{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "3ef3fd9a-9aca-4125-bab4-c9d873e5b8b0", "metadata": {}, "source": [ "# Example-29: Orbit (fixed point computation)" ] }, { "cell_type": "code", "execution_count": 1, "id": "890f08fe-8677-4a03-8b90-bb7ee7484df5", "metadata": {}, "outputs": [], "source": [ "# In this example computation of fixed points is illustrated\n", "# Fixed points are computed for given initial guess using Newton root search method\n", "# Closed orbit is computed, which is special case of period one stable (elliptic) fixed point corresponding to center manifold\n", "# Also, period five fixed point is computed (restricted to horizontal plane)" ] }, { "cell_type": "code", "execution_count": 2, "id": "cf809ec3-f6b7-4fae-841c-e4a19fcb555a", "metadata": {}, "outputs": [], "source": [ "# Import\n", "\n", "import torch\n", "torch.set_printoptions(linewidth=128)\n", "\n", "import matplotlib\n", "from matplotlib import pyplot as plt\n", "matplotlib.rcParams['text.usetex'] = True\n", "\n", "from twiss import twiss\n", "\n", "from ndmap.signature import chop\n", "from ndmap.evaluate import evaluate\n", "from ndmap.pfp import parametric_fixed_point\n", "\n", "from ndmap.pfp import clean_point\n", "from ndmap.pfp import chain_point\n", "from ndmap.pfp import matrix\n", "\n", "from model.library.drift import Drift\n", "from model.library.quadrupole import Quadrupole\n", "from model.library.sextupole import Sextupole\n", "from model.library.dipole import Dipole\n", "from model.library.line import Line\n", "\n", "from model.command.wrapper import group\n", "from model.command.orbit import orbit" ] }, { "cell_type": "code", "execution_count": 3, "id": "e4f1215d-34b7-45b2-8a92-a156a53af311", "metadata": {}, "outputs": [], "source": [ "# Define simple FODO based lattice using nested lines\n", "\n", "DR = Drift('DR', 0.25)\n", "BM = Dipole('BM', 3.50, torch.pi/4.0)\n", "\n", "QF_A = Quadrupole('QF_A', 0.5, +0.20)\n", "QD_A = Quadrupole('QD_A', 0.5, -0.19)\n", "QF_B = Quadrupole('QF_B', 0.5, +0.20)\n", "QD_B = Quadrupole('QD_B', 0.5, -0.19)\n", "QF_C = Quadrupole('QF_C', 0.5, +0.20)\n", "QD_C = Quadrupole('QD_C', 0.5, -0.19)\n", "QF_D = Quadrupole('QF_D', 0.5, +0.20)\n", "QD_D = Quadrupole('QD_D', 0.5, -0.19)\n", "\n", "SF_A = Sextupole('SF_A', 0.25, 0.00)\n", "SD_A = Sextupole('SD_A', 0.25, 0.00)\n", "SF_B = Sextupole('SF_B', 0.25, 0.00)\n", "SD_B = Sextupole('SD_B', 0.25, 0.00)\n", "SF_C = Sextupole('SF_C', 0.25, 0.00)\n", "SD_C = Sextupole('SD_C', 0.25, 0.00)\n", "SF_D = Sextupole('SF_D', 0.25, 0.00)\n", "SD_D = Sextupole('SD_D', 0.25, 0.00)\n", "\n", "FODO_A = Line('FODO_A', [QF_A, DR, SF_A, DR, BM, DR, SD_A, DR, QD_A, QD_A, DR, SD_A, DR, BM, DR, SF_A, DR, QF_A], propagate=True, dp=0.0, exact=False, output=False, matrix=False)\n", "FODO_B = Line('FODO_B', [QF_B, DR, SF_B, DR, BM, DR, SD_B, DR, QD_B, QD_B, DR, SD_B, DR, BM, DR, SF_B, DR, QF_B], propagate=True, dp=0.0, exact=False, output=False, matrix=False)\n", "FODO_C = Line('FODO_C', [QF_C, DR, SF_C, DR, BM, DR, SD_C, DR, QD_C, QD_C, DR, SD_C, DR, BM, DR, SF_C, DR, QF_C], propagate=True, dp=0.0, exact=False, output=False, matrix=False)\n", "FODO_D = Line('FODO_D', [QF_D, DR, SF_D, DR, BM, DR, SD_D, DR, QD_D, QD_D, DR, SD_D, DR, BM, DR, SF_D, DR, QF_D], propagate=True, dp=0.0, exact=False, output=False, matrix=False)\n", "\n", "RING = Line('RING', [FODO_A, FODO_B, FODO_C, FODO_D], propagate=True, dp=0.0, exact=False, output=False, matrix=False)" ] }, { "cell_type": "code", "execution_count": 4, "id": "53ac420b-4eb0-4239-a2e8-43e34ae3f05d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor([5.0000, 5.0000], dtype=torch.float64)\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Correct chromaticity\n", "\n", "# Set parametric mapping\n", "\n", "ring, *_ = group(RING, 'FODO_A', 'FODO_D', ('ms', ['Sextupole'], None, None), ('dp', None, None, None), root=True, alignment=False)\n", "\n", "# Set deviation parameters\n", "\n", "fp = torch.tensor(4*[0.0], dtype=torch.float64)\n", "dp = torch.tensor([0.0], dtype=torch.float64)\n", "ms = torch.tensor(8*[0.0], dtype=torch.float64)\n", "\n", "# Compute first order parametric fixed point with respect to momentum deviation\n", "\n", "pfp, *_ = parametric_fixed_point((0, 1), fp, [ms, dp], ring)\n", "chop(pfp)\n", "\n", "# Define ring around fixed point\n", "\n", "def mapping(state, ms, dp):\n", " return ring(state + evaluate(pfp, [ms, dp]), ms, dp) - evaluate(pfp, [ms, dp])\n", "\n", "# Tune\n", "\n", "def tune(ms, dp):\n", " matrix = torch.func.jacrev(mapping)(fp, ms, dp)\n", " tunes, *_ = twiss(matrix)\n", " return tunes\n", "\n", "# Chromaticity\n", "\n", "def chromaticity(ms):\n", " return torch.func.jacrev(tune, 1)(ms, dp)\n", "\n", "# Initial chomaticity values\n", "\n", "psix, psiy = chromaticity(ms).squeeze()\n", "\n", "# Define target chomaticity values\n", "\n", "psix_target = torch.tensor(5.0, dtype=torch.float64)\n", "psiy_target = torch.tensor(5.0, dtype=torch.float64)\n", "\n", "# Perform correction\n", "\n", "dpsix = psix - psix_target\n", "dpsiy = psiy - psiy_target\n", "\n", "# Set solution\n", "\n", "solution = - torch.linalg.pinv((torch.func.jacrev(chromaticity)(ms)).squeeze()) @ torch.stack([dpsix, dpsiy])\n", "\n", "# Set sextupoles\n", "# Note, ring function in not effected\n", "\n", "SF_A.ms, SD_A.ms, SF_B.ms, SD_B.ms, SF_C.ms, SD_C.ms, SF_D.ms, SD_D.ms = solution.tolist()\n", "\n", "# Check chromaticity\n", "\n", "print(chromaticity(solution).squeeze())\n", "\n", "# Plot tunes vs momentum deviation\n", "\n", "nux, nuy = tune(solution, dp)\n", "\n", "dps = torch.linspace(-5.0E-3, 5.0E-3, 16, dtype=torch.float64)\n", "nuxs, nuys = torch.stack([tune(solution, dp) for dp in dps.reshape(-1, 1)]).T\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.plot(dps.cpu().numpy(), (nux + psix_target*dps).cpu().numpy(), color='red', linestyle='dashed')\n", "plt.scatter(dps.cpu().numpy(), nuxs.cpu().numpy(), color='black', marker='x')\n", "plt.plot(dps.cpu().numpy(), (nuy + psiy_target*dps).cpu().numpy(), color='blue', linestyle='dashed')\n", "plt.scatter(dps.cpu().numpy(), nuys.cpu().numpy(), color='black', marker='x')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "305d9e16-79d6-4e7a-ac71-612b1d50cc3f", "metadata": {}, "outputs": [ { "data": { "image/png": 