{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## GBGPU Tutorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`GBGPU` is a GPU-accelerated version of the `FastGB` waveform which has been developed by Neil Cornish, Tyson Littenberg, Travis Robson, and Stas Babak. It computes gravitational waveforms for Galactic binary systems observable by LISA using a fast/slow-type decomposition. For more details on the original construction of `FastGB` see [arXiv:0704.1808](https://arxiv.org/abs/0704.1808).\n", "\n", "The current version of the code is very closely related to the implementation of `FastGB` in the LISA Data Challenges' Python code package. The waveform code is entirely Python-based. It is about 1/2 the speed of the full C version, but much simpler in Python for right now. There are also many additional functions including fast likelihood computations for individual Galactic binaries, as well as fast C-based methods to combine waveforms into global fitting templates. \n", "\n", "The code is CPU/GPU agnostic. CUDA and NVIDIA GPUs are required to run these codes for GPUs.\n", "\n", "See the [documentation](https://mikekatz04.github.io/GBGPU/html/index.html) for more details. This code was designed for [arXiv:2205.03461](https://arxiv.org/abs/2205.03461). If you use any part of this code, please cite [arXiv:2205.03461](https://arxiv.org/abs/2205.03461), its [Zenodo page](https://zenodo.org/record/6500434#.YmpofxNBzlw), [arXiv:0704.1808](https://arxiv.org/abs/0704.1808), and [arXiv:1806.00500](https://arxiv.org/abs/1806.00500). " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import time\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "from gbgpu.gbgpu import GBGPU\n", "from gbgpu.thirdbody import GBGPUThirdBody\n", "\n", "from gbgpu.utils.constants import *\n", "from gbgpu.utils.utility import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating Galactic binary waveforms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialize the waveform class." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "gb = GBGPU(use_gpu=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Setup all the binary information. GBGPU operates in a vectorized manner, so it takes arrays of parameters as inputs." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "dt = 10.0\n", "Tobs = 1.0 * YEAR\n", "\n", "\n", "# number of points in waveform\n", "# if None, will determine inside the code based on amp, f0 (and P2 if running third-body waveform)\n", "N = None\n", "\n", "# number of binaries to batch\n", "num_bin = 10\n", "\n", "# parameters\n", "amp = 2e-23 # amplitude\n", "f0 = 2e-3 # f0\n", "fdot = 7.538331e-18 # fdot\n", "fddot = 0.0 # fddot\n", "phi0 = 0.1 # initial phase\n", "iota = 0.2 # inclination\n", "psi = 0.3 # polarization angle\n", "lam = 0.4 # ecliptic longitude\n", "beta_sky = 0.5 # ecliptic latitude\n", "\n", "\n", "# for batching\n", "amp_in = np.full(num_bin, amp)\n", "f0_in = np.full(num_bin, f0)\n", "fdot_in = np.full(num_bin, fdot)\n", "fddot_in = np.full(num_bin, fddot)\n", "phi0_in = np.full(num_bin, phi0)\n", "iota_in = np.full(num_bin, iota)\n", "psi_in = np.full(num_bin, psi)\n", "lam_in = np.full(num_bin, lam)\n", "beta_sky_in = np.full(num_bin, beta_sky)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate the waveforms." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "signal length: (128,)\n" ] }, { "data": { "text/plain": [ "(0.0019993, 0.0020007000000000002)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+3olU7qq8GM02dz8PEYWGkExgzp49i1dffRXDhg3D559/jp/97Gf45S9/iTfffLPLx69cuRKJiYnuW25ubpAjJgodDofgPkJgdFcVmAHOpdiDJQ1+6xXpjsmLbdQA3McJdNUDIx4f0FPVKN3PO5HON7RWgiobuYxEFEpCMoFxOByYMGECnn32WRQUFGDp0qVYsmQJVq9e3eXjV6xYAb1e776VlJQEOWKi0FFc1wSj2Qa1Uo4hafGdPp+flQC1Qo76JqtH5w71hXsbdR97YNptn+5i+UiU5sdhdiazrV0vTSX7YIhCSkgmMFlZWRg1alS7+/Lz81FcXNzl4zUaDXQ6XbsbUbQS+1/yMxOgUnT+EdcoFcjPdv6MBHo7des2as97YACgorGl3XEH35cbUNlohlYlx+RByd1+vT+n8Zbr2/fhVLACQxRSQjKBmTp1Kk6ePNnuvh9++AF5eXkSRUQUPsT+l1Fd9L+ICoIwD8Zqd8Bicw6B82QbNQD0i1W5H1ta35pAiNWXqUNSoVV1nwz5cxbM+Yb2CQsbeYlCS0gmMPfffz92796NZ599FqdPn8a7776L119/HcuWLZM6NKKQd6yH/hfRuNzAN/I2mVsrKJ5uo5bJZF32wbj7X3pYPgKAdF3gKjDsgSEKLSGZwFx00UX44IMP8H//938YPXo0/vCHP+Cll17CbbfdJnVoRCFNEAT3EQJd7UASjc91NvIePd/orpL4m9HVwKtWyKFWev5WMyDZOcxO7IPRN1lxoLgBQNfzX9pKi3c28fpjF5JYgVG65uhwFgxRaAnJOTAAMG/ePMybN0/qMIjCSmWjGbUmCxRyGUZmJnT7uIEpsUiMUUHfbMXJCgPG5HSf7PjK5GX/i6hjI++O09WwOwQMS493V2e6E4gKzMisBBwta2QPDFGICckKDBH55qir+jI0Lb7HXhGZTNbmXKT6gMTi7QwYkZjAnKt1JjCtp0/3PnQvLd6ZwNQ3WftcWRJnwBS4qlVcQiIKLUxgiCKIe4BdD/0vIvFk6u8C1Afj7RZqUdseGIdDwLYfxPkvPS8fAUBSrAoqhXPJp6abAyE9Jc6AKRiQBMDZGOxwBHZuDhF5jgkMUQRxHyHQQ/+LaHyAG3m93UItyktxTtktrmvCkTI9aowWxGuUmJjX/fZpkUwmc1dh+rITSRAEdwVmbE4i5DLA7hBQY+JOJKJQwQSGKIK4J/Bm916BGZeTBAA4U22Cvtnq91iavJzCK+qfFAOZDGi22vGv/aUAgKlDUzxuBE7T9X0ab2OzDU0WZwUpp18sUl1JUaWeCQxRqGACQxQh6k0WlLmWPUZ5kMCkxGvc/SZHSvV+j6f1IEfvEhi1Uo7sROdOpP8ccCYws7w4dLK1AuN7z4p4HZPj1NCqFMhMdCZFbOQlCh1MYIgihNj/MjAlFglaz05iDmQjr9HVA+PpDJi2cl1bqU2uKog3p2b7YyeSuAMpy5W4iGcssZGXKHQwgSGKEN70v4jGB3Aib2sFxrseGKB1JxIA5Gfp3BUQT/ijB+a8q/8ly1UJykx0LSExgSEKGUxgiCKENzuQRGIj78ESvd9Ppvb2JOq22iYwszzYfdSWXyowriWk7CRn4pTp6qvhMDui0MEEhihCeDKBt6MLshOhlMtQYzS7+z78xdc5MADaDazzZP5LW/6owJR3qMBk6NgDQxRqmMAQRQCj2YbCWhMA4AIPGnhFWpUC+VnOxx8q8W8jb+scGO+XkIakxQNwznURD570VLor2ajpyxJSxwpMIntgiEINExiiCPB9eSMEwbnUIW759dQ49zKSfxt5+7KENLp/IlbeOAarb78QSoV3b1PiidTVBrPPy2LdVWB4IjVR6GACQxQBxOWjnk6g7o54sKO/G3l93UYtunXSAFw8OMXrr0uNVwMALHaHT/NtHA7B3esi7kISExh9sxUtVnu3X0tEwcMEhigCHHU18I7yov9FJDbyHinTw2b338nU7m3UPiYwvtIoFUiKdW4j96UPptZkgcXugEzWunSk0yoR4zpbio28RKGBCQxRBDjmxQTejganxiNBq0SL1YGTlQa/xdSXbdR9lZ7g+04kcQZMWrwGKtfylUwm4zA7ohDDBIYozJltdpxyJR4X9Pe+AiOXy9zHCvizkdfXowT8QeyD8WUa7/kG1/JRUky7+8WkiI28RKGBCQxRmPuhwgibQ0C/WBWyvRj41lYgGnndhzn6MIm3r8TJuX2pwHS8ltyJRBRaPHpnueuuu3x+AZlMhrVr1/r89UTUs7YTeGUymU/P4e9GXpvdgRars59G0gqMD7uGxB1I2R0qMK3D7LgTiSgUePTOsn79ep9fgAkMUWAdcycw3ve/iMQKzKkqI4xmm887h0RNbXbqxEnZA2P0PtkQZ8BkdajAtG6lZgWGKBR49C61bt26QMdBRD46WiYeIeB9/4soPUGL/kkxKGtoxuHSBlwyJLVPMYkNvCqFDBpl8BOYgFRg2MRLFFI8SmAWLVoU6DiIyAc2uwMnKlwJTB8qMIDzYMeyhmYcKtH7LYHx5SRqf0jrQwWmvNsKDJt4iUIJm3iJwtjZGhNarA7EqRUYlBLXp+fyZyOvOAOmr0tRvkp3V2C8SzZsdgcqXY2/HSsw4hJSVaPvE36JyH/6/O6i1+uxd+9eVFdXIy8vD5dccok/4iIiD4j9L/lZOsjlvjXwivzZyNvkPsgx+MtHAJDm2oXU2GJDi9UOrcqzOKoMZtgdApRyWacjGcSdTRa7A3UmC1K8PLKBiPzL5wqMwWDAT3/6U6Snp+OKK67A7bffjr///e/uz//9739HdnY29uzZ45dAiagzsf9ldB/6X0Sj++ugkMtQ2Wju87RZo8RLSDqtEmql8+3Nm63U4hbqDJ0Wig4JoVopdx9TwD4YIun5lMA0Nzdj5syZeOONN9CvXz/MnTu3U0l13rx5qKysxIcffuiPOImoC2IFZlQf+18AZ7IxPCMBQN+XkcSDHKVaQpLJZK3LSF4kMOIQO/EU6o64E4kodPiUwLz44ov47rvvcOutt+LMmTP45JNPOj0mMzMT+fn52LJlS5+DJKLOBEFoc4RA3yswQOu5SAf7OJHX5OqBkWoJCWh/KrWnxAqMeAp1RzyVmih0+JTAvPfee8jMzMTatWsRF9d94+Dw4cNRWlrqc3BE1L2SumYYWmxQK+QYlhHvl+ccn5sEwA8VGLN0xwiIWs9D8rxa0nqMQM8VGB7oSCQ9nxKYM2fOYNKkSdBqex5bHhsbi5qaGp8CI6KeiRN4R2QmuA8d7CuxkfdIqR52h+87bUwSHiMg6ksFJrubCkwml5CIQoZP73oKhQJWq7XXx5WWlvZYoSEi3/ljAm9HQ9PjoVbKYbLY3RNpfWF0LyFJWYFxbXv2KoFxVWC6OVMqM9GZFLGJl0h6PiUwQ4YMwaFDh2Cz2bp9jNFoxOHDh5Gfn+9zcETUPbH/pS8TeDtSyGVIi/d9CJyoyd3EG149MK1NvF1XYNLZA0MUMnxKYK699lqUl5fj6aef7vYxTz/9NPR6PW644QafgyOi7rmPEPBjBQaAe6twjQ8nOYuk3kYNwOtdSGabHTWupK3bCgyXkIhChk8JzP3334/+/fvjD3/4A66//nq8++67AIDKykr85z//wS233II//elPGDhwIO69916/BkxEzgmzNUYz5DIgP9PfCYzzH/4ao8Xn5xB7YKTaRg14X4GpdJ0yrVHKkRyn7vIxYgJTZ7LAbLN3+RgiCg6f3l2SkpKwadMmXHvttdi4cSM+/vhjyGQybNq0CZs2bYIgCMjLy8PHH3/MHhiiABAbeIekxSNG7d9lGvEf/po+LCGZLKHTA1NjNMPhEHqdVHxe33oGkkzW9WOTYlVQK+Ww2ByoajQjNznWv0ETkcd8fncZNWoUjh49ivXr1+PTTz/F2bNn4XA4kJubi7lz52Lp0qWIjeUPN1EgfF9uAOD/5SOgbQWmDwmMxEcJAEBKvBoyGWBzCKhv6n30f28zYADngLxMnRbFdU2oaGxhAkMkoT79eqTVanHvvfdymYgoyMQ5JIH4B9TdA+OXBEa6CoxKIUdyrBq1JguqDOZeE5jeZsCIMnQaFNc1sQ+GSGIheRr1k08+CZlM1u42cuRIqcMiChlictHxwEF/SPVh905H7m3UEjbxAt71wfQ2A0bEYXZEoUHad5ceXHDBBfjyyy/dHyuVIRsqUdDVuhpsU+K7bjbtC3808TZJfBaSKC1BgxMVBo92IpV7WIHhTiSi0ODzu0txcTFWrlyJL7/8EmVlZTCbu36DkMlkPc6L6TYwpRKZmZm+hkcU0QJagRETGB8rMA6HgCaL9GchAd5VYM67Kiq9VWAyXVusKzgLhkhSPiUwJ06cwNSpU9HQ0NDpFOqOevt8d06dOoXs7GxotVpMmTIFK1euxIABA3x6LqJI05rA+L8CI/6jbzDb0GK1Q6vyLgkRT6IGpO2BAdpO4+29WuJeQupmiJ2IJ1IThQafemB+85vfoL6+Hpdffjl2794NvV4Ph8PR7c1bkydPxvr167Fp0ya8+uqrKCwsxLRp02AwGLp8vNlsRmNjY7sbUaQy2+xobHEmCYGowOi0SqhdZyv50sgrVl8Uchk0Smnb7DytwDRZbGhoch6P0nsTLxMYolDg069H27Ztw4ABA/DRRx9Brfb/b4Bz5851/3ns2LGYPHky8vLy8M9//hN33313p8evXLkSTz31lN/jIApFdSZnb4pSLoNOq/L788tkMqTGq3Fe34Jqgxk5/bzb6WR0H+So6HaeSrB4Oo1X3IEUr1H2ek0z2zTxCoIg+fdIFK18+vWoqakJkyZNCkjy0pWkpCQMHz4cp0+f7vLzK1asgF6vd99KSkqCEheRFGoMrQ28vQ1n81Vqgu+NvKGwhVrkHsrXSwJT3maIXW/Sdc7nNNsc0Df3fqgtEQWGTwnM4MGDYTKZ/B1Lt4xGI86cOYOsrKwuP6/RaKDT6drdiCJVjcn5j3FKnP+Xj0R9GWZnDMEEprcKTOsOpJ77XwBAq1KgX6yzSsNTqYmk41MCc8cdd2D79u2orq72dzwAgIceegjbtm1DUVERvvnmG9xwww1QKBS49dZbA/J6ROFErCaIVZJA6MuBjk1m6Y8REIlLSEazzb21uyvn3TNgeq/AAG37YLgTiUgqPiUwDz74IKZMmYK5c+fi6NGj/o4JpaWluPXWWzFixAjcfPPNSElJwe7du5GWlub31yIKN7WuHpjUbg4c9Ie+nIdkcs+AkXYLtTMGJbQq59tcT4287gpML1uoRe4EhsPsiCTj069Il19+OaxWKw4cOIDx48djwIABGDBgAOTyzvmQTCbD5s2bvXr+DRs2+BIWUVQITgXG9x4YcQkpVuIpvIDz/Sc9wXl2UbXBjLyUrg+XdR/k2MsOJJG7kZdLSESS8ekdZuvWre4/OxwOFBUVoaioqMvHskOfyL/ECkxKACswYgLjy3EC4hKS1FN4RWkJzrOLeuqDKfdwiJ0oI5EJDJHUfHqH2bJli7/jICIPBXIKr8g/TbzSLyEBrX0w3SVjgiCgvMG3CkwVExgiyfiUwMyYMcPfcRCRh2oCeA6SKC3B+dzVvvTAuOfAhE4FBuh+Gm9jiw0m1/A9jyswrq3UrMAQSSckT6Mmou4FswJjaHEeJ+ANsYk3FHYhAb1XYMQZMEmxKsSoPasatZ5IzV1IRFJhAkMURhwOwT2JN5AJTGKMCiqFs39N7LnxlCmEtlEDvc+C8XYHEtB6oGOtyQyr3fvjUoio73x+hzEYDPh//+//uU+jbmnpupQqk8lw5swZnwMkolYNzVbYHc4DUpMD2MTrPE5Ag3J9C2oMZvT3YMCbSFxCCoVt1EDrgY7dVWC8nQEDAMmxaqgUMljtAqq8vD5E5B8+JTDnz5/HpZdeinPnzvV62jR3IRH5T61r+SgxRgV1gA9KFBMYb3cihdI2asCLCoyHDbwAIJc7t2eXNTSjsrGFCQyRBHx6h3nsscdQVFSE8ePH49FHH0V+fj7H9xMFQbW7/yXw55C5p/F62cgrnkYdKtuoxR6YWqMZdocARYfzo9wzYLxYQgKcjbxlDc0cZkckEZ/eYT7//HNkZGRgy5YtSExM9HdMRNSNWvcOpMD1v4h83UodSoc5As6lNpkMcAjOnhVxSUkkVmCyvajAAK19MNyJRCQNn2rQ9fX1mDJlCpMXoiATk4m0ICQwaT6eSN26hBQaPTBKhdx98GVXy2HlPldgmMAQScmnBCY3NxcOBzvviYKtNggzYETuabw+VmBCZQkJ6L4PRhAEr6fwijJ5HhKRpHxKYH784x9jx44dMJlM/o6HiHoQjBkwIvGsJW9OpHY4BDRZQ2sbNdD9LJg6kwVmm/OXsYxE764pT6QmkpZPCcxvf/tb5Obm4uabb0ZVVZW/YyKibgRjCq9IbOL1pgLTbLVD3JgYihWYjgnMeVf/S1qCBhqld0terQkMKzBEUvDpHWb58uUYMmQIPvjgAwwdOhQTJ07s8TTqtWvX9jlQIgpuBUbss/GmAiMuH8llgFYVOnMyu6vA+DIDRtS2iVcQBK9HRqzedgaHSxvw5wXjvU6eiMjHBGb9+vXuH1aj0djudOqOmMAQ+U+tKZjbqJ3/6De22GC22T36R1Y8UyhOrQypGVDdnYfkPsTRy/4XoLUHpslih8Fsg06r8vhrDS1WvPC/k7DaBcyfWItZI9K9fn2iaOdTArNu3Tp/x0FEHqgxBP4YAZF4nIDVLqDWaEG2B8PaQm0Ltai7abxiA683Q+xEMWoFdFolGltsqGps8SqB2f5DDax251rb0VI9ExgiH/j0LrNo0SJ/x0FEvWiy2NDsapANxhwYuVyGlDgNKhpbUGM0e5TAuLdQh8gxAqLudiGd93EHkihDp0VjixEVejOGpid4/HWbv690//lwmd6n1yaKdqGzSE1EPRKrL1qVHHFBmrGSmuDdNN4mS+htoQa674FxLyH5UIEBfBtmZ3cI2HKydfPDUSYwRD5hAkMUJmpc/S8pcZqg9Ze4Z8F42MhrNLf2wIQSsQLTZLG7q0RAmyWkPlRgAO92Ih0orkd9kxUJGiVkMvh03hQR9eE0agAoLy/HRx99hJMnT6KxsbHLgx3ZxEvkH+JuIHE+SzC0Hifg2TTeUO2BidMoEadWwGSxo9pgRrxGCbtDcFdOvD1GQCQ28lZ4MczuS9fy0ez8dBw734jTVUYcLdNj1kj2wRB5w+d3mZdffhkPP/wwrFar+z4xgRF/OxS3FjKBIeq7WpOrgTcu8DuQRN5WYFoTmNDqgQGcVRhTbROqGlswKDUO1YbWwx07no/kqQyd8/p4U4HZ/L1z+eiy/AzIZTKcrjLicCkTGCJv+bSEtHnzZvzqV7+CVqvFo48+iilTpgAAXnvtNTz44IMYOHAgAOC+++7DG2+84bdgiaKZuwIThAZeUet5SJ4mMKE3hVfk3onk+l7EGTAZCZpOJ1R7ytslpHO1JpyuMkIpl2HG8DSM6e88T+4I+2CIvOZTAvOXv/wFMpkMn3/+OZ555hkMGzYMALBkyRL86U9/wvHjx7Fo0SK88cYbmDZtml8DJopWYgUmGFN4ReK8GY8TmBBt4gXa7ERyjf4XT6HO8mB3VXe8beL90lV9uWhgMhJjVBiTIyYwDT7HQBStfEpgvv32W0yYMAGTJ0/u8vMajQavvvoqtFotfv/73/cpQCJyqg7iFF5RmtdNvKF1EnVb7uMEXNex9RRq35aPgNYemGqDGTZ77wfcitunL8t3LheNytJBLnOep1TFIwmIvOJTAlNfX48hQ4a4P1apnAOcmpub3fdpNBpMmzYNmzdv7mOIRAQAta5/eINagUnwrom3KQRPohZ1rMCI5yB5Mt+mOynxzuUnh9BaIetOY4sV3xbWAQDm5GcAcC61DUmLB8BlJCJv+ZTAJCcntzuJul+/fgCA4uLido+z2+2ora3tQ3hEJKp1JRFpQazAiNUefbMVFlvvFQZjSPfA+L8Co5DL3P8/etuJtO1kNWwOAUPS4jAwNc59f+syEhMYIm/4lMAMGDAAJSUl7o9Hjx4NQRDwySefuO8zGo3YsWMHcnJy+h4lEbn7UIIxhVeUFKOC0tXgKp7D1JNQ3UYNtK3AOBON832cASPK8LAPRlw+EqsvIncjbykTGCJv+JTAzJgxA8eOHUNlpfMH8uqrr0ZcXBwee+wxPPzww3j55Zcxc+ZM1NXV4YorrvBrwETRyGZ3oL7JObIgGAc5iuRymXvJSpwE3BOxiTdYk4K9Ie5CEhNBcQqvrzNgRJkebKW22R3YcrIagHP7dFtjWYEh8olPCcz8+fMxc+ZMHDx4EIBzSenFF1+EzWbDiy++iPvuuw8HDhxAXl4ennrqKX/GSxSV6lz9FXIZkBQbvAQGaDvMLjIqMLUmC1qsdvdSUl8rMJ4Ms9t/rh76ZiuSYlWYMCCp3edGZSVCLnOe0+TNPBmiaOfTu8xFF12EL774ot19S5YswYUXXoj3338fdXV1yM/Px+LFi5GYmOiXQImimdhEmxzn+8wSX3kzzE6cAxOKTbzJcWoo5DLYHQKOnddDEAC1Qo6UPg4GFJeQKhu7vz6bTzi3T88akQ6lov3vjTFqBYalJ+BkpQFHSvXIGNW3ihBRtPDru8yECRMwYcIEfz4lEaG1+hHM5SORO4EJ8wqMQi5DSpwaVQYzDpY4l2syE7WQ9zEhzEjofZjdlx22T3c0un8iTlYacLhMjzmjMrp8DBG1x8McicKA2EAbzBkwIk9PpBYEIaR7YAAg3dWvcqikAUDfdiCJehtmV1hjwtlqE5RyGaYPT+vyMWIfDE+mJvJcn39NErdKt7R0/9vHgAED+voyRFFNbKAN5gwYUZqHBzq2WB1wuM5zDcUKDND6vRwubQDQtxkwIvdxAt30wIi7jyYPToZOq+ryMaNdO5EOl+rdZ8gRUc98fpfZu3cvfve732Hbtm0wm7v/zUwmk8Fms3X7eSLqXY2EFRj3eUi99MCIU3hlMiBGFaIVGNdyT1FtE4C+70ACWiswBrMNJrOtU/LmPn16ZPdLQ6OydFDIZagxmlHZaHY/JxF1z6cEZvfu3Zg9e7a76tKvXz/odDq/BkZEraSswHi6C0nsf4lVKfrcVxIoYjIm6usOJMDZsBynVsBksaOysQWDXZN1AUDfZMXeonoAwJxu+l8AsZE3HicqDDhc2oDMxMw+x0UU6XzqgXniiSfQ0tKCu+66C+Xl5aitrUVhYWG3t75YtWoVZDIZ7rvvvj49D1E4k7QHxsMmXnf/S4guHwGtPTAif1RggO6H2W39oQp2h4Ch6fHIS4nr6kvdxIF27IMh8oxPCcyePXswYsQIrFmzBhkZgeuY37t3L1577TWMHTs2YK9BFA6k3YXkfM2GJiusPRxYGMpbqEUdj2HwRwUGaJ0F03En0mbX6dPd7T5qSzxS4DATGCKP+JTA2Gw2jB8/PqCNZkajEbfddhvWrFnjPmuJKFqJ5yBJUYHpF6t2z56p7aGRN5S3UIs6VWD8nMBU6FurVFa7A1tPOhOYjscHdKVtBUYQBL/ERRTJfEpgRo4ciZqaGn/H0s6yZctw9dVXY86cOb0+1mw2o7Gxsd2NKFIIguBOHIJ5DpJI7pqfAvTcByMuIcWG6BZqAEiLb10yilUroIvxT7LVOsyutQKzr6gejS029ItVYcKA3n8Jy3c38lpQ3svBkETkYwKzdOlS7NixA2fOnPF3PACADRs24MCBA1i5cqVHj1+5ciUSExPdt9zc3IDERSSFxhYbLK6lm75OjfWVJ30wYgUmpJeQ2jTxZiVq/VZFzkjofB6SuH161oh0j6Yna1UKDM9IAMBzkYg84XMCc+utt+JHP/oRPv30U9jtdr8FVFJSgl/96lf4xz/+Aa3Wswa7FStWQK/Xu29tT8omCndi1SNBo4RWou3JqR5spTa6emBCeQkpRq1Agis+f8yAEXU1zE48PqDj4Y09GcuTqYk85tE7zeDBg7u8v6ioCNdccw2USiWysrIgl3fOh2QymVeVmv3796OqqqrdkQR2ux3bt2/H3/72N5jNZigU7d/ENRoNNJrgl9aJgsHd/5Ig3d9xsZHXkwpMnCZ0l5AAIE2ngaHa5pcpvKKOw+zOVBtRWGOCSiHD9OGpHj/P6JxEvLevhBUYIg94lMAUFRV1+zlBEGC1WlFcXNzl570t0V522WU4cuRIu/sWL16MkSNH4pFHHumUvBBFOrECI9XyEdBmGq+hhyZe9zECoVuBAZzfy9lqk992IAGtFZgqgxkOh9A6fXdQChK6mb7bFXcFpowTeYl649E7TV9nuXgjISEBo0ePbndfXFwcUlJSOt1PFA1qjdLNgBG5p/F6VIEJ7QRmdP9E7Cmsc58/5A9p8RrIZIDNIaDWZMGXXmyfbmtEZgKUchnqTBac17egvx+XuYgijUfvNHl5eYGOg4i6UW2UbgqvyJNpvOEwBwYAVswdiZ9MHoDBqT0PlvOGUiFHarwG1QYzTlYYsP+cOH3XuzlZWpUCIzITcOx8I46UNjCBIepBaL/TuGzdulXqEIgkEwoVGM8SGNc26hDvgVEq5BjSZty/v2TqtKg2mPHevhLYHQKGZ8QjNznW6+cZ0z/RmcCU6XHl6Cy/x0kUKTzehfToo4/ixhtvxNdff93rY7/++mvceOON+M1vftOn4IhI2im8otQEVxNvD7uQxB6YUK/ABIrYyLvpaDkA73YfteWeyMudSEQ98iiB2bdvH5577jkYDAZMnTq118dPnToVRqMRq1atwqFDh/ocJFE0k3IKr0h87foejhNwb6MO8SbeQMlMdF4jq905Rbenwxt7wom8RJ7xKIF55513IJPJ8Mwzz3j8xCtXroQgCHjrrbd8Do6I2uxCkjCB6RerhjiLrc7U9U6kcFlCCpSMhNZt2clxaozP9e0IlBGZCVApZKhvsqK0vtlf4RFFHI8SmB07diAvLw+TJk3y+IkvvPBCDBw4ENu2bfM5OCJqW4GRbglJIZe5E6julpGawmASbyBltJkr4+n03a5olM5GXoAnUxP1xKME5uzZsxgzZozXTz527FicPXvW668jIqcWqx0GV2IgZQUG6L2R1xgm26gDRTzQEfB9+Ug0pn8SAJ5MTdQTjxIYk8mEhIQEr588Pj4eJpPJ668jIqda13KNWiGHTittYiBWgGq6OJFaEASYLOGxjTpQcvo5tzyrFXJMG57Wp+dq2wdDRF3z6J0mKSkJVVVVXj95VVUVEhP9NyyKKNqIZw+lxKsln8qa1sMSktnmgN3hbDgN5dOoA2lwWjx+O28UshO1fU7ixrbZicSJvERd8+inbMiQIdizZw+sVitUKs/GYlssFuzZswf5+fl9CpAomtWaWhMYqaX2MI1XbOAFoncXEgDcfekgvzzP8IwEqBVy6Judjby+zJMhinQeLSFddtllMBqNeOWVVzx+4ldeeQUGgwFz5szxOTiiaCeePSTlFmpR6xJSVwmMc/koVq2A3MfmVWqlVsoxMsu5bM95MERd8yiBuffee6FSqfDoo49i48aNvT7+o48+wooVK6BWq3HPPff0OUiiaFUjVmDipE9gejoPSWzgjY3i6ou/jW5zsCMRdeZRApOTk4Pf//73sFgsuOGGG3DjjTfiww8/RFlZGaxWK6xWK8rKyvDhhx+6P2+1WvHkk08iNzc30N8DUcRyV2ASQmAJqYcTqZvcU3ijs/8lEFpPpm6QNhCiEOXxr0u//vWvUVdXh+eeew4fffQRPvrooy4fJ06OfOihh/Doo4/6J0qiKCX2wKSGQAWmp23U0b6FOhDcFRg28hJ1yeOzkABg1apV+OKLLzB9+nTIZDIIgtDuJpPJMGPGDPzvf//Dc889F6iYiaKG+xykEKrA1DVZYOtwnIDYA8MExn+GZyRArZSjscWG4romqcMhCjlev9tcdtlluOyyy6DX63HgwAFUV1cDANLS0lBQUICkpCR/x0gUtcQpvKHQA5Mc5zxOwCE4jxNIbzO4TTzIMS5Kt1AHglopR35mAg6V6nGkTI+8lDipQyIKKT7/upSYmIhZs2b5MxYi6qD1JGrpExiFXIbkODVqjBZUG83tExguIQXEmJxEZwJTqse8sdlSh0MUUrxaQiKi4LE7BPfBiVKeg9RWax9M+0ZeU5SfgxQoY7gTiahbTGCIQlR9kwWu4bZIjguNBMa9lbrDNF4je2ACQjwT6UiZ3r1BgoicmMAQhSix/6VfrApKRWj8qHa3E6mJPTABMSwjHmqlHIYWG87VspGXqK3QeFckok5Cqf9FJC5ldTwPiduoA0OlkGNUlg4AT6Ym6ogJDFGIEhOYUDgHSdRdBYZNvIEjHuzIk6mJ2mMCQxSixEbZUKrAtB4n0L6Jt8ki9sBwCcnfxIF2h0sbpA2EKMQwgSEKUbUhuYTUdQXGvYTEs5D8TqzAHCtrhMPBRl4iUcASmNraWvz5z3/GmDFjAvUSRBGttQcmfJaQuI3a/4amxUOrksNgtqGo1iR1OEQhw6/vNoIgYNOmTVi7di0++eQTWK1Wfz49UVRxT+ENpQqM60iDOpMFdocAhdx5Pg+PEggcpauR90BxA46U6TE4LV7qkIhCgl/ebQoLC/HGG29g/fr1OH/+vHtewYQJE7Bw4UJ/vARR1AnFXUjJsWrIXMcJ1JrMSE9wTuN1HyXAHpiAGJXtTGBOVhikDoUoZPicwJjNZvzrX//C2rVrsX379nYHOv7617/GwoULMWrUKH/GShRVatwVmNBZQlIq5EiOVaPWZEGNwdKawHAXUkANSnVWXbiERNTK63eb/fv3Y+3atdiwYQP0eud0SKVSiauuugqHDx/GuXPnsGrVqkDEShQ1BEFwV2DSQqgCAzh3ItWaLO74zDY7rHZn1ZUJTGAMSo0FABTWcJgdkcijd5v6+nq88847WLt2LY4cOQLA+QY7cuRI3HXXXVi4cCHS09Mxbdo0nDt3LqABE0UDk8UOs80BILQqMIC4pGVwJzBNrv4XAIhVcQkpEAa6TqI+V2tyV7qJop1HCUxWVhasVisEQUB8fDwWLFiAu+66C1OmTAl0fERRSTxrKFatQGyIbU0Wd0WJCYy4hVqrkofMkQeRJjc5Fgq5DE0WO6oMZmS0OQmcKFp59M5osVggk8mQk5ODt99+GzNmzAh0XERRrdYUelN4RWJTsXicgNjAyy3UgaNSyJHTLwbnaptQWGNiAkMED+fAjBkzBoIgoLS0FLNnz8b48ePx17/+FbW1tYGOjygqVRtCbwqvKLXDNF428AaHuIxUVMNGXiLAwwTm0KFD+Pbbb7F06VIkJCTg8OHDuP/++9G/f38sWLAAn3/+OY96J/IjdwUmLgQTmA7D7MQZMKG21BVpBqU6E5hC7kQiAuDFJN6JEydi9erVKC8vx7p16zB16lRYLBa8//77uOqqq5CXl4cTJ04EMlaiqFHjqsCkJYTeEpJ4HpJ7Cck9hZcNvIE0MMW5E4kVGCInrzvuYmJisGjRImzfvh0nT57Er3/9a2RkZKC0tNS9pDR16lS8/vrr0Ot5eiqRL0K7AiM28TqTLCOXkIJiYKq4hMSt1ERAH89CGjZsGFatWoWSkhJ8+OGHmDdvHuRyOXbt2oWf/exnyMrKwi233OL187766qsYO3YsdDoddDodpkyZgs8++6wvoRKFlVA8B0kkzqWpM5lhdwitJ1FzCSmgxCWkoloTD3Ukgp8Oc1QoFLj22muxceNGlJSU4JlnnsGQIUPQ0tKC999/3+vny8nJwapVq7B//37s27cPs2fPxnXXXYdjx475I1yikFcTgucgiZLjWo8TqDNZ2lRguIQUSP2TYqBSyGC2OVDe2CJ1OESS8/vQhszMTKxYsQI//PADtmzZgttvv93r57jmmmtw1VVXYdiwYRg+fDieeeYZxMfHY/fu3f4OlygkheI5SCKlQo5+sa2zYLgLKTiUCjlyk9kHQyTyWwLzzTff4K233mp334wZM/Dmm2/26Xntdjs2bNgAk8nEwXkUNcSTqENxCQloXUZqm8BwDkzgDXJtpS5kAkPkvwRmzZo1WLx4sb+eDkeOHEF8fDw0Gg3uvfdefPDBB90eDmk2m9HY2NjuRhSuLDYH9M1WAKFZgQGA1IQ2FRgLt1EHS2sjLxMYopCd+z1ixAgcPHgQe/bswc9+9jMsWrQIx48f7/KxK1euRGJiovuWm5sb5GiJ/KfO5Ky+KOQyJMaoJI6ma+5ZMAYLt1EH0cA2jbxE0S5kExi1Wo2hQ4fiwgsvxMqVKzFu3Dj85S9/6fKxK1asgF6vd99KSkqCHC2R/4j9LylxasjloXloX9thdtxGHTxcQiJqFTbvOA6HA2azucvPaTQaaDShWWon8pY7gQnR5SOg/XlITVxCCpqBqc4m3pK6ZtgdAhQhmuASBUNIvuOsWLECc+fOxYABA2AwGPDuu+9i69at+Pzzz6UOjSjgakK8gRdoja2aTbxBlZ0YA7VSDovNgfMNze5dSUTRyG/vONdffz0GDhzol+eqqqrCwoULUV5ejsTERIwdOxaff/45fvSjH/nl+YlCWW0Ib6EWpbU50JFzYIJHLpchLzkWp6qMKKwxMYGhqOa3BOa6667Ddddd55fnWrt2rV+ehygchfIUXlHbHhib3QGAFZhgGZga505gpg9PkzocIsnwHYcoxNSG8BRekViBqTNZILZhxDKBCYrBqWzkJQI8TGC2b9/epxeZPn16n76eKJpUh8ESUnKcszpkdwiwu+6LZxNvUHArNZGTR+84M2fOhEzmW7e7TCaDzWbz6WuJolFrBSZ0l5BUCjn6xapQ32R13xfLHpigGJjCYXZEgBdzYARB8OnmcDgCGT9RxKk1OSswaSFcgQHaV4jUSjlUipAdKxVRxFOpS+qbYbXz/ZWil0fvOA6Ho083IvKMwyGERQUGaO2DAdjAG0wZOg1iVArYHQJK65ulDodIMvyViSiENLZYYXMIAICUuPCpwHALdfDIZDLkpfBUaiImMEQhRNxCrdMqoVaG9o9nuwSGDbxBNYg7kYh820btcDiwb98+HDt2DLW1tZDJZEhOTsaYMWNw4YUX+tzwSxTt3FN4E0K7+gK0nkgN8BykYONOJCIvExir1YrnnnsOf/7zn1FfX9/lY1JSUvDggw/iwQcfhFLJNzUib7iH2IX48hHQcQmJP+vBxEMdibxIYEwmE66++mrs2LEDguBco1er1UhOTobD4UBDQwMsFgtqamrw2GOP4YsvvsDHH3+MmJiYgAVPFGlq3RWY0G7gBTo28bIHJpgGcgmJyPMemIceegjbt2+HRqPBww8/jEOHDqG5uRnnz59HRUUFmpqacPDgQTz44IPQaDTYsmULHn744UDGThRx3CdRh0EFJo09MJIRe2DONzTDbLP38miiyORRAlNcXIzXX38dOp0OX3/9Nf74xz9izJgx7Xpd5HI5xo4diz/96U/YuXMn4uPj8dprr6G0tDRgwRNFmtaTqEM/geESknRS49WI1yjhEICSuiapwyGShEcJzD/+8Q8AwKpVq1BQUNDr4ydMmIBVq1bBbre7v5aIeueuwIT4DBigfYzcRh1cMpkMA1OdW6kLa5jAUHTyKIHZtWsXtFotFi9e7PETL168GFqtFt98843PwRFFm9owOAdJpFLIkRSrAsAKjBR4pABFO48SmGPHjqGgoAAajedvqlqtFhMmTMDRo0d9Do4o2rQuIYV+BQZoTbTYAxN87lkw3EpNUcqjBKaurg5ZWVleP3l2djbq6uq8/jqiaBVOFRjAOdYeAHQxTGCCjRUYinYevesYDAYkJCR4/eRxcXEwGo1efx1RNGq22GGyOHeUhEMPDAAsmzUU2YkxmD0yQ+pQoo57mB0TGIpSHiUwfTmQkYc5EnlGbODVKOVhczjiJUNSccmQVKnDiErurdT6FrRY7dCq2EhN0cXjd0mj0Yji4mKvnpzVFyLP1bRZPuJxHNSbfrEq6LRKNLbYcK62CSMyva+SE4UzjxOYf//73/j3v/8dyFiIolptmDXwkrRkMhkGpcbhUKkehTVGJjAUdTyexCsIgk83IvJM6wyY8GjgJem1HinAWTAUfTyqwBQWFgY6DqKoV2tiBYa8M4iNvBTFPEpg8vLyAh0HUdSrNrACQ97hLBiKZh4tIc2ePRvPPfdcoGMhimqtFRgmMOQZzoKhaOZRBWbr1q0YOHBggEMhim7lDc0AuIREnhN7YKoMZpjMNh7pQFHF4yZeIgqcHyoN2HeuHjIZMC4nSepwKEwkxqiQHOdMeIu4jERRhgkMUQh4bdtZAMAVozLdv1UTeWJgivNU6iLuRKIowwSGSGLnG5rx0cEyAMC9M4dIHA2FG/eRAqzAUJRhAkMksb/vKITNIWDK4BSMz02SOhwKM4NSxFkwTGAounicwLz55ptQKBRe35RKNpURdaehyYINe51HdLD6Qr5oHWbHBIaii8fZBafqEvnfW7vOoclix6gsHaYP46GI5D0Os6No5XECc+WVV+KRRx4JZCxEUaXZYsf6b4oAOKsvPMCRfCFWYGpNFjS2WKHTqiSOiCg4PE5gMjMzMWPGjEDGQhRV/rmvBHUmC3KTY3DV6Eypw6EwFa9RIi1Bg2qDGUU1JozlNnyKEmziJZKA1e7A69udW6eXTh8CpYI/iuQ7NvJSNOK7JpEE/nu4HGUNzUiNV2P+hTlSh0NhbmAqZ8FQ9AnJBGblypW46KKLkJCQgPT0dFx//fU4efKk1GER+YUgCFi97QwA4M5LBkKrUkgcEYU7zoKhaBSSCcy2bduwbNky7N69G1988QWsVisuv/xymEz84aTwt/WHapyoMCBOrcAdFw+UOhyKAFxComjkUROvw+EIdBztbNq0qd3H69evR3p6Ovbv34/p06cHNRYif3t1q7P68pPJA5AYyx0j1HeswFA0CskKTEd6vR4AkJycLHEkRH1zoLge3xbWQaWQ4e5LB0sdDkWIga4KTEOTFfUmi8TREAVHyI/JdTgcuO+++zB16lSMHj26y8eYzWaYzWb3x42NjcEKj8grq13VlxsK+iMzUStxNBQpYtQKZOq0qGhsQWGtCf1cJ1QTRbKQr8AsW7YMR48exYYNG7p9zMqVK5GYmOi+5ebmBjFCIs+crjLgf8crIZM5t04T+VPrTiQuI1F0COkEZvny5fjkk0+wZcsW5OR0v9V0xYoV0Ov17ltJSUkQoyTyzGvbnHNffpSfgaHp8RJHQ5FmUKrz7xQTGIoWIbmEJAgCfvGLX+CDDz7A1q1bMWjQoB4fr9FooNFoghQdkffK9c348GAZAB7aSIExyFWBKawNzCwYk9mG74obIEDAtGFpAXkNIm+EZAKzbNkyvPvuu/joo4+QkJCAiooKAEBiYiJiYmIkjo7Ie2t3FMJqFzB5UDImDOgndTgUgcRGXn9VYGqNZuwtqsfeojrsLarDsfONsDuch/r+feFEzBmV4ZfXIfJVSCYwr776KgBg5syZ7e5ft24d7rzzzuAHRNQH+iYr/u/bYgDAz1h9oQBpeyq1IAheHQ4qCAJK65vdycq3hXU4U905EYrXKGE02/DCFz9g9sh0yOU8gJSkE5IJjCAIUodA5Ddv7y6CyWJHfpYOM4az9E6BkZscC5kMMJhtqDVZkBrf+7K62WbHqs9O4LMjFahobOn0+eEZ8bhoYLLzNigZsSoFpj23Bd+XN+LzYxWYOyYrEN8KkUdCMoEhihQtVjvWfV0EALh3xmCvfism8oZWpUB2YgzKGppRVGPqNYExmW245+392Hm6BgCglMswun8iJg1yJiwT8/p1uR37rqkD8devTuPPX/6AKy7IZBWGJMMEhiiA3t9XglqTBTn9YnA1f1ulABuUGoeyhmYU1pgwcWD3gz8bmixYvH4vvituQKxagefnj8OsEemIUfd+Ltfd0wZj3TdF+KHSiE+OlOPacdn+/BaIPBbS26iJwpnDIWDNjkIAwNLpg6FU8MeNAkucBdPTmUhVhhbc8vpufFfcgKRYFd5dcjGuGpPlUfICAIkxKiyZ5pwi/dKXP7gbe4mCje+oRAFytsaI4romaFVyzL+QwxUp8Nw7kbo5E6mkrgnzV+/CiQoD0hM0eG/pFIzPTfL6dRZPHYikWBXOVpvwkWs8AFGwMYEhCpD95+oBAONykjz+7ZaoL8SdSIU1nWfBnK4yYP7qXThX24Tc5Bi8f+8UjMhM8Ol1ErQqLJ3urML8ZfMp2OzBPfCXCGACQxQwYgJzYR7nvlBwiAnMuVpTu92cR0r1mL96FyoaWzAsPR7v33MJ8lzVGl8tmjIQKXFqnKttwn8OsApDwccEhihAmMBQsOUmx0Ihl6HJYkeVwXnA7Z6ztbh1zW7UN1kxNicR/7xnil8OEo3TKHHvDOdco79+dQoWG6swFFxMYIgCoN5kcQ8CK+DkXQoSlUKOnH7OaeWFNSZ8daISC9/4FkazDRcPTsY/fjrZrydV335xHtISNCitb8a/9pf67XmJPMEEhigAvitxVl8Gp8Uh2Y//YBD1Rmzk/fuOs1j61n6YbQ7MyU/H+sWTkKBV+fW1YtQK/Nw1XfpvX52C2Wb36/MT9YQJDFEAuJePWH2hIBP7YL78vgo2h4Drxmfj1dsvhFYVmEbyWycNQKZOi/P6Fry3tyQgr0HUFSYwRAHA/heSysCUWPefb794AP5883ioAjiDSKtSYNnsoQCAv311Gi1WVmEoOJjAEPmZ1e7AoRI9ACYwFHyXX5CJ0f11ePBHw/GH60YHZdT/gom56J8UgyqDGf/YUxzw1yMCmMAQ+d2JcgOarXbotEoMSYuXOhyKMtlJMfjkF9Pwi8uGBe3sLbVSjl+4qjCvbj2NJostKK9L0Y0JDJGf7T9XBwCYkNePB91R1LjpwhwMSI5FjdGCt3edkzocigJMYIj8bH9xAwA28FJ0USnk+OVlwwAAq7edgdHMKgwFFhMYIj87wAZeilLXj8/G4NQ41DdZ8eY3RVKHQxGOCQyRH1XoW1DW0Ay5DBjnwyF5ROFMqZDjV3OcVZjXt59FY4tV4ogokjGBIfKjA8XO6svITB3iNEqJoyEKvnljszEsPR76Zive2FkodTgUwZjAEPkR579QtFPIZbhvznAAwNodhdA3sQpDgcEEhsiPmMAQAXNHZ2JkZgIMZhv+vvOs1OFQhGICQ+QnLVY7jp3nADsiuVyG+1y9MOu/KWIvDAUEExgiPzlSpofVLiAtQeM+EZgoWl0+KhPDM+JhaLHhLe5IogBgAkPkJ20PcAzWBFSiUCWXy7BslnM679qdhTBxLgz5GRMYIj9h/wtRe/PGZmOQay7MuzwjifyMCQyRHwiC4B5gN4EJDBEA546kn80cAgB4bftZnlRNfsUEhsgPztU2odZkgVohx+j+OqnDIQoZNxT0R/+kGNQYzXhvb4nU4VAEYQJD5Afi8tGYnERolAqJoyEKHSqF3F2FWb3tDCw2h8QRUaRgAkPkB/uL2f9C1J0fX5iDDJ0G5foW/PtAqdThUIRgAkPkB+7+F55ATdSJVqXA0unOKsz/23oaNjurMNR3TGCI+qixxYqTlQYAwIS8JGmDIQpRP5k0AClxapTUNWPjofNSh0MRgAkMUR8dLG6AIAADkmORnqCVOhyikBSjVuCn0wYDAP625TTsDkHiiCjcMYEh6qP97uWjJGkDIQpxt188AIkxKpytNuGzo+VSh0NhjgkMUR8dYAMvkUcStCosnjoQAPC3r07DwSoM9QETGKI+sDsEHCxuAMABdkSeWHzJIMRrlDhRYcDmE1VSh0NhjAkMUR+cqjLAYLYhTq3AiIwEqcMhCnmJsSosnJIHAHj5q1MQBFZhyDchmcBs374d11xzDbKzsyGTyfDhhx9KHRJRl8T+l/EDkqBUhOSPE1HIufvSQYhRKXC4VI/tp2qkDofCVEi+45pMJowbNw6vvPKK1KEQ9ajtCdRE5JmUeA1umzwAAPDyZlZhyDdKqQPoyty5czF37lypwyDqFQ9wJPLNkumD8dbuc9h3rh67z9ZhypAUqUOiMBOSFRhvmc1mNDY2trsRBVqN0Yyi2iYAQAErMEReydBpsWBiLgDgb1tOSRwNhaOISGBWrlyJxMRE9y03N1fqkCgKiNWX4RnxSIxRSRwNUfi5Z8ZgKOUyfH261r0cS+SpiEhgVqxYAb1e776VlPDIdgo8HuBI1Dc5/WJx04QcAMArW05LHA2Fm4hIYDQaDXQ6XbsbUaDxAEeivvvZzCGQy4CvTlThaJle6nAojEREAkMUbBabA4dKnW+2rMAQ+W5gahyuHZcNAHhy4zE0WWwSR0ThIiQTGKPRiIMHD+LgwYMAgMLCQhw8eBDFxcXSBkbkcuy8HhabA/1iVRiUGid1OERh7ZeXDUOcWoF95+qxcO23MLRYpQ6JwkBIJjD79u1DQUEBCgoKAAAPPPAACgoK8Lvf/U7iyIic3PNf8vpBJpNJHA1ReBucFo93fjoZOq0S+87V47a/70FDk0XqsCjEhWQCM3PmTAiC0Om2fv16qUMjAtB6gCPnvxD5R8GAfnh3ycVIjlPjcKket7y+GzVGs9RhUQgLyQSGKJQJgsAJvEQBMLp/IjYsvRhpCRqcqDBgwWu7UKFvkTosClFMYIi8VNbQjMpGM5RyGcbmJEkdDlFEGZ6RgH/eMwXZiVqcqTbh5td2oaSuSeqwKAQxgSHyklh9GZWtQ4xaIXE0RJFnUGoc3rtnCgYkx6K4rgkLXtuFwhqT1GFRiGECQ+Qlzn8hCrzc5Fj8854pGJIWh/P6Ftz82i78UGmQOiwKIUxgiLx0oLgBAOe/EAVaZqIW790zBSMzE1BtMGPBa7s47I7cmMAQeaHJYsPxcudhoUxgiAIvNV6DDUsvxticRNQ3WXHrmt3uXYAU3ZjAEHlhx6ka2B0CshK1yE6KkTocoqiQFKvGOz+djIl5/WBoseGOv+/BlhNVsDsEqUMjCSmlDoAoXJhtdqz89HsAwDWu0edEFBw6rQpv3T0JP31zH745U4vF6/dCp1Vi8uAUTBmcgilDUjAiIwFyOQdLRgsmMEQeWrP9LIpqm5CeoMEvZg+VOhyiqBOrVuKNOy/CEx8dw3+PlKOxxYYvjlfii+OVAIDkODUmD0rGlCHOpGZoejwnZUcwmSAIEVeDa2xsRGJiIvR6PU+mJr8oqWvCj/68DS1WB/5yy3hcN76/1CERRTWb3YEjZXrsOluLXWdqsa+oHs1We7vHpMZrcPHgZEwenIILsnUYmZmAWDV/bw9l3vz7zQSGyANL3tqHL45X4uLByfi/JRfztzqiEGOxOXC4tAG7ztRi19la7D9XD7PN0e4xMhkwMCUO+VkJyM/UIT9Lh1HZOmQlavkzHSKYwDCBIT/66kQl7lq/D0q5DJ/+ahqGZyRIHRIR9aLFasfBEmdCc6C4Ht+XG7o9WykxRuVMarKcSc3YnEQMTYuHUsF9LsHmzb/frKUR9aDFaseTG48DAO66dBCTF6IwoVUpcPHgFFw8OMV9X7XBjO/LG9vcDDhdbYS+2YrdZ+uw+2yd+7ExKgVG99dhbE4SxuYkYlxOEvJSYlmpCSFMYIh68Nq2syiua0KmTotfXjZM6nCIqA/SEjRIS0jD9OFp7vvMNjtOVRrdCc2x83ocLdPDZLFjb1E99ha1zpxJjFFhbE6i65aEcTlJyEzUSvGtEJjAEHWruLYJ/2/raQDA4/PyEa/hjwtRpNEoFRjdPxGj+ye677M7BJytNuJQqR6HSxtwqFSP7883Qt9sxY5TNdhxqsb92NR4DUZl6zDK1U8zKkuHQalxUHA7d8CxB4aoG3ev34vNJ6owdWgK3rl7MkvHRFHMYnPgZIUBh0obcLi0AYdL9fih0oCuZulpVXKMzNS1S2y4A8oz7IEh6qMvj1di84kqqBQyPHXtaCYvRFFOrZRjTE4ixuQkAsgDADRb7DhR0Yjj5Y04ft753xPlBjS7GogPljS4v14mA/KSYzEkLR5D0uMxJC3O+ee0ePSLU0vzTYU5JjAUcZosNry3twTnaptw74whXq9Rt1jtePLjYwCAuy8djKHp8YEIk4jCXIxagYIB/VDQ5mR6u0NAUa3JndCI/602mFFU24Si2iZsPlHV7nn6xarcycyQ9DgMTo3H4LQ45PSLhVrJnVDd4RISRQx9sxVv7yrCG18Xoc5kAQDEa5R45MoRuG1ynscjxl/84gf8dfMpZCVq8eUDMxDH3hci6qMqQwtOVxpxptqIM9UmnKk24my1CWUNzd1+jUwGZOm0yEmORW6/WAxIjkVucgxyk51/TovXRNzRCZwDwwQmqtQYzXhjZyHe3nUOBrMNADAgORaJMSocKdMDACYMSMKqm8b2ug26qMaEy1/aDovNgVdvm4C5Y7ICHj8RRa8miw2FNSZnUlNldCc2hTWmTpOFO1Ir5cjpF4PcfrHITopBdqIWma6DZjMTtchK1IZd3w0TGCYwUaGsoRlrtp/F/31b7J64OTwjHstmDcXVY7Igk8nw9q4i/OnzkzBZ7FApZPjZjCH4+ayh0KoUnZ5PEAQsXr8XW09WY9qwVLx11yT2vhCRJARBQK3JguK6JpTUNaG0vhnFtU0oqXfezje0eHQad2KMClmuZCYz0ZnkZOi0SNNpkBavQbpOg5Q4TcjsmmICwwQmop2tNmL1tjP4z4Ey2Fw/wONyk7B81lBcNjK9U0n1fEMzfvfRUXz5vXPdeXBaHFbeMAaT2wy4AoDPj1Xgnrf3Q6WQ4fP7pmNwGntfiCg02ewOlOtbUFLXmtBU6FtwXt+MCn0LyvUtMLoq0r2Ry4CUeA3SEzRIS3D+Nz1B65qbo0FKnBop8WqkxGmQGKMK6LIVExgmMGHJ7hDQYrXDbHPAbLOjxer8r9nqQIvVDpPFhn8fKMOnR8oh/q29ZEgKls0aikuGpPRYLREEAZ8drcATG4+h2uAcJ37LRblYMTcfibEqNFvsmPPiNpQ1NGPZrCF4+IqRwfiWiYgCxtBiRbkrmanQN+N8QwvK9c2oMphR1WhGtdGMWqO5y63g3VHIZegXq0ZqvBrJcWqkxLsSnDg1kuPVSIpRIylWhcQYFZJiVUiKVSNOrfC4ms0EhglM0AiCgCaLHfVNFjQ0WaFvdt6MLTYYzDaYzDYYxVuL82OD+GeL8+NmizNpsXnxUzQnPwM/nzUEE9p0/3tC32zFHzedwLt7igE4h1A9ee0ofF/eiFe2nEH/pBh88cD0sFs3JiLyhc3uQJ3JgiqDGdUGM6oMLa7/OpOcGqMZdSYLaoxmNLZ4VtHpSCmXtUlq1M7/xqiQGKtyJzzi55X2Fky7II8JDBOY3pltdpjMdmdi4Uoq2iYbYvJhaLG5EhRnotLQbHV/bLX7/6+QSiGDVqmARiWHps1/8zMTsGT6YORn9e3/67eFdVjxn8M4U21qd/9rd1yIKy7I7NNzExFFIovNgfomC2qNFtSaxMTGgjqT2XWfxflLbJMVDc0W1DdZYelwInhvHOYmlLx0MwfZRRqHQ0CT1Y4mi7Nq0eS6Of9sQ7PVDqNY9WixwehKTMQkpOOfTWY7LHbv/nJ1R62Qt8uiE7QqxGmUiNcoEa9RIF6jQpxGgQStss39zj/HqhXOJEUph1algFopD3hD2aRByfj0V9Pw6tYzeGXLaVjtAmaOSMPlozIC+rpEROFKrZQjQ+dsAvZUi9Xu+qXX9ctvkxWNzW0+bpPwNDRZUVPnQImHz80KjJ84HAJaXH0bLVa76+Zw3efs42h23d9stXdIQGzOP1vbJCNtP+9KWlqs/kk2uhKjUiBOo3QlGArEqZXuZEO8Xyz19YtVIbFN2S8pRg2tSh62O3ZOVxnwv+OVuOWiAUjmREwiIsnwKAGXwhojNE2A2eqAxe6AxdUc6vyv82Zp89+2n7fYHa5kozUhMbdJSDomKv6qZHhCJnMmHLFqBWLUCsSqlM7/qhWdqhvO6kebqkcXFZA4tQJKRfROexyanoCh6T3PhyEiotAS0QnMNS9/DbkmNuivq1bIoVE5l0O0KjliVArnn129HK3Jh3P5pDURUSBW3ZqMOP/rfIz4NbFqZVhXO4iIiPwhohOYeI0CsfFqqBVyqJXOJlDnf50ft/5Z0XqfK/nQKOTQiImHSg6t0plQiH/WiPe7HhPj+lijVITMQCAiIqJIFdEJzO7H5nAXEhERUQSK3sYHIiIiCltMYIiIiCjsMIEhIiKisBPSCcwrr7yCgQMHQqvVYvLkyfj222+lDomIiIhCQMgmMO+99x4eeOABPPHEEzhw4ADGjRuHK664AlVVVVKHRkRERBIL2QTmxRdfxJIlS7B48WKMGjUKq1evRmxsLN544w2pQyMiIiKJhWQCY7FYsH//fsyZM8d9n1wux5w5c7Br1y4JIyMiIqJQEJJzYGpqamC325GR0f5gvYyMDJw4caLT481mM8xms/vjxsbGgMdIRERE0gnJCoy3Vq5cicTERPctNzdX6pCIiIgogEIygUlNTYVCoUBlZWW7+ysrK5GZmdnp8StWrIBer3ffSko8PYybiIiIwlFIJjBqtRoXXnghNm/e7L7P4XBg8+bNmDJlSqfHazQa6HS6djciIiKKXCHZAwMADzzwABYtWoSJEydi0qRJeOmll2AymbB48WKpQyMiIiKJhWwCs2DBAlRXV+N3v/sdKioqMH78eGzatKlTYy8RERFFH5kgCILUQfhbY2MjEhMTodfruZxEREQUJrz59zske2CIiIiIesIEhoiIiMIOExgiIiIKO0xgiIiIKOyE7C6kvhD7knmkABERUfgQ/932ZH9RRCYwBoMBAHikABERURgyGAxITEzs8TERuY3a4XDg/PnzSEhIgEwmkzocNDY2Ijc3FyUlJdzW3QavS/d4bbrHa9M9Xpvu8dp0L5SujSAIMBgMyM7Ohlzec5dLRFZg5HI5cnJypA6jEx5z0DVel+7x2nSP16Z7vDbd47XpXqhcm94qLyI28RIREVHYYQJDREREYYcJTBBoNBo88cQT0Gg0UocSUnhdusdr0z1em+7x2nSP16Z74XptIrKJl4iIiCIbKzBEREQUdpjAEBERUdhhAkNERERhhwlMANTV1eG2226DTqdDUlIS7r77bhiNxl6/bteuXZg9ezbi4uKg0+kwffp0NDc3ByHi4PH12gDOAUdz586FTCbDhx9+GNhAJeDttamrq8MvfvELjBgxAjExMRgwYAB++ctfQq/XBzHqwHjllVcwcOBAaLVaTJ48Gd9++22Pj3///fcxcuRIaLVajBkzBp9++mmQIg0+b67NmjVrMG3aNPTr1w/9+vXDnDlzer2W4czbvzeiDRs2QCaT4frrrw9sgBLy9to0NDRg2bJlyMrKgkajwfDhw0Pv50ogv7vyyiuFcePGCbt37xZ27NghDB06VLj11lt7/JpvvvlG0Ol0wsqVK4WjR48KJ06cEN577z2hpaUlSFEHhy/XRvTiiy8Kc+fOFQAIH3zwQWADlYC31+bIkSPCjTfeKGzcuFE4ffq0sHnzZmHYsGHCTTfdFMSo/W/Dhg2CWq0W3njjDeHYsWPCkiVLhKSkJKGysrLLx3/99deCQqEQnnvuOeH48ePC448/LqhUKuHIkSNBjjzwvL02P/nJT4RXXnlF+O6774Tvv/9euPPOO4XExEShtLQ0yJEHnrfXRlRYWCj0799fmDZtmnDdddcFJ9gg8/bamM1mYeLEicJVV10l7Ny5UygsLBS2bt0qHDx4MMiR94wJjJ8dP35cACDs3bvXfd9nn30myGQyoaysrNuvmzx5svD4448HI0TJ+HptBEEQvvvuO6F///5CeXl5RCYwfbk2bf3zn/8U1Gq1YLVaAxFmUEyaNElYtmyZ+2O73S5kZ2cLK1eu7PLxN998s3D11Ve3u2/y5MnCPffcE9