Optimizing Matrix Multiplication in Python

Question

I'm currently working on a project that involves multiplying large matrices in Python. The matrices have dimensions A (m x n), B (n x p), and C (m x p), where m, n, and p can be very large (e.g., millions).

To perform the matrix multiplication, I have implemented a basic algorithm using nested loops. However, I've noticed that this implementation is quite slow when dealing with these large matrices. Thus, I'm looking for ways to optimize the code and improve its performance.

Here's the current implementation I have:

def matrix_multiplication(A, B):
    m = len(A)
    n = len(A[0])
    p = len(B)

    C = [[0] * p for _ in range(m)]

    for i in range(m):
        for j in range(p):
            for k in range(n):
                C[i][j] += A[i][k] * B[k][j]

    return C

# Example usage
A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
result = matrix_multiplication(A, B)
print(result)

I would greatly appreciate your expertise and suggestions on how I can optimize this matrix multiplication algorithm in Python. Are there any built-in functions or libraries that can significantly improve the performance? Additionally, I'm open to considering alternative programming languages or techniques if they can provide better performance for this specific task.

I tried implementing a matrix multiplication algorithm in Python using nested loops. My expectation was that the code would correctly multiply the matrices and return the resulting matrix. However, when I executed the code, I encountered an error.

Here's the code I used:

def matrix_multiplication(A, B):
    m = len(A)
    n = len(A[0])
    p = len(B)

    C = [[0] * p for _ in range(m)]

    for i in range(m):
        for j in range(p):
            for k in range(n):
                C[i][j] += A[i][k] * B[k][j]

    return C

# Example usage
A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
result = matrix_multiplication(A, B)
print(result)

I expected the code to multiply the matrices A and B correctly and store the result in matrix C. Then, I expected the result variable to contain the multiplied matrix, which I would print to the console.

However, when I ran the code, I encountered the following error:

IndexError: list index out of range

Thank you in advance for your recommendations! This error suggests that there is an issue with the dimensions of the matrices or the indexing within the nested loops. I'm not sure what went wrong and how to resolve this error.

Answer 1

There is a typo in your code:

# p = len(B[0])
p = len(B)

len(B) so that you can iterate on rows of B matrix.

---

Using numpy, it is beautiful:

result = np.dot(A, B)