475 lines
14 KiB
Python
475 lines
14 KiB
Python
"""
|
|
========
|
|
Glossary
|
|
========
|
|
|
|
.. 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 :term:`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
|
|
`Basic Linear Algebra Subprograms <https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms>`_
|
|
|
|
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 <https://docs.python.org/tutorial/>`_.
|
|
|
|
field
|
|
In a :term:`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 :ref:`arrays.dtypes`
|
|
|
|
Fortran order
|
|
See `column-major`
|
|
|
|
flattened
|
|
Collapsed to a one-dimensional array. See `numpy.ndarray.flatten`
|
|
for details.
|
|
|
|
homogenous
|
|
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
|
|
|
|
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 <https://docs.python.org/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 :term:`ndarray` with :term:`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
|
|
See :term:`structured data type`
|
|
|
|
structured data type
|
|
A data type composed of other datatypes
|
|
|
|
subarray data type
|
|
A :term:`structured data type` may contain a :term:`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 :ref:`title <titles>` 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, :term:`vectorized
|
|
<vectorization>` 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 :ref:`vectorization <whatis-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).
|
|
|
|
"""
|