{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a4985796",
   "metadata": {},
   "source": [
    "# Least squares example\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "453030f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "9330a2c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3] \n",
      "\n",
      "\n",
      " [-1.   0.2  0.9  2.1]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([0, 1, 2, 3])\n",
    "y = np.array([-1, 0.2, 0.9, 2.1])\n",
    "\n",
    "print (x,'\\n\\n\\n',y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "29c19510",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1.]\n",
      " [1. 1.]\n",
      " [2. 1.]\n",
      " [3. 1.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.vstack([x, np.ones(len(x))]).T\n",
    "\n",
    "print (A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "c32cb6ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999997 \n",
      "\n",
      " -0.949999999999999\n"
     ]
    }
   ],
   "source": [
    "m, c = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "print (m, '\\n\\n', c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "a855c1ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Original data', markersize=10)\n",
    "y_1st =  m*x + c\n",
    "plt.plot(x, m*x + c, 'g', label='Fitted line')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c245db2f",
   "metadata": {},
   "source": [
    "# Nonlinear polynomial fits - approximation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "d4240d12",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5] \n",
      "\n",
      "\n",
      " [ 2.   4.   3.5  7.5 11.5]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1,2,3,4,5])\n",
    "y = np.array([2, 4, 3.5, 7.5, 11.5])\n",
    "\n",
    "print (x,'\\n\\n\\n',y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "94184b1d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.]\n",
      " [ 4.  2.  1.]\n",
      " [ 9.  3.  1.]\n",
      " [16.  4.  1.]\n",
      " [25.  5.  1.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.vstack([x*x, x, np.ones(len(x))]).T\n",
    "\n",
    "print (A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "a6df0556",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6071428571428578 -1.3928571428571481 3.20000000000001\n"
     ]
    }
   ],
   "source": [
    "a2, a1, a0 = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "print (a2, a1, a0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "4487fea2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Original data', markersize=10)\n",
    "\n",
    "x2=np.linspace(1,5,num=100)\n",
    "y_ls = a0 + a1*x2 + a2*x2**2\n",
    "plt.plot(x2, y_ls, 'g', label='Fitted line')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "983cd906",
   "metadata": {},
   "source": [
    "# Extrapolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "78a875a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Original data', markersize=10)\n",
    "\n",
    "x2=np.linspace(1,10,num=100)\n",
    "y_ls = a0 + a1*x2 + a2*x2**2\n",
    "plt.plot(x2, y_ls, 'g', label='Fitted line')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c76b38e",
   "metadata": {},
   "source": [
    "Let's do way more! Higher order\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "3cc095be",
   "metadata": {},
   "outputs": [],
   "source": [
    "#500 points between 0 and 100\n",
    "x=np.linspace(0,100,num=500)\n",
    "\n",
    "#create points between 0-100 that are spaced by 0.1\n",
    "x2=np.arange(-2,2,0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "dbcf4811",
   "metadata": {},
   "outputs": [],
   "source": [
    "c0=2\n",
    "c1=5\n",
    "c2=17\n",
    "c3=140\n",
    "c4=52\n",
    "mu = 0.0\n",
    "std = 5\n",
    "numpts = len(x2)\n",
    "r = 10*np.random.normal(mu,std,numpts)\n",
    "\n",
    "y2 = c0 + c1*x2 + c2*x2**2 + c3*x2**3 + c4*x2**4 +r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "37222f50",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable   Type       Data/Info\n",
      "-------------------------------\n",
      "A          ndarray    5x3: 15 elems, type `float64`, 120 bytes\n",
      "a0         float64    3.20000000000001\n",
      "a1         float64    -1.3928571428571481\n",
      "a2         float64    0.6071428571428578\n",
      "c          float64    -0.949999999999999\n",
      "c0         int        2\n",
      "c1         int        5\n",
      "c2         int        17\n",
      "c3         int        140\n",
      "c4         int        52\n",
      "d0         float64    184.97580836447645\n",
