{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Units and Quantities\n", "\n", "## Objectives\n", "\n", "- Use units\n", "- Create functions that accept quantities as arguments\n", "- Create new units" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basics\n", "\n", "How do we define a Quantity and which parts does it have?" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "keep": true }, "outputs": [], "source": [ "from astropy import units as u\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "26.2 m\n" ] } ], "source": [ "# Define a quantity length\n", "length = 26.2 * u.meter\n", "# print it\n", "print(length) # length is a quantity" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "astropy.units.quantity.Quantity" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Type of quantity\n", "type(length)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "astropy.units.core.IrreducibleUnit" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Type of unit\n", "type(u.meter)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$26.2 \\; \\mathrm{m}$" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Quantity\n", "length" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "26.2" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# value\n", "length.value" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$\\mathrm{m}$" ], "text/plain": [ "Unit(\"m\")" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# unit\n", "length.unit" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "dtype = float64\n", "unit = m\n", "class = Quantity\n", "n_bad = 0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# information\n", "length.info" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantities can be converted to other units systems or factors by using `to()`" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0262 km\n", "2.76934218514e-15 lyr\n" ] } ], "source": [ "# Convert it to: km, lyr\n", "print(length.to(u.km))\n", "print(length.to(u.lightyear))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do arithmetic operations when the quantities have the compatible units:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "22.99999 km\n" ] } ], "source": [ "# arithmetic with distances\n", "distance_start = 10 * u.mm\n", "distance_end = 23 * u.km\n", "length = distance_end - distance_start\n", "print(length)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantities can also be combined, for example to measure speed" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.53333266667 km / min\n" ] } ], "source": [ "# calculate a speed\n", "time = 15 * u.minute\n", "speed = length / time\n", "print(speed)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "25.5555444444 m / s\n", "25.5555444444 m / s\n" ] } ], "source": [ "# decompose it\n", "print(speed.decompose())\n", "print(speed.si)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Challenges

\n", "\n", "
    \n", "
  1. Convert the speed in imperial units (miles/hour) using:
    \n", "\n", " ```from astropy.units import imperial```\n", "
    2. \n", "
  2. Calculate whether a pint is more than half litre
    \n", " \n", " You can compare quantities as comparing variables.
    \n", " Something strange? Check what deffinition of pint astropy is using.\n", "
    3. \n", "
  3. Does units work with areas? calculate the area of a rectangle of 3 km of side and 5 meter of width. Show them in m^2 and convert them to yards^2
    4. \n", "
" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "57.166124831 mi / h\n" ] } ], "source": [ "#1\n", "from astropy.units import imperial\n", "print(speed.to(imperial.mile/u.hour))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#2\n", "imperial.pint > 0.5 * u.l\n", " # A liquid pint in US is 473 ml; in UK is 568 ml" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "15.0 km m\n", "15000.0 m2\n", "17939.8506945 yd2\n" ] } ], "source": [ "#3\n", "rectangle_area = 3 * u.km * 5 * u.m\n", "print(rectangle_area)\n", "print(rectangle_area.decompose())\n", "print(rectangle_area.to(imperial.yard ** 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Composed units\n", "\n", "Many units are compositions of others, for example, one could create new combinationes for ease of use:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$2555.5544 \\; \\mathrm{\\frac{cm}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create a composite unit\n", "cms = u.cm / u.s\n", "speed.to(cms)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$57.166125 \\; \\mathrm{\\frac{mi}{h}}$" ], "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# and in the imperial system\n", "mph = imperial.mile / u.hour\n", "speed.to(mph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and others are already a composition:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[Unit(\"Hz\"), Unit(\"Bq\"), Unit(\"3.7e+10 Ci\")]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# what can be converted from s-1?\n", "(u.s ** -1).compose()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[Unit(\"J\"), Unit(\"1e+07 erg\"), Unit(\"4.58742e+17 Ry\"), Unit(\"6.24151e+18 eV\")]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# or Jules?\n", "(u.joule).compose()\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.99999996 \\; \\mathrm{R_{\\infty}}$" ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Unity of R\n", "(13.605692 * u.eV).to(u.Ry)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometime we get *no units* quantitites" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$20 \\; \\mathrm{\\frac{cm}{m}}$" ], "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# no units\n", "nounits = 20. * u.cm / (1. * u.m)\n", "nounits" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What happen if we add a number to this?" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$3.2 \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# arithmetic with no units\n", "nounits + 3" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.2 \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# final value of a no unit quantity\n", "nounits.decompose() # It's a unitless quantity\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Equivalencies\n", "\n", "Some conversions are not done by a conversion factor as between miles and kilometers, for example converting between wavelength and frequency." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "ename": "UnitConversionError", "evalue": "'nm' (length) and 'Hz' (frequency) are not convertible", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mUnitConversionError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m# converting spectral quantities\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;33m(\u001b[0m\u001b[1;36m656.281\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnm\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mto\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mu\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mHz\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# Fails because they are not compatible\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;32m/home/dvd/.conda/envs/swc/lib/python2.7/site-packages/astropy/units/quantity.pyc\u001b[0m in \u001b[0;36mto\u001b[1;34m(self, unit, equivalencies)\u001b[0m\n\u001b[0;32m 631\u001b[0m \u001b[0munit\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mUnit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0munit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 632\u001b[0m new_val = self.unit.to(unit, self.view(np.ndarray),\n\u001b[1;32m--> 633\u001b[1;33m equivalencies=equivalencies)\n\u001b[0m\u001b[0;32m 634\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_new_view\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0munit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 635\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;32m/home/dvd/.conda/envs/swc/lib/python2.7/site-packages/astropy/units/core.pyc\u001b[0m in \u001b[0;36mto\u001b[1;34m(self, other, value, equivalencies)\u001b[0m\n\u001b[0;32m 966\u001b[0m \u001b[0mIf\u001b[0m \u001b[0munits\u001b[0m \u001b[0mare\u001b[0m \u001b[0minconsistent\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 967\u001b[0m \"\"\"\n\u001b[1;32m--> 968\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_converter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mequivalencies\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mequivalencies\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 969\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 970\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0min_units\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mequivalencies\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;32m/home/dvd/.conda/envs/swc/lib/python2.7/site-packages/astropy/units/core.pyc\u001b[0m in \u001b[0;36m_get_converter\u001b[1;34m(self, other, equivalencies)\u001b[0m\n\u001b[0;32m 867\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mUnitsError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 868\u001b[0m return self._apply_equivalencies(\n\u001b[1;32m--> 869\u001b[1;33m self, other, self._normalize_equivalencies(equivalencies))\n\u001b[0m\u001b[0;32m 870\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mval\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mscale\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0m_condition_arg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mval\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 871\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;32m/home/dvd/.conda/envs/swc/lib/python2.7/site-packages/astropy/units/core.pyc\u001b[0m in \u001b[0;36m_apply_equivalencies\u001b[1;34m(self, unit, other, equivalencies)\u001b[0m\n\u001b[0;32m 858\u001b[0m raise UnitConversionError(\n\u001b[0;32m 859\u001b[0m \"{0} and {1} are not convertible\".format(\n\u001b[1;32m--> 860\u001b[1;33m unit_str, other_str))\n\u001b[0m\u001b[0;32m 861\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 862\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_get_converter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mequivalencies\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mUnitConversionError\u001b[0m: 'nm' (length) and 'Hz' (frequency) are not convertible" ] } ], "source": [ "# converting spectral quantities\n", "(656.281 * u.nm).to(u.Hz) # Fails because they are not compatible" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$4.5680502 \\times 10^{14} \\; \\mathrm{Hz}$" ], "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# but doing it right\n", "(656.281 * u.nm).to(u.Hz, equivalencies=u.spectral())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other built-in equivalencies are: \n", " - `parallax()`\n", " - Doppler (`dopplr_radio`, `doppler_optical`, `doppler_relativistic`)\n", " - spectral flux density\n", " - brigthness temperature\n", " - temperature energy\n", " - and you can [build your own](http://astropy.readthedocs.org/en/stable/units/equivalencies.html#writing-new-equivalencies)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " Primary name | Unit definition | Aliases \n", "[\n", " Bq | 1 / s | becquerel ,\n", " Ci | 2.7027e-11 / s | curie ,\n", " Hz | 1 / s | Hertz, hertz ,\n", "]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# finding the equivalencies\n", "u.Hz.find_equivalent_units()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " Primary