{ "cells": [ { "cell_type": "markdown", "id": "08184007", "metadata": {}, "source": [ "# Lomb-Scargle Biases\n", "## This can be used to reproduce Figure 1 from the paper" ] }, { "cell_type": "code", "execution_count": 1, "id": "a457c768", "metadata": {}, "outputs": [], "source": [ "from mind_the_gaps.simulator import Simulator\n", "from astropy.timeseries import LombScargle\n", "from mind_the_gaps.fitting import fit_psd_powerlaw, fit_lomb_scargle\n", "import numpy as np\n", "from astropy.modeling.powerlaws import PowerLaw1D\n", "import random\n", "from multiprocessing import Pool\n", "import nifty_ls\n", "import os\n", "np.random.seed(27)" ] }, { "cell_type": "markdown", "id": "485a30a3", "metadata": {}, "source": [ "Below set input beta to 1 or 1.8" ] }, { "cell_type": "code", "execution_count": 2, "id": "b9f6991b", "metadata": {}, "outputs": [], "source": [ "betas = [1, 1.8]\n", "mean = 3\n", "dt = 1\n", "\n", "input_beta = betas[1] # set to betas[1] for the other index\n", "\n", "outdir = \"beta_%.1f\" % input_beta\n", "if not os.path.isdir(outdir):\n", " os.mkdir(outdir)\n", "# 1,000 datapoint lightcurve\n", "timestamps = np.arange(0, 1000, dt)\n", "# amplitude here sets the variance, which does not play a big role\n", "psd_model = PowerLaw1D(amplitude=1, alpha=input_beta)\n", "\n", "simulator = Simulator(psd_model, timestamps, np.ones(len(timestamps)) * dt, mean, aliasing_factor=1,\n", " extension_factor=1.5) # very important to set it to 1" ] }, { "cell_type": "markdown", "id": "04f7d518", "metadata": {}, "source": "## Let's generate a lightcurve to ensure things are working as expected" }, { "cell_type": "code", "execution_count": 3, "id": "d741c529", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lc_rates = simulator.generate_lightcurve() # \n", "# PSD\n", "freqs = np.fft.rfftfreq(len(timestamps), dt)\n", "# For even fourier transforms we need to ignore the nyquist frequency (Vaughan +2005)\n", "if len(freqs) % 2 == 0:\n", " pow_spec = (np.absolute(np.fft.rfft(lc_rates)[1:-1])) ** 2\n", " frequencies = freqs[1:-1]\n", "else:\n", " pow_spec = (np.absolute(np.fft.rfft(lc_rates)[1:])) ** 2\n", " frequencies = freqs[1:]\n", "\n", "plt.figure()\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.scatter(frequencies, pow_spec)\n", "psd_slope, err, psd_norm, psd_norm_err = fit_psd_powerlaw(frequencies, pow_spec)\n", "plt.plot(frequencies, psd_norm * frequencies ** -input_beta, color=\"C1\", label=\"$\\\\beta = %.2f$\" % input_beta)\n", "plt.plot(frequencies, psd_norm * frequencies ** psd_slope, color=\"C2\", label=\"$\\\\beta = %.2f$\" % psd_slope,\n", " ls=\"--\")\n", "plt.legend()\n", "plt.xlabel(\"Frequency\")\n", "plt.ylabel(\"Power Density\")\n", "plt.savefig(\"%s/psd.png\" % outdir, bbox_inches='tight')" ] }, { "cell_type": "markdown", "id": "757355a6", "metadata": {}, "source": "## Generate N lightcurves" }, { "cell_type": "raw", "id": "f433ec30", "metadata": {}, "source": [ "Helper function for parallelization" ] }, { "cell_type": "code", "execution_count": 4, "id": "876b0ac1", "metadata": {}, "outputs": [], "source": [ "def simulate_lc(n):\n", " return simulator.generate_lightcurve()" ] }, { "cell_type": "raw", "id": "4306703c", "metadata": {}, "source": [ "This may take a few seconds, set the cores to the cpus-1 in your machine" ] }, { "cell_type": "code", "execution_count": 5, "id": "2a52ca30", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n", "/home/andresgur/anaconda3/lib/python3.9/site-packages/stingray/utils.py:403: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] } ], "source": [ "simulator = Simulator(psd_model, timestamps, np.ones(len(timestamps)) * dt, mean, aliasing_factor=1,\n", " extension_factor=10, random_state=27) # now 10 times longer\n", "cores = 15\n", "N_sims = 1000\n", "with Pool(processes=cores, initializer=np.random.seed) as pool:\n", " rates = pool.map(simulate_lc, range(N_sims))" ] }, { "cell_type": "markdown", "id": "e0ac29d6", "metadata": {}, "source": "## Check indices of the simulated lightcurves to ensure everything is ok" }, { "cell_type": "code", "execution_count": 6, "id": "4e71a789", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "slopes = np.ones(N_sims)\n", "for index, rate in enumerate(rates):\n", " # For even fourier transforms we need to ignore the nyquist frequency (Vaughan +2005)\n", " if len(freqs) % 2 == 0:\n", " pow_spec = (np.absolute(np.fft.rfft(rate)[1:-1])) ** 2\n", " frequencies = freqs[1:-1]\n", " else:\n", " pow_spec = (np.absolute(np.fft.rfft(rate)[1:])) ** 2\n", " frequencies = freqs[1:]\n", " psd_slope, err, psd_norm, psd_norm_err = fit_psd_powerlaw(frequencies, pow_spec)\n", " slopes[index] = psd_slope\n", "\n", "plt.figure()\n", "plt.hist(slopes, bins=10, facecolor=\"green\", edgecolor=\"black\")\n", "plt.axvline(-input_beta, ls=\"--\", color=\"black\")\n", "plt.xlabel(\"$\\\\beta$\")\n", "plt.ylabel(\"Instances\")\n", "np.mean(slopes)\n", "np.std(slopes)\n", "plt.savefig(\"%s/histo_beta.png\" % outdir, facecolor=\"white\", bbox_inches='tight')\n", "# plot a template lightcurve\n", "plt.figure()\n", "plt.scatter(timestamps, rates[0], marker=\".\")\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Rate\")\n", "plt.savefig(\"%s/template_lc.png\" % outdir, bbox_inches='tight')" ] }, { "cell_type": "markdown", "id": "94a51be3", "metadata": {}, "source": "## Define frequency range" }, { "cell_type": "code", "execution_count": 7, "id": "d7600ee1", "metadata": {}, "outputs": [], "source": [ "fmax = 1 / (2 * dt) # Nyquist\n", "fmin = 1 / (timestamps[-1] - timestamps[0])\n", "samples_per_peak = 1\n", "ls_norm = \"psd\" # not so important\n", "# remove Nyquist frequency as it follows Chi^2_1 not Chi^2_2\n", "frequencies = np.linspace(fmin, fmax, len(rate) // 2)[:-1]" ] }, { "cell_type": "markdown", "id": "a69d5947", "metadata": {}, "source": "## Remove samples and retrieve the index" }, { "cell_type": "raw", "id": "d0c33e8c", "metadata": {}, "source": [ "This may take a few minutes for 1,000 lightcurves..." ] }, { "cell_type": "code", "execution_count": 8, "id": "5de3e334", "metadata": {}, "outputs": [], "source": [ "# up to 501 so remove max 500 samples in batches of 50\n", "rem_samples = np.arange(0, 501, 50, dtype=int)\n", "# Fitting\n", "ls_slopes = np.ones((len(rem_samples), N_sims))\n", "# loop samples to remove\n", "for rem_index, rem in enumerate(rem_samples):\n", " # fix indices used to remove datapoints, keeping first and last datapoints\n", " del_indexes = random.sample(range(1, len(timestamps)), rem)\n", " # timestamps are the same for all lcs\n", " uneven_timestamps = np.delete(timestamps, del_indexes)\n", " # loop all lightcurves\n", " for index, rate in enumerate(rates):\n", " uneven_rate = np.delete(rate, del_indexes)\n", " ls = LombScargle(uneven_timestamps, uneven_rate, fit_mean=True, nterms=1, center_data=True,\n", " normalization=ls_norm)\n", " power = ls.power(frequencies, method=\"fast\")\n", " # Fitting\n", " psd_slope, err, norm, norm_err = fit_lomb_scargle(frequencies, power)\n", " ls_slopes[rem_index, index] = psd_slope" ] }, { "cell_type": "markdown", "id": "77a6c683", "metadata": {}, "source": "## Plot the results" }, { "cell_type": "code", "execution_count": 9, "id": "21f8c602", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.errorbar(rem_samples, -np.mean(ls_slopes, axis=1), yerr=np.std(ls_slopes, axis=1), \n", " color=\"C1\")\n", "plt.axhline(input_beta, ls=\"--\", color=\"C1\")\n", "plt.xlabel(\"$N$ samples removed\")\n", "plt.ylabel(\"$<\\\\beta>$\")\n", "plt.savefig(\"%s/samples_removed.png\" % (outdir), bbox_inches=\"tight\")\n", "outputs = np.asarray([rem_samples, np.mean(ls_slopes, axis=1), np.std(ls_slopes, axis=1)])\n", "np.savetxt(\"%s/best_fit_beta.dat\" % (outdir), outputs.T, delimiter=\"\\t\", fmt=\"%.2f\", header=\"samples\\tbeta\\tstd\")" ] }, { "cell_type": "raw", "id": "cec5b38f", "metadata": {}, "source": [ "Small differences with respect Figure 1 are due to the randomness of the whole process" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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 }