commit 468745733d30d8e920c39312aa93155478d9ff33 Author: ParkSuMin Date: Sun Aug 31 18:41:52 2025 +0200 New files diff --git a/educmm-lab1.ipynb b/educmm-lab1.ipynb new file mode 100644 index 0000000..c762094 --- /dev/null +++ b/educmm-lab1.ipynb @@ -0,0 +1 @@ +{"metadata":{"kernelspec":{"name":"python3","display_name":"Python 3","language":"python"},"language_info":{"name":"python","version":"3.10.12","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[],"dockerImageVersionId":30918,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"# Лабораторная работа №1 (интерполяция полиномами)","metadata":{}},{"cell_type":"markdown","source":"## Базовые функции","metadata":{}},{"cell_type":"code","source":"import numpy as np\n\ndef f(t):\n return np.exp(-t**2)\n\ndef nodes_mulitiply(x, t_nodes):\n return np.prod(x - t_nodes)\n\ndef factorial(n):\n if n == 0:\n return 1\n else:\n return n * factorial(n-1)\n\ndef chebyshev(a, b, k):\n chebyshev = np.zeros(k, dtype=float)\n for m in range(1, k + 1):\n chebyshev[m-1] = (a + b)/2 + (b - a)/2 * np.cos((2*m - 1)/(2*k) * np.pi)\n return chebyshev","metadata":{"execution":{"iopub.status.busy":"2025-03-13T19:46:56.318274Z","iopub.status.idle":"2025-03-13T19:46:56.326780Z","shell.execute_reply.started":"2025-03-13T19:46:56.318716Z","shell.execute_reply":"2025-03-13T19:46:56.325265Z"},"trusted":true},"outputs":[],"execution_count":31},{"cell_type":"markdown","source":"## Производная $n$-ой степени в точке $t$","metadata":{}},{"cell_type":"code","source":"import numpy as np\n\ndef get_derivative(n, t):\n a = np.zeros((n+1, n+1), dtype=float)\n a[0, 0] = 1\n \n for j in range(1, n+1):\n for i in range(n+1):\n if i+1 <= n:\n term1 = (i+1) * a[j-1, i+1]\n else:\n term1 = 0\n \n if i-1 >= 0:\n term2 = -2 * a[j-1, i-1]\n else:\n term2 = 0\n \n a[j, i] = term1 + term2\n \n P_n = np.polyval(a[n, ::-1], t)\n nth_derivative = P_n * np.exp(-t**2)\n return nth_derivative","metadata":{"execution":{"iopub.status.busy":"2025-03-13T19:46:56.328701Z","iopub.execute_input":"2025-03-13T19:46:56.329204Z","iopub.status.idle":"2025-03-13T19:46:56.354655Z","shell.execute_reply.started":"2025-03-13T19:46:56.329147Z","shell.execute_reply":"2025-03-13T19:46:56.353019Z"},"trusted":true},"outputs":[],"execution_count":32},{"cell_type":"markdown","source":"## Базисный полином Лагранжа","metadata":{}},{"cell_type":"code","source":"def l_i(i, x, t_nodes):\n return np.prod((x - t_nodes[t_nodes != t_nodes[i]]) / (t_nodes[i] - t_nodes[t_nodes != t_nodes[i]]))","metadata":{"execution":{"iopub.status.busy":"2025-03-13T19:46:56.357400Z","iopub.execute_input":"2025-03-13T19:46:56.357813Z","iopub.status.idle":"2025-03-13T19:46:56.379527Z","shell.execute_reply.started":"2025-03-13T19:46:56.357777Z","shell.execute_reply":"2025-03-13T19:46:56.378077Z"},"trusted":true},"outputs":[],"execution_count":33},{"cell_type":"markdown","source":"## Интерполяционный полином Лагранжа","metadata":{}},{"cell_type":"code","source":"def L(x, t_nodes, f_nodes):\n n = len(t_nodes)\n\n basis = np.array([l_i(i, x, t_nodes) for i in range(n)])\n return np.sum(np.multiply(basis, f_nodes))","metadata":{"execution":{"iopub.status.busy":"2025-03-13T19:46:56.381051Z","iopub.execute_input":"2025-03-13T19:46:56.381593Z","iopub.status.idle":"2025-03-13T19:46:56.401027Z","shell.execute_reply.started":"2025-03-13T19:46:56.381537Z","shell.execute_reply":"2025-03-13T19:46:56.399544Z"},"trusted":true},"outputs":[],"execution_count":34},{"cell_type":"markdown","source":"## Курс валюты","metadata":{}},{"cell_type":"code","source":"import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.dates as mdates\n\nfrom datetime import datetime\n\nurl = \"https://www.cbr.ru/scripts/XML_dynamic.asp?date_req1=11/02/2025&date_req2=15/02/2025&VAL_NM_RQ=R01235\"\noutput = pd.read_xml(url)\ndates_str = output['Date'].values\nrates = output['Value'].str.replace(',', '.').astype(float)\n\ndates = [datetime.strptime(date, '%d.%m.%Y') for date in dates_str]\nx_nodes = np.array(dates)\ny_nodes = np.array(rates)\n\nx_interp = np.linspace(mdates.date2num(x_nodes[0]), mdates.date2num(x_nodes[-1]), 500)\ny_interp = np.array([L(x, mdates.date2num(x_nodes), y_nodes) for x in x_interp])\n\nx_interp_dates = mdates.num2date(x_interp)\n\nplt.figure(figsize=(8, 6))\nplt.plot(x_interp_dates, y_interp, label=\"$L(x)$\", color=\"blue\")\nplt.scatter(x_nodes, y_nodes, color=\"red\", label=\"Исходные данные\")\n\nplt.gca().xaxis.set_major_formatter(mdates.DateFormatter('%d.%m.%Y'))\nplt.gca().xaxis.set_major_locator(mdates.DayLocator())\n\nplt.xlabel(\"Дата\")\nplt.ylabel(\"Курс доллара США к рублю\")\nplt.legend()\nplt.grid(True)\nplt.savefig(\"lagrange_interpolation_cb.png\", dpi=300)\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-03-13T19:46:56.402316Z","iopub.execute_input":"2025-03-13T19:46:56.402850Z","iopub.status.idle":"2025-03-13T19:46:58.082100Z","shell.execute_reply.started":"2025-03-13T19:46:56.402805Z","shell.execute_reply":"2025-03-13T19:46:58.080526Z"}},"outputs":[{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}}],"execution_count":35},{"cell_type":"markdown","source":"## Равномерное распределение узлов","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt\n\ndlt_uniform = np.array([])\nuniform_borders = np.array([])\nfor num_nodes in range(4, 21):\n #print(f\"Количество узлов интерполяции: {num_nodes}\")\n\n t_values = np.linspace(-5, 5, 200)\n f_values = f(t_values)\n\n t_nodes = np.linspace(-5, 5, num_nodes)\n f_nodes = f(t_nodes)\n \n interpolated_values = [L(t, t_nodes, f_nodes) for t in t_values] # Значения интерполяционного многочлена\n\n if num_nodes in [5, 10, 15, 20]:\n plt.figure(figsize=(8, 6))\n plt.plot(t_values, f_values, label=\"$f(t)$\", color=\"blue\")\n plt.plot(t_values, interpolated_values, label=f\"$L(t)$, равномерные узлы при n = {num_nodes}\", color=\"red\")\n plt.scatter(t_nodes, f_nodes, color=\"green\") # Отмечаем узлы\n plt.xlabel(\"$t$\")\n plt.ylabel(\"$f(t)$\")\n plt.legend(loc='upper left')\n plt.grid(True)\n plt.savefig(f\"uniform-{num_nodes}.png\", dpi=300)\n plt.show()\n\n delta = np.abs(f_values - interpolated_values)\n supremum = np.max(delta)\n dlt_uniform = np.append(dlt_uniform, supremum)\n #print(f\"Расстояние между функциями - {supremum}\")\n\n max_derivative = float('-inf')\n max_multiply = float('-inf')\n \n for t in t_values:\n derivative = np.abs(get_derivative(num_nodes, t))\n tmp = np.abs(nodes_mulitiply(t, t_nodes))\n \n if derivative > max_derivative:\n max_derivative = derivative\n if tmp > max_multiply:\n max_multiply = tmp\n \n upper_bound = max_derivative/factorial(num_nodes) * max_multiply\n uniform_borders = np.append(uniform_borders, upper_bound)\n #print(f\"Итоговая верхняя граница погрешности - {upper_bound}\\n\")\n\n# График зависимости расстояния от числа узлов\nplt.scatter(range(4, 21), dlt_uniform, label='Численная погрешность интерполяции')\nplt.xlabel(\"n\")\nplt.ylabel(\"$|| f - L_{n-1} ||_\\infty$\")\nplt.grid(True)\nplt.legend()\nplt.savefig(\"uniform.png\", dpi=300)\nplt.show()\n \n\nplt.semilogy(range(4, 21), uniform_borders, '-o', label='Аналитическая погрешность интерполяции')\nplt.scatter(range(4, 21), uniform_borders)\nplt.semilogy(range(4, 21), dlt_uniform, '-o', label='Численная погрешность интерполяции')\nplt.scatter(range(4, 21), dlt_uniform)\nplt.grid(True)\nplt.legend(loc='upper left')\nplt.xlabel(\"n\")\nplt.ylabel(\"$|| f - L_{n-1} ||_\\infty$\")\nplt.savefig(\"uniform_borders_log.png\", dpi=300)\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-03-13T19:46:58.083204Z","iopub.execute_input":"2025-03-13T19:46:58.083569Z","iopub.status.idle":"2025-03-13T19:47:03.035001Z","shell.execute_reply.started":"2025-03-13T19:46:58.083526Z","shell.execute_reply":"2025-03-13T19:47:03.034123Z"}},"outputs":[{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"
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qMyzzWYvb133nkn48ePr9QXnCMrD40bN2bPnj1HvX/dunVp165dhT9RUdX7Xn/WWWdx0UUX0a1bN4YNG8acOXM4dOgQ06ZNq9Z2RSRCHS1B9U6SAsjMDF48fhKZPagJCYFtrLVrzRJ/27ZQ8iAaHw8OhznEoLCwUt9mUlJSyvRQetWrV4+DBw+W+z/lJajeUnj9I1/E1XTuuefSsmVLJk+eTJMmTfB4PHTp0oV87ylfD7viiit48MEHyc3N5d133+Wiiy7ijz/+IOnwm8j7d6+XX365TDm6Mm688UZOP/10GjZsyNChQ8uM78s83PazZ8+madOmpf4WGxvr074qE7P3Pnl5ebzzzjuMGjWKjRs3+iWmnj170r17d6ZOncrQoUNZs2YNs2fPLnWff/3rX9x666189913TJgwgQsuuIBOnToV/T01NfWYvYKVeQzBMHXqVLKysrj55puZOHHiMe8f7V054zCHw1Fm6ElJTzzxRLlfMkr6448/aNGiReUCroTatWtz3HHH8ffff/ttmyISQY6WoMbGmh1jhYXm0EMfqpZ2EJkJqsMBx+gxqhZvQpGUVHY/UVHFpzs9RjK0YcMGDh06dNQe1J49e5Y7K3/VqlXlJrWrV6+mWbNmPk/I+Pnnn0v9vnTpUtq3b4/L5WL//v2sW7eOyZMnc/LJJwMcdUZyrVq1aNeuHQDjx4/nueeeY9myZQwePLjM38HszfJq27YtMTExLF68uGh4QkFBAcuXLy8zgee4446jffv2PPDAA2WW+AE4/vjjiY2NZevWreWWzivzuMt7TEfGXN59Hn30UZ5//vlSvb6+xFSeG264gRdffJEdO3YwePBgmjdvXioJa9CgAQ0aNOD444/n7bffZvbs2aUS1OXLl9OzZ88K91GZx1AdlXmus7OzefDBB3n11VfLJJ7+EowS/5EyMzPZsGEDV111lV+3KyIRwjsG9chju8NhlvkPHgzJiVKRmaAG2tHOJAXmWqjeBPUYVqxYAYDL5WK19zRmmGXs4447jmHDhnH//fdz8OBB6tSpU/R3j8fDunXrSE1NpUaNGkWl0EWLFjF06FCfH87WrVsZN24cN910EytWrOCVV14pWvS/Tp06JCcn89Zbb9G4cWO2bt3KfffdV+52srOz2bVrF3l5eUWTYkomdxWpUaMG//znP7n77rupW7cuLVq04JlnniE7O7vcZbaefvppfvzxR0477bQya78mJiZy1113cccdd+DxeBg4cCBpaWksXryYpKSkoslbFT1uX7jdbnJzc8nLy+Ptt98mOjqaDh068OWXX/ocU3kuv/xy7rrrLiZPnszUqVOLbk9LS2PGjBmceOKJxMTE8OWXX7Jq1aqiZHTfvn288MILLF68+JiPqzKPoToq81x/8MEHnHDCCYwYMcIv+yxP3bp1y/2S4YvMzMxSvaGbNm0iJSWl6HV71113FVUdUlNTGT9+PC6Xi8suu6y64YtIpDGMo0+SguIENQQnSilBDYSjLdQPxeNQK7FYvzdBLbmMFMDAgQNZtGgRXbt2pVevXkybNo2bbrqp6O+PP/449957L0888QR33XUXzz77LLm5ucycObPU0k5TpkzhuuuuK7WcT3muvvpqcnJy6Nu3Ly6Xi9tuu63oxAFOp5OPPvqIW2+9lS5dutChQwdefvnlcpcemjx5MpMnTyYmJob27dvz/vvvlznBQEWeeuopPB4PV111FRkZGfTu3Zuvv/66VHLu1bdvX/r27XvUbT322GPUr1+fJ598ko0bN1K7dm169erFAw88UKnH7YtXX32VV199tdTjbt68eZViKk+tWrW48MILmT17dqnkzTAMpk6dyp133kleXh5t2rRh0qRJnHHGGQC8//77fP3113z22WcVPle+PIaqqsxznZ2dHRJnQ/vll19KjfMdN24cANdccw1Tpkxh+/btXHbZZezfv5/69eszcOBAli5d6vehNyISAQ4dKu7wKu8zJIQX63cYx8pOQkB6ejq1atUiLS2taDyjV25uLps2baJ169aVWpam2gwDfv3VvN6jR3FC6rVxIxw4AM2alT3rQxXMnj2bu+++m9WrVxfN1i7PpEmT+Oyzz5g3b17RbePHj+eHH34otT6ol8fjIT09nREjRtCjRw9efPHFascaSgYNGhRSj/uMM86gc+fOvPzyy0Bx+yUlJVX4urCDUHuug6VkG+bn5wf3c0z8oqCggDlz5nD22WcHbFiKBJbt2/Cvv6BDB7OntLxe0hNPhJ9+ghkzoIK1mYOlonztSOpB9beSs47LSwyqsFh/RYYPH8769evZsWNHhT1a0dHRvPLKK6Vu++qrr3j11Vf9EodY4+DBgyxYsIAFCxbw+uuvWx2OiIgE09EW6fcK4cX6laD6mzdBdTiCkqACRz3LT0k33HBDmduWLVvmtxjEGj179uTgwYM8/fTTdOjQwepwREQkmCoafwpKUKWEisafgjlJCvyaoAbSd999Z/sScSCUN+zBjjZv3mx1CNUWKs+1iIjtHG2JKa8QPptU5GUegebtQT1agurDJCkRERGRozpWghrCk6SUoPqbtwf1aL2OASjxi4iISASqbA+qElSpdA+qElQRERGpjqMt0u+lBFWKVLRIPxQnqG53cW+riIiIiK/Ugxr6grbca2V7UEG9qCJSKWGwXLWIBIImSYUu78K62dnZwdnhsWbxOxwq84uIT7yfX7ZcKFxErBPGk6TCfpkpl8tF7dq12bNnDwAJCQk4HI7A7TAvz7w0DMjNLf8+3vJ/dvbRhwJYzOPxkJ+fT25ubkQuMxXq1H6hz+PxkJeXx/79+9m3bx+1a9fGdbQvviISmcJ4DGrYJ6gAjQ6fUtSbpAbUgQPmC6Gg4OgJ6v79xYlsjRqBj6kKDMMgJyeH+Pj4wCb0EhBqv9BXsg3r1KlT9DkmIgKYnVze6nAYjkG1XYL61FNPcf/993Pbbbf57dzcDoeDxo0b06BBAwoCvf7oG2/ArFlw991w/fXl3+eFF2DePHjoIbjyysDGU0UFBQUsXLiQU045RWXFEKT2C33eNjzjjDOIi4uzOhwRsRtveT8mpjgRPZISVP9Yvnw5b775Jt26dQvI9l0uV+BLZFu3wpYt5hjUox1UXC7zPtu2Hf0+FnO5XBQWFhIXF6cEJwSp/UKftw1V1heRcpUcf3q0SlnJSVKGcfT72ZBtBqdlZmZyxRVXMHnyZOrUqWN1OFXn/ZbiHZhcHm9XvPfFJSIiIuKLY02QguJcxOOBnJzAx+RHtklQx4wZw/Dhwxk8eLDVoVSPN0E9Wnc7FA9m9g5uFhEREfHFsSZIQel5LiFW5rdFif+jjz5ixYoVLF++vFL3z8vLI887yQhIP7y+V0FBQeDHmB5DVFoaDqAwPh7jKLE46tQhCvDs2YPb4niPxvs8Wv18StWo/UKf2jD0qQ1Dn53b0LlrFy7Ak5xcYS4RVbMmjsxMCg4cgLp1gxdgOXx5Hi1PULdt28Ztt93G/PnzKz0R4Mknn+TRRx8tc/u8efNISEjwd4g+GbpvH/HAj7/9RlpWVrn3qb9pEycCmZs28f2cOUGNz1fz58+3OgSpBrVf6FMbhj61YeizYxt2+vlnjgM2ZWWxuoJcYlh0NHHA4rlzSWvTJmjxlceXNekdhsWnKJk5cyYXXHBBqYkAbrcbh8OB0+kkLy+vzCSB8npQmzdvzr59+0iqaOxnEETVq4cjPZ2C1avhuOPKv9NvvxHdpw9GgwYUbt8e3AArqaCggPnz5zNkyBBNsglBar/QpzYMfWrD0GfnNnTddBPOd97BPWECngceOOr9ojp3xrF+PYXffotx8slBjLCs9PR06tWrR1pa2jHzNct7UM844wxWrVpV6rbrrruOjh07cu+995Y7gzU2NpbY2Ngyt0dHR1v7AjKMojEe0cnJcLRYGjcGwLF/P9Eul20X6wcbPKdSLWq/0Kc2DH1qw9BnyzY8cAAAV8OGuCqKrVYtAKKys4+elwSJL8+h5QlqYmIiXbp0KXVbjRo1SE5OLnO77WVlmUkqVG6SlNsNhw5ZPiZEREREQkxlZvFDyK6Fat+uu1DkbXynEyoaCxsbW7z0g5aaEhEREV+FeYJqeQ9qeRYsWGB1CFXjbfyaNY+9GG79+ubCuXv3QocOgY9NREREwkeYJ6jqQfWnyqyB6uV9QWktVBEREfFFQYE5RBCUoEolVOYsUl7JyealElQRERHxxcGDxdePdfZNb05yeM34UKEE1Z+8jV+ZHlTvCyotLXDxiIiISPjx9p7WqgXlrHZUinpQxacSf+3a5qX3RSYiIiJSGd7cwZtLVEQJqihBFRERkYBTgio+8WUMqhJUERERqQpfElRvTqIENYKpB1VEREQCrSo9qJokFcF8mSSlBFVERESqQiV+8Yl6UEVERCTQlKCKT6qSoJZcy0xERETkWLy5gxJUqRRNkhIREZFAq8okqdxc8wxUIUIJqj9VZQxqVlZIvWBERETEYlUp8UNI9aIqQfUnX0r8tWoVX9fZpERERKSyfElQo6MhNta8rgQ1QvmSoEZFQc2a5nWV+UVERKSyfElQISTHoSpB9SdfElTQOFQRERHxnRJU8Ykvk6QA6tQxL5WgioiISGV58wZvHnEsIXg2KSWo/pKXB/n55nX1oIqIiEgg5OaaP+B7D2oInU1KCaq/eF8sAAkJlfsfJagiIiLiC+/Eaoej8h1i3rykZK5ic0pQ/SUvr/h6dHTl/kcJqoiIiPjCmzPUqgXOSqZxMTHmZclcxeaUoPqLt7wfHW1+q6kMJagiIiLiC18nSEFxgurNVUKAElR/8Ta6d62xylCCKiIiIr6oSoLqzU2UoEYgb7e591tKZShBFREREV9UpwdVJf4I5P1WogRVREREAkUlfvGJElQREREJNCWo4hNvt7nGoIqIiEigVGcMqkr8EUg9qCIiIhJo6kEVnyhBFRERkUBTgio+qc4yU1lZUFDg95BEREQkzGiZKfFJVZaZSkoqvu49dZmIiIjI0WiZKfFJVUr8UVHF59FVmV9ERESORSV+8UlVSvxQ/AI7eNCv4YiIiEgY8uYLKvFLpVSlxA+aKCUiIiKVpxK/+KQqJX5QgioiIiKVk5tbnGSqxC+VUtUEtU4d81IJqoiIiFTEmys4ncVzWCpDCWoEq8qZpEA9qCIiIlI53lyhVi0zSa0snUkqgqnELyIiIoFUlfGnoB7UiKYEVURERAJJCar4rLrLTClBFRERkYpUNUHVMlMRTMtMiYiISCBVtwdVY1AjkEr8IiIiEkgq8YvPVOIXERGRQFKJX3ymEr+IiIgEkkr84jOV+EVERCSQVOIXn1W3xJ+dHVIvHBEREQmy6pb4CwrAMPwZUcAoQfWXqpb4k5KKr6el+S8eERERCS/V7UGFkOkMU4LqL1Ut8btcxUmqyvwiIiJyNEpQxWdVTVCh+IV28KDfwhEREZEw401Qa9Xy7f+UoEawqo5BheIXWnq6/+IRERGR8OIdCuhrD6rLZf6AEtSIU9UxqFBc4tcYVBERESlPfj7k5prXS85fqawQW2pKCaq/VKfErx5UERERqUjJHKE6Cap6UCNMdUr86kEVERGRinhzhBo1isv1vgixs0kpQfWX6pT4vT2oSlBFRESkPN4eVF8nSHmpxB+hVOIXERGRQPF2YlU3QVUPaoRRiV9EREQCxZsjVGX8KajEH7H8UeJXD6qIiIiURyV+8Zlh+KfErx5UERERKY9K/OKzwsLi61oHVURERPytuiV+JagRqGRj60xSIiIi4m/VLfFrDGoEKjmeQz2oIiIi4m/+6kHVGNQI4v024nBUbfFcjUEVERGRimgMqvis5BJTDofv/+99sWVlgdvtv7hEREQkPKjELz6rzhJTULq7XuNQRURE5Egq8YvPqrPElPf/4uLM6yrzi4iIyJH8tQ6qelAjSHXOIuWlmfwiIiJyNNUdg6oSfwSqbokfNJNfREREjk4lfvFZdUv8oJn8IiIiUj7DUIlfqsCfCapK/CIiIlJSZqaZpIISVPGBP8agqsQvIiIi5fHmBlFRxZOqfaUxqBHIH2NQ1YMqIiIi5SlZ3q/KeuugMagRyR8lfvWgioiISHmqO0EKVOKPSP5cZkoJqoiIiJRU3SWmQCX+iKQSv4iIiARKdWfwg0r8EUklfhEREQkUlfitMWnSJLp160ZSUhJJSUkMGDCAr776yuqwKk8lfhEREQkUf/SgqsTvu2bNmvHUU0/x66+/8ssvv3D66adz/vnns2bNGqtDqxyV+EVERCRQ/DEGNcRK/FFWBwBw7rnnlvp94sSJTJo0iaVLl9K5c2eLovKBSvwiIiISKBFY4rdFglqS2+3mk08+ISsriwEDBlgdTuXoVKciIiISKP6cJKUE1TerVq1iwIAB5ObmUrNmTT777DOOP/74cu+bl5dHXoku6vTDDVdQUEBBQUFQ4i3JmZODC3BHR+Op6v4TEogGjPR0CvPzq74Qr594n0crnk+pPrVf6FMbhj61YeizSxu6Dh7ECbhr1qxynuFwuYgCjLw8Ci16PL48j7ZJUDt06EBKSgppaWlMnz6da665hh9++KHcJPXJJ5/k0UcfLXP7vHnzSEhICEa4pXRZt462wIatW1k7Z06VthGVk8NwwFFYyNczZ+KuzoQrP5o/f77VIUg1qP1Cn9ow9KkNQ5/VbXjixo3UB1Zu2MCOKuYZdf78k1OA7IMH+aaK26iu7OzsSt/XYRiGEcBYqmzw4MG0bduWN998s8zfyutBbd68Ofv27SOpOuMzqsh5yy243nwT90MP4XnkkaptxDCIiovDYRgUbNkCjRv7N0gfFRQUMH/+fIYMGUJ0dLSlsYjv1H6hT20Y+tSGoc8ubegaMADnr79SOHMmxtlnV20jK1YQ3b8/RrNmFG7c6N8AKyk9PZ169eqRlpZ2zHzNNj2oR/J4PKWS0JJiY2OJLaeHMTo62poXUGEhAK6EBFzV2X9SEqSlEZ2TAzb5MLPsORW/UPuFPrVh6FMbhj7L2/DwUMaounWrnh/UqAGAIz/fssfiy35tkaDef//9nHXWWbRo0YKMjAw++OADFixYwNdff211aJXjj2WmwBz8nJamiVIiIiJSLALPJGWLBHXPnj1cffXV7Ny5k1q1atGtWze+/vprhgwZYnVoleOPWfygtVBFRESkLH+ug6pZ/JX39ttvWx1C9fjjTFKgtVBFRESktPx8yM01r1dnno3OJBWB/FniByWoIiIiYipZVfXHQv1ut/ljc0pQ/UElfhEREQkEb6dVzZrgclV9OyVzlBDoRVWC6g8q8YuIiEgg+OM0p1A6R1GCGiH83YOqBFVERETAPzP4ofTyVEpQI4S/xqB6vx2pxC8iIiLgvx5Uh6M4SQ2BpaaUoPqDelBFREQkEPyxxJRXCC01pQTVH/w1BlUJqoiIiJTkrxI/hNRSU0pQ/UElfhEREQkEf5X4IaTOJqUE1R9U4hcREZFA8GcPqkr8EUYlfhEREQkEf45BVYk/wqjELyIiIoGgEr9Umb9L/FlZUFhYvW2JiIhI6FOJX6rE4ylOJv11JilQL6qIiIioxC9VVFBQfL26PagxMRAXZ15XgioiIiKBKPErQY0AJcdxVDdBBU2UEhERkWKBKPFrDGoEKPktxB8JqiZKiYiIiJd6UKVKvI0cFQVOPzyd6kEVERERMOe56ExSUiX+WmLKSwmqiIiIgLmqj2GY11XiF5/4a4kpL5X4RUREBIo7q6KiiidRV4dK/BHEX2eR8lIPqoiIiEDp8r7DUf3tqcQfQVTiFxERkUDw5xqooBJ/RFGJX0RERALBnzP4QSX+iKISv4iIiASCP2fwg0r8EcXfPahKUEVERAQCV+JXghoB/D0GVSV+ERERgcCV+DUGNQKoB1VEREQCwd8lfvWgRhB/j0H1fktSgioiIhLZ/N2DqjGoESRQy0ypxC8iIhLZAtWDqhJ/BAhkid97ejMRERGJPJokJVUWqBK/2w05Of7ZpoiIiIQelfilyvxd4q9ZE5yHm0XjUEVERCKXSvxSZf4u8TscmiglIiIiKvFLNfi7xA9aC1VERERU4pdq8HcPKmgtVBEREdE6qFIN/h6DCirxi4iIRLr8fMjNNa/rTFLis0D2oKrELyIiEplKdlL5O0FVD2oECMQYVJX4RUREIpu3k6pmTXC5/LNNjUGNICrxi4iIiL/5e4IUqMQfUVTiFxEREX/z9wQpUIk/oqjELyIiIv7m7zVQQSX+iKISv4iIiPhboEv8huG/7QaAEtTqUolfRERE/C2QJX6AwkL/bTcAlKBWl0r8IiIi4m+BLPGD7cv8SlCrKxA9qDrVqYiISGQLZIkflKCGvUCMQVUPqoiISGQLRInf5QKHw7xu86WmlKBWVyBK/JokJSIiEtkC0YPqcITMTH4lqNUVyElS2dm2H8QsIiIiARCIMagQMmuhKkGtrkAuMwUahyoiIhKJAlHih5A5m5QS1OoqKDAvo6L8t82YGIiLM6+rzC8iIhJ5AlHiB4iONi+9+YtNKUGtLrfbvPQ2uL9oLVQREZHIFageVG+Hmjd/sSklqNXlHSPqcvl3u5rJLyIiErkCNQbVm6/YfI6LEtTq8jawP0v8oJn8IiIikcrjKe5B9XeJ35uvKEENc94ucn8nqCrxi4iIRKasLDAM87pK/FIlgepBVYlfREQkMnmP/dHRxZOm/UU9qBEiUGNQVeIXERGJTCVn8HvP/OQvGoMaIVTiFxEREX8K1Ax+UIk/IhhG4BJU9aCKiIhEpkCtgQoq8UeEkt8+ArXMlHpQRUREIksge1BV4o8AJRNUTZISERERfwjUGqigEn9EKPntQyV+ERER8QeV+JWgVkvJxlWJX0RERPxBJX4lqNUSjBL/oUP+3a6IiIjYWzB6UFXiD2Mlv304/fxUagyqiIhIZPJ2TtWu7f9tq8QfAUou0u/vhXS9L8r0dPOcvCIiIhIZvJ1TgUhQVeKPAIFaAxWKe1A9HsjM9P/2RURExJ68PaiaxS9V4v32EYgENT7ePAcvqMwvIiISSQLZg6oSfwQoWeL3N4dDE6VEREQiUSB7UCOhxF9QUMC2bdtYt24dBw4c8FdMoSOQJX4o/uakHlQREZHIEYwe1HAr8WdkZDBp0iROPfVUkpKSaNWqFZ06daJ+/fq0bNmS0aNHs3z58kDEaj+BLPGDelBFREQijWEE50xS4dSD+u9//5tWrVrxzjvvMHjwYGbOnElKSgp//fUXP/30E+PHj6ewsJChQ4dy5plnsn79+kDFbQ+BLPGDelBFREQiTWZm8eo9ETyL36euv+XLl7Nw4UI6d+5c7t/79u3LP/7xDyZNmsSUKVNYtGgR7du390ugthToEr96UEVERCKL95gfHQ1xcf7ffoiU+H3KrD788MOi6yeeeCJz584lqZyzHMTFxXHzzTdXPzq7C3SJXz2oIiIikaXk+FN/r7EO4VniL2np0qXk5uaWuT09PZ177723WkGFjECX+NWDKiIiElkCOYMfQqbE73OCOmrUKJ566ikcDgd79uwp8/esrCyee+45n7b55JNP0qdPHxITE2nQoAEjRoxg3bp1voYWfOpBFREREX8K5Ax+CJkeVJ8zqxYtWvDll19iGAbdu3cnOTmZ7t270717d3r06MG6deto3LixT9v84YcfGDNmDH369KGwsJAHHniAoUOH8scff1CjRg1fQwwejUEVERERfwp0D2o4jkEFcyY/QExMDIsXLyY1NZWVK1eSkpLCZ599hsfj4ZlnnvFpm3Pnzi31+5QpU2jQoAG//vorp5xyiq8hBo9m8YuIiIg/BboHNURK/FXu+svKyiL68Kk4zz//fL8FBJB2uHHq1q1b7t/z8vLIy8sr+j09PR0wTxxQUFDg11gq4sjNJQrwuFy4A7BfR40a5vYPHgzI9ivifR6D+XyK/6j9Qp/aMPSpDUOfFW3o3L8fF+BJTAzIsd/pcOAC3Pn5eCzKLSqjygmqNzn1N4/Hw+23385JJ51Ely5dyr3Pk08+yaOPPlrm9nnz5pGQkBCQuMrTcNky+gOHMjNZNGeO37ef/OefDASyUlP5LgDbr4z58+dbsl/xD7Vf6FMbhj61YegLZhsev3Il7YGNBw6wJgDH/uM2bqQTsG3TJn4Lcm6RnZ1d6fv6lKBu3bqVFi1aVPr+O3bsoGnTpr7sgjFjxrB69Wp+/PHHo97n/vvvZ9y4cUW/p6en07x5c4YOHVrusleB4sjPB6B2cjJnn322/3fQuDE8/DA1CwsDs/0KFBQUMH/+fIYMGRKwLyMSOGq/0Kc2DH1qw9BnRRs6v/wSgNY9etAyAMd+5+rVALRo0oSmQc4tvBXvyvApQe3Tpw8jRozghhtuoE+fPuXeJy0tjWnTpvHSSy9x4403cuutt1Z6+2PHjuXLL79k4cKFNGvW7Kj3i42NJTY2tszt0dHRlnwIOKOjcQZiv/XrA+BIS7Psw82q51T8Q+0X+tSGoU9tGPqC2oYZGQC4kpNxBWKfh/Mnp8cTmNylAr48hz4lqMOHD6dmzZoMGTKEuLg4TjjhBJo0aUJcXBwHDx7kjz/+YM2aNfTq1Ytnnnmm0r1+hmFwyy238Nlnn7FgwQJat27tS1jWCdYs/pwcyM+HmJjA7EdERETsQbP4AR8T1Pfee49t27bx2GOPUb9+fRo3bsy+ffvIycmhXr16XHHFFQwbNuyoY0ePZsyYMXzwwQfMmjWLxMREdu3aBUCtWrWIj4/3aVtBFehZ/CWHK6SlFfWoioiISJjSLH7AxwS1SZMmpKSkMGzYMHJycnjiiSdo0KBBtYOYNGkSAIMGDSp1+zvvvMO1115b7e0HTKAX6o+Kgpo1ITPT/EalBFVERCS8BasHNZwS1DvvvJNzzz2Xfv364XA4eP/99xk4cCBdunSpVk+nYRhV/l9LBbrED+Y3qMxMrYUqIiISCYJ1Jimbl/h9OtXpLbfcwi+//MKZZ56JYRi89tprDBgwgKSkJDp16sSll17KU089xVdffRWoeO0l0CV+0NmkREREIkmge1DDscQP0K1bN7p168aUKVP46aefqFGjBr///jspKSmkpKQwa9YsJk6cSMbhWWhhLdAlftDZpERERCJFfr45MRoC34Mabgmq1/r164uu9+vXj379+hX9HrIle18Fo8SvHlQREZHIULIzKlDruodjib+yHA5HIDZrP+pBFREREX/xHusTEwM3fDBEelADkqBGDI1BFREREX8J9PhTCJkxqEpQqyNYs/hBPagiIiLhLtAz+CGyS/wRIxglfvWgioiIRIZg9KCqxB8BglHiVw+qiIhIZAhGD6pK/BFAs/hFRETEX4LZg6oSfxjTLH4RERHxl2COQVUPahjTLH4RERHxF83iL6IEtTo0i19ERET8RbP4iyhBrY5gzuJPS4NIOUOXiIhIJNIs/iJKUKsjmLP4PR7IzAzcfkRERMRamsVfRAlqdQSjxB8fX7x9jUMVEREJX5rFX0QJanUEo8TvcGgcqoiISCTQLP4iSlCrIxglftBMfhERkUigWfxFlKBWRzBK/KAeVBERkXBnGJrFX4IS1OoIRokf1IMqIiIS7jIzzQnRoFn8KEGtnmCV+NWDKiIiEt68x/joaHOCdKCoxB8BglXiVw+qiIhIeCs5/tThCNx+VOKPAMEq8asHVUREJLwFY/wpFOcsHk/xkAIbUoJaHZrFLyIiIv4QjBn8UDpnsXEvqhLU6lAPqoiIiPhDsHtQwdbjUJWgVkewl5k6eDCw+xERERFreI/xge5BLZmzqAc1TAWrxF+njnmpBFVERCQ8eY/xdesGdj8lcxb1oIapYJX4laCKiIiEN+8x3nvMDxSV+CNAsEr8SlBFRETCW7ASVKezeBkrlfjDVLBK/N7u/oMHbb0khIiIiFRRsBJUCInF+pWgVkewS/weD2RkBHZfIiIiEnwHDpiXgR6DCiFxulMlqNURrBJ/fDzExprXVeYXEREJP8HsQQ2Bs0kpQa2OYJX4QeNQRUREwplK/KUoQa2OYJX4ofQ4VBEREQkvVvSgKkENU8Eq8UPxC9Y7RkVERETCQ34+ZGWZ14M5BlUl/jAVzB5UlfhFRETCk/fY7nAE/kxSoB7UsKcxqCIiIlJdJU9z6gxCaqYxqGEumCV+jUEVEREJT8Ecfwoq8Yc9K0r8GoMqIiISXrzH9mAnqOpBDVMq8YuIiEh1eY/twZggBSrxhz0rZvErQRUREQkvKvGXoQS1OrQOqoiIiFSXVQmqelDDlBUlfo1BFRERCS/BHoOqEn8Y83jAMMzrKvGLiIhIVQV7DKpK/GGsZKMGM0FNSzOTYxEREQkPKvGXoQS1qko2ajBL/IZhJqkiIiISHoKdoKrEH8aC3YMaGwsJCeZ1lflFRETCh2bxl6EEtapKfusIRoIKmiglIiISjrzH9WCPQVUPahgKdokfNFFKREQkHKnEX4YS1Krydos7HOAM0tOotVBFRETCS26u+QMq8ZegBLWqgrlIv5d6UEVERMKL95judEJiYnD2qRJ/GAvmIv1eGoMqIiISXrzH9Nq1g1eRVYk/jHm7xdWDKiIiIlUV7EX6QSX+sGZFiV9jUEVERMJLsCdIgUr8Yc3KEr8SVBERkfBgRYKqEn8Ys7LErzGoIiIi4cF7TLeiB1Ul/jCkWfwiIiJSXVaOQVUPahiyosSvMagiIiLhRSX+cilBrSr1oIqIiEh1aZJUuZSgVpWVY1DT0239ohIREZFK0hjUcilBrSorSvy1axdfP3QoePsVERGRwFCJv1xKUKvKihJ/dHTxadBU5hcREQl9miRVLiWoVWVFiR80DlVERCScWDkGVSX+MGRFiR+UoIqIiIQLw1CJ/yiUoFaVFSV+0GL9IiIi4SI7G/LzzeuaxV+KEtSqsqrEr7VQRUREwoP3WB4VBTVrBm+/KvGHMZX4RUREpDpKlvcdjuDtVyX+MGZVid/bg7p/f3D3KyIiIv5lxRqooBJ/WLOqxF+vnnmpBFVERCS07dtnXtavH9z9qsQfxqzqQfUmqN4XtYiIiIQm77Hce2wPFvWghjGrxqAqQRUREQkPViWoGoMaxqwq8Scnm5cq8YuIiIQ2q3tQVeIPQyrxi4iISHVYnaCqBzUMWV3iT0uDgoLg7ltEgsLtcfPj1h8B+HHrj7g99u3lEJFq8FZDVeIvwxYJ6sKFCzn33HNp0qQJDoeDmTNnWh3SsVlV4q9dG5yHm01lfpGwM2PtDFq91IrhHwwHYPgHw2n1UitmrJ1hcWQi4ndW96CqxF+xrKwsunfvzmuvvWZ1KJVnVYnf5SpeC1VlfpGwMmPtDEZNG8X29O2lbt+RvoNR00YpSRUJN97juHd+SbCEQIk/yNlV+c466yzOOussq8PwjVUlfjC/ae3bpwRVJIy4PW5um3sbBkaZvxkYOHBw+9zbOb/D+bicFnzuiIj/aRb/UdkiQfVVXl4eeXl5Rb+np6cDUFBQQEGQxmU68/NxAW6nE0+Qx4K6kpNxAoW7dmEEaN/e5zFYz6f4l9ovtBgeg68+mMEpn7Sg7e52tDlUSJzHICH6Hf5TcALba0axvr6H9c3TWDD4O07pOMjqkKUS9D4MfQFtw7w8ojMyzO3XqhXUeSUOzATQU1iIO4j79eV5DMkE9cknn+TRRx8tc/u8efNISEgISgwd//yTDsCW7dtZNWdOUPbp1bewkMbAmh9+YHN8fED3NX/+/IBuXwJL7WdfhscgZ/Zman2znK7bf+R891bOP9qdDwHbgZWQ/vmFLE4+mV19+hB7ZRecNaODFrNUjd6HoS8QbRh34ADDAI/TyZzFi4vnlwRB/ZUrORFIP3CAH4KYw2RnZ1f6viGZoN5///2MGzeu6Pf09HSaN2/O0KFDSUpKCkoMziVLAGjZti3Nzz47KPv0cn3+Ofz8M10aNeL4AO27oKCA+fPnM2TIEKKjdQAMNWo/+8o/mMXvd79Pw2mv0SZ3bdHtucSyIuY41teoxYba0eTEOemVdAK/H1pBs4MFHJeRSfecLTRgH4P2z4G5czj4dR3W9P8H7V64meReLS18VFIevQ9DX0Db8PffAXDUq8fZ55zj320fgyMuDoBaCQmcHcQcxlvxroyQTFBjY2OJjY0tc3t0dHTQPwRcMTG4gv3B06CBue+DBwO+byueU/EftZ99GG4PK29/l6aTHmSAeycAGdTkl+MuJ3bUeRw/9hQu+eh4dqSvxsAg3hnPh91u4aXfXyHHk4MDB80SmjOrzlL2vzuXdj9NpZV7IwN/ep78/i/zy0m30uOTh4hvXNvaBypl6H0Y+gLShmlpgJmgBv31cThBdXg8Qd23L/uyxSz+kGTVLH7QYv0iIWbzxz/zd+3e9Hr1HzR072SrsxXzzn6R/I07OG3dm5w4cTi1Gyfy0pkvAeDAUer/vb+/eM4L9LyhH4MXjadp5l8svOtzfkkcRAwFDFj8PDnN2rHy5jfBKDvRSkRsxqoJUhASs/htkaBmZmaSkpJCSkoKAJs2bSIlJYWtW7daG1hFrJ7FD0pQRWzOyMvnlzMfovmlJ9I+cyWHqMWc05+jzu4/GTr7NpJblx6SNLLTSKZfPJ2mSU1L3d4sqRnTL57OyE4ji26LjnNxyrPnckLa9yy49yvWRR1PXc9+er55M6uanknGnzuC8hhFpIqsTFBDYBa/LRLUX375hZ49e9KzZ08Axo0bR8+ePXnkkUcsjqwCVi3UD0pQRULAgZ/Xs6FBf3p/PREXHr5tdAVpy9dz9rd3kliv7BAlr5GdRrL5ts3Mvnw2ALMvn82m2zaVSk5Lcjhg0FNn0nz/b3x5xgvkEEfXnfNwd+7KnxM/DchjExE/sEMPqhbqr9igQYMwDKPMz5QpU6wO7ehU4heRo9jw6le4BvShXfpK9lOXOdd9wmk73qNl7/qV+n+X08XAFgMBGNhiYKXWPU1IiuKcb25n7XsrWBVzArU9B+n40ChShj8IHk+1Ho+IBIAdElT1oIYhO5T4dapTEXsxDH6/6hla3zKcWkYaK+IGsPfbVZz931FBW0Gm1xWdaJn6E18cZ6500mPOE6xuex6F+9OCE4CIVI5K/BVSglpVdijxZ2ZCbm7w9y8iZbnd/HbSP+n23r04MZjTdDStN31Px9ObBD2UpORozvnzeWZdOJVcYumyeTZbW59K9sZdQY9FRI7CDj2oKvGHIStL/ElJxftVL6qI5YzcPFZ1uZTuP72JBwfTT32FoZvepE6jo481DTSHA86ffhU/PfMju2lIm4zfONB5IOkpGy2LSURKsEOCqh7UMGRlid/hgORk87rGoYpYypOZzZ/tzqHrn9PJJ5pZl3/Mhd+PJSracex/DoLT7u7Nto8Ws9nRmma5G8jrcxL7Fqy2OiwRUYm/QkpQq8rKEj9oopSIDXgys1nX4Vw67fiGDGoy//Y5XPD+RTjskZsW6X1JW7LmLWZNVDfqF+7CMfh0Dvz4h9VhiUQ2O/SgqsQfhqws8YMSVBGLGdk5rOt0Pp1SvyODmvw0YR7DXxhsdVhH1XlwY+J+WsCq6J4ku/fiOe10Dv209tj/KCL+l50NOTnmdZX4y6UEtaqsLPGDElQRCxl5+aw9fiSdtn9DJjVY/OBXDB0/wOqwjqlt7zrELZzP6qju1CvcTcEpp5O+4m+rwxKJPN5jd0wM1KwZ/P2XLPHb9MxzSlCrSj2oIpHJ42F1n2s5fstcskhg4b1zOPPxgVZHVWnt+ycT88M3ReX+zBOHkrNxp9VhiUSWkuV9K8YElcxdbLpOshLUqtIYVJHIYxisOuN2uq76kAKimP/Pzzj7qVOsjspnx51YD8fXX7PJ2YYmeZvY2fMsrZMqEkxWjj+F0rmLTcehKkGtKpX4RSLO6iuepOuCVwCYecFURrw+1OKIqu740xux97157KIhbdJ/Y0OX8zBy86wOSyQyWJ2glsxdbDoOVQlqVanELxJR/nr0Q7p8+CAAH534EqM+vcziiKqv72VtWfvvuaSRRIddC1l94o22HY8mElasTlBL5i5KUMOMSvwiEWPHtB9pOeFaAD5reycXLbzVdktJVdVpd/Rg4S3TKcRF15VTWXXVM1aHJBL+vCfZsUOCqhJ/mFGJXyQiHPp1AwmXjyCWfL6rdQFDVz5j2ds+UM59eQifnfoSAJ3fv5+/n5tpbUAi4c7qHlSV+MOYSvwiYa/wUCYHTz2fOu79pMT0odOv71EjMTw/Ni/4ZgxftBiDE4Mm91zB7q9TrA5JJHxZnaA6HOA8/FmmBDXM2KXEn5trLvgrIv5lGKwecAOts9aw09GYmDmzaNw2weqoAiYqCk5d+SI/1RhMgpGNce65ZG/Q8lMiAWF1ggq2P5uUEtSqsrrEX6MGxMaa19WLKuJ3K699iR5/fkwBUax99BOOP6Ox1SEFXFLdKJou+YT1rg40KtjO9j4j8GTlWB2WSPixQ4JacrF+G1KCWlVWl/gdDpX5RQJkwzsL6Tr1LgC+GvxvTn/4JIsjCp4W3WqT8cGXHKAOxx1cxu99b9DMfhF/s0OCavPTnSpBrSqrS/ygBFUkAA6uSSVp9MVE4ebbxlcw/KuxVocUdL0ubsevD8ygEBc9/viA365/2eqQRMKHYdgrQVWJP8xY3YMKxS/svXuti0EkjLhz8kkdeBH13btZG9ONnsvewhUVJutJ+WjIxEHMPu05AI5/5y42/2+RxRGJhImMDMjPN68nJ1sXh3pQw5TVY1ABGjY0L3fvti4GkTCy7OQ76XxoCYeoBdM/pW6z8J0UVRnDv76N7xpcSjSFJFx3MenrNGlKpNq8x+zEREiw8DNGY1DDlB1K/I0amZe7dlkXg0iYWHbrewz49VUAfrvrPTqd287iiKwXFe2g68//4c/oLjRw72L7iRfhyc23OiyR0OY9ZnuP4VZRiT9M2aHErwRVxC/+/vQ3urxyIwDz+j/Cqc+eY3FE9lG/VQ0KPppBGkkcf2Axv5x2l9UhiYQ2uyWoNu1BtTC7CnF2KPErQRWpErfHzaKti9iZsZO6abXpdOlYEshhWd0zOX3BI1aHZztdR7bnm1vfY/DL59F36SusvKsPaWObszNjJ40TG3Nyi5NxOcPs9FoigWKXBNXmJX4lqFWlEr9ISJqxdga3zb2N7enbcbjhi+d706JwI1tcLWm79H2iYpVolWfwS+cy58eHOHvF43R4/ib676zLquN2ANAsqRkvnfkSIzuNtDhKkRBglwRVJf4wpRK/SMiZsXYGo6aNYnv6dgAemnoaw7N/IYc4Rpwfzw+FC6wN0OYyJ3dnbmw/Esjh049d1EqPB2BH+g5GTRvFjLUzLI5QJATYLUG1aQ+qEtSqslOJf98+KCiwLg6REOD2uLlt7m0YmIvOn/ldfyZsWQDAzb168lu3ddw+93bcHnv2JljN7XFz5w93cMU/NrPZ0Yz27q28O7kTDg9Fz6meP5FKsEuCavMSvxLUqrJDiT852XyBGYbWQhU5hkVbFxX1nLb+uw0fLFyLE4PXG5zE1PN+wsBgW/o2Fm3Vep/l8T5/Bxru5sJz6pFLLOdnrODeD08E0PMnUll2SVBV4g9DhmGPEr/TWbwWqsr8IhXamWGu4RmfkcinH8ZShzSWxnTijuuXlns/Ka3k87LihBTGdjET08fXL+X0Jd3LvZ+IlMNuCap6UMOIx1N83coSP2gcqkglNU5sDG6YNLk3Pd1r2e2ox6jrdpMf6y57PynjyOfl7Qu/5+06p+DCw0fzttNsW5Ny7yciJXg8xQv1W52gqsQfhkp2h1vZgwpKUEUq6eQWJ3PH9JFck/49hbi45Oy67Gh8oOjvDhw0T2rOyS1OtjBK+zq5xck0S2qGg8OnfnXA2NE/syKqA/XZzydT69I6qq2eP5GK7N9v5hAOB9Svb20sKvGHoZLfNpSgioSEJc8t46m1XwBwX+ee/NDnr6K/eZOuF898Uet5HoXL6eKlM18Cip+v3IQ8LrwqnQPUpn/Bap7/z4k4HXr+RI7Ke6yuVw+io62NRSX+MFSyMVXiF7G9vxfvpu19o4ihgEXNz+Tjf5QeJ9ksqRnTL56udTyPYWSnkUy/eDpNk5oW3ba55U7+b3gXPDi4YPP/+PrK/1kYoYjN2WX8Kdi+xK+F+qvCjiX+nZqYIFKe9AOFHBhyCe2MVDbHd6J/yjQ2104oOpOUzoTkm5GdRnJ+h/NLP38Pn8yysx+j/9ePcsoHN7HstO70vaGb1aGK2I/3WG2HBNXmJX4lqFWhHlSRkODxwHf97mNEzg9kOBKpOW8G0XUTARjUapC1wYUwl9NV5vnrN/sRfm/xM91S51L/ppFs7fsLLbrVtiQ+EduyUw+qSvxhyNuYTqc50NlKSlBFjuqzy6Yx4u/nAdj5xBTqDexocUThy+Fy0v7n90iNaUlrzwY2nnINOVmeY/+jSCSxU4Jq8xK/EtSqsMMi/V5KUEXK9e2/f+PMadcB8PuZ93DcfRpfGmjxzZJxzPiUXGIZlPY5Xwx8GsOwOioRG7FTgmrzEr8S1KqwwyL9Xt4XeWam+SMirPp+H23vGkENslnbYijdvnzC6pAiRuPhJ7D5rtcAuDDlIWaM+dbiiERsxI4JqnpQw4i3Ma0efwpQsyYkJJjXvYv/ikSw3TsKST/rEloZm0mNb0v7Xz6yx3s1gnR89npW978eFx5OmXQpiz/aZnVIIvZgpwRVJf4wZKcSv8OhMr/IYXl5sKD3XZyU9x1ZjprU/HYWUfXrWB1WROr83atsrtuL+uwj/sqR/JWSbXVIItazU4KqEn8YslOJH5SgigCGAe+e8S6X7DIXk097ZSpJAzpbHFXkcsTH0WjxpxyMqkcv9y/8PfBa9u3RpCmJYHl5cPCged1OCap6UMOInUr8oARVBHj/tmVcvfgmADZc+QhNxlxgcUQS17EVfDqDfKI5O+sTPu/9KLm5VkclYhHvMLzoaKhjg8qOSvxhSD2oIrby1dupnPbKBcSRx8au59P23fFWhySH1TnvZPZNfAuAf2z7F5NP/1Az+yUylSzvW71EJagHNSzZaQwqKEGViPbT1+k0GX02TUllZ51OtF401VyjWGyjyQPXsuWSewAY/dN1TL5+qcURiVjATuNPQWNQw5JK/CK2sCalgJxzRtHd+I2DsQ2p//NsHLWSrA5LytHy/SfY0uM84sjjvHdGMP3fW60OSSS47JagqsQfhlTiF7Hc9m0Ga066kdML55PjTCD+my+Jat/a6rDkaFwuWi56n50NutOI3Rx357l8/3mG1VGJBI/dElSV+MOQSvwiljp4EGad8C8uzp6CGyeF731M3MDeVoclx1KzJg1//pxDcQ3pxu8UXnARSxfmWx2VSHDYNUFViT+M2LXEv3s3eLSMi4S33Fx4o987jNk7AYC0J14n8bJzrA1KKs3ZqgUJ8z8n15nAEM/XbBl8PSkr9LklEcBuCapK/GHIbiX+Bg3My4KC4jXWRMJQYSE8fcY87lp/IwB7rr+fuvffZHFU4quYgX1h+nQKHVFcUvAeiwfey7p1VkclEmB2S1BV4g9Ddivxx8ZC3brm9Z07rY1FJEDcbnjs7J+4c8lIoilk9xmX0+Ctx60OS6oo7oKzyH/9bQDG5DzHZ32fZMsWi4MSCSTv8blhQ2vj8FKJPwzZrcQP0LSpebl9u7VxiASAxwOPXbCCO+afRU2y2Nt9MA1n/1fLSYW4hJuvJnPCcwDcl/4A/+v9kobSS3jyeGDHDvN6s2bWxuKlEn8YsluJH6BFC/Nyq5ZukfDi8cC/LlnD2C+GUps09nUcSP3FM83KgYS8muPvJP0O88QKD+27nTdOmMyePRYHJeJvu3ebw/CcTmjSxOpoTCrxhyG7lfgBWrY0L5WgShhxu2H8yFX83/TTqMd+9rfpQ72fZ0ONGlaHJn6U9Px4Dt1wFwCPpN7Eq90nk5pqcVAi/uQ9Njdtap7q1A5U4g9Ddu5B1SAuCROFhfDQ8JXcNus0GrCXA616krx8LiRpIf6w43BQ+61nOHTVLTgx+NeuG3mr+2ts22Z1YCJ+4j02e4/VdqAe1DBkxzGoKvFLGMnJgfvPWMY9X59OPfZzoH1f6q74tngyoIQfh4Pa775E2g13AjBh31je7f68ZvdLePAem+2UoGoMahiyY4lfCaqEiYMH4eHeXzFh4WnU4RAHOp5I3eXzoE4dq0OTQHM4qPXWs6SPuR+Ahw7exdc97uXnn7ROqoQ4OyaoKvGHITuX+Ldvt+2LTeRYtm2DZ7tO5ck/zqMG2RzsM5S6y+ZCrVpWhybB4nCQ9MpEMh96EoBbc59hw8nX8tXnBRYHJlINdk5Q1YMaRuxY4m/SxIynsFCnPJWQ9PNPHj7q9ChP7LiGaAo5NPwK6vz4BSQmWh2aBJvDQc3H7iN30ju4HS4ud/+P6PPP5o0nDmAYVgcnUgV2TFBV4g9Ddizxu1zFa6upzC8hZvqUTHYMvJi7syYAkH7T3dT+fCrExFgbmFgq7uZr8cz8gtyoGgzmG854sB+PXrqWAnWmSqjxHpe9K+7YgUr8YciOJX7QTH4JOQUF8OT1f9PuuoGM9HxKgSOanNfeJumNZ7QIvwAQfd5ZxP6yhLQ6LWnP34yb1o/x3WdqGSoJHVlZsH+/ed1OPagq8YchO5b4QROlJKTs3AkTu33MmP/2oge/kZHQAOeC74n/v39YHZrYjKN7N2qtW87+zqeQRAZPrL2AL9vfzsJv8q0OTeTYvMfkpCR7jadXiT8M2bHED1qsX0LGvBmZzG97ExP+vJQkMtjXcSCJ637FdcpJVocmdlW/Pskr5nPgH+YyVDdmv0T8kJN49ZZ1dj2+ipjsOP4UVOIPS3Yv8StBFYu5PW4WbF7Ah6s+ZMHmBbg95gdgTg68fMH3tLuwG1fnvIUHB/tvfpB6q763z/mpxb5iYqj79nPkffI5mTF16cMvXP9qDya1e54Nf5U+yB7tNSgSdHZPUG36Dc9mGVaIUIlf5KhmrJ3BbXNvY3v69qLbmiU14/b412ly3xxuTXsDgAOJLanx0dskn32GVaFKiIoddS6x/VLYOfwGGq+axy1b7mJZp+ksv3sSF03sway/yn8NvnTmS4zsNNLCyCUi2XGCFKjEH5bsWuLXJCmx2Iy1Mxg1bVSpxMCZncjZL53MNf+8jssOJ6dbh99M3R2riFVyKlXVvDmNf5vL/qcmk+VKpK9nKRc9fQIfNbqBG557oNRrEGBH+g5GTRvFjLUzLApYIpYdT3MKKvGHJbuX+A8dgvR0S0ORyOP2uLlt7m0YHF6o0g3nzjmDlc82480tH1KP/ayJb07arG9o8eUkrW8q1edwkHzvDcRv/IO/e12MCw9X7Hubv/+7h3veHk58elLRXb2vy9vn3q5yvwSXSvxVogS1Kuxa4k9MLD4d5LZt1sYiEWfR1kVsT9+OwwPDF3Zh6VOd+XzZt3Qz1nLIkcitfdvR/a5trOxms/eNhDxni2a0+/Vjvn/5FVbHNKcuB3l622w2/juW2z4+kRrZ5oHYwGBb+jYWbV1kccQSUeyaoKrEH4bsWuIHjUMVy+zZu4Xrvm3N6idb8OV3q+lXsIYsEniidV9aj8vhlbP/xu2CnRk7rQ5VwtSuQcl0v28bV5/YmY3OZjRiLy+uXcLWZ2vw+AddaXLIAeg1KEHkdpunIAf7Jag2L/HbMMMKAXYt8YP5Bvjtt/BMUHfvhr17ITvbnA5ev775eGvWtDqyiGb89jvbxk/mzC//x8XuNADSSeTNRn15/oIUdjdcVur+jRMbWxGmRIDGiY3xOOF/Q9fw0SAX135+Knet2cZxxkYe/GsV9/3l5MuGLWneYAt0LIDoaKtDjlz5+bBjh/njdEKNGmYVsFWr8DpJx+7d5hlJXC7zlOR2YvMSvw0zrBBg1xI/hFcPam4uTJsG8+bB4sWweXP596tbF/r1g1NOgUGDoG/f8PqAsxvDgHXryP9gOplvf0Td1DV4+wU205LXmvTlrfOWkt7o21L/5sBBs6RmnNzi5ODHLBHh5BYn0yypGTvSd1AQ42byqB94+5w4zvvqfO5YtZtTPEs5f/dm+L/7ybrreTwjR5F4/SVw0klKVgNt40b49ltYuBB+/NGcOGQYZe9XuzYMGGB+nl99tf2SOl95j8VNm9qvU8vmJX6bPVshws4lfu8yFqE8k3/fPnjtNXj9ddizp/h2pxOSkyEhwTxH+549kJYGBw7AV1+ZP2B+oF14IVx6qflB53BY8zjCSVoafPcdxtyvyf9iLrE7txAD1AXyiWa26zx2nTMax/+5ef6nc8r8uwOzDV4880VcTht+sZOw4HK6eOnMlxg1bRQOHBgYeOJymXnBLGYOr0HHhVdyy8o6jMr6iAbZe+G9N+C9NyhISMI55AxcZw2DYcPMXjypvi1b4MMP4ZNPYMWKsn+PjTUTNzArYwcPmpN8vZ/njzwCl10G48ZB9+5BDd1v7DqDH1TiD0t2L/FD6PagTpsG//ynmXQCNG8O115rfpvu29c8VVxJ6enw11/mN/JFi+CbbyA1FV55xfzp3Nnc3pVX2usUc3bm8Zi9HStXwooVGIsXw5IlONxuHEAskEcM33Ma39W/lGZjR3D5/9WmXj3z3xs0n17uGpQvnvmi1qCUgBvZaSTTLy77Gmxery4T37qAc9uNZOb0f7P86e/o8NvHjGAmydkHYNZn5g/gOa4DzsFnmF9wBwyANm30Rbey8vNh1iz4z39g/vziXlKXy+ypPvVUOPlk6NYNGjQo/bwWFppD1JYsgY8/NitnU6fC//4Hd94Jjz0GcXHWPK6qsusEKVCJPyypxO9/Bw7AmDHw0Ufm7127woMPwsiRFZfekpKgd2/z5/bbIS/PTFKnTYPp02HNGhg7Fu69Fy6/3ExWe/YMykMKFLfHzaKti9iZsZPGiY05ucXJVe+VLCyEtWuLklFWroSUlFLLlHkPH3/RnrmcyYKYYdQeMYhL/lGDp4aUHU0xstNIzu9wvv9iFPHRsV6DF10WxUWXDeXPP4fy7NtvsfrdX+m592uG8TX9WUrUX+vgr3VmFQegXj3o39/86dXL7M1r3LhaSatf38d2sHs3vPkmTJoEu3YV33766WY1a8QIc95ARaKi4IQTzJ9bboFly+DZZ83P8ueegzlzzIT1hBMC+lD8ys4Jqkr84cXtcbMvLZWGwN/pm2ntcdvrQ+Xwm8DYvo2PV75HozrNbPfBV+aDmZa4hg6D9evNN8yDD8JDD1VtTFhsLAwfbv689JL5zXvSJDMJmzzZ/Onf3/zwGzXKHCpwrPhs9Pwd7SxNlTpDTk4OrFpVOhldtcoc63uEXGJZRVdW0pNf6M2i2CF0PKs1I0fCuyOOvYSpy+liUKtBvj9AET+pzGuwY0d46lkX7qf68sMPffloxsP83+eHaL/tWwbyI/1ZSi9WELtvH3z5pfnjVa+emah6f7p1g+OPL/cz5UjVeh8HSaU/B3/5BV5+2ezxzM83b2vUCK6/3vxp3brqQfTtaw4P+OILGD0a/vjD7IX95BPcw8+27ee0l9vj5uDaFdQD/qqRS1ub5QtupwMXkF+Qy5LNC+z3HBo28uqrrxotW7Y0YmNjjb59+xo///xzpf4vLS3NAIy0tLSAxvfpH58azf7dzPiwM4YBxtizMJr9u5nx6R+fBnS/vvh09SdGdrTDMMBoewsGE6oWY35+vjFz5kwjPz/fv/Edfg6ZYMZ23FiM7bVdhgGG0aKFYSxb5tf9GYZhGB6PYSxYYBiXXGIY0dHmvsAwGjUyjAkTDGPnzqPGV9XnLxA+/eNTwzHBUSo2JmA4JjgMxwRHqRjz9+41Fj3+uFH43HOGcfXVhtGli2G4XMWPvcRPuiPR+IGTjRe4zbiaKUZXfjOiyDc6dzaMW24xjJkzDSMz08IHHqEC9R6Uink8hrF6tWE8/bRhnHyyYcQ5co2+LDVu5UXjfS4z1tDJKMRZ7nvJExVlGF27GsaVVxrGs88aBV99ZcyeOrVUG/ryPrbKMT8Hs7MN4913DaN//9LPQf/+hvHBB4aRl+f/oPbuNYzhww0DDLfLaYy9om5QPqer+j70Pod/1DOfmyFX2udYYhhmfP0famQYYGRGB+9Y50u+5jCM8qbRBd/HH3/M1VdfzRtvvEG/fv148cUX+eSTT1i3bh0NGjSo8H/T09OpVasWaWlpJB05RtFPvKdwNDD45GMYtRb+72x4o69Z4pl+8XTLv/l6Y1wxyaDHbjjnMpjdoXiCii8xFhQUMGfOHM4++2yi/TS7teRzCNBlN3z7LjTIhrX1YPO0tzjrtNF+2ddR7dpllqHeeKO4DBUdDRddxMJhHRm08RGMI6p2VXn+/M3tcdPqpVZlTt8IUD8Teu2CQftrcVvUEJwpK4ndtqHc7eyhPivpyQp6sZKerKQnG2iLw+mkY0cYONCsyA0aBA0bBvhBSYUC8R4U3x08CD//DD/9BEuXmj/56Tl0Zg3d+a3opxu/U4dD5W4jr0EzjO49cfXpzj93TmJ+rf1srUXx+JnDvCtdbLptk2U9WUd+TpeMreNeg8/Th9PuyyXmEwPm5+cll5hVqb59AxtcYSFbLhxMy89/wAP88xx4q3dxfOD/z+mqvA+9z6HLbZA9EaI90OJ22F7b+mNJyfiaphlsewHyXBD3cHCOdb7ka7ZJUPv160efPn149dVXAfB4PDRv3pxbbrmF++67r8L/DXSCemRy8NmHMGId3HgOTO5tjw+VkjF++AlcugbuGgLPn2T+3dcY/X1wPPI5bJQByyZD83T4tTGcdSXENW4evOcwPx9mzDAnUi1ZUnTz+rrw357wYRfYUqf47v5oY7fbHOpTUGD+eK+XvK2gwJzMmpVV+jJl63peXvQWLTIL6XkwjV5p++mZmUqv3M00de8rd39baFEqGV1BL1JpQu3aDjp2NIfi9uhhXnbpAvHxVXpYEiBKUO3J4zFHDC1fblac1641LzdtNGjGtlJJaw9SaM/f5W7ngCORlLhWrKzRjJU1G7Kydl3WJcXjjs/izlNvpnfrDiQmFi9aEhtrXh55veTv1V1dr7wvwom5cP46uGEFnFpycZgWLcyy+w03mCX9IHB73LR+oSV3T9vBLcvAA5x3uCMGAnMs9vV9WPI5PG4frHsVsqIh8X4wnNbnCyXja5QBO58HtwOixpt/D3R8IZeg5ufnk5CQwPTp0xkxYkTR7ddccw2HDh1i1qxZpe6fl5dHXl5e0e/p6ek0b96cffv2BSRB/XHrjwz/YHjR79P+3ZZzDq3m+qQJvJNwgXmjAa3rtKFGdI2i+5X3zAbqtpzCbLalmac3HZ/1KuNzXuM/sRdxY+Jjh+9ofjNqmtSM+Kj4Mv9fdrsG2dnZJCQk4HA4qh1jbmEuuzN3AxBn5PJ95qX0c//GWmdbTqo5g0POWmA4qF+jAXFRsVXaR1Vv65K/giuzXuOC3GkkklV0+1JnL6ZFncecqDNY52gHDgd1YusQ7Sr9IVXeNj2essmocWTXbAWcuGnPenqykl6sONzXuZJkDpTdFw7+4jhW0IsUerCpdk92NupBdryHLl2SadfOQZs2Bm3bQps2BnXrVjoMsVBBQQHz589nyJAhSlBDQE4OrFsHGzY42L7dwbZtsHWrwebfd9Di4BZaHVpJDyOFnqykM2uIpuzElBziisZ+r6Irv9ONVXTlEHXK2WNZTqeBy2UmqpX9KXn/PHcOqZk7SPbsZ1jBj1yQP5/h+QuIwxxb6sbJlzGDmFF3DMsSz8MoJ4Epb96Yv27LLshi06FNYHh4M+MxRud8SoYjgYF13mVVzHFF92tTpzU1ov1zAhfDMMjIyCAxMRFHJSbFZRVksvHgJgDOzV3ArEO3sSKqI73rfVzqfv6M0Rcl46vnOcCePacBED8+AYer+GA2+/LZDGwx0O/7T09Pp169eqGToKamptK0aVOWLFnCgAEDim6/5557+OGHH/j5559L3X/ChAk8+uijZbbzwQcfkJCQEPB46139Eielf881TGEq1wR8f766hI/4iMtYxEBOwW7nnDb4kMu4lI/ZT1368TMbaGd1UADUIJOL+IQreY/T+B5niRLXJlrxDYNZwoks4UTW0x7DD2cKjnbk0ypqG8fzB10dq+hsrOF4Yw3HudcRZ5SdvFTgiGZbUju21e/IrkbHsa95O9JbtyQ2OZratfOoVSuPqCjL39IicgSPBzIzo0lPjyXrAMRtTKXulg002vUXzfauo+XBdcS7s8r931RnU9a4urDG2YXf6cZvnq6scx9HlqdGuff3VX32MICfOJElDGIBfVhe6vPvTzrwAZfzX/7BDpr5ZZ/VFUUBXzOM0/meLbSgL8vYg73GJd3NMzzDvXzAZVzBB1aHU0YdDnCAZAA+m/YpzpjA9+hmZ2dz+eWXh2+CanUPatff21PvUBx/1E4kNaF4TbaJZzxOlwZdSv1vIL9Nlrzt992/c+839wLQbX8Gy2f9zN64aJpdfkqJOxo8O+RZujXsdsxtut2FLF++jD59+hJ1eK206sT42+4Uxn09jtt+387TSzeR73QwfHgXFjUpvTbpi2e+QI9GPY7YXtmXaGVXd6lsfCm7VjL2q7FFvzfMLuCCDQc4Z/MhTt6RQayndAzu+BrktepAbuuO5DdqTmH9xhQkN8STUBNPXALExhJFIVEUEl2YQ3TmQaKy0ojem0rU9q24dmzFuXUr7NiO4yiLJBsJCRjdumH07ImnWzdGrZ/Iwpr7yStn7Q0HDpomNuX3f/6Oy+lS71sYUBuGviPb0O1x03VSV1IzUsuO8fQYtD0Ipx2szfMNr8K5Zg2ONWtwVHDSFaNBAzzNWlDYrAUFjVuS37AZ7qTaFCbWwR1fE48rGrczCqPAjSMnG7KzcR3Yh2vvTqJ3pxK35S/iNq0l5uCeMtv+rW5N5jZLZnrrhvxeN7HUB+fTg5+ma4NuZf4n0BWv1XtW8+C3DxX9Xicvn0VzltA+I4sFDZM5c2h/DIeDx057rMyxuKoKCwtZsWIFvXr1KjoWVmT1ntU8/P3DALy5+Deu3bCNR7sfxxPdjyt1P3/G6IuS8UV5PJy2cx9uh4MfTvoNXMVtbIceVFssM1WvXj1cLhe7d+8udfvu3btpVM7YltjYWGJjY8vcHh0dHZAP8lNan0JyzWR2pO/AwGBZl99L/d07ZuOOK7taNgb1VE93nt/1JzvSd/BHIwNmQf3cAhKTv2V/jeIYx1zUvZJjUA0yMg5y8skuoqOr/zLp7+nJZz/9xb+Wm21821kG35ywqujv3vhGn9fTkuewp+cEHl2/s6iNtwIvtYKXgIR8OH0TnL0rkZsLuuH45VdcOVkkrF1Bwtpyzo7iq+ho6NDBHAha4sfRqhWOw+vUuYBr1jbgi2mjwEOpg5t3YPtTw54iLjbuiE0H5j0hwaM2DH3eNowmmqeHPc2oaaOAsu/j1XVgwk2vEVVygkpaGqxeDb//bi4L9/vv5u9paTj27MG1Zw+uFb9Q9ojoo86d8QwYwF2ZnzKtyUF2JGUCmUBxguz9nL7lksodR/xtiKcrL+3/rehzejdwTn1Y8SYM2r2fMbtn88mZzbnzav8diwsKDAxjL2edVblj4TBPV145mMKO9B0c953Zvn+0/4v8Nn8Bxc+hP2P0Rcn48jGYXbKA6SmO75TWpwQkPl8+y2yRoMbExHDCCSfw7bffFo1B9Xg8fPvtt4wdO7bifw6C8k6f52WXUziWjDEnxsGWWgYt06DDfviphvUxugoK+eSLOGLd8MVx8Ebv4r/Z4TmsqI1zYhzM7gDXPTwFR6eR5qDSjRvNmRHr1sGOHebZq/bsKZ7VlJdnJp5RUeYMhjp1zHNMN2xono625E+jRpU66cPRzpCjszSJhA6f38e1aplrf550UvFthmGeEnTLltI/27ebtx86BBkZxTMzHQ6oUcOcCVmvnnmSgcaNoX176NTJXBC2Zk2cwMC1Z/HitFE4KP+LsN0+p/+qB3cMg7e+hCe+hbPGjLPHsfjjC+l4eP7qn4fPsmfX59DLDvGVZIsEFWDcuHFcc8019O7dm759+/Liiy+SlZXFddddZ3VoQGgkByVj/LPedlqmQcd9sK2LDWJ85BFqr9tCXp0kHrmiBhg7i/5kl+ew0m3s7fHs0MGSGHWWJpHQVu33scNhfumtU8dcisPPsdn5WFdefJNPgIs3xjH4j1wGPzIFhv3T7BiwMMYvBv+Xuo/+Aw/m6jBg7+cQ7BOfly3GoHq9+uqrPPvss+zatYsePXrw8ssv069fv2P+XzDWQfWy81mGvNweNzuvv5hmU2aw9cZLaDrpfZ9j9OsSN0uXwoknmt/6P/sM93nn2vo5DIU2PhYtURT61IahL5Tb0O6fg2Xiiz0OV7fusG+feSbCxx7zy36q3IaLFsEpp5DTrBEz5/w7NJ7DIMTnS75mmx5UgLFjx9qipF+RUDiFo8vpolnfwTBlBi12ZoOVbwi3G/7v/8zk9OqrYcQIXGDr5zAU2lhEJJDs/jlYbnxvvGGewvqZZ8zjTfv2lsQGwJ9/AhDfpQeXdb3MujgqYPc2rv46OWJPHTual4ffJJZ54w3znO+1a8Ozz1obi4iIhK+RI+HMM80TsYwde/SFvoPBe+z1HovFZ0pQw5X3TbFxozlhxwq7d8ODD5rXJ06EY5yyVkREpMocDvPsgDExMG8efPqpdbEoQa02JajhqlEjSEw0S+wbyj8ve8Dde6+5RMoJJ8BNN1kTg4iIRI527cxjD8Dtt0NmpjVxeBNUCybThgslqOHK4bC2zL98Obz7rhnH669XahklERGRarv/fmjVylwC8Jlngr//3FzYZJ5OVD2oVacENZxZlaAaBtx9t3n9qqugb9/g7l9ERCJXfDw895x5/fnnzXWqg2n9evM4WKuWufa1VIkS1HDmTVDXrQvufmfPhh9+MNehe/zx4O5bRERk5Ejo3988ccqECcHdt/eY27Fj5c/LLWUoQQ1n3gR17drg7bOwEO65x7x+++3QvHnw9i0iIgJmYuhdOebtt80z/wWLJkj5hRLUcNali3m5apW57EYwvPOOmRAnJ8N99wVnnyIiIkcaOBBGjACPJ7jHo19/NS+9x2CpEiWo4ax9e/NUeLm58Pvvgd9fdjaMH29ef/hhc+1TERERqzz1lDlJ94svzLM7BZphmGdPBHOIgVSZEtRw5nAUv0G8b5hAmjQJdu6Eli3h5psDvz8REZGKdOgA119vXn/oocAv3r91K+zaBVFR5hKLUmVKUMNdsBLUjAzzmyqYvaixsYHdn4iISGU8/LB5TFq4EL75JrD78h5re/QwVxOQKlOCGu6ClaC+9BLs22cOK7jqqsDuS0REpLKaNSuu6gW6F1Xlfb9Rghru+vUzS/0bNsCePYHZx8GDxWvOPfqoWdoQERGxi/vvh4QEWLbMHI8aKD/9ZF4qQa02JajhrlYt6NTJvP7zz4HZx3PPmac07dIFLrkkMPsQERGpqoYN4dZbzesPP2zO7Pe3vDxYudK8rgS12pSgRoJAlvn37DHL+wCPPQZOvaRERMSG7r4bkpLMVW2mT/f/9leuNJd0rFcP2rTx//YjjLKJSBDIBPWppyArC3r3hvPP9//2RURE/KFuXRg3zrz+yCPmiWX8yXuMHTBAZ5DyAyWokcCboC5bBm63/7a7Ywe8/rp5/fHH9YYUERF7u+MOM1Fdtw7ef9+/29b4U79SghoJjj8eataEzExYs8Z/25040RxzM3AgDB3qv+2KiIgEQlIS3Huvef3RR/17lkXN4PcrJaiRwOWCvn3N6/4q82/aBJMnm9cnTlTvqYiIhIaxY81JU5s2wX//659tpqaai/Q7HNCnj3+2GeGUoEaKAQPMy8WL/bO98ePN8TtDhsApp/hnmyIiIoGWkAAPPmhe/9e/zHkU1eUt73fpAomJ1d+eKEGNGKefbl5++SUUFFRvWytXwnvvmdefeKJ62xIREQm2G2+EVq3M03O/+GL1t/fZZ+blaadVf1sCKEGNHKeeapY0DhyAb7+t+nYMA+65x7y87DJz9r6IiEgoiY0t7mB5+unqncgmJwdmzTKvX3pp9WMTQAlq5HC5YNQo8/pHH1V9O/Pmmecyjo42x56KiIiEoksugRNOgIwMs9RfVXPmmJOQW7bUBCk/UoIaSbzf7D77DHJzff9/t9tc6BjMQeatW/svNhERkWByOuHZZ83rb74Jf/1Vte14O30uvlgThv1ICWokOfFEaNYM0tNh7lzf///tt2HVKqhdGx56yO/hiYiIBNVpp8Hw4eak33HjzOFrvsjIgNmzzesq7/uVEtRI4nSa3/AAPv7Yt/9NTTXHnoI5g79uXf/GJiIiYoVnnzWHrc2eDZ984tv/fvGFOQa1fXvo2TMw8UUoJaiRxvsN7/PPfVta45ZbIC3NXN/tllsCE5uIiEiwdeoEDzxgXr/lFnMycWV5O3suvVTlfT9TghppeveGNm0gO7t41uGxzJhh/kRFwX/+Y064EhERCRf3328mqnv2wF13Ve5/9u+Hr74yr6u873dKUCONwwFXXmlef/BBc+ZhRfbuNSdEgXl6uG7dAhufiIhIsMXGmvMsHA54553ixLMi995rriveo4d5SnHxKyWokeiuu6BFC9i8ucLJTq6cHFznn28uZNyhgyZGiYhI+BowoLhD5pJLICXl6Pf95hszoQV4+eWAhxaJlKBGosREmDzZvP7yy7BkSdn7FBTQ59lncf7yCyQnm8MB4uKCG6eIiEgwPfssDBpkzs4/6yzYtKnsfTIzYfRo8/qYMXDyyUENMVIoQY1UQ4fCtdeaS2pcf73ZS+q1cyeua6+l4YoVGPHx5ulRO3SwLFQREZGgiI2FmTOha1fYtYuoc86h9vr1xX/PzYU77jArkC1awJNPWhVp2IuyOgCx0L//ba6H+uef5hvt/PPN5aOmTsWZl4fhdOJ+/32idGYMERGJFLVqmWNQTzwRx/r1nHr33XjmzDHnYPzvf8Wz/N96y6xISkCoBzWS1aljLjd10knmIsWffmqW/vPy8AwYwJLx4zHOOcfqKEVERIKraVNYuBDPVVfhcblwfv89vPSSmZy2aGGeeWrYMKujDGvqQY10ffrAjz+aZ4iaPNlc63T0aNz9+rFvzhyroxMREbFGy5a4336b7085hTP++APX7t1w2WXm2FQttxhwSlDF1LVr6ZmIBQXWxSIiImITOfXr43n6aVzR0VaHElFU4hcRERERW1GCKiIiIiK2ogRVRERERGxFCaqIiIiI2IoSVBERERGxFSWoIiIiImIrSlBFRERExFaUoIqIiIiIrShBFRERERFbUYIqIiIiIraiBFVEREREbEUJqoiIiIjYihJUEREREbEVJagiIiIiYitKUEVERETEVpSgioiIiIitKEEVEREREVtRgioiIiIithJldQD+YBgGAOnp6RZHEj4KCgrIzs4mPT2d6Ohoq8MRH6n9Qp/aMPSpDUOf2tC/vHmaN2+rSFgkqBkZGQA0b97c4khEREREpCIZGRnUqlWrwvs4jMqksTbn8XhITU0lMTERh8NhdThhIT09nebNm7Nt2zaSkpKsDkd8pPYLfWrD0Kc2DH1qQ/8yDIOMjAyaNGmC01nxKNOw6EF1Op00a9bM6jDCUlJSkt6UIUztF/rUhqFPbRj61Ib+c6yeUy9NkhIRERERW1GCKiIiIiK2ogRVyhUbG8v48eOJjY21OhSpArVf6FMbhj61YehTG1onLCZJiYiIiEj4UA+qiIiIiNiKElQRERERsRUlqCIiIiJiK0pQRURERMRWlKBKpeXl5dGjRw8cDgcpKSlWhyOVtHnzZq6//npat25NfHw8bdu2Zfz48eTn51sdmlTgtddeo1WrVsTFxdGvXz+WLVtmdUhSSU8++SR9+vQhMTGRBg0aMGLECNatW2d1WFJFTz31FA6Hg9tvv93qUCKKElSptHvuuYcmTZpYHYb46M8//8Tj8fDmm2+yZs0aXnjhBd544w0eeOABq0OTo/j4448ZN24c48ePZ8WKFXTv3p1hw4axZ88eq0OTSvjhhx8YM2YMS5cuZf78+RQUFDB06FCysrKsDk18tHz5ct588026detmdSgRR8tMSaV89dVXjBs3jk8//ZTOnTuzcuVKevToYXVYUkXPPvsskyZNYuPGjVaHIuXo168fffr04dVXXwXA4/HQvHlzbrnlFu677z6LoxNf7d27lwYNGvDDDz9wyimnWB2OVFJmZia9evXi9ddf5/HHH6dHjx68+OKLVocVMdSDKse0e/duRo8ezf/+9z8SEhKsDkf8IC0tjbp161odhpQjPz+fX3/9lcGDBxfd5nQ6GTx4MD/99JOFkUlVpaWlAeg9F2LGjBnD8OHDS70XJXiirA5A7M0wDK699lpuvvlmevfuzebNm60OSarp77//5pVXXuG5556zOhQpx759+3C73TRs2LDU7Q0bNuTPP/+0KCqpKo/Hw+23385JJ51Ely5drA5HKumjjz5ixYoVLF++3OpQIpZ6UCPUfffdh8PhqPDnzz//5JVXXiEjI4P777/f6pDlCJVtw5J27NjBmWeeyUUXXcTo0aMtilwkcowZM4bVq1fz0UcfWR2KVNK2bdu47bbbeP/994mLi7M6nIilMagRau/evezfv7/C+7Rp04aLL76YL774AofDUXS72+3G5XJxxRVX8O677wY6VDmKyrZhTEwMAKmpqQwaNIj+/fszZcoUnE59P7Wj/Px8EhISmD59OiNGjCi6/ZprruHQoUPMmjXLuuDEJ2PHjmXWrFksXLiQ1q1bWx2OVNLMmTO54IILcLlcRbe53W4cDgdOp5O8vLxSf5PAUIIqFdq6dSvp6elFv6empjJs2DCmT59Ov379aNasmYXRSWXt2LGD0047jRNOOIH33ntPH642169fP/r27csrr7wCmGXiFi1aMHbsWE2SCgGGYXDLLbfw2WefsWDBAtq3b291SOKDjIwMtmzZUuq26667jo4dO3LvvfdqqEaQaAyqVKhFixalfq9ZsyYAbdu2VXIaInbs2MGgQYNo2bIlzz33HHv37i36W6NGjSyMTI5m3LhxXHPNNfTu3Zu+ffvy4osvkpWVxXXXXWd1aFIJY8aM4YMPPmDWrFkkJiaya9cuAGrVqkV8fLzF0cmxJCYmlklCa9SoQXJyspLTIFKCKhLm5s+fz99//83ff/9d5kuFCij2dMkll7B3714eeeQRdu3aRY8ePZg7d26ZiVNiT5MmTQJg0KBBpW5/5513uPbaa4MfkEgIUolfRERERGxFsyRERERExFaUoIqIiIiIrShBFRERERFbUYIqIiIiIraiBFVEREREbEUJqoiIiIjYihJUEREREbEVJagiIiIiYitKUEVEbOiOO+5g5MiRVochImIJJagiIja0bNkyevfubXUYIiKW0KlORURsJD8/nxo1alBYWFh0W79+/Vi6dKmFUYmIBFeU1QGIiEixqKgoFi9eTL9+/UhJSaFhw4bExcVZHZaISFApQRURsRGn00lqairJycl0797d6nBERCyhMagiIjazcuVKJaciEtGUoIqI2ExKSooSVBGJaEpQRURsZtWqVfTo0cPqMERELKMEVUTEZjweD+vWrSM1NZW0tDSrwxERCTolqCIiNvP4448zZcoUmjZtyuOPP251OCIiQad1UEVERETEVtSDKiIiIiK2ogRVRERERGxFCaqIiIiI2IoSVBERERGxFSWoIiIiImIrSlBFRERExFaUoIqIiIiIrShBFRERERFbUYIqIiIiIraiBFVEREREbEUJqoiIiIjYihJUEREREbGV/wfJNg+O+arNswAAAABJRU5ErkJggg==\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}}],"execution_count":36},{"cell_type":"markdown","source":"## Оптимальное распределение узлов","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt\n\ndlt_chebyshev = np.array([])\nborders_chebyshev = np.array([])\nfor num_nodes in range(4, 21):\n #print(f\"Количество узлов интерполяции: {num_nodes}\")\n \n t_values = np.linspace(-5, 5, 200)\n f_values = f(t_values)\n \n t_nodes = chebyshev(-5, 5, num_nodes)\n f_nodes = f(t_nodes)\n \n interpolated_values = [L(t, t_nodes, f_nodes) for t in t_values]\n \n if num_nodes in [5, 10, 15, 20]:\n plt.figure(figsize=(8, 6))\n plt.plot(t_values, f_values, label=\"$f(t)$\", color=\"blue\")\n plt.grid(True)\n plt.plot(t_values, interpolated_values, label=f\"$L(t)$, чебышевские узлы при n = {num_nodes}\", color=\"red\")\n plt.scatter(t_nodes, f_nodes, color=\"green\") # Отмечаем узлы\n plt.xlabel(\"$t$\")\n plt.ylabel(\"$f(t)$\")\n plt.legend(loc='upper left')\n plt.savefig(f\"chebyshev-{num_nodes}.png\", dpi=300)\n plt.show()\n \n delta = np.abs(f_values - interpolated_values)\n supremum = np.max(delta)\n dlt_chebyshev = np.append(dlt_chebyshev, supremum)\n #print(f\"Расстояние между функциями - {supremum}\")\n \n max_derivative = float('-inf')\n \n for t in t_values:\n derivative = np.abs(get_derivative(num_nodes, t))\n if derivative > max_derivative:\n max_derivative = derivative\n upper_bound = max_derivative*(10**num_nodes)/(2**(2*num_nodes - 1)*factorial(num_nodes))\n borders_chebyshev = np.append(borders_chebyshev, upper_bound)\n #print(f\"Итоговая верхняя граница погрешности - {upper_bound}\\n\")\n\n# График зависимости расстояния от числа узлов\nplt.scatter(range(4, 21), dlt_chebyshev, label='Численная погрешность интерполяции')\nplt.xlabel(\"n\")\nplt.ylabel(\"$|| f - L_{n-1} ||_\\infty$\")\nplt.grid(True)\nplt.legend()\nplt.savefig(\"chebyshev.png\", dpi=300)\nplt.show()\n\nplt.semilogy(range(4, 21), borders_chebyshev, '-o', label='Аналитическая погрешность интерполяции')\nplt.semilogy(range(4, 21), dlt_chebyshev, '-o', label='Численная погрешность интерполяции')\nplt.grid(True)\nplt.legend(loc='lower left')\nplt.xlabel(\"n\")\nplt.ylabel(\"$|| f - L_{n-1} ||_\\infty$\")\nplt.savefig(\"chebyshev_borders_log.png\", dpi=300)\nplt.show()","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Кусочно-линейная интерполяция","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt\n\ndef piecewise_linear_interpolation(x, t_nodes, f_nodes):\n\n i = np.searchsorted(t_nodes, x) - 1\n i = max(i, 0)\n i = min(i, len(t_nodes) - 2)\n \n x0, x1 = t_nodes[i], t_nodes[i + 1]\n y0, y1 = f_nodes[i], f_nodes[i + 1]\n return y0 + (y1 - y0) / (x1 - x0) * (x - x0)\n\n# Основная программа\ndlt_piecewise = np.array([])\nfor num_nodes in range(4, 21):\n #print(f\"Количество узлов интерполяции: {num_nodes}\")\n \n t_values = np.linspace(-5, 5, 200)\n f_values = f(t_values)\n \n t_nodes = np.linspace(-5, 5, num_nodes)\n f_nodes = f(t_nodes)\n \n interpolated_values = [piecewise_linear_interpolation(t, t_nodes, f_nodes) for t in t_values]\n\n if num_nodes in [5, 10, 15, 20]:\n plt.figure(figsize=(8, 6))\n plt.plot(t_values, f_values, label=\"$f(t)$\", color=\"blue\")\n plt.plot(t_values, interpolated_values, label=f\"$L(t)$, равномерные узлы при n = {num_nodes}\", color=\"red\")\n plt.scatter(t_nodes, f_nodes, color=\"green\")\n plt.xlabel(\"$t$\")\n plt.ylabel(\"$f(t)$\")\n plt.legend(loc='upper left')\n plt.grid(True)\n plt.savefig(f\"piecewise-{num_nodes}.png\", dpi=300)\n plt.show()\n \n delta = np.abs(f_values - interpolated_values)\n supremum = np.max(delta)\n dlt_piecewise = np.append(dlt_piecewise, supremum)\n #print(f\"Расстояние между функциями - {supremum}\\n\")\n\nplt.scatter(range(4, 21), dlt_piecewise, label='Численная погрешность интерполяции')\nplt.xlabel(\"n\")\nplt.ylabel(\"$|| f - L_{n-1} ||_\\infty$\")\nplt.grid(True)\nplt.legend()\nplt.savefig(\"piecewise_border.png\", dpi=300)\nplt.show()","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Сравнение численных погрешностей","metadata":{}},{"cell_type":"code","source":"\nimport matplotlib.pyplot as plt\nimport numpy as np\n\nplt.figure(figsize=(12, 8))\nplt.scatter(np.arange(4, 21), dlt_uniform, label='Численная погрешность при равномерных узлах')\nplt.scatter(np.arange(4, 21), dlt_chebyshev, label='Численная погрешность при чебышевских узлах')\nplt.scatter(np.arange(4, 21), dlt_piecewise, label='Численная погрешность при кусочно-линейной интерполяции')\nplt.xlabel('n')\nplt.ylabel('$ || f - L_{n-1} ||_\\infty $')\nplt.legend()\nplt.grid(True)\nplt.savefig('errors.png')\nplt.show()\n","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Аппроксимация функции ошибок при $x=1$","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt\n\ndef trapezoidal_rule(n, a, b):\n t_nodes = np.linspace(a, b, n)\n f_nodes = f(t_nodes)\n integral = 0.0\n for i in range(n-1):\n integral += (f_nodes[i+1] + f_nodes[i]) * (t_nodes[i+1] - t_nodes[i]) / 2\n return integral\n\ndef erf_approx(n, x):\n t_nodes = np.linspace(0, x, n)\n f_nodes = np.exp(-t_nodes**2)\n integral = 0.0\n \n for i in range(n-1):\n integral += (f_nodes[i+1] + f_nodes[i]) * (t_nodes[i+1] - t_nodes[i]) / 2\n return (2 / np.sqrt(np.pi)) * integral\n\nx = 2\nn_values = [i for i in range(3, 13)]\nerf_values = [erf_approx(n, x) for n in n_values]\n\nplt.figure(figsize=(8, 6))\nplt.scatter(n_values, erf_values, color='red', label='Значение функции erf(2)')\nplt.xlabel('n')\nplt.ylabel('erf(2)')\nplt.grid(True)\nplt.legend(loc='upper left')\nplt.savefig('erf.png', dpi=300)\nplt.show()","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Оптимизация вычисления полинома Лагранжа","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport time\nimport matplotlib.pyplot as plt\n\ndef compute_barycentric_weights(x_nodes):\n n = len(x_nodes)\n w = np.ones(n)\n for i in range(n):\n for j in range(n):\n if i != j:\n w[i] /= (x_nodes[i] - x_nodes[j])\n return w\n\ndef optimize_lagrange(x_nodes, y_nodes, w, x):\n numerator = 0\n denominator = 0\n for i in range(len(x_nodes)):\n if x == x_nodes[i]:\n return y_nodes[i]\n diff = x - x_nodes[i]\n numerator += w[i] * y_nodes[i] / diff\n denominator += w[i] / diff\n return numerator / denominator\n\nlagrange_times = np.array([])\noptimize_lagrange_times = np.array([])\n\nfor n in range(4, 21):\n x_nodes = np.linspace(-5, 5, n)\n y_nodes = np.array([f(x) for x in x_nodes])\n w = compute_barycentric_weights(x_nodes)\n\n x = 2.5 # Точка, в которой вычисляем значение полинома\n\n start_time = time.time()\n res2 = L(x, x_nodes, y_nodes)\n end_time = time.time()\n time_for_L = end_time - start_time\n lagrange_times = np.append(lagrange_times, time_for_L)\n #print(f\"Time for L function: {time_for_L} seconds\")\n\n start_time = time.time()\n result = optimize_lagrange(x_nodes, y_nodes, w, x)\n end_time = time.time()\n time_for_optimize_lagrange = end_time - start_time\n optimize_lagrange_times = np.append(optimize_lagrange_times, time_for_optimize_lagrange)\n #print(f\"Time for optimize_lagrange function: {time_for_optimize_lagrange} seconds\")\n\nplt.semilogy(range(4, 21), lagrange_times, 'o-', label='Функция Лагранжа')\nplt.semilogy(range(4, 21), optimize_lagrange_times, 'o-', label='Оптимизированная функция Лагранжа')\nplt.xlabel('n')\nplt.ylabel('Время выполнения (секунды)')\nplt.legend(loc='upper left')\nplt.grid(True)\nplt.savefig('lagrange_times.png')\nplt.show()","metadata":{"trusted":true},"outputs":[],"execution_count":null}]} \ No newline at end of file diff --git a/educmm-lab2.ipynb b/educmm-lab2.ipynb new file mode 100644 index 0000000..efd72ba --- /dev/null +++ b/educmm-lab2.ipynb @@ -0,0 +1,1415 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a19aec9c", + "metadata": { + "papermill": { + "duration": 0.007761, + "end_time": "2025-04-03T08:33:16.495146", + "exception": false, + "start_time": "2025-04-03T08:33:16.487385", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "# Lab 2" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "fd7f6044", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:16.510526Z", + "iopub.status.busy": "2025-04-03T08:33:16.510138Z", + "iopub.status.idle": "2025-04-03T08:33:17.853046Z", + "shell.execute_reply": "2025-04-03T08:33:17.851923Z" + }, + "papermill": { + "duration": 1.352946, + "end_time": "2025-04-03T08:33:17.855271", + "exception": false, + "start_time": "2025-04-03T08:33:16.502325", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import sys\n", + "from IPython.display import display, Math\n", + "from scipy.special import sici" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9fb74cd8", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:17.870511Z", + "iopub.status.busy": "2025-04-03T08:33:17.869963Z", + "iopub.status.idle": "2025-04-03T08:33:17.874543Z", + "shell.execute_reply": "2025-04-03T08:33:17.873476Z" + }, + "papermill": { + "duration": 0.014006, + "end_time": "2025-04-03T08:33:17.876311", + "exception": false, + "start_time": "2025-04-03T08:33:17.862305", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def dm(eq):\n", + " display(Math(eq))" + ] + }, + { + "cell_type": "markdown", + "id": "d0a3060a", + "metadata": { + "papermill": { + "duration": 0.006445, + "end_time": "2025-04-03T08:33:17.889830", + "exception": false, + "start_time": "2025-04-03T08:33:17.883385", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Исходные функции" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c422b962", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:17.904438Z", + "iopub.status.busy": "2025-04-03T08:33:17.904112Z", + "iopub.status.idle": "2025-04-03T08:33:17.908970Z", + "shell.execute_reply": "2025-04-03T08:33:17.907915Z" + }, + "papermill": { + "duration": 0.013954, + "end_time": "2025-04-03T08:33:17.910554", + "exception": false, + "start_time": "2025-04-03T08:33:17.896600", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def g1(x):\n", + " return x*np.exp(x)\n", + "\n", + "def g2(x):\n", + " return x**2 * np.sin(3*x)\n", + "\n", + "def g3(x):\n", + " return np.sin(np.pi / x)" + ] + }, + { + "cell_type": "markdown", + "id": "411e1cc3", + "metadata": { + "papermill": { + "duration": 0.006679, + "end_time": "2025-04-03T08:33:17.924508", + "exception": false, + "start_time": "2025-04-03T08:33:17.917829", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Численное дифференцирование" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "32cf8551", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:17.939781Z", + "iopub.status.busy": "2025-04-03T08:33:17.939455Z", + "iopub.status.idle": "2025-04-03T08:33:17.944389Z", + "shell.execute_reply": "2025-04-03T08:33:17.943371Z" + }, + "papermill": { + "duration": 0.014508, + "end_time": "2025-04-03T08:33:17.945987", + "exception": false, + "start_time": "2025-04-03T08:33:17.931479", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "x0_g1 = 3\n", + "x0_g3 = 0.01\n", + "eps = sys.float_info.epsilon\n", + "low_border = -16\n", + "high_border = 0\n", + "\n", + "# Границы графика\n", + "h_values = np.logspace(-16, 0, 70, endpoint=True)" + ] + }, + { + "cell_type": "markdown", + "id": "23b8b141", + "metadata": { + "papermill": { + "duration": 0.006617, + "end_time": "2025-04-03T08:33:17.959553", + "exception": false, + "start_time": "2025-04-03T08:33:17.952936", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Формулы численного дифференцирования" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "42410c5c", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:17.974802Z", + "iopub.status.busy": "2025-04-03T08:33:17.974425Z", + "iopub.status.idle": "2025-04-03T08:33:17.979902Z", + "shell.execute_reply": "2025-04-03T08:33:17.978855Z" + }, + "papermill": { + "duration": 0.01524, + "end_time": "2025-04-03T08:33:17.981665", + "exception": false, + "start_time": "2025-04-03T08:33:17.966425", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Первая проивзодная 2-го порядка точности\n", + "def diff2(x_0, h, f):\n", + " return (f(x_0 + h) - f(x_0 - h)) / (2 * h)\n", + "\n", + "# Первая проивзодная 4-го порядка точности\n", + "def diff4(x_0, h, f):\n", + " return (f(x_0 - 2*h) - 8*f(x_0 - h) + 8*f(x_0 + h) - f(x_0 + 2*h))/(12*h)" + ] + }, + { + "cell_type": "markdown", + "id": "615f2ab7", + "metadata": { + "papermill": { + "duration": 0.006655, + "end_time": "2025-04-03T08:33:17.995294", + "exception": false, + "start_time": "2025-04-03T08:33:17.988639", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Аналитические выражения для производных" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "435402c6", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:18.010631Z", + "iopub.status.busy": "2025-04-03T08:33:18.010264Z", + "iopub.status.idle": "2025-04-03T08:33:18.019115Z", + "shell.execute_reply": "2025-04-03T08:33:18.017977Z" + }, + "papermill": { + "duration": 0.018532, + "end_time": "2025-04-03T08:33:18.020762", + "exception": false, + "start_time": "2025-04-03T08:33:18.002230", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def g1_derivative(x):\n", + " return (x+1)*np.exp(x)\n", + "\n", + "def g1_third_derivative(x):\n", + " return (x+3)*np.exp(x)\n", + "\n", + "def g1_fifth_derivative(x):\n", + " return (x+5)*np.exp(x)\n", + "\n", + "# ---------------------------------------------------\n", + "def g2_fourth_derivative(x):\n", + " return 27 * (3 * x**2 * np.sin(3 * x) - 8 * x * np.cos(3 * x) - 4 * np.sin(3 * x))\n", + "\n", + "# ---------------------------------------------------\n", + "def g3_derivative(x):\n", + " return -np.pi * np.cos(np.pi/x) / (x**2)\n", + "\n", + "def g3_third_derivative(x):\n", + " return (np.pi * ((np.pi**2 - 6 * x**2) * np.cos(np.pi/x) + 6* np.pi * x * np.sin(np.pi/x)))/x**6\n", + "\n", + "def g3_fourth_derivative(x):\n", + " return (np.pi *(np.pi *(np.pi**2 - 36*x**2) * np.sin(np.pi/x) - 12*x*(np.pi**2 - 2*x**2)* np.cos(np.pi/x)))/x**8\n", + "\n", + "def g3_fifth_derivative(x):\n", + " return -(np.pi * (20 * np.pi * x *(np.pi**2 - 12 * x**2) * np.sin(np.pi/x) + (120 * x**4 - 120 * np.pi**2 * x**2 + np.pi**4) * np.cos(np.pi/x)))/x**10" + ] + }, + { + "cell_type": "markdown", + "id": "cb00880e", + "metadata": { + "papermill": { + "duration": 0.00679, + "end_time": "2025-04-03T08:33:18.034448", + "exception": false, + "start_time": "2025-04-03T08:33:18.027658", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Численная погрешность методов численного дифференцирования" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2d9b2515", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:18.050046Z", + "iopub.status.busy": "2025-04-03T08:33:18.049688Z", + "iopub.status.idle": "2025-04-03T08:33:18.054293Z", + "shell.execute_reply": "2025-04-03T08:33:18.053234Z" + }, + "papermill": { + "duration": 0.014306, + "end_time": "2025-04-03T08:33:18.055905", + "exception": false, + "start_time": "2025-04-03T08:33:18.041599", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def error_machine_O2(h):\n", + " return eps / h\n", + "\n", + "def error_machine_O4(h):\n", + " return (3 * eps)/(2 * h)" + ] + }, + { + "cell_type": "markdown", + "id": "0067139e", + "metadata": { + "papermill": { + "duration": 0.007042, + "end_time": "2025-04-03T08:33:18.069992", + "exception": false, + "start_time": "2025-04-03T08:33:18.062950", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Погрешность метода численного дифференцирования" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4170163b", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:18.085798Z", + "iopub.status.busy": "2025-04-03T08:33:18.085463Z", + "iopub.status.idle": "2025-04-03T08:33:18.091163Z", + "shell.execute_reply": "2025-04-03T08:33:18.090274Z" + }, + "papermill": { + "duration": 