User guide

CHAPTER

ONE

INTRODUCTION

1.1 What is NumPy?

NumPy is the fundamental package for scientiﬁc computing in Python. It is a Python library that provides a multidi-

mensional array object, various derived objects (such as masked arrays and matrices), and an assortment of routines for

fast operations on arrays, including mathematical, logical, shape manipulation, sorting, selecting, I/O, discrete Fourier

transforms, basic linear algebra, basic statistical operations, random simulation and much more.

At the core of the NumPy package, is the ndarray object. This encapsulates n-dimensional arrays of homogeneous

data types, with many operations being performed in compiled code for performance. There are several important

differences between NumPy arrays and the standard Python sequences:

• NumPy arrays have a ﬁxed size at creation, unlike Python lists (which can grow dynamically). Changing the

size of an ndarray will create a new array and delete the original.

• The elements in a NumPy array are all required to be of the same data type, and thus will be the same size in

memory. The exception: one can have arrays of (Python, including NumPy) objects, thereby allowing for arrays

of different sized elements.

• NumPy arrays facilitate advanced mathematical and other types of operations on large numbers of data. Typi-

cally, such operations are executed more efﬁciently and with less code than is possible using Python’s built-in

sequences.

• A growing plethora of scientiﬁc and mathematical Python-based packages are using NumPy arrays; though

these typically support Python-sequence input, they convert such input to NumPy arrays prior to processing,

and they often output NumPy arrays. In other words, in order to efﬁciently use much (perhaps even most)

of today’s scientiﬁc/mathematical Python-based software, just knowing how to use Python’s built-in sequence

types is insufﬁcient - one also needs to know how to use NumPy arrays.

The points about sequence size and speed are particularly important in scientiﬁc computing. As a simple example,

consider the case of multiplying each element in a 1-D sequence with the corresponding element in another sequence

of the same length. If the data are stored in two Python lists, a and b, we could iterate over each element:

c = []

for i in range(len(a)):

c.append(a[i]

b[i])

This produces the correct answer, but if a and b each contain millions of numbers, we will pay the price for the

inefﬁciencies of looping in Python. We could accomplish the same task much more quickly in C by writing (for clarity

we neglect variable declarations and initializations, memory allocation, etc.)

for (i = 0; i < rows; i++): {

c[i] = a[i]

b[i];

}