View source for The N-dimensional array (ndarray)


== The goal ==
Class has a very important job as a core container type in Python. It is really hard to find a good overview how to use them in a good practice manner.

Questions to [mailto:davrot@uni-bremen.de David Rotermund]

== Chaining of (ndarray) methods ==
<syntaxhighlight lang="python">import numpy as np
a = np.ones((3, 3))
b = a.mean(axis=1).max()
print(b) # -> 1.0</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.fill.html numpy.ndarray.fill] ==
<syntaxhighlight lang="python">ndarray.fill(value)</syntaxhighlight><blockquote>Fill the array with a scalar value.</blockquote><syntaxhighlight lang="python">import numpy as np
A = np.ones((3, 3))
A.fill(7)
print(A)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[7. 7. 7.]
 [7. 7. 7.]
 [7. 7. 7.]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.ndim.html numpy.ndarray.ndim] ==
<syntaxhighlight lang="python">ndarray.ndim</syntaxhighlight><blockquote>Number of array dimensions.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.ones((3, 3))
print(A.ndim)  # -> 2</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html numpy.ndarray.shape] ==
<syntaxhighlight lang="python">ndarray.shape</syntaxhighlight><blockquote>Tuple of array dimensions.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.ones((3, 3))
print(A.shape)  # -> (3, 3)</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.size.html numpy.ndarray.size] ==
<syntaxhighlight lang="python">ndarray.size</syntaxhighlight><blockquote>Number of elements in the array.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.ones((3, 3))
print(A.size) # -> 9</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.nbytes.html numpy.ndarray.nbytes] ==
{: .topic-optional} This is an optional topic!<syntaxhighlight lang="python">ndarray.nbytes</syntaxhighlight><blockquote>Total bytes consumed by the elements of the array.</blockquote>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemsize.html numpy.ndarray.itemsize] ==
{: .topic-optional} This is an optional topic!<syntaxhighlight lang="python">ndarray.itemsize</syntaxhighlight><blockquote>Length of one array element in bytes.</blockquote>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.copy.html numpy.ndarray.copy] ==
<syntaxhighlight lang="python">ndarray.copy(order='C')</syntaxhighlight><blockquote>Return a copy of the array.</blockquote>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.view.html numpy.ndarray.view] ==
<syntaxhighlight lang="python">ndarray.view([dtype][, type])</syntaxhighlight><blockquote>New view of array with the same data.</blockquote>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.reshape.html numpy.ndarray.reshape] ==
<syntaxhighlight lang="python">ndarray.reshape(shape, order='C')</syntaxhighlight><blockquote>Returns an array containing the same data with a new shape.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6)
print(A.reshape((2, 3)))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]</syntaxhighlight>'''WARNING!!! Don’t confuse reshape with resize!'''

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.squeeze.html numpy.ndarray.squeeze] ==
<syntaxhighlight lang="python">ndarray.squeeze(axis=None)</syntaxhighlight><blockquote>Remove axes of length one from a.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((4, 1, 1)) 
print(A.shape) # -> (4, 1, 1)
A = A.squeeze()
print(A.shape) # -> (4,)

A = np.zeros((4, 1, 9, 1)) # -> (4, 1, 9, 1)
print(A.shape)
B = A.squeeze(axis=1) # -> (4, 9, 1)
print(B.shape)
print(np.may_share_memory(A, B)) # -> True</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.moveaxis.html numpy.moveaxis] ==
<syntaxhighlight lang="python">numpy.moveaxis(a, source, destination)</syntaxhighlight><blockquote>Move axes of an array to new positions.

Other axes remain in their original order.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((4, 1, 9, 1)) 
print(A.shape) # -> (4, 1, 9, 1)
B = np.moveaxis(A, 0, 1)
print(B.shape) # -> (1, 4, 9, 1)
print(np.may_share_memory(A, B)) # -> True</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.swapaxes.html numpy.ndarray.swapaxes] ==
<syntaxhighlight lang="python">ndarray.swapaxes(axis1, axis2)</syntaxhighlight><blockquote>Return a '''view''' of the array with axis1 and axis2 interchanged.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((4, 1, 9, 1))
print(A.shape) # -> (4, 1, 9, 1)
B = A.swapaxes(0, 1)
print(B.shape) # -> (1, 4, 9, 1)
print(np.may_share_memory(A, B)) # -> True</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.T.html numpy.ndarray.T] (Transposing a 2d matrix) ==
<syntaxhighlight lang="python">ndarray.T</syntaxhighlight><blockquote>View of the transposed array.