A4peDttenIZrMJCQkJwptvvhmoECXjy7Wx2WzCJZdcIvz9738XFi1aFLEJjLfX5tVXXxUGDx4sWCyWYIXoEy4h+dmuXbuQlJSEiRMnuu+bM2cO5HI59uzZ0+XXVFVVYc+ePUhPT8cll1yCjIwMzJgxAzt37gxW2EHhy7UBgKamJvzkJz/BK6+8gszMzGCEGnS+XpuO9Ho9dDodlMrwPCXEYrFg//79mDNnjvs+uVyOOXPmYNeuXV1+za5du9o9HgCuuOKKbh8frny5Nh01NTXBarUiOTk5UGFKwtdr8/vf/x7p6em4++67gxGmJHy5Nhs3bsSUKVOwbNkyZGRkYPTo0Xj22Wdht9uDFbZHmMD4WUVFBdLT09vdp1QqkZycjIqKii6/5uzZswCAJ598EkuWLMGmTZswYcIEXHbZZTh16lTAYw4WX64NANx///245JJLcN111wU6RMn4em3aqqmpwR/+8AcsXbo0ECEGRU1NDex2OzIyMtrdn5GR0e11qKio8Orx4cqXa9PRI488guzs7E4JX7jz5drs3LkTa9euxZo1a4IRomR8uTZnz57Fv/71L9jtdnz66af47W9/ixdeeAFPP/10MEL2GBMYDz366KOQyWQ93k6cOOHTczscDgDAPffcg8WLF6OgoAB//vOfMWLECLzxxhv+/DYCIpDXZuPGjfjqq6/w0ksv+TfoIAnktWmrsbERV199NUaNGoUnn3yy74FTxFm1ahU2bNiADz74AFqtVupwJGUwGHDHHXdgzZo1SE1NlTqckONwOJCeno7XX38dF154IRYsWIDf/OY3WL16tdShtROedWYJPPjgg7jzzjt7fMzgwYORmZmJqqqqdvfbbDbU1dV1u/yRlZUFABg1alS7+/Pz81FcXOx70EESyGvz1Vdf4cyZM0hKSmp3/0033YRp06Zh69atfYg88AJ5bUQGgwFXXnklEhIS8MEHH0ClUvU1bMmkpqZCoVCgsrKy3f2VlZXdXofMzEyvHh+ufLk2oueffx6rVq3Cl19+ibFjxwYyTEl4e23OnDmDoqIiXHPNNe77xF8klUolTp48iSFDhgQ26CDx5e9NVlYWVCoVFAqF+778/HxUVFTAYrFArVYHNGaPSd2EE2nEZsx9+/a57/v88897bMZ0OBxCdnZ2pybe8ePHCytWrAhovMHky7UpLy8Xjhw50u4GQPjLX/4inD17NlihB5wv10YQBEGv1wsXX3yxMGPGDMFkMgUj1ICbNGmSsHz5cvfHdrtd6N+/f49NvPPmzWt335QpUyK2idebayMIgvDHP/5R0Ol0wq5du4IRomS8uTbNzc2d3leuu+46Yfbs2cKRI0cEs9kczNADztu/NytWrBDy8vIEu93uvu+ll14SsrKyAh6rN5jABMCVV14pFBQUCHv27BF27twpDBs2rN122NLSUmHEiBHCnj173Pf9+c9/FnQ6nfD+++8Lp06dEh5//HFBq9UKp0+fluJbCBhfrk1HiMBdSILg/bXR6/XC5MmThTFjxginT58WysvL3TebzSbVt9FnGzZsEDQajbB+/Xrh+PHjwtKlS4WkpCShoqJCEARBuOOOO4RHH33U/fivv/5aUCqVwvPPPy98//33whNPPBHR26i9uTarVq0S1Gq18K9//avd3w+DwSDVtxAw3l6bjiJ5F5K316a4uFhISEgQli9fLpw8eVL45JNPhPT0dOHpp5+W6lvoEhOYAKitrRVuvfVWIT4+XtDpdMLixYvbvWEUFhYKAIQtW7a0+7qVK1cKOTk5QmxsrDBlyhRhx44dQY488Hy9Nm1FagLj7bXZsmWLAKDLW2FhoTTfhJ+8/PLLwoABAwS1Wi1MmjRJ2L17t/tzM2bMEBYtWtTu8f/85z+F4cOHC2q1WrjggguE//73v0GOOHi8uTZ5eXld/v144okngh94EHj796atSE5gBMH7a/PNN98IkydPFjQajTB48GDhmWeeCblfjHgaNREREYUd7kIiIiKisMMEhoiIiMIOExgiIiIKO0xgiIiIKOwwgSEiIqKwwwSGiIiIwg4TGCIiIgo7TGCIiIgo7DCBIYoSH3/8MaZNmwadTuc+CTvUD8P0p/PnzyMhIaHdAX4AUFRU5L4eRUVFPT6HP66b3W7HyJEjkZeXh+bmZp+fh0LD9u3bcc011yA7OxsymQwffvhhwF+zrKwMt99+O1JSUhATE4MxY8Zg3759Pj3XoUOHcOuttyI3NxcxMTHIz8/HX/7yFz9H3N7Jkycxa9YsZGRkQKvVYvDgwXj88cdhtVq9eh6eRk0UBQ4ePIibbroJDocDs2fPRlZWFmQyWcSd2NyThx9+GE1NTXj22WcljUOhUODpp5/G/Pnz8dxzz+GJJ56QNB7qG5PJhHHjxuGuu+7CjTfeGPDXq6+vx9SpUzFr1ix89tlnSEtLw6lTp9CvX79uv2bgwIFYv349Zs6c2elz+/fvR3p6Ot555x3k5ubim2++wdKlS6FQKLB8+fKAfA8qlQoLFy7EhAkTkJSUhEOHDmHJkiVwOBze/XxKfZYBEQXeE088IQAQHnvsMalDkcS3334rABDmz5/f6XPiGVPw4Awp8XE9ndXlqTFjxggxMTFCeXl5n5+LQgO6OKetpaVFePDBB4Xs7GwhNjZWmDRpUp/+/jzyyCPCpZde6tXX5OXlefWaP//5z4VZs2a1u+/DDz8UCgoKBI1GIwwaNEh48sknBavV6lUcPbn//vu9/r64hEQUBYqLiwEAw4YNkzgSabz00ksAgLvvvlvaQNq466670NzcjNdff13qUCiAli9fjl27dmHDhg04fPgw5s+fjyuvvBKnTp3y6fk2btyIiRMnYv78+UhPT0dBQQHWrFnj15j1ej2Sk5PdH+/YsQMLFy7Er371Kxw/fhyvvfYa1q9fj2eeecYvr3f69Gls2rQJM2bM8O4L/ZY+EVHIESsvXd1mzJghCEJrBSIvL0+w2WzCCy+8IIwfP16Ii4sTOr5FnDx5Uli6dKkwePBgQaPRCDqdTpg2bZrw9ttvdxtDbW2t8Ktf/cp9Em5ubq6wbNkyoba2Vli0aJEAQFi3bl27r2lpaRGee+45YcKECUJ8fLygUqmEjIwMYeLEicLDDz8s1NbWenwNKioqBLVaLWRnZwt2u73T5/tagVm3bl2317jtreNzV1VVCUqlUsjOzvbrb7IkHXSowJw7d05QKBRCWVlZu8dddtllwooVK3x6DY1GI2g0GmHFihXCgQMHhNdee03QarXC+vXru/0abyowX3/9taBUKoXPP/+8XbzPPvtsu8e9/fbbQlZWlk/fg2jKlCmCRqMRAAhLly7t8uezJ+yBIYpg48ePx6JFi7Bz506cOXMGU6dOxdChQwEAI0eObPdYQRBw4403YtOmTZg2bRry8/Nx7Ngx9+fff/99LFy4EC0tLRg5ciSuuuoq6PV67NmzB3fccQe++uorvPHGG+2es7KyEtOmTXOv0c+bNw8OhwP/+Mc/sGnTJlxwwQWdYnY4HLj66quxefNm6HQ6TJs2DUlJSaiursapU6fwpz/9CT/5yU/a/YbYk08//RQWiwWzZ8+GXO7/ovPQoUOxaNGiLj9XVlaGL7/8EoCz96WttLQ0jB8/Hvv27cPevXsxZcoUv8dG0jpy5AjsdjuGDx/e7n6z2YyUlBQAwIkTJ5Cfn9/j8zzyyCNYtWoVAOfPx8SJE929IgUFBTh69ChWr17t/nt477334p133nF/fVNTE+bOndvu76DRaOz0OkePHsV1112HJ554Apdffrn7/kOHDuHrr79uV3Gx2+1oaWlBU1MTYmNjcfHFF2PPnj3dfg8ZGRmoqKhod997770Hg8GAQ4cO4eGHH8bzzz+PX//61z1ei7aYwBBFsOuvvx7XX3897rzzTpw5cwY//elPceedd3b52OLiYjgcDhw5cqTTG+6RI0dwxx13QCaT4d///ne7ZsVz587hmmuuwbp16zBz5kwsXLjQ/bnly5fj1KlTmDZtGj7++GMkJiYCAOrq6nDVVVdh48aNneLYuXMnNm/ejIKCAmzbtg0JCQntPr9v3z7k5uZ6fA2++uorAAhYgnDppZfi0ksv7XR/Q0OD+/6HHnqoy5gvueQS7Nu3D5s3b2YCE4GMRiMUCgX279/fKYGNj48HAAwePBjff/99j88jJjsAkJWVhVGjRrX7fH5+Pv7973+7P/7973+Phx56yP3xzJkz8cc//hGTJ0/u9jWOHz+Oyy67DEuXLsXjjz/e6ft46qmnumxS1mq1AJzJSE+76pTKzumG+DMxatQo2O12LF26FA8++GCna9Xtc3r0KCKKCs8++2yn5AUAnnnmGZjNZjz//POd3sTy8vKwdu1aTJo0CX/961/dCUxJSQn+85//QCaTYfXq1e7kBQCSk5OxevVqFBQUdHqtyspKAMC0adM6JS8AMHHiRK++p++++w4Aev0tFwAGDRrk1XN3x2Kx4IYbbsCxY8ewYMECPPfcc10+TqxAHThwwC+vS6GloKAAdrsdVVVVmDZtWpePUavVnaqhPZk6dSpOnjzZ7r4ffvgBeXl57o/T09ORnp7u/lipVKJ///7u6mtHx44dw+zZs7Fo0aIu+1omTJiAkydPdvv1ANq9vi8cDgesViscDgcTGCLy3k033dTpPofDgc8++wwAsGDBgi6/buLEiYiPj8d3332HlpYWaLVabN++HQ6HAxdeeGGn3xgB5/LW2LFjcfjw4Xb3T5gwAQqFAm+88QaGDx+OG2+8EVlZWT5/T2JC1Pa32O7cdNNN7t+Mu/Lmm2/2+hyCIODOO+/E1q1bMX36dLz55puQyWRdPlaMSYyRwo/RaMTp06fdHxcWFuLgwYNITk7G8OHDcdttt2HhwoV44YUXUFBQgOrqamzevBljx47F1Vdf7fXr3X///bjkkkvw7LPP4uabb8a3336L119/3edm8KNHj2L27Nm44oor8MADD7iXeRQKBdLS0gAAv/vd7zBv3jwMGDAAP/7xjyGXy3Ho0CEcPXoUTz/9tNev+Y9//AMqlQpjxoyBRqPBvn37sGLFCixYsAAqlcrzJ+pTBw4RhYXummUFobWJNT09vcuvraqq8qhJVbyVlpYKgiAIq1atEgAIP/7xj7uN67rrrusyrr/+9a/u5j64GoxvueUW4Z133hHMZrNX37tKpeqxQdff26gfeeQRAYAwatQooa6ursfn+9///icAEPLz83v5LihUbdmypcufg0WLFgmCIAgWi0X43e9+JwwcOFBQqVRCVlaWcMMNNwiHDx/2+TU//vhjYfTo0YJGoxFGjhwpvP766z0+vqcm3u4a/fPy8to9btOmTcIll1wixMTECDqdTpg0aVKvr9udDRs2uBv04+LihFGjRgnPPvus0Nzc7NXzsAJDRACAmJiYLu93OBzuP3fXrNqWRqPpcyy/+MUvcPPNN2Pjxo3YuXMndu7ciQ0bNmDDhg144oknsGPHDo+rMmIDcGNjY5/j6s2rr76KP/7xj8jKysKnn37a43AxwLldFUCvj6PQNXPmTAiC0O3nVSoVnnrqKTz11FN+e8158+Zh3rx5Hj++pwnTTz75JJ588slen+OKK67AFVdc4fFr9mTBggXdVnO9wQSGiHqUmpqKmJgYNDc34/nnn0dqaqpHX9e/f38APb959vS5jIwMLFmyBEuWLAHg3K1x1113YdeuXXj00Uc9Ws4BnP0A1dXVqK2t9ejxvvr444/xi1/8AgkJCfjvf//rUU+AGFNGRkZAYyOKRBxkR0Q9UigU+NGPfgQA+Oc//+nx102fPh0ymQwHDhzAiRMnOn3+0KFDnfpfejJy5Eg88sgjAJxHI3hqwoQJAJy7LAJl7969uOWWWyCTyfD+++932