January
12th,
2017
Multiplying Matrices is a good way to practice what you understand about Python
Formular \(c_{ij} = \sum_{k}^{n}{a_{ik}b_{kj}}\)
Example: \(\begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \\ \end{bmatrix} \times \begin{bmatrix} 7 & 8\\ 9 & 10 \\ 11 & 12 \\ \end{bmatrix} = \begin{bmatrix} 58 & 64\\ 139 & 154 \\ \end{bmatrix}\)
Approach #1
def multipleMatrixes(A, B):
B = list(zip(*B))
return [[sum(ai * bj for ai, bj in zip(Ai, Bj)) for Bj in B] for Ai in A]
#[[58, 64], [139, 154]]
multipleMatrixes([[1,2,3],[4,5,6]], [[7,8],[9,10],[11, 12]]) § zip([iterable, ...])1 returns a list of tuples, where the i-th tuple contains the i-th element from each of the argument sequences or iterables
§ *2 is unpack operator, def test(A, B): print A, B, test(*[[1,2],[3,4]])
Approach #2
def multipleMatrixes(A, B):
return [[sum(x * B[i][col] for i,x in enumerate(row))
for col in range(len(B[0]))] for row in A]
#[[58, 64], [139, 154]]
multipleMatrixes([[1,2,3],[4,5,6]], [[7,8],[9,10],[11, 12]]) § enumerate(sequence, start=0)3 returns an enumerate object
Approach #3
def multipleMatrixes(A, B):
result = [[0] * len(A) for _ in range(len(B[0]))]
for i in range(len(A)):
for j in range(len(B[0])):
for k in range(len(B)):
result[i][j] += A[i][k] * B[k][j]
return result
#[[58, 64], [139, 154]]
multipleMatrixes([[1,2,3],[4,5,6]], [[7,8],[9,10],[11, 12]]) § [0] * 3 becomes [0,0,0]
Approach #4: Using Numpy
import numpy as np
#array([[ 58, 64],
# [139, 154]])
np.dot([[1,2,3],[4,5,6]], [[7,8],[9,10],[11, 12]]) Source here
References