Monte-Carlo.ipynb

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   "source": [
    "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
    "\n",
    "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your github nickname below:"
   ]
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   "source": [
    "NICKNAME = \"meedovique\""
   ]
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   "source": [
    "---"
   ]
  },
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   "source": [
    "# Метод Монте-Карло в физике"
   ]
  },
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   "source": [
    "Методами Монте-Карло называют множество различных методов в совершенно разных областях от физики до экономики. Основная суть этих методов заключается в использовании случайных величин для получения различных состояний исследуемой системы. "
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   "source": [
    "Одно из частых применений метода Монте-Карло в физике состоит в расчете интегралов. При этом действительно полезным и незаменимым метод становится при работе с большим количеством измерений, когда построение обычных квадратур приводит к чересчур  огромным сеткам. Например, уже в случае 10 измерений, задание обычной равномерной решетки шириной в $2^4 = 16$ узлов, приводит к общей сетке размера $2^{40} \\simeq 10^{12}$. Массив данных float такого размера будет занимать 4ТБ в памяти компьютера. Оперировать такими интегралами стандартными методами становится принципиально невозможно."
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   "cell_type": "code",
   "execution_count": 3,
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.special as sp\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
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   "source": [
    "## Задание 1\n",
    "Вычислим объем многомерной сферы в большом количестве измерений."
   ]
  },
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   "source": [
    "### Задание 1.1 \n",
    "Напишите функцию, вычисляющую точный объем $d$-мерной сферы с помощью явного выражения. \n",
    "Объем многомерной сферы радиуса $R$ в $d$-измерениях дается формулой: \n",
    "$$\n",
    "V_d = \\frac{\\pi^{d/2}} {\\Gamma(1 + d/2)}\n",
    "$$\n",
    "где $\\Gamma(x)$ - гамма функция, значение которой можно получить из scipy.special."
   ]
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   "execution_count": 4,
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   "source": [
    "def getSphereVolumeExact(D, R = 1.0):\n",
    "    \"\"\"\n",
    "    Функция вычисляет значение объема D-мерной сферы радиуса R по явной формуле\n",
    "\n",
    "    --------\n",
    "    Аргументы:\n",
    "    D - int, количество измерений \n",
    "    R = 1 - float, радиус сферы\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    V - float, объем сферы\n",
    "    \"\"\"\n",
    "    V = np.pi**(D / 2) / sp.gamma(1 + D / 2) * R**D\n",
    "    return V"
   ]
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   "source": [
    "1. Проверьте результат для нескольких известных вам значений. \n",
    "2. Построите график V(D)"
   ]
  },
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   "execution_count": 5,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Объем сферы размерности 1 радиуса 2 по формуле выше: 4.0\n",
      "Объем сферы размерности 1 радиуса 2 по известной формуле: 4\n",
      "\n",
      "Объем сферы размерности 2 радиуса 2 по формуле выше: 12.566370614359172\n",
      "Объем сферы размерности 2 радиуса 2 по известной формуле: 12.566370614359172\n",
      "\n",
      "Объем сферы размерности 3 радиуса 2 по формуле выше: 33.51032163829113\n",
      "Объем сферы размерности 3 радиуса 2 по известной формуле: 33.510321638291124\n",
      "\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dVolume = {\n",
    "    1: lambda r: 2 * r,\n",
    "    2: lambda r: np.pi * r**2,\n",
    "    3: lambda r: 4 / 3 * np.pi * r**3\n",
    "}\n",
    "\n",
    "r = 2\n",
    "for i in range(1, 4):\n",