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LnS2ckXXZ0ccJAAAZnAup0+mkhiaRwTmRQrVarWOhqd1ue4WmpaWlgWa20GqTbjq0mxBRLIITAGAidbvd/rQDMzMz3s1zWYLH0tKSRFF0bEoC12i8OGYTnU9fKJtuOgzpyI5wBCcAwMTRM4MrpSSKIq+RaZodPOxRceZ9nDt3TiqVykDoEZF+hcs3xCwtLfW/j6LIqzKG0SA4AQDG2tLSklSrVZmenpZut+t1nZs3b/ZHps3Ozuaa1+jx48cSRdGxy8rKiuzu7h7rT9Rut+Xw8ND7Pu0O4Z988knmfUX5CE4AgLGlJ4I8OjqS/f19uXnzptd1Hj9+LPV6XZrNZlC1ScvSXBdaZRI5vmaeuRYextPUqHcAAAAXc/ZskdehIm2xW5Hf+wq9fPkydcbtOFtbW9LtduXKlSupI9RC+jHZzMpYpVJh+oETgIoTAGCsdLtdmZ6ePtZZ+vnz50NdSmR5eVmOjo4G5mpyXbKGpqWlJfnpp5+kVqtJs9lMnZQT44GKEwBgrFy/fv3Ygri+zVdmJ+tx1e125fr16/0186IoylwZw/ARnAAAY8OcQkAkvM+P3bQ3blzNf5cuXRrhHiEUTXUAgLFgh4q8fX7Gqb+Qbn5cWVkZeHy+k3JifBCcAABj4YsvvhioxOTt8zMu/YUWFhZkZWVloPkxT5+mbrcr7733nrRaLYmiSBYWForcXaRgrToAwFioVCr94BTSr8k0Tuu12aMCRV7v3yeffJKrylSv1+Xg4GDgd6N+rCcda9UBAE6cTz75RKrVaubQNC708it2aGq323J0dJTrsbVarWOhqVarZb49hCM4AQDGwtramrx69SpXsDArTsMcYaeXX7GnUdD7tLi4WMgacvZaeCIi33zzTe7bhT+CEwBgYpjLlayvrwct05KF7m/0xRdfyO7u7kA/Jh2Y8laZkrTb7bHpy3VaEJwAABNjbW1tYBqC/f19WVlZkSiKcocoPTKuUqlIvV6X6elp+eyzz+TRo0fy4sULEXkdlprNpnQ6nVIC0+LiYr85M8/km8iO4AQAmCi3bt1yzuGUFqLMYDQ1NeVc1Hd/f1+UUnJwcCD7+/tydHQk1WpVPv74Y2m1WnLnzh35+eefS6sCFdGciXwYVQcAmEjdblc+//xzOTw8jN2m3W5Lr9eTFy9eyIsXL/rrxiWJokimpqakVqvJG2+8ITdu3KC57IQLyQwEJwDAxFtaWpLvvvsuddi+7lxeqVSOBa5GoyG3bt0iJE0gpiMAAIylhYWFftPX9PT00O53bW1tYMFe3Veo3W5Ls9mURqMhzWZT7ty5I0dHR/Lq1atji/kOY5HhpaUlmZqaOhFr7p1WVJwAAENjThcgwsSNpm63KysrK/2fOTbDQ8UJADCW2u12//txXIR3lG7evDnqXYAHghMAYGj+4R/+QVqtlnQ6HXn+/Pmod2dk6vV6v8lSj+67du1a/++EyvFFUx0AYCgWFhbk/v37IvK6yc5nBNukMpssW62WPHz4cHQ7A5rqAADjR4cmEfrvmMxKE8YfwQkAMBRm/6bZ2dkR7snodTqdfpMl0xucLAQnAMBQbG1t9Yf27+7u9n/farUkiiKpVqulritXtKWlJalUKpmmV1heXpaHDx8Smk4g+jgBAEbKnqJgcXHxRCwpMjU1dWySzAk9pU48+jgBAE6Mubm5gZ/X19dlYWFhRHtzXLPZ7FeVzpw506+KXbp0aSD0MRLudKDiBAAYObvqJJKterO0tCTff/+9iMjAqL12uy1bW1uF7Buj4CYPFScAwIlidhx3/ZxmaWlJoiiS9fV1OTo6OjbVgTmiL5TZkb1erzMK7pSbGvUOAACQtRqk/fDDD4l/Dw1iJrMjO0DFCQBw4l26dOnY7xqNhnQ6HVFK5Q5mgEYfJwAAcKrRxwkAAKAEBCcAAEZkaWlJpqamZGFhQaanpyWKIpmampJKpSLVarX/VU+HYF6mp6dP1IShk4KmOgAACtDtduWLL76QX3/9VaampqRWq/X/dnBwIK9ever//uDgQA4ODkrZjzxTL5xWNNUBAJBDt9uV9957T7rdrnS7XTl37pxMT0/3L/V6XSqVSr9SVKlU5IsvvpD9/X1RSsnBwYHs7+/3LwcHBwO/t0NTu93uT6CpK0x6OZdKJexUff/+/X5VapwmEp0UVJwAABOv2+3K9evXRUTkww8/lL/+9a/y4sWLY9u98cYbMj8/35/3qdVqiYjIo0ePUu8jiiJ58803gypOjUZDbt26FbxmXbfblX/8x3/0rlqdlGVsRiUkMxCcAABjTYeeFy9e9IPNgwcPpFqtyltvvZUahD788EP54Ycf+uvKVavVY2vMxel0OiIi/fvXdBB6//335d/+7d/k119/lU8++WTk4WRpaUnW19edf6MJLx7BSQhOADBKOuz8v//3/+Tg4GCgAqPDTFzYsb148eLYTOCmtCCk/16pVGRmZsar4vQ//sf/kEuXLo08CGXV7Xbl888/P3ZcCE9uBCchOAFAXua6b0opiaJIlFIyNfV60Qmz6enVq1dycHAg77//vvR6Pdnb20tcay6k6iMiUqlU5I033shccfrb3/4m165dC24SO+kWFhaOLTfT6XRO3XFIQ3ASghMAxDFHf+kwFEVRv6oTGmriRFHU78+Tp+L0xhtvyI0bNzjZZ2Q331WrVXn16tUI92j8hGQG1qoDgAmlA9L+/n7sNvqzs/kZ2g5NlUoluOIkIoSdMbG2tib/83/+z37l6fDwUBYWFmiyy4jgBAATwico2cxQZFecso74wvjZ2tqSarXaf47t5jv4Yx4nADihut1uf7bpKIpkZWXFOzTpBXAPDw/l6OhIDg8PRSklSil59eqVKKXk+fPnhKYJcvv27YGfl5aWRrQnJxt9nADghAmpLFE1gqlerw/M/TShESAYM4cDwIRZWlrqzySdVFnSlSRdPaJq9NrCwkJ/fbcsX5vNpkxNTUmr1ZJqtSr1el3OnDkjlUpFWq2WTE1NSbPZHPvZur/55ptR78KJR8UJAMZY0oSGIq9Hro3DxIvDoIfWNxoN2d/fP/Z1dnZWnjx5IrVard/kGEWRiEjiPFBl0vtmfj/quZT0MRFhagKNihMAnHC6QpI0C7RSSo6Ojk50aIqrBDWbTalUKnLmzBmp1+tSrVb7HZp1ELG/6rmjXr582V8b7ujoaCA06fXgQr/Ozs5KtVqVubk5qVQqUqvVpF6vSxRFMjc3J9VqVWZnZ489PrMyqL/Xa8npCuKwK1RmcPriiy+Get+TgOAEAGNEBwnXqCcdlpRSJ2Ioue68XqlUpFqtSrVa7Tdn6YAUF4bsEOQTfmZnZyWKIqnX61Kr1frhpFKpyOLiYr/pMsvX3d1defXqlTx69EgODw/l5cuX8ttvv8nR0ZE8evRIXr16Jbu7u9LpdPr7Y+6b/b3I7/2LdJCanp6Wbrdb6HPg8sknn/S/DxmBif+gJtTTp0+ViKinT5+OelcAJOh0OqperysRUVEUqSiKVK1WU81mU3U6nYHtGo2GEpH+ZW5uboR7XqzFxUUVRdHA49OXxcXFUe+ek97narWqROTY17jH47ro51Z/nZ2dVVEUqXq9rmq1mqpUKmN7HEK02+3+Y046Pu12u9T9MO8LYZlhYo8YwQk4GVqtVuzJo9VqpW6XptPpqFarNRDCxsni4qKqVCrHHle9Xh+bfV5cXFTValXNzc0NfPUJRjoMVyoVValU1Ozs7EBAKjsgjDszSA0zQBGcBo1FcNrZ2VGrq6tqY2NDra6uqr29vUzbbm9vq9XVVbW6uqouXryYeDsmghNwMpRdcRrXE0RcYBqHCpMdlOICkn6+4ipOjUZjbMLfSZAUoooOUOZzOurX2zgYi+B0/vz5/vc7Ozvq4sWLmbZdXV0d+N7cNgnBCYBSg8Gp0+mMPKC4AuCoQoY+UdvNZK6A5Ko4ccItR1yAKjI8LS4uDjy/p93Ig9POzs6xgDMzMxO87fb29sD1dnZ2lIionZ2d1H0gOAFQ6vdP1lEUHWvuq1arQ9uPcQhMdp+kpAsBafRcAarI8DSu1dhRCMkMpYyq29zclGazOfC7ZrMpDx48CNr2/Pnz8pe//KX/+ydPnvT/DiCbbrcr586dk+np6YHLuXPnhjKiZ9iOjo76w9KvXbs28LdLly6Vfv/dblfee++9YzN9R1Eki4uLpU5QaY9qW19fF6XUsUV87dFp7Xa7P4Ls1atXYzPdgTkJqJ6AUi83Yy4902q1nNvpySr13+zruf5uTnA57CVKtra2RCkl7Xa7/zs9Am+cJ9mceGUkt9XVVXXhwoWB383Pz6sff/wx17ZXr149tq324sUL9fTp0/7lp59+ouKEU093jG632/0KgiRUGczO2Min0+moZrM5UPHSx7nMCo7d/Oa6jFMfJN2fSncaF/l9RF0URWpubq7/fcgovWFcarWaqtfrKoqi0qtyZVSfzD5pp93IK05xdMUoy7ZPnjyRe/fuycbGhnP7r7/+Ws6ePdu/vPvuuzn2FDi5dEWpXq/LysqKPHr0SO7fvy+Hh4fy+PHj/nZRFEmj0ehfms3msYoMwunjf+XKFdnd3e3P1fPmm29Kq9WSTqdTaAVHV7RarZZzXiQROTaf0bAW8V1aWuovU6Lv3/5+fX1dDg8PZW9vr389PYeTUkoeP37c/14/FhHpT0CpmXMkzc3NObfTk1WaE0Ca13P9Xf/O5eDgQF6+fClKKVlfXx+oUhVdndra2hqoPIm8rj7lqTzpyqNdgcxCv/5ORTWsjOR29+5dZ78lVxXJd9vLly8n9m2i4oTTTFeW9Kd3cXwy1hWnKIrGotIwicwOt/oSRdGxEYJF0BWIuCrMMIf7m6Pw7Pv3vfhUnEbZ18pV8dEVp7THVvR+2/uS9bVlPkd59tEedBEXLczneNzmYBvbzuGuqQR8tl1dXe2Hpr29Pa8pCegcjtNEd3rWoalSqaharZYrJOmmpkaj0b80m021uLg48HsdCuzt895/UXSn7DJPvPqx28GlyMDk27G7zKBkBiQz2KQFB3t78/tJ6HyeNHmpHaKLeqzm7dbr9Uy3YQaeSqWSeV9cc6y5gpFPuBqVkQcnpY5PMWD2Tdre3h6oHiVtu7Gx0a8+7e3tqbt373rdP8EJp4lZcQqZ7NEVjvQl7kTgOnG3Wq3EiSzNT+jDDFGuT8JFftKNGylXZBBIOynPzs4WHj7sx1WpVLwqK66K02mc4DJtUssiApRd3cx6nPVcYnmCkzkXW1IwouKUYmdnR129elVtbGyoq1evDlSJLl68ODA/U9y2evoB8xI3rYGN4AT8Tgcks2KkL2lv8HkqTkkn2GGI24e89GO1J7AsqsKkb9+1/2V07LYrSaEVpEmoGpWlzKV07ICWJTyZgxfysD9QjVswSjMWwWnUCE44rVzVJ7MaZL7B6fDkqjgVEQLiKjJFV2XilBHa7E/6RfW/MZsUXftdZFAy78unqU1XnEbdz+ikc/WBy1uVs8NTKHPy0zz0YzuprxGCkyI44XRxdQ7XX3V4clWchtls5jppDHsId54TlKsfU9nhUoeWIo6TrnzoJW3SKknDPvklVSwrlYr3xJ3mdcyfa7VaaiV0GI87rgKV577zBCf9PzKKJtVxWkeS4KQITphcrjcbu3O4bjoZlzclk706fNnyvjnHNcsVVWFynUBda/WFcM2NFHcpu6nNbHZMCj/jNkeTeSljgENcP6gsz4N5W6HXL6KPU1bmB5FarTb0+zcRnBTBCZPDrhaZlSRzmyydw0fBDAvjvEaWPYGlPrnkDTSVSsW5uG/eypJrSgBXOImiSLXb7UJfJ2a1yKcTeVKVaJQVp5BLUUGzqEqseWxCrq+PxyiCi13BHSWCkyI44WQzw5L55mJWlMY5HMWxTxLj2BfCVWHKMxdTWt+lPIEpLSyZFacim2LSmheTgltc+BmXaStCHk+tViukKdXVfBfaFy/ror066Gad0iAPc9QrFacxQHDCSeSqcpgBKmtFyXxTtU9cw+rbYE8NkLczatGKrjAlnYh11SnLCVfvZ1xlp8imN/uErpsQk0ZjuvZr1KEoj9BAlbdqmOd/M8sIOfP59X2OdFA/aSPnkhCcFMEJJ4PZxGGfkLKctF0jvnxGTeX5pOv7OO37GZcTqW7mNI99ngqT2Qnbfi7yTEaadPIuIiy5QlLc/enX7KSEoxDm/2zSMcr6gcT+f52dnfW+rvna830tmO8ZzWbT6zrm/k0KgpMiOGF8mW+8rnmAfEe8ZW0u8eknEvJm7fN4i/xUXuR+mRWmkGPv4mpuiaIod1NcXBNf3ukB0ipXrkveTuuTKGmyy6zPj32bIbeRpeoUMiWB/f88KQhOiuCE8ZK0lpzuEOtzQrL7MaSd6MwlLlwVgbh5ZYp8Q7SbdcZhJulOpzPwPOTpMxYXbrJWYMyqQdxznOUY+i4LMqyQZM82XavV+iPv9Pdx+6W3c3Wy1697/Xdzu7KnG4gLUVnu1x4R6fs8ZGl6CwlO5pxwNNVNGIITiqRHQ2U5GZonaXMtOd+wlDSLtH0izBNK7BCVl6vPUFH9P7I+Tnuf8vRh0iHYfg6yvEbiwpL5u9Bjp1+zaQvR6r8VGSrM+zbXLUwKRKO46GBVdEiM+0ASenztirLP9c379u1HGDKybpzmXioSwUkRnFAM16SH5jQASddzTUjp27m70+mknmCK7lNif8LNwz5x5B0F6DoRhXCNlMu6T3Zg0sEm9PkoIywlhewiqiCu+9MjBuOqP76XYVScQkNV3tesq8IXUqWxm8V8m9/M6/g8htDmvUkMTwQnRXBCPq5qiW9YcVWYfE/ScferTxhmfxmfTt++nzjzdEh1PQbztrJ8kjdPyK7mD9+KU5Ej5VyBKUuHbNfjyRqWzOOkK5iu103e/lB2CHBV2pJeg3GBaJiLPtvNs/q14Ps4iuynFvK4s0zhYf//pQmtOOnHM24jY/MgOCmCE7LJeqItu8JkvlmGfnpO4qrkZA1NrqpOlpNNUr8r36pOkSPlighMcTN552mGc53wdef2PPML2UufpL3ezOpO1nAwaj4V3rwhyv5wElLRCp2jydzeJwyF9HGyq6OTguCkCE7IJuuJVl9Pv6mENAPFdSi17ztr35A4ropVls6errCZtRnMtU8hs1wXNVJOBx0zCIcGprTJKUP6aZlBKe51kLXpVr/+dL87nwqMDpKTOgWBb5NnEdVG39swnxef147vhyelwoJT3gA5rghOiuCEMHETT/peV3/abjQaQW3/cSdV1xtS3Jt3UkXA9YnQHs2UNTS5pkPIM/+R/RhDT8pFjJSzT2xmeAqtMLmeD11x8g1NPiPhQo5TaB8os+J0kipIRUuqgoYGCNf0HD6vh9DBG2UFp5BtTxKCkyI4wZ9r0kjf0W5mc1DoidoOTWkl9bQTnesknfQ4iwxMOmjmPbFmmZHYbiLM0ofJVQnIEpZcnb1DJqf0GQkXOgLMbHpLCmHmOnHM1eQW96EjNEBlXZ8uZHvzNZ0WzCY1DIUgOCmCE/zYJ0zffgd5qkyafZJOu75vYLJXOU+qWoQO6zcft3l/oyjZ520i1MfFFQJDm9HsztJZmvWSQk1IPyjz5F52x+fTLO+ouSwTw5rvVz79i8zbTkJwIjgppQhO8GO+sYQ0eZgnW98mvbjrp72paWknQftknzSjcWizS1yVaVSBye74HVJlch0XHTR8A1NRI+PiTr6hI+F8ZpGnmlSOuP8z3+fNfv7TrhcyL5rvNAMEJ4KTUorgBD/6TS+kwmC/UWY5CZnXL2p5k7STZ71eDz5pukbK6bA47JNv3o7frlnbQzs4J4XRkLCkm+PyVJbM24kL1VlH7SFMngkvQ+dqChlh5zvC1RzcclpDNcFJEZxQniIqLvYbbJ7lPsw3Ud9qlA+7WU4POR/2STjv5JW6QpV1lvW00XG+c3u5FsYNCUzmnE1ps8if5o7co5R1eg/7emmvTd+qk2/IMitfWSrok4DgpAhOKIddccjK1b8h7YRnv7mmza+TNSzp/lrmmlR5Z1HOIm+TnL4N+ziFNEfEVRJ8R0FVKpXY58m3k3faiK6QzuJFvHbLZHawP6lVMlfl1yc8hTTfh1Sdxqm5ztzver0+VuGe4KQITihHEdUmzZ4MMa4SkbaN+eacZSZrpY5XdXR4yjIHUl72vmSZi8k8AZuByacTf97RcUkdvUMWc45rzgsJS0mzy5cldDHhkG19LuMSuOz/77QqoP1hqqiqk+9zXmZwinsd+nwg08exqC4NcQhOiuCEchR94knqM5N20ctF5JmEsMjJK4uQdy4m1/H0rVLlHR0XFxh01cmnKS6pOc83GPhOlJqH/VjzrlNX9mVUYcoOT2mhJGR5Fd+qk96HtP5LZQQnn0ELRQW/vAhOiuCEcpjLqRRNn/TNE1/oiBsf5gna7sOUtbpkzqGUZ5/MZoWQfYkb5eYbKu2TkG9zUd6O3mnzAvlWlrIEFx9pzY1FXFzruLXb7cIrUaMKUvZrM62SZP//J/F5Ps0PIkkLlOsm8SL7OMWFpna7fWxdxbjXOMFpiAhOKIPPP/q4ihshl3XRW/N2s7y5mU2B5ptoyILIcWup+fRByjOMPKk5yjdwJQUJn7URywhKWSug9nMwqgqPz8LX9iXLMkOh7Oc76T7t5zZvNca876T7zTJDfpq05kSfaV18+2jlRXBSBCeUI+/8TcNmVkTMk5ueJbqI/kt2J3IfdpNcSD8mV/+lkMDkmpZAB7as/Zd8KkM+TXFpFbKQ9QrTjoX5WNIqSlnD6TjwDVNljxgNqTyZr5GkwGBul3R7PgGr6IqTOVIvrvnPHLwR19+pjEDnQnBSBCeUw56wblw6oprMYev2ySHvWnJx9+fT6dpVYco7caXvFAl6H+MqKkknHb3friY13+Y4ux+ZHbp8O8imnfiThHba9n18abLcbxn7ofkEqbL+r+0AGseuOsW9PnyrvT79l4ru42T+j6d9oEgLWMNAcFIEJ5THfrMahxXi4/otmSfnLIHJNxT53I5dYfK9XXtqBH0izdJ/KeTkmNSxNe1E3ul0YqtDWcJr3Ak+6USTpaIUGlDyDG4o8pK1+pUWoooOUCHNcObrNul59glOPtukVZxCJgs2992ngmUG61G9lxKcFMEJ8fJ2ZFbKfTIexdwzcSd33ZSVJ9SFrosVt395F+DVj0+/uYZOXGlPDOnbJGcfU58lUJICU56mUbPilLQYdGh1x+dYJj2mcb6ELtAcdztF94Gyw1rS68En8PhUwPV9JlV/0j4khRxbM6iHfrgZVRcIgpMiOCGez5uRj7g327IqUGZVSZ+A7UpMkWuR2Y8rdD+zdvrW7GqGT3hzNcnp5jzfGb6zrMmXNuy6zEDtM+Tbd0oEpYppWivyf8J3SHva4/etbrr6vxX9HJqPJ6ma5BOKzPehuNG+5vtEXDAJCU5pHzqzfDg1PyCNoupEcFIEJ8QrKjgplfymnmVtOKUGO3TrhVldfZb0m5xuniv65GyGj5DJ5+w36ZDJK+NGymWtEvmGHh1I7WOcdsIfVWDyDTdp/afyhqRxmOE7tLnQp4LkmnFepLgO8b6TXdqv6Ti6ohT32Hz6Efk21aWFPfOxhVSqzQ9Zo6g6EZwUwQnxiuq3Y99mUn+YZrOpFhcX+ydofdELtPrOk6Ob38ZthXuzyqQfZ96ZvkNOVvbJ06dJLqmZMy2Ixp2sywwSPiEn7f6zBqWTtvad70i6tOfKdTtFhSc7FOVpIvMZsq+bW+Oaen06h/u8d/pW01y3PcpO4gQnRXDCaCSNaItrAkg6WZkha9zCkmY3byRNsmfLM1Iu7vpZq0Q+nbbj9rfMwKRDadJrJamKkqUDt+9jMfs/VavVxA8AaYHNpzkuy3FOW+vPJ2za1ylq7Ub7/cHFZ0JMnya9tOazokbV5enoPcrmOoKTIjhh9Ow+Sb4Vp3EYpZcm79QCrrmUfDuz6+tmqQbEder3CVuuDtJlVWLSwk7ayT4kLPl2EM/bz6isS8hisUnHJak5Ou75zxuW7f1xPQ6fKQd8+jmlrflWVHDKs7rCKJvrCE6K4AQ/w5qVdlK45iQKmVpAsysTISPlspz845qofJdUyRo4QqQ1o+lJTF37HBKU0sJe1ikGhlFx8rn49GFKeoxJz6srrOdl3lba7NlJr9m0fk5p+1zEBJi+80olXX9UzXUEJ0Vwgp8i3wAnnd0kl2VqAX3CyvLm6Fq2Iq0fU1wYSaswDTMwpVVzkqpLviEn6RjpE+7s7GzmNemG0UE8rckty37F3WZS9ck+5kVMEKpvK67/kc+CvmnvZWkVpSJm6DYrRlmDTxmLDfsgOCmCE/xMWsXJDgpF9MWwq0x5ApN58alSmZ3GQ2ZsT+rHVEbQyiKtwhR3nz4BIulxZgkgZQTGoviEx7RRoa5jkjR9hl15Chl16uLz2k4LRnn/XkTFqYg+Sno/ht3PieCkCE44fewyuRlQst6evShw3rmYQk7C9sksiqLM0xJk6QBcZmAKrZD4hJ24Y5q0ZIx98tfPtU9zVxnzPYUcE5e00XRJJ2OzmSjLc5InWBZRUUr7u/m/6NrXtEpPyIi6PNUis7Kd9b0rC4KTIjjh9LEnwxTJVnFy9WMKrTLlCUyu6/uMpsrajykucBbd/JQUNPJUl1z7GVpVSnpeslaoRh2m4l6DaZMyusJX2jQA+pJnlnHzdlyvhbSqlPl4s1St0ipOadMZKFVcM1sZU8akITgpghMmm7kEhw4VRbzZ5O3HFBcOsgYm3+DjGvGUdVqCIkfKpS1X4rovnyVO0joIp12SRqKNy/pzvpe0sJJ0TEKOo2tbV+jO+tqxXxc2n6pUWteDpA7k5khZ12NICl1aEc19el8ITiNAcEJRfD7JDZv9Zp1l6K/mmjk7Sz8mV2UiZLRclsCVpVkuLjAVPft6XKUma/+juEDnG3RcxzJvNanMiTHjZu8OfYxaXICK65/kOjY+4SlrtcV+Hl3S/p4WnNIqQknBJ+2+04JXCF09p6luyAhOKIrvp9RhclWcsnCtzRXaj8k1QWNI36Csgcv1aT/tenETWBb5nCad8LM0q8WdrH1CRd6pC4oISGZgyXusk9aSMy8+S4/4bO86VnG3W8R7RN7glDYlQdokmEnBKW0eqKKqTUoVM8IvFMFJEZxQHPvNM091Z1y4RsplnZ3crt6EvNm5OoD7zq1kngDTRuBkXccuRFzVLO4xpU1D4AqBaYEp77QFPgF0WE15WZba8b0N1/Ximi9d02C42M99FuZz63ou0/o5pVWc0sJPnsBS5DQCropT2c13BCdFcEKxzJOiXfL3bY6KO1EO81NVESPlNNfJJ2TWcPs4ZpliwKdJ0VWZKrqJKa4ZKO4kG9rvJq3vkuukHxJw4iphwxg1l2cfzX0NvW5cCHVta1Z444KHvQ9Z/q/N16qrKpTWzyktOKUFuzxVoyKDk6vZzxz8UsZ7JsFJEZxQHldTgY+46sKwKlj2G3uWfkxKuQOM76fUrJUfVxNL1s7feUY+2eICTWjlJ64qlRaY7Ov49llyhf0yK0mLi4uFBrGkIfNxFbm4KovvBwCfoG8/p1mkNaclve+Y854lBcAyll0psqlOqeNVJ5/O8XkQnBTBCeXJOn9L3Emj7IqTqw9S1g6crpNM1uVSfGb+dl3P55i5rlNk5++4hXfjpn8InbspKcRk7bdUZFjKO+FjktCAFdekGdds6np+7IqST8UmLrjk/d9OWyQ36f7N62epSOUJTr5NafaxTpp/zLw9e7qVohGcFMEJ4yfPqLOsXJ1pszYh2EHBN4hkCT5alukJQubhySIubIRWmUIDkKtSllaRSpro0Ofi0+fMdwoE18V3njGf+wgZNeja1ueE7vOhyd4mlPn8uKYlSJtPKem+84yqS+MTnEKeD9ftE5xKRnDCaaWbqKIo6r9RZm2WUyr/NANFhSafaQbskFj0zN+uE3jofEiu/lVJFSlXYEqrFGVtwgsNIGVdkppT04KfTx+luPvw6ctkvwZcsrzetbSAYH6Acd12UrBKG3WXp3O4T+hKet5sriCmX/dlfOAkOCmCE04n1yi1PCNR7NsLDV92c4nvUiuh13N1AC+yL1PcpJRxJxjXiTquQ7pr20ql4nzeQgOTT6XGVX3IU0UaVogKbc50PSbX68pemiatL5Nr/+z/wVBpgSLptvX+1+v1oNtVqtzO4a75rpKO47DnciI4KYITThdXU1qeOXP0J8+QhXVdt2Huj++IO5+Tm8nVIbjI0OQ6QSf1ZQqZJ8h1MneNciy6Cc8+ueXtGJ7leGcJZyHVN9/jYr+uXSE87XZseZvr0q6b9Pekfkxp69WVGZzMarDet6TjVOSEmj4ITorghNPBta5clpBjskevhJbuXeHB5/quE1aW0XZFlvF9qxRx28Z1onZVmeIer+9UB2nhxxWk4/Yj7lJ2nzyl4gdRpB1X13HyraalBVWXtJCWdPtp0q6btG9pI+fSAl9Z8zjFPaakzvDDrDoRnBTBCZPP1acnbSLINPYJI2+Vyfc2slwv6zxSvuxQkTT3k2+H9Li+QiGVFNd+JPX7sW/bt9JTZNUuq7TZ0e19dB1fV18fV/85m3lCd4WQtHBlNu0mLYzrYj6focufpAW+pH5OZVWckvptmZVy+zgNcwZxgpMiOGFy2VUm3Qk8b0k7b2hSavBk49tU6DrZpT2OLKPtQtihKSlE+IamuOVefPs9uW43ZCLNrCPTxoGrGpn03NhB0hWM0p5j+z5d4SnpNZtnFJh5XVfoSprrKe0+kwJOnuCU1Cnd7Ddmv8aSjhMVpyEjOGESuUJGUWtD5TmB+nyCjxParJclaIWwH0vSnEX2yTdpFnZ7n32qGHEn9aRmOfu5SwtM41BZ8pVUhbPZnfnTqkquoGE/vzbzb1lCTJKs8zHp5zvutZgUurJWeNJmPE87DnF/p+I0ZAQnTBrXiLkiOk7mDU1KZV8IOXTCwCz9oELYISMuNIV0SPcdCu8731Ncc19oh+9xrS75iAuD9v+CHYzsgGW/ntL6KqU1DSZdN/R1mhRwdBO9a9UBc6JIV1UpqQ9U1opT2hQJacEprvmQitOQEZwwKVxLhxQ1P5H9xp9lxuCssyWHrlWnVL4FhUP3JylY2CfkuIDl24yXp2Oz6zZdUyfEnYRPqrhgaEsbPJBWVUqrSiU9D+Z1Q4+9733a0qYrSLpu1pnD066XNmO52VfTPIZUnIaM4IRJkGcCySy3HRrGsi54nCVsFdEHy3d/4j4ZK3X8MYdMNZBnckZXB3D7RBXXNyrvoIFx5hMO057bpGOa1lfJPs6mPOur+Ya5pCCeVNkscjqCkBF1LnGVOypOQ0ZwwklXZgfoIkak5VmXyyd4FHVfofuTdPt2GIo7Gfo2KfqGK1do8u38fZL6MGVlN5va4SmtI3hIX6a0/mZJ1w2R9FynBTKfuZziZojPUuHJOqLO5NqGitOQEZxwkoUuNxIqb2hSavBTb8jJ2WfJirT9LZJ90ow7zq4wFHfcfOaW8q342c1uSf1WzEuZC/GOo7Q+Z2mvoaTr2rOJJ1035G9JzOc9tMktKTglXS9rhcdnpF7aMXDdBhWnISM44SRyLe1RdCdeO5RlCU1m+AlpgvDpjGsrovN6Ebdth6G442Y/f67tfCtS9n26TkyuuY5OW2jSksJR2msv5LpJ9xvytyR57jOpqS6pc3gZFSezWpp0u677puI0ZAQnnDSuk2kZI5+KuP20E34cO1SE3lfRnZvTqhCab8CyQ2laZ9mk27Ob53yG3PuG0UllV97s45r0fIeMkMv6t9DnJut9Jo26S6pGldHHKWntvLTbyDOvVCiCkyI44WQZVmjyWUoiTZamNqWOP8Ysy7AU2cE5pNrkG7B8tvOdJyrttlz91E7yFANFGUY4sl+HSc9nnnXrsk50mVRx8qkOuf6WVP1Jup5rP13PkWs7gtOQEZxwktjNLWWVpos4yWa9Dfsx+rBnIi+SuS9JlSzfwOcbxHzClU9Fyr6dYTRnnARpwd43ACUtVZM0ei40kCVJqg4lhSqfCTJDl1zJWqmyH3vc+o+uY3Tqmup2dnbU6uqq2tjYUKurq2pvby/TtiG3YyI44aTIOqQ/VJ4lIExZbyPLYywzGCSdQE1p8/i4bs93O59qU9LJL+12Tivz2NhVkKTnKa0puYy/JckajrJ2Dk8KKkVdzz7+5uvc3udT1zn8/Pnz/e93dnbUxYsXM20bcjsmghNOAvuTapn9U7L0L7JlbaZTKtvJo4igl/e2fZ8fn+18jp/PNr4h7bRKOj523zFTWZ3Ay/ifSerHlNQBPGvFKSnEJV3Pvr+44HSSOodXpAS9Xm/g5/n5ednc3AzeNuR2gJNofX194OdHjx6Vdl8HBwf97xcXFzPdxuPHj3Pfhq+lpaXSbnthYSHT9Xyfn7jtzOMXRVHqNj7m5uaCtj8NOp1O7N+eP38e+7fl5eUydqcUh4eHA19Ne3t7A19N//f//t+Br76UUgNfTS9evBj4avrpp58Gvob461//KoeHh/LXv/41+LplKiU4bW5uSrPZHPhds9mUBw8eBG0bcjvASVd2EDGtra0N9Ta63W7w7ZuhstFoBF8/yf379/vfjyp43LlzJ3Ubn9dEmWH7pDpJAWjYkkLOhx9+KNVqVT788MNjf5uamhr4anrjjTcGvpqSApdpfX1dDg8PB/7vk/Z1lEoJTk+ePHH+fnd3N2jbkNv57bff5NmzZwMX4CQpIsyMq3/8x3/sf58lqNy6davI3RkwquDhc3Kf5NcEXmu1WhJFkbRarcJus1qtDnw1vfPOOwNfTX/729/k8PBQ/va3vw38vtvtyqtXr0RE5K233jp2vRs3bkir1ZIbN27k3ndTUiAbpVKCU5y4IBS6retvX3/9tZw9e7Z/effdd8N3EEApzGbC//pf/2vw9akgYFLpptnQJtparTbw1XR0dDTw1fR//s//GfhqunbtmrRaLbl27drA769fvy5KKYmiKDgcJe2nqVKpDHwVSa6AjVIpwWlmZuZYVWh3d1dmZmaCtg25na+++kqePn3av2RpTwVQvu+++y74Olma+oCTzhUmtKRAogsHrgLCpUuXpFqtyqVLl7z3QzeVvfnmm84PMTdv3pRHjx7JzZs3j/1N9+WL69OX5FT1cbpw4YLz9+12O2jbkNs5c+aMvP322wMX4CSZ5HBg9tVJ6+vgYjb1Fc3uRzksPs931k7smAxJ/YOSmrGydsi+fv26PHr0SK5fvx50vT/84Q9SrVblD3/4w7G/vXz5cuBrnKQmxHFTSnCan58f+LnX60m73e5Xih48eNAfMZe0bdrtAJPkypUrQ7uvIkJayKi3LH11zLBlNvUVwfzw5Rp5NAwrKyup25id2OMU2TdmUkzKMUmq1ujzo32eTPPDDz/I4eGh/PDDD97X0f9/cf+HRVSGXGFvXJvqSp0A8+rVq2pjY0NdvXp1YOLKixcvqtXVVa9tk/6WhHmccBLYM+aWOY+TeT+udc98MI+T3zxOcRNSJs0hFLKN+fcS38ZPrKTjY69nl3TdUf8t6ySXSXM16fcc1yS0cfMmJd2XUmEzh9vPjb645oliyZUhIzjhpEhbmLQodkjLuu5bEcHJd0K7LNcpen98l4rxDTM+QczcxrX+lx1gi178+KRLOsZZQ9UwFgG2ZV2rLutklXF/MyfPdb1vdDod1Wq1nH/znQDT9XjGNTgNdVQdgOPsARD3798vpW/L1tbWwM+fffZZ7tsMaa4zO7HaE3/6yHKdJGaH26Tbvn379sDPcc+NPemiT3NR3Eiq2dnZ/vf7+/vHjrM9hcLR0dHENE/lZR+HpOkm7HmyzGZbe9oM8zViN52V1T8xaXRckqTpCLIwpyBwdQBPYjfBufoox81Xduqa6kaNihNOEvvTrJRUebKrTlnuI+tq776L5Sbtb9YqWd79sZ+bOD5Nmfbxc1WUfO7TPjaSUME6TZKOW1ozqO/f7NdK0nJG5vMdunZc1r/V63UlIqperx/7W5amuk6no5rNpmo2m87/wZCmOvt3+vf6uTH/H07dWnWjRnDCSdPpdI69AZcRnvL0U9JCA5DrenH9JZKuk7Vvls9tJx2LkDUFfUKRT/OsT3OcfTunPTzZx8x+bSY930U1xdnPpblItP0c2uE3633akvokJa1xl7VpzBV6fPbT5Ap047pWHcEJGDP2m2mj0Si00qJU8hu9D/OTu28AUur4ycnnDdG+TpHHIqQCZ4eUuH23T86+27nu266QJHUENi9xndMnmatqa7IrjPbxTgvRRfwtJMjlWXA4qXN4UhhJCkBJkq6n/xZFUeL/ruvxjGsfJ4ITMIbsE3ram07e28/yic78JB1S5TCv5xuEdNNDGeEprUphSju5KnX8hBd3m66mNtd2dud03/B02jqM248/pFO4/Xc7VA2jY7j9vOrQEBdIkjqAJ1WckoJTGRWnTqfT35+kQEZwGgMEJ5x09pv1uIWnLNUj1/V83hTtMBJS5fJhn1TjjrN9zOIqO76hyLWdq/Jkh03Xdq5mu9BQe1LZ4TKtScw+gYf0fbKPZ1mhKm0kW9apCpKa6rI2jaVVqtI+bMRtQ1PdkBGcMAlczQ9FNt1lDT+aWenI02Tn01wYUhkKFTK83942Lpj4dvh3BR7f8GTftyuIpYW8ky4tNCkVVm2yX8chwcjug5enuS2tahQXApX6/TXles6TmvGydsbWIS+uD2JacDKPk/l46Rw+ZAQnTAo9osWngpFF3vBkn9B9+0zZj8nner79jLIImYzUfsxxocQVilyh17eTt10ZiTsOrqY7XWUour/cqPg2T9rHzD5W9rG3j09I6LKva1aNXKEi6XZ9muJc95nW4byMipMZXl2vr6THotTgc2Ted9L8UEUjOCmCEyaPq4IxDuEp63759gWy2SfCMvs7xQUi177HBS3XCd61rWs7V/Osb5NcXHhKOoGdFL6hyR6laj+feTuUh1SjXK9T3+tm/VvIlANKZe9TZB4H13WTwlra4xkWgpMiOGEydTod50irIgJUkeHJt9nONQVD2v2anU2LDpBK+TfFufYjpM+TKxTFNbWl9avJGqBEwkdQjVLcY0nq55P0OO3bsZ8PuyqadP3QOZrS/p71b0nNdEolz+OUpzO275QErv9VgtOYIDhhkpVVfcoz9N/Vgdt3n0KDUNZqlS+7qlOpVGKPhetk7toX1z7HncDiqkppFY+kbZP6P6WFxFGLOx6ufXY9Tlczmf282cfLfr5cxybpOfeZKLaM4JSnupOnaSwpOJkfjuz9SuoHRlPdkBGcMOlc1adKpZI7QJi3GVqNyBroslyvzKZLpfwDkVLuE7vrE7+rShUXUOOCTlKHX9fFfg7TKlBp9zUscccqNBy6KkGu6T5s9n3b0iaSNa8fOgo0z0i9tDmc4o6dUuUFJzMc2X83Q5W9T3QOHzKCE04LV4CIWxrBR1q/Dp/9yTJXU5Yg5DvsPytXyIg7HiFLoMSFF1fVw27KTAo1cZ3H424/7rZdl2F0LE+qLKUdV9djd53EXc9TWpNpWrUptBqVxvz/cb3efAJb6DQFSpXXVJe0z3G/T1vmpWgEJ0Vwwuniqj7lCRFFrJ2XNpop7nGEjtJzBbUiw5PrWNRqtdhV4n3mXNK3aw+l1yc1+7aTqi/29j6VGtfxCalEFRGq0kKeb2CKa670DU1pwcQVTtKqTWkj29IkXTdtioOkcJQWbrLOHO5zXdfzmFRZG2a1SSmCk1KK4ITTyTV1QdZPbL4nmaR9yRLkXCd+n7mr7BNxmfNdxQUcLW6EnOvxh0xcmRZu7Nv3CSeu+/EJX8O6xJ2IQ/p3xR1n13Zpy/D4VGTNv2dZXzFp+H5aU3pSU13S35Qqt+Lkmjw26XU4zMkvlSI4KaUITjjdiuz/4+oPEjJLeJZ5nlxNVGkzp8dV3YpaKDmu2Syu+hR3Yo/rWxIXVIoIUD4dw0PCRNmXpE7qac15rv13PW8+4crVHGrfluu5NP8eGt7jJoPU0m47qeKUtN9K5QsrPtWqpOfNRsVpBAhOGCdpE8SVYZyqT3aIiAsbadfzWXam7E7jcYHIdR+u4Jg1oLjCRFqgcR3n0Ca5tGabPKHKpxqTVFnyOf6+29qhqV6vp96e6znRo9qSAkqStDXq0m47KTilTVWQJ6z4VKt8p9tQ6niIK3uEHcFJEZxQvE6n019sdm5uLuif2HyT0G9K5ifLMicktN/ss3byzVvRydqR2xWe0gKg677KbrrT+xZyAk86fnEBxzU1gk+4COkflDWoFCE0iIWMdPQNTSLpE1a6gkveWfiVSv+Qlba8SVJzXFrn8DwVJ9/r+s6TZoe4shf8JTgpghOKFXeCcX0qdXG9Geo3hqyfTEPo6pPeDz1aJUsFKk8ocTX7+bzZ6o7UIZ3A46ZrKPITa0hFQ6n4UBAXuJKqQ67rdDqdYxUP18UVnpNG8I3bJa4KlvT4ffvexD1/Pmsl2q+1LNLeE5KaxMzXo2seJ/3BL+59K084KTrY2EEsT8d1HwQnRXBCsZI6ymY1rIqTfZ+tVutYc0CWEnjW5jsdaOwg5NtxPHSNu7iO3UUuVxPSHBe3T3GBRqn0KkzealLIFAujuiQ9z2mPNW5CUvt5i2sK9pmeIG/fJtf9JO2zK6Ck/T+lVavKHFUXyq44EZyGgOCEIsWNTiqq4/GwdTqdfvVJv9lmqcbEDan3PS6uZrgs69WlXS9uoeR6vV5YBSquKTPueCQFrqQmv9BJIZUqrvlLyzN1QVH7oFR6R/G4ZqCQ0J+2np2Wt2+TUumj8fTrKy7gpTXFpS22Oy4VJ9ccTgSnISA4oUj6H7lWqxUyO3fefdFvrnneRHT1yTzZVyqVwprvfG8jS2fuuGalLLONh+yrj7iQktScmRRE8lSTXMcjSxXJtzN/2Xwfd2h1Km8znr1d1vcHMxSHLgqsVHrn77S/5+njVGTnbVcIIzgNAcEJk8ruG5W307Pd/