Same as self.transpose().</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((4, 9))
B = A.T
print(A.shape)  # -> (4, 9)
print(B.shape)  # -> (9, 4)
print(np.may_share_memory(A, B)) # -> True</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.transpose.html numpy.ndarray.transpose] ==
{: .topic-optional} This is an optional topic!<syntaxhighlight lang="python">ndarray.transpose(*axes)</syntaxhighlight><blockquote>Returns a view of the array with axes transposed.</blockquote>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html numpy.ndarray.flatten] ==
<syntaxhighlight lang="python">ndarray.flatten(order='C')</syntaxhighlight><blockquote>Return a '''copy''' of the array collapsed into one dimension.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6)
A = A.reshape((2, 3))
print(A)
print()
B = A.flatten()
print(B)
print(np.may_share_memory(A, B))  # -> False</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[0 1 2 3 4 5]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flat.html numpy.ndarray.flat] ==
<syntaxhighlight lang="python">ndarray.flat</syntaxhighlight><blockquote>A 1-D iterator over the array.

This is a numpy.flatiter instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6)
A = A.reshape((2, 3))

print(A.flat[0]) # -> 0
print(A.flat[1]) # -> 1
print(A.flat[2]) # -> 2
print(A.flat[3]) # -> 3
print(A.flat[4]) # -> 4
print(A.flat[5]) # -> 5

for i in A:
    print(i)

print("----")

for i in A.flat:
    print(i)</syntaxhighlight>Output:<syntaxhighlight lang="python">[0 1 2]
[3 4 5]
----
0
1
2
3
4
5</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.dtype.html numpy.ndarray.dtype] ==
<syntaxhighlight lang="python">ndarray.dtype</syntaxhighlight><blockquote>Data-type of the array’s elements.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((0, 6), dtype=np.float32)
print(A.dtype) # -> float32
B = A.astype(dtype=np.int64)
print(B.dtype) # -> int64
print(np.may_share_memory(A, B)) # -> False</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.astype.html numpy.ndarray.astype] ==
<syntaxhighlight lang="python">ndarray.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)</syntaxhighlight><blockquote>Copy of the array, cast to a specified type.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.zeros((0, 6), dtype=np.float32)
print(A.dtype) # -> float32
B = A.astype(dtype=np.int64)
print(B.dtype) # -> int64
print(np.may_share_memory(A, B)) # -> False</syntaxhighlight>

== Complex numbers ==

=== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.real.html numpy.ndarray.real] ===
<syntaxhighlight lang="python">ndarray.real</syntaxhighlight><blockquote>The real part of the array.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.array(1 + 0.5j)
print(A.real) # -> 1.0</syntaxhighlight>

=== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.imag.html numpy.ndarray.imag] ===
<syntaxhighlight lang="python">ndarray.imag</syntaxhighlight><blockquote>The imaginary part of the array.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.array(1 + 0.5j)
print(A.imag) # -> 0.5</syntaxhighlight>

=== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.conj.html numpy.ndarray.conj] ===
<syntaxhighlight lang="python">ndarray.conj()</syntaxhighlight><blockquote>Complex-conjugate all elements.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.array(1 + 0.5j)
print(A.conj()) # -> (1-0.5j)</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.sort.html numpy.ndarray.sort] ==
<syntaxhighlight lang="python">ndarray.sort(axis=-1, kind=None, order=None)</syntaxhighlight><blockquote>Sort an array '''in-place'''. Refer to numpy.sort for full documentation.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6)
A = np.concatenate((A, A))

