Python equivalent of MATLAB's "ismember" function

After many attempts trying optimize code, it seems that one last resource would be to attempt to run the code below using multiple cores. I don't know exactly how to convert/re-structure my code so that it can run much faster using multiple cores. I will appreciate if I could get guidance to achieve the end goal. The end goal is to be able to run this code as fast as possible for arrays A and B where each array holds about 700,000 elements. Here is the code using small arrays. The 700k element arrays are commented out.

import numpy as np

def ismember(a,b):
    for i in a:
        index = np.where(b==i)[0]
        if index.size == 0:
            yield 0
        else:
            yield index


def f(A, gen_obj):
    my_array = np.arange(len(A))
    for i in my_array:
        my_array[i] = gen_obj.next()
    return my_array


#A = np.arange(700000)
#B = np.arange(700000)
A = np.array([3,4,4,3,6])
B = np.array([2,5,2,6,3])

gen_obj = ismember(A,B)

f(A, gen_obj)

print 'done'
# if we print f(A, gen_obj) the output will be: [4 0 0 4 3]
# notice that the output array needs to be kept the same size as array A.

What I am trying to do is to mimic a MATLAB function called ismember[2] (The one that is formatted as: [Lia,Locb] = ismember(A,B). I am just trying to get the Locb part only.

From Matlab: Locb, contain the lowest index in B for each value in A that is a member of B. The output array, Locb, contains 0 wherever A is not a member of B

One of the main problems is that I need to be able to perform this operation as efficient as possible. For testing I have two arrays of 700k elements. Creating a generator and going through the values of the generator doesn't seem to get the job done fast.

Answers


Before worrying about multiple cores, I would eliminate the linear scan in your ismember function by using a dictionary:

def ismember(a, b):
    bind = {}
    for i, elt in enumerate(b):
        if elt not in bind:
            bind[elt] = i
    return [bind.get(itm, None) for itm in a]  # None can be replaced by any other "not in b" value

Your original implementation requires a full scan of the elements in B for each element in A, making it O(len(A)*len(B)). The above code requires one full scan of B to generate the dict Bset. By using a dict, you effectively make the lookup of each element in B constant for each element of A, making the operation O(len(A)+len(B)). If this is still too slow, then worry about making the above function run on multiple cores.

Edit: I've also modified your indexing slightly. Matlab uses 0 because all of its arrays start at index 1. Python/numpy start arrays at 0, so if you're data set looks like this

A = [2378, 2378, 2378, 2378]
B = [2378, 2379]

and you return 0 for no element, then your results will exclude all elements of A. The above routine returns None for no index instead of 0. Returning -1 is an option, but Python will interpret that to be the last element in the array. None will raise an exception if it's used as an index into the array. If you'd like different behavior, change the second argument in the Bind.get(item,None) expression to the value you want returned.


sfstewman's excellent answer most likely solved the issue for you.

I'd just like to add how you can achieve the same exclusively in numpy.

I make use of numpy's unique an in1d functions.

B_unique_sorted, B_idx = np.unique(B, return_index=True)
B_in_A_bool = np.in1d(B_unique_sorted, A, assume_unique=True)
  • B_unique_sorted contains the unique values in B sorted.
  • B_idx holds for these values the indices into the original B.
  • B_in_A_bool is a boolean array the size of B_unique_sorted that stores whether a value in B_unique_sorted is in A. Note: I need to look for (unique vals from B) in A because I need the output to be returned with respect to B_idx Note: I assume that A is already unique.

Now you can use B_in_A_bool to either get the common vals

B_unique_sorted[B_in_A_bool]

and their respective indices in the original B

B_idx[B_in_A_bool]

Finally, I assume that this is significantly faster than the pure Python for-loop although I didn't test it.


Try using a list comprehension;

In [1]: import numpy as np

In [2]: A = np.array([3,4,4,3,6])

In [3]: B = np.array([2,5,2,6,3])

In [4]: [x for x in A if not x in B]
Out[4]: [4, 4]

Generally, list comprehensions are much faster than for-loops.

To get an equal length-list;

In [19]: map(lambda x: x if x not in B else False, A)
Out[19]: [False, 4, 4, False, False]

This is quite fast for small datasets:

In [20]: C = np.arange(10000)

In [21]: D = np.arange(15000, 25000)

In [22]: %timeit map(lambda x: x if x not in D else False, C)
1 loops, best of 3: 756 ms per loop

For large datasets, you could try using a multiprocessing.Pool.map() to speed up the operation.


Here is the exact MATLAB equivalent that returns both the output arguments [Lia, Locb] that match MATLAB except in Python 0 is also a valid index. So, this function doesn't return the 0s. It essentially returns Locb(Locb>0). The performance is also equivalent to MATLAB.

def ismember(a_vec, b_vec):
    """ MATLAB equivalent ismember function """

    bool_ind = np.isin(a_vec,b_vec)
    common = a[bool_ind]
    common_unique, common_inv  = np.unique(common, return_inverse=True)     # common = common_unique[common_inv]
    b_unique, b_ind = np.unique(b_vec, return_index=True)  # b_unique = b_vec[b_ind]
    common_ind = b_ind[np.isin(b_unique, common_unique, assume_unique=True)]
    return bool_ind, common_ind[common_inv]

An alternate implementation that is a bit (~5x) slower but doesn't use the unique function is here:

def ismember(a_vec, b_vec):
    ''' MATLAB equivalent ismember function. Slower than above implementation'''
    b_dict = {b_vec[i]: i for i in range(0, len(b_vec))}
    indices = [b_dict.get(x) for x in a_vec if b_dict.get(x) is not None]
    booleans = np.in1d(a_vec, b_vec)
    return booleans, np.array(indices, dtype=int)

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