0l/Yi0iQOWZtsC347iruSWt+uQKXUV2HlcqOaCMoppUVnNcWVVXsypaxL6EzJellP+SO3YQy9rsnjYNgVL5Fg1O+7vZPyzrFABFhSdXSKJz+BAQnDCpXBNLmiP1Go1Gpj48OkCZJ+8sb6B5FvsN7WyddL20+40LDEVXE7OMqMvSp8nnummB+CR1ENeXtPX0kqp5Icc/7nVhb5c1NKRNbJk2Y7i9Ly5JFScdTOKa7H1CUVHhxnU7ZU+ISXBSBCdMPl2hMCsldjXKZ94jm92/IMuaUXk6ZOs3yCzhyVWxSbvfuOsVWUlJCyRx1a60pqm4x+Y7us7nsfpUwoZ98WnKtauo5iUpeOZZ3DlPpSWtmc58/aSNqIt7PpP6QKWFHp9QVFRzmiskUXEaAoITTiNXB+W8M++aYSxkBF5cZ2nfAJVn6gLXiT5r/6ekk2wWaRWhuP306d+TNieUTwBqt9tez/GwqlMhFYa0TutJ1am458W3X1qe14l5Wz5rvWXpGG6OyIsLXkn/X2m3r1QxwSmuyZDgNAQEJ6QxT7Cj7OxdBv1JOEvFyWb2NdFfQybRzBOg8kxdMM79n+L2z+dE7NMnKakzd9Y+TePSQdzk+1jS9t0VuJJe465Qn0daKCqimS5tRF5aMPEJk/o28rzvuJoMs1S9QxGcFMEJyew3Itdkcfid7t9gNqOFdiDPW4FyLXfhW4EKvc+46k5ogLKvH3dfSQEq6T59mtGy9vWKu/gullu0LLOcp1WB4ipUIU15WWfij3tcLmn9n5RKn6MpbSqCtGqR+TqLC1dFjPgdRcdwpQhOSimCE5LZJ/BJqziVye4/EzqFgStARVHk1TyUp/O4K2CkBaG4eap8A1TcCT10YkyfgOIbgLKGxjzByr7/PLefNyylPcakY2OHpiICo3k84vbdvM+4113arOBpUxGkBSezEpu0xqBPk14cs7pthiSC05AQnJDEPBkW3YfFZI5yq9VqqtFo9C/mG1G1WlVRFKlKpTLyeaJ8uDrfhn7yNo+NDmI+n1J11ctnCQzXde0Tt89+J1V2kpqB0k7ycScgn0pSUofykHDi0wSnQ1mtVksNRsO++E7cmjRBqU8IclWn8vJpglMqvRnODIJZpzJICyfmayopFKVVtpLENScWOUdUHIKTIjghmfkmWGQznRkGGo2Gc7Zq34sZtsps28/DDlBZ18CzT/RZZx73vb699p35fKVVoKIocgaTuADi+3xn7ZPkUzULfd3l6ZBdVsUp6zqDeaZ2SDp+RXy48WmC8wlFPv3/0ipKaZ3D7Yly46SNDkwSV60iOA0JwQlx7E95RbwBxnUqbjabwRWnuDd4M5QsLi6W/kYSQr+xmUExpA9U3BQEPgEq7ro+/Z/ihu2nVf3inu+0x+wTEJJmdfYJHUX3acoSpkbN5zGmzf+klLvKVFSF2g5kPq+ZPCPezNtxSas4+UzQqZRfGHQxj4d9PXvdujIQnBTBCfHscn0eSZ/ms47EcjXv6cBkhgL9BjZOFSlXE16z2fQOea4TXqVS8TqWWSe0dE386RsYsj7/vmu9JU1N4BOifKpRefsclTHiMEToY8jTB6qoTvC+H958Oo4r9fvryWckZtxj8JlKwGcb34BlM98z7NdT2ZNfKkVwUkoRnBDPfJPN80YY9+Za1rBtc0iuq8pSqVRKWUvPNdFmyL6aQ5R9A54rBOkmstARePp6vgsBx1WSfK7r6kOT9nz4LCuS1Bk3LTjYfVOydqTPe8n6mhxmuEu6ryL/p+z78Nku7jVg/q/EdTvwuS/fUOTzIUi/N4V0g0gaFUjn8CEhOCFOEZ9eXKFp2J+8zZN1XJ+bIkKUqykrNESZtxHSidzui2Tehk8A0E2gZnDIM4lmSPAIvb5P81LopJRpgcr3tZF3pN0oLiGv+6THV/TgEbvalPThzee593nMPqGoyHAS2s/JPP6u+y97gV+lCE5KKYITymO/yY66qUKp5GqJSHrVI0nSScW3umY34WWdwsAOQb5TGJhVp5ATa1yA8gmlSaO40q4b18E6tI9H2kgy/VhCn0+trOpU2UFJSwqrZfxfm7N369dwHJ9O4Ur5VZN8timyOSypv5JLUjOdUlSchobghDKU0bG8aEkhKmt/qLQTsO9Jxq4+hfR/0uz9yNoB1bcJT18vLiDk6Yzt83yYz2OeE3lch/a0UJW3/5xPeEu75J1kMvQYlPV/bR+HuMcU8j7jE4rS5nBSqvhw4jufU9qkmVm6CmRBcFIEJ5TD7KBdZtm4KHEnrazTBuhQ5jrZ+FZDXP2fQipQup+FGWR8O5Ar5W7C05e0Pm9F9IOKu+6wO/mnVSmTLidplF1RE4MWvR9J9+X7PmNWU5Nub1jrzLluL+mxmh+k4sJxnnmhQhCcFMEJ5dCz8+b99D9sZn8o1wi9LBWoVqul2u12UGhx3Y5ZgcoyhYHd9BHSgdzVFylkDilX+KrX66mPIWkkX+h+FMX1eNJClW6yHIdQlbWyNYx9tZte0+7Tt8roE4jMwJZ3xFyItKqZOUt40hxdBKchIjihDOYbQdE6nc5AMHOdpIqqSNgnbt1cVvZCmkn7knUKg7gO5CHhw7Voa2gAcz1naYEyaTRe0c95VmV2DPcZUVjGZZjBLnSZFvO1mBYWfN6PzG2SXkdldMCOe+3YxySpeTDPEi4hCE6K4IRyFB2cfOfzsS/miTpP2785vFhPMidSXJ+S0H3JM4WBqwN5SICKmwLBt8OsDlB2+PV9DGn9qMZpvi4dVl0Vp3G8DLt6p9mvqbRJN+2g4TuHWBFNcGWNXEurAqbNCD+MOZyUIjgppQhOKEeRn1rLWPMrTzOJXYUKCS1Fs5vwQkeTuUKQbzUtbhTe3NxcUIiyq2Ah82zp66c93+PYzyhkpF3RoWtc+l65mg3TpjWwm7aS5u5Sym+ZFaX8P+yVFZzSOuSPwwcBpQhOSimCE8rhO5Nv6O3oS1Klx/6EmXQCCTnJ21z9jkZxQrKbDrM0JZqL0+rH02g0ggJQnsDiaoYMOcmbTXlpn9zHITDA/ZrxqXjZ4SKtCmO+jpL4TmxprjdZFnO/y5ooOCuCkyI4IV3aMgVxivi0VNRJT3+6d01Smef24074o2wqytOUaIYu/ZhC5oGqVqsDzaohUxmY959lNJ69L0nPsw5Y49Kkd9q4mt59nlv7emnXCZmPzOeDnjm69bS+bghOiuCEdFmDhdmHJesbjXnfPouN+tDNA5VKxfkGnmUuFFeTw6ia8PJOoqnpIKSfx5BP2HmmMjBvI25SzZAgFdJpexwmaZ1kcc1RWZ7HkM7jadUmnzXqlBrOzNzjjuCkCE5IZ75ZhaypZJa19ZtX6EnJfoP1uX7aydG+jbj5a7Lsr/2Y81bK8sgzhYFJf8qu1WrBzZpxUxnMzs4GdyaPez5DKlFmk15aMy4hqlhZF5dW6nho8ql+h9yHT7VJqeHMzD3uCE6K4IR05htelqYse/h86PVDw0xIdcG+r7j+MSGjjeLmHhpF01DeKQz0bbRarYGmuyzTMeQ5cZqPJa4DbRRFQdMS+E5sGXq7+F1Sh+eQyqP9fIReJ43vUP5hjVwbZwQnRXBC+czwlKXq4RpV5zs6JkuAyrNwrf2442Yjz8ucUsCnMpJ3CgOlfj9pmI9JnxRD54Eyn9PQflDm/hRVidK3Z1/f57VDmDouKTDV6/Wg0J4laJvPXZHzQVFxIjgppQhOGI68w+Zdb6BxJ8a4k1xaZcEWVyEJnevGrkCZs5JnPemaHcCzVG7yrINnhrA8xyZpRnOfWcXN/UlqeqvX65mqfebt+szDVKvVTn2H87T+ZKEfPLJcP2QknVJhTXohfZyyDqoZdwQnRXDC8LiGzYecsH2DjO+aW2nBydxve9ssb4b68eZdxkXflquaFbKIcN4KlFLuYx26tEzcfFBZT7ZJ0xHo+8hSKUqbZyftMonNO74d77N82LBfC77HL2QknVJhYShkW5/3lpOI4KQITihWSBjSVZPQE7brTVX/bL5Rhk6cmcR1gsj6SdKuQIVWfOzbsoNC6IifvBUopeLDamhASZpVPPQEbN6WHkVp32atVssVpOxmS5/Zn/V9nsQKlT6mPhNyZj2mrv6BWfpDldEXiuBEcFJKEZxQLLv5JilcuJrvfINXpxO/Xp39hu2zXIvv+k72beUZlqwfq34zzjM3TJ7qk96XIipQrpm8s04MGlfN8J1V3PUYfRa3zTuJaciM4En7oMNV1seblW+n+aKPnev5DvmfCFmGRQvpC6UUwUkpgpNSiuCEYrn6vSSxm++yVKFcJyq7z0uRnXjtYJCXecyyhqe4UBDal0zflhlos8wDVcSCwmm3kzVEmVMSJIWD0PmikuiKnKvilCdgmfuqbzdukldzm7gZ2rMsAVPE/1bc0j9ZQ5PvB6HQhXFDgpN+X5q0AQQEJ0VwQrHsSlDaKBXX9e1mo5C103T/mrgTQ+gnUhe76pSXa+6nIj61513U2J7GIEsFKqnjdtZO9nFhJ+vyOb6VKBHpd2Yv8mQYt2iyWXEqIlwVcSl6SaG4anDoayPLPtrH3UfoBJjmh6JJ6eNGcFIEJ5QjtOO3fV272Ui/Ifr2CbGrUHGfpO1P53En37iJLYsITvr2iwp2RXL1OcnaoT2uH9Tc3Fzwa6WsEOVz28MIFK59Sgp3RVacyp6zKqmTfZZ12ey+jL6yBDX9obBer3ttb1fgJwHBSRGcMN7iOouGNh+FVBXMS9p1ihxqPK7hSanjFag8y8nEBahqtZop7LjWyHM9h6FVDPP29fMSt4yM+ZossolvUvj8/2U5VqHLsJiyLJ8S2rSXpao17ghOiuCEk8Hsl2J+WtYn2tB5kfTt2Z/OfUYLZXmTDnmc9v2MU/+IIvo/aWnTRmQ5vmkhKk8lyr4fu6IZFwzq9fpAheU0BSqfjvJZq4J21SpkLcssgcZsdvbdZ/N/ZVLmcyI4KYITTh67+pG1T1TcbZsnQHu4+TBCjP0petwWFC2q/5Omw05caM0aUPXJMS7QzM3NZR7x55KliU9XsMxK3kkOVfYs3HGPO+/jtJ/TPBNr+r6+slSoJnGJFoKTIjjh5NL9qMyKk9mnQM9HtLi4mLm/1ahkGVo9bK5m1EajkatvW6vVKqzDsCmtEpV12Ze0+9TzSGXt4G1fdxzWzMsz3ULeKq3rvkNv055131eW60wigpMiOGGyuDqW64rUSQtSoZP5jYrZcV6f1PLMSaUV2ZncZIaopBnLzWpVkc2yrj5TIU3EcaHKp6KVdCl6BF+eZlwXV+jNEnLN2wm5fmjH8KLYU7aMGsFJEZwwucyKlLnUiR2kxuHNyGVYHUvNE0meeaTMyTz1bRUxM3ZcgMoym3gcc9mXuCCgg1aZ8/LYFRVXxamoYFPGpYymxrgKVxGdyUPoY1+r1YLvNw+768CoEZwUwQmnR1yQ0pNEupr+RlGdcgWFMt8w7fvKMmmm5ur/VFT1oYzO5Gn3kzQSrOg+Ur5CmgDLqDgN6/EmNQlm7VCe5/WSNXDl4XrNj9rIg9POzo5aXV1VGxsbanV1Ve3t7WXadnt7W62urqrV1VV18eLFxNuxEZxwWtlzTem+D2Znc/29OXqv0Wgcu+QNBUlLyNTr9VKDWxEVJ1vcKMgibl83tcWtRVh081pa/ygdJsq6/9PItfxKkR3Ks3wQMd8LsjJfQ2mj7OKWHBq1kQen8+fP97/f2dlRFy9ezLTt6urqwPfmtmkITphk5qfWtI61cRUn8w0z6ZO4bppyhSpX6DJ/H/fJetgnX/MTblH3bU8e2mg0Ch1pNKxKlFK/j7qsVCpefaTMbYqaCmFSJT2PRUwfYd5elvBeRHgJCUGu95txeO2MNDjt7OwcCzgzMzPB225vbw9cb2dnR4mI2tnZ8doPghMmmevNJ7TvjR2oXOEorSkkLnTF/X5U1YqyPt2aHVzNkFFkh9e06QfKbFazl7pJei0QqH6XNkKviOeriBGqZjNfns7h5v/77Oxs/73DtU/jOrJ2pMHp7t276sKFCwO/m5+fV9vb28Hbbmxs9H+/vb2tRMS7uY7ghElmV5zsN+k8/XlMZtNUlopTEc19RRhGh3RXE0QZHa7TKlFl3a9S7pF7SU19rtA1ieHKdyqDogJuUeHDnuYkK/NDmP0BKm7/x+15H2lwWl1ddYahH3/8Mde2V69ePbat6cWLF+rp06f9y08//URwwqlhBpxxCCrjSAeOMqte+nkYRlOEfjxJJ+zZ2dmhnKCyBqq4apXZz2t2drb/GMsc+efzGF3H2udxFv2as0NpVman+SKOqz2X1DgFozRjGZzM6lHotnt7e2p+fj6x2vQv//IvzhcswQmIl2fRYsRznWTLHLXlu2Zh3rmiQrmaGfOEKzMo6uu7bsu8P9d29m3YVRJ7FF7cAIeyK0tJx7SIwGPeThHMdSlDlooZB6UEp7t376qrV6/GXnSV6O7du85+S64qku+2ly9fTu3bRMUJCKc/Iep+OrrZr8i5hMbJsJsIhtV8Z0urRtVqtX6FaNRNJq5qVVzFKevM3mVehnUMXU20ef8/iw5OJ9lYdg53VYt8tl1dXe2Hpr29Pfo4AQXSFSdX89IkvaGOct6YuGrQMAKUvdxLXGf/KIrGJkglMY/lsCtOo2wCLyM0KUVwMo3ddARmc9z29vZA9Shp242NjX71aW9vT929e9d7HwhOgD9zIddJrDiNQyBcXFx0BpdhTjSpg1S73R4ISmlLswyrrxQGxQ0EKOr/0gyQp93Ig9POzo66evWq2tjYUFevXh2oEl28eHFgfqa4bfX0A+YlbloDF4ITcLKU2d/KVfEZlbhOxsOeqdveJzNIpTVPEajK1el0nLOdFz131zj8P4yLkQencUBwAk4Wc0SOa5mMWq2WOVSVeQLKKi5AjXLkmGZ36vbtW6S3Z5bxcLrqG9cRvehjaf5/8TwRnJRSBCfgpLE/AcddoihKnS3dZjZ5jFt1pOi1y8pg95XKG6gIVr8b5gzxJqpNg0IyQ6SUUjKBnj17JmfPnpWnT5/K22+/PerdAeBhaWlJvv/+e6lWqyIicnBwkLh9q9WShw8fDmHPyqcf+9HR0bG/NRoNuXXrliwvL49gz+J1u125efOmKKXk8ePH0mg0ZH9/v//VR6VSERERpZRMTU1JFEVycHAgMzMzsre317+tdrstW1tbZT6coVhYWJD79++nbhdFkXzyySeytrZWyn5UKhVRSkkURc7X3GkTlBnKzXCjQ8UJmBx25/XQitNJklSBytNcOQp2k5/9NctldnZWVSoVVavV+s1auoO7nsZglBUu19xVIY93GFVG+jcdR8VJqDgBONmWlpbku+++k7i36EmowOgqm0h6xalI+jZnZ2fl2bNn8vd///fS6/XkxYsXA9sdHBzI4eGhvPPOO/K///f/FvW6e8uxylqefRxFNbFer/eruVScXgvJDAQnABhzac07kxCi0uhjMDs7K0+fPpVqtSpRFMnLly+lWq3K0dHRsbBVRLDJyrxP8/txeK6iKOp/v7i4WFpz4EkSkhkqQ9onAEBGW1tb0ul0pNFoOP9+//59iaJIoiiS6elp6Xa7Q97D8m1tbYlSSnZ3d+Xw8FBevnwpv/32myil5NWrV3J0dCS7u7uilJLnz587v7bbbRGR/nGcnZ2VarUq7XZbms2mNBqNgUutVpNKpSJzc3NSqVT6gUNf3/6qv+90Ov37NO9fKTXy0GS/NghN4ag4AcAJs7S0JOvr617blt3JGCfL1NSUHB4eigjNdCYqTgAwwdbW1voVjMXFxcRtlVKyvr7er0jpysmZM2cmsjKFZDo0iYh88sknI9yTk4vgBAAnmBmikprzNN3I8PLlS1lZWekHqiiK+v2GoiiSqakpqVQqsrS0NIyHgSFoNpsDP1OFzIbgBAATYnl5eaA/TafTkWazKbVarb+N2THYZjbbHB4e9qtVlUpF6vW6TE9PS71eH/h5enpazpw5069i6W2q1Sqha4wsLS3J3t5e/2fd3wvh6OMEAKeQa7qDSqXSD0/VanWgWSerpAqYHu5//vx5+bd/+zf59ddf5c0335T//t//u/z1r38dmB7gjTfekBs3bozdJKAnQbfblZWVlYHfTeipPzOmIxCCEwDk1e125YsvvpBff/1VpqampFarycHBgbx69ar/s4jIq1ev5OXLl1Kv12VqakoODg5SZ31PEhfaoiiSN998s//zG2+8IR9++GE/ZNk/m05r8HJNZcEUBMcRnITgBACj1O125fr168cCjCmk4vTixQvnCDA7ZCVVyiqVirzxxhv9n5OClv77SQ1b3W5Xrly5cqyyNDc3J48ePRrRXo0vgpMQnABgkriCWEjFyTd42eywlXTf4xCyWq2WPH782Pm3cZh8c1wRnITgBAD4nU/wssWFLc0OXXbIMitq5pIuurmzVqvJ1NRUptDlu1iwyOsmzjt37ow81I0zgpMQnAAA+SQ1N9qhKy1k+dDzbOkwVqlURCl1bKJKsxN/GqpMfghOQnACAAyPK2T5VJwODg4KH+FGWApHcBKCEwBg/OnA9csvv8irV6+8K04iIh9//DGj4wpCcBKCEwAA8MNadQAAACUgOAEATrxutyvvvfceCxejdDTVAQBOtGq12u8D1Gq15OHDhwN/j+srBGg01QEAToSFhQWJokiiKJKFhYWB3+mf05hh6Nq1a8f+rusDWesEVLNgouIEABiZKIoS/+5zitIVJ3NEmilvxcmsaIn8vtabuVAy67+dbIyqE4ITAJwEScGpVqvJy5cvh7g3bvY+VqvV/kLHZlCbnZ2V3d3dYe8eCkBTHQDgRGi32/2vi4uL/d9Xq1X55ptvRrVbA+bm5gZ+vnTpUv+rGar29vaGul8YDSpOAADk0Gw2ZW9vj4rTCUbFCQAwdlqtlkRRJK1Wa9S7Uqjd3V1RShGaTgmCEwCgdAsLC/L48WMRkf7X067b7cq5c+fkzJkz/ZGFS0tLo94tpCA4AQBKd//+/YGfGd4vcv36ddnd3R3oAL++vu49DQNGg+AEACid7gQu8nqU2qNHj+Tzzz8f4R6NLztkYrwQnAAApdva2hKlVP8iIs45l06TGzduSK1WO/Z7M2Ri/BCcAAAYgeXlZXn58mV/GoYoimRxcVG2trZGvGdIQnACAAzV7OzswNdh052y6/W6RFEkZ86ckenpaZmenpZz584Nve/V2tqaKKXk6OiI2cdPAOZxAgBMvIWFhX7foSiKgtetq1Re1xk+/vhjws0EYh4nAMCp1+12+1Uls8O1UkoqlUq/f1G9XpdGo5G4/MvR0ZEcHR3J+vp6vzo1qgoVRovgBACYKN1uV6anp2VlZUUODg6O/b3RaMjt27fl5cuXopSS3377TZ4/fy537tyRZrPp7LCtK04iIvv7+/3L7u6ufPbZZ0MLUXoS0Wq1SmAbEZrqAAATo9vtysrKivNv7XY7V8frbrcr169flxcvXvR/9+uvvx5r9ms0GnLr1i1ZXl7OfF9x7KpYp9Mp5X5Om5DMQHACAEyM6elp2d/f7/8cRZF88sknpfVLMsOUeb/a4uJioffdarUGZl5vtVry8OHDwm7/tKKPEwDgVPr111/73y8uLpY+Um15eVl+/vlnef78uSwuLg406Ym8ngm8yKVUHj161J/nqVarybVr1wq5XfgjOAEARq5SqUgURceCR5bbERGpVqtDH/22trYmh4eHsri4eKxJTXcqL6Jf0j/8wz9Is9mUt956K/dtIRxNdQCAkTODRp7TUlG3U4SlpSX57rvvBvajUqnI7du3c/VLeu+99+TRo0f9n4tuDjyNaKoDAJwoOvAkTQlw0qytrcnR0VF/ZnCR19MafPbZZ7lG4NnNcz/88EOu/UQYghMAYOSOjo76s2dPmrW1Nel0OtJsNqVSqcjR0ZHs7u7K559/nik8LS8vD8y6funSpSJ3FykITgCAibSwsDDqXejTnchv377dD1CHh4eZw9Pu7m5/wWSa6YaL4AQAmBhms5g5W/i4MAOUDk+fffYZk1meIHQOBwBMlHHqIJ7k3Llzsru7KyKv9/nOnTtMZjkidA4HAEwMvYRKpVLxmg+p0Wj0v88zf9LS0pJEUZR6yXofN27c6E+foJSi8nRCUHECAIw1e/h92mnLXHYliqJMHc4XFhaCm/qq1ar8+c9/Dqoadbtd+eyzz/r72Gw25eeffw66X+RHxQkAMDFCZ8deXl4eqDplqeJk6R91eHgoKysr0mq1vK+zvLwst2/f7jcv7u7uFjbLOMpBcAIAjLXl5WWp1WoiIv2vaW7duiXValWUUnLz5s1c9z83N9cfwWZf9PInpsePH0u9XvcObPb0Auvr6zTZjTGCEwBg7L18+VKUUvLy5Uuv7ZeXl+XPf/6zNJtN+eWXX4KCiF3xMZsJbVtbW6KUkk6nM7BczMHBQVD16caNGwOd2r/44gvv/RV53bQYRdFYTcEwqQhOAICJtLy8LG+99Zbs7u7KlStXvGfrzjIT9/LyshweHh6rQD1+/NjrPpeXl+XOnTv9n/f394PCnm5avH//PtWqktE5HAAwsbrdrnz++edyeHgoIiKtVksePnyYeJ2lpSVZX1/v/xx6mrSvLyIyOzvbn3ogyfT0tOzv74vI69GBz58/97pPs1rl8xgxiM7hAADIYJNdo9HwarbLOxP32tpav/lO29vb86oE3bp1q//9r7/+6n2fuo9UFEXBnekRhooTAOBU0NMa+EwbYFZwFhcXnWGq1WrJ48ePB65jT33QbDZlb2+v/3O73Zatra3E/VxaWpLvvvtO3nzzTbl16xaTYg5BSGYgOAEAToVutytXrlwRpZRUKhW5fft2bCixQ5HrVGmGK1OtVhvoxG7OEB53WzZ9nbT9RDFoqgMAwGIO+z86OpLr16/Hbvvo0aNj/YZ8HRwcSL1e7/9848aNgb+HzNN0dHSUezoFFIvgBAA4Ncxh/7u7u4kj7T755JP+92b1ycfBwUF/aoDl5eWB0Xbr6+up4enGjRvSaDSkUqnIH/7wh6D7RrloqgMAnCr2SLukZU6q1Wq/31Kj0Rjoc2RWpBqNhvyn//SfjgUs8xRrjpiz/+aim+t8l2Hpdrty8+ZNuXbtGk17gWiqAwAghh5ppyesTFrm5Pbt2/3v9/f35Z/+6Z/6P5vBSQcicwZwkddhSTNHzIXwHZG3srIijx496q/Th3JQcQIAnErmYsAiIp1Ox1mpSZrXye4gXqlU+suxpG0/NzeXOCu5uQCwT9XJvO0JPbWXZuQVp16vJ3/605/k3r178qc//UmePHmSe9svv/wy8XYAAAixvLwsi4uL/Z+vXLnirOysra0NrJFnLm1ir513dHSUGFrM+0vrN7W8vCxvvPGGiIi8ePEicVsR6VfQzKVfUAJVgvPnz/e/39nZURcvXsy17fb2thIRtbe3570PT58+VSKinj596n0dAMDp02w2lYgoEVHValV1Op1j23Q6HdVqtfrbiYhaXFxUSik1Nzc38Hv7Ykv6m61erysRUfV6Pf8DRayQzFB4LO31egM/z8/Py+bmZq5te72ezM/PF7eTAAD8hxs3bkiz2ZQoiuTw8FA+//zzY5Wn5eVlefjw4UCF6fvvvxeR11MXzM3NOW877ve+Dg4OBr5i9AoPTpubm9JsNgd+12w25cGDB5m2vXfvnly8eLHo3QQAnDJLS0sSRdFAU5vI61D0888/y507d6RarcaGJxGRb775pt+X6OjoSKIokqWlJXn06FG/b5N5SerD5EPfV9xkmxi+woNTXD8k1+KGads+efJEZmZmvO73t99+k2fPng1cAADQfvjhh/739+/fPzaSTo+2SwpPy8vLcufOnYHfra+vDwSxIqn/6C+l6Ow9NobWgyykY7fe9ocffpALFy54Xefrr7+Ws2fP9i/vvvtuhr0EAEyqS5cuDfy8vr7uDEY+4cns5C3iDmJFoOI0fqZ8N/z2229lZ2cn9u8ffPCBXLhwQWZmZo5Vl3Z3d52Vo6RtNzc3j73Ik3z11Vfyz//8z/2fnz17RngCAPStra3J2trawPQCn3/+uYjIwDQE+ns9SaZrm7W1Nflv/+2/yT/90z/116VbX1+Xe/fuyTfffFPYBJR68k178WCMTuHzOPV6Pfnoo49ke3u7/7vZ2Vn5X//rfx0LT0nb3r9/f6Dz+KeffipXr16Vjz/+WM6fP5+6H8zjBACIY84e3mq15OHDh5m2ETk+z5PI62kH1tbWnNuHzLfE3EzDEZQZyhjWZ08xcOHChf7P29vbamdnx2tbk4gMXC8N0xEAAJLoKQZc0w+Y2zSbTdVsNhO3a7fbzqkI2u12f5vFxcXUqQpslUpFiYiqVCphDw5BQjJDKTOH93o9uXv3riwsLMjW1pZ89dVX/WrTRx99JAsLC3L16tXUbUVe93f69ttv5csvv5TLly/Lp59+SsUJADA07733njx69Cix6iTirjwlabfbsrW1lbiNnok8iiKa60oUkhlYcgUAgATm4rkikrqQ7sLCgty/fz/xNhuNhjx//jz1vuv1uhwcHEitVuv3pULxCE5CcAIAFE9Xn6rVqvz5z39O7AQeV4FK6v9kO3funOzu7nqtVYfsRr5WHQAAJ1m325X33nvv2FQE165dS50kU1tbW3NOiukbmkREPvzwQ6lWq/Lhhx9mfiwoFhUnAAAsSZUec7SdT+WprP1Acag4AQBQgL29PTl37txAZcmeJPOzzz47tk1RXrx4MfAVo0dwAgDAcuPGDalWq6KUkt3dXVlZWRmYGdwMT0dHR7K7u5vadFemhYWFY2vwoRwEJwAALDoYmQvRr6+vO8NTs9mUSqUih4eHxwJWHt1uV3799VevbfUovrTRfMiPPk4AACSYnp6W/f19ERGpVqvy6tWrY9t0u11ZWVnp/9xsNuXGjRu5+j7p/k369pL6ODHDeD70cQIAoCC3bt2SRqMhlUoldg1Ve+Hf3d1duXLlSq6mO92vKYoiuXHjRux25n2wGHD5qDgBAFCQbrcrn332WX+W7yiKZHZ2Nrj6ZE6imVZtMitiIXNE4XdUnAAAGIHl5WW5ffu2NJtNiaKo37n8+vXr3rfR7XYH+iolVZtEfq9MVSoVQtMQEJwAACjQ8vKy/Pzzz3Lnzh2pVF6fZvf29mR6ejp12oJutytXrlzp/1yr1VIrVXr91mq1OrJRfacJwQkAgBLo6pOe1mB/f192d3dj531aWlqSlZWVgc7d33zzTer99Ho9ERE5ODiQmzdvFvsgcAx9nAAAKFG325Xr16/Lixcv5MWLFwP9n958800ReR16Dg4OBq7n219JLwQsItLpdEqbxXySscivEJwAAONHh6i9vb3EaQNCOnkzFUF+dA4HAGAMmf2fms2mNBoNaTQaUqvVJIoiaTQa0ul0vENTUZNtwh8VJwAATqipqSk5PDwUEaYiyIOKEwAAp8ClS5ekWq0SmoaIihMAADjVqDgBAACUgOAEAADgieAEAADgieAEAADgieAEAADgieAEAADgieAEAMAIdbtdmZ6elkqlItPT08cW/8V4ITgBADBCN2/elP39fVFKyf7+vqysrEi1WpVKpcKSKmOI4AQAwAhdu3ZNGo3GwO+Ojo5EKSXr6+tUocYMwQkAgBFaXl6W58+fy+LiovPv+/v7cvPmzSHvFeIQnAAAGANra2vS6XSOVZ8ajYZcu3ZtRHsFG2vVAQCAU4216gAAAEpAcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPBEcAIAAPA0VcaN9no9uXfvnszPz0uv15PLly/LzMxMpm03Nzel1+vJ/Py8iIhcuHChjF0GAABIVUpw+uijj2R7e1tEXgejP/7xj7KxsRG87ebmpmxsbMjdu3el1+vJBx98IDs7O2XsMgAAQKrCg1Ov1xv4eX5+XjY3NzNt++mnn/ZD1fz8vPz4448F7y0AAIC/wvs4bW5uSrPZHPhds9mUBw8eBG3b6/Vkd3dXZmZm5MGDB/LkyZN+cx0AAMAoFB6cnjx54vz97u5u0LYPHjyQZrPZ7//07bffyr1792Lv97fffpNnz54NXAAAAIpUSh8nl7iQFLft7u6u9Ho9uXDhgszMzMjly5dldnZWlFLO63z99dfyr//6rwXtLQAAwHHewenbb79N7Jj9wQcf9EOOXV3STW62pG3Ni95WROTBgwdy/vz5Y7f11VdfyT//8z/3f3727Jm8++67no8OAAAgnXdwunz5std2Fy5ckLt37x77fbvdDtrW1bSX5MyZM3LmzJmg6wAAAIQovI+T3YG71+tJu90eqBjp0XRJ287Pz0u73e438em5nFzVJgAAgGEopY/TxsaGfPnll7KwsCBbW1sDczh9/fXXsrCwIFevXk3dVv/t/fffl+3tbaYjAAAAIxWpuN7WJ9yzZ8/k7Nmz8vTpU3n77bdHvTsAAGBMhWQG1qoDAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwRHACAADwNDXqHSiLUkpERJ49ezbiPQEAAONMZwWdHZJMbHD6+eefRUTk3XffHfGeAACAk+CXX36Rs2fPJm4zscGp2WyKiMjjx49TD8Jp8uzZM3n33Xflp59+krfffnvUuzM2OC5uHBc3josbx8WN4+I2TsdFKSW//PKL/N3f/V3qthMbnCqV1923zp49O/InZBy9/fbbHBcHjosbx8WN4+LGcXHjuLiNy3HxLbLQORwAAMATwQkAAMDTxAanM2fOyL/8y7/ImTNnRr0rY4Xj4sZxceO4uHFc3DgubhwXt5N6XCLlM/YOAAAAk1txAgAAKBrBCQAAwNNETkfw4MED+eMf/yjb29uJ2/V6Pbl3757Mz89Lr9eTy5cvy8zMzHB2cshCHmuv15PNzU1pNpvS6/Xk4sWLMj8/P9wdHpLQ18Dm5qb0er3+8bhw4cKQ9nS4sv5vfPnll/LVV1/xfySv34c2NzdFRGRra0v+8pe/TMRxCX0v4T32uEl9bbhM5HuJmjAbGxtqe3tb+Ty08+fP97/f2dlRFy9eLHPXRirksa6urg78fPny5dL2a9RCjsuPP/7YPxY7Oztqfn6+9P0blSz/G/r/bm9vr8Q9G62s/0erq6sD1z3JQo4B77Fuk/racJnE95KJC05aWnDa2dk59mKdmZkpc5dGJvSx2ttOanAKPS7z8/MD/8g7Oztl7dpIZf3f2NjYOHaMJknIcdne3h74287OjhKRE/+aCTkGvMeerteGy6S+l5zaPk66KcrUbDblwYMHI9qj8oQ+1mazKe+//36/ye6DDz4Yxm4OXchx6fV6sru7KzMzM/LgwQN58uTJxDZfZvnfuHfvnly8eLHsXRupkONy/vx5+ctf/tL/+cmTJ/3tT7KQY8B77Ol6bbhM6nvJqQ1O+sVq293dHe6ODEHoY93Y2BARkf/yX/6LbGxsjP2LOKuQ4/LgwQNpNpv9tvpvv/1W7t27V/Iejkbo6+XJkyfj2Q+hYKHHxfy/+f777+XChQsn/jiFHAPeY0/Xa8NlUt9LJrJzeB5xT/Qkinusm5ubsrq6Kr1eTz799FMREbl79+4Q92y0XMdld3dXer1e/w3u8uXLMjs7K+oUTYMW93r54Ycf5PLly8PdmTGS9p7x5MkTuXfvXupglZMs5H2T99jBv0/6a8PlpL+XnIjg9O2338rOzk7s3z/44IPg0U0zMzPHUq9uijkpfI9LyGPt9XqytbUlq6urIvJ61Nj7778vX3755YlpmirjuMzPz8vMzEz/b/rrgwcP5Pz580XteqnKOC6bm5ty6dKlond1qMo4LqYvv/xSfvzxxxP13hIn5BhMwnusL14bbhP7XjLqTlZlSXtocZ3WxrUzWh4hj3VjY0NtbGwM/G51dVVtb2+XuYsjEXJcdnZ2jnVqFJFTf1x+/PFHdffu3f5FRNTVq1dP/XHRVldX+51+9/b2Tvz7S+j/DO+xe7HXmbTXhsukvpdMdHCyn5zt7e2BkQv2MMkLFy4Ma/eGLumxmsdlZ2dHXb16deC69s+TxPe4KKXUhQsX+q+p0zYdQdJxMcmEjg7SQo7LxsaG+vHHH5VSr0+Md+/eHd6OlijkGPAe+9ppeW24TOJ7ycQFpx9//FFdvXq1n1bN6snFixcH5s/QIWFjY0NdvXp1IhO/lvRY7ePy448/qtXV1X7yH9cXbxFCjsve3p66fPmyunv3rrp8+TLHxbC3t6dWV1eViKjLly+P5afEIvgeFz3E3LxMylD8kNcG77GvnZbXhsskvpewyC8AAICnUzsdAQAAQCiCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgCeCEwAAgKf/DzbdOfXERpjmAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate and plot phase space trajectories\n", "\n", "qx = torch.linspace(0.10, 0.4, 16, dtype=torch.float64)\n", "px = torch.zeros_like(qx)\n", "qy = torch.zeros_like(qx)\n", "py = torch.zeros_like(qx)\n", "\n", "state = torch.stack([qx, px, qy, py]).T\n", "trjs = []\n", "\n", "for _ in range(2**10):\n", " state = torch.vmap(RING)(state)\n", " trjs.append(state)\n", "\n", "qx, px, *_ = torch.stack(trjs).swapaxes(0, -1)\n", "\n", "plt.figure(figsize=(6, 6))\n", "plt.scatter(qx.cpu().numpy(), px.cpu().numpy(), s=1, color='black')\n", "plt.xlim(-1.0, 0.5)\n", "plt.ylim(-0.075, 0.075)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "500d8cf3-8413-463a-802c-d75360e6a686", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[]\n", "tensor([ 2.9857e-18, -2.0620e-19, -2.9122e-19, -3.0706e-20], dtype=torch.float64)\n", "tensor([ 2.6010e-18, 2.2073e-19, 2.7221e-19, -3.4789e-20], dtype=torch.float64)\n", "\n", "tensor([[-3.3823e-01, -1.7512e+01, 4.0542e-19, 7.6920e-18],\n", " [ 5.0572e-02, -3.3823e-01, -7.0284e-20, 1.3939e-19],\n", " [-1.4957e-19, -8.2174e-18, -2.9764e-01, -6.0422e+00],\n", " [ 6.4815e-20, -4.3138e-19, 1.5084e-01, -2.9764e-01]], dtype=torch.float64)\n", "\n", "tensor([[-3.3823e-01, -1.7512e+01, -3.8455e-33, -5.8351e-32],\n", " [ 5.0572e-02, -3.3823e-01, 4.9958e-34, -5.6691e-34],\n", " [ 7.8130e-34, 5.7800e-32, -2.9764e-01, -6.0422e+00],\n", " [-4.8163e-34, 4.4705e-33, 1.5084e-01, -2.9764e-01]], dtype=torch.float64)\n", "\n", "tensor([-1.6398e-15, -1.6398e-15, -1.2069e-16, -1.2069e-16], dtype=torch.float64)\n", "\n", "[(None, ['SF_A', 'SD_A', 'SF_B', 'SD_B', 'SF_C', 'SD_C', 'SF_D', 'SD_D'], 'ms'), (None, None, 'dp')]\n", "tensor([ 2.9857e-18, -2.0620e-19, -2.9123e-19, -3.0706e-20], dtype=torch.float64)\n", "tensor([ 2.6010e-18, 2.2073e-19, 2.7221e-19, -3.4789e-20], dtype=torch.float64)\n", "\n", "[(None, ['SF_A', 'SD_A', 'SF_B', 'SD_B', 'SF_C', 'SD_C', 'SF_D', 'SD_D'], 'ms'), (None, None, 'dp')]\n", "tensor([[ 2.9857e-18, -2.0620e-19, -2.9123e-19, -3.0706e-20],\n", " [-4.4180e-18, 1.0905e-19, -3.0486e-19, 2.7202e-20],\n", " [ 4.8561e-18, 1.2635e-20, 1.6041e-20, 5.5260e-20],\n", " [-4.2013e-18, -1.3148e-19, 3.1934e-19, 2.2679e-20],\n", " [ 2.6010e-18, 2.2073e-19, 2.7221e-19, -3.4789e-20]], dtype=torch.float64)\n", "torch.Size([5, 4])\n", "4\n", "\n", "tensor([0., 0., 0., 0.], dtype=torch.float64)\n", "tensor([ 0.0030, -0.0002, -0.0014, -0.0003], dtype=torch.float64)\n", "\n", "tensor([ 2.5908e-03, -2.2607e-05, -1.1890e-04, -2.1272e-04], dtype=torch.float64)\n", "tensor([ 