      "d1         float64    318.12891295546706\n",
      "e0         float64    -57.223568166598966\n",
      "e1         float64    336.33939239389304\n",
      "e2         float64    182.10479438426702\n",
      "f0         float64    -73.01528495904815\n",
      "f1         float64    21.164693837820465\n",
      "f2         float64    201.89391317179718\n",
      "f3         float64    131.92745858353783\n",
      "m          float64    0.9999999999999997\n",
      "mu         float      0.0\n",
      "np         module     <module 'numpy' from '/op<...>kages/numpy/__init__.py'>\n",
      "numpts     int        40\n",
      "plt        module     <module 'matplotlib.pyplo<...>es/matplotlib/pyplot.py'>\n",
      "r          ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "sns        module     <module 'seaborn' from '/<...>ges/seaborn/__init__.py'>\n",
      "std        int        5\n",
      "x          ndarray    500: 500 elems, type `float64`, 4000 bytes\n",
      "x2         ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y          ndarray    5: 5 elems, type `float64`, 40 bytes\n",
      "y2         ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y2_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y3_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y4_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y_1st      ndarray    4: 4 elems, type `float64`, 32 bytes\n",
      "y_ls       ndarray    100: 100 elems, type `float64`, 800 bytes\n"
     ]
    }
   ],
   "source": [
    "whos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "da856e12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1227844c0>]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XlJSElpaWIb+vtLQUjzzyiO8vhIiIiEKS3wON1WrFPffcgytXrmDTpk1O+5YvX+74c3Z2NsaNG4dJkybh6NGjyMnJAQBIkjTgnEKIQbfblZSUYM2aNY6fOzs7kZGR4e2lEBERUYjya6CxWq246667cObMGbz33ntOrTODycnJgUqlwunTp5GTk4OUlBRcuHBhQLnW1lYkJycPeR61Wg21Wu11/YmIiEgZ/DaGxh5mTp8+jT179uDaa691ecxHH30Eq9WK1NRUAEBubi6MRiMOHz7sKPPBBx/AaDQiLy/PX1UnIiIihfG4haarqwuffvqp4+czZ86grq4Oer0eaWlp+Jd/+RccPXoUb731Fvr6+hxjXvR6PWJiYvDZZ5/h1VdfxQ9/+EMkJCTg5MmTWLt2LW688UZMmzYNAHD99ddjzpw5WL58ueN17nvvvRfz5s3jG05ERETkIAkhhCcH7tu3DzNnzhywvbCwEOvXr0dWVtagx+3duxczZsxAY2Mjli5dihMnTqCrqwsZGRm47bbb8PDDD0Ov1zvKt7W14YEHHsCbb74JAFiwYAE2btw44G2p4XR2dkKn08FoNLrs9iIiIqLQIOf57XGgURIGGiIiIuWR8/zmWk5ERESkeAw0REREpHgMNERERKR4AZkpmIiIiIJDCIF2kxXdll7EqqMRr1UNOzmtUjHQEBERhSGj2YpttU3YWt2As20mx/ZMvRaFeWOxyJAOnUYVxBr6Ft9yIiIiCjNV9a1YUVELc08fAODqB729bUYTE4XNSw3IH58Y8Pq5i285ERERRaiq+lYUlx2G2doHAecwg69+FgDM1j4Ulx1GVX1r4CvpBww0REREYcJotmJFRa0ttLjofxHCFmxWVNTCaLYGonp+xUBDREQUJrbVNsHc0+cyzNgJAZh7+rD9aJN/KxYADDRERERhQAiBrdUNHh1bfrABSh9Sy0BDREQUBtpNVpxtMw0YM+OKAHC2zYQOk7K7nRhoiIiIwkC3pder47u8PD7YGGiIiIjCQKzau6nlrvHy+GBjoCEiIgoD8VoVMvVayJ0DWIJtsr3RWmVPssdAQ0REFAYkSUJh3liPji2aNlbxyyEw0BAREYWJRYZ0aGKi4G42GSHZZgxemJPu34oFAAMNERFRmNBpVNi81AAJcBlq7Pu3LDWExZpODDRERERhJH98IsqKJ0OjirIFm3777ds0qiiUF0/G9BBey0kOZQ9pJiIiogHyxyeipmQWth9tQvlB59W2x+i1KJpmW2171Ejlt8zYcbVtIiKiMCaEQIfJii5LL65RR2O0VqWYAcBynt9soSEiIgpjkiQhPjYG8bExwa6KX3EMDRERESkeAw0REREpHruciIiIFEYIgXaTFd2WXsSqoxGvoHEx/sJAQ0REpBBGsxXbapuwtdr5zaVMvRaFebY3l8JhThlP8C0nIiIiBaiqb8WKilqYe/oAAFc/vO1tM5qYKGxeakB+mMwtI+f5zTE0REREIa6qvhXFZYdhtvZBwDnM4KufBQCztQ/FZYdRVd8a+EoGGQMNERFRCDOarVhRUWsLLS76VISwBZsVFbUwmq2BqF7IYKAhIiIKYdtqm2Du6XMZZuyEAMw9fdh+tMm/FQsxDDREREQhSgiBrdUNHh1bfrABETBM1sHjQLN//37Mnz8faWlpkCQJO3fudNovhMD69euRlpYGjUaDGTNm4KOPPnIqY7FYsGrVKiQkJCA2NhYLFixAU5Nzomxvb0dBQQF0Oh10Oh0KCgrQ0dHhabWJiIgUo91kxdk204AxM64IAGfbTOgwRU63k8eBpru7GzfccAM2btw46P4nnngCzzzzDDZu3IgjR44gJSUFt9xyCy5fvuwos3r1auzYsQOvvfYaDhw4gK6uLsybNw99fX2OMosXL0ZdXR12796N3bt3o66uDgUFBZ5Wm4iISDG6Lb1eHd/l5fFK4pPXtiVJwo4dO3D77bcDsLXOpKWlYfXq1fjlL38JwNYak5ycjN/97nf42c9+BqPRiMTERLzyyiu4++67AQDnz59HRkYGdu3ahVtvvRUff/wxvvOd7+DQoUOYMmUKAODQoUPIzc3FJ598ggkTJrhVP762TUREStTW3YOcDZUeH3/s17coeg2noL+2febMGbS0tGD27NmObWq1Gvn5+aiurgYA1NbWwmq1OpVJS0tDdna2o0xNTQ10Op0jzADA1KlTodPpHGWIiIjCVbxWhUy9FnLnAJZgm2xvtDZyJtnzS6BpaWkBACQnJzttT05OduxraWlBTEwM4uPjhy2TlJQ04PxJSUmOMoOxWCzo7Ox0+hARESmNJEkozBvr0bFF08ZG1HIIfn3Lqf8vUgjh8pfbv8xg5V2dp7S01DGIWKfTISMjQ2bNiYiIQsMiQzo0MVFwN5uMkGwzBi/MSfdvxUKMXwJNSkoKAAxoRbl48aKj1SYlJQU9PT1ob28ftsyFCxcGnL+1tXVA68/VSkpKYDQaHZ/GxkavroeIiChYdBoVNi81QAJchhr7/i1LDRG3ppNfAk1WVhZSUlJQWfn1QKaenh5UVVUhLy8PAGAwGKBSqZzKNDc348SJE44yubm5MBqNOHz4sKPMBx98AKPR6CgzGLVajVGjRjl9iIiIlCp/fCLKiidDo4qyBZt+++3bNKoolBdPxvQwWctJDo9X2+7q6sKnn37q+PnMmTOoq6uDXq/HmDFjsHr1ajz22GMYN24cxo0bh8ceewxarRaLFy8GAOh0Oixbtgxr167FtddeC71ej3Xr1mHixIm4+eabAQDXX3895syZg+XLl+P5558HANx7772YN2+e2284ERERhYP88YmoKZmF7UebUH7QebXtMXotiqbZVtseNTKyWmYchIf27t1rXwvL6VNYWCiEEOLKlSvi4YcfFikpKUKtVovp06