Predavanje 08 - Aproksimacija.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<font size=\"2\"> [github.com/jankoslavic/pypinm](http://github.com/jankoslavic/pypinm)</font>\n",
    "\n",
    "<center>\n",
    "<img width=300 src=\"./fig/ladisk.png\">\n",
    "<br>\n",
    "<font size=\"7\" color=\"f00e0e\" face=\"garamond\"><b>Aproksimacija</b></font>\n",
    "<br><br>\n",
    "<font size=\"4\">\n",
    "[izr. prof. dr. Janko Slavič](http://www.ladisk.si/~slavic)\n",
    "</font>\n",
    "<br><br>\n",
    "<font size=\"2\">November 2017</font>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Uvod\" data-toc-modified-id=\"Uvod-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Uvod</a></div><div class=\"lev1 toc-item\"><a href=\"#Metoda-najmanjših-kvadratov-za-linearno-funkcijo\" data-toc-modified-id=\"Metoda-najmanjših-kvadratov-za-linearno-funkcijo-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Metoda najmanjših kvadratov za linearno funkcijo</a></div><div class=\"lev2 toc-item\"><a href=\"#Uporaba-psevdo-inverzne-matrike\" data-toc-modified-id=\"Uporaba-psevdo-inverzne-matrike-21\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Uporaba psevdo inverzne matrike</a></div><div class=\"lev1 toc-item\"><a href=\"#Metoda-najmanjših-kvadratov-za-poljubni-polinom\" data-toc-modified-id=\"Metoda-najmanjših-kvadratov-za-poljubni-polinom-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Metoda najmanjših kvadratov za poljubni polinom</a></div><div class=\"lev2 toc-item\"><a href=\"#Numerični-zgled\" data-toc-modified-id=\"Numerični-zgled-31\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Numerični zgled</a></div><div class=\"lev2 toc-item\"><a href=\"#Uporaba-numpy-za-aproksimacjo-s-polinomom\" data-toc-modified-id=\"Uporaba-numpy-za-aproksimacjo-s-polinomom-32\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Uporaba <code>numpy</code> za aproksimacjo s polinomom</a></div><div class=\"lev1 toc-item\"><a href=\"#Aproksimacija-s-poljubno-funkcijo\" data-toc-modified-id=\"Aproksimacija-s-poljubno-funkcijo-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Aproksimacija s poljubno funkcijo</a></div><div class=\"lev2 toc-item\"><a href=\"#Aproksimacija-s-harmonsko-funkcijo\" data-toc-modified-id=\"Aproksimacija-s-harmonsko-funkcijo-41\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>Aproksimacija s harmonsko funkcijo</a></div><div class=\"lev1 toc-item\"><a href=\"#Nekaj-vprašanj-za-razmislek!\" data-toc-modified-id=\"Nekaj-vprašanj-za-razmislek!-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Nekaj vprašanj za razmislek!</a></div><div class=\"lev1 toc-item\"><a href=\"#Dodatno\" data-toc-modified-id=\"Dodatno-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Dodatno</a></div><div class=\"lev2 toc-item\"><a href=\"#Aproksimacija-z-zlepki-in-uporabo-SciPy\" data-toc-modified-id=\"Aproksimacija-z-zlepki-in-uporabo-SciPy-61\"><span class=\"toc-item-num\">6.1&nbsp;&nbsp;</span>Aproksimacija z zlepki in uporabo <code>SciPy</code></a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Uvod"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "V strojniški praksi se pogosto srečamo s tabelo podatkov, ki so lahko obremenjeni z merilnimi ali numeričnimi napakami.\n",
    "\n",
    "Oglejmo si primer meritve (linearne) vzmeti ($x$ je raztezek, $y$ je pomerjena sila):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.array([0.1,  1.1, 2.05, 3.2, 3.9  ])\n",
    "y = np.array([0.2, 18.1, 44.3, 75.5, 105.6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Poglejmo si podatke na sliki, najprej uvozimo potrebne pakete:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEMCAYAAADXiYGSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\namJhSJKaWBiSpCYWhiSpiYUhSWry/wFOvRUVf3huOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e29a9cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.plot(x, y, 'o');\n",
