numpy.lexsort#
- numpy.lexsort(keys, axis=-1)#
Perform an indirect stable sort using a sequence of keys.
Given multiple sorting keys, lexsort returns an array of integer indices that describes the sort order by multiple keys. The last key in the sequence is used for the primary sort order, ties are broken by the second-to-last key, and so on.
- Parameters:
- keys(k, m, n, …) array-like
The k keys to be sorted. The last key (e.g, the last row if keys is a 2D array) is the primary sort key. Each element of keys along the zeroth axis must be an array-like object of the same shape.
- axisint, optional
Axis to be indirectly sorted. By default, sort over the last axis of each sequence. Separate slices along axis sorted over independently; see last example.
- Returns:
- indices(m, n, …) ndarray of ints
Array of indices that sort the keys along the specified axis.
See also
argsort
Indirect sort.
ndarray.sort
In-place sort.
sort
Return a sorted copy of an array.
Examples
Sort names: first by surname, then by name.
>>> import numpy as np >>> surnames = ('Hertz', 'Galilei', 'Hertz') >>> first_names = ('Heinrich', 'Galileo', 'Gustav') >>> ind = np.lexsort((first_names, surnames)) >>> ind array([1, 2, 0])
>>> [surnames[i] + ", " + first_names[i] for i in ind] ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']
Sort according to two numerical keys, first by elements of
a
, then breaking ties according to elements ofb
:>>> a = [1, 5, 1, 4, 3, 4, 4] # First sequence >>> b = [9, 4, 0, 4, 0, 2, 1] # Second sequence >>> ind = np.lexsort((b, a)) # Sort by `a`, then by `b` >>> ind array([2, 0, 4, 6, 5, 3, 1]) >>> [(a[i], b[i]) for i in ind] [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]
Compare against
argsort
, which would sort each key independently.>>> np.argsort((b, a), kind='stable') array([[2, 4, 6, 5, 1, 3, 0], [0, 2, 4, 3, 5, 6, 1]])
To sort lexicographically with
argsort
, we would need to provide a structured array.>>> x = np.array([(ai, bi) for ai, bi in zip(a, b)], ... dtype = np.dtype([('x', int), ('y', int)])) >>> np.argsort(x) # or np.argsort(x, order=('x', 'y')) array([2, 0, 4, 6, 5, 3, 1])
The zeroth axis of keys always corresponds with the sequence of keys, so 2D arrays are treated just like other sequences of keys.
>>> arr = np.asarray([b, a]) >>> ind2 = np.lexsort(arr) >>> np.testing.assert_equal(ind2, ind)
Accordingly, the axis parameter refers to an axis of each key, not of the keys argument itself. For instance, the array
arr
is treated as a sequence of two 1-D keys, so specifyingaxis=0
is equivalent to using the default axis,axis=-1
.>>> np.testing.assert_equal(np.lexsort(arr, axis=0), ... np.lexsort(arr, axis=-1))
For higher-dimensional arrays, the axis parameter begins to matter. The resulting array has the same shape as each key, and the values are what we would expect if
lexsort
were performed on corresponding slices of the keys independently. For instance,>>> x = [[1, 2, 3, 4], ... [4, 3, 2, 1], ... [2, 1, 4, 3]] >>> y = [[2, 2, 1, 1], ... [1, 2, 1, 2], ... [1, 1, 2, 1]] >>> np.lexsort((x, y), axis=1) array([[2, 3, 0, 1], [2, 0, 3, 1], [1, 0, 3, 2]])
Each row of the result is what we would expect if we were to perform
lexsort
on the corresponding row of the keys:>>> for i in range(3): ... print(np.lexsort((x[i], y[i]))) [2 3 0 1] [2 0 3 1] [1 0 3 2]