    "    print(f'Объем сферы размерности {i} радиуса {r} по формуле выше: {getSphereVolumeExact(i, r)}')\n",
    "    print(f'Объем сферы размерности {i} радиуса {r} по известной формуле: {dVolume[i](r)}\\n')\n",
    "\n",
    "D = np.linspace(1, 25)\n",
    "V = getSphereVolumeExact(D)\n",
    "\n",
    "plt.figure(figsize = (10, 8))\n",
    "plt.plot(D, V, label=f'$V(D), \\, r = 1$')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "e1f704ef2557c69c68f0ba8306f0a590",
     "grade": false,
     "grade_id": "cell-6746c4683191a10a",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Задание 1.2\n",
    "Напишите функцию, вычисляющую объем сферы методом Монте-Карло на псевдослучайных числах (используя, например `numpy.random.rand`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "7a684a4679d07ffcedf9756be7dc7a70",
     "grade": false,
     "grade_id": "cell-1a0370e3818326f5",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "isInside = lambda p, r: np.sum(p ** 2, axis=1) < r ** 2\n",
    "countInsideNum = lambda points, r: np.count_nonzero(isInside(points, r))\n",
    "\n",
    "def getSphereVolumePseudorandom(N, D, R = 1):\n",
    "    \"\"\"\n",
    "    Функция вычисляет значение объема D-мерной сферы радиуса R методом Монте-Кало на псевдослучайных числах\n",
    "\n",
    "    --------\n",
    "    Аргументы:\n",
    "    N - int, количество случайных точек\n",
    "    D - int, количество измерений \n",
    "    R = 1 - float, радиус сферы\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    V - float, объем сферы\n",
    "    \"\"\"    \n",
    "    points = np.random.uniform(low=-R, high=R, size=(N, D))\n",
    "    NInside = countInsideNum(points, R)\n",
    "    VAll = (2 * R) ** D\n",
    "    V = (NInside / N) * VAll\n",
    "    \n",
    "    return V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "af83d5e086486ba1208528434be0323b",
     "grade": false,
     "grade_id": "cell-470c46d55a104b03",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Постройте график зависимости относительной точности $\\epsilon$ которая достигается при фиксированном $N$ от размерности сферы $D$. Для относительной точности используйте выражение $\\epsilon = (V_{exact} - V_{random})/V_{exact}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "b316d79151ab61c96b0da29d16e959c0",
     "grade": true,
     "grade_id": "cell-bc252a77e4f5fbd7",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000\n",
    "D = np.arange(1, 15)\n",
    "epsList = []\n",
    "\n",
    "for d in D:\n",
    "    eps = abs(getSphereVolumeExact(d) - getSphereVolumePseudorandom(N, d)) / getSphereVolumeExact(d)\n",
    "    epsList.append(eps)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.xlabel('D')\n",
    "plt.ylabel('$\\epsilon$')\n",
    "plt.scatter(D, epsList, label='$\\epsilon(D)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "64d0594d7fc0b8e470108eb2974397c3",
     "grade": false,
     "grade_id": "cell-853f758127514e1d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Задание 1.3\n",
    "Напишите функцию, вычисляющую объем сферы методом Монте-Карло на квазислучайной последовательности Соболя.\n",
    "\n",
    "Для установки библиотеки `sobol_seq`:\n",
    "\n",
    "\n",
    "выполните `pip install sobol_seq` в Jupyter или\n",
    "\n",
    "выполните команду `pip install sobol_seq --user` в командном окне (если вы используете Jupyter Notebook в составе Anaconda откройте Anaconda Prompt и выполните команду pip в ней, после чего перезапустите Jupyter Notebook).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-17T13:15:33.843734Z",
     "start_time": "2022-11-17T13:15:33.527008Z"
    },
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ca2bd60ff215b0c47e8fe9a1f88f2c27",
     "grade": true,
     "grade_id": "cell-cdee67dec70bf876",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "#!pip install sobol_seq <-- uncomment to install sobol_seq\n",
    "import sobol_seq\n",
    "from scipy.stats.qmc import scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "a0708eb7467e9e14de69c825b6267544",
