algorithms/linear_equations_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Численные методы решения систем линейных уравнений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Метод итерации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def iterative_method(A, b):\n",
    "    alpha = -A / A.diagonal().reshape(A.shape[0], 1)\n",
    "    np.fill_diagonal(alpha, 0)\n",
    "\n",
    "    beta = b / A.diagonal()\n",
    "\n",
    "    results_list = []\n",
    "    iterations = 0\n",
    "    \n",
    "    x_prev = b\n",
    "    while (1):\n",
    "        x = beta + np.dot(alpha, x_prev)\n",
    "        \n",
    "        results_list.append(x)\n",
    "        iterations += 1\n",
    "        \n",
    "        if np.sum(np.abs(x - x_prev) / np.abs(x)) == 0:\n",
    "            return (x, iterations, results_list)\n",
    "        else:\n",
    "            x_prev = x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Метод Зейделя"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def seidel_method(A, b):\n",
    "    C = np.dot(A.T, A)\n",
    "    d = np.dot(A.T, b)\n",
    "    \n",
    "    alpha = -C / C.diagonal().reshape(C.shape[0], 1)\n",
    "    np.fill_diagonal(alpha, 0)\n",
    "\n",
    "    beta = d / C.diagonal()\n",
    "    \n",
    "    L = np.tril(alpha)\n",
    "    U = np.triu(alpha)\n",
    "    E = np.eye(alpha.shape[0])\n",
    "    \n",
    "    results_list = []\n",
    "    iterations = 0\n",
    "    \n",
    "    x_prev = b\n",
    "    while (1):\n",
    "        first = np.dot(np.linalg.inv(E - L), U) \n",
    "        second = np.dot(np.linalg.inv(E - L), beta)\n",
    "        x = np.dot(first, x_prev) + second\n",
    "        \n",
    "        results_list.append(x)\n",
    "        iterations += 1\n",
    "\n",
    "        if np.sum(np.abs(x - x_prev) / np.abs(x)) == 0:\n",
    "            return (x, iterations, results_list)\n",
    "        else:\n",
    "            x_prev = x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Проверка"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.array([[0.58, 0.29, 0.05],\n",
    "              [0.05, 0.34, 0.1],\n",
    "              [0.2, 0.44, 0.81]], dtype=float)\n",
    "\n",
    "b = np.array([0.02, 0.32, 0.74], dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метод итерации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result = iterative_method(A, b)\n",
    "answer, iterations, results_list = result[0], result[1], result[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Результат: [-0.43360563  0.83875936  0.565021  ]\n"
     ]
    }
   ],
   "source": [
    "print('Результат:', answer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "line1 = [each_result[0] for each_result in results_list]\n",
    "line2 = [each_result[1] for each_result in results_list]\n",
    "line3 = [each_result[2] for each_result in results_list]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ccRmF7m4WX/sFdrvg02R32mkw5YypgfZiR2cfEvahzF4k7EOZvVAtqJUd8ucADwB3ANcB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152f6ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.plot(np.arange(1, iterations + 1), line1, label='x1')\n",
    "plt.plot(np.arange(1, iterations + 1), line2, label='x2')\n",
    "plt.plot(np.arange(1, iterations + 1), line3, label='x3')\n",
    "legend = plt.legend(loc='center left', bbox_to_anchor=(1, 0.5), frameon=True, borderpad=1, borderaxespad=1)\n",
    "ax.set_ylabel('Value')\n",
    "trash = ax.set_xlabel('Iteration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метод Зейделя"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = seidel_method(A, b)\n",
    "answer, iterations, results_list = result[0], result[1], result[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Результат: [-0.43360563  0.83875936  0.565021  ]\n"
     ]
    }
   ],
   "source": [
    "print('Результат:', answer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "line1 = [each_result[0] for each_result in results_list]\n",
    "line2 = [each_result[1] for each_result in results_list]\n",
    "line3 = [each_result[2] for each_result in results_list]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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59DD45Zq7N5vZPcCtZjYdGEdwn74zYPNh3Q3u3gJcBuxCcL+/aHoZBLODDXkv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\n4QcAsAjhBwCwiEsUySbf7rpQqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11539b5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.plot(np.arange(1, iterations + 1), line1, label='x1')\n",
    "plt.plot(np.arange(1, iterations + 1), line2, label='x2')\n",
    "plt.plot(np.arange(1, iterations + 1), line3, label='x3')\n",
    "legend = plt.legend(loc='center left', bbox_to_anchor=(1, 0.5), frameon=True, borderpad=1, borderaxespad=1)\n",
    "ax.set_ylabel('Value')\n",
    "trash = ax.set_xlabel('Iteration')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}