print(A) # -> [0 1 2 3 4 5 0 1 2 3 4 5]
print()
A.sort()
print(A) # -> [0 0 1 1 2 2 3 3 4 4 5 5]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argsort.html numpy.ndarray.argsort] ==
<syntaxhighlight lang="python">ndarray.argsort(axis=-1, kind=None, order=None)</syntaxhighlight><blockquote>Returns the indices that would sort this array.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6)
A = np.concatenate((A, A))

print(A)  # -> [0 1 2 3 4 5 0 1 2 3 4 5]
print()
idx = A.argsort()
print(idx)  # -> [ 0  6  1  7  2  8  3  9  4 10  5 11]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.sum.html numpy.ndarray.sum] and [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.mean.html#numpy.ndarray.mean numpy.ndarray.mean] ==
<syntaxhighlight lang="python">ndarray.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)</syntaxhighlight><blockquote>Return the sum of the array elements over the given axis.</blockquote><syntaxhighlight lang="python">ndarray.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)</syntaxhighlight><blockquote>Returns the average of the array elements along given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6).reshape((2, 3))

print(A.sum())  # -> 15
print(A.sum(axis=0))  # -> [3 5 7]
print(A.sum(axis=0).shape)  # -> (3,)
print(A.sum(axis=1))  # -> [ 3 12]
print(A.sum(axis=1).shape)  # -> (2,)

print(A.sum(axis=0, keepdims=True))
print(A.sum(axis=0, keepdims=True).shape) # -> (1, 3)
print()
print(A.sum(axis=1, keepdims=True))
print(A.sum(axis=0, keepdims=True).shape) # -> (1, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[3 5 7]]

[[ 3]
 [12]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.cumsum.html numpy.ndarray.cumsum] ==
<syntaxhighlight lang="python">ndarray.cumsum(axis=None, dtype=None, out=None)</syntaxhighlight><blockquote>Return the cumulative sum of the elements along the given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6).reshape((2, 3))

print(A)
print()
print(A.cumsum())  # -> [ 0  1  3  6 10 15]
print(A.cumsum().shape)  # -> (6,)
print(A.cumsum(axis=0))
print()
print(A.cumsum(axis=0).shape)  # -> (2, 3)
print(A.cumsum(axis=1))  
print(A.cumsum(axis=1).shape)  # -> (2, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[0 1 2]
 [3 5 7]]

[[ 0  1  3]
 [ 3  7 12]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.prod.html numpy.ndarray.prod] ==
<syntaxhighlight lang="python">ndarray.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)</syntaxhighlight><blockquote>Return the product of the array elements over the given axis</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(1, 7).reshape((2, 3))

print(A)
print(A.prod())  # -> 720
print(A.prod().shape)  # -> ()
print(A.prod(axis=0)) # -> [ 4 10 18]
print(A.prod(axis=0).shape) # -> (3,)
print(A.prod(axis=1))  # -> [  6 120]
print(A.prod(axis=1).shape)  # -> (2,)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[1 2 3]
 [4 5 6]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.cumprod.html numpy.ndarray.cumprod] ==
<syntaxhighlight lang="python">ndarray.cumprod(axis=None, dtype=None, out=None)</syntaxhighlight><blockquote>Return the cumulative product of the elements along the given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(1, 7).reshape((2, 3))

print(A)
print()
print(A.cumprod())  # -> [  1   2   6  24 120 720]
print(A.cumprod().shape)  # -> (6,)
print(A.cumprod(axis=0)) 
print()
print(A.cumprod(axis=0).shape) # -> (2, 3)
print(A.cumprod(axis=1))  
print(A.cumprod(axis=1).shape)  # -> (2, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[1 2 3]
 [4 5 6]]

[[ 1  2  3]
 [ 4 10 18]]

 [[  1   2   6]
 [  4  20 120]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.clip.html numpy.ndarray.clip] ==
<syntaxhighlight lang="python">ndarray.clip(min=None, max=None, out=None, **kwargs)</syntaxhighlight><blockquote>Return an array whose values are limited to [min, max]. One of max or min must be given.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 8).reshape((2, 4))
print(A)
print()
print(A.clip(min=1, max=6))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2 3]
 [4 5 6 7]]