0.015482, + "end_time": "2025-04-03T08:33:18.092760", + "exception": false, + "start_time": "2025-04-03T08:33:18.077278", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def error_method_O2(x_0, h, third_derivative):\n", + " interval_a_b = np.arange(x_0 - h, x_0 + h, 0.1)\n", + " M = [np.abs(third_derivative(x)) for x in interval_a_b]\n", + " return (h**2) * max(M) / 6\n", + "\n", + "def error_method_O4(x_0, h, fifth_derivative):\n", + " interval_a_b = np.arange(x_0 - h, x_0 + h, 0.1)\n", + " M = [np.abs(fifth_derivative(x)) for x in interval_a_b]\n", + " return (h**4) * max(M) / 30" + ] + }, + { + "cell_type": "markdown", + "id": "c87b4d9a", + "metadata": { + "papermill": { + "duration": 0.00636, + "end_time": "2025-04-03T08:33:18.105938", + "exception": false, + "start_time": "2025-04-03T08:33:18.099578", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Численное дифференцирование фунции $g_1(x) = xe^x$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c4d1e48a", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:18.120529Z", + "iopub.status.busy": "2025-04-03T08:33:18.120186Z", + "iopub.status.idle": "2025-04-03T08:33:18.971450Z", + "shell.execute_reply": "2025-04-03T08:33:18.970383Z" + }, + "papermill": { + "duration": 0.860627, + "end_time": "2025-04-03T08:33:18.973323", + "exception": false, + "start_time": "2025-04-03T08:33:18.112696", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "g1_exact = g1_derivative(x0_g1)\n", + "\n", + "g1_diff2 = [diff2(x0_g1, h, g1) for h in h_values]\n", + "g1_diff4 = [diff4(x0_g1, h, g1) for h in h_values]\n", + "\n", + "g1_errors_2 = np.abs(np.array(g1_diff2) - g1_exact)\n", + "g1_errors_4 = np.abs(np.array(g1_diff4) - g1_exact)\n", + "\n", + "h_M_2 = np.logspace(low_border, -6, 70)\n", + "h_M_4 = np.logspace(low_border, -4, 70)\n", + "h_O_2 = np.logspace(-5, high_border, 70)\n", + "h_O_4 = np.logspace(-3, high_border, 70)\n", + "\n", + "O_2 = [error_method_O2(x0_g1, h_value, g1_third_derivative) for h_value in h_O_2]\n", + "O_4 = [error_method_O4(x0_g1, h_value, g1_fifth_derivative) for h_value in h_O_4]\n", + "M_2 = [error_machine_O2(h) for h in h_M_2]\n", + "M_4 = [error_machine_O4(h) for h in h_M_4]\n", + "\n", + "fig = plt.figure(figsize=(8, 5))\n", + "\n", + "plt.loglog(h_values, g1_errors_2, 'o', color='orange')\n", + "plt.loglog(h_values, g1_errors_4, 'o', color='green')\n", + "\n", + "plt.loglog(h_M_2, M_2, '--', color='red', label='$O(h^{-1})$')\n", + "plt.loglog(h_O_2, O_2, color='black', label='$O(h^2)$')\n", + "\n", + "plt.loglog(h_O_4, O_4, color='purple', label='$O(h^4)$')\n", + "plt.loglog(h_M_4, M_4, '--', color='blue', label='$O(h^{-1})$')\n", + "\n", + "plt.legend()\n", + "plt.xlabel('h')\n", + "plt.ylabel('E')\n", + "plt.grid(True)\n", + "fig.tight_layout()\n", + "plt.savefig('g1_error.png')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c6b71eda", + "metadata": { + "papermill": { + "duration": 0.007892, + "end_time": "2025-04-03T08:33:18.989740", + "exception": false, + "start_time": "2025-04-03T08:33:18.981848", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Численное дифференцирование функции $g_3(x) = sin(\\frac{π}{x})$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "bd3c8c9e", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:19.007406Z", + "iopub.status.busy": "2025-04-03T08:33:19.007057Z", + "iopub.status.idle": "2025-04-03T08:33:20.158804Z", + "shell.execute_reply": "2025-04-03T08:33:20.157677Z" + }, + "papermill": { + "duration": 1.162688, + "end_time": "2025-04-03T08:33:20.160580", + "exception": false, + "start_time": "2025-04-03T08:33:18.997892", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "g3_exact = g3_derivative(x0_g3)\n", + "\n", + "g3_diff2 = [diff2(x0_g3, h, g3) for h in h_values]\n", + "g3_diff4 = [diff4(x0_g3, h, g3) for h in h_values]\n", + "\n", + "g3_errors_2 = np.abs(np.array(g3_diff2) - g3_exact)\n", + "g3_errors_4 = np.abs(np.array(g3_diff4) - g3_exact)\n", + "\n", + "h_M_2 = np.logspace(low_border, -9, 70)\n", + "h_M_4 = np.logspace(low_border, -8, 70)\n", + "h_O_2 = np.logspace(-9, -5, 70)\n", + "h_O_4 = np.logspace(-7, -5, 70)\n", + "\n", + "O_2 = [error_method_O2(x0_g3, h_value, g3_third_derivative) for h_value in h_O_2]\n", + "O_4 = [error_method_O4(x0_g3, h_value, g3_fifth_derivative) for h_value in h_O_4]\n", + "M_2 = [error_machine_O2(h) for h in h_M_2]\n", + "M_4 = [error_machine_O4(h) for h in h_M_4]\n", + "\n", + "fig = plt.figure(figsize=(8, 5))\n", + "\n", + "plt.loglog(h_values, g3_errors_2, 'o', color='green')\n", + "plt.loglog(h_values, g3_errors_4, '^', color='orange')\n", + "\n", + "plt.loglog(h_M_2, M_2, '--', color='brown', label='$O(h^{-1})$')\n", + "plt.loglog(h_O_2, O_2, color='black', label='$O(h^2)$')\n", + "\n", + "plt.loglog(h_O_4, O_4, color='purple', label='$O(h^4)$')\n", + "plt.loglog(h_M_4, M_4, '--', color='blue', label='$O(h^{-1})$')\n", + "\n", + "plt.legend()\n", + "plt.xlabel('h')\n", + "plt.ylabel('E')\n", + "plt.grid(True)\n", + "fig.tight_layout()\n", + "plt.savefig('g3_error.png', dpi=400)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "acc3a405", + "metadata": { + "papermill": { + "duration": 0.009188, + "end_time": "2025-04-03T08:33:20.179293", + "exception": false, + "start_time": "2025-04-03T08:33:20.170105", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Численное интегрирование" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "296c21f8", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:20.199935Z", + "iopub.status.busy": "2025-04-03T08:33:20.199570Z", + "iopub.status.idle": "2025-04-03T08:33:20.204213Z", + "shell.execute_reply": "2025-04-03T08:33:20.203144Z" + }, + "papermill": { + "duration": 0.016646, + "end_time": "2025-04-03T08:33:20.205791", + "exception": false, + "start_time": "2025-04-03T08:33:20.189145", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "low_border = 2**3\n", + "high_border = 2**13\n", + "\n", + "def definite_integral_f(a, b, integral_func):\n", + " return integral_func(b) - integral_func(a)" + ] + }, + { + "cell_type": "markdown", + "id": "9f89ded8", + "metadata": { + "papermill": { + "duration": 0.008924, + "end_time": "2025-04-03T08:33:20.224413", + "exception": false, + "start_time": "2025-04-03T08:33:20.215489", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Составная формула Симпсона для интегрирования функции от $a$ до $b$ с $n$ узлами" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "cca578f2", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:20.244167Z", + "iopub.status.busy": "2025-04-03T08:33:20.243762Z", + "iopub.status.idle": "2025-04-03T08:33:20.249527Z", + "shell.execute_reply": "2025-04-03T08:33:20.248322Z" + }, + "papermill": { + "duration": 0.017644, + "end_time": "2025-04-03T08:33:20.251288", + "exception": false, + "start_time": "2025-04-03T08:33:20.233644", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def composite_simpson(a, b, n, f) :\n", + " h = (b - a) / (n-1)\n", + " x = [a + i * h for i in range(n)]\n", + "\n", + " sum_odd = sum(f(x[i]) for i in range(1, n-1, 2))\n", + " sum_even = sum(f(x[i]) for i in range(2, n-1, 2))\n", + "\n", + " integral = (h / 3) * (f(a) + 4 * sum_odd + 2 * sum_even + f(b))\n", + " # print(f\"Ready integral when n = {n} is {integral}\")\n", + " return integral" + ] + }, + { + "cell_type": "markdown", + "id": "7544d91f", + "metadata": { + "papermill": { + "duration": 0.009191, + "end_time": "2025-04-03T08:33:20.269892", + "exception": false, + "start_time": "2025-04-03T08:33:20.260701", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Аналитические значения интегралов" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "85aeabaf", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:20.289906Z", + "iopub.status.busy": "2025-04-03T08:33:20.289515Z", + "iopub.status.idle": "2025-04-03T08:33:20.294758Z", + "shell.execute_reply": "2025-04-03T08:33:20.293514Z" + }, + "papermill": { + "duration": 0.017284, + "end_time": "2025-04-03T08:33:20.296558", + "exception": false, + "start_time": "2025-04-03T08:33:20.279274", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def integral_g1(x):\n", + " return (2 * x * np.sin(3 * x)) / 9 - ((9 * x**2 - 2) * np.cos(3 * x)) / 27\n", + "\n", + "def integral_g3(x):\n", + " s, ci = sici(np.pi / x) # s = Si(z), ci = Ci(z)\n", + " return x * np.sin(np.pi / x) - np.pi * ci" + ] + }, + { + "cell_type": "markdown", + "id": "bd0106e4", + "metadata": { + "papermill": { + "duration": 0.009203, + "end_time": "2025-04-03T08:33:20.315686", + "exception": false, + "start_time": "2025-04-03T08:33:20.306483", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Погрешности численного интегрирования" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "5a224d2d", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:20.335749Z", + "iopub.status.busy": "2025-04-03T08:33:20.335347Z", + "iopub.status.idle": "2025-04-03T08:33:20.341304Z", + "shell.execute_reply": "2025-04-03T08:33:20.340161Z" + }, + "papermill": { + "duration": 0.017879, + "end_time": "2025-04-03T08:33:20.343047", + "exception": false, + "start_time": "2025-04-03T08:33:20.325168", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def error_method(a, b, n, diff_f):\n", + " h = (b - a) / n\n", + " interval_a_b = np.arange(a, b)\n", + " M = [np.abs(diff_f(x_i)) for x_i in interval_a_b]\n", + " return (b - a) * (h**4) * max(M) / 180\n", + "\n", + "def absolute_error(a, b, n, f, definite_integral_f, num_integral_f, integral_gX):\n", + " definite = definite_integral_f(a, b, integral_gX)\n", + " num_integral = num_integral_f(a, b, n, f)\n", + " # print(f\"definite integral: {definite}\")\n", + " # print(f\"num integral: {num_integral}\")\n", + " return np.abs(definite_integral_f(a, b, integral_gX) - num_integral_f(a, b, n, f))" + ] + }, + { + "cell_type": "markdown", + "id": "ae494c57", + "metadata": { + "papermill": { + "duration": 0.009227, + "end_time": "2025-04-03T08:33:20.361653", + "exception": false, + "start_time": "2025-04-03T08:33:20.352426", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Численное интегрирование функции $g_2(x) = x^2sin(3x)$ на отрезке $[0, π]$" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f8bad02a", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:20.381816Z", + "iopub.status.busy": "2025-04-03T08:33:20.381502Z", + "iopub.status.idle": "2025-04-03T08:33:21.695137Z", + "shell.execute_reply": "2025-04-03T08:33:21.693894Z" + }, + "papermill": { + "duration": 1.325817, + "end_time": "2025-04-03T08:33:21.696848", + "exception": false, + "start_time": "2025-04-03T08:33:20.371031", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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PP791fcGCBfG73/0ug8kAAAAAgIpKaRYAAAAAgFKzbt26uPHGG6NRo0YxadKkKCws3G7PoEGDYv369RlIBwAAAABUZEqzAAAAAACkXUFBQdxzzz2Rk5MTQ4cOjQ0bNnzr3k8++SRuvfXWUkwHAAAAAFQGSrMAAAAAAKRNMpmMp556Klq0aBFXXHFFfP7558WaGzVqVKxYsSLN6QAAAACAyqTMlWYHDRoUTz75ZHzyySeZjgIAAAAAwHcwa9asOOmkk+JHP/pRLFmyJKXZhg0b+joxAAAAAFCisjMd4L8NHz48EolERESceOKJ8fLLL2c4EQAAAAAAqfjXv/4VAwYMiIceeijl2fr168fgwYPj0ksvjezsMvclbAAAAACgHCtzT5r9X8lkMlavXp3pGPCd/e1vf4tEIrHbHyeeeGKm/xEAAAAAoFhWr14dubm50aRJk5QLs3vssUfccMMNkZeXF5dffrnCLAAAAABQ4srsVx3/92mzqdiyZUtUqVIlDWkgcw444IBMRwAAAACAncrPz49nnnkmfv7zn6f8MIREIhE9evSIIUOGRIMGDdKUEAAAAACgDJdmk8lkyjPHHHNM5Ofnx1FHHRVHHXVUXH755WlIBqlp0KBB9OrVq9j7lyxZEi+//PLW1z//+c/TEQsAAAAAvrNkMhl///vf4/e//32sWLEi5fkzzjgjRo8eHS1btkxDOgAAAACAbZXZ0uzuKCgoiHnz5sW8efPigQceUJqlTGjUqFFMmDCh2Pt/9rOfbf3zgQceGGeccUY6YgEAAADAd/L3v/89+vbtG++++27Ks61atYoxY8bEaaedloZkAAAAAAA7VqFKsxFFv8prd55S+786d+4c1apV2/q02lNPPbUE08HOffXVV/H4449vfd2tW7eoUqVKBhMBAAAAwLaWLl0a1113XTzxxBMpzzZo0CCGDx8eF198sa97AQAAAAClrsKVZr+rjz76KObNmxePP/54JBKJKCgoyHQkKpGHHnooNm7cuPV1jx49MpgGAAAAALY3ffr0lAuztWvXjuuvvz6uvvrqqFmzZnqCAQAAAADsQlamA5RFyWRy6weUpgceeGDrn48//vho3LhxBtMAAAAAwPYuvvjiaN26dbH2VqlSJXr16hV5eXkxYMAAhVkAAAAAIKM8aXYHEomEwmwZ8N5778Xs2bPjo48+ig0bNkTNmjXj+9//frRt2zYOP/zwTMcrcYsWLYoZM2Zsff3LX/4yg2kAAAAAYMeysrJi7Nixceqpp+5037nnnhsjR46MJk2alFIyAAAAAICdU5plh5YvXx6zZs2KmTNnxqxZs2LWrFmxatWqbfZ07949pkyZUqL35ufnx/333x8TJkyIxYsXf+u+Zs2aRe/evaNnz55RtWrVEs2QKf/5lNk999wzunbtmsE0AAAAAPDtTjnllPjhD38Yzz333HbvHX300TF27Njo2LFjBpIBAAAAAHw7pVkiImL69Okxbdq0rUXZzz77rNQzLFy4MLp27RqLFi3a5d7FixdHr1694q677opHHnkkmjVrVgoJ06egoCB+//vfb339k5/8JGrVqpXBRAAAAACwc6NHj44XXnghCgsLIyJiv/32i9tvvz26du0aiUQiw+kAAAAAALanNEtERIwcOTKefPLJjN0/ffr0OP3002PdunUpzS1cuDCOOeaYeOmll6J9+/ZpSpd+zz33XKxYsWLr6x49emQwDQAAAACVzccffxxVqlSJ/fffv9gzzZs3j1NPPTXeeuut+MlPfhKdO3eOc889N30hAQAAAAC+I6VZMu7DDz+MTp06bVeYzcrKinPOOSc6dOgQDRs2jM8++yxmzJgRjz76aOTn52/dt3bt2jjrrLPinXfeiYYNG5Z2/BLxwAMPbP1zTk5O/M///E8G0wAAAABQWaxbty5Gjx4d48aNiwsuuGCbr1MVR/fu3aNbt25Rq1atyM725WYAAAAAoGzzVUx2qnbt2tGmTZvIycmJyZMnp+WObt26xapVq7ZZO/zww+PJJ5+MI488crv9I0eOjC5dusQ///nPrWtffPFF/OIXv4iXXnopLRnTaeXKlfHMM89sff2LX/wic2EAAAAAqBQKCgpi4sSJcdNNN8Xnn38eERG/+93v4uqrr45WrVoV+5w6depEQUFBumICAAAAAJSorEwHoOyoUaNG/OAHP4hevXrFlClTYuHChbFmzZp47bXXYtCgQWm589FHH43XXnttm7WGDRvGm2++ucPCbETEQQcdFH/729+2++L9yy+/HE888USx7p04cWIkEokS/djdp9z+8Y9/3Prk3KysrOjevftunQMAAAAAu5JMJuOp/8fenUdXXZ7r4352CKOA4IBa0KqAgMgsqCiOLQ5YREFFqxWcp6rVADKLEKagWKVaFUVt62zrUKtIjxYHpKIIIiBTHcAJFBAEmffvj3zLT8qUHbOzQ3Jda7FW9rvf533vc846EpI7nzz/fDRp0iSuuuqqzYXZ/77Xo0ePDKYDAAAAAEgvT5olIiLGjBkT++yzT5QvX75Y7x06dOhWa/fcc0/ss88+O5yrWrVqjBs3Ltq0abPFkyyGDh0anTp1KuqYafXjX3nXvn37QpdvAQAAAGBH3n333cjJydnqh9h/bMKECTF+/Pg4+eSTizEZAAAAAEDxUJolIiIjRc1333033n///S3WjjzyyDj99NMLNN+iRYvo3LlzPPHEE5vXpkyZEtOmTYvmzZvvcLZGjRrRoEGDlDPvyL777pvyzNSpU+ODDz7Y/Lp79+5FGQkAAAAA4pNPPok+ffrEY489VqD9OTk58Ytf/CLKlSuX5mQAAAAAAMWrRJdm16xZE8uWLYuaNWtmOgpp8OOy639ddtllKZ1x6aWXbnXO448/vtPSbJcuXaJLly4p3ZUOP37K7B577BFnnHFGBtMAAAAAUJosW7Yshg4dGnfeeWesW7euwHMffvhhPPzww3HxxRenMR0AAAAAQPHLynSA7UkkEjFnzpzYa6+9ok6dOnHaaafFzTffHI8++mjMnDkzNm7cmOmI/ETjx4/f4nUikYhOnTqldMaJJ54Yu++++xZrr7zyyk+NVizWrl0bjz766ObX559/flSsWDGDiQAAAAAoDdauXRujR4+OunXrxqhRo1IqzCYSibj44ovj5JNPTmNCAAAAAIDMKLFPmk0mk5s//uKLL+LLL7/comRZoUKFaNiwYTRt2nTznzVr1mQiKoWwYsWK+PDDD7dYa9SoUeyxxx4pnZOVlRVHHXVUvPzyy5vXpk2bFitXroxq1aoVSdZ0ef7552Pp0qWbX3tyBwAAAAA/RTKZjCeffDJ69+4dH3/8ccrzJ598cowcOTKaNm2ahnQAAAAAAJlXYkuziURii9c/LtFG5D8tYfr06fHBBx9s94wJEyZEs2bNolatWmnJSOFNmzZtq/+bHnnkkYU6639Ls8lkMqZPnx7HHHPMT8qYbuPGjdv8cbNmzaJFixYZTAMAAADAruyNN96InJyceOedd1KebdasWeTl5cUvf/nLNCQDAAAAACg5Slxpdv/994+FCxdusZZIJLYq0UbklyP/t3j5Y6ecckpEROyzzz7RvHnzLf4ccsghRRuclMyZM2ertYMPPrhQZ21rbu7cuSW6NPvFF1/EK6+8svm1p8wCAAAAUBhz5syJm2++OZ599