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:

>>> # The element of x in the *second* row, *third* column, namely, 6.
>>> x[1, 2]

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:

ndarray(shape[, dtype, buffer, offset, …]) An array object represents a multidimensional, homogeneous array of fixed-size items.

Indexing arrays¶

Arrays can be indexed using an extended Python slicing syntax, array[selection]. Similar syntax is also used for accessing fields in a structured array.

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}} = \mathrm{itemsize} \prod_{j=0}^{k-1} d_j , \quad s_k^{\mathrm{row}} = \mathrm{itemsize} \prod_{j=k+1}^{N-1} d_j .

where 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:

If self.shape[k] == 1 then for any legal index index[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:

`ndarray.flags`	Information about the memory layout of the array.