{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# %load_ext autoreload\n", "# %autoreload 2\n", "# %matplotlib notebook\n", "\n", "import numpy as np\n", "from stingray.pulse.search import phase_dispersion_search\n", "import matplotlib.pyplot as plt\n", "import seaborn as sb\n", "import matplotlib as mpl\n", "mpl.rcParams['figure.figsize'] = (10, 6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Phase Dispersion Minimization in Stingray\n", "\n", "Phase dispersion minimization (PDM; Stellingwerf (1978)) is a method to search for strictly periodic signals in constant light curves (white noise only). Like Epoch Folding, it relies in folding a light curve at a given trial period, splitting the folded light curve into phase bins, and evaluating the resulting profile. \n", "\n", "Epoch Folding evaluates how much the means in each phase bin deviate from the global sample mean, given the variance of the measurements. A periodic signal will generate a maximum in the Epoch Folding periodogram across many trial periods. In contrast, Phase Dispersion Minimization evaluates the *variance* in each phase bin and compares this to the global sample variance $\\hat{\\sigma}$:\n", "\n", "\\begin{equation}\n", "\\theta_{\\mathrm{PDM}} = \\frac{1}{\\hat{\\sigma}} \\frac{\\sum_{ij}(x_{ij} - \\bar{x}_j)^2}{N - M} \\;\n", "\\end{equation}\n", "\n", "for $N$ measurements in the light curve split into $M$ bins, and $\\bar{x}_j$ the mean of measurements in bin $j$.\n", "\n", "If a periodic signal is present in the data at a given trial period, the PDM statistic should have a *minimum* at that period.\n", "\n", "## Simulate a dataset\n", "\n", "Let us simulate a simple data set: we create a sinusoidal light curve and add Poisson noise:\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def sinusoid(times, frequency, baseline, amplitude, phase):\n", " return baseline + amplitude * np.sin(2 * np.pi * (frequency * times + phase))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from stingray import Lightcurve\n", "\n", "period = 1.203501\n", "mean_countrate = 50\n", "pulsed_fraction = 0.2\n", "bin_time = 0.01\n", "obs_length = 300\n", "\n", "t = np.arange(0, obs_length, bin_time)\n", "\n", "# The continuous light curve\n", "counts = sinusoid(t, 1 / period, mean_countrate, \n", " 0.5 * mean_countrate * pulsed_fraction, 0) * bin_time\n", "\n", "counts = np.random.poisson(counts)\n", "\n", "lc = Lightcurve(t, counts, gti=[[-bin_time / 2, obs_length + bin_time / 2]],\n", " dt=bin_time)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pulsation search with Phase Dispersion Minimization\n", "\n", "Let us assume we have already an estimate of the true period, for example because we found a candidate in the power density spectrum with a period of ~1.2.\n", "We search around that period with the phase dispersion minimization.\n", "\n", "The first thing we need to do is *fold* the light curve: for every data point, we convert the time of that bin to its corresponding phase. We then split the resulting phase-folded light curve into $M$ phase bins, where $M$ should strike a balance between generating enough bins to accurately represent the structure in the phase curve, but also few enough bins that the number of measurements in each bin is meaningful.\n", "\n", "In regular epoch folding, we calculate the mean flux (or counts) within each bin as a useful statistic. Let's do that first, because it gives us a nice visual representation. Note that when using a light curve (rather than event arrival times) in `fold_events`, you need to use set the `weights` keyword to the array of fluxes or counts:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from stingray.pulse.pulsar import fold_events\n", "from stingray.pulse.search import plot_profile\n", "nbin = 16\n", "\n", "ph, profile, profile_err = fold_events(lc.time, 1/period, nbin=nbin, weights=lc.counts)\n", "_ = plot_profile(ph, profile)\n", "\n", "ph, profile, profile_err = fold_events(lc.time, 1/1.1, nbin=nbin, weights=lc.counts)\n", "_ = plot_profile(ph, profile)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, folding at the correct period (blue line) generates a profile that looks approximately sinusoidal, whereas folding at a different period (orange line) does not. \n", "\n", "For Phase Dispersion Minimization, we are not interested in the *mean* in each phase bin, but rather the *variance* in each phase bin, which we'd like to _minimize_, not maximize. We