.. _arrays.ndarray:
******************************************
The N-dimensional array (:class:`ndarray`)
******************************************
.. currentmodule:: numpy
An :class:`ndarray` is a (usually fixed-size) multidimensional
container of items of the same type and size. The number of dimensions
and items in an array is defined by its :attr:`shape `,
which is a :class:`tuple` of *N* positive integers that specify the
sizes of each dimension. The type of items in the array is specified by
a separate :ref:`data-type object (dtype) `, one of which
is associated with each ndarray.
As with other container objects in Python, the contents of an
:class:`ndarray` can be accessed and modified by :ref:`indexing or
slicing ` the array (using, for example, *N* integers),
and via the methods and attributes of the :class:`ndarray`.
.. index:: view, base
Different :class:`ndarrays ` can share the same data, so that
changes made in one :class:`ndarray` may be visible in another. That
is, an ndarray can be a *"view"* to another ndarray, and the data it
is referring to is taken care of by the *"base"* ndarray. ndarrays can
also be views to memory owned by Python :class:`strings ` or
objects implementing the :class:`buffer` or :ref:`array
` interfaces.
.. admonition:: Example
A 2-dimensional array of size 2 x 3, composed of 4-byte integer
elements:
>>> x = np.array([[1, 2, 3], [4, 5, 6]], np.int32)
>>> type(x)
>>> x.shape
(2, 3)
>>> x.dtype
dtype('int32')
The array can be indexed using Python container-like syntax:
>>> x[1,2] # i.e., the element of x in the *second* row, *third*
column, namely, 6.
For example :ref:`slicing ` can produce views of
the array:
>>> y = x[:,1]
>>> y
array([2, 5])
>>> y[0] = 9 # this also changes the corresponding element in x
>>> y
array([9, 5])
>>> x
array([[1, 9, 3],
[4, 5, 6]])
Constructing arrays
===================
New arrays can be constructed using the routines detailed in
:ref:`routines.array-creation`, and also by using the low-level
:class:`ndarray` constructor:
.. autosummary::
:toctree: generated/
ndarray
.. _arrays.ndarray.indexing:
Indexing arrays
===============
Arrays can be indexed using an extended Python slicing syntax,
``array[selection]``. Similar syntax is also used for accessing
fields in a :ref:`record array `.
.. seealso:: :ref:`Array Indexing `.
Internal memory layout of an ndarray
====================================
An instance of class :class:`ndarray` consists of a contiguous
one-dimensional segment of computer memory (owned by the array, or by
some other object), combined with an indexing scheme that maps *N*
integers into the location of an item in the block. The ranges in
which the indices can vary is specified by the :obj:`shape
` of the array. How many bytes each item takes and how
the bytes are interpreted is defined by the :ref:`data-type object
` associated with the array.
.. index:: C-order, Fortran-order, row-major, column-major, stride,
offset
A segment of memory is inherently 1-dimensional, and there are many
different schemes for arranging the items of an *N*-dimensional array
in a 1-dimensional block. Numpy is flexible, and :class:`ndarray`
objects can accommodate any *strided indexing scheme*. In a strided
scheme, the N-dimensional index :math:`(n_0, n_1, ..., n_{N-1})`
corresponds to the offset (in bytes):
.. math:: n_{\mathrm{offset}} = \sum_{k=0}^{N-1} s_k n_k
from the beginning of the memory block associated with the
array. Here, :math:`s_k` are integers which specify the :obj:`strides
` of the array. The :term:`column-major` order (used,
for example, in the Fortran language and in *Matlab*) and
:term:`row-major` order (used in C) schemes are just specific kinds of
strided scheme, and correspond to the strides:
.. math::
s_k^{\mathrm{column}} = \prod_{j=0}^{k-1} d_j ,
\quad s_k^{\mathrm{row}} = \prod_{j=k+1}^{N-1} d_j .
.. index:: single-segment, contiguous, non-contiguous
where :math:`d_j` = `self.itemsize * self.shape[j]`.
Both the C and Fortran orders are :term:`contiguous`, *i.e.,*
:term:`single-segment`, memory layouts, in which every part of the
memory block can be accessed by some combination of the indices.
Data in new :class:`ndarrays ` is in the :term:`row-major`
(C) order, unless otherwise specified, but, for example, :ref:`basic
array slicing ` often produces :term:`views `
in a different scheme.
.. seealso: :ref:`Indexing `_
.. note::
Several algorithms in NumPy work on arbitrarily strided arrays.
However, some algorithms require single-segment arrays. When an
irregularly strided array is passed in to such algorithms, a copy
is automatically made.
.. _arrays.ndarray.attributes:
Array attributes
================
Array attributes reflect information that is intrinsic to the array
itself. Generally, accessing an array through its attributes allows
you to get and sometimes set intrinsic properties of the array without
creating a new array. The exposed attributes are the core parts of an
array and only some of them can be reset meaningfully without creating
a new array. Information on each attribute is given below.