eL48ePO53DbDaLlStXCr1eLzQajZg3b544d+6cU5lLly6JJUuWiLi4OBEXFyeWLFki2tvbZdXVaDQKAMJoNHp6uURERCHjypUroq3LIs5d6hZtXRZx5cqVYFfJL+Q8v30yD02o4zw0REREyhP0eWiIiIiIAomBhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgULzrYFSAiIop0Qgi0m6zotvQiVh2NeK0KkiQFu1qKwkBDREQUJEazFdtqm7C1ugFn20yO7Zl6LQrzxmKRIR06jSqINVQOSQghgl0Jf+vs7IROp4PRaMSoUaOCXR0iIiJU1bdiRUUtzD19AICrH8b2thlNTBQ2LzUgf3xiwOsXCuQ8vzmGhoiIKMCq6ltRXHYYZmsfBJzDDL76WQAwW/tQXHYYVfWtga+kwjDQEBERBZDRbMWKilpbaHHRRyKELdisqKiF0WwNRPUUi4GGiIgogLbVNsHc0+cyzNgJAZh7+rD9aJN/K6ZwDDREREQBIoTA1uoGj44tP9iACBj26jEGGiIiogBpN1lxts00YMyMKwLA2TYTOkzsdhoKAw0REVGAdFt6vTq+y8vjwxkDDRERUYDEqr2b/u0aL48PZww0REREARKvVSFTr4XcOYAl2CbbG63lJHtDYaAhIiIKEEmSUJg31qNji6aN5XIIw2CgISIiCqBFhnRoYqLgbjYZIdlmDF6Yk+7fiikcAw0REVEA6TQqbF5qgAS4DDX2/VuWGrimkwsMNERERAGWPz4RZcWToVFF2YJNv/32bRpVFMqLJ2N6hK7lJAeHSxMREQVB/vhE1JTMwvajTSg/6Lza9hi9FkXTbKttjxrJlhl3+LWFZuxY2wCm/p/7778fAFBUVDRg39SpU53OYbFYsGrVKiQkJCA2NhYLFixAUxOnfyYiIuXTaVQonpaFfT+fgWO/vgXv/2Imjv36Fuz7+QwUT8timJHBr4HmyJEjaG5udnwqKysBAHfeeaejzJw5c5zK7Nq1y+kcq1evxo4dO/Daa6/hwIED6Orqwrx589DX1+fPqhMREQWMJEmIj41Bhl6L+NgYvs3kAb92OSUmOvf5Pf7447juuuuQn5/v2KZWq5GSkjLo8UajES+99BJeeeUV3HzzzQCAiooKZGRkYM+ePbj11lv9V3kiIiJSjIANCu7p6UFFRQV+8pOfOCXPffv2ISkpCePHj8fy5ctx8eJFx77a2lpYrVbMnj3bsS0tLQ3Z2dmorq4e8rssFgs6OzudPkRERBS+AhZodu7ciY6ODhQVFTm2zZ07F6+++iree+89PP300zhy5AhuuukmWCwWAEBLSwtiYmIQHx/vdK7k5GS0tLQM+V2lpaXQ6XSOT0ZGhl+uiYiIiEJDwN5yeumllzB37lykpaU5tt19992OP2dnZ2PSpEnIzMzE22+/jYULFw55LiHEsP2LJSUlWLNmjePnzs5OhhoiIqIwFpBAc/bsWezZswfbt28ftlxqaioyMzNx+vRpAEBKSgp6enrQ3t7u1Epz8eJF5OXlDXketVoNtVrtm8oTERFRyAtIl1NZWRmSkpJw2223DVvu0qVLaGxsRGpqKgDAYDBApVI53o4CgObmZpw4cWLYQENERESRxe8tNFeuXEFZWRkKCwsRHf3113V1dWH9+vVYtGgRUlNT0dDQgIceeggJCQm44447AAA6nQ7Lli3D2rVrce2110Kv12PdunWYOHGi460nIiIiIr8Hmj179uDcuXP4yU9+4rQ9KioKx48fxx//+Ed0dHQgNTUVM2fOxOuvv464uDhHuWeffRbR0dG46667YDabMWvWLJSXlyMqKsrfVSciIvKYEALtJiu6Lb2IVUcjXqvi/DJ+JAkhRLAr4W+dnZ3Q6XQwGo0YNWpUsKtDRERhzGi2YlttE7ZWOy9nkKnXojDPtpwBF5p0j5znNwMNERGRj1TVt2JFRS3MPbbZ7K9+wNrbZjQxUdi81IB8LjjpkpznN1fbJiIi8oGq+lYUlx2G2doHAecwg69+FgDM1j4Ulx1GVX1r4CsZxhhoiIiIvGQ0W7GiotYWWlz0ewhhCzYrKmphNFsDUb2IwEBDRETkpW21TTD39LkMM3ZCAOaePmw/2uTfikUQBhoiIiIvCCGwtbrBo2PLDzYgAoayBgQDDRERkRfaTVacbTMNGDPjigBwts2EDhO7nXyBgYaIiMgL3ZZer47v8vJ4smGgISIi8kKs2rs5aq/x8niyYaAhIiLyQrxWhUy9FnLnAJZgm2xvtJaT7PkCAw0REZEXJElCYd5Yj44tmjaWyyH4CAMNERGRlxYZ0qGJiYK72WSEZJsxeGFOun8rFkEYaIiIiLyk06iweakBEuAy1Nj3b1lq4JpOPsRAQ0RE5AP54xNRVjwZGlWULdj022/fplFFobx4MqZzLSef4tBqIiIiH8kfn4iaklnYfrQJ5QedV9seo9eiaJptte1RI9ky42tcbZuIiMgPhBDoMFnRZenFNepojNaqOABYJjnPb7bQEBER+YEkSYiPjUF8bEywqxIROIaGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4GGiIiIFI+BhoiIiBSPgYaIiIgUj4tTEhERuUEIgXaTFd2WXsSqoxHP1bNDCgMNERHRMIxmK7bVNmFrdQPOtpkc2zP1WhTmjcUiQzp0GlUQa0iAn7uc1q9fD0mSnD4pKSmO/UIIrF+/HmlpadBoNJgxYwY++ugjp3NYLBasWrUKCQkJiI2NxYIFC9DU1OTPahMREQEAqupbkVv6Lja8dRLnrgozAHCuzYQNb51Ebum7qKpvDVINyc7vY2i++93vorm52fE5fvy4Y98TTzyBZ555Bhs3bsSRI0eQkpKCW265BZcvX3aUWb16NXbs2IHXXnsNBw4cQFdXF+bNm4e+vj5/V52IiCJYVX0rissOw2ztgwAg+u23bzNb+1BcdpihJsj8Hmiio6ORkpLi+CQmJgKwtc78/ve/x69+9SssXLgQ2dnZ2Lp1K0wmE/70pz8BAIxGI1566SU8/fTTuPnmm3HjjTeioqICx48fx549e/xddSIiilBGsxUrKmptoaV/kulHCFuwWVFRC6PZGojq0SD8HmhOnz6NtLQ0ZGVl4Z577sE//vEPAMCZM2fQ0tKC2bNnO8qq1Wrk5+ejuroaAFBbWwur1epUJi0tDdnZ2Y4yg7FYLOjs7HT6EBERuWtbbRPMPX0uw4ydEIC5pw/bj3JIRLD4NdBMmTIFf/zjH/HXv/4VL774IlpaWpCXl4dLly6hpaUFAJCcnOx0THJysmNfS0sLYmJiEB8fP2SZwZSWlkKn0zk+GRkZPr4yIiIKV0IIbK1u8OjY8oMNEO6mIPIpvwaauXPnYtGiRZg4cSJuvvlmvP322wCArVu3Osr0f+VNCOHyNThXZUpKSmA0Gh2fxsZGL66CiIgiSbvJirNtpgFjZlwRAM62mdBhYrdTMAR0Yr3Y2FhMnDgRp0+fdrzt1L+l5eLFi45Wm5SUFPT09KC9vX3IMoNRq9UYNWqU04eIiMgd3ZZer47v8vJ48kxAA43FYsHHH3+M1NRUZGVlISUlBZWVlY79PT09qKqqQl5eHgDAYDBApVI5lWlubsaJEyccZYiIiHwpVu3dFG3XeHk8ecavv/V169Zh/vz5GDNmDC5evIj/+q//QmdnJwoLCyFJElavXo3HHnsM48aNw7hx4/DYY49Bq9Vi8eLFAACdTodly5Zh7dq1uPbaa6HX67Fu3TpHFxYREZGvxWtVyNRrcU5mt5MEYIxei9FaTrIXDH4NNE1NTfjxj3+ML774AomJiZg6dSoOHTqEzMxMAMAvfvELmM1m/Nu//Rva29sxZcoUvPPOO4iLi3Oc49lnn0V0dDTuuusumM1mzJo1C+Xl5YiKivJn1YmIKEJJkoTCvLHY8NZJ2ccWTRvL5RCCRBIRMBy7s7MTOp0ORqOR42mIiMglo9mK3NJ3bZPqufGUHCEBI1VRqCmZxWUQfEjO85urbRMREfWj06iweakBEgBXDS72/VuWGhhmgoiBhoiIaBD54xNRVjwZGlWULdj022/fplFFobx4MqaPTwx8JcmBQ7GJiCgiCSHQbrKi29KLWHU04rWqAeNf8scnoqZkFrYfbUL5QefVtsfotSiaZltte9RItswEG8fQEBFRRDGardhW24St1c4BJVOvRWGeLaAM1nUkhECHyYouSy+uUUdj9CABiHxLzvObgYaIiCJGVX0rVlTUwtzTB8B5BW17NNHERGHzUgPy2YUUdBwUTERE1E9VfSuKyw7b3lwCBswxY99mtvahuOwwqupbA19J8hgDDRERhT2j2YoVFbW20OKiX0IIW7BZUVELo5nrMikFAw0REYW9bbVNMPe4N6cMYAs15p4+bD/a5N+Kkc8w0BARUVgTQmBrdYNHx5YfbEAEDDUNCww0REQU1tpNVpyVuS4TYOt2OttmQoeJ3U5KwEBDRERhrdvS69XxXV4eT4HBQENERGEtVu3dHLLXeHk8BQYDDRERhbV4rQqZeu2ApQtckWCbbG+0lrMAKwEDDRERhTVJklCYN9ajY4umjeVswArBQENERGFvkSEdmpgolytn242QbDMGL8xJ92/FyGcYaIiIKOzpNCpsXmqwrZDtItTY929Zahh0TScKTQw0REQUEfLHJ6KseDI0qihbsOm3375No4pCefFkTOdaTorCodtERBQ2hBBoN1nRbelFrDoa8f1WxM4fn4iaklnYfrQJ5QedV9seo9eiaJptte1RI9kyozRcbZuIiBTPaLZiW20TtlY7h5RMvRaFebaQ0r/7SAiBDpMVXZZeXKOOxuh+4YeCT87zm4GGiIgUraq+FSsqamHu6QPgvIq2PZ5oYqKweakB+exGUhQ5z2+OoSEiIsWqqm9FcdlhmK19tpW0++23bzNb+1BcdhhV9a2BryQFBAMNEREpktFsxYqKWltocdHXIIQt2KyoqIXRzLWZwhEDDRERKdK22iaYe/pchhk7IQBzTx+2H23yb8UoKBhoiIhIcYQQ2Frd4NGx5QcbEAHDRyMOAw0RESlOu8mKs22mAWNmXBEAzraZ0GFit1O4YaAhIiLF6bb0enV8l5fHU+hhoCEiIsWJVXs3L+w1Xh5PoYeBhoiIFCdeq0KmXjtg+QJXJNgm2xut5UzA4YaBhoiIFEeSJBTmjfXo2KJpYzkjcBhioCEiIkVaZEiHJibK5erZdiMk24zBC3PS/VsxCgq/BprS0lJ873vfQ1xcHJKSknD77bfj1KlTTmWKioogSZLTZ+rUqU5lLBYLVq1ahYSEBMTGxmLBggVoauI8AkREkUynUWHzUoNtlWwXoca+f8tSw4A1nSg8+DXQVFVV4f7778ehQ4dQWVmJ3t5ezJ49G93d3U7l5syZg+bmZsdn165dTvtXr16NHTt24LXXXsOBAwfQ1dWFefPmoa+vz5/VJyKiEJc/PhFlxZOhUUXZgk2//fZtGlUUyosnYzrXcgpbAV2csrW1FUlJSaiqqsL06dMB2FpoOjo6sHPnzkGPMRqNSExMxCuvvIK7774bAHD+/HlkZGRg165duPXWW11+LxenJCIKb0azFduPNqH84MDVtoum2VbbHjWSLTNKI+f5HdD31oxGIwBAr9c7bd+3bx+SkpIwevRo5Ofn47e//S2SkpIAALW1tbBarZg9e7ajfFpaGrKzs1FdXe1WoCEiovCm06hQPC0LRXlj0WGyosvSi2vU0RitVXEAcIQIWKARQmDNmjX4/ve/j+zsbMf2uXPn4s4770RmZibOnDmDX//617jppptQW1sLtVqNlpYWxMTEID4+3ul8ycnJaGlpGfS7LBYLLBaL4+fOzk7/XBQREYUUSZIQHxuD+NiYYFeFAixggWblypX4+9//jgMHDjhtt3cjAUB2djYmTZqEzMxMvP3221i4cOGQ5xNCDJm6S0tL8cgjj/im4kRERBTyAvLa9qpVq/Dmm29i7969SE8f/nW51NRUZGZm4vTp0wCAlJQU9PT0oL293ancxYsXkZycPOg5SkpKYDQaHZ/GxkbfXAgRERGFJL8GGiEEVq5cie3bt+O9995DVlaWy2MuXbqExsZGpKamAgAMBgNUKhUqKysdZZqbm3HixAnk5eUNeg61Wo1Ro0Y5fYiIiCh8+bXL6f7778ef/vQn/PnPf0ZcXJxjzItOp4NGo0FXVxfWr1+PRYsWITU1FQ0NDXjooYeQkJCAO+64w1F22bJlWLt2La699lro9XqsW7cOEydOxM033+zP6hMREZFC+DXQbN68GQAwY8YMp+1lZWUoKipCVFQUjh8/jj/+8Y/o6OhAamoqZs6ciddffx1xcXGO8s8++yyio6Nx1113wWw2Y9asWSgvL0dUVJQ/q09EREQKEdB5aIKF89AQEREpT8jOQ0NERCSEQLvJim5LL2LV0YjnXDHkAww0RETkFXcDitFsxbbaJmytHjibb2GebTZfrrNEnmKXExEReUROQKmqb8WKilqYe2xr8F394LFHH01MFDYvNSCf6y3RV+Q8vxloiIhINjkBBQCKyw5DABjuiSNJtmPLiicz1BAABpoBGGiIiHynqr7V7YACAcREj0BP35Vhy159jEYVhZqSWex+IlnP74DMFExERL4nhEBbdw8a20xo6+5BIP59ajRbsaKi1mWYwVf7BQBLr3thxn6MuacP2482eVtVijAcFExEpDDBHFy7rbYJ5p4++Ds6lR9sQFHeWL79RG5joCEiUpD+Y1eudq7NhA1vncRT75zyy+BaIQS2Vjf49JyDfg+As20mdJisGK1V8RVvcgsDDRGRQjiNXRlkv32b2dqH4rLDPh9c226yOrUI+VvZwTP4c915vuJNbuEYGiIiBfBk7MqKiloYzVaf1aHb0uuzc7njufc+xbl+AcreCpVb+i6q6lsDWh8KbQw0REQK4Bi7EsTBtbHqwDbqD9YSZd9mb4ViqCE7BhoiohDnzdiV8oMNPnv7KV6rQqZei1AYweKvVihSLgYaIqIQZx+7IjeWXD241hckSUJh3lifnMsX+Io3XY2BhogoxHk7dqXLh2NfFhnSoYmJgrsvGo2QAHX0CIyQ4PYxcvmyFYqUi4GGiCjEeTt25Rofjn3RaVTYvNQACa4Din3/i/86CWXFk6FRRdmO61/Oi/r4uhWKlIuBhogoxHk6dkWC7TXn0Vrfvt6cPz7RZUCRYFvCoLx4MqaPT0T++ETUlMzCb+Z/B2P0WqfyY/Ra/Pusb3lVJ1+2QpEycR4aIqIQZx+7suGtk7KPLZrmn9l27QFl+9EmlB90nrF4jF6Lomm2uWJGjfw6TOk0KhRPy0JR3lh0mKzosvTiGnW0Y/K8/+fdTz2ujy9boUiZ+F8AEVGIEEIMOSvuIkM6nnrnFMxW917dHiEBI1VRWJiT7vLcnhouoAx3bkmSEB8bg/jYGMc2eyvUOZmDnyXYApSvW6FIeRhoiIiCzN21mTYvNaC47DAgubHKNYAtSw0AgJcPnPHruk+DBRRPzhFqrVCkLJKIgKHhcpYfJyLyFXdaRfqvzXT1X8j2kpqYKMfaTO6W37LU4Jinxd1zB5vRbEVu6buyW6FqSmZxGYQwJef5zUBDFEH80e1AA7nb4uK0NpOLFhcJcKzNZDRbBx27knnV2JVj5zo8Onewyf2d2AcdU3hioOmHgYYinbsPWPKeuy0oT915A9a98Te3WyMkyfbW0NWtEUKIQceuyG3pGOzcwSSnFYphJrwx0PTDQEORTG6XBnlOTusCxOArZg9HAvCb+d9B8bSsYcu9fOAMNrx1Uvbg2qvPHezWPHdaoa5+g4rCEwNNPww0FKk87dIg+eS2injC/kbPvp/PGDJcCCEw48l9Hr8t9ObKadh29POQac0bqhWKIoOc5zcn1iMKU0azFSsqal2GGYAL/fmC3NWwPeHOrLjervs0tfQ9bHjrJM5dFWYA4FybCRveOonc0ncDusK1/Q2qDL0W8bExDDM0JAYaojAl9wEb6IX+hBBo6+5BY5sJbd09il6Lx5vVsD0x3Ky43q779KW1zxaC+223bzNb+1BcdjigoYbIHZyHhigMefOALT/YgKI8/83rEY4DlO2tIoEy3Ky43q775CpWCgFAsrXmhcogYiKALTREYcnbbgdPFvpzp8Wlqr4VuaXvhlSXhi942yriLnfWZvJ03Sc5At2aR+QOttAQKdhQb6J4+4DtsvS6PeurR3OuDHYtX/2vvUtDSQOUvW0VkcPVrLjezLgrl79b84jkYKAhUiBXIeKm65O8Or+7C/31fyX8avYWl6feOeWYc8XdAcpK69LwdB0iOfqvzTQcues+eeLq1jxvljwg8hV2OREpjDvdNnN/vx9JcWrZ3Q79uzSG60ayt7iY3RhEev+rR2EK4QHK3rK3inh27NdrLw1XBrCtzeROwLOv+yTB9bm9NdwAZaJAUkyg2bRpE7KysjBy5EgYDAa8//77wa4SUcC5GyK+7L2C1ssWj1oLiqaNReeXvXj5wBnMeHIfcjZU4gdP7EXOhkrMeHIfXj5wBo3tJtmvhHui/GCDYt5+WmRIhyYmyu0AMUICtDFR+O/FOdCoomzho18Z+zaNKkr2FP/54xNRVjzZjXN79xhwtzWPyN8UMbHe66+/joKCAmzatAnTpk3D888/jz/84Q84efIkxowZ4/J4TqxH4cDTidu+mpTWJXuXhmNK/mFmFo6OkmDtC8xfHcd+fYtfuzR8OSOup+sQ+XNWXFfnXpjzDSx47qDHE/ENN8kfkbfCbqbgKVOmICcnB5s3b3Zsu/7663H77bejtLTU5fEMNBQOPJnOHvi6y8GdB+yaW8bjmcp6t1peAuX9X8xEerzG59Pw++v1cW/WIfLnrLjDndsXSyUQ+UNYBZqenh5otVq88cYbuOOOOxzb//3f/x11dXWoqqoacIzFYoHFYnH83NnZiYyMDAYaUixvprNPvEaNrp5elw/Yp++8AWtlLJYYKD+fPQH/34eNQQkdnq5vpbR1iOS2/tlb85QyaJuUS06gCfnOzy+++AJ9fX1ITk522p6cnIyWlpZBjyktLcUjjzwSiOpRhPLnwn2DndvTidsEgItdFuz/+Qy8+8nFAQ/YMVc9YP/3w69mFvbJVfiGBOCpd04N2H71G1RyQ0cgXh/XaVQonpaForyxiliHyD6IuLjsMCC5sbAm3B+gTBQoIR9o7Pr/JSCEGPIvhpKSEqxZs8bxs72Fhshb/pzldrhz/+if07yqtyRJwz5gAz11v7uGeq56Gjrkrm/l7evj9nWIlPBas30QscuWK9Xg3WVEwRbygSYhIQFRUVEDWmMuXrw4oNXGTq1WQ61WB6J6FEHcnXPFk24KV+f+f9/71ON6A1+/iTLUAzbQU/f7itzQ4VjfSsb57a+PR8JYkfzxiagpmTVod9mYEO0uI7IL+UATExMDg8GAyspKpzE0lZWV+NGPfhTEmlEk8Wc3hbvn9oT9TZThpsoHAjh1vxsDlOVyN3T4an0rf3Y3hgKldZcR2YV8oAGANWvWoKCgAJMmTUJubi5eeOEFnDt3Dvfdd1+wq0YRwJ/dFHLO7SlXU+UD/p+6391XwgXcf828P1fT8HszDulsmwmNbSbs+fhiWC2qORwldZcRAQoJNHfffTcuXbqERx99FM3NzcjOzsauXbuQmZkZ7KpRBPBnN4Xcc8shZ6p8f07df/Ug0unjEzHtWwlDdmncNSkdT75TL/s73JmG39tWqFt/vx9fWq8M2O5tdyMR+UbIv7btC5yHhlwZqhvBm9elXU065um53fr+fhO3ucPTeW5UURJ6v5pkz9s5V5razfjBE3tl1uBr7/9iJjL02kH3tXX3IGdDpcfndtVyZP+dK2lRTaJQF1avbVNwhft4AXcWefSmm2K4FgNvB+La74Kv3kSRu6ChvQXor/8xHXtOXpA9iHSwLg1vu76Gm4bf21YoV8cocVFNonDCQEOD8ufryaHCnbeWnvjrJ159R5el129dIA/MGoedxz732Zsons5FkhGv9dkgUk9DhzuDn+0LSG5466SsOskRaW9FEYUSdjnRAP6eRTUUuLvmjreGW4fI2y6QY7++BaO1Kp+/ieLN1P2+4Itp+IdqWfR0PSw5uMYRke+wy4k8FohZVIMtEG8WudNi4IvWCH+8iRLsuUg87fpamJPuVsuiu61QnnKnu5GIfI8tNOQg91+vkmQbq6G08QKeDn6Vw92F+0J9UUB/LpY4HE9WrRaA2y2LcKOsWjVi0Lea3DXcAGUico+c5/eIANWJFMDxCrGbT9erxwsoRSCm+B8h2R6c7rwuvciQDk1MFNzNCHLO7Qv2FqAMvRbxsTEB60KxT8OvUUVBwtchw1Gvrz4aVZQjzBSXHbaFcQxsXbRvs7csAkBNySz8Zv53MKZf6Bij1+I387+Dv66e7tU1DDdAmYh8j/+PIwC+m0VV7ncG+g0qX7xZ5OrVXcD9hfu4KODQ3O36EgLILX3Xo4kPXa1v5a8BykTkeww0BMD7WVTljBcI5htU3r5ZNPKqbghfvS7NRQGH5s40/C8fOOPVxIdDjUPy5q0od2ZnJiLfYpcTAfD+Qd/l5vFV9a3ILX0XG946iXP9ApT9Venc0ndRVd/qVX2G4u08J39dPX3YbopDD83yKHDYWyP8ce5wMFTXl7cti66GEIZ6lyARfY0tNATAvxOa2YXCG1TevlmUoffdnCv9cVFA+fzdssguQSLlYAsNAfj6QS/3sSnB1lXkaryA3AUe7W+sGM1WmTUanr0bwRNXdyP4c7BssAbiKlEgWhblDlCO1FY0omBjoCEAvnvQD8UXb1AJIdDW3YPGNhPauntcdhcMhd0I4SMQLYsAuwSJlIBdTuTgzYRmw/F2nMPCG7+BbUc/99kgYnYjhA9/LpXQH7sEiUIbW2i84KsWA2/P7at62B/0EuCy9ULOg94+zkFurezjHKaWvufRIOLhfi/sRggP/m5ZHOo72SVIFHo4U7AH/PnasZxz+6sevl7Lp7HNhB88sVd2Pa7+Tldzv0iAYxCx3N/hYPOcZAZgin/yDbkzXNtbFpU2wzVRJJLz/GagkcmfCzfKOTfg/jTvnrwp5MsHvbeLMLrDvgzDU3fegHVv/E327yVYU/yTb3iyVAJb3YhCHwNNP74KNHL/0rz6tWNXs+LKOTeE7X89qYdcvnjQCyEw48l9ssc5eMJeNX//XuQIxozIkSjYq4QTke8x0PTji0Dj6cKNf/2P6aj86MKw3R8AZJ1bjlBZQDIQC0LKEYjfSzBnRI5U7EIkCi8MNP34ItB4+kBWRUno7bMdNdS/GO+48Rv40wfn/PawD+TqzEORGwgDwZ+/F392TZJr7EIkCg9cbdvHvHnt2Nonhl3919TTh1f9GGbs3Jnm3Z/kvEEVSP74vdi7D91d+dlfyzxEMr6JRBR5GGjc4Olrx6Hi6mneg8n9V6UD85+lP34voTIjMhFRpGGgcYO306uHCncXkPQnd2dc9WQZBk/58vfiixmRiYhIPs4U7AZvp1cPFe5O8+5v7sy4Wpg3FhveOhmQ+vjq9+LtjMhFeZ5N9EZERGyhcYunCzeGCncXkAy04cY5yF1vyaPvh29/L97OiBzsLkEiIiVjoHGDN9OrhwpPp3kPFrnLMHh6Zb78vQRi5WciIhocA42bAtFi4A9KXilaznpLm5bkQBvkFbQDtfIzERENxEDjpkC9duxua8QIybcLSIYqdwcRz52Y6peFNeXwtGsyVLsEiYiUhBPryeTOhGnRURKsffJ+rRKAxVPGYMexz92aut3+uq8n07wrdSp+dyZLC/b0955MwBgKEx8SEYUizhTcjz9W2x5uevVbvpOM2c/u92j1XwBuT90ud5r3SJmKP5jT33PlZyIi32Gg6cfXgcZuuBYDb1f/lTN1uy9bLrydij+UWn+CNf09V34mIvKNkFj6oKGhAcuWLUNWVhY0Gg2uu+46PPzww+jp6XEqJ0nSgM+WLVucyhw/fhz5+fnQaDT4xje+gUcffTSo0/jbDffasZwBrYM90ORM3e6qbCCm4jearXj5wBnMeHIfcjZU4gdP7EXOhkrMeHIfXj5wJigz4QZr+ntv7z0REcnnt9cqPvnkE1y5cgXPP/88vvWtb+HEiRNYvnw5uru78dRTTzmVLSsrw5w5cxw/63Q6x587Oztxyy23YObMmThy5Ajq6+tRVFSE2NhYrF271l/V9wn7gNbBuj/GBGj1X7lT8UOyjc2R0wXSv/XnaufaTNjw1kk89c6piFqIMRTuPRFRJAlol9OTTz6JzZs34x//+MfXFZAk7NixA7fffvugx2zevBklJSW4cOEC1Go1AODxxx/Hc889h6amJrf+1e2vLic5gtX94e9BqnK7V8qKJ0dMqLHjys9ERJ4JiS6nwRiNRuj1+gHbV65ciYSEBHzve9/Dli1bcOXKFce+mpoa5OfnO8IMANx66604f/48GhoaBv0ei8WCzs5Op0+wBaP7w9up+F1lXS7E6B6u/ExE5H8BCzSfffYZnnvuOdx3331O2zds2IA33ngDe/bswT333IO1a9fisccec+xvaWlBcnKy0zH2n1taWgb9rtLSUuh0OscnIyPDx1ejDP6eip8LMRIRUaiQHWjWr18/6EDeqz8ffvih0zHnz5/HnDlzcOedd+KnP/2p077//M//RG5uLv75n/8Za9euxaOPPoonn3zSqUz/f9HaWw6G+pduSUkJjEaj49PY2Cj3MsOCP6fi93frDxERkRyyBwWvXLkS99xzz7Blxo4d6/jz+fPnMXPmTOTm5uKFF15wef6pU6eis7MTFy5cQHJyMlJSUga0xFy8eBEABrTc2KnVaqcuqkjlz6n47a0/cl3d+hMfG+NF7YiIiL4m+4mXkJCAhIQEt8p+/vnnmDlzJgwGA8rKyjBihOsGoWPHjmHkyJEYPXo0ACA3NxcPPfQQenp6EBNjewC+8847SEtLcwpONJB9Kv5zMrudJNjexBluKn5ftP4w0BARka/4bQzN+fPnMWPGDGRkZOCpp55Ca2srWlpanFpb/vKXv+DFF1/EiRMn8Nlnn+EPf/gDfvWrX+Hee+91tLAsXrwYarUaRUVFOHHiBHbs2IHHHnsMa9as4eBKF7xZJdzVKtRciJGIiEKJ354q77zzDj799FN8+umnSE93XtHYPn5CpVJh06ZNWLNmDa5cuYJvfvObePTRR3H//fc7yup0OlRWVuL+++/HpEmTEB8fjzVr1mDNmjX+qnpYWWRIx1PvnJI9Fb+rVaj92fpDREQkF5c+iAD+moqfCzESEZE/hew8NBQc/pqKf5EhHZqYKLjb8zdCsq0X5ar1h4iISC4Gmghhn4r/N/O/gzF6rdO+MXotfjP/Ozj00CxZ6wrpNCpsXmqwBSIXoca+f8tSA1eVJiIin2OXUwTy9VT87q7kvWWpgQsxEhGR2+Q8vxloyCeMZuugCzFmciFGIiLyEANNPww0gcOFGImIyFfkPL85GQj5lH0hRk6aR0REgcRBwURERKR4DDRERESkeAw0REREpHgMNERERKR4DDRERESkeAw0REREpHgR8dq2faqdzs7OINeEiIiI3GV/brszZV5EBJrLly8DADIyMoJcEyIiIpLr8uXL0Ol0w5aJiJmCr1y5gvPnzyMuLs7ns9Z2dnYiIyMDjY2NYTsLcSRcI8DrDDe8zvARCdcI8DoHI4TA5cuXkZaWhhEjhh8lExEtNCNGjEB6erpfv2PUqFFh/R8gEBnXCPA6ww2vM3xEwjUCvM7+XLXM2HFQMBERESkeAw0REREpHgONl9RqNR5++GGo1epgV8VvIuEaAV5nuOF1ho9IuEaA1+mtiBgUTEREROGNLTRERESkeAw0REREpHgMNERERKR4DDRERESkeAw0MjQ0NGDZsmXIysqCRqPBddddh4cffhg9PT3DHieEwPr165GWlgaNRoMZM2bgo48+ClCtPfPb3/4WeXl50Gq1GD16tFvHFBUVQZIkp8/UqVP9W1EveXKdSryf7e3tKCgogE6ng06nQ0FBATo6OoY9Rgn3c9OmTcjKysLIkSNhMBjw/vvvD1u+qqoKBoMBI0eOxDe/+U1s2bIlQDX1nJxr3Ldv34B7JkkSPvnkkwDWWL79+/dj/vz5SEtLgyRJ2Llzp8tjlHgv5V6nEu9naWkpvve97yEuLg5JSUm4/fbbcerUKZfH+eJ+MtDI8Mknn+DKlSt4/vnn8dFHH+HZZ5/Fli1b8NBDDw173BNPPIFnnnkGGzduxJEjR5CSkoJbbrnFscZUKOrp6cGdd96JFStWyDpuzpw5aG5udnx27drlpxr6hifXqcT7uXjxYtTV1WH37t3YvXs36urqUFBQ4PK4UL6fr7/+OlavXo1f/epXOHbsGH7wgx9g7ty5OHfu3KDlz5w5gx/+8If4wQ9+gGPHjuGhhx7CAw88gG3btgW45u6Te412p06dcrpv48aNC1CNPdPd3Y0bbrgBGzdudKu8Eu8lIP867ZR0P6uqqnD//ffj0KFDqKysRG9vL2bPno3u7u4hj/HZ/RTklSeeeEJkZWUNuf/KlSsiJSVFPP74445tX375pdDpdGLLli2BqKJXysrKhE6nc6tsYWGh+NGPfuTX+viLu9epxPt58uRJAUAcOnTIsa2mpkYAEJ988smQx4X6/Zw8ebK47777nLZ9+9vfFg8++OCg5X/xi1+Ib3/7207bfvazn4mpU6f6rY7eknuNe/fuFQBEe3t7AGrnHwDEjh07hi2jxHvZnzvXGQ738+LFiwKAqKqqGrKMr+4nW2i8ZDQaodfrh9x/5swZtLS0YPbs2Y5tarUa+fn5qK6uDkQVA2rfvn1ISkrC+PHjsXz5cly8eDHYVfIpJd7Pmpoa6HQ6TJkyxbFt6tSp0Ol0Luscqvezp6cHtbW1TvcBAGbPnj3kNdXU1Awof+utt+LDDz+E1Wr1W1095ck12t14441ITU3FrFmzsHfvXn9WMyiUdi+9peT7aTQaAWDY56Sv7icDjRc+++wzPPfcc7jvvvuGLNPS0gIASE5OdtqenJzs2Bcu5s6di1dffRXvvfcenn76aRw5cgQ33XQTLBZLsKvmM0q8ny0tLUhKShqwPSkpadg6h/L9/OKLL9DX1yfrPrS0tAxavre3F1988YXf6uopT64xNTUVL7zwArZt24bt27djwoQJmDVrFvbv3x+IKgeM0u6lp5R+P4UQWLNmDb7//e8jOzt7yHK+up8MNADWr18/6MCrqz8ffvih0zHnz5/HnDlzcOedd+KnP/2py++QJMnpZyHEgG3+5sl1ynH33XfjtttuQ3Z2NubPn4//+7//Q319Pd5++20fXoVr/r5OQHn3c7C6uapzqNzP4ci9D4OVH2x7KJFzjRMmTMDy5cuRk5OD3NxcbNq0CbfddhueeuqpQFQ1oJR4L+VS+v1cuXIl/v73v+N//ud/XJb1xf2Mlle98LRy5Urcc889w5YZO3as48/nz5/HzJkzkZubixdeeGHY41JSUgDYEmhqaqpj+8WLFwckUn+Te53eSk1NRWZmJk6fPu2zc7rDn9epxPv597//HRcuXBiwr7W1VVadg3U/B5OQkICoqKgBLRXD3YeUlJRBy0dHR+Paa6/1W1095ck1Dmbq1KmoqKjwdfWCSmn30peUcj9XrVqFN998E/v370d6evqwZX11PxloYPuLIyEhwa2yn3/+OWbOnAmDwYCysjKMGDF8I1dWVhZSUlJQWVmJG2+8EYCtb7yqqgq/+93vvK67HHKu0xcuXbqExsZGpwd/IPjzOpV4P3Nzc2E0GnH48GFMnjwZAPDBBx/AaDQiLy/P7e8L1v0cTExMDAwGAyorK3HHHXc4tldWVuJHP/rRoMfk5ubiL3/5i9O2d955B5MmTYJKpfJrfT3hyTUO5tixYyFxz3xJaffSl0L9fgohsGrVKuzYsQP79u1DVlaWy2N8dj9lDSGOcJ9//rn41re+JW666SbR1NQkmpubHZ+rTZgwQWzfvt3x8+OPPy50Op3Yvn27OH78uPjxj38sUlNTRWdnZ6AvwW1nz54Vx44dE4888oi45pprxLFjx8SxY8fE5cuXHWWuvs7Lly+LtWvXiurqanHmzBmxd+9ekZubK77xjW+E1XUKocz7OWfOHPFP//RPoqamRtTU1IiJEyeKefPmOZVR2v187bXXhEqlEi+99JI4efKkWL16tYiNjRUNDQ1CCCEefPBBUVBQ4Cj/j3/8Q2i1WvEf//Ef4uTJk+Kll14SKpVK/O///m+wLsEludf47LPPih07doj6+npx4sQJ8eCDDwoAYtu2bcG6BLdcvnzZ8f89AOKZZ54Rx44dE2fPnhVChMe9FEL+dSrxfq5YsULodDqxb98+p2ekyWRylPHX/WSgkaGsrEwAGPRzNQCirKzM8fOVK1fEww8/LFJSUoRarRbTp08Xx48fD3Dt5SksLBz0Ovfu3esoc/V1mkwmMXv2bJGYmChUKpUYM2aMKCwsFOfOnQvOBbhJ7nUKocz7eenSJbFkyRIRFxcn4uLixJIlSwa8CqrE+/nf//3fIjMzU8TExIicnBynV0MLCwtFfn6+U/l9+/aJG2+8UcTExIixY8eKzZs3B7jG8sm5xt/97nfiuuuuEyNHjhTx8fHi+9//vnj77beDUGt57K8n9/8UFhYKIcLnXsq9TiXez6GekVf/Heqv+yl9VQEiIiIixeJbTkRERKR4DDRERESkeAw0REREpHgMNERERKR4DDRERESkeAw0REREpHgMNERERKR4DDRERESkeAw0REREpHgMNERERKR4DDRERESkeAw0REREpHj/Pz6zR+MrC8LeAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2, y2, 'o', label='Original data', markersize=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "4c2603b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.vstack([x2, np.ones(len(x2))]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "fcdd5072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.00000000e+00  1.00000000e+00]\n",
      " [-1.90000000e+00  1.00000000e+00]\n",
      " [-1.80000000e+00  1.00000000e+00]\n",
      " [-1.70000000e+00  1.00000000e+00]\n",
      " [-1.60000000e+00  1.00000000e+00]\n",
      " [-1.50000000e+00  1.00000000e+00]\n",
      " [-1.40000000e+00  1.00000000e+00]\n",
      " [-1.30000000e+00  1.00000000e+00]\n",
      " [-1.20000000e+00  1.00000000e+00]\n",
      " [-1.10000000e+00  1.00000000e+00]\n",
      " [-1.00000000e+00  1.00000000e+00]\n",
      " [-9.00000000e-01  1.00000000e+00]\n",
      " [-8.00000000e-01  1.00000000e+00]\n",
      " [-7.00000000e-01  1.00000000e+00]\n",
      " [-6.00000000e-01  1.00000000e+00]\n",
      " [-5.00000000e-01  1.00000000e+00]\n",
      " [-4.00000000e-01  1.00000000e+00]\n",
      " [-3.00000000e-01  1.00000000e+00]\n",
      " [-2.00000000e-01  1.00000000e+00]\n",
      " [-1.00000000e-01  1.00000000e+00]\n",
      " [ 1.77635684e-15  1.00000000e+00]\n",
      " [ 1.00000000e-01  1.00000000e+00]\n",
      " [ 2.00000000e-01  1.00000000e+00]\n",
      " [ 3.00000000e-01  1.00000000e+00]\n",
      " [ 4.00000000e-01  1.00000000e+00]\n",
      " [ 5.00000000e-01  1.00000000e+00]\n",
      " [ 6.00000000e-01  1.00000000e+00]\n",
