What is the '@=' symbol for in Python?

Question

I know @ 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 tokenizer.py.

Menashem

See cset c553d8f72d65 (GitHub mirror...easier to read) in the CPython repo. – Gilman

SymbolHound is a search-engine which can search on punctuation symbols. However searching on @= python doesn't currently return relevant results, because Python 3.5 documentation contains '@' but not an example of '@=' anywhere. I sent SH a message to help improve that. Python doc could improve too. – Autotype

Combined with the := walrus operator of Python 3.8, you get what's known as the @:= thorny rose operator. (Or in Japan it's known as the Elvis-walrus operator.) – Enravish

Answer 1

From the documentation:

The @ (at) operator is intended to be used for matrix multiplication. No builtin Python types implement this operator.

The @ operator was introduced in Python 3.5. @= is matrix multiplication followed by assignment, as you would expect. They map to __matmul__, __rmatmul__ or __imatmul__ similar to how + and += map to __add__, __radd__ or __iadd__.

The operator and the rationale behind it are discussed in detail in PEP 465.

Levon

That explains why it's in the latest version of tokenizer.py but not the 3.4 docs. – Menashem

This is covered in 3.5's docs - docs.python.org/3.5/reference/… and docs.python.org/3.5/reference/… – Antiworld

Does this have conflict with Python decorators? This is not implemented in Python 2.n, right? – Episcopalism

This does not conflict decorators, because decorators may never be preceded by an expression, and binary operators must always be preceded by an expression. – Levon

Answer 2

@= and @ 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:

• the * operator (and arithmetic operators in general) were defined as element-wise operations on ndarrays and as matrix-multiplication on numpy.matrix type.

• method/function dot was 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.

Pumpernickel

Just for clarification: from your first example, we could think that @ has been implemented for list, which is not the case. – Aerophone

@ is associated with np.matmul, not np.dot. The two are similar but not the same. – Keeling

@A-B-B, perhaps you could provide an example clarifying the nuance and ensuring the answer is then complete? – Emarie

Answer 3

@ is the new operator for Matrix Multiplication added in Python3.5

Reference: https://docs.python.org/3/whatsnew/3.5.html#whatsnew-pep-465

Example

C = A @ B

Rosannrosanna

Answer 4

Numpy 1.25 will support using @= as in place matrix multiplication:

Molt