{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 4.2: Computing things!\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr >\n",
    "\n",
    "We have looked at a data set from Harvey and Orbidans on the cross-sectional area of *C. elegans* eggs. Recall, we loaded the data and converted everything to Numpy arrays like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/c_elegans_egg_xa.csv', comment='#')\n",
    "\n",
    "xa_high = df.loc[df['food']=='high', 'area (sq. um)'].values\n",
    "xa_low = df.loc[df['food']=='low', 'area (sq. um)'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we would like to compute the diameter of the egg from the cross-sectional area. Write a function that takes in an array of cross-sectional areas and returns an array of diameters. Recall that the diameter $d$ and cross-sectional area $A$ are related by $A = \\pi d^2/4$. There should be no `for` loops in your function! The call signature is\n",
    "\n",
    "```python\n",
    "xa_to_diameter(xa)\n",
    "```\n",
    "\n",
    "Use your function to compute the diameters of the eggs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diameters of eggs from well fed mothers:\n",
      " [46.29105911 51.22642581 47.76657057 48.5596503  51.59790585 47.61973991\n",
      " 49.33998388 47.89966242 47.21697198 46.94654036 49.08125119 49.84064959\n",
      " 47.9926071  46.29105911 47.69988539 48.40207395 48.15152345 49.3141717\n",
      " 49.57168871 47.87307365 48.30991705 46.29105911 46.12573337 46.24978308\n",
      " 46.41466697 47.87307365 48.15152345 48.95137203 45.72372833 47.18999856\n",
      " 46.68817945 45.98750791 46.53794651 52.2111661  48.70364742 47.23045291\n",
      " 47.06842687 46.81073869 45.97366251 49.57168871 50.8397116  48.54653847\n",
      " 52.08909166 48.24398292]\n",
      "\n",
      "Diameters of eggs from poorly fed mothers:\n",
      " [48.40207395 51.58556628 52.55146594 50.31103472 53.06982074 54.57203767\n",
      " 50.32368681 52.24773281 53.99739399 49.44309786 53.87936676 47.9926071\n",
      " 52.41804019 47.87307365 52.11352942 51.21399674 52.44232467 50.47526453\n",
      " 50.8397116  51.56087828 49.84064959 55.96578669 50.72688754 50.58864976\n",
      " 52.18677405 52.44232467 51.78264653 52.57568879 51.86863366 52.67246879\n",
      " 49.05530287 52.67246879 50.72688754 50.07003758 52.32078957 49.18490759\n",
      " 53.72554372 46.67454189 49.19784929 51.88090591 51.85635852 54.8280819\n",
      " 52.07686848 51.22642581 51.96673046 48.29673743 53.04582353 52.07686848\n",
      " 52.35727972 50.57606396 51.70882946 53.54750652 52.23554675 53.54750652\n",
      " 53.18964437 51.96673046 55.38261517]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def xa_to_diameter(xa):\n",
    "    \"\"\"\n",
    "    Convert an array of cross-sectional areas\n",
    "    to diameters with commensurate units.\n",
    "    \"\"\"\n",
    "    # Compute diameter from area\n",
    "    diameter = 2 * np.sqrt(xa / np.pi)\n",
    "    \n",
    "    return diameter\n",
    "\n",
    "print('Diameters of eggs from well fed mothers:\\n', xa_to_diameter(xa_high))\n",
    "print('\\nDiameters of eggs from poorly fed mothers:\\n', xa_to_diameter(xa_low))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.9.12\n",
      "IPython version      : 8.3.0\n",
      "\n",
      "numpy     : 1.21.5\n",
      "pandas    : 1.4.2\n",
      "jupyterlab: 3.3.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,pandas,jupyterlab"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
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}