metingen.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Verwerken van experimentele data\n",
    "\n",
    "In dit notebook geven we een voorbeeld van het verwerken van experimentele data.\n",
    "\n",
    "* de meetgegevens vullen we direct in in een Python tabel; dit kan ook op veel andere manieren, bijvoorbeeld door deze uit een tekstbestand in te lezen.\n",
    "* deze tabel geven we weer als pandas-tabel; \n",
    "* we gebruiken matplotlib voor het tekenen van een grafiek, met een raster voor het lezen van de waarden uit de grafiek;\n",
    "* we gebruiken lineaire regressie voor het bepalen van het lineaire verband tussen de meetwaarden;\n",
    "* hiermee tekenen we de benaderende funcie\n",
    "\n",
    "Als voorbeeld gebruiken we een (fictieve) meting aan een weerstand, met een spanningsmeter parallel aan de weerstand, en een stroommeter in serie met de weerstand. De voeding van de schakeling kunnen we regelen: we meten de spanning en de stroom bij een aantal verschillende instellingen van de voeding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We gebruiken de volgende libraries: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ipysheet\n",
    "import ipywidgets as widgets\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## De experimentele data\n",
    "\n",
    "De variabele `measurements` bevat de experimentele data: een array van (spanning, stroom)-metingen.\n",
    "De spanning is in 0.1V, de stroom in mA.\n",
    "\n",
    "> *Opmerking*: dit moet nog aangepast worden naar \"fatsoenlijke eenheden\", maar dat leverde in eerste instantie problemen met de assen van de grafieken. Nog uitzoeken hoe dat beter kan!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "measurements = np.array([ [10.0, 15.1], [20.0, 19.7], [30.0, 29.5], [40.0, 39.5],[50.0, 51.2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We geven deze meetwaarden weer als tabel. Voor tabellen is pandas een handige en flexibele library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>U</th>\n",
       "      <th>I</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>15.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>20.0</td>\n",
       "      <td>19.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>30.0</td>\n",
       "      <td>29.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>40.0</td>\n",
       "      <td>39.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>50.0</td>\n",
       "      <td>51.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      U     I\n",
       "0  10.0  15.1\n",
       "1  20.0  19.7\n",
       "2  30.0  29.5\n",
       "3  40.0  39.5\n",
       "4  50.0  51.2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(data = measurements, columns=[\"U\", 'I'])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De variabelen `measured_u` en `measured_v` zijn de kolommen met de gemeten spanning en stroom. We gebruiken deze bijvoorbeeld voor de x- en y-waarden in de grafiek."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "measured_u = measurements[:,0]\n",
    "measured_i = measurements[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sheet voor uitvoer/invoer\n",
    "\n",
    "Met behulp van een sheet kunnen we de gegevens weergeven.\n",
    "We kunnen via dit sheet de data aanpassen.\n",
    "\n",
    "> In een meer bruikbare versie kunnen we zo'n sheet gebruiken voor de invoer van de data. De data kunnen we dan bewaren in een bestand, dat we een volgende keer weer inlezen in het notebook. Op die manier scheiden we de data van het notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "59c1df301a724d368ca126c8ddeb50fa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Sheet(cells=(Cell(choice=[], column_end=0, column_start=0, row_end=4, row_start=0, squeeze_row=False, type='nu…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sheet = ipysheet.from_dataframe(data)\n",
    "sheet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = ipysheet.to_dataframe(sheet)\n",
    "measured_u = df['U'].values\n",
    "measured_i = df['I'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## De grafiek\n",
    "\n",