    "plt.xlabel('Pomik $x$')\n",
    "plt.ylabel('Sila $y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Za konkreten primer bi bilo, glede na poznavanje fizikalnega ozadja linearne vzmeti, primerno, da bi meritve poskušali popisati z linearno funkcijo:\n",
    "$$f(x) = a_0\\,x+ a_1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Poznamo tabelo $n$ podatkov $x_i, y_i$ za $i=0,1,\\dots,n-1$; teh je več, kot jih potrebujemo za določitev dveh konstant $a_0$ in $a_1$, zato imamo torej predoločen sistem linearnih enačb: \n",
    "\n",
    "$$y_i=a_0\\,x_i+a_1\\quad\\textrm{za}\\quad i=0,1,\\dots,n-1.$$\n",
    "\n",
    "Iščemo taki vrednosti konstanti $a_0$ in $a_1$, da se bo funkcija $f(x)$ v znanih točkah $x_i$ *najbolje* ujemala z $y_i$.\n",
    "\n",
    "Najprej torej potrebujemo kriterij za *najboljše* ujemanje. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Za vrednosti iz tabele $x_i, y_i$ bi lahko iskali vrednosti $a_0$ in $a_1$, pri katerih bi bila vsota absolutne vrednosti odstopkov $S$ najmanjša:\n",
    "\n",
    "$$P(a_0, a_1) = \\sum_{i=0}^{n-1} |y_i - (a_0\\,x_i+a_1)|.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ker pa taka funkcija $P(a_0, a_1)$ ni zvezno odvedljiva,raje uporabimo **metodo najmanjših kvadratov**:\n",
    "\n",
    "$$S(a_0, a_1) = \\sum_{i=0}^{n-1} \\left(y_i - (a_0\\,x_i+a_1)\\right)^2.$$\n",
    "\n",
    "Takšna funkcija $S(a_0, a_1)$ je zvezna in zvezno odvedljiva. S parcialnim odvajanjem po parametrih $a_0$ in $a_1$ lahko najdemo stacionarno točko (parcialna odvoda sta enaka 0). Postopek si bomo za linearno funkcijo pogledali v naslednjem poglavju."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Metoda najmanjših kvadratov za linearno funkcijo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poiskati moramo konstanti $a_0$, $a_1$, da bo vsota kvadratov razlik med funkcijo in tabelirano vrednostjo ($x_i, y_i$, kjer $i=0,1,\\dots, n-1$ in je $n$ število tabeliranih podatkov):\n",
    "\n",
    "$$S(a_0, a_1) = \\sum_{i=0}^{n-1} \\left(y_i - (a_0\\,x_i+a_1)\\right)^2$$\n",
    "\n",
    "najmanjša. Vrednost bo najmanjša v stacionarni točki, ki jo določimo s parcialnim odvodom po parametrih $a_0$ in $a_1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Najprej izvedemo parcialni odvod po parametru $a_0$:\n",
    "\n",
    "$$\\frac{\\partial S(a_0, a_1)}{\\partial a_0} = 2\\,\\sum_{i=0}^{n-1} \\left(y_i - a_0\\,x_i-a_1\\right)\\,(-x_i)$$\n",
    "\n",
    "Izraz uredimo:\n",
    "\n",
    "$$\\frac{\\partial S(a_0, a_1)}{\\partial a_0} =-2\\left(\\sum_{i=0}^{n-1} y_i\\,x_i -a_0\\,\\sum_{i=0}^{n-1} x_i^2- a_1\\,\\sum_{i=0}^{n-1} x_i\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Podobno postopamo še za $a_1$:\n",
    "\n",
    "$$\\frac{\\partial S(a_0, a_1)}{\\partial a_1} = 2\\,\\sum_{i=0}^{n-1} \\left(y_i  - a_0\\,x_i- a_1\\right)\\,(-1)$$\n",
    "\n",
    "$$\\frac{\\partial S(a_0, a_1)}{\\partial a_1} = -2\\left(\\sum_{i=0}^{n-1} y_i -a_0\\,\\sum_{i=0}^{n-1} x_i- a_1\\,\\sum_{i=0}^{n-1}1\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ker v stacionarni točki velja $\\partial S(a_0, a_1)/\\partial a_0=0$ in $\\partial S(a_0, a_1)/\\partial a_1=0$, iz zgornjih izrazov izpeljemo:\n",
    "\n",
    "$$a_0\\,\\sum_{i=0}^{n-1} x_i^2 + a_1\\,\\sum_{i=0}^{n-1} x_i=\\sum_{i=0}^{n-1} y_i\\,x_i$$\n",
    "\n",
    "in\n",
    "\n",
    "$$a_0\\,\\sum_{i=0}^{n-1} x_i+ a_1\\,n=\\sum_{i=0}^{n-1} y_i.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Dobili smo sistem dveh linearnih enačb za neznanki $a_0$ in $a_1$, ki ga znamo rešiti. Imenujemo ga *normalni sistem* (število enačb je enako številu neznank).\n",
    "\n",
    "Zapišimo normalni sistem v matrični obliki:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A: [[ 30.8725  10.35  ]\n",
      " [ 10.35     5.    ]]\n",
      "b: [ 764.185  243.7  ]\n"
     ]
    }
   ],
   "source": [
    "A = [[np.sum(x**2), np.sum(x)], # matrika koeficientov\n",
