The N-dimensional array (ndarray
)¶
An 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 shape
,
which is a tuple
of N positive 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
ndarray
can be accessed and modified by indexing or
slicing the array (using, for example, N integers),
and via the methods and attributes of the ndarray
.
Different ndarrays
can share the same data, so that
changes made in one 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 strings
or
objects implementing the buffer
or array interfaces.
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)
<type 'numpy.ndarray'>
>>> 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 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
Array creation routines, and also by using the low-level
ndarray
constructor:
Indexing arrays¶
Arrays can be indexed using an extended Python slicing syntax,
array[selection]
. Similar syntax is also used for accessing
fields in a record array.
See also
Internal memory layout of an ndarray¶
An instance of 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 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.
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 ndarray
objects can accommodate any strided indexing scheme. In a strided
scheme, the N-dimensional index (n_0, n_1, ..., n_{N-1})
corresponds to the offset (in bytes):
n_{\mathrm{offset}} = \sum_{k=0}^{N-1} s_k n_k
from the beginning of the memory block associated with the
array. Here, s_k are integers which specify the 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:
s_k^{\mathrm{column}} = \prod_{j=0}^{k-1} d_j , \quad s_k^{\mathrm{row}} = \prod_{j=k+1}^{N-1} d_j .
where d_j = self.itemsize * 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:
- If
self.shape[k] == 1
then for any legal indexindex[k] == 0
. This means that in the formula for the offset n_k = 0 and thus s_k n_k = 0 and the value of s_k = self.strides[k] is arbitrary.- 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.
An array is considered aligned if the memory offsets for all elements and the base offset itself is a multiple of self.itemsize.
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 ndarrays
is in the row-major
(C) order, unless otherwise specified, but, for example, basic
array slicing often produces views
in a different scheme.
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.
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:
Data type¶
See also
The data type object associated with the array can be found in the
dtype
attribute:
Other attributes¶
Array interface¶
See also
__array_interface__ |
Python-side of the array interface |
__array_struct__ |
C-side of the array interface |
Array methods¶
An 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
numpy
: all
, any
, argmax
,
argmin
, argpartition
, argsort
, choose
,
clip
, compress
, copy
, cumprod
,
cumsum
, diagonal
, imag
, max
,
mean
, min
, nonzero
, partition
,
prod
, ptp
, put
, ravel
, real
,
repeat
, reshape
, round
,
searchsorted
, sort
, squeeze
, std
,
sum
, swapaxes
, take
, trace
,
transpose
, var
.
Array conversion¶
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.
Item selection and manipulation¶
For array methods that take an axis keyword, it defaults to
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.
Calculation¶
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).
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 ndarray
and have the same number of
elements. It can have a different data type in which case casting will
be performed.
Arithmetic and comparison operations¶
Arithmetic and comparison operations on ndarrays
are defined as element-wise operations, and generally yield
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. For
more information, see the section on Universal Functions.
Comparison operators:
Truth value of an array (bool
):
Note
Truth-value testing of an array invokes
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 .any()
and
.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:
Arithmetic:
Note
- Any third argument to
pow
is silently ignored, as the underlyingufunc
takes only two arguments. - The three division operators are all defined;
div
is active by default,truediv
is active when__future__
division is in effect. - Because
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
set_numeric_ops
.
Arithmetic, in-place:
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.