# Efficient method to calculate the rank vector of a list in Python

I'm looking for an efficient way to calculate the rank vector of a list in Python, similar to R's rank function. In a simple list with no ties between the elements, element *i* of the rank vector of a list l should be *x* if and only if l[i] is the *x*-th element in the sorted list. This is simple so far, the following code snippet does the trick:

def rank_simple(vector): return sorted(range(len(vector)), key=vector.__getitem__)

Things get complicated, however, if the original list has ties (i.e. multiple elements with the same value). In that case, all the elements having the same value should have the same rank, which is the average of their ranks obtained using the naive method above. So, for instance, if I have [1, 2, 3, 3, 3, 4, 5], the naive ranking gives me [0, 1, 2, 3, 4, 5, 6], but what I would like to have is [0, 1, 3, 3, 3, 5, 6]. Which one would be the most efficient way to do this in Python?

Footnote: I don't know if NumPy already has a method to achieve this or not; if it does, please let me know, but I would be interested in a pure Python solution anyway as I'm developing a tool which should work without NumPy as well.

## Answers

Using scipy, the function you are looking for is scipy.stats.rankdata :

In [13]: import scipy.stats as ss In [19]: ss.rankdata([3, 1, 4, 15, 92]) Out[19]: array([ 2., 1., 3., 4., 5.]) In [20]: ss.rankdata([1, 2, 3, 3, 3, 4, 5]) Out[20]: array([ 1., 2., 4., 4., 4., 6., 7.])

The ranks start at 1, rather than 0 (as in your example), but then again, that's the way R's rank function works as well.

Here is a pure-python equivalent of scipy's rankdata function:

def rank_simple(vector): return sorted(range(len(vector)), key=vector.__getitem__) def rankdata(a): n = len(a) ivec=rank_simple(a) svec=[a[rank] for rank in ivec] sumranks = 0 dupcount = 0 newarray = [0]*n for i in xrange(n): sumranks += i dupcount += 1 if i==n-1 or svec[i] != svec[i+1]: averank = sumranks / float(dupcount) + 1 for j in xrange(i-dupcount+1,i+1): newarray[ivec[j]] = averank sumranks = 0 dupcount = 0 return newarray print(rankdata([3, 1, 4, 15, 92])) # [2.0, 1.0, 3.0, 4.0, 5.0] print(rankdata([1, 2, 3, 3, 3, 4, 5])) # [1.0, 2.0, 4.0, 4.0, 4.0, 6.0, 7.0]

This is one of the functions that I wrote to calculate rank.

def calculate_rank(vector): a={} rank=1 for num in sorted(vector): if num not in a: a[num]=rank rank=rank+1 return[a[i] for i in vector]

input:

calculate_rank([1,3,4,8,7,5,4,6])

output:

[1, 2, 3, 7, 6, 4, 3, 5]

This doesn't give the exact result you specify, but perhaps it would be useful anyways. The following snippet gives the first index for each element, yielding a final rank vector of [0, 1, 2, 2, 2, 5, 6]

def rank_index(vector): return [vector.index(x) for x in sorted(range(n), key=vector.__getitem__)]

Your own testing would have to prove the efficiency of this.

There is a really nice module called Ranking http://pythonhosted.org/ranking/ with an easy to follow instruction page. To download, simply use easy_install ranking

Here is a small variation of unutbu's code, including an optional 'method' argument for the type of value of tied ranks.

def rank_simple(vector): return sorted(range(len(vector)), key=vector.__getitem__) def rankdata(a, method='average'): n = len(a) ivec=rank_simple(a) svec=[a[rank] for rank in ivec] sumranks = 0 dupcount = 0 newarray = [0]*n for i in xrange(n): sumranks += i dupcount += 1 if i==n-1 or svec[i] != svec[i+1]: for j in xrange(i-dupcount+1,i+1): if method=='average': averank = sumranks / float(dupcount) + 1 newarray[ivec[j]] = averank elif method=='max': newarray[ivec[j]] = i+1 elif method=='min': newarray[ivec[j]] = i+1 -dupcount+1 else: raise NameError('Unsupported method') sumranks = 0 dupcount = 0 return newarray

[sorted(l).index(x) for x in l]

sorted(l) will give the sorted version index(x) will give the index in the sorted array

for example :

l = [-1, 3, 2, 0,0] >>> [sorted(l).index(x) for x in l] [0, 4, 3, 1, 1]

import numpy as np def rankVec(arg): p = np.unique(arg) #take unique value k = (-p).argsort().argsort() #sort based on arguments in ascending order dd = defaultdict(int) for i in xrange(np.shape(p)[0]): dd[p[i]] = k[i] return np.array([dd[x] for x in arg])

timecomplexity is 46.2us

These codes give me a lot of inspiration, especially unutbu's code. However my needs are simpler, so I changed the code a little.

Hoping to help the guys with the same needs.

Here is the class to record the players' scores and ranks.

class Player(): def __init__(self, s, r): self.score = s self.rank = r

Some data.

l = [Player(90,0),Player(95,0),Player(85,0), Player(90,0),Player(95,0)]

Here is the code for calculation:

l.sort(key=lambda x:x.score, reverse=True) l[0].rank = 1 dupcount = 0 prev = l[0] for e in l[1:]: if e.score == prev.score: e.rank = prev.rank dupcount += 1 else: e.rank = prev.rank + dupcount + 1 dupcount = 0 prev = e