priors[\"amplitude_1\"] = p_whitenoise\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There's a function `set_logprior` in `stingray.modeling` that sets the prior correctly:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import set_logprior" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "lpost.logprior = set_logprior(lpost, priors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also set the priors when you instantiate the posterior object:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "lpost = PSDPosterior(ps.freq, ps.power, plc, priors=priors, m=ps.m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Much like before with the log-likelihood, we can now also compute the log-posterior for various test parameter sets:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-prior: -198.61635344021062\n", "log-likelihood: -2412.2493594640564\n", "log-posterior: -2610.865712904267\n" ] } ], "source": [ "test_pars = [1.0, 2.0, 4.0]\n", "print(\"log-prior: \" + str(lpost.logprior(test_pars)))\n", "print(\"log-likelihood: \" + str(lpost.loglikelihood(test_pars)))\n", "print(\"log-posterior: \" + str(lpost(test_pars)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the prior is zero (so the log-prior is -infinity), it automatically gets set to a very small value in order to avoid problems when doing the optimization:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-prior: -1e+16\n", "log-likelihood: -2534.0567826161864\n", "log-posterior: -1e+16\n" ] } ], "source": [ "test_pars = [6, 6, 3.0]\n", "print(\"log-prior: \" + str(lpost.logprior(test_pars)))\n", "print(\"log-likelihood: \" + str(lpost.loglikelihood(test_pars)))\n", "print(\"log-posterior: \" + str(lpost(test_pars)))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-prior: 1.383646559789373\n", "log-likelihood: -2184.6739536386162\n", "log-posterior: -2183.290307078827\n" ] } ], "source": [ "test_pars = [5.0, 2.0, 2.0]\n", "print(\"log-prior: \" + str(lpost.logprior(test_pars)))\n", "print(\"log-likelihood: \" + str(lpost.loglikelihood(test_pars)))\n", "print(\"log-posterior: \" + str(lpost(test_pars)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do the same parameter estimation as above, except now it's called maximum-a-posteriori instead of maximum likelihood and includes the prior (notice we set `max_post=True`):" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "parest = PSDParEst(ps, fitmethod='BFGS', max_post=True)\n", "res = parest.fit(lpost, starting_pars)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "best-fit parameters:\n", "4.8949 +/- 0.4941\n", "2.0690 +/- 0.0811\n", "2.0547 +/- 0.0680\n" ] } ], "source": [ "print(\"best-fit parameters:\")\n", "for p,e in zip(res.p_opt, res.err):\n", " print(\"%.4f +/- %.4f\"%(p,e))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same outputs exist as for the Maximum Likelihood case:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "The best-fit model parameters plus errors are:\n", " 0) Parameter amplitude_0 : \n", "4.89492 +/- 0.49409 \n", "[ None None]\n", " 1) Parameter x_0_0 : \n", "1.00000 (Fixed) \n", " 2) Parameter alpha_0 : \n", "2.06898 +/- 0.08112 \n", "[ None None]\n", " 3) Parameter amplitude_1 : \n", "2.05471 +/- 0.06803 \n", "[ None None]\n", "\n", "\n", "Fitting statistics: \n", " -- number of data points: 1000\n", " -- Deviance [-2 log L] D = 4367.845868.3\n", " -- The Akaike Information Criterion of the model is: 2188.6889410986737.\n", " -- The Bayesian Information Criterion of the model is: 2203.41220693562.\n", " -- The figure-of-merit function for this model is: 1104.686609.5f and the fit for 997 dof is 1.108011.3f\n", " -- Summed Residuals S = 75870.967955.5f\n", " -- Expected S ~ 6000.000000.5 +/- 109.544512.5\n" ] } ], "source": [ "res.print_summary(lpost)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unlike in the maximum likelihood case, we can also *sample* from the posterior probability distribution. The method `sample` uses the [emcee](http://emcee.readthedocs.io/) package to do MCMC. \n", "\n", "**Important**: Do *not* sample from the likelihood function. This is formally incorrect and can lead to incorrect inferences about the problem, because there is no guarantee that a posterior with improper (flat, infinite) priors will be bounded!\n", "\n", "**Important**: emcee has had a major upgrade to version 3, which came with a number of API changes. To ensure compatibility with stingray, please update emcee to the latest version, if you haven't already.\n", "\n", "Much like the optimizer, the sampling method requires a model and a set of starting parameters `t0`. Optionally, it can be useful to also input a covariance matrix, for example from the output of the optimizer.\n", "\n", "Finally, the user should specify the number of walkers as well as the number of steps to use for both burn-in and sampling:\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Chains too short to compute autocorrelation lengths.\n", "-- The acceptance fraction is: 0.642375.5\n", "R_hat for the parameters is: [0.32313683 0.00732082 0.00479484]\n", "-- Posterior Summary of Parameters: \n", "\n", "parameter \t mean \t\t sd \t\t 5% \t\t 95% \n", "\n", "---------------------------------------------\n", "\n", "theta[0] \t 4.942652228740678\t0.5691486161504021\t4.035143030111889\t5.915733521435971\n", "\n", "theta[1] \t 2.0754546626425574\t0.0856675712513585\t1.9374392067380983\t2.21960029522001\n", "\n", "theta[2] \t 2.052820542793331\t0.06933048478134216\t1.9394014208215005\t2.167009901378628\n", "\n" ] } ], "source": [ "sample = parest.sample(lpost, res.p_opt, cov=res.cov, nwalkers=400,\n", " niter=100, burnin=300, namestr=\"psd_modeling_test\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sampling method returns an object with various attributes that are useful for further analysis, for example the acceptance fraction:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6423749999999999" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample.acceptance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or the mean and confidence intervals of the parameters:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.94265223, 2.07545466, 2.05282054])" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample.mean" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.03514303, 1.93743921, 1.93940142],\n", " [5.91573352, 2.2196003 , 2.1670099 ]])" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample.ci" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method `print_results` prints the results:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "-- The acceptance fraction is: 0.642375.5\n", "R_hat for the parameters is: [0.32313683 0.00732082 0.00479484]\n", "-- Posterior Summary of Parameters: \n", "\n", "parameter \t mean \t\t sd \t\t 5% \t\t 95% \n", "\n", "---------------------------------------------\n", "\n", "theta[0] \t 4.942652228740678\t0.5691486161504021\t4.035143030111889\t5.915733521435971\n", "\n", "theta[1] \t 2.0754546626425574\t0.0856675712513585\t1.9374392067380983\t2.21960029522001\n", "\n", "theta[2] \t 2.052820542793331\t0.06933048478134216\t1.9394014208215005\t2.167009901378628\n", "\n" ] } ], "source": [ "sample.print_results()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the method `plot_results` produces a bunch of plots:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = sample.plot_results(nsamples=1000, fig=None, save_plot=True,\n", " filename=\"modeling_tutorial_mcmc_corner.