{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## `bbhx` Tutorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`bbhx` is a software package that produces black hole binary waveforms. It focuses on LISA and provides the proper LISA response function for MBHBs ([arXiv:1806.10734](https://arxiv.org/abs/1806.10734), [arXiv:2003.00357](https://arxiv.org/abs/2003.00357)). `bbhx` also provides fast likelihood functions. The package is GPU-accelerated for fast analysis. \n", "\n", "If you use this software please cite [arXiv:2005.01827](https://arxiv.org/abs/2005.01827), [arXiv:2111.01064](https://arxiv.org/abs/2111.01064), and the associated [Zenodo page](https://zenodo.org/record/5730688#.YaFvRkJKhTY) Please also cite any consituent parts used like the response function or waveforms. See the `citation` attribute for each class or docstring for functions for more information. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "No CuPy\n", "No CuPy or GPU PhenomHM module.\n", "No CuPy or GPU interpolation available.\n", "No CuPy or GPU response available.\n", "No CuPy\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "from bbhx.waveformbuild import BBHWaveformFD\n", "from bbhx.waveforms.phenomhm import PhenomHMAmpPhase\n", "from bbhx.response.fastfdresponse import LISATDIResponse\n", "from bbhx.likelihood import Likelihood, HeterodynedLikelihood\n", "from bbhx.utils.constants import *\n", "from bbhx.utils.transform import *\n", "\n", "from lisatools.sensitivity import get_sensitivity\n", "\n", "np.random.seed(111222)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GPU accelerated MBHB waveforms for LISA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we will detail how to produce full waveforms for MBHBs to be detected by LISA. We will look at how to generate PhenomHM waveforms ([arXiv:1708.00404](https://arxiv.org/abs/1708.00404), [arXiv:1508.07253](https://arxiv.org/abs/1508.07253), [arXiv:1508.07250](https://arxiv.org/abs/1508.07250)) put through the LISA response function (([arXiv:1806.10734](https://arxiv.org/abs/1806.10734), [arXiv:2003.00357](https://arxiv.org/abs/2003.00357)). More information on generating the waveforms and response separately can be found below. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "wave_gen = BBHWaveformFD(amp_phase_kwargs=dict(run_phenomd=False))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# set parameters\n", "f_ref = 0.0 # let phenom codes set f_ref -> fmax = max(f^2A(f))\n", "phi_ref = 0.0 # phase at f_ref\n", "m1 = 1e6 \n", "m2 = 5e5\n", "a1 = 0.2\n", "a2 = 0.4\n", "dist = 18e3 * PC_SI * 1e6 # 3e3 in Mpc \n", "inc = np.pi/3.\n", "beta = np.pi/4. # ecliptic latitude\n", "lam = np.pi/5. # ecliptic longitude\n", "psi = np.pi/6. # polarization angle \n", "t_ref = 0.5 * YRSID_SI # t_ref (in the SSB reference frame)\n", "\n", "# frequencies to interpolate to\n", "freq_new = np.logspace(-4, 0, 10000)\n", "modes = [(2,2), (2,1), (3,3), (3,2), (4,4), (4,3)]\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, squeeze=True, length=1024)[0] \n", "\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new, np.abs(wave[i]), label=let)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adjust inspiral timing" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# start at the beginning of observation\n", "t_obs_start = 0.0\n", "\n", "t_obs_end = (t_ref - 24 * 3600) / YRSID_SI # 1 day before merger\n", "\n", "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, squeeze=True, length=1024, t_obs_start=t_obs_start, t_obs_end=t_obs_end)[0] \n", "\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new, np.abs(wave[i]), label=let)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Controlling interpolation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The user has the option to control the interpolation by providing the number of frequencies to interpolate over with the `length` keyword argument. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Frequency (Hz)')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk4AAAG1CAYAAAAP5HuyAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAACIEUlEQVR4nO3deXwU9fnA8c/smTshCeQAQrhEEUg0GIR6BIxyKB6I0lYlgKK2xaOp/gRbUVuVWi2lrSjVCqgVRbSClRaRCAa5CQZRLoEAgZCLkGuTbLK78/tjycKSOySZTfZ5v1776s53Zmee3Zrhme+pqKqqIoQQQgghmqTTOgAhhBBCiM5CEichhBBCiGaSxEkIIYQQopkkcRJCCCGEaCZJnIQQQgghmkkSJyGEEEKIZpLESQghhBCimSRxEkIIIYRoJoPWAXQ1DoeDnJwcAgMDURRF63CE6BRUVaWsrIzo6Gh0OnmeuxhyDxKidZp7H5LEqY3l5OTQu3dvrcMQolPKzs6mV69eWofRqck9SIiL09R9SBKnNhYYGAg4f/igoCCNoxGicygtLaV3796uvx/RenIPEqJ1mnsfksSpjdVWjQcFBclNS4gWkqaliyf3ICEuTlP3IelMIIQQQgjRTJI4CSGEEEI0k9c21d1xxx1s2LCBG264gY8//thtX1ZWFjNmzCAvLw+9Xs/WrVvx9/fXKFLhLex2OzU1NVqH0W5MJpOMmBNCdHpemzg99thjzJgxg3feeafOvmnTpvHCCy9w7bXXUlRUhNls1iBC4S1UVSU3N5fi4mKtQ2lXOp2Ovn37YjKZtA5FCCFazWsTp6SkJDZs2FCn/IcffsBoNHLttdcCEBoa2sGRCW9TmzT16NEDPz+/LtlBunZuoVOnThETE9Mlv6MQwjt4ZL15eno6EydOJDo6GkVRWLlyZZ1jFi5cSGxsLD4+PowYMYLt27e3ybV//PFHAgICmDhxIldeeSUvvfRSm5xXiPrY7XZX0hQWFoavry8+Pj5d7uXn50f37t2pqKjAZrNp/bMLIUSreWSNk8ViIS4ujhkzZjBp0qQ6+5cvX05qaiqLFi1ixIgRLFiwgLFjx3LgwAF69OgBQHx8fL036LVr1xIdHd3gtW02Gxs3biQzM5MePXowbtw4rrrqKm688ca2+4JCnFXbp8nPz0/jSNpfbROd3W7HaDRqHI0QQrSORyZO48ePZ/z48Q3unz9/PjNnzmT69OkALFq0iNWrV7N48WJmz54NQGZmZquu3bNnT4YPH+6aeXfChAlkZmY2mDhZrVasVqtru7S0tFXXFd7NG5quvOE7CiG6Po9sqmtMdXU1GRkZJCcnu8p0Oh3Jycls2bLlos9/1VVXkZ+fz5kzZ3A4HKSnp3PZZZc1ePy8efMIDg52vWSpAyGEEKLr6nSJU2FhIXa7nYiICLfyiIgIcnNzm32e5ORk7rrrLv773//Sq1cvV9JlMBh46aWXuO666xg2bBgDBw7klltuafA8c+bMoaSkxPXKzs5u3RcTQgghhMfzyKa6jrBu3boG9zXVVHg+s9ks0xUIIYQQXqLT1TiFh4ej1+vJy8tzK8/LyyMyMlKjqITwTlu2bEGv13PzzTdrHYoQQnSITpc4mUwmEhISSEtLc5U5HA7S0tIYOXKkhpGJzmRV5kkefi+DV77YT2W1XetwOq23336bRx55hPT0dHJycrQOR4hO48SZCub8+zt+89Fu9ubIoKLOxCOb6srLyzl06JBrOysri8zMTEJDQ4mJiSE1NZWUlBSGDx9OYmIiCxYswGKxuEbZCQHw/ckS0vblo1MgsW8oiX1DURSFhesP8Y8vdnGtbg8b93bnYF45b96X4BGjvlRVpbJGm0TO16hv0W9QXl7O8uXL2blzJ7m5uSxdupSnn366HSMUovOosTv4z+4cvj5YQHFFDTGhfiQN6s5PBoTz3z2n+POqbfzMvgp/qnhiz1hefmgyQ3sFax22aAaPTJx27tzJ6NGjXdupqakApKSksHTpUqZMmUJBQQFz584lNzeX+Ph41qxZU6fDuPBOp0oqeWXNATZ8u48huiwsqg+vqX3pGxlGTKgfh/Z9yxrzS0QrRQD84cA9rPm+J+OHRmkcOVTW2Bk89wtNrr3392PxMzX/lvDRRx9x6aWXMmjQIO69914ef/xx5syZ4xEJqBBaqaqx83HGCd5d/x3XlH/BBN0+fLGy90gf/rptBPer/bhcOcaHxr/Q21AAwF3q1zy+TM/rqVMxGTpdQ5DX8cjEKSkpCVVVGz1m1qxZzJo1q4MiEp5OVVWyiypZkZHNRxu/Y4b6KfPMazErzgkmC9Rg3i4Yz7q8K3nX9Cdn0mQKgOpy5hg+4NG1VzNuyH3yj34LvP3229x7770AjBs3jpKSEr7++muSkpK0DawTaWix8QMHDjBlyhS37Q8++IDbb79dgyhFUw7mlbEq8yR7TpRQdHwvt9u/4BP9BgKNla5jrmMPDxs+54QaTg/OYFLsqCEx2E3BBOTv4cnyV/hw6zVMvWaAdl9ENIuiNpWhiBYpLS0lODiYkpISgoKCtA6nyyutqmHhV4f4fHcOSulxbtVt4SHDfwhWKpwHhPaDqlKoKHT/YNgAmPEF1asexXRwNV/YhxM8/SOu7hfWofFXVVWRlZVF37598fHx6TRNdQcOHGDIkCGcPHnSNVv/rFmzKCkp4b333qv3Mxd+1/N569/Nhg0bKCsr45133nFLnM5XXl5ObGwsx44dw9/fv8lzeutvqZXX0g6Q9dVibtNt4nLdUcKUMtc+R/ggdFfeBz7BcGQD6v7/otjOJlOXjIc73gBVpeovV+BTU8yLyoM8NnseAeZzdRoWq43/fZ9LbJgfw2Nl7dT21Ny/HY+scRKiOc5YqnngH+sYV/Qey/Xb6WU+lxypPQaj3Ph7GJAMDhvs+Ri+fhnOZEH0FXD3u+AfjunGZ+Hgam7UZfD0hq1c3a/u6DCHQ0Wn65iaKEVRWtRcppW3334bm83mtnyRqqqYzWZee+01goOlr0ZzNLTY+Pk+++wzbrjhhmYlTaJt2R0qH2dkU1JZw5SrYgj2dV8q6KMth7hsw0PMMn7rKnPoTCix16CM/CW6AclQ+zBy5VSUqlI4nAa+3aDv9a59xjFz4IunSHH8myVfz+CRmy5zXf+BJVsIOP4VhWowN469hV9c319qxjUmjanCY9kdKlsOn+bEmYp69/9l5Te8XPwbZhr+Sy+lEFVngF6JcMebKA9/AwNvdN6Y9EaI/xk8kgG/3gsz10NIjPMk3QdR0fMn6BSViCOfcOy0xXX+sqoaHn4vg0ufWcOUf2zBZnd0xNf2eDabjXfffZc///nPZGZmul67d+8mOjqaDz74QOsQ24SWi42f76OPPnJrthNtr6rGzpd78yipcDbtq6rK59/lMOMfaVSseoLwLx/l4T+/x/y1B/jz2gOs/SGXXceKUP73G27Qf0uNzgxjfgcPfIXu6RMoUz89d/85n08QXH4H9Ety26cfPg2rOYxeSiHZm5ZRZKkGYNHXh/nZyRd5yzSfT83PUrPuBZ5d9T1nzu4X2vD8R1vhlWrsDma9n0H+vk0U6sL5/dSbuHZAODaHio9RzzcHC7hm/wsM0OdQ7R+NaeKfUfpdD6ZGnsp1egjuWafY7+oZ8Mkm7tZv4J/fHObZ24YBMP/Lg5TsS2ORfjUHs3vxy38Z+MfU4V7/tPf5559z5swZ7r///jo1S3feeSdvv/02Dz/8sEbRtR0tFxuvVVpayubNm/nwww8v/gsJNxXVNvxMBhwOlYf/uR6f7I08pQzhlsTLUB02SnZ8xDOGTxlgcE6zcVPNTr7cmEA3yslSIzmCiYcNG3CgQ//TZXBJchNXbITRB+PIh2HDi0xTV/HG+p9yS1xPtqz7lF8Zzy0l9pjhU97fWUrS9p8ztF9vpo2KJXmwDIrqaJI4CU2pqsq8/+1nz4kSnrllMIOjg/j02xP8cfVe/s/6V+40f4NVNfDIO48wRz8Eg72SxPihGPd/xsv6DOzoMd23AiKHtD6IS2+hxhRMz+rTZGesoeSmyygst7J36xd8YHwJnaIyhkw++rGM6155nKfHX8ZNl0ei76DmO0/z9ttvk5ycXG9z3J133smf/vQnvvvuO4YNG6ZBdG1Hy8XGa61atYqbbrqpTp+w88lC441TVZUyq41tR4pYsO4g00bFUlJh5bMvvmBQ3EhKKmt4IGcu15h+oFI18eGO0YQrJUw0bQXA5tcDXWAkAXnfcYd+EwBJ7Hadv3r0M/hcTNJ0li7xAewb5zOYY7y6ZRU/234F7+udCbN61UyUsAGoa2ZzjyGNO9Rv+N+xq/jnkSSK7/wZkxN6XfT1RfNJ4iQ6XH5pFUUV1VwaGcT6A/kc+WYFVynH+OnfxhIa1p0eRRksMn7AFXrnXF5mxcabpr84P6yHLXsGM1R3BBSw/eTX6C8maQIw+mAYNhl2vs3N6gaW77iT3dklzNR9hk45N3bibsPXWEuNPPb+fVRjZOWvfkJ875CLu3Yn9J///KfBfYmJiU2OiO0KahcbnzNnjqusLRcbr/XRRx/x4IMPNnrMvHnzeP7559vsmp1VZbWd0qoaiizVfLj9OHtOlhAZ7MNX32cTpJZzle4AfzOsYNmnN9BfOclnxvVkft+PQCrprz8FgK9SzXTDedOBXHEfhtFPQ0AE7FkBxcfBHITj4BocJ7+FhGn4XPfrtvkCfqHoEu+HLa/xqH4FRls1V5gOoRr9UK57EgIjUML6w9pn8CvYx536b7hT/w0LVx/GccUbHdYPU8ioujYnI1rqqqqx85uPdrPnZAkLfhrPsx+sp6y4iL6XDKPs+G4+cjzpSlAW2Sbyc/06gpRKVEWHcvsiHEfWo9tdt99MZcgl+M76BgxtsFbgiZ3wzxuoVE1caV1EhHKGDebfoKKgPLgB3rze7fAfHH143v+3fPTUxfU9aWykWVfTmUfVKYrCp59+6poOICcnh549e7J582a3FQv+7//+j6+//ppt27Y167zJycns3r0bi8VCaGgoK1ascJ2vpKSESy65hOzsbEwmU4PnqK/GqXfv3h77W7YFu0PlxJkKdh0/w/tbj1NRbefEqVOEKqX0Vgq4RbeVq3T7seDDUN3Rps+nGNDfMh+qLdg3vIzeWoxj5CPoxr7Q/l/mfOUFqH8dhlJzXr/Oa38DN8w9t62qcGIH9q3/QP/Dx5SpvmQ/sIfBvbt3bKxdkIyqE5o4XW7l9Q2H8TcbqLDa+HBHNuVWG7/Ur+QWXRaPv/Fz/mV8iZ6mQt48fAtJut3odOdy94cNztoMW2BPDCmrIHwgurgp8JPHnUN6raXO0XE1VfiOe6ltkiaAngk4QvrgW3yM63TfcYXOWdulDLwJouNh/J/gf//nOvxy3TGetLzKO5tHkDIqtm1iEF6nscXGg4OD66zJWZ+uvtC4qqrkl1n59vgZXl17kEP55RixcZlyjKt0+3lSn0F/JYdwn5Y1UTp6Dkd3cicANSMfR5+QAoD+slsg51t0l97S5t+lSQHdUa75Nax/8ex2hPPedz5Fgd6J6HsOp2RfGsGOMxz9dj2De9/d4eF6K0mcRKuVVdVg0On4YPtx/pr2IyWVNYBKsm4XFZi5VMnmH7pdDDVnEXR2XqXx+h2uz/+iNknS+2K4eyn88Cl852zTN0z6B4QPPHexHpeefRMFkxe3/ZdRFHSDb4PNf+PXfmvoo54EO3D2ZkrCNNQtC1GKj7k+cpXuIGtW/wlGvd728QiPJouNt5/Kajuff5fDC6v3UVJZg4KDPkoe1+m+43PDMnx8alp1XlVvQrn9DRyb/g6hfdHdtQSOb4EjX+Mz6pFzB4bEnBt1q4Vrn3D+b/4+Z22TTwM1HzodeaEJBBeuQz2xA5DEqaNI4iSazWK14VBVlmw6yl/WHaS2kbc7Z/i1YRU3mjPoqZxu8Xl1t78Og8bBJWOhzyjnyLi+17Zx9M0w4iHY8U8urdnv3PYLgwE3Ot8bzCgz18Mr/dw+8ozxfUASJ29z/mLjtc13tYuNy4oGzedwqGSeKObxDzM5XuR8uPKnkhT9WnYbl8PFtF73HgG9rnL+HQ+7G8W/OxjM6IZOPndMn1HOlyfR6eD6/2v6OIDoBChcR/CZPe0bk3AjiZNo1NFCC+9tPcbb32S5yuKVQ8w3fOEaYdJcjoAodOWnqOk5AuPPl8HrV4N/d3SDJzoPUJRzNTxaCO4F16bCV2f7NSTNAcN5fUv8w2D2cfijhk+josPIYuNtr6yqhidXfMeaH3IBMGLjZt1W0k2vX1ySBJAwDSKHQsRQ6BYLgV1/mH7YoBHwHfSrPkhVjR0fo17rkLyCJE7CzelyK+9sPsrfvnL+g6HHTi+lgL8aP+Y2/eYWn09V9Cj9R8OAZHRD74Jd72Ac9lPwD4fHv3fOraQ3Nn2ijjLqMTD4QM/h0Gdk3f0+wfCzD+GDn7qK7A7Va6cm6MpksfGL92NeGTf+Jd21Hclptvo8cvFJ0uWT4Mr7IKiXc/kknXfO5RzaLwGAaOU0+06c5LK+8lDXESRx8nLVNgfvbT3GHz7fe7ZEpbeSz1LjUpL0uxv9bIN6Xw1X3AsxV6MY/dwnnbz2N+feGz1wFJnBBOf3d6jPJePcNi1VVoL8PPC7iIsii4233LfHz3DH67UPWCp36jZy1GfRxZ20XxJc82vnfcUT7xkaUnxDOK0LJ8xRSMGR7yRx6iCSOHkZVVX5/mQpE1/7xlXmRxWvGxcxQX8Ry0VMXgL2ahh8u3OkW1eeXVtRUG/+C8pq5/wtm/dlMy5hYBMfEqLryS2p4up5aQDocPCKcRFHfb5p4lNNuPNtZ42Sl9YitdRpv36ElRdSefJ7QIORgF5IEicvUFZVw12LtrA/17lqtw4HvzZ8wmOGT1t3wv5joM9PnJ25I4e2YaSdhzJ8OpxNnLb8+++MS/ibxhEJ0TEe/eBbPtudA6j82biIoz4bW3+y5Odg5COgl3+KWqs6dBCUb0dfeEDrULyG/NfaRW07cpopb251bQ9RjnDU53etP+HUVRA2EIKiu3ZtUnOd9xs8b3wH8L7Eadq0abzzzjt1yseOHcuaNWs0iEi0l7+n/cifvzxICGVk+jzE31rTYtZzONz3b2c/QdFmzNGXw3EIsRzWOhSvIYlTF/LXdT/yl3UHAWet0jLjS4zS723iUw247XUYNB78QtswQtHVjBs3jiVLlriVdeXJGL3J9ydLuOXv32CihoM+KTzS0mTp8T3azofkJcL6DoOtEGM7JiPrOogkTp2YqqqkLNlB+sECAKIp5KjPo607WfLzznmMjL5tGKH3qLE7MOq9r0+G2WyWCR+7mGdWfs97W48x27CMoz6fN+9DI2fBjb93jpIVHapbH2d3iR5KMfuzT3Bpvz4aR9T1SeLUCT3wzk7W7XPOWHyVsp+jPr9v+UlG/AKSn5VEqY2UlVsIDQ68+BOpKpy/TlVHMvpJM6yXUlWVvnP+C8AThuUc9VnV+Aeunw1Js+W/Fw+g+ARRoOtBd0c+hUcyQRKndieJUyeRXVTBtX9aD0CS7luO+rzSshOExMAvtzpn5RZt49bX4DPnUPTqyhJoi8SppgJeir7487TG0zkt/u/j888/JyAgwP00Tz/N008/3ZaRiXZUOzIugAq+93mg4QOfOgq+3TosLtF8p/370b0sn6qc74HbtA6ny5PEycOt+T6Xh/+VgR9VHPWZ0bIPz85ueJ0jcfGuvI/qVY9jUmzUVFVqHY0mRo8ezRtvvOFWFhoq/eI6i0VfH+aP/9vHUZ97Gj7ouZKOC0g0y9GSo7y15y1yynO4e9Dd9Ay9FMq2ysi6DiKJk4e6843NZBw7Q3/lJEd9nmzeh+5+FwbL00ZHqlZMmLBRY22jxMno56z50YLRr8Uf8ff3Z8CAAe0QjGhXG/8Mab/nYeDhhjp9S8LkMbJLs9lXtI9uPt34Nv9bFu1eRI3DudjxvqJ9vBFxLxyDbjKyrkNI4uRhPsk4wW9W7OYX+s/4xOfDpj/wbLH0M9CQFSMBwKfbD/GbQcMu/oSKIs2pov2lNdIv8tFMCO3bYaGIxu3I3cGDXz6IzWFzKx8VPYrNOZux1Fg40k3HFUCM7SjWGhtmo/zT3p7k1/UQ/951gtSPduPbVJPcgBvh3o87LjDRKLNqBQXu/vH/cDjuQOdla9ZZrVZyc3PdygwGA+Hh4RpFJJrjFeNDPFnzD/fC/mPg3n/Lg5gHcagO/rD1D9gcNiL9IzEoBvyN/ky9fCoT+03kj9v/yLL9y9jryOcOVSFUKefH7GMM7Ndf69C7NEmcNHb+aJY/Gt7kp4YN9R/4u3znUibCowQoVQD01hVQXFFFSIB3jVJcs2YNUVFRbmWDBg1i//79GkUkmmNh2fUs5HoAjv7xZo2jEQ3ZmrOVrJIs/I3+fHrrpwSY3AdiJEYlsmz/MnYV7ibXEEW0PYfCw5mSOLUz75t4xoM4HOeSpqM+P68/aZp7xtnXQJImj1dcqFHfJI0sXboUVVXrvCRp6jx+mST/wGpFVVX+tfdfJK9I5taVt/LV8a/qHPPB/g8AuH3A7XWSJoBh4c7uAUdKjpDj52xedY6sE+1JEicN9Xv6v/hTyVGfn9fdOXWVM2GShS49iqqqrD6ymlHLRjHjixnk6s9N+Gctl860onPI+F0yHz54NQ9e10/rULzWhwc+5OUdL5NXkUdWSRaPr3+cL45+4dqfa8kl/WQ6AFMGTan3HN39utPDrwcO1cGPYc6JaI2nZWRde5OmOi0851yr6WhDo1mkw7dHUVUVgBpHDb/b9Dv+l/U/wNlp86Wwbvwtv9C5v6pMsxiFaImwADNhAVKLrZXs0mz+kvEXAB4Y+gBFVUX8+8d/88ymZxgQMoD+If1ZeWglDtXB8Ijh9A1uuLP+5WGXk1+RT3aQc1SsjKxrf5I4dbTK4sb3yxBgj1JYWcj0NdM5Wnq03v3r/c8N4bdXSuIkhGicQ3XwzOZnqLRVkhiZyCNXPIKqqpwsO8m23G08+tWjvDP+Hf79478BmDRwUqPnGxI+hPXZ6zlhtgLONetqbHaMBln+pr1IO1BHUx31lw+6WZImD+NQHfxf+v81mDRdyGYtb9+AhBCd3uLvF5ORl4GvwZfnRz2PTtGh1+l5+bqXifaP5njZccZ+PJZTllOE+4ZzY58bGz3f4LDBAByx5lCj6glUKjl57FBHfBWvJTVOHc0vlNiqZQDOVcf/L07mTPFQ35z8hh25O5p9fEHRmXaMRgjRWamqytZTW1m2bxkbTmwA4InhT9ArsJfrmDDfMF674TWmfzGdEqvzITo1IRUfQ0N9OpxqE6djZcc5ZOzJZbbjFBzJJLb/oPb5MkISp45mtdld7x9IulSSJg/22eHPALj3snt5POFxVhxYwf6i/eRX5LPl1BbXcVt8zIysshL1/ZtYJz2IWarIhRBnnSw/yTObnnE9hOkUHQ8Pe5i7LrmrzrEDuw3k01s/Ze2xtQwMGUhiVGKT5w/1CSXKP4pTllNkBkVzWdFxrDnfA/V3KBcXz2ub6u644w66devG5MmT6+x79dVXufzyyxkyZAj/+te/2vS6+aVW1/snx8oTgVZsDhuv7HiF8Z+M53ff/I7S6lK3/VW2Kr7O/hqAW/rfgllv5t7B9/LCNS/w5k1vMv3y6a5jXwh3rs0WpztC3gWTQQohvNeBogPcs/oeduTuwEfvw88u/Rmf3vopv4j/BUoDA4C6+3XnnsvuaVbSVKu21ulQsHPgkYysa19emzg99thjvPvuu3XK9+zZw7Jly8jIyGDHjh289tprFBcXt9l1e4f6kTVvArvn3tTgH45of69nvs67e9/lRPkJVh1eReqGVOyOc7WB205to8peRZR/FINDB9f5/KNXPup6f9xodL0vLTjWvoELITqFwspCfpn2S05XneaSbpfw6W2f8vSIp+kX0vZTQNQmTtln59+VkXXty2sTp6SkJAIDA+uU79u3j5EjR+Lj44Ovry9xcXGsWbOmTa+tKArBfsamDxTtIteSy7t7nUnz1MFT8TX4su3UNj758RPXMV9lOyeju67XdfUmuAZd/a3cNeXSz0kIb1fjqOGJr58gvyKf2KBYloxb4tafqa25Eie1GIDetuPYbLZGPiEuhkcmTunp6UycOJHo6GgURWHlypV1jlm4cCGxsbH4+PgwYsQItm/f3ibXHjJkCBs2bKC4uJgzZ86wYcMGTp482SbnFp7h79/+HavdSkJEAk8Mf4LHrnwMgL/u+iunK09jc9hYf3w9QJMjWi5ksxS3dbhCiE7m1R2vkpGXgb/Rn7+O+StBpqB2vV5t4nSi6hSnMeGrVHPqmDTXtRePTJwsFgtxcXEsXLiw3v3Lly8nNTWVZ599ll27dhEXF8fYsWPJz893HRMfH8+QIUPqvHJyGl8WY/DgwTz66KOMGTOGSZMmcfXVV6PXS2ffruJA0QH+c/g/APwm4TcoisKUQVMY1G0QpdWl/GHrH/g2/1vOWM8QZAoiISKhWeetfbZzVBW3T+AeRFGURl/PPfec1iEKoZkl3y9h2X7nyOl518yjX3D7z85e20EcYKNfTwAKD3/b7tf1Vh45qm78+PGMHz++wf3z589n5syZTJ/u7KC7aNEiVq9ezeLFi5k9ezYAmZmZrb7+Qw89xEMPPQTAAw88wMCBAxs81mq1YrWe6/BdWlra4LFCW3aHnRe3vYiKyrjYcQztPhRwNru9cM0L/Ozzn5F2PI2042kAXN/r+gab5ABevvZlntr4FABWRcGgqtisle3/RTR26tQp1/vly5czd+5cDhw493QbEFB3TS0hvMG/f/w38zPmA86pBEbHjO6waw8OG8wpyym+Dwjl9oosrDk/dNi1vY1H1jg1prq6moyMDJKTk11lOp2O5ORktmzZ0sgnm6+25urAgQNs376dsWPHNnjsvHnzCA4Odr169+7dJjGItlViLeHZzc/ybf63+Bv9SU1Iddt/aeilPDjsQde2SWdy6wBen3F9x7neW8/2g3LUWBs6vMuIjIx0vYKDg1EUxa1MEifhjdYdW8fzW54HYPqQ6UwfMr2JT7Qt10SY/iYAjEXSVNdePLLGqTGFhYXY7XYiIiLcyiMiIlq0KntycjK7d+/GYrHQq1cvVqxYwciRIwG47bbbKCkpwd/fnyVLlmAwNPwzzZkzh9TUc/8Il5aWSvLkQRyqg3d/eJc3v3uTshrnkii/u/p3RAVE1Tn2wWEPEu4XzueHP+dnl/6MSP/IRs+tU849dzzdPYxFeQUUHthEVY0dH2PrmndVVaXSpk2tla/BV0Z6CtEKO3J38H/p/4dDdXDnwDv59ZW/7vAYXB3E9c77R6iMrGs3nS5xaivr1q1rcF9Laq7MZjNmsyyW6YlqHDU8lf4UXx77EnBOLvfUVU8xImpEvcfrdXruuuSueiema8omP19U4A79Jr75dhfXJF7VqpgrbZWMWFZ/fO1t28+34Wf0a/pAIYRLTnkOv97wa2ocNdzY50aeufoZTR5AahOnXHsR5YpCT9sJ7DXV6I2mDo+lq+t0TXXh4eHo9Xry8vLcyvPy8oiMbLyGQHiXP277I18e+xKjzsjckXNZccuKBpOmtlBx9mZpPLmt3a4hhPAsf//275RYS7g87HJeuuYl9DptBhOd30H8W5M/JsVG3tG9msTS1XW6GieTyURCQgJpaWncfvvtADgcDtLS0pg1a5a2wQmP8eWxL/no4EcoKPz5+j93SCdNi06Hv92OtdLS6nP4GnzZ9nNtEi9fg68m1xWis/rxzI+sPrIagGdGPtPkunLtrbaD+Fbf7lxrLed01m6iB8ZrGlNX5JGJU3l5OYcOnVvdOSsri8zMTEJDQ4mJiSE1NZWUlBSGDx9OYmIiCxYswGKxuEbZCe9WYi3hxa0vAvDA0Ac6bGSLRaeAHZTKolafQ1EUaS4TopNYmLkQFZUb+9zI5WGXax0Og8MGk3Y8jf1+AVDM2TXrRFvzyMRp586djB597h+72s7XKSkpLF26lClTplBQUMDcuXPJzc0lPj6eNWvW1OkwLrzTKzte4XTVafoG9+XhuIc77LoVZzuLG6pLOuyaQghtfF/4PWnH09ApOmbFe0ZrR20/p6Nm5/JRxtMHtQyny/LIxCkpKQlVVRs9ZtasWdI0J+rYkbuDVYdXoaDw+1G/x6TvuI6RlTpnHyddTeub6oQQnk9VVRZkLADgln63tMv6c61RmzjlU065ohBacaiJT4jW6HSdw4VoSLW9mt9v+T0Adw+6m/ge8R16/V9EdAfAYPOexGnatGltugi2EJ5uc85mZm+czbbcbZh0Jn4Z/0utQ3I5v4P4PrOJKFsOak2VxlF1PZI4iS7j1Z2vcrT0KGE+YU1OXtkeqnQ6SnUKCaVplFfVdPj1hRDtR1VV3sh8g4e+fIj/Zv0XgEevfJSeAT01jszdkPAhAGSYAjAoDvKPygzibc0jm+qEaKnPDn/GB/s/AOD5Uc+3+6KaDSnS6Qly2Nj0+TuMnfyAJjEIIdrO1lNb+eTgJxwrPca+on0A3NzvZu4ceCdXRbZuvrb2NDhsMF8e+5IMnyAoPc3pI5lEDGzempuieaTGSXR6+4v2u5rofhH3C67vfX2HXXtgN/d1DEv1zj+pwDyZy0k0Ljs7m6SkJAYPHsywYcNYsWKF2/477riDbt26MXnyZI0iFJn5mTz85cOsObqGfUX70Ct65o6cyx+v/aNHJk2Aa3TfIR/nfFLVp6TGqa1J4iQ6NUuNhV+v/zVWu5Vre17boaPoAN4b/57bdpnO+SdlV2S2XtE4g8HAggUL2Lt3L2vXruXxxx/HYjnXP+6xxx7j3Xff1TBC71Zjr+GZTc9gV+2Mih7FsyOf5eOJH7dqZYGOVNtBvFBfTYlOh+G0rFnX1qSpTnRq//juH5woP0G0fzTzrp3ntn5cR/A3+rttV52dPVwvUxKIJkRFRREV5ezIGxkZSXh4OEVFRfj7O/+bSkpKYsOGDRpG6L1UVWXe9nkcLT1KqE8or1z/imbN/y0VbA4mJjCG42XH+cFkom+FrFnX1qTGSXRauZZc3tvrrPH57dW/JdgcrHFEsDdyAgCm6jMt+pzD4WiPcDxKU1OMeJr09HQmTpxIdHQ0iqKwcuXKOscsXLiQ2NhYfHx8GDFiBNu3b2/VtTIyMrDb7bJAuIdY/P1iVhxcgYLCb0f8ttMkTbVqm+t+MJuIsOWiVnvPSN+OIDVOotP6cP+H2Bw2EiISuK7XdVqHA8DHyj5mAT41zatxMplM6HQ6cnJy6N69OyaTSZMFQtubqqoUFBSgKApGo1HrcJrFYrEQFxfHjBkzmDRpUp39y5cvJzU1lUWLFjFixAgWLFjA2LFjOXDgAD169AAgPj4em81W57Nr164lOjoagKKiIqZOncpbb73VqjitVitWq9W1XVpa2qrzCCdLjYW3v38bgDkj5nBT7E0aR9Ryl4dfzv+O/o9vzX7olFIKj/5A+CWJWofVZUjiJDqlKlsVH//4MQD3Db5P42jOKXKUs9dkxM/WvH+8dDodffv25dSpU+Tk5LRzdNpSFIVevXqh12uzCGpLjR8/nvHjxze4f/78+cycOdO11NOiRYtYvXo1ixcvZvbs2QBkZmY2eg2r1crtt9/O7NmzGTVqVKvinDdvHs8//3yrPivOKaoq4j+H/8OrO18FoE9QH6YMmqJxVK1T289pr9kMwOmsTEmc2pAkTqJT+ur4V5RYS4jyjyKpV5LW4bjJMxgYU30Mu0NFr2u69shkMhETE4PNZsNut3dAhNowGo2dJmlqSnV1NRkZGcyZM8dVptPpSE5OZsuWLc06h6qqTJs2jTFjxnDffa1P/ufMmeNalgqcNU7S5Ncy646t49cbfu1Wdvcld3d4n8m2MjhsMAoKpw0qhTod1hwZWdeWJHESndKqw6sAuG3Abeh1nvWP8emzUxKkf7KQ0Xc1b1mg2iasztKM5e0KCwux2+111seMiIhg//79zTrHpk2bWL58OcOGDXP1n3rvvfcYOnQoAMnJyezevRuLxUKvXr1YsWIFI0eOrHMes9mM+WzNgmg5u8PO3779m2v7hpgb6B/Sn59e+lMNo7o4/kZ/+gb35UjJEfaaTfQokpF1bUkSJ9HpnCo/xZYc51P9rf1u1TiaukrPTkkQvu9fgKynKOp3zTXXNDooYN26dR0Yjff639H/kVWSRaApkLV3riXAFKB1SG3i8rDLOVJyhB/MJi4tlZF1balz1kMKr3Wy/CQvbXsJFZURkSPoHeR5TRLZum4AqAapBeiqwsPD0ev15OXluZXn5eURGRmpUVSipRyqgze/exOAaZdP6zJJEzg7iAP8YDbTw5GPWiWDBtqKJE6i03jnh3cY/8l4NpzYgILCL+J/oXVI9crrfQUAITX5Gkci2ovJZCIhIYG0tDRXmcPhIC0trd7mNOFZDp45SOqGVOLejSOrJIsAYwA/v/TnWofVpmqnJNhjMqMCxdn7tA2oC5GmOtEp/PfIf12jXYZHDGfa5dNIiPDM9Ze+KfuWHIOeHjUFOOwOdHp5PumMysvLOXTokGs7KyuLzMxMQkNDiYmJITU1lZSUFIYPH05iYiILFizAYrG4RtkJz/X7Lb9nd8Fu1/akgZO6VG0TwKDQQegVPUUGyNPrKT36Pd0GjtA6rC5BEifhsSw1FuZumsumnE1YapwTuE0dPJUnr3pS48ia9qWfHymlZRQWniI8wrNWTxfNs3PnTkaPHu3arh25lpKSwtKlS5kyZQoFBQXMnTuX3Nxc4uPjWbNmTZ0O48JzVNRU8MPpH1xJk0lnIiEigelDul6y62vwpX9Ifw6eOcgPZhPhp5o3aEE0TRIn4bEWZCxg7bG1ru1b+99KakJqI5/wHOX4AmWcOXVEEqdOKikpqcnZzmfNmsWsWTIAoDP49MdPmbt5rmt7dO/R/G3M3xr5ROd3edjlrsRpdNGhpj8gmkUSJ+GRTpSd4OODzgku/3TdnxgRNYJQn1CNo2q+3LNr2JXlHQOu1TYYIbycqqq888M7bmW/Tvh1A0d3HUPCh/DpoU/ZazJx2+ksrcPpMiRxEh7pze/exKbaGBU9ivF9G5692ZP0DOiJXtFzvOw4p41+ANhOfa9xVEJ4twNFB7j787txqM6pH67scSVXR11N3+C+GkfW/mo7iH9vNtHDdhIcDtBJn8uLJb+g8DifH/mcTw99CsCDwx7UOJqmvXnjmwzrPoy/j/k704ZMA6DU19nR1FC4V8PIhPBuqqryxNdPuJKmSQMn8c74dzx2RG5bG9htIAadgRK9ntMGO2dOHdE6pC5BEifhUapsVby07SUAZg6d6bEj5843Mnok7094n4HdBrqaE0/qKwAIrjyhZWhCeK29p/cS/148R0uPAhBoCmTm0JnaBtXBTHoTl3S7BIAfTCbysqQGvC1I4iQ8SvqJdMqqy4j0j+RX8b/SOpwWC/MJA6DQXsJmXx/C7HlNfEII0dbe2/seUz6f4qppGhk1ks0/20yvwF4aR9bxapvr9ppNVOTIyLq2IImT8Bhrj67lN1//BoAJfSd43Bp0zXF+B/YVgQGEUE6VpUTDiITwLkdLjvKnHX9yK3sq8SmNotHeoG6DADhoMsHpHzWOpmuQzuFCc+uOreON3W9w8MxBV9mEvhM0jKj1egacm3rAevbPq/DEYXoNulKrkITwGrvydpGyJsW1Hdc9jqXjlmLQee8/dZeEOpvqDpqM+MnIujYhNU5CUxU1FTz9zdNuSdMdA+5gUOggDaNqPb1Oz8IbFgKQbTQBUJorC2wK0d7e3vO2W9I0sd9E3rrpLa9OmgAGhgwEIN9gwFB9XONougbv/i9KaC7teBqVtkoA3r7pbRKjEjWO6OLV1jrlGxQAKguOahiNEF3fxhMbWbBrgVvZI1c8gq/BV5uAPEiAKYAePhHkV+VRZCiFaguY/LUOq1OTGiehGVVVeW/vewD8Mu6XXSJpAojyjwKgQqdSolNQz8hTnhDtZXPOZn6Z9kvXtoLCd1O/IyogSsOoPMulYZcBzn5OZTkHNI6m85PESWhmS84W9hXtw8/gx08v/anW4bQZP6Ofq5P4EaORwDM/aByREF3T/Iz5PPTlQ67tngE9+fS2T1EURcOoPM/g8EsBOGAyciZbRtZdLEmcRIertFWyu2A3szfOBmBi/4l08+mmcVRtK657HAAb/XwJq5RJ54Roa18c/YIl3y9xbYf6hPKfO/5D/5D+GkblmWrncjpoMmLJkz6XF0v6OIkOZXfY+dnnP+Nwybk/3htibtAwovYxMnok67PXc9BkIlwtwFFdic4k/S2EaAsLMhbw9vdvu5V9dvtnGHVGjSLybLVTEhw2Gqk5LYnTxZIaJ9Ghvs3/1i1p8jf6E98jXruA2kntOlhHDc4b+ZlcGQYsRFv46MBHbknTZaGXsXvqboLNwRpG5dl6BfbCiAGrTsfpCqkBv1hS4yQ61Prs9QDc1Ocmbul3Cz38e3TJkS99AvsAcNKoxwacyTlCWMxgbYMSopN7fsvzfHzwY7eyJeOWoFOkDqAxOkVHT2MkR2tOkO/I1zqcTs9r/2vLzs4mKSmJwYMHM2zYMFasWNGsfaJ1fr/l9wx9Zyjv7n0XgHF9xzE6ZrRrOYCuJsI/ArPejE1ROGUwUJkvT3lCXIzZG2e7JU0KCtt+vg1/owytb46+Ic4O4qcMlWCv0Tiazs1rEyeDwcCCBQvYu3cva9eu5fHHH8disTS5T7RcUVVRnafEMb3HaBRNx9ApOnoH9gbgmNGAreiYxhEJ0TmpqkrqhlRWH1ntVp5xXwZ+Rj+Noup8LoscBsBRuR9dNK9NnKKiooiPjwcgMjKS8PBwioqKmtwnWsbusLN4z2JUVFfZU1c91SnXoWup2KBYwJk46UpPaBuMEJ3UL9N+yZfHvnQr+27qd9IRvIWG9nCOrDtiNFJy8mATR4vGeGzilJ6ezsSJE4mOjkZRFFauXFnnmIULFxIbG4uPjw8jRoxg+/btrbpWRkYGdrud3r17t2ifaJzdYefxDY/zzt53APjZpT9j3eR13Dv4Xo0j6xi1HcS/N5vxqzipcTRCdC4O1cGtK2/lm5PfuJXvnrpb5mlqhQHdnNM0ZBsNFJ+SSTAvhscmThaLhbi4OBYuXFjv/uXLl5Oamsqzzz7Lrl27iIuLY+zYseTnn+v4Fh8fz5AhQ+q8cnJyXMcUFRUxdepU3nzzzTrXaGyfaNqOvB1syN7g2v75pT8nwj9Cs3g6WkJEAgA/mEwEV+dqHI0Qncudn91JVon7aNRd9+6SjuCtFOEXgcmhw6YoHC+USXkvhseOqhs/fjzjx49vcP/8+fOZOXMm06dPB2DRokWsXr2axYsXM3u2c2LFzMzMRq9htVq5/fbbmT17NqNGjWr2vguPs1qtru3S0tKmvppX+Or4Vzy2/jHX9qNXPEpscKx2AWmgtsYp22ggyJEHdhvoPfZPTgiPYHfYiX8vvk75t/d96/UL9l4MRVEIV4PIoZgcy1Gtw+nUOmXqXl1dTUZGBsnJya4ynU5HcnIyW7ZsadY5VFVl2rRpjBkzhvvuu6/Z+y40b948goODXS9p0oP9RfvdkqbfJPyGmcNmahiRNiL9IzHpnCPr8g06qouluU6IxqiqWm/StCdljyRNbSDc6Fy/L9dWoHEknVunTJwKCwux2+1ERLg3+0RERJCb27wmkU2bNrF8+XJWrlxJfHw88fHx7Nmzp8l9F5ozZw4lJSWuV3Z29sV9uU4u/UQ6d/3nLreypN5J2gSjMZ2io09QDOAcyXImR2bsFaIxw94dVqdsT0r9917RcpGBAwDIUypAVZs4WjTEa1P4a665BofD0eJ9FzKbzZjN5rYMrVNbeWil2/b7E973uia688UGx/Jj8Y8cNRqJzssiYqjWEQnhmYa+U/ePQ5KmttWnexyU/IejRh1UFIF/mNYhdUqdssYpPDwcvV5PXl6eW3leXh6RkZEaRSVmb5ztNmx4ydglDOte9wnSm5w/JUF14VFNYxHCEzlUhyRNHWRopHPC4SyjAUexzOXUWp0ycTKZTCQkJJCWluYqczgcpKWlMXLkSA0j8052h53nNj/nNkHd+rvXMzxyuIZReYba2rajRiNqiczlJMT5VFUl7t24OuXf3vetBtF0ffFR/dGrUKXTcfTUd1qH02l5bFNdeXk5hw4dcm1nZWWRmZlJaGgoMTExpKamkpKSwvDhw0lMTGTBggVYLBbXKDvRcTbnbOaTHz9xbQ+PGE64b7iGEXmOmEBnH6cTBgOmEukcLkQtVVXr7dP03dTvZJ6mdtLNz5fwGgN5Jhv7c7+nn9YBdVIemzjt3LmT0aNHu7ZTU1MBSElJYenSpUyZMoWCggLmzp1Lbm4u8fHxrFmzpk6HcdG+TpSd4Jdpv3Rt+xn8+MeN/9AwIs/SK7AXALkGPeaqUxpHI4RnaChpkua59hfs8CePEo6XSFNda3ls4pSUlITaRK//WbNmMWvWrA6KSFzIarcy/t/uc229nvw6Jr1Jo4g8T5hPGCbFRDXVVKmFzpEs8jQtvJjNYeOK966oUy5JU8cIIhQo4VRVfpPHivp1yj5OQntl1WUM/5d7H6a0u9Jcs2ULJ0VRiPTrCUCu0eEcySKEl5KkSXuBtXM52WWy5taSxEm0ylPpT7ltLx67mB5+PTSKxrP1DXH2JDhmNGI9fVTbYITQiKqqkjR5gG5+zjXrcpVqjSPpvCRxEi323Obn2Hhyo2v7jgF3cFXkVRpG5NkGdIsFnFMSlJzKavxgIbogh+qQPk0eIrzbEABOGUCtqdI4ms5JEifRIttPbXcbQTem9xh+/5PfaxiR56tds+6o0YilQBIn4V1sDlu9Uw5I0qSN3j0Go1NVKnU6Cgu+1zqcTkkSJ9FsR4qPcP/a+93K5o6cq1E0nUefoD6Ac9I5W9FxjaMRouPYHXZpnvMwUcGBdLc53x/P261tMJ2UJE6iWWrsNdy26ja3shUTVxDmK1P2N6W2xinfYKCiTOZyEt6h2l7d4IK9Qjs9gnzoVmMEILvooMbRdE6SOIkm2R12rvzXlW5ln9/xOZeGXqpRRJ1LsDkYf3wBKKjJa+Jo4S2ys7NJSkpi8ODBDBs2jBUrVrjtj42NZdiwYcTHx7vNadcZVNRUkPCvuiNsJWnSXvdAM341zvvR0RKpAW8Nj53HSXiOR756xG37tyN+62p+Es0TYejBEdsx8h3FWociPITBYGDBggXEx8eTm5tLQkICEyZMwN/f33XM5s2bCQgI0DDKlrPUWLh62dV1yiVp8gwBZgMmWxBQxomKAq3D6ZSkxkk06m+7/uY2gm5U9Ch+eulPNYyocwr3dc7ldEZX4ZwEU3i9qKgo4uPjAYiMjCQ8PJyios49z1dBRUGdpMmgM0jS5GHMirOLRb6tTONIOidJnESDjpYc5a09b7mVvXbDaxpF07lFBjn7ORUYAKvcrDqD9PR0Jk6cSHR0NIqisHLlyjrHLFy4kNjYWHx8fBgxYgTbt29v1bUyMjKw2+307t3bVaYoCtdffz1XXXUV77//fmu/RofJs+QxZsUYtzKdopMFez2Qz9lJMPMdMh1Ba0hTnahXYWUhE1dOdCvbPXU3OkVy7dboE9oXTkKOQQ9lueATpHVIogkWi4W4uDhmzJjBpEmT6uxfvnw5qampLFq0iBEjRrBgwQLGjh3LgQMH6NHDORlsfHw8NputzmfXrl1LdHQ0AEVFRUydOpW33nJ/SPnmm2/o2bMnp06dIjk5maFDhzJsWN25kDxBdlk2E/49wa3szoF38tyo57QJSDTK1xwLQIHOjqqqsqhyC0niJOqwO+yM/si9M+qnt34qSdNFGBgaA0COwUB18UlM3S/ROCLRlPHjxzN+/PgG98+fP5+ZM2cyffp0ABYtWsTq1atZvHgxs2fPBiAzM7PRa1itVm6//XZmz57NqFGj3Pb17Ols3o2KimLChAns2rWr3sTJarVitVpd26WlHbuUxomyE3WSpsevfJz7h97fwCeE1nwC+qNYVaoVhaLK04T5hWsdUqci/xKKOi4cQvzoFY8yoNsAbYLpIgaE9gLglN5AaUG2xtGIi1VdXU1GRgbJycmuMp1OR3JyMlu2bGnWOVRVZdq0aYwZM4b77rvPbZ/FYqGszNmkW15ezldffcXll19e73nmzZtHcHCw63V+c197O1l+ss5C37MTZ0vS5OF8Q3oTZncAkCtTErSYJE7CTeqGVLftUdGjmDlspkbRdB2RAZEoKlTrFHJPH9Y6HHGRCgsLsdvtREREuJVHRESQm5vbrHNs2rSJ5cuXs3LlSuLj44mPj2fPHmcn6ry8PK655hri4uK4+uqrmTp1KlddVf+yRnPmzKGkpMT1ys7umMT80x8/Zdwn49zKXrrmJe657J4Oub5ovZBAf8JtzkEqkji1nDTVCZcvj33Jl8e+dCv7+5i/axRN12LUGQl0mCjVV5NTcowhWgckNHfNNdfgcDjq3devXz92727erM5msxmz2dyWoTXpP4f/w9zN7qsGvDf+PeJ7xHdoHKJ1wgJMBNn0AOQWyzJQLSU1TgJw9lO4sLZp0882YdKbNIqo6wlSnfPx5Fc2r0ZCeK7w8HD0ej15ee4Tmubl5REZGalRVB1j+f7lPP3N025lq25bJUlTJxLqb8Lf5ky288plNYOWksRJUGmrrNNPYeVtKwkyycivthSk6wZAYU3nnqtHgMlkIiEhgbS0NFeZw+EgLS2NkSNHahhZ+3pp20u8sO0Ft7Iv7vyCfiH9NIpItEaovwmdzTnR6unKQo2j6XykqU6Q+H6i2/a749+lf0h/jaLpukJMkWA7TKFq0ToU0Qzl5eUcOnTItZ2VlUVmZiahoaHExMSQmppKSkoKw4cPJzExkQULFmCxWFyj7Lqa333zO1YdXuVWtuu+XRh1Ro0iEq0V6m/Cbg8AzlBU3bGjMLsCSZy83PXLr3fbjgmM4YoedVczFxevm38slGyiUFftnD1c5k7xaDt37nRbIy411dmUnZKSwtKlS5kyZQoFBQXMnTuX3Nxc4uPjWbNmTZ0O413BnI1z+PzI525lu+6VpKmzCvU3YbcFAnC6Rh7kWkoSJy/2wtYXKKpybzZaPWm1RtF0fT26DYASKNDroKoEfEO0Dkk0IikpCbWJ5XFmzZrFrFmzOigibfxmw29Ye2ytW5lMhtu5mQ16wNl14IyjWttgOiH5L99L7czdyfIDy93Ktv18m0bReIeYbs6FkXNrZw8XwsPN+GJGnaTpu6nfSdLUBRj03QE4g63JBwThTv7r90KnK08z/Qv3fhgb7t6An9FPo4i8Q+0kmKV6PRXFR7UNRogmvJ75Ojtyd7iV7UnZI8tzdBFGs3P0p1VxDhASzSeJk5dxqA6SPkpyK/tH8j8I8w3TJiAv0iskFJ+z0/bkFP6obTBCNOLr7K95Y/cbbmV7UvZoFI1oDyb/SHzOziN2uuq0xtF0LpI4eZm4d+PctsfFjmNUz1ENHC3aUoivkcAaZ2fa42eOaByNEPV7I/MNZn3l3m9LkqauxxgQTsjZxKm4QqYkaAlJnLzITz74SZ2yV65/RYNIvJNBr8PP7gtATplMOic8z4qDK3h99+uu7e6+3SVp6qL8gsIIOJs4Wcqlz2VLSOLkJT468BGlF8zXITfEjuerOocA58ukc8LD7D29l99v+b1b2Vd3f6VRNKK9dQvwxexw9lezWPI1jqZzkcTJC+RacvnD1j+4le28d6dG0Xg3sxIOQIFNJp0TnqOipoIpn09xK5MHq64t1N+EyeFcr84iD3ItIolTF1dtr+bGj290K1t520rM+o5dFFQ4+RidI1kKVBnFIjzHiGUj3LYlaer6wgJMGB3OFKDcWqJxNJ2LJE5dmKqqJPwrwa1sVvwsWU5FQwE+vQEoUBwaRyKE08EzB922JWnyDt38ztU4VVSXaRxN5yKJUxc27N1hdcoeintIg0hEreBA52KoeQYd1Eitk9DenZ/d6Xq/4e4N2gUiOlSYvxm9w7l4SHl1ucbRdC6SOHVREz+dWKfsu6nfaRCJOF9EkDNxsuh0lJVkaxyN8HZ/3P5H1/vhEcNlPjcvEhpgQjmbOL1dsJW/7fqbxhF1HpI4dUF7CvZwtPSoW9mu+3bJjL8eICIomEC7c3mD3KKDTRwtRPt6f9/7rvdv3vSmhpGIjuZv0gMm1/Zbe96ioKJAu4A6Ea9MnLKzs0lKSmLw4MEMGzaMFStWuO2PjY1l2LBhxMfHu62O3hmcqTrDz//7c7ey9Xevl1XMPUSov4lQm/N9XukxbYMRXs2huvezk3uEd1EUBZ3O5Fb21XGZfqI5DFoHoAWDwcCCBQuIj48nNzeXhIQEJkyYgL+/v+uYzZs3ExAQoGGULWd32Llu+XVuZf+48R+E+4ZrFJG4UKi/iSCbAcx2cstOaB2O8GJ///bvrvcZ92ZoGInQik7nPrp608ntTLl0SgNHi1ptljjV1NSQm5tLRUUF3bt3JzQ0tK1O3eaioqKIiooCIDIykvDwcIqKitwSp84o/r14t+3BYYMZFS3LqXiSUH8TZrsJqKRIljkQGvrnnn+63pv0pkaOFF2VonevZdyaswNVVaVbRxMuqqmurKyMN954g+uvv56goCBiY2O57LLL6N69O3369GHmzJns2LGj6RNdID09nYkTJxIdHY2iKKxcubLOMQsXLiQ2NhYfHx9GjBjB9u3bW/UdMjIysNvt9O7d21WmKArXX389V111Fe+//34jn/YcQ98ZWqds+S3LNYhENCbYz4je5gPA6UpZWFMIoR2dQe+2Xek4Q36FzCLelFYnTvPnzyc2NpYlS5aQnJzMypUryczM5ODBg2zZsoVnn30Wm83GTTfdxLhx4/jxx+avBm+xWIiLi2PhwoX17l++fDmpqak8++yz7Nq1i7i4OMaOHUt+/rn/w+Pj4xkyZEidV05OjuuYoqIipk6dyptvuneK/Oabb8jIyOCzzz7jpZde4rvvPHs02oUz/oLMxeKpAkwGsDtrNgutMnu40N6t/W/VOgShkfMTpwHV1QB8fTRTo2g6j1Y31e3YsYP09HQuv/zyevcnJiYyY8YMFi1axJIlS9i4cSMDBw5s1rnHjx/P+PHjG9w/f/58Zs6cyfTp0wFYtGgRq1evZvHixcyePRuAzMzMRq9htVq5/fbbmT17NqNGuTdn9ezZE3A26U2YMIFdu3YxbFjdOZFqz2O1Wl3bpaUd+4/hgaID7D29160s877MDo1BNJ9Op6A7u17dGZtF42iEtzp/9NRvR/xWw0iEls6vcLq0uoZDJhPpxzK5+/Kx2gXVCbS6xumDDz5oMGk6n9ls5uGHH2bGjBmtvZSb6upqMjIySE5OdpXpdDqSk5PZsmVLs86hqirTpk1jzJgx3HfffW77LBYLZWXOWVTLy8v56quvGv2e8+bNIzg42PU6v8mvvVlqLEz+z2S3sm0/34Zep2/gE8IT6BRn/79ih7WJI4VoH/O2z3O99zP6aRiJ0JIDu+v9pVZnjdPBon1ahdNpdLrpCAoLC7Hb7URERLiVR0REkJub26xzbNq0ieXLl7Ny5Uri4+OJj49nzx5n01ZeXh7XXHMNcXFxXH311UydOpWrrrqqwXPNmTOHkpIS1ys7u+MmNbx62dVu26+NeU1ugp2ATucc5XgGm8aRCG+1IXuD1iEID6Cqqut9P9UXgOLq5ner8VataqqrrKykqKjI1aRV64cffmhWLZTWrrnmGhyO+tcK69evH7t37272ucxmM2Zzxy+Ye2Fn8LsuuYvre1/f4XGIllPOLvRbrDhkBIvQRI2jRusQhAdQOJc4Deg+FNQfqdSXUmgpI9w/UMPIPFuLa5w+/vhjBg4cyM0338ywYcPYtm2ba9+FzV7tITw8HL1eT15enlt5Xl4ekZGR7X59T1DfCLq5I+dqEIloDYOP84HDpiiUVUsHcSGENpTzapwi+4wk2O5sukvPkua6xrQ4cXrhhRfIyMggMzOTJUuWcP/997Ns2TLAvdqvvZhMJhISEkhLS3OVORwO0tLSGDlyZLtfX2vPbX6uTpmMoOtc9L498D9b41lUltPE0UK0vVAfZz+7KYNkskNvdn5dt9L7KvrVOGsiM07t1yagTqLFTXU1NTWu/kUJCQmkp6dzxx13cOjQoTZrcigvL+fQoUOu7aysLDIzMwkNDSUmJobU1FRSUlIYPnw4iYmJLFiwAIvF4hpl11XtO72PT378xK1MkqbOx+wbSLcqBxadjjOl2cSGX6Z1SMLLxAbFUlRVxFWRDfffFF2fcv6yO1Hx9K2x8a0PHCmQGqfGtDhx6tGjB999951reH5oaChffvklKSkpbTbf0c6dO93WiEtNTQUgJSWFpUuXMmXKFAoKCpg7dy65ubnEx8ezZs2aOh3Gu5JKWyV3f363W9l3Uz17filRvyBfI0GFgBGKyk5qHY7wQv931f+RW5HLkLAhWociPIVvCL1U5+S8ZyoOaByMZ2tx4vSHP/yhToJiMpn44IMPmDVrVpsElZSU1GSz36xZs9rsep5OVVUS3090K1s3eZ10Ku6kAswG/O3OVvIiS/NGggrRli4Pv5zL8fyBPKKdXfDPbG//3sApytVTMnClES1OnF5//XWOHDnClVdeyU033cQNN9xAYKCz9/1PfvKTNg9QwLB33SfffP2G14nw77q1a11doI8BP7sBcHCmUtarE0JoxT1zujRyGBScotxg4VRpBdHBnXv91vbS4sRp2bJlqKpKRkYGa9eu5e9//zuqqjJ69GhuuukmEhMTJUttQxeOoLss9DKu7XWtRtGIthDoY8RkNwFVFMl6dUIIjVw4KU/vXomY8tZQrYOdJ45wa3DdEdyilRNgKorC8OHDefrpp0lLS+Ozzz4jLi6Od999lxEjRrR1jF7rg/0f1Cn7aOJHGkQi2lKgjwGD3Tn3V5G1RONohBDCSR85lJ4258S8e3IPaxyN52qTmcMDAgK49dZbmTp1Ktu3b2+LU3o9m8PGS9teciuTEXRdQ4CPAWzOWXrLZL06IYSnCBtAT5tzLqcTBTL4qCFtuuTKXXfd1Zan82pXvHeF27YkTV1HkI+RGoczcbLYKjWORgghztIbicQ5sq64/FATB3uvFvdxuvvuu+stV1WVoqKiiw5I1O3XtHtq85eAEZ4vxM9IjcPZ6bJcFvoVQniQSHN3oIBym0zO25AWJ07r1q3jvffeIyAgwK1cVVXS09PbLDBvNW3NNLftXfftQqd0urWYRSNC/U1YHc6/n3JZM0wIoZH6Jv2JCe4D5QVU6Iqx2R0Y9PLvz4VanDglJSURGBjIddddV2df7aSYonWOFB8hIy/Dtf3e+Pcw6owaRiTag69RT40aDECFatc4GiGEOGdAxBAo30mp0cqJMxXEhgc0/SEv0+JU8t///ne9SRPAl19+edEBeasaew23rbrNtX1Z6GXE94jXLiDRbhRFQW8MA6ActUPWeBRCiLrq3nt6R10JQJUO9uSe6uiAOoWLroPLzZWZj9vClf+60m1bph3o2oxm5yKrdgWsdunn5I2ys7NJSkpi8ODBDBs2jBUrVrj2vfrqq1x++eUMGTKEf/3rXxpGKbyNT8Tl9Dg7JcEPObJmXX0uOnG66aab2iIOr/bbb37rti0j6Lq+AN9Q1/vymnINIxFaMRgMLFiwgL1797J27Voef/xxLBYLe/bsYdmyZWRkZLBjxw5ee+01iouLtQ5XdEEXToAJgH93etqcNVH5p2VgUn0uOnGSZoaLo6oqnx3+zLX98rUvaxiN6ChBQcGYHc7bVrW9WuNohBaioqKIj48HIDIykvDwcIqKiti3bx8jR47Ex8cHX19f4uLiWLNmjbbBii6p3jU+FIUInNOllJT/2KHxdBYXnTjJ8ioX5087/uS2PaHfBI0iER0pJDgY09lnjuoamcvJE6WnpzNx4kSio6NRFIWVK1fWOWbhwoXExsbi4+PDiBEjWj0BcEZGBna7nd69ezNkyBA2bNhAcXExZ86cYcOGDZw8efIiv40QzdfD5OyDWWHL0zgSz9TiUXWibf1r37n+C99NlZlavUVoSAimPGfmZJVlVzySxWIhLi6OGTNmMGnSpDr7ly9fTmpqKosWLWLEiBEsWLCAsWPHcuDAAXr06AFAfHw8trP9Rc63du1aoqOjASgqKmLq1Km89dZbAAwePJhHH32UMWPGEBwczNVXX41er2/Hbyq8VUPtRVEBUVCRRwVyb6qPJE4aWvL9Etf7GUNmSO2dF+keEoTpbDN3jbVM42hEfcaPH8/48eMb3D9//nxmzpzJ9OnTAVi0aBGrV69m8eLFzJ49G4DMzMxGr2G1Wrn99tuZPXs2o0aNcpU/9NBDPPTQQwA88MADDBw4sNFzWK3nBhiUlpY2+d2EABighgDH6pT3CR8AxzOxGCopqawh2FemxTnfRTfVyZNQ683PmO96//iVj2sXiOhwkcG+GM4+7j23688cKT6ibUCiRaqrq8nIyCA5OdlVptPpSE5OZsuWLc06h6qqTJs2jTFjxnDfffe57cvPzwfgwIEDbN++nbFjxzZ4nnnz5hEcHOx69e7duxXfSHijIY5QFubm879s96bgmB6XAVBssJNdJOtpXuiiE6dvv/22LeLwOhd2qpfaJu8SFmCitmvmgdIsHt/wuAy06EQKCwux2+1ERES4lUdERDR7ipZNmzaxfPlyVq5cSXx8PPHx8ezZ4xxRe9tttzF48GDuvfdelixZgsHQcOPAnDlzKCkpcb2ys7Nb/8WEV1FQuK6yil4294l4I3vEAWDVKRzIlymHLiRNdRo5Xnbc9X5+0vxGjhRdUYDZQIHh3HNLVkkW2WXZxATFaBiV6EjXXHMNDke9A8KbXWsFYDabMZvNbRWW8CJFvvXfb8yh/Qiz2Tlt0HPs1HdwxaUdHJlna5NFaMaMGcPzzz9fp/zMmTOMGTOmLS7R5by681XX+xv73KhhJEILfiYDVTr3Wsa9p/dqFI1oqfDwcPR6PXl57qOO8vLyiIyM1CgqIVpmb/g4Xqm5m7utz7jv0Bvp4XDenwqLZBLMC7VJ4rRhwwZee+01br/9diyWc+2h1dXVfP31121xiS5nQ/YGrUMQGjIZ6v7pbTshN6jOwmQykZCQQFpamqvM4XCQlpbGyJEjNYxMiOYb2juUhfbb2a5eVmdfuOKcy6m0Iqujw/J4bbbs8bp168jNzeXqq6/m6NGjbXXaLi/cN1zrEISH2J13QOsQxHnKy8vJzMx0jYzLysoiMzOT48edzeypqam89dZbvPPOO+zbt49f/OIXWCwW1yg7ITzd2Msj+fNdcaz9dd31Z7sbQwCw1Egfpwu1WR+nqKgovv76a6ZPn85VV13FihUruOyyulmsgMLKQtf7V657RcNIhCcpsNQdFiy0s3PnTkaPHu3aTk1NBSAlJYWlS5cyZcoUCgoKmDt3Lrm5ucTHx7NmzZo6HcaF8FSKonBnQq9690X5R4Elj0qKOzaoTqBNEqfaEWFms5lly5bxwgsvMG7cOJ566qm2OH2X8+H+D13vEyISNIxEeJJyRy6qqsoISw+RlJTU5EjHWbNmMWvWrA6KSIiO0yesP1gyqTBUUm61EWCWsWS12uSXuPDm8rvf/Y7LLruMlJSUtjh9l2PUnZtMTP6RFACKqmLT2ci3FBIR0F3rcIQQXi6m+yA4DiUGO7klVQzoEaB1SB6jTfo4ZWVlER7u3lfnzjvvZOvWrSxevLgtLtGl7MjboXUIwsNEnZ1HZfvJgxpHIoQQEBV+OQBFBoXsIll65XwXVeNUO7V/t27dKC8vr7M/JiaGmBiZl+ZC205t0zoE4WFibDXkGA18e+pHJg76idbhCCG8XLewQZgcKtU6heO5e+HSnlqH5DEuKnEKCQlptKmptr+G3W5v8BghvJ1OVelTY2OrL/xYeFjrcIQQAsVoJtyhkqNTyD99AJD5BmtdVOK0fv1613tVVZkwYQL//Oc/6dlTMtPmuOuSu7QOQXgAHdDT5nxfUP6jprEIIUStbqqBHBwUl8pcTue7qMTp+uuvd9vW6/VcffXV9OvX76KC8hYOtf7lFoR3UYEoUw+gknJbjtbhCCEEAN0UP6AcS9XJJo/1Jm02AaZonvNHICb3SW7kSOEt7IpCbDfnw4ZFX8LpcqvGEQkhBISZggGosJ/WOBLPIolTB6uyV7neX9HjCg0jEZ6kf3Q8RlXFpnPwn717tA5HCCGI8HdO5mpVSjWOxLO0eeIk8xI1zlJzbi0/X4OvhpEIT6GoKsbul3JJdTUAO3MkcRJCaK9niHNUfIWuispqGeRV66L6OE2aNMltu6qqiocffhh/f3+38n//+98Xc5k2l52dzX333Ud+fj4Gg4FnnnmGu+4611H7L3/5C//85z9RVZXk5GT++te/tllCGGwO5uOJH1Nhq0CnSIWfOCtqGJdW1/CD2Ux2yX6toxFCCHqG9oNssBhsnCqppF93mQQTLjJxCg4Odtu+9957LyqYjmIwGFiwYAHx8fHk5uaSkJDAhAkT8Pf3p6CggNdee40ffvgBo9HIddddx9atW9tsxXOjzsig0EFtci7RhYT2I0znvCnprDIJphBCez3CLgWgyAC5xRWSOJ11UYnTkiVL2iqODhUVFUVUVBQAkZGRhIeHU1RU5Kops9lsVFU5+yLV1NTQo0cPzWIV3iMkoD+oh6lRC7QORQgh6NF9MAAWnY7c3MMwUP4tBA/tHJ6ens7EiROJjo5GURRWrlxZ55iFCxcSGxuLj48PI0aMYPv27a26VkZGBna7nd69ewPQvXt3nnjiCWJiYoiOjiY5OZn+/ftfzNcRolnCg5z9Cap0FRpHIoQQ4O8TjK/DORK88PRejaPxHK1OnI4fP96i40+ebP48EBaLhbi4OBYuXFjv/uXLl5Oamsqzzz7Lrl27iIuLY+zYseTn57uOiY+PZ8iQIXVeOTnn5skpKipi6tSpvPnmm66yM2fO8Pnnn3P06FFOnjzJ5s2bSU9Pb9F3FaI1Qrv1AcCqs2F3qE0cLYQQ7S/M4UwTzpQe1TYQD9LqxOmqq67ioYceYseOhhesLSkp4a233mLIkCF88sknzT73+PHjeeGFF7jjjjvq3T9//nxmzpzJ9OnTGTx4MIsWLcLPz89tQeHMzEy+//77Oq/o6GgArFYrt99+O7Nnz2bUqFGuz61bt44BAwYQGhqKr68vN998M1u3bm0wVqvVSmlpqdtLiNaICHXWelboHJRU1mgcjRBCQChmAMpkEkyXVvdx2rt3Ly+++CI33ngjPj4+JCQkEB0djY+PD2fOnGHv3r388MMPXHnllfzpT39iwoQJbRJwdXU1GRkZzJkzx1Wm0+lITk5my5YtzTqHqqpMmzaNMWPGcN9997nt6927N5s3b6aqqgqj0ciGDRt48MEHGzzXvHnzeP7551v3ZYQAasdrdgtxJk7VOoX8snJC/UO1C0oIIYBu+gCgioqaQq1D8RitrnEKCwtj/vz5nDp1itdee42BAwdSWFjIjz8619q65557yMjIYMuWLW2WNAEUFhZit9uJiIhwK4+IiCA3N7dZ59i0aRPLly9n5cqVxMfHEx8fz549zrlzrr76aiZMmMAVV1zBsGHD6N+/P7feemuD55ozZw4lJSWuV3Z2duu/nPBKtY1ygUG9Uc7OLH+yRG5SQgjthZu6AVChFmsbiAe5qFF1AL6+vkyePJnJkye3RTwd4pprrsHhaHiduBdffJEXX3yxWecym82Yzea2Ck14MZ1/dwIcKmV6hfwzJ4BLtA5JCOHlevj3gOIfqVQsTR/sJTxyVF1jwsPD0ev15OXluZXn5eURGRmpUVRCtJ5ralWDmcCzncLPFLds8IUQQrSHyJCeAFTpq6mqkdnDoRMmTiaTiYSEBNLS0lxlDoeDtLS0NpukUgitBKjOP8my8lMaRyKEEBDVLRYAi95OQZksQA5t0FTXHsrLyzl06JBrOysri8zMTEJDQ4mJiSE1NZWUlBSGDx9OYmIiCxYswGKxMH36dA2jFuLi+WMA7JRX5jV5rBBCtLewbv0AKNFDfkkFvUP9NI5Iex6ZOO3cuZPRo0e7tlNTUwFISUlh6dKlTJkyhYKCAubOnUtubi7x8fGsWbOmTodxITqbAMxABZXVp7UORQghCAsdCECJTkdR4QnoG65xRNprs8SppqaG3NxcKioq6N69O6GhrR9KnZSUhKo2PgHgrFmzmDVrVquvIYQn8tf7ARVU2Uq0DkUIIQjxDUOnqjgUhYKCg0C81iFp7qL6OJWVlfHGG29w/fXXExQURGxsLJdddhndu3enT58+zJw5s9EJMoUQ7kJMQQCUV5dSbWt45KcQQnQEvU5PkMM5hOVMyVFtg/EQrU6c5s+fT2xsLEuWLCE5OZmVK1eSmZnJwYMH2bJlC88++yw2m42bbrqJcePGueZ3EkI0LDq4OwDVSiV7ThZrG4wQQgAhGAEos5zQOBLP0Oqmuq1bt7JhwwaGDh1a7/7ExERmzJjBokWLWLJkCRs3bmTgwIGtDlQIbxAa0AOKwGKs5HCBhYQ+Mnu4EEJbQYoPUENFdX6Tx3qDVtc4rVy5kh49egAwbdo0KirqX9HdbDbz8MMPM2PGjNZeSoguTTnv/dDYGwA44qPy/anvtQlICCHO080QCECVvUjjSDxDqxOn6OhoMjMzAXjvvfcoLy9vq5iE8Fr9YsfQv8bZt+lM/gZtgxFCCKCbj3PZFasqi9jDRSROv/nNb5g4cSLXXnstAO+//z7bt2+nsrKyzYITwusoCn11zqe7MssRjYMRQgjo7u+c6seqq2pyxLs3aHXi9Mgjj7Bz507GjRuHqqosXLiQUaNGERQUxGWXXcZPf/pT/vjHP/K///2vLeMVosuL9Hc2gdsdBdTYZWSdEEJbkUFRAFTqa7BUy7IrFzUdwbBhw/jtb39L//792bp1K2VlZXzzzTc8/vjjdOvWjVWrVnH33Xe3VaxCeIWo4N4AKIYyTpdXaxyNEMLbRXaLAaBM76BI7kltMwHm+VMNjBgxghEjRri2pVpPiJbpEToA8tKxGqoot9YAPlqHJITwYmFBfQDnsiuny8qJCfPuZVfafZFfRVGaPkgI4RLR3TnFR6nBIX0GhRCaCwvpC0CRXk9pYa7G0Wiv1YnT8ePHW3T8yZMnW3spIbxK97BBAOTr9dSckQnnhBDaCvVzrk9nUxSKzsiglVYnTldddRUPPfRQo0uqlJSU8NZbbzFkyBA++eST1l5KCK/S4+wIlmqdQrGlQONohBDezqQ34Xd2nEpxSba2wXiAVvdx2rt3Ly+++CI33ngjPj4+JCQkEB0djY+PD2fOnGHv3r388MMPXHnllfzpT39iwoQJbRm3EF2GA/fmbJPeRJBdpVSvUGg5pVFUQghxToCqowIHZZYcrUPRXKtrnMLCwpg/fz6nTp3itddeY+DAgRQWFro6it9zzz1kZGSwZcsWSZqEaISjnj/DkLOLapZVF3Z0OKKDFBcXM3z4cOLj4xkyZAhvvfVWs/YJoYVATABUVsmyKxc9qs7X15fJkyczefLktohHCK9T3/gJo6oAKtU1lg6PR3SMwMBA0tPT8fPzw2KxMGTIECZNmkRYWFij+4TQQqDOB6ii0ibLrrTJdAQ7duxg9uzZFBQUMGDAAOLj412vmJiYtriEEF2Wvp7MyYAOsGO31b8GpOj89Ho9fn7OYd1WqxVVVV3TtzS2TwgtBBkCwF6M1S7LrjS7qe7hhx9m48aN9e6777770Ov1PPjgg/Tt25evv/6a6dOnExsbK09IQjRBoZ7ESXX+adbYrR0djjgrPT2diRMnEh0djaIorFy5ss4xCxcuJDY2Fh8fH0aMGMH27dtbdI3i4mLi4uLo1asXTz75JOHh4c3aJ0RHCzYHA1CN1II3u8Zp+PDhTJ06laysrDr7srOzWb16Nf3793crP3bsmGshYCFE/Yx6Y50yw9lnmhqHzNKrFYvFQlxcHDNmzGDSpEl19i9fvpzU1FQWLVrEiBEjWLBgAWPHjuXAgQP06OFcNic+Ph6bzVbns2vXriU6OpqQkBB2795NXl4ekyZNYvLkyUREOEdVNrZPiI4W6hcOFVCjVGkdiuaanTht27aNe+65p959P/nJTzhx4kSdxKlPnz706dPn4iIUootaMHoBf9z+R16+9uU6+2oTJ5skTpoZP34848ePb3D//PnzmTlzJtOnTwdg0aJFrF69msWLFzN79myAZj84RkREEBcXx8aNG+v0F21sHzib8qzWczWTpaXSlCLaXvfACCiEKl01ldV2fE16rUPSTLOb6jZv3swDDzzg2p40aRLPPfccn376KQ8//DB/+MMfOHPmTLsEKURXdEPMDXw5+UuujLiyzr5zNU51ayuE9qqrq8nIyCA5OdlVptPpSE5OZsuWLc06R15eHmVlZYBzzrv09HQGDRrU5L4LzZs3j+DgYNerd+/eF/PVhKhX9+CeAFTp7Zy2eHcXgmbXOP3xj3/kt7/9Le+//z4A/fv3Z9OmTbz++usUFjqHTF9yySXcdtttXH311VxxxRUMHToUk8nUPpEL0YW5apxUqXHyRIWFhdjt9jpNZxEREezfv79Z5zh27BgPPvigq+P3I488wtChQ5vcd6E5c+aQmprq2i4tLZXkSbS5bmcXHy/Tw5nSMnp189716pqdOE2cOJGJEye6tl955RXX+5MnT5KZmel6vfzyyxw5cgSDwcCgQYP47rvv2jZqIbo4g+KsBrfaJHHqqhITExtsymts34XMZjNms7ntAhOiHiEBzhqnYp2estO50Md7+9u1yXQEPXv2pGfPntx8882usvLycjIzM9m9e3dbXEIIr6LHmTjlFFt4K/0IM6/rp3FE4nzh4eHo9Xry8vLcyvPy8oiMjNQoKiHaT4hPNwCK9TqqSrx7EsxWzxzelICAAK655hp+9atftdclhOiyFEV39n8dvPjffRpHIy5kMplISEggLS3NVeZwOEhLS2PkyJEaRiZE+wjxCQGcC/2Wl3v3UlBtUuMkhGhbytmmup66fAxIB3EtlJeXc+jQIdd2VlYWmZmZhIaGEhMTQ2pqKikpKQwfPpzExEQWLFiAxWJxjbIToivxNfhiUqFagVJJnIQQnkZ3tjJ4dTcbKRWvAbdpG5AX2rlzJ6NHj3Zt13bATklJYenSpUyZMoWCggLmzp1Lbm4u8fHxrFmzRuZaEl1WgKqnSLFTXundTXWSOAnhiZRzregf9czlGQ1D8VZJSUlNLnMya9YsZs2a1UERCaGtQIwUYaey5rTWoWiq3fo4CSFar7apTgghPIVzoV+oqinWNhCNSeIkhAfSyZ+mEMLDBOj9Aah2lGkcibbk7iyEB9Ip7n+aFdXSQVwIoa1AYwAA1WqFxpFoSxInITyRqrhtLtpwWKNAhBDCKcgcAkCN4t1LrkjiJIQHqrG7bx/MLdEmECGEOCvILxSAGqW6yYETXZkkTkJ4oErcM6eRZV9oFIkQQjiFBYQDUK2zUXnh050X8crEqbi4mOHDhxMfH8+QIUN466233PbfcccddOvWjcmTJ2sUofB2JVS6bV9W9a1GkQghhFNooHOOMqvOTrHFe9fR9MrEKTAwkPT0dDIzM9m2bRsvvfQSp0+fm5fiscce491339UwQuHt9Hb3USuFtsoGjhRCiI4RFOBch7Fcr1Ba5r3dB7wycdLr9fj5+QFgtVpRVdWtvTYpKYnAwECtwhMCOzVu2yt8izSKRAghnAJ9nU11ZTodluICjaPRjkcmTunp6UycOJHo6GgURWHlypV1jlm4cCGxsbH4+PgwYsQItm/f3qJrFBcXExcXR69evXjyyScJDw9vo+iFuHg2xeG2XWKwU+XFfQqEENoLNAcBzsSpqkQSJ49isViIi4tj4cKF9e5fvnw5qampPPvss+zatYu4uDjGjh1Lfv659XNq+y9d+MrJyQEgJCSE3bt3k5WVxbJly8jLy2tVrFarldLSUreXEBdLxX3Eil6xc6bCe/sUCCG0F2hytsSU6XRYSws1jkY7HrlW3fjx4xk/fnyD++fPn8/MmTNdq5AvWrSI1atXs3jxYmbPng1AZmZms64VERFBXFwcGzdubFVn8Hnz5vH888+3+HNCNObCxOmgbw0Wq9Q4CSG0E2Ry1jjZFIUKS+sqG7oCj6xxakx1dTUZGRkkJye7ynQ6HcnJyWzZsqVZ58jLy6OszNn5tqSkhPT0dAYNGtSqeObMmUNJSYnrlZ2d3arzCHE+2wVr1TkUhYpK6SAuhNCOr8EX3dlnuqpK702cPLLGqTGFhYXY7XYiIiLcyiMiIti/f3+zznHs2DEefPBBV6fwRx55hKFDh7r2Jycns3v3biwWC7169WLFihWMHDmy3nOZzWbMZnPrv5AQ9SgwRALuSfjzK9bz8W/uQlGU+j8khBDtSFEU/NBTjp2q6jNah6OZTpc4tYXExMRGm/LWrVvXccEIUY8axVinLK/kFEdPV9A33F+DiIQQAvwxOhOnGu/tz9vpmurCw8PR6/V1OnPn5eURGRmpUVRCtLW6yxmE6k5zuty714gSQmjLTzEBUH3BXHPepNMlTiaTiYSEBNLS0lxlDoeDtLS0BpvThOhsLuwcDvBH8+sUl1k0iEYIIZz8dD4AWB3lGkeiHY9sqisvL+fQoUOu7aysLDIzMwkNDSUmJobU1FRSUlIYPnw4iYmJLFiwAIvF4hplJ0RnF+W4jSP6v7qVWXQ6HIWHgN7aBCWE8Hr+Bn+ohmrVewereGTitHPnTkaPHu3aTk1NBSAlJYWlS5cyZcoUCgoKmDt3Lrm5ucTHx7NmzZo6HcaF6KyC1KHoTo/AEbbNVTYjKoKXK7x37hQhhPb8jc7EyYb3dhvwyMQpKSnJbQmU+syaNYtZs2Z1UERCdDxD/hiqz0ucAE5XZGkUjRBCgJ8pACxgw3sn5O10fZyE8AaqCvVNOlBplRonIYR2AszBANh1No0j0Y4kTkJ4KAtm9BfUvJbbvHckixBCe0F+IQDYFBt2R+MtQ12VJE5CeCAVlUp86GF3X2alyi6j6oQQ2gny6wZAjc5OeVWNxtFoQxInITxQbUVTjeq+9IrN7r0jWYQQ2gvyCwOgQqejvKxY22A0IomTEJ1ITmkpNrtD6zCEEF7K72wfpwpFobLMO5ddkcRJiE5EUWpYveeU1mEIIbyUn8m55FOFTqFKEichhKdoaDaOfvpssk9LPychhDb8DH4AVCg6rJZibYPRiCROQnig+pZcAdAr1XQ/vb2DoxFCCCc/49nESaegVpZoHI02JHESwgPV1jipF0zmVKUoRJbs7viAhBCC82qcdDoc1lKNo9GGJE5CeLCYaveaJ6tOQXXYGzhaCCHal7/xbB8nRcFurdA4Gm1I4iSEB3s03z1J+ndgAHa7964RJYTQVm1TnUNRsFq9c0JeSZyE8EC19Uzd7NCrxn2SuW+VnI4PSAghAB+9j+t9VY0kTkIID9E90AzAPrVPnTXrilUZVSeE0IZep8ekOlMHq61c42i0IYmTEB7o2VsGkzSoO4F3/rXOPocXr0ouhNCe6WzqUGOTPk5CCA/RI8iHpdMTuT7+UmwY3PbZVO9cH0oI4RmMOJeC8tYloCRxEqLTkVF1XUFxcTHDhw8nPj6eIUOG8NZbb7n2HThwgPj4eNfL19eXlStXahesEOcxKs6HOW9NnAxNHyKE8CQ2ZK26riAwMJD09HT8/PywWCwMGTKESZMmERYWxqBBg8jMzASgvLyc2NhYbrzxRm0DFuIs49nUwaZWaRyJNqTGSQgPp1fcu4fbpMapS9Dr9fj5OYd2W61WVFVFrWetnc8++4wbbrgBf3//jg5RiHqZdEYAHA7vnBpFEichPJzugmF1laokTh0hPT2diRMnEh0djaIo9TaVLVy4kNjYWHx8fBgxYgTbt7dsOZzi4mLi4uLo1asXTz75JOHh4XWO+eijj5gyZUprv4YQbc54NnGye2l/S0mchPB0ivufaaCujPX78jQKxntYLBbi4uJYuHBhvfuXL19Oamoqzz77LLt27SIuLo6xY8eSn5/vOqa2/9KFr5wc51xcISEh7N69m6ysLJYtW0Zenvv/r6WlpWzevJkJEya03xcVooWMigkAB96ZOEkfJyE8nBrQAypyXdvVisLxje/BZU9oGFXXN378eMaPH9/g/vnz5zNz5kymT58OwKJFi1i9ejWLFy9m9uzZAK5+Sk2JiIggLi6OjRs3MnnyZFf5qlWruOmmm/Dx8Wnws1arFav1XJNJaal3rh8mOk5tU12N4p39LaXGSQgP182vh9t2tQJxJV9pFI0AqK6uJiMjg+TkZFeZTqcjOTmZLVu2NOsceXl5lJU5Z14uKSkhPT2dQYMGuR3TnGa6efPmERwc7Hr17t27hd9GiJapTZy8tb+lJE5CeLiXrn3JbduBAg6bRtEIgMLCQux2OxEREW7lERER5ObmNvApd8eOHePaa68lLi6Oa6+9lkceeYShQ4e69peUlLB9+3bGjh3b6HnmzJlDSUmJ65Wdnd3yLyREC5h0zqa6YLUAcr7VOJqOJ011Qni4PkF9uMXRn891hwGwAQYvHc3SlSQmJjbalBccHFynz1N9zGYzZrO5DSMTonG1iVOVosDaZ2Da5xpH1LGkxkmITsahgEmVZVe0FB4ejl6vr5PY5OXlERkZqVFUQnQMk96ZOFUrCuqxzRpH0/EkcRKiEzh/RgJ7nWV/RUczmUwkJCSQlpbmKnM4HKSlpTFy5EgNIxOi/dUmTlZFQVHt4PCuTuLSVCdEJ2NXgHomShRtq7y8nEOHDrm2s7KyyMzMJDQ0lJiYGFJTU0lJSWH48OEkJiayYMECLBaLa5SdEF2Vj945ytNaOzlveS4ERWsYUceSxEmITkCvO1c5vM9kkkVXOsDOnTsZPXq0azs1NRWAlJQUli5dypQpUygoKGDu3Lnk5uYSHx/PmjVr6nQYF6KrMejOLrlSmzgVH5fESQjhWSKDfODs9DwOReGgsYZLtQ2py0tKSqp3CZTzzZo1i1mzZnVQREJ4Br2iB5wDVQAozoaYqzWLp6NJHychOgHdBevVpft554y9Qgjt6R3OBwq7q8bpmIbRdDxJnIToBC7sDm6XxjohhFbOVsS6pr8s8a65wyRxEqITGGbu7rZt89KlDoQQ2lNU56NcbR8nR2nzJn3tKrwycSouLmb48OGuBTjfeuutOsdUVFTQp08fnnhC1gMT2hvlG8WM4hLXtl2RUXVCCG3ozy48/r3ZRKlOwe5liZNXdg4PDAwkPT0dPz8/LBYLQ4YMYdKkSYSFhbmOefHFF7n6au/p7CY8nKLwk8oqFocEOzeRxEkIoQ392TqXXIOBX0T0YKmXJU5eWeOk1+vx8/MDnCuLq6rqNnrmxx9/ZP/+/Y2ujC5ER7O59XSSxEkIoQ3defei73zMnLEWedUkmB6ZOKWnpzNx4kSio6NRFIWVK1fWOWbhwoXExsbi4+PDiBEj2L59e4uuUVxcTFxcHL169eLJJ58kPDzcte+JJ55g3rx5F/s1hGg7Qye7bdpk8nAhhEZqm+pqHTDqoOK0RtF0PI9MnCwWC3FxcSxcuLDe/cuXLyc1NZVnn32WXbt2ERcXx9ixY8nPz3cdU9t/6cJXTk4OACEhIezevZusrCyWLVvmWnNq1apVXHLJJVxyySXNitVqtVJaWur2EqLNhfbj2JBfujZrAPb/F0pOahaSEMI76S9IHY4bDc7Zw72ER/ZxGj9+fKPNZPPnz2fmzJmupQ0WLVrE6tWrWbx4MbNnzwZodNXx80VERBAXF8fGjRuZPHkyW7du5cMPP2TFihWUl5dTU1NDUFAQc+fOrffz8+bN4/nnn2/ZFxSiFewG/3PvdQ748GcQMxJmrNEwKiGEt9FfMEHKMYMRyvIgcqhGEXUsj6