3.1. Аппроксимация функции.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Есть функция F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import linalg\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x / 5.) * np.exp(x / 10.) + 5. * np.exp(-x / 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.25221686527\n"
     ]
    }
   ],
   "source": [
    "print f(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.635221419579\n"
     ]
    }
   ],
   "source": [
    "print f(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 1. Сформируйте систему линейных уравнений (то есть задайте матрицу коэффициентов A и свободный вектор b) \n",
    "# для многочлена первой степени, который должен совпадать с функцией f в точках 1 и 15. \n",
    "# Решите данную систему с помощью функции scipy.linalg.solve. Нарисуйте функцию f и полученный многочлен. \n",
    "# Хорошо ли он приближает исходную функцию?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1],\n",
       "       [ 1, 15]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 1], [1, 15]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.25221687],\n",
       "       [ 0.63522142]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[f(1)], [f(15)]])\n",
    "b\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.43914511],\n",
       "       [-0.18692825]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.solve(A, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 2. Повторите те же шаги для многочлена второй степени, который совпадает с функцией f в точках 1, 8 и 15. \n",
    "# Улучшилось ли качество аппроксимации?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   1,   1],\n",
       "       [  1,   8,  64],\n",
       "       [  1,  15, 225]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1], [1, 8, 64], [1, 15, 225]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.25221687],\n",
       "       [ 2.31617016],\n",
       "       [ 0.63522142]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[f(1)], [f(8)], [f(15)]])\n",
    "b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.32512949],\n",
       "       [-0.06531159],\n",
       "       [-0.00760104]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.solve(A, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 3. Повторите те же шаги для многочлена третьей степени, который совпадает с функцией f в точках 1, 4, 10 и 15. \n",
    "# Хорошо ли он аппроксимирует функцию? Коэффициенты данного многочлена (четыре числа в следующем порядке: w_0, w_1, w_2, w_3) \n",
    "# являются ответом на задачу. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1,    1,    1,    1],\n",
       "       [   1,    4,   16,   64],\n",
       "       [   1,   10,  100, 1000],\n",
       "       [   1,   15,  225, 3375]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1, 1], [1, 4, 16, 64], [1, 10, 100, 1000], [1, 15, 225, 3375]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.25221687],\n",
       "       [ 1.74684595],\n",
       "       [ 2.50541641],\n",
       "       [ 0.63522142]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[f(1)], [f(4)], [f(10)], [f(15)]])\n",
    "b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.36264154],\n",
       "       [-1.29552587],\n",
       "       [ 0.19333685],\n",
       "       [-0.00823565]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.solve(A, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Построим графики"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear1(x): \n",
    "    y1 = 3.43914511 -0.18692825 * x \n",
    "    return y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear2(x): \n",
    "    y2 = 3.32512949 - 0.06531159 * x - 0.00760104 * x**2\n",
    "    return y2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear3(x): \n",
    "    y3 = 4.36264154 - 1.29552587 * x + 0.19333685 * x**2 - 0.00823565 * x**3\n",
    "    return y3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1. ,   1.5,   2. ,   2.5,   3. ,   3.5,   4. ,   4.5,   5. ,\n",
       "         5.5,   6. ,   6.5,   7. ,   7.5,   8. ,   8.5,   9. ,   9.5,\n",
       "        10. ,  10.5,  11. ,  11.5,  12. ,  12.5,  13. ,  13.5,  14. ,  14.5])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 15, 0.5)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.sin(x / 5.) * np.exp(x / 10.) + 5. * np.exp(-x / 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xlin=np.arange(1.,15., 0.5)\n",
    "\n",
    "ylin=linear1(xlin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xlin2=np.arange(1.,15., 0.5)\n",
    "\n",
    "ylin2=linear2(xlin2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xlin3=np.arange(1.,15., 0.5)\n",
    "\n",
    "ylin3=linear3(xlin3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['linalg', 'f']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7adfda0>,\n",
       " <matplotlib.lines.Line2D at 0x7adff60>,\n",
       " <matplotlib.lines.Line2D at 0x7aec588>,\n",
       " <matplotlib.lines.Line2D at 0x7aecb00>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gmjgx3xk1l5KSqIWvL428do0eZ2ZqNd7SIiuLaOZM2Szt5k31X3fzyRMy5dlo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\ndFCKe0REB6W4R0R0UIp7REQH/QGhn65VVFQ1jgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x78b5160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(x,y,xlin,ylin, xlin2,ylin2, xlin3,ylin3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7d12ef0>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YiaQhLrssLFQYN07r39Ohde45cMkloTXBjTfGTlI81q2DX/0qFIPRo/XCmgQbNsARR4R+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\ni4gkkIq7iEgC/X9C/iG8DKsx4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7974ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(x,y)"
   ]
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