    "Met behulp van matplotlib maken we een grafiek van deze experimentele data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_plot1(x, y):\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8, 8))\n",
    "\n",
    "    plt.axis(\"equal\") # for square grid (correct angles)\n",
    "    plt.xlabel(\"U (0.1 V)\")\n",
    "    plt.ylabel(\"I (mA)\")\n",
    "    plt.title(\"I as function of V for resistor R\")\n",
    "    \n",
    "    # Major ticks every 2 minor ticks every 1\n",
    "    major_ticks = np.arange(0, 60, 5)\n",
    "    minor_ticks = np.arange(0, 60, 1)\n",
    "\n",
    "    ax.set_xticks(major_ticks)\n",
    "    ax.set_xticks(minor_ticks, minor=True)\n",
    "    ax.set_yticks(major_ticks)\n",
    "    ax.set_yticks(minor_ticks, minor=True)\n",
    "\n",
    "    # And a corresponding grid\n",
    "    plt.grid(which='minor', color=\"b\", alpha=0.2)\n",
    "    plt.grid(which='major', color='b', alpha=0.6)\n",
    "    \n",
    "    plt.ylim(0, 60)\n",
    "    plt.xlim(0, 60)\n",
    "\n",
    "    plt.plot(x, y, 'ro') # de meetpunten.\n",
    "    \n",
    "    # plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_plot1(measured_u, measured_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lineaire regressie: best passende lijn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Met behulp van lineaire regressie bepalen we de best-passende lijn door deze meetpunten.\n",
    "Het punt (0,0) ligt vast: we weten zeker dat als de spanning 0 is, de stroom ook 0 zal zijn.\n",
    "We gebruiken dus een vorm van lineaire regressie waarbij de \"intercept\", het snijpunt met de y-as, vastligt (op 0).\n",
    "Dit is een toepassing van de \"kleinste kwadraten methode\". \n",
    "(Zie: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.01272727])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = measured_u[:,np.newaxis]\n",
    "y = measured_i\n",
    "a, _, _, _ = np.linalg.lstsq(x, y, rcond=None)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0127272727272723"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = a[0]\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De waarde `a[0]` is de gezochte coefficient $R$ in $U = R \\times I$: de waarde van de weerstand. Omdat we de spanning gemeten hebben in 0.1V en de stroom in mA, is de waarde van de weerstand: R = r * 100 (Ohm)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "De weerstand R is  101.3  Ohm\n"
     ]
    }
   ],
   "source": [
    "print(\"De weerstand R is \", \"{:.1f}\".format(r * 100) , ' Ohm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grafiek met benaderende lijn\n",
    "\n",
    "We geven hieronder de grafiek met de meetpunten en de lijn die we bepaald hebben met behulp van lineaire regressie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_plot2(x, y, a):\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8, 8))\n",
    "\n",
    "    plt.axis(\"equal\") # for square grid (correct angles)\n",
    "    plt.xlabel(\"U (0.1 V)\")\n",
    "    plt.ylabel(\"I (mA)\")\n",
    "    \n",
    "    # Major ticks every 2 minor ticks every 1\n",
    "    major_ticks = np.arange(0, 60, 5)\n",
    "    minor_ticks = np.arange(0, 60, 1)\n",
    "\n",
    "    ax.set_xticks(major_ticks)\n",
    "    ax.set_xticks(minor_ticks, minor=True)\n",
    "    ax.set_yticks(major_ticks)\n",
    "    ax.set_yticks(minor_ticks, minor=True)\n",
    "\n",
    "    # And a corresponding grid\n",
    "    plt.grid(which='minor', color=\"b\", alpha=0.2)\n",
    "    plt.grid(which='major', color='b', alpha=0.6)\n",
    "    \n",
    "    plt.ylim(0, 60)\n",
    "    plt.xlim(0, 60)\n",
    "\n",
    "    plt.plot(x, y, 'ro') # de meetpunten.\n",
    "    pts = np.arange(0, 60, 1)\n",
    "    plt.plot(pts, a * pts, 'b-')\n",
    "    plt.suptitle(\"I as function of V for resistor R\")\n",
    "    \n",
    "    # plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_plot2(measured_u, measured_i, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Opdracht\n",
    "\n",
    "* welke meting valt uit de toon?\n",
    "* heb je een verklaring voor deze meetfout?\n",
    "* herhaal deze meting, vul de nieuwe waarde in, en herhaal de berekeningen.\n",
    "* welk verschil maakt dit voor bepaalde waarde van de weerstand?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}