When it comes to performance of your Python code, it often boils down to the difference between interpreted code and compiled code. Python is an interpreted programming language and basic Python code is executed directly without any intermediate compilation to machine code. With a compiled language, the code needs to be translated to machine instructions before execution.

The benefits of an interpreted language are many but interpreted code cannot compete with compiled code for speed. To make your code faster, you can write some parts in a compiled language like FORTRAN, C, or C++. This is what NumPy and SciPy do.

For this reason, it is best to use functions in NumPy and SciPy over interpreted versions whenever possible. NumPy array operations such as matrix multiplication, matrix-vector multiplication, matrix factorization, scalar products, and so on are much faster than any pure Python equivalent. Consider the simple case of scalar products. The scalar product...