Skip to content

Instantly share code, notes, and snippets.

@nmayorov
Last active November 17, 2023 19:59
Show Gist options
  • Save nmayorov/1a9f7d592927999527a971ec51f6f0b0 to your computer and use it in GitHub Desktop.
Save nmayorov/1a9f7d592927999527a971ec51f6f0b0 to your computer and use it in GitHub Desktop.
BVP benchmarks with boundary condition tolerance check
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Qualitative benchmarks for solve_bvp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here I want to establish that `solve_bvp` can solve most of the test problems presented in the literature. It should converge in a few number of iterations to a reasonable and smooth solution.\n",
"\n",
"I list problems in the order they appear in papers."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/nmayorov/anaconda3/lib/python3.6/site-packages/matplotlib/style/core.py:167: UserWarning: In /Users/nmayorov/.matplotlib/stylelib/latex.mplstyle: \n",
"The text.latex.unicode rcparam was deprecated in Matplotlib 2.2 and will be removed in 3.1.\n",
" styles = read_style_directory(stylelib_path)\n"
]
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from scipy.integrate import solve_bvp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Global tolerance setting:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"TOL = 1e-3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problems from \"A BVP Solver Based on Residual Control and the MATLAB PSE.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"mu = 0.02\n",
"l = 0.0279\n",
"eta = 0.01\n",
"def fun(x, y):\n",
" beta = 1575 * (1 + np.cos(2 * np.pi * x))\n",
" return np.vstack((\n",
" mu - beta * y[0] * y[2],\n",
" beta * y[0] * y[2] - y[1] / l,\n",
" y[1] / l - y[2] / eta\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb):\n",
" return ya - yb\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.full((3, x.size), 0.01)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.21e-02 2.17e-19 5 4 \n",
" 2 1.93e-02 1.03e-18 9 4 \n",
" 3 2.67e-02 7.59e-19 13 7 \n",
" 4 2.60e-02 1.48e-18 20 12 \n",
" 5 3.09e-02 1.77e-18 32 24 \n",
" 6 3.79e-04 0.00e+00 56 0 \n",
"Solved in 6 iterations, number of nodes 56, maximum relative residual 3.79e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11f08a278>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def fun(x, y, p):\n",
" A = p[0]\n",
" return np.vstack((\n",
" y[1], y[2], 100 * (y[1]**2 - y[0]*y[2] - A),\n",
" y[4], -100 * y[0] * y[4] - 1, y[6], -70 * y[0] * y[6]\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb, p):\n",
" A = p[0]\n",
" return np.array([ya[0], ya[1], yb[0] - 1, yb[1], ya[3], yb[3], ya[5], yb[5] - 1])\n",
"\n",
"x = np.linspace(0, 1, 10)\n",
"y = np.ones((7, x.size))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.30e+00 8.88e-16 10 18 \n",
" 2 2.42e-02 2.19e-23 28 12 \n",
" 3 3.47e-03 1.18e-20 40 2 \n",
" 4 7.51e-04 4.82e-22 42 0 \n",
"Solved in 4 iterations, number of nodes 42, maximum relative residual 7.51e-04, \n",
"maximum boundary residual 4.82e-22.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[1], tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11f038278>]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"eps = 1e-4\n",
"\n",
"def fun(x, y):\n",
" t = np.pi * x\n",
" return np.vstack((\n",
" y[1], -(x * y[1] + eps * np.pi**2 * np.cos(t) + t * np.sin(t)) / eps\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0] + 2, yb[0]])\n",
"\n",
"x = np.linspace(-1, 1, 10)\n",
"y = np.zeros((2, x.size))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.24e+00 0.00e+00 10 18 \n",
" 2 1.12e+00 0.00e+00 28 54 \n",
" 3 2.44e+00 0.00e+00 82 132 \n",
" 4 1.78e-01 0.00e+00 214 17 \n",
" 5 2.63e-02 0.00e+00 231 24 \n",
" 6 3.08e-03 0.00e+00 255 7 \n",
" 7 9.83e-04 0.00e+00 262 0 \n",
"Solved in 7 iterations, number of nodes 262, maximum relative residual 9.83e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11ec7d710>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problems from \"Solving Boundary Value Problems for Ordinary Differential Equations in Matlab with bvp4c\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def fun(x, y):\n",
" return np.vstack((\n",
" 0.5 * y[0] * (y[2] - y[0]) / y[1],\n",
" -0.5 * (y[2] - y[0]),\n",
" (0.9 - 1000 * (y[2] - y[4]) - 0.5 * y[2] * (y[2] - y[0])) / y[3],\n",
" 0.5 * (y[2] - y[0]),\n",
" -100 * (y[4] - y[2])\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0] - 1, ya[1] - 1, ya[2] - 1, ya[3] + 10, yb[2] - yb[4]])\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.empty((5, x.size))\n",
"y[0] = 1\n",
"y[1] = 1\n",
"y[2] = -4.5 * x**2 + 8.91 * x + 1\n",
"y[3] = -10\n",
"y[4] = -4.5 * x**2 + 9 * x + 0.91"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 6.09e-03 0.00e+00 5 4 \n",
" 2 1.09e-03 0.00e+00 9 1 \n",
" 3 4.89e-04 0.00e+00 10 0 \n",
"Solved in 3 iterations, number of nodes 10, maximum relative residual 4.89e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12022f048>]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAqwAAAH9CAYAAADf+C7/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzs3Xl8VOWh//HPLMkkmSSTPSErIUCAsKMiqAgioG2per1qrW1Ba7W31lptf/baWy0uBe2mtrfXa21F0SvaliK1rS3gRkVcWIIQIOwkZA9ZJjNJZj2/PyYMRBYJApPl+3698oozOTM+Yyl8eM5znmMyDMNARERERKSXMkd6ACIiIiIiJ6NgFREREZFeTcEqIiIiIr2aglVEREREejUFq4iIiIj0agpWEREREenVFKwiIiIi0qspWEVERESkV1OwioiIiEivpmAVERERkV5NwSoiIiIivZo10gM4U4LBINXV1SQkJGAymSI9HBERERH5BMMwaGtrIzs7G7P51OdN+02wVldXk5eXF+lhiIiIiMinqKysJDc395SP7zfBmpCQAIT+AyQmJkZ4NCIiIiLySU6nk7y8vHC3nap+E6yHlwEkJiYqWEVERER6sZ4u39RFVyIiIiLSqylYRURERKRXU7CKiIiISK+mYBURERGRXk3BKiIiIiK9moJVRERERHo1BauIiIiI9GoKVhERERHp1RSsIiIiItKrKVhFREREpFdTsIqIiIhIr6ZgFREREZFeTcEqIiIiIr2aglVEREREejUFq4iIiIj0agpWEREREenVFKwiIiIi0qtZIz0AERERkYEiEAzQ4e/AH/TjN/z4g358AR8+wxd6LujHF/Th8/vw+fx4fX68Xh9+XwCf14/P58fvC+Lz+Qn4ggT8oS+/L0jQHyTgNwiGv8DwQzBgYPjBCJjAb4LAkS9TwMyQi5K5/gtXRPo/zUn1KFgXLVrEn//8Z3bs2EFsbCxTp07lscceo7i4+KSvW7ZsGffffz979uyhqKiIn/zkJ1xzzTXhnxuGwYMPPshvf/tbmpubmTx5Mr/5zW8oKSk5vU8lIiIichYFggHavG20eFpo9bbS6mmlpbMVp6uN1lYXrrZO2ts8eNr9+N0GgQ6g04LFE02UPxarYcUSjMIStIa+Dj82jjzuzgxEd32dmKXrqyeaDzX18BXnXo+C9Z133uGOO+7g/PPPx+/381//9V/Mnj2bbdu2Ybfbj/uadevWccMNN/Dwww9zzTXXsHz5cq6//nreffddJk+eDMBPf/pTfvnLX/Lcc88xfPhwHnnkEWbNmkV5eTkJCQmf/VOKiIiIHIc/6MfpddLqCUXn4X9u7mzB6XbS1tqB29VJp8uPx+0n0A5GpxmTx0qMz06MP77re+ifLUaoh+K7vs4EAwPDHCBoCWCYgxiWIFiM0HezAdYgJgtgMTBbwWQBkxXMVhPmru8Wqzn0PcqMxWrGGmXGEmUhymphWNG4MzTSs8dkGIZxui9uaGggIyODd955h2nTph33mBtuuAGn08nrr78efu6KK64gOTmZpUuXYhgG2dnZfPe73+UHP/gBAB6Ph8zMTB577DFuv/32UxqL0+nE4XDQ2tpKYmLi6X4kERER6eMCwQD17fVUuaqodldT5ariUFszbmcn7a5OOt1+fG6DYIfpqPC0E+OLJ8YfF45QqxF1Wv9+wxqAmACWWIiym7HZrdgTbMQnxJLosJNgj8Nmi8YaZQmFo9UcDsnuQRn6Z7PFhMlkOsP/lSLjdHvtM61hbW1tBSAlJeWEx6xbt467776723Nz5szhiSeeAGDfvn3U1tYye/bs8M9tNhuXXnop77333ikHq4iIiAwMxwvS6pZamuqdtB3yEGg1Y+9MJrEzlQRPCgmefJIDxSSfxr/LsAQxxwaxxpqItluIjY8mLsFGQmIcDkc88QkxxMRHERMfRWx8FDH2KKzRPT0pL5/mtIPVMAzuueceLr74YkaPHn3C42pra8nMzOz2XGZmJrW1teGfH37uk8ccOHDghO/r8XjweDzhx06ns8efQURERHqf4waps5rGxlacjR34W8zYO5NI8KR2RWkWWb5isj7tjc0GllgjPOsZG3941jOOuHjbkegMB2g01mhzv5nd7MtOO1i//e1v8/HHH/Puu+9+6rGf/B/aMIxjnjuVY462aNEiHnzwwR6MWERERHqDQDBAQ0dDKERd1Rx0HaS6rZr6pkO0NrbjazGFgrQzlURPKgmdKaR7h5JlnHzm0hRtEJtiISnNTlpGIo50O4lpMSSmxmJPthEdY1F89lGnFax33nknf/nLX1izZg25ubknPTYrKys8i3pYfX19eEY1Kyv096Ha2loGDRp03GOO57777uOee+4JP3Y6neTl5fX4s4iIiMiZ9ckgPfy9tqWOlsZ2PM1B4jqTumI0FKUpnVPICsac/I3NBjFJFhLTYruCNI7EtNhwlNrsVgVpP9WjYDUMgzvvvJPly5fz9ttvU1hY+KmvmTJlCqtWreq2jnXlypVMnToVgMLCQrKysli1ahUTJkwAwOv18s477/DYY4+d8H1tNhs2m60nwxcREZEz4ERBWu2soelQG53NAewd3YM0wTOJTN+n7/wTlWAiMTWG1IxEEtNjSUztCtK0WOxJNsxmBelA1KNgveOOO3jppZdYsWIFCQkJ4ZlTh8NBbGwsAF/72tfIyclh0aJFANx1111MmzaNxx57jKuuuooVK1awevXq8FICk8nEd7/7XRYuXMiwYcMYNmwYCxcuJC4uji9/+ctn8rOKiIjIKThhkLZV09DUTEezH3tnUtf60cNROoZxnkswf8ouoJYYSEiNITk9PjRDmhoTniVNSI3BGqULluRYPQrWp556CoDp06d3e37x4sXMnz8fgIqKCszmI3d8nTp1Ki+//DI/+tGPuP/++ykqKuKVV14J78EKcO+999LR0cG3vvWt8I0DVq5cqT1YRUREzoITBqmrmtqWejqa/MR1Oo66qCmVxM5iRnumEBU8+dlNkwXsKdEkp9txpB11yj4tloTUGGLsp7dVlAxsn2kf1t5E+7CKiIiEnCxIq501uJo9xHU4up2yPxymsf5P2e7eBLGJVpLS7TjSYkk4KkgTU2OxO6Ix6bS9nEBE9mEVERGRyPEEPOxu2c3Opp3sbN7JrpZdVLdV09LiCgVpeHY0lQRPDkM7xzLOm4QZ80nfNzrOgiMttmt2tOur69R9QkoMlqiTv17kTFOwioiI9HKGYdDQ0UB5UznlzeXsbN7Jzqad1DUeItmVRWp7LmnuHAraZzDak0pU8OT3mzdbTUeCNDUmfHFTQtdMqS1WeSC9i35FioiI9CLegJe9rXuPxGnTTnY17SLYEkVaew6p7hxS3QVc1D6VON8JTqmaID7ZduSUffjCptDp+7jEaG3/JH2KglVERCRCGjsa2dm0k/LmIzOnlYeqcLgzSHXnkObOIbt9KqPb//34s6YmSM6MIy0vgbTceFJz40nKiCU+OQaLVaftpf9QsIqIiJxlvqCPfa37KG8KRWl5UznlTeV0tvlDYdo1czrJPY7LOtMxHWeNqTXaTFpuPGm5CaTlhb6n5NiJ0n3rZQBQsIqIiJxBTZ1N4TA9HKd7W/YR704m1Z3bFafj+UL754k7wUb6cY7oo8I0nvS8BBLTY7VpvgxYClYREZHT4A/62d+6P3wq//B602ZXK6nt2aS5c0l151Di/jyXtA/Cahx7St9kgqQse9fMaXx45jQu8eQXTYkMNApWERGRT9Hqae12hX55Uzl7mvcQ1RlLatfp/LT2Ycx0T8fRmXb8U/o2C2k58eFZ07S8BFKydUpf5FQoWEVERLoEggEOtB04ciFU16n9encDSR0ZpLlDcVrUPoML3F854Sb7dkd0+EKow98d6bHaUF/kNClYRURkQHJ6neEwPTxrurtlN0EvpLqzSW0PXaV/kfsCUtoHYTWOvaWoyQTJg+ykds2cpucmkJobr1P6ImeYglVERPq1oBGksq2y276m5c3l1LhqsHsdXZvuZ5PtPp+x7dfg6Ew/7vtE2SxHrTUNXRCVMsiOVaf0Rc46BauIiPQbLq/ryNX5hzfdb9mFx+vB0ZkZPqU/qf0aUt05Jz6ln2Q7sta062p9R5pO6YtEioJVRET6nKARpKqtqtvp/PLmcqpcVUT5bUddCDWKK92zTnxK32wiOSvuE/ubxhOboFP6Ir2JglVERHq9Dn8Hmxs2s6FuAxvqNlDWWEa7rx27Nyk0a9qewyj3bKa5c3B4TnJKv2vbqMNbSOmUvkjfoGAVEZFex+V1sal+ExvqNrC+bj1ljWWY/BaynIVkO4dxmesC0tpziPHbj/v6+GRbtyv00/LiSUzVKX2RvkrBKiIiEdfqaQ3Pnq6vW8+Oph1Y/FHhQJ3rvIx0dz5mo/v+puFT+nmfOKUfr1P6Iv2JglVERM65xo7GboG6q3kXUQFbOFCvcs45bqAmpMaQMzyJQUVJoVP62XasUTqlL9LfKVhFROSsq3XXsr5ufShQa9ez37n/qEAdwTXOL5w0UHOGJ5M9LInEtNgIfQIRiSQFq4iInFGGYXDQdZD1tevDM6hVrqqjAnUME5zXKFBF5JQpWEVE5DMxDIN9zn3dArW+vT4cqLnOiVzgvJ4Mdz6mTwRqYloM2cOTyRmeFArUVAWqiBxLwSoiIj0SNILsat4VPsW/oW4DTZ1N4UAtdE7mYucw0t15ClQROSMUrCIiclL+oJ/ypnLW161nfd16NtZtxOl1hgN1mPMictqGke5SoIrI2aFgFRGRbnwBH2WHysKBWlpfitvnDgfqSOel5LYNJ82Vq0AVkXNCwSoiMsB1+jvZ0rglvAZ1c8NmOgOd4UAd7byMvLZiUl05ClQRiQgFq4jIANPua6e0vjS8BnVL4xZ8QV84UMc5Z5HfNoIUV7YCVUR6BQWriEg/5/Q62VS3KRyo2w5tI2AEwoE60XkF+a4RpLQpUEWkd1Kwioj0M02dTWys2xgO1PKmcgyMrkAdwnnOzzHYNYqktqzjBmrO4UAdnkxCSkyEPoWIyBEKVhGRPq6+vT58B6kNdRvY07oHIByoFzi/QKG7BIczC5Nh6vZaBaqI9AUKVhGRPqbKVdUtUCvaKoAjgTrZOZch7tEkOjMVqCLSLyhYRUR6McMwOOA8EL6D1Ia6DdS4a4AjgXqh84sMaR9NQmuGAlVE+iUFq4hIL+P2uVlzcA1vVrzJ+rr1NHY0AkcCdYrzAoa0jya+NV2BKiIDgoJVRKQXaPO28Xbl26w6sIq1VWvxBr3hQJ3adjFD2kdjb0lToIrIgKRgFRGJkFZPazhS36t+D1/QR7Q/lsKmCYxunULaocEKVBERFKwiIudUS2cLb1W+xT8P/JMPqj/Ab/iJ9scwuHkcY1ovIv1QIabgkUhVoIqIKFhFRM66ps4m3qx4k5X7V/Jh7YfhTfsHN41jrPNiMhoHQ/DIfqipOXaGTspg6KRMkjLjIjdwEZFeQsEqInIWNHY0hiP1o7qPCBpBrIFoBjePZZzzEjIaCyFwJFKTs+IYel4mQydmkJJtj+DIRUR6HwWriMgZUt9ez+oDq1l1YBUb6jZgYGAJRFHQMoaJbZeS3lAI/iOR6siIZdh5mQydFIpUk8l0kncXERm4FKwiIp9Brbs2HKmb6jeFIjVopaClhEmuGaTXDwHfkUhNTIsJzaROyiAtN16RKiJyChSsIiI9VO2qZtWBVaw6sIrNDZsBMAct5LWO4nzXZaTXdY/UhJSY0JrU8zJIz09QpIqI9JCCVUTkFFS2VYZnUrc0bgHAHDST3zqK890zQ5HqPRKp8ck2iiZlMHRSBpmDExWpIiKfgYJVROQEKpwVrDywkpX7V7K9aTsAJsNMbmsxk9tnkVFXhNF5JFLjHNEMnZjB0PMyySpMxGRWpIqInAk9DtY1a9bws5/9jA0bNlBTU8Py5cu5+uqrT3j8/Pnzef755495ftSoUZSVlQGwYMECHnzwwW4/z8zMpLa2tqfDExH5TPa17mPVgVWs3L+S8uZyAEyGidy24VzYPpv02iKMjlCkGkBsYjRDJ6Qz9LwMBhUlKVJFRM6CHger2+1m3Lhx3HzzzVx77bWfevyTTz7Jo48+Gn7s9/sZN24c1113XbfjSkpKWL16dfixxWLp6dBERE7LnpY9rNy/kpUHVrK7ZTcQitSctmFM6ZhDRm0RwfYjkRoTH0XRhHSGnpdJ9rAkzIpUEZGzqsfBeuWVV3LllVee8vEOhwOHwxF+/Oqrr9Lc3MzNN9/cfSBWK1lZWT0djohIjxmGwa6WXazcv5JVB1axt3Vv1w9M5LiGMqXzCjJqigi6Q5EaBGx2K0Xj0xk6KZOc4iTMFvOJ/wUiInJGnfM1rL///e+5/PLLKSgo6Pb8rl27yM7OxmazMXnyZBYuXMiQIUNO+D4ejwePxxN+7HQ6z9qYRaTvMwyDHU07wlf373fu7/oBZLcXcVHHlWTUFhFoOypS46wUjk9n6KQMckckY1GkiohExDkN1pqaGl5//XVeeumlbs9PnjyZJUuWMHz4cOrq6njkkUeYOnUqZWVlpKamHve9Fi1adMy6VxGRoxmGwbZD21h5IDSTWtlW2fUDGNQ+hEs8nyO9poiAMxSiASAqxsKQcaFIzRuVgsWqSBURiTSTYRjGab/YZPrUi66OtmjRIn7xi19QXV1NdHT0CY9zu90UFRVx7733cs899xz3mOPNsObl5dHa2kpiYmLPPoiI9BuGYbClcUt4JrXKVdX1AxjUOZhpni+QXlOEv+VIiFptFgrHpjF0Ugb5JSlYo7SGXkTkbHA6nTgcjh732jmbYTUMg2effZavfvWrJ41VALvdzpgxY9i1a9cJj7HZbNhstjM9TBHpg4JGkI8bPg7PpNa6u3YYMWCQdzDTOr9ARs1QfM2hi6P8gDXazOAxaQw9L4OCklSs0YpUEZHe6pwF6zvvvMPu3bv5+te//qnHejwetm/fziWXXHIORiYifVEgGKC0oZSV+1ey+sBq6jvqwz8b5C3gUs8XyagpwnsoFKk+wBJlZvDoVIomZTB4TBpRNkWqiEhf0ONgdblc7N69O/x43759lJaWkpKSQn5+Pvfddx9VVVUsWbKk2+t+//vfM3nyZEaPHn3Me37/+99n7ty55OfnU19fzyOPPILT6WTevHmn8ZFEpL8KBANsrN/IP/f/kzcq3qCxozH8s0G+AqZ7v0hGzVA8DaHnvIDZaqKgJJWh54UiNTpG90sREelrevw79/r165kxY0b48eE1pvPmzeO5556jpqaGioqKbq9pbW1l2bJlPPnkk8d9z4MHD3LjjTfS2NhIeno6F154Ie+///4xOwmIyMDjD/r5qPYjVh1YxRsVb9DU2RT+2aBAATO6IrWzLvScBzBbTOSPSmHopAwGj0vHFqtIFRHpyz7TRVe9yeku4hWR3scX9PFhzYfhSG3xtIR/lh0sYIbvKjJqhtJRc+S3L7PZRO7IZIZOyqRwXBox9qhIDF1ERE6i1190JSJyMr6Aj3U161h1YBVvVryJ03tkb+Vso4DL/FeRUT2U9upQpHZgYDKbyC1OYuikTIaMTycmXpEqItIfKVhFJGIMw+D9mvf5696/8lbFW7T52sI/yzblM9N3DRm1Q3FXBgFox8BkguzhoUgtmpBObMLJdx0REZG+T8EqIuecP+hn5f6VLC5bzI6mHeHnc8wFzPRfTWbNMNoqA2CAmyCYIHtoEkMnZTBkQjp2h7a0ExEZSBSsInLOtPvaWb57OS9seyG8oX+SkcpcbmJQXTFt+/0YBrQRACBriIOh52VQNCGD+GRFqojIQKVgFZGz7lDHIZbuWMrL5S/T6mkFIIfBfNE1H3N5KgFvECd+ADILExk6KYOiiRkkpMREctgiItJLKFhF5KypcFbwfNnzrNizAk8gdCvlEeaxXNFyE94dsQQDBgGCpObEM3xyJkMnZpCYFhvhUYuISG+jYBWRM25LwxYWly1m9YHVGISu6p9smc4lDVfj2mmi0wAwyBmexMQrCsgbmYLJZIromEVEpPdSsIrIGWEYBv+q+heLty5mfd36ridhTvS/Ma7qMpx7Ari6jh08No1JVxSQNcQRsfGKiEjfoWAVkc/EF/Dx931/57my59jdErpts5Uoron+KkP2nk9rpRcnAUxmE8POy2DinAJSc+IjPGoREelLFKwiclpcXhd/2vknXtj+AvXt9QDEWxO43nwraeXFOGs9tOLFYjUzcuogJszO1/pUERE5LQpWEemRhvYGXtz+In8o/wMuX+gkf2b0IK4zbsW2NRt3kxcnHqJiLIy5NIexl+Vp31QREflMFKwickr2tu7l+bLneW3Pa/iCPgCG2ou5xnMz/o2JdLT58OMlJj6KcTPzGHNpDrY43SpVREQ+OwWriJzUpvpNPLv1Wd6ufDv83AWOqcx23oBzrYW2jgDgIz7FxoRZ+Yy8KJuoaEvExisiIv2PglVEjhE0grxV+RaLty5mc8NmAEyYmJXyOS5qnEvDGz4afUEgQHJWHBPnFDDsgkwsFnNkBy4iIv2SglVEwjwBD3/d81eeK3uO/c79AESZo7gm9UuMOTidmtfd1ARDNwDIKEhg0hWDKRyXhsmsPVRFROTsUbCKCK2eVv6484+8uO1FDnUeAiAhOoEvJd9M/p4JVK11UtW1i2pOcTKTriggd0SyNvsXEZFzQsEqMoDVuGp4YfsLLNu5jHZ/OwCZsZl8OfEbJG0rouYdJ1U4ASgcl8akKwaTWZgYySGLiMgApGAVGYDKm8p5vux5Xt/3On7DD8CwpGHcEH0rptI0Gg646MCJyWxi+AWZTJxdQEq2PcKjFhGRgUrBKjJAGIbBR7Uf8WzZs6ytWht+fnLGhXzR+AquD2001rYDLixRZkZNHcT4WdrsX0REIk/BKtLP+YN+VlesZvHWxWw7tA0As8nM7Jw5XN5xHbX/8lLZ5AHaiY6xMHp6LuMuyyMuMTqyAxcREemiYBXppzr8HazYvYLny57noOsgADGWGK7Ju5bJzVdy4B9Odre1ARCbENrsf/Sludhi9duCiIj0LvqTSaSfae5s5uUdL7N0x1KaPc0AJNmS+FL+VxhZdRF7lh9ix+GdAFJimDA7n5FTB2HVZv8iItJLKVhF+onKtkqWlC3h1d2v0hnoBCAnPoev5N7MoN2j2fVSA9v99QAkD7IzaU4+Q8/XZv8iItL7KVhF+riyQ2U8t/U5Vh5YSdAIAjAqdRQ3ZdxCzNYcdr/RQGuwDoDMwkQmzimgcKw2+xcRkb5DwSrSBxmGwXvV77F462I+qP0g/PxF2RdxXdLX6Pwonv1/bQRCM6p5I5OZeMVgcoYnabN/ERHpcxSsIn2IL+jjH/v+wXNlz7GzeScAFpOFKwdfyVzbl6hfG2DHzhagE0wwZHw6k64oIKNAm/2LiEjfpWAV6QPafe0s27WMJduWUOuuBSDWGsu1Q6/lssBV7Hu7jU0VoQupzGYTwydnMnFOAclZ2uxfRET6PgWrSC/W2NHIS9tf4uXyl2nzhragSolJ4abhX+E852Vs/3sDH9ZVA2CNMjPq4mzGz8onISUmksMWERE5oxSsIr3Q/tb9PL/tef6y+y94g14ABicO5mvD5zGkZhJb/1DNuuYDAETHWhk7I5exM3KJTdBm/yIi0v8oWEV6kc0Nm1m8dTFvVryJgQHA2PSxzBtyC0l7CtmyuIr3XfsAiE2MZvzMPEZPyyFam/2LiEg/pj/lRCIsaARZc3ANi7cuZmP9xvDz03Onc1PBPAKbHZQ9VY3Psx+AxLQYJswuYMSULKxR2uxfRET6PwWrSIR4A17+tvdvPFf2HHtb9wJgNVuZO2Qu12V9mUPvQ+nyWgJ+JwAp2XYmXVHA0EkZmLXZv4iIDCAKVpFzrM3bxh93/pEXt71IQ0cDAPFR8VxXfB1fcPw7+99p418vVmOEVgSQNcTBpCsKKBidqs3+RURkQFKwipwjde46Xtz+In/c+UfcPjcAGbEZfHXUV5lmncP2N+pZtWV3+Pj8USlMurKAQUO12b+IiAxsClaRs8wX9PHslmd5+uOn8QV9ABQ5iphfcjNjOy5k8z+reH3X9tDBJiiakMGkKwpIz0+I4KhFRER6DwWryFlU3lTO/WvvZ3tTKEgnZkzklpJbGFRfzKY/VPB6ZRkAZouJ4guzmDi7gKTMuEgOWUREpNdRsIqcBb6Aj2e2PMMzHz+D3/DjsDn4z0n3UVg3nk2/q2Br/TYArNFmSi7JYfzlecQna7N/ERGR41Gwipxh2w5t4/6197OzeScAl+dfzvz4Oyl9toYDzeUA2OKsjDm82X+8NvsXERE5GQWryBniDXj5383/y7NbnyVgBEi2JfOD8T8k5oN83l23H4A4RzTjL8+n5JJsomP0fz8REZFToT8xRc6AssYyfrT2R+xuCV3lP2fwHG5JvpOPlhzE1VQLJhh/eT6T5xZijdZm/yIiIj2hYBX5DDwBD0+VPsVzZc8RMAKkxKTww0k/InZDAW8t3QOE7kw1c94osoclRXi0IiIifVOPb5ezZs0a5s6dS3Z2NiaTiVdfffWkx7/99tuYTKZjvnbs2NHtuGXLljFq1ChsNhujRo1i+fLlPR2ayDm1uWEz1792Pb/f+nsCRoArC6/kmbH/R8OSeLa8dRCAkmk53PCjCxSrIiIin0GPZ1jdbjfjxo3j5ptv5tprrz3l15WXl5OYmBh+nJ6eHv7ndevWccMNN/Dwww9zzTXXsHz5cq6//nreffddJk+e3NMhipxVnf5OflP6G5ZsW0LQCJIak8p/nX8/8ZsHs3rpTgwD7Ek2LvvqCPJLUiM9XBERkT7PZBiHbwB5Gi82mVi+fDlXX331CY95++23mTFjBs3NzSQlHX+W6YYbbsDpdPL666+Hn7viiitITk5m6dKlpzQWp9OJw+GgtbW1WxiLnEmb6jfxwNoH2O/cD8DcIXO5LedO3v+/Sg5VuQAYPjmTS64fTow9KoIjFRER6X1Ot9d6vCTgdE2YMIFBgwYxc+ZM3nrrrW4/W7duHbNnz+723Jw5c3jvvfdO+H4ejwen09ntS+Rs6fB38NiHjzHv9Xnsd+4nIzYohF9xAAAgAElEQVSDX0//Nf/muo3Xf7GDQ1UuYuKjuOL20cy6uUSxKiIicgad9YuuBg0axG9/+1smTZqEx+PhhRdeYObMmbz99ttMmzYNgNraWjIzM7u9LjMzk9ra2hO+76JFi3jwwQfP6thFANbXrufH7/2YirYKAK4eejW35d/JBy9VULZvLwCF49KYftMI4hK1p6qIiMiZdtaDtbi4mOLi4vDjKVOmUFlZyc9//vNwsEJoecHRDMM45rmj3Xfffdxzzz3hx06nk7y8vDM4chno2n3tPLnxSV7a8RIAmXGZPHDhAzh2FfL3n27D7wsSHWtl2g3DGD4566S/XkVEROT0RWRbqwsvvJAXX3wx/DgrK+uY2dT6+vpjZl2PZrPZsNlsZ22MMrB9WPMhD7z3AFWuKgCuHXYttw/5Nh8srWBL+S4A8kYmM+OrI0lI0S1VRUREzqaIBOumTZsYNGhQ+PGUKVNYtWoVd999d/i5lStXMnXq1EgMTwYwt8/N4xse55XyVwAYZB/Ej6f8mOT9hbz2aBm+zgDWaDNT/20ooy/N0ayqiIjIOdDjYHW5XOzevTv8eN++fZSWlpKSkkJ+fj733XcfVVVVLFmyBIAnnniCwYMHU1JSgtfr5cUXX2TZsmUsW7Ys/B533XUX06ZN47HHHuOqq65ixYoVrF69mnffffcMfESRU7Oueh0L3ltAtbsagOuHX883h32bD1+poHRLaN/gQUUOLps3kqSMuEgOVUREZEDpcbCuX7+eGTNmhB8fXkc6b948nnvuOWpqaqioqAj/3Ov18v3vf5+qqipiY2MpKSnhb3/7G5/73OfCx0ydOpWXX36ZH/3oR9x///0UFRXxyiuvaA9WOSdcXhc/X/9zlu0K/SUqJz6HB6c+SErVYFYs2oLH7cdsNTH5i0MYf3k+ZrNmVUVERM6lz7QPa2+ifVjldKytWsuCdQuodYfWUN844ka+WXwH6/9Uya719QCk5cVz+fxRpObER3KoIiIifd7p9lpE1rCKRJrT6+RnH/2MV3eHbi2cl5DHg1MfJL2hkBULt9Du9GIym5h0RQHnfW4wFus527JYREREPkHBKgPOmoNrePC9B6nvqMeEiZtG3sTtI/6DjSuq+HDtxwAkZ8Uxc/4oMgdrtl5ERCTSFKwyYLR6WvnpRz/lL3v+AkBBYgEPX/QwGc2D+cujW2lr6gQTjJuZx4VfHII12hLhEYuIiAgoWGWAeKviLR56/yEaOxoxm8x8bdTXuH3UN9n01yree3MTAAmpMcycN5Kc4ckRHq2IiIgcTcEq/VpLZwuLPlzE3/f9HYBCRyEPX/QwWa5CVjy2hZa6dgBGXZLNRdcOJTpG/5cQERHpbfSns/Rbqw+s5uH3H6apswmzycz8kvncPvqbfPyPapb9Yz2GAXGOaC776kgKRqdGergiIiJyAgpW6XeaOptY+MFC/rn/nwAUOYp4+KKHyfYW8trPt9BY6QJg2PmZTPvScGLsUZEcroiIiHwKBav0K//c/09+8v5PaPY0YzFZuGX0Ldw25nbK3qjhD699RDBgEGOP4tIvFzN0UkakhysiIiKnQMEq/UJjRyMLP1jIqgOrABiWPIyHL3qYHH8hf3t8C7V7nQAMHpvG9JuKsTtskRyuiIiI9ICCVfo0wzB4fd/rLPpwES2eFqwmK98Y+w1uLbmVHe/W88qfP8TvCxIdY+Hi64czYkoWJpNurSoiItKXKFilz2pob+Dh9x/mrcq3ABiRMiI0q8pgXv9NGQd3NAOQU5zMzHkjSUiJieRwRURE5DQpWKXPMQyDv+79K49++ChOrxOr2crtY2/nltG3sOeDQ7z8hw/wdgawRpmZ8m9DGXNpDiazZlVFRET6KgWr9Cl17joeev8h1hxcA8Co1FE8fNHD5FoGs+rpHez/uBGAzMJELp8/iqTMuEgOV0REpNeqbulgY0Uz43KTyEvp3X9eKlilTzAMg1d3v8rPPvoZbb42osxRfGv8t5hfMp8DpU0sfekDOl0+zBYTF8wtZMLsAsyaVRUREQHA6w9SVt3KhgPNbKpoYcOBZmqdnQAsmDuK+RcVRniEJ6dglV6v1l3LgnULWFu1FoAxaWNCa1Wj8nlzcTm7PqoDIDU3nsvnjyItNz6SwxUREYm4emcnGyua2VjRwsYDzXxc1YrXH+x2jMVsYtSgROJjev9+5ApW6bUMw2DZrmX8fP3PcfvcRJuj+faEb/PVUV+lalsrL7/wAe5WLyYTTLyigPM/X4jFao70sEVERM4pfyDIjto2NhxoZmNFMxsONHOwueOY45LjophUkMyE/GQmFSQzNtdBXHTfSMG+MUoZcKpd1Sx4bwHratYBMC59HA9d9BC5tnz+tXQ32/5VDUBSZhwz548kq9ARyeGKiIicM01uL5u6wnRjRTObK1vp8AW6HWMyQXFmAhMLkpnYFaiDU+P67NaOClbpVYJGkD/t/BO/WP8L2v3t2Cw27pxwJ18Z+RXq9jh55fkPcTaG1tyMvSyXC68uIiraEuFRi4iInB2BoMGu+q7Z0wMtbKxoZl+j+5jjEmKsTMw/Eqfj8hwk9IFT/adKwSq9xsG2g/z4vR/zYe2HAEzMmMhDFz1ETmwu6/68l81vVIIBCSkxXDZvJLnFyREesYiIyJnV2uGjtLKl6+Ko0AVSLo//mOOK0u1MOmr2tCg9vl9fbKxglYgLGkFe3vEyT2x8gg5/B7HWWO6aeBc3jriRxgoXf/jlRzTXtgMw8qJBXPzvw4iO1S9dERHp24JBg72NbjYetfZ0d4MLw+h+nD3awri8pHCgTshPIikuOjKDjhD9qS8RVeGs4IH3HmBD3QYAzss8j4emPkS2PYeP/rqfDa8fwAgaxCVGM+MrIxg8Ni3CIxYRETk9Lo+fzZUt4UDdWNFCa4fvmOMKUuNCp/cLkpmYn0RxZgJWy8C+qFjBKhERCAZ4acdL/Grjr+gMdBJrjeWeSfdwffH1NFe386dfr6ex0gXA0PMyuPRLxcTE95+1OCIi0r8ZhsG+RndoW6mKZjYeaGZnXRvBT8ye2qxmxuUmheN0YkEyafG2yAy6F1Owyjm3v3U/D7z3AJvqNwEwOWsyC6YuINueQ+mqCj74y16CfgOb3cqlNxYz7LzMCI9YRETk5I6ePd1U2cKmimaa24+dPc1JimVC/pHT+yMHJRKtLRk/lYJVzplAMMCL21/k15t+jSfgwR5l53vnfY9/H/bvOBs7ePXpjdTsbgWgYEwqM74yArtDf8sUEZHe5VRnT6OtZsbkOEIzp12n+DMTYyIz6D5OwSrnxN6Wvdz/3v183PAxAFOzp7JgygKy7FmUrali7bLd+L1BomIsXHzdMEZOHdRn94oTEZH+xX149rRr3emnzZ4ejtNRmj09YxSsclb5g36eL3ue/yn9H7xBL/FR8dx7/r1cPfRq3C0eXvtVKZXbmwHIGZ7EZV8bSWJabIRHLSIiA9Xh2dNNFUcCtbzWqdnTCFOwylmzq3kXD6x9gK2HtgJwSc4lPDDlATLjMtn5QS1rXtmFt8OPJcrMlGuKGDs9F1M/3kNORER6H82e9g0KVjnjfEEfi7cu5n83/y++oI+E6AR+cP4P+GLRF+lo8/GPp7eyt7QBgIzBiVw+fyTJWfYIj1pERPo7wzDYf6i927ZSmj3tGxSsckbtbt7ND9/9IdubtgMwPXc690+5n4y4DPZuauDtl3bQ0ebDbDFx/ucLmTgnH/MA31tORETOjtYOH1sOtlJaGbpj1KbKFprc3mOOy0mKZfzhOM1PoiTbodnTXkbBKmdMaX0p31r9Ldp8bThsDv7zgv/k84Wfx9vhZ/XibZR/UAtAao6dmfNHkZ6XEOERi4hIf+H1BymvbaO0spnSylCk7mlwH3PcJ2dPJ+Qnk+XQ7Glvp2CVM+Kj2o+444076PB3MDFjIr+Y/gvSYtOo2HaIN5fswN3iwWSCCXMKuODzhVii9DdXERE5PYZhUNnUwabKZjZ3xenWaidef/CYY/NSYhmfl8z4vCQm5icxKjsRm9USgVHLZ6Fglc9sbdVa7nrrLjwBDxcOupAnZzyJNRDNOy+Vs3VNFQCOjFgunz+KrCGOCI9WRET6mpZ2L6WVLeE43Xyw9bin9h2xUYzLS2J8roPx+UmMy00iVXeN6hcUrPKZvFXxFt9753v4gj6m5U7jl9N/yaF9Hbzx/GacDR0AjJmey5Rrioiy6W+0IiJych5/gO01bZRWNIci9WAr+xqPc2rfYmZkdmI4TsfnJTM4NU57ePdTClY5bf/Y/w/uW3MffsPPrIJZPHrxo2z+RxUf/nUfGBCfbOOyeSPJG5ES6aGKiEgvdPiq/dLKZkorWig92Mr2aifewLGn9gvT7IzLdTA+L4nx+cmMHJSgU/sDiIJVTsuK3St44L0HCBpBvjDkCzw09SHW/6WCjf88AMCIqYO4+Lph2GL1S0xEREIOuTxsPtjSdVFUC5srW2jtOHbP0+S4qFCY5iUzLi8UqUlx0REYsfQWqgnpsT+U/4GH338YgGuHXcv9F97PB6/uY9PKCgAuvn4Y4y7Li+QQRUQkwjp9AcqqW7vFaUVT+zHHRVvNjM5ODMfphLxk8lJidWpfulGwSo+8sO0FfvrRTwG4aeRN3Hvevaz78x5KV1cCMO1LwxkzPTeSQxQRkXMsGDTY2+imtLIldFFUZSvba5z4P7kjP1CUbu+6at/B+LxkirMStOepfCoFq5yyZz5+hl9t+hUAt4y+hbsm3MV7y/aw+Q3FqojIQNLQ5ukWp5sPttDW6T/muLT46K5T+6HT+2NyHThioyIwYunrFKzyqQzD4Nebfs0zW54B4Fvjv8XtY25n7Z928/GbBwG49MvFjJ6WE8lhiojIWdDhDbClqpXNlS1dkdpCVUvHMcfFRIU25D967WlOkk7ty5mhYJWTMgyDn6//OUu2LQHgnkn3ML9kPv/6wy62vBWK1ek3FVNyiWJVRKSvCwQNdte72FwZuo1paWULO+vaCHzi1L7JBMMy4rvFaXFmAlbdalvOEgWrnFDQCLLwg4W8Uv4KAPddcB83jriRNS/vZOs7VWCCGV8ZwaiLsiM8UhEROR21rZ3hWdPNlS18fLAFtzdwzHGZibZucTo2N4l4mxJCzp0e/2pbs2YNP/vZz9iwYQM1NTUsX76cq6+++oTH//nPf+app56itLQUj8dDSUkJCxYsYM6cOeFjFixYwIMPPtjtdZmZmdTW1vZ0eHKGBIIBfvzej1mxZwUmTCyYuoBriq5hzdKdobtXmeCyr45g5FTFqohIX+D2+Pn44JEr9ksrW6h1dh5zXFy0hbG5DsblJTGhK1KzHDERGLHIET0OVrfbzbhx47j55pu59tprP/X4NWvWMGvWLBYuXEhSUhKLFy9m7ty5fPDBB0yYMCF8XElJCatXrw4/tli0GXCk+II+fvivH/KP/f/AYrLwk4t/wucGf453lpZT9q9qMMHMr41kxJRBkR6qiIgchz8QZGedK7TnaUUoTnfVt/HJi/bNJijOSuy6Yj+JcXlJDMtIwGLWulPpXXocrFdeeSVXXnnlKR//xBNPdHu8cOFCVqxYwWuvvdYtWK1WK1lZWT0djpxh3oCX//fO/+PNyjexmq38bNrPmJk3k7f/bwfb1taACS6fN5LiCxWrIiK9QTBosP+Qm63VTrZWtVJa0cKWqlY6fMee2s92xHTdxjSJcblJjMl1EBetU/vS+53zX6XBYJC2tjZSUrrfrnPXrl1kZ2djs9mYPHkyCxcuZMiQISd8H4/Hg8fjCT92Op1nbcwDRYe/g7vfvpu1VWuJNkfz+IzHuST7Et56cQfb36vBZIKZ80dRPFl/sRARiQR/IMjeRjdbq1rZWuVka3Ur26qduDzHbimVYLMy9vDMaW4oUjMSdWpf+qZzHqy/+MUvcLvdXH/99eHnJk+ezJIlSxg+fDh1dXU88sgjTJ06lbKyMlJTU4/7PosWLTpm3aucvnZfO99+89t8VPsRsdZYfnXZr7ggczJvvrCdHetqMZng8ptHMfwCxaqIyLng9QfZVd/WLU631zjp9AWPOdZmNTMqO5GS7ETG5SYxIT+JIWnxmHVqX/oJk2EYx96G4lRfbDJ96kVXR1u6dCm33norK1as4PLLLz/hcW63m6KiIu69917uueee4x5zvBnWvLw8WltbSUxM7NkHGeDavG38x+r/YHPDZuxRdv5n5v8wPn0Cby7ZTvn7tZjMJmbdMoph52VGeqgiIv1Spy/AjtpQnJZVhwK1vLYNb+DYOLVHWyjJdlCSk8jobAejcxwUpdu1pZT0CU6nE4fD0eNeO2czrK+88gpf//rX+eMf/3jSWAWw2+2MGTOGXbt2nfAYm82GzWY708MccFo6W7h99e1sO7SNxOhEnp71NKNSSnjj+W3s/KBOsSoicoa5PX6214TWmx5ed7qr3nXMXqcAiTFWRuc4GJPjoCTHwejsRAan2jVzKgPOOQnWpUuXcsstt7B06VI+//nPf+rxHo+H7du3c8kll5yD0Q1cjR2N3LbqNnY17yLZlswzs59hmGMYqxdvY9dHdZjNJmZ9vYShkzIiPVQRkT6ptcNHWXUrZV2n9LdWtbK30c3xzm2m2qMZneNg9FEzp7nJulOUCJxGsLpcLnbv3h1+vG/fPkpLS0lJSSE/P5/77ruPqqoqliwJ3Rlp6dKlfO1rX+PJJ5/kwgsvDO+tGhsbi8PhAOD73/8+c+fOJT8/n/r6eh555BGcTifz5s07E59RjqPOXcetK29lv3M/6bHpPDP7GQoTCkOxur4es9nE7G+UUDRBsSoiciqa3N6uWdMjgXrgUPtxj81KjGF0TiIl2aHZ09E5DjITbYpTkRPocbCuX7+eGTNmhB8fXmM6b948nnvuOWpqaqioqAj//Omnn8bv93PHHXdwxx13hJ8/fDzAwYMHufHGG2lsbCQ9PZ0LL7yQ999/n4KCgtP9XHISVa4qbv3nrRx0HWSQfRC/m/07cu25rHp2G7s3hGJ1zm2jGTI+PdJDFRHpleqdnWw56mKosqpWqluP3YQfIC8lNjxjWpIditT0BC1pE+mJz3TRVW9yuot4B5oDzgPcuvJWat215Mbn8vs5vyczNotVv9/Gno31mC0m5nxDsSoiAmAYBlUtHWytcnZdDBVad9rQ5jnu8UPS7OG1pocDNSku+hyPWqT36vUXXUnk7WnZw60rb6Wxo5FCRyHPzHqGtJh0Vv2ujD2bGjBbTVxx2xgKx6ZFeqgiIudcMGhQ0dTetdb0SKA2t/uOOdZsgqEZ8eGZ09E5DkYOSiAhJioCIxfp/xSsA8SOph3ctvI2mj3NDE8ezm9n/ZakqGRWPlPG3tJQrF55+xgGj1Gsikj/Fwga7G1wheN0a1VoA/6242zAH2UxMTwzoStOEynJcTAyK5HYaN1CXORcUbAOAB83fMw3V3+TNm8bJaklPD3raeItCfzzma3s29yIxWrmym+OoWD08W/SICLSl/kCQXbVucJrTbdWO9lW7TzurUujrWZGDkoMn9Ifk+NgWGY8NqviVCSSFKz93Pra9dzxxh20+9uZkDGB38z8DXEmO//47Vb2fxyK1c/9xxjySxSrItL3dfoC7KxrC18QVVbdyo7aNrz+Yzfgj4u2hC+COrydVFF6PFHagF+k11Gw9mPrqtfxnTe/Q2egk8lZk/nVZb/CRgyv/3YLB7YcwhLVFaujFKsi0ve0ew9vwH9kE/5ddW34j7MBf0KMNXxKP3QxlIPCNDsWbcAv0icoWPupdyrf4Z6378Eb9HJxzsU8Pv1xrEYUrz+9hQNbQ7H6+W+NJW9kSqSHKiJyUsFg6Er98to2yuvaKK9tY3uNkz0NLo7TpqTYoynJTgzvbzo620FeijbgF+nLFKz90Mr9K/nBmh/gN/zMzJ/JT6f9FHPQwuv/u4WKsiasUWY+f8dYckcoVkWkdznk8oSjdGddGztq29hZ24bbe+x6U4DMRBujsx3dtpIa5IhRnIr0MwrWfua1Pa/xo7U/ImgEubLwSn5y8U8w+c38/X+3ULmtCWu0mS/cMY6c4uRID1VEBjC3x8+uehfltU7Ka12U14W+N7qOv79plMVEUXo8I7ISGJ6VwMisREpyEslIiDnHIxeRSFCw9iPLdi7jwXUPYmBw9dCrWTBlAUE//O1/PubgjuZQrH57HDnDFasicm74AkH2NbrDM6U7umZOK5qOf8tSkwnyU+IYnpnAiKwEirMSKM5MYHCaXRdDiQxgCtZ+4v+2/x+PfvgoADcU38APJ/+QgM/g74dj1WZh7rfHkj1MsSoiZ97x1pnurGtjT4MLX+D4N1RMT7BRnHkkSouzEhiWGU9ctP5oEpHu9LtCP/Ds1md5fMPjAMwbNY/vnfc9/N4gf/ufzVSVtxBls/CFO8eRPTQpwiMVkf6gp+tM421WhmfGU5yVSPHh71kJpNh1y1IROTUK1j7MMAye2vwUT21+CoDbx97OHePvwO8N8tf/3kz1rhaiYizMvXM8g4ocER6tiPQ1p7vOtDir+6xpTpKu0BeRz0bB2kcZhsHjGx5ncdliAO6aeBe3jrkVb6efv/3m43CsfvE748kaolgVkRP7rOtMD3/XOlMROVsUrH1Q0Aiy6INFvFz+MgD/ecF/ctPIm/B2+vnrf2+mZncr0TEW5ipWReQop7PONC3e1i1Kh2clMFzrTEXkHNPvOH1MIBjgofcf4s+7/owJE/dPuZ/rhl+Ht8PPa7/eTO3eVqJjrXzxO+PJLEyM9HBFJEJOf51p6FT+8K7vqfG2czxyEZFjKVj7EH/Qz3+9+1/8fd/fMZvMPHLRI8wtmtsVq6XU7nVii7PyxbvGk1GgWBUZCLTOVEQGAgVrH+EL+Lh3zb2srliN1WTl0WmPMmfwHDwdfl77VSl1+xSrIv1ZT9eZQmid6dFRWpyVQKHWmYpIH6Rg7QM8AQ93v3U3/6r6F1HmKH45/ZdMz5uOp93HX361mfr9Tmx2K1fdNYH0/IRID1dEPoNOX4ADh9rZ1+hiT4ObnV2n9Xu6znRYRjx2m36LF5H+Qb+b9XLtvna+89Z3+KDmA2IsMTx52ZNMzZ5Kp9vHa78qpf5AWyhWvzuB9DzFqkhfEAgaVDV3sLfRxb5Gd/hrb4Ob6tYOjON3KfZoC8OzjlyZX6x1piIyQChYezGX18Udb9zBxvqNxFnj+O+Z/835WefT6fbxlydLaahoI8YexVV3jyctV7Eq0psYhkGjy9sVoqEw3dsVphWH2vEGgid8bUKMlSHp8RSmxjHsqK2jcpO1zlREBiYFay/V6mnlm6u+ydZDW0mISuCpWU8xLn1c91iNj+Kq704gLTc+0sMVGbDaOn3sb2w/ZrZ0X4ObNo//hK+LtpoZnBpHYZqdwrR4hqTZKUy3U5hmJ9UerTAVETmKgrUXaups4raVt1HeXE6SLYmnZz3NqNRRdLp8rHhyE42VLmITQrGamqNYFTnbPP4AlU3t7G046vR91/eGtuNfjQ+hDfZzk2OPBOlRX9lJsVjMilIRkVOhYO1l6tvr+cbKb7C3dS+pMak8M/sZhiUPo8PlZcUTpRw62BWrd08gNVuxKnKmBIMGNc5O9jW42dfoCgfp3gY3B5vbCZ5gXSmELnoKB2nXLOmQNDt5KXHERFnO3YcQEemnFKy9SLWrmltX3kplWyWZcZn8bvbvGOwYTEeblxVPbOJQlZvYxGiu/u4EUrLtkR6uSJ9jGAbN7b5QkB41W3r4y+M/8bpSe7SFwnQ7Q9LiQ0HaFaaD0+wkxkSdw08hIjLwKFh7iUpnJV9f+XVq3DXkxOfwu9m/Izchl3ZnKFabqt3EJUZz9T0TSM5SrIqcTLvX320t6dGn8Fs7fCd8XZTFRH5KXOgUfvqR0/dD0uykJ9i0rlREJEIUrL3A3pa93LryVho6GhicOJhnZj9Dlj2LdqeXVx/fRHONmzhHNFffrVgVOcwXCHKwueOY2dK9DW5qnZ0nfW1OUmy39aShmVM7OUmxWLWpvohIr6NgjbDypnJuW3UbTZ1NDE0ayjOznyEtNg13q4cVj2+iubYduyOaq++ZSFJmXKSHK3JOGYZBndNz5Ar8o8K0oqkd/0kWlqbYo7tF6eGr8AtS7MRGa12piEhfomCNoLLGMm5bdRtOr5ORKSN5etbTJMckd4vV+GQbV909gaQMxar0X63tPvYd+sR+pQ1u9h9y0+4NnPB1sVEWBnetJ/3kVfhJcdHn8BOIiMjZpGCNkE31m/jW6m/h8rkYmz6Wpy5/isToRNwtHl59fBMtdaFYvfqeCTjSFavSdwWDBg0uD1UtHVS3dFDV/P/bu/f4qOo7/+PvuU/uCYRMJheiUq1UWldIRUBq7XZRum3Fdivdrqh97LZl6/Yn5NeHxbpUoRVa8WfZboUVy6Pqr7tIt67WruwW+uviDbrdstDa4lqtQO6EhCSTkGSu5/fHmZnMJJPLhFwmyev5eHwfc+bMmZNzPATffM73+z3R145eNXT0qbGjd9h+pTZrrF/p4GqpJ88tK1NDAcCMR2CdAv/Z9J/60s+/pN5Qr6o91fruH39XOY4cdbf79fy3/1udLb3KnePSmo2LVTAva6oPFxhWXzAcD6CN0RCaGEqbOnsVDA8zJ1RUab47qT9pLJxWzsmWg36lADCrEVgn2Sv1r2jj4Y3yh/1aXrZcO2/cqSx7lrrb+/T8o8fVea5XeXPcWlNzjfKLCauYWrFpoBraYxVRM4gmBtTW7sCI+7FZLSrNd6us0K3ywiyVFWapvMh8rYi+z3Hx1xEAIDX+DzGJ/t+Z/6cvv/xlhSIhfbDyg/o/N/wfOW1OdZ3v0/PfPi7fuV7lzXVrzUbCKiZHIBTRWV+fGUaTbtX3B9K+4NBzk8bkOG3xABoPpAmh1JPnYvQ9AGDMCKyT5MA7B/TVV7+qsBHWTZfcpO0rt8thdZhh9dH/lpdoFjoAACAASURBVK+1T/nFbt2y8RrlzyWsYnz4+oKDgmhjR58a2nvU2NGns119Mka+W6+SPFe8Klo+MJQWZik/y84cpQCACUNgnQTPvfWcHjjygAwZ+viCj2vr8q2yWW3ytfbq+W8fV1ebGVbX1CxW3hz3VB8upolwxFBLlzloqb49GkQ7zCAaG9zU5Q+NuB+X3RoPoOYt+2zzNRpOSwvcctmZBgoAMHUIrBNs3//s07b/3CZJuu2K23T/dffLarGaYfXR4+o636f8eVm6teYa5RYRVtGvJxCKD2JKHF1fH71V39zZN+w8pDFzcpzJfUcTK6RFWZqb46Q6CgDIaATWCfTU757SI796RJJ0+8Lbde/775XFYpGvtVfPPfrf6j7vV0FJltZsXKzcItcUHy0mk2EYau0OJA1eqo8G0sZOM5y29ww91VOM3WqRt9CtsoLkPqOJ4ZRJ8gEA0x2BdQIYhqHHf/O4HjvxmCTpc+/9nL50zZdksVjUea5Hzz96XN3tfhV6srVm4zXKKSSszgSGYagnENb5CwG1XQjo/AW/zl8I6vwFv9ouBNTWHVBTZ+zWfa8CoZEHM+W57YMqomYQNW/dz8tzycY8pACAGY7AOs4Mw9B3jn9H33v9e5KkL13zJX3+fZ+XJHW09OjH304IqzXXKKeAsJqpDMOQrzektgv+hBBqtrbuaCDtMQPp+W7zc/8oQmiM1SJ58t3RvqOxW/XueCgtK8xSvtsxgWcIAMD0QGAdR4Zh6OH/elg/eOMHkqQvV39Zd151pySp42yPnv/2cV3o8KuoNFu3bCSsTrZQOKL2nqDae2KBMxCvfsYDaWx9T0DtFwKj6iM6kMtu1dwcp+bkOjUnx2UuR5u3wB0Pp6UFbibEBwBgFAis4yRiRPT1X3xdP/r9jyRJf7v0b7X2yrWSpPbmC/rxt4/rQmdARd4crdl4jbLzec75xfKHwgnVzuTWf0u+vzLa2Rsc1RROA+W57CqKBs54+MyNLScH0rm5TmU7+bUCAGA88X/WcRCKhPS1176mn7zzE1ktVm1ZvkVr3rVGkhlWn//2cfV0BjSnLEe3bCCsppKq/+fQQdRs3aOYsmkgi0UqzHJEw6dLRTmOpNA5NzchfEY/Z0onAACmVtqB9eWXX9aOHTt07NgxNTU16bnnntOaNWuG/c5LL72kmpoa/e53v1NZWZnuvfderV+/PmmbXbt2aceOHWpqatJVV12lnTt3auXKleke3qQLhoPa9MomHTxzUDaLTdtXbtfqS1dLks43mZXVHl9Ac8vNsJqVNzvCaiRiyNcXTBk0Y/0/Y+vaL6Tf/zPGbrWoKLHymVjtjFZAE4NoYZaDJy4BADDNpB1YL1y4oKuvvlqf/exn9clPfnLE7U+dOqWPfOQj+tznPqcf/OAHeu211/TFL35R8+bNi39///792rBhg3bt2qUVK1bo8ccf1+rVq3Xy5EnNnz8//bOaJP6wX18+/GUdrj8su9WuR254RH88/48lSecbL+j5ncfV6wtobnmubtnwR1MWViMRQ4FwRP5gRP5QWP6Q+doXjMSXkz5L2i4ifzBhObptX/w7g7/X7Q+rvSeg8Dj3/5wz4Lb83BwXT1gCAGAWsBjGWHr1Rb9ssYxYYf3KV76iF154QW+88UZ83fr16/XrX/9aR48elSQtXbpUixcv1u7du+PbLFy4UGvWrNH27dtHdSw+n08FBQXq7OxUfn7+GM9o9HpDvbrn5/foaNNRuWwu7bxxp64vv16S1NbQrR/vPK7erqCKK3P1sf91texZjpQhsC84fDBMDITxbUcRKBPXB8LpVy7HS67LPihoJvb/nDPglny200YABQBghhprXpvwPqxHjx7VqlWrktbddNNN2rt3r4LBoAzD0LFjx7Rp06akbVatWqUjR44MuV+/3y+/3x9/7/P5xvfAh/Hb37ysB3/5v/Wmo09Ow6q7WivV+o/f1z7j/6q7b478Zz8gS8SloN2nY70v6T+++aL6DIf8cspvOORXQjOcSe8NTeztaotFctttcjmsctmtctltcjvMV5fdGl0fXY5+nrhtbBu3wzZoXWw5y2nTnBynirKdcjvo/wkAAC7OhAfW5uZmeTyepHUej0ehUEitra0yDEPhcDjlNs3NzUPud/v27dqyZcuEHPNI/q32Rb3p6FNuJKLdzc36I/9pSVJr8BL9+PyDshguzbP/QR+f86Dc1u609h2SXUGLU0GLUyGrU2GrU2GrS2GrUxGbSxGbS4bNJcPukmxuye6SHG5Z7G5ZHG5ZHS5ZHVmyOd2yObNkd2bJ7nTL7sqWw2Wut9jdkj363aRXt2SlfycAAMgskzJLwMBbvLFeCBaLJWl54DbD3Rq+7777VFNTE3/v8/lUWVk5Xoc8rHXv/Us1vfyOltvLZL8kT79XQL1dWfrlb65TwHBpTm6rPrjwFYWtS9UXCcga9ssa8csa9ssSMptCfVLIL4V6JaP/lr1dIdmNkLKMHmkq7uRbHUOE2TRenTlS9lwpa46UPcdczp5rrud2PwAASNOEB9bS0tJBldKWlhbZ7XbNnTtXhmHIZrOl3GZg1TWRy+WSyzU1E++XVl2hR9f9c/z9udouvfx3xxUIhVRSlaeP37NSruzbRr/DcCghwPYNWB7t61i+MzgwKxKUAkEp0DWO/8WibK7+8JoYZJPWDVjvyBr/4wAAANPKhAfWZcuW6Sc/+UnSuoMHD6q6uloOh/nYySVLlujQoUO69dZb49scOnRIt9xyy0Qf3kU7V9ulH+88Ln9PSJ5L8/Wx//VHcmWl+Z/VZpdsuZIrd2IOciTjHZgD3VLP+WhrM1vYb7auRrONliN7+ICbNXD9HLPKCwAAZoy0A2t3d7fefvvt+PtTp07pxIkTmjNnjubPn6/77rtPDQ0NevrppyWZMwJ897vfVU1NjT73uc/p6NGj2rt3r/bt2xffR01NjdatW6fq6motW7ZMe/bsUW1t7aC5WjNNyxmfXvi7ExcXVjPBRAdmw5ACF8zg2hsLsQlhNt7OJy9HglKwR+rskTrrRv/znHlDBNyiFOvmSllFks0xMecOAAAuWtrp6le/+pVuvPHG+PtYP9I777xTTz75pJqamlRbWxv//NJLL9WBAwe0ceNGPfbYYyorK9N3vvOdpDlc165dq7a2Nm3dulVNTU1atGiRDhw4oKqqqos5twl19rQZVgO9IZVeVqCPfelqOadjWJ0MFosZhl25UtEor6lhSP6uYcLtgJAbC8JGxOzOEOiSOs6M/hjdBamDbKqAmz1XyiqUrMyAAADAZLioeVgzyWTOw9p8qlM/+bsTCvSF5V1QoI9+6Wo53YTVKReJSP7OUQTchM972yWN5VfAkiLQDhNws+dIrgJmYQAAzGoZOw/rTBToDSkcMuR9V4E++jeE1YxhtZohMqtImrtgdN+JhKXejqEDbm/74HV9nZIMs6rbe15qe2t0P8tik3JLpPwyKc+b4rVcyveasykAAIA4Kqxj1PR2h+ZW5BJWZ6NwMHWQHVi9TVyfzqwLrgIzuMbCbKqAm11MtRYAMO1QYZ1k3ncVTvUhYKrYHGalNLdk9N8J+c3w2tUk+Zqir439r7HlQLfZreFcp3Tuf4ben9URDa/ewWE2tpznlRzuiz9fAACmGIEVmAx2V3+YLB9muz7fgDDbMDjgdreYMyh01pptOFlzEsJstNvBwICbVcQDHQAAGY3ACmQSd77Z5r176G3CQamreXCVNla99TWYy6G+/n62Z3879P7s7gEh1ivllSUH3LxSpv4CAEwZAisw3dgcUmGl2YZiGGY/23gXhMbkrgexdT1tZrBtP2W2IVmknHkDwmxZ/3Ls1ZVPtRYAMO4IrMBMZLH0P+rWc9XQ2wX7zAA7sEobD7jRzyJB6UKL2Zp+PfT+HDnRrg/ewWE2L9olIreEOWwBAGkhsAKzmcMtzbnUbEOJRKIDxhqTuxzEg230ta9TCl4wp/kabqovi03K9QyYCaHcrBgXzDdfc0qYBQEAEEdgBTA8q1XKnWc279VDbxe4MDjEDqzWdp+VjLC5rqtx6H3ZXFJBRTTEVkqFVQnLlWa11sZfXwAwW/A3PoDx4cyRit9ltqFEwuYsB/FqbTS4djZInXVSR535PuyXzv/BbKlYbAlV2UqpcH7yckGFOTMDAGBGILACmDxWW3TAlnfo6b3CQbPbQUddNMTWRpdjr/Wjm9YrtzRFoE0Itq7cCTlFAMD4I7ACyCw2h1R0idlSiUSk7uYBgba2v0LbWScFe8xtupul+v9KvZ+sOUN3OSicL7kLmfEAADIEgRXA9GK19j+EQUsHf24Y5iCxxBCbFGhrzQFisTlqh5r1wJk3dJeDwvnmNF8EWgCYFARWADOLxSLlFJutfHHqbfo6Eyq0dVLHmeQK7YVzUqBLajlptlTsbrOvbKouB4XzzRkQmL4LAMYFgRXA7OMukEoLpNJFqT8P9Jh9ZWP9Zgd2OfA1mg9caHvbbKlY7WYVuGD+gAptNNDmV0h258SdIwDMIARWABjImS3Nu8JsqYQC5sCwQV0Ooq+dDebAsFj/2jOpdmIxH3k7VJeDgkrzOAAABFYASJvdOfwDFyJhqas5ud9sfLaD6LpQb/9Txup/mXo/2XPNAWFFVf2vRZeYywWVVGgBzBoEVgAYb1abVFButvnXDf7cMKQLrQlTddUNCLS1kt9nDh7raZMa/3vwPixW8wEKiSE2MdjmlvK0MAAzBoEVACabxdL/9LDyJam36e0ww2v7GXNQWPvphOUzZoXWV2+2M68N/r7NZXYtSFWdLaqSsoom8gwBYFwRWAEgE2UVmq30vYM/MwxzJoN4iD2dHGw7G8ynhbW9ZbZUXAVS0fxogL1kQJV2vuTImrBTA4B0EVgBYLqxWKTcErNVXjv483DIrLwOVZ290CL5O6Xm182WSm5pcnU2HmyrzMfiMmUXgElEYAWAmcZmH/5pYYELZj/ZxBCbGGwDXf1PCqv7z8Hft9rNOWgTQ2xhQpeDnGIeqgBgXBFYAWC2ceZIJQvNNpBhSL3tZnhNVZ3tqDWn7Go/bbZTLw3ehyNn6OpsYZXkyp3Q0wMw8xBYAQD9LBYpe47ZUj0pLBI2p+Iaqjrb1SQFLwz/lLD4dF2XDA62TNcFIAUCKwBg9Ky26CNpKyStGPx5yB99mMLpFNXZM2b1dqTpuvLLh67O5nqYrguYhQisAIDxY3dJxe8yWyp9nUNXZzvOmI+87YzOR3vm1cHfj0/XdUn/VF3xGQ4ukdz5E3ZqAKYOgRUAMHncBZL3fWYbyDCk7pYBIfZ0f5jtrB95uq6sOamDbNElZlXY5pioMwMwgQisAIDMYLFIeR6zpZyuK2iG1lh1NjbwKxZwe9qk3vNmazyeYv/WAbMbDGjZc5ndAMhQBFYAwPRgc0hzLjVbKv6u/iDbkRBoE7sbdNSa7fQrg7/vyEkIsAOqtIXzJWf2BJ0YgJEQWAEAM4MrTypdZLaBIhGp++zgIBsLt77G6OwGvzNbKrme1F0NiqqkvDIGgwETiMAKAJj5rFYp32u2+dcN/jwYHezVfkZqPzV4Hlq/zwy83WdTP0zB5jSrsImzGiSG26zCCT09YKYjsAIA4HBLxZebbaCUD1M43V+h7ayTwgGp7W2zpeIuHHpmA+aeBUZEYAUAYDgjPUwhHJK6GgcH2VjAvXBO6uuQmk6YbdD+o3PPpupqUHSJlDOPwWCY9QisAABcDJs92h1gvnTpBwZ/7u82B3oNnNUgFm5Dvf1zzyrVYLDs1EE29nAFZ87EnRuQIQisAABMJFeu5HmP2QaKzT07sM9sLND6GqRgj3TuDbOlklMyOMTGXvMrzEANTHP8KQYAYKokzj07f+ngz0N+c+7Z9lOp557t65QutJit/r9S7N8mFUQfdTswzPKoW0wjBFYAADKV3SXNXWC2VHrbU8w9G513tqPWHAwWm3s2VXcDm0sqrEwOsYXzo8uXmP126T+LDEBgBQBgusoqMlvZHw3+LGnu2TPJrx1npM6G6KNuh5ndwJmbEGbnD67SuvIm9vyAKAIrAAAz0Uhzz4aDZh/ZpDBb27/c3SwFuod/mEJWUYquBpf0D0JzuCf0FDF7EFgBAJiNbI7+mQdSCfZKHXX9FdmBVdre9v6WarouScotTdHVgAFhSB9/UgAAwGCOLGneFWZLpc+XXJEd+Bq8YFZpu5tTPx1s2AFh882wy4AwRI0psO7atUs7duxQU1OTrrrqKu3cuVMrV65Mue0HP/hBvfTSS4PWf+QjH9GLL74oSbrrrrv01FNPJX2+dOlS/eIXvxjL4QEAgInmzpdKF5ltIMOQes5LHaeTB4ExIAxjlHZg3b9/vzZs2KBdu3ZpxYoVevzxx7V69WqdPHlS8+fPH7T9v/zLvygQCMTft7W16eqrr9anPvWppO1uvvlmff/734+/dzp5TB0AANOSxSLlzDVb+ZLBn0ciZuV1YL/Z2KuvfvQDwgZ2NWBA2IxkMQzDSOcLS5cu1eLFi7V79+74uoULF2rNmjXavn37iN/fuXOnvva1r6mpqUk5OebTOe666y51dHTo+eefT/Pw+/l8PhUUFKizs1P5+flj3g8AAJhiKQeEJVRpu5tH3sfAAWGxWQ4KK6WCSvOBDph0Y81raVVYA4GAjh07pk2bNiWtX7VqlY4cOTKqfezdu1ef/vSn42E15vDhwyopKVFhYaFuuOEGPfTQQyopKRlyP36/X36/P/7e5/OlcSYAACBjpTMgrP304CrtaAaEZc2JdjmYLxVEZzWIv6+Usgon6OQwFmkF1tbWVoXDYXk8nqT1Ho9Hzc0j/2vnl7/8pX77299q7969SetXr16tT33qU6qqqtKpU6e0efNmfehDH9KxY8fkcrlS7mv79u3asmVLOocPAABmglENCEvRb7ajznz1d0q9583W9OvU+3AVJAfYWKAtiParpQ/tpBrToCvLgAtkGMagdans3btXixYt0rXXXpu0fu3atfHlRYsWqbq6WlVVVXrxxRf1iU98IuW+7rvvPtXU1MTf+3w+VVZWpnMaAABgJnLnS6XvNVsqvR1SZ50ZYDvr+gd/ddSa73vazFB7tlM6+9vU+3BkDw6zidXanHnMcjCO0gqsxcXFstlsg6qpLS0tg6quA/X09OiZZ57R1q1bR/w5Xq9XVVVVeuutt4bcxuVyDVl9BQAAGFJWodmGCrSBCwlh9kx/ZTYWcrubpWCPdO5/zJaKzSUVVKQOs4WV5rRdzEM7amn9l3I6nVqyZIkOHTqkW2+9Nb7+0KFDuuWWW4b97g9/+EP5/X7dfvvtI/6ctrY21dXVyev1pnN4AAAAF8+ZI5VcabZUgn3moLBUYbajVupqNGc5OP8Hs6VisUn5ZWaoTWqV/a9uBpHHpB3ta2pqtG7dOlVXV2vZsmXas2ePamtrtX79eknSHXfcofLy8kEzBuzdu1dr1qzR3Llzk9Z3d3frwQcf1Cc/+Ul5vV6dPn1aX/3qV1VcXJwUigEAADKCwy3NXWC2VGKzHCR1OYhWazvrpM56KRKKLtcN/XNcBcME2gopzztrqrRpn+XatWvV1tamrVu3qqmpSYsWLdKBAwdUVVUlSaqtrZV1QJ+N3//+93r11Vd18ODBQfuz2Wx6/fXX9fTTT6ujo0Ner1c33nij9u/fr7w85lADAADTzEizHETCUneLGVxjATbeou97z5v9aFs6pZbfpd6PxSrlDVelrZDcBTNicFja87BmKuZhBQAAM0bggtTZMCDQ1iW8NkiR4Mj7ceYNH2jzy8yAPUkmZR5WAAAATAJnzvBTd0Ui0oURqrQ9bVKgSzr3htlSsVilG++XPvDliTuXcUBgBQAAmG6sVimv1GwV1am3CfSYfWkHBtqOWvPV1yCFA+ZTwTIcgRUAAGAmcmZLxZebLZVIRLpwzhxEluEIrAAAALOR1SrlDT+PfqbgEQwAAADIaARWAAAAZDQCKwAAADIagRUAAAAZjcAKAACAjEZgBQAAQEYjsAIAACCjEVgBAACQ0QisAAAAyGgEVgAAAGQ0AisAAAAyGoEVAAAAGY3ACgAAgIxGYAUAAEBGI7ACAAAgoxFYAQAAkNEIrAAAAMhoBFYAAABkNAIrAAAAMhqBFQAAABmNwAoAAICMRmAFAABARiOwAgAAIKMRWAEAAJDRCKwAAADIaARWAAAAZDQCKwAAADIagRUAAAAZjcAKAACAjEZgBQAAQEYjsAIAACCjEVgBAACQ0QisAAAAyGgEVgAAAGQ0AisAAAAyGoEVAAAAGY3ACgAAgIw2psC6a9cuXXrppXK73VqyZIleeeWVIbd98sknZbFYBrW+vr4x7xMAAACzR9qBdf/+/dqwYYPuv/9+HT9+XCtXrtTq1atVW1s75Hfy8/PV1NSU1Nxu90XtEwAAALODxTAMI50vLF26VIsXL9bu3bvj6xYuXKg1a9Zo+/btg7Z/8skntWHDBnV0dIzbPlPx+XwqKChQZ2en8vPz0zgjAAAATIax5rW0KqyBQEDHjh3TqlWrktavWrVKR44cGfJ73d3dqqqqUkVFhT760Y/q+PHjF71Pv98vn8+X1AAAADDzpBVYW1tbFQ6H5fF4ktZ7PB41Nzen/M6VV16pJ598Ui+88IL27dsnt9utFStW6K233hrzPiVp+/btKigoiLfKysp0TgUAAADTxJgGXVkslqT3hmEMWhdz3XXX6fbbb9fVV1+tlStX6oc//KGuuOIK/f3f//2Y9ylJ9913nzo7O+Otrq5uLKcCAACADGdPZ+Pi4mLZbLZBlc+WlpZBFdKhWK1Wvf/9749XWMe6T5fLJZfLlc7hAwAAYBpKq8LqdDq1ZMkSHTp0KGn9oUOHtHz58lHtwzAMnThxQl6vd9z2CQAAgJkrrQqrJNXU1GjdunWqrq7WsmXLtGfPHtXW1mr9+vWSpDvuuEPl5eXx0f1btmzRddddp8svv1w+n0/f+c53dOLECT322GOj3icAAABmr7QD69q1a9XW1qatW7eqqalJixYt0oEDB1RVVSVJqq2tldXaX7jt6OjQ5z//eTU3N6ugoEDXXHONXn75ZV177bWj3icAAABmr7TnYc1UzMMKAACQ2SZlHlYAAABgshFYAQAAkNEIrAAAAMhoBFYAAABkNAIrAAAAMhqBFQAAABmNwAoAAICMRmAFAABARiOwAgAAIKMRWAEAAJDRCKwAAADIaARWAAAAZDQCKwAAADIagRUAAAAZjcAKAACAjEZgBQAAQEYjsAIAACCjEVgBAACQ0QisAAAAyGgEVgAAAGQ0AisAAAAyGoEVAAAAGY3ACgAAgIxGYAUAAEBGI7ACAAAgoxFYAQAAkNEIrAAAAMhoBFYAAABkNAIrAAAAMhqBFQAAABmNwAoAAICMRmAFAABARiOwAgAAIKMRWAEAAJDRCKwAAADIaARWAAAAZDT7VB8AAAAAJodhGAp3dCjU1KRgU5OCjU3Kfn+13FdeOdWHNiwCKwAAwAxhBAIKnj2rYGOTgk2NZjBtbFKwsdEMqE1NMnp7k75T8pWvEFgBAABw8WLV0WBjQhCNVUqbGhVqbFKotVUyjBH3ZSsulsPrNVtF+SQc/cUhsAIAAGSAiN+vUHNz/FZ9sMmsioYSgqnR1zfifixudzyM2suiodRbJkd02V5aKqvLNQlnNH4IrAAAABMsXh1taFSwsSFFhbRJ4dbWUe3LPm9eNIiW9VdJy7yye71ylJXJVlgoi8UywWc0ucYUWHft2qUdO3aoqalJV111lXbu3KmVK1em3PaJJ57Q008/rd/+9reSpCVLlmjbtm269tpr49vcddddeuqpp5K+t3TpUv3iF78Yy+EBAABMKsMwFG5tVbChQcHGRgWir7H3wcYmGT09I+7HkpWVFEIdZWVmEI1WSO0ej6xO5yScUWZJO7Du379fGzZs0K5du7RixQo9/vjjWr16tU6ePKn58+cP2v7w4cP68z//cy1fvlxut1sPP/ywVq1apd/97ncqL+/vM3HzzTfr+9//fvy9cxZeDAAAkJmMcFihlpbkENrQYFZMGxrM2/WBwIj7iVdHy8r6K6SxW/Ve74ysjo4Hi2GMomdugqVLl2rx4sXavXt3fN3ChQu1Zs0abd++fcTvh8NhFRUV6bvf/a7uuOMOSWaFtaOjQ88//3yah9/P5/OpoKBAnZ2dys/PH/N+AADA7GMEgwo2N/cH0MbG5HDa3CyFQsPvxGqV3eORo7zMDKRlZXKUl8tRViZnebnsXu+06zs63saa19KqsAYCAR07dkybNm1KWr9q1SodOXJkVPvo6elRMBjUnDlzktYfPnxYJSUlKiws1A033KCHHnpIJSUlQ+7H7/fL7/fH3/t8vjTOBAAAzCYRvz8aQM0+pOZrfygNtbRIkcjwO7Hb5SgtjYfQpNfyMjk8Hlkcjsk5oVkmrcDa2tqqcDgsj8eTtN7j8ai5uXlU+9i0aZPKy8v14Q9/OL5u9erV+tSnPqWqqiqdOnVKmzdv1oc+9CEdO3ZMriH+JbJ9+3Zt2bIlncMHAAAzVLxCWl+vQH29gvUNZnW0vl6BhnqFz408oMnidCZXRssTQmlZmewlJbLYbJNwNhhoTIOuBvatMAxjVP0tHn74Ye3bt0+HDx+W2+2Or1+7dm18edGiRaqurlZVVZVefPFFfeITn0i5r/vuu081NTXx9z6fT5WVlemeCgAAmAaMSEShc+cUrK9PDqX19WYwbW4esUJqyc42+4sm3KZPDKi2uXNlsfLU+kyUVmAtLi6WzWYbVE1taWkZVHUd6JFHHtG2bdv0s5/9TO973/uG3dbr9aqqqkpvvfXWkNu4XK4hq68AAGB6MQxD4fb2/kDa0NAfSOvrFWxslBEMDrsPi9NphtGKCjnKy+SsqIguV8hRUc6ApmksrcDqdDq1ZMkSHTp0SLfeemt8/aFDh3TLLbcM+b0dO3boxuPOZwAAFeFJREFUG9/4hn7605+qurp6xJ/T1tamuro6eb3edA4PAABksHB39+AKafy2fcPI0z7ZbGYf0gozgDorKhICaoXs84qpkM5QaXcJqKmp0bp161RdXa1ly5Zpz549qq2t1fr16yVJd9xxh8rLy+MzBjz88MPavHmz/umf/kmXXHJJvDqbm5ur3NxcdXd368EHH9QnP/lJeb1enT59Wl/96ldVXFycFIoBAEBmi/T1Rad6aki+ZR+9bR/u7BxxH/aSkv4QGg+l0UppqUcWO888mo3Svupr165VW1ubtm7dqqamJi1atEgHDhxQVVWVJKm2tlbWhH/d7Nq1S4FAQH/2Z3+WtJ8HHnhADz74oGw2m15//XU9/fTT6ujokNfr1Y033qj9+/crLy/vIk8PAACMl0EDmxJu2492YJOtsDAaRivkrChPqpA6ystm/bRPSC3teVgzFfOwAgBwcYYc2BS9bT+agU3W7Ox4II1XSGO37ssrZMvNmaSzQSaalHlYAQDA9BUf2BTrNzrwtj0Dm5ChCKwAAMwgiQObzL6kyf1II2MZ2JRQIWVgE6YCgRUAgGnECAYVbGpSoK4uWh2tU6AuGkjr6kY/sCk+wp6BTch8/IkEACCDGIah8PnzCtbVRaujdf3htK5uVP1IGdiEmYbACgDAJIv09vb3Ia2rV6C+P5COZj5Si8sVDaMVclRWmlXSysp4KGVgE2YaAisAAOPMCIcVOns2HkiDDfXmbfu6utFN/2SxyO7xpAik5rJ93jwGNmFWIbACADAGYZ/PvFUfD6TR5fp6BRobpRFG21vz8uSorJCzwqyMOisr+qeDKi+X1emcpDMBMh+BFQCAFIxAQMHGRrMyOjCQ1tcr4vMNvwO73Zz2qdyskvYHUnPZVlAwOScCzAAEVgDArGQYhsKtrdG5SOuTBjYF6usVam6WRni2jq24WM7ycvO2fWW0T2lFpZwV5bKXlspis03S2QAzG4EVADBjRXp64oE0Puq+ri4+yMno6xv2+5asLHOUfdJt+8r4VFDW7OxJOhNgdiOwAgCmLSMcVqi5OToPaV3/IKfobftwW9vwO7BYZPeWDuhH2j/IyTZ3LoObgAxAYAUAZCzDMBTu6EiukCY+576xUQqFht2HtaAg/rSm/kAaXfZ6ZWFwE5DxCKwAgCnVf9s+GkZjU0BFg+mIjxJ1OOQsKxvcjzQ6yMmWnz85JwJgwhBYAQATyggGFWxuTh7YVF+vQIMZUke8ba+ER4kmPka0skLOykrZS0oY3ATMcARWAMBFMQxDoXPnzCDaUJ/0BKdgff2oHiVqzc+PhtHK5GAam5OUR4kCsxqBFQAwonBX16AgGquQBhtGMdre5Yo+z35AhbSC2/YARkZgBQAo4vcr2NCYXCFNeLZ9pLNz+B1YrbKXeuKT5CdXSCtkn1csi9U6OScDYMYhsALALGCEwwq1tETDqBlEgw318VH3oZaWkSfJnzPHHF1fUW5WSBMfJ1paymh7ABOGwAoAM0DS9E+JFdL6enOS/MamEZ9tb8nO7n9q04AKqbOiXNacnEk6GwBIRmAFgGki0tOjYENDQhhNnpc0cuHC8Duw2+UoK0tdIa2okK2oiEnyAWQkAisAZIhIX5+CjU0KNjYq2NBgvtan8dQmSfZ588wAGhvQFAumPNsewDRGYAWASRLu7jYHNjU2RF8TWsPo5iO15uWZYbS8on/6p8roVFBlZbK63ZNwJgAwuQisADAO4n1IGxKqowMCacTnG3E/1uxsc/qnsjI5ysviFdJYn1JbQcEknA0AZBYCKwCMghGJKHSudUB1NBpMo++N3t4R92MrKDADaXmZGUrLyvoDalmZrAUF9CMFgAEIrAAgyQiFFGw+mxBIE6qkDY0KNTXJGGGUvSTZ5hXLWdYfSO1lZebI+1ggZaQ9AKSNwApgVoj4/Um355Nv1zcqdPbsiI8Plc0mu6ckHkjt0RAaC6R2r5dHiALABCCwApgRwt0XEm7RDw6k4dbWEfdhcThkL/PKWV4eD6NJgdTjkcXOX5sAMNn4mxdAxosPaEoVRqOBdMRHh8qcGN9R5k3qMxoLpPayMtmLeXwoAGQiAiuAKWdEIgq1tirU2KjAoOpog4KNTTJ6ekbcj7WgoH90fdngQU22wkIGNAHANERgBTChjEBAoXPnFDzbolDLWYXOnjWXz55V8GyzQtFlIxAYcV+24uJhAmm5bLkMaAKAmYjACmBMDMNQpLs7GjzPKtR8VqGW6HIskLa0mJPhG8bIO7RaZfd4UgTS6Ih7r5dJ8QFgliKwAhjECIfNW/RnkwNoqOWsgs1n42F0NLfpJUkOhxwlJbJ7PLJ7SuQo8fQvezyyl5bK4fHI4nBM7IkBAKYlAiswy0R6evpDaEIANauj0WDa2iqFw6PanzU/Xw5PiezREOoo9USXo2HU45GtqIjBTACAMSOwAjOEEYko3N6uYHNzfxhNvD0f7S8a6eoa3Q5tNtnnzUtdES2JBdMSWbOzJ/bEAACzHoEVmAYifr9CLS0DbtE391dEz55V8Nw5aRRPYpLM59Xbo9VPh6dEdk9pUkXUXuKRvXiuLDbbBJ8ZAAAjI7ACU8gwDEU6O6MhdOCApehAprNnFe7oGN0OLRbZ5s7tD54JFVG7p0SO0lLzFn1u7sSeGAAA44jACowzwzBk9PQo1N6hcHu7wh3tCre3K3T+vEIt5/orotGKqeH3j2q/FpfLrIjGBi+VepLDqMcj+7x5DFwCAMw4BFZgBJG+PjN4trcr1N6ucCyIRsNofF1H//rRzCmayFZYKHtpaer+op5SOTwlshYUMOk9AGBWIrBiVokEAtFw2T4ghCYH0VBHfwg1envH9LMsTqdsc+bIVlQke1GhGUrnzUvRX7REVpdrnM8UAICZg8CKacsIBs2qZkdHcuWzY4hqaHu7IqOdN3Qgh0P2wkLZiooSWqHsRUWyFUbfRz+3F5mvlqwsKqIAAIwDAisyghEOK9zZmXCrvSNl4IxXPtvbRz8900A2WzRcFspeWJQ6hCYEUFtRkaw5OYRPAACmyJgC665du7Rjxw41NTXpqquu0s6dO7Vy5coht3/22We1efNm/eEPf9CCBQv00EMP6dZbb41/bhiGtmzZoj179qi9vV1Lly7VY489pquuumosh4cpZkQiivh8CX0720cMomGfb3SP7xzIYpGtoGD4yueAEGrNy2MSewAAppG0A+v+/fu1YcMG7dq1SytWrNDjjz+u1atX6+TJk5o/f/6g7Y8ePaq1a9fq61//um699VY999xzuu222/Tqq69q6dKlkqSHH35Yjz76qJ588kldccUV+sY3vqE/+ZM/0Ztvvqm8vLyLP8tZyAiHZQQCMvx+RfwBGQF/dNkvY4j38WW/f4j30WW/X5FAwmd+vyKBhOXeXikSGdNxW/PzR658xsNooWz5+cwVCgDADGcxjPTKWkuXLtXixYu1e/fu+LqFCxdqzZo12r59+6Dt165dK5/Pp3/7t3+Lr7v55ptVVFSkffv2yTAMlZWVacOGDfrKV74iSfL7/fJ4PPrWt76lL3zhC6M6Lp/Pp4KCAnV2dio/Pz+dU5oQUxoYA4FRTyA/kay5uQm31QdWPVOE0IICWez0UgEAYKYaa15LKx0EAgEdO3ZMmzZtSlq/atUqHTlyJOV3jh49qo0bNyatu+mmm7Rz505J0qlTp9Tc3KxVq1bFP3e5XLrhhht05MiRIQOr3++XP2H+Sp/Pl86pXJTe3/xGZx9+OOMDY5zVKovbLavTKYvLJYvLJavLKYvTFX3vlDW+PPC9U1aXK3nb+Pvo8sD3WVmyFxbK4nRO9ZkDAIAZIK3A2traqnA4LI/Hk7Te4/Goubk55Xeam5uH3T72mmqbM2fODHks27dv15YtW9I5/HET6elR76+Ojf4Lkx0YYz8j9vOoWgIAgGlsTElm4GhpwzCGHUE9mu3T3ed9992nmpqa+Hufz6fKysoRj308uC6/XOU7dxIYAQAAJkFaSaq4uFg2m21QNbWlpWVQhTSmtLR02O1LS0slmZVWr9c7qn1KZrcB1xRNtm6fO1f5N980JT8bAABgtklrbh+n06klS5bo0KFDSesPHTqk5cuXp/zOsmXLBm1/8ODB+PaXXnqpSktLk7YJBAJ66aWXhtwnAAAAZo+071XX1NRo3bp1qq6u1rJly7Rnzx7V1tZq/fr1kqQ77rhD5eXl8RkD7rnnHn3gAx/Qt771Ld1yyy368Y9/rJ/97Gd69dVXJZldATZs2KBt27bp8ssv1+WXX65t27YpOztbn/nMZ8bxVAEAADAdpR1Y165dq7a2Nm3dulVNTU1atGiRDhw4oKqqKklSbW2trAmTsi9fvlzPPPOM/vZv/1abN2/WggULtH///vgcrJJ07733qre3V1/84hfjDw44ePAgc7ACAAAg/XlYM1WmzcMKAACAZGPNazyfEgAAABmNwAoAAICMRmAFAABARiOwAgAAIKMRWAEAAJDRCKwAAADIaARWAAAAZDQCKwAAADIagRUAAAAZjcAKAACAjEZgBQAAQEYjsAIAACCjEVgBAACQ0exTfQDjxTAMSZLP55viIwEAAEAqsZwWy22jNWMCa1dXlySpsrJyio8EAAAAw+nq6lJBQcGot7cY6UbcDBWJRNTY2Ki8vDxZLJYJ/3k+n0+VlZWqq6tTfn7+hP88jD+u4fTG9Zv+uIbTH9dwepuK62cYhrq6ulRWViardfQ9U2dMhdVqtaqiomLSf25+fj6/pNMc13B64/pNf1zD6Y9rOL1N9vVLp7Iaw6ArAAAAZDQCKwAAADKa7cEHH3xwqg9iurLZbPrgBz8ou33G9KyYdbiG0xvXb/rjGk5/XMPpbbpcvxkz6AoAAAAzE10CAAAAkNEIrAAAAMhoBFYAAABkNAIrAAAAMhqBdRi7du3SpZdeKrfbrSVLluiVV14Zdvtnn31W73nPe+RyufSe97xHzz333CQdKVJJ5/o98cQTWrlypYqKilRUVKQPf/jD+uUvfzmJR4tU0v0djHnmmWdksVi0Zs2aCT5CjCTda9jR0aG7775bXq9XbrdbCxcu1IEDBybpaJFKutdw586deve7362srCxVVlZq48aN6uvrm6SjRaKXX35ZH/vYx1RWViaLxaLnn39+xO+89NJLWrJkidxuty677DL9wz/8wyQc6SgYSOmZZ54xHA6H8cQTTxgnT5407rnnHiMnJ8c4c+ZMyu2PHDli2Gw2Y9u2bcYbb7xhbNu2zbDb7cYvfvGLST5yGEb61+8zn/mM8dhjjxnHjx833njjDeOzn/2sUVBQYNTX10/ykSMm3WsYc/r0aaO8vNxYuXKlccstt0zS0SKVdK+h3+83qqurjY985CPGq6++apw+fdp45ZVXjBMnTkzykSMm3Wv4gx/8wHC5XMY//uM/GqdOnTJ++tOfGl6v19iwYcMkHzkMwzAOHDhg3H///cazzz5rSDKee+65Ybd/5513jOzsbOOee+4xTp48aTzxxBOGw+EwfvSjH03SEQ+NwDqEa6+91li/fn3SuiuvvNLYtGlTyu1vu+024+abb05ad9NNNxmf/vSnJ+wYMbR0r99AoVDIyMvLM5566qmJODyMwliuYSgUMlasWGF873vfM+68804C6xRL9xru3r3buOyyy4xAIDAZh4dRSPca3n333caHPvShpHU1NTXG9ddfP2HHiNEZTWC99957jSuvvDJp3Re+8AXjuuuum8hDGxW6BKQQCAR07NgxrVq1Kmn9qlWrdOTIkZTfOXr06KDtb7rppiG3x8QZy/UbqKenR8FgUHPmzJmIQ8QIxnoNt27dqnnz5ukv//IvJ/oQMYKxXMMXXnhBy5Yt09133y2Px6NFixZp27ZtCofDk3HIGGAs1/D666/XsWPH4l2q3nnnHR04cEB/+qd/OuHHi4s3VJb51a9+pWAwOEVHZcrsxxpMkdbWVoXDYXk8nqT1Ho9Hzc3NKb/T3Nyc1vaYOGO5fgNt2rRJ5eXl+vCHPzwRh4gRjOUavvbaa9q7d69OnDgxGYeIEYzlGr7zzjv6+c9/rr/4i7/QgQMH9NZbb+nuu+9WKBTS1772tck4bCQYyzX89Kc/rXPnzun666+XYRgKhUL667/+a23atGkyDhkXaagsEwqF1NraKq/XO0VHRmAdlsViSXpvGMagdRezPSbWWK/Hww8/rH379unw4cNyu90TdXgYhdFew66uLt1+++164oknVFxcPFmHh1FI5/cwEomopKREe/bskc1m05IlS9TY2KgdO3YQWKdQOtfw8OHDeuihh7Rr1y4tXbpUb7/9tu655x55vV5t3rx5Mg4XFynV9U61frIRWFMoLi6WzWYb9C/IlpaWQf/yiCktLU1re0ycsVy/mEceeUTbtm3Tz372M73vfe+byMPEMNK9hn/4wx90+vRpfexjH4uvi0QikiS73a4333xTCxYsmNiDRpKx/B56vV45HA7ZbLb4uoULF6q5uVmBQEBOp3NCjxnJxnINN2/erHXr1umv/uqvJEnvfe97deHCBX3+85/X/fffL6uVnoiZbKgsY7fbNXfu3Ck6KhN/clJwOp1asmSJDh06lLT+0KFDWr58ecrvLFu2bND2Bw8eHHJ7TJyxXD9J2rFjh77+9a/r3//931VdXT3Rh4lhpHsNr7zySr3++us6ceJEvH384x/XjTfeqBMnTqiysnKyDh1RY/k9XLFihd5+++34PzYk6fe//728Xi9hdQqM5Rr29PQMCqU2m02GOch7wo4V42OoLFNdXS2HwzFFRxU1VaO9Ml1sKo+9e/caJ0+eNDZs2GDk5OQYp0+fNgzDMNatW5c0SvK1114zbDab8c1vftN44403jG9+85tMazWF0r1+3/rWtwyn02n86Ec/MpqamuKtq6trqk5h1kv3Gg7ELAFTL91rWFtba+Tm5hp/8zd/Y7z55pvGv/7rvxolJSXGN77xjak6hVkv3Wv4wAMPGHl5eca+ffuMd955xzh48KCxYMEC47bbbpuqU5jVurq6jOPHjxvHjx83JBmPPvqocfz48fi0ZJs2bTLWrVsX3z42rdXGjRuNkydPGnv37mVaq+ngscceM6qqqgyn02ksXrzYeOmll+Kf3XDDDcadd96ZtP0///M/G+9+97sNh8NhXHnllcazzz47yUeMROlcv6qqKkPSoPbAAw9M/oEjLt3fwUQE1syQ7jU8cuSIsXTpUsPlchmXXXaZ8dBDDxmhUGiSjxqJ0rmGwWDQePDBB40FCxYYbrfbqKysNL74xS8a7e3tU3Dk+I//+I+U/2+LXbM777zTuOGGG5K+c/jwYeOaa64xnE6ncckllxi7d++e/ANPwWIY1OgBAACQuejDCgAAgIxGYAUAAEBGI7ACAAAgoxFYAQAAkNEIrAAAAMhoBFYAAABkNAIrAAAAMhqBFQAAABmNwAoAAICMRmAFAABARiOwAgAAIKMRWAEAAJDR/j9rW6TtzWAMAQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[1])\n",
"plt.plot(res.x, res.y[2])\n",
"plt.plot(res.x, res.y[3] + 10)\n",
"plt.plot(res.x, res.y[4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"p = 1e-5\n",
"\n",
"def fun(x, y):\n",
" return np.vstack((\n",
" y[1],\n",
" -3 * p * y[0] / (p + x**2)**2\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0] + 0.1 * (p + 1e-2)**-0.5, yb[0] - 0.1 * (p + 1e-2)**-0.5])\n",
"\n",
"x = np.linspace(-0.1, 0.1, 10)\n",
"y = np.empty((2, x.size))\n",
"y[0] = 0\n",
"y[1] = 10"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 6.72e-01 0.00e+00 10 12 \n",
" 2 4.29e-01 0.00e+00 22 18 \n",
" 3 1.27e-01 0.00e+00 40 28 \n",
" 4 1.73e-02 0.00e+00 68 23 \n",
" 5 5.74e-03 0.00e+00 91 4 \n",
" 6 1.50e-03 0.00e+00 95 2 \n",
" 7 9.55e-04 0.00e+00 97 0 \n",
"Solved in 7 iterations, number of nodes 97, maximum relative residual 9.55e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12028eda0>]"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"q = 5\n",
"\n",
"def fun(x, y, p):\n",
" l = p[0]\n",
" return np.vstack((\n",
" y[1],\n",
" -(l - 2 * q * np.cos(2 * x)) * y[0]\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb, p):\n",
" return np.array([ya[1], yb[1], ya[0] - 1])\n",
"\n",
"x = np.linspace(0, np.pi, 10)\n",
"y = np.empty((2, x.size))\n",
"y[0] = np.cos(4 * x)\n",
"y[1] = -4 * np.sin(4 * x)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 5.61e-02 4.46e-21 10 9 \n",
" 2 2.48e-02 8.64e-21 19 16 \n",
" 3 2.79e-03 1.29e-19 35 6 \n",
" 4 9.02e-04 2.01e-21 41 0 \n",
"Solved in 4 iterations, number of nodes 41, maximum relative residual 9.02e-04, \n",
"maximum boundary residual 2.01e-21.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[15], tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"17.097331513398718"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res.p[0]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1205ae5f8>]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def fun(x, y, p):\n",
" T = p[0]\n",
" return np.vstack((\n",
" 3 * T * (y[0] + y[1] - y[0]**3/3 - 1.3),\n",
" -T / 3 * (y[0] - 0.7 + 0.8 * y[1])\n",
" ))\n",
"\n",
"def bc(ya, yb, p):\n",
" T = p[0]\n",
" return np.array([ya[0] - yb[0], \n",
" ya[1] - yb[1],\n",
" T * (ya[0] - 0.7 + 0.8 * ya[1]) + 3])\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.empty((2, x.size))\n",
"y[0] = np.sin(2 * np.pi * x)\n",
"y[1] = np.cos(2 * np.pi * x)\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 4.16e+00 5.55e-01 5 8 \n",
" 2 1.23e+00 3.19e-05 13 16 \n",
" 3 2.57e-01 3.89e-10 29 17 \n",
" 4 8.92e-03 6.24e-10 46 17 \n",
" 5 1.79e-03 2.50e-11 63 2 \n",
" 6 9.65e-04 2.66e-15 65 0 \n",
"Solved in 6 iterations, number of nodes 65, maximum relative residual 9.65e-04, \n",
"maximum boundary residual 2.66e-15.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[2 * np.pi], tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10.710846754842603"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res.p[0]"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120612a58>]"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"beta = 0.5\n",
"eta = 6\n",
"\n",
"def fun(x, y):\n",
" return np.vstack((\n",
" y[1],\n",
" y[2],\n",
" -y[0]*y[2] - beta * (1 - y[1]**2)\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0], ya[1], yb[1] - 1])\n",
"\n",
"x = np.linspace(0, eta, 5)\n",
"y = np.empty((3, x.size))\n",
"y[0] = x\n",
"y[1] = 1\n",
"y[2] = 0 "
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 4.08e-03 5.71e-21 5 3 \n",
" 2 7.77e-04 4.94e-19 8 0 \n",
"Solved in 2 iterations, number of nodes 8, maximum relative residual 7.77e-04, \n",
"maximum boundary residual 4.94e-19.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Value reported in the paper matches:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9277320266935143"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res.y[2, 0]"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1207d2400>]"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[1])\n",
"plt.plot(res.x, res.y[2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"phi = 0.6\n",
"gamma = 40\n",
"beta = 0.2\n",
"\n",
"def fun(x, y):\n",
" return np.vstack((\n",
" y[1], \n",
" phi**2 * y[0] * np.exp(gamma * beta * (1 - y[0]) / ( 1 + beta * (1 - y[0]) ) )\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[1], yb[0] - 1])\n",
"\n",
"S = np.array([[0, 0], \n",
" [0, -2]])\n",
"\n",
"x = np.linspace(0, 1, 10)\n",
"y = np.empty((2, x.size))\n",
"y[0] = 0.5\n",
"y[1] = 0"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.95e+00 0.00e+00 10 14 \n",
" 2 3.88e-02 0.00e+00 24 16 \n",
" 3 5.86e-05 0.00e+00 40 0 \n",
"Solved in 3 iterations, number of nodes 40, maximum relative residual 5.86e-05, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, S=S, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120ad3240>]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 7."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"d = 0.1\n",
"\n",
"def fun(x, y, p):\n",
" return np.vstack((\n",
" y[1],\n",
" 0.5 * (y[0]**3 - y[1]) / x\n",
" ))\n",
"\n",
"def bc(ya, yb, p):\n",
" a = p[0]\n",
" return np.array([\n",
" ya[0] - (0.1 + 0.1 * a * d**0.5 + 0.01 * d),\n",
" ya[1] - (0.05 * a * d**-0.5 + 0.01),\n",
" yb[0] - 1 / 6\n",
" ])\n",
"\n",
"x = np.linspace(d, 16, 5)\n",
"y = np.empty((2, x.size))\n",
"y[0] = 1\n",
"y[1] = 1"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.39e+00 5.56e-10 5 5 \n",
" 2 2.20e+00 2.05e-09 10 4 \n",
" 3 5.94e-02 1.22e-10 14 5 \n",
" 4 4.35e-03 1.28e-12 19 1 \n",
" 5 1.44e-03 6.05e-13 20 1 \n",
" 6 3.60e-04 4.34e-14 21 0 \n",
"Solved in 6 iterations, number of nodes 21, maximum relative residual 3.60e-04, \n",