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calibrating Likelihood Ratio Tests\n", "\n", "In order to use likelihood ratio tests for model comparison, one must compute the p-value of obtaining a likelihood ratio at least as high as that observed given that the null hypothesis (the simpler model) is true. The distribution of likelihood ratios under that assumption will only follow an analytical distribution if\n", "* the models are nested, i.e. the simpler model is a special case of the more complex model *and*\n", "* the parameter values that transform the complex model into the simple one do not lie on the boundary of parameter space. \n", "\n", "Imagine e.g. a simple model without a QPO, and a complex model with a QPO, where in order to make the simpler model out of the more complex one you would set the QPO amplitude to zero. However, the amplitude cannot go below zero, thus the critical parameter value transforming the complex into the simple model lie on the boundary of parameter space.\n", "\n", "If these two conditions are not given, the observed likelihood ratio must be calibrated via simulations of the simpler model. In general, one should *not* simulate from the best-fit model alone: this ignores the uncertainty in the model parameters, and thus may artificially inflate the significance of the result.\n", "\n", "In the purely frequentist (maximum likelihood case), one does not know the shape of the probability distribution for the parameters. A rough approximation can be obtained by assuming the likelihood surface to be a multi-variate Gaussian, with covariances given by the inverse Fisher information. One may sample from that distribution and then simulate fake data sets using the sampled parameters. Each simulated data set will be fit with both models to compute a likelihood ratio, which is then used to build a distribution of likelihood ratios from the simpler model to compare the observed likelihood ratio to.\n", "\n", "In the Bayesian case, one may sample from the posterior for the parameters directly and then use these samples as above to create fake data sets in order to derive a posterior probability distribution for the likelihood ratios and thus a posterior predictive p-value.\n", "\n", "For the statistical background of much of this, see [Protassov et al, 2002](http://adsabs.harvard.edu/abs/2002ApJ...571..545P).\n", "\n", "Below, we set up code that will do exactly that, for both the frequentist and Bayesian case.\n" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "import copy\n", "\n", "def _generate_model(lpost, pars):\n", " \"\"\"\n", " Helper function that generates a fake PSD similar to the\n", " one in the data, but with different parameters.\n", "\n", " Parameters\n", " ----------\n", " lpost : instance of a Posterior or LogLikelihood subclass\n", " The object containing the relevant information about the\n", " data and the model\n", "\n", " pars : iterable\n", " A list of parameters to be passed to lpost.model in oder\n", " to generate a model data set.\n", "\n", " Returns:\n", " --------\n", " model_data : numpy.ndarray\n", " An array of model values for each bin in lpost.x\n", "\n", " \"\"\"\n", " # get the model\n", " m = lpost.model\n", "\n", " # reset the parameters\n", " fitter_to_model_params(m, pars)\n", "\n", " # make a model spectrum\n", " model_data = lpost.model(lpost.x)\n", "\n", " return model_data\n", "\n", "def _generate_psd(ps, lpost, pars):\n", " \"\"\"\n", " Generate a fake power spectrum from a model.\n", "\n", " Parameters:\n", " ----------\n", " lpost : instance of a Posterior or LogLikelihood subclass\n", " The object containing the relevant information about the\n", " data and the model\n", "\n", " pars : iterable\n", " A list of parameters to be passed to lpost.model in oder\n", " to generate a model data set.\n", "\n", " Returns:\n", " --------\n", " sim_ps : stingray.Powerspectrum object\n", " The simulated Powerspectrum object\n", "\n", " \"\"\"\n", "\n", " model_spectrum = _generate_model(lpost, pars)\n", "\n", " # use chi-square distribution to get fake data\n", " model_powers = model_spectrum*np.random.chisquare(2*ps.m,\n", " size=model_spectrum.shape[0])/(2.*ps.m)\n", "\n", " sim_ps = copy.copy(ps)\n", "\n", " sim_ps.powers = model_powers\n", "\n", "\n", " return sim_ps\n", "\n", "def _compute_pvalue(obs_val, sim):\n", " \"\"\"\n", " Compute the p-value given an observed value of a test statistic\n", " and some simulations of that same test statistic.\n", "\n", " Parameters\n", " ----------\n", " obs_value : float\n", " The observed value of the test statistic in question\n", "\n", " sim: iterable\n", " A list or array of simulated values for the test statistic\n", "\n", " Returns\n", " -------\n", " pval : float [0, 1]\n", " The p-value for the test statistic given the simulations.\n", "\n", " \"\"\"\n", "\n", " # cast the simulations as a numpy array\n", " sim = np.array(sim)\n", "\n", " # find all simulations that are larger than\n", " # the observed value\n", " ntail = sim[sim > obs_val].shape[0]\n", "\n", " # divide by the total number of simulations\n", " pval = ntail/sim.shape[0]\n", "\n", " return pval\n", "\n", "def calibrate_lrt(ps, lpost1, t1, lpost2, t2, sample=None, neg=True, max_post=False,\n", " nsim=1000, niter=200, nwalker=500, burnin=200, namestr=\"test\"):\n", "\n", "\n", " # set up the ParameterEstimation object\n", " parest = PSDParEst(ps, fitmethod=\"L-BFGS-B\", max_post=False)\n", "\n", " # compute the observed likelihood ratio\n", " lrt_obs, res1, res2 = parest.compute_lrt(lpost1, t1,\n", " lpost2, t2,\n", " neg=neg,\n", " max_post=max_post)\n", "\n", " # simulate parameter sets from the simpler model\n", " if not max_post:\n", " # using Maximum Likelihood, so I'm going to simulate parameters\n", " # from a multivariate Gaussian\n", "\n", " # set up the distribution\n", " mvn = scipy.stats.multivariate_normal(mean=res1.p_opt, cov=res1.cov)\n", "\n", " # sample parameters\n", " s_all = mvn.rvs(size=nsim)\n", "\n", " else:\n", " if sample is None:\n", " # sample the posterior using MCMC\n", " sample = parest.sample(lpost, res1.p_opt, cov=res1.cov,\n", " nwalkers=nwalker, niter=niter,\n", " burnin=burnin, namestr=namestr)\n", "\n", "\n", " # pick nsim samples out of the posterior sample\n", " s_all = sample[np.random.choice(sample.shape[0], nsim, replace=False)]\n", "\n", " lrt_sim = np.zeros(nsim)\n", "\n", " # now I can loop over all simulated