ZzclaNHjwIALrzwwoDFRhSpmMAQUa+eeOIJqNVqPPzww3jzzTfbLSuJjh49iv/85z/ujwcMGIAbbrgBDocDP/vZz9ot4dTX1+PnP/95l6X3r776Cp9++mmng90EQcAnn3wCwLsdD7NmzQIA7Nq1y+Ov8cbZs2cxb948NDU14fXXX/eqzP7NN98AAGbPnh2Q2IgiGZeQiKhXEyZMwDvvvIM777wTd955Jx5//HGMGjUKaWlpqKurw5EjR1BaWooFCxa022b9yiuv4NChQ9i6dSsGDRrk7hfYsmULUlJScO2113aaBXP48GHcf//90Ol0mDBhArKzs9Hc3IwDBw7g3LlzSExMxO9//3uPY7/qqqugUqnw1VdfwW63e7xF01PPPPMMqqqqkJaWhm3btmHbtm1dPq7j8lt1dTUOHz6M7OxsXHTRRX6NiSgaMIEhIo/Mnz8fF110Ef7617/iiy++wNdffw273Y6MjAwMHToUy5cvx49//ON2X5OZmYk9e/bgqaeewgcffIBPPvkE6enpuOWWW/CHP/yh3bAt0TXXXAO9Xo8dO3bg1KlT2L17N2JiYpCbm4tHH30Uy5YtQ05OjsdxZ2RkYP78+Xj33Xfxv//9D3Pnzu3ztWjLbrcDcCYkPfXlPPnkk+0SmHfeeQc2mw333HNPl0O+iKhnMqGn9mkiogC688478eabb2LdunXdTgj2h71792LSpEm48cYb200slYogCBg3bhxOnz6Ns2fPIjMzU+qQiMIOe2CIKOJddNFF+MlPfoIPPvjAq8bhQPnXv/6FI0eO4JFHHmHyQuQjJjBEFBWee+45xMbG4rHHHpM0Drvdjt/+9rcYMGCAVwfXEVF7XHgloqjQv3//Lk/gDTaFQtHltnIi8g57YIiIiCjscAmJiIiIwg4TGCIiIgo7TGCIiIgo7DCBISIiorDDBIaIiIjCDhMYIiIiCjtMYIiIiCjsMIEhIiKisMMEhoiIiMLO/wd8jaSWcJ8vHAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params = np.array(\n", " [amp_in, f0_in, fdot_in, fddot_in, phi0_in, iota_in, psi_in, lam_in, beta_sky_in,]\n", ")\n", "\n", "gb.run_wave(*params, N=N, dt=dt, T=Tobs, oversample=2)\n", "\n", "# signal from first binary\n", "A = gb.A[0]\n", "freqs = gb.freqs[0]\n", "print(\"signal length:\", A.shape)\n", "plt.plot(freqs, np.abs(A))\n", "plt.ylabel(\"TDI-A Channel\", fontsize=16)\n", "plt.xlabel(\"freqs (Hz)\", fontsize=16)\n", "dx = 7e-7\n", "plt.xlim(f0 - dx, f0 + dx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding additional GB astrophysics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible in `GBGPU` to inherit a special class [(`gbgpu.gbgpu.InheritGBGPU`)](https://mikekatz04.github.io/GBGPU/html/user/derivedwaves.html#gbgpu.gbgpu.InheritGBGPU) that allows users to add other types of astrophysics to the FastGB waveform. This requires that the astrophysical effects vary slowly.\n", "\n", "The methods that need to be written when adding astrophysics are `prepare_additional_args`, `special_get_N`, `shift_frequency`, and `add_to_argS`.\n", "\n", "`prepare_additional_args`: Prepares all arguments beyond the base GB parameters.\n", "\n", "`special_get_N`: Implemented if the new setup puts limitations on the sampling rate in the time-domain for the slow part of the waveform. \n", "\n", "`shift_frequency`: Shifts the frequency in the slow computation. \n", "\n", "`add_to_argS`: Adjusts the phasing in the transfer function of the slow waveform. \n", "\n", "See [`gbgpu.thirdbody.GBGPUThirdBody`](https://mikekatz04.github.io/GBGPU/html/user/derivedwaves.html#gbgpu.thirdbody.ThirdBody) for an example and more information." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Third-body in orbit around the inner binary" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "gb_third = GBGPUThirdBody(use_gpu=False)\n", "\n", "A2 = 400.0 # third body amplitude parameter\n", "varpi = 0.0 # varpi phase parameter\n", "e2 = 0.3 # eccentricity of third body\n", "P2 = 1.2 # period of third body\n", "T2 = 0.5 * P2 # time of periapsis passage of third body\n", "\n", "\n", "A2_in = np.full(num_bin, A2)\n", "P2_in = np.full(num_bin, P2)\n", "varpi_in = np.full(num_bin, varpi)\n", "e2_in = np.full(num_bin, e2)\n", "T2_in = np.full(num_bin, T2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Third-body signal length: (128,)\n" ] }, { "data": { "text/plain": [ "(0.0019993, 0.0020007000000000002)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params = np.array(\n", " [amp_in, f0_in, fdot_in, fddot_in, phi0_in, iota_in, psi_in, lam_in, beta_sky_in, A2_in, varpi_in, e2_in, P2_in, T2_in]\n", ")\n", "\n", "gb_third.run_wave(*params, N=N, dt=dt, T=Tobs, oversample=2)\n", "\n", "# signal from first binary\n", "A_third = gb_third.A[0]\n", "freqs = gb_third.freqs[0]\n", "print(\"Third-body signal length:\", A_third.shape)\n", "plt.plot(freqs, np.abs(A), label=\"No third body\")\n", "plt.plot(freqs, np.abs(A_third), label=\"No third body\")\n", "plt.ylabel(\"TDI-A Channel\", fontsize=16)\n", "plt.xlabel(\"freqs (Hz)\", fontsize=16)\n", "dx = 7e-7\n", "plt.xlim(f0 - dx, f0 + dx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the Information Matrix" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10, 8, 8)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "params = np.array(\n", " [amp_in, f0_in, fdot_in, fddot_in, phi0_in, iota_in, psi_in, lam_in, beta_sky_in,]\n", ")\n", "\n", "inds = np.array([0, 1, 2, 4, 5, 6, 7, 8])\n", "\n", "info_matrix = gb.information_matrix(\n", " params,\n", " easy_central_difference=False,\n", " eps=1e-9,\n", " inds=inds,\n", " N=1024,\n", " dt=dt,\n", " T=Tobs,\n", ")\n", "\n", "cov = np.linalg.pinv(info_matrix)\n", "\n", "cov.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Covariance Matrix for first binary:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1.03670758e-02, -3.03751670e-09, -4.34853085e-06,\n", " 9.30287319e-05, -4.16250330e-04, 5.58219344e-04,\n", " -5.55445555e-05, 4.37703212e-04],\n", " [-3.03751670e-09, 2.75957296e-12, 4.60004509e-09,\n", " -1.30903471e-07, 2.27487105e-10, -7.85411493e-07,\n", " 1.13683606e-07, -6.31724576e-08],\n", " [-4.34853085e-06, 4.60004509e-09, 8.78628478e-06,\n", " -2.50761137e-04, 3.73944799e-07, -1.50454902e-03,\n", " 1.72593472e-04, -7.75682309e-05],\n", " [ 9.30287318e-05, -1.30903471e-07, -2.50761137e-04,\n", " 7.17103859e-03, -9.43217244e-06, 4.30257258e-02,\n", " -5.08042272e-03, 1.88810467e-03],\n", " [-4.16250330e-04, 2.27487092e-10, 3.73944776e-07,\n", " -9.43217177e-06, 1.67174837e-05, -5.65945132e-05,\n", " 6.51025824e-06, -1.93069353e-05],\n", " [ 5.58219343e-04, -7.85411493e-07, -1.50454902e-03,\n", " 4.30257258e-02, -5.65945172e-05, 2.58151320e-01,\n", " -3.04822260e-02, 1.13284197e-02],\n", " [-5.55445553e-05, 1.13683606e-07, 