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NumPy is the fundamental package for scientific computing in Python. It is a Python library that provides a multidimensional 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. Typically, 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];
} 3
NumPy User Guide, Release 1.11.2
This saves all the overhead involved in interpreting the Python code and manipulating Python objects, but at the
expense of the benefits gained from coding in Python. Furthermore, the coding work required increases with the
dimensionality of our data. In the case of a 2-D array, for example, the C code (abridged as before) expands to
for (i = 0; i < rows; i++): {
for (j = 0; j < columns; j++): {
c[i][j] = a[i][j]*b[i][j];
} }
NumPy gives us the best of both worlds: element-by-element operations are the “default mode” when an ndarray is
involved, but the element-by-element operation is speedily executed by pre-compiled C code. In NumPy
c = a * b
does what the earlier examples do, at near-C speeds, but with the code simplicity we expect from something based on
Python. Indeed, the NumPy idiom is even simpler! This last example illustrates two of NumPy’s features which are
the basis of much of its power: vectorization and broadcasting.
Vectorization describes the absence of any explicit looping, indexing, etc., in the code - these things are taking place,
of course, just “behind the scenes” in optimized, pre-compiled C code. Vectorized code has many advantages, among
which are:
• vectorized code is more concise and easier to read
• fewer lines of code generally means fewer bugs
• the code more closely resembles standard mathematical notation (making it easier, typically, to correctly code
mathematical constructs)
• vectorization results in more “Pythonic” code. Without vectorization, our code would be littered with inefficient
and difficult to read for loops.
Broadcasting is the term used to describe the implicit element-by-element behavior of operations; generally speaking,
in NumPy all operations, not just arithmetic operations, but logical, bit-wise, functional, etc., behave in this implicit
element-by-element fashion, i.e., they broadcast. Moreover, in the example above, a and b could be multidimensional
arrays of the same shape, or a scalar and an array, or even two arrays of with different shapes, provided that the smaller
array is “expandable” to the shape of the larger in such a way that the resulting broadcast is unambiguous. For detailed
“rules” of broadcasting see numpy.doc.broadcasting.
NumPy fully supports an object-oriented approach, starting, once again, with ndarray. For example, ndarray is a
class, possessing numerous methods and attributes. Many of its methods mirror functions in the outer-most NumPy
namespace, giving the programmer complete freedom to code in whichever paradigm she prefers and/or which seems
most appropriate to the task at hand.
1.2 Installing NumPy
In most use cases the best way to install NumPy on your system is by using an pre-built package for your operating
system. Please see http://scipy.org/install.html for links to available options.
For instructions on building for source package, see Building from source. This information is useful mainly for
advanced users.
4 Chapter 1. Setting up
CHAPTER
TWO
QUICKSTART TUTORIAL
2.1 Prerequisites
Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at
the Python tutorial.
If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please
see http://scipy.org/install.html for instructions.
2.2 The Basics
NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of
the same type, indexed by a tuple of positive integers. In Numpy dimensions are called axes. The number of axes is
rank.
For example, the coordinates of a point in 3D space [1, 2, 1] is an array of rank 1, because it has one axis. That
axis has a length of 3. In example pictured below, the array has rank 2 (it is 2-dimension
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