NumericalMethods/HW3/HW3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ed049dae",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "17da2ee7",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams.update({\"font.size\" : 15, \"font.family\" : \"serif\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdcca142",
   "metadata": {},
   "source": [
    "### Задача 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2fa3961",
   "metadata": {},
   "source": [
    "Пусть $y$ - проекция $v$ на $range(A)$, тогда $v-y$ должно быть ортогонально $range(A)$. Так как $y\\in range(A)$, то $y=Ax$, условие оротогональности переписывается в виде $A^T(v-Ax)=0$, т.е. $x=(A^TA)^{-1}A^T,\\; y = Ax = A (A^TA)^{-1}A^T$. \n",
    "\n",
    "Окончательно $P = A (A^TA)^{-1}A^T$ \n",
    "\n",
    "*(при выводе сделано предположение, что $A^TA$ обратима, что верно, когда столбцы матрицы $A$ независимы)\n",
    "\n",
    "$A=\\begin{pmatrix} 1 & 0\\\\ 0 & 1 \\\\ 1 & 0 \\end{pmatrix}, \\; (A^TA)^{-1}=\\begin{pmatrix} 1/2 & 0 \\\\ 0 & 1\\end{pmatrix}$\n",
    "\n",
    "$P_A = A(A^TA)^{-1}A^T = \\begin{pmatrix} 1/2 & 0 & 1/2\\\\ 0 & 1 & 0 \\\\ 1/2 & 0 & 1/2 \\end{pmatrix}$\n",
    "\n",
    "$B=\\begin{pmatrix} 1 & 2\\\\ 0 & 1 \\\\ 1 & 0 \\end{pmatrix}, B^TB = \\begin{pmatrix} 2 & 2 \\\\ 2 & 5\\end{pmatrix}, (B^TB)^{-1} = \\frac{1}{6}\\begin{pmatrix} 5 & -2 \\\\ -2 & 2\\end{pmatrix}$\n",
    "\n",
    "$P_B =  \\frac{1}{6}\\begin{pmatrix} 1 & 2\\\\ 0 & 1 \\\\ 1 & 0 \\end{pmatrix}\\begin{pmatrix} 5 & -2 \\\\ -2 & 2\\end{pmatrix} \n",
    "\\begin{pmatrix} 1 & 0 & 1\\\\ 2 & 1 & 0 \\end{pmatrix} = \n",
    "\\frac{1}{6}\\begin{pmatrix} 5 & 2 & 1\\\\ 2 & 2 & -2\\\\ 1 & -2 & 5\\end{pmatrix}$\n",
    "\n",
    "Столбцы матрицы А ортогональны, поэтому QR-разложение ищется просто нормировкой столбцов\n",
    "\n",
    "$Q = \\begin{pmatrix} 1/\\sqrt{2} & 0\\\\ 0 & 1 \\\\  1/\\sqrt{2} & 0\\end{pmatrix} , \\; R=\\begin{pmatrix} \\sqrt{2} & 0 \\\\ 0 & 1\\end{pmatrix}$\n",
    "\n",
    "Ортогонализация Грама-Шмидта для B\n",
    "\n",
    "$q_1 = \\frac{1}{\\sqrt{2}}a_1 = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\0\\\\1\\end{pmatrix} = \\frac{1}{r_{11}}\\begin{pmatrix}1\\\\0\\\\1\\end{pmatrix}, \\; r_{11} = \\sqrt{2}$\n",
    "\n",
    "$u_2 = a_2 - \\frac{(a_1, a_2)}{||a_1||^2}a_1 \\Leftrightarrow r_{22}q_2 = a_2 - r_{12}q_1, \\; u_2 = \\begin{pmatrix} 1 \\\\ 1 \\\\ - 1\\end{pmatrix}, \\; q_2 = \\frac{1}{\\sqrt{3}}\\begin{pmatrix} 1 \\\\ 1 \\\\ - 1\\end{pmatrix}$\n",
    "\n",
    "$r_{22} = ||u_2|| = \\sqrt{3},\\; r_{12} = \\frac{(a_1, a_2)}{||a_1||}=\\sqrt{2}$\n",
    "\n",
    "$R = \\begin{pmatrix}\\sqrt{2} & \\sqrt{2}\\\\ 0 & \\sqrt{3}\\end{pmatrix}, \\; Q = \\begin{pmatrix} q1\\; |  \\; q2\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5518f255",
   "metadata": {},
   "source": [
    "### Задача 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b91597f3",
   "metadata": {},
   "source": [
    "$m = 1,\\; a(10) = \\frac{f_1}{2} + \\left(f_1 + \\frac{f_2}{2}\\right) + ... + (f_1+...+\\left(f_9 + \\frac{f_{10}}{2}\\right) = \\frac{1}{2}\\left( 19f_1 + 17f_2 + ... + f_{10}\\right),\\; v(10)=f_1+...+f_{10}$\n",
    "\n",
    "$f = (f_1, ..., f_{10})^T, \\; A = \\begin{pmatrix} \n",
    "\\frac{19}{2} & ... & \\frac{1}{2} \\\\\n",
    "1 & ... & 1\n",
    "\\end{pmatrix}$\n",
    "\n",
    "Для недоопределённой системы $Af = a$ можно искать решение линейной системы с минимальной 2-нормой $||f||_2$. Метод множителей Лагранжа в таком случае даёт решение $f = A^T(AA^T)^{-1} a$ (right pseudoinverse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "18d6765c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[9.5-i for i in range(10)], np.ones(10)])\n",
    "a = np.array([1,0]).T\n",
    "\n",
    "f1 = np.linalg.lstsq(A, a, rcond=None)[0]\n",
    "f2 = A.T@np.linalg.inv(A@A.T)@a\n",
    "\n",
    "print(np.allclose(f1, f2))\n",
    "print(np.allclose(A@f1, a))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9347468",
   "metadata": {},
   "source": [
    "### Задача 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ffd7e107",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 7\n",
    "x = np.sort(np.random.uniform(low=0.0, high=6.0, size=n))\n",
    "y0 = 10*np.sin(x)\n",
    "y = y0 + np.random.normal(size=n)\n",
    "\n",
    "p1 = np.polyfit(x, y, deg=1)\n",
    "p2 = np.polyfit(x, y, deg=3)\n",
    "\n",
    "f1 = np.poly1d(p1)\n",
    "f2 = np.poly1d(p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2c6c9bee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7feb1bd47040>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x, y0, color=\"red\", label=\"True\")\n",
    "plt.scatter(x, y, color=\"black\", label=\"Data\")\n",
    "plt.plot(x, f1(x), color=\"blue\", label=\"Linear\")\n",
    "plt.plot(x, f2(x), color=\"green\", label=\"Cubic\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea9a12e",
   "metadata": {},
   "source": [
    "### Задача 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "dd579bdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25, 60)\n",
      "(1500, 816)\n"
     ]
    }
   ],
   "source": [
    "with np.load(\"data.npz\") as data:\n",
    "    A, C = data[\"A\"], data[\"C\"]\n",
    "    \n",
    "def mat2vec(A):\n",
    "    return A.flatten()\n",
    "\n",
    "def vec2mat(a, shape):\n",
    "    return a.reshape(shape)\n",
    "\n",
    "print(A.shape)\n",
    "print(C.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "c2614e3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7feb0ab32bf0>"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 691.2x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "8e4035fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/h9/ll8t8frd1r575llt96l1glhm0000gn/T/ipykernel_43808/2371967909.py:2: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  a0 = np.linalg.lstsq(C, a)[0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7feb09a9f460>"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = mat2vec(A).T\n",