[[1 1 2 3]
 [4 5 6 6]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.max.html#numpy.ndarray.max numpy.ndarray.max] and [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.html#numpy.ndarray.min numpy.ndarray.min] ==
<syntaxhighlight lang="python">ndarray.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)</syntaxhighlight><blockquote>Return the maximum along a given axis.</blockquote><syntaxhighlight lang="python">ndarray.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)</syntaxhighlight><blockquote>Return the minimum along a given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6).reshape((2, 3))

print(A)
print()
print(A.max())  # -> 5
print(A.max(axis=0))  # -> [3 4 5]
print(A.max(axis=0).shape)  # -> (3,)
print(A.max(axis=1))  # -> [2 5]
print(A.max(axis=1).shape)  # -> (2,)
print(A.max(axis=0, keepdims=True)) # -> [[3 4 5]]
print(A.max(axis=0, keepdims=True).shape) # -> (1, 3)
print(A.max(axis=1, keepdims=True))
print(A.max(axis=0, keepdims=True).shape) # -> (1, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[2]
 [5]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argmax.html#numpy.ndarray.argmax numpy.ndarray.argmax] and [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argmin.html#numpy.ndarray.argmin numpy.ndarray.argmin] ==
<syntaxhighlight lang="python">ndarray.argmax(axis=None, out=None, *, keepdims=False)</syntaxhighlight><blockquote>Return indices of the maximum values along the given axis.</blockquote><syntaxhighlight lang="python">ndarray.argmin(axis=None, out=None, *, keepdims=False)</syntaxhighlight><blockquote>Return indices of the minimum values along the given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.arange(0, 6).reshape((2, 3))

print(A)
print()
print(A.argmax())  # -> 5
print(A.argmax(axis=0))  # -> [1 1 1]
print(A.argmax(axis=0).shape)  # -> (3,)
print(A.argmax(axis=1))  # -> [2 2]
print(A.argmax(axis=1).shape)  # -> (2,)
print(A.argmax(axis=0, keepdims=True))  # -> [[1 1 1]]
print(A.argmax(axis=0, keepdims=True).shape)  # -> (1, 3)
print(A.argmax(axis=1, keepdims=True))
print(A.argmax(axis=0, keepdims=True).shape)  # -> (1, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[2]
 [2]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.std.html numpy.ndarray.std] and [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.var.html numpy.ndarray.var] ==
<syntaxhighlight lang="python">ndarray.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)</syntaxhighlight><blockquote>Returns the standard deviation of the array elements along given axis.</blockquote><syntaxhighlight lang="python">ndarray.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)</syntaxhighlight><blockquote>Returns the variance of the array elements, along given axis.</blockquote><syntaxhighlight lang="python">import numpy as np

rng = np.random.default_rng()
A = rng.random((2, 3))

print(A)
print()
print(A.var())  # -> 0.15743358550255018
print(A.var(axis=0))  # -> [0.19429192 0.15604444 0.00441136]
print(A.var(axis=0).shape)  # -> (3,)
print(A.var(axis=1))  # -> [0.18135622 0.00196335]
print(A.var(axis=1).shape)  # -> (2,)
print(A.var(axis=0, keepdims=True))  # -> [[0.19429192 0.15604444 0.00441136]]
print(A.var(axis=0, keepdims=True).shape)  # -> (1, 3)
print(A.var(axis=1, keepdims=True))
print(A.var(axis=0, keepdims=True).shape)  # -> (1, 3)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0.9804056  0.82416017 0.00909   ]
 [0.09883446 0.03411095 0.1419262 ]]

[[0.18135622]
 [0.00196335]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.round.html#numpy.ndarray.round numpy.ndarray.round] ==
<syntaxhighlight lang="python">ndarray.round(decimals=0, out=None)</syntaxhighlight><blockquote>Return a with each element rounded to the given number of decimals.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.array(np.pi)
print(A)  # -> 3.141592653589793
print(A.round(decimals=0))  # -> 3.0
print(A.round(decimals=1))  # -> 3.1
print(A.round(decimals=2))  # -> 3.14
print(A.round(decimals=3))  # -> 3.142</syntaxhighlight>'''WARNING!!! This might be unexpected behavior for you:'''<syntaxhighlight lang="python">import numpy as np

print(np.round(1.5))  # -> 2.0
print(np.round(2.5))  # -> 2.0
print(np.round(2.5 + 1e-15))  # -> 3.0</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.trace.html numpy.ndarray.trace] ==
<syntaxhighlight lang="python">ndarray.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)</syntaxhighlight><blockquote>Return the sum along diagonals of the array.</blockquote><syntaxhighlight lang="python">import numpy as np

