- matmul(a, b)
Matrix multiplication of tensors representing (batches of) matrices
tensors representing the matrices to contract
- a @ b
matrix product of a and b
The behavior depends on the arguments in the following way.
If both arguments are 2-D they are multiplied like conventional matrices.
If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.
matmul differs from dot in two important ways:
Multiplication by scalars is not allowed, use * instead.
Stacks of matrices are broadcast together as if the matrices were elements, respecting the signature
>>> a = np.ones([9, 5, 7, 4]) >>> c = np.ones([9, 5, 4, 3]) >>> np.dot(a, c).shape (9, 5, 7, 9, 5, 3) >>> np.matmul(a, c).shape (9, 5, 7, 3) >>> # n is 7, k is 4, m is 3
The matmul function implements the semantics of the
@operator introduced in Python 3.5 following PEP 465.