can also calculate that using `fold_profile`, using `mode=\"pdm\"` (the default is Epoch Folding, `mode=\"ef\"`):\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ph, profile, profile_err = fold_events(lc.time, 1/period, nbin=nbin, weights=lc.counts, mode=\"pdm\")\n", "_ = plot_profile(ph, profile)\n", "\n", "ph, profile, profile_err = fold_events(lc.time, 1/1.1, nbin=nbin, weights=lc.counts, mode=\"pdm\")\n", "_ = plot_profile(ph, profile)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, this looks very different, and not quite as easily recognizeable. What you see here is the nominator of the second term in the PDM Equation written in the introduction.\n", "\n", "We'd now like to try calculating this profile for a number of trial periods, and then calculate $\\theta_\\mathrm{PDM}$. Our null hypothesis is that there is no variation in the data except for measurement noise (e.g. Poisson statistics as we have here, or Gaussian noise). This is implemenented in `stingray.pulse.search.phase_dispersion_search`.\n", "\n", "For the frequency resolution of the periodogram, one usually chooses _at least_ the same frequency resolution of the FFT, i. e., $df_{\\rm min}=1/(t_1 - t_0)$. In most cases, a certain degree of oversampling is used.\n", "\n", "Let's do that:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# We will search for pulsations over a range of frequencies around the known pulsation period.\n", "df_min = 1/obs_length\n", "oversampling=15\n", "df = df_min / oversampling\n", "frequencies = np.arange(1/period - 200 * df, 1/period + 200 * df, df)\n", "\n", "freq, pdmstat = phase_dispersion_search(lc.time, lc.counts, frequencies, nbin=nbin)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ---- PLOTTING --------\n", "plt.figure()\n", "plt.plot(freq, pdmstat, label='PDM statistic')\n", "#plt.axhline(nbin - 1, ls='--', lw=3, color='k', label='n - 1')\n", "plt.axvline(1/period, lw=3, alpha=0.5, color='r', label='Correct frequency')\n", "plt.xlabel('Frequency (Hz)')\n", "plt.ylabel('PDM Statistics')\n", "_ = plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A dip is definitely there at the frequency we expect it to be. \n", "\n", "Unlike the Epoch Folding statistic, which follows approximately a $\\chi^2$ distribution, the PDM statistic was shown to follow a beta-distribution (Schwarzenberg-Czerny, 1997). \n", "\n", "We can use this beta-distribution to calculate the significance of a peak found in the PDM periodogram, or to set a detection threshold. In stingray, this is implemented in the `stingray.stats` module, using `stingray.stats.phase_dispersion_detection_level` and `stingray.stats.phase_dispersion_probability`:\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from stingray.stats import phase_dispersion_detection_level, phase_dispersion_probability\n", "\n", "# number of trials (the number of independent frequencies)\n", "# we searched over\n", "ntrial = int((frequencies[-1] - frequencies[0]) / df_min)\n", "\n", "# number of time bins in the light curve\n", "nsamples = len(lc.time)\n", "\n", "pdm_det_level = phase_dispersion_detection_level(nsamples, nbin, epsilon=0.01, ntrial=ntrial)\n", "\n", "# ---- PLOTTING --------\n", "plt.figure()\n", "plt.axhline(pdm_det_level, label='PDM det. lev.', color='gray')\n", "\n", "plt.plot(freq, pdmstat, color='gray', label='PDM statistics', alpha=0.5)\n", "\n", "#for c in cand_freqs_ef:\n", "# plt.axvline(c, ls='-.', label='EF Candidate', zorder=10)\n", "#for c in cand_freqs_z:\n", "# plt.axvline(c, ls='--', label='$Z^2_1$ Candidate', zorder=10)\n", " \n", "plt.axvline(1/period, color='r', lw=3, alpha=0.5, label='Correct frequency')\n", "plt.xlim([frequencies[0], frequencies[-1]])\n", "plt.xlabel('Frequency (Hz)')\n", "plt.ylabel('PDM Statistics')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's also calculate the significance of the deepest dip:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of the minimum at 0.8313536003155265 Hz is: p = 4.221416326686607e-15\n" ] } ], "source": [ "min_idx = np.argmin(pdmstat)\n", "\n", "pval = phase_dispersion_probability(pdmstat[min_idx], nsamples, nbin, ntrial=ntrial)\n", "\n", "print(f\"The probability of the minimum at {freq[min_idx]} Hz is: p = {pval}\")" ] } ], "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": "3.10.11" }, "vscode": { "interpreter": { "hash": "b7a0f0345bf008463265b97b79e6b6ac46fd48f5252c12e26d20b6a21351a366" } } }, "nbformat": 4, "nbformat_minor": 2 }