educmm_labs/educmm-lab2.ipynb

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   "source": [
    "# Lab 2"
   ]
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   "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"
   ]
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   "source": [
    "def dm(eq):\n",
    "    display(Math(eq))"
   ]
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   },
   "source": [
    "## Исходные функции"
   ]
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   "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)"
   ]
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   },
   "source": [
    "## Численное дифференцирование"
   ]
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   "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)"
   ]
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   },
   "source": [
    "### Формулы численного дифференцирования"
   ]
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   "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)"
   ]
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   },
   "source": [
    "### Аналитические выражения для производных"
   ]
  },
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   "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"
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    "tags": []
   },
   "source": [
    "### Численная погрешность методов численного дифференцирования"
   ]
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   "source": [
    "def error_machine_O2(h):\n",
    "    return eps / h\n",
    "\n",
    "def error_machine_O4(h):\n",
    "    return (3 * eps)/(2 * h)"
   ]
  },
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   },
   "source": [
    "### Погрешность метода численного дифференцирования"
   ]
  },
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   "id": "4170163b",
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   "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"
   ]
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   "source": [
    "### Численное дифференцирование фунции $g_1(x) = xe^x$"
   ]
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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "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": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "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": {
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,
      "text/plain": [
       "<Figure size 2800x1750 with 1 Axes>"
      ]
     },
     "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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      "text/plain": [
       "<Figure size 2800x1750 with 1 Axes>"
      ]
     },
     "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",
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   "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"
   ]
  },
  {
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    "tags": []
   },
   "source": [
    "### Значение полинома в точке x и вычисление его интеграла"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "40c2e19a",
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   "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"
   ]
  },
  {
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   },
   "source": [
    "### Генерация случайных полиномов"
   ]
  },
  {
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   "execution_count": 20,
   "id": "544b9d54",
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_0(x) = -5x^0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_1(x) = -5x^0 + -11x^1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_2(x) = -5x^0 + -11x^1 + 0x^2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_3(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_4(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3 + -3x^4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_5(x) = -5x^0 + -11x^1 + 0x^2 + 0x^3 + -3x^4 + -6x^5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "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": [
       "<IPython.core.display.Math object>"
      ]
     },
     "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))"
   ]
  },
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   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Полиномы</th>\n",
       "      <td>P_0</td>\n",
       "      <td>P_1</td>\n",
       "      <td>P_2</td>\n",
       "      <td>P_3</td>\n",
       "      <td>P_4</td>\n",
       "      <td>P_5</td>\n",
       "      <td>P_6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Результаты аналитической формулы</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-51.2</td>\n",
       "      <td>-115.2</td>\n",
       "      <td>-133.486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Результаты формулы квадратуры Гаусса</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-32.0</td>\n",
       "      <td>-51.2</td>\n",
       "      <td>-115.2</td>\n",
       "      <td>-133.44</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "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": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Полиномы</th>\n",
       "      <td>P_0</td>\n",
       "      <td>P_1</td>\n",
       "      <td>P_2</td>\n",
       "      <td>P_3</td>\n",
       "      <td>P_4</td>\n",
       "      <td>P_5</td>\n",
       "      <td>P_6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Абсолютная погрешность</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.046</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "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)"
   ]
  }
 ],
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