NumPy quickstart  Prerequisites You’ll need to know a bit of Python. For a refresher, see the Python tutorial. To work the examples, you’ll need matplotlib installed in addition to NumPy. Learner profile This is a quick overview of arrays in NumPy. It demonstrates how n-dimensional (\(n>=2\)) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this article might be of help. Learning Objectives After reading, you should be able to:  Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays.    The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, the array for the coordinates of a point in 3D space, [1, 2, 1], has one axis. That axis has 3 elements in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[1., 0., 0.],
 [0., 1., 2.]]
 NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are:  ndarray.ndim

the number of axes (dimensions) of the array.  ndarray.shape

the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim.  ndarray.size

the total number of elements of the array. This is equal to the product of the elements of shape.  ndarray.dtype

an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples.  ndarray.itemsize

the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize.  ndarray.data

the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities.    An example >>> import numpy as np
>>> a = np.arange(15).reshape(3, 5)
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])
>>> a.shape
(3, 5)
>>> a.ndim
2
>>> a.dtype.name
'int64'
>>> a.itemsize
8
>>> a.size
15
>>> type(a)
<class 'numpy.ndarray'>
>>> b = np.array([6, 7, 8])
>>> b
array([6, 7, 8])
>>> type(b)
<class 'numpy.ndarray'>
   Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> import numpy as np
>>> a = np.array([2, 3, 4])
>>> a
array([2, 3, 4])
>>> a.dtype
dtype('int64')
>>> b = np.array([1.2, 3.5, 5.1])
>>> b.dtype
dtype('float64')
 A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> a = np.array(1, 2, 3, 4)    # WRONG
Traceback (most recent call last):
  ...
TypeError: array() takes from 1 to 2 positional arguments but 4 were given
>>> a = np.array([1, 2, 3, 4])  # RIGHT
 array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> b = np.array([(1.5, 2, 3), (4, 5, 6)])
>>> b
array([[1.5, 2. , 3. ],
       [4. , 5. , 6. ]])
 The type of the array can also be explicitly specified at creation time: >>> c = np.array([[1, 2], [3, 4]], dtype=complex)
>>> c
array([[1.+0.j, 2.+0.j],
       [3.+0.j, 4.+0.j]])
 Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64, but it can be specified via the key word argument dtype. >>> np.zeros((3, 4))
array([[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]])
>>> np.ones((2, 3, 4), dtype=np.int16)
array([[[1, 1, 1, 1],
        [1, 1, 1, 1],
        [1, 1, 1, 1]],

       [[1, 1, 1, 1],
        [1, 1, 1, 1],
        [1, 1, 1, 1]]], dtype=int16)
>>> np.empty((2, 3))
array([[3.73603959e-262, 6.02658058e-154, 6.55490914e-260],  # may vary
       [5.30498948e-313, 3.14673309e-307, 1.00000000e+000]])
 To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> np.arange(10, 30, 5)
array([10, 15, 20, 25])
>>> np.arange(0, 2, 0.3)  # it accepts float arguments
array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8])
 When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> from numpy import pi
>>> np.linspace(0, 2, 9)                   # 9 numbers from 0 to 2
array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.25, 1.5 , 1.75, 2.  ])
>>> x = np.linspace(0, 2 * pi, 100)        # useful to evaluate function at lots of points
>>> f = np.sin(x)
  See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile    Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout:  the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line.  One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> a = np.arange(6)                    # 1d array
>>> print(a)
[0 1 2 3 4 5]
>>>
>>> b = np.arange(12).reshape(4, 3)     # 2d array
>>> print(b)
[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
>>>
>>> c = np.arange(24).reshape(2, 3, 4)  # 3d array
>>> print(c)
[[[ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]]

