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.. currentmodule:: numpy
.. _how-to-index:
*****************************************
How to index :class:`ndarrays <.ndarray>`
*****************************************
.. seealso:: :ref:`basics.indexing`
This page tackles common examples. For an in-depth look into indexing, refer
to :ref:`basics.indexing`.
Access specific/arbitrary rows and columns
==========================================
Use :ref:`basic-indexing` features like :ref:`slicing-and-striding`, and
:ref:`dimensional-indexing-tools`.
>>> a = np.arange(30).reshape(2, 3, 5)
>>> a
array([[[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]],
<BLANKLINE>
[[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]]])
>>> a[0, 2, :]
array([10, 11, 12, 13, 14])
>>> a[0, :, 3]
array([ 3, 8, 13])
Note that the output from indexing operations can have different shape from the
original object. To preserve the original dimensions after indexing, you can
use :func:`newaxis`. To use other such tools, refer to
:ref:`dimensional-indexing-tools`.
>>> a[0, :, 3].shape
(3,)
>>> a[0, :, 3, np.newaxis].shape
(3, 1)
>>> a[0, :, 3, np.newaxis, np.newaxis].shape
(3, 1, 1)
Variables can also be used to index::
>>> y = 0
>>> a[y, :, y+3]
array([ 3, 8, 13])
Refer to :ref:`dealing-with-variable-indices` to see how to use
:term:`python:slice` and :py:data:`Ellipsis` in your index variables.
Index columns
-------------
To index columns, you have to index the last axis. Use
:ref:`dimensional-indexing-tools` to get the desired number of dimensions::
>>> a = np.arange(24).reshape(2, 3, 4)
>>> a
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
<BLANKLINE>
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> a[..., 3]
array([[ 3, 7, 11],
[15, 19, 23]])
To index specific elements in each column, make use of :ref:`advanced-indexing`
as below::
>>> arr = np.arange(3*4).reshape(3, 4)
>>> arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> column_indices = [[1, 3], [0, 2], [2, 2]]
>>> np.arange(arr.shape[0])
array([0, 1, 2])
>>> row_indices = np.arange(arr.shape[0])[:, np.newaxis]
>>> row_indices
array([[0],
[1],
[2]])
Use the ``row_indices`` and ``column_indices`` for advanced
indexing::
>>> arr[row_indices, column_indices]
array([[ 1, 3],
[ 4, 6],
[10, 10]])
Index along a specific axis
---------------------------
Use :meth:`take`. See also :meth:`take_along_axis` and
:meth:`put_along_axis`.
>>> a = np.arange(30).reshape(2, 3, 5)
>>> a
array([[[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]],
<BLANKLINE>
[[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]]])
>>> np.take(a, [2, 3], axis=2)
array([[[ 2, 3],
[ 7, 8],
[12, 13]],
<BLANKLINE>
[[17, 18],
[22, 23],
[27, 28]]])
>>> np.take(a, [2], axis=1)
array([[[10, 11, 12, 13, 14]],
<BLANKLINE>
[[25, 26, 27, 28, 29]]])
Create subsets of larger matrices
=================================
Use :ref:`slicing-and-striding` to access chunks of a large array::
>>> a = np.arange(100).reshape(10, 10)
>>> a
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],
[30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
[40, 41, 42, 43, 44, 45, 46, 47, 48, 49],
[50, 51, 52, 53, 54, 55, 56, 57, 58, 59],
[60, 61, 62, 63, 64, 65, 66, 67, 68, 69],
[70, 71, 72, 73, 74, 75, 76, 77, 78, 79],
[80, 81, 82, 83, 84, 85, 86, 87, 88, 89],
[90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])
>>> a[2:5, 2:5]
array([[22, 23, 24],
[32, 33, 34],
[42, 43, 44]])
>>> a[2:5, 1:3]
array([[21, 22],
[31, 32],
[41, 42]])
>>> a[:5, :5]
array([[ 0, 1, 2, 3, 4],
[10, 11, 12, 13, 14],
[20, 21, 22, 23, 24],
[30, 31, 32, 33, 34],
[40, 41, 42, 43, 44]])
The same thing can be done with advanced indexing in a slightly more complex
way. Remember that
:ref:`advanced indexing creates a copy <indexing-operations>`::
