arrays - 使用由索引的 kronecker 产品产生的向量构建矩阵，无需 for 循环

Question

我可以通过放弃 for 循环来优化 Matlab 中的以下代码吗？

A = [];
B = randn(4,8);
C = randn(8,4);
I = randperm(8,3);
J = randperm(8,3);
for i = 1:3
    A = [A kron(C(J(i),:)',B(:,I(i)))];
end

Answer 1

是的，您可以，使用三维来存储中间结果并将其转换回二维。这样你也可以避免 kron 本身不是最快的。

Matlab R2016a 或更高版本:

a = C(J,:).' .* permute(B(:,I),[3 2 1]);  %// calculation of the product to 3rd dimension
                                          %// by implicit expansion
b = permute( a, [3 1 2] );                %// permuting
out = reshape( b, [], 3 )                 %// reshape to desired form

短:

out = reshape( permute( C(J,:).' .* permute(B(:,I),[3 2 1]), [3 1 2] ), [], 3 )

在 Matlab R2016a 之前:

a = bsxfun(@times , C(J,:).', permute(B(:,I),[3 2 1])); %// calculation of 
                                          %// the product to 3rd dimension(explicit)
b = permute( a, [3 1 2] );                %// permuting
out = reshape( b, [], 3 )                 %// reshape to desired form

短:

out = reshape(permute(bsxfun(@times , C(J,:).', permute(B(:,I),[3 2 1])), [3 1 2] ), [], 3 )