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numpy.lexsort

numpy.sort

numpy.sort(a, axis=-1, kind=None, order=None)[source]

Return a sorted copy of an array.

Parameters:
a : array_like

Array to be sorted.

axis : int or None, optional

Axis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis.

kind : {‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional

Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort or radix sort under the covers and, in general, the actual implementation will vary with data type. The ‘mergesort’ option is retained for backwards compatibility.

Changed in version 1.15.0.: The ‘stable’ option was added.

order : str or list of str, optional

When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.

Returns:
sorted_array : ndarray

Array of the same type and shape as a.

See also

ndarray.sort
Method to sort an array in-place.
argsort
Indirect sort.
lexsort
Indirect stable sort on multiple keys.
searchsorted
Find elements in a sorted array.
partition
Partial sort.

Notes

The various sorting algorithms are characterized by their average speed, worst case performance, work space size, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The four algorithms implemented in NumPy have the following properties:

kind speed worst case work space stable
‘quicksort’ 1 O(n^2) 0 no
‘heapsort’ 3 O(n*log(n)) 0 no
‘mergesort’ 2 O(n*log(n)) ~n/2 yes
‘timsort’ 2 O(n*log(n)) ~n/2 yes

Note

The datatype determines which of ‘mergesort’ or ‘timsort’ is actually used, even if ‘mergesort’ is specified. User selection at a finer scale is not currently available.

All the sort algorithms make temporary copies of the data when sorting along any but the last axis. Consequently, sorting along the last axis is faster and uses less space than sorting along any other axis.

The sort order for complex numbers is lexicographic. If both the real and imaginary parts are non-nan then the order is determined by the real parts except when they are equal, in which case the order is determined by the imaginary parts.

Previous to numpy 1.4.0 sorting real and complex arrays containing nan values led to undefined behaviour. In numpy versions >= 1.4.0 nan values are sorted to the end. The extended sort order is:

  • Real: [R, nan]
  • Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]

where R is a non-nan real value. Complex values with the same nan placements are sorted according to the non-nan part if it exists. Non-nan values are sorted as before.

New in version 1.12.0.

quicksort has been changed to introsort. When sorting does not make enough progress it switches to heapsort. This implementation makes quicksort O(n*log(n)) in the worst case.

‘stable’ automatically chooses the best stable sorting algorithm for the data type being sorted. It, along with ‘mergesort’ is currently mapped to timsort or radix sort depending on the data type. API forward compatibility currently limits the ability to select the implementation and it is hardwired for the different data types.

New in version 1.17.0.

Timsort is added for better performance on already or nearly sorted data. On random data timsort is almost identical to mergesort. It is now used for stable sort while quicksort is still the default sort if none is chosen. For timsort details, refer to CPython listsort.txt. ‘mergesort’ and ‘stable’ are mapped to radix sort for integer data types. Radix sort is an O(n) sort instead of O(n log n).

Examples

>>> a = np.array([[1,4],[3,1]])
>>> np.sort(a)                # sort along the last axis
array([[1, 4],
       [1, 3]])
>>> np.sort(a, axis=None)     # sort the flattened array
array([1, 1, 3, 4])
>>> np.sort(a, axis=0)        # sort along the first axis
array([[1, 1],
       [3, 4]])

Use the order keyword to specify a field to use when sorting a structured array:

>>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
>>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
...           ('Galahad', 1.7, 38)]
>>> a = np.array(values, dtype=dtype)       # create a structured array
>>> np.sort(a, order='height')                        # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
       ('Lancelot', 1.8999999999999999, 38)],
      dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])

Sort by age, then height if ages are equal:

>>> np.sort(a, order=['age', 'height'])               # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
       ('Arthur', 1.8, 41)],
      dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])