__matmul__() method is called to implement the matrix multiplication operation
@. For example to evaluate the expression
x @ y, Python attempts to call
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.
@ 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 print(c) # ... my result of matmul...
If you hadn’t defined the
__matmul__() method, Python would’ve raised a
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
class Data: pass a = Data() b = Data() c = a @ b print(c)
Running this leads to the following error message on my computer:
Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", 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 @
To perform matrix multiplication between two NumPy arrays, check out the
# 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.
Python __matmul__ vs __rmatmul__
Say, you want to matrix-multiply two objects
print(x @ y)
Python first tries to call the left object’s
x.__matmul__(y). But this may fail for two reasons:
- The method
x.__matmul__()is not implemented in the first place, or
- The method
x.__matmul__()is implemented but returns a
NotImplementedvalue 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.__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
Where to Go From Here?
Enough theory. Let’s get some practice!
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While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
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