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# How to index `ndarrays`

See also

Indexing on ndarrays

This page tackles common examples. For an in-depth look into indexing, refer to Indexing on ndarrays.

## Access specific/arbitrary rows and columns

Use Basic indexing features like Slicing and striding, and 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]],

            [[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 `newaxis`. To use other such tools, refer to 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 Dealing with variable numbers of indices within programs to see how to use slice and `Ellipsis` in your index variables.

### Index columns

To index columns, you have to index the last axis. Use 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]],

           [[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 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 `take`. See also `take_along_axis` and `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]],

            [[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]],

            [[17, 18],
            [22, 23],
            [27, 28]]])
    >>> np.take(a, [2], axis=1)
    array([[[10, 11, 12, 13, 14]],

            [[25, 26, 27, 28, 29]]])

## Create subsets of larger matrices

Use 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 advanced indexing creates a copy:

    >>> 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 `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 `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 `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 `where` to generate indices based on conditions and then use 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 Boolean array indexing:

    >>> a > 14
    array([[[False, False, False, False, False],
            [False, False, False, False, False],
            [False, False, False, False, False]],

           [[ 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]],

           [[  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]],

           [[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]],

           [[0, 1, 2, 3, 4],
            [5, 6, 7, 8, 9]]])

## Fetch indices of max/min values

Use `argmax` and `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]])

    >>> 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]],

           [[0],
            [0],
            [0]]])
    >>> np.argmax(a, axis=1, keepdims=True)
    array([[[2, 2, 2, 2, 2]],

           [[2, 2, 2, 2, 2]]])

To get the indices of each maximum or minimum value for each (N-1)-dimensional array in an N-dimensional array, use `reshape` to reshape the array to a 2D array, apply `argmax` or `argmin` along `axis=1` and use `unravel_index` to recover the index of the values per slice:

    >>> x = np.arange(2*2*3).reshape(2, 2, 3) % 7  # 3D example array
    >>> x
    array([[[0, 1, 2],
            [3, 4, 5]],

           [[6, 0, 1],
            [2, 3, 4]]])
    >>> x_2d = np.reshape(x, (x.shape[0], -1))
    >>> indices_2d = np.argmax(x_2d, axis=1)
    >>> indices_2d
    array([5, 0])
    >>> np.unravel_index(indices_2d, x.shape[1:])
    (array([1, 0]), array([2, 0]))

The first array returned contains the indices along axis 1 in the original array, the second array contains the indices along axis 2. The highest value in `x[0]` is therefore `x[0, 1, 2]`.

## Index the same ndarray multiple times efficiently

It must be kept in mind that basic indexing produces views and advanced indexing produces copies, 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 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.