name | Unit definition | Aliases \n", "[\n", " AU | 1.49598e+11 m | au, astronomical_unit ,\n", " Angstrom | 1e-10 m | AA, angstrom ,\n", " Bq | 1 / s | becquerel ,\n", " Ci | 2.7027e-11 / s | curie ,\n", " Hz | 1 / s | Hertz, hertz ,\n", " J | kg m2 / s2 | Joule, joule ,\n", " Ry | 2.17987e-18 kg m2 / s2 | rydberg ,\n", " cm | 0.01 m | centimeter ,\n", " eV | 1.60218e-19 kg m2 / s2 | electronvolt ,\n", " erg | 1e-07 kg m2 / s2 | ,\n", " k | 100 / m | Kayser, kayser ,\n", " lyr | 9.46073e+15 m | lightyear ,\n", " m | irreducible | meter ,\n", " micron | 1e-06 m | ,\n", " pc | 3.08568e+16 m | parsec ,\n", " solRad | 6.95508e+08 m | R_sun, Rsun ,\n", "]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# but also using other systems\n", "u.Hz.find_equivalent_units(equivalencies=u.spectral())\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Printing the quantities" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.533 km min-1\n", "1.533 $\\mathrm{km\\,min^{-1}}$\n" ] } ], "source": [ "# Printing values with different formats\n", "print(\"{0.value:0.03f} {0.unit:FITS}\".format(speed))\n", "print(\"{0.value:0.03f} {0.unit:latex_inline}\".format(speed))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Arrays\n", "\n", "Quantities can also be applied to arrays" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$1.9130435 \\; \\mathrm{\\frac{m}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# different ways of defining a quantity for a single value\n", "length = 44 * u.m\n", "time = u.Quantity(23, u.s)\n", "speed = length / time\n", "speed" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$[1,~1,~1] \\; \\mathrm{\\frac{m}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# now with lists\n", "length_list = [1, 2, 3] * u.m\n", "\n", "# and arrays\n", "import numpy as np\n", "time_array = np.array([1, 2, 3]) * u.s\n", "\n", "# and its arithmetics\n", "length_list / time_array" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 179.] deg\n", "[ 0. 0.01745241]\n" ] } ], "source": [ "# angles are smart!\n", "angle = u.Quantity(np.arange(180), u.deg)\n", "print(angle[[0, -1]])\n", "print(np.sin(angle[[0, -1]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting quantities\n", "\n", "To work nicely with matplotlib we need to do as follows:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "keep": true }, "outputs": [], "source": [ "# allowing for plotting\n", "from astropy.visualization import quantity_support\n", "quantity_support()\n", "\n", "# loading matplotlib\n", "%matplotlib inline\n", "from matplotlib import pyplot as plt\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TpwiDiYhEbNkyOPlk+OQTP+V2Z6jDKIO8PPj2W78rrYhIOqtXz+9S8dhjYXNk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\nBUNERMpEBUNERMrk/wEjO38XgYtn0gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Ploting the previous array\n", "plt.plot(angle, np.sin(angle))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Creating functions with quantities as units\n", "\n", "We want to have functions that contain the information of the untis, and with them we can be sure that we will be always have the *right* result." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Create a function for the Kinetic energy\n", "@u.quantity_input(mass=u.kg, speed=u.m/u.s)\n", "def kinetic(mass, speed):\n", " return (mass * speed ** 2 / 2.).to(u.joule)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$2.5 \\; \\mathrm{J}$" ], "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# run with and without units\n", "kinetic(5, 10) # Fails! it doesn't specify the units.\n", "kinetic(5 * u.kg, 100 * cms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Challenges

\n", "\n", "
    \n", "
  1. Create a function that calculates potential energy where *g* defaults to Earth value, \n", " but could be used for different planets. \n", " Test it for any of the *g* values for any other \n", " planet.\n", "
    2. \n", "
\n", "
" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#4\n", "@u.quantity_input(mass=u.kg, height=u.m, g=u.m / u.s ** 2)\n", "def potential(mass, height, g=9.8 * u.m / u.s **2):\n", " return (0.5 * mass * g * height).to(u.joule)\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$7.35 \\; \\mathrm{J}$" ], "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# run it for some values\n", "potential(5 * u.kg, 30 *u.cm)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$9.375 \\; \\mathrm{J}$" ], "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# on Mars:\n", "potential(5 * u.kg, 1 * u.m, g=3.75 * u.m/u.s**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create your own units\n", "\n", "Some times we want to create our own units:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "240.0 titter\n" ] } ], "source": [ "# Create units for a laugh scale\n", "titter = u.def_unit('titter')\n", "chuckle = u.def_unit('chuckle', 5 * titter)\n", "laugh = u.def_unit('laugh', 4 * chuckle)\n", "guffaw = u.def_unit('guffaw', 3 * laugh)\n", "rofl = u.def_unit('rofl', 4 * guffaw)\n", "death_by_laughing = u.def_unit('death_by_laughing', 10 * rofl)\n", "print((1 * rofl).to(titter))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Challenges

\n", "\n", "
    \n", "
  1. Convert the area calculated before `rectangle_area` in Hectare\n", " (1 hectare = 100 ares; 1 are = 100 m2).\n", "
    2. \n", "
\n", "
" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.5 hectares\n" ] } ], "source": [ "#5\n", "ares = u.def_unit('ares', (10 * u.m)**2)\n", "hectar = u.def_unit('hectares', 100 * ares)\n", "print(rectangle_area.to(hectar))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python2", "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 }