在Matlab中向嵌套for循环中矢量化更高维 [英] Vectorizing ther higher dimensions in nested for loop in Matlab

问题描述

我有一个5D矩阵 A ，我需要乘以一个向量的3-5维。例如，请参阅以下示例代码：

  A = rand（50,50,10,8,6）; 
 B = rand（10,1）; 
 C = rand（8,1）; 
 D = rand（6,1）; （A，3）
对于j = 1：大小（A，4）
对于K = 1：大小（A，5）$ 
 
 （i，j）* B（i）* C（j）* D（K）; b（b） 
 end 
 end 
 end 
  

不知有没有更好的\矢量化\更快的方法来做到这一点？

解决方案

首先，作为一个注释，这些天在Matlab中，用JIT编译，矢量化的代码不一定更快/更好。对于大问题，特别是内存使用可能会导致性能问题。

然而，这是一个向量化的解决方案，它看起来与您的代码具有相同的结果：

  A = rand（3,4,5,6,7）; 
 B = rand（5,1）; 
 C = rand（6,1）; 
 D = rand（7,1）; 
 
 s = size（A）; 
 [b，c，d] = ndgrid（B，C，D）; 
 F = b。* c。* d; 
 G =零（1,1，prod（s（3：5）））; 
 G（1,1，：）= F（:); 
 A = reshape（A，s（1），s（2），[]）; 
 A = bsxfun（@ times，A，G）; 
 A =重塑（A，s）; 
  

编辑：备用解决方案：

  A = bsxfun（@ times，A，permute（B，[2 3 1]））; 
 A = bsxfun（@ times，A，permute（C，[2 3 4 1]））; 
 A = bsxfun（@ times，A，permute（D，[2 3 4 5 1]））; 
  

I have a 5D matrix A, and I need to multiply the 3rd-5th dimensions with a vector. For example, see the following sample code:

A=rand(50,50,10,8,6);
B=rand(10,1);
C=rand(8,1);
D=rand(6,1);

for i=1:size(A,3)
    for j=1:size(A,4)
        for K=1:size(A,5)
            A(:,:,i,j,K)=A(:,:,i,j,K)*B(i)*C(j)*D(K);
        end
    end
end

I wonder if there's a better \ vectorized \ faster way to do this?

解决方案

Firstly, as a note, these days in Matlab, with JIT compilation, vectorised code is not necessarily faster/better. For big problems the memory usage in particular can cause performance issues.

Nevertheless, here is a vectorised solution that seems to give the same results as your code:

A=rand(3,4,5,6,7);
B=rand(5,1);
C=rand(6,1);
D=rand(7,1);   

s=size(A);
[b,c,d]=ndgrid(B,C,D);
F=b.*c.*d;
G=zeros(1,1,prod(s(3:5)));
G(1,1,:)=F(:);
A=reshape(A,s(1),s(2),[]);
A=bsxfun(@times,A,G);
A=reshape(A,s);

EDIT: An alternate solution:

A=bsxfun(@times,A,permute(B,[2 3 1]));
A=bsxfun(@times,A,permute(C,[2 3 4 1]));
A=bsxfun(@times,A,permute(D,[2 3 4 5 1]));

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