Example

A 2-dimensional array of size 2 x 3, composed of 4-byte integerelements:

>>>x=np.array([[1,2,3],[4,5,6]],np.int32)>>>type(x)<type 'numpy.ndarray'>>>>x.shape(2, 3)>>>x.dtypedtype('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 exampleslicing can produce views ofthe array:

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

Constructing arrays¶

New arrays can be constructed using the routines detailed inArray creation routines, and also by using the low-levelndarray constructor:

Indexing arrays¶

Arrays can be indexed using an extended Python slicing syntax,array[selection]. Similar syntax is also used for accessingfields in astructured array.

Internal memory layout of an ndarray¶

An instance of classndarray consists of a contiguousone-dimensional segment of computer memory (owned by the array, or bysome other object), combined with an indexing scheme that mapsNintegers into the location of an item in the block. The ranges inwhich the indices can vary is specified by theshape of the array. How many bytes each item takes and howthe bytes are interpreted is defined by thedata-type object associated with the array.

A segment of memory is inherently 1-dimensional, and there are manydifferent schemes for arranging the items of anN-dimensional arrayin a 1-dimensional block. NumPy is flexible, andndarrayobjects can accommodate anystrided indexing scheme. In a stridedscheme, the N-dimensional index(n_0, n_1, ..., n_{N-1})corresponds to the offset (in bytes):

from the beginning of the memory block associated with thearray. Here,s_k are integers which specify thestrides of the array. Thecolumn-major order (used,for example, in the Fortran language and inMatlab) androw-major order (used in C) schemes are just specific kinds ofstrided scheme, and correspond to memory that can beaddressed by the strides:

whered_j= self.shape[j].

Both the C and Fortran orders arecontiguous,i.e.,single-segment, memory layouts, in which every part of thememory block can be accessed by some combination of the indices.

While a C-style and Fortran-style contiguous array, which has the correspondingflags set, can be addressed with the above strides, the actual strides may bedifferent. This can happen in two cases:

1. Ifself.shape[k]==1 then for any legal indexindex[k]==0.This means that in the formula for the offsetn_k = 0 and thuss_k n_k = 0 and the value ofs_k= self.strides[k] isarbitrary.
2. If an array has no elements (self.size==0) there is no legalindex and the strides are never used. Any array with no elements may beconsidered C-style and Fortran-style contiguous.

Point 1. means thatself andself.squeeze() always have the samecontiguity andaligned flags value. This also means that even a highdimensional array could be C-style and Fortran-style contiguous at the sametime.

An array is considered aligned if the memory offsets for all elements and thebase offset itself is a multiple ofself.itemsize.

Data in newndarrays is in therow-major(C) order, unless otherwise specified, but, for example,basicarray slicing often producesviewsin a different scheme.

Array attributes¶

Array attributes reflect information that is intrinsic to the arrayitself. Generally, accessing an array through its attributes allowsyou to get and sometimes set intrinsic properties of the array withoutcreating a new array. The exposed attributes are the core parts of anarray and only some of them can be reset meaningfully without creatinga new array. Information on each attribute is given below.

Array methods¶

Anndarray object has many methods which operate on or withthe array in some fashion, typically returning an array result. Thesemethods are briefly explained below. (Each method’s docstring has amore complete description.)

For the following methods there are also corresponding functions innumpy: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.

>>>xarray([[[ 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]]))

Arithmetic, matrix multiplication, and comparison operations¶

Arithmetic and comparison operations onndarraysare defined as element-wise operations, and generally yieldndarray objects as results.

Each of the arithmetic operations (+,-,*,/,//,%,divmod(),** orpow(),<<,>>,&,^,|,~) and the comparisons (==,<,>,<=,>=,!=) is equivalent to the correspondinguniversal function (orufunc for short) in NumPy. Formore information, see the section onUniversal Functions.

Comparison operators:

Truth value of an array (bool):

Unary operations:

Arithmetic:

Arithmetic, in-place:

Matrix Multiplication:

Special methods¶

For standard library functions:

Basic customization:

Container customization: (seeIndexing)

Conversion; the operationscomplex,int,long,float,oct, andhex. They work only on arrays that have one element in themand return the appropriate scalar.

String representations: