Lecturer: Vince Knight

Office: M1.30

email: knightva@cf.ac.uk

chat: https://gitter.im/computing-for-mathematics/Lobby

Office hours: Thursday 1400-1600

What you have learnt this week:

Using numpy to carry out linear algebraic calculations.

Numerical approximation

Some of you carried out the following calculation and noticed that something wasn’t quite right:

>>> import numpy as np
>>> A = np.matrix([[1, 2, 4], [5, 3, 1], [5, 1, 8]])
>>> Ainv = np.linalg.inv(A)
>>> b = np.matrix([[1], [2], [3]])
>>> np.array_equal(Ainv * b, np.linalg.solve(A, b))
False

However:

>>> Ainv * b
matrix([[ 0.35632184],
        [ 0.02298851],
        [ 0.14942529]])
>>> np.linalg.solve(A, b)
matrix([[ 0.35632184],
        [ 0.02298851],
        [ 0.14942529]])

This is due to numerical error which is a normal process when dealing with numerical calculations.

We can however check for equality with a tolerance for numerical error:

>>> np.isclose(Ainv * b, np.linalg.solve(A, b))
matrix([[ True],
        [ True],
        [ True]], dtype=bool)

Including code in LaTeX

There are various ways to include code in LaTeX documents, one of the nicest is to use the minted library, however this might not work on all systems (it works fine on overleaf). The simplest approach is to use the listings package like in the model solution. Here is a small example:

\documentclass{article}

\usepackage{listings}

\begin{document}
Here is some amazing code:

\begin{lstlisting}[language=python]
for i in range(20):
    print(i)
\end{lstlisting}

\end{document}

Searching for LaTeX commands

Keep in mind that overleaf, texworks, cloud.sagemath are just interfaces to LaTeX, so when searching for how to do things don’t include those terms. For example search for “how to change margin size in LaTeX” and not “how to change margin size in overleaf”.

Page limit

3 pages is a strict upper limit.

Ideas

Most of you have come up with great ideas for your projects, if you are still looking for inspiration, here are some blog posts I have written that might be of interest: