{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": true, "input": [ "from pylab import *\n", "%matplotlib inline\n", "from scipy import integrate\n", "from matplotlib.patches import ConnectionPatch\n", "\n", "# nastavitve za izris grafov (http://matplotlib.org/1.3.1/users/customizing.html)\n", "rc('text', usetex=True)\n", "rc('font', size=12, family='serif', serif=['Computer Modern'])\n", "rc('xtick', labelsize='small')\n", "rc('ytick', labelsize='small')\n", "rc('legend', fontsize='medium')\n", "rc('figure', figsize=(5, 3))\n", "rc('lines', linewidth=2.0)\n", "rc('axes', color_cycle=['k'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Diferencialne operacije" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Odvod" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Koli\u010dino, ki je definirana z odvodom merjene koli\u010dine $y$, lahko dolo\u010dimo le pribli\u017eno, saj v tabeli ne moremo izpeljati limitnega procesa $h\\rightarrow0$, ki ga terja matemati\u010dna definicija. Zadovoljimo se z diferen\u010dnim pribli\u017ekom, v katerem je $h$ kar korak na\u0161e tabele merjenih vrednosti: $y_i^\\prime=\\frac{y_{i+1}-y_i}{x_{i+1}-x_i}$. Vrednosti odvoda $y_i^\\prime$ je v tem primeru treba pripisati vrednostim $x$ na sredi intervala, torej smo pripravili novo tabelo parov $y_i^\\prime$, $\\tilde{x}_i=\\frac{x_i+x_{i+1}}{2}$. \n", "\n", "Kadar bi radi obdr\u017eali koli\u010dini $y$ in $y^\\prime$ v isti tabeli, torej pripisani istim $x$, lahko uporabimo naslednji postopek: skozi tri sosednje to\u010dke $(x_{i-1},y_{i-1})$, $(x_i, y_i)$ in $(x_{i+1}, y_{i-1})$ povle\u010demo parabolo\n", "\n", "$$y(x)=y_{i-1}\\frac{(x-x_{i})(x-x_{i+1})}{(x_{i-1}-x_{i})(x_{i-1}-x_{i+1})}+\n", "y_{i}\\frac{(x-x_{i-1})(x-x_{i+1})}{(x_{i}-x_{i-1})(x_{i}-x_{i+1})}+\n", "y_{i+1}\\frac{(x-x_{i-1})(x-x_{i})}{(x_{i+1}-x_{i-1})(x_{i+1}-x_{i})}$$\n", "\n", "in izra\u010dunano njen odvod pri $x=x_i$:\n", "\n", "$$y_i^{\\prime}=y_{i-1}\\frac{x_i-x_{i+1}}{(x_{i-1}-x_{i})(x_{i-1}-x_{i+1})}+\n", "y_{i}\\frac{-x_{i-1}+2x_i-x_{i+1}}{(x_{i}-x_{i-1})(x_{i}-x_{i+1})}+\n", "y_{i+1}\\frac{x_i-x_{i-1}}{(x_{i+1}-x_{i-1})(x_{i+1}-x_{i})}.$$\n", "\n", "Pri ekvidistantni tabeli, $x_{i+1}-x_i=h$ za vsak $i$, se izraz poenostavi:\n", "\n", "$$y_i^{\\prime}=\\frac{y_{i+1}-y_{i-1}}{2h}.$$\n", "\n", "V prvi in zadnji to\u010dki, $x_1$ in $x_N$, zgoraj opisani postopek ne deluje. Tam moramo odvod parabole izra\u010dunati v eni od robnih to\u010dk. Navedimo izraza za ekvidistantno tabelo:\n", "\n", "$$y_1^{\\prime}=-\\frac{3y_1-4y_2+y_3}{2h},$$\n", "\n", "$$y_N^{\\prime}=\\frac{3y_N-4y_{N-1}+y_{N-2}}{2h}.$$\n", "\n", "Odvajanje podatkov prina\u0161a \u0161e eno neprijetnost, izgubo natan\u010dnosti. Pri koli\u010dkaj gladki odvisnosti $y(x)$ sta si sosednji vrednosti v tabeli blizu tudi po velikosti in je njuna razlika v \u0161tevcu odvoda majhna. Njena natan\u010dnost (absolutna napaka) je istega reda velikosti kot napaka izmerkov \u2013 v resnici je za faktor $\\sqrt{2}$ ve\u010dja \u2013 zato pa je relativna napaka lahko dosti ve\u010dja. Povedano druga\u010de, napaka se za\u010dne na dolo\u010deni decimalki merjenega rezultata. Ko dve taki vrednosti od\u0161tejemo, lahko izgubimo eno ali ve\u010d vodilnih decimalk, tako da ima napaka v rezultatu od\u0161tevanja ve\u010dji relativni dele\u017e. Zato so grafi odvodov vedno bolj za\u0161umljeni (zobati) kot grafi izvirnih koli\u010din. \u010ce se zanesemo na gladkost $y$, lahko zobatost odvoda popravimo z zglajenimi formulami, ki upo\u0161tevajo \u0161ir\u0161i interval sosednjih vrednosti. Ob povedanem je o\u010ditno, da potrebujemo za drugi odvod koli\u010dine zelo natan\u010dne podatke, da se po dvakratnem od\u0161tevanju rezultat ne izgubi v \u0161umu meritve." ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Integral" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Integracija, nasprotno, je stabilna operacija, ki ne oja\u010duje \u0161uma meritve. Integralsko koli\u010dino $Y=\\int_{x_1}^{x_N}\\mathrm{d}x\\,y(x)$ lahko aproksimiramo s trapezno integracijo: \n", "\n", "$$Y_1=0,$$ \n", "\n", "$$Y_{i+1}=Y_{i}+\\frac{1}{2}\\left(x_{i+1}-x_{i}\\right)\\left(y_i+y_{i+1}\\right).$$" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Primer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "V datoteki kamen.dat so podatki o poti $s$ (2. stolpec, v m), hitrosti $v$ (3. stolpec, v m/s) in pospe\u0161ku $a$ (4. stolpec, v m/s$^2$) kamna v odvisnosti od \u010dasa $t$ (1. stolpec, v s). Pot, hitrost in pospe\u0161ek so podani na tri signifikantna mesta." ] }, { "cell_type": "code", "collapsed": false, "input": [ "podatki=loadtxt('../podatki/kamen.dat')\n", "t=podatki[:, 0]\n", "s=podatki[:, 1]\n", "v=podatki[:, 2]\n", "a=podatki[:, 3]\n", "print podatki" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 0. 0. 0. 9.81 ]\n", " [ 0.1 0.049 0.978 9.71 ]\n", " [ 0.2 0.195 1.94 9.43 ]\n", " [ 0.3 0.435 2.86 8.99 ]\n", " [ 0.4 0.765 3.73 8.42 ]\n", " [ 0.5 1.18 4.54 7.75 ]\n", " [ 0.6 1.67 5.28 7.02 ]\n", " [ 0.7 2.23 5.94 6.28 ]\n", " [ 0.8 2.86 6.53 5.54 ]\n", " [ 0.9 3.54 7.05 4.84 ]\n", " [ 1. 4.27 7.5 4.18 ]\n", " [ 1.1 5.04 7.89 3.58 ]\n", " [ 1.2 5.84 8.22 3.05 ]\n", " [ 1.3 6.68 8.5 2.58 ]\n", " [ 1.4 7.54 8.74 2.17 ]\n", " [ 1.5 8.42 8.94 1.82 ]\n", " [ 1.6 9.33 9.11 1.52 ]\n", " [ 1.7 10.2 9.24 1.26 ]\n", " [ 1.8 11.2 9.36 1.05 ]\n", " [ 1.9 12.1 9.46 0.869]\n", " [ 2. 13.1 9.53 0.719]\n", " [ 2.1 14. 9.6 0.594]\n", " [ 2.2 15. 9.65 0.49 ]\n", " [ 2.3 16. 9.7 0.404]\n", " [ 2.4 16.9 9.74 0.332]\n", " [ 2.5 17.9 9.77 0.273]\n", " [ 2.6 18.9 9.79 0.225]\n", " [ 2.7 19.9 9.81 0.185]\n", " [ 2.8 20.8 9.83 0.152]\n", " [ 2.9 21.8 9.84 0.125]\n", " [ 3. 22.8 9.85 0.102]]\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Izra\u010dunajmo hitrost in pospe\u0161ek kamna z odvajanjem poti po \u010dasu. Na slikah (b) in (c) vidimo, da pri tem izgubimo natan\u010dnost, kar je \u0161e posebej opazno pri pospe\u0161ku." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def odvod(f, h):\n", " f1=convolve(f, [1, 0, -1], mode='same') / (2 * h)\n", " f1[0] = -(3 * f[0] - 4 * f[1] + f[2]) / (2 * h)\n", " f1[-1] = (f[-3] - 4 * f[-2] + 3 * f[-1]) / (2 * h)\n", " return f1 \n", " \n", "h=t[1] - t[0] \n", "v1=odvod(s, h)\n", "a1=odvod(v1, h)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Izra\u010dunajmo \u0161e hitrost in pot z integriranjem pospe\u0161ka kamna. Na slikah (d) in (e) vidimo, da pri integraciji izgube natan\u010dnosti ni." ] }, { "cell_type": "code", "collapsed": false, "input": [ "v2=integrate.cumtrapz(a, t, initial=0.0)\n", "s2=integrate.cumtrapz(v2, t, initial=0.0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ((axa, axd), (axb, axe), (axc, axf)) = subplots(3, 2, sharex='col', sharey='row', figsize=(10, 9))\n", "\n", "axa.plot(t, s);\n", "axa.set_ylabel(r'Pot (m)')\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axb.plot(t, v, t, v1, 'ro', markersize=5.0);\n", "axb.set_ylabel(r'Hitrost (m/s)')\n", "axb.set_ylim([0, 11])\n", "axb.legend((r'to\\v cno', r'izra\\v cunano'), loc=7, frameon=True)\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axc.plot(t, a, t, a1, 'ro', markersize=5.0);\n", "axc.set_ylabel(r'Pospe\\v sek (m/s$^2$)')\n", "axc.set_xlabel(r'\\v Cas (s)')\n", "axc.set_ylim([-3, 11.5])\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axd.plot(t, s, t, s2, 'bo', markersize=5.0);\n", "axd.grid(alpha=0.5)\n", "axd.annotate('(d)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axe.plot(t, v, t, v2, 'bo', markersize=5.0);\n", "axe.legend((r'to\\v cno', r'izra\\v cunano'), loc=7, frameon=True)\n", "axe.grid(alpha=0.5)\n", "axe.annotate('(e)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axf.plot(t, a);\n", "axf.set_xlabel(r'\\v Cas (s)')\n", "axf.grid(alpha=0.5)\n", "axf.annotate('(f)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "axb.add_artist(ConnectionPatch(xyA=(0.5, 0.1), xyB=(0.5, 0.9), zorder=100, coordsA=\"axes fraction\", coordsB=\"axes fraction\", axesA=axa, axesB=axb, arrowstyle=\"->\", linewidth=5, color=\"red\"))\n", "axc.add_artist(ConnectionPatch(xyA=(0.5, 0.1), xyB=(0.5, 0.9), zorder=100, coordsA=\"axes fraction\", coordsB=\"axes fraction\", axesA=axb, axesB=axc, arrowstyle=\"->\", linewidth=5, color=\"red\"))\n", "axe.add_artist(ConnectionPatch(xyA=(0.5, 0.9), xyB=(0.5, 0.1), zorder=100, coordsA=\"axes fraction\", coordsB=\"axes fraction\", axesA=axe, axesB=axd, arrowstyle=\"->\", linewidth=5, color=\"blue\"))\n", "axf.add_artist(ConnectionPatch(xyA=(0.5, 0.9), xyB=(0.5, 0.1), zorder=100, coordsA=\"axes fraction\", coordsB=\"axes fraction\", axesA=axf, axesB=axe, arrowstyle=\"->\", linewidth=5, color=\"blue\"))\n", "axa.annotate('odvod', xy=(0.52, 0.05), xycoords=\"axes fraction\", color=\"red\", fontsize=\"large\")\n", "axb.annotate('odvod', xy=(0.52, 0.05), xycoords=\"axes fraction\", color=\"red\", fontsize=\"large\")\n", "axe.annotate('integral', xy=(0.30, 0.9), xycoords=\"axes fraction\", color=\"blue\", fontsize=\"large\")\n", "axf.annotate('integral', xy=(0.30, 0.9), xycoords=\"axes fraction\", color=\"blue\", fontsize=\"large\")\n", "\n", "subplots_adjust(hspace=0.05, wspace=0.075)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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lERwczKpVq2jVqpXa0a5JijIhtO3qlZUDr7wyF3iVoKCmrFq1ivbt26sZ77ocaTNkTpkL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\nos7sl18Qx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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Naloge" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "
  1. Nari\u0161i graf diferencialne upornosti $\\mathrm{d}U/\\mathrm{d}I$ za tokovno odvisnost v datoteki Korozija.dat. To je meritev karakteristike $I$-$U$ za kovinsko elektrodo v dolo\u010deni korozivni raztopini. V prvem stolpcu je $U$ (mV), v drugem pa $I$ (A).\n", "\n", "
  2. Datoteka body_acc.txt vsebuje podatke o kartezi\u010dnih komponentah vektorja pospe\u0161ka premikajo\u010de se osebe (komponente $x$, $y$ in $z$ pospe\u0161ka v enotah $g=9.81\\,$m/s$^2$ so v prvem, drugem in tretjem stolpcu datoteke). Akcelerometer v mobilnem telefonu, ki ga je oseba nosila na pasu, je podatke o pospe\u0161ku zapisoval s frekvenco $50\\,$Hz. Nari\u0161i graf polo\u017eaja osebe v odvisnosti od \u010dasa.\n", "\n", "
  3. V datoteki prevajanje.dat je podan temperaturni profil v $0.1\\,$m debeli steni v odvisnosti od \u010dasa. V prvem stolpcu je podana oddaljenost (v metrih) merilne to\u010dke od levega roba stene, v ostalih stolpcih pa so temperature (v stopinjah Celzija) na teh mestih ob \u010dasih od $0\\,$s do $180\\,$s s korakom $1\\,$s. (a) Kako se s \u010dasom spreminjata toplotna tokova na obeh robovih stene? (b) Ob \u010dasu $t=1\\,$min primerjaj krajevno odvisnost odvoda temperature po \u010dasu s krajevno odvisnostjo drugega odvoda temperature po kraju.\n", "
" ] } ], "metadata": {} } ] }