    "     [np.sum(x), len(x)]]\n",
    "b = [np.dot(y,x), np.sum(y)]    # vektor konstant\n",
    "A = np.asarray(A)\n",
    "b = np.asarray(b)\n",
    "print('A:', A)\n",
    "print('b:', b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Sedaj moramo rešiti linearni sistem:\n",
    "\n",
    "$$\\mathbf{A}\\,\\mathbf{a}=\\mathbf{b},$$\n",
    "\n",
    "Opomba, tukaj smo vektor neznank zapisali kot $\\mathbf{a}=(a_0, a_1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Sistem rešimo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(27.490050804403033, -8.1644051651142853)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0, a1 = np.linalg.solve(A, b)\n",
    "a0, a1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Preverimo še število pogojenosti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.200713508702421"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Sedaj si bomo pogledali še rezultat. Najprej pripravimo sliko, ki bo vsebovala tudi informacijo o vsoti kvadratov odstopanja $f(x_i)$ od tabeliranih vrednosti $y_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def slika(naklon=a0, premik=a1):\n",
    "    d=1\n",
    "    def linearna_f(x, a0, a1):\n",
    "        return a0*x+a1\n",
    "    def S(x, y, f):\n",
    "        return np.sum(np.power(y-f,2))\n",
    "    plt.plot(x,y,'.', label='Tabela podatkov')\n",
    "    linearna_f1 = linearna_f(x, naklon, premik)\n",
    "    linearna_f1_MNK = linearna_f(x, a0, a1)\n",
    "    plt.plot(x, linearna_f1, '-', label='Izbrani parametri')\n",
    "    plt.plot(x, linearna_f1_MNK, '-', label='Metoda najmanjših kvadratov')\n",
    "    napaka = S(x, y, linearna_f(x, naklon, premik))\n",
    "    sprememba_napake_v_smeri_a0 = (S(x, y, linearna_f(x, naklon+d, premik))-napaka)/d\n",
    "    sprememba_napake_v_smeri_a1 = (S(x, y, linearna_f(x, naklon, premik+d))-napaka)/d\n",
    "    title = f'S: {napaka:g}, \\\n",
    "            $\\Delta S/\\Delta a_0$: {sprememba_napake_v_smeri_a0:g}, \\\n",
    "            $\\Delta S/\\Delta a_1$: {sprememba_napake_v_smeri_a1:g}'\n",
    "    plt.title(title)\n",
    "    plt.legend()\n",
    "    plt.ylim(-10,110)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8b342f5aaca5483c866894447ae6cfe4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "interact(slika, naklon=(0, 50, 2), premik=(-10, 10, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Uporaba psevdo inverzne matrike\n",
    "\n",
    "Do podobnega rezultata lahko pridemo z uporabo psevdo inverzne matrike. Iščemo $y(x)=a_0\\,x+a_1$ in nastavimo predoločen sistem $\\mathbf{A}\\,\\mathbf{a}=\\mathbf{y}$, kjer je matrika koeficientov $\\mathbf{A}$ definirana glede na vrednosti $x_i$ ($i=0,1,\\dots,n-1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.1 ,  1.  ],\n",
       "       [ 1.1 ,  1.  ],\n",
       "       [ 2.05,  1.  ],\n",
       "       [ 3.2 ,  1.  ],\n",
       "       [ 3.9 ,  1.  ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=np.array([x, np.ones_like(x)]).T\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Vektor konstant smo označili z $\\mathbf{b}$, v našem primeru pa je to kar vektor vrednosti $\\mathbf{y}$ z elementi $y_i$ ($i=0,1,2,\\dots,n-1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0.2,   18.1,   44.3,   75.5,  105.6])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Vektor konstant $\\mathbf{a}$ določimo z uporabo psevdo inverzne matrike:\n",
    "\n",
    "$$\\mathbf{a}=\\mathbf{A}^{+}\\,\\mathbf{y}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 27.4900508 ,  -8.16440517])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(A).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Metoda najmanjših kvadratov za poljubni polinom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linearno aproksimacijo, predstavljeno zgoraj, bomo posplošili za poljubni polinom stopnje $m$:\n",
    "\n",
