MSOMA_application.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "77b9b1fe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:30:50.022959Z",
     "start_time": "2023-07-03T07:30:49.589052Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random as rand\n",
    "import math\n",
    "from tqdm import tqdm\n",
    "from more_itertools import sort_together \n",
    "from statistics import mean \n",
    "\n",
    "from itertools import *\n",
    "\n",
    "import random\n",
    "\n",
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c3025e3b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:30:50.025549Z",
     "start_time": "2023-07-03T07:30:50.024004Z"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fdd07cf",
   "metadata": {},
   "source": [
    "# SOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e2ed1721",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:30:58.040870Z",
     "start_time": "2023-07-03T07:30:58.018171Z"
    }
   },
   "outputs": [],
   "source": [
    "class Soma:\n",
    "    \n",
    "    def __init__(self, func):\n",
    "        self.f = func\n",
    "        \n",
    "    # population creation (создание популяции)\n",
    "    def pop_create(self, pop_size, num_of_x, a, b):\n",
    "        pop = np.empty((num_of_x, pop_size))\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                pop[i][j] = a[i] + random.random() * (b[i] - a[i])\n",
    "        return pop\n",
    "\n",
    "\n",
    "    # sorting by cost function (сортировка по функции присособленности)\n",
    "    def cost_function_sort(self, pop, pop_size, num_of_x):\n",
    "        newpop = np.empty((num_of_x, pop_size))\n",
    "        cost = {}\n",
    "        for j in range(pop_size):\n",
    "            cost[j] = self.f(pop[:, j])\n",
    "        list_cost = list(cost.items())\n",
    "        list_cost.sort(key=lambda i: i[1])\n",
    "        for j in range(pop_size):\n",
    "            newpop[:, j] = pop[:, list_cost[j][0]]\n",
    "        return newpop\n",
    "\n",
    "\n",
    "    # creating a PRT vector (создание вектора PRT)\n",
    "    def create_prt_vector(self, prt, pop_size, num_of_x):\n",
    "        prt_vector = np.zeros((num_of_x, pop_size))\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                if random.random() < prt:\n",
    "                    prt_vector[i][j] = 1\n",
    "        return prt_vector\n",
    "\n",
    "\n",
    "    # movement of individuals towards leaders\n",
    "    def movement(self, pop_size, prt, num_of_x, NStep, new_pop, a, b):\n",
    "\n",
    "        vector_of_steps = np.zeros((num_of_x, NStep))\n",
    "\n",
    "        PRT = self.create_prt_vector(prt, pop_size, num_of_x)\n",
    "\n",
    "        # movement to the first leader\n",
    "        for i in range(pop_size):\n",
    "            for s in range(NStep):\n",
    "                vector_of_steps[:, s] = new_pop[:, i] + ((new_pop[:, 0] - new_pop[:, i])/(NStep//2)) * (PRT[:, i])*s\n",
    "            new_pop[:, i] = self.cost_function_sort(vector_of_steps, NStep, num_of_x)[:, 0]\n",
    "\n",
    "        # catching value out of range\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                if new_pop[i][j] < a[i]:\n",
    "                    new_pop[i][j] = a[i]\n",
    "                if new_pop[i][j] > b[i]:\n",
    "                    new_pop[i][j] = b[i]\n",
    "        return new_pop\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    # SOMA function\n",
    "    def find_min(self\n",
    "                 , pop_size = 100\n",
    "                 , num_of_x = 2\n",
    "                 , a = [-100, -100]\n",
    "                 , b = [100, 100]\n",
    "                 , NStep = 10\n",
    "                 , prt = 0.4\n",
    "                 , Migrations = 20\n",
    "                 , MinDist = 0.0001):\n",
    "        start_time = time.time()\n",
    "\n",
    "        pop = self.pop_create(pop_size, num_of_x, a, b)\n",
    "\n",
    "        new_pop = self.cost_function_sort(pop, pop_size, num_of_x)\n",
    "\n",
    "\n",
    "        MCount = 0\n",
    "        # migration loop\n",
    "        pbar = tqdm(total=Migrations)\n",
    "        while MCount < Migrations and abs(self.f(new_pop[0]) - self.f(new_pop[-1])) >= MinDist:\n",
    "            new_pop = self.movement(pop_size, prt, num_of_x, NStep, new_pop, a, b)\n",
    "            new_pop = self.cost_function_sort(new_pop, pop_size, num_of_x)\n",
    "\n",
    "            MCount += 1\n",
    "            pbar.update(1)\n",
    "        pbar.close()\n",
    "        \n",
    "        return new_pop[:, 0], self.f(new_pop[:, 0]), MCount, time.time() - start_time\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30811157",
   "metadata": {},
   "source": [
    "# MSOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "770c4f39",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:31:00.082113Z",
     "start_time": "2023-07-03T07:31:00.052628Z"
    }
   },
   "outputs": [],
   "source": [
    "class Msoma:\n",
    "    \n",
    "    def __init__(self, func):\n",
    "        self.f = func\n",
    "        \n",
    "    # population creation (создание популяции)\n",
    "    def pop_create(self, pop_size, num_of_x, a, b):\n",
    "        pop = np.empty((num_of_x, pop_size))\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                pop[i][j] = a[i] + random.random() * (b[i] - a[i])\n",
    "        return pop\n",
    "\n",
    "\n",
    "    # sorting by cost function (сортировка по функции присособленности)\n",
    "    def cost_function_sort(self, pop, pop_size, num_of_x):\n",
    "        newpop = np.empty((num_of_x, pop_size))\n",
    "        cost = {}\n",
    "        for j in range(pop_size):\n",
    "            cost[j] = self.f(pop[:, j])\n",
    "        list_cost = list(cost.items())\n",
    "        list_cost.sort(key=lambda i: i[1])\n",
    "        for j in range(pop_size):\n",
    "            newpop[:, j] = pop[:, list_cost[j][0]]\n",
    "        return newpop\n",
    "\n",
    "\n",
    "    # creating a PRT vector (создание вектора PRT)\n",
    "    def create_prt_vector(self, prt, pop_size, num_of_x):\n",
    "        prt_vector = np.zeros((num_of_x, pop_size))\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                if random.random() < prt:\n",
    "                    prt_vector[i][j] = 1\n",
    "        return prt_vector\n",
    "\n",
    "\n",
    "    # movement of individuals towards leaders\n",
    "    def movement(self, pop_size, prt, num_of_x, NStep, new_pop, a, b):\n",
    "\n",
    "        vector_of_steps_1 = np.zeros((num_of_x, NStep * 4))\n",
    "        vector_of_steps_2 = np.zeros((num_of_x, NStep * 2))\n",
    "        vector_of_steps_3 = np.zeros((num_of_x, NStep))\n",
    "\n",
    "        PRT = self.create_prt_vector(prt, pop_size * 3, num_of_x)\n",
    "\n",
    "        # movement to the first leader\n",
    "        for i in range(pop_size):\n",
    "            for s in range(4 * NStep):\n",
    "                vector_of_steps_1[:, s] = new_pop[:, i] + ((new_pop[:, 0] - new_pop[:, i])/(2*NStep)) * (PRT[:, i])*s\n",
    "            new_pop[:, i] = self.cost_function_sort(vector_of_steps_1, 4 * NStep, num_of_x)[:, 0]\n",
    "\n",
    "        # movement to the second leader\n",
    "        for i in range(pop_size, pop_size * 2):\n",
    "            for s in range(2 * NStep):\n",
    "                vector_of_steps_2[:, s] = new_pop[:, i] + ((new_pop[:, pop_size+1] - new_pop[:, i])/NStep) * (PRT[:, i])*s\n",
    "            new_pop[:, i] = self.cost_function_sort(vector_of_steps_2, 2 * NStep, num_of_x)[:, 0]\n",
    "\n",
    "        # movement to the third leader\n",
    "        for i in range(pop_size * 2, pop_size * 3):\n",
    "            for s in range(NStep):\n",
    "                vector_of_steps_3[:, s] = new_pop[:, i] + ((new_pop[:, 2*pop_size+2] - new_pop[:, i])/(NStep/2)) * (PRT[:, i])*s\n",
    "            new_pop[:, i] = self.cost_function_sort(vector_of_steps_3, NStep, num_of_x)[:, 0]\n",
    "\n",
    "        # catching value out of range\n",
    "        for j in range(pop_size):\n",
    "            for i in range(num_of_x):\n",
    "                if new_pop[i][j] < a[i]:\n",
    "                    new_pop[i][j] = a[i]\n",
    "                if new_pop[i][j] > b[i]:\n",
    "                    new_pop[i][j] = b[i]\n",
    "        return new_pop\n",
    "\n",
    "\n",
    "    # refinement function (функция уточнения)\n",
    "    def elaboration(self, pop, NStep, prt, num_of_x):\n",
    "        NStep *= 10\n",
    "        PRT = self.create_prt_vector(prt, 3, num_of_x)\n",
    "        vector_of_steps = np.zeros((num_of_x, NStep))\n",
    "        ans = np.zeros((num_of_x, 3))\n",
    "        for i in range(3):\n",
    "            for s in range(NStep):\n",
    "                vector_of_steps[:, s] = pop[:, i] + ((pop[:, 0] - pop[:, i])/(NStep/2)) * (PRT[:, i])*s\n",
    "            ans[:, i] = self.cost_function_sort(vector_of_steps, NStep, num_of_x)[:, 0]\n",
    "        ans = self.cost_function_sort(ans, 3, num_of_x)\n",
    "        return ans[:, 0]\n",
    "\n",
    "\n",
    "    # MSOMA find min\n",
    "    def find_min(self\n",
    "                 , pop_size = 100\n",
    "                 , num_of_x = 2\n",
    "                 , a = [-100, -100]\n",
    "                 , b = [100, 100]\n",
    "                 , NStep = 20\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 25\n",
    "                 , MinDist = 0.1**10):\n",
    "        start_time = time.time()\n",
    "\n",
    "        pop = self.pop_create(pop_size, num_of_x, a, b)\n",
    "        new_pop = self.cost_function_sort(pop, pop_size, num_of_x)\n",
    "\n",
    "        # cloning\n",
    "        new1_pop = np.concatenate((new_pop, new_pop), axis=1)\n",
    "        new_pop = np.concatenate((new1_pop, new_pop), axis=1)\n",
    "\n",
    "        MCount = 0\n",
    "        # migration loop\n",
    "        pbar = tqdm(total=Migrations)\n",
    "        \n",
    "        while MCount < Migrations and math.sqrt((1/2) * ((self.f(new_pop[:, 1]) - self.f(new_pop[:, 0]))**2 + (self.f(new_pop[:, 2]) - self.f(new_pop[:, 0]))**2)) >= MinDist:\n",
    "            new_pop = self.movement(pop_size, prt, num_of_x, NStep, new_pop, a, b)\n",
    "            new_pop = self.cost_function_sort(new_pop, 3 * pop_size, num_of_x)\n",
    "\n",
    "            # population refreshing\n",
    "            new_pop = new_pop[:, :round(pop_size*(2/3))]\n",
    "            new_pop = np.concatenate((new_pop, self.pop_create(round(pop_size*(1/3)), num_of_x, a, b)), axis=1)\n",
    "            new_pop = self.cost_function_sort(new_pop, pop_size, num_of_x)\n",
    "\n",
    "            # cloning\n",
    "            new1_pop = np.concatenate((new_pop, new_pop), axis=1)\n",
    "            new_pop = np.concatenate((new1_pop, new_pop), axis=1)\n",
    "\n",
    "            MCount += 1\n",
    "            pbar.update(1)\n",
    "            \n",
    "        pbar.close()\n",
    "        last_pop = new_pop[:, :3]\n",
    "\n",
    "        ans = self.elaboration(last_pop, NStep, prt, num_of_x)\n",
    "\n",
    "        return ans, self.f(ans), MCount, time.time() - start_time\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "165d18a2",
   "metadata": {},
   "source": [
    "# Classic task"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ad7821a",
   "metadata": {},
   "source": [
    "## ex1 (50 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3a6d8744",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T06:57:50.911318Z",
     "start_time": "2023-01-08T06:57:50.900921Z"
    }
   },
   "outputs": [],
   "source": [
    "def model(t, x, u):\n",
    "    return x[t] + u[t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1ecaa922",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T06:57:51.178711Z",
     "start_time": "2023-01-08T06:57:51.171925Z"
    }
   },
   "outputs": [],
   "source": [
    "def f(u):\n",
    "    x = [0]       \n",
    "    sumU = 0\n",
    "    for t in range(N):\n",
    "        x.append(model(t, x, u))\n",
    "        sumU += (1.1**(-t)) * (u[t]**2)\n",
    "    return 0.5*(sumU) + x[N]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3d19996e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T07:32:10.006432Z",
     "start_time": "2023-01-08T07:32:09.997844Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_x(u):\n",
    "    x = [0]       \n",
    "    sumU = 0\n",
    "    for t in range(N-1):\n",
    "        x.append(model(t, x, u))\n",
    "        sumU += (1.1**(-t)) * (u[t]**2)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2ed0a280",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T06:57:53.355635Z",
     "start_time": "2023-01-08T06:57:53.352326Z"
    }
   },
   "outputs": [],
   "source": [
    "N = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "063a2566",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T07:37:41.380747Z",
     "start_time": "2023-01-08T07:35:19.326200Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min f(x) =  -581.32586179\n",
      "loop =  70\n",
      "--- run time 142.0469810962677 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# setting paarameters\n",
    "pop_size = 1000\n",
    "num_of_x = 50\n",
    "prt = 0.3\n",
    "NStep = 100\n",
    "Migrations = 70\n",
    "MinDist = 0.001\n",
    "a = [-110]*50\n",
    "b = [0]*50\n",
    "\n",
    "soma = Soma(f)\n",
    "x, f_x, loop, time_run = soma.find_min(pop_size = pop_size,\n",
    "                                       num_of_x = num_of_x,\n",
    "                                       a = a,\n",
    "                                       b = b,\n",
    "                                       NStep = NStep,\n",
    "                                       prt = prt,\n",
    "                                       Migrations = Migrations,\n",
    "                                       MinDist = MinDist)\n",
    "\n",
    "\n",
    "\n",
    "# msoma = Msoma(f)\n",
    "# u, I, iterac, t = msoma.find_min(pop_size = pop_size,\n",
    "#                                        num_of_x = num_of_x,\n",
    "#                                        a = a,\n",
    "#                                        b = b,\n",
    "#                                        NStep = NStep,\n",
    "#                                        prt = prt,\n",
    "#                                        Migrations = Migrations,\n",
    "#                                        MinDist = MinDist)\n",
    "\n",
    "print(\"min f(x) = \", np.round(f(x), 8))\n",
    "print(\"loop = \", loop)\n",
    "print(\"--- run time %s seconds ---\" % time_run)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cdc683da",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T07:37:41.443409Z",
     "start_time": "2023-01-08T07:37:41.381792Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.scatter(list(range(50)), x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c5cb5637",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-08T07:32:14.125785Z",
     "start_time": "2023-01-08T07:32:14.039307Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list(range(50)), f_x(x))\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c60be484",
   "metadata": {},
   "source": [
    "## ex2 (10 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "89298b09",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:49:47.903611Z",
     "start_time": "2023-01-07T13:49:47.892796Z"
    }
   },
   "outputs": [],
   "source": [
    "def eq_x1(x2, t):\n",
    "    return x2[t]\n",
    "\n",
    "def eq_x2(x1, x2, u, N, t):\n",
    "    return 2*x2[t]-x1[t]+((1/(N**2))*u[t])\n",
    "\n",
    "\n",
    "def f(u):\n",
    "    N = 10\n",
    "    x1 = [0]\n",
    "    x2 = [0]\n",
    "    \n",
    "    I_sum = 0\n",
    "    \n",
    "    for t in range(N):\n",
    "        x1.append(eq_x1(x2, t))\n",
    "        x2.append(eq_x2(x1, x2, u, N, t))\n",
    "        \n",
    "        I_sum += u[t]**2\n",
    "        \n",
    "    return (1/(2*N))*I_sum - x1[N]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "caf5692f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:49:49.959706Z",
     "start_time": "2023-01-07T13:49:49.952386Z"
    }
   },
   "outputs": [],
   "source": [
    "def x_counter(u):\n",
    "    N = 10\n",
    "    x1 = [0]\n",
    "    x2 = [0]\n",
    "    \n",
    "    I_sum = 0\n",
    "    \n",
    "    for t in range(N):\n",
    "        x1.append(eq_x1(x2, t))\n",
    "        x2.append(eq_x2(x1, x2, u, N, t))\n",
    "        \n",
    "        I_sum += u[t]**2\n",
    "        \n",
    "    return x1, x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4ddf3848",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:53:34.421906Z",
     "start_time": "2023-01-07T13:53:08.092477Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min f(x) =  -0.1425000000000005\n",
      "loop =  100\n",
      "--- run time 26.324079036712646 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# setting paarameters\n",
    "pop_size = 500\n",
    "num_of_x = 10\n",
    "prt = 0.4\n",
    "NStep = 50\n",
    "Migrations = 100\n",
    "MinDist = 0.00000000001\n",
    "a = [0]*50\n",
    "b = [100]*50\n",
    "\n",
    "\n",
    "soma = Soma(f)\n",
    "x, f_x, loop, time_run = soma.find_min(pop_size = pop_size,\n",
    "                                       num_of_x = num_of_x,\n",
    "                                       a = a,\n",
    "                                       b = b,\n",
    "                                       NStep = NStep,\n",
    "                                       prt = prt,\n",
    "                                       Migrations = Migrations,\n",
    "                                       MinDist = MinDist)\n",
    "\n",
    "\n",
    "\n",
    "# msoma = Msoma(f)\n",
    "# u, I, iterac, t = msoma.find_min(pop_size = pop_size,\n",
    "#                                        num_of_x = num_of_x,\n",
    "#                                        a = a,\n",
    "#                                        b = b,\n",
    "#                                        NStep = NStep,\n",
    "#                                        prt = prt,\n",
    "#                                        Migrations = Migrations,\n",
    "#                                        MinDist = MinDist)\n",
    "# x*, f(x*), number of loops, time = MSOMA function (population size, number of variables, constraints a, constraints b, number of steps, prt, number of migrations, minimum distance)\n",
    "\n",
    "\n",
    "print(\"min f(x) = \", f_x)\n",
    "print(\"loop = \", loop)\n",
    "print(\"--- run time %s seconds ---\" % time_run)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5dc7914a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:53:37.894713Z",
     "start_time": "2023-01-07T13:53:37.813753Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.scatter([t for t in range(10)], x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "24fdd7b5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:53:39.923690Z",
     "start_time": "2023-01-07T13:53:39.849287Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x1')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yNQA9//zzeuSRR/T3f//3WrBggV544QWlpqaqurp62P633HKLdu7cqQ0bNsjlco04rsPhkNvtDtoAAJMnNsahigKPJIWEoKH9igIP6wFhyrAtAPX19ampqUl5eXlB7Xl5eTp16tR1jX3lyhWlpaVp7ty5uv/++9Xc3HzN/r29vfL7/UEbAGBs8jNSVF2UKbcreMbd7XKquiiTdYAwpdi2EGJXV5f6+/uVnJwc1J6cnKyOjo5xjzt//nzt27dP3/zmN+X3+7Vz506tWLFCZ8+e1bx584Z9T1VVlSorK8f9mQCAQfkZKVrtcbMSNKY821eCdjiC/ygsywppG4tly5Zp2bJlgf0VK1YoMzNTu3fv1q5du4Z9z7Zt21RWVhbY9/v9Sk1NHXcNAGCy2BiHcm+bYXcZwDXZFoBmzpyp2NjYkNmezs7OkFmh6xETE6MlS5boo48+GrFPfHy84uPjJ+wzAQDA1GbbNUBxcXHKyspSXV1dUHtdXZ2WL18+YZ9jWZZaWlqUksK5ZwAAMGjCZoDOnz+vtWvX6uOPPx71e8rKylRcXKzs7Gzl5uZq7969am9vV0lJiaTBU1OXLl3Sa6+9FnhPS0uLpMELnT/77DO1tLQoLi5OHs/g3QeVlZVatmyZ5s2bJ7/fr127dqmlpUUvvfTSRB0qAACIcBMWgPr6+nThwoUxvaewsFCff/65tm/fLq/Xq4yMDB05ckRpaWmSBhc+/NM1gRYvXhz476amJh04cEBpaWn65JNPJElffPGFHn30UXV0dMjlcmnx4sWqr69XTk7O9R0gAACIGg7Lskb1ZLqvXiQ8nM8++0wHDhxQf3//hBRmJ7/fL5fLJZ/Pp8TERLvLAQAAozCW3+9RzwDt3LlTd9xxx4gDXrlyZWxVAgAA2GTUAWjevHnasmWLioqKhn29paVFWVlZE1YYAADAZBn1XWBZWVlqamoa8XWHw6FRnk0DAACw1ahngJ577jn19vaO+PqiRYs0MDAwIUUBAABMplHPALndbqWlpendd98dsc8rr7wyIUUBAABMpjEvhLh27Vr94Ac/UF9fX6Dts88+U0FBgbZt2zahxQEAAEyGMQeg+vp61dbWasmSJfrwww/17//+78rIyNCVK1d09uzZyagRAABgQo05AC1dulTNzc26/fbblZWVpb/6q7/SD37wA7333ns8QBQAAESEcT0L7He/+51Onz6tuXPnatq0afrtb3+rP/zhDxNdGwAAwKQYcwD68Y9/rNzcXK1evVqtra06ffp0YEaooaFhMmoEAACYUGMOQDt37tSvfvUr7d69W06nUwsXLlRjY6MeeOAB3X333ZNQIgAAwMQa88NQP/jgA82cOTOo7YYbbtBPfvIT3X///RNWGAAAwGQZ8wzQn4afr7rrrruuqxgAAIBwGNdF0AAAAJGMAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwzjS7CwAAjKx/wFJj22V1dvdodoJTOelJio1x2F0WEPEIQAAwRR1t9aqy9py8vp5AW4rLqYoCj/IzUmysDIh8nAIDgCnoaKtXG/efCQo/ktTh69HG/Wd0tNVrU2VAdCAAAcAU0z9gqbL2nKxhXhtqq6w9p/6B4XoAGA0CEABMMY1tl0Nmfr7KkuT19aix7XL4igKiDAEIAKaYzu6Rw894+gEIRQACgClmdoJzQvsBCEUAAoApJic9SSkup0a62d2hwbvBctKTwlkWEFUIQAAwxcTGOFRR4JGkkBA0tF9R4GE9IOA6EIAAYArKz0hRdVGm3K7g01xul1PVRZmsAwRcJxZCBIApKj8jRas9blaCBiYBAQgAprDYGIdyb5thdxlA1OEUGAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOLYHoD179ig9PV1Op1NZWVk6ceLEiH29Xq8efPBBfeMb31BMTIxKS0uH7Xfo0CF5PB7Fx8fL4/HozTffnKTqAQBAJLI1ANXU1Ki0tFTl5eVqbm7WqlWrtGbNGrW3tw/bv7e3V7NmzVJ5ebkWLVo0bJ+GhgYVFhaquLhYZ8+eVXFxsdavX6/3339/Mg8FAABEEIdlWZZdH7506VJlZmaquro60LZgwQKtW7dOVVVV13zv3XffrTvuuEMvvPBCUHthYaH8fr/efvvtQFt+fr5uuukmHTx4cFR1+f1+uVwu+Xw+JSYmjv6AAACAbcby+23bDFBfX5+ampqUl5cX1J6Xl6dTp06Ne9yGhoaQMe+9995rjtnb2yu/3x+0AQCA6GVbAOrq6lJ/f7+Sk5OD2pOTk9XR0THucTs6OsY8ZlVVlVwuV2BLTU0d9+cDAICpz/aLoB2O4KcaW5YV0jbZY27btk0+ny+wXbx48bo+HwAATG22PQ1+5syZio2NDZmZ6ezsDJnBGQu32z3mMePj4xUfHz/uzwQAAJHFthmguLg4ZWVlqa6uLqi9rq5Oy5cvH/e4ubm5IWMeO3bsusYEAADRxbYZIEkqKytTcXGxsrOzlZubq71796q9vV0lJSWSBk9NXbp0Sa+99lrgPS0tLZKkK1eu6LPPPlNLS4vi4uLk8XgkSZs3b9add96pHTt26Dvf+Y7eeustvfvuuzp58mTYjw8AAExNtgagwsJCff7559q+fbu8Xq8yMjJ05MgRpaWlSRpc+PBP1wRavHhx4L+bmpp04MABpaWl6ZNPPpEkLV++XK+//rqefPJJ/dM//ZNuu+021dTUaOnSpWE7LgAAMLXZug7QVMU6QAAARJ6IWAcIAADALgQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABjH1qfBA0A49Q9Yamy7rM7uHs1OcConPUmxMQ67ywJgAwIQACMcbfWqsvacvL6eQFuKy6mKAo/yM1JsrAyAHTgFBiDqHW31auP+M0HhR5I6fD3auP+MjrZ6baoMgF0IQACiWv+Apcrac7KGeW2orbL2nPoHhusBIFoRgABEtca2yyEzP19lSfL6etTYdjl8RQGwHQEIQFTr7B45/IynH4DoQAACENVmJzgntB+A6EAAAhDVctKTlOJyaqSb3R0avBssJz0pnGUBsBkBCEBUi41xqKLAI0khIWhov6LAw3pAgGEIQACiXn5GiqqLMuV2BZ/mcrucqi7KZB0gwEAshAjACPkZKVrtcbMSNABJBCAABomNcSj3thl2lwFgCuAUGAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDjT7C4AQGTqH7DU2HZZnd09mp3gVE56kmJjHHaXBQCjYvsM0J49e5Seni6n06msrCydOHHimv2PHz+urKwsOZ1O3XrrrXr55ZeDXt+3b58cDkfI1tPTM5mHARjlaKtXK3e8p+/+9Nfa/HqLvvvTX2vljvd0tNVrd2kAMCq2BqCamhqVlpaqvLxczc3NWrVqldasWaP29vZh+7e1tem+++7TqlWr1NzcrCeeeEKPPfaYDh06FNQvMTFRXq83aHM6neE4JCDqHW31auP+M/L6gv9R0eHr0cb9ZwhBACKCw7Isy64PX7p0qTIzM1VdXR1oW7BggdatW6eqqqqQ/lu3btXhw4d1/vz5QFtJSYnOnj2rhoYGSYMzQKWlpfriiy/GXZff75fL5ZLP51NiYuK4xwGiTf+ApZU73gsJP0Mcktwup05u/TanwwCE3Vh+v22bAerr61NTU5Py8vKC2vPy8nTq1Klh39PQ0BDS/95779VvfvMb/fGPfwy0XblyRWlpaZo7d67uv/9+NTc3X7OW3t5e+f3+oA1AqMa2yyOGH0myJHl9PWpsuxy+ogBgHGwLQF1dXerv71dycnJQe3Jysjo6OoZ9T0dHx7D9r169qq6uLknS/PnztW/fPh0+fFgHDx6U0+nUihUr9NFHH41YS1VVlVwuV2BLTU29zqMDolNn9+iupRttPwCwi+0XQTscwdPklmWFtH1d/6+2L1u2TEVFRVq0aJFWrVqlX/7yl/qLv/gL7d69e8Qxt23bJp/PF9guXrw43sMBotrshNFdSzfafgBgF9tug585c6ZiY2NDZns6OztDZnmGuN3uYftPmzZNM2bMGPY9MTExWrJkyTVngOLj4xUfHz/GIwDMk5OepBSXUx2+Hg138eDQNUA56UnhLg0AxsS2GaC4uDhlZWWprq4uqL2urk7Lly8f9j25ubkh/Y8dO6bs7GzdcMMNw77Hsiy1tLQoJSVlYgoHDBYb41BFgUfSYNj5qqH9igIPF0ADmPJsPQVWVlamn/3sZ3r11Vd1/vx5bdmyRe3t7SopKZE0eGpqw4YNgf4lJSW6cOGCysrKdP78eb366qv6+c9/rscffzzQp7KyUu+8844+/vhjtbS06JFHHlFLS0tgTADXJz8jRdVFmXK7gk9zuV1OVRdlKj+Df2wAmPpsXQm6sLBQn3/+ubZv3y6v16uMjAwdOXJEaWlpkiSv1xu0JlB6erqOHDmiLVu26KWXXtKcOXO0a9cu/fVf/3WgzxdffKFHH31UHR0dcrlcWrx4serr65WTkxP24wOiVX5GilZ73KwEDSBi2boO0FTFOkAAAESeiFgHCAAAwC4EIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxptldAACpf8BSY9tldXb3aHaCUznpSYqNcdhdFgBELQIQYLOjrV5V1p6T19cTaEtxOVVR4FF+RoqNlQFA9OIUGGCjo61ebdx/Jij8SFKHr0cb95/R0VavTZUBQHQjAAE26R+wVFl7TtYwrw21VdaeU//AcD0AANeDAATYpLHtcsjMz1dZkry+HjW2XQ5fUQBgCAIQYJPO7pHDz3j6AQBGjwAE2GR2gnNC+wEARo8ABNgkJz1JKS6nRrrZ3aHBu8Fy0pPCWRYAGIEABNgkNsahigKPJIWEoKH9igIP6wEBwCQgAAE2ys9IUXVRptyu4NNcbpdT1UWZrAMEAJOEhRABm+VnpGi1x81K0AAQRgQgYAqIjXEo97YZdpcBAMbgFBgAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwWQkTU6R+wWFUZAHBNBCBElaOtXlXWnpPX1xNoS3E5VVHg4blaAIAAToEhahxt9Wrj/jNB4UeSOnw92rj/jI62em2qDAAw1RCAEBX6ByxV1p6TNcxrQ22VtefUPzBcDwCAaQhAiAqNbZdDZn6+ypLk9fWose1y+IoCAExZBCBEhc7ukcPPePoBAKIbAQhRYXaCc0L7AQCiGwEIUSEnPUkpLqdGutndocG7wXLSk8JZFgBgiiIAISrExjhUUeCRpJAQNLRfUeBhPSAAgCQCEKJIfkaKqosy5XYFn+Zyu5yqLspkHSAAQAALISKq5GekaLXHzUrQAIBrIgCFUSQ+oiESa46NcSj3thl2lwEAmMJsPwW2Z88epaeny+l0KisrSydOnLhm/+PHjysrK0tOp1O33nqrXn755ZA+hw4dksfjUXx8vDwej958883JKn/UjrZ6tXLHe/ruT3+tza+36Ls//bVW7nhvSq9OHIk1AwAwGrYGoJqaGpWWlqq8vFzNzc1atWqV1qxZo/b29mH7t7W16b777tOqVavU3NysJ554Qo899pgOHToU6NPQ0KDCwkIVFxfr7NmzKi4u1vr16/X++++H67BCROIjGiKxZgAARsthWZZtzwZYunSpMjMzVV1dHWhbsGCB1q1bp6qqqpD+W7du1eHDh3X+/PlAW0lJic6ePauGhgZJUmFhofx+v95+++1An/z8fN100006ePDgqOry+/1yuVzy+XxKTEwc7+FJGjyFtHLHeyOuUuzQ4EW6J7d+e8qcWorEmgEAGMvvt20zQH19fWpqalJeXl5Qe15enk6dOjXsexoaGkL633vvvfrNb36jP/7xj9fsM9KYktTb2yu/3x+0TZRIfERDJNYMAMBY2BaAurq61N/fr+Tk5KD25ORkdXR0DPuejo6OYftfvXpVXV1d1+wz0piSVFVVJZfLFdhSU1PHc0jDisRHNERizQAAjIXtF0E7HMGnUCzLCmn7uv5/2j7WMbdt2yafzxfYLl68OOr6v04kPqIhEmsGAGAsbLsNfubMmYqNjQ2Zmens7AyZwRnidruH7T9t2jTNmDHjmn1GGlOS4uPjFR8fP57D+FpDj2jo8PVouIuthq6nmUqPaIjEmgEAGAvbZoDi4uKUlZWlurq6oPa6ujotX7582Pfk5uaG9D927Jiys7N1ww03XLPPSGNOtkh8REMk1gwAwFjYegqsrKxMP/vZz/Tqq6/q/Pnz2rJli9rb21VSUiJp8NTUhg0bAv1LSkp04cIFlZWV6fz583r11Vf185//XI8//nigz+bNm3Xs2DHt2LFDv/3tb7Vjxw69++67Ki0tDffhBUTiIxoisWYAAEbL1tvgpcGFEJ999ll5vV5lZGTon//5n3XnnXdKkh5++GF98skn+q//+q9A/+PHj2vLli368MMPNWfOHG3dujUQmIb827/9m5588kl9/PHHuu222/T000/rgQceGHVNE3kb/FdF4qrKkVgzAMBMY/n9tj0ATUWTFYAAAMDkiYh1gAAAAOxCAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjGPb0+CnsqHFsf1+v82VAACA0Rr63R7NQy4IQMPo7u6WJKWmptpcCQAAGKvu7m65XK5r9uFZYMMYGBjQp59+qoSEBDkcE/vgT7/fr9TUVF28eJHnjE0ivufw4HsOD77n8OG7Do/J+p4ty1J3d7fmzJmjmJhrX+XDDNAwYmJiNHfu3En9jMTERP64woDvOTz4nsOD7zl8+K7DYzK+56+b+RnCRdAAAMA4BCAAAGAcAlCYxcfHq6KiQvHx8XaXEtX4nsOD7zk8+J7Dh+86PKbC98xF0AAAwDjMAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCUBjt2bNH6enpcjqdysrK0okTJ+wuKepUVVVpyZIlSkhI0OzZs7Vu3Tr97ne/s7usqFZVVSWHw6HS0lK7S4lKly5dUlFRkWbMmKEbb7xRd9xxh5qamuwuK6pcvXpVTz75pNLT0zV9+nTdeuut2r59uwYGBuwuLaLV19eroKBAc+bMkcPh0K9+9aug1y3L0lNPPaU5c+Zo+vTpuvvuu/Xhhx+GrT4CUJjU1NSotLRU5eXlam5u1qpVq7RmzRq1t7fbXVpUOX78uDZt2qRf//rXqqur09WrV5WXl6cvv/zS7tKi0unTp7V3717dfvvtdpcSlf7v//5PK1as0A033KC3335b586d03PPPac///M/t7u0qLJjxw69/PLLevHFF3X+/Hk9++yz+slPfqLdu3fbXVpE+/LLL7Vo0SK9+OKLw77+7LPP6vnnn9eLL76o06dPy+12a/Xq1YHncU46C2GRk5NjlZSUBLXNnz/f+uEPf2hTRWbo7Oy0JFnHjx+3u5So093dbc2bN8+qq6uz7rrrLmvz5s12lxR1tm7daq1cudLuMqLe2rVrre9973tBbQ888IBVVFRkU0XRR5L15ptvBvYHBgYst9tt/fjHPw609fT0WC6Xy3r55ZfDUhMzQGHQ19enpqYm5eXlBbXn5eXp1KlTNlVlBp/PJ0lKSkqyuZLos2nTJq1du1b33HOP3aVErcOHDys7O1t/8zd/o9mzZ2vx4sX66U9/andZUWflypX6j//4D/3+97+XJJ09e1YnT57UfffdZ3Nl0autrU0dHR1Bv4vx8fG66667wva7yMNQw6Crq0v9/f1KTk4Oak9OTlZHR4dNVUU/y7JUVlamlStXKiMjw+5yosrrr7+uM2fO6PTp03aXEtU+/vhjVVdXq6ysTE888YQaGxv12GOPKT4+Xhs2bLC7vKixdetW+Xw+zZ8/X7Gxserv79fTTz+t7373u3aXFrWGfvuG+128cOFCWGogAIWRw+EI2rcsK6QNE+f73/++/vu//1snT560u5SocvHiRW3evFnHjh2T0+m0u5yoNjAwoOzsbD3zzDOSpMWLF+vDDz9UdXU1AWgC1dTUaP/+/Tpw4IAWLlyolpYWlZaWas6cOXrooYfsLi+q2fm7SAAKg5kzZyo2NjZktqezszMk/WJi/MM//IMOHz6s+vp6zZ071+5yokpTU5M6OzuVlZUVaOvv71d9fb1efPFF9fb2KjY21sYKo0dKSoo8Hk9Q24IFC3To0CGbKopO//iP/6gf/vCH+tu//VtJ0je/+U1duHBBVVVVBKBJ4na7JQ3OBKWkpATaw/m7yDVAYRAXF6esrCzV1dUFtdfV1Wn58uU2VRWdLMvS97//fb3xxht67733lJ6ebndJUecv//Iv9cEHH6ilpSWwZWdn6+/+7u/U0tJC+JlAK1asCFnG4fe//73S0tJsqig6/eEPf1BMTPDPYWxsLLfBT6L09HS53e6g38W+vj4dP348bL+LzACFSVlZmYqLi5Wdna3c3Fzt3btX7e3tKikpsbu0qLJp0yYdOHBAb731lhISEgKzbi6XS9OnT7e5uuiQkJAQck3Vn/3Zn2nGjBlcazXBtmzZouXLl+uZZ57R+vXr1djYqL1792rv3r12lxZVCgoK9PTTT+vmm2/WwoUL1dzcrOeff17f+9737C4tol25ckX/8z//E9hva2tTS0uLkpKSdPPNN6u0tFTPPPOM5s2bp3nz5umZZ57RjTfeqAcffDA8BYblXjNYlmVZL730kpWWlmbFxcVZmZmZ3Jo9CSQNu/3iF7+wu7Soxm3wk6e2ttbKyMiw4uPjrfnz51t79+61u6So4/f7rc2bN1s333yz5XQ6rVtvvdUqLy+3ent77S4tov3nf/7nsP8/fuihhyzLGrwVvqKiwnK73VZ8fLx15513Wh988EHY6nNYlmWFJ2oBAABMDVwDBAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACYJS7775bpaWldpcBwGYEIAAAYByeBQbAGA8//LD+5V/+Jaitra1Nt9xyiz0FAbANAQiAMXw+n9asWaOMjAxt375dkjRr1izFxsbaXBmAcJtmdwEAEC4ul0txcXG68cYb5Xa77S4HgI24BggAABiHAAQAAIxDAAJglLi4OPX399tdBgCbEYAAGOWWW27R+++/r08++URdXV0aGBiwuyQANiAAATDK448/rtjYWHk8Hs2aNUvt7e12lwTABtwGDwAAjMMMEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACM8/8A/bwb424B0H0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(11)], x_counter(x)[0])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bd8ecf16",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-07T13:53:41.215051Z",
     "start_time": "2023-01-07T13:53:41.099304Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x2')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(11)], x_counter(x)[1])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d34abc02",
   "metadata": {},
   "source": [
    "# Bundles of trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "8c14a3cb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T18:22:01.537638Z",
     "start_time": "2023-03-10T18:22:01.525638Z"
    }
   },
   "outputs": [],
   "source": [
    "def start_parallelepiped(start_conditions : list\n",
    "                         , indent : int\n",
    "                         , step : int) -> list:\n",
    "    \n",
    "    pre_start_conditions = []\n",
    "    for el in start_conditions:\n",
    "        pre_start_conditions.append([n for n in np.arange(el-(step*indent), el+(step*indent)+1, step)])\n",
    "        \n",
    "    if len(pre_start_conditions) == 1:\n",
    "        return pre_start_conditions[0]\n",
    "    \n",
    "    else:  \n",
    "        tmp = list(product(pre_start_conditions[0], pre_start_conditions[1]))\n",
    "        if len(start_conditions) > 2:\n",
    "            for i in range(2, len(start_conditions)):\n",
    "                tmp = list(product(tmp, pre_start_conditions[i]))\n",
    "                for ind in range(len(tmp)):\n",
    "                    ff = list(tmp[ind][0])\n",
    "                    ff.append(tmp[ind][1])\n",
    "                    tmp[ind] = ff\n",
    "        else:\n",
    "            for ind in range(len(tmp)):\n",
    "                tmp[ind] = list(tmp[ind])\n",
    "                \n",
    "        return tmp\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "857df929",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T15:57:54.690059Z",
     "start_time": "2023-03-10T15:57:54.677299Z"
    }
   },
   "outputs": [],
   "source": [
    "def info_print(u, I, iterac, t):\n",
    "    print(f'target function value: {I}')\n",
    "    print(f'final iteration: {iterac}')\n",
    "    print(f'execution time: {t}')\n",
    "    print('--------------------------------')\n",
    "    print(f'U: {u}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f0afbb",
   "metadata": {},
   "source": [
    "## ex1 (50 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "dd18e889",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:23:15.328838Z",
     "start_time": "2023-03-10T19:23:15.316288Z"
    }
   },
   "outputs": [],
   "source": [
    "#1\n",
    "def model(t, x, u):\n",
    "    return x[t] + u[t]\n",
    "\n",
    "\n",
    "all_start_points = start_parallelepiped([0], 2, 100)\n",
    "\n",
    "\n",
    "def f(u):\n",
    "    N = 50\n",
    "    I_sum = 0\n",
    "    for point in all_start_points:\n",
    "        x = [point]\n",
    "        sumU = 0\n",
    "        for t in range(N):\n",
    "            x.append(model(t, x, u))\n",
    "            sumU += (1.1**(-t)) * (u[t]**2)\n",
    "        I_sum += 0.5*(sumU) + x[N]\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    return I_sum \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "cca26e7b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:23:15.899007Z",
     "start_time": "2023-03-10T19:23:15.888021Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_x(u):\n",
    "    N = 50\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x = [point]\n",
    "        sumU = 0\n",
    "        for t in range(N):\n",
    "            x.append(model(t, x, u))\n",
    "            sumU += (1.1**(-t)) * (u[t]**2)\n",
    "        I_sum += 0.5*(sumU) + x[N]\n",
    "        plt.scatter([t for t in range(51)], x, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x')\n",
    "    plt.show()\n",
    "    return I_sum "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87c5f029",
   "metadata": {},
   "source": [
    "### SOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "cf9f998c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T15:43:25.141954Z",
     "start_time": "2023-03-10T15:34:44.604869Z"
    }
   },
   "outputs": [],
   "source": [
    "soma = Soma(f)\n",
    "u, I, iterac, t = soma.find_min(pop_size = 600\n",
    "                 , num_of_x = 50\n",
    "                , a = [-110]*50\n",
    "                , b = [0]*50\n",
    "                 , NStep = 100\n",
    "                 , prt = 0.4\n",
    "                 , Migrations = 100\n",
    "                 , MinDist = 0.1**5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "08731b90",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T15:43:32.947303Z",
     "start_time": "2023-03-10T15:43:32.937936Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target: -581.8247710251362\n",
      "iter: 100\n",
      "time: 520.5289258956909\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "291dcef2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T15:43:25.214614Z",
     "start_time": "2023-03-10T15:43:25.149879Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "-581.8247710251362"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "bd288b7d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T15:43:25.273691Z",
     "start_time": "2023-03-10T15:43:25.215659Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list(range(50)), u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58389802",
   "metadata": {},
   "source": [
    "### MSOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "bc22bc4a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:27:00.923763Z",
     "start_time": "2023-03-10T19:23:56.388295Z"
    }
   },
   "outputs": [],
   "source": [
    "msoma = Msoma(f)\n",
    "u, I, iterac, t = msoma.find_min(pop_size = 600\n",
    "                 , num_of_x = 50\n",
    "                , a = [-110]*50\n",
    "                , b = [0]*50\n",
    "                 , NStep = 40\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 50\n",
    "                 , MinDist = 0.1**10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "ed6d4419",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:28:46.999103Z",
     "start_time": "2023-03-10T19:28:46.985780Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -553.3341\n",
      "final iteration: 19\n",
      "execution time: 2523.330262999271\n",
      "--------------------------------\n",
      "U: [  0.          -3.69759668  -1.8165702   -2.24625741  -2.99919841\n",
      "  -2.09590898  -0.51538814  -0.46757877  -3.75488011  -1.96983561\n",
      "  -0.23814931  -3.80777885  -4.46263792  -3.17408554  -5.95635532\n",
      "  -6.72169467  -8.26147325  -4.78044155  -4.50277957  -6.96114625\n",
      "  -8.56351746  -6.60174825 -10.3746736   -7.09031875 -11.12156943\n",
      " -11.68212002  -9.77695813 -18.79100268 -12.45924727 -22.68833179\n",
      " -15.85901326 -25.20736948 -26.16179595 -23.9839223  -32.75987206\n",
      " -31.82841369 -34.19524922 -42.15516945 -32.47016783 -59.15495506\n",
      " -57.44915828 -47.73595569 -57.68504982 -50.06769757 -73.48141502\n",
      " -65.55338296 -78.73851533 -85.60952212 -80.6945899  -96.70423054]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, -553.3341, 19, 2523.330262999271)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "cdca8670",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:27:01.004418Z",
     "start_time": "2023-03-10T19:27:00.928435Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "-553.3341416428646"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "0bd2d94a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:27:01.064647Z",
     "start_time": "2023-03-10T19:27:01.005748Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list(range(50)), u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "125f6350",
   "metadata": {},
   "source": [
    "## ex2 (10 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "86c464a9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:36:42.265664Z",
     "start_time": "2023-03-10T19:36:42.253779Z"
    }
   },
   "outputs": [],
   "source": [
    "#2\n",
    "def eq_x1(x2, t):\n",
    "    return x2[t]\n",
    "\n",
    "def eq_x2(x1, x2, u, N, t):\n",
    "    return 2*x2[t]-x1[t]+((1/(N**2))*u[t])\n",
    "\n",
    "all_start_points = start_parallelepiped([0, 0], 2, 0.2)\n",
    "\n",
    "\n",
    "def f(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    return I_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "c5c554c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:36:42.749725Z",
     "start_time": "2023-03-10T19:36:42.729440Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_x1(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        plt.scatter([t for t in range(N+1)], x1, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x1')\n",
    "    plt.show()\n",
    "\n",
    "def f_x2(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        plt.scatter([t for t in range(N+1)], x2, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x2')\n",
    "    plt.show()\n",
    "\n",
    "def show_x(u):\n",
    "    f_x1(u)\n",
    "    f_x2(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028f8651",
   "metadata": {},
   "source": [
    "### SOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "66c6432d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:15:01.307043Z",
     "start_time": "2023-03-10T19:11:15.721289Z"
    }
   },
   "outputs": [],
   "source": [
    "soma = Soma(f)\n",
    "u, I, iterac, t = soma.find_min(pop_size = 300\n",
    "                 , num_of_x = 10\n",
    "                , a = [0]*50\n",
    "                , b = [100]*50\n",
    "                 , NStep = 50\n",
    "                 , prt = 0.4\n",
    "                 , Migrations = 50\n",
    "                 , MinDist = 0.1**5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "1c572c02",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:15:01.312349Z",
     "start_time": "2023-03-10T19:15:01.309327Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -0.5424999988097853\n",
      "final iteration: 27\n",
      "execution time: 225.5800199508667\n",
      "--------------------------------\n",
      "U: [8.99909325e-01 7.99987827e-01 7.00020338e-01 5.99970658e-01\n",
      " 5.00044771e-01 3.99970030e-01 3.00103373e-01 2.00005699e-01\n",
      " 1.00021063e-01 9.73545827e-06]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "47b5f381",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:15:01.790863Z",
     "start_time": "2023-03-10T19:15:01.313449Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "b8ccec01",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:15:01.847908Z",
     "start_time": "2023-03-10T19:15:01.792555Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AYMy44qa1tXXEWl9fny677DL94Ac/mPBQAAAA4xWzz9ykpaWpurpaP//5z2P1TwIAAHxpMf1A8X/+8x+FQqFY/pMAAABfyrhOS919991Rzx3HUTAY1OOPP66SkpKYDAYAADAe44qbX//611HPk5KSNHfuXF166aVav359TAYDAAAYj3HFTUdHR6znAAAAiAlu4gcAAKxC3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKuO6zw0AJKJwxFFzR6+6+weUkepRgT9d7iSX6bEAfI7xIze1tbXy+/3yeDzKy8vTjh07jup1r7zyimbMmKHTTz99cgcEAEmNbUEt2fiiLnpwt657aq8uenC3lmx8UY1tQdOjAfgco3Gzbds2lZeXa8OGDWptbdXSpUu1fPlydXZ2HvF1oVBIq1ev1llnnRWnSQEkssa2oNZu2aNgaCBqvSs0oLVb9hA4wBRjNG42bdqkNWvW6Morr9TChQt11113KTs7W3V1dUd83VVXXaWLL75YhYWFcZoUQKIKRxxVNbTLGeVrQ2tVDe0KR0bbAcAEY3Fz8OBBtbS0qLi4OGq9uLhYu3btGvN1jzzyiP7xj3+osrLyqL7P4OCg+vr6oh4AcLSaO3pHHLH5LEdSMDSg5o7e+A0F4IiMxU1PT4/C4bAyMzOj1jMzM9XV1TXqa/7+97/r5ptv1tatWzVjxtF9FrqmpkZer3f4kZ2dPeHZASSO7v6xw2Y8+wBMPuMfKHa5oq80cBxnxJokhcNhXXzxxaqqqtLJJ5981P/++vXrFQqFhh/79++f8MwAEkdGqiem+wBMPmOXgs+ZM0dut3vEUZru7u4RR3Mkqb+/X6+//rpaW1t19dVXS5IikYgcx9GMGTP0wgsv6MwzzxzxupSUFKWkpEzOmwBgvQJ/unxej7pCA6N+7sYlKct7+LJwAFODsSM3ycnJysvLU1NTU9R6U1OTioqKRuxPS0vTm2++qb179w4/ysrK9PWvf1179+7VokWL4jU6gATiTnKpsjRH0uGQ+ayh55WlOdzvBphCjN7Er6KiQpdccony8/NVWFio+vp6dXZ2qqysTNLhU0rvv/++HnvsMSUlJSkQCES9PiMjQx6PZ8Q6AMRSScCnulW5qmpoj/pwcZbXo8rSHJUEfAanA/B5RuNm5cqVOnDggKqrqxUMBhUIBLR9+3bNnz9fkhQMBr/wnjcAEA8lAZ+W5WRxh2JgGnA5jpNQN2fo6+uT1+tVKBRSWlqa6XEAAMBR+DK/v41fLQUAABBLxA0AALAKcQMAAKxC3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKsQNAACwCnEDAACsQtwAAACrEDcAAMAqxA0AALAKcQMAAKxC3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKsQNAACwCnEDAACsQtwAAACrEDcAAMAqM0wPAACIv3DEUXNHr7r7B5SR6lGBP13uJJfpsYCYIG4AIME0tgVV1dCuYGhgeM3n9aiyNEclAZ/ByYDY4LQUACSQxrag1m7ZExU2ktQVGtDaLXvU2BY0NBkQO8QNACSIcMRRVUO7nFG+NrRW1dCucGS0HcD0QdwAQIJo7ugdccTmsxxJwdCAmjt64zcUMAmIGwBIEN39Y4fNePYBUxVxAwAJIiPVE9N9wFRF3ABAgijwp8vn9WisC75dOnzVVIE/PZ5jATFH3ABAgnAnuVRZmiNJIwJn6HllaQ73u8G0R9wAQAIpCfhUtypXWd7oU09ZXo/qVuVynxtYgZv4AUCCKQn4tCwnizsUw1rEDQAkIHeSS4ULZpseA5gUnJYCAABWIW4AAIBViBsAAGAV4gYAAFiFuAEAAFYhbgAAgFWIGwAAYBXiBgAAWIW4AQAAViFuAACAVYgbAABgFeIGAABYhbgBAABWIW4AAIBViBsAAGAV4gYAAFiFuAEAAFYhbgAAgFWIGwAAYBXiBgAAWIW4AQAAViFuAACAVYgbAABgFeIGAABYhbgBAABWmWF6AAAAxisccdTc0avu/gFlpHpU4E+XO8lleiwYRtwAAKalxragqhraFQwNDK/5vB5VluaoJOAzOBlMM35aqra2Vn6/Xx6PR3l5edqxY8eYe5955hktW7ZMc+fOVVpamgoLC/WnP/0pjtMCAKaCxrag1m7ZExU2ktQVGtDaLXvU2BY0NBmmAqNxs23bNpWXl2vDhg1qbW3V0qVLtXz5cnV2do66/+WXX9ayZcu0fft2tbS06Hvf+55KS0vV2toa58kBAKaEI46qGtrljPK1obWqhnaFI6PtQCJwOY5j7Ke/aNEi5ebmqq6ubnht4cKFWrFihWpqao7q3zj11FO1cuVK3XrrraN+fXBwUIODg8PP+/r6lJ2drVAopLS0tIm9AQBA3L36jwO66MHdX7jvyR9/W4ULZsdhIsRDX1+fvF7vUf3+Nnbk5uDBg2ppaVFxcXHUenFxsXbt2nVU/0YkElF/f7/S09PH3FNTUyOv1zv8yM7OntDcAACzuvsHvnjTl9gH+xiLm56eHoXDYWVmZkatZ2Zmqqur66j+jTvvvFMff/yxLrjggjH3rF+/XqFQaPixf//+Cc0NADArI9UT032wj/GrpVyu6Ev2HMcZsTaaJ598Ur/4xS/03HPPKSMjY8x9KSkpSklJmfCcAICpocCfLp/Xo67QwKifu3FJyvIeviwcicnYkZs5c+bI7XaPOErT3d094mjO523btk1r1qzR7373O5199tmTOSYAYIpxJ7lUWZoj6XDIfNbQ88rSHO53k8CMxU1ycrLy8vLU1NQUtd7U1KSioqIxX/fkk0/qsssu0xNPPKHzzjtvsscEAExBJQGf6lblKssbfeopy+tR3apc7nOT4IyelqqoqNAll1yi/Px8FRYWqr6+Xp2dnSorK5N0+PMy77//vh577DFJh8Nm9erV+s1vfqNvf/vbw0d9Zs6cKa/Xa+x9AADiryTg07KcLO5QjBGMxs3KlSt14MABVVdXKxgMKhAIaPv27Zo/f74kKRgMRt3z5oEHHtChQ4e0bt06rVu3bnj90ksv1aOPPhrv8QEAhrmTXFzujRGM3ufGhC9znTwAAJgapsV9bgAAACYDcQMAAKxC3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKsQNAACwCnEDAACsQtwAAACrEDcAAMAqxA0AALAKcQMAAKxC3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKsQNAACwCnEDAACsQtwAAACrEDcAAMAqxA0AALDKDNMDAACQ6MIRR80dveruH1BGqkcF/nS5k1ymx5q2iBsAAAxqbAuqqqFdwdDA8JrP61FlaY5KAj6Dk01fnJYCAMCQxrag1m7ZExU2ktQVGtDaLXvU2BY0NNn0RtwAAGBAOOKoqqFdzihfG1qramhXODLaDhwJcQMAgAHNHb0jjth8liMpGBpQc0dv/IayBHEDAIAB3f1jh8149uH/ETcAABiQkeqJ6T78P+IGAAADCvzp8nk9GuuCb5cOXzVV4E+P51hWIG4AADDAneRSZWmOJI0InKHnlaU53O9mHIgbAAAMKQn4VLcqV1ne6FNPWV6P6lblcp+bceImfgAAGFQS8GlZThZ3KI4h4gYAAMPcSS4VLphtegxrcFoKAABYhbgBAABWIW4AAIBViBsAAGAV4gYAAFiFuAEAAFYhbgAAgFWIGwAAYBXiBgAAWIW4AQAAViFuAACAVYgbAABgFeIGAABYhbgBAABWIW4AAIBViBsAAGAV4gYAAFiFuAEAAFYhbgAAgFWIGwAAYBXiBgAAWIW4AQAAViFuAACAVYgbAABgFeIGAABYZYbpAQAAgB3CEUfNHb3q7h9QRqpHBf50uZNccZ/D+JGb2tpa+f1+eTwe5eXlaceOHUfc/9JLLykvL08ej0cnnXSS7r///jhNCgAAxtLYFtSSjS/qogd367qn9uqiB3drycYX1dgWjPssRuNm27ZtKi8v14YNG9Ta2qqlS5dq+fLl6uzsHHV/R0eHzj33XC1dulStra265ZZbdO211+rpp5+O8+QAAGBIY1tQa7fsUTA0ELXeFRrQ2i174h44LsdxnLh+x89YtGiRcnNzVVdXN7y2cOFCrVixQjU1NSP233TTTXr++ee1b9++4bWysjK98cYbevXVV4/qe/b19cnr9SoUCiktLW3ibwIAgAQWjjhasvHFEWEzxCUpy+vRzpvOnNApqi/z+9vYkZuDBw+qpaVFxcXFUevFxcXatWvXqK959dVXR+w/55xz9Prrr+vTTz8d9TWDg4Pq6+uLegAAgNho7ugdM2wkyZEUDA2ouaM3bjMZi5uenh6Fw2FlZmZGrWdmZqqrq2vU13R1dY26/9ChQ+rp6Rn1NTU1NfJ6vcOP7Ozs2LwBAACg7v6xw2Y8+2LB+AeKXa7oQ1SO44xY+6L9o60PWb9+vUKh0PBj//79E5wYAAAMyUj1xHRfLBi7FHzOnDlyu90jjtJ0d3ePODozJCsra9T9M2bM0OzZs0d9TUpKilJSUmIzNAAAiFLgT5fP61FXaECjfYh36DM3Bf70uM1k7MhNcnKy8vLy1NTUFLXe1NSkoqKiUV9TWFg4Yv8LL7yg/Px8HXPMMZM2KwAAGJ07yaXK0hxJh0Pms4aeV5bmxPV+N0ZPS1VUVOihhx7S5s2btW/fPl1//fXq7OxUWVmZpMOnlFavXj28v6ysTO+++64qKiq0b98+bd68WQ8//LBuuOEGU28BAICEVxLwqW5VrrK80aeesrwe1a3KVUnAF9d5jN6heOXKlTpw4ICqq6sVDAYVCAS0fft2zZ8/X5IUDAaj7nnj9/u1fft2XX/99brvvvs0b9483X333Tr//PNNvQUAAKDDgbMsJ2tK3KHY6H1uTOA+NwAATD/T4j43AAAAk4G4AQAAViFuAACAVYgbAABgFeIGAABYhbgBAABWIW4AAIBViBsAAGAV4gYAAFjF6J9fMGHohsx9fX2GJwEAAEdr6Pf20fxhhYSLm/7+fklSdna24UkAAMCX1d/fL6/Xe8Q9Cfe3pSKRiD744AOlpqbK5YrtH/Pq6+tTdna29u/fz9+tmgL4eUwt/DymHn4mUws/jyNzHEf9/f2aN2+ekpKO/KmahDtyk5SUpOOPP35Sv0daWhr/w5xC+HlMLfw8ph5+JlMLP4+xfdERmyF8oBgAAFiFuAEAAFYhbmIoJSVFlZWVSklJMT0KxM9jquHnMfXwM5la+HnETsJ9oBgAANiNIzcAAMAqxA0AALAKcQMAAKxC3AAAAKsQNzFSW1srv98vj8ejvLw87dixw/RICaumpkbf+ta3lJqaqoyMDK1YsUJ/+9vfTI+F/1NTUyOXy6Xy8nLToySs999/X6tWrdLs2bM1a9YsnX766WppaTE9VkI6dOiQfvazn8nv92vmzJk66aSTVF1drUgkYnq0aY24iYFt27apvLxcGzZsUGtrq5YuXarly5ers7PT9GgJ6aWXXtK6deu0e/duNTU16dChQyouLtbHH39serSE99prr6m+vl6nnXaa6VES1r///W8tXrxYxxxzjP74xz+qvb1dd955p4499ljToyWkjRs36v7779e9996rffv26Y477tCvfvUr3XPPPaZHm9a4FDwGFi1apNzcXNXV1Q2vLVy4UCtWrFBNTY3BySBJ//rXv5SRkaGXXnpJ3/nOd0yPk7A++ugj5ebmqra2VrfddptOP/103XXXXabHSjg333yzXnnlFY4uTxHf//73lZmZqYcffnh47fzzz9esWbP0+OOPG5xseuPIzQQdPHhQLS0tKi4ujlovLi7Wrl27DE2FzwqFQpKk9PR0w5MktnXr1um8887T2WefbXqUhPb8888rPz9fP/zhD5WRkaEzzjhDDz74oOmxEtaSJUv05z//WW+//bYk6Y033tDOnTt17rnnGp5seku4P5wZaz09PQqHw8rMzIxaz8zMVFdXl6GpMMRxHFVUVGjJkiUKBAKmx0lYTz31lPbs2aPXXnvN9CgJ75133lFdXZ0qKip0yy23qLm5Wddee61SUlK0evVq0+MlnJtuukmhUEinnHKK3G63wuGwbr/9dl100UWmR5vWiJsYcblcUc8dxxmxhvi7+uqr9de//lU7d+40PUrC2r9/v6677jq98MIL8ng8psdJeJFIRPn5+frlL38pSTrjjDP01ltvqa6ujrgxYNu2bdqyZYueeOIJnXrqqdq7d6/Ky8s1b948XXrppabHm7aImwmaM2eO3G73iKM03d3dI47mIL6uueYaPf/883r55Zd1/PHHmx4nYbW0tKi7u1t5eXnDa+FwWC+//LLuvfdeDQ4Oyu12G5wwsfh8PuXk5EStLVy4UE8//bShiRLbjTfeqJtvvlkXXnihJOkb3/iG3n33XdXU1BA3E8BnbiYoOTlZeXl5ampqilpvampSUVGRoakSm+M4uvrqq/XMM8/oxRdflN/vNz1SQjvrrLP05ptvau/evcOP/Px8/ehHP9LevXsJmzhbvHjxiFsjvP3225o/f76hiRLbJ598oqSk6F/FbrebS8EniCM3MVBRUaFLLrlE+fn5KiwsVH19vTo7O1VWVmZ6tIS0bt06PfHEE3ruueeUmpo6fFTN6/Vq5syZhqdLPKmpqSM+7/SVr3xFs2fP5nNQBlx//fUqKirSL3/5S11wwQVqbm5WfX296uvrTY+WkEpLS3X77bfrhBNO0KmnnqrW1lZt2rRJV1xxhenRpjcHMXHfffc58+fPd5KTk53c3FznpZdeMj1SwpI06uORRx4xPRr+z3e/+13nuuuuMz1GwmpoaHACgYCTkpLinHLKKU59fb3pkRJWX1+fc9111zknnHCC4/F4nJNOOsnZsGGDMzg4aHq0aY373AAAAKvwmRsAAGAV4gYAAFiFuAEAAFYhbgAAgFWIGwAAYBXiBgAAWIW4AQAAViFuAACAVYgbAABgFeIGgDX+53/+R+Xl5abHAGAYcQMAAKzC35YCYIXLLrtMv/3tb6PWOjo6dOKJJ5oZCIAxxA0AK4RCIS1fvlyBQEDV1dWSpLlz58rtdhueDEC8zTA9AADEgtfrVXJysmbNmqWsrCzT4wAwiM/cAAAAqxA3AADAKsQNAGskJycrHA6bHgOAYcQNAGuceOKJ+stf/qJ//vOf6unpUSQSMT0SAAOIGwDWuOGGG+R2u5WTk6O5c+eqs7PT9EgADOBScAAAYBWO3AAAAKsQNwAAwCrEDQAAsApxAwAArELcAAAAqxA3AADAKsQNAACwCnEDAACsQtwAAACrEDcAAMAqxA0AALDK/wLiYDdsYlWv4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(10)], u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d54a2176",
   "metadata": {},
   "source": [
    "### MSOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "a82df8db",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:51:15.774288Z",
     "start_time": "2023-03-10T19:36:47.415085Z"
    }
   },
   "outputs": [],
   "source": [
    "msoma = Msoma(f)\n",
    "u, I, iterac, t = msoma.find_min(pop_size = 400\n",
    "                 , num_of_x = 10\n",
    "                , a = [0]*50\n",
    "                , b = [100]*50\n",
    "                 , NStep = 40\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 50\n",
    "                 , MinDist = 0.1**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "f3b87328",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:51:15.779702Z",
     "start_time": "2023-03-10T19:51:15.776546Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -0.5424745548007707\n",
      "final iteration: 14\n",
      "execution time: 868.348531961441\n",
      "--------------------------------\n",
      "U: [0.90943877 0.80465411 0.71111912 0.59681182 0.49432263 0.3868026\n",
      " 0.30740015 0.19853583 0.09897847 0.        ]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "3441bad0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T19:51:16.347150Z",
     "start_time": "2023-03-10T19:51:15.780750Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "9dadec99",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-10T20:15:49.554679Z",
     "start_time": "2023-03-10T20:15:49.477098Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(10)], u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3cecc24",
   "metadata": {},
   "source": [
    "# Stochastic systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "858ab381",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T16:13:19.386166Z",
     "start_time": "2023-06-12T16:13:19.375591Z"
    }
   },
   "outputs": [],
   "source": [
    "test_rand = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c0c739df",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T16:13:21.964802Z",
     "start_time": "2023-06-12T16:13:21.938637Z"
    }
   },
   "outputs": [],
   "source": [
    "rand_list = []\n",
    "for _ in range(10000):\n",
    "    rand_list.append(20*np.random.normal(loc=0.0, scale=1.0))\n",
    "    \n",
    "test_rand['test'] = rand_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "abca7132",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T16:13:22.474545Z",
     "start_time": "2023-06-12T16:13:22.375848Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: >"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_rand['test'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b1b03643",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:31:06.774551Z",
     "start_time": "2023-07-03T07:31:06.770443Z"
    }
   },
   "outputs": [],
   "source": [
    "def start_parallelepiped(start_conditions : list\n",
    "                         , indent : int\n",
    "                         , step : int) -> list:\n",
    "    \n",
    "    pre_start_conditions = []\n",
    "    for el in start_conditions:\n",
    "        pre_start_conditions.append([n for n in np.arange(el-(step*indent), el+(step*indent)+1, step)])\n",
    "        \n",
    "    if len(pre_start_conditions) == 1:\n",
    "        return pre_start_conditions[0]\n",
    "    \n",
    "    else:  \n",
    "        tmp = list(product(pre_start_conditions[0], pre_start_conditions[1]))\n",
    "        if len(start_conditions) > 2:\n",
    "            for i in range(2, len(start_conditions)):\n",
    "                tmp = list(product(tmp, pre_start_conditions[i]))\n",
    "                for ind in range(len(tmp)):\n",
    "                    ff = list(tmp[ind][0])\n",
    "                    ff.append(tmp[ind][1])\n",
    "                    tmp[ind] = ff\n",
    "        else:\n",
    "            for ind in range(len(tmp)):\n",
    "                tmp[ind] = list(tmp[ind])\n",
    "                \n",
    "        return tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d16da428",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:31:07.419153Z",
     "start_time": "2023-07-03T07:31:07.409660Z"
    }
   },
   "outputs": [],
   "source": [
    "def info_print(u, I, iterac, t):\n",
    "    print(f'target function value: {I}')\n",
    "    print(f'final iteration: {iterac}')\n",
    "    print(f'execution time: {t}')\n",
    "    print('--------------------------------')\n",
    "    print(f'U: {u}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38339b26",
   "metadata": {},
   "source": [
    "## ex1 (50 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "23a33c8c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:26:33.339250Z",
     "start_time": "2023-07-03T07:26:33.330246Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def model(t, x, u):\n",
    "    return x[t] + u[t] + (20 * np.random.normal(loc=0.0, scale=1.0))\n",
    "\n",
    "\n",
    "all_start_points = start_parallelepiped([0], 2, 100)\n",
    "\n",
    "\n",
    "def f(u):\n",
    "    N = 50\n",
    "    I_sum = 0\n",
    "    for point in all_start_points:\n",
    "        x = [point]\n",
    "        sumU = 0\n",
    "        for t in range(N):\n",
    "            x.append(model(t, x, u))\n",
    "            sumU += (1.1**(-t)) * (u[t]**2)\n",
    "        I_sum += 0.5*(sumU) + x[N]\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    return I_sum "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aa1b30a8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:26:33.825449Z",
     "start_time": "2023-07-03T07:26:33.816098Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_x(u):\n",
    "    N = 50\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x = [point]\n",
    "        sumU = 0\n",
    "        for t in range(N):\n",
    "            x.append(model(t, x, u))\n",
    "            sumU += (1.1**(-t)) * (u[t]**2)\n",
    "        I_sum += 0.5*(sumU) + x[N]\n",
    "        plt.scatter([t for t in range(51)], x, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x')\n",
    "    plt.show()\n",
    "    return I_sum "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "514c36e8",
   "metadata": {},
   "source": [
    "### SOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43d38b47",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T07:26:56.435248Z",
     "start_time": "2023-07-03T07:26:49.009549Z"
    }
   },
   "outputs": [],
   "source": [
    "soma = Soma(f)\n",
    "u, I, iterac, t = soma.find_min(pop_size = 1500\n",
    "                 , num_of_x = 50\n",
    "                , a = [-110]*50\n",
    "                , b = [0]*50\n",
    "                 , NStep = 100\n",
    "            \n",
    "                                , prt = 0.4\n",
    "                 , Migrations = 100\n",
    "                 , MinDist = 0.1**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "4f5d8ca8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T15:23:14.799544Z",
     "start_time": "2023-06-12T15:23:14.795575Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -428.0443840757747\n",
      "final iteration: 100\n",
      "execution time: 3173.59712100029\n",
      "--------------------------------\n",
      "U: [-1.43797455e+00 -9.33943173e-01 -2.77872423e+00 -1.90836168e-03\n",
      " -2.76620573e+00 -1.30188623e+00 -1.95762587e+00 -4.07505561e+00\n",
      " -5.94662191e-04 -4.58038130e+00 -2.94485270e+00 -8.98347760e-01\n",
      " -1.20437360e-03 -5.88439446e+00 -6.54477234e-01 -1.45870248e-05\n",
      " -9.01739672e+00 -1.51294035e-01 -1.40869736e+01 -1.78771084e+01\n",
      " -2.52992732e+00 -8.59201695e+00 -9.44965597e+00 -4.51459358e-04\n",
      " -1.43033055e+01 -1.32709939e-01 -3.08817105e+01 -1.63368826e+01\n",
      " -1.84266040e+01 -5.03659456e-02 -2.21114915e+01 -1.21651462e+01\n",
      " -1.76229187e+01 -3.42318501e+01 -2.60940511e+01 -2.20395824e+01\n",
      " -2.05916119e+01 -2.84085831e+01 -3.16703344e+01 -9.31971741e+01\n",
      " -2.30466300e-01 -5.87243841e+01 -2.69874014e+01 -5.07859982e+01\n",
      " -5.20466149e+01 -4.89474765e+01 -6.48883306e+01 -1.96838578e+01\n",
      " -7.46950728e+01 -9.07338228e+01]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a82e27d9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T15:23:14.871064Z",
     "start_time": "2023-06-12T15:23:14.800511Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "-345.3260659446342"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "661f82c9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T15:23:14.931954Z",
     "start_time": "2023-06-12T15:23:14.872964Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list(range(50)), u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2243a525",
   "metadata": {},
   "source": [
    "### MSOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "bce9d4cb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T14:03:15.070256Z",
     "start_time": "2023-06-12T13:33:11.524896Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████| 50/50 [30:03<00:00, 36.06s/it]\n"
     ]
    }
   ],
   "source": [
    "msoma = Msoma(f)\n",
    "u, I, iterac, t = msoma.find_min(pop_size = 600\n",
    "                 , num_of_x = 50\n",
    "                , a = [-110]*50\n",
    "                , b = [0]*50\n",
    "                 , NStep = 40\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 50\n",
    "                 , MinDist = 0.1**10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5f1a1df0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T14:03:15.076146Z",
     "start_time": "2023-06-12T14:03:15.072770Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -583.9370317480074\n",
      "final iteration: 50\n",
      "execution time: 1803.5392441749573\n",
      "--------------------------------\n",
      "U: [ -3.0883004   -1.39553645  -1.97236609  -5.43609701  -5.07477029\n",
      "  -0.58664172   0.15147878  -4.79907938  -6.49167647  -4.93282996\n",
      "  -5.41228319  -3.4353857   -4.51682063  -3.96412566  -3.11575534\n",
      "  -9.98754594  -6.82329625 -13.89035356  -9.4460306  -12.46885513\n",
      "  -9.00476655  -5.31665373  -7.6126076   -9.97378237 -18.18233345\n",
      " -12.95627603 -13.92444372 -20.03301022 -17.14299848 -35.31002019\n",
      " -21.5251251  -35.31402477 -19.81487601 -24.82519341 -18.40832717\n",
      " -17.68720838  20.35082819 -32.46563832 -34.37856924 -41.0467233\n",
      " -53.61940448 -66.48037022 -56.42212593 -70.28632029 -93.35043661\n",
      " -51.14271206 -83.59603678 -48.27566975 -87.09812389 -53.60101794]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "51b6f7d8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T14:03:15.148451Z",
     "start_time": "2023-06-12T14:03:15.077105Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "-457.0743380297311"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1dead277",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-12T14:03:15.208265Z",
     "start_time": "2023-06-12T14:03:15.150173Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list(range(50)), u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "393504ee",
   "metadata": {},
   "source": [
    "## ex2 (10 dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3fda761b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:57:33.039490Z",
     "start_time": "2023-07-03T13:57:33.026235Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def eq_x1(x2, t):\n",
    "    return x2[t] + (0 *np.random.normal(loc=0.0, scale=1.0))\n",
    "\n",
    "def eq_x2(x1, x2, u, N, t):\n",
    "    return 2*x2[t]-x1[t]+((1/(N**2))*u[t]) + (0 *np.random.normal(loc=0.0, scale=1.0))\n",
    "\n",
    "all_start_points = start_parallelepiped([0, 0], 2, 0.2)\n",
    "\n",
    "\n",
    "def f(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    return I_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "49decc40",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:57:33.875823Z",
     "start_time": "2023-07-03T13:57:33.861244Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_x1(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        plt.scatter([t for t in range(N+1)], x1, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x1')\n",
    "    plt.show()\n",
    "\n",
    "def f_x2(u): \n",
    "    N = 10\n",
    "    I_sum = 0\n",
    "    \n",
    "    for point in all_start_points:\n",
    "        x1 = [point[0]]\n",
    "        x2 = [point[1]]\n",
    "    \n",
    "        sum_U = 0\n",
    "    \n",
    "        for t in range(N):\n",
    "            x1.append(eq_x1(x2, t))\n",
    "            x2.append(eq_x2(x1, x2, u, N, t))\n",
    "\n",
    "            sum_U += u[t]**2\n",
    "        I_sum += (1/(2*N))*sum_U - x1[N]\n",
    "        plt.scatter([t for t in range(N+1)], x2, linewidth = 0.1)\n",
    "        \n",
    "    I_sum /= len(all_start_points)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x2')\n",
    "    plt.show()\n",
    "\n",
    "def show_x(u):\n",
    "    f_x1(u)\n",
    "    f_x2(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fa98615",
   "metadata": {},
   "source": [
    "### SOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0971b969",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T14:02:37.335398Z",
     "start_time": "2023-07-03T13:57:47.342428Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 35%|██████████████▋                           | 35/100 [04:49<08:57,  8.27s/it]\n"
     ]
    }
   ],
   "source": [
    "soma = Soma(f)\n",
    "u, I, iterac, t = soma.find_min(pop_size = 300\n",
    "                 , num_of_x = 10\n",
    "                , a = [0]*50\n",
    "                , b = [100]*50\n",
    "                 , NStep = 20\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 100\n",
    "                 , MinDist = 0.1**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "263bd4e3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T14:02:37.338213Z",
     "start_time": "2023-07-03T14:02:37.336453Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -0.5424999972023219\n",
      "final iteration: 35\n",
      "execution time: 289.9875509738922\n",
      "--------------------------------\n",
      "U: [0.89989331 0.80006371 0.70009257 0.59999257 0.49994338 0.39990961\n",
      " 0.29999732 0.200069   0.10012547 0.        ]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "26d72ea4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T14:02:37.818129Z",
     "start_time": "2023-07-03T14:02:37.339138Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4232f72a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T14:02:37.874095Z",
     "start_time": "2023-07-03T14:02:37.819569Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(10)], u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74dbc94a",
   "metadata": {},
   "source": [