2.5908e-03, -2.2607e-05, -1.1890e-04, -2.1272e-04], dtype=torch.float64)\n", "\n" ] } ], "source": [ "# Compute closed orbit (period one fixed point)\n", "\n", "# Set initial guess\n", "\n", "guess = 1.0E-3*torch.tensor([1.0, -1.0, 1.0, -1.0], dtype=torch.float64)\n", "\n", "# Compute without deviation parameters and groups\n", "\n", "point, table = orbit(RING, guess, [], limit=8, epsilon=1.0E-6)\n", "\n", "print(table)\n", "print(point)\n", "print(RING(point))\n", "print()\n", "\n", "# Compute matrix around closed orbit\n", "\n", "print(torch.func.jacrev(RING)(point))\n", "print()\n", "\n", "print(matrix(1, ring, point, ms, dp, jacobian=torch.func.jacrev))\n", "print()\n", "\n", "# Classify fixed point\n", "\n", "values, _ = torch.linalg.eig(matrix(1, ring, point, ms, dp, jacobian=torch.func.jacrev))\n", "print(values.log().real)\n", "print()\n", "\n", "# Deviation parameters are passed after the initial guess, followed by deviation groups\n", "\n", "point, table = orbit(RING, guess, [ms, dp], ('ms', ['Sextupole'], None, None), ('dp', None, None, None), limit=8, epsilon=1.0E-6)\n", "\n", "print(table)\n", "print(point)\n", "print(RING(point))\n", "print()\n", "\n", "# Track closed orbit\n", "# Note, number of points is equal to the number of lines plus one (full=True, default) or number of lines (full=False)\n", "\n", "points, table = orbit(RING, guess, [ms, dp], ('ms', ['Sextupole'], None, None), ('dp', None, None, None), advance=True, limit=8, epsilon=1.0E-6)\n", "\n", "print(table)\n", "print(points)\n", "print(points.shape)\n", "print(len(RING))\n", "print()\n", "\n", "# Closed orbit with non-zero deviation parameters\n", "# Note, alignment flag should be explicitly passed\n", "\n", "fp = torch.tensor(4*[0.0], dtype=torch.float64)\n", "dx = torch.tensor([-0.001], dtype=torch.float64)\n", "dy = torch.tensor([+0.001], dtype=torch.float64)\n", "dp = torch.tensor([0.0005], dtype=torch.float64)\n", "\n", "ring, *_ = group(RING, 'FODO_A', 'FODO_D', ('dx', None, ['QD_A'], None), ('dy', None, ['QD_A'], None), ('dp', None, None, None), root=True, alignment=True)\n", "\n", "print(fp)\n", "print(ring(fp, dx, dy, dp))\n", "print()\n", "\n", "point, _ = orbit(RING, guess, [dx, dy, dp], ('dx', None, ['QD_A'], None), ('dy', None, ['QD_A'], None), ('dp', None, None, None), alignment=True, limit=8, epsilon=1.0E-6)\n", "\n", "print(point)\n", "print(ring(point, dx, dy, dp))\n", "print()" ] }, { "cell_type": "code", "execution_count": 7, "id": "57417f3d-d4ae-4353-97b4-2351bbd6165e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Locate period five fixed points\n", "\n", "dp = torch.tensor([0.0], dtype=torch.float64)\n", "ms = torch.tensor(8*[0.0], dtype=torch.float64)\n", "\n", "# Set fixed point period\n", "\n", "power = 5\n", "\n", "# Set tolerance epsilon\n", "\n", "epsilon = 1.0E-9\n", "\n", "# Set random initial points\n", "\n", "qx = 1.0*torch.rand(256, dtype=torch.float64) - 0.50\n", "px = 0.1*torch.rand(256, dtype=torch.float64) - 0.05\n", "qy = torch.zeros_like(qx)\n", "py = torch.zeros_like(px)\n", "\n", "points = torch.stack([qx, px, qy, py]).T\n", "\n", "def task(guess):\n", " point, _ = orbit(RING, \n", " guess, \n", " [ms, dp], \n", " ('ms', ['Sextupole'], None, None), \n", " ('dp', None, None, None), \n", " limit=128, \n", " power=power, \n", " epsilon=None)\n", " return point\n", "\n", "# Perform root search iterations for each initial point\n", "\n", "points = torch.func.vmap(task)(points)\n", "\n", "# Set parametric ring\n", "\n", "ring, *_ = group(RING, 'FODO_A', 'FODO_D', ('ms', ['Sextupole'], None, None), ('dp', None, None, None), root=True, alignment=True)\n", "\n", "# Iterate\n", "\n", "for _ in range(128):\n", " locals = torch.vmap(lambda state: ring(state, ms, dp))(points)\n", "\n", "# Remove solutions with large norms\n", "\n", "points = points[locals.norm(1, dim=-1) < 0.5]\n", "\n", "# Remove unconverged solutions\n", "\n", "mask = []\n", "for point in points:\n", " local = point.clone()\n", " for _ in range(power):\n", " local = ring(local, ms, dp)\n", " mask.append((local - point).norm() < epsilon)\n", "\n", "points = points[mask]\n", "\n", "# Clean points (remove nans, duplicates, points from the same chain)\n", "\n", "points = clean_point(power, ring, points, ms, dp, epsilon=epsilon)\n", "\n", "# Generate fixed point chains\n", "\n", "chains = torch.func.vmap(lambda point: chain_point(power, ring, point, ms, dp))(points)\n", "\n", "# Classify fixed point chains (elliptic vs hyperbolic)\n", "# Generate initials for hyperbolic fixed points using corresponding eigenvectors\n", "\n", "kinds = []\n", "for chain in chains:\n", " point, *_ = chain\n", " values, vectors = torch.linalg.eig(matrix(power, ring, point, ms, dp))\n", " kind = values.log().real.prod() < epsilon\n", " kinds.append(bool(kind))\n", " if not kind:\n", " lines = [point + vector*torch.linspace(-epsilon, +epsilon, 128, dtype=torch.float64).reshape(-1, 1) for vector in vectors.real.T]\n", " lines = torch.stack(lines).reshape(-1, 4)\n", "\n", "# Remove vertical plane in chains\n", "\n", "qx, px, *_ = chains.swapaxes(0, -1)\n", "chains = torch.stack([qx, px]).swapaxes(0, -1)\n", "\n", "# Iterate lines and remove vertical plane\n", "\n", "manifold = []\n", "for _ in range(64):\n", " manifold.append(lines)\n", " lines = torch.func.vmap(lambda point: ring(point, ms, dp))(lines)\n", "manifold = torch.stack(manifold)\n", "\n", "# Remove vertical plane in lines (including nonlinear leaking)\n", "\n", "qx, px, qy, py = manifold.swapaxes(0, -1)\n", "qx = qx[qy.abs() + py.abs() < epsilon]\n", "px = px[qy.abs() + py.abs() < epsilon]\n", "manifold = torch.stack([qx, px])\n", "\n", "# Plot \n", "\n", "plt.figure(figsize=(6, 6))\n", "qx, px, *_ = torch.stack(trjs).swapaxes(0, -1)\n", "plt.scatter(qx.cpu().numpy(), px.cpu().numpy(), s=1, color='black')\n", "qx, px = manifold\n", "plt.scatter(qx.flatten().cpu().numpy(), px.flatten().cpu().numpy(), s=1, color='grey', alpha=0.5)\n", "for chain, kind in zip(chains, kinds):\n", " plt.scatter(*chain.T, color = {True:'blue', False:'red'}[kind], marker='o')\n", "plt.xlim(-1.0, 0.5)\n", "plt.ylim(-0.075, 0.075)\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "colab": { "collapsed_sections": [ "myt0_gMIOq7b", "5d97819c" ], "name": "03_frequency.ipynb", "provenance": [] }, "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 5 }