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.
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]])
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.
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]]