 [[12 13 14 15]
  [16 17 18 19]
  [20 21 22 23]]]
 See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> print(np.arange(10000))
[   0    1    2 ... 9997 9998 9999]
>>>
>>> print(np.arange(10000).reshape(100, 100))
[[   0    1    2 ...   97   98   99]
 [ 100  101  102 ...  197  198  199]
 [ 200  201  202 ...  297  298  299]
 ...
 [9700 9701 9702 ... 9797 9798 9799]
 [9800 9801 9802 ... 9897 9898 9899]
 [9900 9901 9902 ... 9997 9998 9999]]
 To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> np.set_printoptions(threshold=sys.maxsize)  # sys module should be imported
   Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> a = np.array([20, 30, 40, 50])
>>> b = np.arange(4)
>>> b
array([0, 1, 2, 3])
>>> c = a - b
>>> c
array([20, 29, 38, 47])
>>> b**2
array([0, 1, 4, 9])
>>> 10 * np.sin(a)
array([ 9.12945251, -9.88031624,  7.4511316 , -2.62374854])
>>> a < 35
array([ True,  True, False, False])
 Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> A = np.array([[1, 1],
...               [0, 1]])
>>> B = np.array([[2, 0],
...               [3, 4]])
>>> A * B     # elementwise product
array([[2, 0],
       [0, 4]])
>>> A @ B     # matrix product
array([[5, 4],
       [3, 4]])
>>> A.dot(B)  # another matrix product
array([[5, 4],
       [3, 4]])
 Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> rg = np.random.default_rng(1)  # create instance of default random number generator
>>> a = np.ones((2, 3), dtype=int)
>>> b = rg.random((2, 3))
>>> a *= 3
>>> a
array([[3, 3, 3],
       [3, 3, 3]])
>>> b += a
>>> b
array([[3.51182162, 3.9504637 , 3.14415961],
       [3.94864945, 3.31183145, 3.42332645]])
>>> a += b  # b is not automatically converted to integer type
Traceback (most recent call last):
    ...
numpy.core._exceptions._UFuncOutputCastingError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind'
 When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> a = np.ones(3, dtype=np.int32)
>>> b = np.linspace(0, pi, 3)
>>> b.dtype.name
'float64'
>>> c = a + b
>>> c
array([1.        , 2.57079633, 4.14159265])
>>> c.dtype.name
'float64'
>>> d = np.exp(c * 1j)
>>> d
array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j,
       -0.54030231-0.84147098j])
>>> d.dtype.name
'complex128'
 Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> a = rg.random((2, 3))
>>> a
array([[0.82770259, 0.40919914, 0.54959369],
       [0.02755911, 0.75351311, 0.53814331]])
>>> a.sum()
3.1057109529998157
>>> a.min()
0.027559113243068367
>>> a.max()
0.8277025938204418
 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> b = np.arange(12).reshape(3, 4)
>>> b
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>>
>>> b.sum(axis=0)     # sum of each column
array([12, 15, 18, 21])
>>>
>>> b.min(axis=1)     # min of each row
array([0, 4, 8])
>>>
>>> b.cumsum(axis=1)  # cumulative sum along each row
array([[ 0,  1,  3,  6],
       [ 4,  9, 15, 22],
       [ 8, 17, 27, 38]])
   Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions” (ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> np.exp(B)
array([1.        , 2.71828183, 7.3890561 ])
>>> np.sqrt(B)
array([0.        , 1.        , 1.41421356])
>>> C = np.array([2., -1., 4.])
>>> np.add(B, C)
array([2., 0., 6.])
  See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where    Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> a = np.arange(10)**3
>>> a
array([  0,   1,   8,  27,  64, 125, 216, 343, 512, 729])
>>> a[2]
8
>>> a[2:5]
array([ 8, 27, 64])
>>> # equivalent to a[0:6:2] = 1000;
>>> # from start to position 6, exclusive, set every 2nd element to 1000
>>> a[:6:2] = 1000
>>> a
array([1000,    1, 1000,   27, 1000,  125,  216,  343,  512,  729])
>>> a[::-1]  # reversed a
array([ 729,  512,  343,  216,  125, 1000,   27, 1000,    1, 1000])
>>> for i in a:
...     print(i**(1 / 3.))
...
9.999999999999998
1.0
9.999999999999998
3.0
9.999999999999998
4.999999999999999
5.999999999999999
6.999999999999999
7.999999999999999
8.999999999999998
 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> def f(x, y):
...     return 10 * x + y
...
>>> b = np.fromfunction(f, (5, 4), dtype=int)
>>> b
array([[ 0,  1,  2,  3],
       [10, 11, 12, 13],
       [20, 21, 22, 23],
       [30, 31, 32, 33],
       [40, 41, 42, 43]])
>>> b[2, 3]
23
>>> b[0:5, 1]  # each row in the second column of b
array([ 1, 11, 21, 31, 41])
>>> b[:, 1]    # equivalent to the previous example
array([ 1, 11, 21, 31, 41])
>>> b[1:3, :]  # each column in the second and third row of b
array([[10, 11, 12, 13],
       [20, 21, 22, 23]])
 When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> b[-1]   # the last row. Equivalent to b[-1, :]
array([40, 41, 42, 43])
 The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i, ...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then
x[1, 2, ...] is equivalent to x[1, 2, :, :, :],
x[..., 3] to x[:, :, :, :, 3] and
x[4, ..., 5, :] to x[4, :, :, 5, :].  >>> c = np.array([[[  0,  1,  2],  # a 3D array (two stacked 2D arrays)
...                [ 10, 12, 13]],
...               [[100, 101, 102],
...                [110, 112, 113]]])
>>> c.shape
(2, 2, 3)
>>> c[1, ...]  # same as c[1, :, :] or c[1]
array([[100, 101, 102],
       [110, 112, 113]])
>>> c[..., 2]  # same as c[:, :, 2]
array([[  2,  13],
       [102, 113]])
 Iterating over multidimensional arrays is done with respect to the first axis: >>> for row in b:
...     print(row)
...
[0 1 2 3]
[10 11 12 13]
[20 21 22 23]
[30 31 32 33]
[40 41 42 43]
 However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> for element in b.flat:
...     print(element)
...
0
1
2
3
10
11
12
13
20
21
22
23
30
31
32
33
40
41
42
43
  See also Indexing on ndarrays, Indexing routines (reference), newaxis, ndenumerate, indices     Shape Manipulation  Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> a = np.floor(10 * rg.random((3, 4)))
>>> a
array([[3., 7., 3., 4.],
       [1., 4., 2., 2.],
       [7., 2., 4., 9.]])
>>> a.shape
(3, 4)
 The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> a.ravel()  # returns the array, flattened
array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.])
>>> a.reshape(6, 2)  # returns the array with a modified shape
array([[3., 7.],
       [3., 4.],
       [1., 4.],
       [2., 2.],
       [7., 2.],
       [4., 9.]])
>>> a.T  # returns the array, transposed
array([[3., 1., 7.],
       [7., 4., 2.],
       [3., 2., 4.],
       [4., 2., 9.]])
>>> a.T.shape
(4, 3)
>>> a.shape
(3, 4)
 The order of the elements in the array resulting from ravel is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0, 0] is a[0, 1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel and reshape can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> a
array([[3., 7., 3., 4.],
       [1., 4., 2., 2.],
       [7., 2., 4., 9.]])
>>> a.resize((2, 6))
>>> a
array([[3., 7., 3., 4., 1., 4.],
       [2., 2., 7., 2., 4., 9.]])
 If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> a.reshape(3, -1)
array([[3., 7., 3., 4.],
       [1., 4., 2., 2.],
       [7., 2., 4., 9.]])
  See also ndarray.shape, reshape, resize, ravel    Stacking together different arrays Several arrays can be stacked together along different axes: >>> a = np.floor(10 * rg.random((2, 2)))
>>> a
array([[9., 7.],
       [5., 2.]])
>>> b = np.floor(10 * rg.random((2, 2)))
>>> b
array([[1., 9.],
       [5., 1.]])
>>> np.vstack((a, b))
array([[9., 7.],
       [5., 2.],
       [1., 9.],
       [5., 1.]])
>>> np.hstack((a, b))
array([[9., 7., 1., 9.],
       [5., 2., 5., 1.]])
 The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> from numpy import newaxis
>>> np.column_stack((a, b))  # with 2D arrays
array([[9., 7., 1., 9.],
       [5., 2., 5., 1.]])
>>> a = np.array([4., 2.])
>>> b = np.array([3., 8.])
>>> np.column_stack((a, b))  # returns a 2D array
array([[4., 3.],
       [2., 8.]])
>>> np.hstack((a, b))        # the result is different
array([4., 2., 3., 8.])
>>> a[:, newaxis]  # view `a` as a 2D column vector
array([[4.],
       [2.]])
>>> np.column_stack((a[:, newaxis], b[:, newaxis]))
array([[4., 3.],
       [2., 8.]])
>>> np.hstack((a[:, newaxis], b[:, newaxis]))  # the result is the same
array([[4., 3.],
       [2., 8.]])
 On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> np.column_stack is np.hstack
False
>>> np.row_stack is np.vstack
True
 In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals :. >>> np.r_[1:4, 0, 4]
array([1, 2, 3, 0, 4])
 When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate.  See also hstack, vstack, column_stack, concatenate, c_, r_    Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> a = np.floor(10 * rg.random((2, 12)))
>>> a
array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.],
       [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]])
>>> # Split `a` into 3
>>> np.hsplit(a, 3)
[array([[6., 7., 6., 9.],
       [8., 5., 5., 7.]]), array([[0., 5., 4., 0.],
       [1., 8., 6., 7.]]), array([[6., 8., 5., 2.],
       [1., 8., 1., 0.]])]
>>> # Split `a` after the third and the fourth column
>>> np.hsplit(a, (3, 4))
[array([[6., 7., 6.],
       [8., 5., 5.]]), array([[9.],
       [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.],
       [1., 8., 6., 7., 1., 8., 1., 0.]])]
 vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split.    Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases:  No Copy at All Simple assignments make no copy of objects or their data. >>> a = np.array([[ 0,  1,  2,  3],
...               [ 4,  5,  6,  7],
...               [ 8,  9, 10, 11]])
>>> b = a            # no new object is created
>>> b is a           # a and b are two names for the same ndarray object
True
 Python passes mutable objects as references, so function calls make no copy. >>> def f(x):
...     print(id(x))
...
>>> id(a)  # id is a unique identifier of an object
148293216  # may vary
>>> f(a)
148293216  # may vary
   View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> c = a.view()
>>> c is a
False
>>> c.base is a            # c is a view of the data owned by a
True
>>> c.flags.owndata
False
>>>
>>> c = c.reshape((2, 6))  # a's shape doesn't change
>>> a.shape
(3, 4)
>>> c[0, 4] = 1234         # a's data changes
>>> a
array([[   0,    1,    2,    3],
       [1234,    5,    6,    7],
       [   8,    9,   10,   11]])
 Slicing an array returns a view of it: >>> s = a[:, 1:3]
>>> s[:] = 10  # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10
>>> a
array([[   0,   10,   10,    3],
       [1234,   10,   10,    7],
       [   8,   10,   10,   11]])
   Deep Copy The copy method makes a complete copy of the array and its data. >>> d = a.copy()  # a new array object with new data is created
>>> d is a
False
>>> d.base is a  # d doesn't share anything with a
False
>>> d[0, 0] = 9999
>>> a
array([[   0,   10,   10,    3],
       [1234,   10,   10,    7],
       [   8,   10,   10,   11]])
 Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> a = np.arange(int(1e8))
>>> b = a[:100].copy()
>>> del a  # the memory of ``a`` can be released.
 If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed.   Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list.  Array Creation

arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like  Conversions

ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat  Manipulations

array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack  Questions

all, any, nonzero, where  Ordering

argmax, argmin, argsort, max, min, ptp, searchsorted, sort  Operations

choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum  Basic Statistics

cov, mean, std, var  Basic Linear Algebra

cross, dot, outer, linalg.svd, vdot      Less Basic  Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting.    Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans.  Indexing with Arrays of Indices >>> a = np.arange(12)**2  # the first 12 square numbers
>>> i = np.array([1, 1, 3, 8, 5])  # an array of indices
>>> a[i]  # the elements of `a` at the positions `i`
array([ 1,  1,  9, 64, 25])
>>>
>>> j = np.array([[3, 4], [9, 7]])  # a bidimensional array of indices
>>> a[j]  # the same shape as `j`
array([[ 9, 16],
       [81, 49]])
 When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> palette = np.array([[0, 0, 0],         # black
...                     [255, 0, 0],       # red
...                     [0, 255, 0],       # green
...                     [0, 0, 255],       # blue
...                     [255, 255, 255]])  # white
>>> image = np.array([[0, 1, 2, 0],  # each value corresponds to a color in the palette
...                   [0, 3, 4, 0]])
>>> palette[image]  # the (2, 4, 3) color image
array([[[  0,   0,   0],
        [255,   0,   0],
        [  0, 255,   0],
        [  0,   0,   0]],

