nested lists - Add two matrices in python

Question

I'm trying to write a function that adds two matrices to pass the following doctests:

  >>> a = [[1, 2], [3, 4]]
  >>> b = [[2, 2], [2, 2]]
  >>> add_matrices(a, b)
  [[3, 4], [5, 6]]
  >>> c = [[8, 2], [3, 4], [5, 7]]
  >>> d = [[3, 2], [9, 2], [10, 12]]
  >>> add_matrices(c, d)
  [[11, 4], [12, 6], [15, 19]]

So I wrote a function:

def add(x, y):
    return x + y

And then I wrote the following function:

def add_matrices(c, d):
    for i in range(len(c)):
        print map(add, c[i], d[i])

And I sort of get the right answer.

Answer 1

Matrix library

You can use the numpy module, which has support for this.

>>> import numpy as np

>>> a = np.matrix([[1, 2], [3, 4]])
>>> b = np.matrix([[2, 2], [2, 2]])

>>> a+b
matrix([[3, 4],
        [5, 6]])

---

Home-grown solution: heavyweight

Assuming you wanted to implement it yourself, you'd set up the following machinery, which would let you define arbitrary pairwise operations:

from pprint import pformat as pf

class Matrix(object):
    def __init__(self, arrayOfRows=None, rows=None, cols=None):
        if arrayOfRows:
            self.data = arrayOfRows
        else:
            self.data = [[0 for c in range(cols)] for r in range(rows)]
        self.rows = len(self.data)
        self.cols = len(self.data[0])

    @property
    def shape(self):          # myMatrix.shape -> (4,3)
        return (self.rows, self.cols)
    def __getitem__(self, i): # lets you do myMatrix[row][col
        return self.data[i]
    def __str__(self):        # pretty string formatting
        return pf(self.data)

    @classmethod
    def map(cls, func, *matrices):
        assert len(set(m.shape for m in matrices))==1, 'Not all matrices same shape'

        rows,cols = matrices[0].shape
        new = Matrix(rows=rows, cols=cols)
        for r in range(rows):
            for c in range(cols):
                new[r][c] = func(*[m[r][c] for m in matrices], r=r, c=c)
        return new

Now adding pairwise methods is as easy as pie:

    def __add__(self, other):
        return Matrix.map(lambda a,b,**kw:a+b, self, other)
    def __sub__(self, other):
        return Matrix.map(lambda a,b,**kw:a-b, self, other)

Example:

>>> a = Matrix([[1, 2], [3, 4]])
>>> b = Matrix([[2, 2], [2, 2]])
>>> b = Matrix([[0, 0], [0, 0]])

>>> print(a+b)
[[3, 4], [5, 6]]                                                                                                                                                                                                      

>>> print(a-b)
[[-1, 0], [1, 2]]

You can even add pairwise exponentiation, negation, binary operations, etc. I do not demonstrate it here, because it's probably best to leave * and ** for matrix multiplication and matrix exponentiation.

---

Home-grown solution: lightweight

If you just want a really simple way to map an operation over only two nested-list matrices, you can do this:

def listmatrixMap(f, *matrices):
    return 
        [
            [
                f(*values) 
                for c,values in enumerate(zip(*rows))
            ] 
            for r,rows in enumerate(zip(*matrices))
        ]

Demo:

>>> listmatrixMap(operator.add, a, b, c))
[[3, 4], [5, 6]]

With an additional if-else and keyword argument, you can use indices in your lambda. Below is an example of how to write a matrix row-order enumerate function. The if-else and keyword were omitted above for clarity.

>>> listmatrixMap(lambda val,r,c:((r,c),val), a, indices=True)
[[((0, 0), 1), ((0, 1), 2)], [((1, 0), 3), ((1, 1), 4)]]

edit

So we could write the above add_matrices function like so:

def add_matrices(a,b):
    return listmatrixMap(add, a, b)

Demo:

>>> add_matrices(c, d)
[[11, 4], [12, 6], [15, 19]]