"maximum boundary residual 4.34e-14.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[0.2], tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120b0d080>]"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 8. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Already solved as #2 in the previous section."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 9."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Multi-point BVP --- not currently implemented."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Proplems from \"A User-Friendly Fortran BVP Solver\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On page 6."
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"eps = 0.1\n",
"\n",
"def fun(x, y, p):\n",
" l = p[0]\n",
" sx = np.sin(x)\n",
" return np.array([(sx**2 - l * sx**4 / y[0]) / eps])\n",
"\n",
"def bc(ya, yb, p):\n",
" return np.array([ya[0] - 1, yb[0] - 1])\n",
"\n",
"x = np.linspace(-0.5 * np.pi, 0.5 * np.pi, 20)\n",
"y = np.empty((1, x.size))\n",
"y[0] = 0.5"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 2.36e-02 0.00e+00 20 4 \n",
" 2 2.56e-03 0.00e+00 24 3 \n",
" 3 7.52e-04 0.00e+00 27 0 \n",
"Solved in 3 iterations, number of nodes 27, maximum relative residual 7.52e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[1], tol=TOL, verbose=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The found parameter matches well with the provided value:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.018646969893715"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res.p[0]"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120e3f518>]"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On page 13."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"def fun(x, y):\n",
" return np.vstack((\n",
" y[1],\n",
" -y[0]**5\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[1], yb[0] - (3/4)**0.5])\n",
"\n",
"S = np.array([[0, 0], [0, -2]])\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.empty((2, x.size))\n",
"y[0] = (3/4)**0.5\n",
"y[1] = 1e-4"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 1.62e-04 0.00e+00 5 0 \n",
"Solved in 1 iterations, number of nodes 5, maximum relative residual 1.62e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, S=S, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120e9e198>]"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problems from \"Test examples for comparison of codes for nonlinear boundary value problems in ordinary differential equations\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"n = 5\n",
"def fun(x, y):\n",
" return np.vstack((\n",
" y[1],\n",
" n * np.sinh(n * y[0])\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0], yb[0] - 1])\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.empty((2, x.size))\n",
"y[0] = x\n",
"y[1] = 1"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 4.97e+00 5.62e-21 5 6 \n",
" 2 3.94e-01 7.34e-21 11 5 \n",
" 3 3.52e-02 1.08e-23 16 5 \n",
" 4 6.33e-03 3.71e-22 21 3 \n",
" 5 9.96e-04 1.76e-23 24 0 \n",
"Solved in 5 iterations, number of nodes 24, maximum relative residual 9.96e-04, \n",
"maximum boundary residual 1.76e-23.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12119cdd8>]"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solution seems to resemble what is expected. For higher values of n the continuation technique should be used."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Already checked as #6 in the second section."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Skipped, because the problem is quite convoluted with a lot of parameters and regimes. I haven't figured out a suitable starting point (not provided). Potentially this problem is hard for collocation methods, may be considered as a failed problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I use boundary conditions type 1 and \"Brusselator mechanism\" for f and g definition."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"A = 2\n",
"B = 4.6\n",
"Dx = 0.0016\n",
"Dy = 0.008\n",
"L = 0.1\n",
"\n",
"def fun(x, y):\n",
" f = A + y[0]**2 * y[2] - (B + 1) * y[0]\n",
" g = B * y[0] - y[0]**2 * y[2]\n",
" return np.vstack((\n",
" y[1],\n",
" -f * L**2 / Dx,\n",
" y[3],\n",
" -g * L**2 / Dy\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb):\n",
" return np.array([ya[0] - A, yb[0] - A, ya[2] - B / A, yb[2] - B / A])\n",
"\n",
"x = np.linspace(0, 1, 10)\n",
"y = np.zeros((4, x.size))"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 5.69e-02 0.00e+00 10 9 \n",
" 2 3.33e-04 0.00e+00 19 0 \n",
"Solved in 2 iterations, number of nodes 19, maximum relative residual 3.33e-04, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1211d2a20>]"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Seems to work well. The problem looks simple."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"R = 100\n",
"s = 0.8\n",
"\n",
"def fun(x, y, p):\n",
" k = p[0]\n",
" return np.vstack((\n",
" y[1],\n",
" R**0.5 * y[4] * y[1] + R * (y[0]**2 - y[2]**2 + k),\n",
" y[3],\n",
" 2 * R * y[0] * y[2] + R**0.5 * y[3] * y[4],\n",
" -2 * R**0.5 * y[0]\n",
" ))\n",
"\n",
"\n",
"def bc(ya, yb, p):\n",
" k = p[0]\n",
" return np.array([ya[0], ya[4], ya[2] - 1, yb[0], yb[4], yb[2] - s])\n",
"\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.ones((5, x.shape[0] ))"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 4.53e-01 2.09e-18 5 8 \n",
" 2 2.92e-02 2.37e-22 13 12 \n",
" 3 6.01e-03 5.02e-20 25 11 \n",
" 4 1.10e-03 2.05e-20 36 1 \n",
" 5 9.23e-04 1.10e-24 37 0 \n",
"Solved in 5 iterations, number of nodes 37, maximum relative residual 9.23e-04, \n",
"maximum boundary residual 1.10e-24.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, p=[1], tol=TOL, verbose=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The parameter value and plots match with ones from the paper."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.8039883615590798"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res.p[0]"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1214fc748>]"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[2] - 1)\n",
"plt.plot(res.x, res.y[4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"B = 6\n",
"Da = 0.053\n",
"gamma = 20\n",
"l = 0.5\n",
"\n",
"def fun(x, y):\n",
" e = Da * (1 - y[0]) * np.exp(y[1] / (1 + y[1] / gamma))\n",
" return np.vstack((\n",
" e,\n",
" B * e\n",
" ))\n",
"\n",
"def bc(ya, yb):\n",
" return ya - (1 - l) * yb\n",
"\n",
"\n",
"x = np.linspace(0, 1, 5)\n",
"y = np.ones((2, x.shape[0]))"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Iteration Max residual Max BC residual Total nodes Nodes added \n",
" 1 3.10e-05 0.00e+00 5 0 \n",
"Solved in 1 iterations, number of nodes 5, maximum relative residual 3.10e-05, \n",
"maximum boundary residual 0.00e+00.\n"
]
}
],
"source": [
"res = solve_bvp(fun, bc, x, y, tol=TOL, verbose=2)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12152fa58>]"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(res.x, res.y[0])\n",
"plt.plot(res.x, res.y[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The problems seems to be easy. The values at x=0 match with the ones reported in the paper."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 7."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It contains one algebraic equation and I got lazy to bother with it."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solver handles well most of the problems. I consider it to be suitable for practical usage."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment