Imagine that we want to add two vectors called a
and b
. The word vector is used here in the mathematical sense, which means a one-dimensional array. We will learn in Chapter 3, Statistics and Linear Algebra, about specialized NumPy arrays that represent matrices. The vector a
holds the squares of integers 0
to n; for instance, if n
is equal to 3
, a
contains 0
, 1
, or 4
. The vector b
holds the cubes of integers 0
to n, so if n
is equal to 3
, then the vector b
is equal to 0
, 1
, or 8
. How would you do that using plain Python? After we come up with a solution, we will compare it with the NumPy equivalent.
The following function solves the vector addition problem using pure Python without NumPy:
The following is a function that solves the vector addition problem with NumPy:
Notice that numpysum()
does not need a for
loop. Also, we used the arange()
function from NumPy, which creates a NumPy array for us with integers from 0
to n. The arange()
function was imported; that is why it is prefixed with numpy
.
Now comes the fun part. Remember that it was mentioned in the Preface that NumPy is faster when it comes to array operations. How much faster is Numpy, though? The following program will show us by measuring the elapsed time in microseconds for the numpysum()
and pythonsum()
functions. It also prints the last two elements of the vector sum. Let's check that we get the same answers using Python and NumPy:
The output of the program for 1000
, 2000
, and 3000
vector elements is as follows:
Clearly, NumPy is much faster than the equivalent normal Python code. One thing is certain; we get the same results whether we are using NumPy or not. However, the result that is printed differs in representation. Notice that the result from the numpysum()
function does not have any commas. How come? Obviously, we are not dealing with a Python list but with a NumPy array. We will learn more about NumPy arrays in the next chapter, Chapter 2, NumPy Arrays.