    "$$f(a_0,a_1,\\dots,a_{m}, x) = \\sum_{s=0}^{m}a_s\\,\\underbrace{x^{m-s}}_{f_s(x)},$$\n",
    "\n",
    "kjer $f_s(x)=x^{m-s}$ imenujemo bazna funkcija ($s=0,1,2,\\dots,m$).\n",
    "\n",
    "Tabela podatkov naj bo definirana z $x_i, y_i$, kjer je $i=0,1,2,\\dots,n-1$. \n",
    "\n",
    "Opomba: zaradi kompaktnosti zapisa bomo konstante $a$ zapisali v vektorski obliki $\\mathbf{a}=[a_0, a_1,\\dots,a_m]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Uporabimo metodo najmanjših kvadratov:\n",
    "\n",
    "$$S(\\mathbf{a}) = \\sum_{i=0}^{n-1} \\left(y_i - f(\\mathbf{a}, x_i)\\right)^2= \\sum_{i=0}^{n-1} \\left(y_i - \\sum_{s=0}^{m}a_s\\,x_i^{m-s}\\right)^2.$$\n",
    "\n",
    "Potreben pogoj za nastop ekstrema funkcije $m+1$ neodvisnih spremenljivk je, da najdemo stacionarno točko za vsak $a_v$, iščemo torej $\\partial S(\\mathbf{a})/\\partial a_v=0$ (namesto $s$ smo uporabili indeks $v$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Najprej določimo parcialni odvod za izbrani $a_v$:\n",
    "\n",
    "$$\\frac{\\partial S(\\mathbf{a})}{\\partial a_v} = \\sum_{i=0}^{n-1} - 2\\,\\left(y_i - \\sum_{s=0}^{m}a_s\\,x_i^{m-s}\\right)\\,x_i^{m-v}$$\n",
    "\n",
    "Opomba: $\\frac{\\partial}{\\partial a_v}\\left(\\sum_{s=0}^{m}a_s\\,x_i^{m-s}\\right)=x_i^{m-v}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ker je parcialni odvod v stacionarni točki enak 0, zgornji izraz preoblikujemo:\n",
    "\n",
    "$$\\sum_{i=0}^{n-1} \\left(\\sum_{s=0}^{m}a_s\\,x^{m-s}\\right)\\,x_i^{m-v}=\\sum_{i=0}^{n-1} y_i\\,x_i^{m-v}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izraz uredimo:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\sum_{i=0}^{n-1} \\sum_{s=0}^m a_s\\,x_i^{2m-s-v}=\\sum_{i=0}^{n-1} y_i\\,x_i^{m-v}$$\n",
    "\n",
    "Zamenjamo vrstni red seštevanja ter izpeljemo:\n",
    "\n",
    "$$\\sum_{s=0}^m \\left(a_s \\sum_{i=0}^{n-1} \\,x_i^{2m-s-v}\\right)=\\sum_{i=0}^{n-1} y_i\\,x_i^{m-v}\\quad\\textrm{za:}\\quad v=0,1,\\dots,m$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Izpeljali smo enačbo $v$ sistema $m+1$ linearnih enačb:\n",
    "\n",
    "$$\\mathbf{A}\\,{\\mathbf{a}}=\\mathbf{b}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Element $A_{v,s}$ matrike koeficientov je:\n",
    "\n",
    "$$A_{v,s}= \\sum_{i=0}^{n-1} x_i^{2m-v-s},$$\n",
    "\n",
    "Element vektorja konstant je:\n",
    "\n",
    "$$b_{v}= \\sum_{i=0}^{n-1} y_i\\,x_i^{m-v}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Numerični zgled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uporabimo podatke iz prve naloge in poskusimo aproksimirati s polinomom 2. stopnje ($m=2$). \n",
    "\n",
    "Tabela podatkov je:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.1 ,  1.1 ,  2.05,  3.2 ,  3.9 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0.2,   18.1,   44.3,   75.5,  105.6])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Izračunajmo matriko koeficientov:\n",
    "\n",
    "$$A_{v,s}= \\sum_{i=0}^{n-1} x_i^{2m-v-s}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 355.32690625,  102.034125  ,   30.8725    ],\n",
       "       [ 102.034125  ,   30.8725    ,   10.35      ],\n",
       "       [  30.8725    ,   10.35      ,    5.        ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 2 #stopnja\n",
    "A = np.zeros((m+1,m+1))\n",
    "for v in range(m+1):\n",
    "    for s in range(m+1):\n",
    "        A[v,s] = np.sum(x**(2*m-v-s))\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Izračunajmo še vektor konstant:\n",
    "\n",
    "$$b_{v}= \\sum_{i=0}^{n-1} y_i\\,x_i^{m-v}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2587.36975,   764.185  ,   243.7    ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.zeros(m+1)\n",
    "for v in range(m+1):\n",
