[Numpy-discussion] A newbie question: How to get the "rank" of an 1-d array

[Tim Hochberg]

CL wrote:

> Hi, group,
>           I need to get the "rank" of an 1-D array (ie. a vector). 
> Note that "rank" here is not the value returned from "rank(a_array)". 
> It is the order of the item in its sorted arrray. For example, I have 
> a python function called "listrank" to return the "rank" as below:

In the future, please include the relevant function. This saves us (me 
anyway) time reverse engineering said function from the description you 
give. Is the function below equivalent to your listrank function?

        def listrank(v):
            rank = {}
            for i, x in enumerate(reversed(sorted(v))):
                if x not in rank:
                    rank[x] = i
            return [rank[x]+1 for x in v]

>
> In [19]: x
> Out[19]: array([1, 2, 5, 3, 3, 2])
>
> In [20]: listrank(x)
> Out[20]: [6, 4, 1, 2, 2, 4]
>
> Somebody suggested me to use "argsort(argsort(x))". But the problem is 
> it does not handle ties. See the output:
>
> In [21]: argsort(argsort(x))
> Out[21]: array([0, 1, 5, 3, 4, 2])
>
> I am wondering if there is a solution in numpy/numarray/numeric to get 
> this done nicely.

Unfortunately, nothing comes to mind immediately. This kind of problem, 
where the values at one index depend on the values at a different index 
is often hard to deal with in the array framework. How large of vectors 
are you typically dealing with? If they are not extremely large or this 
isn't a performance critical a python solution like above, possibly 
somewhat optimized, may well be sufficient.

Perhaps someone else will come up with something though.

Regards,

-tim