tmUZ2vXrh25ublxwQUXRLly5Yo+HAAAAABACVPiSrOffvppLFu2LN5///0t/syZMyc2bdq0xd5tFWkjti7TfvXVVzF+/PgYP3785rUqVapEkyZNtijS+rVjxeeTTz7Zau2AAw4o1FnbmivMr58rTo888khs3LgxIiIqVKgQv/71rzOcCAAAAIBdyeLFi2PQoEFx7733bv46U0FVq1Ytbr755rjhhhuiSpUqaUoIAAAAAFDylLjSbEREzZo148QTT4wTTzxx89oPP/wQH3zwQbz//vsxderUeP/99+PDDz+MtWvXbjG7o6fS/tiqVavi3//+d/z73//evJaVlbXdIi5F6+uvv95qbf/99y/UWXXq1CnQ+SXJQw89tPnjjh07xp577pm5MAAAAADsMlavXh133HFHDB8+PFauXJnSbLly5eLKK6+MAQMGRK1atdKUEAAAAACg5CqRpdltqVy5chxxxBFxxBFHbF7buHFjzJo1a4sn0k6bNi1WrFixxWxBi7T/fSKD4mz6LVu2bKu1qlWrFuqsbc0tXbq0UGcVh0mTJsWcOXM2v+7evXux3l+9evVCz/74GzEbNmyIF198sSgiAUDKNmzYsMXH/k4CAKAs+Oijj2LYsGHx7bffpjx75JFHRrdu3aJOnToxZcqUIsvkc3MAACgZfG4OAJREP/4cpaTYZUqz21KuXLlo0qRJNGnSJH7zm99sXv/Pf/6z+Wm0//3zv08e3V6RluKxatWqrdYqVapUqLMqV6681drq1asLdVZxGDdu3OaPf/azn8XJJ59crPen+gSSHSmJ/1EDoGzydxIAAGVBrVq14ocffkhppn79+tGtW7do3LhxRKT/c2efmwMAQMngc3MAgG3bpUuz23PwwQfHwQcfHF26dNm89tVXX21Ron3//ffj448/3upps4q0xWP9+vVbrRW2NLutuXXr1hXqrOJw//33x/3335/pGAAAAADsYqpXrx6dO3eOP/3pTzvdu88++8SFF14YRx99tK95AgAAAAD8P6WyNLst++67b5x66qlx6qmnbl5bsWLFVkXajz76yE9cZUhhv3i/rbn/LUPz/6tWrVqhZ//3KbXZ2WXmPyEAlDD/+/mav5MAACgrOnXqFC+//HIsWbJkm+9XrVo1unbtGh06dIjy5cunPY/PzQEAoGTwuTkAQMGU6c+SqlevHscdd1wcd9xxm9fWrl0bM2bM2FyiJT229QX7VH+13I7mKlSoUKizyoIVK1YUerZ69eqbi7PZ2dnRoUOHoooFACl58cUXN38B0N9JAACUNatWrYrf/OY3W6xVqFAhfvvb30bfvn2jZs2axZbF5+YAAFAy+NwcACiJSuIP8pS8RBlWsWLFOPzww+Pwww/PdJRSrUqVKlutrVmzplBnbas0u63zAQAAAKA0+PWvfx2jR4/e/EP/Xbt2jaFDh8ZBBx2U4WQAAAAAACVbVqYDUDbtscceW619//33hTpr1apVW63tueeehToLAAAAAIpLMpmM559/Pp544omU5rKysiIvLy+OPfbYeOedd+Kxxx5TmAUAAAAAKABPmiUj9tlnn63WFi1aVKiztjVXq1atQp0FAAAAAMXh3XffjZycnJg4cWLsvffeceqpp0b16tULPH/SSSfFiSeeGIlEIo0pAQAAAABKF0+aJSN+/vOfb7X22WefFeqsbc15sgYAAAAAJdEnn3wS559/frRu3TomTpwYERFLliyJESNGpHyWwiwAAAAAQGqUZsmIBg0abLX2n//8p1BnbWtuW+cDAAAAQKYsW7YsevToEQ0aNIjHHntsq/dvv/32WLhwYQaSAQAAAACUHUqzZETz5s23ehLG5MmTC3XW/84lEolo1qxZobMBAAAAQFFZu3ZtjB49OurWrRujRo2KdevWbXPfmjVron///sWcDgAAAACgbFGaJSN23333OOyww7ZYmzVrVixbtiylc5LJZLz99ttbrDVr1iyqVav2kzMCAAAAQGElk8l48skno1GjRnHjjTcW6OtejzzySEyfPr0Y0gEAAAAAlE1Ks2RM+/btt3idTCbjueeeS+mM1157batvOPzvuQAAAABQnN5888046qij4txzz42PP/64wHPJZDLuvffeNCYDAAAAACjblGbJmHPPPXertfvvvz+lM8aOHbvVWteuXQudCQAAAAAKa+7cuXHmmWdGu3bt4t///ndKs7Vr145x48bFXXfdlaZ0AAAAAAAozZIxrVu3jubNm2+xNmnSpHjppZcKND99+vR4+umnt1hr1apVtGjRoqgiAgAAAMBOLVmyJK699tpo3LhxPPvssynNVqtWLXJzc2Pu3LnRrVu3KFeuXHpCAgAAAACgNEtm9e7de6u1K664IpYsWbLDuVWrVkX37t1j/fr1W6z36dOnSPMBAAAAwPasXr06hg4dGnXr1o0//OEPsWHDhgLPlitXLq6++uqYP39+9OnTJ6pUqZLGpAAAAAAARCjNkmHnnHNOtGvXbou1hQsXRtu2bWPWrFnbnFm4cGGccMIJ8f7772+xfsIJJ8RZZ52VtqwAAAAAEBGxcePGePjhh6NBgwbRt2/fWLlyZUrznTp1ipkzZ8Yf/vCHqFWrVppSAgAAAADwv7IzHYCSo3nz5tt9b926dVutPf/88zucufXWW6Njx447vfeRRx6Jli1bxrJlyzavzZ8/P5o0aRIdO3aMdu3axc9+9rP4+uuvY8qUKfHkk09u9YTZPfbYIx566KGd3gUAAAAAP8WECROiR48eMX369JRn27RpE6NGjdrqh8gBAAAAACgeSrNsluoX+pctW7ZF0fV/LV26tEDnHHjggfHCCy/EKaecEt9///3m9U2bNsWzzz4bzz777A7nq1WrFi+++GIccMABBboPAAAAAFI1Y8aM6NmzZ7z88sspzx500EExbNiwOOeccyKRSKQhHQAAAAAABZGV6QAQEXH00UfHpEmTomHDhinNNWrUKN5+++048sgj05QMAAAAgLJuwYIF0bx585QLszVr1ozbb789Zs+eHeeee67CLAAAAABAhinNUmI0adIkpk+fHnfddVc0aNBgh3sbNmwYd911V0yfPj0aN25cTAkBAAAAKIvq1q0bnTp1KvD+ChUqRE5OTixYsCB+97vfRcWKFdMXDgAAAACAAsvOdABKjmQymekIUaFChbj22mvj2muvjXnz5sXUqVNj0aJFsXr16qhSpUrUqVMnWrVqFfXq1ct0VAAAAADKkOHDh8fzzz8fGzZs2OG+8847L3Jzc+Oggw4qpmQAAAAAABSU0iwlVv369aN+/fqZjgEAAAAAUb9+/bjyyitjzJgx23z/uOOOi7y8vGjdunUxJwMAAAAAoKCyMh0AAAAAAGBXMGDAgKhevfoWaw0bNoznnnsuXnvtNYVZAAAAAIASTmkWAAAAACiTNm3alNL+vffeO3r37h0REbVq1Yp77rknZsyYER07doxEIpGOiAAAAAAAFKHsTAcAAAAAAChOy5Yti9zc3Jg+fXq88sorKRVer7/++kgmk3HttddGtWrV0pgSAAAAAICipjQLAAAAAJQJa9eujbvvvjsGDx4cy5Yti4iI5557Ljp16lTgMypXrrz5abMAAAAAAOxasjIdAAAAAAAgnZLJZDzxxBPRqFGjuPHGGzcXZiMievXqFevXr89gOgAAAAAAiovSLAAAAABQar3xxhtx5JFHRteuXePjjz/e6v25c+fGfffdl4FkAAAAAAAUN6VZAAAAAKDUmTNnTpx55plx7LHHxjvvvLPDvYMGDYoVK1YUUzIAAAAAADJFaRYAAAAAKDUWL14c11xzTTRu3DieffbZAs0sWbIkRowYkd5gAAAAAABkXHamAwAAAAAA/FSrV6+OO+64I4YPHx4rV65MabZcuXKxdu3aNCUDAAAAAKCkUJoFAAAAAHZZGzdujD/96U/Rr1+/+Pzzz1Oe79SpUwwfPjwaNGiQhnQAAAAAAJQkSrMAAAAAwC5pwoQJ0aNHj5g+fXrKs23atIlRo0ZFu3bt0pAMAAAAAICSKCvTAQAAAAAAUjFjxow49dRTo3379ikXZg866KB4/PHHY/LkyQqzAAAAAABljNIsAAAAALBL+Pzzz+OSSy6J5s2bx8svv5zSbM2aNeP222+P2bNnx7nnnhuJRCJNKQEAAAAAKKmyMx0AAAAAAGBHVq5cGSNHjozbbrstfvjhh5RmK1SoENddd1306dMnatasmaaEAAAAAADsCpRmAQAAAIASacOGDTF27NgYOHBgLF68OOX58847L3Jzc+Oggw5KQzoAAAAAAHY1SrMAAAAAQIm0adOmGDVqVMqF2eOOOy7y8vKidevWaUoG+dasiZgxI+L99yMWL45Yty6iQoWIWrUiWrSIaNIkolKlTKcEAAAAAP5LaRYAAAAAKJEqVKgQw4cPj7PPPrtA+xs2bBgjRoyIX/3qV5FIJNKcjrJq9eqIxx+PeOCBiHfeidiwYft7s7Mj2rSJuOSSiK5dI6pUKb6cAAAAAMDWsjIdAAAAAABgezp37hxHHXXUDvfUqlUr7rnnnpgxY0Z07NhRYZa0WL06om/fiNq180uwkybtuDAbkf/+pEn5+2vXzp9fvbp48gIAAAAAW1OaBQAAAABKrEQiEaNGjdrme5UrV45+/frF/Pnz48orr4zsbL9Yi/R4442Ipk0jhg6NWL68cGcsX54/36xZ/nkAAAAAQPFTmgUAAAAASrS2bdtG586dN79OJBJx8cUXx7x582Lw4MFRrVq1DKajNEsmIwYPjjjuuIgFC4rmzPnz888bMiT/fAAAAACg+CjNAgAAAADFJplMxvTp01OeGzZsWGRnZ8fJJ58c06ZNiwceeCBq166dhoSQL5mM6NEjYsCAoi+3JpMR/fvnn684CwAAAADFR2kWAAAAACgWb775Zhx11FHRunXr+M9//pPSbP369WPmzJnx8ssvR9OmTdOUEP5/Q4ZE3HZbeu+47baI3Nz03gEAAAAA/P+UZgEAAACAtJo7d26ceeaZ0a5du/j3v/8d69evj969e6d8ziGHHJKGdLC1N96IGDiweO4aMCD/PgAAAAAg/ZRmAQAAAIC0WLJkSVx77bXRuHHjePbZZ7d478knn4x///vfmQkGO7B6dUT37hHJZPHcl0xGXHxx/r0AAAAAQHopzQIAAAAARWr16tUxdOjQqFu3bvzhD3+IDRs2bHNfTk5OJIurmQgFlJsbsWBB8d45f37+vQAAAABAeinNAgAAAABFYuPGjfHwww9HgwYNom/fvrFy5cod7n/zzTe3egItZNLq1RF3352Zu++5x9NmAQAAACDdlGYBAAAAgJ9swoQJ0apVq+jWrVssWrSowHO9evWK9evXpzEZFNzjj0csX56Zu5cti3jiiczcDQAAAABlhdIsAAAAAFBoM2bMiFNPPTXat28f06dPT2n2oIMOisGDB0d2dnaa0kFqHnggs/ePHZvZ+wEAAACgtFOaBQAAAABS9vnnn8cll1wSzZs3j5dffjml2Zo1a8btt98es2fPjnPPPTcSiUSaUkLBrVkT8c47mc0wZUrE2rWZzQAAAAAApZlHOAAAAAAABbZy5coYOXJk3HbbbfHDDz+kNFuhQoW47rrrok+fPlGzZs00JYTCmTEjYsOGzGZYvz4/x+GHZzYHAAAAAJRWSrMAAAAAwE5t2LAhxo4dGwMHDozFixenPH/eeedFbm5uHHTQQWlIBz/d++9nOkG+qVOVZgEAAAAgXZRmAQAAAIDtSiaT8cILL0SvXr3io48+Snn+2GOPjVGjRkXr1q3TkA6KTiG64GmxZEmmEwAAAABA6aU0CwAAAABs07vvvhs5OTkxceLElGcbNGgQI0eOjF/96leRSCTSkA6K1rp1mU6Qb+3aTCcAAAAAgNJLaRYAAAAA2EIymYxLL700HnzwwZRna9WqFbfccktceumlUb58+TSkg/SoUCHTCfJVrJjpBAAAAABQeinNAgAAAABbSCQSsddee6U0U7ly5bjpppuiZ8+eUa1atTQlg/SpVSvTCfLtvXemEwAAAABA6ZWV6QAAAAAAQMnTu3fv2HPPPXe6L5FIRPfu3WPevHkxePBghVl2WS1aZDpBvpYtM50AAAAAAEovpVkAAAAAYCs1atSI/v3773DPySefHNOmTYsHH3wwateuXUzJID2aNInIzvDvZitfPj8HAAAAAJAeSrMAAAAAwDZdddVVUbdu3a3WmzZtGuPHj4+XX345mjZtmoFkUPQqVYpo0yazGVq3jqhYMbMZAAAAAKA0U5oFAAAAALapQoUKMXz48M2va9euHePGjYupU6dG+/btM5gM0uOSSzJ7/6WXZvZ+AAAAACjtlGYBAAAAoAxYsmRJ9O3bN9asWZPSXOfOnePkk0+O3NzcmDt3bnTr1i3KlSuXppSQWV27RtSokZm7a9aMOPfczNwNAAAAAGVFdqYDAAAAAADp88MPP8Qdd9wRw4YNi5UrV0bNmjUjJyenwPOJRCJeeumlSCQSaUwJJUOVKhFXXx0xdGjx333VVfn3AwAAAADp40mzAAAAAFAKbdq0KR5++OE45JBDok+fPrFy5cqIiMjNzY2lS5emdJbCLGVJ374RdesW75316uXfCwAAAACkl9IsAAAAAJQy//znP6NVq1bRrVu3WLRo0RbvLV++PIYMGZKhZFDyVakSMW5cRHF1xROJ/Ps8ZRYAAAAA0k9pFgAAAABKiRkzZsSpp54av/zlL2PatGnb3TdmzJhYsGBB8QWDXUy7dhGDBhXPXbfeGnHMMcVzFwAAAACUdUqzAAAAALCL++KLL+LSSy+N5s2bx8svv7zT/evXr48+ffoUQzLYdfXrF3HTTem946abIvr2Te8dAAAAAMD/T2kWAAAAAHZRK1eujAEDBkT9+vXjgQceiE2bNhV49rnnnovPP/88jelg15ZIROTlRQwenP9xUZ89eHD++UV9NgAAAACwfUqzAAAAALCL2bBhQ/zxj3+MevXqxeDBg2P16tUpzZ9//vnx0UcfRe3atdOUEEqHRCL/ibMTJ0bUq1c0Z9arF/H66/nnKswCAAAAQPFSmgUAAACAXUQymYznn38+mjRpEldddVUsXrw4pfnjjjsupkyZEn/5y1/iwAMPTE9IKIXatYuYPj2iT5+IGjUKd0bNmvnz06dHHHNMkcYDAAAAAApIaRYAAAAAdgFTpkyJ448/Ps4444z46KOPUppt2LBhPP/88/Haa6/F4YcfnqaEULpVqRKRmxvx+ecRDz4Y0bZtRHb2jmfKl8/f9+CDEYsW5c9XqVI8eQEAAACAre3kS3oAAAAAQCZ9/PHH0adPn3j88cdTnq1Vq1YMGjQoLr300sjeWbsPKJAqVSK6d8//s3ZtxIwZEVOnRixZkv+6YsWIvfeOaNkyokmT/NcAAAAAQMngK+UAAAAAUAItXbo0cnNzY8yYMbFu3bqUZitXrhw33XRT9OzZM6pVq5amhEDFihGHH57/BwAAAAAo+ZRmAQAAAKAEWbNmTfzhD3+IIUOGxPLly1OaTSQS0b1797j11lujdu3a6QkIAAAAAAC7KKVZAAAAAChBLr/88vjTn/6U8twpp5wSI0eOjCZNmqQhFQAAAAAA7PqyMh0AAAAAAPj/3XDDDSntb968eUyYMCFeeuklhVkAAAAAANgBpVkAAAAAKEFatmwZF1xwwU731alTJx5++OF477334he/+EUxJAMAAAAAgF2b0iwAAAAAlDBDhgyJihUrbvO96tWrx7Bhw2Lu3Lnxm9/8JrKyfIkPAAAAAAAKwlfUAQAAAKCE+fnPfx7XXXfdFmvZ2dnx29/+NubPnx8333xzVK5cOUPpAAAAAABg16Q0CwAAAABptmnTppRn+vTpE3vssUdERHTu3DlmzZoVd955Z+y9995FHQ8AAAAAAMoEpVkAAAAASJNkMhn/+Mc/omnTpvGvf/0rpdkaNWrEvffeG2+99VY8/fTTUb9+/fSEBAAAAACAMiI70wEAAAAAoDSaOnVq9OjRI1599dWIiMjJyYl33nknsrIK/nPsXbp0SVc8AAAAAAAoczxpFgAAAACK0GeffRYXXnhhtGrVanNhNiLivffei8cffzyDyQAAAAAAoGxTmgUAAACAIrB8+fLo1atXHHLIIfHnP/95m3v69OkTa9asKeZkAAAAAABAhNIsAAAAAPwk69ati9///vdRr169GDlyZKxdu3a7ez/99NMYM2ZMMaYDAAAAAAD+S2kWAAAAAAohmUzGU089FYceemjccMMN8e233xZoLjc3N5YuXZrmdAAAAAAAwP9SmgUAAACAFL311lvRtm3bOOecc2LBggUpzdapUye++OKLNCUDAAAAAAC2R2kWAAAAAApo7ty5cdZZZ8UxxxwTkydPTml2v/32i7Fjx8a0adPisMMOS1NCAAAAAABge7IzHQAAAAAASrolS5bErbfeGn/84x9jw4YNKc3utttu0atXr7jxxhtjt912S1NCAAAAAABgZ5RmAQAAAGA7Vq9eHXfccUcMHz48Vq5cmdJsuXLl4rLLLotbbrkl9tlnnzQlBAAAAAAACkppFgAAAAD+x8aNG+NPf/pT9O/fPxYtWpTyfMeOHWP48OHRqFGjNKQDAAAAAAAKQ2kWAAAAAH5kwoQJ0aNHj5g+fXrKs61bt468vLw47rjj0pAMAAAAAAD4KbIyHQAAAAAASoIZM2bEKaecEu3bt0+5MHvggQfGo48+GpMnT1aYBQAAAACAEsqTZgEAAAAgIt5+++0YP358SjM1a9aMfv36xTXXXBMVK1ZMUzIAAAAAAKAoeNIsAAAAAETExRdfHI0aNSrQ3goVKsSNN94Y8+fPjxtvvFFhFgAAAAAAdgFKswAAAAAQEdnZ2TFy5Mid7uvatWt89NFHcdttt8Uee+xRDMkAAAAAAICioDQLAAAAAP9Phw4d4oQTTtjme8cee2y888478dhjj8VBBx1UzMkAAAAAAICfSmkWAAAAAP6fRCIReXl5W6w1bNgwnnvuufjXv/4VrVu3zlAyAAAAAADgp1KaBQAAAKDU+s9//hOLFy9OaaZVq1bx61//OmrVqhX33HNPzJgxIzp27BiJRCJNKQEAAAAAgOKgNAsAAABAqfPtt9/GjTfeGA0bNowBAwakPD969OiYP39+XHnllZGdnZ2GhAAAAAAAQHFTmgUAAACg1FizZk3k5eVFvXr1YvTo0bF+/foYO3ZszJ49O6Vz9t5776hWrVqaUgIAAAAAAJmgNAsAAADALm/Tpk3x6KOPRsOGDaNnz56xfPnyze9t3LgxevXqlblwAAAAAABAiaA0CwAAAMAu7V//+le0adMmfv3rX8enn366zT0vvPBCTJw4sZiTAQAAAAAAJYnSLAAAAAC7pFmzZsWvfvWrOOGEE+K9997b6f6cnJzYtGlTMSQDAAAAAABKIqVZAAAAAHYpX331VVxxxRXRpEmT+Pvf/17guXfffTeeeOKJNCYDAAAAAABKsuxMBwAAAACAgvj+++/jtttui7y8vFi1alVKs9nZ2XH11VfHL3/5yzSlAwAAAAAASjqlWQAAAABKtA0bNsS4ceNiwIAB8dVXX6U836VLlxg2bFjUq1cvDekAAAAAAIBdhdIsAAAAACVSMpmMf/zjH9GzZ8+YNWtWyvNt27aNUaNGxVFHHZWGdAAAAAAAwK5GaRYAAACAEmfq1KmRk5MTr732Wsqz9erVi+HDh8dZZ50ViUQiDekAAAAAAIBdUVamAwAAAADAf3366adxwQUXRKtWrVIuzO61115x1113xaxZs6Jz584KswAAAAAAwBY8aRYAAACAjFu+fHkMHTo07rzzzli7dm1Ks5UqVYobbrghbr755th9993TlBAAAAAAANjVKc0CAAAAkFH/93//F+ecc04sXbo0pblEIhEXXnhhDBkyJPbff/80pQMAAAAAAEoLpVkAAAAAMurQQw9N+emyv/jFLyIvLy+aN2+enlAAAAAAAECpk5XpAAAAAACUbfvtt1/k5OQUaO9hhx0WL730UrzyyisKswAAAAAAQEqUZgEAAADIuJycnNh33323+/7PfvazeOCBB2LatGlxyimnRCKRKMZ0AAAAAABAaaA0CwAAAEDGVa1aNQYNGrTN9cGDB8fcuXPj4osvjnLlymUgHQAAAAAAUBoozQIAAABQIlx88cXRqFGjiIgoV65cXHXVVTF//vzo169f7LbbbhlOBwAAAAAA7OqUZgEAAAAoUhs3boxx48bFk08+mdJcdnZ25OXlxRlnnBEffvhh3H333bHPPvukKSUAAAAAAFDWZGc6AAAAAAClxyuvvBI9evSIDz74IPbbb7/o0KFDSk+J7dChQ3To0CGNCQEAAAAAgLLKk2YBAAAA+MmmT58eJ598cpx88snxwQcfRETEl19+GbfffnuGkwEAAAAAAORTmgUAAACg0BYtWhTdu3ePFi1axCuvvLLV+yNHjoyvv/46A8kAAAAAAAC2pDQLAAAAQMpWrFgRffv2jUMOOSQeeuihSCaT29z3/fffxy233FK84QAAAAAAALZBaRYAAACAAlu/fn384Q9/iHr16sXQoUPjhx9+2OnM/fffH7Nnzy6GdAAAAAAAANunNAsAAADATiWTyfjb3/4Whx12WFx77bWxZMmSAs9u3Lgx/vKXv6QxHQAAAAAAwM5lZzoAAAAAACXb5MmTo0ePHvHmm2+mPNuoUaMYOXJkdOjQIQ3JAAAAAAAACs6TZgEAAADYpgULFsQ555wTRx11VMqF2X322Sf++Mc/xgcffBCnn356JBKJNKUEAAAAAAAoGE+aBQAAAGAL3377bQwePDjuvvvuWL9+fUqzVapUiZycnMjJyYlq1aqlKSEAAAAAAEDqlGYBAAAAiIiINWvWxJ133hlDhw6N7777LqXZrKysuPjii2PQoEHxs5/9LE0JAQAAAAAACk9pFgAAAKCM27RpUzz22GPRp0+f+Oyzz1KeP+2002LEiBFx2GGHpSEdAAAAAABA0VCaBQAAACjDXnvttcjJyYmpU6emPNuiRYsYNWpUnHjiiWlIBgAAAAAAULSUZgEAAADKqGnTphWq8HrAAQdEbm5unH/++ZGVlZWGZAAAAAAAAEXPdzUAAAAAyqjmzZvHaaedVuD9u+++e4wYMSLmzJkTF1xwgcIsAAAAAACwS/GdDQAAAIAybOTIkTstv2ZnZ8f1118f8+fPj549e0alSpWKKR0AAAAAAEDRUZoFAAAAKMMaN24cl1xyyXbf79KlS8yePTvuuOOO2GuvvYoxGQAAAAAAQNFSmgUAAAAo4wYNGhS77bbbFmtt27aNSZMmxVNPPRX16tXLUDIAAAAAAICiozQLAAAAUMqsW7cupf377bdf5OTkRERE/fr145lnnok333wzjjrqqHTEAwAAAAAAyIjsTAcAAAAAoGh88skn0bdv31iyZEmMHz8+EolEgWdzcnJi3333jUsuuSTKly+fxpQAAAAAAACZoTQLAAAAsItbtmxZDB06NO68887NT5l9+eWX49RTTy3wGVWrVo0rr7wyXREBAAAAAAAyLivTAQAAAAAonLVr18bo0aOjbt26MWrUqM2F2YiInj17xsaNGzOYDgAAAAAAoGRRmgUAAADYxSSTyXjiiSeiUaNGceONN8ayZcu22vPhhx/GQw89VPzhAAAAAAAASiilWQAAAIBdyBtvvBFHHnlkdO3aNT7++OMd7u3fv3+sWrWqmJIBAAAAAACUbEqzAAAAALuAOXPmxJlnnhnHHntsvPPOOwWa+fLLL+P2229PczIAAAAAAIBdg9IsAAAAQAm2ePHiuPrqq6Nx48bx7LPPpjRbtWrVqFq1anqCAQAAAAAA7GKyMx0AAAAAgK2tXr06Ro8eHcOHD4/vv/8+pdly5crFFVdcEQMHDoxatWqlKSEAAAAAAMCuRWkWAAAAoATZuHFjPPLII9G/f//4/PPPU57v1KlTDB8+PBo0aJCGdAAAAAAAALsupVkAAACAEmL8+PHRo0ePmDFjRsqzbdq0iVGjRkW7du3SkAwAAAAAAGDXl5XpAAAAAABl3fTp06N9+/ZxyimnpFyYPfjgg+OJJ56IyZMnK8wCAAAAAADsgNIsAAAAQIYsWrQounXrFi1atIgJEyakNFuzZs0YPXp0zJo1K84555xIJBJpSgkAAAAAAFA6ZGc6AAAAAEBZs2rVqsjNzY3Ro0fHmjVrUpqtUKFCXHfdddGnT5+oWbNmmhICAAAAAACUPkqzAAAAAMWsXLly8Ze//CXlwuz5558fubm5ceCBB6YnGAAAAAAAQCmWlekAAAAAAGVNpUqVIjc3t8D7jz/++JgyZUr85S9/UZgFAAAAAAAoJKVZAAAAgAw4//zzo2XLljvc06hRo3jhhRfi1VdfjcMPP7yYkgEAAAAAAJROSrMAAAAAGZCVlRV5eXnbfG+fffaJe++9Nz744IM4/fTTI5FIFHM6AAAAAACA0kdpFgAAACBDTjzxxDjttNM2v65SpUoMHDgw5s+fH5dffnlkZ2dnMB0AAAAAAEDpojQLAAAAUATWrFkTr7/+espzI0eOjAoVKsRll10W8+fPj1tuuSWqVq2ahoQAAAAAAABlm8eVAAAAAPwEmzZtikcffTT69u0bixcvjrlz58b+++9f4PnGjRvHp59+Gvvuu28aUwIAAAAAAOBJswAAAACF9Oqrr0br1q3jwgsvjM8++yzWrFkT/fr1S/kchVkAAAAAAID0U5oFAAAASNHMmTPj9NNPj5NOOimmTp26xXt/+tOfYtq0aZkJBgAAAAAAwHYpzQIAAAAU0JdffhmXXXZZNG3aNF588cVt7kkmk9GjR49IJpPFnA4AAAAAAIAdUZoFAAAA2Invv/8+Bg4cGPXq1YuxY8fGpk2bdrj/n//8Z4wfP76Y0gEAAAAAAFAQSrMAAAAA27Fhw4a47777ol69enHrrbfG6tWrCzzbs2fPnZZrAQAAAAAAKD7ZmQ4AAAAAUNIkk8l48cUXo2fPnjF79uyU59u2bRujRo2KrCw/r0z6rVkTMWNGxPvvRyxeHLFuXUSFChG1akW0aBHRpElEpUqZTgkAAAAAAJmnNAsAAADwI++++2706NEj/vWvf6U8W79+/RgxYkR06tQpEolE0YeD/2f16ojHH4944IGId96J2LBh+3uzsyPatIm45JKIrl0jqlQpvpwAAAAAAFCSeNwJAAAAQER88skncf7550fr1q1TLszutddeMWbMmJg5c2aceeaZCrOkzerVEX37RtSunV+CnTRpx4XZiPz3J03K31+7dv786tXFkxcAAAAAAEoSpVkAAACgTFu2bFn06NEjGjRoEI899lhKs5UqVYo+ffrEggUL4pprrony5cunKSVEvPFGRNOmEUOHRixfXrgzli/Pn2/WLP88AAAAAAAoS5RmAQAAgDJp7dq1MXr06Khbt26MGjUq1q1bV+DZRCIR3bp1i3nz5kVubm5Ur149jUkp65LJiMGDI447LmLBgqI5c/78/POGDMk/HwAAAAAAyoLsTAcAAAAAKE7JZDKefPLJ6N27d3z88ccpz//yl7+MvLy8aNasWRrSwZaSyYgePSJuuy09Z/fvn//02by8iESi6O8AAAAAAICSRGkWAAAAKDM2btwYxx9/fLz55pspzzZt2jTy8vKiffv2aUgG2zZkSHoKsz92220RNWpE9OuX3nsAAAAAACDTsjIdAAAAAKC4lCtXLlq2bJnSTO3atWPcuHExdepUhVmK1RtvRAwcWDx3DRiQfx8AAAAAAJRmSrMAAABAmdK/f/+oXr36TvdVq1YtcnNzY+7cudGtW7coV65cMaSDfKtXR3TvHpFMFs99yWTExRfn3wsAAAAAAKWV0iwAAABQpuy1117Rp0+f7b6fnZ0d11xzTcyfPz/69OkTVapUKcZ0kC83N2LBguK9c/78/HsBAAAAAKC0UpoFAAAAypzrrrsu9t9//63WzzzzzJg5c2aMGTMmatWqlYFkkP+017vvzszd99zjabMAAAAAAJReSrMAAABAmVO5cuXI/dEjNY844oh444034q9//WsccsghGUwGEY8/HrF8eWbuXrYs4oknMnM3AAAAAACkm9IsAAAAsEubPn16XHLJJbF+/fqU5n79619H586d48knn4y33347jjnmmDQlhNQ88EBm7x87NrP3AwAAAABAumRnOgAAAABAYSxatCj69esXjzzySCSTyWjRokVce+21BZ7PysqKp59+Oo0JIXVr1kS8805mM0yZErF2bUTFipnNAQAAAAAARc2TZgEAAIBdynfffRd9+vSJ+vXrx8MPPxzJZDIiIgYNGhTfffddhtPBTzNjRsSGDZnNsH59fg4AAAAAAChtlGYBAACAXcL69etjzJgxUa9evRg2bFisWbNmi/e/+eabGDFiRIbSQdF4//1MJ8g3dWqmEwAAAAAAQNFTmgUAAABKtGQyGX/961+jcePG8dvf/ja++eab7e4dPXp0LFy4sBjTQdFavDjTCfItWZLpBAAAAAAAUPSUZgEAAIAS6+2334527dpF586dY968eTvdv2bNmujfv38xJIP0WLcu0wnyrV2b6QQAAAAAAFD0lGYBAACAEmf+/Plx9tlnR9u2beOtt95KaXbChAmxcuXKNCWD9KpQIdMJ8lWsmOkEAAAAAABQ9JRmAQAAgBLjm2++ieuvvz4OPfTQePrpp1OarVKlStxyyy0xZ86cqFatWpoSQnrVqpXpBPn23jvTCQAAAAAAoOhlZzoAlDXvvfdePPzww/H666/HwoUL4/vvv49atWpF3bp148wzz4wLLrgg9txzz0zHBAAAKFY//PBD3HnnnTFs2LD47rvvUprNysqKSy65JAYNGhT77bdfmhJC8WjRItMJ8rVsmekEAAAAAABQ9JRmoZisXLkyLr/88nj88ce3em/RokWxaNGimDhxYgwZMiTuueee6NKlSwZSAgAAFK9NmzbFo48+Gn369ImFCxemPH/66afH8OHDo3HjxmlIB8WvSZOI7OyIDRsyl6F8+fwcAAAAAABQ2ijNQjH4/vvvo127djF9+vTNa/vuu2+0a9cuatSoEV988UW8/vrrsXLlyvjmm2/inHPOiT//+c9x/vnnZzA1AABAer366qvRo0ePmDp1asqzrVq1iry8vDjhhBPSkAwyp1KliDZtIiZNylyG1q0jKlbM3P0AAAAAAJAuWZkOAGXBFVdcsbkwm5WVFSNGjIiFCxfGk08+Gffdd1/8/e9/j4ULF8ZFF10UERHJZDK6desWs2fPzmRsAACAtPjwww/jtNNOi5NOOinlwuwBBxwQf/nLX+Kdd95RmKXUuuSSzN5/6aWZvR8AAAAAANJFaRbS7IMPPojHHnts8+vBgwdHz549Izt7ywc977777vHQQw/Fr371q4iIWL9+ffTs2bNYswIAAKTTF198EZdeemk0a9YsXnrppZRmd9999xg5cmTMmTMnzj///MjK8iUNSq+uXSNq1MjM3TVrRpx7bmbuBgAAAACAdPMdJkizJ554IpLJZERE7L333nHTTTftcP/w4cM3f/z3v/895s+fn9Z8AAAAxeWiiy6KBx54IDZt2lTgmfLly8cNN9wQCxYsiB49ekSlSpXSmBBKhipVIq6+OjN3X3VV/v0AAAAAAFAaKc1Cmr399tubPz7xxBOjYsWKO9x/6KGHxs9//vPNr5966qm0ZQMAAChOgwYNSmn/ueeeGx999FGMHj069txzzzSlgpKpb9+IunWL98569fLvBQAAAACA0ip751sgMxYsWBBTp06NhQsXxurVq6NKlSqx//77R8uWLaNucX/X6Cf46quvNn984IEHFmjm5z//eXz66acRETFhwoTo3bt3OqIBAAAUq7Zt20bnzp3jmWee2eG+Y445JkaNGhVHHHFEMSWDkqdKlYhx4yKOOy7i//0Cm7RKJPLv85RZAAAAAABKM6VZtmnRokXx7rvvxpQpU+Ldd9+Nd999N5YuXbrFnosuuigeeuihIr13/fr1cf/998eYMWNi9uzZ293XqFGjuPbaa+Oyyy6L8uXLF2mGkmbmzJmZjgAAAFBkhg0bFs8991xs2LBhq/cOOeSQGDFiRJxxxhmRSCQykA5KlnbtIgYNihgwIP133XprxDHHpP8eAAAAAADIJKVZIiJi8uTJ8corr2wuyv746ajFZebMmXHOOefErFmzdrp39uzZcc0118Tdd98dTz31VDRq1KgYEhbO3nvvvbkA/MknnxRo5r9PmY2IWLx4cSxdujT22GOPdMQDAAAoVvXr14+rrroq7rr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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# n = np.logspace(np.log2(low_border), np.log2(high_border), 12, True, 2, int)\n", + "# h = [(b - a) / n_i for n_i in reversed(n)]\n", + "# n_o = np.logspace(2, 13, 12, True, 2, int)\n", + "# h_o = [(b - a) / n_i for n_i in reversed(n_o)]\n", + "\n", + "a = 0\n", + "b = np.pi\n", + "\n", + "n = np.logspace(np.log2(low_border), np.log2(high_border), 11, True, 2, int) - 1\n", + "h = [(b - a) / (n_i+1) for n_i in reversed(n)]\n", + "n_o = np.logspace(3, 13, 11, True, 2, int) - 1\n", + "h_o = [(b - a) / (n_i+1) for n_i in reversed(n_o)]\n", + "\n", + "E = [absolute_error(a, b, int(n_i), g2, definite_integral_f, composite_simpson, integral_g1) for n_i in reversed(n)]\n", + "O = [error_method(a, b, int(n_i), g2_fourth_derivative) for n_i in reversed(n_o)]\n", + "\n", + "plt.figure(figsize=(8, 5), dpi=350)\n", + "plt.loglog(h, E, 'o', color=\"blue\")\n", + "plt.loglog(h_o, O, linestyle = \"--\", color=\"black\", label=\"$O({h^4})$\")\n", + "plt.xlabel('$h$')\n", + "plt.ylabel('$E$')\n", + "plt.legend(loc='upper left')\n", + "plt.grid()\n", + "plt.tight_layout()\n", + "plt.savefig('g2_integral_uzly.png')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "fe981b52", + "metadata": { + "papermill": { + "duration": 0.013725, + "end_time": "2025-04-03T08:33:21.723970", + "exception": false, + "start_time": "2025-04-03T08:33:21.710245", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Численное интегрирование функции $g_3(x) = sin(\\frac{π}{x})$ на отрезке $[0.005, 1]$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "c628ad26", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:21.749062Z", + "iopub.status.busy": "2025-04-03T08:33:21.748633Z", + "iopub.status.idle": "2025-04-03T08:33:21.753304Z", + "shell.execute_reply": "2025-04-03T08:33:21.752091Z" + }, + "papermill": { + "duration": 0.019278, + "end_time": "2025-04-03T08:33:21.755134", + "exception": false, + "start_time": "2025-04-03T08:33:21.735856", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "a = 0.005\n", + "b = 1" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "1665e5a6", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:21.780166Z", + "iopub.status.busy": "2025-04-03T08:33:21.779745Z", + "iopub.status.idle": "2025-04-03T08:33:23.191394Z", + "shell.execute_reply": "2025-04-03T08:33:23.190296Z" + }, + "papermill": { + "duration": 1.427638, + "end_time": "2025-04-03T08:33:23.194667", + "exception": false, + "start_time": "2025-04-03T08:33:21.767029", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = np.logspace(np.log2(low_border), np.log2(high_border), 11, True, 2, int) - 1\n", + "h = [(b - a) / (n_i+1) for n_i in reversed(n)]\n", + "n_o = np.logspace(3, 13, 11, True, 2, int) - 1\n", + "h_o = [(b - a) / (n_i+1) for n_i in reversed(n_o)]\n", + "\n", + "E = [absolute_error(a, b, int(n_i), g3, definite_integral_f, composite_simpson, integral_g3) for n_i in reversed(n)]\n", + "O = [error_method(a, b, int(n_i), g3_fourth_derivative) for n_i in reversed(n_o)]\n", + "\n", + "plt.figure(figsize=(8, 5), dpi=350)\n", + "plt.loglog(h, E, 'o', color=\"blue\")\n", + "plt.loglog(h_o, O, linestyle = \"--\", color=\"black\", label=\"$O({h^4})$\")\n", + "plt.xlabel('$h$')\n", + "plt.ylabel('$E$')\n", + "plt.legend(loc='upper left')\n", + "plt.grid()\n", + "plt.tight_layout()\n", + "plt.savefig('g3_integral_uzly.png')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "50e49681", + "metadata": { + "papermill": { + "duration": 0.01451, + "end_time": "2025-04-03T08:33:23.223658", + "exception": false, + "start_time": "2025-04-03T08:33:23.209148", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Квадратура Гаусса" + ] + }, + { + "cell_type": "markdown", + "id": "c9978707", + "metadata": { + "papermill": { + "duration": 0.013702, + "end_time": "2025-04-03T08:33:23.251570", + "exception": false, + "start_time": "2025-04-03T08:33:23.237868", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Формула квадратуры Гаусса 5-го порядка точности" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "b2d76a3d", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:23.280860Z", + "iopub.status.busy": "2025-04-03T08:33:23.280526Z", + "iopub.status.idle": "2025-04-03T08:33:23.285436Z", + "shell.execute_reply": "2025-04-03T08:33:23.284473Z" + }, + "papermill": { + "duration": 0.021513, + "end_time": "2025-04-03T08:33:23.286965", + "exception": false, + "start_time": "2025-04-03T08:33:23.265452", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Квадратура Гаусса 5-го порядка точности\n", + "def gauss_quad5(f):\n", + " x = np.array([1.0, 1.0 + np.sqrt(3/5), 1.0 - np.sqrt(3/5)])\n", + " c = np.array([8/9, 5/9, 5/9])\n", + " \n", + " integral = np.sum(c * f(x))\n", + " return integral" + ] + }, + { + "cell_type": "markdown", + "id": "196f734a", + "metadata": { + "papermill": { + "duration": 0.014083, + "end_time": "2025-04-03T08:33:23.315560", + "exception": false, + "start_time": "2025-04-03T08:33:23.301477", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Значение полинома в точке x и вычисление его интеграла" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "40c2e19a", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:23.345077Z", + "iopub.status.busy": "2025-04-03T08:33:23.344707Z", + "iopub.status.idle": "2025-04-03T08:33:23.349200Z", + "shell.execute_reply": "2025-04-03T08:33:23.348385Z" + }, + "papermill": { + "duration": 0.021039, + "end_time": "2025-04-03T08:33:23.350719", + "exception": false, + "start_time": "2025-04-03T08:33:23.329680", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def analytical_integral(poly_coeffs, a=0, b=2):\n", + " integral = 0.0\n", + " for power, coeff in enumerate(poly_coeffs):\n", + " integral += coeff * (b**(power + 1) - a**(power + 1)) / (power + 1)\n", + " return integral" + ] + }, + { + "cell_type": "markdown", + "id": "c6bff63d", + "metadata": { + "papermill": { + "duration": 0.013638, + "end_time": "2025-04-03T08:33:23.378284", + "exception": false, + "start_time": "2025-04-03T08:33:23.364646", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Генерация случайных полиномов" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "544b9d54", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:23.408082Z", + "iopub.status.busy": "2025-04-03T08:33:23.407707Z", + "iopub.status.idle": "2025-04-03T08:33:23.426405Z", + "shell.execute_reply": "2025-04-03T08:33:23.425399Z" + }, + "papermill": { + "duration": 0.035228, + "end_time": "2025-04-03T08:33:23.427824", + "exception": false, + "start_time": "2025-04-03T08:33:23.392596", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle P_0(x) = -5x^0$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_1(x) = -5x^0 + -11x^1$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_2(x) = -5x^0 + -11x^1 + 0x^2$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_3(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_4(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3 + -3x^4$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_5(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3 + -3x^4 + -6x^5$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle P_6(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3 + -3x^4 + -6x^5 + -1x^6$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "analytical_results = []\n", + "gauss_results = []\n", + "absolute_errors = []\n", + "\n", + "max_degree = 6\n", + "random_coef = [int(rand) for rand in 10 * np.random.randn(max_degree+1)]\n", + "for d in range(7):\n", + " display(Math(f'P_{d}(x) = '+ ' + '.join(f'{random_coef[i]}x^{i}' for i in range(0, d + 1))))\n", + "\n", + "for degree in range(max_degree + 1):\n", + " current_coeffs = random_coef[:degree + 1]\n", + " poly = np.polynomial.Polynomial(current_coeffs)\n", + " \n", + " exact = analytical_integral(current_coeffs)\n", + " numerical = gauss_quad5(poly)\n", + " error = np.abs(exact - numerical)\n", + " \n", + " analytical_results.append(round(exact, 3))\n", + " gauss_results.append(round(numerical, 3))\n", + " absolute_errors.append(round(error, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "1c215abd", + "metadata": { + "execution": { + "iopub.execute_input": "2025-04-03T08:33:23.458702Z", + "iopub.status.busy": "2025-04-03T08:33:23.458330Z", + "iopub.status.idle": "2025-04-03T08:33:23.489546Z", + "shell.execute_reply": "2025-04-03T08:33:23.488508Z" + }, + "papermill": { + "duration": 0.048659, + "end_time": "2025-04-03T08:33:23.491293", + "exception": false, + "start_time": "2025-04-03T08:33:23.442634", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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ПолиномыP_0P_1P_2P_3P_4P_5P_6
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Результаты формулы квадратуры Гаусса-10.0-32.0-32.0-32.0-51.2-115.2-133.44
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" + ], + "text/plain": [ + " 0 1 2 3 4 5 \\\n", + "Полиномы P_0 P_1 P_2 P_3 P_4 P_5 \n", + "Результаты аналитической формулы -10.0 -32.0 -32.0 -32.0 -51.2 -115.2 \n", + "Результаты формулы квадратуры Гаусса -10.0 -32.0 -32.0 -32.0 -51.2 -115.2 \n", + "\n", + " 6 \n", + "Полиномы P_6 \n", + "Результаты аналитической формулы -133.486 \n", + "Результаты формулы квадратуры Гаусса -133.44 " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
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ПолиномыP_0P_1P_2P_3P_4P_5P_6
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" + ], + "text/plain": [ + " 0 1 2 3 4 5 6\n", + "Полиномы P_0 P_1 P_2 P_3 P_4 P_5 P_6\n", + "Абсолютная погрешность 0.0 0.0 0.0 0.0 0.0 0.0 0.046" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "polynomial_names = [f'P_{i}' for i in range(7)]\n", + "\n", + "dataframe_results = pd.DataFrame([\n", + " polynomial_names,\n", + " analytical_results,\n", + " gauss_results\n", + "], index=['Полиномы', 'Результаты аналитической формулы', 'Результаты формулы квадратуры Гаусса'])\n", + "\n", + "dataframe_abs = pd.DataFrame([\n", + " polynomial_names,\n", + " absolute_errors\n", + "], index=['Полиномы', 'Абсолютная погрешность'])\n", + "\n", + "display(dataframe_results)\n", + "display(dataframe_abs)" + ] + } + ], + "metadata": { + "kaggle": { + "accelerator": "none", + "dataSources": [], + "dockerImageVersionId": 30918, + "isGpuEnabled": false, + "isInternetEnabled": true, + "language": "python", + "sourceType": "notebook" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + }, + "papermill": { + "default_parameters": {}, + "duration": 10.532706, + "end_time": "2025-04-03T08:33:24.126351", + "environment_variables": {}, + "exception": null, + "input_path": "__notebook__.ipynb", + "output_path": "__notebook__.ipynb", + "parameters": {}, + "start_time": "2025-04-03T08:33:13.593645", + "version": "2.