    "a0 = np.linalg.lstsq(C, a)[0]\n",
    "A0 = vec2mat(a0, (16, 51))\n",
    "plt.matshow(A0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "d10f062c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(816,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feafa778dc0>]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAD8CAYAAABqxe1QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAvoElEQVR4nO3deXxU1f3/8ddntmyEQCCA7Ksgi4hG2ZWKdS2tftVaW+tWRa0VrbW2tf1a+6vVb7W2dasWd9uq1VattIorqCyyKEVEEQQRAYEAEiCBrOf3x0xwiJOQwCR37sz7+XjwCPfOnTufO5mb95x7zz3XnHOIiIhI+gh4XYCIiIgkl8JdREQkzSjcRURE0ozCXUREJM0o3EVERNJMyOsCkqVjx46ud+/eXpchkvLefvvtzc65Iq/raIj2ZZGmaWxfTptw7927NwsXLvS6DJGUZ2afeF1DY7QvizRNY/uyDsuLiIikGYW7iIhImlG4i4iIpBmFu4iISJpRuIuIiKQZ34e7mU0ys6mlpaVelyIiIpISfB/uzrlpzrnJBQUFXpciIiKSEnwf7k31xvIS7nx1hddliMgB2lVZw+9fXs7bn3zudSkiKStjwn3ex1u4/dUVVFTXeF2KiByAqtpa7nh1BYvWKNxFGpIx4T6wS1uqax0fby7zuhQROQBZoeifrYrqWo8rEUldGRPuXdpmA7Bpe4XHlYjIgYgEFe4i+5Ix4d6xTQSAzTsV7iJ+ZmZEQgGdYhNpROaEe34WoHAXSQdZwQCVarmLNChjwj0/K0QkFGDzzkqvSxGRA5QVVriLNMb34d7UQWzMjKI2WWq5i6SBSDCgc+4ijfB9uDdnEJv2eWE+L1PLXcTvoufcFe4iDfF9uDdH+9wIn5dXeV2GiBygcDBAdY3CXaQhGRXuRW2y+Kx0l9dliMgBCgaM6lrndRkiKSujwn14j3Zs3F7B259s9boUETkAoaBRo3AXaVBGhfsxBxcB8NGmnR5XIiIHIhgIqOUu0oiMCvcuBdFR6nQ5nIi/hQJGTa3OuYs0JKPCPTscJD87RMkOXQ4n4mfBgFFdo5a7SEMyKtwh2qlO4S7ib9GWu8JdpCEZF+5dCrKZvXIzzukPg4hfqbe8SOMyLtyP6NWebeVV7KrSTSdE/Eotd5HGZVy4d2uXA8A2DWYj4lvBQEDhLtII34d7U8eWr9MuNwwo3EX8TC13kcb5PtybM7Y8QLvc6H3dt+3S5XAifhUMGtW6FE6kQb4P9+aqa7mXquUu4ltquYs0LvPCPSfactcNZET8S73lRRqXeeEea7l/Xq7D8iJ+pZa7SOMyLtyzw0HyIkG2aAhaEd/S2PIijcu4cAfo0CaLzTs1Sp2IX6nlLtK4jAz3fkV5LN+4w+syRGQ/RceWV295kYZkZLgP61bA8o072FWpUepE/Egtd5HGZWS4H3JQW2odrCzRfd1F/Ch6nbvCXaQhGRnuvTvmAbB6S5nHlYikJzMbaWaPmNmbZjbDzJaY2V/NrHsy1q+Wu0jjQl4X4IXeHaLh/nGJwl2khZxJtPEwwTlXY2Y5wEzgKWD0ga68rre8cw4zO9DViaSdjAz3nEiQHoU5vP/Zdq9LEUlX9wHbnHM1AM65XWY2G7ggGSsPBaKBXusgqGwX+ZKMPCwPUNyrkAWrP9d93UVagHPuQ+fcxrppMxsKnA7ckoz1B2PhrvHlRRLL2HAf1CWfzTsrKFOPeZEWY2ZnmNkyYC7wB+fczQ0sN9nMFprZwpKSkn2ut67lrvPuIollbLgX5ESHod2xW2PMi7QU59w/nHODgJHA5WZ2fwPLTXXOFTvniouKiva53i9a7gp3kURSMtzN7GAze87MpprZ38wsN9mvkZ8dDfftu6qTvWoRqcc59z5wHfA9MxtzoOvb03KvUbiLJJKS4Q7cC9zmnJsMLAd+lOwXaJsT7Uu4XS13kaQzs6wEs5fGfh52oOsPBqN/utRyF0ks6eFuZheY2RYzu6GBxweb2StmNtvMFpnZTWYWinu8iOghvFmxWdOBs5JdZ9s9LXeFu0gL+NDMOtWb1y32c8uBrlzn3EUal7RwN7P2ZvYiMAIobGCZImAG8KxzbiwwDjgFuC1usZ7A1rpLaICNsXlJ1TZ2zl0td5EW83MzCwKYWQHwS+BT4D8HuuK6c+5VGl9eJKFkttzzgBucc1MaWWYKYMA9AM65MqLBfrmZdU1iLfvUNjt2WF7n3EVawk+Ag4H5ZvYG0QFsPgDGOucOeNznL65zV8tdJJGkDWLjnFsLrN3HYicDC+Na5QBzgCBwPPAw0W/2hWYWjC3XGViTaGVmNhmYDNCzZ/Ma921zwoSDxvptu5r1PBHZN+fc34G/t9T61VtepHGt3aGuP7C+3rx1sZ8DAJxzm4D5RA/ZA5wIPJloZc29fCZeOBhgePd2vPXx1mY9T0S8FwpE/3TpnLtIYq0d7m2Ainrz6qbz4uZdBlxjZlOBQex9Tj5phnYrYNUm3RlOxG/2tNx1KZxIQq09tvxOoP4lMnXTe+7i4pxbBkxqygrNbBIwqX///s0uJi8rSHlVjW4+IeIz6i0v0rjWbrl/BNTvOFc3vWJ/Vuicm+acm1xQUNDs5+ZGQtTUOirV41bEVzS2vEjjWjvcnweK6y6PiRkD1AAvtXIt5EaiZZRXaHx5ET8JquUu0qjWDvc7AAdcAhAbVvZq4G7nXP2Odi2uLty3lle29kuLyAHQYXmRxiU13M3sKTObGZs838xmmtnX6x53zpUAxwKnx+7tPIfoCHTXHMBrTjKzqaWlpc1+bue22QC8uHTD/r68iHhALXeRxiW1Q51z7swmLLMUmJjE15wGTCsuLr64uc895uAi8iJB/vbWGr4/ofkd8kTEG6GgrnMXaUyq3jimVZgZZxzRnXXbdjFj2SavyxGRJgrqOneRRmV0uANcc8JAciNBfvr0u+yuUsc6ET8IaYQ6kUb5PtwP5Jw7RO/rft+5xWzcXsEDsz5OcnUi0hK+OOeuS+FEEvF9uB/Ide51xvbvyFcGFvHwnNU43YhCJOV9cVc47a8iifg+3JPl2EM6U7KjgrWf60YyIqkuKxT901VZrZa7SCIK95gje7cH4J7XV3pciYjsS24keqFPeaVu2SySiMI9ZlCXtgw+qC0vLd2oQ/MiKS4vKzoAVVmlOsGKJOL7cD/QDnXxjh/Smc07K7jw4QVUVOuPhkiqygkHMYPyCrXcRRLxfbgno0NdnYvH9+XKiQOY8WEJ/178WRKqE5GWYGbkRUJs361wF0nE9+GeTHlZIaZMHEB2OMAzi9Z5XY6INKJfUR4ffLbd6zJEUpLCvZ5gwBjXvyOL1nyu0a9EUlhRfrZa7iINULgncPrh3SmrrOFBDWojkrIiIaOqRpfCiSTi+3BPZoe6OscN7sygLvnc8eoK9ZwXSVGhQIBqhbtIQr4P92R2qKsTDgb4ZnEPdlRUs3mn7vUukorCwYBGqBNpgO/DvaUM6doWgPveXOVxJSKSSDiow/IiDVG4N2Bk3w6cVdyD+99cxawVm70uR0TqibbcFe4iiSjcG3H9pMEM6JTPZX99m5UlO70uR0TihIJGtQ7LiySkcG9EXlaI3581nMqaWk784xv899NtXpckIjGRYIBKtdxFElK478OQrgX86wdjqapxPL9Eo9aJpIpQ0KjWWBQiCfk+3FviUrj6BnVpy4SBRUx9YxUvKOBFUkI4GKCm1lGrgBf5Et+He0tcCpfIXd8+nE75Wfzm+Q9Yur7lvkiISNOEg9E/X1W1OjQvUp/vw721tMkKcds3h7Nu2y5Ou3sOi3X+XcRT4aAB6Fp3kQQU7s0wfkAR/7liPMGA8T/3zOGxeWu8LkkkY9W13DVKnciXKdybaXDXtrz0w6MZ0KkN1z2zhG9NnctHm3Z4XZZIxgnFwl095kW+TOG+H3oU5vLUpaO5bEI/3l+/nbP+/Babd1Z4XZZIRonosLxIgxTu+yk/O8xPThzEQxccybZdVXzl1pm8s+Zzr8sSyRihgA7LizRE4X6AjuhVyGMXjSQQMM5/cD4fbtAhepHWEA7Fessr3EW+ROGeBCP7duC+c4u
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u, s, vh = np.linalg.svd(C, full_matrices=False)\n",
    "print(s.shape)\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.semilogy(s)\n",
    "plt.subplot(122)\n",
    "plt.plot(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "da03e7f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/h9/ll8t8frd1r575llt96l1glhm0000gn/T/ipykernel_43808/88012303.py:3: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  w = np.linalg.lstsq(s1, u1.T@a)[0]\n",
      "/var/folders/h9/ll8t8frd1r575llt96l1glhm0000gn/T/ipykernel_43808/88012303.py:6: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
      "  plt.matshow(A1)\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEaCAYAAABzZLM+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAm20lEQVR4nO3deZRcZ3nn8d9Ta2/qTWrZkrzgBezYYMyJwNhhEdgxSzIkMwzMhNVMguCMgwdyEjgDQ+ITGBOCIcEJSY6CHZg4ZxIMZPAhQAAHsdgGW47NYrCNwZYsWbaklnqt7lqf+aOqod1utaoeXXX3pb+fc3TqVNX99fvWve+996mre2+ZuwsAAABAumRWugMAAAAAOkchDwAAAKQQhTwAAACQQhTyAAAAQApRyAMAAAApRCEPAAAApBCFPADgqMzspWa2z8x2tjFtv5n9nZm5mW07xrQvMrNvmtkBM9tvZh83s/UJdRsA1gQKeQDAk5hZr5n9laS/kbS5jem3SfqepEvbmPZySV+R9HlJJ0u6QNL5kr5hZn3xXgPA2kIhDwBYzEckdatZZC/JzLZI+ntJb5V0wzGmzUn6a0l3ufsH3b3h7gclvUXSeZL+4Hg7DgBrBYU8AGAx73P3N7n7RBvTjkm6wN2/1Ma0l0o6U9I/z3/R3b8n6UFJv21m1mlnAWAtopAHgBVmZpeZ2WNmVjGzh83sfDP7qpk93jrf/BPL3Sd339vBtNPufqTNyV/QevzeIu99V9IWSWe12zYArGW5le4AAKx17v5VSSe3Lih9uqQPSLpC0j41T1lZkpl9VtIlbTZ3rbtfG+tpIp7Wety/yHuPth6fqubReQDAEijkAWB1WS/p/XNHxM3sg5I2LRVw9/+0HB1LyEDrsbTIe3OvDS5PVwAg3SjkAWB1mXX3O+aeuPv3JX1/BfsDAFilOEceAFaXgyvdgRNsvPXYs8h7PQumAQAsgSPyALC6NDoNpOwc+Qdaj5sk3b3gvbn71f94+boDAOlFIQ8AKZeyc+S/Iendat6f/gsL3rtAzQt8udAVANrAqTUAgOV0i6SHJP3H+S+a2QVq3q3mBnf3legYAKQNhTwAYNm4e03NX4D9ZTN7l5llzGyDpL+R9ENJH1rRDgJAilDIA8AKM7Nnmtljap7nfmrrx6GOef/4E9yn57f68VjrpUvmnptZcZHpP9ea9vdbL322Ne17Fk7r7l+W9KuS/oOkx9S8K8+PJL3A3SdPyAcCgF9Axv9gAgAAAOnDEXkAAAAghSjkAQAAgBSikAcAAABSiEIeAAAASCEKeQAAACCFVmUhb2bnmdlXzexWM7vbzK4xM36FFj9jZm8ys1Ezu3qR98zM3tMaO98ys2+a2dYV6CZWkJm91Mw+a2Y7W+Pg383sSjOzRabd3nr/G2Z2h5m9ZCX6jJVhZheZ2Sdb24qvmdn3zexGMztlwXSMEzyBmZ1uZhNmtnOR9xgva5yZbTOzh1v7ofn/fnveNMdVs6y64tjMRiR9TdL73P0vzaxX0m2SeiX9jxXtHFacmQ1J+kdJ90saPspk75X0eknPdvcxM3udpFvM7Jnu/vDy9BSrwI2SPuDuH5YkM3uOpG9K6pf0gbmJzOwNkv5E0oXuvsfMXiDpy2b2Qnf/zgr0G8vvVWoe2Nrm7nUz65a0U9JNki6WGCd4stZBgesl1Rd5j/GCOZ9w96uXeP+4apbVeET+Kkkm6a8lyd2nJX1Y0pVmtnklO4ZVoVfS1e5+1WJvmtk6Se+S9BfuPiZJ7n6jpEOS3rlcncSqcKek6+aeuPsdkm6R9Ma511o74vepuaHd05ruG2oePPijZe0tVtLfSvp9d69LkrvPSLpV0rkS4wRH9VZJuyV9d/6LjBe0K4maZTUW8i+XtGtug9pym6SspMtXpktYLdx9r7vfvsQk2yT1SPr2gtdvV3NsYY1w95e5e3XByzOSCvOeP13SaXryeLlN0mVmVhB+4bn7/e7++NxzM3u6pFdK+tPWS4wTPIGZnaHmgcffW+RtxgvatU3HWbOsxkL+bEmPLnhtX+vxqcvcF6TP2a3HxcbQ6WxA1y4zy6p5msSN815earzkJZ2+DF3DKmFm/9nM7lNzJ/pn7j53ChbjBD8z75Sad7j7+CKTMF4w33PN7Iutc9+/YmZvm3fd53HXLKuxkO+TVF7w2tzz3mXuC9Knr/V4tDHUs4x9werydkmjkq6Z99qxxgvbnDXE3T/t7udKukjN0zk/3nqLcYL5rpT0kLt/6SjvM14wZ1zSXkmvdffnS/pdSe+Q9LnW+8dds6y6i10lTUkqLnht7vn0MvcF6TPVejzaGCotY1+wSpjZy9Q8n/VF7j47761jjRe2OWuQu//QzN4t6VNmdoMYJ2gxs7PULMYuWmIyxgskSe5+t6Tfmff8fjN7v6TrzewiJVCzrMZC/kFJCy9qnXv+42XuC9LnwdbjZjW/BWve893uXln+LmEltW75dq2ky9x974K354+X+TZLqqp5IRt+wZlZ0d0XHhG7t/V4oZp3O5IYJ5B+XVJF0ufm3cn2Qklq3YJyj6QPtV5nvGAxc7XsmUqgZlmNp9Z8QdLW1vmscy5R8/ZOX16ZLiFFdqp5QePCoyUXS/risvcGK8rMfk3NIv4l7r679dr21m1MJekHkh7Rk8fLJZJu4YvfmnG/mW1c8NqW1uOoGCdocfePuvsF7r5t7p+keyTd03r+BjFe0GJmH2hdGD3f3O9T7FMCNctqLOSvk+SS3iJJZtaj5lXhH3P3hRcDAE/g7pNq3rv3bWY2IElm9hpJI5I+uJJ9w/Iys9+QdIOkd0s62cy2tn5k4y2SBiTJ3V3S/5J0hZmd2so9T9KvSLp6JfqNFfOeuQNIrW3HH6lZjP0L4wSdYLxgnoslvd3MMpJkZsOS/kDSLknfSqJmWXWn1rj7QTN7saTrzOy1al4U8kVJf7iyPcNqYWY3qTnIpeaGcpukj7j7za3X3iepIenrZjal5hfDy/gxqDXnJjXvEHHzUhO5+/8xsy41/6t8SlKXpN/kR1vWlHdJukLSHWY2LWmdmjva33L3KYlxgiczsyvUHDcXtp7vlPT37n494wUt16h5fdbtZlZWs6a9RdL/dvdGa5rjqlms+cURAAAAQJqsxlNrAAAAABwDhTwAAACQQhTyAAAAQApRyAMAAAApRCEPAAAApBCFPAAAAJBCq76QN7PtK90HpAfjBe1irKATjBe0i7GCThzveFn1hbwkVgh0gvGCdjFW0AnGC9rFWEEnfuELeQAAAAALrIpfds3193h+4+Ci79UnSsr29yz6XiFbD7VXa8S+v5jF5lW1kgvlcvnY58tkYv0sZmqh3FSlGMpF5+dSn682XlJuYPHxUqvFlnsu2zj2RAtE16qeXDWUiy6DXHAdqtaCYzrYXjbT+TKQpPoS6/pSY0UWak7RzWnDYw3mgvOlL18J5aaqhVAuE1zX6x5bZ2uzsfGpJbYt9clpZdf1LvpeoRjbdkY3FN3B7UQtOj+D+8zouA6ufqHZub4wHWprotZ91PfKYzMqDi7+fqmSD7UX3a83gvs91YPLLrZJkheC9UBg/yxJ+WWuH7tyR99GlI/MqjjUteh7R+47dMjdR5b628GtXbLyGwd15off3HHu1MGxUHuHSotvjI8l+sVh3571odyGzeOhXF+xHMqd3X8olPvWnjNDuWxwBezrin2+0bG+UG6wv9RxphHcQV8wsj+Uu33PU0K5Df2xndijBwZj7a2fDOWGumZCucMzRynUjyH6haNSy4ZyM+VYgTzU1/nYlKTnnfTTUO72A2eEcsUldmJLmarE5suB+5bc7x1Voy+23M884/FQbqkvmkt5+lBsO3G4ElsfDpdjudIyf/GLfHF43WnfCbX15UPnhXJ37z41lOvrmw3lJkZj9U5mPHiwZjr2BaB6Wmy/vm4gtm/Y1D8Ryh2YitURT1t/MJS76ZIdu481TaKn1pjZeWb2VTO71czuNrNrzGxVfFkAAAAAfpEkVsib2Yikr0n6f+7+K5KeJ+nXJH04qTYAAAAANCV5RP4qNU9t+2tJcvdpNYv4K81sc4LtAAA
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEaCAYAAABzZLM+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAApg0lEQVR4nO3de5RkZXnv8d/T1dX3e8/9znAfuacBES+DAooaTYKYFQiKiWd0LSOHuJK4oseEFQ1EgyQSTU4mweA5eE4UxcDRKCgBJIAww01QGBhg7tee6e7p+6X6OX9UdWx6enqqntkz3Zv+ftZiFbVr/+p9q+qtXU/v2fvd5u4CAAAAkC5l090BAAAAAKWjkAcAAABSiEIeAAAASCEKeQAAACCFKOQBAACAFKKQBwAAAFKIQh4A8BpmVmVm15jZ/WbWbmadZvaimd1oZnWHyFxiZveZ2X4z6zCzR8zs16do4wNm9oSZ7TGzrWZ2k5nVHL1XBQCvPxTyAICJbpb0dUnfkrRQUoukP5b0SUkPmFnl+JXN7BpJ90h6RtISSQskfV/S3WZ25cQnN7Pfk/RtSTe7+zxJb5X0fknfN7PMUXpNAPC6Y1wQCgAwnpn9T0mN7v47E5bfIOlPJa1x938qLKuTtFXSfkknuvvouPUfl7RS0gp37yksa5b0qqR73f2D49Z9n6S7JP2eu//L0Xx9APB6wR55AMBE/y7pq5Msf7Rwe+64ZW+S1CTpwfFFfMGPJbVKet+4ZR+U1Cjpzgnr/lBSv6SPxroMALMPhTwATDMzu9jMdpnZkJltMrM3mNlPzGy3mbmZ3XYs++Pud7v7w5M8VFG47Ri3bG7htn2S9fcUbt84btlbC7c/n9DmsKRfSnrjxEN3AACTo5AHgGnm7j9x9wWSHpFUJ+lGSdcof6z5Nw+XN7M7C38IFPPfHx1BV9sKt+P3po8V8PMmWb+1cLt83LKTCrc7J1l/h/K/SyujHQSA2aR8ujsAAHiNVklfcPdtkmRmX1T+hNNDcvffOtqdMrN6SR+WdKe7PzbuoUck9Ui6yMwy7p4b99jbC7e145Y1Fm77JmlmbFnTkfcYAF7/2CMPADPLgLs/PnbH3Z9193uns0MFX5I0JOnj4xe6e7fyJ8Auk/Q1M2sxs3oz+6x+tfd9sqIdAHCEKOQBYGbZO90dmMjM/kDSb0t6t7sf1D93/6qkKySdJulF5Y9/XyppbNab3eNW7yrcTjZnfM2EdQAAU+DQGgCYWSbO/HJYZnan8rPHFOMmd7+phOe+StIXJF3q7r881Hru/h1J35mQfWfhf58Zt/hF5Y+1X6jXnjQrSYuUf/2vFNs/AJjNKOQBIOWO1jHyZvabkv5e0nvHDvcpHCu/yN03FPEU50hySf9v3LKfSrpS0hnKz1Iz1lZW0qmSfubuA8m8AgB4fePQGgDAQczsXZJuk/QBd39o3EO/JukfJ6x7s5ldPWFZufInx37L3TePe+gOSQck/eaEJi9T/tCaWxN5AQAwC7BHHgDwGmb2NuWnmFwv6UIzu3DcwysmiSyT9D4ze9TdN5rZHElfUX5v/CfHr+ju+83sU5LWmtlV7v5NM1sh6SZJ90v6RuIvCABep8zdp7sPADCrmdmZku6R1CIpo/wJrz9296unDB69/vybpPdPscqD7r563PpXK39F1lWScsrvcf+epL909wOHaOMK5We7WaL8bDjfkvQ5d2eGGwAoEoU8AAAAkEIcIw8AAACkEIU8AAAAkEIU8gAAAEAKUcgDAAAAKUQhDwAAAKTQjCzkzWyVmf3EzB42s6fM7IbCxUUASZKZfcTM9pnZ9ZM8Zmb22cLY+U8ze8jM2qahm5hGZvYuM7vTzB4ojIMnzewTZmaTrLum8PhPzexxM3vndPQZ08PMzjezbxS2Ffeb2bNmdruZLZmwHuMEr2Fmy83sgJk9MMljjJdZzsxWm9mmwu/Q+P9+f9w6R1SzzLji2MzmKn9RkM+7+1fNrFbSI5JqJf33ae0cpp2ZNUv6V0kblJ9zezKfk3S1pHPdvdPMflfSfWZ2prtvOjY9xQxwu6Qb3f3LkmRm50l6SFKDpBvHVjKzD0n6K0lnufsWM3urpHvN7G3u/tg09BvH3hXK79ha7e45M6uW9IDyV6G9QGKc4GCFnQK3Kn/thImPMV4w5jZ3v36Kx4+oZpmJe+SvlWSS/kGS3L1X0pclfcLMFk1nxzAj1Eq63t2vnexBM6uX9GlJf+funZLk7rdLapf0J8eqk5gR1km6ZeyOuz8u6T5JHx5bVvgh/rzyG9othfV+qvzOgz8/pr3FdPonSX/k7jlJcvd+SQ9LOkVinOCQPi5ps6Rnxi9kvKBYSdQsM7GQf7ek9WMb1IJHlL/a4aXT0yXMFO6+zd0fnWKV1ZJqJP1swvJHlR9bmCXc/TJ3H56wuF9Sxbj7p0lapoPHyyOSLjazCuF1z903uPvusftmdpqkyyV9qbCIcYLXMLPjlN/x+KlJHma8oFirdYQ1y0ws5E+QtGPCsu2F2xOPcV+QPicUbicbQ8vZgM5eZpZR/jCJ28ctnmq8ZCUtPwZdwwxhZh8wsxeU/xH9G3cfOwSLcYL/Mu6Qmj90965JVmG8YLw3mtkPC8e+/9jMPjnuvM8jrllmYiFfJ2lwwrKx+7XHuC9In7rC7aHGUM0x7Atmlusk7ZN0w7hlhxsvbHNmEXf/jrufIul85Q/n/OfCQ4wTjPcJSa+6+48O8TjjBWO6JG2TdJW7v0XSH0j6Q0l3FR4/4pplxp3sKqlHUuWEZWP3e49xX5A+PYXbQ42hvmPYF8wQZnaZ8sezXuTuA+MeOtx4YZszC7n7L83sM5K+bWZfF+MEBWZ2vPLF2PlTrMZ4gSTJ3Z+S9NFx9zeY2Rck3Wpm5yuBmmUmFvIbJU08qXXs/kvHuC9In42F20XK/xWscfc3u/vQse8SplNhyrebJF3s7tsmPDx+vIy3SNKw8iey4XXOzCrdfeIesV8Ubs9SfrYjiXEC6b2ShiTdNW4m27MkqTAF5RZJf11YznjBZMZq2ZVKoGaZiYfW/LuktsLxrGPepPz0TvdOT5eQIg8of0LjxL0lF0j64THvDaaVmb1H+SL+ne6+ubBsTWEaU0l6TtJWHTxe3iTpPv7wmzU2mNm8CcsWF273iXGCAnf/iruf4e6rx/6T9LSkpwv3PyTGCwrM7MbCidHjjV2fYrsSqFlmYiF/iySX9DFJMrMa5c8K/5q7TzwZAHgNd+9Wfu7eT5pZoySZ2ZWS5kr64nT2DceWmb1f0tclfUbSAjNrK1xk42OSGiXJ3V3S/5B0jZktLeTeLOlCSddPR78xbT47tgOpsO34c+WLsR8wTlAKxgvGuUDSdWZWJklm1iLpjyWtl/SfSdQsM+7QGnffa2Zvl3SLmV2l/EkhP5T0Z9PbM8wUZnaH8oNcym8oV0u62d3vLiz7vKRRSQ+aWY/yfxhezMWgZp07lJ8h4u6pVnL3/2VmVcr/U3mPpCpJv8FFW2aVT0u6RtLjZtYrqV75H9rfcfceiXGCg5nZNcqPm7MK9x+Q9L/d/VbGCwpuUP78rEfNbFD5mvY+SX/p7qOFdY6oZrH8H44AAAAA0mQmHloDAAAA4DAo5AEAAIAUopAHAAAAUohCHgAAAEghCnkAAAAghSjkAQAAgBSa8YW8ma2Z7j4gPRgvKBZjBaVgvKBYjBWU4kjHy4wv5CXxhUApGC8oFmMFpWC8oFiMFZTidV/IAwAAAJhgRlzZtb4563MWV076WHfHsOqbs5M+lgv+HTIwOvnzHc6oWyi3KNsVym0abAnlBgdjr6+6aiiUW1zRGcqVx95ObR9qOORjA50DqmqqmvSxqsxwqL3B0fKSM33DFaG2omPsxJq9ody+XG0o15uLvb6cx76z5TZ6+JUmMdVn3tcxqJrmybc7tWWDofaGvPSxIkn9wW1SXbCf0W1nT27y9+twyhT7nWnN9oRynSM1oVzX0OTbDknKdfUp0xh73kNZXr0/lIt+H7YONodyGYt9fnXlA6HciGdCuY6B0j+fivKRUFutFb2HfKx7/7DqWyb/TreWxdrbOXLosTm
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEaCAYAAABzZLM+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAo/klEQVR4nO3de3hcd33n8c9XMxpJI1k3W7Et27Gd2LmTBOIkOFBwLkChLe2WhT7l0oZta3iakoU+FHbp0mZLG0oJtKRl2cdbUrpNu13SwhLKPWmchCSQOAkkcYgTx/FVvut+10jf/WNGoMiypfn62NKx3q/n8TPPzJzP/H4z8ztnvjo+53fM3QUAAAAgXSpmuwMAAAAAykchDwAAAKQQhTwAAACQQhTyAAAAQApRyAMAAAApRCEPAAAApBCFPADgZcwsZ2bvNrO7zOx5MztgZnvM7Ktm9qoT5OrN7O/MzM1swzRtXGtmD5rZITPbb2Z/a2YLk34vAHAmo5AHAEzWKukfJGUkvcbdl0i6WlKDpEfMbP3kQKlwf0rS9dO9uJm9UdL3JP2bpCWSLpV0saQHzKwumbcAAGc+CnkAwFRGJN3o7oclyd3bJP2upJykmyYuaGbLVCz83y/pjhO9qJllJX1B0uPu/il3Hyu18T5JF0n6g6TfCACcqSjkAQCT7Zd0jbt3T3p8T+m2YdLjnZIudfdvz+C1r5d0jqSvTnzQ3Z+StF3Sb5mZld1jAJiHKOQBYJaZ2Q2l49CHzWynmV1sZveY2cHS8eZfOp39cfchd98yxVPjx8c/OGn5PnfvmOHLv650+9QUz/1Y0jJJ587wtQBgXsvOdgcAYL5z93skLTGzzZIukfRJSTdK2qfiISsnZGZfkXTNDJu7zd1vK6d/ZlYtab2k/ynpm5JuLyc/yXml2/1TPNdWul2r4t55AMAJUMgDwNyyUNKfuvteSTKzT0laeqKAu//qqeqMmd0q6cOSKiV9UdJH3H3wJF5y/LCc/imeG3+s8SReHwDmDQ6tAYC5ZdDdHx2/4+5Pu/t3Z6sz7v4xSTWSLlPx2PatZnb1bPUHAPAzFPIAMLccnu0OTObuo6WTUX9VxVlr7izNPhPRVbrNT/FcftIyAIAToJAHgLllrNyAmX2ldLLsTP59ONoxd++U9JikNSoexx7xfOl2qsOFWku3LwRfGwDmFY6RB4CUS/oYeTO7TlKlu39niqcHSrdNwZd/QNLHVLwI1DcnPXepiif4cqIrAMwAe+QBAJO9TtLNkx80sxpJV0kalrQ1+Nr3SnpJ0n+Y9NqXqriX/w539+BrA8C8QiEPAJjKW8zsv5hZrSSZ2VIVp8JslfTf3T10HLu7F1S8AuwVZvZRM6sws0UqTm35rKRPJ9N9ADjzGTs+AGB2mdllkr4jqVlSRsUTXr/n7u+Zpf60SHq3iie3rpZULckkPSnpC+7+r1Nkvibpakl1kmoldai45/6v3f3Pplj+WkmfUHFe+VEVD7P5iLsfPRXvCQDORBTyAAAAQApxaA0AAACQQhTyAAAAQApRyAMAAAApRCEPAAAApBCFPAAAAJBCc7KQN7OLzOweM3vIzJ40s1vNjKvQ4qfM7L1mdtTMbpniOTOzPyyNne+b2YNmtm4WuolZZGY/b2ZfMbPNpXHwhJndZGY2xbIbS88/YGaPmtmbZqPPmB1mdrWZ/X1pW3GfmT1tZnea2fJJyzFO8DJmttLMus1s8xTPMV7mOTPbYGY7S79DE//91oRlTqpmmXPFcWn+4vskfcLd/6Z0MZKHVZyX+D/Paucw68ysSdI/S9qm4pzbU/m4pPdIutLdO83s3ZLuNbPL3H3n6ekp5oA7JX3S3T8jSWZ2laQHJdVL+uT4Qmb2G5L+XNLl7r7bzF4n6btm9np3/+Es9Bun39tV3LG1wd1HS1ew3SzpLknrJcYJjlXaKfBFFa+DMPk5xgvGfcndbznB8ydVs8zFPfI3q3jhkS9Ikrv3SfqMpJvMrHU2O4Y5oVbSLe5+zOXjJcnMFkj6qIoXoemUJHe/U9IRSR85XZ3EnPCYpNvH77j7o5LulfSb44+Vfog/oeKGdndpuQdU3Hnwx6e1t5hN/0vSh919VJLcfUDSQ5IukBgnOK73S9ol6ccTH2S8YKaSqFnmYiH/FklbxjeoJQ+reLXDN85OlzBXuPted3/kBItskJSX9INJjz+i4tjCPOHub3b3kUkPD0jKTbh/iaSzdex4eVjSDWaWE8547r7N3Q+O3zezSyS9TdJflB5inOBlzGy1ijsef3+KpxkvmKkNOsmaZS4W8msktU16bF/pdu1p7gvSZ03pdqoxtJIN6PxlZhkVD5O4c8LDJxovlZJWnoauYY4ws/9oZs+p+CP6l+4+fggW4wQ/NeGQmg+5e9cUizBeMNGrzexbpWPfv2dmH5hw3udJ1yxzsZCvkzQ06bHx+7WnuS9In7rS7fHGUP409gVzywclHZV064THphsvbHPmEXf/F3e/QNLVKh7O+belpxgnmOgmSS+5+7eP8zzjBeO6JO2V9C53/zlJvyfpQ5K+Vnr+pGuWOXeyq6ReSVWTHhu/33ea+4L06S3dHm8M9Z/GvmCOMLM3q3g867XuPjjhqenGC9ucecjdnzWzj0n6spndIcYJSszsXBWLsatPsBjjBZIkd39S0m9PuL/NzP5U0hfN7GolULPMxUJ+u6TJJ7WO33/hNPcF6bO9dNuq4l/BmnB/l7sPn/4uYTaVpny7TdIN7r530tMTx8tErZJGVDyRDWc4M6ty98l7xLaWbi9XcbYjiXEC6RclDUv62oSZbC+XpNIUlLslfbr0OOMFUxmvZc9RAjXLXDy05puS1pWOZx13jYrTO313drqEFNms4gmNk/eWrJf0rdPeG8wqM/sFFYv4N7n7rtJjG0vTmErSM5L26Njxco2ke/nDb97YZmZnTXpsWen2qBgnKHH3z7n7pe6+YfyfpB9J+lHp/m+I8YISM/tk6cToicavT7FPCdQsc7GQv12SS3qfJJlZXsWzwj/v7pNPBgBext17VJy79wNm1iBJZvZOSS2SPjWbfcPpZWa/LOkOSR+TtMTM1pUusvE+SQ2S5O4u6b9JutHMVpRyr5X0Gkm3zEa/MWv+cHwHUmnb8ccqFmPfYJygHIwXTLBe0gfNrEKSzKxZ0h9I2iLp+0nULHPu0Bp3P2xm10m63czepeJJId+S9Eez2zPMFWZ2l4qDXCpuKDdI+qy731167BOSxiTdb2a9Kv5heAMXg5p37lJxhoi7T7SQu/9vM6tW8b/KeyVVS/oVLtoyr3xU0o2SHjWzPkkLVPyh/XV375UYJziWmd2o4ri5vHR/s6R/cPcvMl5QcquK52c9YmZDKta090r6M3cfKy1zUjWLFf9wBAAAAJAmc/HQGgAAAADToJAHAAAAUohCHgAAAEghCnkAAAAghSjkAQAAgBSikAcAAABSaM4X8ma2cbb7gPRgvGCmGCsoB+MFM8VYQTlOdrzM+UJeEisEysF4wUwxVlAOxgtmirGCcpzxhTwAAACASebElV2rG6u9bmndlM8Ndg6qurH6NPdoaj1DVaFca74rlDswWB/KjQ1nQrlsdSGUO7u6PZSrNQvltg8d/3MZ7hxQrrFmyueGCtlQexFjhdjfyJaJrY8tNT2hXMFjY6WvkAvlhgYrQzmrHJt+oSlUZ48/pk80VhZkB0PtZRT7/npHY9uWrMU+l4LHxmfvcKyfZrHPpbmqP5TrHJn6e51O4QTbztGePmUW1E75XEU29j00Vg2EctUVI6FcW19DKFdVGfttqM0Oh3L9we3L4Ej52/jqXOy9neg7GOgYUk3T1OtKriLW3pHBqWuk6VRUxNa9sbHY7/Pp/u2ryw2FcrWZWC76m3mi8dLdXlB989Rjd8cz/UfcveVEr336KpsTqFtap1/6+186be2NKTZAH9i+JpT743VfD+Vue+4NoVzfS7GNdcv5R0K5z1/4T6HcFVWxjfVbX/j5UG5nR1MoFxkt3YdjG93KutgP3+9een8od2RkQSi3pf3sUG7btmWhXE1LrKA7r+VwKLdh0bZQbkFF7A+Ah7t
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEaCAYAAABzZLM+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAplklEQVR4nO3deZhcZ3Xn8d/p6n1vba3FkmxL8iLLtmzLGzbGWwCDJ4GAyQQDMYEIJg6OWYZMyDA4gZiQGCcYGGZE7HEmZgYwhOABbLwK79gyXmXkXfvWWlq9r3Xmj6qGdqkkdR1dqfu6v5/n6aeeunV/9b5d9dZbp2/fxdxdAAAAANKlbLw7AAAAAKB0FPIAAABAClHIAwAAAClEIQ8AAACkEIU8AAAAkEIU8gAAAEAKUcgDAF7HzCrN7ANmdquZvWhmW81sg5n9yMxOLbL++WbWm1+v8Oer+2jjvWb2hJltzz/3dWZWe+h/OwB446CQBwAUmi3pXyVlJJ3j7jMlnSmpSdIjZnZ2kcz33H1mkZ9PF65oZn8s6fuSrnf3GZLOk/R7kn5iZplD9UsBwBsNhTwAoJhBSVe4e5skuftmSX8qqVLSldEnNbMWSddL+oG7fyf/3K9J+rSkCyR96CD7DQCTBoU8AKDQFklvcveOguUb8rdNB/Hc78vn/61g+e2SeiV99CCeGwAmFQp5ABhnZnZxfn/yATNba2YnmNndZrbNzNzMbj6c/XH3fndfVeShkf3jHziIpz8vf/tMQZuDkp6XdJaZVR3E8wPApEEhDwDjzN3vzu+H/rCkeklflnSFpJmSvnOgvJn92z4ONC3285lS+2dm1WZ2gaR/lvQzSTcUWW2hmf3QzF7NH8D6oJl9uMh6x+RvtxR5bLNy30tHl9pHAJiMyse7AwCA15kq6UvuvlGSzOwrkmbtL+Duv3+oOmNm10r6jKQKSTdK+qy79xVZ9UhJfyPpbknNkv6TpBvN7Ex3//io9UZ2y+kp