     "grade": false,
     "grade_id": "cell-a4e83154a99b336c",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Используйте функцию `i4_sobol_generate`. Документацию по ней можно получить выполнив следующую строчку кода:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "4dd80d4e49a11c30ff18fa6a94acc980",
     "grade": false,
     "grade_id": "cell-c2e083778576396c",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "sobol_seq.i4_sobol_generate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "fd6332fd33d93a423b00d29d4c5ec2cf",
     "grade": false,
     "grade_id": "cell-a47b8ac1df1c3aa2",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def getSphereVolumeQuasirandom(N, D, R = 1):\n",
    "    \"\"\"\n",
    "    Функция вычисляет значение объема D-мерной сферы радиуса R методом Монте-Кало на квазислучайных числах\n",
    "\n",
    "    --------\n",
    "    Аргументы:\n",
    "    N - int, количество случайных точек\n",
    "    D - int, количество измерений \n",
    "    R = 1 - float, радиус сферы\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    V - float, объем сферы\n",
    "    \"\"\"\n",
    "    points = sobol_seq.i4_sobol_generate(D, N)\n",
    "    NInside = countInsideNum(points, R)\n",
    "    VAll = (2 * R) ** D\n",
    "    V = (NInside / N) * VAll\n",
    "    \n",
    "    return V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "e832833a2abf17f3a31f0b502d0c6269",
     "grade": false,
     "grade_id": "cell-c78358c73e3552e1",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Сравните точность вычисления объема для квазислучайной и псевдослучайной последовательностей, рассчитав  $\\epsilon(D)$, при таком же значении $N$, как в предыдущем задании. Постройте обе зависимости $\\epsilon(D)$ на одном графике в логарифмической шкале по $\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "cea5e5d71d2557210c2c83a3575595a3",
     "grade": true,
     "grade_id": "cell-fa2634c16c9366de",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000\n",
    "D = np.arange(1, 15)\n",
    "epsUniformList = []\n",
    "epsSobolList = []\n",
    "\n",
    "for d in D:\n",
    "    VTrue = getSphereVolumeExact(d)\n",
    "    \n",
    "    eps = abs(VTrue - getSphereVolumePseudorandom(N, d)) / VTrue\n",
    "    epsUniformList.append(eps)\n",
    "    \n",
    "    eps = abs(VTrue - getSphereVolumeQuasirandom(N, d)) / VTrue\n",
    "    epsSobolList.append(eps)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.xlabel('D')\n",
    "plt.ylabel('$\\epsilon$')\n",
    "plt.yscale('log')\n",
    "plt.scatter(D, epsUniformList, label='Uniform $\\epsilon(D)$')\n",
    "plt.scatter(D, epsSobolList, label='Sobol $\\epsilon(D)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "e383870464ab39ce5a420a82b0d9126f",
     "grade": false,
     "grade_id": "cell-e969d95dbed841c4",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Сделайте вывды о работе псевдослучайной и квазислучайной последовательностях. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "df94c0084812a2d9671fe006d76698bd",
     "grade": true,
     "grade_id": "cell-38edaea06714934d",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "заметно, что последовательности Соболя дают немного лучше точность, т.к точки расположены плотнее к друг другу, чем случайный набор чисел"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "fe4e91df7e49b802f59fe84cad36d487",
     "grade": false,
     "grade_id": "cell-5190799a80fee19b",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "# Задание 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "cc52dbc64e89d296d8859c43503ba17c",
     "grade": false,
     "grade_id": "cell-b514f20dc52808b3",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Задание 2.1\n",
    "Вычислите значение интеграла \n",
    "$$\n",
    "\\int d^d\\mathbf{r} \\frac{e^{-\\mathbf{r}^T\\mathbf{r}}}{1 + \\mathbf{r}^T\\mathbf{r}}, \\;\\mathbf{r} = (r_1, r_2, ..., r_d)\n",
    "$$\n",
    "по всему пространству, используя генерацию случайной величины с гауссовой плотностью.\n",
