303 - Arbeiten mit Physikalischen Größen.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 303 - Arbeiten mit Physikalischen Größen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numpy und Matplotlib brauchen wir immer\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(xdata, ydata, xerr=None, yerr=None, ax=plt, **kwargs):\n",
    "    # retrieve errors from data\n",
    "    xdata, xerr = unp.nominal_values(xdata), unp.std_devs(xdata)\n",
    "    if (xerr == 0).all():\n",
    "        xerr = None\n",
    "    ydata, yerr = unp.nominal_values(ydata), unp.std_devs(ydata)\n",
    "    if (yerr == 0).all():\n",
    "        yerr = None\n",
    "    # default plot style\n",
    "    if not ('ls' in kwargs or 'linestyle' in kwargs):\n",
    "        kwargs['ls'] = 'none'\n",
    "    if not 'marker' in kwargs:\n",
    "        kwargs['marker'] = '.'\n",
    "    # plot\n",
    "    return ax.errorbar(xdata, ydata, xerr=xerr, yerr=yerr, **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_data(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Physikalische Einheiten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pint\n",
    "units = pint.UnitRegistry()\n",
    "Q_ = units.Quantity\n",
    "units.default_format = '~P' # Abgekürzte Einheiten-Namen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import uncertainties.unumpy as unp\n",
    "t = Q_(unp.uarray([1,2,3], 2), units.seconds)\n",
    "l = Q_(unp.uarray([1,2,3], 2), units.meters)\n",
    "print(format(l/t, \"~L\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = (10 * units.m/units.s).plus_minus(2)\n",
    "print(a)\n",
    "print(\"{:~L}\".format(a))\n",
    "print(\"{:Lx}\".format(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(0, 10, 100) * units.seconds\n",
    "a = -9.81 * units.meter / units.seconds**2\n",
    "s = a / 2 * t**2\n",
    "plt.plot(t, s)\n",
    "plt.xlabel(\"Zeit $t \\, [{:~L}]$\".format(t.units))\n",
    "plt.ylabel(\"Position $s \\, [{:~L}]$\".format(s.units))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_data(date, T)\n",
    "plt.ylabel('Temperatur $T [{:~L}]$'.format(T.units))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "T_0 = Q_(23.5, units.degC)\n",
    "print(T_0, T_0.to(units.K))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "heating_rate = 0.5 * units.delta_degC / units.s\n",
    "print(heating_rate, heating_rate.to(units.K / units.s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(T_0 + 10 * units.minute * heating_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = x * units.s\n",
    "v = y * units.m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_labels(xdata, ydata):\n",
    "    plt.xlabel(\"${:~P}$\".format(xdata.units))\n",
    "    plt.ylabel(\"${:~P}$\".format(ydata.units))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_data(u.magnitude, v.magnitude)\n",
    "plot_labels(u, v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tabellen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tabulate import tabulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(tabulate([x, y]))"
   ]
  }
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