    "### MSOMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2771cd45",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:50:48.784192Z",
     "start_time": "2023-07-03T09:52:58.397708Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████| 50/50 [3:57:47<00:00, 285.35s/it]\n"
     ]
    }
   ],
   "source": [
    "msoma = Msoma(f)\n",
    "u, I, iterac, t = msoma.find_min(pop_size = 600\n",
    "                 , num_of_x = 10\n",
    "                , a = [0]*50\n",
    "                , b = [100]*50\n",
    "                 , NStep = 50\n",
    "                 , prt = 0.3\n",
    "                 , Migrations = 50\n",
    "                 , MinDist = 0.1**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cc577c62",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:50:48.790658Z",
     "start_time": "2023-07-03T13:50:48.786607Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target function value: -0.527295296270643\n",
      "final iteration: 50\n",
      "execution time: 14270.38245010376\n",
      "--------------------------------\n",
      "U: [0.90968184 0.7251045  0.70847773 0.71064074 0.43375787 0.39085757\n",
      " 0.35906478 0.26445178 0.02305616 0.        ]\n"
     ]
    }
   ],
   "source": [
    "info_print(u, I, iterac, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "35c2db5b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:50:49.284251Z",
     "start_time": "2023-07-03T13:50:48.791698Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_x(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e1e20e8a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-03T13:50:49.384621Z",
     "start_time": "2023-07-03T13:50:49.285155Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'u')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pbGxUZWWl1q9fr46ODpWUlGjJkiXq7u4+4ef8fr9WrFihSy65ZIomBQAAsWJcTwWPlPnz56ugoEANDQ3D2/Ly8rR06VLV1dWN+bkrr7xSX/jCF+R0OvX73/9ee/fuHXPfwcFBDQ4ODr8PBALKycnhqeAATlkwZHHXF2CTSX8qeCQcPXpU7e3tWrduXdj20tJS7d69e8zPPfHEE3r77be1ZcsWbdy48TO/T11dnWpqaiY8L4D41rLPp5qmzrCHgWa7XdpQls96PUCUse20VF9fn4LBoDIzM8O2Z2ZmqqenZ9TP/OMf/9C6deu0detWJSaeXJdVV1fL7/cPvw4ePDjh2QHEl5Z9Pq3asmfEU857/ANatWWPWvb5bJoMwGhsX+fG4Qg/pGtZ1ohtkhQMBnXVVVeppqZG55577kl//eTkZCUnJ094TgDxKRiyVNPUqdHO31s6/iiJmqZOLcrP4hQVECVsi5sZM2bI6XSOOErT29s74miOJPX39+u1115TR0eHbrzxRklSKBSSZVlKTEzUiy++qIsvvnhKZgcQP9q6jow4YvNJliSff0BtXUdYqBCIEradlkpKSlJhYaFaW1vDtre2tqq4uHjE/qmpqXrjjTe0d+/e4VdFRYW++MUvau/evZo/f/5UjQ4gjvT2jx0249kPwOSz9bRUVVWVrr76ahUVFWnBggXatGmTuru7VVFRIen49TLvvfeennzySSUkJMjr9YZ9PiMjQy6Xa8R2AIiUjBTXZ+90CvsBmHy2xk15ebkOHz6s2tpa+Xw+eb1eNTc3Kzc3V5Lk8/k+c80bAJhM8zxpyna71OMfGPW6G4eOP+V8nidtqkcDMAZb17mxw6ncJw8A0v/ulpIUFjhDlw83LC/gdnBgkp3K32/bH78AANFusTdbDcsLlOUOP/WU5XYRNkAUsv1WcACIBYu92VqUn8UKxUAMIG4A4CQ5ExzG3O7NoyRgMuIGAOIMj5KA6bjmBgDiCI+SQDwgbgAgTnzWoySk44+SCIbi6iZaGIi4AYA4cSqPkgBiGXEDAHGCR0kgXhA3ABAneJQE4gVxAwBxYuhREmPd8O3Q8bumeJQEYh1xAwBxwpng0IayfEkaEThD7zeU5bPeDWIecQMAcYRHSSAesIgfAMQZHiUB0xE3ABCHTHqUBPBpnJYCAABGIW4AAIBRiBsAAGAU4gYAABiFuAEAAEYhbgAAgFGIGwAAYBTiBgAAGIW4AQAARiFuAACAUYgbAABgFOIGAAAYhbgBAABGIW4AAIBRiBsAAGAU4gYAABiFuAEAAEYhbgAAgFGIGwAAYBTiBgAAGIW4AQAARiFuAACAUYgbAABglES7BwAAYLyCIUttXUfU2z+gjBSX5nnS5Exw2D0WbEbcAABiUss+n2qaOuXzDwxvy3a7tKEsX4u92TZOBrtxWgoAEHNa9vm0asuesLCRpB7/gFZt2aOWfT6bJkM0IG4AADElGLJU09Qpa5R/G9pW09SpYGi0PRAPiBsAQExp6zoy4ojNJ1mSfP4BtXUdmbqhEFWIGwBATOntHztsxrMfzEPcAABiSkaKK6L7wTzEDQAgpszzpCnb7dJYN3w7dPyuqXmetKkcC1GEuAEAxBRngkMbyvIlaUTgDL3fUJbPejdxjLgBAMScxd5sNSwvUJY7/NRTltulhuUFrHMT51jEDwAQkxZ7s7UoP4sVijECcQMAiFnOBIcWzEm3ewxEGU5LAQAAoxA3AADAKMQNAAAwCnEDAACMQtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAo9geN/X19fJ4PHK5XCosLNTOnTvH3Pf555/XokWLNHPmTKWmpmrBggX605/+NIXTAgCAaGdr3DQ2NqqyslLr169XR0eHSkpKtGTJEnV3d4+6/44dO7Ro0SI1Nzervb1d3/zmN1VWVqaOjo4pnhwAAEQrh2VZll3ffP78+SooKFBDQ8Pwtry8PC1dulR1dXUn9TXmzp2r8vJy3XHHHSe1fyAQkNvtlt/vV2pq6rjmBgAAU+tU/n7bduTm6NGjam9vV2lpadj20tJS7d69+6S+RigUUn9/v9LS0sbcZ3BwUIFAIOwFAADMZVvc9PX1KRgMKjMzM2x7Zmamenp6Tupr3Hffffrwww+1bNmyMfepq6uT2+0efuXk5ExobgAAEN1sv6DY4XCEvbcsa8S20TzzzDP6+c9/rsbGRmVkZIy5X3V1tfx+//Dr4MGDE54ZAABEr0S7vvGMGTPkdDpHHKXp7e0dcTTn0xobG3X99dfr2Wef1aWXXnrCfZOTk5WcnDzheQEAQGyw7chNUlKSCgsL1draGra9tbVVxcXFY37umWee0cqVK/X000/r8ssvn+wxAQBAjLHtyI0kVVVV6eqrr1ZRUZEWLFigTZs2qbu7WxUVFZKOn1J677339OSTT0o6HjYrVqzQL37xC331q18dPuozbdo0ud1u234OAAAQPWyNm/Lych0+fFi1tbXy+Xzyer1qbm5Wbm6uJMnn84WtefPoo4/q2LFjWr16tVavXj28/ZprrtGvf/3rqR4fAABEIVvXubED69wAABB7YmKdGwAAgMlA3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAAAwCnEDAACMQtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAAAwCnEDAACMQtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAAAwCnEDAACMQtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAAAwCnEDAACMQtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjJJo9wAAAMS7YMhSW9cR9fYPKCPFpXmeNDkTHHaPFbOIGwAAbNSyz6eapk75/APD27LdLm0oy9dib7aNk8UuTksBAGCTln0+rdqyJyxsJKnHP6BVW/aoZZ/PpsliG3EDAIANgiFLNU2dskb5t6FtNU2dCoZG2wMnQtwAAGCDtq4jI47YfJIlyecfUFvXkakbyhDEDQAANujtHztsxrMf/oe4AQDABhkprojuh/8hbgAAsME8T5qy3S6NdcO3Q8fvmprnSZvKsYxA3AAAYANngkMbyvIlaUTgDL3fUJbPejfjQNwAAGCTxd5sNSwvUJY7/NRTltulhuUFMbfOTTBk6eW3D+sPe9/Ty28ftu1OL9sX8auvr9e9994rn8+nuXPn6oEHHlBJScmY+2/fvl1VVVV68803NWvWLP3kJz9RRUXFFE4MAEDkLPZma1F+VsyvUBxNixHaeuSmsbFRlZWVWr9+vTo6OlRSUqIlS5aou7t71P27urp02WWXqaSkRB0dHbr99tu1Zs0aPffcc1M8OQAAkeNMcGjBnHT9vwvO1II56TEZNtG0GKHDsizbVgeaP3++CgoK1NDQMLwtLy9PS5cuVV1d3Yj9b7vtNm3btk379+8f3lZRUaHXX39dL7/88kl9z0AgILfbLb/fr9TU1In/EAAAxLFgyNJFd/9lzDV7HDp+mm3XbRdPKNpO5e+3bUdujh49qvb2dpWWloZtLy0t1e7du0f9zMsvvzxi/29961t67bXX9PHHH4/6mcHBQQUCgbAXAACIjGhcjNC2uOnr61MwGFRmZmbY9szMTPX09Iz6mZ6enlH3P3bsmPr6+kb9TF1dndxu9/ArJycnMj8AAACIysUIbb9byuEIP0RlWdaIbZ+1/2jbh1RXV8vv9w+/Dh48OMGJAQDAkGhcjNC2u6VmzJghp9M54ihNb2/viKMzQ7KyskbdPzExUenp6aN+Jjk5WcnJyZEZGgAAhBlajLDHPzDqQ0CHrrmZysUIbTtyk5SUpMLCQrW2toZtb21tVXFx8aifWbBgwYj9X3zxRRUVFem0006btFkBAMDoonExQltPS1VVVemxxx7T5s2btX//fq1du1bd3d3D69ZUV1drxYoVw/tXVFTonXfeUVVVlfbv36/Nmzfr8ccf1y233GLXjwAAQNyLtsUIbV3Er7y8XIcPH1Ztba18Pp+8Xq+am5uVm5srSfL5fGFr3ng8HjU3N2vt2rV65JFHNGvWLD344IO64oor7PoRAACAomsxQlvXubED69wAABB7YmKdGwAAgMlA3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAAAwCnEDAACMYuvjF+wwtCBzIBCweRIAAHCyhv5un8yDFeIubvr7+yVJOTk5Nk8CAABOVX9/v9xu9wn3ibtnS4VCIR06dEgpKSlyOCL7MK9AIKCcnBwdPHiQ51ZFAX4f0YXfR/ThdxJd+H2cmGVZ6u/v16xZs5SQcOKrauLuyE1CQoJmz549qd8jNTWV/2FGEX4f0YXfR/ThdxJd+H2M7bOO2AzhgmIAAGAU4gYAABiFuImg5ORkbdiwQcnJyXaPAvH7iDb8PqIPv5Powu8jcuLugmIAAGA2jtwAAACjEDcAAMAoxA0AADAKcQMAAIxC3ERIfX29PB6PXC6XCgsLtXPnTrtHilt1dXX6yle+opSUFGVkZGjp0qX6+9//bvdY+D91dXVyOByqrKy0e5S49d5772n58uVKT0/X9OnTdcEFF6i9vd3useLSsWPH9NOf/lQej0fTpk3TOeeco9raWoVCIbtHi2nETQQ0NjaqsrJS69evV0dHh0pKSrRkyRJ1d3fbPVpc2r59u1avXq1XXnlFra2tOnbsmEpLS/Xhhx/aPVrce/XVV7Vp0yadf/75do8St/79739r4cKFOu200/THP/5RnZ2duu+++3TGGWfYPVpcuvvuu/XLX/5SDz/8sPbv36977rlH9957rx566CG7R4tp3AoeAfPnz1dBQYEaGhqGt+Xl5Wnp0qWqq6uzcTJI0r/+9S9lZGRo+/bt+trXvmb3OHHrgw8+UEFBgerr67Vx40ZdcMEFeuCBB+weK+6sW7dOL730EkeXo8S3v/1tZWZm6vHHHx/edsUVV2j69Ol66qmnbJwstnHkZoKOHj2q9vZ2lZaWhm0vLS3V7t27bZoKn+T3+yVJaWlpNk8S31avXq3LL79cl156qd2jxLVt27apqKhI3/ve95SRkaELL7xQv/rVr+weK25ddNFF+vOf/6y33npLkvT6669r165duuyyy2yeLLbF3YMzI62vr0/BYFCZmZlh2zMzM9XT02PTVBhiWZaqqqp00UUXyev12j1O3Prtb3+rPXv26NVXX7V7lLh34MABNTQ0qKqqSrfffrva2tq0Zs0aJScna8WKFXaPF3duu+02+f1+nXfeeXI6nQoGg7rzzjv1/e9/3+7RYhpxEyEOhyPsvWVZI7Zh6t14443629/+pl27dtk9Stw6ePCgbr75Zr344otyuVx2jxP3QqGQioqKdNddd0mSLrzwQr355ptqaGggbmzQ2NioLVu26Omnn9bcuXO1d+9eVVZWatasWbrmmmvsHi9mETcTNGPGDDmdzhFHaXp7e0cczcHUuummm7Rt2zbt2LFDs2fPtnucuNXe3q7e3l4VFhYObwsGg9qxY4cefvhhDQ4Oyul02jhhfMnOzlZ+fn7Ytry8PD333HM2TRTfbr31Vq1bt05XXnmlJOlLX/qS3nnnHdXV1RE3E8A1NxOUlJSkwsJCtba2hm1vbW1VcXGxTVPFN8uydOONN+r555/XX/7yF3k8HrtHimuXXHKJ3njjDe3du3f4VVRUpB/84Afau3cvYTPFFi5cOGJphLfeeku5ubk2TRTfPvroIyUkhP8pdjqd3Ao+QRy5iYCqqipdffXVKioq0oIFC7Rp0yZ1d3eroqLC7tHi0urVq/X000/rD3/4g1JSUoaPqrndbk2bNs3m6eJPSkrKiOudTj/9dKWnp3MdlA3Wrl2r4uJi3XXXXVq2bJna2tq0adMmbdq0ye7R4lJZWZnuvPNOnXXWWZo7d646Ojp0//3367rrrrN7tNhmISIeeeQRKzc310pKSrIKCgqs7du32z1S3JI06uuJJ56wezT8n69//evWzTffbPcYcaupqcnyer1WcnKydd5551mbNm2ye6S4FQgErJtvvtk666yzLJfLZZ1zzjnW+vXrrcHBQbtHi2mscwMAAIzCNTcAAMAoxA0AADAKcQMAAIxC3AAAAKMQNwAAwCjEDQAAMApxAwAAjELcAAAAoxA3AADAKMQNAGN84xvfUGVlpd1jALAZcQMAAIzCs6UAGGHlypX6zW9+E7atq6tLZ599tj0DAbANcQPACH6/X0uWLJHX61Vtba0kaebMmXI6nTZPBmCqJdo9AABEgtvtVlJSkqZPn66srCy7xwFgI665AQAARiFuAACAUYgbAMZISkpSMBi0ewwANiNuABjj7LPP1l//+lf985//VF9fn0KhkN0jAbABcQPAGLfccoucTqfy8/M1c+ZMdXd32z0SABtwKzgAADAKR24AAIBRiBsAAGAU4gYAABiFuAEAAEYhbgAAgFGIGwAAYBTiBgAAGIW4AQAARiFuAACAUYgbAABgFOIGAAAY5f8DfyxsHRUKO0YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t for t in range(10)], u)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c18672d1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9 (tensorflow)",
   "language": "python",
   "name": "tensorflow"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.15"
  },
  "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": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "290.391px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}