docs/python_docs/python/api/np/arrays.ndarray.rst
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.. _arrays.ndarray:
The N-dimensional array (:class:ndarray)
.. currentmodule:: mxnet.np
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 <ndarray.shape>,
which is a :class:tuple of N non-negative integers that specify the
sizes of each dimension. The type of items in the array is specified by
a separate 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 <arrays.indexing> the array (using, for example, N integers),
and via the methods and attributes of the :class:ndarray.
.. index:: view, base
Different :class:ndarrays <ndarray> 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.
.. 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) <class 'mxnet.numpy.ndarray'> x.shape (2, 3) x.dtype dtype('int32')
The array can be indexed using Python container-like syntax:
The element of x in the second row, third column, namely, 6.
x[1, 2] array(6, dtype=int32) # this is different than the official NumPy which returns a np.int32 object
For example :ref:slicing <arrays.indexing> can produce views of
the array if the elements to be sliced is continguous in memory:
y = x[1,:] y array([9, 5, 6], dtype=int32) # this also changes the corresponding element in x x array([[1, 2, 3], [9, 5, 6]], dtype=int32)
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::
ndarray
Arrays can be indexed using an extended Python slicing syntax,
array[selection].
.. seealso:: :ref:Array Indexing <arrays.indexing>.
.. _memory-layout:
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 <ndarray.shape> of the array. How many bytes each item takes and how
the bytes are interpreted is defined by the data-type object
associated with the array.
.. index:: C-order, Fortran-order, row-major, column-major, stride, offset
.. note::
`mxnet.numpy.ndarray` currently only supports storing elements in
C-order/row-major and contiguous memory space. The following content
on explaining a variety of memory layouts of an ndarray
are copied from the official NumPy documentation as a comprehensive reference.
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 <ndarray.strides> of the array. The column-major order (used,
for example, in the Fortran language and in Matlab) and
row-major order (used in C) schemes are just specific kinds of
strided scheme, and correspond to memory that can be addressed by the strides:
.. math::
s_k^{\mathrm{column}} = \mathrm{itemsize} \prod_{j=0}^{k-1} d_j , \quad s_k^{\mathrm{row}} = \mathrm{itemsize} \prod_{j=k+1}^{N-1} d_j .
.. index:: single-segment, contiguous, non-contiguous
where :math:d_j = self.shape[j].
Both the C and Fortran orders are contiguous, i.e., single-segment, memory layouts, in which every part of the memory block can be accessed by some combination of the indices.
While a C-style and Fortran-style contiguous array, which has the corresponding flags set, can be addressed with the above strides, the actual strides may be different. This can happen in two cases:
1. If ``self.shape[k] == 1`` then for any legal index ``index[k] == 0``.
This means that in the formula for the offset :math:`n_k = 0` and thus
:math:`s_k n_k = 0` and the value of :math:`s_k` `= self.strides[k]` is
arbitrary.
2. If an array has no elements (``self.size == 0``) there is no legal
index and the strides are never used. Any array with no elements may be
considered C-style and Fortran-style contiguous.
Point 1. means that self and self.squeeze() always have the same
contiguity and aligned flags value. This also means
that even a high dimensional array could be C-style and Fortran-style
contiguous at the same time.
.. index:: aligned
An array is considered aligned if the memory offsets for all elements and the
base offset itself is a multiple of self.itemsize. Understanding
memory-alignment leads to better performance on most hardware.
.. note::
Points (1) and (2) are not yet applied by default. Beginning with
NumPy 1.8.0, they are applied consistently only if the environment
variable ``NPY_RELAXED_STRIDES_CHECKING=1`` was defined when NumPy
was built. Eventually this will become the default.
You can check whether this option was enabled when your NumPy was
built by looking at the value of ``np.ones((10,1),
order='C').flags.f_contiguous``. If this is ``True``, then your
NumPy has relaxed strides checking enabled.
.. warning::
It does *not* generally hold that ``self.strides[-1] == self.itemsize``
for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
Fortran-style contiguous arrays is true.
Data in new :class:ndarrays <ndarray> is in the row-major
(C) order, unless otherwise specified, but, for example, :ref:basic array slicing <arrays.indexing> often produces views
in a different scheme.
.. seealso: :ref:Indexing <arrays.ndarray.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 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.
The following attributes contain information about the memory layout of the array:
.. autosummary::
ndarray.shape ndarray.ndim ndarray.size
The data type object associated with the array can be found in the
:attr:dtype <ndarray.dtype> attribute:
.. autosummary::
ndarray.dtype
.. _array.ndarray.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:argpartition, :func:argsort, :func:choose,
:func:clip, :func:compress, :func:copy, :func:cumprod,
:func:cumsum, :func:diagonal, :func:imag, :func:max <amax>,
:func:mean, :func:min <amin>, :func:nonzero, :func:partition,
:func:prod, :func:ptp, :func:put, :func:ravel, :func:real,
:func:repeat, :func:reshape, :func:round <around>,
:func:searchsorted, :func:sort, :func:squeeze, :func:std,
:func:sum, :func:swapaxes, :func:take, :func:trace,
:func:transpose, :func:var.
.. autosummary::
ndarray.item ndarray.copy ndarray.tolist ndarray.astype
For reshape, resize, and transpose, the single tuple argument may be
replaced with n integers which will be interpreted as an n-tuple.
.. autosummary::
ndarray.reshape ndarray.transpose ndarray.swapaxes ndarray.flatten ndarray.squeeze
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::
ndarray.nonzero ndarray.take ndarray.repeat ndarray.argsort ndarray.sort
.. 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::
ndarray.max ndarray.argmax ndarray.min ndarray.argmin ndarray.clip ndarray.sum ndarray.mean ndarray.prod ndarray.cumsum ndarray.var ndarray.std ndarray.round ndarray.all ndarray.any
.. index:: comparison, arithmetic, matrix, operation, operator
Arithmetic and comparison operations on :class:ndarrays <ndarray>
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
universal function (or ufunc for short) in NumPy.
Comparison operators:
.. autosummary::
ndarray.lt ndarray.le ndarray.gt ndarray.ge ndarray.eq ndarray.ne
Truth value of an array (:func:bool()):
.. autosummary::
ndarray.bool
.. note::
Truth-value testing of an array invokes
:meth:ndarray.__bool__, which raises an error if the number of
elements in the array is larger than 1, because the truth value
of such arrays is ambiguous.
Unary operations:
.. autosummary::
ndarray.neg ndarray.abs ndarray.invert
Arithmetic:
.. autosummary::
ndarray.add ndarray.sub ndarray.mul ndarray.truediv ndarray.mod ndarray.pow ndarray.and ndarray.or ndarray.xor
.. note::
Any third argument to :func:pow() is silently ignored,
as the underlying :func:ufunc <power> 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 :class:__array_ufunc__ <numpy.class.__array_ufunc__>.
Arithmetic, in-place:
.. autosummary::
ndarray.iadd ndarray.isub ndarray.imul ndarray.itruediv ndarray.imod 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.
Matrix Multiplication:
.. autosummary::
ndarray.matmul
For standard library functions:
.. autosummary::
ndarray.reduce ndarray.setstate
Basic customization:
.. autosummary::
ndarray.new
Container customization: (see :ref:Indexing <arrays.indexing>)
.. autosummary::
ndarray.len ndarray.getitem ndarray.setitem
Conversion; the operations :func:index(), :func:int() and :func:float().
They work only on arrays that have one element in them
and return the appropriate scalar.
.. autosummary::
ndarray.index ndarray.int ndarray.float
String representations:
.. autosummary::
ndarray.str ndarray.repr