8hwjy5oPuuMAMAmwRR4AJpY+d39s5I67P+vud45XZ9z9c5JqJJ2s3Jby1WZ2ZsFqj0g63t3vdPesu+9y97+V9CNJHzOzcw9vrwFgcqCQB4CJpW28O1DI3Yfd/RlJv6/cWWtuMbPyUY/3u3tnkeht+dtLRy3bk78tds742oJ1AAD7QSEPABNLttTAod5HfoS7t0t6XNJCSYvGENmWv50xatmL+dtiuwvNVu73fzXYRQCYVNhHHgBSLul95M3sQkkV7v7zIg/35m9bRq1/taTvjJxzfpTW/O2OUcvul/R+SScpd5aakeeokHS8pEf3sQ8+AKAAW+QBAIXOk3RV4UIzq5F0hqQBSatHPXS1pDcXeZ535m/vGLXsVkkdkt5dsO4lyu1ac2OoxwAwCVHIAwCKeYeZ/Rczq5MkM5sl6V+V2/3lr929cD/2vzezZfl1a8zs05LeK+m77n7vyEruvkvSpyS918wuz69/pKTrJN0n6V8O7a8FAG8c5u7j3QcAmNTM7GRJP5c0RVJGuQNe73L3D45Tf6ZL+oByB7ceJalakkl6UtK33P2HBeufLumPJF2g3Okz65TbF/5mSd909732+zezyyT9paQjlNvC/z1Jn3f3YqelBAAUQSEPAAAApBC71gAAAAApRCEPAAAApBCFPAAAAJBCFPIAAABAClHIAwAAACk0IQt5M1tsZneb2UNm9qSZXWtmXIUWv2FmHzaznWZ2TZHHzMz+Kj92HjSzB0bOb43Jw8zebmb/ZmYr8+PgV2Z2pZlZkXWX5x+/38weM7O3jUefMT7M7Ewz+5f8XHGfmT1rZreY2REF6zFO8DpmNt/MOsxsZZHHGC+TnJmdb2Zr899Do38+Mmqdg6pZJlxxnD9/8X2Svuju38hfjORh5c5L/Ofj2jmMOzNrkfRdSS8od87tYj4v6YOSTnf3djP7gKR7zOxkd197eHqKCeAWSV92969KkpmdIekBSY2Svjyykpl9SNLfSVrq7uvN7DxJd5rZW9z9l+PQbxx+lym3Yet8dx/OX8F2pXJXoT1bYpxgb/mNAjdKGi7yGOMFI25292v28/hB1SwTcYv8VcpdeORbkuTu3ZK+KulKM5s9nh3DhFAn6Rp33+vy8ZJkZg2S/kLS1929XZLc/RZJOyR99nB1EhPC45JuGLnj7o9Juke5CxdJ+s0X8ReVm2jX59e7X7mNB184rL3FePq2pM+4+7AkuXuvpIckHScxTrBPH5e0TtLToxcyXjBWSdQsE7GQf4ekVSMTat7Dyl3t8K3j0yVMFO6+0d0f2c8q50uqlfRowfJHlBtbmCTc/RJ3HyxY3CupctT9JZLmae/x8rCki82sUnjDc/cX3H3byH0zWyLpPZL+Pr+IcYLXMbOjlNvw+KkiDzNeMFbn6yBrlolYyC+UtLlg2ab87aLD3Bekz8L8bbExNJ8JdPIys4xyu0ncMmrx/sZLhaT5h6FrmCDM7L1mtka5L9F/dPeRXbAYJ/iNUbvUfNLd9xRZhfGC0c4ys9vz+77fZWafGHXc50HXLBOxkK+X1F+wbOR+3WHuC9KnPn+7rzFUexj7gonlakk7JV07atmBxgtzziTi7j9w9+Mknanc7pz/nH+IcYLRrpT0mrvfsY/HGS8YsUfSRkmXu/ubJf2ZpE9K+nH+8YOuWSbcwa6SuiRVFSwbud99mPuC9OnK3+5rDPUcxr5ggjCzS5Tbn/UCd+8b9dCBxgtzziTk7s+b2eckfd/MbhLjBHlmtkC5YuzM/azGeIEkyd2flPTRUfdfMLMvSbrRzM5UAjXLRCzkX5ZUeFDryP2XDnNfkD4v529nK/dXsEbdX+fuA4e/SxhP+VO+XSfpYnffWPDw6PEy2mxJg8odyIY3ODOrcvfCLWKr87dLlTvbkcQ4gXSppAFJPx51JtulkpQ/BeV6Sf+QX854QTEjtezRSqBmmYi71vxM0rL8/qwj3qTc6Z3uHJ8uIUVWKndAY+HWkrMl3X7Ye4NxZWbvVK6If5u7r8svW54/jakkPSdpg/YeL2+SdA9/+E0aL5jZjIJlc/K3O8U4QZ67f83dT3L380d+JD0l6an8/Q+J8YI8M/ty/sDo0UauT7FJCdQsE7GQv0GSS/qYJJlZrXJHhX/T3QsPBgBex907lTt37yfMrEmSzOz9kqZL+sp49g2Hl5n9nqSbJH1O0kwzW5a/yMbHJDVJkru7pP8q6Qozm5vPnSvpHEnXjEe/MW7+amQDUn7u+IJyxdhPGScoBeMFo5wt6WozK5MkM5si6T9LWiXpwSRqlgm3a427t5nZhZJuMLPLlTso5HZJ/218e4aJwsxuVW6QS7mJ8nxJ17v7bfllX5SUlfQLM+tS7g/Di7kY1KRzq3JniLhtfyu5+/82s2rl/lXeJala0ru4aMuk8heSrpD0mJl1S2pQ7ov2D929S2KcYG9mdoVy42Zp/v5KSf/q7jcyXpB3rXLHZz1iZv3K1bT3SPpbd8/m1zmomsVyfzgCAAAASJOJuGsNAAAAgAOgkAcAAABSiEIeAAAASCEKeQAAACCFKOQBAACAFKKQBwAAAFJowhfyZrZ8vPuA9GC8YKwYKygF4wVjxVhBKQ52vEz4Ql4SHwiUgvGCsWKsoBSMF4wVYwWleMMX8gAAAAAKTIgru1Y213jtzIaijw2096qyuaboY+4Waq+2fCCU29VVF8pNq+8K5fYMVodygz0VoZxVD4dyx9XtCOU6s7F+bh8oPlYkabC9RxXNtUUfq8vE3vfdnYH3PRP7XGUqsgdeqQhTrL2FtTtDuTWd00M5649tO8jUDoVy5Zl9v577m1uay3tC7VVarJ8beqaEcg1VfaFcdO7sz5aHcgODmVCuoao/lOsaqArlfGjfr8twV7cy9cXngvLK2NxZXT4YyjVkYu/7ls7mUK6iKjauj6jeHcq9FpxfKitL72d0bDZW7/s96Nvdr+qW4mOwuiz2nm/vbgzlyvYzB+5PTUWsn91dsbqlrCr6GYqNzWxwDmyq6A3lamzf9Uf7rmE1Tyk+Dl98rn+Hu+/3AxGblRNWO7NB5337fSXnBrKxD+DS5o2h3P999KxQ7iP
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEaCAYAAABzZLM+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAp30lEQVR4nO3deZhcZZn38d/d+5akOwtZICuJLLIEaQhBhLAv4jqCIwjiFpxBGHQcvcZ5UdQZcAFmhHGYN4rbMPMygM4LiAiCBBCIEGRLIAuB7AlZO+ktvd7zR1Vr0+mt7pxO96G/n+vqq646dX71PF311Km7T5/zHHN3AQAAAEiXvMHuAAAAAIDcUcgDAAAAKUQhDwAAAKQQhTwAAACQQhTyAAAAQApRyAMAAAApRCEPAOiVmVWY2RozczOb1sM6R5jZ3Wa21sy2mNlSM7vGzMp6WP8jZvZcdt11ZnZDT+sCALpHIQ8A6Ms/SZrS04NmdrSkZyRVSap29wMkXSHp7yTdb2bWZf1PSbpT0k3ZdU+W9AFJvzKz/IH5FQDg7YdCHgDQIzObI+njkh7qZbWrJJVKusrdt0iSuy+UtEDSPElzOz1flaSbJN3t7v+ZXfcNSX8r6VRJlyb+SwDA2xSFPACgW2ZWKOmHkv5e0qZeVj0we/t6l+WrsreTOy27UNIoSb/ssu4DkholfSbUWQAYhijkAWCQmdkZZrbZzJrNbLWZvdPMHjazN7PHpf90kLr2FUk1yhTzvVmSvX1Hl+Ud95d1WnZy9valziu6e4ukVySdYGbFOfcUAIYhCnkAGGTu/rC7T5D0lKQKSddLukzSBEn/2VfezH6Z/UOgPz9f6k+fzOwQZY5xn+/u3sfq35X0qqRbzGyqmeWb2XmSPivp/7r7i53W7Sjuu9vDv1GZ76UZ/ekjAAx3BYPdAQDAW4yR9I/uvl6SzOw7kib2FnD3DyfZgezJqQsk3ejuy/pa3923mNlZ2cxqSc2SWiV9092/02X1Udnbhm6eqmNZZaDbADDssEceAIaWPe7+TMcdd3/Z3Xs70XQgfFbSWEnf7s/KZnaypBck1UqapMx/FS6U9GUzu4OZaABgYFDIA8DQsnUwGzezicoU8J919+Z+rF8o6eeS2iRd5u6b3L3F3e+X9E1JH1XmD4MOu7K33c0ZX9ZlHQBALyjkAWBoac81kPAx8qcpc9jlW55TmYJckp7NLvt+9v4sSVMlLXb3xi7P9UT29qxOy1Zkb7s7XGiSMr9/19lvAADd4Bh5AEi5JI+Rz87tvtcJttmZcz4h6Th3X93poYqOaDdP195lHUl6XNJFko5SZpaajucvlHSYpEXuvifYfQAYVtgjDwDYF0uVmf/9XWZW1OWxjgtBPddp2V2Sdkv6UJd1z1Xm0JrbBqKTAPB2RCEPAAhz93pJ31LmUJl/M7ORlvEeSV9XZprJ73daf4ekL0r6iJldLElmNk3SDZIelfSz/fsbAEB6Wd/TAwMABpKZHS3pQUmjJeUrc8Lrb939kkHtmCQzu1OZiziNklQiaZsyJ7a+v/PsOmb2MUl/rcwhM67MDDYPSvqGu6/r5nkvUOaKsQcpM13lf0u6xt27m5YSANANCnkAAAAghTi0BgAAAEghCnkAAAAghSjkAQAAgBSikAcAAABSiEIeAAAASKEhWcib2eFm9rCZPWlmz5vZdWbGVWjxJ2b2STPbbmbXdvOYmdk/ZMfO783sCTOrHoRuYhCZ2Tlm9kszW5gdB380syvMzLpZd3728cfN7BkzO3sw+ozBYWZzzOxn2W3Fo2b2spndbmYHdVmPcYK3MLOpZrbbzBZ28xjjZZgzs3lmtjr7PdT559Od1tmnmmXIFcdmNk6Zi4J8y93/1czKJT0lqVzS3wxq5zDozKxK0h2Slisz53Z3rpF0iTKXkq8xs49LesTMju5yaXm8vd0u6Xp3v1GSzOx4SU9IGinp+o6VzOxSSd+WNNvd15rZyZIeMrNT3P0Pg9Bv7H8XKLNja567t5lZqaSFylyFdq7EOMHesjsFblPmugpdH2O8oMNP3f3aXh7fp5plKO6Rv0qSSbpV+tNVA2+UdIWZTRrMjmFIKJd0rbtf1d2DZjZC0lck3eLuNZLk7rcrcxGbL++vTmJIeFbSzR13shcvekTSJzqWZb+Iv6XMhnZtdr3Hldl58PX92lsMph9K+pK7t0mSuzdKelLSoRLjBD36nKQ1kl7svJDxgv5KomYZioX8eZIWd2xQs55S5mqHZw1OlzBUuPt6d3+6l1XmSSqTtKjL8qeVGVsYJtz9XHdv6bK4UVJRp/tHSJqivcfLU5LOMLMi4W3P3Ze7+5sd983sCEl/Iem72UWME7yFmU1XZsfjF7t5mPGC/pqnfaxZhmIhP1PSxi7LNmRvZ+3nviB9ZmZvuxtDU9mADl9mlq/MYRK3d1rc23gplDR1P3QNQ4SZfcTMlinzJfrP7t5xCBbjBH/S6ZCaL7j7rm5WYbygsxPM7IHsse+/NbMrO533uc81y1As5CskNXVZ1nG/fD/3BelTkb3taQyV7ce+YGi5WtJ2Sdd1WtbXeGGbM4y4+93ufqikOcoczvmj7EOME3R2haQ33P03PTzOeEGHXZLWS7rY3d8j6fOSviDpnuzj+1yzDLmTXSXVSSrusqzjfv1+7gvSpy5729MYatiPfcEQYWbnKnM866nuvqfTQ32NF7Y5w5C7v2JmX5V0p5n9WIwTZJnZwcoUY3N6WY3xAkmSuz8v6TOd7i83s3+UdJuZzVECNctQLORfk9T1pNaO+yv3c1+QPq9lbycp81ewOt1f4+7N+79LGEzZKd9ukHSGu6/v8nDn8dLZJEktypzIhrc5Myt29657xJZmb2crM9uRxDiBdL6kZkn3dJrJdrYkZaegXCvpe9nljBd0p6OWnaEEapaheGjNryVVZ49n7XCiMtM7PTQ4XUKKLFTmhMaue0vmSnpgv/cGg8rM3qtMEX+2u6/JLpufncZUkpZIWqe9x8uJkh7hD79hY7mZHdBl2YHZ2+1inCDL3b/v7ke5+7yOH0kvSHohe/9SMV6QZWbXZ0+M7qzj+hQblEDNMhQL+ZsluaTLJcnMypQ5K/wH7t71ZADgLdy9Vpm5e680s1GSZGYXSRon6TuD2TfsX2b2AUk/lvRVSRPMrDp7kY3LJY2SJHd3Sf9H0mVmNjmbO0nSuyVdOxj9xqD5h44dSNltx9eVKcbuZ5wgF4wXdDJX0tVmlidJZjZa0t9JWizp90nULEPu0Bp332pmp0m62cwuVuakkAckfW1we4ahwszuUmaQS5kN5TxJN7n7vdll35LULukxM6tT5g/DM7gY1LBzlzIzRNzb20ru/nMzK1HmX+V1kkokfZCLtgwrX5F0maRnzKxe0ghlvmg/5u51EuMEezOzy5QZN7Oz9xdK+g93v43xgqzrlDk/62kza1Kmpn1E0j+5e3t2nX2qWSzzhyMAAACANBmKh9YAAAAA6AOFPAAAAJBCFPIAAABAClHIAwAAAClEIQ8AAACkEIU8AAAAkEJDvpA3s/mD3QekB+MF/cVYQS4YL+gvxgpysa/jZcgX8pL4QCAXjBf0F2MFuWC8oL8YK8jF276QBwAAANDFkLiya/6Ici8YU9XtY2119cqvKO/2MWu2UHsFFS2hXLvH2ju4dFsot2LnhFBOBbH3NC+/ve+VujGyaE8oV1NfFsqpl/eht/FSWBJ731vrC3PO5Je3xtpqLAjlyiti70FFflMot6VxRCjnTcF9B7GPnorKen7PW2oaVFjZ/Rhsbsj9PZekiuD7UN9cFGuvKPb+NbbGfr/oNrAguG1pboz102LNyUraenysbXeD8kcGt1kJG1UcG2e1m7vfNvZpTGx7Vpof2+bW7SoN5bwk9zc+Pzg2xxQ39PhY3Y5mVYzu/jNd0xL73Zpb8kM5tcW2uVYQe12sLtZee0mwFg1uk8rLY5+hQut5G9Gb4ryeP0N1O5tVUdX9eFm3tHabu4/r7bljVUPCCsZUacLXr8w5V7Im9uU35sTNoVxDc+xL5RdH3xbKnXnnF0K5trHNodyIqp43TL05c/LyUO6
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for r in range(10, 501, 10):\n",
    "    u1, s1, vh1 = u[::, :r], np.diag(s[:r]), vh[:r, ::]\n",
    "    w = np.linalg.lstsq(s1, u1.T@a)[0]\n",
    "    a1 = vh1.T@w\n",
    "    A1 = vec2mat(a1, (16, 51))\n",
    "    plt.matshow(A1)\n",
    "    plt.title(\"r = {}\".format(r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "4781d689",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/h9/ll8t8frd1r575llt96l1glhm0000gn/T/ipykernel_43808/696818349.py:3: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  w = np.linalg.lstsq(s1, u1.T@a)[0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'r = 360')"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 918x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 360\n",
    "u1, s1, vh1 = u[::, :r], np.diag(s[:r]), vh[:r, ::]\n",
    "w = np.linalg.lstsq(s1, u1.T@a)[0]\n",
    "a1 = vh1.T@w\n",
    "A1 = vec2mat(a1, (16, 51))\n",
    "plt.matshow(A1)\n",
    "plt.title(\"r = {}\".format(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a13c391",
   "metadata": {},
   "source": [
    "__Вывод:__\n",
    "\n",
    "- Авторы задачи предложили мне поботать\n",
    "\n",
    "\n",
    "- Найден субъективный оптимум $r=360$. Раньше ботать не получается, позже уже не надо"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37bc433a",
   "metadata": {},
   "source": [
    "### Задача 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfd89287",
   "metadata": {},
   "source": [
    "$Cx = 0 \\Leftrightarrow ||Cx||_2^2=x^TC^TCx=0$\n",
    "\n",
    "$L = ||Ax-b||_2^2 - \\lambda ||Cx||_2^2 =x^TA^TAx + b^Tb - 2b^TAx - \\lambda x^TC^TCx$\n",
    "\n",
    "$\\frac{\\partial L}{\\partial x} = 0 \\Leftrightarrow x^TA^TA - b^TA - \\lambda x^TC^TC = 0 $\n",
    "\n",
    " Считаем, что $A^TA$ обратима, домножаем на $(A^TA)^{-1}$ справа\n",
    " \n",
    "$(1)\\;\\;\\;x^T - b^TA(A^TA)^{-1} - \\lambda x^TC^TC(A^TA)^{-1}=0$ \n",
    "\n",
    "Теперь домножаем на $C^T$ справа\n",
    "\n",
    "$x^TС^T - b^TA(A^TA)^{-1}C^T - \\lambda x^TC^TC(A^TA)^{-1}C^T=0$\n",
    "\n",
    "Пользуемся условием\n",
    "\n",
    "$(2)\\;\\;\\;\\frac{\\partial L}{\\partial \\lambda} = 0 \\Leftrightarrow x^TC^TCx=0 \\Leftrightarrow Cx=0$\n",
    "\n",
    "Получаем\n",
    "\n",
    "$- b^TA(A^TA)^{-1}C^T - \\lambda x^TC^TC(A^TA)^{-1}C^T=0 \\Leftrightarrow$\n",
    "\n",
    "$\\Leftrightarrow\\lambda x^TC^TC(A^TA)^{-1}C^T = - b^TA(A^TA)^{-1}C^T$\n",
    "\n",
    "\n",
    "Считая что $С(A^TA)^{-1}C^T$ обратима, получаем \n",
    "\n",
    "$\\lambda Cx = - (C(A^TA)C^T)^{-1}C(A^TA)^{-1}A^Tb$\n",
    "\n",
    "Подставляем $\\lambda Cx$ в $(1)$, получаем\n",
    "\n",
    "$x = (A^TA)^{-1}A^Tb-(A^TA)^{-1}C^T(C(A^TA)^{-1}C^T)^{-1}C(A^TA)^{-1}A^Tb$\n",
    "\n",
    "$A^{+}=(A^TA)^{-1}A^T$, тогда\n",
    "\n",
    "$x = (I-(A^TA)^{-1}C^T(C(A^TA)^{-1}C^T)^{-1}C)A^{+}b$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62219b46",
   "metadata": {},
   "source": [
    "### Задача 6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90769187",
   "metadata": {},
   "source": [
    "$(\\overline{r_j}-\\overline{r_i}, \\overline{r_k}-\\overline{r_i})=|\\overline{r_j}-\\overline{r_i}||\\overline{r_k}-\\overline{r_i}|\\cos\\theta_{ijk}$\n",
    "\n",
    "Введём обозначение $x_{ab}=x_a-x_b$\n",
    "\n",
    "Пренебрегаем слагаемыми второго порядка малости и выше, получаем уравнение\n",
    "\n",
    "$(r_{ki},r_{ji})+(r_{ji},dr_{ki})+(r_{ki},dr_{ji})=|r_{ji}||r_{ki}|\\left( 1 + \\frac{(dr_{ji}, r_{ji})}{|r_{ji}|^2} +\\frac{(dr_{ki}, r_{ki})}{|r_{ki}|^2}\\right)\\cos\\theta_{ijk}$\n",
    "\n",
    "\n",
    "Введём обозначения\n",
    "\n",
    "$A_{ikj} = r_{ik} - \\frac{r_{ij}}{|r_{ij}|}|r_{ik}|\\cos\\theta_{ijk}$\n",
    "\n",
    "$A_{ijk} = r_{ij} - \\frac{r_{ik}}{|r_{ik}|}|r_{ij}|\\cos\\theta_{ijk}$\n",
    "\n",
    "$B_{ijk} = B_{ikj}=\\frac{1}{2}\\left(|r_{ij}||r_{ik}|\\cos\\theta_{ijk}-(r_{ik}, r_{ij})\\right)$\n",
    "\n",
    "В новых обозначениях получаем уравнение\n",
    "\n",
    "$(dr_i, A_{ijk}+A_{ikj})-(dr_j, A_{ikj})-(dr_k, A_{ijk})=B_{ijk}+B_{ikj}$\n",
    "\n",
    "Если угол $\\theta_{ijk}$ не измерен, считаем, что $A_{ijk}=A_{ikj}=B_{ijk}=B_{ikj}=0$. Видно, что при таком выборе обозначений уравнение превращается в тождество при подстановке неизмеренных углов. Также видно, что при совпадении двух индексов константы равны $0$, что эквивалентно незаданным углам\n",
    "\n",
    "Пользуемся методом множителей Лагранжа\n",
    "\n",
    "$L = \\sum_{i=1}^n||dr_i||^2_2 - \\sum_{i=1}^n \\lambda_i \\sum_{j,k} \\left[ (dr_i, A_{ijk}+A_{ikj})-(dr_j, A_{ikj})-(dr_k, A_{ijk})-B_{ijk}-B_{ikj}\\right]$\n",
    "\n",
    "\n",
    "$(1)\\;\\;\\; \\frac{\\partial L}{\\partial dr_i} = 0 \\Leftrightarrow dr_i = \\frac{\\lambda_i}{2}\\sum_{j, k}\\left(A_{ijk}+A_{ikj}\\right)$(коэффициенты с повторяющимися индексами занулены)\n",
    "\n",
