{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4a525e24-4923-479f-82d7-bad69a76b456",
   "metadata": {},
   "source": [
    "## Задача 2.  Периодичность появления интервалов переворота намагниченности в  $Ф0$ джозефсоновском переходе под воздействием импульса тока\n",
    "### Python-realization \n",
    "Рассмотрим _Python_- реализацию программного кода, на основе которого получены результаты в статье:\n",
    " \n",
    "[1] _P. Kh. Atanasova, S.A. Panayotova, I.R. Rahmonov, Yu. M. Shukrinov, E.V. Zemlyanaya, and M. V. Bashashin_. __Periodicity in the Appearance of Intervals of the Reversal\n",
    "of the Magnetic Moment of a $ϕ_0$ Josephson Junction.__ , JETP Letters, __2019__, Vol. 110, No. 11, pp. 722–726\n",
    "\n",
    "***\n",
    "#### Схема перехода $ϕ_0$: \n",
    "\n",
    "![fig1-SFS2.png](https://disk.jinr.ru/index.php/apps/files_sharing/publicpreview/wBpNftN4cp4L9d3?x=2474&y=958&a=true&file=SFS.png&scalingup=0)\n",
    "\n",
    "\n",
    "* (S) сверхпроводящие слои \n",
    "* (F) ферромагнитный слой\n",
    "* (M) магнитный момент ферромагнитного слоя, ось которого направлена вдоль оси $z$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f42932f-b041-4046-9818-ba37d0c94ae2",
   "metadata": {},
   "source": [
    "### Математическая постановка задачи\n",
    "\n",
    "Основные уравнение представлены в работе [1]. Ниже приведена задача Коши для системы уравнений в безразмерном виде.\n",
    "Динамика магнитного момента $M$ рассматриваемой системы описывается уравнением Ландау–Лифшица–Гильберта:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "&& \\frac{dm_x}{dt}=-\\frac{1}{1+M^2\\alpha^2} \\left\\{ m_y H_z -m_z H_y +\\alpha [m_x  (M,H) - H_x] \\right\\},\\\\\n",
    "&& \\frac{dm_y}{dt}=-\\frac{1}{1+M^2\\alpha^2} \\left\\{ m_z H_x -m_x H_z +\\alpha [m_y  (M,H) - H_y] \\right\\},\\\\\n",
    "&& \\frac{dm_z}{dt}=-\\frac{1}{1+M^2\\alpha^2} \\left\\{ m_x H_y -m_y H_x +\\alpha [m_z  (M,H) - H_z] \\right\\},\n",
    "\\label{eq7}\n",
    "\\tag{7}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "где $ M=[m_x, m_y, m_z] $ -компоненты магнитного момента. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "424824cf-d825-4e32-829e-3cddb52a69d0",
   "metadata": {},
   "source": [
    "Компоненты эффективного поля $H=[H_x,H_y,H_z]$ зависит от джозефсоновской разности фаз $\\phi $  определются следующим образом:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "&& H_x (t)=0,\\\\\n",
    "&& H_y = G r \\sin( \\phi(t)-r m_y(t) ),\\\\\n",
    "&& H_z (t)= m_z(t),\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "при этом уравнение на джозефсоновскую разность фаз $\\phi (t)$ определяется из уранения на электрический ток $I$ определяется через джозефсоновский контакт, измеренный в единицах критического тока $I_c$:\n",
    "\n",
    "$$\n",
    " I= w \\left( \\frac{d\\phi}{dt} - r \\frac{dm_y}{dt}\\right) +\\sin(\\phi- r m_y),\n",
    "$$\n",
    "\n",
    "а именно:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\frac{d\\phi}{dt}= -\\frac{1}{w}\\left( \\sin(\\phi- r m_y) + r \\frac{dm_y}{dt} \\right)+\\frac{1}{w} I, \n",
    "\\label{eq8}\n",
    "\\tag{8}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "с параметрами модели:\n",
    "* G - отношение энергии Джозефсона к энергии магнитной анизотропии;\n",
    "* r - константа спин-орбитального взаимодействия;\n",
    "* $\\alpha$ - диссипация Гилберта;\n",
    "* $\\omega_F$ - частота ферромагнитного резонанса;(не входит в уравнения!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3155eba-fa46-4dd9-af01-da614d055acc",
   "metadata": {},
   "source": [
    "### Начальные условия\n",
    "Начальные условия предполагают, что все компонентны магнитного момента, кроме $m_z$, равны нулю:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "m_x(0)=0, m_y(0)=0, m_z(0)=1, \\phi(0) =0.\n",
    "\\label{eq9}\n",
    "\\tag{9}\n",
    "\\end{eqnarray}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2131f4ba-15ee-4510-8749-d49bd7a47260",
   "metadata": {},
   "source": [
    "### Вид тока\n",
    "\n",
    "Ток $I$ в уравнении (8) представляется в виде прямоугольного импульса:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "I = I(t) = \n",
