Exercise 4.2: Computing things!

---

import pandas as pd

---

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:

df = pd.read_csv('data/c_elegans_egg_xa.csv', comment='#')

xa_high = df.loc[df['food']=='high', 'area (sq. um)'].values
xa_low = df.loc[df['food']=='low', 'area (sq. um)'].values

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

xa_to_diameter(xa)

Use your function to compute the diameters of the eggs.

Solution

import numpy as np

def xa_to_diameter(xa):
    """
    Convert an array of cross-sectional areas
    to diameters with commensurate units.
    """
    # Compute diameter from area
    diameter = 2 * np.sqrt(xa / np.pi)

    return diameter

print('Diameters of eggs from well fed mothers:\n', xa_to_diameter(xa_high))
print('\nDiameters of eggs from poorly fed mothers:\n', xa_to_diameter(xa_low))

Diameters of eggs from well fed mothers:
 [46.29105911 51.22642581 47.76657057 48.5596503  51.59790585 47.61973991
 49.33998388 47.89966242 47.21697198 46.94654036 49.08125119 49.84064959
 47.9926071  46.29105911 47.69988539 48.40207395 48.15152345 49.3141717
 49.57168871 47.87307365 48.30991705 46.29105911 46.12573337 46.24978308
 46.41466697 47.87307365 48.15152345 48.95137203 45.72372833 47.18999856
 46.68817945 45.98750791 46.53794651 52.2111661  48.70364742 47.23045291
 47.06842687 46.81073869 45.97366251 49.57168871 50.8397116  48.54653847
 52.08909166 48.24398292]

Diameters of eggs from poorly fed mothers:
 [48.40207395 51.58556628 52.55146594 50.31103472 53.06982074 54.57203767
 50.32368681 52.24773281 53.99739399 49.44309786 53.87936676 47.9926071
 52.41804019 47.87307365 52.11352942 51.21399674 52.44232467 50.47526453
 50.8397116  51.56087828 49.84064959 55.96578669 50.72688754 50.58864976
 52.18677405 52.44232467 51.78264653 52.57568879 51.86863366 52.67246879
 49.05530287 52.67246879 50.72688754 50.07003758 52.32078957 49.18490759
 53.72554372 46.67454189 49.19784929 51.88090591 51.85635852 54.8280819
 52.07686848 51.22642581 51.96673046 48.29673743 53.04582353 52.07686848
 52.35727972 50.57606396 51.70882946 53.54750652 52.23554675 53.54750652
 53.18964437 51.96673046 55.38261517]

Computing environment

%load_ext watermark
%watermark -v -p numpy,pandas,jupyterlab

Python implementation: CPython
Python version       : 3.11.3
IPython version      : 8.12.0

numpy     : 1.24.3
pandas    : 1.5.3
jupyterlab: 3.6.3