    "Проведите результаты для $d=1,2,3,4,5$, используя разумной количество точек.\n",
    "Для $d=1,2$ сравните с ответом, полученным \\textit{любым} другим способом."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "03b3f3f41ff9c708a754cad6ef9b0e0e",
     "grade": true,
     "grade_id": "cell-1a5d7fa2b658a67f",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "normal\td = 1:\tintegral = 1.3483128274291394\n",
      "normal\td = 2:\tintegral = 1.8749161018588723\n",
      "normal\td = 3:\tintegral = 2.7071362954839997\n",
      "normal\td = 4:\tintegral = 4.000143204259882\n",
      "normal\td = 5:\tintegral = 5.989145670208055\n",
      "quad\td = 1:\tintegral = 1.3432934216467354\n",
      "dblquad\td = 2:\tintegral = 1.873480492462358\n"
     ]
    }
   ],
   "source": [
    "from scipy import integrate\n",
    "\n",
    "func = lambda r: 1 / (1 + np.sum(r**2, axis=1))\n",
    "\n",
    "n = 10000\n",
    "mu = 0\n",
    "sigma = 1 / np.sqrt(2)\n",
    "fD1 = lambda x: np.e ** (-x**2) / (1 + x**2)\n",
    "fD2 = lambda x, y: np.e ** (-x**2 - y**2) / (1 + x**2 + y**2)\n",
    "quad = lambda f: integrate.quad(f, -np.inf, np.inf)[0]\n",
    "dblquad = lambda f: integrate.dblquad(f, -np.inf, np.inf, -np.inf, np.inf)[0]\n",
    "\n",
    "for d in range(1,6):\n",
    "    points = np.random.normal(mu, sigma, size=(N, d))\n",
    "    i = np.pi**(d / 2) * np.sum(func(points)) / N \n",
    "    print(f'normal\\td = {d}:\\tintegral = {i}')\n",
    "\n",
    "print(f'quad\\td = 1:\\tintegral = {quad(fD1)}')\n",
    "print(f'dblquad\\td = 2:\\tintegral = {dblquad(fD2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "ccee63c4b03c4d79f02913b7313ba608",
     "grade": false,
     "grade_id": "cell-ce2fa89765e2cb96",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Задание 2.2\n",
    "Реализуйте функцию, возвращающую выборку случайной величины с плотностью $\\omega(x) \\propto \\sqrt{1-x^2}, x\\in[-1,1]$, используя rejection method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-17T13:05:20.564428Z",
     "start_time": "2022-11-17T13:05:20.558161Z"
    },
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6e0d4d3b87a8503dafd0bb5847b17532",
     "grade": false,
     "grade_id": "cell-7e3e16764a1a98d5",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "w = lambda x: np.sqrt(1 - x**2)\n",
    "\n",
    "def getSample(N):\n",
    "    \"\"\"\n",
    "    Функция возвращает выборку случайных величин с распределнием ~sqrt(1-x^2) \n",
    "\n",
    "    --------\n",
    "    Аргументы:\n",
    "    N - int, количество случайных точек\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    sample - numpy ndarray of float, массив случайных величин размера N\n",
    "    \"\"\"\n",
    "    sample = []\n",
    "    while len(sample) < N:\n",
    "        x = np.random.uniform(low=-1, high=1)\n",
    "        y = np.random.uniform(low=0, high=1)\n",
    "        \n",
    "        if y < w(x):\n",
    "            sample.append(x)  \n",
    "    return sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "b20ba7e8d517e79fc84955c12a4f96ff",
     "grade": false,
     "grade_id": "cell-6e7e433d4b66c555",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Проверьте правильность, сгенерировав достаточно большой sample, и построив гистограмму."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ad5194f981453ca90fb070574e726017",
     "grade": true,
     "grade_id": "cell-bf9f681eae8300e9",
     "locked": false,
     "points": 3,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.hist(getSample(100000), 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "efa058240c57aa7bb6cf5420101cb234",
     "grade": false,
     "grade_id": "cell-b74adc6677b414a1",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "# Задание 3\n",
    "\n",
    "Рассмотрим решетку $n\\times n$, в которой каждой ячейке соответствует спин $\\sigma_i$ равный $+1$ или $-1$. При этом между соседними ячейками существует энергия взаимодействия\n",
    "$$\n",
    "E_i = -J \\sigma_i \\sigma_j\n",
    "$$\n",
