{ "cells": [ { "metadata": {}, "cell_type": "raw", "source": "", "id": "6d622050078fe199" }, { "cell_type": "markdown", "id": "6339b291", "metadata": {}, "source": [ "# Celerite Variance\n", "## This notebook helps explain the celerite normalization (variance)" ] }, { "cell_type": "raw", "id": "efe365d3", "metadata": {}, "source": [ "When integrating the model in frequency to obtain the variance, we need to add a factor \n", "2 / np.sqrt(2 * np.pi) # this factor accounts for the fact that we only integrate positive frequencies and the 1 / sqrt(2pi) from the Fourier transform\n", "Another factor 2 * np.pi enters because we are integrating angular frequencies\n", "Below is just a simulated lightcurves fited with celerite and showing we get the same variance (amplitude) as we had put in" ] }, { "cell_type": "code", "execution_count": 1, "id": "875bbda9", "metadata": {}, "outputs": [], "source": [ "import celerite\n", "from celerite.terms import JitterTerm\n", "from mind_the_gaps.models import DampedRandomWalk as DRW, Lorentzian\n", "from mind_the_gaps.models import BendingPowerlaw as BPL, SHO, Lorentzian as Lor, Matern32, Jitter\n", "from mind_the_gaps.lightcurves import GappyLightcurve\n", "from mind_the_gaps.gpmodelling import GPModelling\n", "import corner\n", "import astropy.units as u\n", "from mind_the_gaps.simulator import *\n", "import numpy as np\n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt\n", "\n", "def neg_log_like(params, y, gp):\n", " gp.set_parameter_vector(params)\n", " return -gp.log_likelihood(y)\n", "\n", "def log_probability(params):\n", " \"\"\"https://celerite.readthedocs.io/en/stable/tutorials/modeling/\"\"\"\n", " gp.set_parameter_vector(params)\n", "\n", " lp = gp.log_prior()\n", " if not np.isfinite(lp):\n", " return -np.inf\n", " return lp + gp.log_likelihood(y)\n", "\n", "cores = 12" ] }, { "cell_type": "code", "execution_count": 2, "id": "47ab06c0", "metadata": {}, "outputs": [], "source": [ "normalization_factor = 2 / np.sqrt(2 * np.pi) # this factor accounts for the fact that we only integrate positive frequencies and the 1 / sqrt(2pi) from the Fourier transform" ] }, { "cell_type": "markdown", "id": "0e92faea", "metadata": {}, "source": "## Generate lightcurve with given variance and a DRW" }, { "cell_type": "code", "execution_count": null, "id": "d1633e10", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lightcurve duration: 5001.25\n", "Model variance: 1.00000\n", "Integrated variance: 0.99204\n", "Sample Variance: 0.97372\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Beware! Stingray only supports poisson err_dist at the moment in many methods, and 'gauss' in a few more. \n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, 'Period')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(45)\n", "Npoints = 5000\n", "times = np.linspace(0, 5000, Npoints)\n", "exposures = 0.5 * np.ones(Npoints) \n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "print(\"Lightcurve duration: %.2f\" % (duration))\n", "sim_dt = 1 / 2 * np.min(exposures)\n", "\n", "logS0 = 0\n", "S0 = np.exp(logS0)\n", "break_timescale = 100\n", "w0 = 2 * np.pi / break_timescale\n", "logw0 = np.log(w0)\n", "psd_model = BPL(S0=S0, omega0=w0)\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "\n", "extension_factor = 1.0\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "\n", "simulator = Simulator(psd_model, times, exposures, mean=0, pdf=\"Gaussian\", extension_factor=extension_factor)\n", "rates = simulator.generate_lightcurve()\n", "\n", "#lc = simulate_lightcurve(times, psd_model, dt=0.5, \n", " # extension_factor=extension_factor)\n", "\n", "#segment = cut_random_segment(lc, duration)\n", "#plt.plot(segment.time, segment.countrate)\n", "plt.plot(times, rates)\n", "plt.gca().ticklabel_format(useOffset=False)\n", "print(\"Model variance: %.5f\" % S0)\n", "print(\"Integrated variance: %.5f\" % var)\n", "#print(\"LC variance: %.5f\" % np.var(lc.countrate))\n", "print(\"Sample Variance: %.5f\" % np.var(rates))\n", "\n", "plt.figure()\n", "plt.plot(1 / int_freq, psd_model(w_int))\n", "plt.axvline(1 / minimum_frequency, color=\"green\", alpha=0.5, ls=\"--\")\n", "plt.axvline(1 / maximum_frequency, alpha=0.5, color=\"blue\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Period\")" ] }, { "cell_type": "markdown", "id": "12d13088", "metadata": {}, "source": "## Fit it with celerite" }, { "cell_type": "code", "execution_count": 5, "id": "f3ca5026", "metadata": {}, "outputs": [], "source": [ "\n", "y = rates\n", "time = times\n", "S0 = np.var(rates)\n", "y = rates\n", "time = times\n", "S0 = np.var(rates)\n", "S_0_N_bounds = (-10, 10)\n", "log_omega0_N_bounds = (-10, 10)\n", "bounds = dict(log_S0=S_0_N_bounds, log_omega0=log_omega0_N_bounds)\n", "kernel = DRW(log_S0=np.log(S0), log_omega0=np.log(w0),\n", " bounds=bounds)\n", "cols = [\"kernel:log_S0\", \"kernel:log_omega0\"]\n", "labels = [r\"log $S_N$\", r\"log $\\omega_N$\"]\n", "gpmodel = GPModelling(GappyLightcurve(times, rates, dy=np.ones(len(rates)) * 1e-12), kernel)" ] }, { "cell_type": "markdown", "id": "344c3c72", "metadata": {}, "source": [ "fit" ] }, { "cell_type": "code", "execution_count": 6, "id": "38bd6a53", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 9%|â–‰ | 4500/50000 [05:10<52:20, 14.49it/s] " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Convergence reached after 4500 samples!\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "gpmodel.derive_posteriors(max_steps=50000, fit=True, cores=cores)" ] }, { "cell_type": "code", "execution_count": 7, "id": "cc2227a6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corner_fig = corner.corner(gpmodel.mcmc_samples, labels=gpmodel.gp.get_parameter_names(), title_fmt='.1f',\n", " quantiles=[0.16, 0.5, 0.84], show_titles=True, truths=[np.log(S0), logw0],\n", " title_kwargs={\"fontsize\": 18}, max_n_ticks=3, labelpad=0.08,\n", " levels=(1 - np.exp(-0.5), 1 - np.exp(-0.5 * 2 ** 2))) # plots 1 and 2 sigma levels\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "8c273d84", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('kernel:log_S0', 'kernel:log_omega0', 'mean:value')\n", "[-0.02605619 -2.90922302]\n", "Ratio ampltiudes\n", "1.000578571036844\n", "Ratio breaks\n", "0.867682082322184\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(gpmodel.gp.parameter_names)\n", "print(gpmodel.max_parameters)\n", "df = 1 / (duration)\n", "fnyq = 1 / (2 * exposures[0])\n", "frequencies = np.arange(df, fnyq, df)\n", "w = frequencies * 2 * np.pi\n", "\n", "kernel.set_parameter_vector(gpmodel.max_parameters)\n", "psd = kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Fit model\")\n", "plt.yscale(\"log\")\n", "plt.xscale(\"log\")\n", "plt.xlabel(\"Frequency\")\n", "\n", "kernel.set_parameter_vector((logS0, logw0))\n", "psd = kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Input model\")\n", "plt.legend()\n", "print(\"Ratio ampltiudes\")\n", "print(np.exp(gpmodel.max_parameters[0]) / S0)\n", "print(\"Ratio breaks\")\n", "print(np.exp(gpmodel.max_parameters[1]) / w0)" ] }, { "cell_type": "markdown", "id": "937da991", "metadata": {}, "source": "## Same thing but with a Lorentizan now" }, { "cell_type": "code", "execution_count": null, "id": "e16cbaad", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lightcurve duration: 5001.25\n", "Model variance: 1.00000\n", "Integrated variance: 0.99921\n", "Sample Variance: 0.96105\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Beware! Stingray only supports poisson err_dist at the moment in many methods, and 'gauss' in a few more. \n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, 'Period')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(4)\n", "Npoints = 5000\n", "times = np.linspace(0, 5000, Npoints)\n", "exposures = 0.5 * np.ones(Npoints) \n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "print(\"Lightcurve duration: %.2f\" % (duration))\n", "sim_dt = 1 / 2 * np.min(exposures)\n", "\n", "\n", "logS0 = 0\n", "S0 = np.exp(logS0)\n", "break_timescale = 100\n", "w0 = 2 * np.pi / break_timescale\n", "logw0 = np.log(w0)\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "Q = 5\n", "logQ = np.log(Q)\n", "psd_model = Lor(S0=S0, omega0=w0, Q=Q)\n", "\n", "extension_factor = 1.0\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "\n", "simulator = Simulator(psd_model, times, exposures, mean=0, pdf=\"Gaussian\", extension_factor=extension_factor)\n", "rates = simulator.generate_lightcurve()\n", "\n", "#lc = simulate_lightcurve(times, psd_model, dt=0.5, \n", " # extension_factor=extension_factor)\n", "\n", "#segment = cut_random_segment(lc, duration)\n", "#plt.plot(segment.time, segment.countrate)\n", "plt.plot(times, rates)\n", "plt.gca().ticklabel_format(useOffset=False)\n", "print(\"Model variance: %.5f\" % S0)\n", "print(\"Integrated variance: %.5f\" % var)\n", "#print(\"LC variance: %.5f\" % np.var(lc.countrate))\n", "print(\"Sample Variance: %.5f\" % np.var(rates))\n", "\n", "plt.figure()\n", "plt.plot(1 / int_freq, psd_model(w_int))\n", "plt.axvline(1 / minimum_frequency, color=\"green\", alpha=0.5, ls=\"--\")\n", "plt.axvline(1 / maximum_frequency, alpha=0.5, color=\"blue\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Period\")" ] }, { "cell_type": "markdown", "id": "63e1ce7d", "metadata": {}, "source": "## Prepare fit with celerite" }, { "cell_type": "code", "execution_count": null, "id": "c5b270a7", "metadata": {}, "outputs": [], "source": [ "y = rates\n", "time = times\n", "S0 = np.var(rates)\n", "S_0_N_bounds = (-10, 10)\n", "Q = 200\n", "log_omega0_N_bounds = (-10, 1)\n", "log_Q_bounds = (np.log(1.5), np.log(5000))\n", "\n", "bounds = dict(log_S0=S_0_N_bounds, log_omega0=log_omega0_N_bounds, log_Q=log_Q_bounds)\n", "kernel = Lorentzian(log_S0=np.log(S0), log_omega0=np.log(w0), log_Q=np.log(Q),\n", " bounds=bounds)\n", "cols = [\"kernel:log_S0\", \"kernel:log_omega0\", \"kernel:log_Q\"]\n", "labels = [r\"log $S_N$\", r\"log $\\omega_N$\", \"log_Q\"]\n", "gpmodel = GPModelling(GappyLightcurve(times, rates, dy=np.ones(len(rates)) * 1e-12), kernel)" ] }, { "cell_type": "markdown", "id": "9e168ad7", "metadata": {}, "source": "## fit" }, { "cell_type": "code", "execution_count": 11, "id": "ab71c4a3", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 50000/50000 [59:37<00:00, 13.98it/s] \n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/mind_the_gaps/gpmodelling.py:214: UserWarning: The chains did not converge after 50000 iterations!\n", " warnings.warn(f\"The chains did not converge after {sampler.iteration} iterations!\")\n" ] } ], "source": [ "gpmodel.derive_posteriors(max_steps=50000, fit=True, cores=cores)" ] }, { "cell_type": "code", "execution_count": 18, "id": "9dc68995", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corner_fig = corner.corner(gpmodel.mcmc_samples, labels=gpmodel.gp.get_parameter_names(), title_fmt='.1f',\n", " quantiles=[0.16, 0.5, 0.84], show_titles=True, truths=[np.log(S0), np.log(Q), np.log(w0)],\n", " title_kwargs={\"fontsize\": 18}, max_n_ticks=3, labelpad=0.08, range=0.9 * np.ones(gpmodel.k),\n", " levels=(1 - np.exp(-0.5), 1 - np.exp(-0.5 * 2 ** 2))) # plots 1 and 2 sigma levels\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "f72db19c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('kernel:log_S0', 'kernel:log_Q', 'kernel:log_omega0', 'mean:value')\n", "[-0.08662917 1.68480537 -2.77819922]\n", "Ratio ampltiudes\n", "0.9541861557182113\n", "Ratio breaks\n", "0.9891531574824449\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(gpmodel.gp.parameter_names)\n", "print(gpmodel.max_parameters)\n", "df = 1 / (duration)\n", "fnyq = 1 / (2 * exposures[0])\n", "frequencies = np.arange(df, fnyq, df)\n", "w = frequencies * 2 * np.pi\n", "\n", "\n", "kernel.set_parameter_vector(gpmodel.max_parameters)\n", "psd = kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Fit model\")\n", "plt.yscale(\"log\")\n", "plt.xscale(\"log\")\n", "plt.xlabel(\"Frequency\")\n", "\n", "kernel.set_parameter_vector((logS0, logQ, logw0))\n", "psd = kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Input model\")\n", "plt.legend()\n", "print(\"Ratio ampltiudes\")\n", "print(np.exp(gpmodel.max_parameters[0]) / S0)\n", "print(\"Ratio breaks\")\n", "print(np.exp(gpmodel.max_parameters[2]) / w0)" ] }, { "cell_type": "markdown", "id": "c43f9828", "metadata": {}, "source": "## Same with Matern" }, { "cell_type": "code", "execution_count": null, "id": "c6682acc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lightcurve