{ "cells": [ { "cell_type": "markdown", "id": "743457ef", "metadata": {}, "source": [ "# EMRI Example with FEW" ] }, { "cell_type": "markdown", "id": "5a19c7d4", "metadata": {}, "source": [ "To run this example you will have to have few installed.\n", "This can done by installing this package with the dev option.\n", "\n", "`pip install . [dev]`" ] }, { "cell_type": "code", "execution_count": 1, "id": "e0a56d39", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.interpolate import CubicSpline\n", "\n", "import jax.numpy as jnp\n", "\n", "from few.amplitude.romannet import RomanAmplitude\n", "from few.trajectory.ode.flux import SchwarzEccFlux\n", "from few.trajectory.inspiral import EMRIInspiral\n", "from few.utils.ylm import GetYlms\n", "from few.waveform import FastSchwarzschildEccentricFlux\n", "from few.summation.interpolatedmodesum import CubicSplineInterpolant\n", "from few.utils.constants import *\n", "\n", "import WDM\n", "\n", "import TimeFrequencyWaveforms as TFW\n", "\n", "import time" ] }, { "cell_type": "code", "execution_count": 2, "id": "0357beb7", "metadata": {}, "outputs": [], "source": [ "traj = EMRIInspiral(func=SchwarzEccFlux)\n", "amp = RomanAmplitude()\n", "ylm_gen = GetYlms()\n", "\n", "inspiral_kwargs = {\"DENSE_STEPPING\": 0, \"max_init_len\": int(1e3)}\n", "amplitude_kwargs = {}\n", "Ylm_kwargs = {}\n", "sum_kwargs = {\"pad_output\": False}" ] }, { "cell_type": "markdown", "id": "a473e96b", "metadata": {}, "source": [ "__Source Parameters__" ] }, { "cell_type": "code", "execution_count": 3, "id": "1f4a80d4", "metadata": {}, "outputs": [], "source": [ "M = 1.0e6 # Central black hole mass [Msun]\n", "mu = 5.0e1 # Compact object mass [Msun]\n", "p0 = 10.0 # Initial semi-latus rectum [M]\n", "e0 = 0.4 # Initial eccentricity \n", "theta = np.pi/4. # Polar viewing angle [rad]\n", "phi = np.pi/3. # Azimuthal viewing angle [rad]\n", "dist = 1.0 # Luminosity distance [Gpc] \n", "T = 1.0 # Maximum duration [yr]" ] }, { "cell_type": "markdown", "id": "a98c1599", "metadata": {}, "source": [ "__Trajectory__\n", "\n", "Compute the trajectory of the compact object using `few`." ] }, { "cell_type": "code", "execution_count": 4, "id": "f8d2b9d9", "metadata": {}, "outputs": [], "source": [ "t, p, e, x, Phi_phi, Phi_theta, Phi_r = traj(M, mu, 0.0, p0, e0, 1.0, T=T)" ] }, { "cell_type": "markdown", "id": "a9554d4e", "metadata": {}, "source": [ "Plot the trajectory." ] }, { "cell_type": "code", "execution_count": 5, "id": "fc30a76a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(figsize=(5,4), nrows=2, sharex=True)\n", "axes[0].plot(t/3.154e7, p, 'k-')\n", "axes[0].set_ylabel(r\"Semi-latus rectum $p$ [M]\")\n", "axes[0].set_ylim(6, 10)\n", "axes[1].plot(t/3.154e7, e, 'k-')\n", "axes[1].set_ylabel(r\"Eccentricity $e$\")\n", "axes[1].set_ylim(0, 0.5)\n", "axes[1].set_xlabel(r\"Time $t$ [yr]\")\n", "axes[1].set_xlim(0, t[-1]/3.154e7)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "c34af020", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5,4))\n", "ax.plot(p, e, 'k-')\n", "ax.set_xlabel(r\"Semi-latus rectum $p$ [M]\")\n", "ax.set_ylabel(r\"Eccentricity $e$\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "f17c6376", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(figsize=(9,4), ncols=2)\n", "for