numpy: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
=========== ======= ============= ============ ========

For performance, sort makes a temporary copy if needed to make the data contiguous in memory along the sort axis. For even better performance and reduced memory consumption, ensure that the array is already contiguous along the sort 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.

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.

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).

NaT now sorts to the end of arrays for consistency with NaN.