    "    b[v] = np.dot(y,x**(m-v))\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Preverimo število pogojenosti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "963.21258562906587"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rešimo sistem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.18393375,  14.64106847,  -1.22621065])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.linalg.solve(A, b)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Glede na definicijo aproksimacijskega polinoma:\n",
    "\n",
    "$$f(a_0,a_1,\\dots,a_{m}, x) = \\sum_{v=0}^{m}a_v\\,x^{m-v}$$\n",
    "\n",
    "Kar v konkretnem primeru je aproksimacijski polinom:\n",
    "\n",
    "$$f(x)=3.18393375\\,x^2 + 14.64106847\\,x -1.22621065$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Definirajmo numerično implementacijo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apr_polinom(x, a):\n",
    "    \"\"\"Vrne vrednosti aproksimacijskega polinoma\n",
    "\n",
    "    :param x: vrednosti kjer računamo aproksimirani rezultat\n",
    "    :param a: koeficienti aproksimacijskega polinoma\n",
    "    \"\"\"\n",
    "    m = len(a) - 1\n",
    "    return np.sum(np.asarray([_*x**(m-v) for v,_ in enumerate(a)]), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prikažemo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPvNAhLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e66bc358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_g = np.linspace(np.min(x), np.max(x), 100) # več točk za prikaz\n",
    "plt.plot(x, y, 'o', label='Tabela podatkov')\n",
    "plt.plot(x_g, apr_polinom(x_g, a), lw=5, alpha=0.5, label='Aproksimacija s kvadratno funkcijo')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Poglejmo še napako aproksimacije:\n",
    "$$e_i=y_i - f(x_i)$$\n",
    "\n",
    "za $i=0,1,2,\\dots,n-1$.\n",
    "\n",
    "Pri pravilno izvedni aproksimaciji je nekaj $e_i$ pozitivnih in nekaj negativnih. Poglejmo, če je to res v našem primeru:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.06973553, -0.6315245 ,  2.13153872, -2.72869002,  1.29841133])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e = y - apr_polinom(x, a)\n",
    "e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Opomba: višje stopnje polinoma kot uporabimo, večja je verjetnost slabe pogojenosti. Iz tega razloga s stopnjo polinoma ne pretiravamo (v praksi uporabljamo predvsem nizke stopnje)!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Uporaba `numpy` za aproksimacjo s polinomom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poglejmo si, kako uporabimo knjižnico `numpy` za polinomsko aproksimacijo. \n",
    "\n",
    "Najprej uporabimo funkcijo `numpy.polyfit` ([dokumentacija](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html)):\n",
    "\n",
    "```python\n",
    "polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False)\n",
    "```\n",
    "\n",
    "ki zahteva tri parametre: `x` in `y` predstavljata tabelo podatkov (lahko tudi v obliki seznamov vektorjev), `deg` pa stopnjo polinoma. Ostali parametri so opcijski (npr. `w` za uporabo uteži pri aproksimaciji). \n",
    "\n",
    "Funkcija `polyfit` vrne seznam koeficientov polinoma (najprej za najvišji red); rezultat je lahko tudi seznam seznamov (če so vhodni podatki seznam vektorjev)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Poglejmo si uporabo za predhodno obravnavani primer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.18393375,  14.64106847,  -1.22621065])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "koef = np.polyfit(x, y, deg=2)\n",
    "koef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.18393375,  14.64106847,  -1.22621065])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a # rezultat lastne implementacije"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ko imamo koeficiente, lahko ustvarimo objekt polinoma s klicem ``numpy.poly1d`` ([dokumentacija](https://docs.scipy.org/doc/numpy/reference/generated/numpy.poly1d.html#numpy.poly1d)):\n",
    "\n",
    "```python\n",
