Indexing NumPy Arrays

Index an ndarray with standard Python x[obj] syntax, where x is the array and obj selects part of it.

Like lists and tuples, arrays use zero-based indices. Multidimensional arrays extend the same idea across multiple axes.

NumPy supports basic indexing, advanced indexing, and field access for structured arrays.

Basic and single element indexing

Single-element indexing is zero-based and accepts negative indices from the end of an axis.

Reshape a one-dimensional array by assigning a compatible tuple to shape.

x = n.arange(10)
# array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
x.shape = (2, 5)
# array([[0, 1, 2, 3, 4],
       [5, 6, 7, 8, 9]])
x[1, 3]
# 8

Indexing a multidimensional array with fewer indices than dimensions returns a lower-dimensional subarray.

x
# array([[0, 1, 2, 3, 4],
       [5, 6, 7, 8, 9]])
       
x[0]
# array([0, 1, 2, 3, 4])

x
# array([[0, 1, 2, 3, 4],
       [5, 6, 7, 8, 9]])

Basic indexing returns a view that shares memory with the original array; changes through the view can change the source.

x[0, 2] and x[0][2] select the same element, but the second form creates an intermediate view before the final lookup.

Slicing

Basic slicing extends Python's slice syntax across any number of dimensions.

Each axis accepts start:stop:step notation.

Indices can also include integers, Ellipsis, and newaxis.

Python's sequence-slicing rules apply independently to each dimension.

In i:j:k, i is the start, j is the exclusive stop, and nonzero k is the step.

Striding

Credit: Kathryn

A sliding window reads a fixed-width region at each position; its stride controls how far that position advances between reads.

Ellipses

An ellipsis (... or Ellipsis) inserts as many full slices (:) as needed to cover unspecified dimensions.

A slice expression can contain only one ellipsis.

Create a four-dimensional 2 × 2 × 2 × 2 array:

from numpy import arange
a = arange(16).
# result array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])
a.reshape(2,2,2,2)
# result array([[[[ 0,  1],
         [ 2,  3]],
        [[ 4,  5],
         [ 6,  7]]],
       [[[ 8,  9],
         [10, 11]],
        [[12, 13],
         [14, 15]]]])

Select index 0 from the fourth dimension with an ellipsis:

a[..., 0].flatten()
# result array([0, 2, 4, 6, 8, 10, 12, 14])

This explicit slice is equivalent:

a[:,:,:,0].flatten()
# result array([0, 2, 4, 6, 8, 10, 12, 14])

Number of Dimensions

The numpy.ndarray.ndim attribute reports an array's number of dimensions.

a = np.array([1, 2, 3, 4])
arr.ndim
# result 1