i, phase in enumerate([Phi_phi, Phi_r]):\n", " axes[i].plot(t/3.154e7, np.gradient(phase, t), 'k-')\n", " axes[i].set_xlabel(r\"Time $t$ [yr]\")\n", " label = [r\"$\\Omega_\\phi$\", r\"$\\Omega_r$\"][i]\n", " axes[i].set_ylabel(r\"Frequency \"+label)\n", " axes[i].set_xlim(0, t[-1]/3.154e7)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2aa610bb", "metadata": {}, "source": [ "__Full EMRI Waveform__\n", "\n", "Use `few` to compute the full waveform (inc. all harmonics)." ] }, { "cell_type": "code", "execution_count": 8, "id": "eec47d9e", "metadata": {}, "outputs": [], "source": [ "few = FastSchwarzschildEccentricFlux(\n", " inspiral_kwargs=inspiral_kwargs,\n", " amplitude_kwargs=amplitude_kwargs,\n", " Ylm_kwargs=Ylm_kwargs,\n", " sum_kwargs=sum_kwargs\n", ")\n", "\n", "dt = 10.0 # sampling interval [s]\n", "times = np.arange(t[0], t[-1], dt)\n", "\n", "wave = few(M, mu, p0, e0, theta, phi, dt=dt, T=T) / ((dist * Gpc) / (mu * MRSUN_SI))" ] }, { "cell_type": "markdown", "id": "f03a5b01", "metadata": {}, "source": [ "Plot the full EMRI waveform." ] }, { "cell_type": "code", "execution_count": 9, "id": "2decf9eb", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5,4))\n", "ax.plot(times/3.154e7, np.real(wave), 'k-', lw=1)\n", "ax.set_xlabel(r\"Time $t$ [yr]\")\n", "ax.set_xlim(0, t[-1]/3.154e7)\n", "ax.set_ylabel(r\"Waveform strain $h_+$\")\n", "ax.set_ylim(-2.5e-21, 6.0e-21)\n", "\n", "# inset Axes....\n", "x1, x2, y1, y2 = 0.01, 0.0103, -2.0e-21, 2.0e-21 # subregion of the original image\n", "axins = ax.inset_axes(\n", " [0.1, 0.6, 0.3, 0.35],\n", " xlim=(x1, x2), ylim=(y1, y2), xticklabels=[], yticklabels=[])\n", "axins.plot(times/3.154e7, np.real(wave), 'k-', lw=1)\n", "ax.indicate_inset_zoom(axins, edgecolor=\"black\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ff9a0cac", "metadata": {}, "source": [ "__Discrete Wavelet Transform__\n", "\n", "Perform the discrete wavelet transform numerically on the entire EMRI signal (inc. all harmonics)." ] }, { "cell_type": "code", "execution_count": 10, "id": "d4e49f32", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WDM_transform(Nf=3600, N=864000, q=8, d=4, A_frac=0.25, calc_m0=True)\n", "self.Nt = 240 time cells\n", "self.Nf = 3600 frequency cells\n", "self.dT = 36000.0 time resolution\n", "self.dF = 1.388888888888889e-05 frequency resolution\n", "self.K = 57600 window length\n" ] } ], "source": [ "dt = 10.0 # sampling interval [s]\n", "num_samples_per_dT = 3600 # wavelet length \\Delta T = 10 hours\n", "\n", "desired_length = WDM.utils.next_multiple(times.shape[0], num_samples_per_dT)\n", "\n", "Nt = desired_length // num_samples_per_dT\n", "Nf = desired_length // Nt\n", "\n", "assert Nt * Nf == desired_length, \"Desired length not achieved!