# Multidimensional collections

Martin McBride, 2020-02-27
Tags len 2d list
Categories magic methods

In the article on magic methods for collections we saw how to implement collection behaviours for our example matrix class. We implemented support of built-in function len, support for for loops and the in operator. We also saw how to might implement del, although our 2 by 2 matrix doesn't allow it.

For getting and setting elements, we implemented __getitem__ and __setitem__ as if the matrix was a list of 4 elements. In thi sarticle we will see how to improve that.

## Supporting two dimensional selection

Our Matrix is a 2D array, so wouldn't it be nice to support (row, column) style selection? It would be nice if we could use a syntax like:

a[0, 1]     #row 0, columns 1


Well we can! The numpy library does exactly this, and we can easily support this with our Matrix class.

If you are familiar with dictionaries, you will know that a dictionary is indexed by keys rather than integers. A key can be an integer, or a string, but it can also be a tuple:

d = dict()
d = 0
d['two'] = 2
d[(0, 1)] = 3
print(d)


This gives the result:

{0: 0, 'two': 2, (0, 1): 3}


Thanks to the magic of tuple packing we can write d[(0, 1)] as d[0, 1]. So we can do this:

d[0, 1] = 10
print(d)


which gives:

{0: 0, 'two': 2, (0, 1): 10}


We need to do a similar thing with our matrix class.

## Two dimensional getters and setters

Previously our getter and setter accepted and index of the item in list of length 4:

def __getitem__(self, i):
return self.data[i]


But now instead we want to pass in a tuple (row, col). So we need to modify our code like this:

def __getitem__(self, t):
row, col = t
return self.data[row*2 + col]


We can now do this:

m = Matrix(1, 2, 3, 4)
print(m[1, 0])


This prints matrix row 1, column 0, which is the value 3.

We can do a similar thing with the setter:

def __setitem__(self, t, value):
row, col = t
self.data[row*2 + col] = value


which allows us to do this:

m[0, 1] = 5
print(m)


The matrix has now been updated, with row 0 column 1 set to 5:

[1, 5][3, 4]


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