Numpy Array Rank All Elements

Question

I have a two-dimensional numpy array and I am wondering how I can create a new two-dimensional numpy array represent the ranking of the values based on all items in the original 2d array.

I would like to use the following array :

anArray = [[ 18.5,  25.9,   7.4,  11.1,  11.1]
           [ 33.3,  37. ,  14.8,  22.2,  25.9]
           [ 29.6,  29.6,  11.1,  14.8,  11.1]
           [ 25.9,  25.9,  14.8,  14.8,  11.1]
           [ 29.6,  25.9,  14.8,  11.1,   7.4]]

to create a new rank ordered array [based on all values and having same rank for multiple numbers] :

anOrder = [[ 6,  4,  9,  8,  8]
           [ 2,  1,  7,  5,  4]
           [ 3,  3,  8,  7,  8]
           [ 4,  4,  7,  7,  8]
           [ 3,  4,  7,  8,  9]]

Thank you.

Warren Weckesser · Accepted Answer · 2016-03-24 04:54:31Z

5

You can use scipy.stats.rankdata with method='dense'. It ranks the values of the flattened input, so you'll have to restore the shape of the array returned by rankdata.

For example,

In [21]: anArray
Out[21]: 
[[18.5, 25.9, 7.4, 11.1, 11.1],
 [33.3, 37.0, 14.8, 22.2, 25.9],
 [29.6, 29.6, 11.1, 14.8, 11.1],
 [25.9, 25.9, 14.8, 14.8, 11.1],
 [29.6, 25.9, 14.8, 11.1, 7.4]]

In [22]: a = np.array(anArray)

In [23]: r = rankdata(a, method='dense').reshape(a.shape)

In [24]: ranks = (r.max()+1) - r

In [25]: ranks
Out[25]: 
array([[6, 4, 9, 8, 8],
       [2, 1, 7, 5, 4],
       [3, 3, 8, 7, 8],
       [4, 4, 7, 7, 8],
       [3, 4, 7, 8, 9]])

Note that rankdata ranks from low to high, starting with 0, so the ranks r are reversed and set to start at 1 with the line ranks = (r.max()+1) - r.

edited Mar 24, 2016 at 4:54

answered Mar 24, 2016 at 4:49

Warren Weckesser

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Comments

Divakar · Accepted Answer · 2016-03-24 04:46:53Z

That's a routine work for np.unique with its optional argument return_inverse that tags each element based on the uniqueness among other elements, like so -

_,id = np.unique(anArray,return_inverse=True)
out = (id.max() - id + 1).reshape(anArray.shape)

Sample run -

In [17]: anArray
Out[17]: 
array([[ 18.5,  25.9,   7.4,  11.1,  11.1],
       [ 33.3,  37. ,  14.8,  22.2,  25.9],
       [ 29.6,  29.6,  11.1,  14.8,  11.1],
       [ 25.9,  25.9,  14.8,  14.8,  11.1],
       [ 29.6,  25.9,  14.8,  11.1,   7.4]])

In [18]: _,id = np.unique(anArray,return_inverse=True)

In [19]: (id.max() - id + 1).reshape(anArray.shape)
Out[19]: 
array([[6, 4, 9, 8, 8],
       [2, 1, 7, 5, 4],
       [3, 3, 8, 7, 8],
       [4, 4, 7, 7, 8],
       [3, 4, 7, 8, 9]])

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