parameter sets to generate a PSD\n", " for i,s in enumerate(s_all):\n", "\n", " # generate fake PSD\n", " sim_ps = _generate_psd(ps, lpost1, s)\n", "\n", " # make LogLikelihood objects for both:\n", " if not max_post:\n", " sim_lpost1 = PSDLogLikelihood(sim_ps.freq, sim_ps.power,\n", " model=lpost1.model, m=sim_ps.m)\n", " sim_lpost2 = PSDLogLikelihood(sim_ps.freq, sim_ps.power,\n", " model=lpost2.model, m=sim_ps.m)\n", " else:\n", " # make a Posterior object\n", " sim_lpost1 = PSDPosterior(sim_ps.freq, sim_ps.power,\n", " lpost1.model, m=sim_ps.m)\n", " sim_lpost1.logprior = lpost1.logprior\n", "\n", " sim_lpost2 = PSDPosterior(sim_ps.freq, sim_ps.power,\n", " lpost2.model, m=sim_ps.m)\n", " sim_lpost2.logprior = lpost2.logprior\n", "\n", "\n", " parest_sim = PSDParEst(sim_ps, max_post=max_post)\n", "\n", " lrt_sim[i], _, _ = parest_sim.compute_lrt(sim_lpost1, t1,\n", " sim_lpost2, t2,\n", " neg=neg,\n", " max_post=max_post)\n", "\n", " # now I can compute the p-value:\n", " pval = _compute_pvalue(lrt_obs, lrt_sim)\n", " return pval" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "scrolled": true }, "outputs": [], "source": [ "pval = calibrate_lrt(ps, loglike, starting_pars,\n", " loglike_bplc, bplc_start_pars,\n", " max_post=False, nsim=100)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The p-value for rejecting the simpler model is: 0.9\n" ] } ], "source": [ "print(\"The p-value for rejecting the simpler model is: \" + str(pval))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the p-value for rejecting the powerlaw model is fairly large: since we simulated from that model, we would be surprised if it generated a small p-value, causing us to reject this model (note, however, that if the null hypothesis is true, the p-value will be uniformely distributed between 0 and 1. By definition, then, you will get a p-value smaller or equal to 0.01 in approximately one out of a hundred cases)\n", "\n", "We can do the same with the Bayesian model, in which case the result is called a *posterior predictive p-value*, which, in turn, is often used in posterior model checking (not yet implemented!).\n", "\n", "We have not yet defined a `PSDPosterior` object for the bent power law model, so let's do that. First, let's define some priors:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "import scipy.stats\n", "\n", "# flat prior for the power law indices\n", "p_alpha1 = lambda alpha: ((-1. <= alpha) & (alpha <= 5.))\n", "p_alpha2 = lambda alpha: ((-1. <= alpha) & (alpha <= 5.))\n", "\n", "# flat prior for the break frequency\n", "p_x_break = lambda xbreak: ((0.01 <= xbreak) & (10.0 >= xbreak))\n", "\n", "# flat prior for the power law amplitude\n", "p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0))\n", "\n", "# normal prior for the white noise parameter\n", "p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise)\n", "\n", "priors = {}\n", "priors[\"alpha_1_0\"] = p_alpha\n", "priors[\"alpha_2_0\"] = p_alpha\n", "\n", "priors[\"amplitude_0\"] = p_amplitude\n", "priors[\"amplitude_1\"] = p_whitenoise\n", "priors[\"x_break_0\"] = p_x_break\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can set up the `PSDPosterior` object:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "lpost_bplc = PSDPosterior(ps.freq, ps.power, bplc, priors=priors, m=ps.m)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2230.14039643262" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lpost_bplc(bplc_start_pars)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And do the posterior predictive p-value. Since we've already sampled from the simple model, we can pass that sample to the `calibrate_lrt` function, in order to cut down on computation time (if the keyword `sample` is not given, it will automatically run MCMC:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "scrolled": true }, "outputs": [], "source": [ "pval = calibrate_lrt(ps, lpost, starting_pars,\n", " lpost_bplc, bplc_start_pars,\n", " sample=sample.samples,\n", " max_post=True, nsim=100)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The posterior predictive p-value is: p = 0.99\n" ] } ], "source": [ "print(\"The posterior predictive p-value is: p = \" + str(pval))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we find that the p-value does not suggest rejecting the powerlaw model.\n", "\n", "Of course, a slightly modified version is implemented in `stingray` as a subclass of the `PSDParEst` class:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import PSDParEst" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "parest = PSDParEst(ps, fitmethod=\"BFGS\")" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "scrolled": true }, "outputs": [], "source": [ "pval = parest.calibrate_lrt(lpost, starting_pars, lpost_bplc, bplc_start_pars,\n", " sample=sample.samples, nsim=100, max_post=True, seed=200)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.22\n" ] } ], "source": [ "print(pval)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian-ish QPO Searches\n", "\n", "When searching for quasi-periodic oscillations (QPOs) in light curves that are not constant (for example because they are bursts or have other types of variability), one must take care that the variable background is accurately modelled (most standard tools assume that the light curve is constant). \n", "\n", "In [Vaughan et al, 2010](http://adsabs.harvard.edu/abs/2010MNRAS.402..307V), a method was introduced to search for QPOs in the presence of red noise (stochastic variability), and in [Huppenkothen et al, 2013](http://adsabs.harvard.edu/abs/2013ApJ...768...87H) it was extended to magnetar bursts, and in [Inglis et al, 2015](http://adsabs.harvard.edu/abs/2015ApJ...798..108I) and [Inglis et al, 2016](http://adsabs.harvard.edu/abs/2016ApJ...833..284I) a similar approach was used to find QPOs in solar flares.\n", "\n", "Based on a model for the broadband spectral noise, the algorithm finds the highest outlier in a test statistic based on the data-model residuals (under the assumption that if the broadband model is correct, the test statistic $T_R = \\max_j(2 D_j/m_j)$ for $j$ power spectral bins with powers $D_j$ and model powers $m_j$ will be distributed following a $\\chi^2$ distribution with two degrees of freedom). The observed test statistic $T_R$ is then compared to a theoretical distribution based on simulated power spectra without an outlier in order to compute a posterior predictive p-value as above for the likelihood ratio.