    "$(2)\\;\\;\\; \\frac{\\partial L}{\\partial \\lambda_i} = 0 \\Leftrightarrow \\sum_{j,k} \\left[ (dr_i, A_{ijk}+A_{ikj})-(dr_j, A_{ikj})-(dr_k, A_{ijk})-B_{ijk}-B_{ikj}\\right]=0$\n",
    "\n",
    "После подстановки $(1)$ в $(2)$ вылезет система из $n$ линейных уравнений на $\\lambda_i$, из которых можно будет найти $\\lambda_i$, получить $dr_i$. Можно ожидать, что матрица системы будет разреженной, т.е. для неё есть хорошее малоранговое приближение\n",
    "\n",
    "$(i-\\text{ое уравнение})\\;\\;\\;\\lambda_{i}||\\sum_{j, k}(A_{ijk}+A_{ikj})||^2 - \\sum_{j,k}\\lambda_j\\left( \\sum_{\\alpha, \\beta}(A_{j\\alpha\\beta}+A_{j\\beta\\alpha}), A_{ikj}\\right)-\\sum_{j, k}\\lambda_k\\left( \\sum_{\\alpha, \\beta}(A_{k\\alpha\\beta}+A_{k\\beta\\alpha}), A_{ijk}\\right)=\\sum_{j,k}(B_{ijk}+B_{ikj})$\n",
    "\n",
    "Видно, что третье слагаемое при замене индексов $k\\leftrightarrow j$ переходит во второе слагаемое. Также видно, что второе и третье слагаемые не содержат $\\lambda_i$, так как зануляются коэффициенты с одинаковыми индексами. $i$-ое уравнение имеет вид\n",
    "\n",
    "$\\lambda_{i}||\\sum_{j, k}(A_{ijk}+A_{ikj})||^2 - 2\\sum_{j}\\lambda_j\\sum_{\\alpha, \\beta, k}\\left((A_{j\\alpha\\beta}+A_{j\\beta\\alpha}), A_{ikj}\\right)=\\sum_{j,k}(B_{ijk}+B_{ikj})$\n",
    "\n",
    "В удобоваримом виде выглядит вот так\n",
    "\n",
    "$\\lambda_1 \\left(\\sum_{\\alpha, \\beta}(A_{1\\alpha\\beta}+A_{1\\beta\\alpha}), \\sum_{k}A_{ik1})\\right) + ...-\\frac{\\lambda_i}{2}||\\sum_{j, k}(A_{ijk}+A_{ikj})||^2+...= -\\frac{1}{2}\\sum_{j,k}(B_{ijk}+B_{ikj})=-\\sum_{j,k}B_{ijk}$\n",
    "\n",
    "Осталось все это запрогать)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "id": "fef71fb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7feafc704040>"
      ]
     },
     "execution_count": 440,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABITklEQVR4nO3dd3gU1dvG8e9JJYWEFnogQOglIYBBpARElCLSSwDFhtIFC4gK+KKCBVGqDX9Y6EgTEBAEFVBq6DX0Egg1JCF9z/vHhBhCyiaQTMrzua5ccWfm7Nw7Lk92z8yco7TWCCGEyP9szA4ghBAiZ0jBF0KIAkIKvhBCFBBS8IUQooCQgi+EEAWEndkB0lKiRAnt5eVldgwhhMhTdu/efU1r7ZHaulxb8L28vNi1a5fZMYQQIk9RSp1Na5106QghRAEhBV8IIQoIKfhCCFFASMEXQogCIlMFXyn1vFLqulJqvJXbF1FK/U8ptVsptVMptUApVSpLSYUQQjwQqwq+UqqoUmodUB8olonn/wVwARpqrRsB4cBvSinbTCcVQgjxQKz9hO8CjNdaD7P2iZVSjwOtgA/0f0NyTsD4o9E1UymFEEI8MKsKvtb6gtb6n0w+dzsgEjiQ7HnOARcT1wmRp0XHJbBo53kiYuLNjiKEVbLzpK03cFnfP+D+RaBqag2UUgOUUruUUruuXr2ajdGEeHDjVx7irV/2M2rJfmReCZEXZGfBdwViUlkeg9FFdB+t9Tda64Za64YeHqneGSxErrAs6AILdp6ndlk3Vh8I4ad/07y5UYhcIzsLfgTgmMpyR4yuHiHypODQcMYsPcgjlYqxfPBjtKpRkg9WHeHAhTCzowmRruws+MFAaaWUSrG8LHAiG/crRLa5ExvPoLl7cHawZVrv+tjb2jC5uw8lXB0YNG83YVFxZkcUIk3ZWfDXYHTd1Lm7QCnlCZQHfsvG/QqRbd5bfogToRF82as+pdwKAVDUxYHpffwIuRXNW0v2SX++yLUeSsFXShVSSh1QSs2+u0xrvRHYBLyT7FP+u0AQsORh7FeInLRo13l+2XOBYa2q0rRqiXvW+VUoyui2NVh36Arfbz1jTkAhMmB1wVdKLVZKbU582F8ptVkp1fHuasAZcErRrCsQDexSSu0EigBttdYJD5RaiBx29PJtxq44yGPexRn2eKoXmfFi00q0qVWKiWuOsOfczRxOKETGVG79+tmwYUMt4+GL3CAiJp6O07cQHh3PmmHN8Cic2rUIhrA7cYz4cg5d49fQdNAs3IuXzsGkQoBSarfWumFq62TwNCHSobXmnWUHOHMtkqm96qdb7AHcYy/ztc3HtE/4gwvfBmKJl5uyRO4hBV+IdMzfcZ4Vey8x8olqPFqlePobx4TD/F7YW2I4UOkFakfvZu9Pb+ZMUCGsIAVfiDQcuhTG+F8P0byaB4MCvNPf2JIAS16E0CPQ/X/UefZztri1x+/s9wT/uSBnAguRASn4QqQiPDqOwXP3UMzZgSk9fLCxSXk7SQrr34UT66Dtx+DdGqUU9QZ8w2GbqpTZ9Bo3zx3KmeBCpEMKvhApaK0Z/csBzt+MYlpgfYq7pt9vz87Z8O9M8H8VHnk5abGbqyu2PX8iWttz58deWKJuZ3NyIdInBV+IFH769yyrD4Tw5pPVaeSVwfQPwRthzZtQtQ08+dF9q6tXr0mQ/+eUjjvPqdn9IZdeFScKBin4QiSz/8ItJqw6TKsaJRnQrHL6G4cehcX9waMGdPsebFKf1+fxtt34teQreF/byNlfJz380EJYSQq+EInCouIYPG8PHq6OTO6eQb995DWY1wPsCkHgQnAsnOamSilav/gBm+0eo/yeT7h1aEM2pBciY1LwhcDot39ryT5CbkUzvY8fRV0c0t44LhoWBELEFei9AIp4Zvj8roXsKfPcbE7pstj88gIJN889xPRCWEcKvhDA91vPsO7QFUa3rYFfhaJpb6g1rBwC57dD56+gfAOr91HdswzBAbMgIZars3safziEyEFS8EWBt+fcTSauOUKbWqV4sWml9Df+8xM4sBhavQu1O2d6X08FNGNxhXcpHXGYywuGZjGxEFkjBV8UaLfuxDJ0XhBlihTi024+3D99QzIHlsDmj8CnNzR7I0v7U0rRu9+rzHXoQemTi7i95dssJhci86TgiwLLYtG8vmgfV8NjmBHoh7uzfdobn98BywdBhSbw9JeQ3h+GDDg72PHI85/yt/bBacPbxJ/bmeXnEiIzpOCLAuubv0+x8Wgo77SvSb3yRdLe8OZZmN8b3MpCz5/BLoMbsaxQtUwRwtrO5LKlCHd+DoSIqw/8nEJkRAq+KJB2nrnBp+uO0b5uGZ59tGLaG0aHwbyeYImDwEXgksEAapnQoXEdllWbhEPMTW7+2BcSZGRNkb2k4IsC53pEDEPnBeFZ1IlJXeum3W+fEA+Ln4frJ6DHj+BR7aFnGdCzM9NdBlM09F8i1rz70J9fiOSk4IsCxWLRjFi0jxt3YpnRx4/ChdLpt187Gk5uhPaToXJAtuQpZG9Ll+ffZL5ug+vuWcQfWJot+xECpOCLAmbm5mD+On6VcU/XonZZ97Q33P417PwWHh0CDfpna6bKHq64dvqU3ZaqWJYNMoZYFiIbSMEXBcY/J6/z+e/Heca3LIGPVEh7w+PrjU/31dvBE/+XI9meru/FhrqfEpbgQORPvY1zB0I8ZFLwRYFwNTyGYQuC8Crhwked0+m3v3IIlrwApWpDl2/THBAtOwzv1JxP3d7GIfwcUYteBoslx/YtCgYp+CLfS7Bohi8IIjw6jpl9/HBxtEt9w/ArxhU5jq7Qe6HxOwcVsrdlcP9nmaz74XRqHfF/Tc7R/Yv8Twq+yPembjzBtpPX+b9n6lCjtFvqG8VFGQOi3bkOveeDe7mcDZmoYnEXfLqOYnlCE2w3fwjBMrKmeHik4It8bcuJa0z94wRd/crTo2Eao1paLLB8IFzcDV2+gbL1czZkCm3rleWQ3wSOWjyJXfQi3Dxjah6Rf0jBF/nWldvRDF8QhLeHKxM61U57w80fwaFl0Ho81Hw6x/Kl582n/fii+FiiY+OIndvH+AYixAOSgi/ypfgEC0PnB3EnNoGZffxwdkij337fAvjrU6jfFx4bnrMh0+FgZ8O7/dozmqHYXTtEwsrXZHpE8cCk4It8acqG4+w4fYOPutShaqk0ZqM6+w+sHApezaD9lAcaEC07eBZzpnOPF/gyrgu2BxbAzu/MjiTyOCn4It/ZdCyUGZtO0quRJ53rl099oxunjJO0RSoYwybYpTPDlYmeqFWKO4+OZENCfSy/vQ3ntpsdSeRhVhV8pVQtpdQGpdRWpVSQUuojpVQa35HvaddQKbVOKbVdKfWnUmqLUqr1g8cWInWXbkUxcuFeapQuzPiOafTbR90yLr9EGwOiORfLyYiZ9lbbWswp9TYXLMWIX9DPuHxUiCzIsOArpTyATcByrfVjQFOgPZDuRcJKKTfgd+C41tpfa90C+AJYpZSq9aDBhUgpLrHfPjbewsw+fhSyT+WmqYQ4WPQs3DhtDHVcvErOB80ke1sbPunbnDds3iT+zi0si54zXocQmWTNJ/xhgAJmAWitIzGK/WClVNl02lUFigBrky37DXAE2mQlrBDp+WzdMXafvcmkrvWo7JHKTVNaw5o34PSfxiQmXk1zPmQWlS3ixMBez/BW7MvYnP8H1r9ndiSRB1lT8NsBu7TWCcmWbQNsSb9wHwQOAH2UUnc7SF9I/B2S2aBCpGfD4St8/dcp+jauwNM+aXwO+WcG7J4DTUdA/T45mu9haFm9JOWa92N2fFvYPgv2LzY7kshjrCn43sClFMsuJv6umlYjrXUM0AJwBa4opU4BU4A5wJJMJxUiDRdu3uH1xfuoXdaNd9un0Vt4dA2sfxdqdoRWY3M24EP0+hPV2FBuMDt1TSwrh8Dlg2ZHEnmINQXfFYhJsezuY5e0GimlXICNQCxQVmtdGaP/fweQ6qhQSqkBSqldSqldV6/KlG8iY7HxFgbPC8Ji0Wn324fsh19egrK+0PlrsMm7F6fZ2dowJbA
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with np.load(\"data_1.npz\") as data:\n",
    "    r, p, theta, dr = data['r'], data['p'], data['theta'], data['dr']\n",
    "    \n",
    "x, y = r.T\n",