\"\n", "\n", "wdm = WDM.WDM.WDM_transform(dt=dt, Nf=Nf, N=desired_length, q=8, calc_m0=True)\n", "\n", "print(wdm)\n", "\n", "wave_padded, padding_mask = WDM.utils.pad_signal(wave, desired_length)\n", "\n", "w_plus_nm = wdm(np.real(wave_padded))\n", "w_cross_nm = wdm(np.real(wave_padded))" ] }, { "cell_type": "markdown", "id": "8fb68b10", "metadata": {}, "source": [ "Plot the discrete wavelet transform. You can see all the harmonics in this time-frequency representation." ] }, { "cell_type": "code", "execution_count": 11, "id": "3a0f0773", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5,4))\n", "im = ax.imshow(w_plus_nm.T, aspect='auto', origin='lower',\n", " extent=[0., wdm.T, 0., wdm.f_Ny], cmap='jet')\n", "ax.set_xlabel('Time [yr]')\n", "ax.set_xticks(np.arange(0, 0.26, 0.05)*3.154e7, labels=[f\"{f:.2f}\" for f in np.arange(0, 0.26, 0.05)])\n", "ax.set_ylabel('Frequency [Hz]')\n", "ax.set_ylim(0, 0.007)\n", "fig.colorbar(im, ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ae7a5d20", "metadata": {}, "source": [ "__Isolate a Specific Mode__" ] }, { "cell_type": "code", "execution_count": 26, "id": "243b2fc5", "metadata": {}, "outputs": [], "source": [ "ell, m, n = 2, 2, 0\n", "\n", "specific_modes = [(ell, m, n)]\n", "\n", "phase_sparse_data = m*Phi_phi + n*Phi_r\n", "A = amp(0., p, e, x, specific_modes=specific_modes)[(ell, m, n)] / ((dist * Gpc) / (mu * MRSUN_SI))\n", "Ylm = ylm_gen(np.array([ell]), np.array([m]), theta, phi)\n", "amplitude_sparse_data = A * Ylm\n", "\n", "phase_interp = CubicSpline(t, phase_sparse_data, extrapolate=True)\n", "amplitude_phase_interp = CubicSpline(t, np.unwrap(np.angle(amplitude_sparse_data)), extrapolate=True)\n", "amplitude_interp = CubicSpline(t, np.abs(amplitude_sparse_data), extrapolate=True)" ] }, { "cell_type": "markdown", "id": "6d6ec64b", "metadata": {}, "source": [ "Plot this single mode." ] }, { "cell_type": "code", "execution_count": 27, "id": "90a34d1d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mode = amplitude_interp(times) * np.exp((1j)*(phase_interp(times)+amplitude_phase_interp(times)))\n", "\n", "fig, ax = plt.subplots(figsize=(5,4))\n", "ax.plot(times/3.154e7, np.real(mode), 'k-', lw=1)\n", "ax.set_xlabel(r\"Time $t$ [yr]\")\n", "ax.set_xlim(0, t[-1]/3.154e7)\n", "ax.set_ylabel(r\"Mode strain $h_+$\")\n", "ax.set_ylim(-4.0e-22, 8.0e-22)\n", "\n", "# inset Axes....\n", "x1, x2, y1, y2 = 0.01, 0.0103, -2.0e-22, 2.0e-22 # subregion of the original image\n", "axins = ax.inset_axes(\n", " [0.1, 0.6, 0.3, 0.35],\n", " xlim=(x1, x2), ylim=(y1, y2), xticklabels=[], yticklabels=[])\n", "axins.plot(times/3.154e7, np.real(mode), 'k-', lw=1)\n", "ax.indicate_inset_zoom(axins, edgecolor=\"black\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e03ee9e1", "metadata": {}, "source": [ "__Fast TD -> TFD Transform__\n", "\n", "Set up the transformer object." ] }, { "cell_type": "code", "execution_count": null, "id": "087a9e9b", "metadata": {}, "outputs": [], "source": [ "fdot_grid_spec = (0.0, 3.0e-9, 3)\n", "\n", "transformer = TFW.code.TD_to_TFD_transform.Transformer(wdm, num_freq_points=40, num_pixels=21, fdot_grid_spec=fdot_grid_spec)" ] }, { "cell_type": "markdown", "id": "54170bcc", "metadata": {}, "source": [ "Evaluate the harmonic amplitude, phase, frequency, and frequency derivative on the sparse grid of wavelet times." ] }, { "cell_type": "code", "execution_count": 28, "id": "032037d4", "metadata": {}, "outputs": [], "source": [ "t_n = jnp.arange(wdm.Nt) * wdm.dT\n", "A_n = jnp.array(amplitude_interp(t_n))\n", "Phi_n = jnp.array(phase_interp(t_n) + amplitude_phase_interp(t_n))\n", "f_n = jnp.array(phase_interp.derivative()(t_n) + amplitude_phase_interp.derivative()(t_n)) / (2.0 * jnp.pi)\n", "fdot_n = jnp.array(phase_interp.derivative(nu=2)(t_n) + amplitude_phase_interp.derivative(nu=2)(t_n)) / (2.0 * jnp.pi)" ] }, { "cell_type": "markdown", "id": "ce7e6229", "metadata": {}, "source": [ "Compute the fast transform of a single mode." ] }, { "cell_type": "code", "execution_count": 29, "id": "eaaf9c74", "metadata": {}, "outputs": [], "source": [ "mode = transformer.transform(A_n, Phi_n, f_n, fdot_n)\n", "w_plus_mode_nm, w_cross_mode_nm = jnp.real(mode), jnp.imag(mode)" ] }, { "cell_type": "markdown", "id": "b92789a5", "metadata": {}, "source": [ "Plot this single mode in the time-frequency representation." ] }, { "cell_type": "code", "execution_count": 30, "id": "9841ee68", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5,4))\n", "im = ax.imshow(w_plus_mode_nm.T, aspect='auto', origin='lower',\n", " extent=[0., wdm.T, 0., wdm.f_Ny], cmap='jet')\n", "ax.set_xlabel('Time [yr]')\n", "ax.set_xticks(np.arange(0, 0.26, 0.05)*3.154e7, labels=[f\"{f:.2f}\" for f in np.arange(0, 0.26, 0.05)])\n", "ax.set_ylabel('Frequency [Hz]')\n", "ax.set_ylim(0, 0.007)\n", "fig.colorbar(im, ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "249cca4b", "metadata": {}, "source": [ "__Apply the Fast Transform to the Full EMRI Signal__\n", "\n", "Apply the transform to each mode one by one.\n", "\n", "Included modes: $(2,2,n)$ for $n\\in\\{-1,0,1,2,3\\}$." ] }, { "cell_type": "code", "execution_count": 42, "id": "9f89b22e", "metadata": {}, "outputs": [], "source": [ "w_plus_allmodes_nm = np.zeros_like(w_plus_nm)\n", "w_cross_allmodes_nm = np.zeros_like(w_cross_nm)\n", "\n", "for n in np.arange(-1, 3+1):\n", "\n", " ell, m = 2, 2\n", "\n", " specific_modes = [(ell, m, n)]\n", "\n", " phase_sparse_data = m*Phi_phi + n*Phi_r\n", " A = amp(0., p, e, x, specific_modes=specific_modes)[(ell, m, n)] / ((dist * Gpc) / (mu * MRSUN_SI))\n", " Ylm = ylm_gen(np.array([ell]), np.array([m]), theta, phi)\n", " amplitude_sparse_data = A * Ylm\n", "\n", " phase_interp = CubicSpline(t, phase_sparse_data, extrapolate=True)\n", " amplitude_phase_interp = CubicSpline(t, np.unwrap(np.angle(amplitude_sparse_data)), extrapolate=True)\n", " amplitude_interp = CubicSpline(t, np.abs(amplitude_sparse_data), extrapolate=True)\n", "\n", " A_n = jnp.array(amplitude_interp(t_n))\n", " Phi_n = jnp.array(phase_interp(t_n) + amplitude_phase_interp(t_n))\n", " f_n = jnp.array(phase_interp.derivative()(t_n) + amplitude_phase_interp.derivative()(t_n)) / (2.0 * jnp.pi)\n", " fdot_n = jnp.array(phase_interp.derivative(nu=2)(t_n) + amplitude_phase_interp.derivative(nu=2)(t_n)) / (2.0 * jnp.pi)\n", "\n", " mode = transformer.transform(A_n, Phi_n, f_n, fdot_n)\n", " w_plus_onemode_nm, w_cross_onemode_nm = jnp.real(mode), jnp.imag(mode)\n", "\n", " w_plus_allmodes_nm += w_plus_onemode_nm\n", " w_cross_allmodes_nm += w_cross_onemode_nm\n", "\n", "# For reasons that I don't understand, the whole signal is off by a minus sign\n", "w_plus_allmodes_nm *= -1.0\n", "w_cross_allmodes_nm *= -1.0" ] }, { "cell_type": "markdown", "id": "fd67df72", "metadata": {}, "source": [ "Plot the discrete wavelet transform. You can see the 5 included modes in this representation." ] }, { "cell_type": "code", "execution_count": 