5.3. Assignment. Polynomial approximation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import interpolate\n",
    "from scipy import optimize\n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": "markdown",
   "metadata": {},
   "source": [
    "$$ Ax = b $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.array([1, 15])\n",
    "b = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.4391451113923299, -0.18692824612091097)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_1 = (f(15.) - f(1.)) / 14.\n",
    "w_0 = f(1.) - w_1\n",
    "w_0, w_1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  1.]), True)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([\n",
    "    [w_0, w_1 * 1.],\n",
    "    [w_0, w_1 * 15.]\n",
    "])\n",
    "x_ = np.linalg.solve(a, b)\n",
    "x_, np.allclose(np.dot(a, x_), b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIQ13EZE49P8BNTo3OAapkZ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109768490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x__ = np.arange(1, 15, 0.1)\n",
    "y__ = w_0 + w_1 * x__\n",
    "plt.plot(x, f(x), 'o', x__, y__, '-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIQ13EZE49P8BNTo3OAapkZ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c040f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([1, 15])\n",
    "fnew = interpolate.interp1d(x, f(x), kind=1)\n",
    "xnew = np.arange(1, 15, 0.1)\n",
    "ynew = fnew(xnew)\n",
    "plt.plot(x, f(x), 'o', xnew, ynew, '-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.25221687  1.74684595  2.50541641  0.63522142]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 4, 10, 15])\n",
    "b = f(x)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[   1    1    1    1]\n",
      " [   1    4   16   64]\n",
      " [   1   10  100 1000]\n",
      " [   1   15  225 3375]]\n",
      "[ 3.25221687  1.74684595  2.50541641  0.63522142]\n"
     ]
    }
   ],
   "source": [
    "points = np.array([1, 4, 10, 15])\n",
    "A = np.array([[x_**0, x_**1, x_**2, x_**3] for x_ in points])\n",
    "b = f(points)\n",
    "print(A)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.36264154 -1.29552587  0.19333685 -0.00823565]\n"
     ]
    }
   ],
   "source": [
    "weights = np.linalg.solve(A, b)\n",
    "print(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c16bd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_approx3 = np.arange(1, 15, 0.1)\n",
    "y_approx3 = weights[0] + weights[1] * x_approx3 + weights[2] * (x_approx3**2) + weights[3] * (x_approx3**3)\n",
    "plt.plot(x, f(x), 'o', x_approx3, y_approx3, '-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}