From 5590a57bb997948a3473b8d783602ca12c144b4b Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Fri, 22 Aug 2014 07:37:47 -0700 Subject: [PATCH] Switch to np.array. I switched all the equations to use np.array instead of np.matrx. Also, I am starting to write the Kalman Math chapter in earnest. --- Designing_Kalman_Filters.ipynb | 367 ++++++++++++++++++--------- Extended_Kalman_Filters.ipynb | 436 ++++++++++++++++++++++++++++++--- Kalman_Filter_Math.ipynb | 80 +++++- ekf_internal.py | 38 ++- exp/RungeKutta.py | 58 +++-- stats.py | 5 +- 6 files changed, 815 insertions(+), 169 deletions(-) diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb index 3a0e264..31e863c 100644 --- a/Designing_Kalman_Filters.ipynb +++ b/Designing_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:9d11bcd4ef99a8c59d3debbacc1dd13ef2280c966fe5c9e19cd4963b8e29bdea" + "signature": "sha256:4543c870ab0c051c4385acc09b0cc240e855d61acec8a6789fb611a90a05eca3" }, "nbformat": 3, "nbformat_minor": 0, @@ -41,10 +41,10 @@ " margin-right: auto;\n", " }\n", " div.text_cell code {\n", - " background: #FFFFFF;\n", + " background: transparent;\n", " color: #000000;\n", " font-weight: 600;\n", - " font-size: 13pt;\n", + " font-size: 11pt;\n", " font-style: bold;\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", " }\n", @@ -248,13 +248,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 16, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 16 + "prompt_number": 1 }, { "cell_type": "heading", @@ -316,7 +316,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -343,13 +343,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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"text": [ - "" + "" ] } ], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -414,40 +414,40 @@ "cell_type": "code", "collapsed": false, "input": [ - "from KalmanFilter import KalmanFilter\n", + "from filterpy.kalman import KalmanFilter\n", "import numpy as np\n", "\n", "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", "dt = 1. # time step\n", "\n", - "f1.F = np.mat ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])" + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### **Step 3**: Design the Motion Function\n", - "We have no control inputs to our robot (yet!), so this step is trivial - set the motion transition function $\\small\\mathbf{B}$ to zero. This is done for us by the class when it is created so we can skip this step, but for completeness we will be explicit." + "We have no control inputs to our robot (yet!), so this step is trivial - set the motion input $\\small\\mathbf{u}$ to zero. This is done for us by the class when it is created so we can skip this step, but for completeness we will be explicit." ] }, { "cell_type": "code", "collapsed": false, "input": [ - "f1.B = 0." + "f1.u = 0." ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 6 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -498,8 +498,8 @@ "cell_type": "code", "collapsed": false, "input": [ - "f1.H = np.mat ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", "print(f1.H)" ], "language": "python", @@ -514,7 +514,7 @@ ] } ], - "prompt_number": 7 + "prompt_number": 13 }, { "cell_type": "markdown", @@ -533,8 +533,8 @@ "cell_type": "code", "collapsed": false, "input": [ - "f1.R = np.mat([[5,0],\n", - " [0, 5]])\n", + "f1.R = np.array([[5,0],\n", + " [0, 5]])\n", "print (f1.R)" ], "language": "python", @@ -549,7 +549,7 @@ ] } ], - "prompt_number": 8 + "prompt_number": 14 }, { "cell_type": "markdown", @@ -584,7 +584,7 @@ ] } ], - "prompt_number": 9 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -603,7 +603,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "f1.x = np.mat([0,0,0,0]).T\n", + "f1.x = np.array([[0,0,0,0]]).T\n", "f1.P = np.eye(4) * 500.\n", "print(f1.x)\n", "print()\n", @@ -628,7 +628,7 @@ ] } ], - "prompt_number": 10 + "prompt_number": 15 }, { "cell_type": "heading", @@ -652,18 +652,18 @@ "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", "dt = 1.0 # time step\n", "\n", - "f1.F = np.mat ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])\n", - "f1.B = 0.\n", - "f1.H = np.mat ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])\n", + "f1.u = 0.\n", + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", "\n", "f1.R = np.eye(2) * 5\n", "f1.Q = np.eye(4) * .1\n", "\n", - "f1.x = np.mat([0,0,0,0]).T\n", + "f1.x = np.array([[0,0,0,0]]).T\n", "f1.P = np.eye(4) * 500.\n", "\n", "# initialize storage and other variables for the run\n", @@ -675,7 +675,7 @@ "\n", "for i in range(count):\n", " pos = s.read()\n", - " z = np.mat([[pos[0]],[pos[1]]])\n", + " z = np.array([[pos[0]],[pos[1]]])\n", "\n", " f1.predict ()\n", " f1.update (z)\n", @@ -696,13 +696,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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g6WiL6ZF+6OXnALv162H36aco2bMHUKnqfX1ryelGMSdxTR1dEG50hw8fjtWr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\nh5jBMWOS04mxhdMnLUQ+84zCPvzQm2VZDveTObI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kVexN+1JQZcT8P3Lw4sBwqOQyaP/xD1gDAlD76qtil9Yi7E+yFwy/RERENiYI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\nNRjdg924Jy8REZEd48wv2TeTCR7x8bB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"text": [ - "" + "" ] } ], - "prompt_number": 11 + "prompt_number": 17 }, { "cell_type": "markdown", @@ -722,18 +722,18 @@ "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", "dt = 1.0 # time step\n", "\n", - "f1.F = np.mat ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])\n", - "f1.B = 0.\n", - "f1.H = np.mat ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])\n", + "f1.u = 0.\n", + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", "\n", "f1.R = np.eye(2) * 5\n", "f1.Q = np.eye(4) * .1\n", "\n", - "f1.x = np.mat([0,0,0,0]).T\n", + "f1.x = np.array([[0,0,0,0]]).T\n", "f1.P = np.eye(4) * 500.\n", "\n", "# initialize storage and other variables for the run\n", @@ -745,7 +745,7 @@ "\n", "for i in range(count):\n", " pos = s.read()\n", - " z = np.mat([[pos[0]],[pos[1]]])\n", + " z = np.array([[pos[0]],[pos[1]]])\n", "\n", " f1.predict ()\n", " f1.update (z)\n", @@ -756,8 +756,8 @@ " pys.append(pos[1]*.3048)\n", "\n", " # plot covariance of x and y\n", - " cov = np.mat([[f1.P[0,0], f1.P[2,0]], \n", - " [f1.P[0,2], f1.P[2,2]]])\n", + " cov = np.array([[f1.P[0,0], f1.P[2,0]], \n", + " [f1.P[0,2], f1.P[2,2]]])\n", " \n", " #e = stats.sigma_ellipse (cov=cov, x=f1.x[0,0], y=f1.x[2,0])\n", " #stats.plot_sigma_ellipse(ellipse=e)\n", @@ -777,9 +777,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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uatZ0Ubu2i0WL0m9JHzmi5fffDTz+uMpouFuY9VqMusxTu5QU+OEHI4MH3/l+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6K9+aYTh8MkGDzzJrZWKwwa7GPSx4X84ZW/MXLhJiJb99J5o5XXZz3FnFv+zorVXiB64lqTJiGy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\nMrp27cqNN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GY9b+/tasMTB0qC8LFyZQqtT9s3NbZsmcXyGEEEI8MLZs0fP8835ERcWRP3/W\nUpw//9QxerQv69fHA3Al0cHuc/HsPhvP7nMJ6LRQ2hjI2m8K8+0sPeUDrOiOH8cdHg6k3/ML8Oqr\nvpQs6WHEiJsJcmIiVKyYjxMnYjAaQVEUEh1uYm0uYmzepDk2yUWs/b8/bS7cCvSpXZzi/ibAW93t\n3NnCo4+6mDo1icBA79f9xhs+GI0K48enP0btBrsd3nvPzIIFJhYuTOCRR3Jw3MVdJHN+hRBCCPFQ\nslph6FBf3n/fmuXEF6BsRTvntTY+3nyBfRfiibW5CCvhT80S/jxXszglAoxoNBoMe3yYOl7L3Ln6\n5MQXUrcm3K5vXzvPPmth2DBb8gNk+/frCA29WZ3VaDRYTHosJj0lAzO37jJlPKxfH8fEiT40bBjA\nxIlWmjd3snixkd9/j8/w8x4PrF+v5803fQkJcbNxYxxFiz54Fd8bsp38fvLJJ/z8888AtG7dmiFD\nhuTYosSDSXr4hBqJC6FG4kKoySguFi0yUbmymyeeyPxYLofbw6I9F/nrTBynYmyUahJI0lU/xjQt\nSEhBbzsBADZbckPw2LFJ1K4dyIEDugwnQNyqenU3JUt6WLHi5oiyzZsN1KmTftKcGf7+MGNGEu3b\nO5k+3cyrr/pSpIjCxYsaChcmVfuH0wn//KNj40Y9X39twsdHYeTIJDp2dD5wPb63y1bye/r0aVas\nWMGaNWtwu920bt2ajh07UrJkyZxenxBCCCFEhhQFvvzSxPTp1ix97udDV9lzLp4BdUpQuagf8+f5\nELVcT4WnEr1viIvD5+230R0/TsKyZYA3kezd287cuSbefz9r93vrLSv9+ll47LE4AgMVvv7axKJF\nObeVcuPGLsqVS6RRowBq1nTx2mu+HDmio2xZD/nyeecax8drOHpUR6lSHurUcTF7diJ167of+KT3\nhmwlvxaLBb1ej81mw+PxYDAY8M/so5TioSVVHKFG4kKokbgQatKLi+3bdXg80LBh5quoDreHb/dd\nZELzYCoV9s7H7drVzpQpZs6dhTK7VuI7ZgzOFi1InDs3xWd79rTToEEAb78Nfn5qV1dXr56bjh0d\njBrly1NPOShZ0kP16jnXW+vxwPDhfgwebGfkSG+vr80GR47oiIvToCjg56dQoYIbiyXHbntfyVby\nmz9/fnr16sVjjz2Gx+Nh9OjRBAQE5PTahBBCCCEy5Y8/DLRqlbVf2a+Jvkpwfp/kxBcgIACGdz5G\nYotX8fEx4bDnAAAgAElEQVSPJvGLL3DVr5/qs8WLK5Qv72HfPj3162etbWHcuCRatfJn2DBfZs/O\nWuU4PYoCr7/uQ1ISDBt28yE3s5kcTbDvd6kHyWXCmTNnWLx4Mb///ju//vorX375JZcvX87ptYkH\nzJ3uyS4eTBIXQo3EhVCTXlzs3asjLCzzSajT7WHx3ov0qFUs1bmXa29km6MWC1/bqpr43hAe7mLP\nHl2m73mDry/Uru3C7dbw11/eivWdcrngtdd8+PNPPZGRiXe8HfODLFuV33379lG9enUs/9XLq1Sp\nwsGDB2nSpEnyewYNGkRQUBAAgYGBVK9ePfnXFTeCV44fruMb8sp65DhvHO/fvz9PrUeO88bxDXll\nPXKcN47T++/F/v062rb9k6ioxExd79cj1/AniauHdxN1+DEiIlw3zz/TmUrldHTrZiLBuYXu3cNV\nr+fjE81vvxVg4EBLlr6e69ebsnatkenTf2fWrHD+/DOAmTOtnD27KVt/PwULNmboUD8U5Rpjxuwk\nMLBenvh+3c3/PkRFRXHq1CkABgwYQFZka87v/v37eeONN1iyZAkej4cOHTrw6aefUq5cOUDm/Aoh\nhBAid5UrF8jOnZmb7evyKPT97iBjHitD1WIWpk0zp9qcAmDxYiOTJ/uwdGk8lSqlLs+uWmVg0SIj\nCxYkZnqdq1cbGD7cl++/T6BGDTduN3z2mYkPPzTTv7+dPn3sFC+eudTs1CktX35pIjLSyLhxSfTu\n7XhoHlq7Va7M+a1evTotWrSgY8eOAHTt2jU58RVCCCGEyG0eT+qtidPy25FrlAgwcv1IIPOn/c30\n+Q2Sz0VEuLgxr/eZZ7xbBrdv78+0aVY6dkw5Qk2r9W6lnBlOJ3z0kZm5c01895038QXQ6WDwYDut\nWzv5v/8z0bBhABERLpo2dRIW5qZqVTcm714WWK3eXdv27tWzbp2ev/7S07Wrg/Xr4x7IndjuFtnh\nTeSaqCiZ2ylSk7gQaiQuhJr04qJq1UDWrMk4CXR7FPotOciIxmWos/wbjJGRvNl6K6Ned6X5mR07\ndAwZ4kflym4mT7Ym32PJEiM//2xg7tz0K7+7d+t49VVfChVS+PDDxHTXGBcHy5cb+fNPPXv36jh8\nWIfuv7ZijwdCQ92Eh7upV89F+/YOfH3TvfVDQXZ4E0IIIcRDw2YDq1VDcLCbvXt1lCqVdhIL8Pux\naxT2M/LIvj8wf/IJ8b/8QoOT6d+jTh03GzbEMWOGmSZNAmjY0EWfPnb27vXuzqbm+nUNv/5q4Msv\nTZw7p2X06CSeey7jtoSAAOjVy0GvXt6qs8dzc38Nk8lbbRZ3Riq/QgghhLhvxMZq+P57I9u2eSuj\np05p8fVVSErS4HJBcLCHsDA3jz7q4umnHeTLdzPNcXsUBnz/D6+UdNGo79MkREbirl07S/dPSIDv\nvzeycKGJ3bt1lCzp4dFHXVgs3kT12jUN+/fruHpVS7163iS5ZUtn8nbGIudJ5VcIIYQQD5wjR7TM\nmmVm5UoDzZp5e2KHD7dRqZIbvR5++snA55+beOcdK3v26Fm/3sCUKWaefNLJ0KE2Klb0sOH4dfLr\nPUS89BzW6dOznPgCWCzQp4+Drl0dVKkSyEcfWbl4UYvV6q3K+vsrvPmmm5AQj1Rp8yhJfkWukR4+\noUbiQqiRuBA3uN0we7aJWbPMPPHEYbZvL0aRIql/ad2ihZMRI3wxGuHZZx08+6yDy5c1zJ9vok0b\nf4YMTWJ/iQsMKe7BPnQozqeeuqN1LVtmpH59F02bpt9mIfIe+ZlECCGEEPeEkkHj5dWrGtq29Wfd\nOgO//RZPt25HVBNf8PbDPvecnblzTcmvFS6sMGKEjd9/j+e36BhOHzNRqlIN7C+8cMfrnjvXRL9+\n9ju6jrg3pPIrco1UcYQaiQuhRuLiwXPtmoYffzSwa5e3V/foUR1JSRr0eoUCBRSqV3cTHu6icWPv\nqLErVzS0a+dP27YOxo2zodVCmTLpx0X//naaNAmgd297irm8pUq7Kfb4SQJPlOXJJwNYuTI+zSQ6\nM7791ojTCc2aSdX3fiTJrxBCCCHumv37dXz2mYlVqww0b+6ifn0XvXrZqVTJjZ+ft63h4kUN+/bp\n2b1bx+jRvjidkJSkoWtXO2++mXrzibSULKkwdqyNIUP8+OWX+OQRYVH/xuBj0DJjpJl33Q66dLHw\nyy/x+Phk/es5f17D+PE+fP99gvT03qfk2yZyze3blgoBEhdCncTF/c9mg7fe8qFLFwuVKrnZuTOO\nL75IpH9/O7Vru/H39z4gZjBAqVIKbdo4GTfOxh9/xBEW5sbjgZUrjWzbpku+Zmbiom9fO35+Cm+/\n7c1slUuXiNx9gR41i6HRaBg92kZIiIepU7Oe+dps8MILfvTta0/epELcfyT5FUIIIUSOOnpUS5Mm\nAZw4oWXz5jheftlOwYKZazP46y8dUVF6Nm6MY/z4JPr2tTB5sjnD/uAbtFr48stE1q418MVrp9jT\n71V0Tid1SwcA3nm506db+f57I9u36zK42k1JSdC7t4XChRVGjcp8NVrkPTLnVwghhBA55tAhLZ06\n+TNqVBK9e2e8qcPt2re38OyzjuStha9c0fDssxaqVnXzwQfWTF/vSvR1DE1a8dKIj+nftgrNqwSm\nOP/dd0bmzzfy008JGV7r6FEtAwf6ERzsZvZsKwZD1r4mcXdldc6vVH6FEEIIkSPOntXw9NP+vPVW\nEn36ZD3xPXRIy5EjOjp1ciS/VqiQwrJl8Rw8qEtuZciQ3U7ZV3twaHBfEn0KMLxraVavNqSoHnfs\n6ODECR0HD6adCtnt8MknJlq39qdrVweffSaJ74NAkl+Ra6SHT6iRuBBqJC7uP4oCw4b50bOnna5d\nHRl/QMVXX5no2dOO0ZjydYsFFi9OYOFChc2bM3hWX1HwfeUVPAUKML9aU0a1Lcr//Z+VKVN8qFcv\ngP/9z8SVKxoMBujZ085XX5lu/zjHjml5+20zNWoEsmmTgbVr43n+ebs84PaAkGkPQgghhLhjCxYY\nuXpVw5AhNpxOslUh3bDBwOefJ6qey59fYeDAfbz8cm02b47DYlG/hubKFTQJCawfPwPnvms0KBuI\nNthFVFQc27bp+eILE1OnmgkIUChXzsO+fTpMJm+V9+hRHXv36jCb4amnHKxaFU/58h71G4n7lvT8\nCiGEECJbYmM1LF9uYPt2PUuWGNFovJVTRQEfH6ha1Tu7t0EDF0884UxV0b1VQgKEhubjxImYdBPn\n55/3IzTUzYgRaT90pigKw348zNPVi9C4XP5U5z0eOHFCy65dOoYM8WPkyCQCA6FMGQ9hYS6KFcvx\n1EjcRdLzK4QQQoi7Kjpay/DhvoSHB7BhgzdTrVnTzcmTMVy+7P3n779jGTcuiZIlPXz+uYmwsECm\nTjVz5Yp6I/CBAzoqVXJnWDEeMsTGV1+ZcN82aSwq6uYvs3eejSfJ6SEiOJ/qNbRaCAnx0KWLkxo1\n3DRq5OKFF+y0auWUxPchIMmvyDXSwyfUSFwINRIXeZPTCe+/b+bJJ/0pVcrDtm1xzJuXyJEjOl55\nxZa8aYRGA4GBCo0auRg61M7KlQksWxbPlStaIiICWL48dYZ77ZqWIkXSbzGIiooiLMxN8eIe1q41\n3HbOm/wqisKCXRd4tmZRtJl44q5IEQ/Xrkk69DCRnl8hhBBCZOjcOQ09e1rIn19h/fo4SpXyVkhj\nYzVER+to0cKZ7ucrV/bwwQdWnnlGx9ChfqxebWDWLCum/543c7tJ3pEtXXFxDK/2Bz7v78Ay9w9i\nrniY0WoV06d7M+8SNa8RZ3fRODh1u4ManQ5cskvxQ0V+1BG5JiIi/T3ZxcNJ4kKokbjIW86c0dC2\nrT9PPulkyZKE5MQXYO9eHdWqudBnspxWt66bDRvicDg0dO9uwfZf667ZrGC1pl2p1cTE0HrsWPJV\nrUrrHVOJO5OIvXdvNJGzeX5oPAPHXqF5j0v8ZTvNs+HF0GkzN2fNatXg4yOtDg8TqfwKIYQQIk2x\nsRo6dfLn+eftDBpkT3V+zx4dYWFZ2+rXx8e7C9sLL/jRqZOFVasSKF/ew6l/bOii/iC+Tl1i7B6u\nJzmJSXJxPclFTJKT2JEfc903kKtWD7sOevj6uh3r6vMEmi9jKGbg+/16KhX2pWlI5qq+ANHROkJC\nZKLDw0SSX5FroqKipJojUpG4EGokLvKOceN8aNTIpZr4Aly5oqV48cwnjx5FYfupOM7H26n3bAzr\nf7jEa1NicOrdVO5rovXfBdAeOUA+XwP5ffTkMxvI56Mnn48eu8ZBRLkC5PfRs2pSfub/ZKd0UW2m\nenvV164hIQGCgyX5fZhI8iuEEEIIVb/+qicqSk9UVFya73G5MtmrC5yNtfH+5lM4XAr53BZKrV1L\nnZN2zu4rQ4Ongvl+Rzh9uhl4+in1ZDQq6jgR/1V1lVg/fLRutJrstyxs26YnPNyd5Z3oxP1Nkl+R\na6SKI9RIXAg1Ehf3lt0O//yj49VXfenVy86ePXpCQtwUL5460TSbFWy29LNHt0fhhwOXWbznAs/W\nLEaHKoW9PbmdBjPtXR8KKhB1QsvTT7lYvMDI008lqF7nRlwoCthsGszmO+vVnT/fRLdu2duNTty/\nJPkVQgghBCdOaPn6axMbN+o5fFhH4cIerl/Xsm2bgQ0bDERH6zAYoFYtF126OGjb1onBAGXLeti6\nNe104lSMjQ82nUKv1TCzQyVKBNyynfB/JdcBA+zUrRvAG28k8eabPhw7pk23D/fcOW/i6+9/Z1/v\n7t065s+X5PdhI9MeRK6RuZ1CjcSFUCNxkXv279fRtauFli398Xhg2jQrR47EEB7uZuLEJJYuTWDV\nqgSOHIllzZp4OnRw8sUX3k0rPv7YRLVqbvbsSZ38uj0K3+69yIifjvB4SH6mP1Y8ZeL7n4gIF4UL\nK7Rs6WTpUiP9+tmZONEHRaWoeyMu9u7VExZ2Z+0KEyf60LevHbM5+9cQ9ydJfoUQQoiHkMMB06aZ\n6dzZQuvWDvbti+Xtt5N49FE3Pj6wYYOe9u1vVkU1GggK8tC1q4Offkrg++/j2bLFwLBhvpw6peXa\ntZuZ6IlrSQxfeZhdZ+P5pHERuk9+Gb/p01XXERHhHbLboYOT9esNDB9u48gRHcuWpb3V244demrW\nzP5w3h9+MPzX1pH2FsniwSXJr8g10sMn1EhcCDUSF3fX9esannzSn9279WzYEEffvo7k3dnA2xLg\n7w+FC6fdU1uliofFixMYONCO2w1jxvjg8igs3H2BUauP0rpSQWb4X6Bim2Z4KlYk6Y030l1TWJiL\nvXt1mEwwe3Yir7/uy9GjKdOUiIgInE749lsjnTplr13h+HEtY8f6Mnt2olR9H1LS8yuEEELcxy5d\n0rB3r45//9Vht4PBAIULewgPdxMc7EnVGhATo6FDBwtNmrh4++0k1daBvXt1hIdnXFnVaODZZx0Y\nDAoj3lboMe8w5Urq6FusEp2WzcC0YAGJs2bhatYsw2uVKKGg0Xj7eWvVcvPGG0l07mzhhx8SKFfu\nZv/vqlUGQkLcVK6c9fFkJ05o6dTJwtixSdSunbXZxOLBIZVfkWukh0+okbgQaiQu0nfihJbx432o\nXj2QevUC+L//MxMdreX8eS0nTmhZvtzIU09ZCA4OpH9/P7Zs0aMo4PFAr15+RESknfgCXL2qpWjR\nzCeXTVtbqfTiHg6uKE0rn0r4fr4I/Y4dxK1fn6nEF7yJdNGiHq5e9aYmPXs6eOUVG+3a+bNhg7dW\nt379FqZP9+Gll9RnDqdn40Y9Tz7pz7BhNnr3lofcHmZS+RVCCCHuE6dOaRkzxoe//tLz7LMOli6N\np0KF1NXdGy5f1vDDD0ZeecUXvR4aNHDidGqYNCntxBe8s3szu10xwKfbz9AypBAf7ypBz54KSQlD\nGPna8zQ84iGiaOZ7cw0GcDpvHvfp4yAoyMPQoX60aOEkJiaUkBA3bdo4077IbeLiYOJEX9asMfDx\nx4k0b579XmHxYJDKr8g10sMn1EhcCDUSFykpCsyda+Txx/2pW9fFvn2xvPVWEhUrpp34grdn94UX\n7GzbFscLL9iYN89EqVJurNb072c2KyQlZW6UwtaTsRy7msTLLYrw8ss2/Pygag0YPdaR/DBbZlmt\nmlR9uI8/7uKPP2I5f17DihXlCAxUOHQo4/Tl0CEto0f7EB4eiMsFW7bESuIrAKn8CiGEEHmaywUv\nv+zLoUM6fvopntDQrPe6ajTekWaDB9u5ckVD69b+LF2aQNGi6g+0lSvn4bvvMk4wk5xuZv9xihFN\nymLSa3n1VRs7d+pZt07PyZMaypTJ/CYUTiecPq2lTJnUvbjR0Tp27tTzv/8lcviwjs6d/dFovA/J\nVavmJjDQe5/YWA0HDujYs8fb5tGjh53Nm+MoWfLONsMQDxap/IpcIz18Qo3EhVAjceHl8cDgwb5c\nuKBl5crsJb7g/dX/smVGXnrJxiefWGnXzkn79v5cvape3Q0Lc/P333rc6T0TlpjIwg++5ZF//qRm\nCQvgbZX4+usEChVS6NjRn4sXMz+I99AhHaVLe7BYUr7+ww8GnnvOwuzZiRQtup6xY20cOBDL6tXx\ndOvm+O8hOS1nz3pTmq5dHaxeHc+BA7G8/rpNEl+RilR+hRBCiDzqgw/MnDqlY+nSeHx9s3+dZcuM\nNG7sSt6eePRoGzabhr59/Vi+PAHtbaWwwECFokU9HDigo0aN1BmwbscOTr/5Dr91GMGcflW4tffC\nbIbvvounbdsAGjcOYMoUK507OzPckGL79pSzey9f1vDaa77884+OxYsTqFXLzY2fiTQaKFPGQ5ky\nHjp0yHz/rxAglV+Ri6SHT6iRuBBqJC7gwAEdc+aY+OKLhDtKfMGbWDZrljJJfOONJOx2DV9+mXrX\nNYDOnR18840x5YsOB+YpUzD36s2UZ0bTv3kogYXzp/psjRoeAgIUPvzQykcfmXnsMX++/tpIYqL6\n+hQFvvnGyNNPOzh4UMuIEb7UrRtAmTIeNm6Mo1YtbwIucSFyglR+hRBCiDzG44EhQ3yZMCEpR35t\nv2ePnkGDUo4H0+ngk08Sad3anyeecFK6dMqWil697EREBDB+fBL+/t7X9H/9hW7/fuZ/uRJLjIfm\n5Qukec+wMBcuF2zaFM+GDXrmzjXx5pu+VK3qJjzcRaVKbvz8vD3Nu3bpOH5cy2uv+WKzaejd286W\nLXHJlWohcpIkvyLXREVFyU/tIhWJC6HmYY+LNWv0xMVpiI/X8MorvlitoNV62xG8yaOb0FA3hrR3\nAE7mcMC//2oJDU3dvlChgodnnnHwxRcmJk5MSnGuRAmFZs1cjBjhy//+5x0P4WrQgDPVH2HR8mg+\nbl8RTTq9DNWqufn7bx3t2zt5/HEXjz/uIibGuyHH3r3eB9hsNg06nUJUlJ62bZ0MG2ajYkUPOp36\nNR/2uBA5Q5JfIYQQIg9QFNixQ8fcuSaWLjVSsqSHo0d1VKvmxmJRUBS4elXDH3/omT3bzLVrGp59\n1kGfPnbKlk37QTjv+DAlzUS5Xz87Tzzhz9ixSSnHjLndTJ5s5ZFHAtm1y06tWm4UReGTLWfoVK0I\nJQPT3xs4Xz6FM2e0qV5r0sRFkyY3e3u//NLE8eM6Zs+2ppn0CpGTJPkVuUZ+WhdqJC6EmoctLo4d\n0zJsmHeqQ7dudnx9ISoqLtXkg1sdP65l3jwTzZv706aNk8mTrQQEpH6fkkHnQLlyHqpVdfHHgrO0\n9o9Cv20b+m3bOFO2AfPCZmO1auja1cKsWYn4VrrMxQQHE5oHZ+rr8mQwnOLAAR3vvGNm9er4TCW+\nD1tciLtDkl8hhBDiHlEUmDPHxIwZZkaOtPHCC3bWr9cTHu5KN/EFb9I6aVISr72WxFtv+dKwYSAz\nZybStGnKjRx8fb0bVqS1a5tu925W7OqBskNB3+JRYus15HK33lwpVZZ69vM8Y4ZEl5MPNrsIvHKV\niS2DMegyfl4+Lk6Dv3/amfehQ1q6drXw3ntWKlbM3gg3IbJDkl+Ra6RXS6iRuBBqHoa48Hhg5Ehf\n9uzRsXZtPOXKeRPAPXv0hIWlN2A3pYAA+OADK+vX6xk0yI/x45Po3t2RfN5kgoplY9mzfC++jcpz\nLcnJdauT60kuric5uRbvx+kJizmToMPo70Cv1ZD/lIH8Vy6R38dA/lJGGobo2PCzhcM/FENfVw9F\nM05WDxzQ0bGjQ/Xcb7/pGTLEj7ffTqJjx8yPKnsY4kLcfZL8CiGEELlMUWD0aB+io7WsWBGfPE0B\n4PBhbarqbVribC4uJDi4bnViL+Fi0CwXH32vIcoag4/+GtesDq4regJ66/jwdCIFt5m9Ca2vngI+\nBsoV8OGRUgEoZQy81Cc/f/2RhI9Bvf/g2XD46isjTz7pw9ChNgYNsqtWkm/Ys0fPW2+lfIguLg7G\njfNl0ybvbm2NG8t2wyL3SfIrco38tC7USFwINQ96XCxebGTLFgM//xyXIvEF7wNqfn4Zj/j651Ii\nb6w5RlGL0ZvQ+ujJH2ggtJQPbRd+QKlSfhStWZ7AR2oQuf8Rth8KYOYrVtVrxcdD3HlffAzqlVrw\nbizRt6+DZs1cDB/uyxdfmOjTx0GPHnaKFEm53qNHtdjtEBzsrRBHR3v7k5csMdKhg5OoqNRfd2Y8\n6HEhcockv0IIIUQuOndOw4QJPixdmqD6gJpGk/FDahfi7Uz87TijmpTh0aBAoqL0REXpuQys/MAH\nW/P5nDysJ2puHHo9dKyuYdIMA1evaihYMPXFFYVUu7ylJSjIw7JlCezdq+PLL03Urh1ImTJuwsLc\nVK3qnUyxbJmRSpXcDBjgx549OqxWDT172tm4MY5SpWR2r7i3ZIc3kWuibuxLKcQtJC6Emgc5Ll5/\n3Ze+fe1Ur67e1xsYqHDtWtrzcxMdbt5cc5xnworxaFAgABERLsaMsTFmjI1Ro5JYtNhKsWIe5s71\n7t6WP79C27bO1Du2/efaNS0BAVlLSsPC3MycaeXw4Rg+/tjKI4+4+PdfLX/8oWfbNj0hIR5atXKy\naFECBw7EMm6c7Y4T3wc5LkTukcqvEEIIkUtOn9ayebOe2bPT2OcX7+YQ+/bpgdQtCC6PwqR1Jwgv\nYeGpqoXRHj2Kkj8/SsGCye+JiHCh1cK4cUkMHOjHgAF2tFoYMsRGu3b+PP20I1USunevjurVs9d/\nazZDrVru5C2Ix4714amnHHz0kXqLhRD3WrYrv3v37qVdu3a0adOG4cOH5+SaxANKerWEGokLoeZ+\njQtF8W7V+/HHJvr08eORRwIIDg4kKCgflSoF0qaNhVKlPPzyi4HENPLf8HAXe/emfuhMURRmbzmN\nTqPhpXql0P31F/7t2qH/888U74uI8CaxtWt7WxDWr/fWuUJDPbz4op3hw/1StVXs3avL0oSJtGzd\nqmfFCiNTpiRl/OZsuF/jQuQt2Up+PR4Po0aNYuLEiaxevZoJEybk9LqEEEKI+4bDAQsWGGnWzJ8B\nA/y4dElL27ZOIiMT2LUrjr//jmHDhjhcLg0NGzpZssRIjRqBjBnjw7FjKf9XXKOGmxMntJw7l7L1\nYdnflzl4MZHXHy+Lad1vWLp3x/rRRzhbt1Zdk0YDPXo4WLbsZqvDsGE2rl/XMGPGzd3ZFAXWrjXQ\nsOGdTV44c0bDiy/6MmOGlQIFpK9X5F3ZSn7//vtvChQoQK1atQDInz9/ji5KPJikV0uokbgQau6n\nuNizR0fTpgEsW2Zk7Ngk/vorjilTkujSxUGlSh7y51cICPDO27VaNUyebGPx4kQ2bozDYlF44gl/\nPvjAjOu/3NPHB55+2sH8+abke2w9GcvS/ZeY1CqE/MuW4DdkCAkLF+Js1SrdtdWt62L37psdjgYD\nREYm8O23Rj780JsAb9+uw+nU3FHye/q0lo4d/XnxRTtt2mR+bm9W3U9xIfKubCW/58+fx9/fnwED\nBtCxY0ciIyNzel1CCCFEnqYo8P77Zrp1szB8uI2lSxNo0cKV5tSEPXt01Khx83ypUgpvvGFj/fo4\noqL0tGrlz5kz3mpv37525s83YbXCwYuJfLD5FB0Kl6fE7u2Yp04l/scfcdetm+EaQ0PdnDypTdFi\nUbSowsqV8SxZYmTgQF9mzjTTt68dTdrP2KXrl18MPPGEP/372xk82J69iwiRi7L1wJvdbmfXrl38\n9NNPWCwWOnfuTKNGjShdunROr088QKRXS6iRuBBq8npcKIr3wa7t2/Vs3BhHsWIZ/5r/xAkd5cun\n3hmtVCmFpUsTmDXLRNu2/qxYkUDlyh4aRDgY9H+XSSx2gZGNg1gfmQ/XqIbE//47SqFCmVqn0Qil\nS3s4eVJLlSo37128uMLatXE8/7wfv/1moEMHB2436NT3t1B19qyGyZO9fwf/+1/iHbdNZEZejwtx\nf8hW8lu4cGHKly9PsWLFAKhWrRrHjx9PkfwOGjSIoKAgAAIDA6levXpy0N74tYUcy7Ecy7Ecy/H9\neLx5c3P+/FPPmDG/cvSoi2LFMv68zQbXrp0lKuqA6vmXX7Zz4cJR2rQJYe7yGDzN/uHITl+6Bmh4\nNCiQ9UDUli1ZXq/b3Qi7XZvqvNutYedON717H+bzz0OZOtWHpk0PU7/+ebp0qYlWm/p6a9du459/\nCrBzZ02iovQ0bXqc6dMP07Bh/Tz1/ZHjB/v4xr+fOnUKgAEDBpAVmujo6Cx3pcfHx9O2bVtWrlyJ\nj48PnTt3ZubMmQQHBwNw+vTp5H5gIW6IipI92UVqEhdCTV6Oi61b9fTv78emTXEUKpT5/4XOmWPi\n2DEt06enPQnB7vLw4szLXDBfZnTLEiQdLsLw4X506uTgf/8zM2pUEhERLm5MdMiMiAh/PvvMSrVq\nN6c52GzQvbuFSpXcTJvmXc/u3TrmzTOxcaOemBgtNWq4KFxYwWBQSEzUEB2t4/x5LdWru+nWzc7T\nT0bgyJEAACAASURBVDuwWDK9jByRl+NC3Du7du3KUveBPjs38ff35/XXX6d37964XC7atWuXnPgK\nIYQQd8JuB6tVT1KSd4ZsdntR7warFYYM8U40yEriC1C4sIc//kj7f7sHLibw/qZTBFfzoczYUzT9\nvxdgyy9cGKPlo4/M9O/v3cQiKxQFLlzQUqjQzZaHxETo3dtC/vxKipFkNWu6qVnTO5v36lUN+/bp\nuHZNg9utwWxWKF/eTcWKHvTZyhyEyDuyVfnNiFR+hRBCZNahQ1pWrDCyZ4+OvXv1XL2qwWQClwuM\nRoWwMO/WuS1bOmnY0HVXk2GrFRITNWg04Oen4OOT8vyHH5rZv1/H3Llpb1KRlmPHtHTsaGHfvrgU\nr9tcHr766xwbjl1nSAk3raePJfGanZ7XZvHFwaoYDN4xam+84cOkSUn06OHI9N/B/7N339FRVVsA\nh393ejKZhBJa6EU6JIAKKoJUpUoTRAERkBZA8CEgKlgRBUGpAlItKCqggiJNxCCiAgkoofcQWiDJ\nZCbT7/tjBIyZNIyRsr+1XOsl3Lm54R1Odvbss/epUxpat7YQH58CwK+/ahk2zEzDhh6mTbNLICtu\nCQWS+RVCCCH+CVWFb77RM2+ekUOHtHTr5qJnTxdvvplO2bK+q8HdxYsKsbFadu/WMXp0MAADBjjp\n08eJIfCk3jxJSlL47DMDO3boiIvTcvasBrPZnxOy2RRKl/YRGemlUSMPnTu7WLzYwAcf5D3wBahY\n0UdqqsLFi8rVrPGexDSm/XiSaqFalu38gGKvfU36+PH4HnuMpIfDWLvWSadObnr1clGvnpfo6GC+\n/NLfUq1Bg5yHUsTGaomM9HD6tMKcOSZWrjQwebKdTp3+vXZkQtzornvCmxB59ddCdSGukHVx+zl7\nVuHxx81MmhRE375O4uJSePXVdDp2dFOunD/wvbIuwsNVWrb08OyzDrZvT2XqVDvffaenRQsLe/bk\noTXB3+zbp2HIkGDuvDOUPXu0tGnjZvnyNE6dSubQoRQOHUrh5Mlkli5No0ULNzt26IiMDMXhUK4G\nx3ml0cADD3j48ksD6W4vs386xRvfH2dgwwheKOshLNhAyo4duHr3Bq2Wfv2cLFp0rddvrVpeNmyw\n0ry5mwEDzLRoYWHhQiN79mhx/W0SsqrCsWMaZs0ycfq0hiZNQvH5ICYm9aYOfGW/EPlBMr9CCCEK\nzKZNOoYMMfPEE06WLLHlKXurKNC4sYf77ktjxQoD3bqF8PTTjjz1lnW7/aULCxYYGT7cweuvp2c5\njUyng5o1fdSs6c9KDxkSTFKSwkMPWXj6aQdDhzrz1BoMoH9/J+PfcfJDyH5qlwxhXpfqhJp0eClE\n+muvZbi2XTs3w4ebSUvj6sEyvR6GDnUyaJCTzZt1rFpl4P33jZw8qaFMGR8mk4rbrZCYqBAU5M+c\nv/yynd69C/5wmhA3Kqn5FUIIUSDWrtXzzDPBLF2aRqNGOb9ln5PTpxW6dbPw8MMunnsu54NgZ88q\nPPZYCEWLqrzzjo3SpfP2469FCwuvv26nZEmVESOCcbsVPvooLdejfG0uLwt+SWDNb1a6VSzP4Idz\njkZbtrTw2mv2HP++bDY4eVKDy6Wg16sUK6by3ntGLl3SMH26PVfPJ8TNKq81v1L2IIQQ4l+3fbuO\nUaOC+fTT/Al8wT8cYs0aK6tXG5g/35jttWfOKLRrZ6FtWzcrVqTlOfB1u2H/fi21a3upUMHH6tVp\nNGzooX17CxcvZn/6LNXh4fXV5+j76R8oO3ex+NePmDshAqs1568bGeklNjbnN2nNZqhRw1+fXLOm\nj7NnNXzwgZExY7JuqybE7UrKHkSBkf6MIhBZF7e+tDQYMiSYmTPtREXlLvDN7boID1dZujSNhx6y\ncO6cgkYDbreCwaBSoYKPqCgPERE+una10KePk6efvr7xuykpCkFB6tXSAY0GXnopHZ1OpXv3EL79\n1orxb/H3+TQXX+w9z8ZDl6hw4jILvnuViLpVSZ/6Ik0meXjxxWDeeSf7rGzp0j4uXMhbewunE6Kj\ng3n55XRKlcr3N3f/U7JfiPwgmV8hhBD/qpdfDuK++zw8+GD+HbRyu+HLL/V06hRCixahhIaqfPCB\nEZ0OwsJUFAU2b9bzxBMhVKtWCKfTXy+sXmcs6HYTsC3Y8887iIjwMWWK6ernjl1K560txxmyaj+2\n7fuZ/fZoBk6fzDf1p7H+sfmopUrx+ut2tm/XMWNG9hlrnU7F5cp98Ot2w4ABZqpW9fHoo66cXyDE\nbUgyv6LAyG/rIhBZF7e2o0c1rF5t4NdfU3O++C+yWheqCqtW6XnxxWAqVvTSr5+TTz9NQ6+Hdu0s\nVK7spVu3a0F2TIyOp54y06OHkwEDzBQrpjJ9up1atfJWemE0+qei/Z2iwNtv22nSJJSaTS+x257I\noYt2Hq5VjKH3lKHIiji8815hyfdNGfecE/BPZgsNhZUrrXTsaMHhUBg92oEmQDrK6fQPmMgNmw2e\nesqMqsLChbYbajhIfpH9QuQHyfwKIYT41yxebOSxx1wUKvTP336/cEHhiSfMvPVWEIsXp7FmTRpd\nurgxGv1lCEOGODK0BgN/1vmNN+yMHetk585Uevd20qlTCFOmmPDkfkLw1ef/e32vT1U56kjmzjG/\nMW/XCRqWC2NZj1r0jCpJiFGHq3dvvI0aBRxTV7q0ytq1VjZs0NOlSwgnT2b+kXzkiIZy5XyZPv93\n27bpuP/+UIoWVVm2LG9dNIS43UjwKwqM9GcUgci6uHU5HLB8uYEnn8x7ne3f18Xx4/5JZRUq+Niy\nJZW7786cuW3Txs2JE1r27fP/aIuN1XLunEKHDv5MsEYDvXu72LIllZ9+0tGnjzlgNjcQjebK4TN/\nbzO318f6g0kM+jyejzbtY+ipdRyb05Dq+uIYdJl/tDZuHDjSLllS5dtv/b17W7SwMGmSiYSEa4Hy\n7t066tXLOku9Z4+W6OhgBg40M2lSOjNn2tHrc/c93YxkvxD5QcoehBBC/Cvi4rSULeujQoWcM5fZ\nOX1aoWPHEEaOdNCvX9Z1rHo9tG3rYssWPTVrOlm82MiTT7oy9eItXVrl00/TGDzYTN++Zj74wJar\ngDEqysv23xSSS5xn1Z6zlE+9wOiv5lHf5MY1aBCPK26WLDHy2muZOyxkFfyCv5Z4xAgn7dq5mTfP\nyP33h3LvvR7q1/dw8qSGiAgvPp+/5OPSJYW4OP8Y6O++05OYqKFvXyevv56aL9l1IW4H0udXCCHE\nv2L+fCP792uZNu36+8y63fDggxY6d3YxfHjOGeQPPzTw44865s2zExUVyooVaVStGjj4drvh8cdD\nqFHDy8svZ98S7HK6m/mbk9hw9CLN1RP0XT6NKnfVwjF4ML6aNQHYuVPLqFHBbN2aix5m2bBa4euv\nDSxbZuDQIS1Op0L6n48XFqZSp46XyEgv993noUULd8CDeELcTvLa51f+yQghhAjoxAkNv/2mJTZW\nx4EDWux2/9v/YWEqtWp5iYryctddHooWDZxDiYvTctddeSis/ZuYGB07dugoXFhl2LDclU5ERXmZ\nNcvEpUsKly5pqFIl66yzXg+zZ9u4//5Q2rd3cdddmcsLElOdfL73PFuOXqZJxUKwKYqHmtkp/fWn\n2MPDM1xbq5aXI0e0pKdDUFDevte/sljg0UddTJ9u4qOP/H2Rr3SpuBUPsQlR0CT4FQVG+jOKQGRd\n3FjcblizRs+iRUYOHtTSsKGHqCh/V4WQEBVVhaQkhb17tSxYYGTIkGBatPDQv7+TRo08GYKzS5cU\nSpa8vjcXY378ka++bs2qVQbWb0pm79k0dp9JY3eCFaNOw5ttqwR8XfHiPi5d8j9fnTqegB0U/qpY\nMZXJk+0MH25m27bUqyUSn290cVCTwM4EK+2qh7Ogaw2KBOspfVZh9JwWrI+2ZvoBajJB5cpe4uO1\n1K//zwZ5rFhhwGJRadjQfx8Jev1kvxD5QYJfIYQQAPz8s5YRI8wUL+6jf38n7du7s6yF7dTJf4gs\nJUVh+XIDI0YEU66cj3fftVGmjD/g9XgUtNq8Bb/x7/1M+Ly32F67F2vSzlGpbxLDN6ZSoYiJeqUt\n9K5fkik/nOB0ioMyYaZMr9fp/AH8pUsKxYrl7mt36uRm1iwTGzfquadpOm+vi+ePU1Z6H/mBp998\nFrPx2o/Krl3dfPSRkZkzTYwalfm0XLFiKpcv/7NINTFRYcKEID77LE2CXiH+BRL8igIjv62LQGRd\n/PfcbnjllSA+/9zAm2/a6dgx98MowsJUBg920r+/kxkzTDRrFsrLL6fz2GMugoJU7PacozdVVTn7\n/U/sWb2ZnSGl2BX9HBaLmaCNDqIfKkKz2mWx/CUAbVKpMFuOJtOrXslM97Lb/SUHXi+ZDrplZ1SH\nfSS8tZ6n95bhvn07KP21nrMD+rH7V1OGw2qKAjNm2Gne3ELTpu5MGV6dzv+1r5fHA8OHm+nb10lk\nZP6Mgb6VyH4h8oMEv0IIcRtzOqF/fzMOh0JMTGqW9bs50evhf/9z0KaNi969Qzh7VkOlSj4OHtQC\nmYPpJJub3Wes7D5yjrhD58DrpV79+7n7nloMLBPG5rUh/B5romODa8MxtLt2YXrnHZr3jWZqgoXH\no0qg/C01euCAlsqVvZhM/kA4t+7YPZX57R/liQiFLqOeZ/IUM+PGObgylOKvypb1MWOGnccfD+GL\nL6zUrHmtrthu95c/XA+Pxz+WWFFg9Ohc9mATQuSZBL+iwEitlghE1sV/x+uFgQPNaDTw8cdp+TIY\noWZNH2vXWnn4YQv16nlIS/MX3VqdHuIS04g9Y2V3gpVkh4fIUhbqlS5M79RDlOjcBuUvNRZr1pyj\nSZOIjM9btSqeJk24a0w0rl5vcnrFYcp2acNfazPi4nRERnqpUsXLgQMBUr8BUsIbD11iXssBqFuq\nE1IrCLSebFuTgb+ncHq6nc6dLcyZY6NFC//o5P37tVSpkveM7aVLCsOHB+NwKHzwQf78f3Erkv1C\n5AcZciGEELep994zcv68hgUL8nciWMmSKstXpLDtsJUDhpMMW32AXp/8wdr4ixQ3GxjbrAIrHq/D\nhJYV6VCnJCW7d8wQ+AIcPlzoal3xVSEhOAcMwPrLLzxQ0sAPO48RFhWF9tdfr16yY4eOevU83HGH\nj4sXNSQnK2hOnMA4YwaWFi0wTZ169VpVVVm6M5FluxKZ2q4KDcqGEhvrzwnlFPwCdOni5v33bYwa\nFczTTwezf7+CVgulSuUte/7NN3ruvz+UcuV8fPxxGsHBeXq5ECKPJPMrCoz8ti4CkXXx3zh8WMP0\n6SY2bLBiNOZ8fU68PpWDF+3sTrCy+4yVgxft1OsVzJ6NRanhLMuMsjswOhJwR7bN1f3Ony9E9eqp\ngf9Qo6FJywa8qhShz+MPoJYvD/iHYfz2m5annlLRJSfxRtH5hLb8DEvqCdzt25M+YQKe++4DwOXx\n8faPJzlrdfJuh6oUDtZTvbqXjRvzNh7t/vs9xMSkMnFiMA89FEZ4uI+TJzWUL5/9YA+nE77+Ws/C\nhSYuXFB4/30b99xz/W3hbheyX4j8IMGvEELchsaODWb0aAcVK17f9DVVVTmR7Lga7O49a6NEiJ6o\nCAvd6hSnTskQgvUaXpizgzYjX6FQuSTSX3op1/dPT1cIDs46g1q5aBBajUJ8RBWqFTIDsHSpkUce\ncfHbbzpaV06laekDTHW9ypif7+SvkyCS0928tOEYxcx63mp7B8Y/xxGbzerVYRJ5ERoK06fb2bNH\nQ/HiKi1aWChTxkdkpJeoKA/h4So6nb8eeP9+f9/kXbu01K3rJTrawUMPyaAKIQqS/HMTBUZqtUQg\nsi4K3sGDGv74Q8vHH6fl6XXnrC7/IbUzVuLOWDHoNNSLsNC8chFG3V+OwkF/Zk1VFd3mzQS9+SZv\nua085ZpI51fb0LJ1XsoBvNl2TVAUhQcqFWbLkctUK2YmIUFhwQIj3bu7eOutIKAGrrtns3ChiUfP\npFKunD/IP5ns4MXvjvBApcI8cWcpNH85MOfx5K1DxF/t26chMVHLunUpeL2wd69/BPGuXTqSkxU8\nHn8XiipV/D2TZ8zw5Lk8Qsh+IfKHBL9CCHGbWbTISK9ezlyXO8QcS+b9XxOwu3xERYRQL8JC3ztL\nUcqS9Q0Mn36KY/Bg3A8/TGyTQqyP1rBzZwqhobn7mhaLi4sXNYSGZp2ZblqpEM99e4QBd5dm5MgQ\noqOdPPusgyJF1D87Nfi98koQ779vY/cZK29sPs6AuyNoXbVopvtdvKihcOG8B6SqCi+9FMzAgQ70\nev/5u7vu8gacGCeE+O9J8CsKjPy2LgKRdVHwvv7awJdfWnN1rdvrY+7Pp3m6cVnuKhOaqbVYQIqC\nff78qx8OGeLk7bdN/O9/ZubNs+U4dQ3grrt0xMX5qFQp6+C3fOEgLEYtb8x3ceGCwsiR/oD3r4fV\nRo920LRpKG+uSGan6xTPN69AZIQl4P3i4rTUr5/3utuPPzZw7pxCdHTuRjCL6yf7hcgP0u1BCCFu\nI+fOKTgcULly7mp9vz9ymTJhRu4uG5Y58FVVNMeO5XiPBg38Y49Pn9YwZkwQvlx86chI79XOC9kp\nZA3n2z+SWbrUdrXj2V+DX1OQSscXDrDuxFmeqVcty8AXIDZWm+fBEvHxGl56KYhZs+xZTsMTQtxY\nJPgVBSYmJua/fgRxA5J1UbDi4vwBXm4SuD5V5dO4czwaeW2SWkyMDlQV/bp1WFq2JHjYMP/7/tmo\nWtXfdmz+/DTi47X062fOcQRwWNhOvvlGn2Wg7HbDpEkm1i+MoOSd5ylTNnPQ6vT4eH3zcS5rrHQv\nUoMhvcI5cSLwj71jxzScPauhVq3cB78HD2ro1s3C66+nU6eOlDgUBNkvRH6Q4FcIIW4jJ09qc93h\n4afjKQQbtERFhPg/oaokLV6HpXlzTK+/juPpp0n7+mtyiqS1Wv9UtNRUDZ9/nkapUj4aNw5l7Vp9\nlnFz9eqXMZlUtm7NnP3du1dLy5YW4uJ0fLPCQ0QhA7FnMpZxXLa7Gb32EHqNwuS2VRjSXyU62km7\ndhZ+/DHzPRcvNvLYY65c10Fv2KDj4YctvPBCOt27u3L3IiHEDUFqfkWBkVotEYisi4LldILRmPOh\nLlVV+STuHI/+ZYRw0PPP82BMDI63x+Bu25ZcFe/+yWhUcTr9HQ/eeCOdDh3cjBoVzJQpJvr1c9Kt\nmyvDcIf7729M//5O5swx0bRpGj4fbNigZ+FCI3FxWl56KZ2ePV0oCjStVJgtRy/ToIz/NN3xy+m8\n+N1RWlctQq96Ja8+/4ABTsqX9zJkiJmHHnIxYUI6oaGQkqKwfLmB9etzroO+fFnhhReC2LZNx/z5\nNu6/X3rzFiTZL0R+kOBXCCFuIwaDv2QgJ7vPWHF4fNxbPgzwlzv8YnqFKRcsPP27SuNCOY8A/iuX\niwxT5O6918P27als3qxj0SIj48cHU726l8hIL5UrezGZVOx2hZ07tdx7r4XERA1VqvgYMMDJsmUu\ngoKu3atppUIMXnmW4V4fexPTmLzlBIMblaZFlSKZnqNVKw/btqXy4otB1KsXRrduLhITNXTs6M4y\nI66q8PvvWhYtMrJ6tZ5HHnERE5NKSEiuv30hxA1Egl9RYKQ/owhE1kXBKlHCx9q1er79Vs/Fiwpe\nLxiNULGilzp1vJj98yL4JO4c3esWv9oHt3FjD40b63AZMrYRyw1V9R92K1kyY3Cp0UDLlh5atvSQ\nluYPMGNjdZw4oeHEibOUK1eSTp1crFxpYN06K9WrBw5Oi5kNlC9sYvqPJ9mVYGVCy4rUKZl1ZBoW\npjJjhp2xYxVeeimIb7/VU7SoypkzZmrX9mKx+DPjKSkKe/fqiIvTYjSq9Onj4uefUylRQvrz/ldk\nvxD5QYJfIYS4xakq/PKLliVLjGzYoOfyZQW93h8I63TgcMD77xvZv19LhQo+WnZP4lS4k2aVC2e6\nV16yvVccO6bBYoHw8KyDxpAQaNTIS6NG/oNjMTF7adzYn3UuVkxl2DAzq1ZZsWTRrKHVHUX5bM85\nprWvSumw3BXuJidr2LpVz8qVaVSo4GP3bi3x8VouXNCgKBASovLEE04iIz2ULq3m6pCgEOLGpxw4\ncCDff4U9deoU9evXz+/bCiGEyKOtW3W8+GIQNpvCk0866djRRfPmoXz/fSplymTc/l0uf7uvyT8e\n5ejPRWhcogQvv5xO0aL/7MfEF1/oWb3awAcf2K7r9aoKo0cHs2ePlk8/TaNIkczPo6oqKmSY2Jad\nXbu0PPZYCJMn2+nUKRd1IEKIG9auXbsoW7Zsrq+Xbg9CCHELSkuD0aODGDrUzJgxDn75JZXoaCdl\ny6q0bu3miy8MmV5jMEDJO2zoSqTy3dwQShmTaNVYz5o1/6yB7WefGWjd+voDTEWBqVPtNG7s4f77\nQ9mwIfObloqi5Crw9Xhg+nQT3buHMH26BL5C3I4k+BUFRvozikBkXeS/xESF1q1DSU9X2LYtlXbt\n3BkaM/Tv72TxYiPeAK1pP91zjodrFaNEUZh0fiDftp/OxIlBvPqqKad2vgGdOKHht990dO2at3Zg\nf18XigITJ6Yzd66NZ58NZuDAYH7/XZvr+3m98N13eh580MLWrTq+/95KmzYS+N5sZL8Q+UFqfoUQ\n4hZy/rzCww9bePRRF888E/hgWv36XsLDVVauNPDII9eC0vNpLn4+mcKS7jXRr1yJ9sgRSrz/PuvT\nrHTrFoLXq/DSS+l5ep4ZM0z07Jmxjdk/0aSJh5iYVObONdGjRwjlyvno3NlFvXoeatf2ZugCkZSk\nEBur5ddfdSxfbqBYMZXBg/1t1aR+V4jbl9T8CiHELcLrhbZtLTzwgJvnnsu+I8POnVoefzyErVtT\nKV7c/2Ng9k+nMWgVBlbQEdqkCWmffIK3Xj0ALl1SaNfOQnS0g169cpfFjYnRMWiQmW3bUilUKP87\nJHg88O23ejZt0hMbq+XQIS0hIerVQ3wej0Lduh6iorx07uyifn2ZwibErSivNb+S+RVCiFvE7NlG\nTCaVsWNzbkXWoIGXnj1d/O9/wSxdaiPV6WbzkUvM71Kd4MH9cfbufTXwBShSRGXhwjQeftgfXP/9\nsNzfpaQojBgRzPTptn8l8AXQ6aBDBzcdOvjLF5xO/9d1ucBk8j9zHuZwCCFuE7ItiAIjtVoiEFkX\n+ePIEQ0zZpiYMcOe64Bv7Nh0LlzQMH58EKt+v0CTioUoEfsr2iNHcDz7bKbra9b0MXiwk2eeMWd7\n37Q06NnTzEMPuWnd+vomoF3PujAaoXhxlTJlVMLDJfC9Fcl+IfKDbA1CCHELmDvXSP/+TsqXDzwI\nIhCTCT79NI3fYmHFziQerl4Cz333Yf3mG38kGcCIEQ727dOyd2/gw2bnzil06WLhjjt8vPZa3uqD\nhRCiIEjNrxBC3ETcboiP1xIbq+X337WkpCg4nQrr1ukZOdJBkyYe6tTxZDkMIpAPfjnHZxvdXPi6\nJrNn23KsjZ0yxcSZMxqmT7df/ZyqwsqVesaPD+bJJ52MHeuQQ2VCiAIhNb9CCHELOnZMw5IlRj7+\n2EB4uEpUlIc6dbwULary0086qlXzkpSkMHFiEAcOaHnwQTf9+zto2NCbbRDq8vhYe/g80wdVIbZa\nOj17htCypZv+/Z1ZBsG9eztp2DCMyZPt6HSwfr2e+fONnDun4ZNP0qhXTw6WCSFuXBL8igIjM9lF\nILIuspeSovDCC0GsW6enZ08X69dbqVgxY2nDTz/p6N3bxYABTgCSkxWWLzcwfLiZ8HCVGTNs3HFH\n4HKI9YcuUaVoMJWLBlG5q5tmzVL58EMD/fqZKVxY5b77PERFeahZ04vFAj6fv/NDSIiPp54yExur\npUQJlf79nXTu7MqqWiLPZF2IQGRdiPwgwa8QQtygNm/WMWKEmQcfdLNrV0qWpQxxcVp69XJe/bhQ\nIZUhQ5wMGuRk4UIjbdpYGDXKwdChzgxZYK9PZcWec4ytea0Jb5EiKiNGOImOdrJtm47fftPx1VcG\npkzRYrMpaLUqoaEqRiPodCoff2yjdm3J9Aohbh5S8yuEEDeg5csNvPJKEHPn2njggew7JpQsWYij\nR5OzHCRx/LiGAQPM1KrlZdo0O1otnLU6mbP9NMmHzrJ41USsGzaQlyLduXONHD+u4c035VCbEOK/\nldea3+vu9pCWlkbjxo1ZtGjR9d5CCCFEAF98oee114L48ktrjoGv2+0fbpHdBLUKFXysXm3l6FEN\n/xtj4sNdZ4lefYCaahrvvDUI+9SpeQp8ASwWFZtNTrQJIW4+1x38vvfee9SuXRtFjvOKXJL+jCIQ\nWRcZHTigYdy4YD77zErVqjm3LVMUf6cFNYf38EJC4H9TE/i99G5+2G3ntR0b6N2/O8OtU3h9XSMm\nTzYRE5P7SjifL8/xcp7IuhCByLoQ+eG6an6PHj3KpUuXqF27NmpOO64QQohc8Xph2DAzzz2XTs2a\nuevXq9P5+/VarRAaGvias1Ync39O4MRlB4PvLktkl0ep1qw4nt9+oOySCowbl/NEuL9LTlYIDZX9\nXwhx87muzO+0adMYPnx4fj+LuMXJCV0RiKyLaxYtMhIcrNK3rytPr6tVy8uePZlzGS6Pjw93n2XY\n6gNUCw9mftfqdGtsYfPgZfQyrkAtWZLGja9vAtuePbp/9aCbrAsRiKwLkR/ynPndvHkzFSpUoFSp\nUpL1FUKIbLhcYLMp+HwQFKRerct1ufy9cXfs0BEbq2XfPi2pqQpeL5jNKu3bhxAV5eXuuz20aePO\nsX1YVJSH2FhthkD2l1MpzNl+moqFg5jdqTolLIarf9Z7XFGm1NVx8qTmuoPfuDgtzzwjh92EEDef\nPAe/e/bsYf369WzatInLly+j0WgoXrw47du3z3Dd0KFDKVeuHABhYWHUqVPn6m9sV2p25OPbYy1S\npwAAIABJREFU6+Mrn7tRnkc+vjE+njt37i2zP9hsMGXKCX7/vSiJiREcPapBr3ejKOBy6QkP96Eo\ndpKSTNSqpfDQQ25at97JoEEpGI338uqrQYwdu4njx0PxeCJZutTIqFF6WrY8ycsvFyMiQg349QsX\nLsWGDZEMG+ZkzeZtfHfegFVjZljNUBxJRzkUd4YSf3veHj1asWSJgebNN+b5+01IMJOS8gBVq/pk\nv5CPC/TjW2m/kI//2f4QExPDyZMnARgwYAB58Y9anc2aNQuz2cyTTz6Z4fPS6kwEEhMjzclFZrfC\nukhIUJg1y8SKFQYaNfLQurWbqCgvNWp4MRj8h9E+/1zPuHHB1K3rJTRUZetWHc2aeRg+3EG9el6i\no4OJjPQycKAzw70PH9awcKGRzz83MGFCOr16uTIdNHM6IbJ+CEPeOcKPZ8/RpXYxHvvje8JeeYm0\nDz7A27BhpmeOj9fQo0cIe/ak5vn7ff75IAwGmDjx38v83grrQuQ/WRciEBlvLG5YsmGJQG7mdaGq\n8OGH/n68jz3mYssWK2XLZjyoZrfD0KFmDh7U8vnn10b/pqbCJ58YeeyxELp3d7Frly5T4AtQpYqP\nN97wB73R0cGsWWNgwYK0DIfb4s6nUHX4PmJ+NzP3ITMVxw9FSU4m7fPP8datG/DZq1XzkZqqcPGi\nQnh47nMgVit8+qmBTZusuX7N9biZ14X498i6EPnhHwW/w4YNy6/nEEKIm4rNBgMGmDl7VsPq1WnU\nqpX58FdaGvToEUK5cj6+/z41Q+1uaCgMHOikSxcXzzwTzMGDGoKDsw5Ca9XysmGDlXHjgunUycKq\nVWk4tU5mbz/NgTMOht8TwR/tv6DCu2/g/t/TOIcM8beCyIJGA5GRXmJjtbRs6cn19/3SS8G0aeOm\nfPncdaMQQogbzXX3+RUir/5aqyPEFTfjukhLg65dLRQtqrJ+vTVg4Ov1whNPhFCxoo/Zs+1ZHloL\nD1cZPz6d8HCVTp0sHD6c9bas18PUqXbuvttD9xEuhq0+wB1Fg6ibGEWrOqF0u+c47YpuJ3Xg8GwD\n3yvuuMPLsWPaXH/fP/ygY/16Pa+/bs/1a67XzbguxL9P1oXIDxL8CiFEHvh8/qD2jju8zJhhR68P\nfN2cOUZcLnj3XTuaHHZap1OhZEkfY8em07VrCElJWU+PUFGp1f0Y3H2QColV6VW/FBo0oNFQ+tNX\nMdetwLBhZny5SMyaTODIZYvfw4c1DBli5p13bFn2ExZCiJuB1PyKAiO1WiKQm21dLFhgxG5XeOed\nrIPagwc1vPuuiY0brWhzkVjV6cDjUejTx8XBg1rGjAlm4UJbpuusTg9vbTlBmsvL9LZVadc8HFeC\ni2XLTAA0buxhzhwbPXqEEB0dzMyZ9mwTwB4PWQbvf3XggIZu3Sw891w6LVrkvkTin7jZ1oUoGLIu\nRH6QzK8QQuTS0aMapkwxMXOmLdug9tVXg3jmGQcVKuSuLjY83MfZswqqCs8/n87evVq++ipjVHok\nyc6w1QeI0LiZvXY6tcyXeeWVdI4f1zJmTDrjxjlo3NhDUBB88kkaly5paNfOwqFDWW/ziYkaihXL\n+hmvHOhr397C88+n07t33oZvCCHEjUiCX1FgpFZLBHIzrYu33jIxdKiTKlWyDhhPn1b46Scdffpk\n7tyQlRIlVEwmOHVKQ1AQTJtm56WXgq6WLqw/mMS4bw7z1MU9jBvSHk3lSqhhYfTo4WL/fm2mw2fB\nwbB8eRpdu7po08bCtGkmkpMzl1LExWmJjAw8pW3PHi3du4fw/vtGVq9O49FHCzbwvZnWhSg4si5E\nfpCyByGEyIWLFxW++07PG29k3xd36VIjjzziIiQk858l2d18uCuRJ++MINSUcfuNjPSwa5eWcuV8\n3Hefh9BQlQ2bNcSbjrP36AXmfjKJCmYN1g0b8FWsCIAB6N3bSVyclp49M34tjcbfTaJVKzdvvGGi\nXr1QOnRw8/DDLqKi/AHv5csaKlXyB84+n7+u95dfdCxbZiQxUcPAgQ4GD3bmqjRCCCFuFv9oyEVW\nZMiFEOJWM2OGkYMHtcyalX2ng+bNLUyaZKdRo4wZ1R+PJTNz2yk8PpUJLSsSFWHJ8Ofvv28kJkbH\nkiX+Wt+5S1W+TjrMPXe4eOnlfmheHI+7Y0f+PuFi3z4NffuG8Msv2QflFy4ofPihke+/1xEXp0Or\n9W/91at7cTgUDh/WEh7uIyrKS7duLlq3duemYYQQQvznZMiFEEL8C7Zs0TNoUPalDC4XHDigpU6d\na4GvzeVl9vbT7Dtn4+XWlVj1+3mS7O5Mr+3e3cnrr5tITFRI8KawWXOCMz+XZ/zTFrwPxeDNIv1a\ntaqPM2c0pKaSbReGYsVURo1yMGqUvw1bw4ahDBzooHZtHyaTSsWKPgoXzvdciBBC3HCk5lcUGKnV\nEoHcDOtCVa/Ux2bf6eDAAX/Zgtns/3hPopXBK/dj1CrM7VyNGsXNFA3WcylA8BsaCo3ucfPCxxd4\ne+tJXmxZAQ6W4ehRbbYtGXQ6qFnTy969uc9lbN6sQ6uFp55yce+9HurX995wge/NsC5EwZN1IfKD\nZH6FECIHCQkKBgOULJl9gHjunEKpUj5cXh9Lf0tk05FLjGpcDvfJogTp/YFz0WA9F/8e/Doc2BLO\nElLnDAesJXi1cQ3qlvIfRtuzR8sdd2TfNaJUKR8XLmTdG/ivrFYYPTqYadPsf6+gEEKI24JkfkWB\nkf6MIpCbYV0kJWkoXjzntmUej4KmsI0RXx4gIdXJe52r07BcGDEx1/IMRc16ktJchLRrR+jddxNW\noQJnGzZn6Bf7Cd1/nApHajBycGHS06F4cR+XLuW8Tev1/p69ufHii8E0beopsH691+tmWBei4Mm6\nEPlBMr9CiNuG1wt792qJjdUSG6sjIUGD2+0PHiMifERFeYiM9FK3rjfDYS+vlxyHVfhUlbj0RFLr\nJ/JU7QhaVynM0bfWsDS9JW/NLAz4h1AUrawnyeHBMX48vvBw1tmDWPBHMkPvKcsOXymmjnUweLCO\n/v3NlC7ty1VQ63CQ5fjkv5oxw8j27To2bMj+cJwQQtzKJPMrCozUaolACmJdXLyo8M47RurXD2Xw\nYDO//qqjVi0vAwc6GDXKwcCBDurW9bJzp45hw8zUqxfG22+bOH/eXxdgMqnY7VnXCJyzuhj7zWFO\neC9z9sMGtNGnYnnkEaLWTmFUr4QMQyiu1PzaG93DtAtBfHI4jSnt7qBZZX+ArCgwc6a/JGHdOj0a\nTc61uIcOaa+2LAvE5/P3KF661MjKldabYjyx7BciEFkXIj9I5lcIccvyemHePCNTp5po29bNkiU2\n6tULPNQBrqVY4+K0LFpkpFGjUEaOdPDkk05OndLgdGbMsKqqyqbDl5m3I4FudYrTtWoh5o54F3OL\nt3GNHIFzyBDQ62nc+Nq9iwTruWBz8781hyhmNjDz4WqYDf608pXrDAZYssRG7dphvPNOEDVr+rj/\n/sApYKsVEhI0VKsW+Ps6eVLDiBHB2GwKa9dac6xbFkKIW530+RVC5IrP5397XVH8AaDmBn/f6MQJ\nDYMGmdFqVWbOtGebGc3uHlcCx9RUhfnzbVcHRKQ6PMzYdooTlx2MfaA8VcwKllat+O1seRLGT6F5\nv4gs7/vEp3/QoUY4XesUR8ni1JnHAxUrFmLmzDSef95MkyZuBg1yXv36V2zZomPSpCDWr7dm+HxC\ngsLSpUYWLzYyfLiDoUOd0rdXCHFLkj6/Qoh8kZKisGqVnl9/1REbq+PQIQ06nb/tF0CNGl4iI73c\nc4+HDh1cBAX9t8/7V/HxGrp1szB4sIPoaOd1B+rly/tYtSqNBQuMvPJKEKtWGYiKSue306lM23qS\nJpUKMaZpeQw6/xewz5rFb7/fxddrDDTvZ8vyvku618wy6L0iLk5LRISPTp08NGuWyuLFBp54wkyx\nYioPPugmKspDnTpePvjASOfOLlJSFPbt89czb9um46efdDzyiIt166xUrpz3wF8IIW5VkvkVBSYm\nJkZO6t4EDh7UMHu2ia++0tOsmYcmTdxERXmpUcN79S1/mw1+/91/aGzjRj2xsVoefdTFkCEOIiLy\ntqXk97o4flxDu3YWJk5Mp3t3V77d9403TLwzS8/wBfHEpyQzukl56pW2ZLrOboe6dcPYtMlK+fLX\nH3Q+/XQw5cr5+N//HFc/5/X6e/T+9JP/7zwuTktysoKigNkMVat6iYrycOedXtq3Dzxi+WYh+4UI\nRNaFCEQyv0KI6+LxwIwZJubONTJokJMdO1IpXjxwIGs2Q8OGXho29DJokJNjxzQsXGikadNQJk5M\n5/HHXZl6yKqqf8RuerqCVqsSGqrm+8ErjwcGDDAzbJgjXwNfgC79L7Fec5INWyx8+XRJCgUIfAGC\ng6FPHyeTJpmYNy/7UchZSUlR+OorPT//nLErg1YLrVp5aNXKX//77LP+dPtbb6VLz14hhMglyfwK\nITh7VqFXrxBCQ1VmzLBRpsz1bQt//KElOjqYUqV8LFhg4+xZDZ9+amDnTh1xcdo/M5QqPp9CcrJC\nsWI+oqK8NG7spls3V5bBcHKyQlyclj17tCQlafB4ICjIP5I3KspD1ao+dDp45x0jP/ygZ+XKtHwL\nBr0+leVx5/jyjwtEOstQ+IWPGKmdiSd2G2p4eMDX2GzQpEkor72WTps2mae55WT8+CBSUxVmzco6\neN66VcfQoWa2bUslLEwOsQkhbl+S+RVC5ElCgkLHjhZ69nTxv/85/lHQWKuWlw0brDz2mJnatcMw\nGKBnTxeDBzuIjPRSosS1IM3rhcOHNcTF6fjmGz2vvRZE585uRo50ULasj/R0WLnSwOLFRg4e1FK7\ntoe6db2UKuVDo4H0dIXvv9fzzjsmzp7V0KqVi02b9Pz4ozXfAt+EFAdvbjlBkF7L/LJWyo1tw3ZT\nFe507mB5WhEqhAcuazCb/e3KBgwwU6dOap5+mdi+Xcfq1QZiYrLuxXv+vMKIEcFMn26TwFcIIfJI\ngl9RYKRW68aTmgpdulh44gknI0Y4//H9kpMVnn8+iMOH/aN5VRVefDE9YJcBrRaqVfNx4cJmlixp\nTGKiwqJFRpo1s9CsmZstW/Q0aOBh7Nh0mjf3ZDtk4sIFhQEDzPh8MGSIf3Rv1arXX2+rqirfHEhi\nyW+J9KoeSo9lb2PctAn75MmE1O7IifvCmDzZxXvvZZ2ZvfdeD9HRDrp2tbB6tZVSpXIOUs+fV4iO\nDmbKFDtFigS+/uJFhW7dQujRw3W1/OFWJPuFCETWhcgPN3izIiHEv2nChGAaNvTkS+C7Z4+Wxo1D\nCQ5W+fHH1KulB3Pm5GL0GFCqlErv3i4qVPDx7bcGqlXzsHChjVatsg98AcLCVA4e1PLdd1Y6dXLT\ntq2FmTON+K4j/r1kdzNh/VHWxl9karsqdKoYglK4MCnbt+Pu0IEKFVUmT7bz2WcGfvkl+weLjnbS\ns6eTdu0s7N6d/bUXLviD2u7dXbRrF7hUYt8+/2G+Vq3cjBvnCHiNEEKI7EnNrxC3qc2bdYwcGUxM\nTOo/Pni2e7eWHj1CmDrVTseO1wK3Eyc0tGhhYe1aK9WqZR+J7t3rv8egQQ4GD3byzDPBHDum4bPP\n0jCbs//6P/6o45VXgtiwwd/r9vhxDYMHmylXzsvs2Xb0+tx9H9uOJzNj2ykeqlaUXvVKotdmnR+4\n5x4LiYkapk2z07mzO9tSiy++0DN+fDC9ezt59llHplHEu3drGTjQTOfOLp57LnPpidsN775rYt48\nIxMnptOrV/4e5hNCiJtZXmt+JfMrxG3IX44QzJQp6f848D15UkPPniG8+27GwBf8fXKfecbBa69l\n3wQ4Pl7DI4+E8MYbdp5+2onR6K+ZrVjRR79+IVd7C2dl924td955rQSgQgUfq1ZZSU7WMHSoGW9W\nQ93+ZHd5eXvrCebvSGBCy4o8eWdEtoEvQOvWHrp0cfHmm0H07Wvm3Lmso9+uXd1s3ZrKwYNa6tcP\n4803TSQmKjgc8NprJh59NISxY9MZPz5j4HvhgsL06SYaNAhlxw4d33+fKoGvEEL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X/Xe7s9nMrgQwD6MUEWLVWR0Yd7RZCYWke+5JUv/+Xp11FucVxzvWFtTXkbJS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\nIV5dcYVPbu4qDgC1qm3GmB1jIEYlJ0s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"text": [ - "" + "" ] } ], - "prompt_number": 14 + "prompt_number": 24 }, { "cell_type": "markdown", @@ -922,30 +922,56 @@ "collapsed": false, "input": [ "from math import radians, sin, cos\n", + "import math\n", + "\n", + "def rk4(y, x, dx, f):\n", + " \"\"\"computes 4th order Runge-Kutta for dy/dx.\n", + " y is the initial value for y\n", + " x is the initial value for x\n", + " dx is the difference in x (e.g. the time step)\n", + " f is a callable function (y, x) that you supply to compute dy/dx for\n", + " the specified values.\n", + " \"\"\"\n", + " \n", + " k1 = dx * f(y, x)\n", + " k2 = dx * f(y + 0.5*k1, x + 0.5*dx)\n", + " k3 = dx * f(y + 0.5*k2, x + 0.5*dx)\n", + " k4 = dx * f(y + k3, x + dx)\n", + " \n", + " return y + (k1 + 2*k2 + 2*k3 + k4) / 6.\n", + "\n", + "def fx(x,t):\n", + " return fx.vel\n", + " \n", + "def fy(y,t):\n", + " return fy.vel - 9.8*t\n", + "\n", + "\n", "class BallTrajectory2D(object):\n", " def __init__(self, x0, y0, velocity, theta_deg=0., g=9.8, noise=[0.0,0.0]):\n", - " theta = radians(theta_deg)\n", - " self.vx0 = velocity * cos(theta)\n", - " self.vy0 = velocity * sin(theta)\n", + " self.x = x0\n", + " self.y = y0\n", + " self.t = 0\n", " \n", - " self.x0 = x0\n", - " self.y0 = y0\n", + " theta = math.radians(theta_deg)\n", + "\n", + " fx.vel = math.cos(theta) * velocity\n", + " fy.vel = math.sin(theta) * velocity\n", " \n", " self.g = g\n", " self.noise = noise\n", " \n", - " def position(self, t):\n", - " \"\"\" returns (x,y) tuple of ball position at time t\"\"\"\n", " \n", - " x = self.vx0*t + self.x0\n", - " y = -0.5*self.g*t**2 + self.vy0*t + self.y0\n", - " \n", - " return (x +random.randn()*self.noise[0], y +random.randn()*self.noise[1])" + " def step (self, dt):\n", + " self.x = rk4 (self.x, self.t, dt, fx)\n", + " self.y = rk4 (self.y, self.t, dt, fy)\n", + " self.t += dt \n", + " return (self.x +random.randn()*self.noise[0], self.y+random.randn()*self.noise[1])" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 15 + "prompt_number": 25 }, { "cell_type": "markdown", @@ -969,7 +995,7 @@ " t = 0\n", " dt = 0.25\n", " while y >= 0:\n", - " x,y = ball.position(t)\n", + " x,y = ball.step(dt)\n", " t += dt\n", " if y >= 0:\n", " plt.scatter(x,y)\n", @@ -986,21 +1012,21 @@ { "metadata": {}, "output_type": "display_data", - "png": 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6CmjFkbfpdblsZWa2vASC7MxGfubqqdl98olLF12UqylT8vXEE2kKBJyeUdfo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\nWWedRX5JbPny5frggw+UnZ2tG264QVL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PAe04/Da9Lpet9PS2l0CQndnIz1y9NbuPP3bpoouyNW1arh5/PEV+v9Mz6h69\nNT90HEU00ItdfHFQ3/52kyZMCOv3v/dr7FhupgKge/3ud6n64AOP6ust3X57hj7+mHfA0DtRRCMu\n6A1LTEOGRPWznzWqrMynCy4Iyett+xiyMxv5mStZsrN66X2ckiU/HB1FNNDLud1iD2gAPWbRooBO\nOSWk3NyoHnigQSecwI2c0DuxTzTQC9TWSg0NlvLzbaWlOT0bAMmutlZqbLRUUGC3+w4Y4LR47BPN\nSjRguK1bYzc9mDo1V7/5Tap8PqdnBCDZ9e0rDRhAAY3ejSIacUFvmHOeeSZFf/+7Vw0Nlu69N0Mf\nfdS5i3jIzmzkZy6yMxv5gSIaMNyRF+301ot4AJivstLSPfek6dJLM7VunVt2QjSUAl1DTzRguH/+\n06Wbb87Q5s1u3XRTk664IqCsLKdnBQBt3Xdfmh58MF2SlJZma+3aOo0ezdab6Hnx6In2xGkuABwy\ncmRUTz5ZL7/fUr9+tlJSnJ4RALTv8D2jm5os+f28dQZz0c6BuKA3zFm5ubGLeLpSQJOd2cjPXMmY\n3dVXNykjI/YG+Pz5AQ0ZYu72d8mYH1pjJRoAAPSIadMievXVOvn9lgYPjig/3+kZAV1HTzRgAL9f\nevddj3btsnTSSVGNH2/u6g0AAE6jJxpIEm+84dGll2ZLknJyolq1yqcxY7gYBwAAp9ATjbigN6x7\nvf12y++7dXUu7dkTv1OX7MxGfuYiu7a2bnXpgw9cOnDA6Zl8OfIDRTRggNNPD8uyYp1Xxx0X1fHH\nswoNoHdZv96tM8/M0cyZubrvvnTV1jo9I+CL0RMNGCAQkDZudGvvXpdOOCHCvqoAehXbli65JFMv\nv9yyxdCrrx7UxIm81qF70BMNJInUVGnq1IgkLigE0PtYVmzP+5dfjo3T021lZjo7J+DL0M6BuKA3\nzFxkZzbyMxfZtfbd7wZ0zTVN+upXg3r6aZ9GjUrsVWjyAyvRAADAcUOGRHXffY2y7djKNJDo6IkG\nEsS+fZZWrPDq7bc9+uY3g/q3fwvL63V6VgAA9D70RAO9yGuvebRkSawJ8NlnU7R6tU+TJtEDDQBA\nIqInGnFBb9ix277d3fxxJGLpwIGeeT+T7MxGfuYiu44LhaTycpfeesut6urE6PUgP1BEAwli1qyQ\ncnJiF9JMnhzSyJGsQgOAJL3yikdf/WqOzjknR3fcka79+52eEUBPNJBQtm51qabG0qBBUQ0YkBCn\nJgA4KhK5uwPEAAAcg0lEQVSRzj8/S2+91XKRyGuvHdT48Ym9ewcSGz3RQC+T6Fs6AUBPc7ulyZMj\nzUV0375RZWc7PClAtHMgTugNMxfZmY38zEV2HXfVVU368Y8b9J3vNOm55+o1dKjzCw7kB1aiAQBA\nQhs0yNZ11wWcngbQCj3RQA/y+6W33/Zo2zaXJk2KaPLkCDcVAACgh9ETDRjmb3/z6OKLY818aWm2\nXnqpjotjAAAwED3RiAt6wzrmww9b9oJuarK0e7fzpyDZmY38zEV28bNnj6WqKkuhUM99T/KD8z/B\ngSQydWpYHk+sg6qgIJoQF8cAgMk2bnRr1qwcTZ2aq2ee8SoYdHpGSBb0RAM9KBKRysvd+uwzSyNG\nRHXCCRTRANBVoZD0jW9k6o03UiRJlmVr/fo6jR7Nayu+GD3RgGHcbmnSJO5ECADxYFlSamrL2O2W\nXLzHjh7CPzXEBb1h5iI7s5Gfucju2Hk80l13NWrixJAGDIjq8cfrNXx4z6xCkx+6VETv2bNH8+fP\n17nnnqu5c+dq/fr1kqSysjKVlJSopKREa9eubX780Y4DAAAcixNPjOr55+u1dm2dSkvDcru//GuA\neOhST/T+/fu1b98+jR49Wrt27dK8efP0yiuv6Oyzz9by5csVCAS0YMECrVmzRsFgUHPmzGlz/Ej0\nRKM3qa62VFcn5efb6tPH6dkAAIDDOdYTnZ+fr/z8fEnSgAEDFAqFtHHjRo0aNUp5eXmSpKKiIlVU\nVKi+vr7d42PGjDmmiQOJ6l//cunKKzNVXu7R178e0H33NaqoKCGu3wUAAHFyzD3Rb7zxhsaNG6f9\n+/eroKBAy5Yt08qVK1VQUKC9e/dq37597R5H70JvWIt16zwqL4/9fvr886natCmx31skO7ORn7nI\nzmzkh2PanaO6uloPPPCAfvOb3+jDDz+UJM2bN0+S2rRsHH7cOsp9jhcvXqzBgwdLknJzczV+/HgV\nFxdLavnHyjgxx5s2bUqo+Tg5zshoveqclpZY82PMmHFijA9JlPn0xvHBg9K6dU1qbHTptNNSdfzx\nNvkl6fjQx5WVlZKkRYsW6Vh1eZ/oQCCgK664QosXL1ZxcbHee+89Pfroo/qv//ovSdK3v/1t3XHH\nHfL7/e0eP7Kdg55o9Ba7dln6+c/TtHatV5dfHtCCBQHl5jo9KwBIPv/1XylaujRTknTGGSE9+qhf\n/frRXgcHe6Jt29btt9+uc889t7nSHz9+vLZu3aqamhoFAgHt2bNHY8aMUTAYbPc40FsNGGDrvvsa\n5fc3KidHXCkOAA7w+6U//7llE+nXXvNq3z6LIhpx06We6Pfee0+rV6/W008/rQsvvFBf//rXdeDA\nAS1ZskTz58/XwoULtXTpUklSSkpKu8fRuxz59layS0mR+vY1o4AmO7ORn7nIrntlZEglJaHm8Ykn\nhtW3b/wKaPJDl1aiTz31VG3evLnN8dLSUpWWlnb4OAAAQHewLOk73wno5JMj8vksTZkS1nHHsQqN\n+OlyT3S80RMNAACAnuBYTzQAads2l6qrLQ0YENWgQQnxuygAAOghx7xPNCAlX2/YRx+5NGdOtubM\nydHFF2dp2zZzT6Vky663IT9zkZ3ZyA/m/uQHHPTuux5VV8dOn48/9qiiglMJAIBkQjsH4uLQVofJ\n4rjjooeNbOXlmdvOkWzZ9TbkZy6yc1Z1taUNG9xqbLQ0aVJEQ4ZEv/yLDkN+oIgGumDKlLB++Uu/\n/ud/PLrwwpBOPjni9JQAAB0UiUi//32qHnggXZI0fXpITzzBjVjQObwHjbhItt6wvn2lb30rqEcf\nbdA554SUnu70jLou2bLrbcjPXGTnnPp66YUXUprH69d7VVtrdeo5yA8U0QAAIKlkZUkXXhhsHs+Y\nETK6LQ/OYJ9oAACQdPbtO7wnOqzBgxOiHEIPYZ9oAACALujXz9bs2WGnpwGD0c6BuOitvWH791va\nts1Sba3TM+k+vTW7ZEF+5iI7s5EfKKKBo/jkE5cWLMjUqafm6tprM7VrV+cuOgEAAL0XPdHAUSxf\n7tV3v5vVPH7ySZ/OOYe3/gAAMB090UA3Sk394jEAoHcKhaSPP3YpHJZGjIgqK+vLvwbJh3YOxEVv\n7A2bMiWsq69u0pAhEd1yS6MmTeqdq9C9MbtkQn7mIrvEZNtSWZlXZ5yRo5kzc/W736WqoaHt48gP\nFNHAURQV2br77ka98kqdlixpUn6+0zMCAHS32lrpnnvSFY3GroO555507dnDNTFoiyIacVFcXOz0\nFLqF1yvl5cX+31v11uySBfmZi+wSU1qaNGxYpHlcWGgrLa3t48gP9EQDAAB8LiND+slPGvXrX0d1\n8KBLN97YqP79E2IPBiQYVqIRF/SGmYvszEZ+5iK7xDVyZFQ//3mjHnvMrwkTou0+hvxAEQ0AAAB0\nEvtEI6kFg9KGDW5t2eLW2LERTZ4ckYcmJwAAejX2iQaO0fvvu3XuudmKRi253bZWrvTp1FMjX/6F\nAAAgqdHOgbgwtTesqsrVvI1RJGKpqir5TglTs0MM+ZmL7My2fv16p6cAh7ESjaQ2YkRUaWm2mpos\nZWbaGjGi/QtIAACQpKoqS+vWeXTw4DQVFVkaPjwhumLhAHqikdRsW9q0ya3KSktDhkQ1fjxFNACg\nfY2N0s03Z+j//b9USdKUKSH9+c/1ystzeGLoNHqigWNkWdKECRFNmOD0TAAAia6+3tIbb7Tcfevv\nf/fI57OUl5cQ65HoYcnXAIpuQW+fucjObORnLrIzT58+tq64ItA8vuyyIAV0EmMlGgAAoAO8XunK\nK5s0ZUpYNTU+TZuWoexsp2cFp9ATDQAAgKQSj55o2jkAAACATqKIRlwkcm+f3y+VlXm1ZEm6/vpX\nr/x+p2eUWBI5O3w58jMX2ZmN/EBPNHq9999367LLMiVZevxxWy+84NPpp3NXQgAA0HWsRCMuiouL\nnZ7CUe3d65JkfT6yVF3NP/vDJXJ2+HLkZy6yMxv5gZVo9HrjxkVUVBTVZ5+5VFgY1YknsgoNAIi/\nHTtcWr3ao1DIUklJiLvg9nIsySEuErk3bPToqP76V59WrKjTf/+3T2PH8qJ2uETODl+O/MxFdmY7\nMj+/X1q6NF233pqpO+/M0LXXZqimxqHJoUewEo2kMHx4VMOHOz0LAEBv5fNZevfdlrLq/fc98vu5\nm2Fvxko04oLeMHORndnIz1xkZ7Yj88vLs3X11U3N46uuaqKA7uVYiQYAADhGKSnSv/97QFOmhBWJ\nWDrppLAyM52eFboTK9GIC3r7zEV2ZiM/c5Gd2drLLzdXmjEjotNPDysvz4FJoUdRRAMAAACdZG3Z\nsiUhGnaqqqo0efJkp6cBQ9m2tHGjW9u2uTRkSFQTJ0bkoVkJAAC0Y8OGDRo0aNAxPQdlBnqFDz5w\nq7Q0W4GAJbfbVlmZT1/5CvtBAwCA7kE7B+LC6d6+HTtcCgRidyWMRCxt28Y/7Y5yOjscG/IzF9mZ\njfzASjR6hSFDokpLs9XUZMnjsTV8ODdUAQAkjro6afNmt6TYnXRzcx2eEI4ZPdHoFQ71RG/fHuuJ\nPvlkeqIBAIkhEJB+/etU3XtvhiTp1lsb9b3vNSktzeGJJbF49ETznjd6BcuSJk2KaO7ckE45hQIa\nAJA49u+39MtftlTMv/pVmvbvtxycEeKhy0X0/fffrxkzZui8885rPlZWVqaSkhKVlJRo7dq1X3oc\nvQe9YeYiO7ORn7nIzmydyS8z09bJJ7dc7H7yyWFlZiZEIwCOQZfX62bPnq1zzjlHt99+uyQpGAzq\nwQcf1PLlyxUIBLRgwQLNnDnzqMcBAACSQW6u9LOf+bViRYqiUemCC0Lq08fpWeFYdbmInjRpknbu\n3Nk8Li8v16hRo5T3+S16ioqKVFFRofr6+naPjxkz5hinjkRSXFzs9BTQRWRnNvIzF9mZrbP5DR9u\n63vfC3TTbOCEuHWOVldXq6CgQMuWLVNubq4KCgq0d+9eNTQ0tHucIhoAAACmivuFhfPmzdOcOXO+\n8Lhl0Uzf2/RUb19Tk7Rnj6WGhh75dkmBvkyzkZ+5yM5s5Ie4rUQXFhaqurq6eVxdXa3CwkL5/f42\nxwsKCtp9jsWLF2vw4MGSpNzcXI0fP7757ZJD/1gZJ+Z406ZN3f79vN4BWrnyRD31VKrOPLNR//7v\nn2jq1AEJ8ednzJgx486OD0mU+TAmv948PvRxZWWlJGnRokU6Vse0T/TOnTt1zTXXaMWKFQoGg5oz\nZ07zBYSXX365Vq9efdTjR2KfaHyZV17x6OKLs5vHv/tdvebODTk4IwAAYKJ47BPt6eoX3n333Vqz\nZo0OHDigM844Qz/60Y+0ZMkSzZ8/X5K0dOlSSVJKSkq7x4HOCoe/eAwAANBTuGMh4mLdunXNb510\nl88+s3Tvvel6+ukUnXFGWA8+2KDBg7m997HqiezQfcjPXGRntnjmt3WrS88+myKXS7rooqBGjOBn\nW3dzdCUa6GlFRbZ+8pMG3Xprk7Kzo+yxCQAwXm2tdO21GXr3Xa8kaf16j/74x3rl5Dg8MXwpVqIB\nAAAcsnOnpalTc9XYGNu5rE+fqN58s079+ydEedZrxWMlOu5b3AEAAKBj+vWzddNNTc3jm29uUn4+\nBbQJKKIRF0du+QNzkJ3ZyM9cZGe2eOWXliZddVWTVq6s06pVdVq4MKCUlLg8NboZPdEAAAAOysmR\npk6NOD0NdBI90QAAAEgq7M6BXungQWn/fks5ObFeMQAAgERDTzTiIl69YZ99ZukHP8jQqafm6tJL\nM7VtmxWX58XR0ZdpNvIzF9mZjfxAEY2EUl7u1jPPpEqy9O67Xr35ptfpKQEAALRBEY24iNddm468\nIjktjXaO7sYd08xGfuYiO7ORH+iJRkKZODGsO+9s0B//mKqZM0OaPj3s9JQAAHDMxx+7tGxZilJT\npYsvDmj4cBaXEgUr0YiLePWG9ekjXX99QK+84tN//mejBg7kxaK70ddnNvIzF9mZrSfy27/f0pVX\nZuqhh9J1//3puu22DNXXd/u3RQdRRCPheL1Sfr6t1FSnZwIAgHP8fktbtribx5s3e9TQwAX3iYIi\nGnFBb5i5yM5s5GcusjNbT+TXr19UN9986Jbgtm66qVF9+/IObaKgJxoAACABZWRI11zTpJkzQ3K7\npbFjI/KyaVXCYCUacUFvn7nIzmzkZy6yM1tP5ZebG7sl+KmnRpSZ2SPfEh1EEQ0AAAB0krVly5aE\naK6pqqrS5MmTnZ4GelBDg5SeLllcIwEAAHrQhg0bNGjQoGN6Dlai0eP8fulPf0rRuedm68c/TtPu\n3VTRAADALBTRiIvO9IaVl7t1ww0Z2rjRo1/8Il1vvsn1rU6iL9Ns5GcusjMb+YEiGj3O77cktaw+\n19SwEg0AAMxCTzR63O7dlm68MUNr1qRo6NCwnnrKr9Gjo05PCwAAo+zbZ+nDD93yem2NHx9RdrbT\nMzJHPHqieR8dPa5/f1u//nWDqqsblZtra8CAhPg9DgAAY/h80k9+kqbHH0+TJN1zT4O++92APFR2\nPYZ2DsRFZ3vD+vWzNXZslAI6AdDXZzbyMxfZmc3p/Pbvt/T446nN49/+NlUHDtAe2ZMoogEAAAyT\nlSVNmBBpHk+bFlZmJgtTPYmeaAAAAAP9858urVnjVXq6rbPOCmnw4IQo6YxATzQAAECSGjkyqpEj\nA05PI2nRzoG4cLo3DF1HdmYjP3ORndnIDxTRAAAAQCfRE41us3Onpaoql/LybPaBBgAACYOeaCSs\nykpLCxZkqbzco+xsWy++6NPEiZEv/0IAAAAD0M6BuDiyN2zrVrfKy2O/o/l8ll591evEtNAB9PWZ\njfzMRXZmIz9QRKNb5OXZcrtbOoWGDWMVGgAA9B70RKNbhELSunUePf+8V1/5SkSlpUHl5zs9KwAA\nksM//uHSsmUpys21NXduSEOHcm3S4eiJRsLyeqWZM8OaOTPs9FQAAEgqn31m6dJLM7VjR6zM+/DD\noH7zG79SU7/kC9EptHMgLugNMxfZmY38zEV2Zkvk/BoapB073M3j8nK3GhsdnFAvRRENAADQixQW\n2rrmmkN3MrR1442Nys11dEq9Ej3RAAAAvUxtrVRR4VZqqjR2bETp6U7PKLHQEw0AAIA2+vaVpk1j\nZ6zuRDsH4iKRe8PwxcjObORnLrIzG/mBIhoAAADoJHqiAQAAkFTi0RPNSjQAAADQSRTRiAt6w8xF\ndmYjP3ORndnIDxTRAAAAQCfREw0AAJBEPvrIpWefTVFenq1zzw1qyJCEKAV7FPtEAwAAoMN277Z0\nySVZ+vTT2G3BKypc+vnPG+WhIuy0HmvnKCsrU0lJiUpKSrR27dqe+rboIfSGmYvszEZ+5iI7s5ma\nn89nNRfQkrRhg1cNDQ5OyGA9UkQHg0E9+OCDeuqpp/TEE0/oP/7jP3ri2wIAAOAwxx0X1cKFTZ+P\nbF1/faNychydkrF6ZPG+vLxco0aNUl5eniSpqKhIFRUVGjNmTE98e/SA4uJip6eALiI7s5GfucjO\nbKbml5sr3XFHky66KKi0NGncOG4N3lU9UkTv27dPBQUFWrZsmXJzc1VQUKC9e/dSRAMAAPSw/Hxb\nM2ZQPB+rHt3ibt68eZozZ44kybKsnvzW6Gam9oaB7ExHfuYiO7ORH3pkJbqgoEDV1dXN4+rqahUU\nFLR53OLFizV48GBJUm5ursaPH9/8dsmhf6yME3O8adOmhJoPY8aMGSf6+JBEmQ9j8uvN40MfV1ZW\nSpIWLVqkY9Uj+0QHg0HNmTNHy5cvVyAQ0OWXX67Vq1e3egz7RAMAAKAnGLNPdEpKipYsWaL58+dL\nkpYuXdoT3xYAAADoFj3WE11aWqqXXnpJL730ks4888ye+rboIUe+vQVzkJ3ZyM9cZGc28kOPXlgI\nAAAA9AY90hPdEfREAwAAoCfEoyealWgAAACgkyiiERf0hpmL7MxGfuYiO7ORHyiiAQAAgE6iJxoA\nAABJhZ5oAAAAwAEU0YgLesPMRXZmIz9zkZ3ZyA8U0QAAAEAn0RMNAACApEJPNAAAAOAAimjEBb1h\n5iI7s5GfucjObOQHimgAAACgk+iJBgAAQFKhJxoAAABwAEU04oLeMHORndnIz1xkZzbyA0U0AAAA\n0En0RAMAACCp0BMNAAAAOIAiGnFBb5i5yM5s5GcusjMb+YEiGgAAAOgkeqIBAACQVOiJBgAAABxA\nEY24oDfMXGRnNvIzF9mZjfxAEQ0AAAB0Ej3RAAAASCr0RAMAAAAOoIhGXNAbZi6yMxv5mYvszEZ+\noIgGAAAAOomeaAAAACQVeqIBAAAAB1BEIy7oDTMX2ZmN/MxFdmYjP1BEAwAAAJ1ETzQAAACSCj3R\nAAAAgAMoohEX9IaZi+zMRn7mIjuzkR8oogEAAIBOoicaAAAASYWeaAAAAMABFNGIC3rDzEV2ZiM/\nc5Gd2cgPFNEAAABAJ9ETDQAAgKRCTzQAAADgAIpoxAW9YeYiO7ORn7nIzmzkB4poAAAAoJPoiQYA\nAEBSoScaAAAAcECXiuj7779fM2bM0HnnndfqeFlZmUpKSlRSUqK1a9d+6XH0HvSGmYvszEZ+5iI7\ns5EfPF35otmzZ+ucc87R7bff3nwsGAzqwQcf1PLlyxUIBLRgwQLNnDnzqMfRu3z22WdOTwFdRHZm\nIz9zkZ3ZyA9dKqInTZqknTt3tjpWXl6uUaNGKS8vT5JUVFSkiooK1dfXt3t8zJgxxzh1JJLU1FSn\np4AuIjuzkZ+5yM5s5IcuFdHt2bdvnwoKCrRs2TLl5uaqoKBAe/fuVUNDQ7vHKaIBAABgqi8sop94\n4gk9++yzrY7NmjVL3/ve9476NfPmzZMkrVmz5qjHLcvq0mSRuCorK52eArqI7MxGfuYiO7ORH76w\niF64cKEWLlzYoScqKChQdXV187i6ulqFhYXy+/1tjhcUFLT5ep/Ppw0bNnRw2kg006ZNIz9DkZ3Z\nyM9cZGc28jObz+c75ueIWzvH+PHjtXXrVtXU1CgQCGjPnj0aM2aMgsFgu8ePdOKJJ8ZrKgAAAEC3\n6lIRfffdd2vNmjU6cOCAzjjjDN11112aOXOmlixZovnz50uSli5dKklKSUlp9zgAAABgqoS5YyEA\nAABgCu5YCAAAAHQSRTQAAADQSXG7sLCj6urqtGzZMjU1Ncnj8Wj27NkaOXKkJGnTpk16+eWXZVmW\nzj777OYLEI92HM4jm8R3tHOO880cgUBADz30kGbMmKHi4mKyM0hVVZVeeOEFRaNRFRUV6ZJLLiE/\ng7z66qvavHmzJOmkk07SWWedRX4JbOXKlfrggw+UmZmp66+/XlLna8vO5NjjRbTL5dL555+voqIi\nHThwQI888ohuueUWhcNhrV69WldffbVCoZAee+wxjRkz5qjH4TyyMUN759ySJUs43wzyP//zPxo4\ncKAsy+K10iDRaFTPPvus5s6dq8GDB6u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vpWrp0hr17UvrBgBn9OzZ9vjTTz2aPTtTa9emaMiQkP7854AGDmTrTCQmVqLh\nCHrD4k9Dg7RxY+vr5F27PKqvP3pliOzMRn7mSsTsNmzwau3aFEnS1q0+rV2buFcaJmJ+iA1FNJCg\ncnOluXMbZFnRlecbbmjk1r0AulROTtt3unJzXZoI0A0oouEIesPi05QpzXrttVotXlyj73+/QTk5\nR38O2ZmN/MyViNmNGBHSz34W0KhRIf3oR/UaNarZ7Sl1mUTMD7GhJxpIYKmp0W3sAKA75OVJs2c3\n6ZprmpSW5vZsgK5lbd26NS6uMtq5c6dGjhzp9jQA4+zfL61alaLt2z0aNy6kESMomgEA+DLr1q1T\n//79O/UYrEQDhnvllRRdf322JCkry9ayZTUqLqb3GQCArkRPNBxBb5h71q1rfS0cCFiqqoptb1ay\nMxv5mStZs9u3z1J1tduz6LxkzQ+tKKIBw5WVNcvrjXZlDR4c0te+xio0gPi0apVXEybkqLQ0V+++\nm7jb3yE50BMNGC4UkjZu9GrfPkuDBkV04okU0QDiz65dlsaNy9W+fdH1u5NPDmvp0lrl58dFGYIk\nQ080APl84mJCAHEvEoneSfWQpqboGGAq2jngCHrDzEV2ZiM/cyVbdn362Hr66YBycmz17BnR//2/\n9TrhBHNXoZMtPxyNlWgAANDlLEuaMCGk1asPyrKiRTVgMnqiAUN89pmlf/7To549bQ0dGpEV2yYc\nAADgC/REA0nis88sXXddlt59N0Vpabb+/vdajRlDHzSAxFNbK6WkSOnpbs8E+HL0RMMR9IZ1rX/+\n06N3302RJAWDlp5/PtWxxyY7s5GfuciurUhEevVVnyZNytXMmVn66KP4LlHID6xEAwbo2dNWWpqt\nYDDaw3H66axCA0gs27d7dNVV2WpqsvThh15lZUm//W1AnviupZHEKKLhiJKSErenkNCGDo3o73+v\n1f/7f6kaOjSs0tLmr/6i40R2ZiM/c5FdW83N0W3vDtm3z1IkorgtoskPFNGAASxLGjMmrDFjGtye\nCgB0iRNPjOiBBxp0110ZysuzdffdDfJRpSCOxenrO5iG3jBzkZ3ZyM9cZNdWZqZ03XVBvfPOQa1Y\nUaNRo+K7bY38wGs8II7s2yctWpSqt9/26fLLm3T++SGlpLg9KwDoHhkZ0sCBcbHzLvCV2CcaiCPP\nP5+ib30rW5Lk8dhaurRWI0fG92oMAACmYZ9oIMH885+tHVaRiKXqau6oAgAVFZYOHrRUVBRRQYHb\nswGi6ImET/U8AAAdb0lEQVSGI+gNc8b48c3KyYm+OTRsWEinnNL1q9BkZzbyMxfZHZ8PPvBo0qQc\nnX9+nm6+OVO7dsXH4gL5gZVoII6ccUZEy5bVaN8+S/37R9SvX1x0WwGAa15+OVWff+6VJC1alKbZ\ns5vUu3fI5VkBFNFwCPtlOueUUyLd+v3IzmzkZy6yOz5+/+HPibaysuJjcYH8QDsHAACIWxdf3Kzv\nfrdRZ50V0pNPBrhjK+IGRTQcQW+YucjObORnLrI7Pn362PrRjxq0cGGtvvnNZmVkuD2jKPIDRTQA\nAIh76eluzwBoi32iAQAAkFSc2CealWjABbYd/Q8AAJiJIhqOoDfs+G3e7NE112Rp1qwsffCB+6cg\n2ZmN/MxFds45eFDaudNSXV33fU/yA1vcAd1o3z5L3/52lj76KHrq7djh0Qsv1KpnT5cnBgCGKi+3\n9IMfZOr111M0Y0ZQP/hBo3r14q0+dD33l8GQENgv8/g0NqrlpgGS9PnnHjU2unv3LbIzG/mZi+yc\nsWaNT0uWpCoYtPTMM+lav9771V/kAPIDRTTQjQoLbf30pwFZli3LsvWTn9TL72fFBAA6yuP58mOg\nq/CjBkfQG3Z8UlKkadOa9eabNVq5skbf+EazfC43VZGd2cjPXGTnjDFjQpo2LaiePSOaM6dBZ57Z\nPTdjIT90qIjes2ePZsyYoUsvvVRXXHGFVq9eLUlatGiRSktLVVpaquXLl7d8/rHGgWSUliYNHRrR\nqadGlJrq9mwAwGz9+tl67LF6rVxZox/+sFEnnMC7e+geHdonet++fdq7d6+GDBmizz//XNOnT9er\nr76qSZMmacGCBQoGg5o5c6aWLVumpqYmTZ48+ajxI7FPNAAAALqDE/tEd+iN5IKCAhUUFEiS+vTp\no+bmZr3//vsaPHiw8vPzJUlFRUXasmWL6urq2h0vLi7u1MSBeNXYKG3a5FUgYGnIkLCKilgVAQAg\n0XS6J/rNN9/Uaaedpn379snv92v+/PlavHix/H6/KisrtXfv3nbHkVjoDWv10kspmjgxR5dfnqO5\nczO1b5+7u298FbIzG/mZi+y63ocfevTccylatcqr+npnH5v80KlLmqqqqvSzn/1Mv/71r7V582ZJ\n0vTp0yXpqJaNw8ctq/2iYs6cORowYIAkKS8vT8OGDWvZQubQDyvH8Xm8cePGuJqPW8fnnFOip55K\nlxT9GV+8OFW7djXoww/fjIv5ccwxx/FzfEi8zCfRjouKxukb38jR3r0eSbaefbZOX/96iPyS9PjQ\nn8vLyyVJs2fPVmd1qCdakoLBoK677jrNmTNHJSUlWrt2rZ5++mk98cQTkqRrrrlGP/zhDxUIBNod\nP7Kdg55oJIr77kvXL3+ZIUkqKopoyZIa9e9PSwcAdKcVK7y67LLcluMbb2zQj3/c6OKMEE9c64m2\nbVt33nmnLr300pZKf9iwYdq2bZuqq6sVDAa1Z88eFRcXq6mpqd1xIFH9+78HdfLJEe3e7dEllzRR\nQAOAC3r3tlVQENG+fdGV6JKSkNtTQoLpUBG9du1aLV26VJ988on+93//V5Zl6cknn9TcuXM1Y8YM\nSdK8efMkSampqe2OI7GsXLmy5QVVsuvd29Y11zS5PY3jRnZmIz9zkV3XGjw4ohdeqNWWLV716hXR\niBHO7h9NfuhQEX322Wdr06ZNR42XlZWprKzsuMcBAAC6ytChEQ0dGnF7GkhQHe6Jdho90QAAAOgO\nTvREc9tvoANsWzp4UGoyp2sDAAA4iCIajjhyy59EVl8v/fd/p2rixFzdckumPv00vveB/irJlF0i\nIj9zkZ3ZyA8d6okGktkHH3j13e9mSrK0bZtXw4aF9Z3vBN2eFgAA6EYU0XBEMl2h3NgoHbqZiiQd\nPGj2SnQyZZeIyM9cZOeuUEiqqPDI67U7tBUp+YF2DiBGp54a0XXXNUqydeKJIV1+OY3RAGCScFh6\n8cUUjR6dq/POy9Mbb7CmiNhRRMMRydQbVlBg6957G/TOOzVatKhOQ4aYvX1SMmWXiMjPXGTnns8+\nszRnTpaamy0FApa+971MVVfH9q4i+YGXXkAH5OZKublmF88AkKx8Pikjw1ZjY7Rwzsqy5fXGxY6/\nMAj7RAMAgKSzZo1Xc+dmKT09okcfrdfw4SyMJBMn9olmJRoAACSdMWPCWrSoRh6PlJPj9mxgInqi\n4YhE7A3bssWj++9P169+laZPP03cUyURs0sm5GcusnNfXl7HC2jyAyvRQDt277b0b/+WpR07oqfI\n5s1B/epX9UpLc3liAAAgLtATDbRj+3ZLo0bl6dB+0IMGhbV0aY169HB3XgAAoPOc6IlO3PeogU4o\nLLQ1e/ahuxDauvnmBuXluTolAEA32bjRo0cfTdNf/5qiqiqzb6iFrkMRDUckWm9YTo50xx0NevHF\nGi1bVqsrrmiWlaDPo4mWXbIhP3ORXXzavt2jyy7L0f33Z+rf/z1bf/tbSrufR36giAaOIT9fOu+8\nsM46K6yMDLdnAwDoDvv3W9q/v7U8Wr26/SIaoIiGI0pKStyeAjqI7MxGfuYiu/jUt29E55zTLEmy\nLFszZgTb/TzyA7tzAAAAfKF3b1tPPx3Qtm1e5eXZGjYs7PaUEKdYiYYj6A0zF9mZjfzMRXbxq39/\nW+PHh3TWWWGlprb/OeQHimgAAAAgRuwTjaS2fbtHK1b4lJVlq6QkpD594uJ0AAAAXciJfaLpiUbS\nqqqy9O1vZ2nDhuhp8K1vNerBBxuO+dYdAADAIbRzwBEm9obV1KilgJak119PUSDg4oRcYmJ2aEV+\n5iI7s5EfKKKRtAoKbF1+eevWRbNmBZWb6+KEAABGqKy0lJZ2smw6AJMaPdFIart3W9q0yau0NGn4\n8BC39gYAfKl33/XquuuyFQhIv/51QBMnhuRhSdI49EQDnVRUZKuoKOT2NAAABqitlb73vUx99lm0\nar7uumytWVOjr30t4vLM4AZeO8ER9IaZi+zMRn7mIjszWVbbPx9+jORCEQ0AAHAccnKkxx6r10kn\nhVVYGNEf/lCn/v1ZhU5W9EQDAADEYO9eS6GQ1KuXzUq0oeiJBgAA6GYnnBAX649wGe0ccES89/bt\n3m3ppZdS9PzzKdq5k2WDw8V7dvhy5GcusjMb+YGVaCS8xkbpkUfS9ZvfpEuSSkub9PjjAfXo4fLE\nAACAseiJRsKrrLR04YW52r07+saLx2Nr7Vq2JAIAIFk50RNNOwcSXm6urcsvb2o5vuSSJvXoQQEN\nAHCebUshbj+QFCii4Yh47g1LT5duvrlR//M/tfrDH+r04IMN3JnwMPGcHb4a+ZmL7MzWXn6ffGLp\nxhszdcUV2Vq92uvCrNCd6IlGUigstDVpEksDAICuYdvSz3+eoWefTZMk/eu/+vTGGwc1cGBcdM2i\nC7ASDUeUlJS4PQV0ENmZjfzMRXZmOzK/UEj69NPWsqq+3lJjI7tBJTKKaAAAgE5KSZHmzWtURkZ0\n5fm22xq4gD3BUUTDEfT2mYvszEZ+5iI7s7WXX0lJSG+8UaM33zyom25qVHa2CxNDt6EnGgAAwCGD\nBrH6nCzYJxoJIRSSNm70qrra0qBBEd5CAwAAx+TEPtGsRCMhrF7t07Rp2QqHLQ0ZEtKzz9ZpwIC4\neH0IAIAkac8eSzU1lvz+CHfNTQD0RMMRbvf2vfhiisLh6FXQW7f6tHMnP9rHy+3s0DnkZy6yM1us\n+W3b5tFll2Vr9Og83XZbpvbsYecO01FpICGcfXbrHtDZ2bYKCliFBgDEj9de82nr1mgDwHPPpWnT\nJm7GYjraOeAIt/c7nTChWX/4Q50++cSjceNCKi6mJ/p4uZ0dOof8zEV2Zos1v5yctos76eks9piO\nIhoJIT9fmjKl2e1pAADQrgsuCOlb32rUypUp+va3G3XGGWG3p4RO6nA7x0MPPaSxY8dqypQpLWOL\nFi1SaWmpSktLtXz58q8cR+Kgt89cZGc28jMX2Zkt1vz69rX10582aMmSGs2e3cQe0gmgwyvREydO\n1CWXXKI777xTktTU1KSHH35YCxYsUDAY1MyZM3XRRRcdcxwAACCZ+HxSXp7bs4BTOlxEjxgxQhUV\nFS3HGzZs0ODBg5Wfny9JKioq0pYtW1RXV9fueHFxcSenjnhCb5+5yM5s5GcusjMb+cGxnuiqqir5\n/X7Nnz9feXl58vv9qqysVH19fbvjFNEAAAAwleNb3E2fPl2TJ0/+0nHLYm/ERNOdvX21tdE7FMIZ\n9GWajfzMRXZmIz84thJdWFioqqqqluOqqioVFhYqEAgcNe73+9t9jDlz5mjAgAGSpLy8PA0bNqzl\n7ZJDP6wcx+fxxo0bu/z7pabmqLz8bD36aIaGDw/q2mvLNXp0r7j4+3PMMcccx3p8SLzMh2PyS+Tj\nQ38uLy+XJM2ePVudZW3durXDGxVWVFToO9/5jhYuXKimpiZNnjy55QLCWbNmaenSpcccP9LOnTs1\ncuTITv1lkNjee8+rCRNyZNvRdzLuuadet9wSdHlWAADANOvWrVP//v079Ri+jn7hfffdp2XLlunA\ngQO64IILdO+992ru3LmaMWOGJGnevHmSpNTU1HbHgVgFg2opoCWpspIbbgIAAHd0aiXaSaxEm23l\nypUtb510lepq6ac/zdBvfpOuPn3CevbZOp12Gncm7KzuyA5dh/zMRXZmczK/QEA6cMBSbq6tnBxH\nHhJfwYmVaJbyYIz8fOmHP2zQmjUHtWRJLQU0AMB4e/ZYuueeDJ13Xp5uuSVTFRVsvmAKVqIBAABc\nsmSJTzNmtC4///a3dbr88mYXZ5QcWIkGAAAwmG1/+THiF0U0HHHklj8wB9mZjfzMRXZmcyq/ESPC\nuu66RmVn27r88qDOOSfkyOOi63V4dw4AAAB0Tq9etn784wbdemsjFxYahp5oAAAAJBV6ogEAAAAX\nUETDEU729lVWWvrsM0vhsGMPiS9BX6bZyM9cZGc28gNFNOLK++9Hb+09ZkyeXnghRc3s8gMAAOIQ\nPdGIG8GgdNll2XrrrRRJktdr6x//qNGgQdxUBQCQnD7+2KPyco/69ImouJjfh05xoiea3TkQNyxL\nSklpe2xZcfEaDwCAbrd1q0dTp+aoqsqjnBxbCxfWavhweh3jBe0ccIQTvWGpqdJ//Ee9iotDKiyM\n6Jln6nTiiRTRXY2+PrORn7nIzmzdkd9HH3lVVRUt1WprLW3a5O3y74njx0o04sqwYRG9+GKtmpst\nFRbasiy3ZwQAgDt69YrIsmzZtiXJVr9+tHPEE3qiAQAA4lBTk7RmjU+rVvl09tkhnXdeSFlZbs8q\nMdATDQAAkKBSU6Vx40IaN45bgccjeqLhCHr7zEV2ZiM/c5Gd2cgPFNEAAABAjOiJBgAAQFJxoiea\nlWi4pqEheovvxka3ZwIAABAbimg4ItbesF27LN11V4YuvDBXDzyQrqoq9rJzC319ZiM/c5Gd2cgP\nFNFwxTvv+PT736dr926Pfv3rDK1bxwbyAADAHBTRcERJSUlMnx8Kffkxuk+s2SG+kJ+5yM5s5AeK\naLhi1KiQJkxoksdj6/LLgxoxIuz2lAAAMEZTk/Tyyz5dfXWWnngilbZIF1BEwxGx9ob172/rqacC\nWreuRo8+Wq8+feJik5ikRF+f2cjPXGRnNrfz27jRq6uuytaiRamaNy9LK1Zw/7zuxr84XNOjh9Sj\nR8TtaQAAYJwDByzZduvq886drIt2N/7F4Qh6w8xFdmYjP3ORndnczu+UU8I655xmSVLPnhFdfHGz\nq/NJRqxEAwAAGKZ/f1u//31An33mUX6+rZNP5p3d7sZKNBzhdm8YOo7szEZ+5iI7s8VDfr172zr7\n7DAFtEsoogEAAIAYWVu3bo2LbRF27typkSNHuj0NAAAAJLh169apf//+nXoMeqLRZTZu9Ortt73q\n1y+i0aND6tHD7RkBAAA4g3YOOOLI3rCPPvJo6tRsff/7WZoxI0fLlqW4NDN8lXjo60PHkZ+5yM5s\n5AeKaHSJqipLBw+2/nitXs2bHgAAIHHQE40uUV5uadq0bG3f7pNl2Xr22TpNmBBye1oAACSF7ds9\neucdr7KzpXPOCamwMC7KvbhBTzTi1oABtp59NqCPPvKooMDWGWeE3Z4SAABJYfduS7NmZemDD6Jl\n3u23N+iOOxpdnlXioZ0DjmivN+zkkyOaNCmkUaPCSk11YVI4LvT1mY38zEV2Zovn/Pbvt1oKaEla\nvDhF9fUuTihBUUQDAAAkEL/fVklJ623AZ8wIKjPTxQklKHqiAQAAEszOnZY2bPAqK0saMSKkvDy3\nZxRf6IkGAADAUfr3t9W/Pxf0dyXaOeCIeO4Nw5cjO7ORn7nIzmzkB4poAAAAIEb0RKNTdu60VF4e\n3cauuDji9nQAAAC+Ej3RcNWnn3p01VXRfSizsmy98EKtRo5kP2gAAJD4aOdAh338sadlH8pAwNLy\n5SkuzwgdQV+f2cjPXGRnNvIDRTQ6rKDAls/X2g00aBCr0AAAxLtQSGpu/urPw5ejJxodFgpJ//iH\nTwsXpmjkyJAmTmxWfr7bswIAAMfywQce3XtvhoJBSz/+cYPOPDM5F8DoiYarfD7p/PNDOv989qEE\nACDeHTwozZmTqQ0bou2X11zj1Suv1KhXr7hYTzVOt7VzLFq0SKWlpSotLdXy5cu769uim9AbZi6y\nMxv5mYvszGZifsGgpb17vS3H+/ZZampycUKG65YiuqmpSQ8//LD+8pe/6JlnntGDDz7YHd8WAAAA\nX/D7bT30UEA+ny3LsvXIIwEVFbEK3VHd0s6xYcMGDR48WPlfNMwWFRVpy5YtKi4u7o5vj25QUlLi\n9hTQQWRnNvIzF9mZzcT8LEuaNCmkVatqFIlIJ50UUQoba3VYtxTRe/fuld/v1/z585WXlye/36/K\nykqKaAAAgG7k9UqDB3NzNCd06xZ306dP1+TJkyVJlmV157dGFzOxNwxRZGc28jMX2ZmN/NAtK9F+\nv19VVVUtx1VVVfL7/Ud93pw5czRgwABJUl5enoYNG9bydsmhH1aO4/N448aNcTUfjjnmmON4Pz4k\nXubDMfkl8vGhP5eXl0uSZs+erc7qln2im5qaNHnyZC1YsEDBYFCzZs3S0qVL23wO+0QDAACgOxiz\nT3Rqaqrmzp2rGTNmSJLmzZvXHd8WAAAA6BLd1hNdVlamJUuWaMmSJbrwwgu769uimxz59hbMQXZm\nIz9zkZ3ZyA/demEhAAAAkAi6pSf6eNATDQAAgO7gRE80K9EAAABAjCii4Qh6w8xFdmYjP3ORndnI\nDxTRAAAAQIzoiQYAAEBSoScaAAAAcAFFNBxBb5i5yM5s5GcusjMb+YEiGgAAAIgRPdEAAABIKvRE\nAwAAAC6giIYj6A0zF9mZjfzMRXZmIz9QRAMAAAAxoicaAAAASYWeaAAAAMAFFNFwBL1h5iI7s5Gf\nucjObOQHimgAAAAgRvREAwAAIKnQEw0AAAC4gCIajqA3zFxkZzbyMxfZmY38QBENAAAAxIieaAAA\nACQVeqIBAAAAF1BEwxH0hpmL7MxGfuYiO7ORHyiiAQAAgBjREw0AAICkQk80AAAA4AKKaDiC3jBz\nkZ3ZyM9cZGc28gNFNAAAABAjeqIBAACQVOiJBgAAAFxAEQ1H0BtmLrIzG/mZi+zMRn6giAYAAABi\nRE80AAAAkgo90QAAAIALKKLhCHrDzEV2ZiM/c5Gd2cgPFNEAAABAjOiJBgAAQFKhJxoAAABwAUU0\nHEFvmLnIzmzkZy6yMxv5gSIaAAAAiBE90QAAAEgq9EQDAAAALqCIhiPoDTMX2ZmN/MxFdmYjP1BE\nAwAAADGiJxoAAABJhZ5oAAAAwAUdKqIfeughjR07VlOmTGkzvmjRIpWWlqq0tFTLly//ynEkDnrD\nzEV2ZiM/c5Gd2cgPvo580cSJE3XJJZfozjvvbBlramrSww8/rAULFigYDGrmzJm66KKLjjmOxLJ7\n9263p4AOIjuzkZ+5yM5s5IcOFdEjRoxQRUVFm7ENGzZo8ODBys/PlyQVFRVpy5Ytqqura3e8uLi4\nk1NHPElLS3N7CuggsjMb+ZmL7MxGfuhQEd2evXv3yu/3a/78+crLy5Pf71dlZaXq6+vbHaeIBgAA\ngKm+tIh+5pln9Le//a3N2IQJE3TzzTcf82umT58uSVq2bNkxxy3L6tBkEb/Ky8vdngI6iOzMRn7m\nIjuzkR++tIi+9tprde211x7XA/n9flVVVbUcV1VVqbCwUIFA4Khxv99/1NfX1tZq3bp1xzltxJtz\nzz2X/AxFdmYjP3ORndnIz2y1tbWdfgzH2jmGDRumbdu2qbq6WsFgUHv27FFxcbGampraHT/S0KFD\nnZoKAAAA0KU6VETfd999WrZsmQ4cOKALLrhAP/rRj3TRRRdp7ty5mjFjhiRp3rx5kqTU1NR2xwEA\nAABTxc0dCwEAAABTcMdCAAAAIEYU0QA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NjXTjjVnavt2tykq35s3L0u7dvOcKoGcFg9GLD3m+QaKjiEZMlJaWOj0FHCES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\nY+J0duge8jMX2ZmN/EARjYR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"text": [ - "" + "" ] } ], - "prompt_number": 16 + "prompt_number": 26 }, { "cell_type": "markdown", @@ -1107,7 +1133,6 @@ "cell_type": "code", "collapsed": false, "input": [ - "from KalmanFilter import KalmanFilter\n", "from math import sin,cos,radians\n", "\n", "def ball_kf(x, y, omega, v0, dt):\n", @@ -1119,25 +1144,27 @@ "\n", " ay = .5*dt**2\n", "\n", - " f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", - " [0, 1, 0, 0, 0], # dx = dx\n", - " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", - " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", - " [0, 0, 0, 0, 1]]) # ddy = -g.\n", + " f1.F = np.array ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", + " [0, 1, 0, 0, 0], # dx = dx\n", + " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", + " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", + " [0, 0, 0, 0, 1]]) # ddy = -g.\n", " \n", " # compute velocity in x and y\n", " omega = radians(omega)\n", " vx = cos(omega) * v0\n", " vy = sin(omega) * v0\n", + " \n", + " f1.Q *= 0.\n", "\n", - " f1.x = np.mat([x, vx, y, vy, -g]).T\n", + " f1.x = np.array([[x, vx, y, vy, -g]]).T\n", " \n", " return f1" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 17 + "prompt_number": 36 }, { "cell_type": "markdown", @@ -1158,12 +1185,11 @@ "\n", "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[0,0])\n", "f1 = ball_kf(x,y,theta,v0,dt)\n", - "\n", "t = 0\n", "while f1.x[2,0] > 0:\n", " t += dt\n", " f1.predict() \n", - " x,y = ball.position(t)\n", + " x,y = ball.step(dt)\n", " p1 = plt.scatter(f1.x[0,0], f1.x[2,0], color='black', marker='+', s=75)\n", " p2 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", "\n", @@ -1178,11 +1204,11 @@ "output_type": "display_data", "png": 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65s6bC4CKyswxM/nHa/8xvDT7SMtIKXcoxDByIXOS5ZNAiCHoU+en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"text": [ - "" + "" ] } ], - "prompt_number": 18 + "prompt_number": 41 }, { "cell_type": "markdown", @@ -1263,11 +1289,11 @@ "metadata": {}, "source": [ "##### Step 6: Design the Process Noise Matrix\n", - "Finally, we design the process noise. As with the robot tracking example, we don't yet have a good way to model process noise. However, we are assuming a ball moving in a vacuum, so there should be little to no process noise. For now we will assume the process noise is 0.02 for each state variable. This is a bit silly - if we were in a perfect vacuum then our predictions would be perfect, and we would have no need for a Kalman filter. We will soon alter this example to be more realistic by incorporating air drag and ball spin. \n", + "Finally, we design the process noise. As with the robot tracking example, we don't yet have a good way to model process noise. However, we are assuming a ball moving in a vacuum, so there should be no process noise. For now we will assume the process noise is 0 for each state variable. This is a bit silly - if we were in a perfect vacuum then our predictions would be perfect, and we would have no need for a Kalman filter. We will soon alter this example to be more realistic by incorporating air drag and ball spin. \n", "\n", "We have 5 state variables, so we need a $5{\\times}5$ covariance matrix:\n", "\n", - "$$\\mathbf{Q} = \\begin{bmatrix}0.02&0&0&0&0\\\\0&0.02&0&0&0\\\\0&0&0.02&0&0\\\\0&0&0&0.02&0\\\\0&0&0&0&0.02\\end{bmatrix}$$" + "$$\\mathbf{Q} = \\begin{bmatrix}0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\end{bmatrix}$$" ] }, { @@ -1292,10 +1318,9 @@ "cell_type": "code", "collapsed": false, "input": [ - "from KalmanFilter import KalmanFilter\n", "from math import sin,cos,radians\n", "\n", - "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.02):\n", + "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.):\n", "\n", " g = 9.8 # gravitational constant\n", " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", @@ -1325,7 +1350,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 19 + "prompt_number": 75 }, { "cell_type": "markdown", @@ -1341,10 +1366,10 @@ "y = 1.\n", "x = 0.\n", "theta = 35. # launch angle\n", - "v0 = 50.\n", + "v0 = 80.\n", "dt = 1/10. # time step\n", "\n", - "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[1,1])\n", + "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[.2,.2])\n", "f1 = ball_kf(x,y,theta,v0,dt)\n", "\n", "t = 0\n", @@ -1352,7 +1377,7 @@ "ys = []\n", "while f1.x[2,0] > 0:\n", " t += dt\n", - " x,y = ball.position(t)\n", + " x,y = ball.step(dt)\n", " z = np.mat([[x,y]]).T\n", "\n", " f1.update(z)\n", @@ -1361,7 +1386,7 @@ " \n", " f1.predict() \n", " \n", - " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + " p1 = plt.scatter(x, y, color='green', marker='.', s=75, alpha=0.5)\n", "\n", "p2, = plt.plot (xs, ys,lw=2)\n", "plt.legend([p2,p1], ['Kalman filter', 'Measurements'])\n", @@ -1373,13 +1398,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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9n+qjrKUMh8dBYnAiocbQQT+HkM/OQCezWwghxEXIjMgkM2L0FcSfp6oqL5x8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W6jrfPJutzVjtVqzOYI5Up9HYHgZAqK+BGyZEMC3BgL/xAow6o1oluzU5P0/v\nxrGX8w/tP4gIzqO8PoOm9nBe2VXF2/vLiDXnEmmqYV7SXCZGTjzpOMlTPQORpaIoJ91dT4hvcjqd\nZ39QH/T5i3sLFx6f+fr2SMU398vJLIToLUVRTrrDmhY/KurGc6wpEQUtOq2Ni5Kd3D1zLN5yhVD8\nnwi/CO6bch8dtg58Db7srerk2S+LqG7Tc7hiHJUNzdS2bSY5KNktbxIjesdkMtHY2EhoaKirSxFu\nxul0UllZSUREhOrPfc5Ncnh4OHV1dT3bdXV1hIeH09HRccp+s/n0d61ZunQp8fHHf2VqMpnIyMjo\n+RR64s49st277RP73KUeT96eOXOmW9Xj6dvnkueUC6bwyv5XyM7PBkXDlGG383mBkWZLMuAkJqSM\nS4c7SWgKY/fX293i/blznkNxO9ArsGf76vH1bDzSypFjybR2BXGw7GL+vLWC6YaD+OklT0/c9vf3\nJz8/n5qaGoKCggBoaWkBjvcRsj00txVFISgoiIiICHbu3MkJ27Zto6ysDIBbbrmFvurVzUQqKiq4\n/fbbT/vFvSVLlrB+/frv3P9t8sU9IcS3fVj4Iftq92HpDqOgaiStXcf/Jzgqwo/l02MZFurr4gqF\nJ8lvyOeNQ2/gpQ3kaF0y5fXHfxvha9CSHHmEYP88Ar38uWHUDYT4hJz9CYUQHut8vrh31t9ZPvro\noyxcuJCSkhJmzZrFtm3buOeee1i0aBE33ngjK1asAMBoNJ52v+hfJz5pi/MnWarrTHl2O7rpsnf1\nbNd1tFFSM5bdRdNo7QrCoOti+fQw/nhFqjTI/0fOz95LC00jKzmLAC8jY+Oq+PW8ACbFBtBpc5Jb\nnkxO8YXsKWjkzUNvurrUQUHOTXVJnu5Df7YHPPzwwzz88MOn7M/KyjrtvtPtF0KIEz47+hlbK7YC\nkGwaRpRXFp/sT6e9+8QyXiUMjyrj8hFT5XsNos8uiLmAC2Iu6NmeHqfwwOevc6gyhQ5rAB1cheZo\nGR0ZDvyMZ7/5iBBi6OnVuIWaZNxCiKGrvrOeP+3+EwHGADosfhyuHEFr1/FVKxKCFUbEHCYqUMOV\nKVfib/R3cbVisHnr0FvkNxRxrHEkpXVJKGgJ8zWwbHo0kaYmABJNib26Y58QwjP06zrJQgihlpbu\nFhwKFNek9DQp3gYHyy9IYm5qCBqNfIAW/ed7ad/j/YL3CfGpZHSUk/yqDArrLTz6WSnB/uXEm/eQ\nFGLmp2MmYp8/AAAgAElEQVR/il4r/3sUYqiTdZQ8nMwuqUeyVNfp8rRYQ8gvm8fRumEoaAg3FfO7\nrFDmDQ+V0YqzkPPz/Bl1Rn4w8gfcOelOJnRH8+yVI7hqtAatxk5TexwHyzI5UKVnb80+V5fqUeTc\nVJfk6T7ko7IQol84FSerDq+ipLkErdaAtz2LT/OsOJRA/L2sTEku5eoRYxkRmuTqUsUQpdNqmJzQ\nTVnn55TWTqSx3UzRscm8vtvBsEttBPsa5AYWQgxhMpMshOgX60vWs71yO3Z7GIcqMmi3BAJwVbqZ\nmyZH4WOQuU/heha7hZXZK7HYrNS0xFFSMwqH04C/UUty5H78fYsJ9QnhJxk/kTl5ITyQzCQLIdxO\nZfsxqptGUlKbgqJoMeo7uH92MjMTo11dmhA9vPXe3DHhDr6s/BIlViFtehp//bqOnMo29peNxhwY\nhhKZy+r81fwk4yeuLlcIMYBkJtnDyeySeiRL9VS2WPg0J5HimuEoipbo4DKmpHzJtPhwV5fmseT8\nVNc38/Q1+DI3cS7zEueREGziycuGkRq1H53WTl1rJNnFF1JUJ7/5+C5ybqpL8nQfciVZCHHeLHYL\n7+a/S0NXI01taWSXRmC1B+JndDAyNpfYoE6uHb5EVgwQHkGj0TA2xkqQ32YKqsbT0hnCzuIMXvCp\n4MaJ4ZS2FaEoCsNDhss5LcQgJjPJQojz9sq+Vzja3MSRY+NobD++7vElw4JZNj2WAC9pIoTn6bJ3\n8V7+ezR2NVHTlE5OWQgOBQK8O4iP2I6vVwsRfhHcPu52DDqDq8sVQnwHmUkWQrjUwWoN+VUXYXcY\nMei6GRVXyP0X/9jVZQnRZz56H3486n/ncEFdJ498lk99hx+Hyi4lJaIADYfYV7uPSVGTXFipEKK/\nyEyyh5PZJfVIlr2jKAqt1lbau9vpsjn4w5ZSDpZPwO4wEuJfx8TkrQwPt0ieKpM81XWueQ43+7J8\npoNwUwmKoqWwegSFVRfQarX3U4WeQ85NdUme7kOuJAshes2pOHn94OsUNRXR3hVCee0MWi0GDFpI\njSokJDCfEJ9gFo5YyN6de11drhCqmhiVwbiETZQ21HHk2Dia2qP4+1d6Qo1N1HbvpsvWxczYmYT4\nhLi6VCGECmQmWQjRazuqdvBx0SfUNI3iaO0wFLTEmnT8ek4qicE+cuMFMehZ7BZ2HNtBc6eGDYfN\nFNRb0OAkPvwwCaGlOBQ7yycuJ9Qn1NWlCiE4v5lkGbcQQvRaVWsz+RXTKalNRUFLRHABP7tQQ2Kw\nD4A0yGLQ89Z7MytuFlelXcSfFqQxd7gXClpKa0dxsGISiuLDtgr5dbkQg4E0yR5OZpfUI1me2eHa\nDt7OiaKpIxyDrpsxCbsYHlXA8NBhp3285KkuyVNdauRp0Gn54XgTKdHb0OtsNLSFk108nbYuPxUq\n9BxybqpL8nQfMpMshDitvIY8Piz8kG6HjW7LRLJLo7A7FYaF6hmbkE+gtz+ZSdfja/B1dalCuEy0\nfzQzE0PxMa6j6Nh0Oq0hvJ3jT6xfE7OHBbu6PCHEeZCZZCHEKSx2C0/veBotPuRVjqK2NQqAa0ab\nuWVyNAad/BJKiBMURaGyvZKO7m4+2K/h86JmAK4dHUq8+RAWRyczYmYQ4Rfh4kqFGHpknWQhhKra\nu9tptRgoqppKhzUAndbOjJQqbp823tWlCeF2NBoNsQGxANw3WyEtvJ4Xv67gP7kNBPlpGRVbxL7a\nfSwdv1QaZSE8iFwO8nAyu6QeyfJ/Shp0HCq7hA5rAL5e7WQkbOTSYeHn9BySp7okT3X1V54ajYar\nR5m5d7YJvc5Cc4eZ7OLp2G2hg/YLfXJuqkvydB9yJVkIgc1ho8HSgK/el88LLby0oxKnYiTS1MjY\n+DzGRIxnWvQ0V5cphMfIiPInPf4tSo7NpM1iIqdkGtF+ra4uSwhxDmQmWYghrsXSwot7X6TZ0k5Z\n3QTqWhIBWDQ2giWTotDKsm5CnDNFUfhPwX/YeWwvR6sn09Qeh1YDt02LZcHIEDrtnfjqfdFpda4u\nVYhBTWaShRB99lHRR3TZdBypupiWzmC0Gjv3zkri0pQwV5cmhMfSaDRcl3YdM2NnYrFb+bxAy6p9\ndbzwVQUf5G0n1pyDn8GbxaMXExMQ4+pyhRCnITPJHk5ml9QzVLOsbdOSU3wBLZ3BeBm6GJWwlemJ\n57/O61DNs79InuoaqDwj/CJIMMVz0+RY7p+dgFbjpKopnsLKC7E59Lyb/+6A1NGf5NxUl+TpPqRJ\nFmKI6XZ0U99ZT7ejm13lrWzKS8di8yXQp5kxiVsYaQ7EW+ft6jKFGHQuSQlhUnI2Bp2Vpo5Q9pRM\npaXL1VUJIb6LzCQLMYSUt5bzz9x/YnFYaGhJo7h6NAowPkbL6NjDmP2CmJM4B71WJrGE6A/v5b/H\nrqoj5FVMp9Pqj6/Rxp+uyCApxMfVpQkxKMlMshCiV/5T8B806Kmsm0xlYzwAPxwXweKJUWg1Y11c\nnRCD3zXDr8HfuIF4UxG7ikZQ2eLF3WsK+NWcBJJCnPgZ/PDSe7m6TCEEMm7h8WR2ST1DIUuL3cHB\n8vFUNsaj0TgZFXuAGydF98sKFkMhz4EkearLVXlqNVrmJ81n6YQbeemaKVyYFESnzcmKT4t48It3\neGrHU+TW57qktr6Sc1Ndkqf7kCZZiCGi3WrncPkF1LeFo9fZGBX3JRclB7i6LCGGLKNey4OXJJIa\nUYOiaCk6NpXqplQ+OvKRq0sTQiAzyUIMCQ2dNh789AjFjRYCvJzMHlFERkQ4s+JmoZF1kIVwqedz\nnudgVQhHqkcAEBtayCtXfQ+tVq5jCXG+ZCZZCHEKq93Krupd1Lc7eW9vCDXtNmJNXjx5WQoRARNd\nXZ4Q4v+kh6ZT27kJo76bQxWjqWhI5bntlSybHotOKx9ihXAV+Zjq4WR2ST2DKctuRzcv7HmBD/J2\n8vJXBmrabaSEevPHK1KJCDAOSA2DKU93IHmqy53ynB0/m8zkTCbEarhqTAtGnYb/5tXz1Kaj2BxO\nV5d3Vu6U5WAgeboPuZIsxCCU35BPcYOGI1UzcTj1mHxruWacD0E+I11dmhDiWzQaDdOipzEtehoA\nF8a18ev1xWwqbuZgXREj47JJMsXyg5E/kOUZhRhAMpMsxCC0av8BXt1lRVF0hAdWkxixg6yUeUyP\nme7q0oQQvZBf187P/3sQm8OIybeJEbFfMSV6DAtSFri6NCE8yvnMJMu4hRCDzLqCBl7bZUdRdJhN\nRcRHbMPsF8ykyEmuLk0I0UuxQRpGxW/BS99FS2cwh8pmUNpS5+qyhBhSpEn2cDK7pB5PzdLhdLDm\nyBpe2vsSD3/xBX/YUoZTgR+OC+ehi0fxw/RFLB2/FKNuYGaRT/DUPN2V5Kkud8/TV+9LqL+TCUk7\n8DZ00mYxsb1gNE1dNleXdgp3z9LTSJ7uQ5pkITzc+wXvs7s6m11HzXxVHAzA0gtiuXFSDCPDRjLa\nPBqDzuDiKoUQ50Kj0XBzxs1EBHgxLXUPQT7d1HcY+MV/C6ltt9JkacJit7i6TCEGNZlJFsLD/X7H\nHzhYmXL8Lno4GRmby58vW+LqsoQQKmrqsvHA2uNrnfsYu0iL3YSvsZusYVlMiZri6vKEcFsykyzE\nEOVUFPKPjaKyMR6txkFGfA5JYc2uLksIobJgHwNPZ6US5m+hq9uHw+WzcTpCWFu8FpvD/UYwhBgM\npEn2cDK7pB5Py9LhVPjjljJK6yPQahykxX5NuKmJ74/4vqtLAzwvT3cnearLE/MM9NYzK60Ak28T\nVpsPOSWT6bB4Y3G4duzCE7N0Z5Kn++jzgovPPfcca9euBSAzM5Ply5fzySefsHLlSgDuv/9+Lr74\nYnWqFEIA4FScHKw/SIulnc2FZjYXt+Gl1/KbucNIj8jAqDPKbaaFGMQmR2dQ2voRRyovpLkzhLyK\ni2i3GBigewQJMaT0aSa5vLycm266iXXr1uFwOMjMzOTll1/mlltuYfXq1VitVhYvXsyGDRtOe6zM\nJAtx7hRF4Z8H/0lhYxHFx6bQ0BaLl17D4/NTGBPl7+ryhBADZG/NXrKrc9mcP4zqVm8iA4z8/vJU\nwv2lUxbi2wZ8Jtnf3x+9Xo/FYsFqtWIwGKivryc1NZWQkBCioqKIjIwkLy+vT0UJIU5V31VPfkMh\npdXTaWiLRae1My+9XBpkIYaYcRHjuHnsj/nr1VNIM/tS3dbNfZ8coaFDZpOFUFOfmuTg4GAWL17M\n7NmzmT17NjfddBMNDQ2YzWZWrVrF2rVrMZvN1NbWql2v+BaZXVKPu2fpdCqUVE+htjUSndbGmIRd\nRAa67xJQ7p6np5E81TUY8vQz6njismGkhPpQ1Wrltg9y+NuetyhsLBzQOgZDlu5E8nQffWqSKyoq\nWLVqFV988QUbNmzg73//O1arFYCFCxeSmZkJILORQqjEqSi8nt1FY1s8Wo2NkXHb8fOpZ27iXFeX\nJoRwoQAvPb+dl4C/dxstXUbW5sby932rKG4qdnVpQni8Pn1xb//+/WRkZODvf/zXvOnp6VRUVFBX\n979bZtbV1WE2m097/NKlS4mPjwfAZDKRkZHBzJkzgf99gpLt3m2f2Ocu9Xjy9syZM92qnhPbigLZ\nmng2FDZi0ChcbC5nRvpUMswZ7N251+X1eVqenroteUqe37WdPC6ZYdEbOXT0QjqswRRWXsiX5myq\nDla5RX2yLdsDuX3iz2VlZQDccsst9FWfvrh34MABHnroIVavXo3T6eSqq65i5cqVLFu2rOeLe0uW\nLGH9+vWnHCtf3BPi7PIa8thUtgmnotDUfCGbi20YdRp+O38Y46MDXF2eEMKNNFua+f2u32MghJyS\nqXR1+xJj6uav10zGWy8rvYqhbcC/uJeRkcHcuXO55ppruO666/j+97/PiBEjuOeee1i0aBE33ngj\nK1as6FNB4tx885OTOD/ukmV1ezVvHXqLJksz2aURbC62odfCI3OTPapBdpc8BwvJU12DKc8g7yBm\nx83GoWlmeOxmvA3dVLYY+c1nxXQ7nP3++oMpS3cgeboPfV8PXL58OcuXLz9pX1ZWFllZWeddlBBD\nWUFTATqtjpLaYZQ3JKHByQ/GO5gUG+jq0oQQbmpO4hymx0zH5rTR3GnkFx8fYXdFG7/beJRbpwXg\nbTBi8jK5ukwhPEqfxi3Oh4xbCHFmhU2FPLN1G0drxwEKw6K+4pczLyfRlOjq0oQQHqKooZNffFxI\nR7eT0MCjJEdmMzlqElenXu3q0oQYUAM+biGE6D9VTWEcrR0LQErkfq4dNVwaZCHEORkW6st141rR\nauw0tCZyrH4SO6p2Ut1R7erShPAY0iR7OJldUo87ZJlT2cpTm0oBDT+ZFMXzly/BU5d5c4c8BxPJ\nU11DIU9/nwZGx+eg0TipaEygqiGdju4O1V9nKGQ5kCRP99HnmWQhhDo2l21mb+1e2rpM7Cgah92p\ncM0oMwvHRsha40KIPpsWNY2c6hcYFasnt3w8xxpHkVPuw7BgV1cmhGeQmWQhXGhPzR7eL3gfnGFk\nF0/B5vDiouRAVlycjFYaZCHEeapsq2Rz+WZK6kLZXBgOwD0XxmA2VeBUnGSYM/DSe7m4SiH6z/nM\nJMuVZCFcKL8xHx1BZB+diM3hRaBvNTdMMEuDLIRQRUxADD9M/yEAacE1/G1nFX/cWkFqzFcE+1ez\nqXwTd0y4QxplIU5DZpI9nMwuqccVWYb7xLH36HgsNl8CfFoYGbubUN+gAa+jP8i5qS7JU11DMc/v\njYng0lQNChqOVE2luzuWNmsb2TXZ5/W8QzHL/iR5ug9pkoVwEbtT4bO8CDqsQXgbOxiXuIfrR1yF\nv9Hf1aUJIQapzBFazKZinIqO/aUT6LDK2slCfBeZSRbCBRRF4Y9by1hX0IjJW8+fFwwnxiS/7hRC\n9C+bw8bzOS/wdXEyjW2xeOkt/PWaDGJN8uFcDE4ykyyEB2jvbuetw2/RYmmhqmEUB6ui8NJp+M28\nZGmQhRADwqAzsGzCUqZF7ePvO52UNnrz6Gfl/OmKVPy9pCUQ4ptk3MLDyeySevo7yzcOvUFdRx3l\nDZEcrIpCg8KKS5IYGe7Xr6/rKnJuqkvyVNdQztOgMzAtdhJ/yBpLnMmL0iYLv/m8BJvD2afnG8pZ\n9gfJ031IkyzEAGmyNNHcEU5+VToAI2PyuSBB5gGFEK4R6K3n8cuGEeyjZ29VO3/cUkpDZwNd9i5X\nlyaEW5CZZCEGyNNf/ZONh0ficBqICz3ChSkd3Jhxo6vLEkIMcQX1ndzz3wKsdoXokMMkhOeTmZzJ\ntOhpri5NiPN2PjPJciVZiAHQ1GVj/9EJOJwGwgNrmJ7cxg9G/sDVZQkhBMPDfJk1vAJQqGocSVNr\nCp8Wf4rVbnV1aUK4lDTJHk5ml9TTX1l22508uqGE2g47aWZfXrl2HjePvQkfvU+/vJ67kHNTXZKn\nuiTPk4UF1JMWfQiA/Kp0mjuDsTp61yRLluqSPN2HNMlC9ANFUWiyNNHU1cQftpZxqLYDs5+BR+Ym\n462Xv3ZCCPcyLnwcQQH5xIWWoKClsPIC2i1GV5clhEvJTLIQKnMqTl4/+DpHmo5QWT+CyoZR+Bi0\n/PGKVIaF+rq6PCGEOK0DdQfIqdnL1oJhlDX6kBDszZ8XDMfPqHN1aUL0mcwkC+FG9tbupaipiI7O\nFCobRgEKSyYZpUEWQri1DHMGS0bfwMorphIf5E1pk4XfbTyKwzmg19KEcBvSJHs4mV1Sj1pZtlpb\n6bKGcrhiNAAJ5gMkhHaq8tyeRM5NdUme6pI8v5ufUcejc5MJ8NKxo7yVV3dXnfHxkqW6JE/3IU2y\nECqL9x9NXsUUnIqOqKBy4sLKSAtJc3VZQgjRazEmL351aRI6Dbyzv5YntnxKVfuZm2UhBhuZSRZC\nRVa7k198XEh+XScRgZ1cNqqcy4ddRpB3kKtLE0KIc+JwOrhvw3scKE9Fo3GSHr+VX0y7npiAGFeX\nJkSvyUyyEG5AURT+uLXseIPsb+QvC6bwo1ELpUEWQnik2s5avH32ERNShqJoKaycyvrir11dlhAD\nRppkDyezS+rpa5aFjYW8cfANHv5iExuLmvDWa3l0bjJBPgaVK/Qscm6qS/JUl+R5dkadEY1GQ2pU\nHkF+jXTbvfk8L4Zuu/Okx0mW6pI83Yc0yUKch4LGAl4/+Dp7Kq18XWICFH45O57k0MF9oxAhxOAX\n6hPK5MjJdNhaSYjYio/BQm2bFyu/LEdRZMULMfjJTLIQ5+GNg2+QV9dEdvE0HE49sWG5PDM/i1Cf\nUFeXJoQQqqjrrMPqsNJpMXHPx8VY7U5umxbDtaPDXV2aEGd1PjPJepVrEWJI0RPA/tJEHE494aZj\nxIYcwUvn5eqyhBBCNWZf8/E/BMC9F8Xz2BdHeWlHJRUdu0kMsTMncQ6+BlkHXgw+Mm7h4WR2ST3n\nmqXDqbCndCQWmx++Xk0khO/i4sTZ+Bv9+6lCzyLnprokT3VJnn1zUXIw144OQlHg00Oh7Kg8wr3v\n34vVbnV1aYOGnJvuQ64kC9FHr2UfY09VB4HeOn47P51Y02QCjAGuLksIIfpVYngBIf5OGtsjOVQ+\niQDdYYpbihkZOtLVpQmhKrmS7OFmzpzp6hIGjXPJcnNxE2/vq0GrgYcuSWKkOVIa5G+Rc1Ndkqe6\nJM++8zf6MSxqN75e7XRYA7BqF+CllTEztci56T6kSRailxRFoaGrgd2Vlfx+SxkAt06NYVy0NMdC\niKFjWvQ0YgJDSY7ahlZro6k9jt1lfq4uSwjVSZPs4WR2ST1nylJRFFYdXsXTXz/HI58d/3b3nJRg\nrh5lHsAKPYucm+qSPNUlefadXqvn1rG3cs/Uxdwx4/gKF//YXUV2RauLKxsc5Nx0H9IkC9ELxS3F\nHKjL5Wj1dLpt/vh5NTEjpRaNRuPq0oQQYsDptDpiAmK4PC2RC0O7cSrwxMajbCnNZXvldlosLa4u\nUYjzJuskC9EL+2r38cethzjWNAKDzsq4pC1ckjiRSxMvdXVpQgjhUk5F4dfritlZ0YqvVzMZCdvQ\na50snbD0f8vHCeEi57NOslxJFqIX6lojOdY0AnCSHrcXo6GLiZETXV2WEEK4nFajYdmMELwM7XRa\ngzhaMwGD1sj6kvWuLk2I8yJNsoeT2SX1fFeWZU0W/vJlNQDTkhqZFBvMsvHLCPIOGsjyPI6cm+qS\nPNUleapn27Zt+Bl1pMZ8hU5rp6YlmsrGeFeX5bHk3HQfsk6yEGfQ0e3gkc+K6bI5mZUcxIqLx8kc\nshBCfEuAMYDJ0XF0WbMpOjaVIzVpLB4b5eqyhDgvMpMsxGnYnXYsdgt/2FzLl6UtJAZ7s/LK4fgY\ndK4uTQgh3JKiKBxuOMybOR3sKtMT4W/khWvSCPCS63HCdWQmWQgV7a/dz5NfPcldaz/gy9IWfA1a\nHp6TJA2yEEKcgUajIT0snYcvnUhqmA817d38fksZijKg1+KEUI00yR5OZpfUs23bNuxOOx8UfkBb\nVwRldekAzEipIMbk7eLqPI+cm+qSPNUlearn21kadVoeujQJP6OOr0pbeO9ArYsq80xybrqPPjfJ\n+/btY8GCBWRlZXH33XcD8MknnzB//nzmz5/Pxo0bVStSiIFisVvo7NZzsHwMoCHRXERoQI2ryxJC\nCI8SFeDFvbOOf3nvlV1VvHVgO4WNhXJVWXiUPs0kO51OMjMzefLJJ5kwYQJNTU34+fmRmZnJ6tWr\nsVqtLF68mA0bNpxyrMwkC3dmdzj58TubaewIItivgeExW7g8JYtp0dNcXZoQQnicZzYfYkOhFaO+\ni1EJnzEjbhxXplzp6rLEEDLgM8m5ubmEhIT0NLvBwcHs37+f1NRUQkJCiIqKIjIykry8vD4VJYSr\n/CunmsaOIHwMdi4aXknWsEymRk11dVlCCOGRAgO3E+jTRLfdh9KaaWQfy8HutLu6LCF6pU9N8rFj\nxwgICOCWW27hmmuu4a233qK+vh6z2cyqVatYu3YtZrOZ2lqZQ+pvMruknlc//Yp/76tBq4HfzhvB\nsolLuCDmAlnyrY/k3FSX5KkuyVM9Z8pSq1UYFbcXg66bxnYzVY3DBrAyzyTnpvvo07osVquVnJwc\n/vvf/+Lv7891113H9773PQAWLlwIwIYNG76zuVi6dCnx8cdnlUwmExkZGcycORP438kh273bPnDg\ngFvV46nbw8dN4YNjXgDMCu1mTFSAW9Un27It27LtrtsnnO7nQZYgyr3LGRaVQ17FNMrq0jlSb2VE\nuN5t6ne37TPlKdu9y2/btm2UlZUBcMstt9BXfZpJ/uqrr1i5ciWrVq0C4J577iE5OZkDBw7w4osv\nAnDDDTfw4IMPMmLEiJOOlZlk4U7qO+v5pOhT1h1Moq7dl0mxATw2fxhauXoshBCqaOhqIL8xn82F\ngWw8YiMywMhfrxmBn1GW1RT9b8BnkkePHk1VVRUtLS10d3dTUFDAnDlzKCwspLGxkWPHjlFTU3NK\ngyyEO2nvbueFPS+w+YgPde2+GPVd/L+pgdIgCyGEikJ9QpkeM517LkwnJdSH6rZu/rxV1k8W7q9P\nTXJAQAArVqxgyZIlXHvttVxxxRWkpaVxzz33sGjRIm688UZWrFihdq3iNL796xnRe/mN+dS2hlLe\nkIwGJ8GGtRS3HHB1WYOGnJvqkjzVJXmqp7dZGnVaHrwkER+Dls0lzazNb5BG+TTk3HQf+r4eeNll\nl3HZZZedtC8rK4usrKzzLkqIgaA4Ayk6NhGA5IhCrB2VBPsEu7gqIYQYvGJM3vxsRhxPbSrl2S+P\nsrXqDcZGRfL9Ed9Hq5H7mwn3ImekhzsxsC7OjcOp8Ga2gsPpRZBfNSGmXC7OuJjx4eNdXdqgIeem\nuiRPdUme6jnXLKfGGzGbSnEqOvIqJ3KwvpCt5Vv7qTrPI+em++jzlWQhPNnr2cc4WNNBqK+BZy6/\ngECvGQQYA2S5NyGE6Get3a3EmXPo6Aqlw+pPRd0YqsKqXF2WEKeQK8keTmaXzt3uilZW/d96yA9c\nnEhsYBCBXoF8+eWXri5tUJFzU12Sp7okT/Wca5ah3qH4G42kx+5Do3FS2RiPs1u+6H+CnJvuQ5pk\nMWQ4FSdlzU08tekoCnDDhCjGRPm7uiwhhBhSvPRe3DLmFuJD9KRHH1/L9oMDeho6bS6uTIiT9Wmd\n5PMh6yQLV2ixtPDS3r+xs3gsrZ1m0sK1/PmKMei0Ml4hhBCu4lQUVnxaRE5lGxNiAnjiMlmnXqhr\nwNdJFsLTvFfwHkdq42ntNGPUWwkL/kwaZCGEcDGtRsO9FyUQ6KUjp7KN/+TWubokIXpIk+zhZHap\ndyqb9ZTWpgAK6bH7Qdt+yvqckqW6JE91SZ7qkjzVc75ZhvoZuOeiBAD+vrOSv+x8j8+Pfo5TcapR\nnseRc9N9SJMsBr12q519ZekoaIkPO4qfzzFiA2JlJQshhHATFySYmBRnw6HA5/nhbCrbzr8P/dvV\nZYkhTpaA83CynuKZKYrCym3ltFp0RAU6mJrYQrjfOLKST73pjWSpLslTXZKnuiRP9aiVZURoNr61\no+m0+lNRPwaDbh+Kogy5CxpybroPaZLFoLauoJHNJc34GLQ8MT+dGNMkV5ckhBDiNHz0OkbF7mN3\n8QVUNsYT7Ffj6pLEECfjFh5OZpe+W1mzhee/qgDgjulxxJi8zvh4yVJdkqe6JE91SZ7qUSvLq1Ov\nxte7hdjQgwCU1k6m1epQ5bk9iZyb7kOaZDHoHG44zJ93PcfPP96F1e7kkmHBzEkNcXVZQgghziDc\nL5z/396dh0dZ33sff8+WfU8mJMEEEEICGJBVVI5IpSBo3Z4+p6CCVmlrsVy2pcee6tWnnvOc6znn\n6qmtetpq9bjUVg+VurS2ULGKG4gLEcIWZAtJyDbZ98lkZp4/KFQDKEx+yT0z+bz+4h6dyacfh/Ll\nnu32guIAACAASURBVO/c9/dmf49//cJCJmfH0eGFB9+pPOVL1iLDRddJlqjS1N3Eg9sf5FjjdKqa\nxhLr6uQnV+VTlDXW6mgiInKW6jq83PFCOd2+AP80v4AvFmZaHUkilK6TLPI3Fe0VtHVnUdU0FhsB\nikd/RFXnQatjiYjIOchJjmX1xecB8Iut1dR1eC1OJCORhuQIp92lT0uPzeFQ7fFPKsa4DxMX66Eg\nueCsnqsuzVKfZqlPs9SnOUPV5RcLM7h0TCrdvgB3/WkLP/3gZxxoPjAkPyuc6L0ZPjQkS1R5cVc/\nff2JJMe1ke8+wGX5lzExc6LVsURE5BzZbDbmFzbhcvTS0pXOgbocnt33LF2+LqujyQihnWSJGu8e\nbeNHrx7G5bDx8HXFFKTHWR1JREQG4Xflv+ODqg7Kjs7EZgswqWAT35u7gvOSz7M6mkQI7STLiNfa\n4+Nnb1cCcPvsPA3IIiJRYFzKOBLjqshLryIYtHO0fi5JrlSrY8kIoSE5wml36fhd9R7aUkVrbz/T\ncpO4boo7pNdRl2apT7PUp1nq05yh7HJ27mzm5M2hKPcgca4eunrT+PO+6F630HszfGhIlojW1NPE\nrz/axTsVbSS47Ky9rAD7CLuFqYhItLLZbFw1/ip+cMl3+ZeFJQA881Edh5q6LU4mI4F2kiViba/b\nzrq9f2F3xUL8gRiWT3fy1ZklVscSEZEh8tCWKv60r5HxmfE8dM1EXA6d65PPpp1kGZH+WvEaVQ1z\n8AdiyEpuoDXwmtWRRERkCH1tTh6jkmI41NTD/+yotzqORDkNyRFuJO8uHWvOo7kzC6ejj6K8PcDg\nPhQZyV0OBfVplvo0S32aM5xdxrscfO+y49e+f3ZHLU/ueIW6zrph+/nDQe/N8KEhWSJSXYeXQ/WT\nACjM2UM/LczNm2txKhERGWpTc5MoymkiELTxx11x/FfpL6loq7A6lkQh7SRLxAkEg3x/w0F21nYy\nLc/O/InVFGcUMSFjgtXRRERkiHX2dfLv797P7qML6elLYEzWQeaN7+aWklusjiZhaDA7yU7DWUSG\n3B/3NrKztpPUOCf3LigmLX6a1ZFERGSYOOwOHHY/k0bvovTIHI42ns8FeYetjiVRSOsWEW6k7S4d\na+vl8fePAXDXvHzS4l3GXnukdTnU1KdZ6tMs9WnOcHcZ74xnTu4cHK4qstMOAnZ2V03C5w8Ma46h\novdm+NCZZIkI/oCf0vodPLIFvH47XxifzryxaVbHEhERC1w94Wqmj5pOQ1crP30jyNEWH7/bWc/N\nM3KtjiZRRDvJEvb8AT+P7nyUDysTqPJMJcbZy+NfnsKopBSro4mIiMV21HRw94aDOO02fnFdEeMy\n4q2OJGFE10mWqFbVUcWBphaONU4BoDCnjNKGLRanEhGRcHBhXjJXF2fRHwjyk7eO4g8M67k/iWIa\nkiPcSNhdCgSDVNTPJBB0kJN2jPTkemyYv/X0SOhyOKlPs9SnWerTnHDo8vY5ebgTXRxo7OHuTX/i\nsZ2Pcbg1Mr/MFw59ynEakiXs7alJpLMnG6ejl9FZO4hxxHBZ/mVWxxIRkTCRGONg1ZwMAHYfy+No\nSw9P7XoKT7fH4mQSybSTLGGtobOPrz+/j25fgBWz7BSN8lLiLiHeqZ0zERH5u/dq3uOhLbV42saQ\nEt/KBWPeYkHB5cwvmG91NLGQrpMsUSkYDPLgO1V0+wJcOiaVm6eNw2Yzv2YhIiKRLys+i/ysv9DW\nNYr2njSONY3BXey2OpZEMK1bRLho3l167WALH1S3kxTj4FuX5g/5gBzNXVpBfZqlPs1Sn+aES5fj\n08fzD/mzGDdqBwDHmkpIjznf4lTnLlz6FA3JEobave1srSzjF+9WAnDH3NFkJpi7aYiIiESnqyZc\nxU8XreIfxqbQH7DzX1urCQZ1tQsJjXaSJawcbTvKE7ueYH/1TJo78xmX6eOR62ZrzUJERM5aS7eP\nVc/vo8Pr5+75Y1hYmGF1JLGIrpMsUWPjkY10dufT3JmPw95PZvqbVkcSEZEIk57g4hsXjQbg4W3V\ntPT4LE4kkUhDcoSLtt2l/n47H9dOBuD87APEuroJMjwfdkRbl1ZTn2apT7PUpznh2uUXCzOYnpdM\nh9fPz945yPa67RFxSbhw7XMkGtSQ3NnZybx583jiiScA2LBhA4sXL2bx4sVs3rzZSEAZWdo65uD1\nxZMU10pGSjkXZl+I3aa/y4mIyLmx2Wx8e14+LnuQbUd7eeqjbTy0/SF21O+wOppEiEHtJP/kJz/h\n4MGDXHTRRdx0000sWbKE9evX4/V6WblyJa+++uopz9FOspzJoaZu7nxpP0Fg+cxGZuSNosRdon1k\nEREJ2Z1/+h0H6iYS6+rhoglbSIhx8N3Z37U6lgwTS3aSDx8+THNzMxdccAHBYJCysjIKCwvJyMgg\nNzeXnJwcysvLQ315GWH8gSAPvFNFIAjXTXZz64VfZGr2VA3IIiIyKPlZlSTHt+H1xXO4vtDqOBJB\nQh6Sf/rTn7JmzZqTx42NjbjdbtatW8fGjRtxu900NDQYCSlnFi27S38ub2S/p5usBBe3zMy1JEO0\ndBku1KdZ6tMs9WlOuHd5yeiLGJP9IRCgurmAgsRLrI70mcK9z5EkpDvuvf7664wdO5bc3NxTrj+4\nbNkyAF599dUzngVcvXo1BQUFAKSmplJSUsK8efOAv785dHx2x7t27QqrPKEcd/hsPFGZBMAX0jso\nff/dsMqnYx3rWMc6PvPxCeGSZ+DxZfMuY3TSaH7cuIcjXfls/jiN64uDvLt1S1jki7Q+w/34xK8r\nK4/fa2HVqlWEKqSd5AceeIANGzbgcDhoaWnBbrdz4403snv3bh555BEAVqxYwb333ktxcfGnnqud\nZDmhz9/HpiOb+OOuZCqaUphbkMK/fPF8rViIiIhxPT4/q36/D0+Xj9UXn8d1U3TL6pFg2HeSv/3t\nb7Np0yY2btzIzTffzNe+9jW+8Y1vcODAAZqbm6mtraW+vv6UAVnkhEAwwKM7H+Wvh6qpaErBbuvn\nykleDcgiIjIk4l0O7rzkPACe+rCGpi5dO1k+m7Fra7lcLtauXcvy5cu59dZbueeee0y9tHyGgR/P\nRIp2bzu1HR4O15UAcP6ogxxq325ppkjtMlypT7PUp1nq05xI6vKSMWlcPCaVbl+AR7ZVWx3ntCKp\nz2jnHOwLfOtb3zr566VLl7J06dLBvqSMADGOGGqai+n1JZAU10Fu+mHiHBOtjiUiIlHuzovPo/RY\nB28eaWVRVTuz81OsjiRhalDXSQ6FdpIF4FhbL6t+vxd/0Mak/DfIT/ezevpqElwJVkcTEZEot76s\nnsferyEx1su10w5xfdHVpMamWh1LhsBgdpIHfSZZ5FwFg0F+vrUaf9DGgvHJ3H7RTWTEZeC06+0o\nIiJDb3JuMwmxrXR503jncAwNPb/iO7O+g8vhsjqahBHd7zfCReLu0ttHWtl+rIPkWAffnDuG7ITs\nsBiQI7HLcKY+zVKfZqlPcyKxyzLPDiaNPn7Ds6qm86nvCNLY02hxquMisc9opSFZhlV3n59Hth0D\n4Kuz8kiL19/aRURkeKXHpRMf6yEvvYpg0M7RhgtJcGrdTz5NO8kyrB597xi/39VAkTuBB740EYdd\nl3wTEZHh1R/o58myJznSVs+Owwvp98fygwVjWDA+w+poYph2kiWsBYNBXq14lfeqK3hn/yxs2Fhz\nSb4GZBERsYTT7mTVtFX09PfwenYHD22p4VfvHWNOfiqJMQ6r40mY0LpFhIuE3aVttdt4p2oLZVXj\nCWIjJ72CsRnh9/ezSOgykqhPs9SnWerTnEjt0mazkeBKYGlxNpOzE2nu7ufp0lqrY0Vsn9FIQ7IM\nuUMth2jrOp+27gxcDi+5mWW0elutjiUiIoLdZmPNpedht8Ef9ng41NRtdSQJExqSI9y8efOsjvC5\nMuPyOFh3/EYhE3I+JsFlIyUm/C7eHgldRhL1aZb6NEt9mhMNXY7PTOBLk9wEgvDQlipae9sIBAOW\nZImGPqOFhmQZctWNE/H540iOb2V0ej1fmfQV4pxxVscSERE56dZZuaTE2tjX0M0//3U9//nef9LU\n02R1LLGQhuQIF+67S9Vtvby45/i1J//fojncPfefKMoosjjV6YV7l5FGfZqlPs1Sn+ZES5eJMQ4K\nsncBUOUpoddnZ335+mHPES19RgMNyTKkHtl2jP5AkMUTMyhyJ1odR0RE5IwykipJS2zG54+hwjMR\nr99rdSSxkIbkCBfOu0vvVbbxflU7CS47t83KszrO5wrnLiOR+jRLfZqlPs2Jpi7HpBYwbtRObAQ4\n1pxPirN42DNEU5+RTkOyDIk+f4CH/3ZnvRUzcklP0J31REQkvC2fvJzLCoooHNUI2CirGkcwOKz3\nXJMwoiE5woXb7lIgGGBv417+a+tH1LR7KUiL49opbqtjnZVw6zLSqU+z1KdZ6tOcaOrSaXdy1YSr\n+I9FV5Aa52RPfRevH2oZ1gzR1Gek05AsxgSDQZ7e8zRP7XyBVz8+fumclTPTcOrOeiIiEkGSYp3c\nPvv4muBj7x+ju89vcSKxgobkCBdOu0sN3Q0caDpAbfN0AkEnWcl1NPm2WR3rrIVTl9FAfZqlPs1S\nn+ZEa5eLJmZQ5E6gubuf/9lRN2w/N1r7jEQaksWYIEE6etOpb8vDbvMzPqfcsouxi4iIDIbdZuPO\ni88D4PndHqrbei1OJMNNQ3KEC6fdJXd8Ng3NFwGQm3EIl6uDK8ZcYXGqsxdOXUYD9WmW+jRLfZoT\nzV0WZyeyeGIG/YEgP3lrP/ub9uMPDO3qRTT3GWk0JIsxbxxupbkrieTYIDdPH823Z36btLg0q2OJ\niIiEbMWMbJz2fvbWB3jovVf51c5fDfmgLOHBtn///mG9tklVVRUzZswYzh8pw6DH5+f29fto7Pax\n9rICFk/MtDqSiIjIoG2r2cbjH+7naMNU4mO6mVzwF26c8o+UuEusjiZnobS0lPz8/JCeqzPJYsTv\ndzXQ2O1jQmY8XyzMsDqOiIiIEf6An5z0IyTGdtLTl0BDayH9gX6rY8kw0JAc4cJhd8nT1cdzO+sB\nuGPuedhtkXnJt3DoMpqoT7PUp1nq05xo73JGzgySYuIZk70LgJrmSeQlFg3Zz4v2PiOJhmQZtCc+\nqMHrD/IP49KYmptkdRwRERFj4p3xrJmxhmsnTWKC24c/4OSZ0karY8kw0E6yDMq+hi7u+uPHuOw2\n/vt/TyI3OdbqSCIiIkOiuq2Xrz9fjj8Q5OfXFVGYlWB1JPkc2kkWS5Q3lvMfb+wG4IaSbA3IIiIS\n1c5LjePayVkEgYffrSYYHNbzjDLMNCRHOKt2lzYf3cyD771BbXsMLkcvY92HLclhkvbAzFKfZqlP\ns9SnOSOty5um55Aa52R3fRdvHWk1/vojrc9wpiFZQrKtZjvVjVMBGD/qIDs971ucSEREZOglxTq5\nZWYuAI+9d4wOr+7EF620kywhuePl33O4fjxJce3MHv8ucc5YvjP7O1bHEhERGXL+QJDbf7+TmvYg\n+Vl7mVnQxm1TbyPOGWd1NBlAO8kyrDxdfVQ1ng/AeVkf0d3fxcKxCy1OJSIiMlwCZKZvBeBY00Rq\n2rt4+eDLFmcS0zQkRzgrdpcef78Gn9/GnPx4vjbjCr47+7tRcech7YGZpT7NUp9mqU9zRmKXXr+X\npPh63Cn1BIJOKhsn0dbXZuS1R2Kf4cppdQCJLPsaunj9UAsuh407LxmnK1qIiMiIE++MJz02nbHZ\ne2jscFPXOpoUe7rVscQw7STLWQsEg9z1x4/Z7+lm2bRR3DY7z+pIIiIilujydfHixy/y7uEMDtTn\nMjUnkf+8qhBbhN51NlppJ1mGxesHW9jv6SYj3smyaaOsjiMiImKZRFciN0+5mf9YtIjkWAdldV28\nW2lm5ULCg4bkCDccu0vBYJD6zhb++4NqAG6bnUdCjGPIf+5w0x6YWerTLPVplvo0Z6R3mRzrZMWM\nE5eEq8HnDwzq9UZ6n+FEQ7J8pmAwyLN7n+WfX91Ic7efzMQerpigvSsREZETrp6UxXmpsRxr9/Kn\nfY1WxxFDNCRHuHnz5g3p6+9p3MOOugpqmycCkJ3xHh837x/Sn2mVoe5ypFGfZqlPs9SnOeoSnHYb\nX5szGoDfflRHh7c/5NdSn+FDQ7J8pjZvGzVNJQSCDrJTa0lLbDV2mRsREZFoMbcghWm5SXR4/Tz7\nUZ3VccSAkIbk+vp6li9fztVXX80NN9zA1q3HL6i9YcMGFi9ezOLFi9m8ebPRoHJ6Q727lGArxNOe\nj80WYFz2fhw2B5MyJw3pz7SK9sDMUp9mqU+z1Kc56vI4m83G1y8aDQR5YU89/+fNB3mj8o1zfh31\nGT5Cuk6y0+nkvvvuo6ioiJqaGpYtW8Zrr73G/fffz/r16/F6vaxcuZIFCxaYzivDKBgM8uyO42eN\nJ+e2MNmdwxfHriA1NtXiZCIiIuEnIbaFrJSjNLaP5VD9RIL21yhIKeD8tPOtjiYhCGlIzszMJDMz\nE4C8vDx8Ph87duygsLCQjIwMAHJycigvL6e4uNhcWjnFUO4uvV/Vzs7aTpJjHfzrFZeTHBvd957R\nHphZ6tMs9WmW+jRHXf5ddUc1BVnlNHfk42nPISfdzdH2o+c0JKvP8DHoneS3336bKVOm0NTUhNvt\nZt26dWzcuBG3201DQ4OJjGIBfyDIY+/XAHDT9JyoH5BFREQGa1zaOFyubgqyKgA4Uj+ZCakTrA0l\nIRvUkOzxePjxj3/Mj370o5OPLVu2jCVLlgDorjPDYKh2l/7ycROVrb3kJsfwpUlZQ/Izwo32wMxS\nn2apT7PUpznq8u+yE7L5ctGXmZhTS4yzj87eTI42J5/Ta6jP8BHy6UGv18tdd93F97//ffLz82lo\naMDj8Zz85x6PB7fbfdrnrl69moKCAgBSU1MpKSk5+fHCiTeHjs/ueNeuXcZf3+uHp6uP7x1fmtzO\ne+9uDZv/vTrWsY51rOPwOj4hXPKEw/G07Gk4GraxsR4e/6CGuWNS2bZ1i/ochuMTv66srARg1apV\nhMq2f//+4Lk+KRgMsnbtWmbNmsWNN94IQF9fH0uWLDn5xb1bbrmFTZs2nfLcqqoqZsyYEXJgGVq7\nPLv4TWk9O6oymeRO4IFrJuoTARERkXPUHwjy9ef3Ud3m5c6Lz+PaKac/cShDq7S0lPz8/JCeG9K6\nxfbt29m0aRPPPfcc1113Hddffz2tra2sXbuW5cuXc+utt3LPPfeEFEiss6V6C7/d9UfKqtMAKMz9\nWAOyiIhICJx2G7fPzgOO32Ckq89vcSI5VyENybNmzWL37t289NJLvPTSS7z44otkZ2ezdOlSXnnl\nFV555RUuv/xyw1HldAZ+PDMYpQ2l1DVPJRB04E6po7V/J8HgOX/QELFMdinq0zT1aZb6NEddntkl\nY1KZMiqRtt5+nttZf1bPUZ/hQ3fck5O6vcnUto7GRoDxow5gt9l1JllERCREf7/BCDy/u4HdDVV0\n9nVanErOVkg7yYOhneTwdfeGPeyo6cOdeoAJuXu4dsK1zMjRfysREZHBuPeVfXxQ1UtWyhEKc3dy\nbaH+fB0ug9lJdhrOIhFqT10nO2r6iHPauOfyueSnXElKbIrVsURERCJeRup72KpLaGwfy/nZNWw8\nvJHpo6br09owp3WLCGdidykYDPLfHxy/cciXS0YxxV0wIgdk7YGZpT7NUp9mqU9z1OXni4vpYnRG\nFWDjUN1E/MEzf4lPfYYPDcnCtsp29tR3kRrn5H+VZFsdR0REJKpMHzWd7LRdOOz9NHW6SbJP1Vnk\nCKCd5BHOHwhyxwvlHG3t5ZtzR3P9BRqSRURETNtRv4P/2dHAR1Vuit0JPKj7EAyLYb9OskSPvx5s\n5mhrLznJMVw1Qm4/LSIiMtwuHHUh933hCtLinJR7utlytM3qSPI5NCRHuFB3l5p7mvnZ+z/n51v3\nA7D8wkxiHCP77aA9MLPUp1nq0yz1aY66PHvxLgc3Tc8B4MkPavAHTv0wX32Gj5E9FY1gT+9+mo/r\nM/H2x5MY20aD79RbiIuIiIhZS4szyU2OoarNy6YDzVbHkc+gITnCzZs3L6Tntfb2crRxPAATcg7S\n1ttqMlZECrVLOT31aZb6NEt9mqMuz43LYefWWbkA/GZ7Ld7+wKf+ufoMHxqSRyhP2xT6/S7SEptI\njD9GTlKO1ZFERERGhPnnpzMhM57Gbh9/2OuxOo6cgYbkCBfK7lJTt4+jnuPf9JyUW0FR5kSuL7ze\ndLSIoz0ws9SnWerTLPVpjro8d3abjdtm5wHw1IdH+bet9/PusXcB9RlOdMe9EejZj+ro8we5ZEwq\n912+yuo4IiIiI05qfD0pCQ20d2dT0TCWP/v/zLi0cVbHkk/QmeQId667S7XtXjaUN2KDkztRcpz2\nwMxSn2apT7PUpznqMjRHO44yLvv4Faaqm8bQ35/AsY5j6jOMaEgeYZ4urcUfhCsKMxibHm91HBER\nkRGpML2Q2NgG3Cn1BIIOjjUVMSZljNWx5BM0JEe4c9ldOtLcw+sHW3DabaycoS/qDaQ9MLPUp1nq\n0yz1aY66DM2Y1DFcO+FaivMqgSCetvPx+ZPVZxjRkDyCPPlhDUHgquJMcpJjrY4jIiIyos3Onc0P\n532dhRMyCATht6V1VkeST7Dt37//1Nu9DKGqqipmzJgxnD9yxKvtrOX1w4f49fuJxDrtPP2Pk0lP\ncFkdS0RERDj+faHb1u8lCDx6wyQK0uOsjhQ1SktLyc/PD+m5OpMc5XZ7dvOL0l/y4u4eAC48r0MD\nsoiISBjJTYllSVEWgSD8urTW6jjyNxqSI9zn7S69VfUWXm8B7d1ZOB0+HLHvEAwO64cHEUN7YGap\nT7PUp1nq0xx1acaN00cR47Dx9pFWDjR2Wx1H0JAc9YJBOFxfCMCYrMM4nf0WJxIREZGBshJjuGay\nG4CnPtTZ5HCgITnCfd71FDNc8+noTcXl7CEtZR8X512MzWYbpnSRRdemNEt9mqU+zVKf5qhLc74y\nbRTxLjsfVLezq67T6jgjnobkKOYPBHn94+P/iRcXObnjwtu4YswVFqcSERGR00mNc3L9lEwA/u/r\n7/Pz7b+gqafJ4lQjl4bkCPdZu2BvHWnlaGsv2Uku7pgzizGpukj5Z9FenVnq0yz1aZb6NEddmlVZ\n/SxORx+t3elUNMXw5K4nrY40YmlIjlL+QJDf/O0bsjdemEOMQ/+pRUREwl2H38OYrCMAHPEU0u7t\noD+g7xNZQZNThDvTLtjmQy1Ut3nJSY5h0cTMYU4VmbRXZ5b6NEt9mqU+zVGXZl18wcVkpx0ixuml\noyeVXu84nHan1bFGJA3JUcgfCPLbj47fteem6Tk47fqinoiISCT40oQvUZQ5jrHuCgBa2mYR0KVb\nLaEhOcIN3AXrD/SzYX8dNe1e8lJiWDghw6JkkUd7dWapT7PUp1nq0xx1adZ7777HjZNv5KeL/5HM\nBBdHW3xsqWizOtaIpCE5imyv286/bf13Hn3/EABfmZaFQ2eRRUREIk6M087yC0cB8HRprc4mW0BD\ncoQ7sQvm7ffyp0N/orl9LF5fIvExnfTatlmcLrJor84s9WmW+jRLfZqjLs36ZJ9XFmXiTnRxtKWX\nNw+3WphqZNKQHCV6+nvo8/s54hkPwLjsQ7T36TeUiIhIpIpx2Llpeg4AvymtxR/Q2eThpCE5wp3Y\nBUuJTaGraxJeXzyJsZ0kJhzkgqwLLE4XWbRXZ5b6NEt9mqU+zVGXZg3sc9HETHKSY6hu87L5UItF\nqUYmDclRot8P9S3Hh+Jp+Q1cV3gtM3NmWpxKREREBsNpt3Hz384mP/7hUfZ6ygkEAxanGhls+/fv\nH9Zz91VVVcyYMWM4f+SI8Ic9Hn7xbjXj0uN4+IZi7DZ9YU9ERCQadPX1cNO67XT3JTJ21IfMLoDb\np96O3aZznZ+ntLSU/Pz8kJ6rdqPEgcZuAFbMzNWALCIiEkW21WzlvKxyAOqap3CotYKKtgprQ40A\nGpIj3Indpe/NH8PPry3i0jGpFieKXNqrM0t9mqU+zVKf5qhLs07XZ3+wn+yUWhJjO4l19dDfH4c/\n6Lcg3cii+xxGkYnuBKsjiIiIiGGXjr6UD+s+ZErBO9jtvWQlZDIudZzVsaKedpJFREREwlyXr4v3\na98n1hHL7JzZuBwuqyNFhMHsJOtMsoiIiEiYS3QlsqBggdUxRhTjO8kbNmxg8eLFLF68mM2bN5t+\neRlAu2DmqEuz1KdZ6tMs9WmOujRLfYYPo2eS+/r6uP/++1m/fj1er5eVK1eyYIH+1iMiIiIikcXo\nmeSysjIKCwvJyMggNzeXnJwcysvLTf4IGeCT93iXwVGXZqlPs9SnWerTHHVplvoMH0bPJDc2NuJ2\nu1m3bh2pqam43W4aGhooLi42+WNERERERIbUkFwnedmyZSxZsgQAm25sMaS0u2SOujRLfZqlPs1S\nn+aoS7PUZ/gweibZ7Xbj8XhOHns8Htxu9yn/3urVqykoKAAgNTWVkpKSkx8vnHhz6Pjsjnft2hVW\neXSsYx3rWMcj6/iEcMkT6ccnhEueSDs+8evKykoAVq1aRaiMXie5r6+PJUuWnPzi3i233MKmTZs+\n9e/oOskiIiIiMhzC5jrJMTExrF27luXLlwNwzz33mHx5EREREZFhYXwneenSpbzyyiu88sorXH75\n5aZfXgYY+PGMhE5dmqU+zVKfZqlPc9SlWeozfAzJF/dERERERCKZ0Z3ks6GdZBEREREZDoPZSdaZ\nZBERERGRATQkRzjtLpmjLs1Sn2apT7PUpznq0iz1GT40JIuIiIiIDKCdZBERERGJStpJFhEREREx\nSENyhNPukjnq0iz1aZb6NEt9mqMuzVKf4UNDsoiIiIjIANpJFhEREZGopJ1kERERERGDNCRHutxM\nxQAACLxJREFUOO0umaMuzVKfZqlPs9SnOerSLPUZPjQki4iIiIgMoJ1kEREREYlK2kkWERERETFI\nQ3KE0+6SOerSLPVplvo0S32aoy7NUp/hQ0OyiIiIiMgA2kkWERERkaiknWQREREREYM0JEc47S6Z\noy7NUp9mqU+z1Kc56tIs9Rk+NCSLiIiIiAygnWQRERERiUraSRYRERERMUhDcoTT7pI56tIs9WmW\n+jRLfZqjLs1Sn+FDQ7KIiIiIyADaSRYRERGRqKSdZBERERERgzQkRzjtLpmjLs1Sn2apT7PUpznq\n0iz1GT40JIuIiIiIDKCdZBERERGJStpJFhERERExSENyhNPukjnq0iz1aZb6NEt9mqMuzVKf4UND\nsoiIiIjIANpJFhEREZGopJ1kERERERGDNCRHOO0umaMuzVKfZqlPs9SnOerSLPUZPjQki4iIiIgM\noJ1kEREREYlK2kkWERERETHonIfk+vp6li9fztVXX80NN9zA1q1bT/6zDRs2sHjxYhYvXszmzZuN\nBpXT0+6SOerSLPVplvo0S32aoy7NUp/hw3nOT3A6ue+++ygqKqKmpoZly5bx1ltv0dfXx/3338/6\n9evxer2sXLmSBQsWDEVm+YS6ujqrI0QNdWmW+jRLfZqlPs1Rl2apz/BxzkNyZmYmmZmZAOTl5eHz\n+fD5fJSVlVFYWEhGRgYAOTk5lJeXU1xcbDaxfEpsbKzVEaKGujRLfZqlPs1Sn+aoS7PUZ/g45yH5\nk95++22mTJmCy+XC4/HgdrtZt24dqampuN1uGhoaNCSLiIiISMT5zCH5qaee4vnnn//UYwsXLuSu\nu+7C4/Hw4x//mF/+8pcA2Gw2AJYtWwbAq6++evIxGTqVlZVWR4ga6tIs9WmW+jRLfZqjLs1Sn+Ej\npEvAeb1evvrVr7J69WrmzZsHwPbt23nsscd45JFHAFixYgX33nvvKWeS9+7dS3JysoHoIiIiIiJn\n1tHRweTJk0N67jmvWwSDQX7wgx9w9dVXnxyQAUpKSjhw4ADNzc14vV7q6+tPu2oRalARERERkeFy\nzkPy9u3b2bRpE4cPH+a5554D4LHHHsPtdrN27VqWL18OwD333GM2qYiIiIjIMBn2O+6JiIiIiIQ7\n3XFPRERERGQADckiIiIiIgMM6jrJn2fjxo3s3LmTxMRE1qxZc/LxXbt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"text": [ - "" + "" ] } ], - "prompt_number": 22 + "prompt_number": 74 }, { "cell_type": "markdown", @@ -1417,7 +1442,7 @@ "source": [ "Our first step is to implement the math for a ball moving through air. There are several treatments available. A robust solution takes into account issues such as ball roughness (which affects drag non-linearly depending on velocity), the Magnus effect (spin causes one side of the ball to have higher velocity relative to the air vs the opposite side, so the coefficient of drag differs on opposite sides), the effect of lift, humidity, air density, and so on. I assume the reader is not interested in the details of ball physics, and so will restrict this treatment to the effect of air drag on a nonspinning baseball. I will use the math developed by Nicholas Giordano and Hisao Nakanishi in *Computational Physics* [1997]. \n", "\n", - "**Important**: Before I continue, let me point out that you will not have to understand this next piece of physics to proceed with the Kalman filter. My goal is to create a reasonably accurate behavior of a baseball in the real world, so that we can test how our Kalman filter performs with real-world behavior. In real world applications it is usually impossible to completely model the physics of a real world system, and we make do with a process model that incorporates the large scale behaviors. We then tune $\\mathbf{Q}$ and $\\mathbf{R}$ until the filter works well with our data. There is a real risk to this; it is easy to finely tune a Kalman filter so it works perfectly with your test data, but performs badly when presented with slightly different data. This is perhaps the hardest part of designing a Kalman filter, and why it gets referred to with terms such as 'black art'. \n", + "**Important**: Before I continue, let me point out that you will not have to understand this next piece of physics to proceed with the Kalman filter. My goal is to create a reasonably accurate behavior of a baseball in the real world, so that we can test how our Kalman filter performs with real-world behavior. In real world applications it is usually impossible to completely model the physics of a real world system, and we make do with a process model that incorporates the large scale behaviors. We then tune the measurement noise and process noise until the filter works well with our data. There is a real risk to this; it is easy to finely tune a Kalman filter so it works perfectly with your test data, but performs badly when presented with slightly different data. This is perhaps the hardest part of designing a Kalman filter, and why it gets referred to with terms such as 'black art'. \n", "\n", "I dislike books that implement things without explanation, so I will now develop the physics for a ball moving through air. Move on past the implementation of the simulation if you are not interested. \n", "\n", @@ -1453,7 +1478,7 @@ "\n", "I will not belabor this issue further because the computational physics is beyond the scope of this book. Recognize that a higher fidelity simulation would require incorporating things like altitude, temperature, ball spin, and several other factors. My intent here is to impart some real-world behavior into our simulation to test how our simpler prediction model used by the Kalman filter reacts to this behavior. Your process model will never exactly model what happens in the world, and a large factor in designing a good Kalman filter is carefully testing how it performs against real world data. \n", "\n", - "The code below computes the behavior of a baseball in air, at sea level, in the presense of wind. I plot the same initial hit with no wind, and then with a tail wind at 10 mph. Baseball statistics are universally done in US customary units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 50 m/s corresponds to a velocity of 110 mph, which is a typical exit speed for a baseball for a home run hit." + "The code below computes the behavior of a baseball in air, at sea level, in the presense of wind. I plot the same initial hit with no wind, and then with a tail wind at 10 mph. Baseball statistics are universally done in US units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 110 mph is a typical exit speed for a baseball for a home run hit." ] }, { @@ -1462,13 +1487,16 @@ "input": [ "from math import sqrt, exp, cos, sin, radians\n", "\n", + "def mph_to_mps(x):\n", + " return x * .447\n", + "\n", "def drag_force(velocity):\n", " \"\"\" Returns the force on a baseball due to air drag at\n", " the specified velocity. Units are SI\"\"\"\n", "\n", " return (0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))) * velocity\n", "\n", - "v = 50.\n", + "v = mph_to_mps(110.)\n", "y = 1\n", "x = 0\n", "dt = .1\n", @@ -1500,7 +1528,7 @@ "x,y = solve(x=0, y=1, vel=v, v_wind=0, launch_angle=theta)\n", "p1 = plt.scatter(x, y, color='blue')\n", "\n", - "x,y = solve(x=0, y=1,vel=v, v_wind=4.47, launch_angle=theta) # roughly 10 mph wind\n", + "x,y = solve(x=0, y=1,vel=v, v_wind=mph_to_mps(10), launch_angle=theta)\n", "p2 = plt.scatter(x, y, color='green', marker=\"v\")\n", "plt.legend([p1,p2], ['no wind', '10mph wind'])\n", "plt.show()" @@ -1511,13 +1539,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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EPMLixYvp378/9erV4/bbby93X3FxMZMmTSIxMZHWrVvz0UcfueSYFovlrB+jfL4aNGhA\nRkbGee3fnfX9mUYjTOYpn7fuDZSVMcrJuD9ntX69lW++8adz5xI6djzz+EBysp0ffrDidJZ+k24Q\nH0TPpME8v/45nDjpktCFBuENznrMlOgU5g2eV+lqsKf5c059+9rp27cZpUPC5cdCnE4oLLRAbhz8\ncjE0+pI6mx/jTOMYD65+sNxl4jrGd+TzkZ+7/i9QQ/S1Z5yyOi0yMpI777yT1atXk5eXV+6+l156\nie3bt7N161a2bNnC6NGj6dixI/Xr1zep2tpHK8IiIsA//xnIqFFhPPZYCKNGhfHXF7M4lHuo7M+x\n/GMAvPBCHtdeW0TnzsUMHFjEvHk53NtpCkl1kqgXWo8ZPc690tsloYu7/zqmsVigeXM74IQVT8Ha\ne2mVHFThcWvW+BO9/V6sztKRjjpBdXiy15M1XK1I5W5deivd53Wnx7we9JjXg7Q30jiYc9Clx+je\nvTuDBw8mKiqqwn0ff/wxt912GxEREXTv3p20tDQ+++wzoHS8YeTIkbRo0YJZs2bRokUL7r77bgAy\nMjKIjo7m2Wef5cILL6RXr15s2bKl3L7Xrl1LWloaTZs25fXXXz9nnW+++SZ/+ctfKtz+z3/+k8mT\nJwMwYMAAGjZsSHR0NA5H+Q/jadOmDX/729/OeMzjx48zevRoGjVqxPXXX09RUdF5jVZUhRphk2lO\nyjhlZYxyMu6PWc2bZyu7pu/x4348n30Jveb3Kvsz5L9DAAgMLG2GlyzJYd68XGJjnQT7BzO46WA6\n1+tc6Wqwt6rqOfWf/+Ry3XVF9E6rw7i2N/HSS7nl7l+4MIBbbglj3Su3YD/YEoDWMa3pEN/BZTWb\nQV97xnlCVjlFOfSY14O+C/qW/bn+s+vLPebm1Js5mHOQbUe3se3oNhqEN6BeWL2y+w/nHmbh9oXl\n/mw+vNllNe7cuZNmzZpx22238cEHH5CcnMzOnaWvolgsFiZMmMCYMWNYvXo169at4/3336eoqKjs\n+cePH2fnzp1cd9113HLLLWW3O51ONmzYQHp6Oi+++CLTpk2r0Lj+WceOHdm0aVOF2zdv3kzHjh0B\n+Pzzz1m7du0Zn2+xWM56zJkzZxIcHMzOnTsZOXIk3333nUYjRERqksNR/ptuxI7bOB7xECXOEoKs\nQTze/fFKn/9A5wcosBdU+hhfERxc+svC2bz1ViBHjvy+DvPd7TBgCn9p/NgZHzs9fTrHCo6VbUcG\nRjKz50xXlis+KswWRmJEIkv3LAUgyBrELa1vKfeYLvW70Cq2Fen70okKjOKRbo+Uu7/QXsjUNVPL\nzlGrxcq07tNoE9fGJTXm5eURGhrKTz/9RJs2bQgLC+PAgQNl9zdu3Jh9+/Zx8OBBIiIiiIyM5Nix\n018v48ePx9/fn5tuuonp06ezZ88eGjdujMViYezYsQQFBdGvXz9ycnI4dOgQ9erVO1MZACQnJ3Ps\n2DFOnjzJG2+8wZYtW5g7dy6bN2/mnnvuKXtcZSu5Zzvm8uXLefXVVwkICGDw4MFceOGF5xdcFWhF\n2GSakzJOWRmjnIz7Y1a9ehUTHFz6DTw42Mng2PFlV1lIiU5hZMrISvcVYA0g3BbuvmJN5OpzqtxC\nz6YbCd40mbaxZ77u/PZj23l729tlf3Yc2+HSWlxJX3vGeUpW07tPJzY4Fij9Or+mxTUVHvNQ54eI\ntEXSOrY1afFp5e5rGNGQHg1O/11SolMY33a8y+oLCQkhLy+PNWvWMHHiRLKzswkLCyu732q1YrVa\ny1ZP/f39KSk5/SE4sbGxZbdHRUVx+PDhsvvq1KkDgM1mA6CwsOJlHP/Iz8+Ptm3bsmnTJtLT09m/\nfz8nTpzg8OHDpKSkGPr7nO2YR48eJSYmpkLdNaHSRvj48eOMGDGCYcOGMXToUBYvXgyUvsNxwIAB\nDBgwgJUrV9ZIoSIi1bF7tx9jx4YycmQYCxac/QoMs2fnM2NGHlddVchjj+Xx92dKGJUyimD/YG5r\nc1uNvUznCyZPzqdevdI3zwXaLAwMmUr9+hVXkXJy4LEuM4gNKf2hGB0czWPdzrxyLFIdzes2p0N8\nBwKtgdza5lb8LBXboi71u9C8bvMKq8GnPN79ceJD4/G3+DMqZRT+fq57sb1Zs2b83//9X9n2jh07\naNasmeHnn2p8S0pKOHHixHk3mGlpaXzzzTdYLBa6du3Km2++Sbt27c5rnwAxMTFkZp6+7vgf/9vd\nKm2Ew8PDefvtt/n444954403mDlzJsXFxTz77LPMnz+f119/nSef1JsbzocnzEl5C2VljHI67fhx\nC6NGhbJkiY0VKwK4+7//4PK5dzBx2UQmLpvIqHmjyCsufQnfYoFx44p49dU8brutCIsFbm1zKxc3\nvPicq8G1navPqb597fz3vzlMnZrPnDm5zJ2bV26VOCcHhg0Lo0uXCK69rCMxBaWrcO3i2tEqtpVL\na3Elfe0Z50lZzegxg8SIRK5JqbgafMpnV31WYTX4lMTIRDrV60TTOk25re1tVT6+w+GgoKAAu92O\nw+GgsLAQu730F8Vhw4bxyiuvkJWVRXp6Ot9//z2XX3654X2//PLLFBcX89prr9GgQQOaNGlS5fr+\nqGPHjrzxxht069aNiy++mJdffpm0tDPnUpU3uw0YMIC5c+dSVFTEokWL+OWXX86rzqqo9NcWf39/\n/P1LH5KdnY3NZmPz5s0kJSVRt25dAOLj49m+fbvhZXERkZry9ddWdu48/W2u0HaAr/Pf4evtpdvN\nQ5oT7B981ucHWAOYN2Seu8v0SSkpDlJSzjxT/eCDIXz55enV+5h3niLyum+0GixukVQnidWjV1f6\nqs+5Vnmf6PkE6w6sq9Zq8IIFC5g0aVLZ9nvvvccDDzzA/fffz8SJE/n5559p1aoVUVFRvPjii2Uf\nL3zqWruVXXM3OjqapKQkEhMTmTt37llrMPqKV4cOHTh8+DB9+vQhJSWFnJycsjfKpaenM2bMGJxO\nJxaLhcaNSy8RuWrVqjM24H885iOPPMKECRNISkri4osvplOnTobqcQXLjh07Km3Zc3NzGTVqFBkZ\nGTzzzDPY7Xa++uorWrZsSWRkJMuXL2f48OH06tWr3PP27t1L+/ZnnvkSEakJ69dbGT48jLy831/8\nCjxJ2JQO5Nh2EeIfwpxL5zC8+XBzi5QKRowIY+XK041wQICTx9/+hNv69arwWKfTSdqb5Vekwm3h\nrBq9yt1lihc5cOBAWQPpCzIyMmjXrh2ZmZn4+dWut4Od7d9yw4YNNGzYsMr7O2c6oaGhLFq0iA8+\n+ICnnnqqbLB51KhRDBxY+hGamp0TEU/UoYOd4cOLiYx0EBjopE1KKFem9gWgRXQLhiUNM7lCOZM2\nbUrw9z+9RtOwoYNrOvY+42MtFgsDmwxkz8k97Dm5h33Z+xhz0ZiaKlVEvJzhNfymTZuSkJBA/fr1\nWbJkSdntmZmZZx2+njhxIomJiUDpJ6ekpqaWvVP01HyQr2+fus1T6vHk7S1btjBhwgSPqcdTt/98\nbpldjzu3O3ToQVAQfPXV2R8/Z04e3btvIi/Pn7FjW1FkeZhFu97nkuBL+Oqrr/T1Z2D7pZdeqtHv\n3717r2D79lQOHmyAzeZkxIhv2br12Nkf7+jNR4EfcaDwAMl1k0nOSiY9PV3fzz14u6a/n0dHR/vU\nijDU3kXKkydPsnv3bqD03zYjIwOAcePGVWt/lY5GHDp0CJvNRp06dcjMzGTEiBF8+OGHjBw5koUL\nF1JYWMgNN9zAsmXLKjxXoxHG/PGbtVROWRnjCznt3u3HzTeHcuSIhchIeO65XDp1OvNHIp9J+r50\nutfvXtYIS+U87ZzKz4eJE0PZudOP0FB45plcFhx/iLmb5zKz50xubXOrKXV5Wk6erKaz8rXRiNrM\n1aMRlTbCmzZt4tFHHy3bnjBhAoMGDWLx4sW88MILAEydOpWLL764wnPVCIuIuwwaFMY33/w+Q3pz\nDwLq/EaDBqWfUGR32Fl33ToC/QNNrFDcafz4EN57zwaUrnilpJSweMVBhn88mC+u+QKrn9XcAsXj\nqBGuPVzdCFc6GtG2bVsWLVpU4fZBgwYxaNCgKh9MRMQVTp78w0t+39xJ8RU3sedk6WXQrrvoOjXB\ntdwvv1g51QQDZGb6kX00gpWjVp7x5eD92fu59fNbCbSWnhdOnLSObc2MHjNqqmQR8VC1662EXuiP\ns2VSOWVljC/kVL++4/TGtqsJyS69tmyjiEY81t34JbZ8IStX8LScoqMd5bYjI53ExDjOOhOZEJZA\nob2QVXtXsWrvKr47+B0dLujg8ro8LSdPVtNZOZ3OKl3XVjyTw+E494OqSI2wiHidV1/No3//Ilq1\nKqFnzxJmDBhPsDWYXg16ER0cbXZ54mYvvphHp07F1K9vJymphMcfzyf47JeDxmKxMKHthLJrRreI\nbsGQZkNqqFrxBJGRkRw7dszsMuQ8OBwO9u/fX+6jmF3hnNcRri7NCItITXE6nfR7rx/vDn1XjbAP\nKSiAwEA425vjHQ44dQnVU+fI9qPb+Ve/fzE0aWjNFSoe4ejRo2WXgBXvFBMTg81mO+N9bpkRFhGp\nST/95Menn9po2tTOFVcUn7XB+TOLxcLykctr7eWC5MyCgs58+3ffWZkyJYTsbAvx8Q7eeCOXuDiY\n0HYCz61/TqvBPio6Wr8kS0UajTCZZsqMU1bGeGtOy5b5c9VVYfz1abjt/Rl0nvYoU1dPZerqqby8\n6eVzPr86TbC3ZlXTvCknpxMmTw5l61Z/fv3Vyrp1AUyYEALAlc2v5P3h77vtFyZvyslsysoY5eR+\nWhEWEY8wZ04QBw9agSDsif9jZ8wGdm4uvW9si7Gm1ibeIzsbTp4sf9vRo6VrPhaLhfjQ+DM+798/\n/JuP/u8j/P1KfywW2AuY1m0aXet3dWu9ImIuzQiLiEcYPDiMtWt/vzZwq3kw7BYIyCcxPJEvRn2h\n2V8xxOmEXr3C+fHH0+s8AwYUMX9+bqXP23l8J4P/O5jDeYcBaF6nOStHryx7g52IeLbqzghrNEJE\nPMLYsYVll8Xy+2k0EQUXAdCroa4EIcZZLPDqq7mkpZXQvLmdvn2LeOmlvHM+r1mdZmWXVLNgYUjT\nIWqCRXyAGmGTaf7HOGVljLfmNHp0Ma+8ksOYMYU8NLWAv11xK7HBsUzrPs1tx/TWrGqat+XUooWD\nZcuy+eabLN5/P5eoKGMvfM7oMYO4kDiS6iRxT6d7qnxcb8vJTMrKGOXkfpoRFhGP0bevnb59S1fv\nnM6rqBMcodVgcbmTJy28804Afn4wdmwRYWGltzer04x2F7SjVXQrrQaL+AjNCIuIiM84ftzCkCFh\nbNtWug7Upk0Jn3ySTXh46f0nCk4QEhCCzXrma5WKiGfSjLCIeJz8fLj99hAGDQrj5ptDycoyuyLx\ndS+8EFjWBANs3uzP//t/gWXbUUFRZ22CC0oKyC/JL/tTWKIPZxDxdmqETab5H+OUlTGelNNtt4Uy\nf76Nb0If5aPEFFr8szOd3uxE6mupfHfwO7PL86isPFltyqmoqOI1hAsLz31dYYfTQee3OtPxzY5l\nf/q916/cY2pTTu6mrIxRTu6nRlhE3GbnTitggXV3gZ+d/NCf2XliJ/Gh8aTFp5ldnvigiRMLaNzY\nXradlGTn5pvPvbLrZ/FjRPIIDuYc5EDOAY7lH+P2dre7s1QRqQGaERYRt7n00nA2bPj9Zejh10Pb\ntwjxD+Efl/6DK5pfYW5x4rP27rXw3HNB+PnBffcVcMEFxn4M5hXn0WdBH34+/jPt4tqx4poV+lhv\nEQ+hGWER8Th//WseSUklREY6aLjjr8T4N6RFdAuGJw03uzTxYQ0bOvn73/N55pl8w00wQEhACJc3\nvZxAayC3trlVTbBILaBG2GSa/zFOWRnjSTl17Ghn1apsVqzIZu2yEC5p1o3b293uMQ2EJ2XlyXwt\np7w8yMjwo7i44n33dryXjvU6MjJlZIX7fC2n86GsjFFO7qfrCIuIWwUHQ9OmpZ8Y969+//KYJljk\nTD76KICZM4PJyrIQF+fktddySE52lN0fEhDCJ1d+YmKFIuJKmhEWEREB7Hbo0iWCXbusZbd161bM\np5/mmFg2RPUFAAAgAElEQVSViBhR3RlhrQiLSJVlZ5decio62okWeKW2yM0tvfZ1+duMn+Bzvp/D\nl/u+LHvVo8hexJO9niQlOsWVZYqIC2lG2GSa/zFOWRnj7pweeyyYjv2O0e6u5+kw5TmeXDub2etm\nsypjlVuP6w46p4zxlZzCw6FevT++SOokKcl+1sdXcAjWHVzHsl+WseyXZRzKO0STqCYur7M28JVz\n6nwpJ/fTirCIGPbdd1befNNGliMUBs8lN+IAz6wHm5+NZ/s8a3Z5IufFYoF583K4664Qjh3zo1kz\nO88+m2f4+W0j2tIypiVfH/gaq8XKVc2v0kc1i3g4zQiLiGFvv23jzjtDSzd+vy4wQJu4NnxxzRf4\nWfQik/i2VRmruHHxjdQPr8/KUSvVCIvUEF1HWETcrlevEhISfn+peMVTWE4m4k8g41LHqQkWAS5O\nvJjmdZtrNVjES+gnl8k0/2OcsjLGnTklJjp4/vk8unQppmOLGFqGdSMlJonRF4122zHdSeeUMcrp\ntPx82LbNjyNHKr6J7lRO/xn4H25vr49frozOKWOUk/tpRlhEquTSS0u49NLSy0kdzpvOj5k/ajVY\nfMLOnX5cf30Y+/dbCA93cscdhYwfX1jhcfXD65tQnYhUh2aERUREDLjyylBWrTo97tCwoZ309CzC\nw00sSkQAXUdYRETErfLzy49D5OVZOHHCj/Bwx1meUd6mw5t4at1TBPgFAODAwaAmgxjdwjtHi0Rq\nA72eaTLN/xinrIxRTsYpK2OUU6n27e0EBJx+EbVBAwcJCaeb4HPl1CSyCTuO7WDRrkUs2rWIr/Z9\nRZNI37zOsM4pY5ST+2lFWET46isrmzZZ6d27hFatjK1uifiamTPzCQhwsmGDP5GRTp59Ng+r9dzP\nOyUiMIJLG13K3B/mAtA6tjWdEzq7qVoRMUIzwiI+7vHHg3h10Vby+o3Dn2AaNHAQVbeY/hf258Eu\nD5pdnkitklWYRZ8FfThecJz5Q+arERZxEc0Ii0iVlZTAhx/ayMtoDw5/ShLW8UsJxGbHMiJ5hNnl\nidQ6p1aFtx3dpiZYxANoRthkmv8xTlkZU5Wc7HZwOACnFb6/BUpK3xGfFp9GUp0kN1XoOXROGaOc\njDGa0yPdHmHOpXPcXI1n0zlljHJyv0pXhA8dOsRdd91FdnY2NpuNe++9l27dutGiRQuSk5MB6Nix\nIw8//HCNFCsirhUYCGlpJfz2mx/FG27Br+OrBMUdYHqP6WaXJuJ1Nm6M4T//CSUqysG0aflERJz5\nceG2cMJtuuaaiCeodEb46NGjHDlyhOTkZA4cOMCoUaNYs2YN7dq1Y+PGjZXuWDPCIt7B4YAXXghk\n2zYr/l1e4Vjsp7w79F2zyxLxKkuWBDB5cghHjpS+0NquXQmffZZNUJDJhYn4CLfMCEdHRxMdHQ1A\nQkICxcXFFBUVVa9CEfFIfn5w992ln47ldF5Lfolmg0Wq6s03bWVNMMDWraVXYunSxW5iVSJyLoZn\nhL/88ktatmyJzWajqKiIK6+8ktGjR7N+/Xp31lfraf7HOGVlzPnkZLFYCAkIcWE1nk3nlDHK6dz+\nfBm1gAAnwcFV28eBnAN0erMTvd/pTe93etPrnV5MXDbRdUV6EJ1Txign9zN01YjMzEyeeuop/vWv\nfwGwZs0aoqOj2bJlC3fccQfLly/HZrOdYy8iIiK107Rp+WzcWMTBg2EEBjrp27eE1q2rthqcEJZA\nfGg86ftLm5+owChm957tjnJF5HfnbIQLCwuZPHkyDzzwQNnsxalxidTUVOLi4ti3bx9NmlT8dJyJ\nEyeSmJgIQGRkJKmpqfTo0QM4/VuOtrVdle1TPKUeT9zu0aOHR9Wjbe/fPnWbp9TjqdsrV/bk889z\nOXJkC2lpmVgsVd/f1C5TGfnRSHLtubSKaUXX+l095u+n7+f6fu5J26f+OyMjA4Bx48ZRHZW+Wc7p\ndDJlyhTS0tIYM2YMACdPniQwMJCgoCD27dvHmDFjWLZsGUF/ekeA3iwnIiJSdUP/O5QtR7bwzuB3\n6Fq/q9nliHiF6r5ZrtIZ4e+//55ly5bx3nvvMXz4cK644gp2797N8OHDGTp0KJMmTWLWrFkVmmAx\n7s+/GcvZKStjVq9OZ8bsfK4Z/xuzX93H7hN72HNiD/kl+WaX5nF0ThmjnIxxVU5Tu0wlqU5SrW6C\ndU4Zo5zcz7+yO9PS0ti6dWuF25cuXeq2gkTk/DzzTHvW+r+Gs+szLD/ux/OvQ2iIhflD5tOxXkez\nyxORc+havyufjfjM7DJEfEKloxHnQ6MRIjWvqAg6doxg78FiuLU9xP0EQPf63Vk0YpHJ1Yn4rqNH\nLaxe7U98vIOuXe1YLGZXJFK7uGU0QkS8i9X6+2WcSoJg21XgsOBXFMn9ne83uzQRn7Vzpx8DB4Yz\nblwYV10VzvjxITjdsgQlIlWlRthkmv8xTlmdm9UKXbv+TFSUA9IfwnoimWZhqfRs0NPs0jySzilj\nlJMxZ8tp2rRgdu4svdBwQYGFzz8PYPt23/7xq3PKGOXkfpXOCIuI9xk9+mduvjmBzZut7K43ikGt\n08wuScSnFReX3y4stJCXV/XZiGP5x5j1zSzsjtPXJ24T24abWt90viWK+CzNCIuIiLjRwoUBTJ0a\nwrFjpavAbduWsGRJNoGBVdtPsb2YPgv6sO3oNgAsWLi3071M7TLV1SWLeB3NCIuIiHigq68u5rnn\n8hgypIhrry3kgw9yqtwEAwRYAxjdYjT+ltIXc5vXbc7daXe7uFoR36JG2GSa/zFOWRmjnIxTVsYo\nJ2Mqy2nIkGLeeCOXF1/MIyqq+i/E3trmVpKjk/HDj2HNhhHk753X8dc5ZYxycj81wiIiIl4iwBrA\nqJRR1A+vz11pd5ldjojX04ywiIiIFym2F/P1ga/p1bCX2aWIeAzNCIuIiPiAAGuAmmARF1EjbDLN\n/xjnq1n9vNtOr3veodvkN5n05n+Yu3kun/z8yVkf76s5VYeyMkY5GVPdnL791srjjwfx0UcBPvNB\nGzqnjFFO7qfrCIt4sOPHLYwdHcHOfv+CuG1sPwHzVsOAxgMYmjTU7PJE5Dy9/baNmTODycz0IyTE\nwerVRTz3XL7ZZYn4DM0Ii3iwjz8O4KabwqDdXLj8DvAvIrAogXW3LCYxMtHs8kTkPPXrF873359e\nk6pf3866dVmEhJhYlIgXqu6MsFaERTxYbKyDoCAnBZv+Ah1fhoQNxBV2VhMsUkv8eRTC6ax4m1F7\ns/YyZ8McnJzeQbeEbgxvPvw8KhSp3TQjbDLN/xjni1l17Wpn0KAiwkLBb+N4rIXRvHXt9Eqf44s5\nVZeyMkY5GVOdnK6+uoioKAcANpuT7t1LCA2t3vEjAyNZ9ssy/v3Dv/n3D//mra1vkVWUVb2duZnO\nKWOUk/tpRVjEg1ksMHduHlu3WsnKvpofg3Jo3ajqL/2IiGe67bZCLrzQzpIlAbRqZecvfymq9r4i\nAiPof2F/5v4wF4CU6BSubXmtq0oVqZU0IywiIlJLZBVm0WdBHw7kHGB279lc3+p6s0sSqRG6jrCI\niIiPiwiM4NJGl9IksolWg0UMUCNsMs3/GKesjFFOxikrY5STMZ6S08NdH+bpPk/jZ/HcH/GekpWn\nU07u57lfJSIiIlJlEYERdKvfzewyRLyCZoRFRERExKtpRlhERKQWWbfOyiWXhNO1awTXXhtKXp7Z\nFYnUPmqETab5H+OUlTHKyThlZYxyMsaVOeXnw513hrBxoz87dlhZvNjGlCm15+PmdE4Zo5zcT9cR\nFqlBDgeM+vtr7Mw8QESEkx49Sgi22bi/0/0EWAPMLk9EPMTBg35kZpZfq/r1V61dibiaZoRFatB9\n9wXzWvb1OC9aWHZbu7h2rLhmBRaLxcTKRMST5OZC794R7N5tLbtt+PAiXnstt9r7fH3L67y25TUC\nrYEA5Jfk82i3RxnQeMB51ytiNs0Ii3iBb7/1x7nkOTjZoPSG4lDuaHO3mmARKSc0FJ58Mo8WLUpo\n1MhOr17FPP989ZtggMFNB5NVmMX3h77n+0PfU+IooVfDXi6qWMQ7qRE2meZ/jKsNWQUEANn14dee\nAAQeb8XQ5pe79Bi1IaeaoqyMUU7GuDqn/v1L+OqrbL7/PouPPsohIuL89hcTEkPPBqXfeyxYGNJ0\nCMH+wS6otOp0ThmjnNxPjbBIDbr//nwaNrTD8qex5MdwZfxkrFatBovI2fm58Cf1tO7TSIxIJKlO\nEvd0usd1OxbxUpoRFqlhBw9a2LrVSkbIx9zcbZDGIkSkRk1aPon40Hge7vaw2aWIuEx1Z4R11QiR\nGlavnpN69UoA145EiIgY8UyfZ7D6Wc/9QBEfoNEIk2n+xzhlZYxyMk5ZGaOcjPGWnAL9A/H3M3cd\nzFuyMptycj81wiIiIiLikzQjLCIi4mWeey6QpUttWK1O7r03n7597WaXJGIqt1xH+NChQ4wePZrB\ngwdz5ZVXsnbtWgAWL17MgAEDGDBgACtXrqxexSIiIlJlb79t4/nng/juO3+++SaAyZND2btXL/CK\nVEelXzn+/v5Mnz6dTz/9lDlz5vDggw9SXFzMs88+y/z583n99dd58skna6rWWknzP8YpK2OUk3HK\nyhjlZExN5fTFFwFkZ5/+8b1/v5U1a7zrve86p4xRTu5X6VdOdHQ00dHRACQkJFBcXMymTZtISkqi\nbt26AMTHx7N9+3ZSUlLcX62IiIiPa9jQgcXixOksvfRieLiD5s3PfzRixlcz2Ju1t2zb38+fFy99\nEZvVdt77FvFUhn+F/PLLL2nZsiVHjx4lNjaWBQsWEBkZSWxsLIcPH1YjXE09evQwuwSvoayMUU7G\nKStjlJMxNZXTww/ns22bla1brfj7Oxk+vJiOHc+/Ec4qyuKDnz8o2+6W0M1tTbDOKWOUk/sZaoQz\nMzN56qmn+Ne//sWPP/4IwKhRowBYvny5PhBAfNaTn77HmvVZ1K3rpHv3EkICgrgx9UZ9TYiI2wQG\nwsKFORw5YiEw0HneH718yqNdH2Xlryv5JesXImwR3N/5ftfsWMSDnbMRLiwsZPLkyTzwwAM0bNiQ\nw4cPk5mZWXZ/ZmYmsbGxZ3zuxIkTSUxMBCAyMpLU1NSy325Ozb34+vap2zylHk/e3rJlCxMmTPCY\ner7+Op4XMhdQ3GAVAEu/gjaxbbgx9UZT6/vzueUpeXni9p8zM7seT91+6aWX9P3bwPap2zylnups\n92nUh/9s+Q8NbQ3p1bCX247nad/PPXVb388r/3pLT08nIyMDgHHjxlEdlV4+zel0MmXKFNLS0hgz\nZgwARUVFDBw4kIULF1JYWMgNN9zAsmXLKjxXl08zJj09vewfVyrnaVkNHx7Gmh0/wvX9IPQIFIbz\n9+5zubFbf1Pr8rScPJmyMkY5GVMbcjpRcILOb3Vm7mVzyxphd6gNWdUE5WRcdS+fVmkjvH79em68\n8UaaNWtW+mCLhVdeeYX169fzwgsvADB16lQuvvjiCs9VIyy13RVXhLF6dQCMHQhJS7Ee6Ma6Wz+j\nSRO3XJpbRKRGbPhtA+3j9fNbvItbGuHzoUZYarsvvvDnzjtDOOjYAjf2pUPG/2PZnIvReLCIiEjN\ncssHaoj7/XHWRSrnaVldckkJ776bw12jkxlZdwZLX+ztEU2wp+XkyZSVMcrJGOVknLIyRjm5n7/Z\nBYh4s1atHLRqVQBca3YpIiIA5OfDiRMWLrjAiZ+Wu0QqpdEIERGRWuL112288EIQeXkWEhIcLFiQ\nwwUX6H0LUvtpNEJERMSHnTxp4bnngvj1VyuZmX5s3uzPPfeEmF2WiEdTI2wyzf8Yp6yMUU7GKStj\nlJMxZueUmWkhK6v8GxVOnPCANy6cgdlZeQvl5H6aERYREakFGjZ0kJDg4OTJ0jUuq9VJaur5f/Qy\nwLYj27h/9f0EWgMBcDgd9Ensw50d7nTJ/kXMohlhERGRWmLXLj/uvTeE3FwLqaklzJ6dj78LlryK\n7EX0XdCXbUe3ARAVGMWCIQvolNDp/Hcu4gLVnRHWirCIiEgt0bSpgw8/zHH5fm1WG1clX8Wsr2dh\nd9ppHdtaTbDUCpoRNpnmf4xTVsYoJ+OUlTHKyZjantPEdhNJrptMVGAUD3V56Lz2VduzchXl5H5q\nhEVEROScTq0Kt4huodVgqTU0IywClDhK2HPkNw4csBAX5yQ8HMICwogKijK7NBERj1FsL+Z44XHi\