如何实现对所有子矩阵元素的加法? [英] How to implement addition to all submatrix elements?

问题描述

我正在尝试通过简单的python(没有numpy等)实现矩阵类，以实现简单的操作.

I'm trying to implement matrix class for simple operations with plain python (no numpy and etc.).

这是其中的一部分:

class Matrix(list):
    def __getitem__(self, item):
        try:
            return list.__getitem__(self, item)
        except TypeError:
            rows, cols = item
            return [row[cols] for row in self[rows]]

它允许执行以下操作:

m = Matrix([[i+j for j in [0,1,2,3]] for i in [0,4,8,12]])
print(m[0:2, 0:2])
will print: [[0, 1], [4, 5]]

我还希望能够将所有子矩阵元素添加/乘以给定值，例如:

I also want to be able to add/multiply all submatrix elements by given value, like:

m[0:2, 0:2] += 1
print(m[0:2, 0:2])
should print: [[1, 2], [5, 6]]

目前尚不清楚我应该采用哪种魔术方法使其起作用?

It's not clear which magic methods should I implement to make it work?

推荐答案

首先，从list继承是一个不好的举动.矩阵不支持列表所执行的操作；例如，您不能append到或extend矩阵，并且项目分配完全不同.您的矩阵应包含一个列表，而不是列表.

First, inheriting from list is a bad move here. A matrix doesn't support the kinds of operations a list does; for example, you can't append to or extend a matrix, and item assignment is completely different. Your matrix should contain a list, not be a list.

关于所需的魔术方法，m[0:2, 0:2] += 1大致翻译为以下内容:

As for what magic methods you need, m[0:2, 0:2] += 1 roughly translates to the following:

temp = m.__getitem__((slice(0, 2), slice(0, 2)))
temp = operator.iadd(temp, 1)
m.__setitem__((slice(0, 2), slice(0, 2)), temp)

其中operator.iadd尝试使用temp.__iadd__，temp.__add__和(1).__radd__进行加法.

where operator.iadd tries temp.__iadd__, temp.__add__, and (1).__radd__ to perform the addition.

您需要实现__getitem__和__setitem__来检索子矩阵并分配新的子矩阵.另外，__getitem__将需要返回矩阵，而不是列表.

You need to implement __getitem__ and __setitem__ to retrieve the submatrix and assign the new submatrix. Additionally, __getitem__ will need to return a matrix, rather than a list.

您可能应该同时实现__add__和__iadd__；在这种情况下，仅__add__就足够了，但__iadd__对于像m += 1这样的操作就地工作而不是用新的矩阵对象替换m来说是必要的.

You should probably implement both __add__ and __iadd__; while __add__ alone would be sufficient for this case, __iadd__ will be necessary for operations like m += 1 to work in-place instead of replacing m with a new matrix object.

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