       [[  0,   0,   0],
        [  0,   0, 255],
        [255, 255, 255],
        [  0,   0,   0]]])
 We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> a = np.arange(12).reshape(3, 4)
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>> i = np.array([[0, 1],  # indices for the first dim of `a`
...               [1, 2]])
>>> j = np.array([[2, 1],  # indices for the second dim
...               [3, 3]])
>>>
>>> a[i, j]  # i and j must have equal shape
array([[ 2,  5],
       [ 7, 11]])
>>>
>>> a[i, 2]
array([[ 2,  6],
       [ 6, 10]])
>>>
>>> a[:, j]
array([[[ 2,  1],
        [ 3,  3]],

       [[ 6,  5],
        [ 7,  7]],

       [[10,  9],
        [11, 11]]])
 In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> l = (i, j)
>>> # equivalent to a[i, j]
>>> a[l]
array([[ 2,  5],
       [ 7, 11]])
 However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> s = np.array([i, j])
>>> # not what we want
>>> a[s]
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
IndexError: index 3 is out of bounds for axis 0 with size 3
>>> # same as `a[i, j]`
>>> a[tuple(s)]
array([[ 2,  5],
       [ 7, 11]])
 Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> time = np.linspace(20, 145, 5)  # time scale
>>> data = np.sin(np.arange(20)).reshape(5, 4)  # 4 time-dependent series
>>> time
array([ 20.  ,  51.25,  82.5 , 113.75, 145.  ])
>>> data
array([[ 0.        ,  0.84147098,  0.90929743,  0.14112001],
       [-0.7568025 , -0.95892427, -0.2794155 ,  0.6569866 ],
       [ 0.98935825,  0.41211849, -0.54402111, -0.99999021],
       [-0.53657292,  0.42016704,  0.99060736,  0.65028784],
       [-0.28790332, -0.96139749, -0.75098725,  0.14987721]])
>>> # index of the maxima for each series
>>> ind = data.argmax(axis=0)
>>> ind
array([2, 0, 3, 1])
>>> # times corresponding to the maxima
>>> time_max = time[ind]
>>>
>>> data_max = data[ind, range(data.shape[1])]  # => data[ind[0], 0], data[ind[1], 1]...
>>> time_max
array([ 82.5 ,  20.  , 113.75,  51.25])
>>> data_max
array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ])
>>> np.all(data_max == data.max(axis=0))
True
 You can also use indexing with arrays as a target to assign to: >>> a = np.arange(5)
>>> a
array([0, 1, 2, 3, 4])
>>> a[[1, 3, 4]] = 0
>>> a
array([0, 0, 2, 0, 0])
 However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> a = np.arange(5)
>>> a[[0, 0, 2]] = [1, 2, 3]
>>> a
array([2, 1, 3, 3, 4])
 This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> a = np.arange(5)
>>> a[[0, 0, 2]] += 1
>>> a
array([1, 1, 3, 3, 4])
 Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires a += 1 to be equivalent to a = a + 1.   Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> a = np.arange(12).reshape(3, 4)
>>> b = a > 4
>>> b  # `b` is a boolean with `a`'s shape
array([[False, False, False, False],
       [False,  True,  True,  True],
       [ True,  True,  True,  True]])
>>> a[b]  # 1d array with the selected elements
array([ 5,  6,  7,  8,  9, 10, 11])
 This property can be very useful in assignments: >>> a[b] = 0  # All elements of `a` higher than 4 become 0
>>> a
array([[0, 1, 2, 3],
       [4, 0, 0, 0],
       [0, 0, 0, 0]])
 You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> def mandelbrot(h, w, maxit=20, r=2):
...     """Returns an image of the Mandelbrot fractal of size (h,w)."""
...     x = np.linspace(-2.5, 1.5, 4*h+1)
...     y = np.linspace(-1.5, 1.5, 3*w+1)
...     A, B = np.meshgrid(x, y)
...     C = A + B*1j
...     z = np.zeros_like(C)
...     divtime = maxit + np.zeros(z.shape, dtype=int)
...
...     for i in range(maxit):
...         z = z**2 + C
...         diverge = abs(z) > r                    # who is diverging
...         div_now = diverge & (divtime == maxit)  # who is diverging now
...         divtime[div_now] = i                    # note when
...         z[diverge] = r                          # avoid diverging too much
...
...     return divtime
>>> plt.imshow(mandelbrot(400, 400))
    The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> a = np.arange(12).reshape(3, 4)
>>> b1 = np.array([False, True, True])         # first dim selection
>>> b2 = np.array([True, False, True, False])  # second dim selection
>>>
>>> a[b1, :]                                   # selecting rows
array([[ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>>
>>> a[b1]                                      # same thing
array([[ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>>
>>> a[:, b2]                                   # selecting columns
array([[ 0,  2],
       [ 4,  6],
       [ 8, 10]])
>>>
>>> a[b1, b2]                                  # a weird thing to do
array([ 4, 10])
 Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a.   The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> a = np.array([2, 3, 4, 5])
>>> b = np.array([8, 5, 4])
>>> c = np.array([5, 4, 6, 8, 3])
>>> ax, bx, cx = np.ix_(a, b, c)
>>> ax
array([[[2]],