    "dx, dy = dr.T\n",
    "\n",
    "plt.plot(x, y, label=\"data\")\n",
    "plt.plot(x+dx, y+dy, label=\"after correction\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "id": "e51c2fb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "def AB(r, theta, p):\n",
    "    n = r.shape[0]\n",
    "    A = [[[[0.0, 0.0] for _ in range(n)] for _ in range(n)] for _ in range(n)]\n",
    "    B = [[[0.0 for _ in range(n)] for _ in range(n)] for _ in range(n)]\n",
    "    p0 = (p-1).tolist()\n",
    "    #Не знаю, как это адекватно через numpy организовать, буду быдлокодить\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            for k in range(n):\n",
    "                idx = -1\n",
    "                try:\n",
    "                    idx = p0.index([i,j,k])\n",
    "                except ValueError:\n",
    "                    try:\n",
    "                        idx = p0.index([i,k,j])\n",
    "                    except ValueError:\n",
    "                        pass\n",
    "                \n",
    "                if idx > -1:\n",
    "                    A[i][k][j] = r[i]-r[k]-np.linalg.norm(r[i]-r[k],ord=2)/np.linalg.norm(r[i]-r[j],ord=2)*np.cos(theta[idx])\n",
    "                    A[i][j][k] = r[i]-r[j]-np.linalg.norm(r[i]-r[j], ord=2)/np.linalg.norm(r[i]-r[k], ord=2)*np.cos(theta[idx])\n",
    "                    B[i][j][k] = 0.5*np.linalg.norm(r[i]-r[j], ord=2)*np.linalg.norm(r[i]-r[k], ord=2)*np.cos(theta[idx])-0.5*np.dot(r[i]-r[k], r[i]-r[j])       \n",
    "    \n",
    "    return np.array(A), np.array(B)\n",
    "\n",
    "\n",
    "def sum1(A, i, j):\n",
    "    n = A.shape[0]\n",
    "    temp = np.array([0.0, 0.0])\n",
    "    for k in range(n):\n",
    "        temp += A[i,k,j]\n",
    "    return temp\n",
    "\n",
    "\n",
    "def sum2A(A, i):\n",
    "    n = A.shape[0]\n",
    "    temp = np.array([0.0, 0.0])\n",
    "    for j in range(n):\n",
    "        for k in range(n):\n",
    "            temp += A[i, j, k] + A[i, k, j]\n",
    "    return temp\n",
    "\n",
    "def sum2B(B, i):\n",
    "    n = B.shape[0]\n",
    "    temp = np.array(0.0)\n",
    "    for j in range(n):\n",
    "        for k in range(n):\n",
    "            temp -= 0.5*(B[i, j, k] + B[i, k, j])\n",
    "    return temp\n",
    "    \n",
    "    \n",
    "def system_b(r, theta, p):\n",
    "    A, B = AB(r, theta, p)\n",
    "    n = A.shape[0]\n",
    "    S = np.zeros((n,n))\n",
    "    b = np.zeros((n,1))\n",
    "    for i in range(n):\n",
    "        b[i] = -sum2B(B, i)\n",
    "        for j in range(n):\n",
    "            if i == j:\n",
    "                S[i, j] = -0.5*np.linalg.norm(sum2A(A, i),ord=2)\n",
    "            else:\n",
    "                S[i, j] = np.dot(sum2A(A, j), sum1(A,i,j))\n",
    "    return A, B, S, b\n",
    "\n",
    "\n",
    "def sol_lasso(r, theta, p):\n",
    "    n = r.shape[0]\n",
    "    A, B, S, b = system_b(r, theta, p)\n",
    "    model = Lasso(alpha=1.0, fit_intercept=False)\n",
    "    model.fit(S, b)\n",
    "    l = model.coef_\n",
    "    dr = [[0.0, 0.0] for _ in range(n)]\n",
    "    for i in range(n): \n",
    "        dr[i] = l[i]/2 * sum2(A, i)\n",
    "    return np.array(dr)\n",
    "\n",
    "def sol_lstsq(r, theta, p):\n",
    "    n = r.shape[0]\n",
    "    A, B, S, b = system_b(r, theta, p)\n",
    "    l = np.linalg.lstsq(S, b, rcond=None)[0]\n",
    "    \n",
    "    dr = [[0.0, 0.0] for _ in range(n)]\n",
    "    for i in range(n): \n",
    "        dr[i] = l[i]/2 * sum2(A, i)\n",
    "    return np.array(dr)\n",
    "\n",
    "def angles(r, p):\n",
    "    theta = np.zeros(p.shape[0])\n",
    "    count = 0\n",
    "    p0 = (p-1).tolist()\n",
    "    for i, j, k in p0:\n",
    "        temp = np.dot(r[i]-r[j], r[i]-r[k])/np.linalg.norm(r[i]-r[j], ord=2)/np.linalg.norm(r[i]-r[k],ord=2)\n",
    "        theta[count] = np.arccos(temp)\n",
    "        count += 1\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "id": "4c63f481",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7feb00d6d1b0>"
      ]
     },
     "execution_count": 479,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with np.load(\"data_2.npz\") as data:\n",
    "    r, p, theta, dr = data['r'], data['p'], data['theta'], data['dr']\n",
    "    \n",
    "x, y = r.T\n",
    "dx, dy = dr.T\n",
    "dx_lasso, dy_lasso = sol_lasso(r, theta, p).T\n",
    "dx_lstsq, dy_lstsq = sol_lstsq(r, theta, p).T\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(x, y, color=\"black\", label=\"data\", s=400, alpha=0.2)\n",
    "plt.scatter(x+dx, y+dy, color=\"blue\", label=\"after correction\", s=100)\n",
    "plt.scatter(x+dx_lasso, y+dy_lasso, color=\"red\", label=\"after sol_lasso\", s=100)\n",
    "plt.scatter(x+dx_lstsq, y+dy_lstsq, color=\"green\", label=\"after sol_lstsq\", s=100)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "id": "2e9048f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sol_lasso :  [1.60244721 1.78332771 0.14900583 1.21385168]\n",
      "sol_lstsq :  [1.34827534 2.30829296 0.29572171 1.62005206]\n",
      "data      :  [1.5708   1.5708   0.523599 1.0472  ]\n"
     ]
    }
   ],
   "source": [
    "r_lasso = r+sol_lasso(r, theta, p)\n",
    "r_lstsq = r+sol_lstsq(r, theta, p)\n",
    "\n",
    "print(\"sol_lasso : \", angles(r_lasso, p))\n",
    "print(\"sol_lstsq : \", angles(r_lstsq, p))\n",
    "print(\"data      : \", theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e4339f9",
   "metadata": {},
   "source": [
    "__Вывод:__\n",
    "\n",
    "- видимо, я где-то ошибся, пока не могу понять где\n",
    "\n",
    "\n",
    "- sklearn.linear_model.Lasso используется, чтобы найти разреженное решение на $\\lambda$, что должно хорошо работать, когда матрица $S$ разрежена"
   ]
  }
 ],
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  "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",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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