    "poly1d(c_or_r, r=False, variable=None)\n",
    "```\n",
    "\n",
    "kjer `c_or_r` predstavlja seznam koeficientov polinoma oz. ničle polinoma v primeru, da je `r=True`. Funkcija vrne instanco objekta, s klicem katere lahko izračunamo vrednosti aproksimacijskega polinoma pri `x`, lahko pa izračunamo tudi druge stvari, kot na primer ničle polinoma."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Poglejmo si primer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.poly1d(koef) # p je instanca objekta poly1d. Aproksimacijo sedaj dobimo z y = p(x)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Izrišimo vrednosti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPvNAhLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e66fc0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Tabela podatkov')\n",
    "plt.plot(x_g, p(x_g), lw=5, alpha=0.5, label='Aproksimacija s kvadratno funkcijo')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Izračunajmo ničle polinoma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.68070044,  0.08227923])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.roots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Aproksimacija s poljubno funkcijo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pri aproksimaciji nismo omejeni zgolj na polinome. Tabele podatkov lahko aproksimiramo:\n",
    "\n",
    "* z linearno kombinacijo linearno neodvisnih baznih funkcij ali \n",
    "* s funkcijo, v kateri nastopajo parametri v nelinearni zvezi (npr. $a_0\\,\\sin(a_1\\,x+a_2)$).\n",
    "\n",
    "Za podrobnosti glejte vir J. Petrišič: Uvod v Matlab za inženirje, Fakulteta za strojništvo 2013, str 145. \n",
    "\n",
    "Osredotočili se bomo na uporabo `scipy` paketa za aproksimacijo z nelinearno fukcijo, ki temelji na metodi najmanjših kvadratov."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Aproksimacija s harmonsko funkcijo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tabela podatkov je definira kot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([ 0.1, 0.8, 1.7, 2.5, 3.4, 4.2,  5.1])\n",
    "y = np.array([ 0.01, -1.13, 0.02, 0.92, -0.01, -0.98, 0.1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Prikažimo tabelo podatkov:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQID+H3mriGrZuj0qAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e66bedd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Tabela podatkov')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Aproksimacijo z nelinearno funkcijo bomo izvedli s pomočjo ``scipy.optimize.curve_fit`` ([dokumentacija](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html)):\n",
    "\n",
    "```python\n",
    "curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, check_finite=True, bounds=(-inf, inf), method=None, jac=None, **kwargs)\n",
    "```\n",
    "\n",
    "\n",
    "katera zahteva tri parametre: `f` predstavlja definicijo Python funkcije, s katero želimo aproksimirati, in katere parametre spreminjamo z uporabo metode najmanjših kvadratov. `xdata` in `ydata` predstavljata tabelo podatkov. Priporočeno je tudi, da definiramo približek iskanih parametrov `p0`. Ostali parametri so opcijski.\n",
    "\n",
    "Funkcija vrne dve numerični polji: `popt`, ki predstavlja najdene parametre ter `pcov`, ki predstavljajo ocenjeno kovarianco `popt`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Definirajmo najprej Python funkcijo, katere prvi parameter je neodvisna spremenljivka `x`, nato pa sledijo parametri, ki jih želimo določiti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, A, ω, ϕ):\n",
    "    return A*np.sin(ω*x+ϕ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "kjer je `A` amplitua, `ω` krožna frekvenca in `ϕ` faza harmonske funkcije. S pomočjo slike lahko ugibamo prve približke: `A=1`, `ω=1`, `ϕ=0`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Sedaj uvozimo `curve_fit` in izvedemo optimizacijski postopek:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.01461945,  1.89652046, -3.27943097])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt, pcov = curve_fit(func, x, y, p0=[1, 1, 0])\n",