       [[3]],

       [[4]],

       [[5]]])
>>> bx
array([[[8],
        [5],
        [4]]])
>>> cx
array([[[5, 4, 6, 8, 3]]])
>>> ax.shape, bx.shape, cx.shape
((4, 1, 1), (1, 3, 1), (1, 1, 5))
>>> result = ax + bx * cx
>>> result
array([[[42, 34, 50, 66, 26],
        [27, 22, 32, 42, 17],
        [22, 18, 26, 34, 14]],

       [[43, 35, 51, 67, 27],
        [28, 23, 33, 43, 18],
        [23, 19, 27, 35, 15]],

       [[44, 36, 52, 68, 28],
        [29, 24, 34, 44, 19],
        [24, 20, 28, 36, 16]],

       [[45, 37, 53, 69, 29],
        [30, 25, 35, 45, 20],
        [25, 21, 29, 37, 17]]])
>>> result[3, 2, 4]
17
>>> a[3] + b[2] * c[4]
17
 You could also implement the reduce as follows: >>> def ufunc_reduce(ufct, *vectors):
...    vs = np.ix_(*vectors)
...    r = ufct.identity
...    for v in vs:
...        r = ufct(r, v)
...    return r
 and then use it as: >>> ufunc_reduce(np.add, a, b, c)
array([[[15, 14, 16, 18, 13],
        [12, 11, 13, 15, 10],
        [11, 10, 12, 14,  9]],

       [[16, 15, 17, 19, 14],
        [13, 12, 14, 16, 11],
        [12, 11, 13, 15, 10]],

       [[17, 16, 18, 20, 15],
        [14, 13, 15, 17, 12],
        [13, 12, 14, 16, 11]],

       [[18, 17, 19, 21, 16],
        [15, 14, 16, 18, 13],
        [14, 13, 15, 17, 12]]])
 The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the broadcasting rules in order to avoid creating an argument array the size of the output times the number of vectors.   Indexing with strings See Structured arrays.    Tricks and Tips Here we give a list of short and useful tips.  “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> a = np.arange(30)
>>> b = a.reshape((2, -1, 3))  # -1 means "whatever is needed"
>>> b.shape
(2, 5, 3)
>>> b
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],
        [27, 28, 29]]])
   Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> x = np.arange(0, 10, 2)
>>> y = np.arange(5)
>>> m = np.vstack([x, y])
>>> m
array([[0, 2, 4, 6, 8],
       [0, 1, 2, 3, 4]])
>>> xy = np.hstack([x, y])
>>> xy
array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4])
 The logic behind those functions in more than two dimensions can be strange.  See also NumPy for MATLAB users    Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np
>>> rg = np.random.default_rng(1)
>>> import matplotlib.pyplot as plt
>>> # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2
>>> mu, sigma = 2, 0.5
>>> v = rg.normal(mu, sigma, 10000)
>>> # Plot a normalized histogram with 50 bins
>>> plt.hist(v, bins=50, density=True)       # matplotlib version (plot)
>>> # Compute the histogram with numpy and then plot it
>>> (n, bins) = np.histogram(v, bins=50, density=True)  # NumPy version (no plot)
>>> plt.plot(.5 * (bins[1:] + bins[:-1]), n)
    With Matplotlib >=3.4 you can also use plt.stairs(n, bins).    Further reading  The Python tutorial
 Command Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary
 tutorial-svd


numpy.ndarray.newbyteorder method   ndarray.newbyteorder(new_order='S', /)

Return the array with the same data viewed with a different byte order. Equivalent to: arr.view(arr.dtype.newbytorder(new_order))
 Changes are also made in all fields and sub-arrays of the array data type.  Parameters

new_orderstring, optional

Byte order to force; a value from the byte order specifications below. new_order codes can be any of:  ‘S’ - swap dtype from current to opposite endian {‘<’, ‘little’} - little endian {‘>’, ‘big’} - big endian {‘=’, ‘native’} - native order, equivalent to sys.byteorder
 {‘|’, ‘I’} - ignore (no change to byte order)  The default value (‘S’) results in swapping the current byte order.    Returns

new_arrarray

New array object with the dtype reflecting given change to the byte order.


numpy.ndarray.nonzero method   ndarray.nonzero()

Return the indices of the elements that are non-zero. Refer to numpy.nonzero for full documentation.  See also  numpy.nonzero

equivalent function


numpy.ndarray.partition method   ndarray.partition(kth, axis=- 1, kind='introselect', order=None)

Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.  New in version 1.8.0.   Parameters

kthint or sequence of ints

Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.  Deprecated since version 1.22.0: Passing booleans as index is deprecated.
axisint, optional

Axis along which to sort. Default is -1, which means sort along the last axis.
kind{‘introselect’}, optional

Selection algorithm. Default is ‘introselect’.
orderstr or list of str, optional

When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.      See also  numpy.partition

Return a parititioned copy of an array.  argpartition

Indirect partition.  sort

Full sort.    Notes See np.partition for notes on the different algorithms. Examples >>> a = np.array([3, 4, 2, 1])
>>> a.partition(3)
>>> a
array([2, 1, 3, 4])
 >>> a.partition((1, 3))
>>> a
array([1, 2, 3, 4])


numpy.ndarray.prod method   ndarray.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)

Return the product of the array elements over the given axis Refer to numpy.prod for full documentation.  See also  numpy.prod

equivalent function


numpy.ndarray.ptp method   ndarray.ptp(axis=None, out=None, keepdims=False)

Peak to peak (maximum - minimum) value along a given axis. Refer to numpy.ptp for full documentation.  See also  numpy.ptp

equivalent function


numpy.ndarray.put method   ndarray.put(indices, values, mode='raise')

