Python中矩阵元素的双重求和 [英] Double summation of matrix elements in Python

问题描述

基于下面的简化示例

我想要我的代码

from sympy import*
import numpy as np
init_printing()

x, y = symbols('x, y')

mat = Matrix([[x,1],[1,y]])

X = [1, 2, 3]
Y = [[10, 20, 30], [40, 50, 60], [70, 80, 90]]

将符号x和y替换为X和Y值，并且当然会计算给定矩阵的两倍总和.

to substitute the symbolic x and y with values of X and Y and ofcourse calculate the double summation of the given matrix.

我正在尝试解决这个问题，但是在每个步骤中我都遇到了麻烦. 任何帮助将不胜感激.

I'm trying to solve this but I'm having a rough time with the substitution in each step. Any help would be highly appreciated.

推荐答案

您已经导入了SymPy和NumPy，因此可以在此处选择工具.对于将一堆数字矩阵相加的工作，numpy是正确的工具.这是在numpy中求和的方式:

You've imported both SymPy and NumPy, so you have a choice of tools here. And for the job of adding together a bunch of numeric matrices, numpy is the right tool. Here is how the summation happens in numpy:

sum([sum([np.array([[x,1], [1,y]]) for y in yr]) for x, yr in zip(X,Y)])

这里yr代表Y的一行元素.外部的总和超过i索引，内部的总和超过j，尽管列表理解消除了将它们拼出的必要.

Here yr stands for a row of elements of Y. The outer sum is over i index, the inner is over j, although the list comprehension eliminates the need to spell them out.

结果是一个NumPy数组:

The result is a NumPy array:

 array([[ 18,   9],
       [  9, 450]])

，但是您只需将Matrix()放在它周围，就可以将其转换为SymPy矩阵:

but you can turn it into a SymPy matrix just by putting Matrix() around it:

Matrix(sum([sum([np.array([[x,1], [1,y]]) for y in yr]) for x, yr in zip(X,Y)]))

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