duration: 5001.25\n", "Period: 1.61 d\n", "Model variance: 0.96105\n", "Integrated variance: 0.00000\n", "Sample Variance: 0.00001\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Beware! Stingray only supports poisson err_dist at the moment in many methods, and 'gauss' in a few more. \n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, 'Period')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(4)\n", "Npoints = 5000\n", "times = np.linspace(0, 5000, Npoints)\n", "exposures = 0.5 * np.ones(Npoints) \n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "print(\"Lightcurve duration: %.2f\" % (duration))\n", "sim_dt = 1 / 2 * np.min(exposures)\n", "\n", "logS0 = 1\n", "sigma = np.exp(logS0)\n", "logrho = np.log(32.17 / 20 * 3600 * 24)\n", "rho = np.exp(logrho)\n", "break_timescale = rho / 3600 / 24 \n", "print(\"Period: %.2f d\" % break_timescale)\n", "psd_model = Matern32(sigma=sigma, rho=rho)\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "\n", "extension_factor = 10\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "\n", "\n", "simulator = Simulator(psd_model, times, exposures, mean=0, pdf=\"Gaussian\", extension_factor=extension_factor)\n", "rates = simulator.generate_lightcurve()\n", "\n", "plt.plot(times, rates)\n", "plt.gca().ticklabel_format(useOffset=False)\n", "print(\"Model variance: %.5f\" % S0)\n", "print(\"Integrated variance: %.5f\" % var)\n", "#print(\"LC variance: %.5f\" % np.var(lc.countrate))\n", "print(\"Sample Variance: %.5f\" % np.var(rates))\n", "\n", "plt.figure()\n", "plt.plot(1 / int_freq, psd_model(w_int))\n", "plt.axvline(1 / minimum_frequency, color=\"green\", alpha=0.5, ls=\"--\")\n", "plt.axvline(1 / maximum_frequency, alpha=0.5, color=\"blue\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Period\")" ] }, { "cell_type": "markdown", "id": "4984e4fa", "metadata": {}, "source": "## Jitter" }, { "cell_type": "code", "execution_count": 36, "id": "eae112dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lightcurve duration: 1000.06 d\n", "Model variance: 54.59815\n", "Integrated variance: 54.59815\n", "Sample Variance: 56.21669\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, 'Period')" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Npoints = 1000\n", "times = np.linspace(0, 1000, Npoints) * 3600 * 24 # seconds\n", "exposures = 2000 * np.ones(Npoints) # seconds\n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "print(\"Lightcurve duration: %.2f d\" % (duration / 3600 /24))\n", "aliasing_factor = 1\n", "sim_dt = np.min(exposures) / aliasing_factor\n", "\n", "logS0 = 2\n", "sigma = np.exp(logS0)\n", "psd_model = Jitter(sigma=sigma)\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "\n", "extension_factor = 2\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "\n", "w_int = int_freq * 2 * np.pi\n", "var = np.sum(psd_model(w_int)) * (df_int * 2 * np.pi) * normalization_factor\n", "simulator = Simulator(psd_model, times, exposures, mean=0, pdf=\"Gaussian\", extension_factor=extension_factor, \n", " aliasing_factor=aliasing_factor)\n", "# Note the power is diluted by a factor aliasing_factor, if you want the lightcurve with the original variance, you need to simulate the regularly sampled lightcurve\n", "rates = simulator.generate_lightcurve()\n", "\n", "#lc = simulate_lightcurve(times, psd_model, dt=0.5, \n", " # extension_factor=extension_factor)\n", "\n", "#segment = cut_random_segment(lc, duration)\n", "#plt.plot(segment.time, segment.countrate)\n", "plt.plot(times, rates)\n", "plt.gca().ticklabel_format(useOffset=False)\n", "print(\"Model variance: %.5f\" % sigma**2)\n", "print(\"Integrated variance: %.5f\" % var)\n", "print(\"Sample Variance: %.5f\" % np.var(rates))\n", "\n", "plt.figure()\n", "plt.plot(1 / int_freq, psd_model(w_int))\n", "plt.axvline(1 / minimum_frequency, color=\"green\", alpha=0.5, ls=\"--\")\n", "plt.axvline(1 / maximum_frequency, alpha=0.5, color=\"blue\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Period\")" ] }, { "cell_type": "markdown", "id": "c1be9aca", "metadata": {}, "source": [ "fit with celerite" ] }, { "cell_type": "code", "execution_count": 37, "id": "3a964a6e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n", " success: True\n", " status: 0\n", " fun: 3433.545361920608\n", " x: [ 2.015e+00]\n", " nit: 6\n", " jac: [ 2.592e-03]\n", " nfev: 18\n", " njev: 9\n", " hess_inv: <1x1 LbfgsInvHessProduct with dtype=float64>\n" ] } ], "source": [ "y = rates\n", "time = times\n", "S0 = np.var(y)\n", "nwalkers = 12\n", "kernel = JitterTerm(log_sigma=np.log(3))\n", "\n", "gp = celerite.GP(kernel, mean=np.mean(y))\n", "gp.compute(time) # You always need to call compute once.