Set a.flat[n] = values[n] for all n in indices. Refer to numpy.put for full documentation.  See also  numpy.put

equivalent function


numpy.ndarray.ravel method   ndarray.ravel([order])

Return a flattened array. Refer to numpy.ravel for full documentation.  See also  numpy.ravel

equivalent function  ndarray.flat

a flat iterator on the array.


numpy.ndarray.real attribute   ndarray.real

The real part of the array.  See also  numpy.real

equivalent function    Examples >>> x = np.sqrt([1+0j, 0+1j])
>>> x.real
array([ 1.        ,  0.70710678])
>>> x.real.dtype
dtype('float64')


numpy.ndarray.repeat method   ndarray.repeat(repeats, axis=None)

Repeat elements of an array. Refer to numpy.repeat for full documentation.  See also  numpy.repeat

equivalent function


numpy.ndarray.reshape method   ndarray.reshape(shape, order='C')

Returns an array containing the same data with a new shape. Refer to numpy.reshape for full documentation.  See also  numpy.reshape

equivalent function    Notes Unlike the free function numpy.reshape, this method on ndarray allows the elements of the shape parameter to be passed in as separate arguments. For example, a.reshape(10, 11) is equivalent to a.reshape((10, 11)).


numpy.ndarray.resize method   ndarray.resize(new_shape, refcheck=True)

Change shape and size of array in-place.  Parameters

new_shapetuple of ints, or n ints

Shape of resized array.
refcheckbool, optional

If False, reference count will not be checked. Default is True.    Returns
 None
  Raises
 ValueError

If a does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.  SystemError

If the order keyword argument is specified. This behaviour is a bug in NumPy.      See also  resize

Return a new array with the specified shape.    Notes This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set refcheck to False. Examples Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C')
>>> a.resize((2, 1))
>>> a
array([[0],
       [1]])
 >>> a = np.array([[0, 1], [2, 3]], order='F')
>>> a.resize((2, 1))
>>> a
array([[0],
       [2]])
 Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]])
>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
>>> b
array([[0, 1, 2],
       [3, 0, 0]])
 Referencing an array prevents resizing… >>> c = a
>>> a.resize((1, 1))
Traceback (most recent call last):
...
ValueError: cannot resize an array that references or is referenced ...
 Unless refcheck is False: >>> a.resize((1, 1), refcheck=False)
>>> a
array([[0]])
>>> c
array([[0]])


numpy.ndarray.round method   ndarray.round(decimals=0, out=None)

Return a with each element rounded to the given number of decimals. Refer to numpy.around for full documentation.  See also  numpy.around

equivalent function


numpy.ndarray.searchsorted method   ndarray.searchsorted(v, side='left', sorter=None)

Find indices where elements of v should be inserted in a to maintain order. For full documentation, see numpy.searchsorted  See also  numpy.searchsorted

equivalent function


numpy.ndarray.setfield method   ndarray.setfield(val, dtype, offset=0)

Put a value into a specified place in a field defined by a data-type. Place val into a’s field defined by dtype and beginning offset bytes into the field.  Parameters

valobject

Value to be placed in field.
dtypedtype object

Data-type of the field in which to place val.
offsetint, optional

The number of bytes into the field at which to place val.    Returns
 None
    See also  getfield
  Examples >>> x = np.eye(3)
>>> x.getfield(np.float64)
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])
>>> x.setfield(3, np.int32)
>>> x.getfield(np.int32)
array([[3, 3, 3],
       [3, 3, 3],
       [3, 3, 3]], dtype=int32)
>>> x
array([[1.0e+000, 1.5e-323, 1.5e-323],
       [1.5e-323, 1.0e+000, 1.5e-323],
       [1.5e-323, 1.5e-323, 1.0e+000]])
>>> x.setfield(np.eye(3), np.int32)
>>> x
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])


numpy.ndarray.setflags method   ndarray.setflags(write=None, align=None, uic=None)

Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), respectively. These Boolean-valued flags affect how numpy interprets the memory area used by a (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)  Parameters

writebool, optional

Describes whether or not a can be written to.
alignbool, optional

Describes whether or not a is aligned properly for its type.
uicbool, optional

Describes whether or not a is a copy of another “base” array.     Notes Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array. All flags can be accessed using the single (upper case) letter as well as the full name. Examples >>> y = np.array([[3, 1, 7],
...               [2, 0, 0],
...               [8, 5, 9]])
>>> y
array([[3, 1, 7],
       [2, 0, 0],
       [8, 5, 9]])
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False
>>> y.setflags(write=0, align=0)
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : False
  ALIGNED : False
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False
>>> y.setflags(uic=1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: cannot set WRITEBACKIFCOPY flag to True


numpy.ndarray.shape attribute   ndarray.shape

Tuple of array dimensions. The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.  See also  numpy.reshape

similar function  ndarray.reshape

similar method    Examples >>> x = np.array([1, 2, 3, 4])
>>> x.shape
(4,)
>>> y = np.zeros((2, 3, 4))
>>> y.shape
(2, 3, 4)
>>> y.shape = (3, 8)
>>> y
array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
>>> y.shape = (3, 6)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: total size of new array must be unchanged
>>> np.zeros((4,2))[::2].shape = (-1,)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: Incompatible shape for in-place modification. Use
`.reshape()` to make a copy with the desired shape.


numpy.ndarray.size attribute   ndarray.size

Number of elements in the array. Equal to np.prod(a.shape), i.e., the product of the array’s dimensions. Notes a.size returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested np.prod(a.shape), which returns an instance of np.int_), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type. Examples >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
>>> x.size
30
>>> np.prod(x.shape)
30


numpy.ndarray.sort method   ndarray.sort(axis=- 1, kind=None, order=None)

