along an axis

Axes are defined for arrays with more than one dimension. A 2-dimensional array has two corresponding axes: the first running vertically downwards across rows (axis 0), and the second running horizontally across columns (axis 1).

Many operations can take place along one of these axes. For example, we can sum each row of an array, in which case we operate along columns, or axis 1:

>>> x = np.arange(12).reshape((3,4))

>>> x
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

>>> x.sum(axis=1)
array([ 6, 22, 38])

A homogeneous container of numerical elements. Each element in the array occupies a fixed amount of memory (hence homogeneous), and can be a numerical element of a single type (such as float, int or complex) or a combination (such as (float, int, float)). Each array has an associated data-type (or dtype), which describes the numerical type of its elements:

>>> x = np.array([1, 2, 3], float)

>>> x
array([ 1.,  2.,  3.])

>>> x.dtype # floating point number, 64 bits of memory per element

# More complicated data type: each array element is a combination of
# and integer and a floating point number
>>> np.array([(1, 2.0), (3, 4.0)], dtype=[('x', int), ('y', float)])
array([(1, 2.0), (3, 4.0)],
      dtype=[('x', '<i4'), ('y', '<f8')])

Fast element-wise operations, called a ufunc, operate on arrays.

Any sequence that can be interpreted as an ndarray. This includes nested lists, tuples, scalars and existing arrays.

A property of an object that can be accessed using obj.attribute, e.g., shape is an attribute of an array:

>>> x = np.array([1, 2, 3])
>>> x.shape
When storing a multi-byte value in memory as a sequence of bytes, the sequence addresses/sends/stores the most significant byte first (lowest address) and the least significant byte last (highest address). Common in micro-processors and used for transmission of data over network protocols.
Basic Linear Algebra Subprograms

NumPy can do operations on arrays whose shapes are mismatched:

>>> x = np.array([1, 2])
>>> y = np.array([[3], [4]])

>>> x
array([1, 2])

>>> y

>>> x + y
array([[4, 5],
       [5, 6]])

See numpy.doc.broadcasting for more information.

C order
See row-major

A way to represent items in a N-dimensional array in the 1-dimensional computer memory. In column-major order, the leftmost index “varies the fastest”: for example the array:

[[1, 2, 3],
 [4, 5, 6]]

is represented in the column-major order as:

[1, 4, 2, 5, 3, 6]

Column-major order is also known as the Fortran order, as the Fortran programming language uses it.


An operator that transforms a function. For example, a log decorator may be defined to print debugging information upon function execution:

>>> def log(f):
...     def new_logging_func(*args, **kwargs):
...         print("Logging call with parameters:", args, kwargs)
...         return f(*args, **kwargs)
...     return new_logging_func

Now, when we define a function, we can “decorate” it using log:

>>> @log
... def add(a, b):
...     return a + b

Calling add then yields:

>>> add(1, 2)
Logging call with parameters: (1, 2) {}

Resembling a language dictionary, which provides a mapping between words and descriptions thereof, a Python dictionary is a mapping between two objects:

>>> x = {1: 'one', 'two': [1, 2]}

Here, x is a dictionary mapping keys to values, in this case the integer 1 to the string “one”, and the string “two” to the list [1, 2]. The values may be accessed using their corresponding keys:

>>> x[1]

>>> x['two']
[1, 2]

Note that dictionaries are not stored in any specific order. Also, most mutable (see immutable below) objects, such as lists, may not be used as keys.

For more information on dictionaries, read the Python tutorial.

In a structured data type, each sub-type is called a field. The field has a name (a string), a type (any valid dtype, and an optional title. See Data type objects (dtype)
Fortran order
See column-major
Collapsed to a one-dimensional array. See numpy.ndarray.flatten for details.
Describes a block of memory comprised of blocks, each block comprised of items and of the same size, and blocks are interpreted in exactly the same way. In the simplest case each block contains a single item, for instance int32 or float64.
An object that cannot be modified after execution is called immutable. Two common examples are strings and tuples.

A class definition gives the blueprint for constructing an object:

>>> class House(object):
...     wall_colour = 'white'

Yet, we have to build a house before it exists:

>>> h = House() # build a house

Now, h is called a House instance. An instance is therefore a specific realisation of a class.


A sequence that allows “walking” (iterating) over items, typically using a loop such as:

>>> x = [1, 2, 3]
>>> [item**2 for item in x]
[1, 4, 9]
It is often used in combination with enumerate::
>>> keys = ['a','b','c']
>>> for n, k in enumerate(keys):
...     print("Key %d: %s" % (n, k))
Key 0: a
Key 1: b
Key 2: c
The size of the dtype element in bytes.

A Python container that can hold any number of objects or items. The items do not have to be of the same type, and can even be lists themselves:

>>> x = [2, 2.0, "two", [2, 2.0]]

The list x contains 4 items, each which can be accessed individually:

>>> x[2] # the string 'two'

>>> x[3] # a list, containing an integer 2 and a float 2.0
[2, 2.0]

It is also possible to select more than one item at a time, using slicing:

>>> x[0:2] # or, equivalently, x[:2]
[2, 2.0]

In code, arrays are often conveniently expressed as nested lists:

>>> np.array([[1, 2], [3, 4]])
array([[1, 2],
       [3, 4]])

For more information, read the section on lists in the Python tutorial. For a mapping type (key-value), see dictionary.

When storing a multi-byte value in memory as a sequence of bytes, the sequence addresses/sends/stores the least significant byte first (lowest address) and the most significant byte last (highest address). Common in x86 processors.

A boolean array, used to select only certain elements for an operation:

>>> x = np.arange(5)
>>> x
array([0, 1, 2, 3, 4])

>>> mask = (x > 2)
>>> mask
array([False, False, False, True,  True])

>>> x[mask] = -1
>>> x
array([ 0,  1,  2,  -1, -1])
masked array

Array that suppressed values indicated by a mask:

>>> x =[np.nan, 2, np.nan], [True, False, True])
>>> x
masked_array(data = [-- 2.0 --],
             mask = [ True False  True],
       fill_value = 1e+20)

>>> x + [1, 2, 3]
masked_array(data = [-- 4.0 --],
             mask = [ True False  True],
       fill_value = 1e+20)

Masked arrays are often used when operating on arrays containing missing or invalid entries.


A 2-dimensional ndarray that preserves its two-dimensional nature throughout operations. It has certain special operations, such as * (matrix multiplication) and ** (matrix power), defined:

>>> x = np.mat([[1, 2], [3, 4]])
>>> x
matrix([[1, 2],
        [3, 4]])

>>> x**2
matrix([[ 7, 10],
      [15, 22]])

A function associated with an object. For example, each ndarray has a method called repeat:

>>> x = np.array([1, 2, 3])
>>> x.repeat(2)
array([1, 1, 2, 2, 3, 3])
See array.
record array
An ndarray with structured data type which has been subclassed as np.recarray and whose dtype is of type np.record, making the fields of its data type to be accessible by attribute.
If a is a reference to b, then (a is b) == True. Therefore, a and b are different names for the same Python object.

A way to represent items in a N-dimensional array in the 1-dimensional computer memory. In row-major order, the rightmost index “varies the fastest”: for example the array:

[[1, 2, 3],
 [4, 5, 6]]

is represented in the row-major order as:

[1, 2, 3, 4, 5, 6]

Row-major order is also known as the C order, as the C programming language uses it. New NumPy arrays are by default in row-major order.


Often seen in method signatures, self refers to the instance of the associated class. For example:

>>> class Paintbrush(object):
...     color = 'blue'
...     def paint(self):
...         print("Painting the city %s!" % self.color)
>>> p = Paintbrush()
>>> p.color = 'red'
>>> p.paint() # self refers to 'p'
Painting the city red!

Used to select only certain elements from a sequence:

>>> x = range(5)
>>> x
[0, 1, 2, 3, 4]
>>> x[1:3] # slice from 1 to 3 (excluding 3 itself)
[1, 2]
>>> x[1:5:2] # slice from 1 to 5, but skipping every second element
[1, 3]
>>> x[::-1] # slice a sequence in reverse
[4, 3, 2, 1, 0]

Arrays may have more than one dimension, each which can be sliced individually:

>>> x = np.array([[1, 2], [3, 4]])
>>> x
array([[1, 2],
       [3, 4]])
>>> x[:, 1]
array([2, 4])
See structured data type
structured data type
A data type composed of other datatypes
subarray data type

A structured data type may contain a ndarray with its own dtype and shape:

>>> dt = np.dtype([('a', np.int32), ('b', np.float32, (3,))])
>>> np.zeros(3, dtype=dt)
array([(0, [0., 0., 0.]), (0, [0., 0., 0.]), (0, [0., 0., 0.])],
      dtype=[('a', '<i4'), ('b', '<f4', (3,))])
In addition to field names, structured array fields may have an associated title which is an alias to the name and is commonly used for plotting.

A sequence that may contain a variable number of types of any kind. A tuple is immutable, i.e., once constructed it cannot be changed. Similar to a list, it can be indexed and sliced:

>>> x = (1, 'one', [1, 2])
>>> x
(1, 'one', [1, 2])

>>> x[0]

>>> x[:2]
(1, 'one')

A useful concept is “tuple unpacking”, which allows variables to be assigned to the contents of a tuple:

>>> x, y = (1, 2)
>>> x, y = 1, 2

This is often used when a function returns multiple values:

>>> def return_many():
...     return 1, 'alpha', None
>>> a, b, c = return_many()
>>> a, b, c
(1, 'alpha', None)
>>> a
>>> b
Universal function. A fast element-wise, vectorized array operation. Examples include add, sin and logical_or.
Optimizing a looping block by specialized code. In a traditional sense, vectorization performs the same operation on multiple elements with fixed strides between them via specialized hardware. Compilers know how to take advantage of well-constructed loops to implement such optimizations. NumPy uses vectorization to mean any optimization via specialized code performing the same operations on multiple elements, typically achieving speedups by avoiding some of the overhead in looking up and converting the elements.

An array that does not own its data, but refers to another array’s data instead. For example, we may create a view that only shows every second element of another array:

>>> x = np.arange(5)
>>> x
array([0, 1, 2, 3, 4])

>>> y = x[::2]
>>> y
array([0, 2, 4])

>>> x[0] = 3 # changing x changes y as well, since y is a view on x
>>> y
array([3, 2, 4])

Python is a high-level (highly abstracted, or English-like) language. This abstraction comes at a price in execution speed, and sometimes it becomes necessary to use lower level languages to do fast computations. A wrapper is code that provides a bridge between high and the low level languages, allowing, e.g., Python to execute code written in C or Fortran.

Examples include ctypes, SWIG and Cython (which wraps C and C++) and f2py (which wraps Fortran).

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