Python NumPy 中@ at 符号的意思

小鱼儿 2022-04-16 03:42 205阅读 0赞

除了python标准的@的功能（**decorator** ），一直不知道干什么的，后来查了一下，可以理解成矩阵乘法，见下面的官方文档

[https://docs.python.org/3/whatsnew/3.5.html\#whatsnew-pep-465][https_docs.python.org_3_whatsnew_3.5.html_whatsnew-pep-465]

### PEP 465 - A dedicated infix operator for matrix multiplication ###

[**PEP 465**][PEP 465] adds the `@` infix operator for matrix multiplication. Currently, no builtin Python types implement the new operator, however, it can be implemented by defining [`__matmul__()`][matmul], [`__rmatmul__()`][rmatmul], and [`__imatmul__()`][imatmul] for regular, reflected, and in-place matrix multiplication. The semantics of these methods is similar to that of methods defining other infix arithmetic operators.

Matrix multiplication is a notably common operation in many fields of mathematics, science, engineering, and the addition of `@` allows writing cleaner code:

S = (H @ beta - r).T @ inv(H @ V @ H.T) @ (H @ beta - r)

instead of:

S = dot((dot(H, beta) - r).T,
            dot(inv(dot(dot(H, V), H.T)), dot(H, beta) - r))

NumPy 1.10 has support for the new operator:

>>>

>>> import numpy
    
    >>> x = numpy.ones(3)
    >>> x
    array([ 1., 1., 1.])
    
    >>> m = numpy.eye(3)
    >>> m
    array([[ 1., 0., 0.],
           [ 0., 1., 0.],
           [ 0., 0., 1.]])
    
    >>> x @ m
    array([ 1., 1., 1.])

See also

[**PEP 465**][PEP 465] – A dedicated infix operator for matrix multiplication

PEP written by Nathaniel J. Smith; implemented by Benjamin Peterson.

另一个参考：

[https://alysivji.github.io/python-matrix-multiplication-operator.html][https_alysivji.github.io_python-matrix-multiplication-operator.html]

2017 will forever be etched in our memories as the year [Python overtook R to become the leading language][] for Data Science. There are many factors that play into this: Python's simple syntax, the fantastic [PyData ecosystem][], and of course buy-in from Python's [BDFL][].

[PEP 465][PEP 465 1] introduced the `@` infix operator that is designated to be used for matrix multiplication. The acceptance and implementation of this proposal in Python 3.5 was a signal to the scientific community that Python is taking its role as a numerical computation language very seriously.

I was a Computational Mathematics major in college so matrices are very near and dear to my heart. Shoutout to [Professor Jeff Orchard][] for having us implement matrix algorithms in C++. His [Numerical Linear Algebra course][] was the best class I've ever taken.

In this post, we will explore the `@` operator.

In \[1\]:

import numpy as np

In \[2\]:

A = np.matrix('3 1; 8 2')
    A

Out\[2\]:

matrix([[3, 1],
            [8, 2]])

In \[3\]:

B = np.matrix('6 1; 7 9')
    B

Out\[3\]:

matrix([[6, 1],
            [7, 9]])

In \[4\]:

A @ B

Out\[4\]:

matrix([[25, 12],
            [62, 26]])

Let's confirm this works

In \[5\]:

# element at the top left. i.e. (1, 1) aka (0, 0) in python
    A[0, 0] * B[0, 0] + A[0, 1] * B[1, 0]

Out\[5\]:

In \[6\]:

# element at the top right. i.e. (1, 2) aka (0, 1) in python
    A[0, 0] * B[0, 1] + A[0, 1] * B[1, 1]

Out\[6\]:

In \[7\]:

# element at the bottom left. i.e. (2, 1) aka (1, 0) in python
    A[1, 0] * B[0, 0] + A[1, 1] * B[1, 0]

Out\[7\]:

In \[8\]:

# element at the top right. i.e. (2, 2) aka (1, 1) in python
    A[1, 0] * B[0, 1] + A[1, 1] * B[1, 1]

Out\[8\]:

In \[9\]:

# let's put it in matrix form
    result = np.matrix([[A[0, 0] * B[0, 0] + A[0, 1] * B[1, 0], A[0, 0] * B[0, 1] + A[0, 1] * B[1, 1]],
                        [A[1, 0] * B[0, 0] + A[1, 1] * B[1, 0], A[1, 0] * B[0, 1] + A[1, 1] * B[1, 1]]])
    result

Out\[9\]:

matrix([[25, 12],
            [62, 26]])

In \[10\]:

A @ B == result

Out\[10\]:

matrix([[ True,  True],
            [ True,  True]], dtype=bool)

Looks good!

The [Python Data Model][] specifies that the `@` operator invokes `__matmul__` and `__rmatmul__`.

We can overload `@` by defining custom behavior for each of the special methods above, but this would result in our API not being Pythonic.

[https_docs.python.org_3_whatsnew_3.5.html_whatsnew-pep-465]: https://docs.python.org/3/whatsnew/3.5.html#whatsnew-pep-465
[PEP 465]: https://www.python.org/dev/peps/pep-0465
[matmul]: https://docs.python.org/3/reference/datamodel.html#object.__matmul__
[rmatmul]: https://docs.python.org/3/reference/datamodel.html#object.__rmatmul__
[imatmul]: https://docs.python.org/3/reference/datamodel.html#object.__imatmul__
[https_alysivji.github.io_python-matrix-multiplication-operator.html]: https://alysivji.github.io/python-matrix-multiplication-operator.html
[Python overtook R to become the leading language]: https://www.kdnuggets.com/2017/08/python-overtakes-r-leader-analytics-data-science.html
[PyData ecosystem]: http://numfocus.wpengine.com/open-source-projects/
[BDFL]: https://en.wikipedia.org/wiki/Benevolent_dictator_for_life
[PEP 465 1]: https://www.python.org/dev/peps/pep-0465/
[Professor Jeff Orchard]: https://cs.uwaterloo.ca/~jorchard
[Numerical Linear Algebra course]: http://www.ucalendar.uwaterloo.ca/0607/COURSE/course-CS.html#CS372
[Python Data Model]: https://docs.python.org/3/reference/datamodel.html#emulating-numeric-types