Sort an array in-place. Refer to numpy.sort for full documentation.  Parameters

axisint, optional

Axis along which to sort. Default is -1, which means sort along the last axis.
kind{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional

Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.  Changed in version 1.15.0: The ‘stable’ option was added.
orderstr or list of str, optional

When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.      See also  numpy.sort

Return a sorted copy of an array.  numpy.argsort

Indirect sort.  numpy.lexsort

Indirect stable sort on multiple keys.  numpy.searchsorted

Find elements in sorted array.  numpy.partition

Partial sort.    Notes See numpy.sort for notes on the different sorting algorithms. Examples >>> a = np.array([[1,4], [3,1]])
>>> a.sort(axis=1)
>>> a
array([[1, 4],
       [1, 3]])
>>> a.sort(axis=0)
>>> a
array([[1, 3],
       [1, 4]])
 Use the order keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
>>> a.sort(order='y')
>>> a
array([(b'c', 1), (b'a', 2)],
      dtype=[('x', 'S1'), ('y', '<i8')])


numpy.ndarray.squeeze method   ndarray.squeeze(axis=None)

Remove axes of length one from a. Refer to numpy.squeeze for full documentation.  See also  numpy.squeeze

equivalent function


numpy.ndarray.std method   ndarray.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)

Returns the standard deviation of the array elements along given axis. Refer to numpy.std for full documentation.  See also  numpy.std

equivalent function


numpy.ndarray.strides attribute   ndarray.strides

Tuple of bytes to step in each dimension when traversing an array. The byte offset of element (i[0], i[1], ..., i[n]) in an array a is: offset = sum(np.array(i) * a.strides)
 A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.  See also  numpy.lib.stride_tricks.as_strided
  Notes Imagine an array of 32-bit integers (each 4 bytes): x = np.array([[0, 1, 2, 3, 4],
              [5, 6, 7, 8, 9]], dtype=np.int32)
 This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array x will be (20, 4). Examples >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
>>> y
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]]])
>>> y.strides
(48, 16, 4)
>>> y[1,1,1]
17
>>> offset=sum(y.strides * np.array((1,1,1)))
>>> offset/y.itemsize
17
 >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
>>> x.strides
(32, 4, 224, 1344)
>>> i = np.array([3,5,2,2])
>>> offset = sum(i * x.strides)
>>> x[3,5,2,2]
813
>>> offset / x.itemsize
813


numpy.ndarray.sum method   ndarray.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)

Return the sum of the array elements over the given axis. Refer to numpy.sum for full documentation.  See also  numpy.sum

equivalent function


numpy.ndarray.swapaxes method   ndarray.swapaxes(axis1, axis2)

Return a view of the array with axis1 and axis2 interchanged. Refer to numpy.swapaxes for full documentation.  See also  numpy.swapaxes

equivalent function


numpy.ndarray.take method   ndarray.take(indices, axis=None, out=None, mode='raise')

Return an array formed from the elements of a at the given indices. Refer to numpy.take for full documentation.  See also  numpy.take

equivalent function


numpy.ndarray.tobytes method   ndarray.tobytes(order='C')

Construct Python bytes containing the raw data bytes in the array. Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the order parameter.  New in version 1.9.0.   Parameters

order{‘C’, ‘F’, ‘A’}, optional

Controls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for Any) means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.    Returns

sbytes

Python bytes exhibiting a copy of a’s raw data.     Examples >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
>>> x.tobytes()
b'\x00\x00\x01\x00\x02\x00\x03\x00'
>>> x.tobytes('C') == x.tobytes()
True
>>> x.tobytes('F')
b'\x00\x00\x02\x00\x01\x00\x03\x00'


numpy.ndarray.tofile method   ndarray.tofile(fid, sep='', format='%s')

Write array to a file as text or binary (default). Data is always written in ‘C’ order, independent of the order of a. The data produced by this method can be recovered using the function fromfile().  Parameters

fidfile or str or Path

An open file object, or a string containing a filename.  Changed in version 1.17.0: pathlib.Path objects are now accepted.
sepstr

Separator between array items for text output. If “” (empty), a binary file is written, equivalent to file.write(a.tobytes()).
formatstr

Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.     Notes This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size. When fid is a file object, array contents are directly written to the file, bypassing the file object’s write method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support fileno() (e.g., BytesIO).


numpy.ndarray.tolist method   ndarray.tolist()

Return the array as an a.ndim-levels deep nested list of Python scalars. Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the item function. If a.ndim is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.  Parameters
 none
  Returns

yobject, or list of object, or list of list of object, or …

The possibly nested list of array elements.     Notes The array may be recreated via a = np.array(a.tolist()), although this may sometimes lose precision. Examples For a 1D array, a.tolist() is almost the same as list(a), except that tolist changes numpy scalars to Python scalars: >>> a = np.uint32([1, 2])
>>> a_list = list(a)
>>> a_list
[1, 2]
>>> type(a_list[0])
<class 'numpy.uint32'>
>>> a_tolist = a.tolist()
>>> a_tolist
[1, 2]
>>> type(a_tolist[0])
<class 'int'>
 Additionally, for a 2D array, tolist applies recursively: >>> a = np.array([[1, 2], [3, 4]])
>>> list(a)
[array([1, 2]), array([3, 4])]
>>> a.tolist()
[[1, 2], [3, 4]]
 The base case for this recursion is a 0D array: >>> a = np.array(1)
>>> list(a)
Traceback (most recent call last):
  ...
TypeError: iteration over a 0-d array
>>> a.tolist()
1


numpy.ndarray.tostring method   ndarray.tostring(order='C')

