Python __matmul__() Magic Method

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object.__matmul__(self, other)

The Python __matmul__() method is called to implement the matrix multiplication operation @. For example to evaluate the expression x @ y, Python attempts to call x.__matmul__(y).

We call this a “Dunder Method” for Double Underscore Method” (also called “magic method”). To get a list of all dunder methods with explanation, check out our dunder cheat sheet article on this blog.

The @ operator was introduced to Python’s core syntax from 3.5 onwards thanks to PEP 465. Its only goal is to solve the problem of matrix multiplication. It even comes with a nice mnemonic – @ is * for mATrices. 

It is unusual that @ was added to the core Python language when it’s only used with certain libraries. Fortunately, the only other time we use @ is for decorator functions. So you are unlikely to get confused. 


In the following example, you create a custom class Data and overwrite the __matmul__() method that simply returns a dummy string. The real computation could be much more sophisticated, of course.

class Data:
    def __matmul__(self, other):
        return '... my result of matmul...'

a = Data()
b = Data()
c = a @ b

# ... my result of matmul...

If you hadn’t defined the __matmul__() method, Python would’ve raised a TypeError.

How to Resolve TypeError: unsupported operand type(s) for @

Consider the following code snippet where you try to multiply two custom objects without defining the dunder method __matmul__():

class Data:

a = Data()
b = Data()
c = a @ b


Running this leads to the following error message on my computer:

Traceback (most recent call last):
  File "C:\Users\xcent\Desktop\", line 7, in <module>
    c = a @ b
TypeError: unsupported operand type(s) for @: 'Data' and 'Data'

The reason for this error is that the __matmul__() dunder method has never been defined—and it is not defined for a custom object by default. So, to resolve the TypeError: unsupported operand type(s) for @, you need to provide the __matmul__(self, other) method in your class definition as shown previously:

class Data:
    def __matmul__(self, other):
        return '... my result of matmul...'

NumPy Matrix Multiplication @

np.matmul() vs vs @ Matrix Multiplication Operators

To perform matrix multiplication between two NumPy arrays, check out the @ operator:

# Python >= 3.5
# 2x2 arrays where each value is 1.0
>>> A = np.ones((2, 2))
>>> B = np.ones((2, 2))

>>> A @ B
array([[2., 2.],
      [2., 2.]]) 

I’ll give you a more detailed introduction in the following video or this blog tutorial.

NumPy Matrix Multiplication -- np.matmul() and @ [Ultimate Guide]

Python __matmul__ vs __rmatmul__

Say, you want to matrix-multiply two objects x and y.

print(x @ y)

Python first tries to call the left object’s __matmul__() method x.__matmul__(y). But this may fail for two reasons:

  1. The method x.__matmul__() is not implemented in the first place, or
  2. The method x.__matmul__() is implemented but returns a NotImplemented value indicating that the data types are incompatible.

If this fails, Python tries to fix it by calling the y.__rmatmul__() for reverse matrix multiplication on the right operator y. If this method is implemented, Python knows that it doesn’t run into a potential problem of a non-commutative operation. If it would just execute y.__matmul__(x) instead of x.__matmul__(y), it could cause an error if the multiplication is non-commutative. That’s why y.__rmatmul__(x) is needed which indicates that matrix multiplication is possible after all.

So, the difference between x.__matmul__(y) and x.__rmatmul__(y) is that the former calculates x @ y whereas the latter calculates y @ x — both calling the respective matrix multiplication method defined on object x.


Where to Go From Here?

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