    "popt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunali smo pričakovane vrednosti (glejte zgoraj)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.0525477 , -0.99608783, -0.05612665,  1.00860622, -0.02753942,\n",
       "       -1.01426499,  0.1110182 ])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func(x, *popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e6ad4cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_g = np.linspace(np.min(x), np.max(x), 50)\n",
    "y_g = func(x_g, *popt) # bodi pozorni kako smo v funkcijo posredovali parametre\n",
    "plt.plot(x, y, 'o', label='Tabela podatkov')\n",
    "plt.plot(x_g, y_g, label='Aproksimacija')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Nekaj vprašanj za razmislek!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Podatki:\n",
    "$$x = [-1.00, -0.50, 0.00, 0.50, 1.00]$$\n",
    "$$y = [−1.00, −0.55, 0.00, 0.45, 1.00]$$\n",
    "uporabite linearne zlepke in določite prvi odvod.\n",
    "2. Na zgornjih podatkih izračunajte linearno aproksimacijo ter določite parametra aproksimacije.\n",
    "3. Na nateznem testu ste testirali aluminijeve vzorce; rezultati testa so podani spodaj.\n",
    "\n",
    "    Napetost [MPa]:\n",
    "$$\\sigma = [34.5, 69.0, 103.5, 138.0]$$\n",
    "\n",
    "    Specifična deformacija [mm/m]\n",
    "$$vzorec_1 = [0.46, 0.95, 1.48, 1.93]$$\n",
    "$$vzorec_2 = [0.34, 1.02, 1.51, 2.09]$$\n",
    "$$vzorec_3 = [0.37, 1.00, 1.51, 2.05]$$\n",
    "    S pomočjo linearne aproksimacije določite elastični modul (napetost/specifična deformacija) vsakega posameznega vzorca.\n",
    "4. Za vzorce zgoraj linearno aproksimirajte elastični modul čez vse vzorce. Določite tudi standardno napako (glejte ``np.std``).\n",
    "5. Raziščite pomoč za funkcijo ``np.polyfit`` in utežite različne vzorce z različno utežjo (npr. da prvi meritvi zaupate manj). Izračunajte nato linearno aproksimiran elastični modul.\n",
    "6. Pojasnite bistvo metode najmanjših kvadratov na primeru linearne aproksimacije. \n",
    "7. Podatki:\n",
    "$$x = [1.0, 2.5, 3.5, 4.0, 1.1, 1.8, 2.2, 3.7]$$\n",
    "$$y = [6.008, 15.722, 27.130, 33.772, 5.257, 9.549, 11.098, 28.828$$\n",
    "    Pripravite in pojasnite funkcijo za linearno aproksimacijo.\n",
    "8. Nadaljujte zgornjo nalogo in z vgrajeno funkcijo ``np.polyfit`` izvedite linearno, kvadratno in kubično polinomsko aproksimacijo. \n",
    "9. Nadaljujte zgornjo nalogo in aproksimacije narišite ter določite standarno napako. Katera aproksimacija najbolje popiše podatke?\n",
    "10. Definirajte polinom 2. ali 3. stopnje. Dodajte šum (enakomeren ``np.random.rand`` ali normalen ``np.random.randn``) ter nato aproksimirajte s polinomom 1., 2. in 3. stopnje. Vse rezultate narišite in jih vrednotite.\n",
    "11. Podatke iz prejšnje točke aproksimirajte s pomočjo kubičnih zlepkov. Uporabite vgrajeno funkcijo in preučite vpliv parametra `s`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Dodatno"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naredite *.exe* svojega programa:\n",
    "\n",
    "* https://pypi.org/project/py2exe/\n",
    "* http://www.pyinstaller.org/\n",
    "* http://pinm.ladisk.si/323/kako-iz-python-kodo-prevedem-v-exe-datoteko\n",
    "\n",
    "Poglejte [pandas paket](http://pandas.pydata.org/).\n",
    "<img src=\"http://pandas.pydata.org/_static/pandas_logo.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Aproksimacija z zlepki in uporabo ``SciPy``"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Tabela podatkov naj bo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.        , -2.68421053, -2.36842105, -2.05263158, -1.73684211,\n",
