@ is for decorators, but what is
@= for in Python? Is it just reservation for some future idea?
This is just one of my many questions while reading
From the documentation:
@(at) operator is intended to be used for matrix multiplication. No builtin Python types implement this operator.
@ operator was introduced in Python 3.5.
@= is matrix multiplication followed by assignment, as you would expect. They map to
__imatmul__ similar to how
+= map to
The operator and the rationale behind it are discussed in detail in PEP 465.
@ are new operators introduced in Python 3.5 performing matrix multiplication. They are meant to clarify the confusion which existed so far with the operator
* which was used either for element-wise multiplication or matrix multiplication depending on the convention employed in that particular library/code. As a result, in the future, the operator
* is meant to be used for element-wise multiplication only.
As explained in PEP0465, two operators were introduced:
- A new binary operator
A @ B, used similarly as
A * B
- An in-place version
A @= B, used similarly as
A *= B
Matrix Multiplication vs Element-wise Multiplication
To quickly highlight the difference, for two matrices:
A = [[1, 2], B = [[11, 12], [3, 4]] [13, 14]]
Element-wise multiplication will yield:
A * B = [[1 * 11, 2 * 12], [3 * 13, 4 * 14]]
Matrix multiplication will yield:
A @ B = [[1 * 11 + 2 * 13, 1 * 12 + 2 * 14], [3 * 11 + 4 * 13, 3 * 12 + 4 * 14]]
Usage in Numpy
So far, Numpy used the following convention:
*operator (and arithmetic operators in general) were defined as element-wise operations on ndarrays and as matrix-multiplication on numpy.matrix type.
dotwas used for matrix multiplication of ndarrays
Introduction of the
@ operator makes the code involving matrix multiplications much easier to read. PEP0465 gives us an example:
# Current implementation of matrix multiplications using dot function S = np.dot((np.dot(H, beta) - r).T, np.dot(inv(np.dot(np.dot(H, V), H.T)), np.dot(H, beta) - r)) # Current implementation of matrix multiplications using dot method S = (H.dot(beta) - r).T.dot(inv(H.dot(V).dot(H.T))).dot(H.dot(beta) - r) # Using the @ operator instead S = (H @ beta - r).T @ inv(H @ V @ H.T) @ (H @ beta - r)
Clearly, the last implementation is much easier to read and interpret as an equation.
@ is the new operator for Matrix Multiplication added in Python3.5
C = A @ B