    "\\begin{cases}\n",
    "   A_s, & t \\in \\left[ t_s - \\Delta t / 2, t_s + \\Delta t / 2 \\right], \\\\\n",
    "   0, & otherwise.\n",
    "\\end{cases}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "* с амплитудой $A_s$, \n",
    "* локализацией $t_s$,\n",
    "* длительностью $\\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3e49d946-02cf-4783-9ea2-25ce857bd4f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import partial\n",
    "from scipy.integrate import solve_ivp\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "sns.set(style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4659b1a-a76a-42c5-911e-434c4c7291db",
   "metadata": {},
   "source": [
    "__Определим функцию импулься тока и построим ее график__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4d071a20-070f-4202-858a-e552d5e19b1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def I_pulse(t, As, t_s, delta_t):\n",
    "    ''' Определяет пимпульс тока. Параметры\n",
    "    As - амплитуда,\n",
    "    t_s -локализация\n",
    "    delta_t -длительность'''\n",
    "    Ipuls = 0\n",
    "    if t_s-1/2*delta_t <= t <= t_s+1/2*delta_t:\n",
    "        Ipuls = As\n",
    "    return Ipuls"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77919f2e-333e-4f99-9499-bcca4a08413b",
   "metadata": {},
   "source": [
    "__Параметры импульса тока и численного решения__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "465c7d9d-60b6-4124-9828-c7bc03dcc916",
   "metadata": {},
   "outputs": [],
   "source": [
    "As = 1.5\n",
    "t_s = 25\n",
    "delta_t = 6\n",
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 100\n",
    "nt = 1000\n",
    "# Массивы точек, в которых находим значения тока\n",
    "y_I = np.zeros([nt])\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "for i in range(nt):\n",
    "    y_I[i] = I_pulse(t_e[i], As, t_s, delta_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "de7b1248-98c5-4d1b-9937-eccf38c1275c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t_e, y_I, label='Прямоугольный импульс тока с ' +\n",
    "         '\\n амплитудой $A_s = $%4.2f' % As +\n",
    "         '\\n локализацией $t_s = $ %i' % t_s +\n",
    "         '\\n шириной $\\Delta_t =$ %4.1f' % delta_t)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$I(t)$', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "859f21c4-48aa-49b0-a558-dadc9a8a1a19",
   "metadata": {},
   "source": [
    "### Определим  правые части уравнений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "70508a96-5357-4b0f-9126-1fc3f18df4c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_sfs(t, S,  G, r,  alpha, As, t_s, delta_t):\n",
    "    ''' Определяет правые части ДУ Задачи 2.\n",
    "    G, r, alpha, omegaF,omegaJ - параметры модели\n",
    "    As, t_s, delta_t - параметры импульма тока\n",
    "    S=[mx, my, mz, phi] - искомая вектор-фунция'''\n",
    "    w = 1\n",
    "    mx = S[0]\n",
    "    my = S[1]\n",
    "    mz = S[2]\n",
    "    ph = S[3]\n",
    "    Hx = 0\n",
    "    Hy = G*r*np.sin(ph-r*my)\n",
    "    Hz = mz\n",
    "    H = [Hx, Hy, Hz]\n",
    "    M = [mx, my, mz]\n",
    "    m2 = np.dot(M, M)\n",
    "    HdM = np.dot(H, M)\n",
    "    alpha2 = -1/(1+alpha*alpha*m2)\n",
    "    Iv = I_pulse(t, As, t_s, delta_t)\n",
    "    dmx = alpha2 * ((my*Hz-mz*Hy) + alpha * (mx*HdM-Hx))\n",
    "    dmy = alpha2 * ((mz*Hx-mx*Hz) + alpha * (my*HdM-Hy))\n",
    "    dmz = alpha2 * ((mx*Hy-my*Hx) + alpha * (mz*HdM-Hz))\n",
    "    dph = r * dmy - 1/w * np.sin(ph-r*my) + Iv/w\n",
    "    dS = [dmx, dmy, dmz, dph]\n",
    "    return dS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36bf73f3-df8e-4d4a-9315-de96491b4673",
   "metadata": {},
   "source": [
    "__Проверяем на правильность__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f8b8285d-bb2e-4606-b5c4-6dc7b65feb48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.0, -0.0, -0.0, 0.0]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = np.array([0, 0, 1, 0])\n",
    "dS = my_sfs(0, s, 0.1, 0.1, 0.1, 1.5, 25, 5)\n",
    "dS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "366e9b47-3bb4-4749-8842-01fc635ed220",
   "metadata": {},
   "source": [
