# Glossary¶

- 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])

- array
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 dtype('float64') # 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.

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

- attribute
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 (3,)

- big-endian
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.

- BLAS
- broadcast
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 array([[3], [4]]) >>> x + y array([[4, 5], [5, 6]])

See

`numpy.doc.broadcasting`

for more information.- C order
See

*row-major*- column-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.

- decorator
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) {} 3

- dictionary
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] 'one' >>> 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.

- field
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*- flattened
Collapsed to a one-dimensional array. See

`numpy.ndarray.flatten`

for details.- homogeneous
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.

- immutable
An object that cannot be modified after execution is called immutable. Two common examples are strings and tuples.

- instance
A class definition gives the blueprint for constructing an object:

>>> class House: ... 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.- iterable
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

- It is often used in combination with
- itemsize
The size of the dtype element in bytes.

- list
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' '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*.- little-endian
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.

- mask
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.ma.masked_array([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.

- matrix
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]])

- method
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])

- ndarray
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.- reference
If

`a`

is a reference to`b`

, then`(a is b) == True`

. Therefore,`a`

and`b`

are different names for the same Python object.- row-major
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.

- self
Often seen in method signatures,

`self`

refers to the instance of the associated class. For example:>>> class Paintbrush: ... 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!

- slice
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])

- structure
- 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,))])

- title
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.

- tuple
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] 1 >>> 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 1 >>> b 'alpha'

- ufunc
Universal function. A fast element-wise, vectorized array operation. Examples include

`add`

,`sin`

and`logical_or`

.- vectorization
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.

- view
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])

- wrapper
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).