>>> a[np.arange(5)[:, None], np.arange(5)[None, :]]
array([[ 0, 1, 2, 3, 4],
[10, 11, 12, 13, 14],
[20, 21, 22, 23, 24],
[30, 31, 32, 33, 34],
[40, 41, 42, 43, 44]])
You can also use :meth:`mgrid` to generate indices::
>>> indices = np.mgrid[0:6:2]
>>> indices
array([0, 2, 4])
>>> a[:, indices]
array([[ 0, 2, 4],
[10, 12, 14],
[20, 22, 24],
[30, 32, 34],
[40, 42, 44],
[50, 52, 54],
[60, 62, 64],
[70, 72, 74],
[80, 82, 84],
[90, 92, 94]])
Filter values
=============
Non-zero elements
-----------------
Use :meth:`nonzero` to get a tuple of array indices of non-zero elements
corresponding to every dimension::
>>> z = np.array([[1, 2, 3, 0], [0, 0, 5, 3], [4, 6, 0, 0]])
>>> z
array([[1, 2, 3, 0],
[0, 0, 5, 3],
[4, 6, 0, 0]])
>>> np.nonzero(z)
(array([0, 0, 0, 1, 1, 2, 2]), array([0, 1, 2, 2, 3, 0, 1]))
Use :meth:`flatnonzero` to fetch indices of elements that are non-zero in
the flattened version of the ndarray::
>>> np.flatnonzero(z)
array([0, 1, 2, 6, 7, 8, 9])
Arbitrary conditions
--------------------
Use :meth:`where` to generate indices based on conditions and then
use :ref:`advanced-indexing`.
>>> a = np.arange(30).reshape(2, 3, 5)
>>> indices = np.where(a % 2 == 0)
>>> indices
(array([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]),
array([0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 1, 1, 1, 2, 2]),
array([0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3]))
>>> a[indices]
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28])
Or, use :ref:`boolean-indexing`::
>>> a > 14
array([[[False, False, False, False, False],
[False, False, False, False, False],
[False, False, False, False, False]],
<BLANKLINE>
[[ True, True, True, True, True],
[ True, True, True, True, True],
[ True, True, True, True, True]]])
>>> a[a > 14]
array([15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29])
Replace values after filtering
------------------------------
Use assignment with filtering to replace desired values::
>>> p = np.arange(-10, 10).reshape(2, 2, 5)
>>> p
array([[[-10, -9, -8, -7, -6],
[ -5, -4, -3, -2, -1]],
<BLANKLINE>
[[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9]]])
>>> q = p < 0
>>> q
array([[[ True, True, True, True, True],
[ True, True, True, True, True]],
<BLANKLINE>
[[False, False, False, False, False],
[False, False, False, False, False]]])
>>> p[q] = 0
>>> p
array([[[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]],
<BLANKLINE>
[[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]]])
Fetch indices of max/min values
===============================
Use :meth:`argmax` and :meth:`argmin`::
>>> a = np.arange(30).reshape(2, 3, 5)
>>> np.argmax(a)
29
>>> np.argmin(a)
0
Use the ``axis`` keyword to get the indices of maximum and minimum
values along a specific axis::
>>> np.argmax(a, axis=0)
array([[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1]])
>>> np.argmax(a, axis=1)
array([[2, 2, 2, 2, 2],
[2, 2, 2, 2, 2]])
>>> np.argmax(a, axis=2)
array([[4, 4, 4],
[4, 4, 4]])
<BLANKLINE>
>>> np.argmin(a, axis=1)
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])
>>> np.argmin(a, axis=2)
array([[0, 0, 0],
[0, 0, 0]])
Set ``keepdims`` to ``True`` to keep the axes which are reduced in the
result as dimensions with size one::
>>> np.argmin(a, axis=2, keepdims=True)
array([[[0],
[0],
[0]],
<BLANKLINE>
[[0],
[0],
[0]]])
>>> np.argmax(a, axis=1, keepdims=True)
array([[[2, 2, 2, 2, 2]],
<BLANKLINE>
[[2, 2, 2, 2, 2]]])
Index the same ndarray multiple times efficiently
=================================================
It must be kept in mind that basic indexing produces :term:`views <view>`
and advanced indexing produces :term:`copies <copy>`, which are
computationally less efficient. Hence, you should take care to use basic
indexing wherever possible instead of advanced indexing.