    "### Определим параметры модели"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4db5146b-aeca-498d-81d1-2e7b3985056c",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = 18\n",
    "r = 0.1\n",
    "alpha = 0.1\n",
    "As = 1.5\n",
    "t_s = 25\n",
    "delta_t = 6\n",
    "t0 = 0\n",
    "tf = 200"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6abc5203-e43a-4891-94db-2ac77f504464",
   "metadata": {},
   "source": [
    "__Находим численное решение с использованием библиотекой Scipy__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f975d62c-307f-47b8-b5c3-661b1ffb5261",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 100\n",
    "nt = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ce64913a-2f0f-4691-95d6-1f26d0a1fd25",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = partial(my_sfs, G=G, r=r, alpha=alpha,\n",
    "            As=As, t_s=t_s, delta_t=delta_t)\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "s0 = np.array([0, 0, 1, 0])\n",
    "sol_1 = solve_ivp(f, [t0, tf], s0, t_eval=t_e,\n",
    "                  method='BDF', rtol=1e-8, atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7916fea2-b206-4b68-aa15-dffe8cf0de70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.plot(t_e,y_I,  label= 'Прямоугольный импульс тока')\n",
    "plt.plot(sol_1.t, sol_1.y[2], label= 'Компонента $m_z $ при G=%4.2f' %G)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$m_z(t),~I(t)$', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7eba5c3c-359f-4650-9ae6-0395f08c5915",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Вывод графиков\n",
    "plt.figure(figsize=(18, 6))\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.plot(sol_1.t, sol_1.y[0], label='Компонента $m_x $')\n",
    "plt.xlabel('t', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.plot(sol_1.t, sol_1.y[1], label='Компонента $m_y $')\n",
    "plt.xlabel('t', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.plot(sol_1.t, sol_1.y[2], label='Компонента $m_z $')\n",
    "plt.xlabel('t', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ebe3279-7aac-48ca-b367-1635100b015c",
   "metadata": {},
   "source": [
    "__Проверка условия $|m|=1$__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "38e86dac-2f3a-4e0a-a737-de33c40a0f93",
   "metadata": {},
   "outputs": [],
   "source": [
    "M_1 = 1 - np.sqrt(sol_1.y[0]**2 + sol_1.y[1]**2 + sol_1.y[2]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7bee840e-d3c8-4b25-b7a9-e0049bff0186",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(sol_1.t, M_1, label='Проверка условия $|m|=1 $ при G=%4.2f' % G)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$1-|m(t)|$', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8605e0e-c38d-49e5-9f80-94fb102969c9",
   "metadata": {},
   "source": [
    "### Расчеты при различных значениях параметров\n",
    "\n",
    "Для анализа возможности обращения магнитного момента джозефсоновского перехода $Ф0$ при различных зачениях параметров, проведем расчеты для _G_=8,9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3e975c2c-79e7-403b-ab9c-9e889d52b724",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = 8\n",
    "f = partial(my_sfs, G=G, r=r, alpha=alpha,\n",
    "            As=As, t_s=t_s, delta_t=delta_t)\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "s0 = np.array([0, 0, 1, 0])\n",
    "sol_1 = solve_ivp(f, [t0, tf], s0, t_eval=t_e,\n",
    "                  method='BDF', rtol=1e-8, atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a3b640f5-14f1-4982-8cf6-422d1738f8e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t_e, y_I, label='Прямоугольный импульс тока')\n",
    "plt.plot(sol_1.t, sol_1.y[2], label='Компонента $m_z $ при G=%4.2f' % G)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$I(t), m_z(t)$', size=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f29476f8-364e-44fe-b124-2b0cd167de26",
   "metadata": {},
   "source": [
    "### Проведение расчетов при различных знечениях параметров: плоскость $(\\alpha, G)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c19ade7d-ee5b-49e4-856f-b68a00c4ea3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# количество точек по каждому параметру при значении которых проводим расчеты\n",
