矩阵乘法中的 bsxfun 实现 [英] bsxfun implementation in matrix multiplication

问题描述

一如既往地向您学习更多信息，我希望我能在以下代码方面得到一些帮助.

As always trying to learn more from you, I was hoping I could receive some help with the following code.

我需要完成以下工作:

1) 我有一个向量:

x = [1 2 3 4 5 6 7 8 9 10 11 12]

2) 和一个矩阵:

A =[11    14    1
    5     8    18
    10    8    19
    13    20   16]

我需要能够将 x 的 each 值与 A 的 every 值相乘，这意味着:

I need to be able to multiply each value from x with every value of A, this means:

new_matrix = [1* A
              2* A
              3* A
               ...
              12* A]

这将给我这个 new_matrix 大小为 (12*m x n) 假设 A (mxn).在这种情况下 (12*4x3)

This will give me this new_matrix of size (12*m x n) assuming A (mxn). And in this case (12*4x3)

如何使用 matlab 中的 bsxfun 来做到这一点?并且，这种方法会比 for-loop 更快吗?

How can I do this using bsxfun from matlab? and, would this method be faster than a for-loop?

关于我的 for-loop，我在这里也需要一些帮助......我无法在循环运行时存储每个 "new_matrix" :(

Regarding my for-loop, I need some help here as well... I am not able to storage each "new_matrix" as the loop runs :(

for i=x
new_matrix = A.*x(i)
end

提前致谢！！

在给出解决方案之后

第一个解决方案

clear all
clc
x=1:0.1:50;
A = rand(1000,1000);
tic
val = bsxfun(@times,A,permute(x,[3 1 2]));
out = reshape(permute(val,[1 3 2]),size(val,1)*size(val,3),[]);
toc

输出:

Elapsed time is 7.597939 seconds.

第二种解决方案

clear all
clc
x=1:0.1:50;
A = rand(1000,1000);
tic
Ps = kron(x.',A);
toc

输出:

Elapsed time is 48.445417 seconds.

推荐答案

将 x 发送到三维，这样在使用 bsxfun 时，单例扩展就会生效对于与 A 的乘法，将乘积结果扩展到第三维.然后，执行bsxfun乘法-

Send x to the third dimension, so that singleton expansion would come into effect when bsxfun is used for multiplication with A, extending the product result to the third dimension. Then, perform the bsxfun multiplication -

val = bsxfun(@times,A,permute(x,[3 1 2])) 

现在，val 是一个 3D 矩阵，期望的输出是一个 2D 矩阵，通过第三维沿列连接.这是在下面实现的 -

Now, val is a 3D matrix and the desired output is expected to be a 2D matrix concatenated along the columns through the third dimension. This is achieved below -

out = reshape(permute(val,[1 3 2]),size(val,1)*size(val,3),[])

希望这是有道理的！传播 bsxfun 字！呜！！:)

Hope that made sense! Spread the bsxfun word around! woo!! :)

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