Lesson 20: Practice with Numpy

(c) 2016 Justin Bois. This work is licensed under a Creative Commons Attribution License CC-BY 4.0. All code contained herein is licensed under an MIT license.

This tutorial was generated from a Jupyter notebook. You can download the notebook here.

In [2]:
# NumPy, the engine of scientific computing
import numpy as np

Numpy arrays can take a while to get the hang of. Therefore, it's important to practice practice practice!

Practice 1: Generating arrays of sequential numbers

The functions np.arange() and np.linspace() are really useful.

  1. Read their documentation (either using your IPython shell, e.g., np.arange?, or by reading the respective webpages (np.arange, np.linspace)).
  2. Use np.arange() to make an array of numbers 0 through 10.
  3. Do the same using np.linspace().
  4. Make sure the data type of each of those arrays is a float.

Practice 2: Computing things!

In the last lesson, we looked at a data set from Harvey and Orbidans on the cross-sectional area of C. elegans eggs. Recall, we loaded the data like this:

In [3]:
# Load in data
xa_high = np.loadtxt('data/xa_high_food.csv', comments='#')
xa_low = np.loadtxt('data/xa_low_food.csv', comments='#')

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!

Below, is a skeleton for your function for you to fill in.

In [ ]:
def xa_to_diameter(xa):
    """
    Convert an array of cross-sectional areas
    to diameters with commensurate units.
    """
    
    # Compute diameter from area
    diameter = ____
    
    return diameter

Use your function to compute the diameters of the eggs.

Practice 3: Working with two-dimensional arrays

Numpy enables you do to matrix calculations on two-dimensional arrays. In exercise, you will practice doing matrix calculations on arrays. We'll start by making a matrix and a vector to practice with. You can copy the code below into your script or IPython shell.

In [7]:
A = np.array([[6.7, 1.3, 0.6, 0.7],
              [0.1, 5.5, 0.4, 2.4],
              [1.1, 0.8, 4.5, 1.7],
              [0.0, 1.5, 3.4, 7.5]])

b = np.array([1.1, 2.3, 3.3, 3.9])

First, let's practice slicing.

  1. Print row 1 (remember, indexing starts at zero) of A.
  2. Print columns 1 and 3 of A.
  3. Print the values of every entry in A that is greater than 2.
  4. Print the diagonal of A. using the np.diag() function.

The np.linalg module has some powerful linear algebra tools.

  1. First, we'll solve the linear system $\mathsf{A}\cdot \mathbf{x} = \mathbf{b}$. Try it out: use np.linalg.solve(). Store your answer in the Numpy array x.
  2. Now do np.dot(A, x) to verify that $\mathsf{A}\cdot \mathbf{x} = \mathbf{b}$.
  3. Use np.transpose() to compute the transpose of A.
  4. Use np.linalg.inv() to compute the inverse of A.

Sometimes you want to convert a two-dimensional array to a one-dimensional array. This can be done with np.ravel().

  1. See what happens when you do B = np.ravel(A).
  2. Look of the documentation for np.reshape(). Then, reshape B to make it look like A again.