How to use __add__ method to add sparse vectors in python

Question

I am given an assignment to add two sparse vectors using special methods in SparseVec(length) class.I have limited understanding of special methods and method overloading, can you please describe what i am missing in the following code and what exactly is method overloading? I have two alternatives: using stand alone functions and class methods(OOP). I want to know the advantage of the later (OOP).

Stand-alone function (Works fine)

def SparseVec(numbers):
    dic={}
    for key,val in enumerate(numbers):
        if val:
            dic[key]=val
    return dic

numbers=[-1,0,9.2,0]
a=SparseVec(numbers)
print(a)

numbers2=[0,1,0,0,0]
b=SparseVec(numbers2)
print(b)

#Adds and merges values with keys in two dictionaries
def merged_dictionaries(a,b):
    merged_dict={}
    for key in a:
        if key in b:
            new_value=a[key]+b[key]
        else:
            new_value=a[key]
        merged_dict[key]=new_value
    for key in b:
        if key not in merged_dict:
            merged_dict[key]=b[key]
    return merged_dict
c=merged_dictionaries(a,b)
for key, val in c.items(): # SparseVec iterator
    print ('c[%d]=%g ' % (key,val))
print(c)

class method(OOP)-(Defective)

#Implements a Sparse vector (vector with many zero values) and adds two sparse vectors
class SparseVec:
    #initializes the instance with given length
    def __init__(self,length):
        self.length=length
        self.data={}
    def __str__(self):
        return 'Dense Vector {}'. format(self.data)
    #Returns the length of the vector
    def __len__(self):
        return len(self.data)
    # Returns nonzeros from the given(self) dictionary
    def __getitem__(self, item):
        return self.data
    def __setitem__(self, key, val):
        #To set a value by its key
        self.data[key]= val

    def nonzeros(self):
        nonzerodict = {}
        for key, val in enumerate(self):
            if val:
                nonzerodict[key] = val
        return nonzerodict
    def __add__(self, other):
        c = {}
        for key in self:
            if key in other:
                new_value = self[key]+ other[key]
            else:
                new_value = self[key]
            c[key] = new_value
        for key in other:
            if key not in c:
                c[key] = other[key]
        return c

a = SparseVec(4)
a[2] = 9.2
a[0] = -1
print(a)
print(a.nonzeros())
b = SparseVec(5)
b[1] = 1
print(b.nonzeros())
c=a+b
print(c)

Answer 1

You need to add the components of each vector pairwise, and return a SparseVector object:

class SparseVec:

    def __init__(self, dimension):
        self.dimension = dimension
        self.data = {}

    def __str__(self):
        return 'Sparse Vector {}'. format(self.data)

    def __len__(self):
        return self.dimension    # what matters is the size of the vector, not the length of the stored data

    def __getitem__(self, key):
        assert isinstance(key, int)
        assert 0 <= key < self.dimension, 'the key must be compatible with the vector dimension' 
        try:
            return self.data[key]
        except KeyError:
            return 0     # must return zero if valid key but no entry

    def __setitem__(self, key, val):
        assert isinstance(key, int)
        assert 0 <= key < self.dimension, 'this vector does not have an appropriate dimension'
        if val != 0:     # avoid cluttering with zero values
            self.data[key] = val

    def purge_zeros(self):  # <-- resparsifies a vector by purging the zero values
        nonzerodict = {}
        for key, val in self.data.items():
            if val != 0:
                nonzerodict[key] = val
        self.data = nonzerodict

    def __add__(self, other):
        assert self.dimension == other.dimension, 'vectors must have the same dimension'
        resulting_vector = SparseVec(self.dimension)
        c = {k:v for k, v in self.data.items()}  # <-- copies self data
        for k, v in other.data.items():
            try:
                c[k] += v
            except KeyError:
                c[k] = v
        resulting_vector.data = c
        resulting_vector.purge_zeros()
        return resulting_vector

tests:

a = SparseVec(4)
b = SparseVec(4)
a.data = {0: 2, 1: 1}
b.data = {0: -2, 1: 2, 2: 4}
print(a + b)
print(a[0], a[1], a[2], a[3])
print(b[0], b[1], b[2], b[3])
a[3] = -3
print(a[0], a[1], a[2], a[3])

output:

Sparse Vector {1: 3, 2: 4}
2 1 0 0
-2 2 4 0
2 1 0 -3

Answer 2

Overloading a class method is essentially writing a method that would usually be handled by a default method in Python and replacing it with your own method for that class.

This is the default add method from Python 3 docs: https://docs.python.org/3/reference/datamodel.html#emulating-numeric-types

I'm not sure on why you are using a dict for this rather than a list without more context, but the following should work:

c = a.add(b)
print(c)

a is an instance of the SparseVec class, so in order to access the add method we call a.add() and pass in the other object we wish to add to it.