Last time we saw how to use a set intersection to check for clusters of DNA/protein sequences and their genome intersections. We going to use the same example but this time we will see how we can change it and create a function that would calculate an arbitrary number of intersections at a time and also be able to check the intersection of more than two sets. Our previous code to calculate intersections was

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from sets import Set #for Python 2.3 and below
genA, genB, genC = Set([]), Set([]), Set([])

#populate the sets ...

print len(Set.intersection(genA, genB))
print len(Set.intersection(genA, genC))
print len(Set.intersection(genB, genC))

and that’s does not gives us the most important piece of information: the intersection of A, B and C. Let’s see how we can do it. Python has a function that can help us this time: reduce. This function allows to reduce a series of values to a single one, by employing a function defined in its parameters. From the file tutorial

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reduce(function, iterable[,initializer])

Basically reduce will make the function modify the values of a iterable (i.e. list). In our case reduce helps us calculate the intersection of many sets at once (our sets are genA, genB and genC)

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reduce(Set.intersection, [genA, genB, genC])

where reduce is applying the Set method intersection to a list of sets passed to the function. Python’s reduce might not be available in 3.0, but it is worth knowing. Now that we have a Pythonic way of checking the intersections we need to put reduce in a function, to make our code more elegant.

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def get_intersection(my_set1, my_set2, my_set3):
  return reduce(Set.intersection, [my_set1, my_set2, my_set3])

Done. In this function reduce will operate by first checking the intersection between my_set1 and my_set2 and storing it internally, then checking for the intersection between the previous result and my_set3. But wait … get_intersection receives three arguments, so it will be able to return the intersection only when three sets are sent, thus we would have to create another function that can receive two items in order to calculate the intersection between two items. And if we have more than three genomes to compare … There is a trick. If we define our function receiving only one argument and put a star/asterisk on it, this means that an arbitrary number of arguments will be provided to this function in a tuple (and a tuple is iterable, so it can be used in a reduce). Changing our function accordingly, we will have

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def get_intersection(*my_sets):
  return reduce(Set.intersection, my_sets)

so we can send 2, 3, 4, 5 or n number of sets to this function and it will return the intersection among all of them. Our simple script would be (including the above function)

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from sets import Set #for Python 2.3 and below 

def get_intersection(*my_sets):
  return reduce(Set.intersection, my_sets)

genA, genB, genC = Set([]), Set([]), Set([])

#populate the sets ...

print len(get_intersection(genA, genB))
print len(get_intersection(genA, genC))
print len(get_intersection(genB, genC))
print len(get_intersection(genA, genB, genC))