Memory layout
-------------
The following attributes contain information about the memory layout
of the array:
.. autosummary::
:toctree: generated/
ndarray.flags
ndarray.shape
ndarray.strides
ndarray.ndim
ndarray.data
ndarray.size
ndarray.itemsize
ndarray.nbytes
ndarray.base
Data type
---------
.. seealso:: :ref:`Data type objects `
The data type object associated with the array can be found in the
:attr:`dtype ` attribute:
.. autosummary::
:toctree: generated/
ndarray.dtype
Other attributes
----------------
.. autosummary::
:toctree: generated/
ndarray.T
ndarray.real
ndarray.imag
ndarray.flat
ndarray.ctypes
__array_priority__
.. _arrays.ndarray.array-interface:
Array interface
---------------
.. seealso:: :ref:`arrays.interface`.
========================== ===================================
:obj:`__array_interface__` Python-side of the array interface
:obj:`__array_struct__` C-side of the array interface
========================== ===================================
:mod:`ctypes` foreign function interface
----------------------------------------
.. autosummary::
:toctree: generated/
ndarray.ctypes
.. _array.ndarray.methods:
Array methods
=============
An :class:`ndarray` object has many methods which operate on or with
the array in some fashion, typically returning an array result. These
methods are briefly explained below. (Each method's docstring has a
more complete description.)
For the following methods there are also corresponding functions in
:mod:`numpy`: :func:`all`, :func:`any`, :func:`argmax`,
:func:`argmin`, :func:`argsort`, :func:`choose`, :func:`clip`,
:func:`compress`, :func:`copy`, :func:`cumprod`, :func:`cumsum`,
:func:`diagonal`, :func:`imag`, :func:`max `, :func:`mean`,
:func:`min `, :func:`nonzero`, :func:`prod`, :func:`ptp`,
:func:`put`, :func:`ravel`, :func:`real`, :func:`repeat`,
:func:`reshape`, :func:`round `, :func:`searchsorted`,
:func:`sort`, :func:`squeeze`, :func:`std`, :func:`sum`,
:func:`swapaxes`, :func:`take`, :func:`trace`, :func:`transpose`,
:func:`var`.
Array conversion
----------------
.. autosummary::
:toctree: generated/
ndarray.item
ndarray.tolist
ndarray.itemset
ndarray.tostring
ndarray.tofile
ndarray.dump
ndarray.dumps
ndarray.astype
ndarray.byteswap
ndarray.copy
ndarray.view
ndarray.getfield
ndarray.setflags
ndarray.fill
Shape manipulation
------------------
For reshape, resize, and transpose, the single tuple argument may be
replaced with ``n`` integers which will be interpreted as an n-tuple.
.. autosummary::
:toctree: generated/
ndarray.reshape
ndarray.resize
ndarray.transpose
ndarray.swapaxes
ndarray.flatten
ndarray.ravel
ndarray.squeeze
Item selection and manipulation
-------------------------------
For array methods that take an *axis* keyword, it defaults to
:const:`None`. If axis is *None*, then the array is treated as a 1-D
array. Any other value for *axis* represents the dimension along which
the operation should proceed.
.. autosummary::
:toctree: generated/
ndarray.take
ndarray.put
ndarray.repeat
ndarray.choose
ndarray.sort
ndarray.argsort
ndarray.searchsorted
ndarray.nonzero
ndarray.compress
ndarray.diagonal
Calculation
-----------
.. index:: axis
Many of these methods take an argument named *axis*. In such cases,
- If *axis* is *None* (the default), the array is treated as a 1-D
array and the operation is performed over the entire array. This
behavior is also the default if self is a 0-dimensional array or
array scalar. (An array scalar is an instance of the types/classes
float32, float64, etc., whereas a 0-dimensional array is an ndarray
instance containing precisely one array scalar.)
- If *axis* is an integer, then the operation is done over the given
axis (for each 1-D subarray that can be created along the given axis).
.. admonition:: Example of the *axis* argument
A 3-dimensional array of size 3 x 3 x 3, summed over each of its
three axes
>>> x
array([[[ 0, 1, 2],
[ 3, 4, 5],
[ 6, 7, 8]],
[[ 9, 10, 11],
[12, 13, 14],
[15, 16, 17]],
[[18, 19, 20],
[21, 22, 23],
[24, 25, 26]]])
>>> x.sum(axis=0)
array([[27, 30, 33],
[36, 39, 42],
[45, 48, 51]])
>>> # for sum, axis is the first keyword, so we may omit it,
>>> # specifying only its value
>>> x.sum(0), x.sum(1), x.sum(2)
(array([[27, 30, 33],
[36, 39, 42],
[45, 48, 51]]),
array([[ 9, 12, 15],
[36, 39, 42],
[63, 66, 69]]),
array([[ 3, 12, 21],
[30, 39, 48],
[57, 66, 75]]))
The parameter *dtype* specifies the data type over which a reduction
operation (like summing) should take place. The default reduce data
type is the same as the data type of *self*. To avoid overflow, it can
be useful to perform the reduction using a larger data type.