\n", "initial_params = gp.get_parameter_vector()\n", "bounds = gp.get_parameter_bounds()\n", "solution = minimize(neg_log_like, \n", " initial_params, method=\"L-BFGS-B\", bounds=gp.get_parameter_bounds(), args=(y, gp))\n", "print(solution)" ] }, { "cell_type": "code", "execution_count": 40, "id": "8f7ac0b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('kernel:log_sigma', 'mean:value')\n", "[2.01460783]\n", "Ratio ampltiudes\n", "1.0147150492551757\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(gp.parameter_names)\n", "print(solution.x)\n", "frequencies = np.arange(df_int, fnyq, df_int)\n", "w = frequencies * 2 * np.pi\n", "gp.set_parameter_vector(solution.x)\n", "psd = gp.kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Fit model\")\n", "\n", "gp.set_parameter_vector((logS0))\n", "psd = gp.kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Input model\")\n", "plt.legend()\n", "print(\"Ratio ampltiudes\")\n", "print(np.exp(solution.x)[0] / np.exp(logS0))" ] }, { "cell_type": "markdown", "id": "efd844d3", "metadata": {}, "source": "## Generate lightcurves with different lengths --> dispersion on the variance should go up" }, { "cell_type": "code", "execution_count": null, "id": "f55365c2", "metadata": {}, "outputs": [], "source": [ "np.random.seed(42)\n", "\n", "n = 50 # simulations to perform per sampling\n", "#### Model ###\n", "logS0 = 0\n", "S0 = np.exp(logS0)\n", "logw0 = -13\n", "w0 = np.exp(logw0)\n", "break_timescale = 1 / (w0 / 2 / np.pi) / 3600 / 24 \n", "print(\"Break timescale: %.2f d\" % break_timescale)\n", "psd_model = BPL(S_0=S0, w_0=np.exp(-13))\n", "\n", "### Lightcurve N = 1000 ###\n", "Npoints = 1000\n", "length = 1000\n", "times = np.linspace(0, length, Npoints) * 3600 * 24 # seconds\n", "exposures = 1000 * np.ones(Npoints) # seconds\n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "sim_dt = 1 / 10 * np.min(exposures)\n", "print(\"Lightcurve duration: %.2f d\" % (duration / 3600 /24))\n", "\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "extension_factor = 5\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "normalization_factor = 2 / np.sqrt(2 * np.pi) # this factor accounts for the fact that we only integrate positive frequencies and the 1 / sqrt(2pi) from the Fourier transform\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "print(\"Integrated variance: %.5f\" % var)\n", "\n", "variances = []\n", "for i in range(n): \n", " lc = simulate_lightcurve(times, psd_model,\n", " dt=sim_dt, \n", " extension_factor=extension_factor)\n", "\n", " segment = cut_random_segment(lc, duration)\n", " variances.append(np.var(segment.countrate))\n", "print(\"Dispersion for %d length: %.3f\" % (length, np.std(variances)))\n", "# plot results\n", "plt.hist(variances, label=\"L = %d\" % (length), facecolor=\"None\", edgecolor=\"C0\")\n", "### Lightcurve N = 1000 ###\n", "length=100\n", "times = np.linspace(0, length, Npoints) * 3600 * 24 # seconds\n", "exposures = 1000 * np.ones(Npoints) # seconds\n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "sim_dt = 1 / 10 * np.min(exposures)\n", "print(\"Lightcurve duration: %.2f d\" % (duration / 3600 /24)) \n", "\n", "minimum_frequency = 1 / (duration)\n", "\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "normalization_factor = 2 / np.sqrt(2 * np.pi) # this factor accounts for the fact that we only integrate positive frequencies and the 1 / sqrt(2pi) from the Fourier transform\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "print(\"Integrated variance: %.5f\" % var)\n", "\n", "variances = []\n", "for