    "N = 10\n",
    "G0 = 1\n",
    "delta_G = 1\n",
    "alpha0 = 0.1\n",
    "delta_alpha = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "91834cb3-e6ac-4161-8514-dbf9ccee6b90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpG = np.zeros((N, N, 1)) + 1\n",
    "alpG[1, 1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9511b90d-8661-48c2-a78b-310bbc59f543",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 1)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpG.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4b2505b7-e5fe-4681-8a49-ad061a7384bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 100\n",
    "nt = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e4d164cf-30b4-4242-94ad-34b2af994a04",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20.4 s, sys: 47 ms, total: 20.4 s\n",
      "Wall time: 20.5 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "for j in range(N):\n",
    "    for i in range(N):\n",
    "\n",
    "        G = G0 + delta_G*i\n",
    "        alpha = alpha0+delta_alpha*j\n",
    "        f = partial(my_sfs, G=G, r=r, alpha=alpha, \\\n",
    "                As=As, t_s=t_s, delta_t=delta_t)\n",
    "        t_e = np.linspace(t0, tf, nt)\n",
    "        s0 = np.array([0, 0, 1, 0])\n",
    "        \n",
    "        sol_i = solve_ivp(f, [t0, tf], s0, t_eval=t_e, method='BDF', rtol=1e-8, atol=1e-8) \n",
    "        if sol_i.y[2][nt-1] < 0:\n",
    "            alpG[i, j, 0] =- 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "06f89677-594f-4fac-b64d-6ebf5850b283",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z1 = alpG.reshape(N, N)\n",
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "im = ax.imshow(Z1, cmap='Blues')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d3fa90c7-aea8-4a9e-b35f-6d12d34a761c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_16340/2074255536.py:5: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
      "  fig.colorbar(pos, ax=ax1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(8, 8))\n",
    "# mask out the negative and positve values, respectively\n",
    "Zpos = np.ma.masked_less(alpG[:, :, 0], 0)\n",
    "pos = ax1.imshow(Zpos, cmap='Blues', interpolation='none')\n",
    "fig.colorbar(pos, ax=ax1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81a0a085-1ca2-42aa-8e51-7070ceb21221",
   "metadata": {},
   "source": [
    "__Требуется параллелизация: можно провести расчеты для каждого набора параметров независимо__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b92296ee-b63b-4f40-8e7b-66ae05c59623",
   "metadata": {},
   "source": [
    "### Параллельная реализация"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "19e715ed-4270-41e4-bcf4-652e6691b90f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocessing as mp\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "99cebc5b-ed49-49a8-8ca9-94dd55461105",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cpu: 80\n"
     ]
    }
   ],
   "source": [
    "print(f\"Number of cpu: {mp.cpu_count()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "43616d7a-085b-4910-92ac-9ae953df0b05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_cpu = mp.cpu_count()\n",
    "n_cpu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f9690fb-6daf-4594-b7b8-cc4206f63918",
   "metadata": {},
   "source": [
    "### Пример использования библиотеки Joblib "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "20c6e68e-2b94-4125-a032-ed32c8b8dd5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from joblib import Parallel, delayed\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def random_square(seed):\n",
    "    np.random.seed(seed)\n",
    "    random_num = np.random.randint(0, 10)\n",
    "    return random_num**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0e1ac6fa-ff90-48ff-8631-4d9e704c3cee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 0.41432976722717285 s\n"
     ]
    }
   ],
   "source": [
    "time_s = time.time()\n",
    "results = Parallel(n_jobs=1)(delayed(random_square)(i) for i in range(10000))\n",
    "time_f = time.time()\n",