1.72593472e-04,\n", " -5.08042272e-03, 6.51025872e-06, -3.04822260e-02,\n", " 1.08018147e-02, -8.85702255e-04],\n", " [ 4.37703212e-04, -6.31724576e-08, -7.75682309e-05,\n", " 1.88810467e-03, -1.93069355e-05, 1.13284197e-02,\n", " -8.85702255e-04, 9.57210495e-03]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Standard deviation on the marginalized parameters:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2.03637676e-24, 3.32239249e-09, 2.23448704e-20, 8.46819850e-03,\n", " 8.17740391e-04, 1.52425781e-01, 4.15727117e-02, 4.89185674e-02])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "params[inds, 0] * cov[0].diagonal() ** (1/2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the Information Matrix ellipse for the intial frequency and frequency derivative:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ind1 = 1 \n", "ind2 = 2\n", "inds_get = np.array([\n", " [ind1, ind1],\n", " [ind1, ind2],\n", " [ind2, ind1],\n", " [ind2, ind2]\n", "]).T\n", "sub_mat = cov[0][tuple(inds_get)].reshape(2, 2)\n", "\n", "# calculate and draw covariance ellipse\n", "a, b, b, c = sub_mat.flatten()\n", "\n", "lam1 = (a + c) / 2. + np.sqrt(((a-c)/2) ** 2 + b ** 2)\n", "lam2 = (a + c) / 2. - np.sqrt(((a-c)/2) ** 2 + b ** 2)\n", "\n", "if b == 0. and a >= c:\n", " theta = 0.0\n", "elif b == 0. and a < c:\n", " theta = np.pi / 2.\n", "else:\n", " theta = -np.arctan2(lam1 - a, b)\n", "\n", "t_vals = np.linspace(0., 2 * np.pi, 1000)\n", "x = np.sqrt(lam1) * np.cos(theta) * np.cos(t_vals) - np.sqrt(lam2) * np.sin(theta) * np.sin(t_vals)\n", "y = np.sqrt(lam1) * np.sin(theta) * np.cos(t_vals) + np.sqrt(lam2) * np.cos(theta) * np.sin(t_vals)\n", "\n", "x_in = params[1, 0] * (1 + x)\n", "y_in = params[2, 0] * (1 + y)\n", "plt.plot(x_in, y_in)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Utility functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`GBGPU` provides many utility functions. Below are some examples of `GBGPU` utility functions. This may not include all utility functions. See the [utility documentation](https://mikekatz04.github.io/GBGPU/html/user/utils.html#gbgpu-utility-functions) for all included utility functions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Get the instantaneous gravitational wave frequency" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given $f_0$, $\\dot{f}_0$, and $\\ddot{f}_0$ calculate the instantaneous frequency of the gravitational waves approximating the frequency evolution to quadratic order:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$f_{gw}$ (Hz)')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num = 15\n", "f0 = np.random.uniform(0.001, 0.002, num)\n", "fdot = np.random.uniform(1e-17, 2e-17, num)\n", "fddot = np.random.uniform(1e-28, 2e-28, num)\n", "\n", "t = np.arange(0.0, 10 * YEAR, YEAR/200)\n", "\n", "# cast t to be for all binaries\n", "t = t[None, :]\n", "\n", "f = get_fGW(f0, fdot, fddot, t)\n", "\n", "plt.plot(t[0], f[0])\n", "plt.xlabel(r\"$t$ (s)\")\n", "plt.ylabel(r\"$f_{gw}$ (Hz)\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Get amplitude (for slowly evolving source)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[6.37190427e-23 6.37190427e-23 6.37190427e-23 6.37190427e-23\n", " 6.37190427e-23 6.37190427e-23 6.37190427e-23 6.37190427e-23\n", " 6.37190427e-23 6.37190427e-23 6.37190427e-23 6.37190427e-23\n", " 6.37190427e-23 6.37190427e-23 6.37190427e-23]\n" ] } ], "source": [ "m1 = np.full(num, 0.2)\n", "m2 = np.full(num, 0.1)\n", "f0 = np.full(num, 0.1)\n", "d = np.full(num, 6.0) # kpc\n", "amp = get_amplitude(m1, m2, f0, d)\n", "\n", "print(amp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Get $\\dot{f}$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.73056526e-19 1.73056526e-19 1.73056526e-19 1.73056526e-19\n", " 1.73056526e-19 1.73056526e-19 1.73056526e-19 1.73056526e-19\n", " 1.73056526e-19 1.73056526e-19 1.73056526e-19 1.73056526e-19\n", " 1.73056526e-19 1.73056526e-19 1.73056526e-19]\n" ] } ], "source": [ "m1 = np.full(num, 0.2)\n", "m2 = np.full(num, 0.1)\n", "f0 = np.full(num, 0.001)\n", "\n", "fdot = get_fdot(f0, m1=m1, m2=m2)\n", "\n", "print(fdot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Determine necessary sampling rate in the time-domin" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "get_N(amp, f0, Tobs, oversample=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Citations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can access the necessary citations for the specific waveforms with the `citation` property." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "@software{michael_l_katz_2022_6500434,\n", " author = {Michael L. Katz},\n", " title = {mikekatz04/GBGPU: First official public release!},\n", " month = apr,\n", " year = 2022,\n", " publisher = {Zenodo},\n", " version = {v1.0.0},\n", " doi = {10.5281/zenodo.6500434},\n", " url = {https://doi.org/10.5281/zenodo.6500434}\n", "}\n", "\n", "@article{Cornish:2007if,\n", " author = \"Cornish, Neil J. and Littenberg, Tyson B.\",\n", " title = \"{Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy}\",\n", " eprint = \"0704.1808\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " doi = \"10.1103/PhysRevD.76.083006\",\n", " journal = \"Phys. Rev. D\",\n", " volume = \"76\",\n", " pages = \"083006\",\n", " year = \"2007\"\n", "}\n", "\n", "@article{Robson:2018svj,\n", " author = \"Robson, Travis and Cornish, Neil J. and Tamanini, Nicola and Toonen, Silvia\",\n", " title = \"{Detecting hierarchical stellar systems with LISA}\",\n", " eprint = \"1806.00500\",\n", " archivePrefix = \"arXiv\",\n", " primaryClass = \"gr-qc\",\n", " doi = \"10.1103/PhysRevD.98.064012\",\n", " journal = \"Phys. Rev. D\",\n", " volume = \"98\",\n", " number = \"6\",\n", " pages = \"064012\",\n", " year = \"2018\"\n", "}\n", "\n" ] } ], "source": [ "print(gb.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 }