A compatibility alias for tobytes, with exactly the same behavior. Despite its name, it returns bytes not strs.  Deprecated since version 1.19.0.


numpy.ndarray.trace method   ndarray.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)

Return the sum along diagonals of the array. Refer to numpy.trace for full documentation.  See also  numpy.trace

equivalent function


numpy.ndarray.transpose method   ndarray.transpose(*axes)

Returns a view of the array with axes transposed. For a 1-D array this has no effect, as a transposed vector is simply the same vector. To convert a 1-D array into a 2D column vector, an additional dimension must be added. np.atleast2d(a).T achieves this, as does a[:, np.newaxis]. For a 2-D array, this is a standard matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and a.shape = (i[0], i[1], ... i[n-2], i[n-1]), then a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0]).  Parameters

axesNone, tuple of ints, or n ints

 None or no argument: reverses the order of the axes. tuple of ints: i in the j-th place in the tuple means a’s i-th axis becomes a.transpose()’s j-th axis.
n ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)     Returns

outndarray

View of a, with axes suitably permuted.      See also  transpose

Equivalent function  ndarray.T

Array property returning the array transposed.  ndarray.reshape

Give a new shape to an array without changing its data.    Examples >>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.transpose()
array([[1, 3],
       [2, 4]])
>>> a.transpose((1, 0))
array([[1, 3],
       [2, 4]])
>>> a.transpose(1, 0)
array([[1, 3],
       [2, 4]])


numpy.ndarray.var method   ndarray.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)

Returns the variance of the array elements, along given axis. Refer to numpy.var for full documentation.  See also  numpy.var

equivalent function


numpy.ndarray.view method   ndarray.view([dtype][, type])

New view of array with the same data.  Note Passing None for dtype is different from omitting the parameter, since the former invokes dtype(None) which is an alias for dtype('float_').   Parameters

dtypedata-type or ndarray sub-class, optional

Data-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as a. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the type parameter).
typePython type, optional

Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.     Notes a.view() is used two different ways: a.view(some_dtype) or a.view(dtype=some_dtype) constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory. a.view(ndarray_subclass) or a.view(type=ndarray_subclass) just returns an instance of ndarray_subclass that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For a.view(some_dtype), if some_dtype has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of a (shown by print(a)). It also depends on exactly how a is stored in memory. Therefore if a is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
 Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix)
>>> y
matrix([[513]], dtype=int16)
>>> print(type(y))
<class 'numpy.matrix'>
 Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
>>> xv = x.view(dtype=np.int8).reshape(-1,2)
>>> xv
array([[1, 2],
       [3, 4]], dtype=int8)
>>> xv.mean(0)
array([2.,  3.])
 Making changes to the view changes the underlying array >>> xv[0,1] = 20
>>> x
array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
 Using a view to convert an array to a recarray: >>> z = x.view(np.recarray)
>>> z.a
array([1, 3], dtype=int8)
 Views share data: >>> x[0] = (9, 10)
>>> z[0]
(9, 10)
 Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16)
>>> y = x[:, 0:2]
>>> y
array([[1, 2],
       [4, 5]], dtype=int16)
>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
Traceback (most recent call last):
    ...
ValueError: To change to a dtype of a different size, the array must be C-contiguous
>>> z = y.copy()
>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
array([[(1, 2)],
       [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])


numpy.ndindex.ndincr method   ndindex.ndincr()[source]

Increment the multi-dimensional index by one. This method is for backward compatibility only: do not use.  Deprecated since version 1.20.0: This method has been advised against since numpy 1.8.0, but only started emitting DeprecationWarning as of this version.


numpy.nditer.close method   nditer.close()

Resolve all writeback semantics in writeable operands.  New in version 1.15.0.   See also  Modifying Array Values


numpy.nditer.copy method   nditer.copy()

Get a copy of the iterator in its current state. Examples >>> x = np.arange(10)
>>> y = x + 1
>>> it = np.nditer([x, y])
>>> next(it)
(array(0), array(1))
>>> it2 = it.copy()
>>> next(it2)
(array(1), array(2))


numpy.nditer.debug_print method   nditer.debug_print()

Print the current state of the nditer instance and debug info to stdout.


numpy.nditer.enable_external_loop method   nditer.enable_external_loop()

When the “external_loop” was not used during construction, but is desired, this modifies the iterator to behave as if the flag was specified.


numpy.nditer.index attribute   nditer.index


numpy.nditer.iternext method   nditer.iternext()

Check whether iterations are left, and perform a single internal iteration without returning the result. Used in the C-style pattern do-while pattern. For an example, see nditer.  Returns

iternextbool

Whether or not there are iterations left.


numpy.nditer.itersize attribute   nditer.itersize


numpy.nditer.multi_index attribute   nditer.multi_index


numpy.nditer.operands attribute   nditer.operands

operands[Slice] The array(s) to be iterated over. Valid only before the iterator is closed.


numpy.nditer.remove_axis method   nditer.remove_axis(i, /)

Removes axis i from the iterator. Requires that the flag “multi_index” be enabled.


numpy.nditer.remove_multi_index method   nditer.remove_multi_index()

When the “multi_index” flag was specified, this removes it, allowing the internal iteration structure to be optimized further.


numpy.nditer.reset method   nditer.reset()

Reset the iterator to its initial state.


numpy.nditer.value attribute   nditer.value