       "       -1.42105263, -1.10526316, -0.78947368, -0.47368421, -0.15789474,\n",
       "        0.15789474,  0.47368421,  0.78947368,  1.10526316,  1.42105263,\n",
       "        1.73684211,  2.05263158,  2.36842105,  2.68421053,  3.        ])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(-3, 3, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.08832603,  0.02075073,  0.0526001 ,  0.12684217,  0.14234432,\n",
       "        0.08387244,  0.34226064,  0.52862107,  0.79385312,  0.99590738,\n",
       "        0.98257964,  0.87172774,  0.57424082,  0.30083997,  0.15492949,\n",
       "        0.06565014,  0.08950146, -0.00659471,  0.01639626, -0.04258138])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(0) # seme generatorja naključnih števil\n",
    "y = np.exp(-x**2) + 0.1 * np.random.normal(scale=.5, size=len(x))\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poglejmo si objekt ``scipy.interpolate.UnivariateSpline`` ([dokumentacija](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html)), ki omogoča tako interpolacijo kot aproksimacijo z zlepki:\n",
    "\n",
    "```python\n",
    "UnivariateSpline(x, y, w=None, bbox=[None, None], k=3, s=None, ext=0, check_finite=False)\n",
    "```\n",
    "\n",
    "Parametra `x` in `y` predstavljata tabelo podatkov. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Opcijski parameter `s` določa vrednost, katere vsota kvadratov razlik aproksimacijskega zlepka in aproksimacijskih točk ne sme preseči:\n",
    "\n",
    "```python\n",
    "sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) <= s\n",
    "```\n",
    "\n",
    "`w` so uteži posameznih točk.\n",
    "\n",
    "Če definiramo `s=0`, zahtevamo interpolacijo. \n",
    "\n",
    "Parameter `k` definira stopnjo polinomskega zlepka (privzeto je `k=3`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Aproksimacijo z zlepki izvedemo tako, da ob tabeli podatkov `x` in `y` definiramo še parameter `s`.  Izvedimo interpolacijo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import UnivariateSpline\n",
    "spl = UnivariateSpline(x, y, s=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e703ccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_g = np.linspace(-3, 3, 100)\n",
    "plt.plot(x, y, 'o', ms=5, label='Aproksimacijkse točke')\n",
    "plt.plot(x_g, spl(x_g), lw=3, label='Zlepek', alpha=0.6)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izvedimo še aproksimacijo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "spl_a = UnivariateSpline(x, y, s=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e703cb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', ms=5, label='Aproksimacijske točke')\n",
    "plt.plot(x_g, spl(x_g), lw=3, label='Interpolacija (s=0)');\n",
    "plt.plot(x_g, spl_a(x_g), lw=3, label='Aproksimacija (s=2)');\n",
    "plt.plot(spl_a.get_knots(), spl_a(spl_a.get_knots()), 'o', label='Vozli pri aproksimaciji');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dejanski preostanek:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0999987185545532"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spl_a.get_residual()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "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": "3.6.4"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "livereveal": {
   "theme": "sky",
   "transition": "default",
   "width": 1200
  },
  "nav_menu": {},
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "navigate_num": "#000000",
    "navigate_text": "#333333",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700",
    "sidebar_border": "#EEEEEE",
    "wrapper_background": "#FFFFFF"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "263px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": "2",
   "toc_cell": true,
   "toc_section_display": "block",
   "toc_window_display": false,
   "widenNotebook": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}