xxakx1dTUZGRkkJye7ynQ6HcnJyWzZsqVZ58jLy6OsrAyAkpIS0tPTGTRoEOBMhLKzszl69CivvvoqM2fObDBpApgzZw4lJSWuV3a2d81nIbRRXTvx3PEt8OM6bYMRQngV3QWpw0mpcfJshYWF2O32OutBRUREsH///mad49ixYzz44IOuTuGPPPIIQ4e2LlM2m82YzeZWfVaIlvA1nbtZWc+fSXz5vfDbU6BIxychRPvT9xgMeee28/V6KJPEqUtLTExsVlPetGnT2j0WIZorKsjH9d5thJ2tEmoqwORfz6eEEKJt9Y/qDnvObecb9NI53JOFh4ej1+tdnblr5eXlERkZqVFUQnQsx4WVS9YyTeIQQnif2kV+axXp9VSX5zdwdNfT6RInk8lEQkICaWlprjKHw0FaWhojR47UMDIh2tu5bMl+4S5JnIQQHUSps3omFFR4T+LkkU115eXlHDp0yLWdlZVFZmYmoaGhxMTEkJqaSkpKCsOHDycxMZEFCxZgsVhco+yE6JrOTXppv7A/kyROQogOolPq1rnkV52mpwaxaMEjE6edO3cyevRo13ZqaioAKSkpLF26lClTplBQUMDcuXPJzc0lPj6eNWvW1OkwLkSX4n9uod86NU4OW4eGIoTwXsp5D276Gn/sRgt51SWNfKJr8cjEKSkpyW0JlPrMmjWLWbNmdVBEQniAoHPPczZF4Z/BQQyvqiLeWg32ag0DE0J4E7emOlsgGC0U2SzaBdTBOl0fJyG8VaAp0PW+SK/nr6Eh3Bd9dkCEpUCjqIQQ3ub8GifV0Q2AMzig2juSJ0mchOgkhoQP4drIn9QpT+0RDiumwb7PYf1LYJPaJyFE+zm/Rcisc67zWqTXgaVQq5A6lCROQnQSiqLwWFzd5ukv/f2ca9ctvwe+fhm+/7jDYxNCeA+H6nC9DzE7E6czeu+Zy0kSJyE6Eb1Sf7fEUt15f8oFzZtBXwghWsOunhue0sPPOWilSKeTxEkI4XkM+voTJ8v5iVM9Q4WFEKKtnN9UF+XfA3D2u5SmOiGEx7lwxt5a5brzRrnojB0UjRDC28WEOKcBOqOXGichhAfS6+tPnGrOnxBT5nQSQrSj80fV9Q91Jk7Fej02i3fMHi6JkxCdiL6BqdfOT5xs1RUdFY4QwstdEh7pWtSguDxX22A6iCROQnQiir7+P9ma895nFxR3SCxCCBEV4ofJ7uwekCd9nIQQnkbXwJ+sTVFQAQdwuqyyQ2MSQngvH4MBk+oDQEFlkcbRdAxJnIToRPS6+v9kfxnZg2fCQ7kmphendZI4CSHaz/lLriiKghk/AEq8ZLFxSZyE6EQaSpwAVgUGUKbXsc3gHU99QghtnN85XEHBR+dcDqrc7h39KyVxEqIT0TVjqoFStx5PQgjRfhRFwccQDIBFtWocTceQxEmITkRppMaplum8yemEEKK9+ZpCAShX7GDv+g9ukjgJ0Ymc37egwWMkcRJCtCP1gntMoK9zvbpSvQ4qizWIqGNJ4iREF1ONvemDhBCijYT6OWucSnQ6qCrWNpgOIImTEJ2Irhnr0KnnrVwuhBBtTcW9xqm7XwhwNnGqPKNBRB1LEichOpHzR7M0xI401QkhOk5kQBgApTppqhNCeJjm9HFSkRqnzqSiooI+ffrwxBNPuJXfcccddOvWjcmTJ2sUmRDNExV0tqlOr0OVGichhCdpTuJkl8SpU3nxxRe5+uqr65Q/9thjvPvuuxpEJETLxAQ7a5xKdDqqyk5rHE37k8RJiM6k6bwJhzTVdRo//vgj+/fvZ/z48XX2JSUlERgYqEFUQrRMd/9uAFTqdJSW5GscTfuTxEmITqShterOJ4lT20hPT2fixIlER0ejKAorV66sc8zChQuJjY3Fx8eHESNGsH379hZd44knnmDevHltFLEQHaPOdASmQGpvO2fK8zSIqGNJ4iREJ6LX6fn9qN83eox0Dm8bFouFuLg4Fi5cWO/+5cuXk5qayrPPPsuuXbuIi4tj7Nix5Oefe+KOj49nyJAhdV45OTmsWrWKSy65hEsuuaSjvpIQbeLCUXU6RYePagCg2AsW+jVoHYAQomVu6XcLczfPbXC/vRnNeaJp48ePr7cJrdb8+fOZOXMm06dPB2DRokWsXr2axYsXM3v2bAAyMzMb/PzWrVv58MMPWbFiBeXl5dTU1BAUFMTcuQ3/f1sfq9WK1XpuqYvS0tIWfV6ItmBWzVRho7y6WOtQ2p3UOAnRyeh1+kb3S9fw9lddXU1GRgbJycmuMp1OR3JyMlu2bGnWOebNm0d2djZHjx7l1VdfZebMmS1OmmrPExwc7Hr17t27xecQoiUurHEC8FF8ASiv6fqJuyROQnQyTU2CaZOmunZXWFiI3W4nIiLCrTwiIoLc3Nw2uUZycjJ33XUX//3vf+nVq1eDCdmcOXMoKSlxvbKzs9vk+kI0pL7RvWadPwDl9oqODqfDSVOdEF2MpE2dz7Rp0+qUrVu3rlmfNZvNmM3mNo5IiIZdGXElA0IG0C+4n6vMVx8EdqhUqzSMrGNI4iREF+OQPk7tLjw8HL1eT16e+wiivLw8IiMjNYpKiI5h1Bn5963/dlvJwNcYCHaookbDyDqGNNUJ0cVIjVP7M5lMJCQkkJaW5ipzOBykpaUxcuRIDSMTomNcuPyTnykEgErFDo6uvdC41DgJ0cVI5/C2UV5ezqFDh1zbWVlZZGZmEhoaSkxMDKmpqaSkpDB8+HASExNZsGABFovFNcpOCG8S6BsGpVCu04G1DHxDtA6p3UjiJEQXIzVObWPnzp2MHj3atZ2amgpASkoKS5cuZcqUKRQUFDB37lxyc3OJj49nzZo1dTqMC+ENQvycs4c7E6dSSZyEEJ2H9HFqG0lJSXVmSL7QrFmzmDVrVgdFJITnCvUNAqBMpzhrnLowr+zjVFxczPDhw12z+r711luufQcOHCA+Pt718vX1rXepBSG01Duw4bl6pMZJCNHRwv2DgbM1TlVdey4nr6xxCgwMJD09HT8/PywWC0OGDGHSpEmEhYUxaNAg12y/5eXlxMbGcuONN2obsBAXWHXbKspryhn+8r/wi33TbZ/0cRJCdLQe/iEAlCs6bJXFXTq58MoaJ71ej5+fH+BcrkBV1Xqr5D/77DNuuOEG/P39OzpEIRpl1Bvp5tMNe2W/OvukxkkI0dFqE6cynY6KsmJNY2lvHpk4dcSq5MXFxcTFxdGrVy+efPJJwsPD6xzz0UcfMWXKlNZ+DSHa3aJ7r6xTpiqSOgkhOlawTyAA5ToFa/kZjaNpXx6ZOLX3quQAISEh7N69m6ysLJYtW1ZnIrvS0lI2b97MhAkTGo3VarVSWlrq9hKio4wbEqV1CEIIQYAxAACrTkd52WmNo2lfHtkM2d6rkp8vIiKCuLg4Nm7cyOTJk13lq1at4qabbsLHx6fRz8+bN4/nn3++WdcSQgghuqLaxAmgtLJIw0jan0fWODWmLVYlz8vLo6zMOVyypKSE9PR0Bg0a5HZMc5vpZIFNIYQQ3k6v02Ny6AEor+raTXUeWePUmMZWJd+/f3+zznHs2DEefPBBV6fwRx55hKFDh7r2l5SUsH37dj755JMmzyULbAohhBBgxkA1diqqS7QOpV11usSpLSQmJjbalBccHFynz5MQQgghGmbGTBlWLLZyrUNpV52uqU5WJRdCCCE8j4/i7BNstVs0jqR9dbrESVYlF0IIITyPj945P2KVo1LjSNqXRzbVyarkQgghROfiqw8AB1SqVq1DaVcemTjJquRCNN/Q8GHsKfxO6zCEEF7OzxgENWClWutQ2pVHJk6yKrkQzffX0QsYs2KM1mEIIbycnzkEKqBKsYGqgqJoHVK76HR9nIQQ7rr7dWeQtWveoIQQnUeAbzcAKnQK1HTdfk6SOAnRBeTpZekVIYS2gv3CAOdCv1R33SkJJHESoguoUhpfGkgIIdpbN99gACyKAtVdd0oCSZyE6AIa7xEohBDtL9Q3CIByna7JfsqdmSROQnQJXfcmJYToHML8AgFnH6dqu0PjaNqPJE5CCCGEuGjhfs6munKdjnKrTeNo2o8kTkJ0AXqdjKoTQmgrwOQPgEXRUVVj1zia9iOJkxBdQO9uvlqHIITwcgHGAAAsOkX6OAkhPJvJIH/KQght+RudNU4ORcHq6Lqzh8vdVgghhBAXzdfgi3K2pqnCLhNgCiE82C39btE6BCGEl1MUBd+ziVOVvUrjaNqPJE5CdAE/vfSnTAz6idZhCCFElyeJkxBdgE7RcZk5VuswhBCiy5PESQghhBCimSRxEkIIIYRoJkmchBBCCCGaSRInIYQQQohmksRJCCGEEKKZJHESQgghhGgmSZyEEEIIIZpJEichhBBCiGaSxEkIIYQQopkkcRJCCCGEaCZJnIQQQgghmkkSJyGEEEKIZpLESQghhBCimQxaB9DVqKoKQGlpqcaRCG9TWVGFvdJOTXXn+++vNt7avx/RenIPElqyV9qx61TKyy2d7r/B5t6HFFXuVG3qxIkT9O7dW+swhOiUsrOz6dWrl9ZhdGpyDxLi4jR1H5LEqY05HA5ycnIIDAxEURStw2lzpaWl9O7dm+zsbIKCgrQOx2t09d9dVVXKysqIjo5Gp5MeBBdD7kGiPXjD797c+5A01bUxnU7nFU/MQUFBXfaPx5N15d89ODhY6xC6BLkHifbU1X/35tyH5NFOCCGEEKKZJHESQgghhGgmSZxEi5jNZp599lnMZrPWoXgV+d2FcJK/BW3I736OdA4XQgghhGgmqXESQgghhGgmSZyEEEIIIZpJEichhBBCiGaSxEkIIYQQopkkcRJCCCGEaCZJnES7KC4uZvjw4cTHxzNkyBDeeustrUPyGnfccQfdunVj8uTJWocihKbkPqSdrnwfkukIRLuw2+1YrVb8/PywWCwMGTKEnTt3EhYWpnVoXd6GDRsoKyvjnXfe4eOPP9Y6HCE0I/ch7XTl+5DUOIl2odfr8fPzA8BqtaKqKpKjd4ykpCQCAwO1DkMIzcl9SDtd+T4kiZOXSk9PZ+LEiURHR6MoCitXrqxzzMKFC4mNjcXHx4cRI0awffv2Fl2juLiYuLg4evXqxZNPPkl4eHgbRd95dcTvLkRnIfchbch96OJI4uSlLBYLcXFxLFy4sN79y5cvJzU1lWeffZZdu3YRFxfH2LFjyc/Pdx1T22/gwldOTg4AISEh7N69m6ysLJYtW0ZeXl6HfDdP1hG/uxCdhdyHtCH3oYukCq8HqJ9++qlbWWJiovqrX/3KtW2329Xo6Gh13rx5rbrGL37xC3XFihUXE2aX056/+/r169U777yzLcIUokPIfUgbch9qOalxEnVUV1eTkZFBcnKyq0yn05GcnMyWLVuadY68vDzKysoAKCkpIT09nUGDBrVLvF1FW/zuQnQVch/ShtyHmmbQOgDheQoLC7Hb7URERLiVR0REsH///mad49ixYzz44IOuzpiPPPIIQ4cObY9wu4y2+N0BkpOT2b17NxaLhV69erFixQpGjhzZ1uEK0a7kPqQNuQ81TRIn0S4SExPJzMzUOgyvtG7dOq1DEMIjyH1IO135PiRNdaKO8PBw9Hp9nU6UeXl5REZGahRV1ye/uxDnyN+DNuR3b5okTqIOk8lEQkICaWlprjKHw0FaWlqXqWr1RPK7C3GO/D1oQ373pklTnZcqLy/n0KFDru2srCwyMzMJDQ0lJiaG1NRUUlJSGD58OImJiSxYsACLxcL06dM1jLrzk99diHPk70Eb8rtfJG0H9QmtrF+/XgXqvFJSUlzH/P3vf1djYmJUk8mkJiYmqlu3btUu4C5CfnchzpG/B23I735xZK06IYQQQohmkj5OQgghhBDNJImTEEIIIUQzSeIkhBBCCNFMkjgJIYQQQjSTJE5CCCGEEM0kiZMQQgghRDNJ4iSEEEII0UySOAkhhBBCNJMkTkK0g+rqagYMGMDmzZvb9Lxr1qwhPj4eh8PRpucVQnQtcg9qP5I4iSZNmzYNRVHqvM5f60i4W7RoEX379mXUqFGuMkVRWLlyZZ1jp02bxu23396s844bNw6j0cj777/fRpEK4fnkHtRycg9qP5I4iWYZN24cp06dcnv17du3znHV1dUaROdZVFXltdde4/7772+X80+bNo2//e1v7XJuITyV3IOaT+5B7UsSJ9EsZrOZyMhIt5derycpKYlZs2bx+OOPEx4eztixYwH4/vvvGT9+PAEBAURERHDfffdRWFjoOp/FYmHq1KkEBAQQFRXFn//8Z5KSknj88cddx9T3dBQSEsLSpUtd29nZ2dx9992EhIQQGhrKbbfdxtGjR137a5+kXn31VaKioggLC+NXv/oVNTU1rmOsVitPPfUUvXv3xmw2M2DAAN5++21UVWXAgAG8+uqrbjFkZmY2+rSbkZHB4cOHufnmm1v4K8PRo0frfbJOSkpyHTNx4kR27tzJ4cOHW3x+IToruQedI/cgbUniJC7aO++8g8lkYtOmTSxatIji4mLGjBnDFVdcwc6dO1mzZg15eXncfffdrs88+eSTfP3116xatYq1a9eyYcMGdu3a1aLr1tTUMHbsWAIDA9m4cSObNm0iICCAcePGuT11rl+/nsOHD7N+/Xreeecdli5d6nbjmzp1Kh988AF/+9vf2LdvH//4xz8ICAhAURRmzJjBkiVL3K67ZMkSrrvuOgYMGFBvXBs3buSSSy4hMDCwRd8HoHfv3m5P1N9++y1hYWFcd911rmNiYmKIiIhg48aNLT6/EF2R3IPcyT2onalCNCElJUXV6/Wqv7+/6zV58mRVVVX1+uuvV6+44gq34//whz+oN910k1tZdna2CqgHDhxQy8rKVJPJpH700Ueu/adPn1Z9fX3Vxx57zFUGqJ9++qnbeYKDg9UlS5aoqqqq7733njpo0CDV4XC49lutVtXX11f94osvXLH36dNHtdlsrmPuuusudcqUKaqqquqBAwdUQP3yyy/r/e4nT55U9Xq9um3bNlVVVbW6uloNDw9Xly5d2uDv9dhjj6ljxoypUw6oPj4+br+jv7+/ajAY1Ntuu63O8ZWVleqIESPUW265RbXb7W77rrjiCvW5555rMAYhuhK5B8k9yJMYtEvZRGcyevRo3njjDde2v7+/631CQoLbsbt372b9+vUEBATUOc/hw4eprKykurqaESNGuMpDQ0MZNGhQi2LavXs3hw4dqvNUVVVV5VaFfPnll6PX613bUVFR7NmzB3BWeev1eq6//vp6rxEdHc3NN9/M4sWLSUxM5D//+Q9Wq5W77rqrwbgqKyvx8fGpd99f/vIXkpOT3cqeeuop7HZ7nWNnzJhBWVkZX375JTqde+Wwr68vFRUVDcYgRFcj9yC5B3kKSZxEs/j7+zdYLXz+DQygvLyciRMn8vLLL9c5NioqqtkjYRRFQVVVt7Lz+wWUl5eTkJBQ7+iO7t27u94bjcY6560dSuvr69tkHA888AD33Xcff/nLX1iyZAlTpkzBz8+vwePDw8NdN8ULRUZG1vkdAwMDKS4udit74YUX+OKLL9i+fXu91e1FRUVu31GIrk7uQXIP8hSSOIk2d+WVV/LJJ58QGxuLwVD3P7H+/ftjNBrZtm0bMTExAJw5c4aDBw+6PXV1796dU6dOubZ//PFHtyecK6+8kuXLl9OjRw+CgoJaFevQoUNxOBx8/fXXdZ7Cak2YMAF/f3/eeOMN1qxZQ3p6eqPnvOKKK3jjjTdQVRVFUVoc0yeffMLvf/97/ve//9G/f/86+2ufZq+44ooWn1sIbyD3ILkHtSfpHC7a3K9+9SuKior42c9+xo4dOzh8+DBffPEF06dPx263ExAQwP3338+TTz7JV199xffff8+0adPqVAWPGTOG1157jW+//ZadO3fy8MMPuz253XPPPYSHh3PbbbexceNGsrKy2LBhA48++ignTpxoVqyxsbGkpKQwY8YMVq5c6TrHRx995DpGr9czbdo05syZw8CBAxk5cmSj5xw9ejTl5eX88MMPLfjVnL7//numTp3KU089xeWXX05ubi65ubkUFRW5jtm6dStms7nJOITwVnIPkntQe5LESbS56OhoNm3ahN1u56abbmLo0KE8/vjjhISEuG5Mr7zyCtdeey0TJ04kOTmZa665pk4/hT//+c/07t2ba6+9lp///Oc88cQTbtXTfn5+pKenExMTw6RJk7jsssu4//77qaqqatHT3xtvvMHkyZP55S9/yaWXXsrMmTOxWCxux9x///1UV1czffr0Js8XFhbGHXfc0aoJ4nbu3ElFRQUvvPACUVFRrtekSZNcx3zwwQfcc889jVbVC+HN5B4k96D2pKgXNuAKoZGkpCTi4+NZsGCB1qHUsXHjRm644Qays7OJiIho8vjvvvuOG2+8kcOHD9fbQbW1CgsLGTRoEDt37qx38j8hROvJPahpcg+SGichGmW1Wjlx4gTPPfccd911V7NuWADDhg3j5ZdfJisrq03jOXr0KK+//rrX3rCE8DZyD/I80jlciEZ88MEH3H///cTHx/Puu++26LPTpk1r83iGDx/O8OHD2/y8QgjPJPcgzyNNdUIIIYQQzSRNdUIIIYQQzSSJkxBCCCFEM0niJIQQQgjRTJI4CSGEEEI0kyROQgghhBDNJImTEEIIIUQzSeIkhBBCCNFMkjgJIYQQQjSTJE5CCCGEEM30/3+2fz+MXCNvAAAAAElFTkSuQmCC", "text/plain": [ "<Figure size 640x480 with 2 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# number of points is too small\n", "length = 128\n", "\n", "wave1 = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, squeeze=True, length=length,\n", " )[0] \n", "\n", "# high number of points is good\n", "length = 16384\n", "\n", "wave2 = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, squeeze=True, length=length,\n", " )[0] \n", "\n", "fig, ax = plt.subplots(1, 2)\n", "plt.subplots_adjust(wspace=0.4)\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " ax[0].loglog(freq_new, np.abs(wave1[i]), label=let)\n", " ax[1].loglog(freq_new, np.abs(wave2[i]), label=let)\n", "ax[0].legend()\n", "ax[0].set_ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")\n", "ax[0].set_xlabel(\"Frequency (Hz)\")\n", "ax[1].set_xlabel(\"Frequency (Hz)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Check number of points that is good for interpolation:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generally, most reasonable numbers of points are fine for interpolation. We usually put 1024 to be conservative. It can slightly affect the waveform timing." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Mismatch')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute directly first (see below)\n", "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=True, compress=True, squeeze=False,\n", " ) [0]\n", "\n", "lengths_in = 2**np.arange(5, 15)[::-1]\n", "mismatch = np.zeros_like(lengths_in, dtype=float)\n", "for j, length in enumerate(lengths_in):\n", " # compute directly first (see below)\n", " wave_temp = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes,\n", " direct=False, fill=True, squeeze=False, length=length\n", " )[0]\n", " \n", " num = np.sum([np.dot(wave_temp[i].conj(), wave[i]) for i in range(3)])\n", " den1 = np.sum([np.dot(wave[i].conj(), wave[i]) for i in range(3)])\n", " den2 = np.sum([np.dot(wave_temp[i].conj(), wave_temp[i]) for i in range(3)])\n", " overlap = num / np.sqrt(den1 * den2)\n", " mismatch[j] = 1 - overlap.real\n", "\n", "plt.loglog(lengths_in, mismatch) \n", "plt.xlabel(\"Number of initial frequencies\")\n", "plt.ylabel(\"Mismatch\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate waveforms without interpolation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When interpolating, frequencies between $10^{-4}/M$ and $0.6/M$ are evaluated. Therefore, when not interpolating, the evaluation of the waveform will stretch outside these limits if frequencies outside those limits are given by the user. \n", "\n", "With `compress=True`, all modes will be directly combined. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=True, compress=True, squeeze=True,\n", " ) \n", "\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new, np.abs(wave[i]), label=let)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `compress=False`, it will keep the modes separate." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1e-27, 1e-14)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=True, compress=False, squeeze=True,\n", " ) \n", "\n", "for i, mode in enumerate(wave_gen.amp_phase_gen.modes):\n", " plt.loglog(freq_new, np.abs(wave[0][i]), label=mode)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")\n", "\n", "plt.xlim(1e-4, 1e-1)\n", "plt.ylim(1e-27, 1e-14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adjusting mode content" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can adjust the mode content with the `modes` keyword argument. You will receive an error if the requested mode indices $(l,m)$ are not available for the given waveform model chosen. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1e-27, 1e-14)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wave = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=[(3,3),(4,4)], direct=True, compress=False, squeeze=True,\n", " ) \n", "\n", "for i, mode in enumerate(wave_gen.amp_phase_gen.modes):\n", " plt.loglog(freq_new, np.abs(wave[0][i]), label=mode)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")\n", "\n", "plt.xlim(1e-4, 1e-1)\n", "plt.ylim(1e-27, 1e-14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### All of these functions can take arrays for parameters" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# set parameters\n", "f_ref = np.array([0.0, 0.0]) # let phenom codes set fRef -> fmax = max(f^2A(f))\n", "phi_ref = np.array([0.0, 1.0])\n", "m1 = np.array([1e6, 4e5])\n", "m2 = np.array([5e5, 1e5])\n", "a1 = np.array([0.2, 0.8])\n", "a2 = np.array([0.4, 0.7])\n", "dist = np.array([10e3, 1e3]) * PC_SI * 1e6 # 3e3 in Mpc \n", "inc = np.array([np.pi/3, np.pi/4])\n", "beta = np.array([np.pi/4., np.pi/5])\n", "lam = np.array([np.pi/5., np.pi/6])\n", "psi = np.array([np.pi/6., np.pi/7])\n", "t_ref = np.array([0.5, 1.2]) * YRSID_SI # in the SSB reference frame\n", "\n", "# frequencies to interpolate to\n", "freq_new = np.logspace(-4, 0, 10000)\n", "modes = [(2,2), (2,1), (3,3), (3,2), (4,4), (4,3)]\n", "\n", "waves = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, squeeze=False, length=1024)\n", "\n", "for j, ls in enumerate([\"solid\", \"dashed\"]):\n", " for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new, np.abs(waves[j][i]), label=let + f\" bin {j}\", ls=ls)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The `fill` keyword argument" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `fill` keyword argument allows the user to fill the data stream as in the first example above. However, it can give two other returns. (It is only available when `direct=False`.\n", "\n", "If `fill=False`, it will return special information used in the fast likelihood function. This includes templates as shortened arrays (only the values where $\\tilde{h}(f)$ is non-zero), the information on which frequency each array starts at and its length." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[array([[-3.14154099e-19+2.93930145e-19j, -4.11910745e-19-2.31073392e-19j,\n", " 7.18639789e-20-4.30372868e-19j, ...,\n", " -1.21330575e-43-4.29769485e-44j, 6.36570618e-46-1.07049893e-43j,\n", " -1.51012483e-45-8.87380319e-44j],\n", " [-3.77142996e-19+6.09479474e-19j, -7.23835376e-19-1.45368093e-19j,\n", " -9.26662932e-20-7.14586769e-19j, ...,\n", " 2.57629108e-43-8.19014428e-44j, 1.33780103e-43+1.81800785e-43j,\n", " 1.11242618e-43+1.49366094e-43j],\n", " [-2.82108635e-28+4.25544336e-28j, -5.89161226e-28+6.21183363e-30j,\n", " -9.93313342e-29-5.74008671e-28j, ...,\n", " -3.89107774e-44-4.92386953e-44j, 2.82041850e-44-4.37426151e-44j,\n", " 2.24209609e-44-3.62845654e-44j]]), array([[-3.07245461e-20+6.26998385e-21j, 2.18054463e-20-2.25976697e-20j,\n", " -4.29271950e-21+3.11543715e-20j, ...,\n", " -2.78259785e-20-8.22146447e-20j, 7.77498602e-20+3.89050092e-20j,\n", " -7.88818912e-20+3.68982312e-20j],\n", " [ 1.30420115e-20+4.61283100e-22j, -1.09311648e-20+7.26757282e-21j,\n", " 4.32441893e-21-1.24795359e-20j, ...,\n", " 9.23185723e-20+2.51389976e-20j, -8.34510053e-20+4.74818772e-20j,\n", " 1.43365804e-20-9.52734595e-20j],\n", " [ 3.26882976e-30+8.96343560e-29j, -5.51509029e-29-7.21135974e-29j,\n", " 8.84898291e-29+2.47851396e-29j, ...,\n", " -2.76775148e-26+4.58288676e-26j, -1.27450933e-26-5.22741814e-26j,\n", " 4.91910732e-26+2.24536166e-26j]])] [0 0] [8026 1681]\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "templates, start_inds, lengths = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=False, squeeze=False, length=1024)\n", "\n", "print(templates, start_inds, lengths)\n", "\n", "# plot the first binary\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new[start_inds[0]:start_inds[0] + lengths[0]], np.abs(templates[0][i]), label=let)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The binaries can also be combined into one data stream with `fill=True` and `combine=True`. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\tilde{h}(f)$ (Hz$^{-1/2}$)')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "waves = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=freq_new,\n", " modes=modes, direct=False, fill=True, combine=True, squeeze=False, length=1024)\n", "\n", "for i, let in enumerate([\"A\", \"E\", \"T\"]):\n", " plt.loglog(freq_new, np.abs(waves[i]), label=let)\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\tilde{h}(f)$ (Hz$^{-1/2}$)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating PhenomHM waveforms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Now we will create PhenomHM waveforms in the source frame, but scaled for the distance. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "phenomhm = PhenomHMAmpPhase(use_gpu=False, run_phenomd=False)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "f_ref = 0.0 # let phenom codes set f_ref -> fmax = max(f^2A(f))\n", "phi_ref = 0.0 # phase at f_ref\n", "m1 = 1e6 \n", "m2 = 5e5\n", "a1 = 0.2\n", "a2 = 0.4\n", "dist = 18e3 * PC_SI * 1e6 # 3e3 in Mpc \n", "t_ref = 0.95 * YRSID_SI\n", "\n", "modes = [(2,2), (3, 3), (4, 4), (2, 1), (3, 2), (4, 3)]\n", "\n", "phenomhm(\n", " m1,\n", " m2,\n", " a1,\n", " a2,\n", " dist,\n", " phi_ref,\n", " f_ref,\n", " t_ref,\n", " 1024,\n", " modes=modes\n", ")\n", "\n", "# get important quantities\n", "freqs = phenomhm.freqs_shaped # shape (num_bin_all, num_modes, length)\n", "amps = phenomhm.amp # shape (num_bin_all, num_modes, length)\n", "phase = phenomhm.phase # shape (num_bin_all, num_modes, length)\n", "tf = phenomhm.tf # shape (num_bin_all, num_modes, length)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Amplitudes" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x13660aa20>" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i, mode in enumerate(modes):\n", " plt.loglog(freqs[0, i], np.sqrt(freqs[0, i]) * amps[0, i], label=mode)\n", " \n", "plt.ylabel(\"Characteristic Strain\")\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fast FD Response" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A large amount of the Fast FD Response codes were provided by Sylvain Marsat, so thank you to him! Detailed information on the response can be found in [arXiv:1806.10734](https://arxiv.org/abs/1806.10734) and [arXiv:2003.00357](https://arxiv.org/abs/2003.00357). The response works by applying an effective transfer function, $\\mathcal{T}(f, t(f))$, to the waveform to get the TDI channels: \n", "$$\\tilde{h}^{AET}(f) = \\mathcal{T}(f, t(f))\\tilde{h}^\\text{SSB}(f),$$\n", "where $t(f)$ is the time-frequency correspondence. This determines where the LISA constellation is in its orbit. This response function assumes the arms of the constellation are constant in time.\n", "\n", "The response function operates directly on information coming from the base waveform generation in PhenomHM when you run `BBHWaveformFD`. To run the response separately you need to provide a phase and tf vector. The phase is adjusted inside the response code. If you do not want that to happen, you can add the keyword argument `adjust_phase=False`. If you are just running the response function to use it itself and not using to adjust phase, you can just put in zeros for the phase, it will not affect the computation. All parameters for the response are in the SSB frame. This function can take 1D arrays for the parameters as well. In this case, you need `freqs.shape=(num_bin_all, length)`, `phases.shape=tf.shape=(num_bin_all, num_modes, length)` with `num_bin_all` the total number of binaries, `num_modes` the number of harmonics, and `length` number of frequencies to evaluate per binary. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\mathcal{T}(f, t(f))$')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# use phase/tf information from last waveform run\n", "freqs = phenomhm.freqs.copy()\n", "phase = phenomhm.phase.copy()\n", "tf = phenomhm.tf.copy()\n", "modes = phenomhm.modes\n", "\n", "phi_ref = 0.0\n", "inc = np.pi/4\n", "beta = np.pi/5\n", "lam = np.pi/6\n", "psi = np.pi/7\n", "\n", "length = phenomhm.freqs_shaped.shape[-1]\n", "freqs_shaped = phenomhm.freqs_shaped\n", "response = LISATDIResponse()\n", "response(freqs,\n", " inc,\n", " lam,\n", " beta,\n", " psi,\n", " phi_ref,\n", " length,\n", " phase=phase,\n", " tf=tf,\n", " modes=modes)\n", "\n", "# plot parts of the response\n", "for i in range(1, 4):\n", " \n", " # (2, 2) mode\n", " index = response.modes.index((2,2))\n", " # response.transferL1\n", " transfer = getattr(response, f\"transferL{i}\")\n", " plt.loglog(freqs_shaped[0, index], np.abs(transfer[0, index]), label=f\"L{i} Real\", ls=\"solid\", color=f\"C{i-1}\")\n", " #plt.loglog(freqs, transfer.imag[0, index], label=f\"L{i} Imag\", ls=\"dashed\", color=f\"C{i-1}\")\n", "plt.legend()\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(r\"$\\mathcal{T}(f, t(f))$\")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10, 6, 1024) (10, 6, 1024) (10, 6, 1024) (10, 6, 1024)\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'Phase Difference from Response Function')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# use phase/tf information from last waveform run\n", "\n", "num_bin_all = 10\n", "\n", "freqs = np.tile(phenomhm.freqs_shaped.copy(), (num_bin_all, 1, 1))\n", "phase = np.tile(phenomhm.phase.copy(), (num_bin_all, 1, 1))\n", "tf = np.tile(phenomhm.tf.copy(), (num_bin_all, 1, 1))\n", "\n", "phi_ref = np.full(num_bin_all, 0.0)\n", "inc = np.full(num_bin_all, np.pi/4)\n", "beta = np.full(num_bin_all, np.pi/5)\n", "lam = np.full(num_bin_all, np.pi/6)\n", "psi = np.full(num_bin_all, np.pi/7)\n", "\n", "length = phenomhm.freqs_shaped.shape[-1]\n", "\n", "response(\n", " freqs,\n", " inc,\n", " lam,\n", " beta,\n", " psi,\n", " phi_ref,\n", " length,\n", " phase=phase,\n", " tf=tf,\n", " modes=None, # defaults to phenomhm modes\n", " adjust_phase=True, # if you want to keep the phase array you input the same, set this to false. \n", ") # You can get adjusted phases with response.phase\n", "print(freqs.shape, phase.shape, tf.shape, response.transferL1.shape)\n", "\n", "# get phase adjustment by response function\n", "phase_diff = phase - phenomhm.phase\n", "\n", "plt.semilogx(freqs[0, 0], phase_diff[0, 0])\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(\"Phase Difference from Response Function\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If building a waveform, you can also put a larger buffer object directly into the response code. This larger buffer object would be carrying amplitudes, phases, and tf from the source-frame waveform generator in a flattened 1D array. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2074.3644391335547" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phenomhm.tf.min()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.70824294e-13 4.14100197e+03 1.65814682e+01 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00]\n", "[ 1.70824294e-13 4.14087439e+03 1.65814682e+01 -3.09383403e-06\n", " 2.34941055e-06 4.04192751e-06 1.44557752e-06 2.79724168e-16\n", " -4.52904052e-15]\n" ] } ], "source": [ "num_bin_all = 10\n", "\n", "length = 1024\n", "num_modes = len(response.modes)\n", "buffer_shape = (9, num_bin_all, num_modes, length)\n", "out_buffer = np.zeros(buffer_shape).flatten()\n", "\n", "f_ref = np.full(num_bin_all, 0.0) # let phenom codes set f_ref -> fmax = max(f^2A(f))\n", "phi_ref = np.full(num_bin_all, 0.0) # phase at f_ref\n", "t_ref = np.full(num_bin_all, 3e6) # time at f_ref\n", "m1 = np.full(num_bin_all, 1e6) \n", "m2 = np.full(num_bin_all, 5e5)\n", "a1 = np.full(num_bin_all, 0.2)\n", "a2 = np.full(num_bin_all, 0.4)\n", "dist = np.full(num_bin_all, 3e3) * PC_SI * 1e6 # 3e3 in Mpc \n", "\n", "inc = np.full(num_bin_all, np.pi/4)\n", "beta = np.full(num_bin_all, np.pi/5)\n", "lam = np.full(num_bin_all, np.pi/6)\n", "psi = np.full(num_bin_all, np.pi/7)\n", "\n", "phenomhm(\n", " m1,\n", " m2,\n", " a1,\n", " a2,\n", " dist,\n", " phi_ref,\n", " f_ref,\n", " t_ref,\n", " length,\n", " out_buffer=out_buffer\n", ")\n", "\n", "print(out_buffer.reshape(buffer_shape)[:, 0, 0, 0])\n", "\n", "response(\n", " freqs,\n", " inc,\n", " lam,\n", " beta,\n", " psi,\n", " phi_ref,\n", " length,\n", " out_buffer=out_buffer,\n", " modes=None, # defaults to phenomhm modes\n", ") \n", "\n", "print(out_buffer.reshape(buffer_shape)[:, 0, 0, 0])\n", "# these are all numbers at the first frequency for (2,2) mode for\n", "# amp, phase, tf, transferL1re, transferL1im, transferL2re, transferL2im, transferL3re, transferL3im" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the Likelihood" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The gravitational-wave likelihood, $\\mathcal{L}$, is given by\n", "$$\\log{\\mathcal{L}}\\propto -\\frac{1}{2}\\langle d-h|d-h\\rangle = -\\frac{1}{2}\\left( \\langle d|d\\rangle + \\langle h|h\\rangle - 2\\langle d|h\\rangle \\right),$$\n", "where $\\langle a|b\\rangle$ is the noise-weighted inner product between time-domain strain signals $a(t)$ and $b(t)$. This inner product is given by\n", "$$ \\langle a|b\\rangle = 4\\text{Re}\\int_0^\\infty\\frac{\\tilde{a}(f)^*\\tilde{b}(f)}{S_n(f)}df,$$\n", "where $S_n(f)$ is the one-sided Power Spectral Density in the noise. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the log-Likelihood for MBHBs directly against the Fourier transform of data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One option in `bbhx` for computing the likelihood is a direct Likeihood computation: `bbhx.likelihood.Likelihood`. You will need `lisatools` if you want to compute the sensitivity curves. Otherwise, put in your own sensitivity functions or np.ones to get it to work. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -1.07304677 -9.67441448 -0.82049942 -6.35227414 -10.27292833\n", " -0.18575894 -0.35926129 -2.60369419 -1.14904283 -5.69420711] [764982.31202969 -591.06049369j 764946.22578225-1778.38208222j\n", " 765008.20318771 +516.83052761j 764957.38520581-1439.90214805j\n", " 764944.36630292-1832.8289125j 764991.18762188 -245.87126849j\n", " 765004.61719784 +341.9503657j 764973.14459642 -921.03288148j\n", " 765010.06945941 +611.6637902j 764959.82211007-1363.06563164j]\n" ] } ], "source": [ "######## generate data\n", "# set parameters\n", "f_ref = 0.0 # let phenom codes set f_ref -> fmax = max(f^2A(f))\n", "phi_ref = 0.0 # phase at f_ref\n", "m1 = 1e6 \n", "m2 = 5e5\n", "a1 = 0.2\n", "a2 = 0.4\n", "dist = 18e3 * PC_SI * 1e6 # 3e3 in Mpc \n", "inc = np.pi/3.\n", "beta = np.pi/4. # ecliptic latitude\n", "lam = np.pi/5. # ecliptic longitude\n", "psi = np.pi/6. # polarization angle \n", "t_ref = 0.9 * YRSID_SI # t_ref (in the SSB reference frame)\n", "\n", "T_obs = 1.2 # years\n", "dt = 10.0\n", "\n", "n = int(T_obs * YRSID_SI / dt)\n", "data_freqs = np.fft.rfftfreq(n, dt)[1:] # remove DC\n", "\n", "# frequencies to interpolate to\n", "modes = [(2,2), (2,1), (3,3), (3,2), (4,4), (4,3)]\n", "waveform_kwargs = dict(modes=modes, direct=False, fill=True, squeeze=True, length=1024)\n", "\n", "data_channels = wave_gen(m1, m2, a1, a2,\n", " dist, phi_ref, f_ref, inc, lam, \n", " beta, psi, t_ref, freqs=data_freqs,\n", " **waveform_kwargs)[0]\n", "\n", "######## get noise information (need lisatools)\n", "PSD_A = get_sensitivity(data_freqs, sens_fn=\"A1TDISens\")\n", "PSD_E = get_sensitivity(data_freqs, sens_fn=\"E1TDISens\")\n", "PSD_T = get_sensitivity(data_freqs, sens_fn=\"T1TDISens\")\n", "\n", "df = data_freqs[1] - data_freqs[0]\n", "\n", "psd = np.array([PSD_A, PSD_E, PSD_T])\n", "\n", "# initialize Likelihood\n", "like = Likelihood(\n", " wave_gen,\n", " data_freqs,\n", " data_channels,\n", " psd,\n", " use_gpu=False,\n", ")\n", "\n", "# get params\n", "num_bins = 10\n", "params_in = np.tile(np.array([m1, m2, a1, a2, dist, phi_ref, f_ref, inc, lam, beta, psi, t_ref]), (num_bins, 1))\n", "\n", "# change masses for test\n", "params_in[:, 0] *= (1 + 1e-4 * np.random.randn(num_bins))\n", "\n", "# get_ll and not __call__ to work with lisatools\n", "ll = like.get_ll(params_in.T, **waveform_kwargs)\n", "\n", "print(ll, like.d_h)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also phase marginalize. This occurs in the $\\langle d|h \\rangle$ term in the Likelihood. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ -1.07304677 -0.84470656]\n", " [ -9.67441448 -7.60718515]\n", " [ -0.82049942 -0.64591713]\n", " [ -6.35227414 -4.99708991]\n", " [-10.27292833 -8.07717584]\n", " [ -0.18575894 -0.14624693]\n", " [ -0.35926129 -0.28283688]\n", " [ -2.60369419 -2.04922946]\n", " [ -1.14904283 -0.90451498]\n", " [ -5.69420711 -4.47979925]]\n" ] } ], "source": [ "# get_ll and not __call__ to work with lisatools\n", "ll_marg = like.get_ll(params_in.T, phase_marginalize=True, **waveform_kwargs)\n", "\n", "print(np.array([ll, ll_marg]).T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also return the signal-to-noise ratio: $\\langle d|h \\rangle / \\sqrt{\\langle h|h \\rangle}$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-1.07304677e+00 8.74639879e+02]\n", " [-9.67441448e+00 8.74630045e+02]\n", " [-8.20499422e-01 8.74640167e+02]\n", " [-6.35227414e+00 8.74633843e+02]\n", " [-1.02729283e+01 8.74629361e+02]\n", " [-1.85758940e-01 8.74640893e+02]\n", " [-3.59261290e-01 8.74640695e+02]\n", " [-2.60369419e+00 8.74638129e+02]\n", " [-1.14904283e+00 8.74639792e+02]\n", " [-5.69420711e+00 8.74634595e+02]]\n" ] } ], "source": [ "# get_ll and not __call__ to work with lisatools\n", "out = like.get_ll(params_in.T, return_extracted_snr=True, **waveform_kwargs)\n", "\n", "# first column is log-Likelihood, second is snr\n", "print(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Heterodyned Likelihoods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Heterodyned Likelihoods are also available. See [arXiv:2109.02728](https://arxiv.org/abs/2109.02728) for details on Heterodyning in general. We specifically implement the method used in [arXiv:1806.08792](https://arxiv.org/abs/1806.08792). The practical reason for using a Heterodyned Likelihood method is the computation can be performed along a sparse array of frequencies, rather than a dense array comming from a Fourier transform. \n", "\n", "It is reasonably accurate with higher modes and produces the same posteriors as the full Likelihood. It uses a direct sum of modes prior to residual computation. It gets more accurate as modes are removed. " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ -1.07304677 -1.00832284]\n", " [ -9.67441448 -8.90280807]\n", " [ -0.82049942 -0.74911253]\n", " [ -6.35227414 -5.85909352]\n", " [-10.27292833 -9.45085245]\n", " [ -0.18575894 -0.18590962]\n", " [ -0.35926129 -0.32960139]\n", " [ -2.60369419 -2.41820795]\n", " [ -1.14904283 -1.04894937]\n", " [ -5.69420711 -5.25570331]]\n" ] } ], "source": [ "reference_index = ll.argmax()\n", "\n", "reference_params = params_in[reference_index]\n", "\n", "# how many frequencies to use\n", "length_f_het = 128\n", "\n", "# initialize Likelihood\n", "like_het = HeterodynedLikelihood(\n", " wave_gen,\n", " data_freqs,\n", " data_channels,\n", " reference_params,\n", " length_f_het,\n", " use_gpu=False,\n", ")\n", "\n", "\n", "# get_ll and not __call__ to work with lisatools\n", "ll_het = like_het.get_ll(params_in.T, **waveform_kwargs)\n", "\n", "print(np.array([ll, ll_het]).T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Utility functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are some utility functions in `bbhx` than can be very useful." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transformation functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When sampling on MBHBs, it can be useful to sample in the LISA constellation reference frame where the posterior modes in the sky have a generally predictable structure. In the LISA constellation referenence frame, the sky localization for a source generally has 8 sky modes: 4 longitudinal and 2 latitudinal. Longitudinal modes involve $\\lambda + (0, 1, 2, 3)\\times\\pi/2$ and $\\psi + (0, 1, 2, 3)\\times\\pi/2$, where $\\lambda$ is the ecliptic longitude and $\\psi$ is the polarization angle. The latitudinal modes are at $(\\pm\\beta, \\pm\\cos{\\iota}, \\pm\\cos{\\psi})$ where $\\beta$ and $\\iota$ are the ecliptic latitude and inclination, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Transformations to and from LISA and SSB reference frames" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we will examine transformations of coordinates to and from the LISA and SSB reference frames. All of these functions can take arrays as input as well." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "31557992.305078838 2.3277015675208466 1.0933520437673625 2.3134690745168953\n" ] } ], "source": [ "# start in the LISA frame\n", "tL = YRSID_SI # time\n", "lambdaL = 0.5\n", "betaL = 0.8\n", "psiL = 0.3\n", "\n", "tSSB, lambdaSSB, betaSSB, psiSSB = LISA_to_SSB(tL, lambdaL, betaL, psiL)\n", "print(tSSB, lambdaSSB, betaSSB, psiSSB)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From SSB to LISA:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "31558149.7635457 0.4999999999999887 0.8000000000000038 0.29999999999999005\n" ] } ], "source": [ "tL, lambdaL, betaL, psiL = SSB_to_LISA(tSSB, lambdaSSB, betaSSB, psiSSB)\n", "print(tL, lambdaL, betaL, psiL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Posterior sky-mode transformation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can transform your sky mode parameters to all longitudinal modes. If `inplace==False`, the first dimension will be 4 times as long as the input array. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "start params: [0.4 3.42 0.6 1. ]\n", "end params: [[0.4 3.42 0.6 1. ]\n", " [0.4 4.99079633 0.6 2.57079633]\n", " [0.4 0.27840735 0.6 1. ]\n", " [0.4 1.84920367 0.6 2.57079633]]\n" ] } ], "source": [ "inc = 0.4\n", "lam = 3.42\n", "beta = 0.6\n", "psi = 1.0\n", "\n", "coords = np.array([inc, lam, beta, psi])\n", "\n", "# if we had the whole mbh parameter array like used in BBHWaveformFD,\n", "# it would be dict(inc=7, lam=8, beta=9, psi=10) included f_ref as a parameter \n", "ind_map = dict(inc=0, lam=1, beta=2, psi=3) \n", "\n", "print(f\"start params: {coords}\")\n", "\n", "out_coords = mbh_sky_mode_transform(coords, ind_map=ind_map, inplace=False, kind=\"long\", cos_i=False)\n", "print(f\"end params: {out_coords}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or latitudinal transforms. If `inplace==False`, the first dimension will be 2 times as long as the input array. " ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "start params: [0.4 3.42 0.6 1. ]\n", "end params: [[ 0.4 3.42 0.6 1. ]\n", " [ 2.74159265 3.42 -0.6 2.14159265]]\n" ] } ], "source": [ "print(f\"start params: {coords}\")\n", "\n", "out_coords = mbh_sky_mode_transform(coords, ind_map=ind_map, inplace=False, kind=\"lat\", cos_i=False)\n", "print(f\"end params: {out_coords}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or both transforms. If `inplace==False`, the first dimension will be 8 times as long as the input array. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "start params: [0.4 3.42 0.6 1. ]\n", "end params: [[ 0.4 3.42 0.6 1. ]\n", " [ 2.74159265 3.42 -0.6 2.14159265]\n", " [ 0.4 4.99079633 0.6 2.57079633]\n", " [ 2.74159265 4.99079633 -0.6 0.57079633]\n", " [ 0.4 0.27840735 0.6 1. ]\n", " [ 2.74159265 0.27840735 -0.6 2.14159265]\n", " [ 0.4 1.84920367 0.6 2.57079633]\n", " [ 2.74159265 1.84920367 -0.6 0.57079633]]\n" ] } ], "source": [ "print(f\"start params: {coords}\")\n", "\n", "out_coords = mbh_sky_mode_transform(coords, ind_map=ind_map, inplace=False, kind=\"both\", cos_i=False)\n", "print(f\"end params: {out_coords}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also do these transformations in-place. When you do this, the input binaries will be assigned to new sky modes based on the transformation. Every 2, 4, or 8 binaries will be given the same sky mode transformation if latitudinal, longitudinal, or both transformations are applied, respectively. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "start params: [[0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]\n", " [0.4 3.42 0.6 1. ]]\n", "end params: [[ 0.4 3.42 0.6 1. ]\n", " [ 2.74159265 3.42 -0.6 2.14159265]\n", " [ 0.4 4.99079633 0.6 2.57079633]\n", " [ 2.74159265 4.99079633 -0.6 0.57079633]\n", " [ 0.4 0.27840735 0.6 1. ]\n", " [ 2.74159265 0.27840735 -0.6 2.14159265]\n", " [ 0.4 1.84920367 0.6 2.57079633]\n", " [ 2.74159265 1.84920367 -0.6 0.57079633]\n", " [ 0.4 3.42 0.6 1. ]\n", " [ 2.74159265 3.42 -0.6 2.14159265]\n", " [ 0.4 4.99079633 0.6 2.57079633]\n", " [ 2.74159265 4.99079633 -0.6 0.57079633]\n", " [ 0.4 0.27840735 0.6 1. ]\n", " [ 2.74159265 0.27840735 -0.6 2.14159265]\n", " [ 0.4 1.84920367 0.6 2.57079633]\n", " [ 2.74159265 1.84920367 -0.6 0.57079633]]\n" ] } ], "source": [ "in_coords = np.tile(np.array([inc, lam, beta, psi]), (16, 1))\n", "print(f\"start params: {in_coords}\")\n", "\n", "out_coords = mbh_sky_mode_transform(in_coords, ind_map=ind_map, inplace=True, kind=\"both\", cos_i=False)\n", "print(f\"end params: {out_coords}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Citations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can access citations for each class with the `citation` property. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "@article{Katz:2020hku,\n", " author = \"Katz, Michael L. and Marsat, Sylvain and Chua, Alvin J. K. and Babak, Stanislav and Larson, Shane L.\",\n", " title = \"{GPU-accelerated massive black hole binary parameter estimation with LISA}\",\n", " eprint = \"2005.01827\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " doi = \"10.1103/PhysRevD.102.023033\",\n", " journal = \"Phys. Rev. D\",\n", " volume = \"102\",\n", " number = \"2\",\n", " pages = \"023033\",\n", " year = \"2020\"\n", "}\n", "\n", "@article{Katz:2021uax,\n", " author = \"Katz, Michael L.\",\n", " title = \"{A fully-automated end-to-end pipeline for massive black hole binary signal extraction from LISA data}\",\n", " eprint = \"2111.01064\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " month = \"11\",\n", " year = \"2021\"\n", "}\n", "\n", "@article{michael katz_2021,\n", " title={mikekatz04/BBHx: First official public release},\n", " DOI={10.5281/zenodo.5730688},\n", " abstractNote={No description provided.},\n", " publisher={Zenodo},\n", " author={Michael Katz},\n", " year={2021},\n", " month={Nov}\n", "}\n", "\n", "@article{Marsat:2018oam,\n", " author = \"Marsat, Sylvain and Baker, John G.\",\n", " title = \"{Fourier-domain modulations and delays of gravitational-wave signals}\",\n", " eprint = \"1806.10734\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " month = \"6\",\n", " year = \"2018\"\n", "}\n", "\n", "@article{Marsat:2020rtl,\n", " author = \"Marsat, Sylvain and Baker, John G. and Dal Canton, Tito\",\n", " title = \"{Exploring the Bayesian parameter estimation of binary black holes with LISA}\",\n", " eprint = \"2003.00357\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " doi = \"10.1103/PhysRevD.103.083011\",\n", " journal = \"Phys. Rev. D\",\n", " volume = \"103\",\n", " number = \"8\",\n", " pages = \"083011\",\n", " year = \"2021\"\n", "}\n", "\n", "@article{London2018,\n", " archivePrefix = {arXiv},\n", " arxivId = {gr-qc/1708.00404},\n", " author = {London, Lionel and Khan, Sebastian and Fauchon-Jones, Edward and Garc'ia, Cecilio and Hannam, Mark and Husa, Sascha and Jim{'{e}}nez-Forteza, Xisco and Kalaghatgi, Chinmay and Ohme, Frank and Pannarale, Francesco},\n", " doi = {10.1103/PhysRevLett.120.161102},\n", " eprint = {1708.00404},\n", " journal = {\\prl},\n", " keywords = {General Relativity and Quantum Cosmology},\n", " month = {apr},\n", " number = {16},\n", " pages = {161102},\n", " primaryClass = {gr-qc},\n", " title = {{First Higher-Multipole Model of Gravitational Waves from Spinning and Coalescing Black-Hole Binaries}},\n", " volume = {120},\n", " year = {2018}\n", "}\n", "\n", "@article{Husa2016,\n", " archivePrefix = {arXiv},\n", " arxivId = {gr-qc/1508.07250},\n", " author = {Husa, S and Khan, S and Hannam, M and P{\"{u}}rrer, M and Ohme, F and Forteza, X.$\\sim$J. and Boh{'{e}}, A},\n", " doi = {10.1103/PhysRevD.93.044006},\n", " eprint = {1508.07250},\n", " journal = {\\prd},\n", " month = {feb},\n", " number = {4},\n", " pages = {44006},\n", " primaryClass = {gr-qc},\n", " title = {{Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal}},\n", " volume = {93},\n", " year = {2016}\n", "}\n", "\n", "\n", "@article{Khan2016,\n", " archivePrefix = {arXiv},\n", " arxivId = {gr-qc/1508.07253},\n", " author = {Khan, S and Husa, S and Hannam, M and Ohme, F and P{\"{u}}rrer, M and Forteza, X.$\\sim$J. and Boh{'{e}}, A},\n", " doi = {10.1103/PhysRevD.93.044007},\n", " eprint = {1508.07253},\n", " journal = {\\prd},\n", " month = {feb},\n", " number = {4},\n", " pages = {44007},\n", " primaryClass = {gr-qc},\n", " title = {{Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era}},\n", " volume = {93},\n", " year = {2016}\n", "}\n", "\n" ] } ], "source": [ "print(wave_gen.citation)" ] } ], "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": "3.12.1" } }, "nbformat": 4, "nbformat_minor": 4 }