    "print(f'Execution time {time_f - time_s} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "49e343fe-3914-47e5-8b31-ca50e961daf4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 0.860107421875 s\n"
     ]
    }
   ],
   "source": [
    "time_s = time.time()\n",
    "results = Parallel(n_jobs=4)(delayed(random_square)(i) for i in range(10000))\n",
    "time_f = time.time()\n",
    "print(f'Execution time {time_f - time_s} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dab444f-7941-40dc-ac2f-c043c5a42ad4",
   "metadata": {},
   "source": [
    "### Нахождение решений задачи при различных значениях параметров в параллельном режиме"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7b847805-fd5a-42d6-b388-476286a9ee4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10\n",
    "G0 = 1\n",
    "delta_G = 1\n",
    "alpha0 = 0.1\n",
    "delta_alpha = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5088a912-b47c-4b0d-8d72-f8ebe4887c1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpG = np.zeros((N, N, 1)) + 1\n",
    "alpG[1, 1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c3f0f764-f5e5-4f8c-a422-d59e8ca1c2ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметры численного счета\n",
    "t0 = 0.0\n",
    "tf = 100.0\n",
    "nt = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "921d6310-bf79-43d6-b78c-a6e905f62ab7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def funk_parall(k):\n",
    "    i = k % N\n",
    "    j = k // N\n",
    "    mz_sol = 1\n",
    "    G = G0 + delta_G*i\n",
    "    alpha = alpha0 + delta_alpha*j\n",
    "\n",
    "    f = partial(my_sfs, G=G, r=r, alpha=alpha,\n",
    "                As=As, t_s=t_s, delta_t=delta_t)\n",
    "\n",
    "    s0 = np.array([0, 0, 1, 0])\n",
    "    t_e = np.linspace(t0, tf, nt)\n",
    "    sol_i = solve_ivp(f, [t0, tf], s0, t_eval=t_e,\n",
    "                      method='BDF', rtol=1e-8, atol=1e-8)\n",
    "\n",
    "    if sol_i.y[2][nt-1] < 0:\n",
    "        mz_sol = -1\n",
    "\n",
    "    return mz_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "0d55b8ea-5f4d-42b7-9f3e-e76054e3db90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 20.439760446548462 s\n"
     ]
    }
   ],
   "source": [
    "time_s = time.time()\n",
    "rez = Parallel(n_jobs=1)(delayed(funk_parall)(k) for k in range(N * N))\n",
    "time_f = time.time()\n",
    "print(f'Execution time {time_f - time_s} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "71884433-f661-40dc-8a4e-4066985e5349",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 5.909954071044922 s\n"
     ]
    }
   ],
   "source": [
    "time_s = time.time()\n",
    "rez = Parallel(n_jobs=4)(delayed(funk_parall)(k) for k in range(N*N))\n",
    "time_f = time.time()\n",
    "print(f'Execution time {time_f - time_s} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2c414df2-709c-42e0-af75-1e9a3e3388b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpGxy = np.zeros((N*N, 3)) + 1\n",
    "alpGxy.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e6afa0e4-594e-4d3a-a793-4eda40a49c5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in range(N):\n",
    "    for i in range(N):\n",
    "        G = G0+delta_G*i\n",
    "        alpha = alpha0+delta_alpha*j\n",
    "        alpGxy[i+j*N, 0] = G\n",
    "        alpGxy[i+j*N, 1] = alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "70b46adf-2315-4c2f-be36-715a1e01392c",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpGxy[:, 2] = rez"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "7b4b2519-e003-4f85-ac06-6b76e535ffa1",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = alpGxy[:, 0]\n",
    "Y = alpGxy[:, 1]\n",
    "Z = alpGxy[:, 2]\n",
    "Zc = (Z+1)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "781c3660-5a87-45bd-a84a-80a72e4375c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z1 = Zc.reshape(N, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eac3375c-4d84-4131-a107-74ec65853ce2",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "im = ax.imshow(Z1, cmap='Blues')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56f62fb6-0342-4455-a30a-1a6e66eafa10",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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