Re: FYI: nth_element

[Shai Ayal]

On Thu, Oct 15, 2009 at 12:36 PM, Jaroslav Hajek <address@hidden> wrote:
> On Thu, Oct 15, 2009 at 9:56 AM, Shai Ayal <address@hidden> wrote:
>> On Thu, Oct 15, 2009 at 9:15 AM, Jaroslav Hajek <address@hidden> wrote:
>>> hi all,
>>>
>>> Octave has just got a new function: nth_element:
>>> http://hg.savannah.gnu.org/hgweb/octave/rev/aea3a3a950e1
>>>
>>> the docstring:
>>>
>>>  -- Built-in Function:  nth_element (X, N)
>>>  -- Built-in Function:  nth_element (X, N, DIM)
>>>     Select the n-th smallest element of a vector, using the ordering
>>>     defined by `sort'.  In other words, the result is equivalent to
>>>     `sort(X)(N)'.  N can also be a contiguous range, either ascending
>>>     `l:u' or descending `u:-1:l', in which case a range of elements is
>>>     returned.  If X is an array, `nth_element' operates along the
>>>     dimension defined by DIM, or the first non-singleton dimension if
>>>     DIM is not given.
>>>
>>>     nth_element encapsulates the C++ STL algorithms nth_element and
>>>     partial_sort.  On average, the complexity of the operation is
>>>     O(M*log(K)), where `M = size(X, DIM)' and `K = length (N)'.  This
>>>     function is intended for cases where the ratio K/M is small;
>>>     otherwise, it may be better to use `sort'.
>>>
>>>     See also: sort, min, max
>>>
>>> In short, it allows extracting a small portion of sort(X) without
>>> actually doing the full sort.
>>> This is sometimes useful for statistics when computing quantiles and
>>> the like... statisticians can surely tell better.
>>>
>>> Maybe it can be used to boost some existing functions. As an example,
>>> it can be readily used to speed up the "median" function:
>>> http://hg.savannah.gnu.org/hgweb/octave/rev/b7b89061bd0e
>>>
>> It can also help hist quite a lot.
>>
>
> I don't see how. Can you clarify?

You are right -- I was confused. hist needs the number of elements
smaller than a given value (and uses sort to find out), while
nth_element gives the value of the nth element.
Writing hist in c++ is not hard and would really help since it uses
(M+K)log(M+K) sort in order to avoid a M*K loop just because looping
is slow in the scripting language. One of these days I'll get down to
doing that ...

Shai