nQuLMLkWkHM0Ii5yH5d9kcv2X/bA77fhZICjEzuDkfrzc/2WzSxMR8RgB1gA1wVKraDTCZJr/Mc6d\nWT0/Iwn7nm4QcgRH8BGKssOZ3m2G247nTjqnjFNWxignY5STccrKGOXkfmqERYC8PAssfxqy6gFg\nO9iTKP8LTK5KRERE3EkzwiLArbeG8N//2nBePQLqf0faxrUs+yDM7LJERFwiLw8mTw5hzx4rUVEO\nXnwxj4QEt/z4FzGFZoRFzsM//pFHaCj8sO9JTsT+g4X/CQf0Q0JEaodJk0L58ENb2fZ11/mxYkU2\nFs/8BGaRGqPRCJNp/sc4d2YVGAjPPZfHFwsv4PuZTxAZ6b1NsM4p45SVMcrJGE/Oadeu8j/uDx2y\nkJ1tUjF4dlaeRDm5n1aERUREarnw8PK/3IeGOglz4fTXhkMbyCvOK9v2s/jRJaELfhatt4ln04yw\niIhILbdrlx833hhKZqYf4eFOZs7M57LLil22//7v9Wf9b+vLtptENuHb679VIyw1RjPCIiIickZN\nmzpYvTqbo0ctREU5CQhw7f6f7PUkIz8eyYnCE9j8bExsN1FNsHgFnaUm0/yPccrKGOVknLIyRjkZ\n4+k5+flBbKzrm2CAtPg0Wse2BiAlOoUbWt1Q6eM9PStPoZzcT42wiIiInLdHuj1CpC2S61tej9XP\nanY5IoZoRlhERERc4om1TzC1y1Q1wlLjNCMsIiIipnqk2yNmlyBSJRqNMJnmf4xTVsYoJ+OUlTHK\nyRjlZJyyMkY5uZ8aYRERERHxSZoRFhERERGvphlhkd/d/OHdfLXlNxwOqFfPQewFJcwbPI8g/yCz\nSxMR8SgFBfCXv4SyfbuVwEAn995bwJVXuu6DNkQ8nUYjTKb5H+OMZHXsmIXVnzUgM2IZR+t+ztbC\n5RzOxKeaYJ1TxikrY5STMd6Y08MPB7NkSQB79ljZvt2fGTOCycy0uP243piVGZST+6kRllpl1Sp/\njn/yMBxJKb0hL5q6G2aZW5SIiIf65RcrcLrx/e03P/bsUWsgvkOjESbr0aOH2SV4DSNZxcU5CPIP\npeCnERAzCw62p1FAeyDP/QV6CJ1TxikrY5STMd6YU7Nmdlat8sfpLG2G69Vz0KSJw6XH2Ju1l/05\n+8vd1iqtlUuPUVt54znlbdQIS63Svbudyy8v4vP/PUhOu/+QlPE4j/8n3+yyREQ80syZ+WRm+rFt\nmxWbzcmDDxYQE+Pa99B/+POHzPp6FnaHHYAwWxifjfiMqKAolx5HpDr0+ofJNP9jnJGsLBZ49dU8\nlnxi583en7N6fjJRUW65MIrH0jllnLIyRjkZ44052Wzw2mu5fPNNFmvWZDNokOvfKDeh7QSa1WmG\n4/f/dazXkeM7jrv8OLWRN55T3uacjfDs2bPp3r07Q4YMKbutRYsWDB8+nOHDhzNrluYvxbNYLNCy\npZ3BPRMI8p33yImIeKQAawAjk0fib/EnJjiGx7o9ZnZJImXOeR3hjRs3EhAQwNSpU1m0aBEA7dq1\nY+PGjZXuWNcRFhEREYBiezG95/emfnh9Fg5baHY5Ugu57TrC7dq1Y9++fdUqSkRERCTAGsD4tuPp\nEN/B7FJEyqnWjHBRURFXXnklo0ePZv369a6uyado/sc4ZWWMcjJOWRmjnIxRTpW7vtX1tIxpCSgr\no5ST+1XrqhFr1qwhOjqaLVu2cMcdd7B8+XJsNluFx02cOJHExEQAIiMjSU1NLbsUyKl/XF/fPsVT\n6vHk7S1btnhUPdr2/u1TPKUeT93esmWLR9XjqduneEo9nryt7+fadsXXW3p6OhkZGQCMGzeO6jjn\njDDAvn37mDBhQtmM8B9dffXVzJ49myZNmpS7XTPCIiIiIlITqjsjXOXRiBMnTlBQUACUNsiHDh0i\nISGhygcWERERETHTORvhGTNmMGrUKPbs2UPv3r2ZN28ew4cPZ+jQoUyaNIlZs2YRpGtUVdufX1KT\ns1NWxign45SVMcrJmNqW0//+Z+Xmm0O5++5gTp60nPsJVVDbsnIX5eR+/ud6wLRp05g2bVq5226/\n/Xa3FSQiIiLmWrIkgLvuCiEzs3S9bNMmf5Ysyda12aXWMTQjXB2aERYREfFOY8aEsnTp6TfBW61O\nPvooh+7dS0ysSuTsamxGWERERGo3/z+9XmyzOQkN9a2PqxffoEbYZJr/OTu7w06xvZiikmKK7cWs\n+nIVTqe+EZ+LzinjlJUxysmY2pTT9On5NG1qByAw0Mkll5TQpo3dZfs/ldW6A+u44sMruObja7jm\n42u46qOrePvHt112HG9Xm84pT3XOGWERs1w5/2a+3rsBp8MPqx8EheWQ3nY1DcIbmF2aiEit1qSJ\ngyVLslm+PIDYWAeXXFKCxbXvlwOgRXQL9mXtY9fJXQDEBsfyRM8nXH8gkbPQjLB4JKcTOg08yK6e\nl0D4bwDUPTKInY9rpUBEpDZ5aM1DvLzpZQAGXDiA+UPnm1yReCPNCEutUlAA+fuSYX+n0hty4qi7\n/m/mFiUiIi73YOcHaRrZlNiQWKZ1n3buJ4i4kBphk2n+58yCgyE62gnLnobsC2B/JyKK4swuyyvo\nnDJOWRmjnIxRTsb9MauIwAj6Ne5H29i2pESnmFiV59E55X6aERaPNXduLpMmNeGnY91pcWIak+/Z\nCHQ2uywREXGxR7o+Qm5xrtlliA/SjLCIiIiIeDXNCIuIiIiIVIEaYZNp/sc4ZWWMcjJOWRmjnIxR\nTsYpK2OUk/upERYRERERn6QZYRERETHstddsrFgRQN26TmbNyicyUp/4Kear7oywrhohIiIihsyZ\nE8jTTweRnV36gvKOHVaWLMnGX92EeCmNRphM8z/GKStjlJNxysoY5WSML+S0fHlAWRMMsGuXH3v2\nVL2V8IWsXEE5uZ8aYRERETEkIKD8GERgoJOwMI1GiPfSjLCIiIgY8uOPftxwQxi7d/sRGelkzJgi\nZs3Kd8uxdh3fxZPfPImfpXTNzomT3g17c13L69xyPPFumhEWERERt2rZ0sGyZdls2GAlIcHBRRc5\n3Has+LB4tmRuYeeJnQCE+IcwtOlQtx1PfJNGI0ym+R/jlJUxysk4ZWWMcjLGV3KqW9fJpZeWnFcT\nbCSr0IBQBjUZVLbdIroFQ5oNqfYxvZGvnFNmUiMsIiIiHum+zvfRLKoZIf4hTGo/CYvFYnZJUsto\nRlhEREQ81vT06azau4qVo1aqEZaz0oyweKzfcn8ju6CArJMW6tRxYvWzkBiRqG9oIiJyTvd3vp+R\nKSP1M0PcQqMRJvOF+Z9h826k62uX0H/hJXT+96UMfHcoxY7iKu/HF7JyBeVknLIyRjkZo5yMq0pW\nIQEhXBRzkRur8Vw6p9xPjbC4lcMBeR/PxmF34gw+hj3gONZto7FZbWaXJiIiIj5OM8LiVjk50KVL\nBAf6XQqNV0FmCi2/WseX/7ObXZqIiIjUEtWdEdaKsLhVWBjExzth5eNQEAE/XUGzRkFmlyUiIiKi\nRthsvjD/89ZbOfRt1pm6mUMYVvc+/vnP3GrtxxeycgXlZJyyMkY5GePrOWVlwbZtfmRlnfuxvp6V\nUcrJ/XTVCHG7evWcvP9+LvAPs0sRERE3WLbMn6lTQ8jMtBAb6+Spp3K55BKNwInn04ywiIiInJee\nPcP58cfTa2upqSWsXp1tYkXiazQjLCIiIqbIz7dUui3iqdQIm0zzP8YpK2OUk3HKyhjlZIwv59Ss\n2R/HIJx/2q7Il7OqCuXkfpoRFhERkfPy2mu53Hefk4wMPxo1cvDUU3luPd7639Zzy9JbCPYPBqDY\nUczQZkN5tNujbj2u1D7nnBGePXs2n3zyCXXr1mXRokUALF68mBdeeAGABx98kD59+lR4nmaERURE\nxB2cTieXvnspGw9vBKB+WH0+H/k5CWEJJlcmZnHbjHD//v155ZVXyraLiop49tlnmT9/Pq+//jpP\nPvlklQ8qIiIiUl0Wi4Xb2t5GkLX0uvRdErqoCZZqOWcj3K5dO6Kiosq2f/jhB5KSkqhbty716tUj\nPj6e7du3u7XI2kzzP8YpK2OUk3HKyhjlZIxyMs4VWV2dfDUtoltQP6w+M3rMcEFVnkfnlPtVeUY4\nMzOT2NhYFixYQGRkJLGxsRw+fJiUlBR31CciIiJSwalV4aV7lmo1WKqt2m+WGzVqFADLly/HYtFl\nUqqrR48eZpfgNZSVMcrJOGVljHIyRjkZ56qsRqaM5Krkq1yyL0+kc8r9qtwIx8XFkZmZWbZ9aoX4\nTCZOnEhiYiIAkZGRpKamlv2jnlru17a2ta1tbWtb29qu7vbar9Z6VD3arpntU/+dkZEBwLhx46gO\nQ58st2/fPiZMmMCiRYsoKipi4MCBLFy4kMLCQm644QaWLVtW4Tm6aoQx6enpZf+4UjllZYxyMk5Z\nGaOcjFFOxikrY5STcdW9aoT/uR4wY8YMli9fzokTJ+jduzfTpk1jypQpjB49GoCHHnqo6tWKiIiI\niJjM0IpwdWhFWERERERqgtuuIywiIiJSXXv2+LF1q5WiIrMrEalIjbDJ/jj07cl2n9hN4ospxD3Z\nlrgn29Lg2VRu+3x8jdbgLVmZTTkZp6yMUU7GKKeKJk8OoV+/cC67LIxBg8LJyiq9XVkZo5zcT42w\nGJL1SxIFGamUhGVQEpZBXoGTxJ+nm12WiIh4qPXrrXzwQQDHjvmRl+fHhg3+PPpoiNlliZSjRthk\n3itYDPEAABVOSURBVPJu0G+/tVKy9EnIq1t6Q0ZXdm9sWqM1eEtWZlNOxikrY5STMcqpvIMHLeTm\nlm8zjh8v/dwBZWWMcnI/NcJiSKdOdqIL0+Bge8iqh23106SlFZtdloiIeKhu3ew0aWIv246KcjBk\niAaFxbOoETaZt8z/tG1rZ8qUAhJ/nknYsR6MHliP8eNr9huat2RlNuVknLIyRjkZo5zKi4528vbb\nOfTrV8TFFxczbVo+V19duoDizqw+/L8P6f9ef4b8dwhD/juE/u/155Odn7jteO6kc8r9znkdYZFT\nxo8vZPz4ZOAVIN/sckRExMOlpDh4993cGj1mr4a9mPHVDDKySz9xrFFEI3o26FmjNYj30HWERURE\npFa5c8WdvL3tbQBubHUjf+/7d5MrEnfTdYRFREREgGndp5EYnkijiEY82u1Rs8sRD6ZG2GSa/zFO\nWRmjnIxTVsYoJ2OUk3Huzio6OJreib3pk9iHOkF13Hosd9I55X6aERYREZFa56+9/orFYjG7DPFw\nmhEWEREREa+mGWERERERkSpQI2wyzf8Yp6yMUU7GKStjlJMxysk4ZWWMcnI/NcIiIiIi4pM0Iywi\nIiIiXk0zwiIiIuLxHA544okghg0L49prQ/ntN13ZQcyjRthkmv8xTlkZo5yMU1bGKCdjlJMxM2cG\n8eKLNr78MoDFi22MGhVGcbHZVXkmnVPup0ZYREREasy33/pTUmIt287I8GPvXrUjYg7NCIuIiEiN\nufrqUL74wla2Xb++nTVrsqlTxy3tiPiI6s4I65PlREREpMY8/XQ+Y8eWrgKHhzsZN66wxprgrMIs\nCuwF5W6LCY7Bz6IVaV+lf3mTaf7HOGVljHIyTlkZo5yMUU7GXHihg8cf/5wlS3JYuTKbyZMLa+zY\nk1ZMose8HvR8pyc93+lJr3d6cTjvcI0dv6p0TrmfVoR9zKQVd/L9tixOnvAjKspBy+aBvHrZK2aX\nJSIiPiQw0EHLlvYaP+7jPR5n4PsD+S33NwCGNRtGfGh8jdchnkMzwj6m/awJ/BL+btl2w9whbJ76\nhokViYiI1JwbPruBRbsWUS+0Hp+P/JwG4Q3MLklcQNcRFkOcnz8NJ38/UbLj8fviaXMLEhERqUGP\n93icuJA4OtXrpCZY1AibrabnfwKLEuDXnqUb+7oQkt+0Ro9/PjQrZYxyMk5ZGaOcjFFOxpmZVaPI\nRlza6FJm9pxpWg1G6ZxyPzXCPub66wuJ+m425MYQ9d1sbrqp5t6kICIi4gnm9Juj1WABNCPsk374\nwcqn6/6PoV2TaNXKYXY5IiIiIudF1xEWw1q3ttO6dVNATbCIiIj4Lo1GmEzzP8YpK2OUk3HKyhjl\nZIxyMk5ZGaOc3E+NsIiIiIj4JM0Ii4iIiIhX03WERURExGulp1sZMiSMyy8P49VXbWaXIz6i2o1w\nixYtGD58OMOHD2fWrFmurMmnaP7HOGVljHL6/+3db2xUdb7H8c90hplpy9CxtaV/vN27RJaitl0Q\nBEsVrb0EeYBsVxQkwZtIdgmRrCtEBOON2d3evYbVxQe7JjxA3Wy83SCFqFFCFZCt7soiFy10ieYS\nrCPIn1jL0EJnpp37gNvalhn8dZzpmel5vxISTin0l3d/nPwyfDljjlZm6GSGTuZGturoyNKaNbl6\n//0J+tvfJui3v81Wc/MEi1aXPthTqZfwUyO8Xq927dqVzLUAAAAb2rvXpUDAOXjd1ZWlN990q6Eh\nbOGqYAeMRlistrbW6iVkDFqZoZM5Wpmhkxk6mRvZ6sYb+5Sb++0jPR2OqG64gUd8sqdSL+GDcCgU\nUkNDg5YvX65Dhw4lc00AAMBGamv79MADIU2e3KeCgn7dcUdETz11yeplwQYSPggfOHBAzc3N2rRp\nk9atW6dQKJTMddkG8z/maGWGTuZoZYZOZuhkLlar5567pAMHgtq374J27rwoj2fs1tMb6dXMl2dq\n9p9mD/5Y9NqisVtAHOyp1Et4RrigoECSVFlZqaKiIgUCAU2ZMmXY56xZs0bl5eWSpLy8PFVWVg6+\nzD/wzbX79YB0WU86X7e1taXVerjO/OsB6bKedL1ua2tLq/Wk6/WAdFlPOl/Hu58XFkbV2tqqkyfH\nfn01ZTV69Z+vSpLcDrc2zNmQNr24jv33rbW1VR0dHZKkVatWKREJPUe4q6tLHo9HXq9XgUBADz30\nkPbs2SOv1zv4OTxHGAAAZIrzPedV/5d6dQQ7NLNoploebJHD4bB6WTCU6HOEXYl8sRMnTmjjxo1y\nu91yOp1qbGwcdggGAADIJNfnXK/aG2q149MdWj1jNYdgm0hoRnjGjBnavXu3Xn/9de3cuVN33HFH\nstdlGyP/SQ3x0coMnczRygydzNDJXLq2embeM6r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Dh2v+wLSarTy5/ll2le6AvKrbrmn/O4a2H9qgnMU3hfqHkhyezMqdKwEItARy83k313hM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\nsJfQLJFxlKWxlKexlKdxlKW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MJr3Z7k30t+UlNEvUMFtfzMRREoEzZD/2oP3Y95xL0Y9F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\nkact8rRDlrbIM3YdHb5B67NnacXcRPqjnL/1Vun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"text": [ - "" + "" ] } ], - "prompt_number": 29 + "prompt_number": 72 }, { "cell_type": "markdown", @@ -1587,13 +1615,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 30 + "prompt_number": 66 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can test the Kalman filter against measurements created by this model. There is truly a significant difference in the predictions by the process model; the Kalman filter assumes that the ball is in a vacuum, and thus predicts that the ball would travel about twice as far as it actually does." + "Now we can test the Kalman filter against measurements created by this model." ] }, { @@ -1642,34 +1670,137 @@ { "metadata": {}, "output_type": "display_data", - "png": 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jR44wbtw4evbsSWRkpOuYRx99lBUrVjBy5Mjrv7jrJEaEm4hb8S7ypkrE0rtE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FMs5ikOsxSrPs/NZzZDBx0i9BG+zyRJgiXCgkPXDuH8zfOq76XfZUbfpCjUumV8dlngK5EjI+Gc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\nWYrFPMVin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sNnafqGb/Vz+Q+vaLDDzueTqxzLZR7EjtzO7+nksfjpUf4x+9/sFvhb+RVZ6F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"text": [ - "" + "" ] } ], - "prompt_number": 48 + "prompt_number": 70 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of $\\textbf{R}$ on the output, they are not intended to imply a correct design.\n", + "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n", "\n", - "With R=0.5 we see that the Kalman filter follows the measurements quite closely, albeit slightly overshooting at the end of the trajectory. This small value of R tells the Kalman filter that we expect there to be about 1/2 meter error in the ball measurements, which is quite small, so the Kalman filter prefers the position implied by the measurement vs the process model. The small amount of overshoot is attributable to the incorrect assumption that the ball is travelling in a vacuum during the predict step. We see the effect of this when we set R=10, which incorrectly tells the Kalman filter that the noise in the measurments is on order of 10 meters. In this case the Kalman filter weights the prediction more, and the trajectory ends up overshoooting the measurements because air drag is not being considered by the filter. \n", + "We can see that neither filter does very well. At first both track the measurements well, but as time continues they both diverge. This happens because the state model for air drag is nonlinear and the Kalman filter assumes that it is linear. If you recall our discussion about nonlinearity in the g-h filter chapter we showed why a g-h filter will always lag behind the acceleration of the system. We see the same thing here - the acceleration is negative, so the Kalman filter consistently overshoots the ball position. There is no way for the filter to catch up so long as the acceleration continues, so the filter will continue to diverge.\n", "\n", - "At this point we should question the value of $\\textbf{Q}$, which tells the Kalman filter how much process noise there is in the system. We can think of air drag as process noise, and setting $Q=\\verb,I*0.1,$, for example, would cause the Kalman filter to fit the measurements quite well. If you are reading this in IPython Notebook I urge you to modify the code above to see the effects of various values for $\\textbf{Q}$ and $\\textbf{R}$. \n", + "What can we do to improve this? The best approach is to perform the filtering with a nonlinear Kalman filter, and we will do this in subequent chapters. However, there is also what I will call an 'engineering' solution to this problem as well. Our Kalman filter assumes that the ball is in a vacuum, and thus that there is no process noise. However, since the ball is in air the atmosphere imparts a force on the ball. We can think of this force as process noise. This is not a particularly rigorous thought; for one thing, this force is anything but Gaussian. Secondly, we can compute this force, so throwing our hands up and saying 'it's random' will not lead to an optimal solution. But let's see what happens if we follow this line of thought.\n", "\n", - "However, the errors caused by our process model are anything but Gaussian, so a large $\\textbf{Q}$ is a poor representation of the errors in the model. A better approach is to redesign the Kalman filter to model the behavior of a ball in air.\n", - "\n", - "This is where Kalman filter design becomes an 'art'. I prefer to think of it as emperical engineering. We try designs, measure their performance, work to understand the limits of the mathematical model that we are using, make changes based on that new understanding, and measure the performance of that new system to see if it matches our expectations. Blithely changing $\\textbf{Q}$ and $\\textbf{R}$ will eventually give you a filter that performs very well for a specific set of data, but the filter is likely to perform badly in different situations. Much of this theory and practice was developed by the radar folks in the 1960s and beyond. They were trying to develop filters to track aircraft and missles based on signals generated by radar. Testing was (and is) cumbersome and expensive, and they endlessly faught against overtuning their filters to the rather sparse data they had available. Your application may be less expensive and difficult to test, and you must do everything you can to ensure that your filter is robust in the presense of various process noise. There is significant literature devoted to this topic, and you will have to read it and master it if your application is critical. An excellent introduction to the topic (and excellent introduction to Kalman filters taking a g-h filters approach is the book *Tracking and Kalman Filters Made Easy* by Eli Brookner. I highly recommend this book even if tracking is not your primary interest, as its approach to the math is very clear, yet still rigorous." + "The following code implements the same Kalman filter as before, but with a non-zero process noise. I plot two examples, one with `Q=.1`, and one with `Q=0.01`." ] }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_ball_with_q(q, r=1., noise=0.3):\n", + " y = 1.\n", + " x = 0.\n", + " theta = 35. # launch angle\n", + " v0 = 50.\n", + " dt = 1/10. # time step\n", + "\n", + " ball = BaseballPath(x0=x, \n", + " y0=y, \n", + " launch_angle_deg=theta, \n", + " velocity_ms=v0, \n", + " noise=[noise,noise])\n", + " f1 = ball_kf(x,y,theta,v0,dt,r=r, q=q)\n", + " t = 0\n", + " xs = []\n", + " ys = []\n", + "\n", + " while f1.x[2,0] > 0:\n", + " t += dt\n", + " x,y = ball.update(dt)\n", + " z = np.mat([[x,y]]).T\n", + "\n", + " f1.update(z)\n", + " xs.append(f1.x[0,0])\n", + " ys.append(f1.x[2,0]) \n", + " f1.predict() \n", + "\n", + "\n", + " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + "\n", + " p2, = plt.plot (xs, ys,lw=2)\n", + " plt.legend([p1,p2], ['Measurements', 'Kalman filter'])\n", + " plt.show()\n", + " \n", + "plot_ball_with_q(0.01)\n", + "plot_ball_with_q(0.1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AcHAwb731Fi+99BJZWVlMmjSJt99+u1/0VVYOHz7cI8/Yi4uLT7lgWwghBjtN\n09hVuYutZVtpcDZg1BlJDU3lwrQLCQ0IbXfcV8VN/Dl7P/X2tieVJkMrCeGlxIeXYjE5gLb64bMS\nz+L81PMB2Fi8kc8KP+t0UphH9ZASmsINY27ohU/a/5S1lPH83ucx6oztVoZzeByMiBjBtaOuPaVf\nyJqm8eftf8atdv6EV9M0QgNCuXXyrQAcrbHz5t5KsvMb0ACdAuekh3P1hFjSIgZ3h4nTUVZWRkJC\nQl8PQ/RjXd0ju3bt6vBHwqmSGmEhhOhhmqbx9uG32V+9n0BjIHpFj6qpHKk7Qm5dLksnLCU6MJod\nJc38Z1c5h6vtgBWToZWU6HwSwkvQ69ovOezyukgOTfa9njNsDkfrjlLYVNhupTWX14XZYOaKEV2v\n5DbYJQQlcPvk2/k4/2PyG/Pxql5CAkKYmzSXWQmzTvmplKIozEiYwacFn3Y6ac/hcXDpiEt9rxND\nYXzyPrzGEvIqk6lqTODzvHo+z6tndkooiybGkhXdef9jIUTvkER4gBjq/Rv9SWLpXxLPkztcd5h9\n1fs61KIadAZUVePvX31MU/NMDlbZAAgzG7hkdDCHml8kOKDjk0NN0wgzhzE87JtZ6TpFx03jb2Jr\n2Va2V2zH7rJjMpgYHz2e81LO63bJ4sHq2/dmhCWCa0dfe8bXPCvxLOpa69hevp0AfQAGnQGX14VH\n83B+yvmMjhwNtK1g98yuZ9r+EDEZGZN0gPTYPPKrkqhqTGVLYSNbChuZlBDM9ZPjGBfXfWlLfyA/\n62Iw6jYRrq+vZ8mSJXg8HjRNY+nSpSxYsIA1a9bw1FNPAXD//fdz7rnn9spghRBiINpUsqnTllz1\nLeEcrxpOoz0CsBFqNjAt2MbtC8ZjMerZUnohHx3/CIvB4vtK36260dC4cdSNHZ5k6hQdsxNnMztx\ndof3Ev6hKAqXDL+EucPmsrFkI03OJqIsUcwZNqddi7Z3jryDR/X4Vq0DsJhaGT3sKMOijmD0nMve\nUgu7y5rZXdbMeRnh3DIjkfBAY2dvK4ToId3WCJ9Yfs9isVBfX8+CBQvYuHEjF110EW+99RZOp5Mb\nb7yRdevWdThXaoSFEKLNX3b8pa0P8NcabGEcr8qkwda2OpRe5+SirEB+Pn0MFqO+3bmlTaV8WvQp\nNfYadIqO9LB0zks5b0hOfBsoHB4HK7au6HalPrPBzM3jbmNVTjUr91Xi8mpYTXp+OjWeBSOj0Ov6\nfhJRb5PNkyvPAAAgAElEQVQaYXEyvV4jbDAYfD3dmpubMZlM7N27l8zMTN/yfnFxceTm5jJy5OBs\nIC6EEGcqQB+A0+Ok2RHMsYoR1NuiADDo3CRHFRAWfIAfj7u5QxIMkBiSyOKxi3t7yOIMNLuacWtu\nAug6EW5xtWDQu0mIPMD8MRXsLEyivDGEp7eUsPZoHXeclcTwqI7fIggh/Ouk7dNsNhsLFy5k4cKF\nPPTQQ9TU1BAdHc2bb77JRx99RHR0dIeVQYT/Sf9G/5FY+pfE8+TSgieyv3gk2/NmUW+LQq9zkxZz\njNlZG0mNOU6kNYik4LanGRJP/+mrWFoMFnQn+fXa4m7hyW1PsrlkM3a1hKzELWQmbCPA2Mrhaju3\nvXeY//tlCTbXqS3A0Bt6I56qqp78IDEkaZrWI4uJnDQRtlqtrF69mnfffZcVK1b4lu+75pprfGto\n94c+cEII0d/YXV5e2lHGs5sCqW5MQUEjKbKA2SM2kRaTh0Hvwe62Mz91vvw7OogEm4KJs8Z13bvY\nbaekqQST3uQrn9DpFJIiGpia/gUZMWUArDpQzZK3D7Exv77PVxPrDVFRUb6lhIX4rrq6unZLSvvL\nKXeNyMjIICEhgcTExHbNk6urq4mOju70nFtvvZXk5Lb2PqGhoYwbN8434/TEX5by+tRen9jWX8Yz\nkF/PmTOnX41noL8eyvGcOH0i+6r3sWvvLpLMSVx6XlvrrI2bstndYGBzo5WGVg8AI4NcjBlRTKXj\nIHlFx1EUhYnDJ7Jw+ELqc+vJPpI95OM5mF7HueKoNFVi1pspLi4GIDk5Ga/qZW/+XiKNkfD1r86i\noiLf/gAjtNrf5n8SrmSfK4PcajvLPysgw+rh0R9NIDbY1C8+X0+9jo2NJScnB4PBQFhYGIBv9bET\nSZC8HnqvNU0jNjaWoKAgsrOz2b9/v++4oqIilixZwunqdrJcZWUlJpOJ8PBwqqurueKKK1i1ahVX\nXXWVb7Lc4sWLWbt2bYdzZbKcEGKwUjWVdw+/y/7a/aC1dWtwq27irPGMCb2c13Y3UNTQtpzx6Bgr\nP5uRwJjYto4CTo+TBmcDJr2JcHN4X34M0cOKm4pZnbeaipYKVE3FqG9bRKXF1UKzq7nL804slnJu\nynmsya3l39vLaHF5CTTquHXWMC7IjJBvEIT4lh6bLFdeXs7DDz/se33//fcTGRnJ3XffzaJFiwD4\n9a9/fVpvLL4f6d/oPxJL/xqK8Xz78NscqjnUbhU3lyuKjbkjeN9eAUB8sImbpydwdmpYu6QlwBBA\nrCG2y2sPxXj2lL6OZVJIErdOupVmVzMOj4NgUzAWg4V/7ftXt4mwpmkYdAZ0isKPRkVxVmooT28u\nJrugkT9uLGJrUSN3zEkm1HzKX+r6RV/Hc7CRePYP3f4UTZw4kdWrV3fYvmDBAhYsWNBjgxJCiP6q\n2dXMgZoDviS41WXmeNVwKhoSAAW9zsWFI/XcOmMUJv1Jp2GIISDYFNyu3d2YqDG+/tCdUVGZFDvJ\n9zrcYuTh89P49Fgdz2wpIbugkQOVh/jl2cnMSPZ/zaQQQ0m3pRFnQkojhBCD0eaSzawrWIdBsVJU\nk0ZRTSqqpkdRVIZFFJIac5yE4HBuHn9zXw9V9FMe1cOftv8Jr+r1LZRygtPrJDM8s8tV8CqbXTz5\nRSH7KloAWDAykltmJHbaek+IoeJMSiPkcYUQQnwPDncr1Y3JbD06h4LqDFRNT0xIOTMzs8mMP4JR\n70HVZNa76JpBZ+CWCbdgNVqxuW14VA8urwu7205GWAZXjbyqy3Njg02s+OFwfj49AaNOYU1uLf+7\nKpeDlbZe/ARCDB6SCA8QJ2bVijMnsfSvoRTPAxUtrNwVw9HySbg8ZoItjUxJ38bY5H1YTA6gbaJT\nfFD8ab/HUIpnT+vPsQwzh/GLKb9gyfglTImbwlmJZ3H39Lu5fsz1GHTd1/7qFIX/GR/L3y/LIj3C\nTFmTi19+cIQXd5ThUXuuzVp/judAJPHsH3q30l4IIQagymYX/9peyobjDQCYjU5SY3KJD6vgu5P3\nVU3lnKRzen+QYsBRFIWU0BRSQlNO6/y0CAt/uzSLV3aWs3JfFW/sqeRojZ2Hz0+TUgkhTpHUCAsh\nRBccbi//3VvJ2/urcHk1THqFK8fHcmGWmf8ceB6b2+ab8OTyuvBqXq4aeRVjosb08cjFYGFz21hf\ntJ7jDcfxal4iLZHMS55HQnBCu+P2lbfwu8/yaWz1kBUdyPILM3q9q4QQfeVMaoQlERZCiO9QNY3P\njtXx7+3l1NrdAJyTHsaS6YnEBJmAtglPOyp2kFOdg4pKgjWBc5LPIcgU1JdDF4NIpa2Sf+75Jxoa\nJn3bfadqKg6Pg4vTL2Z24ux2x5c2tnL/R3lUtrgYFhrA4xcNJzbY1BdDF6JXyWS5IUBqifxHYulf\ngy2emwqK+MlbO3jyiyJq7W5GRAXyl4WZ/Pq8NF8SDG0TnmYmzGTJhCX8fMLP+dHwH/klCR5s8exL\nAzmWmqbx2sHXMOgMviQY2hZvsRqtfHT8I+ocde3OSQw189dLRpAeYaak0cmdq4+QX+fw25gGcjz7\nI4ln/yCJsBBCAAX1jfz03XX87tNaKpoMGA2tZMTtYMbw7YyICujr4YkhprCpkHpHfZcryAXoA1hf\ntL7D9shAI3/8YSbj4oKotbu5+4OjHPi61ZoQoiMpjRBCDGk2l5c391bw1r4KVE2HTvGSHFVAclQ+\nBr0Xl9dFSkgKi8ct7uuhiiFkfdF6NhVvavc0+LvCzeHcMvGWTvc5PSqPry9gS2EjJr3Cg+elMStF\nFt8Qg5OURgghxPfkVTU+zK3hppUH+e/eKlRNR0xoOTMys0mPPYZB7wXApDdxrOEYNfaaPh6xGEqs\nRise1dPlfk3TMOqMXe4PMOh4+Pw0Ls6KxOXV+M2nx/nkSG1PDFWIAU0S4QFCaon8R2LpXwMxnjtK\nmvjfVbk8lV1MQ6uH6CA7k9O+ZGzSPiym1g7HB+gD2Fa+rVfGNhDj2V8N5FiOjx6PQd911weHx8GU\nuCl4VA9NziZaPR3vW71O4c45SSyaGIuqwZ82FvHfvZVo2ul9ETyQ49kfSTz7B+mtIoQYMgrrHfxz\nWxnbS5oAiA0ysWR6Avm296mwNXV5nk7R4VbdvTVMITAbzEyPm86XZV/6WvSd4Pa6CTOHcbTuKKvz\nVuP0ONEpOuKt8fww44ckhXzzFbGiKNw0NYFwi5FnvyzhX9vLaPWoLJ5y+ou+CDGYSI2wEGLQq3e4\neWVXBWtya1A1CDTquHZiHJeNicZk0LGxeCOfF36O2WDu9Hyby8YNY29gRMSIXh65GMo0TePzos/Z\nWrYVm8uGoigYdAZSQlJodDbS7GpuV0OsaRoOj4Obxt1EWlhah+t9fqyOFV8UomrwkynxXDsprjc/\njhA95kxqhOWJsBBi0HJ5VFYdqOaNPRXY3So6BRaOiuKGyXGEWb6pr5yZMJMvir5A07QOs/Q1TSPM\nHEZmeGZvD18McYqicH7K+fwg6QcUNxXj8rpIDE5kZ+VOPi/8vMOTYkVRsBgsrD62ml9M/UWH6503\nPAINWLGhkJd2lmPQK1w1PraXPo0Q/ZPUCA8QUkvkPxJL/+qP8dQ0jQ159dz89iH+tb0Mu1tlelII\nz10+ktvPSmqXBEPbhLjrRl+HR/Xg9Dh92x2eth6sPxn3ky7bWPlbf4znQDVYYmnQGUgLSyMrMosg\nUxD7qvZ1SIJPUBSFKntVl5M7zx8ewd1zkwF44asyVuVUnfI4Bks8+wuJZ/8gT4SFEINKYb2Dv2wq\n5mCVDYDUcDM/n5HI1GEh3Z6XHp7OPTPuYXPJZvIb81FQGBU5iunx0zHqu56dL0Rv62xi3Ld5NS8t\nrhaiAqM63T9/RCRuVeOp7GL+79ZSDDqFhaOje2KoQvR7UiMshBg0vixs5A8bCnC4VcItBhZPiefC\nEZHodb3zNFeI3vDsrmdpcnU9udPmtvHLab8k3Bze7XXeO1DNM1+WAHDX2clcnBXp13EK0VukRlgI\nMaRpmsabeyt5aUc5GnBOehh3zkkm0KT3HeP2uslvyMfpdZISmkJIQPdPiIXor6bGT+WDvA8INAR2\n2KdpGvHW+JMmwQCXjonGo2o8t62Uv24qwqCDCzIlGRZDi9QIDxBSS+Q/Ekv/6ut4Oj0qf9hQyIs7\nygG4aWo8D5yb6kuCNU1jXcE6Vny1gpcPvMx/c//LH7/6I//e92/sbnsfjrxzfR3PwWSwxnJq3FRS\nQ1I7lEiomopbdXNF1hWnfK0rxsXw02nxaLT1GV6fV9/lsYM1nn1F4tk/SCIshBiwqm0ufvnBEdbn\n1WMx6nj0gnQWTYxrN7FtbcFaskuy0St6gk3BBJmCCDQGUtZSxnN7nut29S4h+iOdomPx2MWcPexs\njDojrd5WPJqH5JBkbpt8G7HW79cJ4poJcdw4OQ5Vgyc2FJBd0NBDIxei/5EaYSHEgFDnqKPKXkWQ\nMYjE4ERyq+38Zt1x6hwe4oNN/GZ+Oqnh7WfSOz1OVmxb0eVkN7vbzo+G/4jp8dN74yMI0SNUTUVB\nOaPOJpqm8dLOct7YU4lJr/DnhSMYEdWx9EKI/khqhIUQg1ado443c9+kvKUcVVMBsDtGkVs6Bq8K\nE+KDePj8NELMHf85O1h7EJfq6jIRDjQGsrdqryTCYkDTKWf+5a6iKPxkSjx1djefHKnj0bXHefqy\nLCIDpWOKGNykNGKAkFoi/5FY+ldPxrPF1cKze56lobUBq9FKkDGYyropHChuS4Jnpyo8fvHwTpNg\naOsDrFf0ne47ob+VRsj96T8Sy+9HURRuPyuJMbFWauxufrPuOC6P6tsv8fQviWf/IImwEKLf+qzw\nMzRNQ6focHsN7C2cTFFNGgoqWQkHCA1dj76bb4NTQlLwaF0nul7VS6RFZsmLwc3tdfNl6Ze8euBV\n3jz0JgWNBWha51WRJr2OR+alERNkJLfazl+yi7o8VojBQGqEhRD91p+++hNu1Y3dGci+wknYXUEY\n9S7GJu8h3FpPi7uFO6fc2eXCAQB/2/k3WlwtnX59bHPbuGPKHd2eL8RAdrz+OK8feh2X6iLQEIim\nadg9dhKDE/npuJ9i0ps6PS+v1s5dq4/S6lFZMi2BqybIUsyi/zqTGmF5IiyE6Lfcqpva5kh25M3E\n7grCGtDM1IythFvbWjxpmobT6+z2GtePvh6g3dLJqqbS4m7h4vSLJQkWg5bNbePVg6+iV/S+nsOK\nomA1WqmyVfHGoTe6PDcjMpB7z0kB4F/by9ha1NgrYxait0kiPEBILZH/SCz9q6fiqWkaVQ0j2Fs4\nBY9qJDqkkinp27CYHL5jTHoTEZaIbq8TYYngrml3MWvYrLbWaYZAX5up2Ymze2TsZ0LuT/8Z6rH8\nougLgE67SZj0Jo43HKfJ2fUKdXNSw1g8pa3H8B/WF/DuZ5t7aqhD0lC/P/sL6RohhOh3nB6Vp7KL\nyClJAyA1Oo+0mGN8+/e5R/WQHpaOxWDp4irfsBgszE+dz/zU+T01ZCH6naKmoi5LH044WHuQmQkz\nu9x/7cRYCuodfHG8gf+WmJnX6ulycqoQA5E8ER4g5syZ09dDGDQklv7l73hWtbQtkvHpsXoCDDrm\njawkNmIv8M10hlZPK1ajlf/J+h+/vnd/IPen/0gsT+IUZggpisLdc1PIjLJQ79bxu8/y8agyec4f\n5P7sHyQRFkL0G/vKm1n2/w5ztMZBfLCJv10ygl+ddSHXj76eqMAoAgwBBJuCOS/lPG6bfNspPQ0W\nYqhKD0/vvoZegTFRY9ptanY1s75oPWvy1nC0/iiapmE2tK3aGGExsLe8hWe/LOnhkQvRe+T7jQEi\nOztb/nr0E4mlf/kjnpqm8d7BGv6xtQRVgymJwTxwbqrvK9isyCyyIrP8MNr+T+5P/xnqsTx72Nls\nK9uGpmkd6oRdXhcjIkYQbAoG2iaQrjqyin3V+9ApOvSKni2lWwgzh3HDmBuItcZyWUwzr5QE8sGh\nGpLDzFw2JrovPtagMdTvz/5CnggLIfqUy6Pyx41FPPtlWxJ81fgYll+YIXWIQpwhi8HCT8f+FJS2\n5cQ1TWvrmOJqISkkiauyrvIdu/rYanJqcrAYLAToAzDoDASZgnB73Ty/73kcHgfDLCp3n50MwD+2\nlrBNOkmIQUD6CAsh+kxVi4vffprPkRo7AQYdd5+dzDkZ4X09LCEGFa/qZV/1Po7WH8WkNzEzYSZx\n1jjf/lZPKyu2rehyYp3T4+SsYWcxL3UeAK/sKueVXRWYDTr+sjCTjMjAXvkcQnTlTPoIyyMXIUSf\n2FfewvLP8mlo9RAbZOLRC9LkF6oQPUCv0zMpdhKTYid1uv9w3WFcXlenibCmaVQ7qvn3/n+zs3In\nAfoARkWO5pz04Ww43sjDnxznb5eOIMrafXcKIforKY0YIKTfoP9ILP3r+8ZT0zTeP1jNfWuO0tDq\nYVJCMM9cliVJ8Nfk/vQfieWp8aieTlde1DSNfVVtT5KdHieFhYW0elrZWvolhsBVjI6xUGN388ja\n4zjc3j4Y+cAm92f/IImwEKLXuDwqf95UxN+3lODVYERsOcGhK3l69xP8a9+/KGws7OshCjHkDA8f\n3un24uZi6p316BU9QaYg3/YAQwAu1cHY5N0khJg4Vuvg8fUFeKWtmhiApEZYCNErqm1t9cCHq+0Y\ndBopsdtJjqjzzWbXNA27x86PM3/M5Dj5t0OI3vTvff+mtKUUo87o27atbBtu1Y1bdTMrYRZmg7nd\nOS6vi+tH3smv1hTQ7PTy47HR/O/MYb09dCHOqEZYnggLIXpcTkULt/2/wxyuthMTZGB00gZSIuvb\ntXRSFAWr0coHeR/g9HTT+1QI4XfXjr6WsIAwbG4bmtb2fMzuseNRPYyOHN0hCQZwqS6CLK38n3lp\nGHQKq3Kqef9gdW8PXYgzIonwACG1RP4jsfSvk8Vz3dFafvXhUeodHiYmBHHFxDJCAlu6PF5F5avy\nr/w9zAFD7k//kVieOrPBzLLJy7hm1DUkBCUQExhDUnASZw07i1hrLABFRUXtztGhw6w3Mz4+mLvO\nbnsa9+yXJXxVLG3VToXcn/1Dt10jKisrufPOO2lubsZkMnHPPfcwe/ZsRo0aRVZWW3P7adOm8eCD\nD/bKYIUQA8ua3Bqeyi5GAy4fG83PpifyxqFtXbZpAjDrzZTbyntvkEIIAHSKjjFRY3yrzYUGhHKo\n9lCnx2qaRpw1jpCAEAAuyIyktNHJ63sqeezzAv7yoxGkR8rKj6L/67ZGuLa2lpqaGrKysigrK+Oa\na65h48aNTJo0id27d3d7YakRFmJoe/9gNX/f0rYU68+mJ3Dl+LanSquOrOJgzUH0On2n57m9bqbF\nT+Oi9It6baxCiI5aXC08tfMpFJR2XSU0TaPV08risYtJD09vt/3x9QVsON5AlNXI05dkEWk1dnZp\nIfyqx2qEIyMjfU9+ExIScLvduFyu03ojIcTg51W9aJrGO/urfEnw/85M9CXB0Lbsa6u3tetraF7O\nGnZWj49VCNG9IFMQyyYtIzowGofbQZOriRZ3C1ajlRvH3tguCYa2Ov975qYwOsZKjc3Nw2vzpK2a\n6PdOuUZ406ZNjBkzBpPJhMvl4vLLL2fRokXs2LGjJ8cnvia1RP4jsfSvTZs2sblkM3/Z/hd+u+W3\n/Pz9N3huWykAvzgriR+PjWl3fFRgFBNjJnaaDDs8DqbGTyXYFNwrY++P5P70H4nlmQszh/GzCT/j\nnhn3MM0zjV9O/SW/mPoLMsIzOj3eZNDx6AVpxAe3tVX7w4ZCaavWBbk/+4dTWlmuurqaFStW8Oyz\nzwKwceNGIiMj2b9/P7fddhvr1q3DZJJVZYQYajRNY33deryKF4vBQkXdWAqrhwMaGXG7GRFrBaI6\nnHf5iMsJM4exvXw7Le4W0NrqEeelzGPOsDm9/jmEEN0LNgUTbYomwhJx0mPDLEaWX5jBnauP8GVh\nI89/VcpSaasm+qmTJsJOp5M77riD++67z1d/ERkZCcC4ceOIiYmhpKSE9PT0DufeeuutJCcnAxAa\nGsq4ceOYM6ftl9yJv4Tk9am9PrGtv4xnIL+eM2dOvxrPQH4dPyYed7ibmtJa6pxTqXe1JcEx5g0o\n9mP8v6O1/Gr6r9i8eXO78zdv3kwAAdx71r3Ut9azbds2gl3BnJ10dr/6fHJ/ymt5ffqvHzl/Ag98\nnMe7OdU4qku4a+HMfjU+eT1wX+/fv5/GxrbuJEVFRSxZsoTT1e1kOU3TuPvuu5k6dSrXXnstAI2N\njQQEBGA2mykpKeHaa69l7dq1mM3tewzKZDkhBr+X979MaXMZx6uyKKpJQ0FldNJ+YkMrgLbJNj8Z\n95MuV64SQgxu647W8uQXRegU+O38dKYnhfb1kMQg1GOT5Xbu3MnatWtZuXIll112GT/+8Y85fvw4\nl112GZdccgm33347jz32WIckWPjfib+IxJmTWPpPi9vG7mPDfEnwmKS9viQYwKAzUG2XBvvfh9yf\n/iOx9K/TiecFmZFcPykOVYPHPi8gr9beAyMbmOT+7B8M3e2cOnUqOTk5HbZ//PHHPTYgIcTAoGoa\nB0qG0+iKRlFUxiXtISqkfdLrUT1EmE9eUyiEGPhOrEj37RUjAW6YHEdpk5P1efU8/Mlx/nbpCKKs\nMq9I9A/dlkacCSmNEGLw8qoaf80u4pMjdSiKl/HJe4gMrun02Htn3NuuB6kQYnApaynjk/xPKG0u\nxaN6CDeHMyNhBjPiZ/iSYpdX5f41x8iptJERaeHPP8rEYuy8l7gQ31ePlUYIIcR3eVWNP20s5JMj\ndQToFc4dWYDVUtLuGE3TcHgcLEhfIEmwEIPYsfpj/GPPP6hoqcCgM2A2mHF4HHx0/CPePfKu7ymx\nSa/j0QvSSQwJIK/WwRMbCn37hOhL8htqgJBaIv+RWJ4+j6rxhw0FfHqsHrNBx2MXZTBbjWFW4ix0\nig67247D4yA0IJTrR1/P+JjxfT3kAUfuT/+RWPrXd+OpaRrvHnkXi97SoRzCYrCwu2o3hU2Fvm0h\nZgPLL0zHatKzpbCRD3Nre2Xc/ZXcn/1DtzXCQghxgtur8vj6ArILGgk06njswgzGxAWRnafjwrQL\nuSD1AmxuG0adEbNBJtAKMdjlNeTR5GwiyBTU6X6rwcoXxV+QGprq25YYauaOs5L4/foCnttawvj4\nIJLD5N8L0XekRlgIcVIur8ryz/LZWtREkEnP7y/KYGSMta+HJYToQ1tKt7A2f223f/iGBIRw66Rb\nO2xf8UUhnx6tY3ikhacuGYFRL19Qi9MnNcJCiB7j8qj8Zl1bEhwcoOeJBcMlCRZCEB4Qjlfzdrlf\n0zTM+s6T5GWzhhH39TLM/9lZ3lNDFOKkJBEeIKSWyH8klqfO5VF59NPjbC9pItRs4MkFmWRGBbY7\nRuLpXxJP/5FY+td34zkiYgRWY9d/FNs8NmYnzu50n9Wk575zUtApsHJfFXvLmv061oFA7s/+QRJh\nIUSnTiTBO0qaCTUbWLFgOOmRlr4elhCin9Dr9MxPm4/D4+iwz+l1khGaQVZEVpfnj4kN4tqJcWjA\nE18U0uz09OBoheic1AgLITroLAlOi5AkWAjRUW5tLp8Wfkq1rRoVFavRyrjocVyUdhF6Xfe9gr2q\nxi8/OMKhKjs/SAvj1+elduhAIcTJnEmNsHSNEEK04/SoPLruODtLJQkWQpzcyMiRjIwcic1tw6N6\nCDYFn3L/cL1O4b5zUvnfVbl8kd/A9GN1XJAZ2cMjFuIbUhoxQEgtkf9ILLvm9Kj8n28lwU/+8ORJ\nsMTTvySe/iOx9K+TxdNqtBIaEPq9F9FJCAlg2axhAPx9SwnlTc7THuNAIvdn/yCJsBAC+CYJ3lXa\nTNjXSXBquDwJFkL0vAsyIzg7LQyHW+WJDYV4VVl1TvQOqREWQuD0qDz0yVH2ltsJNev54w8zSZEk\nWAjhR3a3naP1R1E1leHhwwk2Bbfb39TqYem7udTY3dw4OY7rJ8f30UjFQCM1wkKI01bZUsc9a/ZT\n2RSCQd9KSlw2HxZkc5nxMhKCEvp6eEKIAc6rell1ZBU5tTl4vB4URUGv6BkePpyrRl6FSW8C2pZg\n/tU5Kdy35hiv7a7grNQwmZ8gepyURgwQUkvkPxLLb1TbGrh99U4qm0IwGZxMSdtBVJCXxtZGntvz\nHOUtJ290L/H0L4mn/0gs/et04/nmoTc5WHsQs95MkCkIq9GK2WDmeMNxXs55GU375ovpSQnB/GhU\nFF4N/rSxaFCXSMj92T9IIizEENXqUfnVmgM02KIwGZxMSt2O1WwDQFEUzHozH+R90MejFEIMZDX2\nGnLrcn1Pfb/NpDdR1FREUVNRu+03T0sg2mrkSI2dd3OqemuoYoiSRHiAmDNnTl8PYdCQWLYlwY+s\nzaOsMbAtCU77Jgk+QVEUSppLaPW0dnstiad/STz9R2LpX6cTzy/LviRAH9Dl/kBDIFvKtrTbZjXp\nuWNOW73nyzvLKW0cnF0k5P7sHyQRFmKIcbi9PPxJHnvKWjDqW9uS4ABbp8eqmnrSRFgIIbri9DrR\nK10vqqEoCl7V22H79KRQ5g0Px+XV+MumIlRt8JZIiL4lifAAIbVE/jOUY+lwe3lk7XH2lrcQYTEw\nLWNXl0kwQIA+AKvR2u01h3I8e4LE038klv51OvHMCMvodAnmE1q9rSQFdz7bf+nMYYSZDeyraGFN\nbu33fu/+Tu7P/kESYSGGiHZJcKCBJ3+YyezkTJzezr929KgeMsIzMOqNvTxSIcRgMT56PBajpd2E\nuG/To2dmwsxO94WYDdw2u22hjRe+KqWqxdVj4xRDl/QRFmII8Koaj647zrbiprYkeEEmSWFmPKqH\n5/c+T4WtAovhmzZFTq+TIFMQt066td12IYT4voqbinlx/4sAvklzbtWNV/WyaPQisiKyujxX0zR+\n8ygFC4AAACAASURBVGk+WwobmZ4Uwu/mp6MoSq+MWwwcZ9JHWH/77bc/6t/htGlqaiI+XpphC9HX\nNE3j71+WsD6vnpAAPX/60QiSwswA6BQdk2InoVf01NhrcKpOAvQBTIydyNUjr8ZsMPfx6IUQA11o\nQChT4qbgUl04PA5MehMjwkdw7ehrSQxOBNrmIxypO/L/27vv8LjKM23g95k+I41G3SqWZMuWLRfZ\nuHcbiMEl4DVeIBgSIFkIgUAC8WYTyO7H5kvILqnkS5YQSAJhE+LQQ8cG3LvlJhe5S6PeNdL0dr4/\nhASyRm30jqbdv+va69ozZ8qT28fWw9Ez74szrWfg9DiRqk+FJEmQJAkl2Yn44GwLKtqcyDVpUci1\nhekKdXV1MJlMQb2Wd4SjxO7du/kNU0FiOUtZlnGy+ST21OyB1WWFWqWGzToH288nQK2U8NM1EzEt\nK1HoZ8ZynuHAPMVhlmKFKs9TzafwzoV30OnuhFqhhsfvQaImETdMuAHTM6YDAD4424Jf7jIjSavE\nczdPQYo++ke2eH2KM5I7wpwRJooRsizj5fKX8XL5y2hztMEre1HZnITt57u+7PbtpVnCm2AiopG4\n3H4ZL5e/DBkyEjWJ0Kq0SNR0/Tv1cvnLuNh2EQCwalIqZuUY0eHy4el91eEsmWIMG+Eowf9qFCdW\nszzWeAynmk8hQZ0ASZJgsSfjdHUJAGB85hnUuT4MyefGap7hwjzFYZZihSLPLRVboFMGHsHSq/TY\nWrkVQNcyaw8vy4NWpcCOS+3YW9kuvJbRxuszMrARJooR+2r39Xyxze4y4ETlLPhlJXJTzRiXYcbl\n9suwe+xhrpKIqIvX70WttbbfL79JkoQ6ax08Pg8AINuoxdfmdn336Dd7qmFz911/mGi42AhHCa43\nKE6sZtnh6oAkSXB71TheORsenwZpiU0oyi6HJAFunxutzlbhnxureYYL8xSHWYolOs9AG2kEfJ78\n2fPWTc1AcYYBLXYP/nioVmg9o43XZ2RgI0wUI9QKNXx+BcrMs+BwJyBR14FpecehkLq+D6uQFFwK\njYgihkapQZImacDnGDXGXls0KxUSHlmWD6UEvHOmGafqraEuk2IcG+EowVkicWI1y4kpRThVNQ0W\newq0agdmFhyBSvnZnZR0QzpSdanCPzdW8wwX5ikOsxRLdJ6SJGFO1px+t3F3ep2YPWZ2n9GJ8al6\n3DpjDADgV7ur4Pb5hdY1Wnh9RgY2wkQxoqZ5Bpo7c6BUeDCz4Ai06s92jLN77bhu3HVciJ6IIsqK\nvBWYnDYZNretZ/c5WZZhdVsxKXUSrsm/JuDr7piVhdwkLcztTrx8vGE0S6YYw0Y4SnCWSJxYzPLt\n001481QblBKweOIlKJSNsLgsPety3jr5VkxLnxaSz47FPMOJeYrDLMUKRZ6SJOG24tvw1ZKvIicx\nByatCTmJOfhqyVexccpGSJIEj8+DfTX78HL5y3j34ruwuCzQqBR4eGnXurF/O9YAc1vgu8qRjNdn\nZFCFuwAiGpkDZgv+59N1NR9elo9Vk2ahw9WBFkcL9Go9xhjG8E4wEUUsSZJQmFKIwpTCPudONZ/C\n6+deh9fvhV6lh9fvxYHaA5iZORMbJm3A6klp+OBcC57abcbPbyiCgv/W0TBxZzmiKHa+2Y5N75yH\n0+vHHbOycNccbmtORLGh0d6I35b+Fga1oc85p9eJRbmLsDjnC7jn1TNoc3jxrSV5uGFKehgqpXDj\nznJEcajR6sZ/fHgRTq8fKyem4M7ZWeEuiYhImK0VW6FTBd5sQ6fSobS+FHo18MCisQCAPxysQYvN\nM5olUgxgIxwlOEskTixkaXP78IMPL6LV4cXM7EQ8siw/bOMPsZBnJGGe4jBLsUY7z7rOOiik/tsU\nq8eKBlsDlo9PxoK8JNg9fvzPvqpRrHBkeH1GBjbCRFHG4/Pj/350CZVtTuQn6/B/Vo6HWsm/ykQU\nW2QMMrkpdz1HkiQ8tCQPerUCuyss2FMR/dsv0+jhT88owfUGxYnmLGVZxq93V+ForRUpehV+vKoQ\nRm14v/MazXlGIuYpDrMUa7TzHJMwBn65/zWCDRoDxhi61hPOTNTgq3NzAAC/3Rsd2y/z+owMbISJ\noshfj9Zjy/lWaFUK/Oj6Ccgyagd/ERFRFFpZsLLfzTZcPhdmZsyEWqnueezGKek92y+/cDi6t1+m\n0cNGOEpwlkicaM1y28VWvHikHgoJeOyacZiU0feb1OEQrXlGKuYpDrMUa7TzzDHmYH3Reji9Tri8\nXRsE+fw+WN1WTEyZiC9O+GKv5ysVEh5emg+FBLx1uhnljbZRrXe4eH1GhgEb4YaGBmzcuBE33HAD\nNmzYgL179wIA3nvvPaxatQqrVq3Ctm3bRqVQonh2ptGGn+80AwDuW5CLRQWmMFdERBR6s7Nm43sL\nv4elY5dirHEsitOK8eCcB3HH1DsCfpGuME2Pm0syIQN4ancVfP6QrBBLMWTAdYRbWlrQ3NyMyZMn\no7a2Frfddhs+/vhjrF69Gq+88gpcLhfuvPNObN26tc9ruY4wkRiNVje+9Y+zaHV4sbY4Dd9ekscN\nMoiI+uHw+PD118rRYHXj6/NzcPOMMeEuiUJsJOsID/gtm7S0NKSlpQEAcnJy4PF4cOzYMRQVFSE1\nNRUAkJWVhfLychQXFwdVABH1JssyLrVfwsnmkwA0ePdEXs8yaQ8uZhNMRDQQvVqJh5aMxb9/eAl/\nPlKPZeNTMMaoCXdZFKGGPCO8a9cuTJs2DS0tLcjIyMDmzZvx/vvvIyMjA42NjaGskcBZIpEiOct2\nZzueOvwUXjj5Ak42ncLfj8ioaPMgUevC968eC5Ui8prgSM4zGjFPcZilWNGU5/w8E1YUJsPl9eO3\ne6sgy5E3IhFNecayIa271NTUhJ/+9Kd4+umncerUKQDAbbfdBgDYunVrv3eoHnjgAeTn5wMATCYT\nSkpKepYL6b4AeDy047Kysoiqh8fij32yD/s1++Hz+9BS14IW51y0ubOhUniQpHwNT219Fz9a/6OI\nqZfHPI70426RUk+0H3eLlHoGO/7GwgU4XN2JA1Ud+MP7+3Hv2kURVV+05RlJx2VlZbBYLAAAs9mM\ne+65B8EacEYYAFwuF7761a/igQcewNKlS1FaWornnnsOzzzzDADgK1/5Cn7wgx/0GY3gjDDR8Bys\nO4h3LrwDg9qA+vZsnK6eAQl+zCg4gjRjC2weGx6Z+whS9anhLpWIKCq8c6YZ/29PFVINKvzx5qlI\n0CjDXRKFwEhmhAccjZBlGY8++ihuuOGGnk68pKQE58+fR2trK+rq6tDQ0MD5YCIBTjafhEFtgMVu\nQnnNNABAUfZZpBlbAABqhRpHGo6Es0QioqiytjgNUzINaLV7ubYwBTRgI1xaWootW7bg5Zdfxvr1\n63HTTTehvb0dmzZtwsaNG3H33XfjscceG61a49qVv0qh4EVsljLgdOtQZp4Fv6xEbqoZuanmntOS\nJMHr94axwMAiNs8oxTzFYZZiRWOeCqlrbWHlp2sLn4mgtYWjMc9YpBro5Ny5c3Hy5Mk+j69duxZr\n164NWVFE8Sg3cTzeOi7B7dUiJaEFRdnl+Pz4vcvnQkl6SfgKJCKKQuNTu9YW/vuJRvx6txm/XV8c\nkV88pvAYdEY4WJwRJho6vyzjP7dewH6zFXqNDXMLD0Ct8vSc9/l9MOlMeHD2g2GskogocsiyjMvt\nl3Gw/iC8fi8mJE/A3Ky5vbZd7ub0+nHvq2fQYHXj3vk5uIVrC8eUkM0IE9HoeOFwHfabrTCoJUwd\nexA+dALo+ofe5rFBr9bj7ul3h7dIIqII4fK68MyxZ/D8yedxuf0yqjur8cHlD/DkgSdRYano83yd\nSoGHlowFAPz1aD06nJE3ZkbhwUY4SnCWSJxIy/Kj863YfLwBCgn4PysL8cMVD+LagmuRnZCNXGMu\nbi2+FQ/PfRiJmsRwlxpQpOUZ7ZinOMxSrEjK86XTL6HZ3owEdULPEq56lR5KSYkXT74Iu8fe5zXz\n80yYnWuE3ePHK2Xh3/8gkvKMZwPOCBNRaJ1usOFXu7q+EPfAorGYnZsEAFietxzL85aHszQioojU\n5mjDJcslJKgT+pyTJAkyZOys2onVhav7nL97TjaO1HTizVNNuGlaBlINfccoKL7wjnCU6F6+jkYu\nUrJs6HTjP7degscvY93UdKybmhHukoISKXnGCuYpDrMUK1LyPNN6Bkqp//WAtUotKjsqA54rzkzA\nonwTXF4//n68IVQlDkmk5Bnv2AgThYHD48PjWy+i3enFrBwj7l84NtwlERFFBQldd32DddecbABd\nm200Wt2iyqIoxUY4SnCWSJxwZ+mXZfz3tkpcanVirEmLf//COCijeCmfcOcZa5inOMxSrEjJc1r6\ntAHPO71OTEye2O/5wjQ9VhQmw+OX8dej9aLLG7JIyTPesREmGmXPH6rFPrMFRq0SP7q+EEYtR/WJ\niIYqSZuEopQiuHyuPudkWYZKocKSsUsGfI87Z2dDIQEfnmtBjaXv+1D84DrCRKNo6/kW/GyHGQoJ\n+K81EzErxxjukoiIoo7H58FfTv8FF9suwqA2QIIEh9cBg9qAO6ffiZzEnEHf4+c7KrHlfCu+MDEF\n37t6XOiLppAZyTrCvBVFNErONtnw1O4qAMCDi/PYBBMRBUmtVOOrJV9Fva0e+2v3w+PzYFLqJJRk\nlEAhDe2X3V+enYVPLrbhkwtt+NLMMRiXog9x1RSJOBoRJThLJM5oZWl1W/GP8//ALw/9Ej/e8yv8\n2/tl8Phk3FCcjhumpI9KDaOB16ZYzFMcZilWJOaZlZCF9UXrcUvxLZiZOXPITTAAZBm1WDM5DTKA\nF0vrQldkPyIxz3jERpgoBJrtzXjq8FM40XQCTq8HJ8wz4HBrkahrwbjME+Euj4iIANx+VRY0Sgm7\nKyw419x3Ew6KfZwRJgqB35T+Bla3FZIk4XzdZFS1jING5cK8CfvgQQvunXEvCkwF4S6TiCjuPXug\nBq+WNWLe2CQ8sXpCuMuhIIxkRph3hIkEa7A1oMHWAEmSUN+ehaqWcZDgx/S8Y9CqXUhQJWC7eXu4\nyyQiIgC3zsiEXq3AoeoOnKq3hrscGmVshKMEZ4nECXWWNdYaSJIEqzMR5TXTAQBF2eVITmgH0LUF\nqMVtCWkNo4nXpljMUxxmKVas5pmsV+OmaV07e74wirPCsZpntGEjTCSYUW2E26vEicpZ8MtKZCXX\nIDe1qtdzNApNmKojIqIr3VySiQSNEsfrrDjXxFnheMJGOEpwT3JxQp1lQdJ4VDYshtNjgFFnweSc\n05A+t3Gcw+vAzMyZIa1hNPHaFIt5isMsxYrlPBO1KqyelAoAeONU46h8ZiznGU3YCBMJ9tKxRrRa\nM6BSujA9/xiUCn/POY/fg1RdKuZlzwtjhUREdKV10zKgkIAdl9rRYveEuxwaJWyEowRnicQJZZZ7\nKtrx0rEGKCTgzrkqJGo96HR3wuKywOlzYrxpPO676j6oFLGzlw2vTbGYpzjMUqxoydPr9+JIwxG8\nf+l9HK47DI9vaE1ttlGLxQUmeP0y3jnTHOIqoyfPWBc7P42Jwszc7sTPdlQCAL42Lwe3loyBLM9B\no72x506wQW0Ic5VERLHrWMMxvHvpXTi9TmiVWrj9bnxw+QNcN+46LMhZMOjr10/LxO4KC94504yN\nM8dAo+L9wljHdYSJBLC7fXjoH2dRZXFh+fhk/ODacZA+PxhMREQhdbHtIl489SL0qr5bJdu9dtw6\n+VZMz5g+4HvIsoxvvnkWF1oc2LQ8H6smpYWqXBKI6wgThZEsy/j5zkpUWVwoSNFh0/J8NsFERKNs\na+VW6JS6gOcMKgO2mbcN+h6SJOGm6V1Lqb1xshGyHJJ7hRRB2AhHCc4SiSM6y83HG7C7woIEjRL/\nuXI89Gql0PePdLw2xWKe4jBLsSI5T7/s79nIqD/NjmY4vI5B32tFYQpS9CpcanXieF3oNtiI5Dzj\nCRthohE4XN2BFw53LcD+vasLkGsKfDeCiIhCR5blQe/eyrIMn9836HtplArcMCUdAPDGqSYh9VHk\nYiMcJbjeoDiisqzrcOG/tlVABvCV2VlYmG8S8r7RhtemWMxTHGYpViTnqVQokaJLGfA5SdokJKgT\nhvR+NxSnQ62QsL/SgtoOl4gS+4jkPOMJG2GiIDi9fvzwo8vodPmwIC8Jd8zKCndJRERxbVHOIjg8\ngUcfnD4n5mbNHfL3N1IMalw9IQUygH/wrnBMYyMcJThLJM5Is5RlGU/tMuNSqwO5SVp87+oCKOL4\ny3G8NsVinuIwS7EiPc952fMwJ3sOrB5rzwiEX/bD6rFiSuoUrMhbMaz3u2la15fmPjzXApt78JGK\n4Yr0POMF1xEmGqY3TzXhk4tt0KkUePy68UjU8q8REVG4SZKEdRPXYX72fOww70CnpxMJqgQsH7sc\nuUm5w36/iekGzMhKxIl6K7aca8FN0zNDUDWFG9cRJhqCFkcLWh2tqLXo8F+fNMMvA/9+7TgsLxx4\nJo2IiKLX7op2/N+PLiMnSYM/3jwVSkX8/vYvko1kHWHeyiIaQK21Fq+dfQ31tnq4PFqcNl8Hv6zD\n9ZO0bIKJiGLconwTxiRqUNvhxsGqDiwqiM8vRccyzghHCc4SiTPULJvtzXju2HOwuq1IUCehsmEp\nvD4dUhKaYZH+jqqOqhBXGh14bYrFPMVhlmLFY55KhYT1n84Kv1bWKPS94zHPSMRGmKgf7116D2ql\nGpIk4VJDESz2FGhVTkzLOwGDSof3Lr0X7hKJiCgIsiyjuqMab51/C2+dfws1HTX9Pnf15DQY1Aqc\nqLfiXLN9FKuk0cAZYaIAZFnGj/f9GGqFGs0dGThhng0JfswafwjJCe0AAKfXiUcXPgqtShvmaomI\naKhsHhueL3se9bZ66JV6AIDD50BuYi7umn4XDGpDn9c8e6AGr5Y14poJKXj0mnGjWzANaiQzwrwj\nTBSAX/bD6/fC4dbhdE0JAKBwzPmeJhgA/PDD7XeHq0QiIhomWZbxx+N/hMVpQaI6EUqFEkqFEonq\nRLQ4WvDHsj8G3KFu/bQMKCRgx6U2NFr5734sYSMcJThLJM5QslQqlEhUmXCqaia8PjXSjI3IT6/o\n9RydUgeDqu+dg3jDa1Ms5ikOsxQrFvK80HYBTfYmKBXKPudUChUarY2o7Kjscy4zUYMVhSnwy8Ab\nJ8XMCsdCnrGAjTBRP1otC9HhSIZW7cDU3JP4/J4Zbp8b09KnBfzHlIiIIlNpQ2nA0YduBrUBh+oO\nBTx3c0nXOsLvnw3NBhsUHmyEowT3JBdnKFnuvtyO0io9FJIfE7P3Q63y9JxzeB1IN6RjbeHaUJYZ\nNXhtisU8xWGWYsVCnoHGHq7khz/g40XpBszMToTd48d75c0jriUW8owFbISJrlDb4cIvdpkBAPfO\nH4svz1gBk9YEtUINo8aI1eNX476Z90GtVIe5UiIiGo6p6VPh8Dr6PW/32jE9fXq/57vvCr9xqgle\nf0jWGqBRxkY4SnCWSJyBsnR7/fjxx5dhc/uwpMCEDdMzMSdrDu6fdT82zd+Eb87+JhblLuJIxOfw\n2hSLeYrDLMWKhTxLMkqQqEkMeGdYlmUkaZIwJW1Kv6+fl5eEPJMWzTYPdlxqG1EtsZBnLBi0EX7y\nySexZMkS3HjjjT2PTZkyBevXr8f69evxxBNPhLRAotH0+wM1uNDiQJZRg03L8yFJ3E6TiChWKCQF\n7p5+NyRJgt3z2ZrAdq8dSoUSX5vxNSik/lsjhST13BV+raxxSKMWFNkGXUf46NGjUKvVePTRR/H2\n228DAGbNmoWjR48O+MZcR5iizfaLbfjJtgqoFRJ+tW4SJqVzRQgioljk9XtxtOEozrScgSzLmJ4x\nHVdlXjWk3/a5vX58efMptDu9+OnaibgqxzgKFdNARrKOsGqwJ8yaNQvV1dVBvTlRtKi2OPGr3V1z\nwfctzGUTTEQUw1QKFeZlz8O87HnDfq1GpcC6aRl4sbQOr5Y1shGOckHNCLvdbmzYsAEbN27E4cOH\nRddEAXCWSJwrs3R9Ohfs8PixojAZN05JD1Nl0YnXpljMUxxmKRbz/MyNU9KhVUo4WNWByrb+v3w3\nEOYZGQa9IxzIzp07kZaWhrKyMjz44IPYunUrNBpNn+c98MADyM/PBwCYTCaUlJT0LBfSfQHweGjH\nZWVlEVVPLB0/va8al1qdSFX78fDSrrngSKqPxzzmcXDH3SKlnmg/7hYp9YT7+LpJBXjnTDOe/qgM\nN2a7mecoHpeVlcFisQAAzGYz7rnnHgRr0BlhAKiursb999/fMyP8ebfccguefPJJFBYW9nqcM8IU\nDT4634qf7qiERinh1+smYUIaRyKIiGhwNRYnvvbKGagUEv5y2zSkGLikZriMZEZ42KMR7e3tcDqd\nALoa5IaGBuTk5AT14UThVNnmwK/3VAEAvrloLJtgIiIaslyTDosKTPD4Zbx9ZuQbbFB4DNoI//CH\nP8Rtt92Gy5cvY8WKFfjrX/+K9evXY926dXjooYfwxBNPQKfTjUatce3KX6VQ8Hbv3g2Hx4cff1wB\nl9ePL0xMwerJaeEuK2rx2hSLeYrDLMVinn1tmJ4BAPjgbAt8w9xgg3lGBtVgT3j88cfx+OOP93rs\nm9/8ZsgKIgo1WQZ+s7cale1O5Cfr8K0leVwvmIgoTsmyjAvtF7CrahesHit0Sh3mZs/FzIyZgy6n\nVpKViNwkLWo6XDhc3YEF+aZRqppEGdKMcDA4I0yR6oOzLfjlLjO0KgV+80+TMC5FH+6SiIgoDGRZ\nxqtnX8WJxhMwqA2QJAmyLMPutSPXmIt/KfkXqJUDz/6+fLwBfzhUi8UFJvzndYUDPpdCI6TrCBNF\nK7/sx/HG4zhUfwgurwuJ6kQUJi3Bb/d27Sb00OKxbIKJiOLYobpDONl8EgmahJ7HJElCgjoBjbZG\nvHPxHdw06aYB32NlUSqeP1yL/WYLWu0epPJLc1ElqHWEafRxlmh4vH4vnjv+HN449wZa7C2weWyo\n7mjCL3bUw+2TsWpSKq6fxLlgEXhtisU8xWGWYsVinvtr90OvCnxDRKPU4HTLaXj93gHfI9WgxsJ8\nE/wysPV865A/OxbzjEZshCkmvXvxXTTYGj73qy7gbN10OD1GqBXNWDC+IdwlEhFRmFnclgHPO71O\nWFwDPwcA1hR33Vh5/2wLZDkkE6cUImyEo0T3QtI0OK/fi5PNJ6FRfrbJS11bLhot2VAqvJg94QyO\nNh4IY4WxhdemWMxTHGYpVizmqZQG/jIcAKgVg486zMlNQrpBjdoOF8rqrUP67FjMMxqxEaaY0+Hq\ngMP72ZaXdpcB5+qKAQCTc04jQWtHu6s9XOUREVGEyE/Kh1/293s+Q5+BJG3SoO+jVEi4flIqgK67\nwhQ92AhHCc4SDZ1KoYKEruXQ/LKEU9Uz4JdVGGOqRVZyHcxm85DuAtDQ8NoUi3mKwyzFisU81xSu\ngdvvDjjOYPfYsXLcyiG/16pP16Pfdbkdna6B54qB2MwzGrERppiTpE1Chr5rkfOKxgnodJigVTsw\nKecMgK7VJPKT8sNZIhERRYA0fRruKbkHWpUWVo8Vdo8dVo8VCkmBDZM2YGr61CG/V7ZRi1k5Rrh9\nMrZdbAth1SQS1xGmmHS6+TSeLd2K01XLAACzxh9CSkIbZFmGy+fCg7MfRLohPcxVEhFRJJBlGbXW\nWtTb6pGsS8Z403gopOHfK9x+sQ0/2VaBCWl6/O6m4hBUSoFwHWGiKxQkTUZdswsAkJ1aDq2mBla3\nH6n6VHx52pfZBBMRUQ9JkpBrzEWuMXdE77N4nAlGrRIXWxw432xHUbpBUIUUKhyNiBKcJRqe/9lb\nhTYHUJSux/eXz8G6ietw31X34ZG5j6DyRGW4y4spvDbFYp7iMEuxmOfgNEoFVhYN7UtzzDMysBGm\nmLP9Yhs+utAGrUqB7189DlPSJ2Fu9lzkJeVBkqRwl0dERDFs9aebNX1yoRVOb/8rUlBk4IwwxZRG\nqxvfeL0cVrcP31qShxumcASCiIhG17ffOoszjXZ8d0U+riviLqahNpIZYd4Rppjh88v42Y5KWN0+\nLMxPwheL+Y8PERGNvu67wu+Xc03hSMdGOEpwlmhwr5U14nidFck6FR5Zlt/vGASzFIt5isU8xWGW\nYjHPri2XnV7noNsoryhMgU6lwMkGG6ranQGfwzwjA1eNoJhwvtmOF0rrAAD/uiIfKfrBt8QkIiIa\nimMNx7CzaidanF13eFN0KVicsxjzc+YHfL5Bo8TVhSn44FwLPjjbgnsXjGw1CgodzghT1HN6/fjm\nG+Wosriwbmo6Hlwc3JwQERHRlbabt+MT8ycwqHovheb0OrEgZwHWFK4J+LrTDTY8/PY5JOtUeOn2\n6VAp+GXtUOGMMMW1PxysQZXFhfxkHe6dz//qJiIiMeweO7abt/dpggFAp9Jhb81eWFyWgK+dkmlA\nQbIO7U4v9psDP4fCj41wlOAsUWAHqyx463QzVAoJj15TAK1q8EuaWYrFPMVinuIwS7HiMc99NfsG\nXHZTq9RiR9WOgOckScLqyV1fmvsgwJrC8ZhnJGIjTFGrzeHBz3eYAQB3z83GhDTu4ENEROK0OFug\nVWr7Pa9SqNDh6uj3/MqiVKgUEg5Xd6DJ5g5FiTRCbISjxNKlS8NdQkSRZRm/3GlGu9OLmdmJuLkk\nc8ivZZZiMU+xmKc4zFKseMwzXZ8Ol9fV73mP34NkbXK/5006FRYXmOCXgS3nWnudi8c8IxEbYYpK\n75a34EBVBxI1Snx3RQEU3DGOiIgEW5S7CDL6X1PA4/Nged7yAd+jezziw3Mt8A+y7BqNPjbCUYKz\nRJ8519yG3+2vAgB8fUE6MhM1w3o9sxSLeYrFPMVhlmLFY556lR5fKPgC7B57n3MOrwNLxy5FvGkJ\nYQAAIABJREFUkjZpwPeYnWtEZqIa9Z1uHK+19jwej3lGIjbCFDV8fh9ePvMavvf+MXh8QHpSJfY1\n/R7/e+p/4fZx9oqIiMRblrcMtxbfCqPG2LOhhkFlwLqJ63D9+OsHfb1CkrCqe6e5s82hLpeGiesI\nU9R46fRL+OisEtUtk6BT2zF/4l6olD64fW5kJmTivpn3DfjtXiIiopHw+DwAALVyeJs2NVrd+Mrm\nU1ApJPzt9ulI0nE/M5G4jjDFvFZHKw5UNaK6pQiAjKljy6BS+gAAGqUGNZ01uNx+ObxFEhFRTFMr\n1cNuggEgM1GDOWON8PhlfHyhdfAX0KhhIxwl4n2WaHvlflyqnwdAwriMS0hOaO913qAy4EDdgSG9\nV7xnKRrzFIt5isMsxWKeI/P5NYVlWWaeEYL35ikqfHQ2ES6PAUn6dozLvNjnvCRJ8Pg9YaiMiIji\nnSzLsHqskGUZRo0x4JjeonwTTDoVLrc5ca6575fvKDw4I0wR7+MLrXhyeyUUkhfzJ+6DQdv3HxCn\n14kV+StwTf41YaiQiIji1aG6Q9hVvQvtznZAAkwaE+Zlz8Oyscv6NMS/31+N1042YW1xGh5emh+m\nimMPZ4QpZtV2uPCbPV1LpU3KPgu9xhbweQpJgUU5i0azNCIiinMfVXyEdy6+A7fPDYPaAIPKAI/f\ng48rP8ZbF97q8/zu8YjtF9vg8PhGu1wKgI1wlIjHWSKvX8Z/bauA3ePHsvHJ+O6SFfDK3l5LpXn8\nHji8DtxafCt0Kt2Q3jceswwl5ikW8xSHWYrFPHuzeWzYVb0LepW+zzm9So9D9YfQ6uj9xbiCFD2m\nZibA7vHjjx8eGq1SaQBshCli/bm0Dmeb7MhMVOPhpXnIM+XhO/O+g7lZc2HUGGHUGDEjYwY2zduE\n4rTicJdLRERxZH/Nfiik/tsonVKHndU7+zy+prjrrvARC7+mFQn4pxAl4m1P8qM1nXj5eAMUEvD9\nq8fBqO26VBPUCVg7Ye2I3jvesgw15ikW8xSHWYrFPHtrcbZAq9T2e16lUMHqtvZ5fPn4ZPxuXzWq\nHUBlmwMFKX3vKNPo4R1hijjtDg+e3FEBGcAds7IwPSsx3CURERH1kpWQBZfP1e95j8+DZG1yn8f1\naiWunpACoGspNQovNsJRIl5ms2RZxi93mdFq92L6mATcflWW8M+IlyxHC/MUi3mKwyzFYp69zc+e\nDwn972bqkT1Ynrc84Lk1n35p7qMLbXD7/CGpj4aGjTBFlLdON2O/uQOJGiW+f804KBXcMpmIiCKP\nTqXDqvGrYPPYIMufrUQryzLsXjuuzrsaSdqkgK+dlG7AGK0PFqcX+ysto1UyBcB1hCliXGpx4KG3\nzsLjk/EfXxiPZeP7/kqJiIgokpxvPY+PzR+jwdYAAMjQZ2B53nJMz5g+4OvePNWEp/dVY3auEf+9\nZuJolBqzRrKOML8sRxHB6fXjJ9sq4PHJWFucxiaYiIiiQlFqEYpSi3ruCgfaVS6QL0xMwXMHa3Ck\nphN1nS5kG/v/4h2FzqCjEU8++SSWLFmCG2+8seex9957D6tWrcKqVauwbdu2kBZIXWJ9NuuZ/dUw\ntzuRn6zDNxaODelnxXqWo415isU8xWGWYjHPgUmSNOQmGACOH9qPZeO6bvpsOdc6yLMpVAZthK+/\n/nr8/ve/7zl2u934xS9+gb/97W944YUX8JOf/CSkBVLs2325He+Vt0CtkPDoNQXQqTi6TkREsa/7\nS3Mfnm2Bzx+SSVUaxKAdx6xZs5Cc/NmvqU+cOIGioiKkpqYiOzsbWVlZKC8vD2mRFLvrNzZa3fjl\nLjMA4N4FuZiQZgj5Z8ZqluHCPMVinuIwS7GYp1hLly7FjOxE5CRp0Wz3oLSmI9wlxaVh33prampC\nRkYGNm/ejPfffx8ZGRlobGwMRW0U43x+Gf+9vQJWtw8L8pLwT1PTw10SERHRqJEkCasnpwIA3ivn\nmsLhEPTvoG+77TasWbMGwNAHwyl4sTib9bdj9ThZb0OqQYVNy/NH7TqKxSzDiXmKxTzFYZZiMU+x\nuvO8rigNCgnYb7ag1e4Jc1XxZ9irRmRmZqKpqannuPsOcSAPPPAA8vPzAQAmkwklJSU9v1rpvgB4\nPLTjsrKyiKpnpMcvbdmL/zXrIEHC91aMw8nSAxFVH495zOPoP+4WKfVE+3G3SKknmo5lWcbiJYuh\nVCj75HnmyAEUJWhx1qrC1vOtyO08H/Z6I/24rKwMFkvX+stmsxn33HMPgjWkdYSrq6tx//334+23\n34bb7caaNWvwyiuvwOVy4a677sKWLVv6vIbrCFN/Ol1e3P9GORqtHnxpRib+ZX5uuEsiIiISrt3Z\njncvvYvLlsvw+rxIUCegJKME1427DkqFsud5B8wW/MeWS8hJ0uL5W6bwN+3DFNJ1hH/4wx9i69at\naG9vx4oVK/D4449j06ZN2LhxIwDgscceC+qDKX64vC4cazwGi9uCvMQ8vHpci0arB5MzDLhrbk64\nyyMiIhKu2d6Mp489DZWk6vo/lQo+2YcDdQdQ2VGJe2bc09MMzx2bhHSDGrUdLpTVWzEj2xjm6uMH\nd5aLErt37+75tUA0+bjyY+yp3gOf7INKoUJ1Sw4uN8yGTgU8s2EqcpJGfwHxaM0yUjFPsZinOMxS\nLOY5PM8cfQZtzraAd3cdXgeyOrJw/9r7ex574XAtXjrWgGsnpOD714wbvUJjwEjuCHPBVgqZvTV7\nsbNqJzRKDfQqPdyeZFQ2zgAA5GWUQqe2hblCIiIi8TpcHai11vY74qBX6XHecb7XY6s+XVN4d0U7\nrC5vyGukLmyEo0S0/Ve4X/Zjd/Vu6FV6AIDPr8CpqhnwyyqMMdUiJ6UBWyr6zpaPhmjLMtIxT7GY\npzjMUizmOXQd7g545YGb2czczF7H2UYtZmYnwu2Tsf1SeyjLo89hI0wh0WRvgsVl6Tm+2DAJVmcS\n9Bo7JuechlKhhLnDHMYKiYiIQiNRnQilpBzwOTqVrs9jqyZ9utPcOa4pPFrYCEeJK5dbiXQ+2dfz\n/zd3pqO6pQAS/Jg29jhUyq5zftkfltqiLctIxzzFYp7iMEuxmOfQJeuSkZWQBVkO/DUsp9cJRUPf\nFmzp+GQY1AqcbbKjos0R6jIJbIQpRNL16dCpdHB5NDhTXQIAKBxzHkmGri0kZVlGmj4tnCUSERGF\nzD9N/Cc4fc4+zbDb50aKLgUzkmb0eY1OpcDVE1IAAFvOtY5KnfGOq0ZQyLxW/jr+fjQR7bYMpCQ0\n46pxpej+3oDNY8Nd0+/CxJSJ4S2SiIgoRGqttXj34ruosdbA7/dDo9JgSuoU3DDhBmhVgVdNOtNo\nw7ffOgeTToW/3T4dKgXXFB5MSNcRJgqWx7UI7bZ6qJQuTMktgyQBXr8XTp8T1+ZfyyaYiIhiWk5i\nDu6deS9cXhdcPhcS1Am9NtIIpDjDgIJkHSrbnThgtmDJuORRqjY+cTQiSkTbbNalFgdeLG0AANw7\n34TC1HSk6dNQnFqMR+Y8gmsLrg1bbdGWZaRjnmIxT3GYpVjMM3halRZJ2qReTXB/eUqShOsnpQLg\neMRo4B1hEs7rl/HznZXw+mXcMCUdN03LAzAl3GURERFFhZUTU/HHQ7U4UGVBq92DVIM63CXFLM4I\nk3B/OVqPF0vrMCZRg2f/uRh69cC/BiIiIqLeHt96CfsqLbh3fg5umTEm3OVENO4sRxHjUosDLx2t\nBwB8Z3k+m2AiIqIgrPp0POLDc639LsNGI8dGOEpEw2zWlSMRs3KM4S4poGjIMpowT7GYpzjMUizm\nKdZgec7PMyFZp4K53YnyJvsoVRV/2AiTMC8fb8CFFgfGJGpwz7yccJdDREQUtVQKCSuLuu8Kc6e5\nUOGMMAlxudWBb755Fl6/jCfXTMSs3Mi8G0xERBQtKtscuPe1chjUCmy+owQ6Fe9fBsIZYQor3+dG\nIr5YnMYmmIiISICCFD2KMwywe/zYfbk93OXEJDbCUSKSZ7NePtGA880OZCaqcc/83HCXM6hIzjIa\nMU+xmKc4zFIs5inW9l3bsaNqB35T+hv87MDP8PSRp3Gw7iD8sr/X81ZNTgPA8YhQYSNMI1LR5sBf\njnStEvHI0nwkaLhKBBER0UDcPjfeangL2yq3weaxwSf70OHuwDsX38ELZS/0aoavLkyBVinheJ0V\ndZ2uMFYdm9gIR4mlS5eGu4Q+fH4Zv9hphscvY83kNMwZmxTukoYkErOMZsxTLOYpDrMUi3mK8/aF\nt5GcnQydStfrcYPKAHOHGdvN23seS9AosfjTbZY/vtA2mmXGBTbCFLRXyxpxtsmOjAQ1vr4g8kci\niIiIws3r96K8tRwapSbgeZ1Kh6MNR3s9tnJi1+oRH5/nmsKisRGOEpE2m1XZ5sCLpXUAgEeWRddI\nRKRlGe2Yp1jMUxxmKRbzFMPmscHlc8FsNvf7nE53Z6+Gd3auESl6FWo6XFxTWDA2wjRsXatEfDYS\nMTdKRiKIiIjCTaPUQJKkAZ+jVqp7PUepkHDNhBQAwMcXWkNaX7xhIxwlwj2b5fV7YbaYUdFegc3H\na3G2yY70KB2JCHeWsYZ5isU8xWGWYjFPMfQqPbIN2f2ue+uX/RhnGtfn8e7xiO0X2+Dx+fucp+Co\nwl0ARTZZlrG1YisO1x+G1WOFw2XEafN1AJT41pLcqBqJICIiigRfnPBFPHfiOeiV+l53fmVZhs/v\nw5rxa/q8ZkKaHgUpOlS2OXG4uhOLCkyjWXLM4h3hKBGu2ay3L76NPTV7oJAUMKqTUNW4ELKsxBiT\nGSfbXovKoX3OuYnFPMVinuIwS7GYpzh5SXkocZbAoDag090Ji8sCm8cGk9aE+666D6n61D6vkSSp\n567wRxyPEIZ3hKlfVrcVpQ2l0Kv0AICqlnHocCRDq3JiUs55VHZYcLn9MgpTCsNcKRERUXTJ1mXj\nlrm3oNneDKvbimRdMpJ1yQO+5tqJKfjToVrsN1tgdXmRqGUbN1K8IxwlwjGbdaj+EBSfXiI2VwIu\nNUwEAEzOPQW10guDyoC9tXtHva6R4pybWMxTLOYpDrMUi3mK1Z1nuiEd45LHDdoEA0BGggZX5STC\n45Oxk1suC8FGmPrV6eqEWqGGLANnqqfBLyuRlVyDdGMzgK5f03j8njBXSUREFD++wPEIodgIR4lw\nzGaNTx4Ph9eBqpYCdDhSoFE5UZRd3nPe7XMjQ58x6nWNFOfcxGKeYjFPcZilWMxTrGDzXDouGVql\nhJP1Nm65LAAbYerXtPRpgD8DlxqKAADFn45EdPP6vViRvyJc5REREcUdA7dcFoqNcJQIx2yWLEto\nbr0aflmJMaaqnpEIv+yHzWPDjRNvhFFjHPW6RopzbmIxT7GYpzjMUizmKdZI8uSWy+Lw64bUrzdP\nNeFiiw8peiXWTPGhwaGFX/YjIyEDK/NXIseYE+4SiYiI4s6VWy5PyUwId0lRi3eEo8Roz2bVWJx4\n/nAtAODhpQW4ffpNeGTeI9g0fxPunHZnVDfBnHMTi3mKxTzFYZZiMU+xRpKnUiHhWm65LAQbYerD\n55fx851muH0yVk5M4e41REREEWZlEbdcFkE6e/ZsSIZLqqqqMHv27FC8NYXYGycb8bv9NUjVq/Ds\nP09Bko4TNERERJFElmXc93o5Ktqc+OF1hXF90+rIkSPIy8sL6rW8I0y91Fhc+NOhrpGIby/NZxNM\nREQUgSRJwrUTu8Yj9lRwc41gsRGOEqMxm+WXZfxqlxkun4xrJ8TuSATn3MRinmIxT3GYpVjMUywR\neS7M7/o5fbCqA36uHhEU3u6jHu+Vt+BEvRXJOhUeWDQ23OUQERHFBZfXhdKGUjTaGzHGMAZzsuZA\no9QM+rqCZB3GJGrQYHXjXJMdxVw9Ytg4I0wAgCabG/e+egZ2jx//fu04LC9MCXdJREREMW9fzT58\nVPkRfH4ftEotnD4nVAoVrht3HRbmLBz09b/dW4W3TjfjjllZuGtO9ihUHHk4I0wjIssy/t/uKtg9\nfiwuMGHZ+ORwl0RERBTzTjWfwvuX34daoYZOpYMkSdCr9FAr1Hj34rs403Jm0Pe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f2rZsQv5JHLZPoiG2kYyEahJjWtBqQr1eKzs2O8zvbuQ7n1HccLJYLMTGxnL/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\ntdUAfGHBmL4mGCDNm0aaN82p0kREZARo7m7mpaqXONLVgM9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+ "text": [ + "" + ] + } + ], + "prompt_number": 90 + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "However, for now we must leave this problem as it is. The effects of air drag are nonlinear, and so we have to bring nonlinear Kalman filters to bear on the problem. We will revisit this design problem once we have discussed the theory behind these filters." + "The second filter tracks the measurements fairly well. There appears to be a bit of lag, but very little.\n", + "\n", + "Is this a good technique? Usually not, but it depends. Here the nonlinearity of the force on the ball is fairly constant and regular. Assume we are trying to track an automobile - the accelerations will vary as the car changes speeds and turns. When we make the process noise higher than the actual noise in the system the filter will opt to weigh the measurements higher. If you don't have a lot of noise in your measurements this might work for you. However, consider this next plot where I have increased the noise in the measurements." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_ball_with_q(0.01, r=3, noise=3.)\n", + "plot_ball_with_q(0.1, r=3, noise=3.)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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w/shNjEg6TFRoPTqdQq2rlrc/flvT655Kip+eP4J/3zCeO6alkhBmpLjBzW/X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PSQN/zyrgj7PSZNxgIYYISYQHCKkl0o7EUlsST231RjxVVeXD7Eqe/qoQp1cl\nPsTEnTNSGTMsqEf7sxr1JIXpSQqzdHjMJrcPm1HX60llR/vvSjz1OoU7zk/hxrcPsCmvlo8PVTE3\nQyZ1+CF5rWtL4hkY5BZZIYQYxOqaPfz3pzk8llWA06syKz2Sf142usdJcFcpikKQST9gelZjQ0ws\nP6fla9WnviqkqLZ3p/gtb3Txu4+O8Mc1x6hsdHe+gRCiV0iNsBBCDFI7i+t5aEMeFU1ubEYdv56e\nzIwRkf3drIClqip/WZ/LhmM1jI6x8T/zR3U469wPVTe5MRl0nZZ/7Ctp4L8/y6Ha0VJrHWYxcPt5\nds60y416QvSU1AgLIYQAwONTeWnbcd7YVYoKZA4L4s4ZKcSFmDvddihTFIXl5ySzt7SRg+VNvLaz\nhGsmxXe4TYPTw8acGj49Us2ekgYSQk08eenodpPhDw5W8OSmQjw+lQkJwegVhW1F9fxhzTGuGBfD\n9VMSMOrly1oh+oq82gaIrKys/m7CoCGx1JbEU1unGs+iWie/WX2I/+wqRVHg5xPjePRH6UM2Ce5u\nPEPMBu44PwUFeHVHCQfKGk96jtvr46u8Wu77LIefvraX/8kq8I+/XFzn4p9fFba5zeNZBTyWVYDH\np3LZuBj+cvFI7r94BDdMSUCnwFt7y/nN6sMU1/VuWUZPyWtdWxLPwCA9wkIIMQioqsraw1U8samQ\nZo+P2GAT/3VBCuPigvu7aQPOhIQQrhg/jDf3lPHghjyeuiwDi0HHwfImPjtSxYaj1dQ5vUDLRCAT\nEoKZNTKSlAgLt71/mLWHqzjLHsa5aS0z3VU3ufnzZznsLW3EqFdYMT2Zi9K/uxnvp6fHMj4umL+s\nz+VQRRM3v3OQX0+3M2NERH+cvhBDitQICyHEANfg9PDYlwV8fqxl0ovzh4fz63OSCTb3vK+joK6A\nz/I+o7ypHEVRSApJYnbqbCKtQ6PG2OX1sfzdbHKqmxkfF0xVk5ui7/XUpkRYmDUykhkjIlqNwfze\nvnKe/KqQULOeZ64YQ2Wjm3s/PUZFo5tom5F7ZqUxup0bFRucHv62sYCs3Jaf48Wjorjp7MRem+Za\niMGkpzXCkggLIcQAtrekgb9uyKWswY3FoOOWaUlclB55SqM1fFX0FR8e+7DVrG1enxeXz8U1Y69h\nZMRIrZof0HKqHNzyXjZub8uvyUirgRkjIrhwZCQjoqxtxtinqtz98VG2FdUzPNJKYW0zLq9K5rAg\n7pmVRqSzelqJAAAgAElEQVSt48k6VFXlg4OVPP11IS6vij3cwt0zU0mL7HymPCGGsp4mwlIjPEBI\nLZF2JJbaknhqq7N4Oj0+DpQ1smp/OQ9uyOX2Dw5T1uBmVLSNpy4bzexRUaeUBNe76vko5yOCjEGt\n9qPX6bHoLaw8uBKvz9vj/fe1U7k+0yKt3DUjlR+NjuaBi0fw6qJx3HhWEiOjbe3GWKco3HaenRCz\nnmNVDlxelbkZUTx0ychOk2BouWHvR2Oi+cfCDOzhFvJrmln+XjbvH6jwTxzSX+S1ri2JZ2CQGmEh\nhAhQTo+PY1UODlc0+f/mVjfzvVmLUWipMV08KU6T0QY+z/8co9J2wqYoCk3uJvZW7OX0Yaef8rG0\n5vF52FG6g7y6PIKNwUxLnHbK+zwnNZxzUsO7tU10kIk7zk/h+W+KWTg2hh+Nie72cdMirfxj4Sie\n+qqIjw9V8viXBeworuc300+t5EUI0ZqURgghRABweXwcbZX0OsitdrRKegF0CiSHW0iPtpEeZWVC\nQoimX5u/uOdFShtL213vU31kRmdyafqlmh1TCwcrD/Jm9pu4vC6sBisenwePz8OE2Alcmn7pgJnY\noy3rj1bxWFYBTe6WmyDvmtnzWQGFGKxkHGEhhBhgiuucZOXW8GVuDYfKm/C2kfSmRHyX9I6KtjE8\nytrjm6d8qo8j1Uc43nCcSGskY6LGYNC1/jVg1ptRVbXdxNHtcxNu7l4PaW8rbyrntQOvYTPY/Odj\n1Bsx6o3sKt9FkDGI2Wmz+7mVPTdjRCQZMUE8sK5lVIlbVx/iuskJXHnaMHQDOMEXIhB0mAhXV1ez\nZMkSPB4PqqqydOlS5s2bx4cffshjjz0GwJ133smMGTP6pLFDmcxJrh2JpbYknl2nqip5Nc1k5daS\nlVPDsSqHf92JpDfMW885mamnnPT+0OGqw7x96G3q3fUYdUbcXjc2o42LUi9iSvwU//OmJU7jQOUB\ngoxt9zj6VF+r5weCT3M/xaxre5zksqIytuq2cmHKheh1/Tv6gqqqHKk5wv6K/Zj0JqbGTSXKFtX5\nhkBCqJn/mZ/Ov7YU89becl7YUsyO4nruvCCFcGvntcdakNe6tiSegaHDRDgkJIRXXnkFq9VKdXU1\n8+bN46KLLuLRRx9l5cqVOJ1OFi9eLImwEKLXqKpKXl0eByoPYNKZmBw/mTDzwJmKVlVVDlc6yMqp\nISu3hsLa74bgshl1nGkPY3pqOJOTQrAa9S2/HMcNa3NfVY4qKhwVhJhCiAuK6/LX/cUNxfzv/v/F\nqrcSbGwZV9isb0kcVx9djdVgZVzMOABSQlMYHjac/Pp8/3NOcHgcTImb0m6S3F+KGoo6THIb3A2U\nNJaQGJLYh61qrdJRyUt7X6K6uRqrwYpX9fJV0VeMiBjBzzJ/dlLPfFuMeh03npXEhIQQHvkin+1F\n9fx61SHumzOC5HBLH5yFEINPh688g8GAwdDylPr6ekwmE7t27SI9PZ3IyJaxJOPi4jh48CCjR4/u\n/dYOYfKpUTsSS231Zjxrmmv4995/U+moxKw341W9fF7wOWOixvCT0T/p9x6+9qiqypFKB+uOVJGV\nW0tpg8u/LtSs5+yUluR3YmIIph/c4NZWPCuaKvjPwf9Q0liC1+dFURQiLBHMHT6XsdFjO23Pmpw1\nWPVtD/dlM9hYl7fOnwgrisLicYt57/B77KvcR5OnCQWFEFMI5yWfx0z7zO6Go9d1NJqC3W6n1lWL\nSv+NuOD2unlu13P4VJ//Q4RO0WHUGcmrzeP1A6/z87E/7/L+zrSH8dRlGfxx7TEOVzhYsfoQf5yV\nxmnxIb11CoC8d2pN4hkYOv0I2tjYyFVXXUV+fj6PPPIIFRUVxMTE8PrrrxMWFkZMTAxlZWWSCAsh\nNOX2unlm5zN4Va8/eTBgAD0cqj7EyuyVXDXmqn5uZWu1zR7WHanik0OVHKtq9j8eaTNwTko401PD\nOS0+GL2u63Wdtc5antrxFAadoVVPrMfn4T8H/sPVmVczOqrj99/C+sIOexwrHBXUu+oJMbUkUnqd\nnsszLudH3h9R1lSGTtERa4sN2A8esUGxFNYXolPaHjUjyBBErC22j1v1nS0lW3B4HFgNJ9/UaNKb\nOFx9mDpnHaHm0C7vMzrIxCOXpPPXDXl8lVfLnR8d5dZz7cxKHxoTngihlU4T4aCgIFavXs3Ro0dZ\nunQpt9xyCwBXXdXyC2jt2rXtfj138803Y7fbAQgLC2P8+PH+T0Anxs+T5a4tP/XUUxI/jZa/P3Zj\nILRnoC/3Vjz31u+lKaQJq8FKfn4+gP/9pLSolPyCfC4ZcQkhppB+PX+vT+XlNV+zs9bA4UYjnm+H\nebDqVWZnDOOC4eFUHd6JotYyMTG52/Fcm7OWwsJC9Iref/7fj8eanDVUHKhod3+qqpJXkIdRMba5\nPUBhUSFfbvqSiy+4+KTtk0KSyMrK4hjHAuJ6a2s5pCyEI2VHGJU66qTzO5p3lHRbOpu/2txv7Vu9\neTW1ntp2419UWMQrda9w87ybu73/ey5M4953trC52shDn+dRXOckrekoiqL9+Zx4rL9/3oNlWeJ5\n6vHLysryv56WLFlCT3Rr+LRrr72W5cuX8/zzz/P0008DcM0113D33Xef1CMsw6dpKytLiuq1IrHU\nVm/F87ldz1HpqGx3fbOnmVmps5ie1D8/y6LaZj45VMXaw1VUNrmBlhveJieFMntUJGfZw04qe+iK\nH8bzoc0P4VN97T6/0d3I7VNv77Bu+h/b/kGju7HD4/526m8Dtse3K7Ye38r7R99HURTMejM+1UeT\npwldhY4/Lvxjv55bZ9eyy+tietJ0Zqb0vOzkvX3lPPV1IT4VZo2M4LbzUrr1zUNXyHuntiSe2uqV\n4dNKS0sxmUxERERQXl5OTk4OaWlpHD58mKqqKpxOJ6WlpVIW0QfkxaIdiaW2eiuendV0KoqC2+fu\nlWO3x+H28kVODZ9kV7K39LvEMszqJjOuiSvHDmdcnP2UjvHDeLq97g6TOFVVafY0d5gIn514NqsO\nr8JmtJ20zulxMjl+8oBOggEmx08mMzqTjYUbKWsqw6w3c07iOf16g9wJ9lA7xQ3FJ918eILb5+5S\nrXdHFo6NITbExAPrcvn0SDUZMUEsHBtzSvv8IXnv1JbEMzB0mAgfP36cP/zhD/7lO++8k6ioKG67\n7TYWLVoEwF133dW7LRRCDElJwUmUNJRg0pvaXO/2uhkTNaZP2nK0sol395Xz+bEamj0tvbMWg8Kw\nsFKCbPuJCW5CUeD1w5+ScDyB68Zd12bS2ROh5tAOe3NNelOn4/qeEXsGRfVFfFPyDUGGIHSKDlVV\naXQ3MiJiBHOHz9Wkrf3NZrQxJ21OfzfjJOcmncvXxV+3OT6zx+chITiB2KBTr2E+yx7G7efbue+z\nXN7aW8aPxkRr3issxGDT4fd2EyZMYPXq1f6/8+bNA2DevHl88sknfPLJJ1xwwQV90c4h7/s1MeLU\nSCy11VvxPN9+fru9wl6fl4SQBOKC4nrl2N+XU+XgV+8d4pNDVTR7fIyNDeLWc5M5f0wWwyI/J9RW\nhV6vQ6/TE2wMpspRxQt7XuhwJIOO/DCeU+On4vA42nyu2+cmPSIds6HtnsYTFEVhYfpCbj79ZlJC\nUwg3hxMfHM+1467lunHXtXuT2WAQCK93m9HGzzN/jlt14/S2DJ934oNIsDGYxeMWa3asc1LCSQg1\nU1LvIiu3RrP9QmDEcjCReAaGDnuEhRCivwQZg7hqzFW8fuB14LsZzxweB+GWcBaP1S55aI/Hp/Lw\n53m4fSrnpIRx/ZQEksLMvLz3ZT7JXQXfdraZ9CYSgxNJC0vDoDNQ1lhGTk0OwyOGn3IbpsZPJac2\nh30V+7AZbP4exWZPM+HmcC4bdVmX95UYmsjPxv7slNskum9ExAj+a+p/8XXx1+TW5qJTdEyMm0hm\nVKamH0T0OoUfjx/G418WsHJ3GeelhQ/o6aWF6G3dulmuO+RmOSGEFhweB1mFWRTUFaBTdEwYNoHx\nMeP7pKb1f7cf53+3lxAbbOKZy0djM+l5M/tN3jz4JvWu+lYJhsfnIS4ojtFRo1FVlRERI/jJ6J9o\n0g5VVdlbsZdNRZtodDdi0pk4bdhpnJ1wNkZ938wqJgKfx+dhW8k2DlXlsHLrSJo9eh65ZGSvjy8s\nRCDolZvlhBCiv1kNVi5KvajPj3ukoonXdpQAcNt5dmwmPZVNlewu291mEm7QGTjeeJy08DRMOlOH\nIz10l6IojI8Zz/iY8ZrtUwwuubW5vLL/FdxeN1aDlbgIHbnl6fwtaxvPXX6OfGASoh2DtzBskJFa\nIu1ILLU1GOPp8vp4+PM8vCoszIxmQkJLj1pWURZmvZlhtmFtjlihV/Tk1eXh8Dp6PArAYIxnfxoK\n8WxwNfDy3pfRo/dP2pEUVYBO8VJcG8bzO1ZpcpyhEMu+JPEMDJIICyHED7y6o4Sc6mYSQk1cPyXB\n/3iDqwG9Ts8w2zB/zfL36RQdTo+TYGPwKQ+HJURXbcjfANCqVMdkcBMfUQRAVo6eBldDfzRNiIAn\nifAAIeMNakdiqa3BFs/s8kb+s6sUBbj9vBSsxu/KIOKC4nB6nCiKwsTYiSeNZdzsbSbUHMr146/v\n8Q1Qgy2e/W0oxDO/Pr/NYQaTo3IBlYraZLYUZ5/ycYZCLPuSxDMwSCIshBDfcnl8PPx5Pj4VLh8X\nw7i44FbrpyVN8w/pZjPamJY4jfSIdEJMIYSYQkgPT+eRCx4h2hbdH80XohWzqYGokOOo6NiUIyNH\nCNEWSYQHCKkl0o7EUluDKZ4vbTtOfk0zSWFmrpuccNJ6q8HKJSMuocnThKqq6BQdSSFJnBZzGukR\n6fxywi8JMgWdUhsGUzwDwVCIZ3JIMi6vy7/s8DjYWbaTrMIsKr3vALAp10dl06mVRwyFWPYliWdg\nkERYCCGAfaUNvLmnDJ0Cvz0/BbOh7bfHKfFTWDJ+CbFBsajf/okPjuf/nf7/mBQrQ0aKvjfDPgNV\nVf3jbH9z/BvqXfXoFT16YxFGYwFur5571r9Pk7upv5srRECRcYSFEENaRaOLj7MrWbW/gppmDz89\nbRg3TE3s72YJ0S0nhk/bXrK9ZfY6tWXmwQhLBAmWWewrmIzZ4ODas0r58eiuT8IixEAh4wgLIUQX\neX0q24rq+OBgJZvza/F92x2QOSyIaybF92/jhOiB1LBUfnPGb7h13a00uFtGN0kOTibEHIKqVpJj\nbqDJGUxWbh0/Ht3frRUicEhpxAAhtUTakVhqayDFs7LJzas7Srjujf38/pNjfJVXiwKcmxbOX+eO\n4G/z0zG1UxLRVwZSPAeCoRRPt8/NsKBhjI8ZT2ZUJiHmlvGvFQXsUbkA5Jan4PP1bLKXoRTLviDx\nDAzSIyyEGNR8qsr2ono+OFDBV9/r/Y0LMTE3I4o5o6KItMmsW2Lgsxlt7c4gFxt+nGNl6TQ5w/j0\nSDWzR0X1ceuECExSIyyEGJSqmtx8cqiSj7IrKalvuaNep8DZ9jAuGRPNpMQQdIoMKSUGl5f3vUxB\nbUGb04AXVA7j8PGJWI06/nnpaBLDzP3QQiF6h9QICyGGPJ+qsrO4ng8OVrIptwbvtx/zY4O/7f3N\niCJKen/FIHZZ+mU8se0JPD4PBt13v+JdXhcjY+qINYeSlVvHgxty+dv8URh08mFQDG1SIzxASC2R\ndiSW2urPePpUldxqB+8fqOCv63P5+ev7uPOjo2zMqUEFzk4J4745w/n3TzK5emLcgEiC5frU1lCL\nZ4gphOVnLGdU5Ci8Pi8OjwMUOH3Y6dw86SZ+c24KMUFGDpY38cr2493a91CLZW+TeAYG6REWQgwY\nLq+PwxVN7CtpZE9JA/vLGql3els9JybIyNyMKC7OiCI66ORpZ4UY7IJNwfxk9E9QVRWv6kWv6FG+\nLQMyG+C/Lkjhtx8c4fVdpZyRFMr4H8ygKMRQIjXCQoiA1ejysq+0gX0ljewtbSS7vBGXt/VbVrTN\nyLi4IMbFBTMuNpiUCAt6+bpXiA69uKWY/9tVyrBgI09fNppg83f9Yj7VR5WjCoBIayQ6RUd2ZTZf\nFH5BnbMOo95IZlQm5yadi9kgdcYiMEiNsBBiwPOpKpvyatlZXM/ekkZyqhz88JN6SoSFcbHfJb7D\ngo3+3q6uqnfVU+usxWqwEmWVu+eHgipHFVtLt+LxehgXM47kkORuXzeDyTVnxLO9uJ7s8iYe/7KA\n381IBWB9/nq2lGyh3lUPtJRauL1umj3NBBmDUBQFt8/Nl4Vfsr10OzdPvJlgk/Qoi4FLEuEBIisr\ni+nTp/d3MwYFiaW2tIpnTpWDv2flc6DsuylgDTqFUdE2xsUFMTY2mLGxQYRaev62VdtcyxvZb1BY\nV4hbdaNDR4wthktGXMLIiJGnfA5akOtTWxs2biAvIo8j1Ucw6ozoFB2bijcRa4tl8bjFhJnD+ruJ\n/cKgU7jzglRueucgG47VMDW5mkY2sr10O1aDlWBjS3Jb1ljGzrKdJIckY2u0YbfbATAbzLi9bv5z\n8D/ccNoN/XkqA5a81gODJMJCiH7V7PHx6o4S3txdileFSJuBBWNiGBcXTEaMDbNGE1w0uBp4cseT\nAFiNVqxYAWhyN/Hyvpe5duy1jIgYocmxROD4rPIzDDoDQcYg/2PBumDqXfU8u/NZbp1ya5tDjQ0F\niWFmlk1L4tEv8vnHpnwykg4QGWRt9ZyCugIsegvHG4+T7Gv9tbNepye/Np86Zx2h5tC+bLoQmpFE\neICQT43aCdRYNrgaWJe/jry6PFRVJTE4kZn2mURYI/q7aR06lXhuLazjH18WcLzehQIsyIzmF5MT\nCDJpn5iszV2LV/Vi1LUeOUJRFKx6Kx/lfMQtEbdoftzuCtTrcyCqclRBFJj1J9ex6hQd9e56dpXv\nYlLs0L2fZXZ6JN8U1LExp4ajJVMJH74FnfJdQVKztxlFUdCjxxvqPWl7l89FhaNCEuEekNd6YJBE\nWIgAUFBXwIt7XgTApG8Z6eBA5QF2l+3mJ2N+wtjosf3ZPM1VN7l5enMR649WA5AWYWHFuXbGDAvq\nZMueO1x9+KQk+ARFUShtLJWerUFma+lWTLr2Rw6xGWzsLts9pBNhRVH49TnJbCsqp94Rwe68iSRE\nFBIVUoFe50On6PCpLf+6vK6Tt0fBYrD0Q8uF0IaMIzxAyHiD2gm0WPpUH6/sfwWjzuhPggEMOgNW\no5W3st+i2dPcjy3sWHfi6VNVPjpYwZK3DrD+aDVmvcKSKQk8ednoXk2CAdxed4frVVVtGXO1nwXa\n9TmQebweCgsLO3yOT/X1UWt6X7OnmUpHJU3ups6f/D2hFgOXndaMonipaohhb8FEsg7OYH/hOIKU\nSbi9Prw+L001J+83whpBfFC8VqcwpMhrPTBIj7AQ/WxP+R4cbgc2o63N9T7Vx5eFX3Jh6oV93DJt\n5Vc38/cv89lb0gjA5KQQlk9LJj60b4ZfCjGHdJggGPXGIXvj1GA1LmYcK30r213v9DoZHj68D1vU\nO2qba3nn8Dvk1uXi8XnQ6/QkBSdxWfplRNuiu7SPn46bSnbNY9Q0pFBaE0d9cxglNYlAIigz8Vre\nYJjJ2WqbJk8TC0cuHNKjb4iBT798+fJ7e2PHdXV1xMfLp0StnLhTV5y6QIvll4VfUuesa/eXyYlp\nUk8fdnpfNqvLOouny+PjlR0lPLghj5J6F+EWA785N5kbpiQQcgojQHSXV/VysOpgm+URHp+HtPA0\nzog7o8/a055Auz4HslBTKAWuApxe50mvL1VVUVG5avRVraYiHmjqnHU8seMJGlwN/m+VjDojTe4m\nvj7+NeNjxrf7Ifv7DDoDYWYLBY4sUqJKiAs/jtHgwuUx4fYEo/OOJzm+Ho9ag8vnwma0MTdtbkC8\nZgYqea1r6/jx44SFdb8zY+C++oUYJCwGC17Vi0Fp++Woqmq7ta2BbkdxPY9nFVBU19KTNDcjihum\nJPiHQCtuKGZ76XZQYeKwiSSGJvZaW85KOIsj1Uc4Un2kVWLg9DoJMgZxxagreu3Yon8oisLicYt5\nduez1LvrsRlafu5OrxOdouOasdcM+AkhPjj2Aaig07WudFQUBaPOyKojq/jF+F90aV+T4ycTY4vh\ns7zPKKGElJgjTEmpJ7/0LL7Oh5KKOdx2vpmYYBuJwYnSEywGBUmEBwgZb1A7gRbLsxPO5uvir9vt\nlWpyN3F24tl93Kquayuetc0ent1cxNrDLbNT2cMt/Hp6sn8qV4fHwUt7XqKooQiLvuVGm6+Pf01C\nUALXjb+uSz1Y3XUi8dlaspUtx7dQ767HrDczKW4S5yedHzAJUaBdnwPdni17uHXarews28me8j34\nVB9p4WlMS5gWMD/znlJVlWM1x9od/k2n6Mivy8fldbW6/6AjKWEpXH/a9a0ec3p83Pr+IQ5XOPi/\nHRb+crEkwVqQ13pg6DQRLi0tZcWKFdTX12Mymbj99tuZNm0aY8aMISMjA4ApU6Zw991393pjhRiM\nIq2RZEZlcqjq0Em/mF1eF8mhyaSEpvRT67rHp6qsOVTF898UUef0YtQrXD0hjp+cNgyjvqXHSlVV\n/rX7X1Q3V580tmtVcxUv7H6BWybd0iu/aBVFYUr8FKbET9F83yJw6XV6zog7Y9B9je9Vvbi9bvSG\n9ocb9KpenF5nlxPhtpgNOu69aDj/74097Cxu4NnNRdx0dlKP9ydEIFGys7N/OINpK5WVlVRUVJCR\nkUFxcTFXXXUVX3zxBRMnTmTHjh3tbldQUMCkSUN3SBohusOn+njv8HvsKd/TUs+Igl6nJyMygysz\nrsSoD/zSiN3H63n66yKOVLaMvDAhIZhfnZNMUljroZVya3N5YdcLBJnaHiWi0d3IdeOuk8ktxJDn\n8XnYVbaLgvoCws3hTI2f2urbElVVeeibh1DV9n+Ne3we7jzrTk3qoPeVNPDbD4/g8ancdp6dOaNk\nenIROLZv305ycnLnT/yBTl8ZUVFRREW1XOwJCQm43W5crpPHEhRC9JxO0XHZqMuYO3wuR6uP+r++\nDTYF93fTOnW8zslz3xSTlVsDQHSQkRumJDBzRESbvbpbjm/psPTBZrCxtXSrJMJiSDtQeYC3s9/G\n6XNi0Vtwe91syN/AmQlncnHaxSiKgqIoZEZlsr10e5uThnh8HtIj0zW7GXBsXDC3TEvi71kFPJ5V\ngD3c0uvDHgrR27o1jvDGjRsZO3YsJpMJl8vF5ZdfzqJFi9i6dWtvtU98S8Yb1E4gx9JisDA2Zizj\nh40P+CS40eXl+W+KuH7lPrJyazAbdCyeFMe/rszkwpGR7ZY2+Oh83Fafb/CM7dpdgXx9DkQDMZ4l\nDSW8vv919Do9NoMNnaLDbDBjMVj4uuhrsgq/O6c5aXOIsETg9LQe2szldWExWFgwcoFm7crKymLe\n6GgWZEbj9qn86dNjVDZ2PD63aN9AvDYHoy5/TCwvL+ehhx7in//8JwBffPEFUVFR7Nmzh1tuuYW1\na9diMvW8BkkIMTB4fSofH6rk31uPU9vsARRmpUdy/eR4ooM6fw/IjMpkX8U+/x38P+TwOBgTNUbj\nVgsxcKzJW9PujXxWo5Wvir/inKRz0Ck6THoTSycsZV3eOvZV7KPR3YjVYGVC7ARmp87ulVnflp6V\nRG5VM7tLGvjTp8d45JJ0TAaZn0sMTJ3WCAM4nU5+8YtfcPPNN7d5h+OVV17Jgw8+yPDh3w1MXlBQ\nwPPPP+8fJy8sLIzx48f7tz/xSUiWZVmWB85yUNrpPLO5kGNVLTPdZQ4L4qazEynP3tHl/flUH79a\n+Su8qpeUlJabAPPz8wFITk5Gr9NzlussdIqu389XlmW5P5ZvfuNm4LtxZk+8Pk4sZ+dmc0XsFfxo\nxo/6rb2NHvjfknDKGtycHupmQbyLc88NjPjJ8tBYPvH/E6+PJUuW9KhGuNNEWFVVbrvtNiZPnszV\nV18NQG1tLWazGYvFQmFhIVdffTVr1qzBYvnuk6fcLCfE4FFU28yzm4v5Kr8WgNhgE0umJnBeWniP\nRneoaKrghd0v0Ohu9NcLN7mbsBqs3HDaDQwLGqZp+4UYSP7y9V9QaP91Ve+q51dn/IrYoNg+bNXJ\njlY2sWLVIZxelZvOSuSycfK6Ff2npzfLdfpdxrZt21izZg1vvPEGl156KZdddhnHjh3j0ksvZcGC\nBSxfvpz777+/VRIstPf9T0Di1Egsu67e6eHprwv55VsH+Sq/FqtRxy8mx/P8j8dw/vCWm+F6Es9o\nWzS3Tb2NH438EfFB8cQHxzNvxDx+e+Zvh3wSLNentgZiPKOt0R2OBBFkDCLK2vcjNvwwliOibNx+\nfsu3Os9sLmJ7UV2ft2kgG4jX5mBk6OwJkydPZu/evSc9/vHHH/dKg4QQ/c/rU/ngYAUvbztOndOL\nAswZFcl1kxOIsmkzlJtBZ2Bq/FSmxk/VZH9CDBYz7TP5995/txpn+4RmTzOT4yYHzLTQ5w+P4Fil\ng//bVcr963J5YmEG8aEDe6ISMbR0qUa4J6Q0QoiBaWthHc98XUReTUsd8GlxwSw9K5GR0drP9tZT\nDo+DHaU7qHfVMzxsOCMjRspMV2JQ2ViwkbW5azHqjRh1RnyqjyZPExmRGfws82folMC5Oc2nqvxx\nzTE2F9RhD7dw98xU0iKt/d0sMcT0tDRCEmEhBNAyHNr/bMzni5yW8YDjQ0z8cmoi56SGBUySqaoq\nH+V8xJbiLfhUHwa9AZfXRagplKszryYxJLG/myiEZuqcdWwo2ECVowqzwcy5ieeSFJrU381qU6PL\ny69XHSK/phmdAgsyY1g8KY5gc2D0XIvBr9dqhEVgkFoi7UgsT3aooomb3znIFzk1WI06lkxN4Lkf\nj2F6F26G68t4rstfx+bizZgNZqxGK0adkSBjEB6fhxd2v0Cdc+DXKMr1qa2BHM9QcygLRi7guvHX\nsfcHIssAACAASURBVGjMon5PgjuKZZBJz//MT2dhZjQA7+4r5/qVB1hzqBJfB/XOQ9lAvjYHE0mE\nhRjCVFXlvX3l/GbVIY7XuxgZZeWpy0bzk9NiMel7/vZQ2ljKnrI95Nfld3jTT3d4fB42F2/Gajj5\nK9cTs2ytz1+vybGEEN0XYjawbFoyT16awbjYIGqaPTzyRT63rj7M3pIGzd4LhNCSlEYIMUT9sBRi\n/phobjwzkVMZGL+koYQ3Dr5BmaMMvn1nCbOEMSd1DqcNO+2U2ptXm8czu54h1BTa7nMsegsrpqw4\npeMIIU6dqqp8dqSa578posrhAWB4pJX5mdHMHBGB1ajv5xaKwaanpRFSvCPEEHS4oon71+VQXOfC\nZtSxYrqdC0ZEnNI+a5preHbXsxh1RoKN300P7fV5eTP7TQw6A5nRmT3ev1f1dtqj1JXpm4UQp05V\nVfZX7ufLoi9pcDVg0pkYP2w80xKmYdQbUZSWGSfPTglj5e5SPjhYybEqB49lFfDc5iJmj4piYWY0\niWEy9KroX1IaMUBILZF2hnIsVVVl9f5yVqw6RHGdixFRVp68NOOUkuAT8fw452P0ir7NmmKb0can\neZ/2+BgAcUFx7U47C+BTfURbo0/pGIFgKF+fvUHiqZ0TsVRVlZXZK3l9/+tUNlXi8rpocDewPm89\nT2x/gmZPs3+bIJOe6yYn8Oqisdx5QQqZw4Jocvt4d185N759kGOVjv46nX4n12ZgkERYiCGi0eXl\ngfW5/GNTIW6fyo9GR/PY/FGa9cjk1uai17X/dWdFUwW1ztoe799mtJERkYHL62pzvcPj4MKUC3u8\nfyH+f3t3HhhVea8P/DlzZstM9mSyJ0Ag7GGTRQFBkcpSpVTrVfS29tdiq1RvW3Gp2lvbXvUq1ltr\nrdblql2lerVWEQQEAVEWIaxC2AIkQ/aQZTKTWc/5/RESCdkz72S25/OPnpk5Z948OWS+Ofme96W+\nKaoqwuGawzDrzR1+8TVqjWj2NOP/jv1fp330sgbzRiTj2SUj8eI3R2FGbjzcPhW/2XYWXoW9wxQ8\nLITDRNsa2+S/aMzyVJ0Dd793DFtLWmeFeOjqIfiP2bl+9QO3acvTq3h7fJ0Cpdsitq9uHHUjUk2p\nsHvs7W0SXsULu8eOxfmLI2L6tGg8PwOJeYrTluXO8p3tS6NfSqfRoaShpMNV4UsNTzHhoauHIj1W\nj5N1LfjHgapADDfk8dwMDewRJopgqqriw+I6vLjTCo9PRX6yEY/MG4bcRPF9eQmGBNg99m6fN8gG\nJBgS/HoPvazHXZPuwrHzx7CrfBfcihsWkwVX513t97GJqG+aXE09Tqvo8rlQ76xHZmxmt68x6WXc\nOycPD649ib/tq8TMIQlchIOCgleEwwR7icSJliwdbh+e3HIWz31WBo9PxaJRKfjdklHtRbBP8WFv\n5V68eeRN/KP4HyipLxnQ9EZteV6edTkcXkeXr3H73BiVPAp6WT/wL+gCSZIwOmU0bi+8HXdMvANL\nC5ZGVBEcLefnYGGe4rRlqZV7voYmSRIMcu/LLE/OisN1o1PhVVQ8vTX6WiR4boYGXhEmikAldS14\nbPNpWBtdMGo1+PHsXFwzIrn9+fLmcvzp0J/Q4muBSWuCqqo4XHMYGeYMfG/C97qcq7c3UzOm4nTj\naRysPgiz7qveQYfHAYvZgqUFS4V9fUQUPMMThuNI3RFoNV2XEJYYC5KMfbsBd/n0LOy2NuJkXQve\nOlCFWydniBwqUa84jzBRBFFVFR8dq8Mfdljh9qkYmmTEz68ZhryLWiHcPjdW7VrV5QwPXsWLdHM6\n7ph4x4Df/9j5Y9hu3Y5mTzOMshGT0idhasbUbj80iSi8NLub8eyeZ6GRNNBIHf+w7PA6cPPomzEu\ndVyfj1d0rgk/W3cKWo2EPywdxRYJGhDOI0wU5XyKij98bsWa4loAwMKRKVgxMwfGS26I21m+E17F\nC6228z9/rUaL0qZS1DhqYDFZ+j2GtraF0SmjB/ZFEFHIi9XH4q7Jd+Efxf9ARXMFfIoPAJASk4Kb\nRt3UryIYAKZkx+Pro1PwYXEdfrPtLJ5bMgqypuel3YlEYY9wmGAvkTiRmKXD7cMvNpRgTXEtdLKE\n++fm4d45eZ2KYAA4WX8SRm33N8vpNDocqD7Q5/eOxDyDiXmKxTzFuTjLlJgUrJi8AvdOuxffLfwu\nfjTlR7h32r0otBQO6NjLp2cjLVaHE7UteOtgdMwiwXMzNLAQJgpzNXY37l1zAl9YmxBvkLFq8Qh8\nrSAl2MMioiiQZEzCyOSRyI7L7nEmid6Y9TJ+OjsPAPDXokqcPh+9C23Q4GKPMFEYO1XnwM/Xl6DO\n4UF2vAGPLRiO7ISe79bebt2OjWc2dntDnN1jx48v+zFSTeG/ShsRhZffflqKdcfqMDLVhN8tGckW\nCeqzgfYI84owUZjaXdaIe9ecQJ3Dg/HpZvxuychei2AAmJ45HQbZ0OVUaR7Fg6HxQ1kEE1FQ/GBG\nNixmHY7XOvD2oehokaDgYiEcJthLJE4kZLnmaC1+saEELR4FVw9PwpOLRiDe2Ld7X/WyHt+f8H3I\nGrl9hTZFVdDsaYbFZMFt427r11giIc9QwjzFYp7iDEaWZr2Mn17Z2iLxl72VOFsfuS0SPDdDA2eN\nIAojiqrif3eX4+1D1QCAZZPScftlmdD0szcv3ZyO+6bfh0M1h1B8vhiyJGNG5gzkxOX41edHROSv\nqTnxWDQqBeuO1eE320rx3JKR/LlEAcMeYaIw4fIqWLX1LD493QBZAn48Ow8LR/GmOCKKPHa3D99/\n+wjOt3ixavEITMqKC/aQKMSxR5gogjW0ePDA2hP49HQDTDoNHl84nEUwEUUMr+LtcN+CWS9j8ejW\nexXWXpgbnSgQWAiHCfYSiRNuWZY1OPHj94/jaLUDFrMOv71+JKZkxwd7WO3CLc9QxzzFYp7iiM7S\nq3ixrmQdVu1ahcc+fwyP73gcf/3yr2hwNgAAFo5KgUYCPjvTiIYWj9D3DgU8N0MDC2GiEHawohk/\n+eA4KmxujEiJwXPf4PKjRBT+vIoXrxx4BbsrdkNRFRi1xvaVLX9f9HvUOmqRFqvHtJx4eBQVH584\nH+whU4RijzBRiNpaUo9VW87Co6i4PC8eD109FDE6OdjDIiLy29bSrdhcurnL+cxVVUVSTBLunHQn\ndpxtxKMbS5CTYMD/fmsMb5qjbrFHmCiCVNhceHpraxH8jbEWPDo/n0UwEUWM/dX7u13UR5IkVDRX\nwOa2YXpuPFJMOlgbXThU2TzIo6RowEI4TLCXSJxwyPKPO87B7VNx9fAk/GhmTkivrhQOeYYT5ikW\n8xRHZJYOr6PH5z2KBza3DbJGar8x+MPiOmHv3xeqqqKkvgTrT6/HtrJtaHaLLcR5boYGziNMFGJ2\nljZiR2kjDFoVRvMm/KHIiURjIublzUNmbGawh0dE5DejbITL5+r2ea2kRawuFgCwcGQK/r6vEttP\nN6DpCm+fFw/yR62jFn/+8s+od9ZDL+vhU3zYVLoJE1MnYunIpdBIvI4YKXr9TlZVVWHZsmW47rrr\ncMMNN+Dzzz8HAKxduxYLFizAggUL8MknnwR8oNFu9uzZwR5CxAjlLN1eBS/sKAMAZCQfhkupgc1t\nw9nGs/hD0R+w+ezmII+ws1DOMxwxT7GYpzgisyy0FMLpdXb5nKqqyDBnIN7QOjtOepweUy/cNLdx\nEG6ac3qdePnAy3B5XTDrzNBpdDBqjYiRY3Cw9iA+OPmBkPfhuRkaei2EtVotfvnLX2LNmjV4/vnn\n8bOf/QwejwfPPPMM3nzzTbzxxht44oknBmOsRBHvrYNVqLR5YDI0YZilov1xjaRBrD4Wm89uRmlT\naRBHSETkvzm5c5BkTILb5+7wuKqqcCkuLB25tMPji0e3tkesLa7tMN9wIHxm/Qxun7vLG/OMshEH\nqg90W8RT+Om1EE5JScGoUaMAAFlZWfB4PNi/fz8KCgqQnJyMzMxMZGRkoLi4OOCDjWbsJRInVLOs\naHJh9YEqAMCorGJopM4/7M06Mzad3TTYQ+tRqOYZrpinWMxTHJFZ6mU97px0J8aljoNP9aHF2wKX\n1wWL2YK7Jt2FrNisDq+fkZeAZJMWZY0uHK6yCxtHV47XH4dRa+z2ebfPjWPnj/n9Pjw3Q0O/Gm0+\n/fRTjBs3DnV1dbBYLFi9ejUSEhJgsVhQXV2N0aNHB2qcRBHvxZ1WuH0qkuPOIslc3+VrJElCvbPr\n54iIwolBa8CNo26ET/HB4XXAIBugl/VdvlarkbBgZAre3F+FtcW1KMyIFT4eVVVxtO4oPjv3GZpc\nTdBIGqTEpGBowlDoNLr212kkTacr2RS++tztXVNTg1WrVuHRRx9tf+yWW27BokWLAIBz+wUYe4nE\nCcUsd5xtxM7SJhi1EnIsB3t8rVYTWve4hmKe4Yx5isU8xQlUlrJGRpw+rtsiuM3CUSmQAGw73YAm\np1foGFRVxb9O/At/P/p3aKCBV/HCq3hRbivHrvJdnVohCpIK/H5PnpuhoU+fqC6XCz/+8Y/x4IMP\nIjc3F9XV1aipqWl/vqamBhaLpdN+K1asQF5eHgAgISEBhYWF7d/4tj8JcJvb0b7t8ir47ZaTADT4\nzmUZOGnXo7S0tQ+47d9P23ZGdgYmpk0MqfFzm9vc5vZgbV+WE4c9Vhte2bAHK5dcLuz4ZS1lOGI4\nglh9LPTNetQ31yMlMQWyRkZDQwO227Zj/pj58CpeeGo9OLzncEjkEc3bbf/f9vm4fPlyDESvK8up\nqoqVK1di6tSpuPXWWwEAbrcbixYtwttvvw2Xy4Xbb78dGzZs6LAfV5YTa/v27e0nAfkn1LL8894K\n/HVfJYYlGfHCN0fj83Pb8fGZjxGj6zjZvKIqUKHip1N/CpPOFKTRdhZqeYY75ikW8xQnFLLcfroB\nv950GkMSjXj5xtHC/hr9yoFXUOuobT9elb0KR+uOQpIkyJIMt8+NSWmTkB2XjR9M+kG3i4H0Ryjk\nGUkGurKctrcX7N27Fxs2bEBJSQneeustSJKEl156CStXrsSyZcsAAA8//HD/R0xEqGhy4R8HW2+Q\n+9HMXMgaCVfmXgmf6sP2c9vh9DghSzJ88CHdlI5bx94aUkUwEdFgunxIApJitDjb4MSRKjvGCeoV\ntrltHYrqdHM6koxJONN4Bs2eZsgaGXNy5mDxiMWcQzjC9HpFeKB4RZiod/+5/hR2lTXhmhFJePCq\noR2e8/g8OH7+OOxeO/Li85BhzgjOIImIQshrX5Rj9YEqzC9IxgNzhwg55u/3/h52T/ezUTS5m7Bi\n8grkxOUIeT8Sb6BXhPlrDVGQ7DjbiF1lTTDpNLhjenan53WyDuMs4zA9czqLYCKiCxZdWHJ5W0m9\nsJvmxqaM7XFu4CRjErJjO/+cpvDHQjhMXNwcTv4JhSxdXgUv7LACAG6/LBPJJl0ve4SuUMgzkjBP\nsZinOKGSZWa8AVNz4uD2qVh3rE7IMWfnzIZJZ4JP8XV6zuF14Joh1wifHStU8ox2LISJguAfB6pQ\n1ezGsCQjloztPOMKERF1b+m41p+b/zpSA6/S/w5PVVVRUl+Ct4rfwptH3sSRuiP44cQfIjM2Ey3e\nFjS5m2Bz26DT6PDNgm9iSjpbPSMVe4SJBll5kwt3vHMUHp+KZ64rCMjE8EREkUxRVSz/v6OwNrrw\nyLyhmJuf1Od9W7wteO3ga6i0V8Kkbb352OF1wKwz47vjvwuz3ow6Rx0MWgMyzBlcJyFMsEeYKAyo\nqooXdljh8amYPyKJRTAR0QBoJKn9qvA/D9f08uqO/nL4L6h31sOsM0OSJEiSBLPODFVV8dqh12CQ\nDRiaOBSZsZksgqMAC+EwwV4icYKZ5c7SJuy+cIPc8i5ukAtHPDfFYp5iMU9xQi3LrxUkw6yXcaTa\njuM1jj7tU2WvQpmtrMsVOiVJgsvnwhcVX4geapdCLc9oxUKYaJA4I+gGOSKiYIvRye0zSPzzy+o+\n7XOg5gD0mu6Xco7RxuDY+WNCxkfhgYVwmODqM+IEK8u2G+TykyPrBjmem2IxT7GYpzihmOWSsanQ\nSMDWkgbUOTzBHk6/hGKe0YiFMNEgONfowlsHWleQu/vCCnJEROSfjDgDrshLgFdRseZoba+vn2iZ\nCLfi7vb5Fm8LRqeMFjlECnEshMMEe4nEGews22+QU1R8rSAZ4yPsBjmem2IxT7GYpzihmuU3x6cB\nANYcrYXbq/T42nRzOvLi8+BROl89VlUVBtmAaRnTAjLOS4VqntGGhTBRgO0obcQX1iaY9TKWT8sK\n9nCIiEKKzW3DmpNr8MqBV/Daodewr2pflwtbdKcww4zhKTFodHqxpaS+19d/e9y3kRKTArvHDlVV\noaoqHB4HZI2M70/4PnQy79+IJpxHmCiAnF4Fd/zfUVQ1u7Hiipz26X6IiAg4UH0A7x5/F7IkQy/r\nW4tSrwPJxmT8cNIPYdKZ+nScDcfr8JttpRieEoMXlo7qddozVVVR2lSK3RW74VN9GJMyBoWWQmgk\nXh8MV5xHmCgErd5feeEGuRhcPyY12MMhIgoZja5GvHP8HcRoY6CXW2dyaJvT1+6x429H/tbnY12V\nn4QEoxan6lpwqNLe6+slScKQhCG4afRNuGXMLZiYNpFFcJTidz1MsJdInMHK8lyjE28fbJ3S556Z\nORF7gxzPTbGYp1jMUxzRWW46s6nbqcy0Gi1Km0pR56jr07H0Wk37xYZ/Hu7bVGrBxnMzNLAQJgqA\n1hvkzsGjqLi2IBnjIuwGOSIif1U6Krtc2KKNBhqcbDjZ5+NdNyYVWo2EHaWNqLS5RAyRogAL4TDB\n+QbF6S5Lm9sGq82K8y3n/X6PjSfOt98g9/3pkX2DHM9NsZinWMxTHNFZ9taK4FN97X3DitrzbBAA\nkGzSYW5+IhQVeGNPBXxKQG6BEobnZmjo/lcxoijR6GzEW8fewjnbObgUF2RJRlpMGr4+/OsYnjS8\n38crbXDi95+3riB35+XZSIrhHchERJcalTwKW0u3wqg1dvl8k7sJ28q24f2T7wMALDEWzMmdg/GW\n8d0e81uFadhyqh6bT9Wjxu7Bw/OGIoWreFIPeEU4TLCXSJyLs7R77PjDvj+gxlEDo9aIBH0CYnWx\nsHvs+POXf8ap+lP9OrbLq+DxTafh8iq4ZkQSri1IFj38kMNzUyzmKRbzFEd0ljOzZsIgG7q82nuq\n4RRqHbVweBwwyAYYZAMaXY14q/gtbC3d2u0xh6eYsOrrBUg2aXGoshkr/lmMA+U2oeMWhedmaGAh\nTFFtw+kN8Km+Tn+ikyQJRtmIdafX9et4L+08h9P1TmTHG3DPzNxep/AhIopWBq0BP5j0A5i0Jtg9\ndnh8Hji9TtjcNtg9dhSmFXb4GSpJEkw6EzaXbkazu7nb4xZmxOLFpaMxMTMW9S1ePLjuJFYfqISi\nhnarBAUH5xGmqLZq16oee8/sHjvun34/4g3xvR5rW0k9Htt8BjqNhOe+MRLDU/o2/yURUTRrm9P3\nRP0JGLVGNDobsadyDwxaQ5evd/vcmJ45HQvzF/Z4XJ+i4s9FFXhzf+vy9jNy4/HAVUMQZ2BXaCTi\nPMJEA+DxdV5m82KqqqLF29LrcSqaXPifT0sBAD+Ykc0imIioj9rm9J0/dD5m58yGzWPrtggGAL2s\nR11L79OqyRoJ/29qFv7r2nzEGWTsKmvCin8ew/Fah8jhU5hjIRwm2EskzsVZxhp6ntZMJ+uQYEjo\n8TUen4InPjkDh0fBrCEJWDI2uhbO4LkpFvMUi3mKM1hZJhoS4fa5u33eq3gRZ4jr8/Fm5CXgD0tH\nYWSqCVXNbvz0/eNYc7QWapBbJXhuhgYWwhTVpmVM6/aKr1fxIj8xv9s7mtu8vqcCx2ocSIvV4d45\neewLJiLyw6ycWfDB1+3zbp8bc3Pn9uuYGXEG/M/1BbhuTCo8iornPivD01vPosXT/fuEmvqWerx/\n8n38/cjf8fGZj+Hw8Mq2COwRpqimqAr+/OWfUdJQApP2q3YGl88Fk9aEH035UY9r3e8qbcR/biiB\nRgL+57qRGJtuHoxhExFFtA2nN+Czc58hRhvT4XGn14mpmVNx3fDrBnzsTSfP49ntZXB5FeQnG/Hf\ni0YMaJpLj8+DPZV7cKrhFGRJxtSMqRiRNEL4xRBVVfGvE/9CUVUR9LIeWo0WLp8LqqpiUf4izMia\nIfT9wtVAe4Tle+6555fihwM0NTUhMzMzEIcmEkaSJEywTIBZZ0ZdSx08igcG2YDJ6ZNx8+ibEaOL\n6XbfGrsbD390Ci6fiu9Ny8LVw5MGceRERJFreNJwmLVmnGs+B5vbBo/igUlnwtV5V2Ne3jy/is38\n5BjMGpKAfeU2nG1w4YuyJlw5NBExOrnPx7A2WfHC/hdw7PwxtHhb0OBswJ6qPfiy9ksUWgqhk8XN\nXbyldAt2VuyESWdqn+FIq9FCq9HiSN0RDIkfgiQjP38qKiqQkNBzK2NXeEU4TGzfvp2r0AgiIkuf\nouKBtSdxqLIZU3Pi8NiC4dBEaUsEz02xmKdYzFOcYGSpqirsHjtUqIjVxQq92lrf4sEDa0/ibL0T\neYlGrFo8Asl9WHzD6XXi6V1PQ6vRdhqPV/HCYrLgh5N+2Otx+pKnoir4ze7fdDu7kaqqSDWl4o6J\nd/T6fpGOs0YQDaK/7avEocpmJMdocf/cIVFbBBMRBZIkSYjVxyJOHye85SApRoenF4/AsCQjShuc\nuO/DE6iz9zyTEADsKN8Bn+rrcjxajRZWmxVV9iohY6x31qPJ3dTt85IkodpRLeS9ohUL4TDBKxri\n+Jvl/nIb/ravEhKAB68aGvVLKPPcFIt5isU8xYnELBNjdFj19QLkJ8fA2ujCfR+eQK29+xkrAKCk\noaTHm6h1Gh0O1Rzq9b37kqeE3ot/FVwoxB+9FsJPPfUUZs2aheuvv779sTFjxmDp0qVYunQpHn/8\n8YAOkKivWrwt2HRmE9488iY+OPkBGl2Nwt+jvsWDJ7ecgQrg1skZmJzd9yl8iIgo9CQYtVi1eASG\np8TgXJML9314EjU9FMO9Facq1E6rlQ5UojER8fruF3RSVRUZ5gwh7xWtev1OXXvttXjppZc6PGY0\nGvHee+/hvffewyOPPBKwwdFXON9gz3aV78JTO5/Cdut2nG06iwPVB/DM7mfwrxP/6jRX5ECzVFQV\nT289i/MOL8ZnmPHvk/nDB+C5KRrzFIt5ihPJWcYbtXhq0QiMSIlBeZML9605germrovhUcmjelxo\nyaf6MCltUq/v2Zc8NZIGMzJndPt+Ld4WXJN3Ta/Hoe71WghPnjwZiYmJgzEWogEpaSjBmlNrYNQa\n21cj0mq0MOlM2Fe1D9vKtgl5n/87WI09VhviDTIeunooZA37gomIIkW8UYunFo/AyFQTKmxu3Pfh\nCVTZOhfD0zOnw6g1drkgh9vnRn5CPpJjkoWNa07uHFyWcRlavC3wKK09zE6vEy6fC9ePuB7DEocJ\ne69o1KdZI6xWK+666y588MEHAIBx48Zh1KhRMBgMWLlyJaZOndppH84aQYPllQOvoNZR2+2NFBpJ\ng/um3+fXn6r2nbPh4Y9OwqcCv742H5fn9X+KFiIiCn3NLi8e+ugUjtU4kB6rx9NfH4GMuI5LPtc6\navH64dfR5GqCSWuCChUt3hYMiR+C74z/DvSyXvi4mlxN2GbdBpvbhgxzBq7IuqLXBZ+iyUBnjdAO\n5M22bduGlJQUHDp0CHfffTc2btwIvV78N52oL6od1ZCl7ud/bHI1ocHZ0K/f0FVVRYOrAS6fC+UN\nBjy6sRQ+FfhWYRqLYCKiCBZr0OLJRSPw8EcncbTagfs+PIGnFxcgM/6rYjjVlIqV01aiuK4YR+qO\nQKvRYkbmDGTGBm79hHhDvF8LiVDXBlQIp6SkAAAKCwuRlpYGq9WK/Pz8Tq9bsWIF8vLyAAAJCQko\nLCxsv0uyrTeG233bfvHFF5lfD9ulpaUA0H6+Xbq9c9dOxGvjMXv27A59WV0d73DNYby69VU0ehoR\nnzIOx61z4FN0KIx3Y/n0rJD4ekNpu7c8uc08mWdkbLc9FirjCfT2EwuvwCMfncKRajvuefcwnrth\nPLLiDR1ePzZ1LKqOnEeDR4I2K4V5DuJ22/+3fd4vX74cA9Hv1oiGhgYYjUYYjUZYrVbceuut2LBh\nA4zGjpfn2Roh1vbtnBS+O/1tjegpy/1V+/HuiXdh0prQ7IxF0enp8Pp0SI0/hxn5JfjRlBXQarQB\n+1rCEc9NsZinWMxTnGjM0uH24ZH1p/BllR2pJh1umZSOWrsHlTYXKm1uVNrcaHB6AQAaCVg8OhW3\nX5aJBGPvnxPRmGcgDbQ1otdC+Fe/+hU2btyIhoYGpKSk4N/+7d/wwQcfQK/XQ5Zl3Hvvvbjyyis7\n7cdCmAZLSUMJXj/0Osw6c6fnWrwtuDrvalyVd1Wvx1FUBc/sfgY+1Qe7y4yikmnw+AxIjavG+Lz9\ncPkcWDhsIa7IviIAXwUREYUih9uHn284hcOV9i6f12okpMXqUGlzQ1GBWL2Mb0/JwPVjLdDypupB\nE7BCeKBYCNNg2lW+C+tK1kGCBIPWAK/ihdvnxmUZl2HJiCV9WpHobONZvHLgFWhUC4pOT4fba0Ry\nbC0K8/ZB1rQub5lgSMBdk+8K9JdDREQhpMXjw9/2VaKhxYuMOD3S4/TIiDMgI06P5BgdZI2EM/Ut\n+OPOcyg6ZwMA5CUacefl2Zia0/08wCQOl1iOcBf3xFBnM7Jm4MHLH8TsnNkYEj8EE9MmYuX0lfhG\nwTc6FcHdZdnkboLLE4P9Z6bB7TUi0XS+QxEMAC6fK6BfRzjiuSkW8xSLeYoTzVnG6GQsn56N++YO\nwb9PycTXClJQmBELi1nfPpXm0KQY/PfC4fjV1/KRFW9AaYMTD390Cv+5/hSsjc5Ox4zmPEMJTZtI\nRQAAIABJREFUmx0pYsRoY3DN0IFPLG6QUlFsvRIuTwziYxowYUhRhyJYVVXE6bmSHBERdU2SJFwx\nJAGX5cThvS9r8Pd9ldhV1oS952xYOs6C2yZnwKzvfpYjGnxsjSAC0Oj04r4PT+BsvROxxiZMHvYF\ndLK3w2uaPc34zrjvYGTyyCCNkoiIwsl5hwev7ynHhuPnoaJ1OefvTc3EtSNT2q8kV9pc+Pu+Knxz\nvAXDkmOCO+AwxtYIogFqdnnx0LqTOFvvRFa8FuNyd0CSOv4Zy+6xY1LaJBQkFQRplEREFG6STTqs\nnDMEv186CuPSzWh0evHb7WW451/HcKiyGW6fgl9/fBofHa/D6gNVwR5uVGIhHCbYSyTOxVm2TY1z\nsq4FWfEGPHPdaNx3+V0YnTwaGkkDRVUQp4/D0oKluHHkjX266S7a8NwUi3mKxTzFYZYDNzLVhP+5\nrgAPXz0UFrMOJ+tasHLNCdz1bjFO1rUAAL6sag7uIKMUe4Qparm8Ch7dWIKj1Q6kxeqwavEIpJh0\nABLwrdHfCvbwiIgogkiShKuGJ+HyIQl4+2AV3txXgbJGF2QJ0MoaVDd7UN3sRlosV+odTOwRpqjk\n9in45cYS7LHakGzS4pmvj0R2gqH3HYmIiASobnbj3cPVGJtuxobj57G7rAkPXT0UVw9PCvbQwhJ7\nhIn6yKuoeGLzGeyx2pBg1OKpRSNYBBMR0aBKi9XjzstzMGdYEsalty4IxfaIwcdCOEywN0sMn6Li\n/rf34POzjYjVy3hy0XAMSeJduv7guSkW8xSLeYrDLMW6OM/xGbEA0O3qdRQ4LIQpaiiqime3l+JL\nmxYmnQZPLByO4SmmYA+LiIii3KhUE3QaCafPt8Du9gV7OFGFhXCYmD17drCHENZUVcULO6xYf/w8\nDLKE/1owHKPTzMEeVkTguSkW8xSLeYrDLMW6OE+9VoOCVBNUAEeqeFV4MLEQprB3znYO60rW4aOS\nj1Bl73oexr/tr8L7R2qh00j45dfyUXjhz1BEREShoK1P+DD7hAcVC+Ewwd6szhweB17Y9wL+uP+P\n2Fu5F19UfoHni57HKwdegdP71YIYR6vt+GtRBSQAP79mGFrOHAzeoCMQz02xmKdYzFMcZinWpXm2\n9Ql/yT7hQcVCmMKSqqp49cCrON9yHmadGVqNFjqNDmadGZX2Srxx+A0AgNOr4OmtZ6GowI2Fabhi\nSEJwB05ERNSFsReuCBfX2OHxKUEeTfRgIRwm2JvV0Yn6E6hpqYFW03lNGJ1GB6vNCmuTFa99UQ5r\nowtDkoz47mWZAJilaMxTLOYpFvMUh1mKdWmeCUYt8hKNcPvU9tXmKPBYCFNY2lu5FyZt9zM+mLQm\nvHv0IN77sgayBDwwdwj0Wp7uREQUutrnE65kn/BgYWUQJtib1ZFP9UGSpO6f9+nwyfFUAMBtUzJR\nkPpV0cwsxWKeYjFPsZinOMxSrK7yHJ/RdsMc+4QHCwthCkujkkehxdv9n46OlhfA7tJhlMWEZRPT\nB3FkREREAzMu/cINc1V2qKoa5NFEB+nYsWMBSbqsrAxTpkwJxKGJ4FW8eHrX0wDQ6cpwdaMFh8um\nQC9LeOGbo5GXaAzGEImIiPpFVVUs+/thnG/x4n+/NQa5/Pzqs6KiIuTm5vZ7P14RprCk1Whxe+Ht\nUKB0uDLc2OLFsfJxAIDvT8tiEUxERGFDkiSMa1tume0Rg4KFcJhgb1ZnWbFZuH/6/bh26LVIN6cj\nzZQOR/NCeHwGTMyMxTfGWbrcj1mKxTzFYp5iMU9xmKVY3eU5njfMDarOc08RhRG9rMesnFmYlTML\nH584j9VVZ2HSaXDfnCHQ9HAzHRERUSjq7oqwV/HC6XUiRhsDWSMHY2gRiT3CFBGqm934wTtH4fAo\nWDknDwtGpgR7SERERP3mU1Tc8JeDaPEoeGrRCAxL8eH9k+/jTOMZeBUv9LIeI5NH4rrh18Gk634a\n0WjDHmGKWoqq4pltpXB4FFyeF49rC5KDPSQiIqIBkTUSvlWYBgD4709O45ndL8Fqs0Iv62HSmaDV\naHH8/HE8X/R8j7MnUd+wEA4T7M3q3pqjtdhXbkOCUYufzs7rcX5hgFmKxjzFYp5iMU9xmKVYPeV5\n66QMFGbEosHpw4nyyZAuKde0Gi1cXhc2nN4Q6GFGPBbCFNasjU68suscAOA/ZuUiyaQL8oiIiIj8\nI2sk3HtlJrSyG+ebLSirG9rpNTpZh6Pnjw7+4CIMC+EwwTXeO/MpKp7eehYun4p5w5Nw5bDEPu3H\nLMVinmIxT7GYpzjMUqze8jQbvMjP2AMAOFVZgCZHQqfXOD1OLrzhJxbCFLbeOliFo9UOpJp0+NHM\nnGAPh4iISBiTzoS0+DrkppyBCg0Ol02A19dxsq8YXUyv7YDUs14L4aeeegqzZs3C9ddf3/7Y2rVr\nsWDBAixYsACffPJJQAdIrdib1dGpOgf+UlQJALh3Th7iDH2fCZBZisU8xWKeYjFPcZilWL3lqZf1\nGJowFEMtxYgzNsLpMaH43Fi0XQB2+9wYkzJmEEYa2XothK+99lq89NJL7dtutxvPPPMM3nzzTbzx\nxht44oknAjpAoku5fQpWbTkLr6Li+jGpmJoTH+whERERCfeNgm9AllWMzt4HWeNFdVMmyutz4Pa5\nEaePw4KhC4I9xLDXayE8efJkJCZ+1Xt58OBBFBQUIDk5GZmZmcjIyEBxcXFAB0nszbrYX/ZW4HS9\nE1nxBiyfntXv/ZmlWMxTLOYpFvMUh1mK1Zc8EwwJuHvK3RifkYERmYcAACcqRiPbNAUrJq+AQWsI\n9DAjXr97hGtqamCxWLB69WqsW7cOFosF1dXVgRgbUSdfVjbj7UPV0EjA/XPzEKPj6jpERBS54g3x\nWDZmGZ5b+P8wf0QiFFXGzpLhUMFZkkQY8M1yt9xyCxYtWgQAbNQeBOzNAlo8Pjy97SwUFbhpQjrG\npccO6DjMUizmKRbzFIt5isMsxepvnpIk4Z5ZechJMOBsvRN/3GkN0MiiS9/vMLogLS0NNTU17dtt\nV4i7smLFCuTl5QEAEhISUFhY2P6ngLYTgNt92z506FBIjScY22sr9Shv0iE/2YjhLSXYvr0kpMbH\nbW5zm9uRvN0mVMYT7ttt+rN/jE7G4qQG/G+TEWuL6zA3Pwn2kgMh8fUEI7/t27ejtLQUALB8+XIM\nhHTs2LFeJ6CzWq2466678MEHH8DtdmPRokV4++234XK5cPvtt2PDhs4rm5SVlWHKlCkDGhTRpXaX\nNeLn60ug1Uj4/TdGYngK11cnIqLQ4fQ6saV0C4rPF8Pj8yDOEIdZ2bMwPnW88L+cP7e9DGuKa/GD\nGdntyzFHu6KiIuTm5vZ7P21vL/jVr36FjRs3oqGhAXPnzsWjjz6KlStXYtmyZQCAhx9+uP+jJeqH\nSpsLT205CwD49pQMFsFERBRSbG4bXih6AU6fEwa59Qa2+pZ6vHX0LRxPP44bRt4gtBiOM7TeH+Py\nKsKOGa167RF+9NFHsX37dhw+fBhbt27FvHnzsHjxYqxfvx7r16/HVVddNQjDpEv/lBItXF4Fv/74\nNGwuH6bnxuPmiel+HzNaswwU5ikW8xSLeYrDLLu3+uhqeBVvexEMtPb0mvVm7KvahyN1Rzrt40+e\nBm1r+cZC2H9cWY5ClqqqeP7zMpysa0FGnB4PzB0CDW/MJCKiENLkaoK1yQpZ0/UsRmadGZ9aPxX6\nnvq2QtjHQthfvbZGUGhoaxKPJmuP1WH98fPQyxIenT8M8UYxp2s0ZhlIzFMs5ikW8xSHWXbtfMt5\n2L12NHuaIUsyEgwJHYpiSZLQ7GrutJ8/eRp5RVgYFsIUkoqr7XjhcysA4Mezc9kXTEREIcfpdeL9\nU++jqLIIWo0WKlToNXpkxWYhPzG/vS9YK4sttwza1uOyEPYfWyPCRDT1ZjW0ePBfm07Dc2EJ5a8V\npAg9fjRlORiYp1jMUyzmKQ6z7Min+PDygZfR6GpEnD4OelkPg2yAJEkos5XhZMNJAIDL58LY1LGd\n9verR1huuyLc68Rf1AsWwhRSfIqKJz45gxq7B2PTzLjz8uxgD4mIiKiTgzUHUeuohU6jQ35iPjyK\np/05rUaLcls5XF4XYrQxmJMzR+h782Y5cdgaESaipTfrjT3l2F/ejESjFj+/Zih0svjf1aIly8HC\nPMVinmIxT3GYZUf7qvYhRhsDAEg3t85oVNJQghZvC1SoUFQFXtWLFZNXwKg1dtrfnzxZCIvDQphC\nxvbTDfjHwWpoJODn1wxFqlkf7CERERF1yaN4OswNnG5OR7o5HXaPHR6fB1qNFvOGzEOsPlb4exs4\na4QwbI0IE5Hem1Xa4MRvtrUumrF8ejYmZMYF7L0iPcvBxjzFYp5iMU9xmGVHqTGp8CreTo+bdWYk\nGhMhSRLyE/K73V9MjzALYX+xEKagc7h9+PXHp+HwKJg7LBE3jrcEe0hEREQ9mpc3D26fu8vnVFVF\nsjEZefF5AXlvtkaIw0I4TERqb5aqqnjm01KUNjgxJNGIe+fkCV+T/VKRmmWwME+xmKdYzFMcZtlR\nUkwSFuUvgt1jh6J+VZC6fC74VB/+fdy/9/h5JmQeYbZG+I09whRU7xyqxqenG2DSafCL+cMQo+t6\nZR4iIqJQc0X2FRiWOAybzm5CjaMGskbGpMRJmJM7ByZd4Oa/17fPI8zp0/zFK8JhIhJ7sw6U2/Dq\nF+UAgPvmDkFuYue7agMhErMMJuYpFvMUi3mKwyy7lmHOwG1jb8NPpv4E90y5BwvzF/apCParR5it\nEcLwijAFRY3djcc2n4GiAjdPTMfsoYnBHhIREVHIqW+px+bSzahtqYWskTE5bTImWiZCIwFeRYVP\nUSFrAttSGMmkY8eOBeS6ellZGaZMmRKIQ1OYc/sU3P/hCRytdmByVhyeWDic/4iJiIgusat8F9ac\nWgODbIBW03rt0uF1IMmQhE++vBpOr4r3vjMBJj3bCouKipCbm9vv/dgaQYPujzvP4Wi1A2mxOjw8\nbyiLYCIioktUO6qx5tQamHXm9iIYAExaE+weO1S0zljB9gj/sBAOE5HSm7XheB3WHK2FTiPhF9fk\nI8E4+N05kZJlqGCeYjFPsZinOMxSrN7y3HRmE4xy1/fOaDXarwphzhzhF/YI06A5WevAc5+VAQDu\nnpmDkZbWmwk8Pg9Km0rhVbzIic+BWWcO5jCJiIiCrqaldRaK7mg0PgC8IuwvFsJhItznb2xyevHr\nTafh9qlYNCoFi0anQlVVrD+9Hnsr98LutUOCBK1Gi5HJI3HTqJuglwOzxHK4ZxlqmKdYzFMs5ikO\nsxSrtzxlqee+X43UVghzCjV/sDWCAk5RVTy15SwqbW6MTDXhR1fkAADWnFqDnRU7IWtkxOvjEaeP\nQ4w2BqfqT+HVg69CVfmPm4iIolNBcgFcPle3z2s1rZ+RbI3wDwvhMBHOvVl/LarEF9YmxBtk/Oc1\nw6DXamD32LG3cm+X/U96WY+K5gocO38sIOMJ5yxDEfMUi3mKxTzFYZZi9ZbnlTlXQqfRdVi1rk2L\ntwVJxtY2QrZG+IeFMAXUztJG/HVfJTQS8PC8oUiPa213KKos6nE/k9aE3RW7B2OIREREISdGG4Mf\nTvohzDozmj3NcPlccHgccPvcmJ45HVlxFgCAk4WwX9gjHCbCsTervMmFVVvOAgC+OzUTU7Lj259r\n9jR3mA7mUpIkwaN4AjKucMwylDFPsZinWMxTHGYpVl/yTIlJwX9c9h84ZzuHkoYSGHVGTLBMgFFr\nxMHSMwB4RdhfLIQpIOrsHjz80Uk0u32YOSQBN09I7/D88MTh+OzcZ4jVxHa5v8fngcVkGYyhEhER\nhSxJkpATn4Oc+JwOj+vl1jn43SyE/cLWiDARTr1Z9Q4PHlh7AuVNboxIicH9c4dAkjoumlGQVIAE\nfUK3N8R5VA+uyr0qIOMLpyzDAfMUi3mKxTzFYZZi+ZunUdtawrE1wj8shEmoRqcXD647ibJGF/KT\njXhy0QiYu1j6UZIk3Dr2VngVLzy+r1ogFFWB3WPH9cOvR7whvtN+REREBBguFMKcNcI/0rFjxwIy\nR1VZWRmmTJkSiENTiLK5vHhg7UmcqmvBkEQjVn19BJJidD3u0+xuxubSzTjdcBoKFKSZ0jB/yHyk\nm9N73I+IiCia/aWoAn8pqsS/T87Ady7LDPZwgq6oqAi5ubn93o89wiSE3e3Dwx+dwqm6FmTHG/Dk\n4t6LYACI1cdiyYglgzBCIiKiyKFr6xHmFWG/sDUiTIRyb5bD7cMjH53CsRoHMuL0WPX1EUgx9V4E\nB0soZxmOmKdYzFMs5ikOsxRLVJ5S7y+hHrAQJr84vQp+saEER6rtSIvVYdXiEbCYA7M0MhEREbVq\nv9dcYinsD79aI8aMGYNRo0YBAKZNm4ZHHnlEyKCos1Ccv9HtVfDohhIcrGxGikmHVYsLkBFnCPaw\nehWKWYYz5ikW8xSLeYrDLMXyN0/lQiHMK5r+8asQNhqNeO+990SNhcKI26fg15tOY1+5DUkxWqxa\nPAJZ8aFfBBMREUWC9pkOeEHYL/xFIkyEUm+WV1Hx+OYz2F3WhHiDjCcXjUBuojHYw+qzUMoyEjBP\nsZinWMxTHGYplr95ts3Dr2FrhF/8KoTdbjduuOEGLFu2DHv27BE1JgphPkXFk5+cwY6zjYgzyHhq\n8QgMS44J9rCIiIiiUrPLF+whhDW/5hGuq6tDSkoKDh06hLvvvhsbN26EXt96o1RZWRleffVV5OXl\nAQASEhJQWFjY3hPT9psQt8NnW1GBz7052HyqHgaNim/nOvFvX5sZMuPjNre5zW1ucztatuPyJ+L+\ntSehgYrlQ5341vzo+jxu+//S0lIAwPLlywc0j7CwBTVuuukmPPXUU8jPzwfABTUijaKq+O2npVh/\n/DyMWg2eXDQCY9PNwR4WERFR1HpuexnWFNdiWJIRv//GKOi10dvxOtAFNQacWGNjI5xOJwDAarWi\nqqoKWVlZAz0c9eLi34AGm6qqeP4zK9YfPw+DLOGxBcPDuggOZpaRiHmKxTzFYp7iMEuxROR5x4ws\nZMUbcLreiTf2VggYVfTRDnTHkpISPPTQQ9Dr9ZBlGY8//jiMxvC5YYr6RlEUPL7lID4tUaGRFEzN\nL4YTbviUyyBr5GAPj4iIKGrF6GQ8eNUQ/PSD43jnUDVm5MZjYlZcsIcVVoS1RlyKrRHhT1EUrPzo\nY3xZboEkKZiQtw8pcbVweBzIiM3AHRPugE4O3RXkiIiIosGf91bgr/sqYTHr8PKNY2DWR9+FqkFv\njaDI9/jWL1qLYCgYn7sfKXG1AACTzoRaRy3WnFoT5BESERHRrZMzMMpiQo3dgz98Xhbs4YQVFsJh\nYrB7s/6+rxKfntIDUDEu9yAs8TUdntfLehypOwKv4h3UcYnAPjexmKdYzFMs5ikOsxRLZJ5ajYQH\n5g6BQZbw8cl67CxtFHbsSMdCmDp5+2DVhaZ7FWNzDiEtoarL1zm9TjS7mwd3cERERNRJbqIRNxSm\nAQD2l9uCPJrwMeCb5Whwtc2fF2jvfVmDV3aXAwBGZh1ERmJlt6/VQBOWPcKDlWW0YJ5iMU+xmKc4\nzFKsQOTZ1hvM1eb6jleEqd264lq8sMMKAPiPWbmYMUSGoipdvlZVVaSb02HWhe80akRERJHkwqrL\nYBncdyyEw0Sge7N2nG3E7z5rbbC/6/JsXDcmFYuGLYLb525fz/xiTp8TC4YtCOiYAoV9bmIxT7GY\np1jMUxxmKVYg8lQufF5rNCyF+4qFMOFotR1PbD4NRQVum5yBb45v7TFKNaXijol3wKQzweaxodnd\njGZ3M7QaLZaNWYbhScODPHIiIiJqo1y4bsU6uO84j3CUO9foxE8+OIFGpxfXFiRj5Zw8SF30FlXZ\nq1DjqEGiMRHZsdldvoaIiIiC5y9FFfhLUSVum5yB2y/LDPZwBtVA5xHmzXJRrL7Fg0fWn0Kj04up\nOXH4yZVdF8EAkG5OR7o5fZBHSERERH3FK8L9x9aIMCG6l6jF48MvNpSgvMmNESkx+Pm8YdBGyb8c\n9rmJxTzFYp5iMU9xmKVYgewR5l9t+46FcBTyKSqe2HwGx2ocSI/V47EFw2GKwuUYiYiIIknbFWGZ\ndXCfsRAOE6LmG1RVFc99VoZdZU2IM8h4YuFwJJvCby5gf3AuTLGYp1jMUyzmKQ6zFCsQebbN8sR5\nhPuOhXCU+dv+Kqw7Vge9LOHX1+YjN9EY7CERERGRAG1XhFkH9x0L4TAhopdo/fE6/HlvBSQAP7t6\nKMalx/p9zHDEPjexmKdYzFMs5ikOsxQrEHn6eEW431gIR4kvyprw209LAQA/mpmD2UMTgzwiIiIi\nEkllj3C/sRAOE/70Eh2vdeC/NrUumHHzhDQsGWsROLLwwz43sZinWMxTLOYpDrMUKxB5ctaI/mMh\nHOEqbC785/pTcHoVzBuehP83LSvYQyIiIqIAUJTW/0bJbKhCsBAOEwPpJWp0evHIR6dQ3+LF5KxY\nrJyTx74hsM9NNOYpFvMUi3mKwyzFCsg8wmCPcH+xEI5QTq+CRzeUwNroQn6yEb+Ynw+dzG83ERFR\npOIV4f5jZRQm+tNL5FNUPPnJGRyptsNi1uHxBSNg5oIZ7djnJhbzFIt5isU8xWGWYgVkHmFeEe43\nFsIRRlVVvLDDis/PNiJW37pgRoo5uhbMICIiika+C7NG8Ipw37EQDhN97SV662A1PjhaC51Gwi+/\nlo8hSTEBHln4YZ+bWMxTLOYpFvMUh1n2bF/VPjxf9Dx+/dmv8djnj+H1Q6/jnO1ct68PSI+wwivC\n/cVCOIJsOnke//tFOSQAD141BBMyo3PBDCIiosH04akP8c/j/0Szuxl6WQ+tRovK5kq8fOBlFNcV\nD9o4LlwQ5hXhfmAhHCZ66yXad86GZ7a1Lpjxw8uzMSc/aTCGFZbY5yYW8xSLeYrFPMVhll2rsldh\nR/kOmHSmDo9LkoQYbQz+eeKfUFSl034BmUdY4TzC/aUN9gDIf6fqHPjVxyXwKipuHG/BDePTgj0k\nIiKiqPBJ6SeIkbtvQ3R4HDhSewTjLeMDPpbvXJaJJeMsyE0wBPy9IgWvCIeJ7nqJqpvd+Pn6Ejg8\nCubmJ+KOGdmDPLLwwz43sZinWMxTLOYpDrPsms1tg6zpfmYmvUaPCntFp8cDkWduohGFGbFIjOFN\n8n3FQjiM2VytC2bUOTyYkBGL++cOYYM8ERHRIDJqjVBVtdvn3YobycbkQRwR9Yd07Nix7r97figr\nK8OUKVMCcWi6oMXjw+Obz6Cq2Y3fXleAWIOYTpdKeyUO1hyEBhpMSpuEVFOqkOMSERFFmpL6Erx+\n6HWY9eYun/cqXjw440HoZF6lDaSioiLk5ub2e78BV05r167F7373OwDAz372M1x99dUDPRQNUIxO\nxq++lo8ml1dIEdzibcGfDv8J1iYrDLIBKlRsKduCofFD8e1x34ZBy54jIiKiiw1LHIaRKSNR0lAC\ng9zxc9LhdWDRsEUsgkPYgFoj3G43nnnmGbz55pt444038MQTT4geF12iu14iWSMhSUAvkKqqePXg\nq6h11CJWHwudrINe1iNWF4uK5gq8cfgNv98jVLDPTSzmKRbzFIt5isMsuyZJEm4bexumZ04HANg9\ndji8Dhi1Rnyz4Ju4IvuKLvdjnqFhQJcRDx48iIKCAiQnt/a8ZGRkoLi4GKNHjxY6OBo8JxtOotpe\nDbOu8592dLIOZbYyWJusyInPCcLoiIiIQpdG0mBR/iJcO/RaNLmbIEsy4vRxnMYsDAyoEK6trYXF\nYsHq1auRkJAAi8WC6upqFsIBFOj5G/dU7oFJa+r2eZPWhN2VuyOiEOZcmGIxT7GYp1jMUxxm2TtZ\nIyPJ+NU8/tYmKzaXbkaDswFajRZjU8diZvZM6GU98wwRfjWW3nLLLQCAjRs38reeMKcoSo/fQwkS\nvIp3EEdEREQUvjad3YRPSj+BSWuCRmrtRN1StgW7K3ZjxeQViNVz9ddQMKBC2GKxoKampn27pqYG\nFoul0+tWrFiBvLw8AEBCQgIKCwvbfwNq643hdt+2X3zxxYDm11LWghMNJ1AwtAAAUFraukpd2/fv\nxJkTyLZlAxcu+gc7D3+2L+7LCoXxhPs282SeobzNPMVttz0WKuMJ5e1qVzWKdEWI1cd2+Dw1ykaU\nnCnBY+cew3Vp1zFPP7bb/r8t3+XLl2MgBjR9mtvtxqJFi/D222/D5XLh9ttvx4YNGzq8htOnibV9\n+/b2kyAQvIoXq3atggSp05VhVVUha2TcN/2+9t9qw1mgs4w2zFMs5ikW8xSHWfbdnw7/Ceds57r9\nzLR77Jjlm4WFVy0c5JFFrkGdPk2v12PlypVYtmwZAODhhx8eyGGoHwL9w0er0eK7hd/Fa4deg9fr\nhVFrBNA6pZpRNuK7478bEUUwEPgsow3zFIt5isU8xWGWfVfvrO/xM1NVVeSMyxnEEVF3BlQIA8Di\nxYuxePFikWOhIMuKzcID0x/AzvKdOFl/EgAwOmU0pmVM4xyIREREfaSVei6vVKiI0cYM0mioJ5Fx\niS8KXNwTE0h6WY85uXPwvQnfw/cmfA8zs2dGXBE8WFlGC+YpFvMUi3mKwyz7bkzKGDi9zm6fj9XF\nwnrYOogjou6wECYiIiISaHbObMRoY+BTfJ2ea/G0YHbObMiSHISR0aUGdLNcX/BmOSIiIopWja5G\nvHn0TZTbyqGoClSoiNXFYlbOLMzJnRPs4UWcQb1ZjoiIiIi6l2BIwJ2T7sT5lvOw2qyI0cUgPyEf\nsoZXgkMJWyPCBHuzxGGWYjFPsZinWMxTHGY5MMkxyZiQNgEFSQUdimDmGRpYCBMRERFRVGKPMBER\nERGFtYH2CPOKMBERERFFJRbCYYK9ROIwS7GYp1jMUyzmKQ6zFIt5hgYWwkREREQUldhL7Xk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+ "text": [ + "" + ] + } + ], + "prompt_number": 91 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This output is terrible. The filter has no choise but to give more weight to the measurements than the process (prediction step), but when the measurements are noisy the filter output will just track the noise. This inherent limitation of the linear Kalman filter is what lead to the development of nonlinear versions of the filter.