\n", "\n", "Since the concept is very similar to that above, we do not show the full code here. Instead, the p-value can be calculated using the method `calibrate_highest_outlier`, which belongs to the `PSDParEst` class:" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "# compute highest outlier in the data, and the frequency and index\n", "# where that power occurs\n", "max_power, max_freq, max_ind = parest._compute_highest_outlier(lpost, res)" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([16.79715764])" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max_power" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "scrolled": true }, "outputs": [], "source": [ "pval = parest.calibrate_highest_outlier(lpost, starting_pars, sample=sample,\n", " max_post=True,\n", " nsim=100, niter=200, nwalkers=500,\n", " burnin=200, namestr=\"test\")" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.24" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pval" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convenience Functions\n", "\n", "For convenience, we have implemented some simple functions to reduce overhead with having to instantiate objects of the various classes.\n", "\n", "Note that these convenience function use similar approaches and guesses in all cases; this might work for some simple quicklook analysis, but when preparing publication-ready results, one should approach the analysis with more care and make sure the options chosen are appropriate for the problem at hand.\n", "\n", "### Fitting a power spectrum with some model\n", "\n", "The code above allows for a lot of freedom in building an appropriate model for your application. However, in everyday life, one might occasionally want to do a quick fit for various applications, without having to go too much into details. Below is a convenience function written for exactly that purpose.\n", "\n", "Please note that while this aims to use reasonable defaults, this is unlikely to produce publication-ready results!\n", "\n", "So let's fit a power law and a constant to some data, which we'll create below:" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "from stingray import Powerspectrum\n", "\n", "m = 1\n", "nfreq = 100000\n", "freq = np.linspace(1, 1000, nfreq)\n", "\n", "np.random.seed(100) # set the seed for the random number generator\n", "noise = np.random.exponential(size=nfreq)\n", "\n", "model = models.PowerLaw1D() + models.Const1D()\n", "model.x_0_0.fixed = True\n", "\n", "alpha_0 = 2.0\n", "amplitude_0 = 100.0\n", "amplitude_1 = 2.0\n", "\n", "model.alpha_0 = alpha_0\n", "model.amplitude_0 = amplitude_0\n", "model.amplitude_1 = amplitude_1\n", "\n", "p = model(freq)\n", "power = noise * p\n", "\n", "ps = Powerspectrum()\n", "ps.freq = freq\n", "ps.power = power\n", "ps.m = m\n", "ps.df = freq[1] - freq[0]\n", "ps.norm = \"leahy\"\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What does this data set look like?" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.loglog(ps.freq, ps.power, ds=\"steps-mid\", lw=2, color=\"black\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to fit this, we'll write a convenience function that can take the power spectrum, a model, some starting parameters and just run with it:" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import PSDLogLikelihood, PSDPosterior, PSDParEst\n", "\n", "def fit_powerspectrum(ps, model, starting_pars, max_post=False, priors=None,\n", " fitmethod=\"L-BFGS-B\"):\n", "\n", " if priors:\n", " lpost = PSDPosterior(ps, model, priors=priors)\n", " else:\n", " lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m)\n", "\n", " parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post)\n", " res = parest.fit(lpost, starting_pars, neg=True)\n", "\n", " return parest, res\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see if it works. We've already defined our model above, but to be explicit, let's define it again:" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "model_to_test = models.PowerLaw1D() + models.Const1D()\n", "model_to_test.x_0_0.fixed = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we just need some starting parameters:" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "t0 = [80, 1.5, 2.5]" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "parest, res = fit_powerspectrum(ps, model_to_test, t0)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([108.97152923, 2.07017797, 2.00200459])" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.p_opt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like it worked! Let's plot the result, too:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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PbN++Hf369TPss2fmX2O5ubkOnUdERMrinRcVuwhgJPQrVpub5zYcwP8A/ADgTgt1XL5sdp1rh23btq3GMkeOHDG7XwiB7du3AwC+/PJLSeMiIiLPweTFC+wCEA/gBQDmUpFuAH6Cvk9McJVjYWGuf7g0ZcoUl7dJ5OlOnDiBNWvW4No1c/Nwk7f766+/7J4lvSohBL766iusW7dO0ZGqAJMXr1EBYB70iz2uMXO8FvSjkY4CGIJ/lhmoXGBRsjhsqG/fvn2StkmkduXl5WjXrh0GDRqE1157TelwyA0cPnwYWq0WFy9exN69exEVFYWoqChcuHDB4TozMzPRt29f9O7du1pfQldj8iKjxMREpUOo5jSAQdCvRv2HmeNNAHwEYDv0I5ekdOLECXz99dcS16qc2bNno0uXLtiyxdyCDUSuc+TIEZSWlgIA5syZo3A0JKWrV6+iW7duiI2NxZkzZ2w6R6fTISYmBunp6RgyZAgGDhyIiooKXL58ucZBEdYYJ8ZTp051uB4pMHnxUpnQ93N5A0CZmeP3ANgH4AMoMyrJ3ZWUlGD8+PHYvXs3Ro0ahc8++wwvvvii2RFUAJCfn48VK1ZIttI3ea7vvvsOjzzyiKH/FrleSUkJli5disOHDztcR3FxsSR3pmua7+qtt97C9u3b8csvv+DZZ5+1qc4rV64YXm/YsAEXL/6zmExlkuvpVJO8uGKSOrW5BmAy9EnMOjPHfQGMAnDs5r9KXizXrl1DaqrlxQ6+/fZblJSUYPLkyahduzYyMjJknQTv6tWrhtfHjh3D4MGDMXfuXAwbNqxaWSEE4uPj8dRTTyEkJAQzZ87kJHkqY3w91KRnz55YvXo1unXrJmNEytDpdDh69Kji/SFqMm7cOIwYMQIxMTEoKzP355t1Go0GISEhiIqKQnl5ucmxI0eOYNmyZYZRkOXl5fj111/NfiZZWVkIDw/Hgw8+aHJ869atmDdvHi5fvmySYO3cudPpnx2LFy922QShshIqU1RUJACIoqIiWepfsmSJgH5kcY1bYmKizWXdYfs3IH4DhLCw7QfEPS6KxZHPvUOHDibvly9fbrgezG0JCQk1fr8txVRQUGBz7BUVFdXKDBkyxPGLkNzK66+/Lvz8/MSkSZNqLHvixAmr14qjfv75Z1nqtdeTTz4pAIj09HTFYrCF8We1cuVKi+Vu3Lhh8r68vFz85z//MTl/0aJFhuPXrl0z7E9LSxNCCHHvvfcKAOK///2v1Ti2bNkijh07Jvbv32/Y9+yzz4pHHnnEpNztt98uSkpKqtW1e/du8f333wudTicuX75sck7dunWr1VH1azPn4sWLIj8/XwghTOICIP71r3/VeL697Pn9zeTFTmpOXgCIQEBMBEQJLCcxywHRROY41q1bZ/K5v/rqq3bX0aZNm2r/aY03JZMXc+XIM9nzPW3RooWk18D+/fvFzJkzxXfffSf7tXXw4EFx4cIFk32//fab+PDDD8XFixeFEPZ9FkoyjjMoKKjacZ1OJ/r06SMaNmwotm7datg/b968av+PZ82aZTh+8OBBk2MXL140eZ+fny9Onz5tNg5LW9XkBYCYMmWKSbzGyeumTZuqJS/mNuO4zSksLBT169cXvr6+YteuXdXOZ/IiMTUlLzExMZIkAo5szQHxKSwnMJcB8SoggmRqPzw83PCZnzx5UoSFhUnehr3Jy/Tp08W3334rtmzZImbOnGmx3qrsSV6KiorErFmzqiVv5Jjr16/L3kZN39NKCxcutOkasNX169cN9TRu3LjGeq9cuSLef/99sXnz5mrHZs6cKZKSksRPP/1k9twvvvhCABANGjQw/NWv0+lEUFCQACD69OkjhLD9s5g/f76YNGmSKC0tNdm/f/9+MWLECJOEwVhhYaFYuHChOHnypNX6a1LT92H79u0mx1etWiWuXr1q9v+xteSlsLDQ7DkvvfSS2TjMbeaSl2effdYk3t69exuO3XLLLTYlL5Vft06nE0IIsWPHDrFw4UJx5coVIYQQ48aNs3oukxeJMXmRdksCxAFYTmJOAOJRmdquJNfnYJy8XLt2TaxevVocPXrU5PvtTNyV7Ele/u///k8AEL6+vuKPP/4wW6byh42Sdu7cKYYPHy52796tdChm6XQ60bt3bxESEiK+/fZbWduq6XsqhLD4y8Sc/fv3i7S0NJGdnW213fPnz9t8DQohxGuvvWY4/vvvvxv2nz592rC/Xr16NX6N06dPF0IIUVZWZrK/6t1ISzZv3mwoM3bsWIvtGDt79qx46qmnDMeaNGli9bOpSdXPq/LOUaWvv/66Wpnx48eb/ayTk5MN51X9/ZCVlWXxe7Rv3z6bfp6YS16GDh1qEq9x8mLP9uyzz4rIyEixePFiw74JEyYIIYQYMmSI1XOZvEhMLcnLgAED3CJ5ASD8ATEWEJdgOYnZCYhEids9ePCgeOihh2T92oqLi4UQQkyaNEkA+h/exteOI3VWZSl5WbNmjRgwYIDIyckx297ChQur1bVz504RGRkpevXqJSoqKmS4wm1j6evNzs4W99xzj5g/f76s7df0vH7Pnj1WvydSqqmd3Nxc8eOPP9p0rQghDH23mjVrZrVde5MX4+Nz5swReXl54sUXXxRz5syx61wA4vTp09WSl6qPaC2p7Bdjrpyl/eZ+OVuzdu1aMWLECHHs2DGbvp5NmzYZ/ijIzc21+07vvHnzRK9evartDwkJcfpnlLnkBdDfna78A8fR5MXS9scff9RYhsmLxNwpebn//vsdvnjGjRvnNslL5dYYEIsBUQHLScxKQERJ1F7Pnj1l/5pefvllIYTpD7NNmzYZvt+O1FmVpeTF3DnG+8wlLx07djQcz8zMlOEKt42lr9d4f1lZmWTt7dixQyxfvlxcu3ZNPPzwwyIsLExs2bLFYnnjv+4BCJ1OJ06fPi2mTZtm8dGIo6x976v2RanpWqmpPmPnzp1z+BqcM2eOaNu2rcVzL126JEaPHi2mTp0qdDpdtTKPPfZYteTFWgznzp0TX3zxhSgtLRVt2rSx6fqxtL+mz+bo0aOGMlFRUUKr1YrbbrvN0DHX0ufWrl07kZeXJ/vPHHs3Hx8fi8datWolhJA+ebFlu/XWW61en45g8mLjF+8IW5OXwMBA8eWXXzp8YaxZs8btkpfKLQ4Q38NyAnMFEFMBUdcNYrVlO3TokMn7TZs2iWvXrgkhpElezP3wN3dO1XLGoxgqGR9ftmyZLNe4LSx9vcb7zY2IEEL/i3ThwoVi0aJFhr92v/jiCzFhwgRx/vz5auVPnjxpqLNPnz5WP+tKVZOXO+64w+S9lI/erMVTu3Ztu66VmuozZmvysm7dumrHq95tMd7KyspErVq1DO/vvvvuamWSkpJMHjfVFEPlz7Jhw4ZZTF7+/PNPk/3Gd9fM1f/FF1+Y/VyaNm1qMab8/HxZfoYouWVkZCjWttSYvNj4xTvCluRl+vTp4tKlS0IIx375zZw5U1RUVLht8lK5PQzrQ6vPAGI4IPzcIFZrW5cuXUzeP/jggyIgIECMHDlSkv/QtiYvM2bMMNm3ePHianUZH3d18vLDDz+IxMRE8c4771j8eo33W0peVq5caSizatUqcerUKcP7fv36GcpduXJF6HQ6MXfuXIufW69evUzaOX78uJg2bZrQarVWP29bhonaqupncf78ebFgwQJx4sQJ4e/vb9e1Yq4+S2xNXswdt5a8OHPHuGoM5n5eVk1eXn31VZM+F5VbUlKSOH/+vElfnZo+vxs3bkgSOzfbv8dS8vjkpW/fviI0NFQMGDDA7nOVSF6qZvrvv/++ofz7779v9wVx6NAhIYR8HVWl3GoB4gVA/A3LScyvgOjjBrFa2qr+VS71f2hbk5eq+2pKXtLS0kRhYaEs17k5tny9xvstJS/Gj766du0q1q5da3Le559/LgYMGCACAgJEQkKCmDVrltXP7pVXXhE6nU5cvXpVRERE2PQ9spa85OXlif79+4tNmzaJ3bt3ix07dli9U1P1s7jvvvsEANGoUSOnk5c1a9YY5tmoytbh+uaOP//887L/vzpz5ozsbXz66adixYoVYtGiReLKlStWE11u0m9S8/jkZcuWLeLrr7/2iOTlueeeE+Xl5Sb7jJMXIey/+1L5w0rpC9OerSEg5gPiOiwnMdvhuknu7NmkThKrsiV5qXoNATUnL4B+6GpZWZm4ePGimDBhgtUJtxyh0+kMnQItxV5SUiI++OADsWPHjmr7zakpeam61XQn4N577xXt27cXoaGhNn+PqiYvFy5cENu2bbPYP2nHjh0WP5+q33vj984mL5VbTk6O+PDDD8XYsWMNCevZs2et1qvT6cTAgQMV+T8FoNqjO27q26Tm8cmLEPoExhOSl3PnzgkhTH/gOJu8OHqeO2xtAbEBlhMYAYi1N8spHatc29GjR03+UrcleRkwYEC1fbYkLwDE9u3bxRNPPGF437BhQ5GcnCyuXLki/vvf/4oxY8Y4/P9h8ODBAoCYOHGi3Z+DLcnLvffeW2PyEhcXJ/n3yHiklvFjK0t3eeLj4w3lr1+/LpYtWyauXr0qNmzYYFJu+PDhJu/9/PysxlE5D82hQ4fEqVOnxN9//11j7I8++qjIz88Xf/31l8UyQgjx7bffKvr/wBV3d7gpu0lN0eTlhx9+EA899JDhUcqXX35Zrcz8+fPFLbfcIgIDA0VCQoL48ccfq5XxlOSlckSF8T5nkpfatWs7dJ67bT0BkQPLCcwN6EcuNXODWOXYnn32WVFcXCwOHjxocXKrmrZRo0ZVu/7Mldu2bZvZ/cYdLW2Zrr2goED8/fffDl+7VbeqE5BV6tSpk6GMLclLbGys5N+f06dPi5deesnmzo7GyYvxfmd/QT/66KNi/fr1Dp07evRoi8f+/PNP8fbbb0v+uXHjZrxJTdHkZcOGDeI///mPYUbGqsnLp59+KgICAsTSpUvFr7/+KtLS0kRoaKgoKCgwKWdr8nLt2jVRVFRk2Cp7k3tr8jJo0CDFL+jKzQcQjwHiOKyPTJoFiHA3iFfqrTKBb926tcN1GE8lbumaqDobqLnN39/fpJ7169eLoUOHigMHDgghhPjpp59ErVq1RN26dcWff/7p1DVYublz8mJvp1RLyQs3bt68Sc1tHhsB1ZOXhIQEodFoDO8rKipEZGSkYdbGSrYmL1OmTDH7oXpr8mI8ksNdtlqASAfEOVhOYi4DYhogwtwgXnfb/vrrL6udVqv2NTG3VU1ejI8999xzIikpyfD++eefd+oarNxKSkrE999/L5o3by6eeeYZQ53Gycs999yjSPJi7xYWFibJZ8KNm5o2qdmTvPjChcrLy5GTk4Pk5GTDPl9fXyQnJ2PXrl0O1Tlx4kQUFRUZtvz8fKnCdZifn59ibYeFhSnWtiXXAcwHcBuA1wGUmClTD8CrAPJulglxWXTur2nTphg/frxTdfj4+Fg89v7772Pr1q2G9//73/+caqvSlStX0KNHD/z5559YvHgxjh07ZrbchQsXrNajzxeUdfHiRaVDICIjLk1eCgsLUVFRgYiICJP9EREROHv2rOF9cnIyBg0ahA0bNqB58+ZWE5vAwEAEBwdjxYoV6Ny5M+6//37Z4rfm+eefBwA0atQIqampisRgzUMPPaR0CLgM4P8AtAKghT6pqSoYwGQAJwC8BqC+i2LzZN9++63NZW1JBC5fvuxMOAYffPCByfszZ85g1KhR2Lt3r2Gfj48PxowZI0l7cps/fz7ef/99pcMgIkCG+z5GANPHRpUzMu7cudOk3Pjx421a4dcWSnXYFUL/9VXOzGoMdtyGM35sZM/Qz8pt48aNZvcrMX10TVtLQPwP+s67wsJWCP3q1SFuEK8nb7Vq1RIvvPCCCAsLE6tXr66xvCPXbk1bampqtX3x8fE1nte+fXvFPz9u3LhV36RcAkQIN35sFB4eDj8/PxQUFJjsLygoQJMmTVwZiiwiIyMRGBgoWX2LFy+WrC539AeAYQDaAlgJQGemTEMA0wCcBPAmgEYui05drl+/jrfffhsXL17EoEGDFIlh48aN1fbl5OTUeN4vv/wiRzhE5KTz588r1rZLk5eAgADEx8cjKyvLsE+n0yErKwtdunRxqm6tVouYmBh06tTJ2TDdxoABA8zuf+CBB1wcibx+A/AkgHYAVlkoEwLgP9A/TpoHoLkrAiMiIouEgv3RJE9eSkpKkJubi9zcXABAXl4ecnNzcerUKQBARkYGFi1ahOXLl+Pw4cMYPXo0SktLMWzYMKfa1Wg0OHTokMnzdPIshwE8CqA9gC8slKkDYCyA4wAWA2jtmtCIiKgKawMB5OYvdYX79u1D9+7dDe8zMjIAAEOHDsWyZcswePBgnD9/HpMnT8bZs2cRFxeHzMzMap14yXsdADAAQByAiQAGonqWHQBgBPSPnb4EMBfATteF6BWMRyAREVWlZPIi+Z2XpKQkCP38MSbbsmXLDGXS09Nx8uRJlJWV4ccff0RiYqLT7arxsZElSo2ocrVcAIOh7xOzFOZHJ/lCn+jsAPDjzfKSZ+ReqG3btiZ/hBARuROX9nmRkzc9NurWrRt27tyJ1157TelQXOIY9HdZbgPwHoCrFsolAPgU+o7AL4FzxTjjyJEjSodARGSRapIXbxIeHo4uXbqgb9++NpXv3LmzvAG5SD6A5wFEA5gOoNhCuSgAswD8Cf3keHe6IjgiInIZ1SQv3vDYqGHDhnjrrbfQurXt3VTHjRsn2Yyp7uIc9LPxNgfwAvQjkMypB0AD4CCAbACPQd9XhoiIPJtqkhdveGy0efNmvPzyy3ad8/bbb+OOO+6QKSJlXYZ+2HQr6Dv1Wuuw2w3Ax9DfjZkB4Fa5gyMiItmoJnkh+/Tv31/pECRTAeBzAPcC6Az9XDE3LJRtBOAV6PvFbIb+bkxtF8RIRETSYfLiperWrat0CLL4Efq5YlpCPyPvWStle0J/N+YsgIUA7pE9OiIikoJqkhdv6PNCtssHMAlACwCPAPjeStlgAGnQD7c+Bv1MvnysRETkvlSTvHhDnxdnFBUVKR2CIq4DWA3gfgB3QN9H5m8r5VtDf8fmD+jv4rwI/eglIiIypapJ6sg9NW/O1YCOQj86qRmAxwFsgvnFICslAJgN4BT0nYHHAoiUOUYiIk/B5IVkFxcXZ/Lez89PmUDcwFUAnwDoBf1jpYkAapqSrQv0d21OQ39H5jXo12AiIiLXU03ywj4v5IjT0A+dbgv9SKUPANS0yHsCgDcA/AzgJPSz/j4AziFDROQqqkle2OdFPq1bt0azZs2UDkN2PwJ4DkBT6EciLQZwsYZzWgBIh/4R1EUAG6B/NNVOvjCJiLyeapIXksezzz6Lo0eP4tSpU0qH4jIVAL6DfgRSBIBUAP8DcKmG8+reLDsX+pWxzwD4CMBTYKdfIiIpcQFelalfv77hdXBwsFN1nTx5Ei1atACgbMcsJd0AkHlzGwn9TL19bm4tazi3KYAhNzdA3/F3u9H2K6x3GCYiIvN458UNBAUFOXReYGBgtX0dOnTAyJEjceedd2LZsmUOxzRx4kRD4kJ6NwBsgf6x0G3QL/g4EcAu2JaEtIB+lNP7AH4BcAH6x0z/B+AhAE0kj5iISJ1450Vhb7zxBvLz87Fw4UK7z73zzjvRsWNH7Nu3z7DPx8cHH374oZQhkgWHbm4zADQE0ANAMvT9ZWyZ5C4U+sdMqUb7TgPIAbDv5vbLzX1ERPQP1SQvWq0WWq0WFRUVSofiMj4+Pti2bRsaNWqEkpISREZGmr0bQ/K7AP1keKtvvr8N/yQySdAnN7ZodnPrY7TvEvQrY1fdLjgZMxGRp1JN8qLRaKDRaFBcXIyQkBClw3GZoKAgbNmyBd988w0GDhwIX18+CXQHx29uHwLwAdAGQFej7TY76go1Os/YeQC/Afj95vab0b/eOZ8yEXkL1SQv3qxjx47o2LGj0mGQBQL6SfCOQD/8GtB35u0K/ZwxHQHEA6hv9mzLGt3czC0oWQggD/pOwvlV/j0FoOBmXEREjlJyIAeTFyIF/AXTx0w+0K+r1NFoi4P9CU2l8JubpSkby6HvS3MW+kSmwOi18b4CACUOxkBEJBcmL0RuQEC/ovUxAB8b7W8B/YR3xltbAI6NT/tHAPSdim3pWFwG/WKWF422v828LgJw2cx21clYiYiqYvJC5MYqH/NsMNrnB/0cM60BtKryb/TN41IKhH4Yt6NDuSugT2JKYJrUlEKf2FwFcM2G15Xvr0F/5+j6zc3aa86jQ6ROTF7IrG7duikdAllQAX2n3N/MHKsFfQLTCvpZfVvc3KKM/q3lkij/4Qd9p+NQF7cL6JMXSwnODeg/S+NNZ2ZfTces7RcWNkvHHDnH3mNVVd0nVxkl25ayjNLcKaaA7Gxg0CBF2mbyorDIyEjk5+crHYaJJUuWICUlRbb6Q0JCUFTE8TByuA7LiQ2gn5UyAvpEJvLm6wjo76pUfV1X7mBdwBf6O0ecQIBIeuVvv83kxdsMGzYMzZo1w6OPPooff/xR6XAMgoODMXz48BrLzZgxA0FBQRg3bpzdbeTk5OCuu+7C1avsDeFqOug7C/9lQ9m6ABoDCLu5NTB6be59MPQdjOuDP1iISF6q+RnjaZPULVq0CH5+9vVOcHatIimNHDkS3377rUPnRkdH44cffkBCQoLEUZGUSqEfbp3nwLlB0Ccx9fBPQlO/yr46AGobbUFW3ld9XQv6Tsec1YjIO6kmeVHrJHULFy7EvHnz8OCDD6JVq1aKxjJgwAB8/vnnSEhIQGhoqMP1+Pn5oVMnS4N4SQ0qO9ael7kdX+gTmcpkxvhfS68r//WHvj+O8eZrZp+1/TWd41PDVlMZqeswZm6GjprKuKIOd42Lqmtzyy2Kta2a5EWt0tLSkJaWpnQYAIDPPvsM+/fvR2xsrNeuMk3uRQf9UO4ypQMh8kIF77yD2gq1zeSFbObr68uZfImISHF8ZExERER2U/IOPJMXIiIi8ihMXoiIiMijMHkhxfz73/9WOgQiIvJATF5IMbNnz1Y6BCIi8kBumbysW7cObdq0QevWrbF48WKlwyGZtG3blvO9EBGR3dxuqPSNGzeQkZGBLVu2ICQkBPHx8ejXrx8aNmyodGhERER0E0cbGdmzZw/uvPNONGvWDPXq1UNqaio2b96sdFhkhvGMv4MUWpyLiIi8j+TJS3Z2Nnr37o3IyEj4+Phg7dq11cpotVpER0cjKCgIiYmJ2LNnj+HYmTNn0KxZM8P7Zs2a4fTp01KHSRK4++67MX/+fIwaNQozZ85UOhwiIvISkj82Ki0tRWxsLIYPH47+/ftXO75q1SpkZGRgwYIFSExMxLx585CSkoKjR4+icePGdrdXVlaGsrJ/JgcvLi52Kn4lxMbGGl4/8cQTCkZiP41Go3QIRETkZSRPXlJTU5Gammrx+Ny5c5GWloZhw4YBABYsWID169dj6dKlmDBhAiIjI03utJw+fdrq6sPTp0/H66+/Lt0XoICnn34apaWlKCoqwpgxY5QOh4iIyK25tM9LeXk5cnJykJyc/E8Avr5ITk7Grl27AAAJCQk4ePAgTp8+jZKSEmzcuBEpKSkW65w4cSKKiooMW35+vuxfh7MaNmwIX99/Pvo6depg/PjxePPNNxEREaFgZNKaMWMG10IiIiLJuXS0UWFhISoqKqr9go6IiMCRI0f0Afn7Y86cOejevTt0Oh1efvllqyONAgMDERgYCK1WC61Wi4qKClm/Bil8/fXXXrEq8yuvvIK77roLDz74oNKhEBGRxDjaqIo+ffrg2LFj+P333zFy5EibztFoNDh06BD27t0rc3TOeeONN3DPPfcoHYYs3nzzTaVDICIiL+DS5CU8PBx+fn4oKCgw2V9QUIAmTZq4MhSywJkOz95wN4mIiJTn0uQlICAA8fHxyMrKMuzT6XTIyspCly5dnKpbq9UiJiaGM7Y6Sa13hYiISD0kT15KSkqQm5uL3NxcAEBeXh5yc3Nx6tQpAEBGRgYWLVqE5cuX4/Dhwxg9ejRKS0sNo48c5SmPjdxd8+bNlQ7Bozz22GNKh0BE5HUk77C7b98+dO/e3fA+IyMDADB06FAsW7YMgwcPxvnz5zF58mScPXsWcXFxyMzMVNUoG/IOkyZNwqhRo/DJJ58oHQoRkVeRPHlJSkqCEMJqmfT0dKSnp0varieNNvJmLVq0UDoESbRv3x5Tp05VOgwiIq/klqONHMHHRp5h3rx5SodAREQeTjXJC3mGu+++2+R9cHCwQpEQEZEzanrKIifVJC8cbWRdnTp1DK8jIyMVjMTUhAkTFG3fnT4LIiKyjWqSFz42sm7gwIFo3rw5goKC8M4771gsFxoa6rqgACQnJ+Obb76xufz9998vaftXr151ug5ry1cQEZH0VJO8kHURERHIy8vDuXPnMHDgwGrH/f39Ubt2bUVWia76KMmSPn36YPz48ZK2LcXkiP7+Ll1lg4jILXB5AHIJf39/1K9fv9r+0NBQnD59GmfOnEH79u0ViMw21u4YOapevXpO16Hkc18iIm+kmuSFfV6c07hxY5c/MrJXdHS05HU+8cQTktdJRETyUk3ywj4vyjO+q3PrrbdKWvfMmTMlra9Su3btZKmXiIjko5rkxVVat25teB0VFcX+DkYef/xxNG3aFIGBgZI+4vnss88k7+tSKSoqSpZ6iYhIPvzNa6euXbvi008/xS+//ILHHnsMvr7M/yo1bNgQJ0+eRGlpqV2PoOrWrWv1uBT9Uizx8/Nz6DyuoE1EpBzV/OZ1VZ8XHx8fDB48GNOmTeMjBzNq1apld9+ZkJAQzJ8/36H27rjjDofOc5ZxJ1122CUici3VJC/s8+LZrA3RbtOmjQsjISIid6ea5MWdDRkyxPA6NjZWwUg8k/EjGqkX3gwKCnLoPOOY+AiJiMi12OfFBbRaLZKSkhAZGYkHHnhA6XA8mnGHaSk0a9bMofP42IiISDlMXlygfv36GD58uNJhqIKjHWyJiEg9+NiIZNWyZUulQzBYuXIlRo0aJUldxo+Kahpu/e6770rSJhGRO+HyAKRaSo0GqqpJkyZ4/PHHJRt2bfyoaOLEiVbLhoeHS9ImERHpqSZ54fIA5KjatWs7dX50dDTuvPNOiaIhIqKaqCZ54VBp99W/f38A+jsQUqziLDVHbn1WPSc4OFiqcIiIqAbssEuyW7JkCR566CF069YNgYGBSocjiaZNm5q853BpIiLXUc2dF3JfoaGhGDZsGFq1aqV0KGZ17NjR5rK+vr7w8fHB1KlTZYyIiIisYfJCXm/WrFk2l/3jjz9w/Phx9q0iIlIQkxfyegkJCUhMTLSp7C233IJbb71V0vbdaTg5EZGtOFSaSGG2dLiVa3Xr7OxsWeolIlIrJi9EsD7Ff3BwMHr27Int27dbLGP8F0jVR0p///23xfM0Go3DSxQQEXkr1SQvnOfFO0RERBjugDz++OMYMGCA7G2OHTsWmzdvdnhRTWuLSbZo0cLRsIiIvJZqhkprNBpoNBoUFxcjJCRE6XBIJnXr1sXWrVuxbds2PPnkk/Dx8cHvv/+O4uJibNy4Uenw7Ga84jgREdlGNckLeY/4+HjEx8cb3n/66acoLCxEo0aNHK7T2mMjZzulWTs/KCjIqbqJiLyRah4bEVnzzDPPOHyuvcmLtUSIiEgtONqISGJV524ZN26cw3XZ8h+0apn//ve/htf9+vVzuG0iIqqOj43IbQQHB6O4uFiSuqqu5NywYUOH63Lkr4sXX3wRzZs3R+vWrTmaiIhIYrzzQm5j5cqVirUt9aOegIAADBkyBJ07d7apvLMrWxMReRMmL+Q2HnroISxfvlzpMKrhootERO6FyQtRDeTssMvEiIjIfm6ZvPTr1w8NGjTAwIEDlQ6FvISzj41qSkLGjBkDAHjwwQedaoeIiNw0eRk7diw++ugjpcMgAiDN3ZF3330XhYWFWLJkidnjcgyvttQWEZEUOFS6iqSkJNSvX1/pMIgASPcftGHDhoiIiJCkrppERUVh+PDhLmmLiMjV7E5esrOz0bt3b0RGRsLHxwdr166tVkar1SI6OhpBQUFITEzEnj17pIiVyG01b97c8DoqKkrBSIiI1M/u5KW0tBSxsbHQarVmj69atQoZGRmYMmUK9u/fj9jYWKSkpODcuXOGMnFxcWjXrl217cyZM45/JUR28vPzM7x2dnmASZMmISAgALVq1cLrr78uSXz26tatmyLtEhG5mt2T1KWmpiI1NdXi8blz5yItLQ3Dhg0DACxYsADr16/H0qVLMWHCBABAbm6uY9GaUVZWhrKyMsN7qSY5I/dQq1Ytp9Ysqqp///6YPXs2AGDGjBk2nWNL8tK2bVvk5+dDCGHXoyEpnxnbuk7Siy++iDlz5kjWLhGRq0na56W8vBw5OTlITk7+pwFfXyQnJ2PXrl1SNmUwffp0hISEGDbesleXzMxM1KtXT7L6unTpghUrVmDWrFkYPXq0TefYmmA0btzY4T4t9nTYrVOnjtn9tsY5ffp0ZGZm2tweEZG7kXR5gMLCQlRUVFT7AR4REYEjR47YXE9ycjJ+/vlnlJaWonnz5li9ejW6dOlituzEiRORkZFheF9cXMwERkV69OgheZ1PPvlktX1yriotlWHDhqG4uBiLFy9GmzZtTB7F2qNWrVpISUmRODoiItdxy7WNvvvuO5vLBgYGIjAwEFqtFlqtFhUVFTJGRt7IuG+MkpYuXWp43aFDB2zatMnkuLskWUTkHVQzVDo8PBx+fn4oKCgw2V9QUIAmTZpI2VQ1Go0Ghw4dwt69e2Vth+TVuHFjw+uOHTsqEkOrVq1M3ntKUuApcRKROih5s0DS5CUgIADx8fHIysoy7NPpdMjKyrL42EcqWq0WMTEx6NSpk6ztkLx69uyJAQMGoE2bNnj33XcdrqdBgwaG161bt7br3Lp16zrcrlJ69uzpkXETkecqKSlRrG27k5eSkhLk5uYaRgzl5eUhNzcXp06dAgBkZGRg0aJFWL58OQ4fPozRo0ejtLTUMPpILrzzog5+fn5Ys2YNjhw54lTC++9//xuJiYkIDQ3F+++/X2N5pfu8NGzY0KnzN27cKFEkRETuz+4+L/v27UP37t0N7ys7yw4dOhTLli3D4MGDcf78eUyePBlnz55FXFwcMjMzXTazKBGg75S6a9cuXL9+HQEBAXad68rHL5VtffHFF+jatStu3Lhh13kAcMcdd1TrlyPHcgNERO7C7uQlKSmpxh+M6enpSE9PdzgoR7DDLlXl4+Njd+KilMTEROTn5+Ppp5+u1hHXVuzzQkTewi3XNnIEHxuRXFyVFDRp0oRrehGRx1DNaCMiT2V8N1HJ/5COtO3oI6LJkyc7dB4RkdJUk7xwtBHJxR0fx0gRk6U1mHr37o0VK1Y4XT8RkVxUk7zwsRGpgTt0tP36668xcOBApcMgIrJINckLkTOUShrc8a4OYPsij0RESmDyQlRF1YTCXROMSnIlXvHx8bLUS0TkLNUkL+zzQt7E3RMqIiI5qSZ5YZ8XkosnJwrr1q1z+Fx36H9DRO5LyZ8RqkleiJyh1l/UDz74oNIhEBFJjskLURXeMs8LANlXeycikgOTF6IauDKZsTURqSkmW+sJCwtzuA1runXr5vC5REQ1UU3ywg675IwGDRqYfQ2g2qKHUpIyMZI6yXLmjk6/fv0kjISIyJRqkhd22CVnvPfee6hTpw5q166NDz/8EKtWrQIAhIaG4qmnnlI4OmWotR8QEXk+u1eVJlKj6OhonD59GkIINGjQAC1btkTr1q3RvHlz1K1bV+nwJBMXF2fyngkKEXki1dx5IXJWaGioySOjDh06oFGjRgpGZJuaEpCEhATD6zp16khWr1znEhHVhMmLlzLuH8Gp4D2PXJ2IU1NTLR6Ts+8PEZE9mLx4qUGDBhlev/LKKwpGQnKLiIgwvG7cuLHVspV9fYDqCdKOHTuwevVqJCYmShugnT799FNF2yci5akmeeFoI/v06tULmZmZ+Oyzz6DRaJQOx2u5Yhj2/PnzERISgtDQULz33nsWy6WkpKB+/foWY0tMTMTAgQPh7+9cV7nbbrut2r4OHTrYfH6fPn2cap+IPJ9qOuxqNBpoNBoUFxcjJCRE6XDcno+PD1JSUpQOgyRQU/+SFi1a4PTp0/Dx8XGLPi8HDhzA6dOn8dBDD+Ho0aMAoKpO0UQkP9UkL0TexN47NpaSA2tJhlydbmvXro1WrVqZ7PPk9aOIyPVU89iIiJzj6gTC0eTIXTsOjxgxQukQiLwGkxciMkvu4c7G9duTOAUEBMgRjtMCAwPx4YcfKh0GkVdg8kLk4cwlGZ42z4oaHhsJIeDra9uP1C5dusgcDZG6MXkh8kDmftm7UwJgS/I0fvx4w+uRI0eaLTNp0iR88803ksXlLnr06KF0CEQejR12iRRUNeHwtFE3nTp1cng9sWHDhuH69esICgpC7969zZaZOnWqM+HJIjo6GidOnHCqDndKNIk8kWruvHCeF1KDl19+WekQDOR+9OTv74/nnnsOw4cPt/mXeXBwsKwx1cTX1xcLFixQNAYiUlHywlWlSQ1iYmLw888/Y+fOnXZN3OYoT+kbs337dowZMwa7d+92qp6kpCSnzj958qTF+ZFq1apl8+fJOy9EzuFjIyI30759ewC2/4KTKgGRsj2pk6J7770X9957r6R1OqJ58+YWj40ZMwZbtmxxYTRE3ks1d16IvIkr/nK3JQFR6g5CfHy8w+d+8sknkg+3Xrt2bbWJ94hIPkxeiNxUo0aNFG3flYmJvXdqnBmB9Oijj+LixYsOn29O165dJa2PiKxj8kKkIGsJQosWLVwYiWOU6jPTtGlTp853t1Fdq1atQnBwMGJiYpQOhcgjMHkh8gDWftm6OoFgZ1PpPfLII7h48SLmz5+vdChEHoHJC5EHkiqBkGthRqVHMQ0aNMil7dn7/TBX3l3XbCJyR0xeiAiAuu6oPPjgg2b3y/W4SE2fHZEncLvkJT8/H0lJSYiJiUH79u2xevVqpUMiUoQn3/lwRwEBAXjvvfeUDsMgOzsbI0aMQE5OjtKh2GTUqFFKh0Bk4HbJi7+/P+bNm4dDhw5h8+bNGDduHEpLS5UOi0hRVf+y79y5s+F15V0Gqf/6V1MCNGrUKOTn5+PWW2+VtR17PrNu3bph8eLFuPvuu2WMyD4tW7a0eOyDDz7AAw884MJoiCxzu+SladOmiIuLAwA0adIE4eHhkg9rJPJ0Go0G9913Hzp16oRXX31VljZuueUWs/tt+QVt6+rKckpLSzO8fuKJJ9C4cWPJ6vbWUUGffPKJ0iEQAXAgecnOzkbv3r0RGRkJHx8frF27tloZrVaL6OhoBAUFITExEXv27HEouJycHFRUVCAqKsqh84ncnaN3S+rVq4etW7diz549iIyMlDgqvdtvv73GMpbiT0tLQ7169QAAPXv2lDQuW82aNQsZGRmYP3++5POwZGZmSlqfIywtZumM5ORkq8fDwsIkb5PIEXYnL6WlpYiNjYVWqzV7fNWqVcjIyMCUKVOwf/9+xMbGIiUlBefOnTOUiYuLQ7t27aptZ86cMZS5ePEinnrqKSxcuNCBL4uIbCHXo6GQkBAcPXoUe/fuxcCBA2VpwxofHx+EhIRgzpw50Gg0ktdf9Q8qKUYb2VvP119/bVebtnjrrbckr5NIDnavbZSamorU1FSLx+fOnYu0tDQMGzYMALBgwQKsX78eS5cuxYQJEwAAubm5VtsoKytD3759MWHCBNxzzz01li0rKzO8Ly4utvErIXJvSs/f4mz7kZGRiIyMxE8//eRUPeQ6oaGhSodAZBNJH0yXl5cjJyfH5Najr68vkpOTsWvXLpvqEELg6aefRo8ePTBkyJAay0+fPh0hISGGjY+YSI04FJeI6B+SJi+FhYWoqKhARESEyf6IiAicPXvWpjp27NiBVatWYe3atYiLi0NcXBwOHDhgsfzEiRNRVFRk2PLz8536GoiIvJm1EUdE7sLux0Zy69q1K3Q6nc3lAwMDERgYCK1WC61Wi4qKChmjI/IelR1uASA8PFzWtsw9oqqpw/CLL76IOXPmIDg4mI+LibyMpHdewsPD4efnh4KCApP9BQUFaNKkiZRNVaPRaHDo0CHs3btX1naIpOTOj4NeeuklhIWFwd/f32LnULn65UyYMAGbNm2yWmbSpEl45513sHnzZllisAen9idyLUmTl4CAAMTHxyMrK8uwT6fTISsrC126dJGyqWq0Wi1iYmLQqVMnWdshcpXY2FjD6/vvv9/l7YeEhODkyZPIz883+f9rb8JlPEz58ccft+mc6dOnIzo6usb4nn/+eSQmJtoVj1QWLFgAX19f9O/fH/Xr1wdgezLnzklrTYMkiNyB3Y+NSkpK8Pvvvxve5+XlITc3F2FhYWjRogUyMjIwdOhQdOzYEQkJCZg3bx5KS0sNo4/kotFooNFoUFxcjJCQEFnbInKF0aNHY+vWrSgsLMQHH3wgSxs1/bKtV6+eyeMjR7Rt2xYrVqzAL7/8YhhxKDdXJAfPPvssHnnkEZeN0GnXrh0OHjwoeztvv/02/t//+38m++rUqSNpGwEBASgvL5e0TvIudt952bdvHzp06IAOHToAADIyMtChQwdMnjwZADB48GDMnj0bkydPRlxcHHJzc5GZmVmtEy8RWefv74/PP/8cP/zwg02PXY2nbh8+fLjd7dn6C79qwmPLbLNPPvkkZs6cqbpJzho0aCBpomSpLn9/fyxYsKDa/l27dhnu+jRr1gwNGjSosY2aki25+ze1a9cO//rXv2RtQ079+/dXOgSCA3dekpKSavxrLT09Henp6Q4H5Qh22CVvN2TIEOzYsQPFxcXIyMhwSZs+Pj7YuHGjxaUEPFGPHj3w/fffKx2GicolU6rq3LkziouLUVJSgsDAQLRu3Rp///23a4PzMp9//rlbP/bzFsovQCIRdtglb1erVi0sWbIEq1evdukdjhYtWrisLVcYMGCA0iEYdOrUCS1atMDHH39stVy9evVQq1YtF0XlHDUt+EnKUU3yQkSkNj/++CPy8vLQunVryX7pu0Py0LBhQ5vLbty4UcZIyFOpJnnhaCPyRGq5/aymx0auYOv33cfHx64Vuj3lepo7d67NZT25fwzJRzXJCx8bEdlPqr/CFy9eLEk9aqOWgQq2dMq2h60rodeuXVvykU6kDqpJXojIOc781e5u/V6UugNRdbSPq+8Ey/F1R0ZGYuXKlZLXawslViQnz+B2ywMQESnJmbtRVTv72ptMGK8r1K5dO4fjkNLJkyfh789fFeReVHPnhX1eiDyXO3QilYKfn59NCxta+nqjoqKwcOFCPP744/jqq6+kDs+qIUOGmN3vCYnL/PnzlQ6BXEw1yQv7vBC5Rt26dQ2vK/sjqCX5cAdpaWlYuXJltSRI7s/YeDmKpk2bAgAaNWokeTtyfB0ajcZlcxuRe1BN8kLkiTxldIgxrVYLf39/+Pn5mZ31lf5h6fvr7t/3HTt24K233sLu3bsVjcOez2nOnDlcXdyLuP/9QCJyK61bt8bJkychhECzZs2UDoeMSJUU3XrrrXj55ZclqcuVKpdKIPXjnRciL/bWW28ZXtvzyyoyMtIkceFjI8/x3HPPKR0CkdNUk7ywwy6R/fr164c1a9Zgw4YN6Nq1q9LhSMbdH8so6aGHHlI6BCKnqSZ5YYddIvv5+vpiwIABSE1NVToURcXHx6Nly5bIyspSOhTZ+fj44N5771U6DCKnqCZ5ISJy1OzZs3H8+HH06NFD6VAskurRnLvMWBsUFKR0COTBmLwQkddz9WMmpR5r9ezZE+3bt1ek7aqkWnCxY8eOktRD9pNjKL2tmLwQKYh9M9yPmjsfb9q0SfFrrnJEUFJSktnjxneGLMVaOQ8NUH1JBnIdJe+eMXkhIpKQOyc/UicuoaGhCA4Otrm8v78/li5danjfq1cvh9oNCwszvHbnz5vko5rkhaONvJvxrK9xcXHKBUJkRI2Po4xXyi4oKMB9991n87mnTp0yWaH6o48+whtvvIGnnnoKtWrVwogRI1CrVq0a61H67hEpTzXJC0cbebfatWvjk08+weDBg7Fo0SKlwyE7Sf3XM3+5yWfbtm0YP348fvzxRwQEBKBv3742n2v8uAfQ95l47bXXsHz5chQVFWHx4sUSR0tqxRl2STUeffRRPProo0qHQSSL5s2bG16Hh4crFkfr1q0xc+ZMw/unn34aJ06cwNWrV7Fu3TocOXLEoXpr164tVYjkBVRz54WIyFM4cmeoZcuWmDZtGnr06IEtW7bIEJVjfH19MXXqVMyaNQsbNmxA3759MWPGDIfrM56DxvgRE5ExJi9ELqbRaAAAXbt2hb+/Om5+Kt1pMioqStH2XeXVV19FVlYW2rVrp3QoZt1666348ssv8corrzhcx6JFixAfH48HHngA48aNky44UhUmL0Qu9u6772LPnj347rvvlA5FNVauXKl0CCSRyMhI7Nu3D5s2bUJAQAAAYMmSJZLU3bZtW6vHv/zyS0na8QZKProEmLwQuZyvry86deqEwMBApUNRjW7duikdAsmoSZMmktTTuHFjq8ft6XxMymLyQkSqMGjQIMPrxMREBSMx9cgjj7isLWdGWQ0YMEDCSFzHnkeWSj/eVELXrl2xefNmpcOQnGqSF87zQuTdPvjgA7zyyiv49NNPcdtttykdjsGSJUuwevVql7RlLXmZNGmSxWPZ2dmIjo6WISJ5WPs6K/uUkd62bdvQs2dPyeu99dZbJa/THqpJXjjPC5F3a9iwIWbMmIHBgwc7VY/Uf53Xq1cPAwcONNnn6nlotm/fjv/7v/8z237Hjh1V9djtnXfewe7du5UOwyGzZs1SOgSbde/eXdH2VZO8EBHZw3jETsuWLSWrt1WrVobXLVq0kKxeZ9x7773w9fWOH/d+fn5u9djQHhkZGRg/frzSYXgE77iaiYiq+Oqrr/D4449j4cKFkg61XrRoESIjI9GyZUtMnTpVsnq9mfGSH3369FEuEJn5+vrWeBesR48eDtUtdZeKhIQESeuzF5MXIvJKLVu2xMqVK5GWliZpvbfccgtOnjyJ3377DaGhoZLW7a0iIyPx1VdfYeLEiYosIVC5evL8+fMBAJmZmRgyZIjL4wAc79OzYcMGyWJ44YUX0L9/f8nqc4Q6ZsgiInIjapl80J306dPHqbsu9evXd/jcQ4cO4dixY0hOTgYApKSkICUlBStWrHC4TkdVzn1jr/DwcAgh8Ouvvzo1yeGNGzfg5+fn8PlS4Z0XIlJcSEgI2rdvDwCYMGGCorFwUUd1Wrlypdnk54EHHgAAPPzwwxbPvfXWW5GSkuKSX9o1XX89e/Y0rOz9/vvvyx5PVe6QuABMXojIDfj4+CA7Oxvff/893nzzTaXDkZ1cCZK3JF6PPfaY4bWtE8vVq1cPzz//PP7973+b7J8zZw5++eUXfP7552bb2bNnj1OxSi0wMBAHDhzA9u3bMWrUKKXDUQzvbRKR06QYXhwSEqL48EvyDBkZGTh//jz8/f3t+gVeq1YtvPvuuyb9P3x8fCw+Rvn444+t1jd8+HAsXbrU5val0qhRIzRq1Mihc9WS4DJ5ISIijxIYGIi5c+cqHYbDCQQ5z+0eG126dAkdO3ZEXFwc2rVrh0WLFikdEhEREbkRt7vzUr9+fWRnZ6NOnTooLS1Fu3bt0L9/fzRs2FDp0IjIC3jj+jfehN9fdXC7Oy9+fn6oU6cOAKCsrAxCCF5sREQerqYVneXmKX09PCVOpdmdvGRnZ6N3796IjIyEj48P1q5dW62MVqtFdHQ0goKCkJiYaHdv7UuXLiE2NhbNmzfH+PHjER4ebm+YRERuyxt+QTVp0sTw+v7770dWVpaC0Vj+zCv/WJbbkiVLEBgYaPK5kOPsTl5KS0sRGxsLrVZr9viqVauQkZGBKVOmYP/+/YiNjUVKSgrOnTtnKFPZn6XqdubMGQBAaGgofv75Z+Tl5eHjjz9GQUGBxXjKyspQXFxsshERSSUsLAxxcXHYunWr0qHUyJ2SouzsbLzwwgvYsWMHvvvuO6cmRpOTq1ZHTkxMxJkzZ5CXl+eS9tTO7j4vqampSE1NtXh87ty5SEtLw7BhwwAACxYswPr167F06VLD5FO5ubk2tRUREYHY2Fhs27at2qqslaZPn47XX3/dvi+CiMhGx44dY587B7Ru3dotRgS5k7CwMKVDqKZZs2Y4ffq00mHYTdI+L+Xl5cjJyTFMoQzoF5pKTk7Grl27bKqjoKAAly9fBgAUFRUhOzsbbdq0sVh+4sSJKCoqMmz5+fnOfRFEREaYuJCa1a5dW+kQHCLpaKPCwkJUVFQYpi6uFBERgSNHjthUx8mTJzFy5EhDR90xY8bgrrvuslg+MDAQgYGB0Gq10Gq1qKiocOprICL7sVM9eQpvv1bd6dGiM9xuqHRCQoLNj5WMaTQaaDQaFBcXIyQkRPrAiIicEBgYiLKyMgDOLRJI3kvKlaEreWoyI+ljo/DwcPj5+VXrYFtQUMAe1kQq5u1/zdri22+/RUBAAFq0aIFnnnlG6XDIgs8//xydO3fG6tWrFWnfWjJhrb+pt5E0eQkICEB8fLzJkDidToesrCx06dJFyqaq0Wq1iImJQadOnWRth4jIEd26dcOZM2fw22+/ISgoSOlwyIL+/ftj165dFgeJGEtKSjK8Hj58uNWyTPClZXfyUlJSgtzcXMOjnby8POTm5uLUqVMA9AtmLVq0CMuXL8fhw4cxevRolJaWGkYfyUWj0eDQoUPYu3evrO0QETmqYcOGCAgIkK3+t99+W7a6PU3VP5jleDySkpKC//73vxg1ahRmz54tef1kmd19Xvbt22ey8mtGRgYAYOjQoVi2bBkGDx6M8+fPY/LkyTh79izi4uKQmZlZrROv1Nhhl4ik4Ml/Iffq1QsbN27E8ePHkZ6ebrHc9OnT0a1bNwDAzJkzXRWeS23cuBGhoaGytuHj44OJEyfaVNaTryt3ZHfykpSUVOM3IT093ep/HDmwwy4ReTsfHx/06tULhw8ftlqua9euyMrKgk6nM3n0oSZK/B6IiYnBoUOHXN6uN3K7tY2IiMg5bdq0QatWrQAAb7zxhtkyPXr0QHJysseONnGUu98BsXfelcWLF8sUiXtj8kJEpDK+vr748ccfsWXLFrz66qtKh0N2uO+++xAbGwtfX1+bRqWNGDHCrvrlfpTmKqpJXjjaiIjoH2FhYUhKSoKvr2p+zKtadHQ0AH3imZOTg7/++gsDBgyQvJ2mTZvi1VdfxZ133ons7GzJ63cV1VzVHG1ERESeqHfv3sjMzDS89/PzQ+PGjdG6dWvDPmszzdtr2rRpOHjwoKHTtidSTfJCRERkidKzGlvra/P111+bXcPvtttuw3vvvYdHHnkEa9eutXh+3759JYjQszB5ISIiVdq4cSPq16+PPn36oEOHDrK3J0dn4PT0dKxatQotW7a0WGblypWSt+vu3G5tI0dxnhci5bj7CA7yTr169cKFCxdQq1Ytwz53u1almFiwTp06EkTiWVRz54V9XoiIqCrjxEVujiRGGo1GhkjUTzXJCxGRFNztL3Miqo7JCxEREZlo1qwZVqxYoXQYFqkmeeE8L0RE5K487Y5eaGgonnzySaXDsEg1yQv7vBAREcnn+eefVzoEA9UkL0RERCSfylmA3QGTFyIi8hpKPb6x1K7Sj5MCAwPN7lc6rpoweSEiIvJSy5cvB6BfU+m2225TOBrbMXkhIiLyUnfffTeOHj2K48ePe1Tywhl2iYiIJODuj1osuf3225UOwW6qufPC0UZEyvHUH9pEZJ67/59WTfJCRERE3oHJCxGREXf/i5Ocw++vZT4+PkqHYDMmL0RERORRmLwQERHJzN9fNeNj3AKTFyIiIpndeeedSoegKkxeiIiIZPTMM89Y7E/irn1wKuMaO3asYV9KSopS4VTD+1hEREQy8pRHRuYSrDfffBMRERG4/fbbERMTo0BU5qnmzotWq0VMTAw6deqkdChEROSm/Pz8ZKt73LhxstWtlHr16mHixIkYMGCA0qGY8Ix00AYajQYajQbFxcUICQlROhwiInJDrVu3RlxcHHJzc/HOO+9IWvczzzyDsrIyBAYGYty4cSgrK5O0fldy18dZlVSTvBAREdXEx8cHu3fvxh9//IG2bdtKWre/v7+hj8gLL7wgad2uwHleiMiruPtfaUTGAgMDJU9cqnrkkUcMr++55x5Z2/JGvPNCRE5TU/Kipq+FlPP222+jvLwcjRo1whNPPKF0OKrD5IWIiEhiYWFh+OSTT5QOQ7X42IiIiIg8CpMXIiIihfAxpWOYvBAREZEJd0+q3DZ5uXLlCm655Ra89NJLSodCRESkesZDpZm8OGjatGno3Lmz0mEQERGRm3HL5OW3337DkSNHkJqaqnQoREREXkHVk9RlZ2ejd+/eiIyMhI+PD9auXVutjFarRXR0NIKCgpCYmIg9e/bY1cZLL72E6dOn2xsaEREReQG753kpLS1FbGwshg8fjv79+1c7vmrVKmRkZGDBggVITEzEvHnzkJKSgqNHj6Jx48YAgLi4ONy4caPauZs3b8bevXtx++234/bbb8fOnTtrjKesrMxk/Yji4mJ7vyQiIiLyIHYnL6mpqVYf58ydOxdpaWkYNmwYAGDBggVYv349li5digkTJgAAcnNzLZ6/e/dufPrpp1i9ejVKSkpw/fp1BAcHY/LkyWbLT58+Ha+//rq9XwYRERF5KEn7vJSXlyMnJwfJycn/NODri+TkZOzatcumOqZPn478/HycOHECs2fPRlpamsXEBQAmTpyIoqIiw5afn+/010FE9nH3kQn2UNPXQqRWkiYvhYWFqKioQEREhMn+iIgInD17VsqmDAIDAxEcHIwVK1agc+fOuP/++2Vph4iISGpSJctr165FdHQ03njjDUnqc3duOdqo0tNPP43Zs2fbVFaj0eDQoUPYu3evzFERERE5rrKrw7/+9S/Url1bkjoffvhh5OXl4bXXXpOkPncnafISHh4OPz8/FBQUmOwvKChAkyZNpGyKiIjII02aNAkHDhzAd999p3QoJvr06WN4/eijjyoYSc0kXVU6ICAA8fHxyMrKQt++fQEAOp0OWVlZSE9Pl7KparRaLbRaLSoqKmRth4iIyBk+Pj5o166d0mFUM2LECBw/fhxXr17FxIkTlQ7HKruTl5KSEvz++++G93l5ecjNzUVYWBhatGiBjIwMDB06FB07dkRCQgLmzZuH0tJSw+gjuWg0Gmg0GhQXFyMkJETWtoiIiNTGz88Pb731ltJh2MTu5GXfvn3o3r274X1GRgYAYOjQoVi2bBkGDx6M8+fPY/LkyTh79izi4uKQmZlZrRMvERERkSPsTl6SkpJq7B2dnp4u+2OiqvjYiIiIyDu49Wgje3C0EREREdCtWzcAwGOPPaZwJPKRtMMuERERKeubb75Bdna2quc9U82dF61Wi5iYGHTq1EnpUIjIg3GGXfJ0ISEh6N27N+rUqaN0KLJRTfLCx0ZEyuEvfCJyJdUkL0REROQdmLwQERGRR1FN8sI+L0RERN5BNckL+7wQERF5B9UkL0REROQdmLwQERGRR1FN8sI+L0RERN5BNckL+7wQERF5B9UkL0REROQdmLwQERkZMGCA4fW0adMUjISILOHCjETkND8/P6VDkEx0dDSys7Px+++/4/HHH1c6HCIyg3deiMhp7du3x1133QUAWLBggcLROK9bt24YNmwYAgMDlQ6FiMxQzZ0XrVYLrVaLiooKpUMh8jo+Pj7Yu3cvTp06hdatWysdDhGpnI9Q2XKwxcXFCAkJQVFREYKDg5UOh4iIiGxgz+9vPjYiIiIij8LkhYiIiDwKkxciIiLyKExeiIiIyKMweSEiIiKPwuSFiIiIPAqTFyIiIvIoqkletFotYmJi0KlTJ6VDISIiIhlxkjoiIiJSHCepIyIiItVi8kJEREQehckLEREReRQmL0RERORR/JUOQGqV/Y+Li4sVjoSIiIhsVfl725ZxRKpLXi5fvgwAiIqKUjgSIiIistfly5cREhJitYzqhkrrdDqcOXMG9evXh4+Pj9kynTp1wt69ey3WYel4cXExoqKikJ+f71HDsGv6et2xHWfqsvdcW8vbUs5aGV5X7tGWo3XxunIdb/qZ5a7XlbXjcl1bQghcvnwZkZGR8PW13qtFdXdefH190bx5c6tl/Pz8rH7gNR0PDg72qB8GNX097tiOM3XZe66t5W0pZ60Mryv3aMvRunhduY43/cxy1+vKluNyXFs13XGp5JUddjUajVPHPY2rvh4p23GmLnvPtbW8LeWsleF15R5tOVoXryvX8aafWe56XdnTlhJU99hITpy9l+TA64rkwOuK5OIO15ZX3nlxVGBgIKZMmYLAwEClQyEV4XVFcuB1RXJxh2uLd16IiIjIo/DOCxEREXkUJi9ERETkUZi8EBERkUdh8kJEREQehckLEREReRQmLxJZt24d2rRpg9atW2Px4sVKh0Mq0q9fPzRo0AADBw5UOhRSifz8fCQlJSEmJgbt27fH6tWrlQ6JVODSpUvo2LEj4uLi0K5dOyxatEi2tjhUWgI3btxATEwMtmzZgpCQEMTHx2Pnzp1o2LCh0qGRCmzduhWXL1/G8uXLsWbNGqXDIRX466+/UFBQgLi4OJw9exbx8fE4duwY6tatq3Ro5MEqKipQVlaGOnXqoLS0FO3atcO+fftk+V3IOy8S2LNnD+688040a9YM9erVQ2pqKjZv3qx0WKQSSUlJqF+/vtJhkIo0bdoUcXFxAIAmTZogPDwcFy9eVDYo8nh+fn6oU6cOAKCsrAxCCMh1f4TJC4Ds7Gz07t0bkZGR8PHxwdq1a6uV0Wq1iI6ORlBQEBITE7Fnzx7DsTNnzqBZs2aG982aNcPp06ddETq5OWevLSJzpLyucnJyUFFRgaioKJmjJncnxXV16dIlxMbGonnz5hg/fjzCw8NliZXJC4DS0lLExsZCq9WaPb5q1SpkZGRgypQp2L9/P2JjY5GSkoJz5865OFLyNLy2SA5SXVcXL17EU089hYULF7oibHJzUlxXoaGh+Pnnn5GXl4ePP/4YBQUF8gQryAQA8eWXX5rsS0hIEBqNxvC+oqJCREZGiunTpwshhNixY4fo27ev4fjYsWPFypUrXRIveQ5Hrq1KW7ZsEQMGDHBFmORhHL2url27Jrp16yY++ugjV4VKHsSZn1eVRo8eLVavXi1LfLzzUoPy8nLk5OQgOTnZsM/X1xfJycnYtWsXACAhIQEHDx7E6dOnUVJSgo0bNyIlJUWpkMlD2HJtEdnLlutKCIGnn34aPXr0wJAhQ5QKlTyILddVQUEBLl++DAAoKipCdnY22rRpI0s8/rLUqiKFhYWoqKhARESEyf6IiAgcOXIEAODv7485c+age/fu0Ol0ePnllznSiGpky7UFAMnJyfj5559RWlqK5s2bY/Xq1ejSpYurwyUPYct1tWPHDqxatQrt27c39GtYsWIF7rrrLleHSx7Cluvq5MmTGDlypKGj7pgxY2S7ppi8SKRPnz7o06eP0mGQCn333XdKh0Aq07VrV+h0OqXDIJVJSEhAbm6uS9riY6MahIeHw8/Pr1qno4KCAjRp0kShqEgNeG2RHHhdkRzc7bpi8lKDgIAAxMfHIysry7BPp9MhKyuLt+7JKby2SA68rkgO7nZd8bERgJKSEvz++++G93l5ecjNzUVYWBhatGiBjIwMDB06FB07dkRCQgLmzZuH0tJSDBs2TMGoyRPw2iI58LoiOXjUdSXLGCYPs2XLFgGg2jZ06FBDmffee0+0aNFCBAQEiISEBLF7927lAiaPwWuL5MDriuTgSdcV1zYiIiIij8I+L0RERORRmLwQERGRR2HyQkRERB6FyQsRERF5FCYvRERE5FGYvBAREZFHYfJCREREHoXJCxEREXkUJi9ERETkUZi8EBERkUdh8kJEREQehckLEREReZT/D5pgWacZTFuAAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.figure()\n", "plt.loglog(ps.freq, ps.power, ds=\"steps-mid\", lw=2, color=\"black\")\n", "plt.plot(ps.freq, res.mfit, lw=3, color=\"red\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can find the function in the `scripts` sub-module:" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling.scripts import fit_powerspectrum" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([109.03139888, 2.07028842, 2.00200906])" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parest, res = fit_powerspectrum(ps, model_to_test, t0)\n", "res.p_opt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fitting Lorentzians\n", "\n", "Fitting Lorentzians to power spectra is a routine task for most astronomers working with power spectra, hence there is a function that can produce either Maximum Likelihood or Maximum-A-Posteriori fits of the data." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "l = models.Lorentz1D" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('amplitude', 'x_0', 'fwhm')" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l.param_names" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [], "source": [ "def fit_lorentzians(ps, nlor, starting_pars, fit_whitenoise=True, max_post=False, priors=None,\n", " fitmethod=\"L-BFGS-B\"):\n", "\n", " model = models.Lorentz1D()\n", "\n", " if nlor > 1:\n", " for i in range(nlor-1):\n", " model += models.Lorentz1D()\n", "\n", " if fit_whitenoise:\n", " model += models.Const1D()\n", "\n", " parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post)\n", " lpost = PSDPosterior(ps.freq, ps.power, model, priors=priors, m=ps.m)\n", " res = parest.fit(lpost, starting_pars, neg=True)\n", "\n", " return parest, res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make a dataset so we can test it!" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(400)\n", "nlor = 3\n", "\n", "x_0_0 = 0.5\n", "x_0_1 = 2.0\n", "x_0_2 = 7.5\n", "\n", "amplitude_0 = 150.0\n", "amplitude_1 = 50.0\n", "amplitude_2 = 15.0\n", "\n", "fwhm_0 = 0.1\n", "fwhm_1 = 1.0\n", "fwhm_2 = 0.5\n", "\n", "whitenoise = 2.0\n", "\n", "model = models.Lorentz1D(amplitude_0, x_0_0, fwhm_0) + \\\n", " models.Lorentz1D(amplitude_1, x_0_1, fwhm_1) + \\\n", " models.Lorentz1D(amplitude_2, x_0_2, fwhm_2) + \\\n", " models.Const1D(whitenoise)\n", "\n", "p = model(ps.freq)\n", "noise = np.random.exponential(size=len(ps.freq))\n", "\n", "power = p*noise\n", "\n", "plt.figure()\n", "plt.loglog(ps.freq, power, lw=1, ds=\"steps-mid\", c=\"black\")\n", "plt.loglog(ps.freq, p, lw=3, color=\"red\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make this into a `Powerspectrum` object:" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "import copy" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [], "source": [ "ps_new = copy.copy(ps)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [], "source": [ "ps_new.power = power" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So now we can fit this model with our new function, but first, we need to define the starting parameters for our fit. The starting parameters will be `[amplitude, x_0, fwhm]` for each component plus the white noise component at the end:" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [], "source": [ "t0 = [150, 0.4, 0.2, 50, 2.3, 0.6, 20, 8.0, 0.4, 2.1]\n", "parest, res = fit_lorentzians(ps_new, nlor, t0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the output:" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.48980332e+02, 1.02031369e+00, -2.04742273e-04, 4.70694020e+01,\n", " 1.90076129e+00, 1.08562751e+00, 1.35701826e+01, 7.50135744e+00,\n", " 5.44356694e-01, 1.99448241e+00])" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.p_opt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cool, that seems to work! For convenience `PSDParEst` also has a plotting function:" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "parest.plotfits(res, save_plot=False, namestr=\"lorentzian_test\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function exists in the library as well for ease of use:" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling import fit_lorentzians" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [], "source": [ "parest, res = fit_lorentzians(ps_new, nlor, t0)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.47775222e+02, -1.95500403e-01, -1.76819873e-03, 4.02910804e+01,\n", " 1.89163457e+00, 1.20856451e+00, 1.05610820e+01, 7.49861477e+00,\n", " 6.35659323e-01, 1.99437212e+00])" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.p_opt" ] } ], "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 1 }