q/task1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Callable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "precision = 3\n",
    "eps = 1 / precision\n",
    "\n",
    "def dichotomy(a: float, b: float, func: Callable[[float], float]) -> float:\n",
    "    while True:\n",
    "        x = (a + b) / 2\n",
    "\n",
    "        x1 = x - eps / 2\n",
    "        f1 = func(x1)\n",
    "\n",
    "        x2 = x + eps / 2\n",
    "        f2 = func(x2)\n",
    "\n",
    "        if f1 > f2:\n",
    "            a = x1\n",
    "        else:\n",
    "            b = x2\n",
    "        \n",
    "        if abs(a - b) <= 2 * eps:\n",
    "            break\n",
    "    return round(func((a + b) / 2), precision)\n",
    "\n",
    "\n",
    "def fibonacci(a: float, b: float, func: Callable[[float], float]) -> float:\n",
    "    n: int = 1000\n",
    "    fibonacciSequence = [1, 1]\n",
    "    \n",
    "    for i in range(1, n - 1):\n",
    "        fibonacciSequence.append(fibonacciSequence[i - 1] + fibonacciSequence[i])\n",
    "    \n",
    "    L = b - a\n",
    "    while n > 2:\n",
    "        x1 = a + L * fibonacciSequence[n - 2] / fibonacciSequence[n - 1]\n",
    "        x2 = b - L * fibonacciSequence[n - 2] / fibonacciSequence[n - 1]\n",
    "\n",
    "        f1 = func(x1)\n",
    "        f2 = func(x2)\n",
    "\n",
    "        if f1 > f2:\n",
    "            b = x1\n",
    "            f1 = f2\n",
    "            x1 = x2\n",
    "            L = b - a\n",
    "            x2 = a + (b - x1)\n",
    "            f2 = func(x2)\n",
    "        else:\n",
    "            a = x2\n",
    "            f2 = f1\n",
    "            x2 = x1\n",
    "            L = b - a\n",
    "            x1 = b - (x2 - a)\n",
    "            f1 = func(x1)\n",
    "        \n",
    "        n -= 1\n",
    "    return round(min(f1, f2), precision)\n",
    "\n",
    "\n",
    "def goldenRatio(a: float, b: float, func: Callable[[float], float]) -> float:\n",
    "    ratio = 0.618\n",
    "    while True:\n",
    "        L: float = abs(a - b)\n",
    "\n",
    "        x1 = a + L * ratio\n",
    "        x2 = b - L * ratio\n",
    "\n",
    "        f1 = func(x1)\n",
    "        f2 = func(x2)\n",
    "\n",
    "        if f1 > f2:\n",
    "            b = x1\n",
    "            f1 = f2\n",
    "            x1 = x2\n",
    "            L = b - a\n",
    "            x2 = a + (b - x1)\n",
    "            f2 = func(x2)\n",
    "        else:\n",
    "            a = x2\n",
    "            f2 = f1\n",
    "            x2 = x1\n",
    "            L = b - a\n",
    "            x1 = b - (x2 - a)\n",
    "            f1 = func(x1)\n",
    "        \n",
    "        if L <= eps:\n",
    "            break\n",
    "    return round(min(f1, f2), precision)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Исходные данные:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "func = lambda x: (x - 15)**2 + 5\n",
    "a = 12\n",
    "b = 20"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Метод дихотомии:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0003370667"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dichotomy(a, b, func)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Метод фибоначчи:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fibonacci(a, b, func)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Метод золотого сечения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0000883205"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "goldenRatio(a, b, func)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "d68a9a56d9a25e4bd7befbd53d862537883bbf75717698e3f2bd31fa571ddf98"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}