是否可以使用mldivide“\"?在 Matlab 中的 3D 矩阵上 [英] Is it possible to use mldivide "\" on a 3D matrix in Matlab

问题描述

是否可以在 MATLAB 的 3D 矩阵上使用 mldivide (\)?我想避免使用 for 循环?

Is it possible to use mldivide (\) on a 3D matrix in MATLAB? I would like to avoid using a for loop?

示例:

A = rand(4, 100, 5);
B = rand(4,4);

我需要执行:

C = B\A;

我现在在做什么:

在 for 循环上为每个切片"i 应用 mldivide:

Apply the mldivide on a for loop for each "slice" i:

for i = 1:size(A, 3)    
    C(:,:,i) = B \ A(:,:,i); 
end

推荐答案

您可以将 A 重塑为二维矩阵以执行除法，然后再恢复到预期大小.reshape 操作应该相对较快，因为 MATLAB 不会改变底层数据.

You can reshape A into a 2D matrix to perform the division and then back to the expected size afterwards. The reshape operations should be relatively quick due to the fact that MATLAB doesn't alter the underlying data.

C = reshape(B \ reshape(A, size(A, 1), []), size(B, 1), size(A, 2), []);

如果我们把它分解:

%// Reshape A to be 4 x 500
Anew = reshape(A, size(A, 1), []);

%// Perform left division
C = B \ Anew;

%// Reshape C to be the expected size (4 x 100 x 5)
C = reshape(C, size(B, 1), size(A, 2), []);

这应该适用于任何有效的 (size(A, 1) == size(B, 2)) 矩阵 A 和 B任何大小.

This should work for any valid (size(A, 1) == size(B, 2)) matrices A and B of any size.

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