Further reading
===============
Nicolas Rougier's `100 NumPy exercises <https://github.com/rougier/numpy-100>`_
provide a good insight into how indexing is combined with other operations.
Exercises `6`_, `8`_, `10`_, `15`_, `16`_, `19`_, `20`_, `45`_, `59`_,
`64`_, `65`_, `70`_, `71`_, `72`_, `76`_, `80`_, `81`_, `84`_, `87`_, `90`_,
`93`_, `94`_ are specially focused on indexing.
.. _6: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#6-create-a-null-vector-of-size-10-but-the-fifth-value-which-is-1-
.. _8: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#8-reverse-a-vector-first-element-becomes-last-
.. _10: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#10-find-indices-of-non-zero-elements-from-120040-
.. _15: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#15-create-a-2d-array-with-1-on-the-border-and-0-inside-
.. _16: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#16-how-to-add-a-border-filled-with-0s-around-an-existing-array-
.. _19: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#19-create-a-8x8-matrix-and-fill-it-with-a-checkerboard-pattern-
.. _20: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#20-consider-a-678-shape-array-what-is-the-index-xyz-of-the-100th-element-
.. _45: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#45-create-random-vector-of-size-10-and-replace-the-maximum-value-by-0-
.. _59: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#59-how-to-sort-an-array-by-the-nth-column-
.. _64: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#64-consider-a-given-vector-how-to-add-1-to-each-element-indexed-by-a-second-vector-be-careful-with-repeated-indices-
.. _65: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#65-how-to-accumulate-elements-of-a-vector-x-to-an-array-f-based-on-an-index-list-i-
.. _70: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#70-consider-the-vector-1-2-3-4-5-how-to-build-a-new-vector-with-3-consecutive-zeros-interleaved-between-each-value-
.. _71: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#71-consider-an-array-of-dimension-553-how-to-mulitply-it-by-an-array-with-dimensions-55-
.. _72: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#72-how-to-swap-two-rows-of-an-array-
.. _76: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#76-consider-a-one-dimensional-array-z-build-a-two-dimensional-array-whose-first-row-is-z0z1z2-and-each-subsequent-row-is--shifted-by-1-last-row-should-be-z-3z-2z-1-
.. _80: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#80-consider-an-arbitrary-array-write-a-function-that-extract-a-subpart-with-a-fixed-shape-and-centered-on-a-given-element-pad-with-a-fill-value-when-necessary-
.. _81: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#81-consider-an-array-z--1234567891011121314-how-to-generate-an-array-r--1234-2345-3456--11121314-
.. _84: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#84-extract-all-the-contiguous-3x3-blocks-from-a-random-10x10-matrix-
.. _87: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#87-consider-a-16x16-array-how-to-get-the-block-sum-block-size-is-4x4-
.. _90: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#90-given-an-arbitrary-number-of-vectors-build-the-cartesian-product-every-combinations-of-every-item-
.. _93: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#93-consider-two-arrays-a-and-b-of-shape-83-and-22-how-to-find-rows-of-a-that-contain-elements-of-each-row-of-b-regardless-of-the-order-of-the-elements-in-b-
.. _94: https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises_with_solutions.md#94-considering-a-10x3-matrix-extract-rows-with-unequal-values-eg-223-
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