For several methods, an optional *out* argument can also be provided
and the result will be placed into the output array given. The *out*
argument must be an :class:`ndarray` and have the same number of
elements. It can have a different data type in which case casting will
be performed.
.. autosummary::
:toctree: generated/
ndarray.argmax
ndarray.min
ndarray.argmin
ndarray.ptp
ndarray.clip
ndarray.conj
ndarray.round
ndarray.trace
ndarray.sum
ndarray.cumsum
ndarray.mean
ndarray.var
ndarray.std
ndarray.prod
ndarray.cumprod
ndarray.all
ndarray.any
Arithmetic and comparison operations
====================================
.. index:: comparison, arithmetic, operation, operator
Arithmetic and comparison operations on :class:`ndarrays `
are defined as element-wise operations, and generally yield
:class:`ndarray` objects as results.
Each of the arithmetic operations (``+``, ``-``, ``*``, ``/``, ``//``,
``%``, ``divmod()``, ``**`` or ``pow()``, ``<<``, ``>>``, ``&``,
``^``, ``|``, ``~``) and the comparisons (``==``, ``<``, ``>``,
``<=``, ``>=``, ``!=``) is equivalent to the corresponding
:term:`universal function` (or :term:`ufunc` for short) in Numpy. For
more information, see the section on :ref:`Universal Functions
`.
Comparison operators:
.. autosummary::
:toctree: generated/
ndarray.__lt__
ndarray.__le__
ndarray.__gt__
ndarray.__ge__
ndarray.__eq__
ndarray.__ne__
Truth value of an array (:func:`bool()`):
.. autosummary::
:toctree: generated/
ndarray.__nonzero__
.. note::
Truth-value testing of an array invokes
:meth:`ndarray.__nonzero__`, which raises an error if the number of
elements in the the array is larger than 1, because the truth value
of such arrays is ambiguous. Use :meth:`.any() ` and
:meth:`.all() ` instead to be clear about what is meant
in such cases. (If the number of elements is 0, the array evaluates
to ``False``.)
Unary operations:
.. autosummary::
:toctree: generated/
ndarray.__neg__
ndarray.__pos__
ndarray.__abs__
ndarray.__invert__
Arithmetic:
.. autosummary::
:toctree: generated/
ndarray.__add__
ndarray.__sub__
ndarray.__mul__
ndarray.__div__
ndarray.__truediv__
ndarray.__floordiv__
ndarray.__mod__
ndarray.__divmod__
ndarray.__pow__
ndarray.__lshift__
ndarray.__rshift__
ndarray.__and__
ndarray.__or__
ndarray.__xor__
.. note::
- Any third argument to :func:`pow()` is silently ignored,
as the underlying :func:`ufunc ` takes only two arguments.
- The three division operators are all defined; :obj:`div` is active
by default, :obj:`truediv` is active when
:obj:`__future__` division is in effect.
- Because :class:`ndarray` is a built-in type (written in C), the
``__r{op}__`` special methods are not directly defined.
- The functions called to implement many arithmetic special methods
for arrays can be modified using :func:`set_numeric_ops`.
Arithmetic, in-place:
.. autosummary::
:toctree: generated/
ndarray.__iadd__
ndarray.__isub__
ndarray.__imul__
ndarray.__idiv__
ndarray.__itruediv__
ndarray.__ifloordiv__
ndarray.__imod__
ndarray.__ipow__
ndarray.__ilshift__
ndarray.__irshift__
ndarray.__iand__
ndarray.__ior__
ndarray.__ixor__
.. warning::
In place operations will perform the calculation using the
precision decided by the data type of the two operands, but will
silently downcast the result (if necessary) so it can fit back into
the array. Therefore, for mixed precision calculations, ``A {op}=
B`` can be different than ``A = A {op} B``. For example, suppose
``a = ones((3,3))``. Then, ``a += 3j`` is different than ``a = a +
3j``: while they both perform the same computation, ``a += 3``
casts the result to fit back in ``a``, whereas ``a = a + 3j``
re-binds the name ``a`` to the result.
Special methods
===============
For standard library functions:
.. autosummary::
:toctree: generated/
ndarray.__copy__
ndarray.__deepcopy__
ndarray.__reduce__
ndarray.__setstate__
Basic customization:
.. autosummary::
:toctree: generated/
ndarray.__new__
ndarray.__array__
ndarray.__array_wrap__
Container customization: (see :ref:`Indexing `)
.. autosummary::
:toctree: generated/
ndarray.__len__
ndarray.__getitem__
ndarray.__setitem__
ndarray.__getslice__
ndarray.__setslice__
ndarray.__contains__
Conversion; the operations :func:`complex()`, :func:`int()`,
:func:`long()`, :func:`float()`, :func:`oct()`, and
:func:`hex()`. They work only on arrays that have one element in them
and return the appropriate scalar.
.. autosummary::
:toctree: generated/
ndarray.__int__
ndarray.__long__
ndarray.__float__
ndarray.__oct__
ndarray.__hex__
String representations:
.. autosummary::
:toctree: generated/
ndarray.__str__
ndarray.__repr__