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/educmm-lab3.xpynb b/educmm-lab3.xpynb new file mode 100644 index 0000000..06d7405 Binary files /dev/null and b/educmm-lab3.xpynb differ diff --git a/educmm-lab4.ipynb b/educmm-lab4.ipynb new file mode 100644 index 0000000..b8a18d6 --- /dev/null +++ b/educmm-lab4.ipynb @@ -0,0 +1,680 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b0171fe2", + "metadata": { + "id": "6e-MGk_sYwto", + "papermill": { + "duration": 0.005395, + "end_time": "2025-05-26T12:00:42.929552", + "exception": false, + "start_time": "2025-05-26T12:00:42.924157", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "# Лабораторная работа №4. LU-разложение" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e55ed6ed", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:42.939088Z", + "iopub.status.busy": "2025-05-26T12:00:42.938689Z", + "iopub.status.idle": "2025-05-26T12:00:42.948722Z", + "shell.execute_reply": "2025-05-26T12:00:42.947046Z" + }, + "id": "gsnd8FCUYwtq", + "papermill": { + "duration": 0.016723, + "end_time": "2025-05-26T12:00:42.950660", + "exception": false, + "start_time": "2025-05-26T12:00:42.933937", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "c9cdfebd", + "metadata": { + "id": "TqOkW3yn6CfL", + "papermill": { + "duration": 0.003345, + "end_time": "2025-05-26T12:00:42.958714", + "exception": false, + "start_time": "2025-05-26T12:00:42.955369", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Исходные СЛАУ" + ] + }, + { + "cell_type": "markdown", + "id": "edde8bd8", + "metadata": { + "id": "eaWRRTBS6Ht-", + "papermill": { + "duration": 0.003509, + "end_time": "2025-05-26T12:00:42.966538", + "exception": false, + "start_time": "2025-05-26T12:00:42.963029", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "$A_1x = b_1$:\n", + "\\begin{equation}\n", + "\t\\begin{bmatrix}\n", + "\t\t1 & 1 & 0 & 3 \\\\\n", + "\t\t2 & 1 & -1 & 1 \\\\\n", + "\t\t3 & -1 & -1 & 2 \\\\\n", + "\t\t-1 & 2 & 3 & -1\n", + "\t\\end{bmatrix}\n", + "\t\\begin{bmatrix}\n", + "\t\tx_1 \\\\\n", + "\t\tx_2 \\\\\n", + "\t\tx_3 \\\\\n", + "\t\tx_4\n", + "\t\\end{bmatrix}\n", + "\t=\n", + "\t\\begin{bmatrix}\n", + "\t\t4 \\\\\n", + "\t\t1 \\\\\n", + "\t\t-3 \\\\\n", + "\t\t4\n", + "\t\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "$A_2x = b_2$:\n", + "\\begin{equation}\n", + "\t\\begin{bmatrix}\n", + "\t\t3 & 1 & -3 \\\\\n", + "\t\t6 & 2 & 5 \\\\\n", + "\t\t1 & 4 & -3\n", + "\t\\end{bmatrix}\n", + "\t\\begin{bmatrix}\n", + "\t\tx_1 \\\\\n", + "\t\tx_2 \\\\\n", + "\t\tx_3\n", + "\t\\end{bmatrix}\n", + "\t=\n", + "\t\\begin{bmatrix}\n", + "\t\t-16 \\\\\n", + "\t\t12 \\\\\n", + "\t\t-39\n", + "\t\\end{bmatrix}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "id": "4e2397fc", + "metadata": { + "id": "4RjiYoOFYwtq", + "papermill": { + "duration": 0.00338, + "end_time": "2025-05-26T12:00:42.974269", + "exception": false, + "start_time": "2025-05-26T12:00:42.970889", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## LU-разложение" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "00dfff6f", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:42.984367Z", + "iopub.status.busy": "2025-05-26T12:00:42.984067Z", + "iopub.status.idle": "2025-05-26T12:00:42.990634Z", + "shell.execute_reply": "2025-05-26T12:00:42.989637Z" + }, + "id": "80D9G2G0Ywtr", + "papermill": { + "duration": 0.014196, + "end_time": "2025-05-26T12:00:42.993087", + "exception": false, + "start_time": "2025-05-26T12:00:42.978891", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def lu(A):\n", + " n = A.shape[0]\n", + " U = A.copy()\n", + " L = np.eye(n)\n", + " for i in range(n):\n", + " M = np.eye(n)\n", + "\n", + " for j in range(i+1, n):\n", + " m_i = U[j, i] / U[i, i]\n", + " M[j, i] = -m_i\n", + "\n", + " U = M @ U\n", + " L = L @ np.linalg.inv(M)\n", + " return L, U" + ] + }, + { + "cell_type": "markdown", + "id": "6ec9cd52", + "metadata": { + "id": "-xXPAM5kYwts", + "papermill": { + "duration": 0.004751, + "end_time": "2025-05-26T12:00:43.002932", + "exception": false, + "start_time": "2025-05-26T12:00:42.998181", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Решение СЛАУ с использованием LU-разложения" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a4fa7355", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.011657Z", + "iopub.status.busy": "2025-05-26T12:00:43.011325Z", + "iopub.status.idle": "2025-05-26T12:00:43.017980Z", + "shell.execute_reply": "2025-05-26T12:00:43.016791Z" + }, + "id": "I6zZuT9zYwts", + "papermill": { + "duration": 0.01353, + "end_time": "2025-05-26T12:00:43.020024", + "exception": false, + "start_time": "2025-05-26T12:00:43.006494", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def solve(L, U, b):\n", + " n = L.shape[0]\n", + " y = np.zeros(n)\n", + " for i in range(n):\n", + " y[i] = b[i] - np.dot(L[i, :i], y[:i])\n", + "\n", + " x = np.zeros(n)\n", + " for i in range(n-1, -1, -1):\n", + " x[i] = (y[i] - np.dot(U[i, i+1:], x[i+1:])) / U[i, i]\n", + " return x" + ] + }, + { + "cell_type": "markdown", + "id": "144e122d", + "metadata": { + "id": "zMPnLeRL6tkA", + "papermill": { + "duration": 0.003144, + "end_time": "2025-05-26T12:00:43.026992", + "exception": false, + "start_time": "2025-05-26T12:00:43.023848", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Решение СЛАУ $A_1x = b_1$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "11241f71", + "metadata": { + "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19", + "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5", + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.036794Z", + "iopub.status.busy": "2025-05-26T12:00:43.036450Z", + "iopub.status.idle": "2025-05-26T12:00:43.136912Z", + "shell.execute_reply": "2025-05-26T12:00:43.135576Z" + }, + "id": "dbxDrIfqYwts", + "outputId": "eedc32fe-e354-4603-947a-37d0e57394fe", + "papermill": { + "duration": 0.108266, + "end_time": "2025-05-26T12:00:43.138788", + "exception": false, + "start_time": "2025-05-26T12:00:43.030522", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solve is: [ -1.000000, 2.000000, 0.000000, 1.000000 ]\n" + ] + } + ], + "source": [ + "A1 = np.array([[1., 1., 0., 3.],\n", + " [2., 1., -1., 1.],\n", + " [3., -1., -1., 2.],\n", + " [-1., 2., 3., -1.]])\n", + "b1 = np.array([4., 1., -3., 4.])\n", + "\n", + "L, U = lu(A1)\n", + "# print(\"L:\\n\", L)\n", + "# print(\"U:\\n\", U)\n", + "ans_1 = solve(L, U, b1)\n", + "print(f\"Solve is: [ {ans_1[0]:.6f}, {ans_1[1]:.6f}, {ans_1[2]:.6f}, {ans_1[3]:.6f} ]\")" + ] + }, + { + "cell_type": "markdown", + "id": "e6479df1", + "metadata": { + "id": "Zp1o80eLYwtt", + "papermill": { + "duration": 0.003615, + "end_time": "2025-05-26T12:00:43.146164", + "exception": false, + "start_time": "2025-05-26T12:00:43.142549", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Модифицированная функция LU-разложения" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "54c475c9", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.155575Z", + "iopub.status.busy": "2025-05-26T12:00:43.154704Z", + "iopub.status.idle": "2025-05-26T12:00:43.163273Z", + "shell.execute_reply": "2025-05-26T12:00:43.162006Z" + }, + "id": "ilUYjY2uYwtt", + "papermill": { + "duration": 0.01488, + "end_time": "2025-05-26T12:00:43.165046", + "exception": false, + "start_time": "2025-05-26T12:00:43.150166", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def lu(A, Permute):\n", + " n = A.shape[0]\n", + " U = A.copy()\n", + " L = np.eye(n)\n", + " P = np.eye(n)\n", + "\n", + " for i in range(n):\n", + " if Permute:\n", + " max_idx = np.argmax(np.abs(U[i:, i])) + i\n", + " if max_idx != i:\n", + " U[[i, max_idx], :] = U[[max_idx, i], :]\n", + " P[[i, max_idx], :] = P[[max_idx, i], :]\n", + " if i > 0:\n", + " L[[i, max_idx], :i] = L[[max_idx, i], :i]\n", + "\n", + " M = np.eye(n)\n", + " for j in range(i+1, n):\n", + " m_i = U[j,i] / U[i,i]\n", + " M[j, i] = -m_i\n", + "\n", + " U = M @ U\n", + " L = L @ np.linalg.inv(M)\n", + "\n", + " return L, U, P" + ] + }, + { + "cell_type": "markdown", + "id": "a7df72b9", + "metadata": { + "id": "NqXdkl5fYwtu", + "papermill": { + "duration": 0.003428, + "end_time": "2025-05-26T12:00:43.172590", + "exception": false, + "start_time": "2025-05-26T12:00:43.169162", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Модифицированная функция решения СЛАУ" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "eb7d00ab", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.181226Z", + "iopub.status.busy": "2025-05-26T12:00:43.180948Z", + "iopub.status.idle": "2025-05-26T12:00:43.188210Z", + "shell.execute_reply": "2025-05-26T12:00:43.187079Z" + }, + "id": "_XJZmPHqYwtu", + "papermill": { + "duration": 0.013904, + "end_time": "2025-05-26T12:00:43.190207", + "exception": false, + "start_time": "2025-05-26T12:00:43.176303", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "def solve(L, U, P, b):\n", + " b = P @ b\n", + " n = L.shape[0]\n", + " y = np.zeros(n)\n", + " for i in range(n):\n", + " y[i] = b[i] - np.dot(L[i, :i], y[:i])\n", + "\n", + " x = np.zeros(n)\n", + " for i in range(n-1, -1, -1):\n", + " x[i] = (y[i] - np.dot(U[i, i+1:], x[i+1:])) / U[i, i]\n", + " return x" + ] + }, + { + "cell_type": "markdown", + "id": "abb5725d", + "metadata": { + "id": "4wPzZedyYwtu", + "papermill": { + "duration": 0.003396, + "end_time": "2025-05-26T12:00:43.197774", + "exception": false, + "start_time": "2025-05-26T12:00:43.194378", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Решение СЛАУ $A_2x = b_2$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a03aaca6", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.207494Z", + "iopub.status.busy": "2025-05-26T12:00:43.207184Z", + "iopub.status.idle": "2025-05-26T12:00:43.215774Z", + "shell.execute_reply": "2025-05-26T12:00:43.214371Z" + }, + "id": "UGd1L6_uYwtv", + "outputId": "9c43ee6a-7ad5-4561-90fd-6058c4f55505", + "papermill": { + "duration": 0.015323, + "end_time": "2025-05-26T12:00:43.217345", + "exception": false, + "start_time": "2025-05-26T12:00:43.202022", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solve is: [ 1.000000, -7.000000, 4.000000 ]\n" + ] + } + ], + "source": [ + "A2 = np.array([[3., 1., -3.], [6., 2., 5.], [1., 4., -3.]])\n", + "b2 = np.array([-16., 12., -39.])\n", + "L, U, P = lu(A2, True)\n", + "# print(\"L:\\n\", L)\n", + "# print(\"U:\\n\", U)\n", + "# print(\"P:\\n\", P)\n", + "ans_2 = solve(L,U,P,b2)\n", + "print(f\"Solve is: [ {ans_2[0]:.6f}, {ans_2[1]:.6f}, {ans_2[2]:.6f} ]\")" + ] + }, + { + "cell_type": "markdown", + "id": "dec771fa", + "metadata": { + "id": "kzQVvJK-Ywtv", + "papermill": { + "duration": 0.005275, + "end_time": "2025-05-26T12:00:43.226907", + "exception": false, + "start_time": "2025-05-26T12:00:43.221632", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Log-log график относительной погрешности $E = \\frac{\\|\\hat{x} - \\tilde{x}\\|_\\infty}{\\|\\hat{x}\\|_\\infty}$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4e11a9a1", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.237058Z", + "iopub.status.busy": "2025-05-26T12:00:43.236762Z", + "iopub.status.idle": "2025-05-26T12:00:43.259392Z", + "shell.execute_reply": "2025-05-26T12:00:43.257833Z" + }, + "id": "SUIa1a90Ywtv", + "outputId": "18ace28c-a8d9-4ae8-b1f7-0fdb5b5cf313", + "papermill": { + "duration": 0.031268, + "end_time": "2025-05-26T12:00:43.262442", + "exception": false, + "start_time": "2025-05-26T12:00:43.231174", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solve for FALSE, when p = 0, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 1, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 2, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 3, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 4, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 5, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 6, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 7, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 8, is: 1.000000, -7.000001, 4.000000\n", + "Solve for FALSE, when p = 9, is: 1.000000, -7.000000, 4.000000\n", + "Solve for FALSE, when p = 10, is: 0.999982, -6.999947, 4.000000\n", + "Solve for FALSE, when p = 11, is: 1.000089, -7.000266, 4.000000\n", + "Solve for FALSE, when p = 12, is: 1.000333, -7.000999, 4.000000\n", + "\n", + "Solve for TRUE, when p = 0, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 1, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 2, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 3, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 4, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 5, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 6, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 7, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 8, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 9, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 10, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 11, is: 1.000000, -7.000000, 4.000000\n", + "Solve for TRUE, when p = 12, is: 1.000000, -7.000000, 4.000000\n" + ] + } + ], + "source": [ + "relative_errors_false = []\n", + "relative_errors_true = []\n", + "for p in range(0, 13):\n", + " k = 10**(-p)\n", + " A1 = np.array([[3 + k, 1., -3.], [6., 2., 5.], [1., 4., -3.]])\n", + " b1 = np.array([-16 + k, 12., -39.])\n", + "\n", + " L = np.eye(len(A1))\n", + " L,U,P = lu(A1, False)\n", + " x = solve(L,U,P,b1)\n", + " print(f\"Solve for FALSE, when p = {p}, is: {x[0]:.6f}, {x[1]:.6f}, {x[2]:.6f}\")\n", + " error = np.linalg.norm(ans_2 - x) / np.linalg.norm(ans_2)\n", + " relative_errors_false.append(error)\n", + "\n", + "print()\n", + "for p in range(0, 13):\n", + " k = 10**(-p)\n", + " A1 = np.array([[3 + k, 1., -3.], [6., 2., 5.], [1., 4., -3.]])\n", + " b1 = np.array([-16 + k, 12., -39.])\n", + "\n", + " L = np.eye(len(A1))\n", + " L,U,P = lu(A1, True)\n", + " x = solve(L,U,P,b1)\n", + " print(f\"Solve for TRUE, when p = {p}, is: {x[0]:.6f}, {x[1]:.6f}, {x[2]:.6f}\")\n", + " error = np.linalg.norm(ans_2 - x) / np.linalg.norm(ans_2)\n", + " relative_errors_true.append(error)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "f1eeafa4", + "metadata": { + "execution": { + "iopub.execute_input": "2025-05-26T12:00:43.273202Z", + "iopub.status.busy": "2025-05-26T12:00:43.272878Z", + "iopub.status.idle": "2025-05-26T12:00:44.298708Z", + "shell.execute_reply": "2025-05-26T12:00:44.297579Z" + }, + "id": "pBjDPqvyYwtv", + "outputId": "310fd01f-5f13-4a67-ca26-8e64d81f86d1", + "papermill": { + "duration": 1.032378, + "end_time": "2025-05-26T12:00:44.300492", + "exception": false, + "start_time": "2025-05-26T12:00:43.268114", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(8, 5))\n", + "plt.loglog(range(0,13), relative_errors_false, 's', color=\"green\", label=r'$\\frac{||\\hat{x} - \\tilde{x}||_{\\infty}}{||\\hat{x}||_{\\infty}}$, False')\n", + "plt.loglog(range(0,13), relative_errors_true, 'o', color=\"red\", label=r'$\\frac{||\\hat{x} - \\tilde{x}||_{\\infty}}{||\\hat{x}||_{\\infty}}$, True')\n", + "plt.xlabel('$p$')\n", + "plt.ylabel(\"$E$\")\n", + "plt.grid(True)\n", + "fig.tight_layout()\n", + "plt.savefig('E.png',dpi=350)\n", + "plt.show()" + ] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [ + "HHs70jNEYwtv" + ], + "provenance": [] + }, + "kaggle": { + "accelerator": "none", + "dataSources": [], + "dockerImageVersionId": 31040, + "isGpuEnabled": false, + "isInternetEnabled": true, + "language": "python", + "sourceType": "notebook" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.11" + }, + "papermill": { + "default_parameters": {}, + "duration": 7.337637, + "end_time": "2025-05-26T12:00:44.825729", + "environment_variables": {}, + "exception": null, + "input_path": "__notebook__.ipynb", + "output_path": "__notebook__.ipynb", + "parameters": {}, + "start_time": "2025-05-26T12:00:37.488092", + "version": "2.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}