      " [ 7.00000000e-01  1.00000000e+00]\n",
      " [ 8.00000000e-01  1.00000000e+00]\n",
      " [ 9.00000000e-01  1.00000000e+00]\n",
      " [ 1.00000000e+00  1.00000000e+00]\n",
      " [ 1.10000000e+00  1.00000000e+00]\n",
      " [ 1.20000000e+00  1.00000000e+00]\n",
      " [ 1.30000000e+00  1.00000000e+00]\n",
      " [ 1.40000000e+00  1.00000000e+00]\n",
      " [ 1.50000000e+00  1.00000000e+00]\n",
      " [ 1.60000000e+00  1.00000000e+00]\n",
      " [ 1.70000000e+00  1.00000000e+00]\n",
      " [ 1.80000000e+00  1.00000000e+00]\n",
      " [ 1.90000000e+00  1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "27cbe7ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "d1, d0 = np.linalg.lstsq(A, y2, rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "3cecbdc1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "319.74117269970185 177.8700818420195\n"
     ]
    }
   ],
   "source": [
    "print(d1,d0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "10514d06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1227ff760>]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2, y2, 'o', label='Original data', markersize=10)\n",
    "\n",
    "y2_LS = d0+d1*x2\n",
    "plt.plot(x2,y2_LS,'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c4fa6c80",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.vstack([x2*x2, x2, np.ones(len(x2))]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "ef439467",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4.00000000e+00 -2.00000000e+00  1.00000000e+00]\n",
      " [ 3.61000000e+00 -1.90000000e+00  1.00000000e+00]\n",
      " [ 3.24000000e+00 -1.80000000e+00  1.00000000e+00]\n",
      " [ 2.89000000e+00 -1.70000000e+00  1.00000000e+00]\n",
      " [ 2.56000000e+00 -1.60000000e+00  1.00000000e+00]\n",
      " [ 2.25000000e+00 -1.50000000e+00  1.00000000e+00]\n",
      " [ 1.96000000e+00 -1.40000000e+00  1.00000000e+00]\n",
      " [ 1.69000000e+00 -1.30000000e+00  1.00000000e+00]\n",
      " [ 1.44000000e+00 -1.20000000e+00  1.00000000e+00]\n",
      " [ 1.21000000e+00 -1.10000000e+00  1.00000000e+00]\n",
      " [ 1.00000000e+00 -1.00000000e+00  1.00000000e+00]\n",
      " [ 8.10000000e-01 -9.00000000e-01  1.00000000e+00]\n",
      " [ 6.40000000e-01 -8.00000000e-01  1.00000000e+00]\n",
      " [ 4.90000000e-01 -7.00000000e-01  1.00000000e+00]\n",
      " [ 3.60000000e-01 -6.00000000e-01  1.00000000e+00]\n",
      " [ 2.50000000e-01 -5.00000000e-01  1.00000000e+00]\n",
      " [ 1.60000000e-01 -4.00000000e-01  1.00000000e+00]\n",
      " [ 9.00000000e-02 -3.00000000e-01  1.00000000e+00]\n",
      " [ 4.00000000e-02 -2.00000000e-01  1.00000000e+00]\n",
      " [ 1.00000000e-02 -1.00000000e-01  1.00000000e+00]\n",
      " [ 3.15544362e-30  1.77635684e-15  1.00000000e+00]\n",
      " [ 1.00000000e-02  1.00000000e-01  1.00000000e+00]\n",
      " [ 4.00000000e-02  2.00000000e-01  1.00000000e+00]\n",
      " [ 9.00000000e-02  3.00000000e-01  1.00000000e+00]\n",
      " [ 1.60000000e-01  4.00000000e-01  1.00000000e+00]\n",
      " [ 2.50000000e-01  5.00000000e-01  1.00000000e+00]\n",
      " [ 3.60000000e-01  6.00000000e-01  1.00000000e+00]\n",
      " [ 4.90000000e-01  7.00000000e-01  1.00000000e+00]\n",
      " [ 6.40000000e-01  8.00000000e-01  1.00000000e+00]\n",
      " [ 8.10000000e-01  9.00000000e-01  1.00000000e+00]\n",
      " [ 1.00000000e+00  1.00000000e+00  1.00000000e+00]\n",
      " [ 1.21000000e+00  1.10000000e+00  1.00000000e+00]\n",
      " [ 1.44000000e+00  1.20000000e+00  1.00000000e+00]\n",
      " [ 1.69000000e+00  1.30000000e+00  1.00000000e+00]\n",
      " [ 1.96000000e+00  1.40000000e+00  1.00000000e+00]\n",
      " [ 2.25000000e+00  1.50000000e+00  1.00000000e+00]\n",
      " [ 2.56000000e+00  1.60000000e+00  1.00000000e+00]\n",
      " [ 2.89000000e+00  1.70000000e+00  1.00000000e+00]\n",
      " [ 3.24000000e+00  1.80000000e+00  1.00000000e+00]\n",
      " [ 3.61000000e+00  1.90000000e+00  1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "f906fa9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x122a3b3a0>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2, e1, e0 = np.linalg.lstsq(A, y2, rcond=None)[0]\n",
    "\n",
    "plt.plot(x2, y2, 'o', label='Original data', markersize=10)\n",
    "\n",
    "y3_LS = e0+e1*x2+e2*x2**2\n",
    "\n",
    "plt.plot(x2,y2_LS,'k')\n",
    "\n",
    "plt.plot(x2,y3_LS,'g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "98aebd0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122a74d90>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.vstack([x2**3, x2*x2, x2, np.ones(len(x2))]).T\n",
    "\n",