    "Тогда энергия каждой ячейки \n",
    "$$\n",
    "E_i = -J \\sigma_i \\sum_j \\sigma_j\n",
    "$$\n",
    "где суммирование подразумевается только по соседним с $i$-ой ячейкой.\n",
    "\n",
    "При нулевой температуре энергитически более выгодным состоянием является состояние, когда все спины одинаково ориентированы. Однако при ненулевой температуре вероятность перехода в более возбужденное состояние пропорциональна $\\sim \\exp(-\\Delta E/ k T)$.\n",
    "\n",
    "Явное численное моделирование такой системы (модели Изинга) является проблематичным, поскольку количество возможных состояний системы $2^N$, где $N$ - общее число узлов, и уже для двумерной сетки $16\\times 16$ это число становится астрономически большим. "
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    "На помощь приходят методы Монте-Карло. Одна из простейших его реализаций (алгоритм Метрополиса — Гастингса):\n",
    "1. Задаем случайное начальное состояние\n",
    "2. Выбираем случайную ячейку\n",
    "3. Переворачиваем её спин и считаем изменение энергии $\\delta E$ данной ячейки.\n",
    "4. Если изменение энергии отрицательное, оставляем спин перевернутым\n",
    "5. Если изменение энергии положительное, оставляем спин перевернутым с вероятностью $\\exp(-\\delta E/kT)$\n",
    "6. Повторяем пункты 2-5 нужное количество раз\n",
    "\n",
    "Спустя достаточно большое количество повторений устанавливается равновесное состояние. "
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    "Реализуем данный алгоритм: \n",
    "1. Задайте начальное случайное расраспределение в виде матрицы из $+1$ и $-1$ размерности $N\\times N$:"
   ]
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   "source": [
    "def getInitialState(N):\n",
    "    '''\n",
    "    Функция задает случайное начальное состояние\n",
    "    ---------\n",
    "    Аргументы:\n",
    "    N - int, линейный размер решетки \n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    state - numpy ndarray of ints, массив состояния системы размера NxN\n",
    "    '''\n",
    "    state = np.random.randint(2, size=(N, N))\n",
    "    state[state == 0] = -1\n",
    "    return state"
   ]
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    "2. Напишите функцию, которая для ячейки $(i,j)$ расчитывает изменение её энергии, если изменить её знак. При этом для простоты предполагаем, во-первых, что $J=1$ (на него отнормируем kT), и во-вторых, что элементы находящиеся на верхней и нижней (левой и правой) границах находятся рядом друг с другом (топология тора).  \n"
   ]
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   "source": [
    "def getDeltaE(i, j, state):\n",
    "    '''\n",
    "    Функция расчитывает и возвращает изменение энергии ячейки (i,j) в случае ее переворота (не меняя состояния state)\n",
    "    \n",
    "    ---------\n",
    "    Аргументы:\n",
    "    i - int, адресс ячейки вдоль оси 0\n",
    "    j - int, адресс ячейки вдоль оси 1\n",
    "    state - numpy ndarray of ints, массив состояния системы размера NxN\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    dE - float, изменение энергии\n",
    "    '''\n",
    "    N = len(state)\n",
    "    iBottom = (i - 1) % N\n",
    "    iTop = (i + 1) % N\n",
    "    jBottom = (j - 1) % N \n",
    "    jTop = (j + 1) % N\n",
    "    neadrStateSum = state[iTop][j] + state[iBottom][j] + state[i][jTop] + state[i][jBottom]\n",
    "    E = -state[i][j] * neadrStateSum\n",
    "    dE = -float(2 * E)\n",
    "    return dE"
   ]
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    "3. Напишите функцию, которая $N^2$ раз для разных случайных $(i,j)$ меняет спин в зависимости от изменения энергии, согласно пунктам 4. и 5. "
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   "source": [
    "def makeFlip(T, state):\n",
    "    '''\n",
    "    Функция N^2 раз переворачивает спин, и принимает решение оставить его перевернутым или нет, согласно правилам 4. и 5.\n",
    "    \n",
    "    ---------\n",
    "    Аргументы:\n",
    "    T - float, положительное число, безразмерный коэфициент, характеризующий температуру, равный kT/J\n",
    "    state - numpy ndarray of ints, массив состояния системы размера NxN\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    state - numpy ndarray of ints, массив нового состояния системы размера NxN\n",
    "    '''\n",
    "    N = len(state)\n",
    "    iList = np.random.randint(0, N, N**2)\n",
    "    jList = np.random.randint(0, N, N**2)\n",
    "    for t in range(N**2):\n",
    "        i = iList[t]\n",
    "        j = jList[t]\n",
    "        dE = getDeltaE(i, j, state)\n",
    "        if dE <= 0:\n",
    "            state[i][j] = -state[i][j]\n",
    "            continue\n",
    "        \n",
    "        w = np.random.uniform(0, 1)\n",
    "        if w <= np.e**(-dE / T):\n",
    "            state[i][j] = -state[i][j]\n",
    "        \n",
    "    return state"
   ]
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    "4. Напишите функцию, которая будет рассчитывать значение энергии всей системы (предполагаем $J=1$)."
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   "source": [
    "def getEnergy(state):\n",
    "    '''\n",
    "    Функция, рассчитывает значение энергии всей системы\n",
    "    ---------\n",
    "    Аргументы:\n",
    "    state - numpy ndarray of ints, массив состояния системы размера NxN\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    E - float, значение энергии системы\n",
    "    '''\n",
    "    E = 0\n",
    "    N = len(state)\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            iBottom = (i - 1) % N\n",
    "            iTop = (i + 1) % N\n",
    "            jBottom = (j - 1) % N \n",
    "            jTop = (j + 1) % N\n",
    "            neadrStateSum = state[iTop][j] + state[iBottom][j] + state[i][jTop] + state[i][jBottom]\n",
    "            E += -state[i][j] * neadrStateSum\n",
    "            \n",
    "    return E"
   ]
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   "source": [
    "5. Напишите функцию, которая будет рассчитывать значение намагниченности всей системы $M=\\sum \\sigma$"
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    "def getMagnetization(state):    \n",
    "    '''\n",
    "    Функция, рассчитывает значение намагниченности всей системы\n",
    "    ---------\n",
    "    Аргументы:\n",
    "    state - numpy ndarray of ints, массив состояния системы размера NxN\n",
    "    --------\n",
    "    Функция возвращает:\n",
    "    M - float, значение намагниченности системы\n",
    "    '''\n",
    "    M = np.sum(state)\n",
    "    return M"
   ]
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   "source": [
    "В следующей ячейке кода зададим начальные параметры: \n",
    "\n",
    "**Nt** - количество точек по температуре, \n",
    "\n",
    "**N** - линейный размер решетки, \n",
    "\n",
    "**eqStep** - количество попыток переворота спина, в течение которых система приводится к равновесному сосотоянию. Обратите внимание, что это число должно увеличиваться пропорционально размеру всей сетки,\n",
    "\n",
    "**steps** - количество попыток переворота спина, в течение которых рассчитывается значения энергии и намагниченности (нужно для усреднения расчитанных значений по ансамблю состояний, близких к равновесному)"
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   "source": [
    "N       = 10         # размер решетки NxN\n",
    "Nt      = 10         # количество точек температуры\n",
    "eqSteps = 150        # количество раз выполнения makeFlip для установления равновесия\n",
    "steps   = 30         # количество раз выполнения makeFlip для усреднения энергии и намагниченности\n",
    "\n",
    "T = np.linspace(0.5, 5, Nt); \n",
    "E, M = np.zeros(Nt), np.zeros(Nt)"
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done              \r"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for t in range(Nt):\n",
    "    print(\"Complete\", t/Nt*100, '%\\r', end='')\n",
    "    \n",
    "    Esum = Msum = 0\n",
    "    state = getInitialState(N)\n",
    "    \n",
    "    for i in range(eqSteps):         # установление статистического равновесия\n",
    "        makeFlip(T[t], state)          \n",
    "\n",
    "    for i in range(steps):           # суммирование по разным состояниям близким к равновеснсому\n",
    "        makeFlip(T[t], state)          \n",
    "        Esum += getEnergy(state)       \n",
    "        Msum += getMagnetization(state) \n",
    "\n",
    "    E[t] = Esum / (steps * N * N)\n",
    "    M[t] = Msum / (steps * N * N)\n",
    "\n",
    "print(\"Done              \\r\", end='')\n",
    "\n",
    "_, ax = plt.subplots(1,2,figsize=(10, 5));\n",
    "\n",
    "ax[0].scatter(T, E)\n",
    "ax[0].set_xlabel(\"Temperature\");\n",
    "ax[0].set_ylabel(\"Energy \");\n",
    "\n",
    "ax[1].scatter(T, abs(M), color = 'blue')\n",
    "ax[1].set_xlabel(\"Temperature\"); \n",
    "ax[1].set_ylabel(\"Magnetization \");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "1fb7063da5118c9fe84ad7ba058f95f5",
     "grade": false,
     "grade_id": "cell-856d7c9bc2ed3bc4",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Интерпретируйте с точки зрения физики полученные графики. Описывают ли они поведение ферромагнетиков и фазовые переходы?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "29e314b20907367c58419147f6573eb4",
     "grade": true,
     "grade_id": "cell-b0c53c58b53735de",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "Из графиков следует вывод, что с ростом температуры намагниченность уменьшается.\n",
    "При повышении температуры возрастает роль теплового движения, что приводит к уменьшению намагниченности\n",
    "фазовый переход упорядоченное-разупорядоченное происходит при температуре Кюри\n",
    "выше этой тепературы ферромагнетик ведёт себя как парамагнетик (подчиняется закону Кюри-Вейса)\n",
    "простешая модель описания энергии взаимодействия $- E_{int} = -A(N_{up}-N_{down})^2$, переход от ферромагнетика к парамагнетику происходит при равенстве среднего значения разности энок нулю, что происходит с ростом температуры"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "83e3a6d5bf845bfae57a49e8eb3e655d",
     "grade": false,
     "grade_id": "cell-a66eaf8d2e060a5a",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Задайте новое сосотояние системы с достаточно большим $N$ и визуализируйте его думя цветами (например с помощью `plt.scatter`). Примените несколько раз к этому сосотоянию функциию makeFlip с низкой и с высокой температурами. Объясните наблюдаемое"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "7fe95d7a138a398d72810b8aa6fc1aa3",
     "grade": false,
     "grade_id": "cell-03dc4ad9f46d8e42",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "N = 64\n",
    "state = getInitialState(N)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "sns.heatmap(state)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "fc631ae525a93d79c509eb1d68d30908",
     "grade": true,
     "grade_id": "cell-48a4ce67380bd407",
     "locked": false,
     "points": 4,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2000x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "times = 10\n",
    "stateHigh = getInitialState(N)\n",
    "stateLow = getInitialState(N)\n",
    "fig, ax = plt.subplots(1, 2, figsize=(20, 8))\n",
    "\n",
    "for _ in range(times):\n",
    "    stateLow = makeFlip(0.5, stateLow)\n",
    "    stateHigh = makeFlip(20, stateHigh)\n",
    "    \n",
    "sns.heatmap(stateHigh, ax=ax[0])\n",
    "sns.heatmap(stateLow, ax=ax[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "9087c7c2f501fcdc5b5fb1d4b67c05d7",
     "grade": true,
     "grade_id": "cell-72a37af61409d074",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "На первом графике при высоких температурах магнетические свойства увеличиваются и появляются большие группы близко раположенных спинов. которые ориентированны одинаково. На втором высокие температуры - происходит обратное."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": true,
   "autocomplete": false,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}