i in range(n): \n", " lc = simulate_lightcurve(times, psd_model,\n", " dt=sim_dt, \n", " extension_factor=extension_factor)\n", "\n", " segment = cut_random_segment(lc, duration)\n", " variances.append(np.var(segment.countrate))\n", "plt.hist(variances, label=\"L = %d\" % (length), facecolor=\"None\", edgecolor=\"C1\")\n", "print(\"Dispersion for %d length: %.3f\" % (length, np.std(variances)))\n", "plt.legend()\n", "plt.xlabel(\"$\\sigma^2$ (ct/s)$^2$\")" ] }, { "cell_type": "code", "execution_count": null, "id": "41bf14e8", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "Npoints = 1000\n", "times = np.linspace(0, 1000, Npoints) * 3600 * 24 # seconds\n", "exposures = 1000 * np.ones(Npoints) # seconds\n", "duration = times[-1] + 1.5 * exposures[-1] - (times[0] - exposures[0])\n", "print(\"Lightcurve duration: %.2f d\" % (duration / 3600 /24))\n", "sim_dt = 1 / 10 * np.min(exposures)\n", "\n", "logS0 = 0\n", "S0 = np.exp(logS0)\n", "logw0 = -13\n", "w0 = np.exp(logw0)\n", "logQ = np.log(1000)\n", "Q = np.exp(logQ)\n", "break_timescale = 1 / (w0 / 2 / np.pi) / 3600 / 24 \n", "print(\"Period: %.2f d\" % break_timescale)\n", "print(\"log_Q: %.3f\" % (logQ))\n", "psd_model = Lor(S_0=S0, w_0=w0, Q=Q)\n", "minimum_frequency = 1 / (duration)\n", "maximum_frequency = 1 / (sim_dt)\n", "fnyq = maximum_frequency\n", "\n", "extension_factor = 10\n", "df_int = 1 / (duration * extension_factor)\n", "int_freq = np.arange(minimum_frequency, fnyq, df_int) # frequencies over which to integrate\n", "w_int = int_freq * 2 * np.pi\n", "normalization_factor = 2 / np.sqrt(2 * np.pi) # this factor accounts for the fact that we only integrate positive frequencies and the 1 / sqrt(2pi) from the Fourier transform\n", "var = np.sum(psd_model(w_int)) * df_int * 2 * np.pi * normalization_factor\n", "\n", "n = 50\n", "variances = []\n", "for i in range(n):\n", " lc = simulate_lightcurve(times, psd_model,\n", " dt=sim_dt, \n", " extension_factor=extension_factor)\n", "\n", " segment = cut_random_segment(lc, duration)\n", " variances.append(np.var(segment.countrate))\n", "\n", "plt.figure()\n", "plt.hist(variances)\n", "plt.axvline(np.mean(variances))\n", "plt.xlabel(\"$\\sigma^2\")\n", "print(\"Dispersion in variance: %.2f\" % np.std(variances))\n", "print(\"Mean variance: %.2f\" % np.mean(variances))" ] }, { "cell_type": "markdown", "id": "f4e91fd6", "metadata": {}, "source": "## Simulate from solution" }, { "cell_type": "code", "execution_count": null, "id": "9251b55e", "metadata": {}, "outputs": [], "source": [ "duration = (times + 1.5 * exposures[-1] - (times[0] - exposures[0]))\n", "\n", "sim_dt = 1 / 10 * np.min(exposures)\n", "mean = np.mean(y)\n", "std = np.std(y)\n", "Q = 1 / 2\n", "psd_model = BPL(S0=np.exp(logS0), omega0=np.exp(logw0), Q=Q)\n", "extension_factor = 20\n", "lc = simulate_lightcurve(times, psd_model,\n", " dt=sim_dt, \n", " extension_factor=extension_factor) # this is just to get tseg for df\n", "plt.plot(lc.time, lc.countrate)\n", "plt.gca().ticklabel_format(useOffset=False)" ] }, { "cell_type": "code", "execution_count": null, "id": "5b63835e", "metadata": {}, "outputs": [], "source": [ "print(\"Generated variance: %.2f\" % np.var(lc.countrate))" ] }, { "cell_type": "code", "execution_count": null, "id": "c000baf7", "metadata": {}, "outputs": [], "source": [ "psd_model = BPL(S_0=np.exp(logS0) * lc.dt * lc.n / 2, w_0=np.exp(logw0), Q=Q)\n", "lc = simulate_lightcurve(timestamps.to(u.s).value, psd_model,\n", " dt=sim_dt.to(u.s).value, \n", " extension_factor=extension_factor) # this is just to get tseg for df\n", "plt.plot(lc.time, lc.countrate)\n", "print(np.var(lc.countrate))" ] }, { "cell_type": "code", "execution_count": null, "id": "3ea0e456", "metadata": {}, "outputs": [], "source": [ "y = lc.countrate\n", "time = lc.time\n", "Q = 1/ 2\n", "w0 = 2 * np.pi / (10 * u.d).to(u.s).value\n", "S0 = np.var(y) / (w0 * Q)\n", "S_0_N_bounds = (-20, 5)\n", "log_omega0_N_bounds = (-20, -5) # 0 to 200 in period (days)\n", "nwalkers = 12\n", "bounds = dict(log_S0=S_0_N_bounds, log_omega0=log_omega0_N_bounds)\n", "kernel = BPL_celerite(log_S0=np.log(S0), log_Q=np.log(Q), log_omega0=np.log(w0),\n", " bounds=bounds)\n", "kernel.freeze_parameter(\"log_Q\")\n", "initial_samples = np.array([np.random.uniform(S_0_N_bounds[0], S_0_N_bounds[1], nwalkers),\n", " np.random.uniform(log_omega0_N_bounds[0], log_omega0_N_bounds[1], nwalkers)])\n", "cols = [\"kernel:log_S0\", \"kernel:log_omega0\"]\n", "labels = [r\"log $S_N$\", r\"log $\\omega_N$\"]\n", "initial_samples = initial_samples.T" ] }, { "cell_type": "code", "execution_count": null, "id": "830380b5", "metadata": {}, "outputs": [], "source": [ "gp = celerite.GP(kernel, mean=np.mean(y))\n", "gp.compute(time) # You always need to call compute once.