2017 will forever be etched in our memories as the year Python overtook R to become the leading language for Data Science. There are many factors that play into this: Python's simple syntax, the fantastic PyData ecosystem, and of course buy-in from Python's BDFL.
PEP 465 introduced the @ infix operator that is designated to be used for matrix multiplication. The acceptance and implementation of this proposal in Python 3.5 was a signal to the scientific community that Python is taking its role as a numerical computation language very seriously.
I was a Computational Mathematics major in college so matrices are very near and dear to my heart. Shoutout to Professor Jeff Orchard for having us implement matrix algorithms in C++. His Numerical Linear Algebra course was the best class I've ever taken.
In this post, we will explore the @ operator.
In [2]:
A = np.matrix['3 1; 8 2'] A
In [3]:
B = np.matrix['6 1; 7 9'] B
Out[4]:
matrix[[[25, 12],
[62, 26]]]In [5]:
# element at the top left. i.e. [1, 1] aka [0, 0] in python A[0, 0] * B[0, 0] + A[0, 1] * B[1, 0]
In [6]:
# element at the top right. i.e. [1, 2] aka [0, 1] in python A[0, 0] * B[0, 1] + A[0, 1] * B[1, 1]
In [7]:
# element at the bottom left. i.e. [2, 1] aka [1, 0] in python A[1, 0] * B[0, 0] + A[1, 1] * B[1, 0]
In [8]:
# element at the top right. i.e. [2, 2] aka [1, 1] in python A[1, 0] * B[0, 1] + A[1, 1] * B[1, 1]
In [9]:
# let's put it in matrix form result = np.matrix[[[A[0, 0] * B[0, 0] + A[0, 1] * B[1, 0], A[0, 0] * B[0, 1] + A[0, 1] * B[1, 1]], [A[1, 0] * B[0, 0] + A[1, 1] * B[1, 0], A[1, 0] * B[0, 1] + A[1, 1] * B[1, 1]]]] result
Out[9]:
matrix[[[25, 12],
[62, 26]]]Out[10]:
matrix[[[ True, True],
[ True, True]], dtype=bool]The
Python Data Model specifies that the @ operator invokes __matmul__ and __rmatmul__.
We can overload @ by defining custom behavior for each of the special methods above, but this would result in our API not being Pythonic.
To build Pythonic objects, observe how real Python objects behave.
- Luciano Ramalho, Author of Fluent Python