\n", + "\n", + "With that said, it is certainly possible to use the process noise to deal with small nonlinearities in your system. This is part of the 'black art' of Kalman filters. Our model of the sensors and of the system are never perfect. Sensors are non-Gaussian and our process model is never perfect. You can mask some of this by setting the measurement errors and process errors higher than their theoretically correct values, but the trade off is a nonoptimal solution. Certainly it is better to be nonoptimal than to have your Kalman filter diverge. However, as we can see in the graphs above, it is easy for the output of the filter to be very bad. It is also very common to run many simulations and tests and to end up with a filter that performs very well under those conditions. Then, when you use the filter on real data the conditions are slightly different and the filter ends up performing terribly. \n", + "\n", + "For now we will set this problem aside, as we are clearly misapplying the Kalman filter in this example. We will revisit this problem in subsequent chapters to see the effect of using various nonlinear techniques. In some domains you will be able to get away with using a linear Kalman filter for a nonlinear problem, but usually you will have to use one or more of the techniques you will learn in the rest of this book." ] }, { diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb index 8119b67..c5e904c 100644 --- a/Extended_Kalman_Filters.ipynb +++ b/Extended_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:2703ec2a794449aaabf6044e38967bdacd2cadc551c734b81dfa513e4ae2ea54" + "signature": "sha256:8cbcb6e649c23718ffea2f8ea7b974233a106f2a4079bd1aea11f0c7aa86e976" }, "nbformat": 3, "nbformat_minor": 0, @@ -248,13 +248,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 1, + "prompt_number": 2, "text": [ - "" + "" ] } ], - "prompt_number": 1 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -341,13 +341,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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NfWkkGHmznZVqnjKZfKqGZTLLCEO/QBA1ARMmfnf1PE9vvPGGCoWCzp07p3v3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\nGZZPnDihTz75ROVyWa7r6u7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/vyB7wHPSY8MNSIaj6mprzY5gGVb782eGji6HHvjnAdW0dOp/v3cWBbGHmGPG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\nzcWDIJ6FynqwYiCXlmYjigejmfhjN1mnh2Lw12J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z5s3z9UcAsLg/7zyqdw80SJKam2P0TE1Jj59Py05QdESY2p0unZmbrB/MGmFG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\nXvPGperKwiw5XR6cdg4RzDHjUBQDAAC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W/3Z69tlnkZiYiFOnTuGnn36Sfed59UdpIpNTVkBeeeWUFbB93tIaLVLzq5Ca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\nhIQEhIeHAwC8vLwQFxeH+Ph4AFfq+Lp7u+k+qd6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vnLIC9sm7v6ASx4pqOnyupKYRt6WEdficu0qBaI2nxceRW9u64kxvV0Tts0U9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\n4uocGtPwWEJej0s+l0vFebn6zcl+vfJun9qHitS694zmhnI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O9FKHahsMqGt2a94f00owNbaxPGFIiLtUsYiISCBqpQJ3xgdhTIQX3vhfJg5m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\nvXu31XEUCoV08OBB2Ww2bd26VStWrLA6kiTzzpNk7uvK1Ot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YhH/szMePJ8vxp8tiEenvKXU0Irtxppc6+ORQEXw17dduTE0IRJi26xs9ELkb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\nqbkkc7ORKzvkulF1cYGqi69di+6vv/Zw666GCp082bXgn0H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"text": [ - "" + "" ] } ], - "prompt_number": 5 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -472,12 +472,12 @@ "output_type": "stream", "stream": "stdout", "text": [ - "input mean, variance: 0.0010, 1.0013\n", - "output mean, variance: -0.0291, 2.2439\n" + "input mean, variance: 0.0009, 1.0005\n", + "output mean, variance: -0.0293, 2.2432\n" ] } ], - "prompt_number": 6 + "prompt_number": 7 }, { "cell_type": "markdown", @@ -502,20 +502,20 @@ { "metadata": {}, "output_type": "display_data", - "png": 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6qacorqrHuwfTkVZcgycn9cJAf55oS/Jj05reF198EXv37kVJSQkmTZqEtWvX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\nbF2vdDD0AgCslZubq55YXH3DCbmuq5sqAtrVPiivx9FH/WP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gJycHADptA0r4lDYg7XAuhngbMDZxKCbF+glzPNtvZ2VlCZWnq3zV1dUAAJ1O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\nAgAAIOv9PxwlSlq79+U1AAAAAElFTkSuQmCC\n", "text": [ - "" + "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ - "output mean, variance: -0.0015, 2.2530\n" + "output mean, variance: -0.0014, 2.2510\n" ] } ], - "prompt_number": 7 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -544,12 +544,12 @@ "output_type": "stream", "stream": "stdout", "text": [ - "linear output mean, variance: -0.0877, 7491.7787\n", - "nonlinear output mean, variance: -2.0078, 26241.0351\n" + "linear output mean, variance: -0.0794, 7485.2514\n", + "nonlinear output mean, variance: -1.9762, 26213.4745\n" ] } ], - "prompt_number": 8 + "prompt_number": 9 }, { "cell_type": "markdown", @@ -572,13 +572,393 @@ "source": [ "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n", "\n", - "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. \n", + "\n", + "Consider the function $f(x)=x^2\u22122x$, which we have plotted below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(0,2,0.01)\n", + "ys = [x**2 - 2*x for x in xs]\n", + "plt.plot (xs, ys)\n", + "plt.xlim(1,2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want a linear appoximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation of the Kalman filter we know it's current state, so if we linearize the function at that value we will have a close approximation. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n", + "\n", + "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x\u221212.75 as the linearization, as in the plot below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def y(x): \n", + " return 8*x - 12.75\n", + "plt.plot (xs, ys,c='k')\n", + "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n", + "plt.xlim(1,2)\n", + "plt.ylim([-1.5, 1])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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fa+/evRowYIDGjh2r3//+9xo4cCA/AhuwKHaeASBARS5cqKCqKlW//rrZpfg9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\nSkosOTw7HA7V1dXJbrc7v9b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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n", + "\n", + "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n", + "\n", + " $$f(x) = x^2 -2x \\\\\n", + " \\frac{df}{dx} = 2x - 2$$, \n", + " \n", + " so the slope at 1.5 is $2*1.5-2=1$. Let's plot that." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def y(x): \n", + " return x - 2.25\n", + "\n", + "plt.plot (xs, ys,c='k')\n", + "plt.plot ([1,2], [y(1),y(2)], c='r')\n", + "plt.xlim(1,2)\n", + "plt.ylim([-1.5, 1])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AoAuqr6/Xxo0btW7dOh09elR5eXl65ZVXNH78eOaY7wMzzwAAAF1E+/sxv/POO9q5c6ce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\nmWcYYEYZAAB0Zcw8w2PsKAM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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n", + "\n", + "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$m we will need to include that term:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "F \n", + "&\\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_{{x_t},{u_t}} \\\\\n", + "H &\\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_{x_t} \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at x. \n", + "\n", + "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** orphan text\n", + "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n", "\n", "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n", "\n", "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF." ] }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Tracking a Flying Airplane" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will start by simulating tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n", + "\n", + "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import ekf_internal\n", + "ekf_internal.show_radar_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As discussed in the introduction, our measurement model is the nonlinear function $x=\\sqrt{slant^2 - altitude^2}$. Therefore we will need a nonlinear \n", + "\n", + "Predict step:\n", + "$$\n", + "\\begin{array}{ll}\n", + "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n", + "x = Fx & x = \\underline{f(x)} \\\\\n", + "P = FPF^T + Q & P = FPF^T + Q\n", + "\\end{array}\n", + "$$\n", + "\n", + "Update step:\n", + "$$\n", + "\\begin{array}{ll}\n", + "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n", + "K = PH^T(HPH^T + R)^{-1}& K = PH^T(HPH^T + R)^{-1}\\\\\n", + "x = x + K(z-Hx) & x = x + K(z-\\underline{h(x)}) \\\\\n", + "P = P(I - KH) & P = P(I - KH)\\\\\n", + "\\end{array}\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see there are two minor changes to the Kalman filter equations. The first change replaces the equation $\\mathbf{x} = \\mathbf{Fx}$ with $\\mathbf{x} = f(\\mathbf{x})$. In the Kalman filter, $\\mathbf{Fx}$ is how we compute the new state based on the old state. However, in a nonlinear system we cannot use linear algebra to compute this transition. So instead we hypothesize a nonlinear function $f()$ which performs this function. Likewise, in the Kalman filter we convert the state to a measurement with the linear function $\\mathbf{Hx}$. For the extended Kalman filter we replace this with a nonlinear function $h()$, giving $\\mathbf{z}_x = h(\\mathbf{x})$.\n", + "\n", + "The only question left is how do we implement use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system. For example, consider the function $f(x) = x^2 -2x$\n", + "\n", + "\n", + "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:\n", + "\n", + "\n", + "$$\n", + "F \\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_x, \\\\\n", + "H \\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_x \n", + "$$\n", + "\n", + "All this means is that at each update step we compute F as the partial derivative of our function $f()$ evaluated at the point of f. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(0,2,0.01)\n", + "ys = [x**2 - 2*x for x in xs]\n", + "plt.plot (xs, ys)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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c3yAiInJFb+8pRVp0ANc1JMPyrFKKouD+y+Ow/lgtjla1io7j8ri7R7LibJKs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\nsDf+OiPJpYozZ5PUineeiVTGx1OLh8f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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we want to linearlize this equation so we can evaluate it's value at 1.5. In other words, we want to create a linear function of the form $y_l(x) = ax+b$ such that $y_l(1.5)$ gives the same value as $y(1.5)$. Obviously there is not single linear equation that will do this. But if we linearize $y(x)$ at 1.5, then we will have a perfect answer for $y_l(1.5)$, and a progressively worse answer as our evaluation point gets further away from 1.5.\n", + "\n", + "The simplest way to linearize a function is to take a partial derivative of it. In geometic terms, the derivative of a function at a point is just the slope of the function. Let's just look at that, and then reason about why this is a good choice.\n", + "\n", + "The derivative of $f(x) = x^2 -2x$ is $\\frac{\\partial{f}}{\\partial{x}} = 2x - 2$, so the slope at 1.5 is $2*1.5-2=1$. Let's plot that." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def y(x): \n", + " return x - 2.25\n", + "\n", + "plt.plot (xs, ys)\n", + "plt.plot ([1,2], [y(1),y(2)], c='r')\n", + "plt.ylim([-1.5, 1])\n", + "\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 71 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a nice visual demonstration of how the slope of the function gives the ideal linear approximation of the function near a point. We could use any linear function such that $f(1.5)=-0.75$, here, but as x varies the value computed by the function would potentially be very far from the functions value. For example, consider using $f(x) = 8x - 12.75$ as the linearization, as in the plot below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def y(x): \n", + " return 8*x - 12.75\n", + "plt.plot (xs, ys)\n", + "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n", + "plt.ylim([-1.5, 1])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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PbdfcCWn68Y3FKilIM7usmMDMs4W96e3Uo68d0IUTM/SlsonKZrFyAEAcSLv1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\nB3QsEJIvMPi21z+gYyfeDwyou39A3X1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+ "text": [ + "" + ] + } + ], + "prompt_number": 73 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the linearization is exactly correct for $x=1.5$, but very quickly diverges as x varies from 1.5. This does not constitute a proof that taking the derivative is a good linearization, but it should be fairly convincing. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will begin by writing a simulation for the radar." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import random\n", + "import math\n", + "\n", + "class Radar(object):\n", + " def __init__(self, pos, vel, alt, dt):\n", + " self.pos = pos\n", + " self.vel = vel\n", + " self.alt = alt\n", + " self.dt = dt\n", + " \n", + " def get(self):\n", + " \"\"\" Simulate radar range to object at 1K altidue and moving at 100m/s.\n", + " Adds about 5% measurement noise. Returns slant range to the object.\n", + " Call once for each new measurement at dt time from last call.\n", + " \"\"\"\n", + " \n", + " # add some process noise to the system\n", + " vel = self.vel + 5*random.gauss(0,1)\n", + " alt = self.alt + 10*random.gauss(0,1)\n", + " self.pos = self.pos + vel*self.dt\n", + " \n", + " # add measurment noise\n", + " err = self.pos * 0.05*random.gauss(0,1)\n", + " return math.sqrt(self.pos**2 + alt**2) + err" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$F = I + \\begin{bmatrix}0 & 1 & 0\\\\ 0 & 0 & 0\\\\0&0&0\\end{bmatrix}dt$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{aligned}\n", + "H&=\\begin{bmatrix}\n", + "\\frac{\\partial h}{\\partial x_{pos}} & \n", + "\\frac{\\partial h}{\\partial x_{vel}} &\n", + "\\frac{\\partial h}{\\partial x_{alt}}\\end{bmatrix} \\\\\n", + "&= \\begin{bmatrix}\n", + "\\frac{x_{pos}}{\\sqrt{x_{pos}^2 + x_{alt}^2}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n", + "\\end{bmatrix}\n", + "\\end{aligned}\n", + "$$" + ] + }, { "cell_type": "heading", "level": 3, @@ -599,7 +979,7 @@ "collapsed": false, "input": [ "import ekf_internal\n", - "ekf_internal.plot_ball()b" + "ekf_internal.plot_ball()" ], "language": "python", "metadata": {}, diff --git a/Kalman_Filter_Math.ipynb b/Kalman_Filter_Math.ipynb index 2d5eaab..2694645 100644 --- a/Kalman_Filter_Math.ipynb +++ b/Kalman_Filter_Math.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:dd34f4987a60a8a3c453361b731ac3f9a06c88bce6e4f0c67907f60ea9ab99fc" + "signature": "sha256:e3462ab986f9dc643d523b8cb2a8312877c7122edff3d6d7accda49234359e80" }, "nbformat": 3, "nbformat_minor": 0, @@ -260,11 +260,68 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This chapter is optional, especially the first time you go through this material. If you are a hobbiest you will be able to get quite far by just skipping this chapter and going on to learn the examples. However, to have any hope of reading the literature or to design more sophsticated kilters you will have to acquire some of the more formal mathematics. I will not endevour to teach linear algebra, statistics, or calculus here as each topic deserves a book on its own. \n", + "If you've gotten this far I hope that you are thinking that the Kalman filter's fearsome reputation is somewhat undeserved. Sure, I handwaved some equations away, but I hope implemention has been fairly straightforward for you. The underlying concept is quite straightforward - take two measurements, or a measurement and a prediction, and choose the output to be somewhere between the two. If you believe the measurement more your guess will be closer to the measurement, and if you believe the prediction is more accurate your guess will lie closer it it. That's not rocket science (little joke - it is exactly this math that got Apollo to the moon and back!). \n", "\n", - "blah blah blah\n", + "Well, to be honest I have been choosing my problems carefully. For any arbitrary problem finding some of the matrices that we need to feed into the Kalman filter equations can be quite difficult. I haven't been *too tricky*, though. Equations like Newton's equations of motion can be trivially computed for Kalman filter applications, and they make up the bulk of the kind of problems that we want to solve. If you are a hobbiest, you can safely pass by this chapter for now, and perhaps forever. Some of the later chapters will assume the material in this chapter, but much of the work will still be acceessible to you. \n", "\n", - "**authors note: need to start with continuous equations with $\\phi$, etc. Then discuss linearization into discrete case.**" + "But, I urge everyone to at least read the first section, and to skim the rest. It is not much harder than what you have done - the difficulty comes in finding closed form expressions for specific problems, not understanding the math in this chapter. \n" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Modelling a Linear System that Has Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We need to start by understanding the underlying equations and assumptions that the Kalman filter uses. We are trying to model real world phenomena, so what do we have to consider?\n", + "\n", + "First, each physical system has a process. For example, a car travelling at a certain velocity goes so far in a fixed amount of time, and it's velocity varies as a function of it's aceleration. We describe that behavior with the well known Newtonian equations we learned in high school.\n", + "\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "v&=at\\\\\n", + "d &= \\frac{1}{2}at_2 + v_0t + d_0\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "But, of course we know this is not all that is happening. First, we do not have perfect measures of things like the velocity and acceleration - there is always noise in the measurements, and we have to model that. Second, no car travels on a perfect road. There are bumps that cause the car to slow down, there is wind drag, there are hills that raise and lower the speed. If we do not have explicit knowledge of these factors we lump them all together under the term \"process noise\".\n", + "\n", + "Trying to model off of those factors explicitly and exactly is impossible for anything but the most trivial problem. I could try to modify Newton's equations for things like bumps in the road, the behavior of the car's suspension system, heck, the effects of hitting bugs with the windshield, but the job would never be done - there would always be more effects to add. What is worse, each of those models would in themselves be a simplification - do I assume the wind is constant, that the drag of the car is the same for all angles of the wind, that the suspension act as perfect springs, and so on?\n", + "\n", + "\n", + "So control theory makes a mathematically correct simplification. We acknowledge that there are many factors that influence the system that we either do not know or that we don't want to have to model. At any time $t$ we say that the actual value (say, the position of our car) is the predicted value plus some unknown process noise:\n", + "\n", + "$$\n", + "x(t) = x_{pred}(t) + noise(t)\n", + "$$\n", + "\n", + "This is not meant to imply that $noise(t)$ is a function that we can derive analytically or that it is well behaved. If there is a bump in the road at $t=10$ then the noise factor will just incorporate that effect. Again, this is not implying that we model, compute, or even know the value of *noise(t)*, it is merely a statement of fact - we can *always* describe the actual value as the predicted value plus some other value. \n", + "\n", + "Let's express this in linear algebra. Using the same notation from previous chapters, we can say that our model of the system (without noise) is:\n", + "\n", + "$$ f(x) = Fx$$\n", + "\n", + "That is, we have a set of linear equations that describe our system. For our car, \n", + "$F$ will be the coefficients for Newton's equations of motion. \n", + "\n", + "Now we need to model the noise. We will just call that *w*, and add it to the equation.\n", + "\n", + "$$ f(x) = Fx + w$$\n", + "\n", + "Finally, we need to consider inputs into the system. We are dealing with linear problems here, so we will assume that there is some input $u$ into the system, and that we have some linear model that defines how that input changes the system. For example, if you press down on the accelerator in your car the car will accelerate. We will need a matrix $G$ to convert $u$ into the effect on the system. We just add that into our equation:\n", + "\n", + "$$ f(x) = Fx + Gu + w$$\n", + "\n", + "And that's it. That is the equation that Kalman set out to solve, and he found a way to compute an optimal solution if we assume certain properties of $w$.\n", + "\n", + "\n" ] }, { @@ -392,9 +449,20 @@ ] }, { - "cell_type": "markdown", + "cell_type": "heading", + "level": 2, "metadata": {}, - "source": [] + "source": [ + "Design of the Process Noise Matrix" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/ekf_internal.py b/ekf_internal.py index 2608a2c..dff0f58 100644 --- a/ekf_internal.py +++ b/ekf_internal.py @@ -125,4 +125,40 @@ def plot_ball(): p2, = plt.plot (xs, ys,lw=2) p3, = plt.plot (xs2, ys2,lw=4, c='r') plt.legend([p1,p2, p3], ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)']) - plt.show() \ No newline at end of file + plt.show() + + +def show_radar_chart(): + plt.xlim([0.9,2.5]) + plt.ylim([0.5,2.5]) + + plt.scatter ([1,2],[1,2]) + #plt.scatter ([2],[1],marker='o') + ax = plt.axes() + + ax.annotate('', xy=(2,2), xytext=(1,1), + arrowprops=dict(arrowstyle='->', ec='r',shrinkA=3, shrinkB=4)) + + ax.annotate('', xy=(2,1), xytext=(1,1), + arrowprops=dict(arrowstyle='->', ec='b',shrinkA=0, shrinkB=0)) + + ax.annotate('', xy=(2,2), xytext=(2,1), + arrowprops=dict(arrowstyle='->', ec='b',shrinkA=0, shrinkB=4)) + + + ax.annotate('Aircraft', xy=(2.04,2.), color='b') + ax.annotate('altitude', xy=(2.04,1.5), color='k') + ax.annotate('X', xy=(1.5, .9)) + ax.annotate('Radar', xy=(.95, 0.9)) + ax.annotate('Slant\n (r)', xy=(1.5,1.62), color='r') + + plt.title("Radar Tracking") + ax.xaxis.set_ticklabels([]) + ax.yaxis.set_ticklabels([]) + ax.xaxis.set_ticks([]) + ax.yaxis.set_ticks([]) + + + plt.show() + +show_radar_chart() \ No newline at end of file diff --git a/exp/RungeKutta.py b/exp/RungeKutta.py index 2196634..0a2fa8c 100644 --- a/exp/RungeKutta.py +++ b/exp/RungeKutta.py @@ -5,18 +5,44 @@ Created on Sat Jul 05 09:54:39 2014 @author: rlabbe """ -from __future__ import division +from __future__ import division, print_function import matplotlib.pyplot as plt from scipy.integrate import ode import math +import numpy as np +from numpy import random, radians, cos, sin +class BallTrajectory2D(object): + def __init__(self, x0, y0, velocity, theta_deg=0., g=9.8, noise=[0.0,0.0]): + theta = radians(theta_deg) + self.vx0 = velocity * cos(theta) + self.vy0 = velocity * sin(theta) + + self.x0 = x0 + self.y0 = y0 + self.x = x + + self.g = g + self.noise = noise + + def position(self, t): + """ returns (x,y) tuple of ball position at time t""" + + self.x = self.vx0*t + self.x0 + self.y = -0.5*self.g*t**2 + self.vy0*t + self.y0 + + return (self.x +random.randn()*self.noise[0], self.y +random.randn()*self.noise[1]) + + + class BallEuler(object): - def __init__(self, y=100., vel=10.): + def __init__(self, y=100., vel=10., omega=0): self.x = 0. self.y = y - self.vel = vel - self.y_vel = 0.0 + omega = radians(omega) + self.vel = vel*np.cos(omega) + self.y_vel = vel*np.sin(omega) @@ -48,7 +74,7 @@ def rk4(y, x, dx, f): k3 = dx * f(y + 0.5*k2, x + 0.5*dx) k4 = dx * f(y + k3, x + dx) - return y + (k1 + 2*k2 + 2*k3 + k4) / 6 + return y + (k1 + 2*k2 + 2*k3 + k4) / 6. def rk2 (y,x,dx,f): """computes the 2nd order Runge-kutta for dy/dx""" @@ -78,8 +104,9 @@ class BallRungeKutta(object): self.x = rk4 (self.x, self.t, dt, fx) self.y = rk4 (self.y, self.t, dt, fy) self.t += dt + print(fx.vel) return (self.x, self.y) - + def ball_scipy(y0, vel, omega, dt): @@ -104,22 +131,25 @@ if __name__ == "__main__": dt = 1./30 y0 = 15. vel = 100. - omega = 0. + omega = 30. vel_y = math.sin(math.radians(omega)) * vel def f(t,y): return vel_y-9.8*t - be = BallEuler (y=y0, vel=vel) + be = BallEuler (y=y0, vel=vel,omega=omega) + #be = BallTrajectory2D (x0=0, y0=y0, velocity=vel, theta_deg = omega) ball_rk = BallRungeKutta (y=y0, vel=vel, omega=omega) - while be.y >= 0: be.step (dt) ball_rk.step(dt) + + print (ball_rk.y - be.y) - plt.scatter (be.x, be.y, color='red') - - plt.scatter (ball_rk.x, ball_rk.y, color='blue', marker='v') - #plt.scatter (brk.x, y[0], color='green', marker='+') - #plt.axis('equal') +''' + p1 = plt.scatter (be.x, be.y, color='red') + p2 = plt.scatter (ball_rk.x, ball_rk.y, color='blue', marker='v') + + plt.legend([p1,p2], ['euler', 'runge kutta']) +''' \ No newline at end of file diff --git a/stats.py b/stats.py index d32c0dc..e4aa50a 100644 --- a/stats.py +++ b/stats.py @@ -12,7 +12,8 @@ faster, at least on my machine. For example, gaussian average 794 ns, whereas stats.norm(), using the frozen form, averages 116 microseconds per call. """ -from __future__ import division +from __future__ import (absolute_import, division, print_function, + unicode_literals) import math import numpy as np @@ -252,4 +253,4 @@ if __name__ == '__main__': plot_covariance_ellipse((2,7), cov=cov, variance=[1,2], title='my title') plt.show() - print "all tests passed" + print("all tests passed")