    "f3, f2, f1, f0 = np.linalg.lstsq(A, y2, rcond=None)[0]\n",
    "\n",
    "plt.plot(x2, y2, 'o', label='Original data', markersize=10)\n",
    "\n",
    "y4_LS = f0 + f1*x2 + f2*x2**2 + f3*x2**3\n",
    "\n",
    "plt.plot(x2,y2_LS,'k',label='1st order')\n",
    "\n",
    "plt.plot(x2,y3_LS,'g',linestyle='dashed',label='2nd order')\n",
    "\n",
    "plt.plot(x2,y4_LS,'m',linestyle='dotted',label='3rd order')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a328f394",
   "metadata": {},
   "source": [
    "# Error analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f22e30b",
   "metadata": {},
   "source": [
    "Let's take a look at a few ways to compute 'goodness of fit'\n",
    "\n",
    "We need statistics and proper criteria to decide if these are good fits from a statistical perspective, but these methods can be useful in practical ways as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "2972dfba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable   Type       Data/Info\n",
      "-------------------------------\n",
      "A          ndarray    40x4: 160 elems, type `float64`, 1280 bytes\n",
      "a0         float64    3.20000000000001\n",
      "a1         float64    -1.3928571428571481\n",
      "a2         float64    0.6071428571428578\n",
      "c          float64    -0.949999999999999\n",
      "c0         int        2\n",
      "c1         int        5\n",
      "c2         int        17\n",
      "c3         int        140\n",
      "c4         int        52\n",
      "d0         float64    177.8700818420195\n",
      "d1         float64    319.74117269970185\n",
      "e0         float64    -72.51537514173693\n",
      "e1         float64    338.56714690900617\n",
      "e2         float64    188.25974209304974\n",
      "f0         float64    -86.68851184246537\n",
      "f1         float64    55.69644032553819\n",
      "f2         float64    206.02056502629333\n",
      "f3         float64    118.40548622162714\n",
      "m          float64    0.9999999999999997\n",
      "mu         float      0.0\n",
      "np         module     <module 'numpy' from '/op<...>kages/numpy/__init__.py'>\n",
      "numpts     int        40\n",
      "plt        module     <module 'matplotlib.pyplo<...>es/matplotlib/pyplot.py'>\n",
      "r          ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "sns        module     <module 'seaborn' from '/<...>ges/seaborn/__init__.py'>\n",
      "std        int        5\n",
      "x          ndarray    500: 500 elems, type `float64`, 4000 bytes\n",
      "x2         ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y          ndarray    5: 5 elems, type `float64`, 40 bytes\n",
      "y2         ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y2_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y3_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y4_LS      ndarray    40: 40 elems, type `float64`, 320 bytes\n",
      "y_1st      ndarray    4: 4 elems, type `float64`, 32 bytes\n",
      "y_ls       ndarray    100: 100 elems, type `float64`, 800 bytes\n"
     ]
    }
   ],
   "source": [
    "whos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "3d20adb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_1st =  m*x2 + c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0548f87b",
   "metadata": {},
   "source": [
    "We are going to fit a simple difference error first. We will take this further in another class. But looking at the below results can tell us quite a bit about the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "89754aca",
   "metadata": {},
   "outputs": [],
   "source": [
    "error_1st = y2-y_1st\n",
    "\n",
    "error_2nd = y2-y2_LS\n",
    "\n",
    "error_3rd = y2-y3_LS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "90691991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124878ac0>]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2, error_1st)\n",
    "\n",
    "plt.plot(x2,error_2nd,'g')\n",
    "\n",
    "plt.plot(x2,error_3rd,'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "5c1159cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "MSE1 = np.sum(error_1st**2)/len(error_1st)\n",
    "MSE2 = np.sum(error_2nd**2)/len(error_2nd)\n",
    "MSE3 = np.sum(error_3rd**2)/len(error_3rd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "c0d82d80",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "240092.7313974852 78185.26852909166 27936.691870808754\n"
     ]
    }
   ],
   "source": [
    "print(MSE1, MSE2, MSE3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03f1af2c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