\n", "initial_params = gp.get_parameter_vector()\n", "par_names = list(gp.get_parameter_names())\n", "bounds = gp.get_parameter_bounds()\n", "solution = minimize(neg_log_like, \n", " initial_params, method=\"L-BFGS-B\", bounds=gp.get_parameter_bounds(), args=(y, gp))" ] }, { "cell_type": "code", "execution_count": null, "id": "13abafd3", "metadata": {}, "outputs": [], "source": [ "print(solution.x)\n", "df = 1 / (lc.tseg)\n", "fnyq = 1 / (2 * lc.dt)\n", "frequencies = np.arange(df, fnyq, df)\n", "w = frequencies * 2 * np.pi" ] }, { "cell_type": "code", "execution_count": null, "id": "672ce7c7", "metadata": {}, "outputs": [], "source": [ "print(gp.parameter_names)\n", "gp.set_parameter_vector(solution.x)\n", "psd = gp.kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Fit model\")\n", "plt.yscale(\"log\")\n", "plt.xscale(\"log\")\n", "\n", "gp.set_parameter_vector((logS0, logw0))\n", "psd = gp.kernel.get_psd(w)\n", "plt.plot(frequencies, psd, label=\"Input model\")\n", "plt.legend()\n", "print(\"Ratio ampltiudes\")\n", "print(np.exp(solution.x)[0] / np.exp(logS0))\n", "print(\"Ratio breaks\")\n", "print(np.exp(solution.x)[1] / np.exp(logw0))" ] }, { "cell_type": "markdown", "id": "3d902f5a", "metadata": {}, "source": "## Bowman et al 2020 gives the std of the SHO" }, { "cell_type": "code", "execution_count": null, "id": "619fca0d", "metadata": {}, "outputs": [], "source": [ "from mind_the_gaps.lightcurves import PatchedLightcurve as Lightcurve\n", "import pyfftw\n", "\n", "\n", "def simulate_lightcurve_(timestamps, psd_model, dt, extension_factor=50):\n", " \"\"\"Simulate a lightcurve regularly sampled N times longer than original using the algorithm of Timmer & Koenig+95\n", "\n", " Parameters\n", " ----------\n", " timestamps: array\n", " Timestamps, same units as dt\n", " psd_model: astropy.model\n", " The model for the PSD. Has to take angular frequencies\n", " dt: float\n", " Binning to which simulate the lightcurve in seconds\n", " extension_factor: int\n", " How many times longer than original\n", " \"\"\"\n", " if exddtension_factor < 1:\n", " raise ValueError(\"Extension factor needs to be higher than 1\")\n", "\n", " duration = timestamps[-1] - timestamps[0]\n", " # generate timesctamps sampled at the median exposure longer than input lightcurve by extending the end\n", " sim_timestamps = np.arange(timestamps[0] - 2 * dt,\n", " timestamps[0] + duration * extension_factor + dt,\n", " dt)\n", "\n", " n_datapoints = len(sim_timestamps)\n", "\n", " complex_fft = get_fft(n_datapoints, dt, psd_model)\n", "\n", " countrate = pyfftw.interfaces.numpy_fft.irfft(complex_fft, n=n_datapoints) # it does seem faster than numpy although only slightly\n", " \n", " countrate *= np.sqrt(n_datapoints) * np.sqrt(dt) * np.sqrt(np.sqrt(2 * np.pi))\n", " \n", " return Lightcurve(sim_timestamps, countrate, input_counts=True, skip_checks=True, dt=dt, err_dist=\"gauss\")" ] }, { "cell_type": "code", "execution_count": null, "id": "89b3f09d", "metadata": {}, "outputs": [], "source": [ "data = readPCCURVE('%s/xray_data/%s/lc/PCCURVE.qdp' % (home, ulx_dir),\n", " minSNR=0)\n", "\n", "time_column = data.dtype.names[0]\n", "filtered_data = data[np.where((data[\"%s\" % time_column] >= tmin) &\n", " (data[\"%s\" % time_column] <= tend))]\n", "exposure_column = data.dtype.names[12]\n", "\n", "timestamps = filtered_data[time_column]\n", "if time_column == 'MJD':\n", " units = u.d\n", "else:\n", " units = u.s\n", "timestamps = filtered_data[time_column] * units\n", "rate_column = data.dtype.names[3]\n", "corr_factor = data.dtype.names[9]\n", "bkg_counts_column = data.dtype.names[11]\n", "y_units = u.ct / u.s\n", "rate = filtered_data[rate_column] * y_units\n", "errors = (-filtered_data[\"%sneg\" % rate_column] +\n", " filtered_data[\"%spos\" % rate_column]) / 2 * y_units\n", "corr_factor = filtered_data[corr_factor]\n", "exposures = filtered_data[exposure_column] * u.s / corr_factor\n", "bkg_counts = filtered_data[bkg_counts_column] << u.ct\n", "half_bins = exposures / 2\n", "duration = (timestamps[-1] + 1.5 * exposures[-1] - (timestamps[0] - exposures[0])).to(u.s).value\n", "\n", "sim_dt = 1 / 2 * np.min(exposures)\n", "logS0 = 3\n", "bend = 60 * 3600 * 24 # 55 days to seconds\n", "logw0 = np.log(2 * np.pi / bend) # rad/s\n", "Q = 1 / 2\n", "psd_model = BPL(S_0=np.exp(logS0), w_0=np.exp(logw0))\n", "extension_factor = 15\n", "lc = simulate_lightcurve_(timestamps.to(u.s).value, psd_model,\n", " dt=sim_dt.to(u.s).value, \n", " extension_factor=extension_factor) # this is just to get tseg for df\n", "plt.plot(lc.time, lc.countrate)\n", "print(\"Lightcurve duration: %.2f days\" %(lc.tseg / 3600 / 24))" ] }, { "cell_type": "code", "execution_count": null, "id": "52e86096", "metadata": {}, "outputs": [], "source": [ "#variance = psd_model.S_0 * psd_model.w_0 / np.sqrt(2)\n", "variance = psd_model.S_0.value\n", "print(\"Theoretical variance: %.8f\" % variance)\n", "#var_factor = 1 / lc.dt**2\n", "#var_factor = lc.n * (lc.dt)\n", "var_factor = lc.n * lc.dt\n", "var_factor = 1\n", "factor = np.sqrt(2 * np.pi)\n", "factor = 1\n", "print(\"Lightcurve variance: %.8f\" % (np.var(lc.countrate) * var_factor * factor))\n", "df = 1 / (lc.tseg)\n", "fnyq = 1 / (2 * lc.dt)\n", "frequencies = np.arange(df, fnyq, df)\n", "w_int = frequencies * 2 * np.pi\n", "factor = 4 / np.sqrt(2 / np.pi)\n", "factor = 2 * np.sqrt(2 * np.pi)\n", "factor = 2 / np.sqrt(2 * np.pi)\n", "integrated_variance = np.sum(psd_model(w_int) * df) * factor * 2 * np.pi # * factor * 2 * np.pi \n", "print(\"Integrated variance: %.8f\" % integrated_variance)" ] }, { "cell_type": "markdown", "id": "f8d1e5ee", "metadata": {}, "source": "## Fit data with celerite" }, { "cell_type": "code", "execution_count": null, "id": "e6b8e95d", "metadata": {}, "outputs": [], "source": [ "y = lc.countrate\n", "time = lc.time\n", "\n", "S_0_N_bounds = (logS0 - 5, logS0 + 5)\n", "log_omega0_N_bounds = (logw0-5, logw0+5) # 0 to 200 in period (days)\n", "nwalkers = 12\n", "bounds = dict(log_S0=S_0_N_bounds, log_omega0=log_omega0_N_bounds)\n", "kernel = DRW(log_S0=logS0, log_omega0=logw0,\n", " bounds=bounds)\n", "initial_samples = np.array([np.random.uniform(S_0_N_bounds[0], S_0_N_bounds[1], nwalkers),\n", " np.random.uniform(log_omega0_N_bounds[0], log_omega0_N_bounds[1], nwalkers)])\n", "cols = [\"kernel:log_S0\", \"kernel:log_omega0\"]\n", "labels = [r\"log $S_N$\", r\"log $\\omega_N$\"]\n", "initial_samples = initial_samples.T\n", "gp = celerite.GP(kernel, mean=np.mean(y))\n", "gp.compute(time) # You always need to call compute once.\n", "initial_params = gp.get_parameter_vector()\n", "par_names = list(gp.get_parameter_names())\n", "bounds = gp.get_parameter_bounds()\n", "solution = minimize(neg_log_like, \n", " initial_params, method=\"L-BFGS-B\", \n", " bounds=gp.get_parameter_bounds(), \n", " args=(y, gp))\n", "print(solution.x)\n", "power = gp.kernel.get_psd(1 / lc.time * 2 * np.pi)\n", "plt.plot(1 / time, power, color=\"blue\")\n", "plt.plot(1/time, psd_model(1 / lc.time * 2 * np.pi), label=\"Input\")\n", "plt.axvline(1 / bend, ls=\"--\", color=\"black\")\n", "plt.axvline(np.exp(solution.x[1]) / 2 / np.pi, ls=\"solid\", color=\"blue\", label=\"Found\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "id": "2b58f563", "metadata": {}, "outputs": [], "source": [ "power = gp.kernel.get_psd(1 / lc.time * 2 * np.pi)\n", "plt.plot(1 / lc.time, power, color=\"blue\")\n", "plt.axvline(np.exp(solution.x[1]) / 2 / np.pi, ls=\"solid\", color=\"blue\", label=\"Found\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.legend()" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.9.19" } }, "nbformat": 4, "nbformat_minor": 5 }