43, "id": "84ae4294", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5,4))\n", "im = ax.imshow(w_plus_allmodes_nm.T, aspect='auto', origin='lower',\n", " extent=[0., wdm.T, 0., wdm.f_Ny], cmap='jet')\n", "ax.set_xlabel('Time [yr]')\n", "ax.set_xticks(np.arange(0, 0.26, 0.05)*3.154e7, labels=[f\"{f:.2f}\" for f in np.arange(0, 0.26, 0.05)])\n", "ax.set_ylabel('Frequency [Hz]')\n", "ax.set_ylim(0, 0.007)\n", "fig.colorbar(im, ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8f5d427f", "metadata": {}, "source": [ "__Mismatch__\n", "\n", "Compute the mismatch between the exact numerical transform and the fast approximation including 5 modes." ] }, { "cell_type": "code", "execution_count": 44, "id": "5ec8dc22", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mismatch = 2.35e-01\n" ] } ], "source": [ "def wavelet_inner_product(wdm : WDM.WDM.WDM_transform,\n", " Anm : jnp.ndarray, Bnm : jnp.ndarray, \n", " f_low : float=None, f_high : float=None, \n", " t_low : float=None, t_high : float=None) -> float:\n", " \"\"\" \n", " Compute white TF noise inner product between two signals with wavelet\n", " coefficients Anm and Bnm. This is a sum over the time-frequency grid.\n", " The optional arguments allow this sum to be restricted to a sub-region\n", " of the time-frequency grid.\n", "\n", " Parameters\n", " ---------- \n", " wdm : WDM.WDM.WDM_transform\n", " An instance of the WDM wavelet transform class.\n", " Anm : jnp.ndarray\n", " Wavelet coefficients of first signal, shape=(Nt, Nf).\n", " Bnm : jnp.ndarray\n", " Wavelet coefficients of second signal, shape=(Nt, Nf).\n", " f_low : float\n", " Lower frequency bound of inner product. Optional.\n", " f_high : float\n", " Upper frequency bound of inner product. Optional.\n", " t_low : float\n", " Lower time bound of inner product. Optional.\n", " t_high : float\n", " Upper time bound of inner product. Optional.\n", "\n", " Returns\n", " -------\n", " AB : float\n", " The inner product.\n", " \"\"\"\n", " tn = wdm.dT * jnp.arange(wdm.Nt)\n", " fm = wdm.dF * jnp.arange(wdm.Nf)\n", "\n", " t_low = t_low if t_low is not None else 0.0\n", " t_high = t_high if t_high is not None else wdm.T\n", " f_low = f_low if f_low is not None else 0.0\n", " f_high = f_high if f_high is not None else wdm.f_Ny\n", "\n", " mask = jnp.outer( jnp.logical_and(tn > t_low, tn < t_high),\n", " jnp.logical_and(fm > f_low, fm < f_high) )\n", "\n", " AB = jnp.sum(Anm[mask]*Bnm[mask])\n", "\n", " return AB\n", "\n", "\n", "edge = 25\n", "f_low, f_high = 0.001, 0.01\n", "\n", "wW = wavelet_inner_product(wdm, w_plus_allmodes_nm, w_plus_nm, \n", " f_low=f_low, f_high=f_high, t_low=edge*wdm.dT, t_high=wdm.T-edge*wdm.dT)\n", "ww = wavelet_inner_product(wdm, w_plus_allmodes_nm, w_plus_allmodes_nm, \n", " f_low=f_low, f_high=f_high, t_low=edge*wdm.dT, t_high=wdm.T-edge*wdm.dT)\n", "WW = wavelet_inner_product(wdm, w_plus_nm, w_plus_nm, \n", " f_low=f_low, f_high=f_high, t_low=edge*wdm.dT, t_high=wdm.T-edge*wdm.dT)\n", "\n", "MM = 1.0 - wW/jnp.sqrt(ww*WW)\n", "\n", "print(f\"Mismatch = {MM:.2e}\")" ] }, { "cell_type": "code", "execution_count": null, "id": "21e40bf8", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "WDM", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }