Matrix Multiplication

Implement matrix multiplication without using @, np.dot or np.matmul.

For A of shape (n, k) and B of shape (k, m), the product C has shape (n, m) and

C[i, j] = sum over p of A[i, p] * B[p, j]

If the inner dimensions do not agree, return None.

Loops are fine here. The point is to see the contraction over the shared axis before letting BLAS hide it from you.

Function signature

def matmul(A, B):

Example

Input

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
matmul(A, B)

Output

array([[19., 22.],
       [43., 50.]])

Reasoning

C[0, 0] = 1 * 5 + 2 * 7 = 19 and C[0, 1] = 1 * 6 + 2 * 8 = 22. The second row is computed the same way from [3, 4].

Constraints and notes

• Return None when A.shape[1] != B.shape[0].
• Do not use @, np.dot or np.matmul.