A = np.eye(3)

print(A)
print(A.trace())  # -> 3.0</syntaxhighlight><syntaxhighlight lang="python">[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.diagonal.html numpy.ndarray.diagonal] ==
<syntaxhighlight lang="python">ndarray.diagonal(offset=0, axis1=0, axis2=1)</syntaxhighlight><blockquote>Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.</blockquote><syntaxhighlight lang="python">import numpy as np

rng = np.random.default_rng()
A = rng.random((3, 3))
print(A)
print(A.diagonal())  # -> [0.7434178  0.11672896]
print(A.diagonal(offset=1))  # -> [0.7434178  0.11672896]
print(A.diagonal(offset=2))  # -> [0.84915636]
print(A.diagonal(offset=-1))  # -> [0.10826248 0.50223328]
print(A.diagonal(offset=-2))  # -> [0.43068892]</syntaxhighlight>Output<syntaxhighlight lang="python">[[0.82574583 0.7434178  0.84915636]
 [0.10826248 0.39898052 0.11672896]
 [0.43068892 0.50223328 0.63444263]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#array-methods Array methods] ==

=== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#array-conversion Array conversion] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.item.html#numpy.ndarray.item ndarray.item(*args)]
|Copy an element of an array to a standard Python scalar and return it.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tolist.html#numpy.ndarray.tolist ndarray.tolist()]
|Return the array as an a.ndim-levels deep nested list of Python scalars.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemset.html#numpy.ndarray.itemset ndarray.itemset(*args)]
|Insert scalar into an array (scalar is cast to array’s dtype, if possible)
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tostring.html#numpy.ndarray.tostring ndarray.tostring([order])]
|A compatibility alias for tobytes, with exactly the same behavior.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tobytes.html#numpy.ndarray.tobytes ndarray.tobytes([order])]
|Construct Python bytes containing the raw data bytes in the array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tofile.html#numpy.ndarray.tofile ndarray.tofile(fid[, sep, format])]
|Write array to a file as text or binary (default).
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.dump.html#numpy.ndarray.dump ndarray.dump(file)]
|Dump a pickle of the array to the specified file.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.dumps.html#numpy.ndarray.dumps ndarray.dumps()]
|Returns the pickle of the array as a string.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.astype.html#numpy.ndarray.astype ndarray.astype(dtype[, order, casting, …])]
|Copy of the array, cast to a specified type.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.byteswap.html#numpy.ndarray.byteswap ndarray.byteswap([inplace])]
|Swap the bytes of the array elements
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.copy.html#numpy.ndarray.copy ndarray.copy([order])]
|Return a copy of the array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.view.html#numpy.ndarray.view ndarray.view([dtype][, type])]
|New view of array with the same data.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.getfield.html#numpy.ndarray.getfield ndarray.getfield(dtype[, offset])]
|Returns a field of the given array as a certain type.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.setflags.html#numpy.ndarray.setflags ndarray.setflags([write, align, uic])]
|Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.fill.html#numpy.ndarray.fill ndarray.fill(value)]
|Fill the array with a scalar value.
|}

=== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#shape-manipulation Shape manipulation] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.reshape.html#numpy.ndarray.reshape ndarray.reshape(shape[, order])]
|Returns an array containing the same data with a new shape.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.resize.html#numpy.ndarray.resize ndarray.resize(new_shape[, refcheck])]
|Change shape and size of array in-place.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.transpose.html#numpy.ndarray.transpose ndarray.transpose(*axes)]
|Returns a view of the array with axes transposed.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.swapaxes.html#numpy.ndarray.swapaxes ndarray.swapaxes(axis1, axis2)]
|Return a view of the array with axis1 and axis2 interchanged.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html#numpy.ndarray.flatten ndarray.flatten([order])]
|Return a copy of the array collapsed into one dimension.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.ravel.html#numpy.ndarray.ravel ndarray.ravel([order])]
|Return a flattened array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.squeeze.html#numpy.ndarray.squeeze ndarray.squeeze([axis])]
|Remove axes of length one from a.
|}

=== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#item-selection-and-manipulation Item selection and manipulation] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.take.html#numpy.ndarray.take ndarray.take(indices[, axis, out, mode])]
|Return an array formed from the elements of a at the given
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.put.html#numpy.ndarray.put ndarray.put(indices, values[, mode])]
|Set a.flat[n] = values[n] for all n in indices.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.repeat.html#numpy.ndarray.repeat ndarray.repeat(repeats[, axis])]
|Repeat elements of an array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.choose.html#numpy.ndarray.choose ndarray.choose(choices[, out, mode])]
|Use an index array to construct a new array from a set of choices.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.sort.html#numpy.ndarray.sort ndarray.sort([axis, kind, order])]
|Sort an array in-place.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argsort.html#numpy.ndarray.argsort ndarray.argsort([axis, kind, order])]
|Returns the indices that would sort this array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.partition.html#numpy.ndarray.partition ndarray.partition(kth[, axis, kind, order])]
|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.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argpartition.html#numpy.ndarray.argpartition ndarray.argpartition(kth[, axis, kind, order])]
|Returns the indices that would partition
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.searchsorted.html#numpy.ndarray.searchsorted ndarray.searchsorted(v[, side, sorter])]
|Find indices where elements of v should be inserted in a to maintain order.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.nonzero.html#numpy.ndarray.nonzero ndarray.nonzero()]
|Return the indices of the elements that are non-zero.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.compress.html#numpy.ndarray.compress ndarray.compress(condition[, axis, out])]
|Return selected slices of this array along given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.diagonal.html#numpy.ndarray.diagonal ndarray.diagonal([offset, axis1, axis2])]
|Return specified diagonals.
|}

=== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#calculation Calculation] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.max.html#numpy.ndarray.max ndarray.max([axis, out, keepdims, initial, …])]
|Return the maximum along a given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argmax.html#numpy.ndarray.argmax ndarray.argmax([axis, out, keepdims])]
|Return indices of the maximum values along the given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.html#numpy.ndarray.min ndarray.min([axis, out, keepdims, initial, …])]
|Return the minimum along a given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.argmin.html#numpy.ndarray.argmin ndarray.argmin([axis, out, keepdims])]
|Return indices of the minimum values along the given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.ptp.html#numpy.ndarray.ptp ndarray.ptp([axis, out, keepdims])]
|Peak to peak (maximum - minimum) value along a given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.clip.html#numpy.ndarray.clip ndarray.clip([min, max, out])]
|Return an array whose values are limited to [min, max].
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.conj.html#numpy.ndarray.conj ndarray.conj()]
|Complex-conjugate all elements.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.round.html#numpy.ndarray.round ndarray.round([decimals, out])]
|Return a with each element rounded to the given number of decimals.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.trace.html#numpy.ndarray.trace ndarray.trace([offset, axis1, axis2, dtype, out])]
|Return the sum along diagonals of the array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.sum.html#numpy.ndarray.sum ndarray.sum([axis, dtype, out, keepdims, …])]
|Return the sum of the array elements over the given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.cumsum.html#numpy.ndarray.cumsum ndarray.cumsum([axis, dtype, out])]
|Return the cumulative sum of the elements along the given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.mean.html#numpy.ndarray.mean ndarray.mean([axis, dtype, out, keepdims, where])]
|Returns the average of the array elements along given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.var.html#numpy.ndarray.var ndarray.var([axis, dtype, out, ddof, …])]
|Returns the variance of the array elements, along given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.std.html#numpy.ndarray.std ndarray.std([axis, dtype, out, ddof, …])]
|Returns the standard deviation of the array elements along given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.prod.html#numpy.ndarray.prod ndarray.prod([axis, dtype, out, keepdims, …])]
|Return the product of the array elements over the given axis
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.cumprod.html#numpy.ndarray.cumprod ndarray.cumprod([axis, dtype, out])]
|Return the cumulative product of the elements along the given axis.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.all.html#numpy.ndarray.all ndarray.all([axis, out, keepdims, where])]
|Returns True if all elements evaluate to True.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.any.html#numpy.ndarray.any ndarray.any([axis, out, keepdims, where])]
|Returns True if any of the elements of a evaluate to True.
|}

== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#arithmetic-matrix-multiplication-and-comparison-operations Arithmetic, matrix multiplication, and comparison operations] ==
<blockquote>Each of the arithmetic operations (+, -, *, /, //, %, divmod(), ** or pow(), &#x3C;&#x3C;, &#x3E;&#x3E;, &#x26;, ^, |, ~) and the comparisons (==, &#x3C;, &#x3E;, &#x3C;=, &#x3E;=, !=) is equivalent to the corresponding universal function in NumPy.</blockquote>for in-place operations see [https://numpy.org/doc/stable/reference/arrays.ndarray.html#arithmetic-matrix-multiplication-and-comparison-operations here]
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__lt__.html#numpy.ndarray.__lt__ ndarray.__lt__(value, /)]
|Return self&#x3C;value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__le__.html#numpy.ndarray.__le__ ndarray.__le__(value, /)]
|Return self&#x3C;=value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__gt__.html#numpy.ndarray.__gt__ ndarray.__gt__(value, /)]
|Return self&#x3E;value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__ge__.html#numpy.ndarray.__ge__ ndarray.__ge__(value, /)]
|Return self&#x3E;=value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__eq__.html#numpy.ndarray.__eq__ ndarray.__eq__(value, /)]
|Return self==value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__ne__.html#numpy.ndarray.__ne__ ndarray.__ne__(value, /)]
|Return self!=value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__bool__.html#numpy.ndarray.__bool__ ndarray.__bool__(/)]
|True if self else False
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__neg__.html#numpy.ndarray.__neg__ ndarray.__neg__(/)]
| -self
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__pos__.html#numpy.ndarray.__pos__ ndarray.__pos__(/)]
| +self
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__abs__.html#numpy.ndarray.__abs__ ndarray.__abs__(self)]
|
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__invert__.html#numpy.ndarray.__invert__ ndarray.__invert__(/)]
|~self
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__add__.html#numpy.ndarray.__add__ ndarray.__add__(value, /)]
|Return self+value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__sub__.html#numpy.ndarray.__sub__ ndarray.__sub__(value, /)]
|Return self-value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__mul__.html#numpy.ndarray.__mul__ ndarray.__mul__(value, /)]
|Return self*value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__truediv__.html#numpy.ndarray.__truediv__ ndarray.__truediv__(value, /)]
|Return self/value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__floordiv__.html#numpy.ndarray.__floordiv__ ndarray.__floordiv__(value, /)]
|Return self//value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__mod__.html#numpy.ndarray.__mod__ ndarray.__mod__(value, /)]
|Return self%value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__divmod__.html#numpy.ndarray.__divmod__ ndarray.__divmod__(value, /)]
|Return divmod(self, value).
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__pow__.html#numpy.ndarray.__pow__ ndarray.__pow__(value[, mod])]
|Return pow(self, value, mod).
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__lshift__.html#numpy.ndarray.__lshift__ ndarray.__lshift__(value, /)]
|Return self&#x3C;&#x3C;value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__rshift__.html#numpy.ndarray.__rshift__ ndarray.__rshift__(value, /)]
|Return self&#x3E;&#x3E;value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__and__.html#numpy.ndarray.__and__ ndarray.__and__(value, /)]
|Return self&#x26;value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__or__.html#numpy.ndarray.__or__ ndarray.__or__(value, /)]
|Return self
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__xor__.html#numpy.ndarray.__xor__ ndarray.__xor__(value, /)]
|Return self^value.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.ndarray.__matmul__.html#numpy.ndarray.__matmul__ ndarray.__matmul__(value, /)]
|Return self@value.
|}

=== [https://numpy.org/doc/stable/reference/arrays.ndarray.html#special-methods Special methods] ===
[https://numpy.org/doc/stable/reference/arrays.ndarray.html#special-methods special methods]