arrays.ndarray.rst

numpy

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 <ndarray.shape>, which is a 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) <arrays.dtypes>, 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 <arrays.indexing> the array (using, for example, N integers), and via the methods and attributes of the ndarray.

view, base

Different ndarrays <ndarray> 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 <str> or objects implementing the memoryview or array <arrays.interface> 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) <class '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] 6

For example slicing <arrays.indexing> can produce views of the array:

>>> y = x[:,1] >>> y array([2, 5], dtype=int32) >>> y[0] = 9 # this also changes the corresponding element in x >>> y array([9, 5], dtype=int32) >>> x array([[1, 9, 3], [4, 5, 6]], dtype=int32)

Constructing arrays

New arrays can be constructed using the routines detailed in routines.array-creation, and also by using the low-level ndarray constructor:

ndarray

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 data type.

Array Indexing <arrays.indexing>.

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 <ndarray.shape> of the array. How many bytes each item takes and how the bytes are interpreted is defined by the data-type object <arrays.dtypes> associated with the array.

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 ndarray objects can accommodate any strided indexing scheme. In a strided scheme, the N-dimensional index (n₀, n₁, ..., 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 <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:

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

single-segment, contiguous, non-contiguous

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.

Note

Contiguous arrays and single-segment arrays are synonymous and are used interchangeably throughout the documentation.

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 n_k = 0 and thus s_kn_k = 0 and the value of 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.

aligned

An array is considered aligned if the memory offsets for all elements and the base offset itself is a multiple of self.itemsize <ndarray.itemsize>. Understanding memory-alignment leads to better performance on most hardware.

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 <ndarray> is in the row-major (C) order, unless otherwise specified, but, for example, basic array slicing <arrays.indexing> often produces views <view> 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 ndarray.shape ndarray.strides ndarray.ndim ndarray.data ndarray.size ndarray.itemsize ndarray.nbytes ndarray.base

Data type

Data type objects <arrays.dtypes>

The data type object associated with the array can be found in the dtype <ndarray.dtype> attribute:

ndarray.dtype

Other attributes

ndarray.T ndarray.real ndarray.imag ndarray.flat

Array interface

arrays.interface.

~object.__array_interface__	Python-side of the array interface
~object.__array_struct__	C-side of the array interface

ctypes foreign function interface

ndarray.ctypes

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 <amax>, mean, min <amin>, nonzero, partition, prod, put, ravel, real, repeat, reshape, round <around>, searchsorted, sort, squeeze, std, sum, swapaxes, take, trace, transpose, var.

Array conversion

ndarray.item ndarray.tolist ndarray.tostring ndarray.tobytes 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.

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 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.

ndarray.take ndarray.put ndarray.repeat ndarray.choose ndarray.sort ndarray.argsort ndarray.partition ndarray.argpartition ndarray.searchsorted ndarray.nonzero ndarray.compress ndarray.diagonal

Calculation

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).

Example of the axis argument

A 3-dimensional array of size 3 x 3 x 3, summed over each of its three axes

>>> x = np.arange(27).reshape((3,3,3)) >>> 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.

ndarray.max ndarray.argmax ndarray.min ndarray.argmin 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, matrix multiplication, and comparison operations

comparison, arithmetic, matrix, operation, operator

Arithmetic and comparison operations on ndarrays <ndarray> 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 <ufuncs>.

Comparison operators:

ndarray.__lt__ ndarray.__le__ ndarray.__gt__ ndarray.__ge__ ndarray.__eq__ ndarray.__ne__

Truth value of an array (bool() <bool>):

ndarray.__bool__

Note

Truth-value testing of an array invokes 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. Use .any() <ndarray.any> and .all() <ndarray.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:

ndarray.__neg__ ndarray.__pos__ ndarray.__abs__ ndarray.__invert__

Arithmetic:

ndarray.__add__ ndarray.__sub__ ndarray.__mul__ 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 pow() is silently ignored, as the underlying ufunc <power> takes only two arguments.
• 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 __array_ufunc__ <numpy.class.__array_ufunc__>.

Arithmetic, in-place:

ndarray.__iadd__ ndarray.__isub__ ndarray.__imul__ 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.

Matrix Multiplication:

ndarray.__matmul__

Note

Matrix operators @ and @= were introduced in Python 3.5 following 465, and the @ operator has been introduced in NumPy 1.10.0. Further information can be found in the matmul documentation.

Special methods

For standard library functions:

ndarray.__copy__ ndarray.__deepcopy__ ndarray.__reduce__ ndarray.__setstate__

Basic customization:

ndarray.__new__ ndarray.__array__ ndarray.__array_wrap__

Container customization: (see Indexing <arrays.indexing>)

ndarray.__len__ ndarray.__getitem__ ndarray.__setitem__ ndarray.__contains__

Conversion; the operations int() <int>, float() <float> and complex() <complex>. They work only on arrays that have one element in them and return the appropriate scalar.

ndarray.__int__ ndarray.__float__ ndarray.__complex__

String representations:

ndarray.__str__ ndarray.__repr__

Utility method for typing:

ndarray.__class_getitem__